diff --git "a/data_all_eng_slimpj/shuffled/split2/finalzzgjqx" "b/data_all_eng_slimpj/shuffled/split2/finalzzgjqx" new file mode 100644--- /dev/null +++ "b/data_all_eng_slimpj/shuffled/split2/finalzzgjqx" @@ -0,0 +1,5 @@ +{"text":"\\section*{List of the acronyms}\nWe introduce here the acronyms used throughout the document:\n\\begin{itemize}\n \\setlength{\\itemsep}{0pt}%\n \\setlength{\\parskip}{0pt}%\n\\item AD: Avalanche Diode\n\\item B\\&L: Box-and-Line dynode\n\\item BSM: Beyond the Standard Model\n\\item CC: charged currents\n\\item CCSNe: Core-Collapse Supernovae \n\\item CCQE: charge current quasi-elastic\n\\item CE: Collection Efficiency\n\\item CPL: Concrete Protective Liner\n\\item DAQ: Data Acquisition\n\\item DR: Design Report\n\\item DT: deuterium-tritium\n\\item EBU: Event Building Unit\n\\item ECal: ND280 Electromagnetic Calorimeter\n\\item FC: Fully Contained\n\\item FCFV: Fully Contained in Fiducial Volume \n\\item FGD: Fine Grained Detector\n\\item FRP: Fiber Reinforced Plastics\n\\item FV: Fiducial Volume\n\\item GUT: Grand Unified Theory\n\\item HDPE: High Density PolyEthylene\n\\item HK: Hyper-Kamiokande\n\\item HPD: Hybrid Photodetector\n\\item HPTPC: High Pressure Time Projection Chamber\n\\item HQE: High Quantum Efficiency\n\\item Hyper-K: Hyper-Kamiokande\n\\item IBC: International Board Representatives \n\\item IBD: Inverse Beta Decay\n\\item ID: Inner Detector\n\\item INGRID: Interactive Neutrino GRID\n\\item ISC: International Steering Committee\n\\item IWCD: Intermediate Water Cherenkov Detector\n\\item LAPPD: Large Area Picosecond PhotoDetector \n\\item LBNE: Long Baseline Neutrino Experiment\n\\item LAr: Liquid Argon calorimeter\n\\item LD: Laser Diode\n\\item LLDPE:Linear Low-Density PolyEthylene\n\\item LV: Lorentz Violation\n\\item MC: Monte Carlo\n\\item MLF: Material Science Facility\n\\item mPMT: Multi-channel Optical Module\n\\item MR: Main Ring synchrotron\n\\item NC: neutral currents\n\\item ND280: Near Detector 280m\n\\item NF: Nano Filter\n\\item OD: Outer Detector\n\\item PC: Partially Contained\n\\item PE: Photo Electron\n\\item PS: Power Supply\n\\item PTF: Photosensor Testing Facility\n\\item MH: neutrino mass hierarchy\n\\item QA: quality assurance\n\\item RBU: Readout Buffer Unit\n\\item RO: Reverse Osmosis\n\\item RCS: Rapid Cycling Synchrotron\n\\item SK: Super-Kamiokande\n\\item SM: Standard Model\n\\item Super-K: Super-Kamiokande\n\\item SUS: Stainless Steel (or Steel Use Stainless)\n\\item TITUS: Tokai Intermediate Tank for Unoscillated Spectrum\n\\item TPU: Trigger Processing Unit\n\\item TS: Target Station\n\\item UF: Ultra Filter\n\\item UPW: Ultra Purified Water\n\\item WAGASCI: Water Grid And SCIntillator detector\n\\item WC: Water Cherenkov\n\\end{itemize}\n\n\n\\subsection{Immersion test}\nSpecimens of HDPE lining sheet (GSE Gundle sheet, whose material is\nidentical to that for the CPL), with artificial extrusion-welded seam,\nwere immersed into the ultra-purified water (UPW) for certain periods\n(1, 2 to 7, and 8 to 31 days), and absorbance was compared to a\ncontrol sample without specimens. Amount of eluted materials into UPW,\ni.e. total organic carbon (TOC), anions and metals, were also\nmeasured.\nFigure \\ref{fig:liner-immersion} show the specimen and an example of\nmeasurements, where increase of the light absorbance were observed\nbetween the wavelength range of 200$\\sim$300\\,nm. Some amount of\nmaterial elution were observed, where eluted amounts per unit area and\ntime were significantly less for later periods. Although relation\nbetween the increase of light absorbance and the material elusion\nshould be studied, it is noted that range of PMT-sensitive wavelength\nis somewhat higher (300$\\sim$650\\,nm), so the effect to the\nexperiment may be limited. Similar results were obtained for\nGadolinium sulfate solutions.\n\n\\subsection{Measurements on material strength}\nTension tests were carried out for the CPL to estimate yield strength,\ntensile strength, and Young's modulus. Since HDPE has large elongation\nbefore breaking ($\\sim$500\\%), 1.0\\% proof stress was used as the\nyield strength (instead of 0.2\\% proof stress which is generally used\nfor other materials). Here, varying measurement conditions were\nexamined for tensioning velocity (0.05\\,mm\/min and 0.5\\,mm\/min) and for temperature (typical room temperature 23.5$^\\circ$\nCelsius and 15$^\\circ$ Celsius simulating water temperature).\nIt was found that measured yield strengths were smaller by a few to\nseveral tens of percent than the specification value (15.2\\,MPa as\nlisted in Table~\\ref{tab:liner-spec}). In general, lower tensioning\nspeed gives lower strength, due to large plasticity of HDPE. Strength\nalso depends significantly on temperature: HDPE becomes harder with\nlowering temperature, as common properties in high-polymer\nmaterials. The measurement in 15$^\\circ$ Celsius gave about 20\\%\nhigher strengths than those at 23.5$^\\circ$ Celsius.\nThe tension tests were also repeated on the samples with an\nextrusion-welded seam. For the most cases, none of peeling, fracture,\nnor other troubles were observed on welded seams, but the deformation\noccurred at the base material. The yield\/tensile strength were almost\nidentical to the values for base material.\n\n\\subsection{Creep test}\nCreep tests were performed with various tensile loads: 1\/4$\\times$M,\n3\/8$\\times$M, or 1\/2$\\times$M, where M = 18.2\\,MPa is the observed\nyield strength as 1.0\\% proof stress with tensioning speed of 5.0\\,cm\/min in 20$^\\circ$ Celsius. For the tests with load of 1\/4$\\times$M\n({\\it i.e.} 4.6 MPa), creep was not observed for about 30 days. Meanwhile, for tests with load of 3\/8$\\times$M (6.8\\,MPa) and\n1\/2$\\times$M (9.1\\,MPa), clear generation of creep was observed with 5\nand 10 days, respectively.\n\n\\subsection{Resistivity to localized water pressure}\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-pressure-test.pdf}\n\\caption{Setup for the test applying localized water pressure to the lining material.}\n \\label{fig:liner-pressure}\n \\end{center}\n\\end {figure}\nIdeally, the CPL sheet should be closely attached to the surface of\nflatly-backfilled concrete walls and thus firmly supported by\nthem. However, it is probable that cracks or rough holes exist or\nhappen in the backfill concrete wall, and thus the liner should\nlocally stand for water pressure by itself. To simulate the situation,\ntests to apply localized water pressure for the lining were performed\nwith variety of slit widths (2 to 8\\,mm) and hole diameters (40\nto 120\\,mm-$\\phi$), as illustrated in\nFig.~\\ref{fig:liner-pressure}. It is found that the liner survived for\n0.8\\,MPa water pressure without breaking for all cases. Although the\ntest load was applied only in a short period and durability for longer\nperiod should be examined, it is probable that the expected water\npressure is enough lower than the critical pressure causing creep.\n\n\\subsection{Water permeability}\nGenerally, plastic materials have a property to pass water as moisture\nvapor through molecules. It is referred as moisture permeability, or\nwater vapor transmission rate (WVTR), being represented with\ntransferred mass through unit area and time (g\/m$^2$\/24-hours). The\npermeability was studied for the GSE geomembrane (Gundle sheet, whose\nmaterial is quite simmilar to that for CPL\nStudliner)~\\cite{liner:JAEA-Tech-2013-036}. For the sheet with\nthickness $t$= 1.5\\,mm, WVTR ($P_{a1}$) was obtained to be\n1\\,g\/m$^2$\/24-hours at most for standard testing temperature\n(40$^\\circ$\\,Celsius). The water permeability coefficient ($k$) was\nthen deduced to be\n\\[\nk = P_{a1} \\times t \\times \\frac{g}{\\Delta P_v} = 2.5 \\times 10^{-12} cm\/s,\n\\]\nwhere $g$ is standard gravitational acceleration (9.8\\,m$^2$\/s) and\n$\\Delta P_v$ is difference of the water-vapor pressures of both sides\nof the geomembrane (90\\% of saturated vapor pressure at\n40$^\\circ$\\,Celsius, 75.22\\,hPa). Since the CPL is 5\\,mm thick, time\nuntil water permeates to backside of the CPL is:\n\\[\n0.5 {\\rm [cm]} \\times \\frac{1}{2.5 \\times 10^{-12} {\\rm [cm\/s]}} = 2 \\times 10^{11} {\\rm [s]},\n\\]\n{\\it i.e.} about 6,300 years. Since the total inner surface area of\nthe tank is 18,259 (54,750)\\,m$^2$ for 1 (3) tank options, amount of\nwater permeation through the entire liner surface will be:\n\\begin{eqnarray}\n&~& 18,250 (54,750) \\times 10^4\\ {\\rm [cm^2]} \\times 2.5 \\times 10^{-12}\\ {\\rm [cm\/s]} \\nonumber \\\\\n&=& 4.6 \\times 10^{-4}(1.4 \\times 10^{-3}){\\rm [cm^3\/s]} = 40 (120) \\ {\\rm [cm^3\/day]}, \\nonumber\n\\end{eqnarray} \nthus being negligible amount. \n\n\n\\subsection{Penetration structure}\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-penetration.pdf}\n\\caption{Schematic drawing for the penetration structure of a water pipe and \n a photo of its prototype.}\n \\label{fig:liner-penetration}\n \\end{center}\n\\end {figure}\nThe leak can happen around the components which penetrate the water\ntank lining, such as anchors to support PMT framework columns, water\nsupply\/return pipes, and so on. A possible design of the penetration\nstructure for the water pipes is illustrated in\nFig.~\\ref{fig:liner-penetration}. A metal pipe with a flange is coated\ntogether with PE resin of about 1.5\\,mm thickness, which can be\nextrusion-welded to adjacent CPLs. A prototype was made for the\ndesign as shown together in the figure, and tested with pressure up to\n1 MPa for 30 minutes. Tests with cyclic pressure (0.5\\,MPa, repeating\non\/off in a day for 5 days) and with continuous pressure (3 months\nwith applying 0.5\\,MPa were also performed. For all of the cases, no\nwater leak was observed.\n\n\n\\subsection{Rock Quality Information for Hakamagoshi and its Surroundings} \n\nThe Hakamagoshi area is characterized by Mount Hakamagoshi (elev. 1,159~m), Mount Mikata (elev. 1,142~m),\nand Mount Sarugayama (elev. 1,448~m), which form a mountain chain running from northeast to southwest. \nMountain streams along the north side of these peaks form part of the Oyabegawa river system, while \nsimilar streams on the southern side running to the east and south form the network of waterways feeding the Shogawa\nriver. \nIn short, the area around Hakamagoshi is the watershed for the Oyabegawa and Shogawa rivers, which is a \nstrong indicator of abundant underground water.\nIndeed, measurements have yielded spring water flows in excess of 100~tons per hour. \nHakamagoshi and its surroundings are formed from the \nprimary Futomiyama formation (from the Paloegene-Paleocene), sporadically covered with so-called Hida bedrock \n(a mixture of Shirakawa granite and Nohi ryolite). \nThe rock types in the Futomiyama formation as it is distributed throughout Hakamagoshi are primarily\nryholitic tuff, ryholitic welded tuff, and ryholitic lava. \nIn addition, quartz porphyry, porphyrite, dorelite and other rock intrusions of no known era are found \nwithin the formation. \nThe upper layers of the formation are inconsistently covered by Tori conglomerate from the Neogene-Miocene eras.\nIn particular this conglomerate is found above the Hakamagoshi tunnel at elevations around 900~m.\nThe upper most layers are composed of andesite and andesitic pyroclast from the same eras. \nOn site investigations of the lithic fragments from the Futomiyama formation indicate large amounts of CH$\\sim$CM class\nhardness rock. \n\nFigure~\\ref{fig:hakamagoshi_layer} shows the rock quality distribution around Hakamagoshi in hardness classes.\nIn the lower layers of the Futomiyama formation Shogawa granodiorite is widespread, and in \naddition to this formation, at 1000~m depths other distributions of Shogawa granodiorite and \nKose diorite may be found.\nSince it is generally thought that diorite layers are higher quality in comparison to the Futomiyama formation,\nthe key to realizing the Hakamagoshi option lies in determining whether or not such layers exist at the site. \n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{hakamagoshi_layer.pdf}\n\\caption{ Overhead and cross sectional views of the rock quality in the Hakamagoshi area appear in the upper and lower panels, respectively. \nThe dark pink color shows the diorite layer which is thought to extend to \nto areas where the rock overburden is 1000~m. \n}\n \\label{fig:hakamagoshi_layer} \\end{center}\n\\end {figure}\n\n\n\\subsection{Physics sensitivities}\n\\subsubsection{Muon rate at Mt. Hakamagoshi} \n\nFor the moment we assume that a detector is placed directly beneath the peak of Mount Hakamagoshi at the same \nlevel as the expressway tunnel and calculate the expected muon rate.\nIn order to study the reliability of these estimates the calculation is additionally performed for \nthe area inside of the tunnel and then compared with measurements made with a plastic scintillator-based detector.\nThe estimation uses 30~m elevation data from the ALOS database in the same way as calculations performed for the \nTochibora site. \nMUSIC and FLUKA are used for the muon simulation. \nWith a peak elevation of 1,159~m and a tunnel elevation of approximately 300~m, here the rock overburden is taken to be \nroughly 850~m. \nSimilarly the rock density is assumed to be the same as in Kamioka, 2.7~g\/$\\mbox{cm}^{3}$.\nFigure~\\ref{fig:hg_mu_rate} shows zenith, azimuthal, and energy distributions from the simulation.\nComparing to the Tochibora site, the muon rate at the Hakamagoshi site is roughly a factor of two times smaller \nand the mean muon energy is reduced by about 10\\%.\nThe following sensitivity studies have been performed based on these results.\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{hakamagoshi_mu.pdf}\n\\caption{ Muon zenith (left top) and azimuthal (left bottom) angular distributions as well as the energy distributions (right) for the Hakamagoshi site assuming an 850~m rock overburden are shown in thick red lines. Results for the Hyper-K Tochibora and \nMozumi sites, as well as the Super-K site are shown in thin red lines. \nBlue lines show measured values. \n}\n \\label{fig:hg_mu_rate} \\end{center}\n\\end {figure}\n\n\nTo validate the results of these simulations the muon rate inside the Hakamagoshi tunnel was measured \nin cooperation with NEXCO Central Nippon in an air conditioning chamber from January 18-20, 2016. \nThis chamber is not located beneath the mountain peak and has an overburden of only 450~m.\nTwo plastic scintillators of dimension $1000\\times200\\times45\\mbox{mm}^{3}$ and separated by \n100~mm were used for coincident muon identification. \nFor comparison the same measurement was repeated at the Super-Kamiokande experimental site.\nUsing this apparatus the muon rates were measured to be $1.9\\pm 0.1 \\times 10^{-3}$~Hz \nand $1.9\\pm 0.2\\times 10^{-4}$~Hz at the Hakamagoshi and Super-K sites, respectively.\nThat is, the air conditioning chamber's muon rate is $10.0\\pm1.1$ times larger.\nBased on the simulations outlined above the expected difference is a factor of 8.9, indicating \nthat the data and simulation are consistent within errors.\nFor this reason the simulation of the Hakamagoshi site below the mountain peak is taken to be reasonable.\n\n\n\\subsubsection{Neutrino beam from J-PARC} \n\nIn the following the Hakamakoshi detector is assumed to be beneath the peak of the mountain, as in the simulations above, \nand the sensitivity neutrino oscillations using the J-PARC neutrino beam is estimated.\nHakamagoshi has an off-axis angle of $2.4^\\circ$ and a baseline of 335~km.\nThe corresponding flux and $\\nu_{\\mu} \\rightarrow \\nu_{e}$ oscillation probabilities are shown in Figure~\\ref{fig:hg_flux_osc}.\nSince the off-axis angle is sightly smaller than that for the Tochibora site, the flux peak has shifted to slightly \nhigher energies, but since the baseline is correspondingly larger the oscillation maximum is found at nearly the same energy.\nUsing this information the sensitivity to CP violation has been estimated as shown in Figure~\\ref{fig:hg_cpv}.\nHere the first tank is assumed to be located in Tochibora with the second tank beginning operations six years later.\nA comparison is made between a second tank in Tochibora and one in Hakamagoshi.\nDue to the larger baseline to Hakamagoshi there is a corresponding decrease in event rate, resulting in a slightly larger \nstatistical error, though the systematic errors are taken to be the same.\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{hakamagoshi_beamflux.pdf}\n\\caption{ The neutrino flux at the Tochibora (TB) and Hakamagoshi (HG) sites from the J-PARC beam is\nshown in the left figure.\nIn the right figure the electron neutrino appearance probability for both sites is shown \nas a function of energy.}\n \\label{fig:hg_flux_osc} \\end{center}\n\\end {figure}\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{hakamagoshi_beamsens.pdf}\n\\caption{ Sensitivity to CP violation as a function of the true value of $\\delta_{cp}$ and for \nvarious assumed values of $\\mbox{sin}^{2}\\theta_{23}$. \nBoth plots assume a single detector operating for five years with a second detector \nbeginning operations in the sixth year. \nThe left (right) plot shows the result assuming the second detector is placed in Hakamagoshi (Tochibora).\nSolid lines show the sensitivity assuming only statistical errors and dashed lines \ninclude both systematic and statistical uncertainties.\n}\n \\label{fig:hg_cpv} \\end{center}\n\\end {figure}\n\n\n\n\n\\subsubsection{Low Energy Neutrino Observations} \n\nSpallation products from cosmic ray muons form the main background to low energy neutrino physics in Hyper-K, including \nsupernova and solar neutrino measurements.\nSince the muon background at Hakamagoshi is lower than that at Tochibora, the former is expected to have improved sensitivity \nto these neutrinos.\nUsing the muon simulation results presented above to derive the spallation backgrounds, Hyper-K's sensitivity \nto the observation of supernova relic neutrinos has been estimated.\nIn this analysis an analysis sample selected using neutron tagging (70\\% tagging efficiency) \nto identify the inverse beta decay signal in an energy window of 16 to 30~MeV has been assumed.\nFigure~\\ref{fig:hg_srn} shows the expected sensitivity assuming only one tank at at the Hakamagoshi site.\nAssuming a standard model of the relic neutrino flux and the first detector in Tochibora, the signal can \nbe observed with $3\\sigma$ ($5\\sigma$) significance after 4 (11)~years. \n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{hakamagoshi_srn.pdf}\n\\caption{ Sensitivity to supernova relic neutrinos as a function of operation time.\nThe left figure shows the number of relic neutrino candidate events and \nthe right figure shows the ability to discern this flux from the \nbackground in units of $\\sigma$.\n}\n \\label{fig:hg_srn} \\end{center}\n\\end {figure}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\\section{Background rate estimation} \\label{section:background}\n\n\\subsection{Background rate estimation for low energy neutrino study \\label{sec:lowe_bg}}\n\nIn this subsection, we will show the background rate estimation used\nfor the study of low energy neutrinos, such as solar neutrinos,\nsupernova neutrinos, and relic-supernova neutrinos. The most important\nbackground sources are the radioactive isotope of $^{222}$Rn contained\nin water, and radioactive spallation products created by cosmic-ray\nmuons. Other important radioactive isotopes\nare U and Th in the water, and $^{40}$K in the PMT glass; we need to\nsuppress the concentration of those isotopes to the similar level in\nSuper-K as well. On the other hand, the major background sources for\nthe anti-neutrino measurement is anti-neutrino backgrounds from\nnuclear power reactors, which limit the energy threshold at around\n10\\,MeV; the smaller contribution comes from the radioactive\nbackground of $(\\alpha, n)$ reactions. In the background calculation,\nthe most complicated task is the estimation of the muon spallation\nproductions and its background reduction by the analyses, because it\ndepends on the detector location and the detector performance. In the\nfollowing paragraphs, after discussing radon backgrounds,\nwe focus on the discussion of the muon spallation backgrounds.\n\n\\subsubsection{Radon background}\n\nRadon ($^{222}$Rn) is a radioactive noble gas, with a half-life of 3.8 days. \n$^{222}$Rn occurs as a daughter nuclide in the $^{238}$U decay scheme,\nvia the decay of $^{226}$Ra ($\\tau_{1\/2} = 1599$ years).\nSmall but finite quantities of $^{226}$Ra exist in all materials and\ntherefore, every material can produce $^{222}$Rn.\nAs a gaseous isotope, $^{222}$Rn can easily escape from materials used\nin the construction of Hyper-K and the radioactivity content\nof construction materials must be carefully screened.\nThe decay of $^{222}$Rn produces several daughter isotopes,\nmost of which are not sufficiently energetic to produce Cherenkov\nlight in the Hyper-K detector. \nThe most serious background for solar neutrino measurements\nis the radon daughter bismuth-214 ($^{214}$Bi)\nwhich decays via beta emission with a Q-value of 3.27 MeV.\nThis limits the energy threshold of the solar neutrino\nmeasurements in which a neutrino-electron elastic scattering reaction\nis used.\n\nIn the same energy region, $^{208}$Tl in thorium series could become\nanother serious source of the background.\nHowever, from the results of radon assay with special radon\ndetectors~\\cite{70Lradon,700Lradon} in Super-K, \nthe contamination of the radon in thorium series ($^{220}$Rn)\nlooks much smaller than that of $^{222}$Rn in Super-K water.\nSo, we discuss only $^{222}$Rn in this section. \n\nTypical radon concentrations in Mozumi mine and Super-K are\nsummarized in Table~\\ref{tab:radon_concentrations}.\n\\begin{table}[htbp]\n \\caption{\\label{tab:radon_concentrations}\n Typical radon concentrations in Mozumi mine and in\n Super-K.}\n\\begin{ruledtabular}\n\\begin{tabular}{lc}\nDetector site & Radon concentration \\\\\n\\hline\nMine air in Mozumi~\\cite{Takeuchi:1999} & $\\sim1200$ [Bq\/m$^3$]\\\\\nSK-I inner detector water (upper half)~\\cite{Takeuchi:1999} & $<1.4$ [mBq\/m$^3$]\\\\\nSK-I inner detector water (bottom)~\\cite{Takeuchi:1999} & $3 \\sim 5$ [mBq\/m$^3$]\\\\\nSK-IV supply water & $< \\sim 1$ [mBq\/m$^3$]\\\\\nSK-IV return water & $8 \\sim 10$ [mBq\/m$^3$]\\\\\n\\hline\n\\end{tabular}\n\\end{ruledtabular}\n\\end{table}\nThe SK-IV return water is taken at $\\sim 18$ ton\/hour from inner detector\nand at $\\sim 42$ ton\/hour from outer detector~\\cite{Abe:2013gga}.\nSo, we think the radon concentration in the SK-IV outer detector\nis close to (or larger than) that in the SK-IV return water.\nFrom the event rate comparison between SK-IV and SK-I, the radon concentration\nin SK-IV inner detector is similar or less than that of SK-I.\nTherefore, the radon concentration would be different by several factors\nbetween inner and outer detectors in SK-IV.\nHowever, in Super-K detector, water flow is controlled well by temperature and flow\nrate balances~\\cite{Abe:2013gga}, and then the water condition in inner\ndetector has been stable.\nFigure~\\ref{fig:sk4-vertex} shows a vertex distribution of the final\ndata sample of the solar neutrino analysis in SK-IV.\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=1.00\\textwidth]{background\/figs\/sk4-vertex.pdf}\n \\caption{\n Vertex distribution of the SK-IV 2645-day final data sample in\n solar neutrino analysis in different electron kinetic energy regions.\n The black lines indicate fiducial volume region in each energy range.\n Whole area corresponds to 22.5 kton volume,\n and the fiducial volume above 5.0 MeV is 22.5 kton.\n The color shows the event rate (\/day\/bin). The R and Z correspond to\n the detector horizontal and vertical axis, respectively.}\n \\label{fig:sk4-vertex}\n \\end{center}\n\\end {figure}\nThe remaining event rate in the central detector is kept low\nwhile the barrel and bottom of the detector are higher than that.\nThis shows the water flow control in Super-K detector works well.\nFor the solar neutrino measurements, a threshold of 4.5 MeV (electron\nkinetic energy) in 22.5 kton fiducial volume was achieved in Super-K I.\n\nIn this design report, we estimate the radon concentration in\nthe Hyper-K tank water would be about 1.6\\,${\\rm mBq}\/{\\rm m}^{3}$\nin average in whole detector, as described in section~\\ref{sec:radon-in-water}. \nWhen applying the same water flow control technique as Super-K,\nthe radon concentration in the central Hyper-K detector will be reduced.\n\nMoreover, we could suppress $^{214}$Bi events thanks to better\nphoton yield in Hyper-K. \nFigure~\\ref{fig:bi214} shows expected observed energy spectrum of\nbeta decay of $^{214}$Bi in Super-K and Hyper-K.\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.70\\textwidth]{background\/figs\/bi214-kin.pdf}\n \\caption{An estimation of expected Bi-214 energy spectrum.\n The black, red and blue lines are the original beta decay spectrum,\n the expected observed spectrum in SK-IV,\n and expected observed spectrum in Hyper-K, respectively.\n The black histogram is observed event rate of the SK-IV final data\n sample in 22.5 kton fiducial volume.\n The vertical axis is event rate in arbitrary unit.}\n \\label{fig:bi214}\n \\end{center}\n\\end {figure}\nAt 4.5 MeV (electron kinetic energy), a suppression about factor 10 is expected\nin Hyper-K detector comparing to Super-K detector. \nActually, we have observed an expected energy resolution difference\ndue to photon yield change between SK-I and SK-II.\n\nAnother possible difference among Super-K and Hyper-K detectors related\nto radon background would be the lining material of the detector.\nAs discussed in section~\\ref{section:tank-liner}, 5 mm thickness HDPE\nwill be used to line the Hyper-K detector, and radon could permeate a HDPE sheet.\nTypical radon permeability through a HDPE sheet \nis reported by various groups as $O(10^{-8}) \\sim O(10^{-7})$\ncm$^2$\/s~\\cite{radon1,radon2,radon3,radon4,radon5}. \n\nAs shown in Table~\\ref{tab:radon_concentrations}, the typical radon\nconcentrations are different by about 5 order of magnitude\nbetween mine air and Super-K OD water.\nFor Hyper-K, radon concentration in OD water through the\nradon permeation from outside detector into Hyper-K detector\ncould be estimated as $O(10)$ mBq\/m$^3$ in Hyper-K OD water\nunder several assumptions, like\n(1) a radon permeability of the Hyper-K HDPE sheet is $10^{-8}$ cm$^2$\/s,\n(2) radon concentration in mine water (spring water in the mine) is $10^{3}$ Bq\/m$^3$,\n(3) there is no water flow between Hyper-K ID and Hyper-K OD, and\n(4) the volumes of mine water and Hyper-K OD water contributing to this effect are similar.\nThis estimation gives a similar radon concentration in Super-K OD detector,\nthough the uncertainty is large.\n\nIn order to reduce the uncertainty of (1) in this estimation, we are planning to\nmeasure radon permeability of a Hyper-K HDPE sheet.\nFigure~\\ref{fig:radon-permeation} shows a device to assay radon\npermeability through a sheet in Kamioka.\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.70\\textwidth]{background\/figs\/radon-permeation.pdf}\n \\caption{A system to measure radon permeation of a sheet in Kamioka.}\n \\label{fig:radon-permeation}\n \\end{center}\n\\end {figure}\nThe performance of the device is still under tuning, but\nthe current sensitivity on radon permeation assay is about $O(10^{-9})$ cm$^2$\/s\nfor a 1 mm thickness sheet. Therefore, this device has enough\nsensitivity to test the Hyper-K HDPE sheet.\n\nIn order to achieve (3) in Hyper-K, we are designing more hermetic ID\ndetector to reduce water flow between ID and OD.\nWe also apply the same water flow control techniques realized in Super-K\nto keep radon around detector wall in Hyper-K ID.\n\nAs a summary, applying the same radon reduction techniques developed in\nSuper-K, a similar radon concentration in Hyper-K inner detector water is expected.\nThe radon permeation through lining material might increase, but an\ninitial estimation shows a similar level of the radon concentration in\nouter detector water in Hyper-K. In order to avoid increase of radon in inner\ndetector, we are planning more hermetic inner detector.\nWe are going to measure radon permeation of our liner candidates, too.\nMoreover, about factor 10 tolerance is expected at 4.5 MeV\nthanks to improvement of the energy resolution.\nTherefore, we think 4.5 MeV (electron kinetic energy)\nthreshold for solar neutrino measurements\nwould be feasible in the Hyper-K detector.\n\n\n\\subsubsection{Muon spallation}\n\t \nRadioactive isotopes produced by cosmic-ray muon-induced spallation\nare potential backgrounds for low energy neutrinos. Generally, the\nproduction rate depends strongly on the muon flux and the average\nenergy, and the delayed radioactive decays cause the backgrounds in\nthe energy region below about 20\\,MeV. If the lifetime of radioactive\nisotope is relatively short on the order of a few seconds or less, the\nspallation backgrounds can be mitigated by time\/volume cuts based on\nthe reconstructed muon track. Therefore, the detailed estimation of\nthe cosmic-ray muon intensity and the spallation production rate are\nof great importance in demonstrating the sensitivity of Hyper-K to low\nenergy neutrinos.\n\nThe muon intensity at the planned site can be estimated using the\ncalculated surface muon flux and energy, the mountain profile, the\nrock density and compositions. The muon flux ($J_{\\mu}$) and average\nenergy ($\\overline{E}_{\\mu}$) at underground sites are estimated by\nthe muon simulation code (\\texttt{MUSIC})~\\cite{Antonioli:1997}, a\nthree-dimensional MC tool dedicated to muon transportation in\nmatter. In this MC, surface muons are generated according to\nthe \\textit{Modified Gaisser Parameterization}~\\cite{Tang:2006}\nsea-level muon flux distribution. A digital map of the topological\nprofile of Nijuugo-yama with a 5\\,m mesh\nresolution~\\cite{GeographicalSurvey:2010} is shown in\nFig.~\\ref{fig:profile_nijuugoyama}. The Hyper-K detector will be\nlocated around the basing point at the altitude of 508\\,m, referenced in\nSection~\\ref{section:location} corresponds to a position under the old mountain peak\nbefore the surface mining. Based on this elevation data, we calculate\nslant depths as a function of zenith and azimuth angle at an arbitrary\npoint of Hyper-K candidate sites, and estimate the survival probability of muons\nafter the muon transportation through the rock for each angle using\nthe \\texttt{MUSIC} simulation.\n\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.70\\textwidth]{background\/figs\/Altitude-HyperK-figure2-PeakSearch-Center-WithoutLine.pdf}\n \\caption{Topological profile of Nijuugo-yama~\\cite{GeographicalSurvey:2010}. The black point is the basing point for the Hyper-K site.}\n \\label{fig:profile_nijuugoyama}\n \\end{center}\n\\end {figure}\n\n\nPreviously, the value of $J_{\\mu}$ and $\\overline{E}_{\\mu}$ at KamLAND\nin Ikeno-yama are evaluated based on the \\texttt{MUSIC} simulation for\nvarious rock types~\\cite{Tang:2006,Abe:2010}. The value of $J_{\\mu}$\nis dependent on the type of rock. Varying the specific gravity of rock\nfrom 2.65 to 2.75\\,${\\rm g}\/{\\rm cm}^{3}$ in the \\texttt{MUSIC}\nsimulation yields values of $J_{\\mu}$ that agree with the KamLAND muon\nflux measurement~\\cite{Abe:2010}. As both Nijuugo-yama and Ikeno-yama\nare skarn deposit, which are common characteristic in the Kamioka\nmine, the simulation for Hyper-K assumes the same rock type used in\nRef.~\\cite{Abe:2010}. Figure~\\ref{fig:muon_flux_and_energy} shows the\ncalculated $J_{\\mu}$ and $\\overline{E}_{\\mu}$ for Hyper-K at the\naltitude of 508\\,m for 2.70\\,${\\rm g}\/{\\rm cm}^{3}$ specific gravity\nIkeno-yama rock. The values of $J_{\\mu}$ and $\\overline{E}_{\\mu}$ vary\ngreatly depending on the shallowest rock thickness on the west or\nsouth side, as indicated in Fig.~\\ref{fig:profile_nijuugoyama}.\n\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.48\\textwidth]{background\/figs\/MuonFlux-HyperK-from-MountainDepth-xy-Fine-figure2-WithoutLine.pdf}\n \\includegraphics[width=0.48\\textwidth]{background\/figs\/MuonFlux-HyperK-from-MountainDepth-xy-Fine-figure3-WithoutLine.pdf}\n \\caption{Calculated muon flux ($J_{\\mu}$) and average energy ($\\overline{E}_{\\mu}$) at the altitude of the Hyper-K (508\\,m) detector. The black point is the basing point for the Hyper-K site.}\n \\label{fig:muon_flux_and_energy}\n \\end{center}\n\\end {figure}\n\n\nTable~\\ref{tab:muon_simulation} summarizes the calculated $J_{\\mu}$\nand $\\overline{E}_{\\mu}$ in Hyper-K and Super-K for 2.70\\,${\\rm\ng}\/{\\rm cm}^{3}$ specific gravity. Considering the variation of\n$J_{\\mu}$ for different rock types, we assume uncertainties of\n$\\pm$20\\% for $J_{\\mu}$. Because the Super-K site is deeper, the value\nof $J_{\\mu}$ for Hyper-K is higher than Super-K by a factor of 4.9. On\nthe other hand, the value of $\\overline{E}_{\\mu}$ for Hyper-K is\nsmaller than Super-K as indicated in Fig.~\\ref{fig:muon_flux_energy},\nbecause the relative contribution of lower energy muons becomes larger\nat a shallower site. Figure~\\ref{fig:muon_flux_angle} shows the muon\nflux as a function of zenith angle $\\theta$ (upper) and azimuth angle\n$\\phi$ (lower) for Super-K and Hyper-K at the basing point. We\nconfirmed that the \\texttt{MUSIC} Monte Carlo simulation has been shown to be in good agreement with the Super-K data, as shown in Figure~\\ref{fig:muon_flux_angle}. In Hyper-K, the major contribution of muon flux is introduced by\nthe flux in the west and the south.\n\n\n\\begin{table}[t]\n\\caption{\\label{tab:muon_simulation}Calculated muon flux ($J_{\\mu}$) and average energy ($\\overline{E}_{\\mu}$) in Hyper-K and Super-K for 2.70\\,${\\rm g}\/{\\rm cm}^{3}$ specific gravity Ikeno-yama rock based on the simulation method~\\cite{Tang:2006}. The basing point in Hyper-K is illustrated in Fig.~\\ref{fig:profile_nijuugoyama}.}\n\\begin{ruledtabular}\n\\begin{tabular}{lccc}\nDetector site & Vertical depth (m) & $J_{\\mu}$ ($10^{-7}\\,{\\rm cm}^{-2} {\\rm s}^{-1}$) & $\\overline{E}_{\\mu}$ (GeV) \\\\\n\\hline\nHyper-K (basing point) & 600 & 7.55 & 203 \\\\\nSuper-K & 1,000 & 1.54 & 258 \\\\\n\\end{tabular}\n\\end{ruledtabular}\n\\end{table}\n\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.60\\textwidth]{background\/figs\/MuonFlux-HyperK-Energy-figure1-WithSuperK-a.pdf}\n \\caption{Calculated muon energy spectra for Super-K and Hyper-K at the basing point based on the \\texttt{MUSIC} simulation.}\n \\label{fig:muon_flux_energy}\n \\end{center}\n\\end {figure}\n\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[angle=270,width=0.60\\textwidth]{background\/figs\/MuonFlux-HyperK-Theta-figure1-WithSuperK-a.pdf}\n \\includegraphics[angle=270,width=0.60\\textwidth]{background\/figs\/MuonFlux-HyperK-Phi-figure1-WithSuperK-a.pdf}\n \\caption{Muon flux as a function of zenith angle $\\theta$ (upper) and azimuth angle $\\phi$ (lower) for Super-K and Hyper-K at the basing point. The east corresponds to the azimuth angle of zero degree. The blue lines show the data for Super-K, and the red lines show the MC predictions for Super-K and Hyper-K based on the \\texttt{MUSIC} simulation. The absolute flux and the shape of the Super-K data, which are determined by slant depths for each angle, are well reproduced by MC.}\n \\label{fig:muon_flux_angle}\n \\end{center}\n\\end {figure}\n\n\nBased on the muon flux and energy spectrum calculated by\nthe \\texttt{MUSIC} simulation, we can estimate the isotope production\nrates by muon spallation in a planned detector. \\texttt{FLUKA} can be \nused to reliably model nuclear and particle physics processes\ninvolved in muon spallation. Previously, the measured isotope\nproduction rates in a underground detector were compared with\nthe \\texttt{FLUKA} simulation~\\cite{Abe:2010}. However, owing to\nlarge uncertainties on the isotope production cross sections by muons\nor their secondaries, the production rate between data and MC differ\nby up to a factor of two, as shown in Table V of\nRef.~\\cite{Abe:2010}. In order to minimize the uncertainties, we use\nthe isotope production rates observed in Super-K as a basis, and the\nvalues in Hyper-K are estimated based on the muon flux ratio\ncalculated by \\texttt{MUSIC} and the isotope yield ratio\nby \\texttt{FLUKA},\n\\begin{equation}\nR_{i} ({\\rm Hyper\\mathchar`-K}) = R_{i} ({\\rm Super\\mathchar`-K}) \\times \\frac{J_{\\mu} ({\\rm Hyper\\mathchar`-K})}{J_{\\mu} ({\\rm Super\\mathchar`-K})} \\times \\frac{Y_{i}({\\rm Hyper\\mathchar`-K})}{Y_{i} ({\\rm Super\\mathchar`-K})}\n\\end{equation}\nwhere $R_{i}$ is the production rate per unit volume for isotope $i$,\n$J_{\\mu}$ the muon flux (${\\rm cm}^{-2} {\\rm s}^{-1}$), $Y_{i}$ the\nyield per muon track length ($\/\\mu\/{\\rm m}$) for isotope\n$i$. We use \\texttt{FLUKA} version 2011.2b to estimate the isotope\nyields in Hyper-K and Super-K. A water-filled volume of 40-m square\nand 40-m length is used in the simulation, and the analysis of isotope\nproductions is limited within the inner volume of 40-m square and 20-m\nlength in order to avoid a boundary effect. To include the muon charge\nand energy dependence in isotope production yields, beams of both\n$\\mu^{+}$ and $\\mu^{-}$ with a calculated energy spectrum produced\nby \\texttt{MUSIC} were simulated, and the isotope yields by $\\mu^{+}$\nand $\\mu^{-}$ are combined based on their weighted average assuming\nthat a relative intensity of $\\mu^{+}$ to $\\mu^{-}$ is\n1.3. Table~\\ref{tab:isotope_yield_estimation} shows the estimation of\nisotope production yields for Hyper-K and Super-K, the ratio of\nisotope yields, $Y_{i} ({\\rm Hyper\\mathchar`-K}) \/ Y_{i} ({\\rm\nSuper\\mathchar`-K})$. The ratio of the production rates, $R_{i} ({\\rm\nHyper\\mathchar`-K}) \/ R_{i} ({\\rm Super\\mathchar`-K})$, are also\ncalculated by multiplying the isotope yield ratio by the muon flux\nratio, $J_{\\mu} ({\\rm Hyper\\mathchar`-K}) \/ J_{\\mu} ({\\rm\nSuper\\mathchar`-K}) = 4.9 \\pm 1.0$, which was evaluated from\nthe \\texttt{MUSIC} simulation. We assume uncertainties of $\\pm$20\\%\nfor the muon flux ratio considering the possibility of different rock\ntypes for the Hyper-K and Super-K sites. The resulting increase in\nisotope production rate per unit volume from Super-K is approximately\na factor of $4 \\pm 1$ in Hyper-K, which is used for studies of the\nHyper-K physics potential in the following sections.\n\n\n\\begin{table}[t]\n\\caption{\\label{tab:isotope_yield_estimation}Estimation of isotope production yields for Hyper-K and Super-K by muon spallation with \\texttt{FLUKA}. The ratio of the production yields for Hyper-K compared with Super-K are also listed. The ratio of the production rates are calculated by multiplying the isotope yield ratio by the muon flux ratio of $4.9 \\pm 1.0$, evaluated by the \\texttt{MUSIC} simulation.}\n\\begin{ruledtabular}\n\\begin{tabular}{lcccc}\n & \\multicolumn{2}{c}{Isotope yield by \\texttt{FLUKA} ($\\mu$\/m)} &Ratio of isotope yield & Ratio of production rate \\\\\n\\raisebox{1.5ex}[1.5ex][0.75ex]{Isotope} & Hyper-K & Super-K & (Hyper-K \/ Super-K) & (Hyper-K \/ Super-K) \\\\\n\\hline\n$^{12}$B & $8.05 \\times 10^{-5}$ & $9.93 \\times 10^{-5}$ & $0.811 \\pm 0.078$ & $3.98 \\pm 0.88$ \\\\\n$^{12}$N & $8.70 \\times 10^{-6}$ & $1.11 \\times 10^{-5}$ & $0.785 \\pm 0.075$ & $3.84 \\pm 0.85$ \\\\\n$^{9}$Li & $1.23 \\times 10^{-5}$ & $1.68 \\times 10^{-5}$ & $0.732 \\pm 0.070$ & $3.59 \\pm 0.80$ \\\\\n$^{8}$Li & $8.67 \\times 10^{-5}$ & $1.08 \\times 10^{-4}$ & $0.805 \\pm 0.077$ & $3.95 \\pm 0.87$ \\\\\n$^{15}$C & $5.12 \\times 10^{-6}$ & $6.68 \\times 10^{-6}$ & $0.768 \\pm 0.073$ & $3.76 \\pm 0.83$ \\\\\n$^{16}$N & $2.74 \\times 10^{-4}$ & $3.41 \\times 10^{-4}$ & $0.804 \\pm 0.077$ & $3.94 \\pm 0.87$ \\\\\n$^{11}$Be & $5.32 \\times 10^{-6}$ & $7.76 \\times 10^{-6}$ & $0.685 \\pm 0.065$ & $3.36 \\pm 0.74$ \\\\\n\\end{tabular}\n\\end{ruledtabular}\n\\end{table}\n\n\\subsubsection{Muon spallation background reduction}\n\nThe spallation products as backgrounds have their origin in the\nspallation reaction of the cosmic muons. Therefore, we can identify\nand remove these spallation products if we compare their\nfour-dimensional correlation with corresponding muons. In this\nsection, we will discuss the muon spallation backgrounds using\nthese correlations. The spallation reduction method is being used in\nsupernova relic neutrino searches at Super-K.\n\n\\paragraph{Method of muon spallation background reduction\\\\}\n\nWe apply a likelihood ratio test on low-energy events to reduce\nspallation backgrounds. The detail is discussed below.\\\\ With water\nCherenkov detectors, such as Super-K or Hyper-K, we\ncan measure the times, positions and energies of the spallation\nproducts and their preceding muon tracks. It is also possible to\nmeasure the energy deposit per unit length $dE\/dx$ along muon tracks,\nby deconvoluting Cherenkov ring hits. The peak position of $dE\/dx$\ndistribution can be assumed as the position where muon spallation\noccurs.\\\\\n\nWe use following valiables for spallation background reduction. \n\\begin{itemize}\n\t\\item Time difference $\\delta t$, between the low-energy event and the preceding muon.\n\t\\item Transverse distance $l_{trans}$, which is defined as the perpendicular distance from the muon track to the low-energy event.\n\t\\item Longitudinal distance $l_{long}$, which is defined as the horizontal distance from the peak position of $dE\/dx$ on reconstructed muon track and the low-energy event.\n\t\\item Residual charge $Q_{peak}$, which is the amount of light seen in $the$ dE\/dx distribution in a width of 4.5 m centered on the peak.\n\\end{itemize}\n\n\\begin {figure}[htbp]\n\\begin{center}\n\t\\includegraphics[width=0.35\\textwidth]{background\/relic_spacut.pdf}\n\t\\caption{\n\t\tSchematic figure for showing spallation distance variables\\cite{KirkRyanDrThesis}.\n\t}\n\t\\label{fig:relic_spacut}\n\\end{center}\n\\end {figure}\n\nA schematic figure of spallation distance variables are shown in Figure~\\ref{fig:relic_spacut}.\nTheir actual distributions can be found in a reference \\cite{KirkRyanDrThesis}.\nThe probability density functions $PDF_{spa}$ and $PDF_{rand}$ of each valuables are given from the fitting results of actual spallation candidates and non-spallation (random) event samples, respectively.\nThe likelihood ratio $\\Lambda$ is defined using PDFs as follows:\n\\begin{equation}\n\\begin{split}\n\t\\Lambda = -2\\log{\\frac{PDF_{spa}(Q_{peak}) \\times PDF_{spa}(\\delta t) \\times PDF_{spa}(L_{trans}) \\times PDF_{spa}(L_{long})}\n\t{PDF_{rand}(Q_{peak}) \\times PDF_{rand}(\\delta t) \\times PDF_{rand}(L_{trans}) \\times PDF_{rand}(L_{long})}}\n\\end{split}.\n\\end{equation}\nBecause any preceding cosmic muon can be a cause of spallation backgrounds, we calculate the likelihood ratio $\\Lambda$ with all muons within 30\\,seconds before the low energy event.\nThe largest likelihood ratio $\\Lambda$ is adopted as the $\\Lambda$ value for the low energy event.\nWe can arbitrarily choose the cut value for the likelihood ratio, which defines the reduction efficiency and the signal efficiency. \n\n\\paragraph{Estimated muon spallation background after reduction\\\\}\\label{par:spallation_reduction}\nWhen we have more cosmic muon flux, the number of preceding muons\nthat are randomly paired with a low-energy event will be increased. As a result, we\nwill have more chance to have ``more spallation like'' $\\Lambda$ value\nfor a low-energy event even if it is a non-spallation event. On the\nother hand the likelihood ratio is not changed for real spallation\nevents, because they will be paired to their mother muons regardless\nof the number of preceding muons. Consequently we will have worse\nseparation between the likelihood distribution of spallation\nbackgrounds and that of non-spallation events with more cosmic muon flux.\nHere we studied the spallation reduction efficiency and the signal efficiency in Hyper-K, based on the data of SK-II.\nThe spallation reduction efficiency is defined as the rate of spallation events that survived the likelihood cut.\nThe likelihood distribution of\nnon-spallation event sample is also made from the data, pairing the\nlow energy events with muons which were detected 300$\\sim$330\\,s before these events.\nThe effect of shallower Hyper-K location on the spallation reduction method is studied by increasing the proceding muons with random muon data.\n\\\\\nIn following, we will show two cases of spallation cuts.\nOne is defined to keep the signal efficiency of 80\\%, which is applied for usual analysis, e.g. solar neutrino analysis.\nTo estimate the performances of this cut, those are signal efficiency and background reduction efficiency,\nwe use the real events of SK-II between 17.5 and 20\\,MeV.\nWe assume the same signal efficiency and the same reduction efficiency below 17.5\\,MeV.\n\nAs the result, the spallation reduction efficiency ($\\epsilon_{reduction}$) will be 1.2\\% and 3.9\\% for the same and 5 times larger amount of the\ncosmic muons for this criteria, respectively.\nFinally, the ratio of remaining spallation events in the solar neutrino analysis is calculated as follows:\n\\begin{equation}\n\tR_{spallation}({\\rm Hyper\\mathchar`-K\/}{\\rm Super\\mathchar`-K}) = \\frac{R_{production}({\\rm Hyper\\mathchar`-K})}\n\t{R_{production}({\\rm Super\\mathchar`-K})} \\times\n\t\\frac{\\epsilon_{reduction}({\\rm Hyper\\mathchar`-K})}\n\t{\\epsilon_{reduction}({\\rm Super\\mathchar`-K})}.\n\t\\label{eq:spallation_production_rate}\n\\end{equation}\nHere, $\\epsilon_{reduction}({\\rm Hyper\\mathchar`-K})$ is found to be 3.9\\% for Hyper-K at Tochibora-site as discussed above.\n${\\epsilon_{reduction}({\\rm Super\\mathchar`-K})}$ of $\\sim$6\\% is taken form SK-II solar neutrino analysis.\n$R_{production}({\\rm Hyper\\mathchar`-K})$ and\n $R_{production}({\\rm Super\\mathchar`-K})$ are the rate of spallation isotope production per unit volume in Hyper-K and Super-K respectively.\n\tReferring to the result of the former section, ${R_{production}({\\rm Hyper\\mathchar`-K})}\/{R_{production}({\\rm Super\\mathchar`-K})}$ is assumed to be $4\\pm1$.\n\tSince, we conclude the ratio of remaining spallation events of Hyper-K to Super-K is $R_{spallation}({\\rm Hyper\\mathchar`-K\/}{\\rm Super\\mathchar`-K})=2.7$.\\par\nMore strict spallation cut is applied for very low background analysis, e.g. supernova relic neutrino search.\nIn this case, the cut value is defined to remove the spallation backgrounds to the level of less than 1 event left between 17.5 and 20\\,MeV or between 20 and 26 MeV.\nSo, the signal efficiency will be affected by the increased amount of muons.\nThe signal efficiency will be 79\\% (29\\%) for the energy range of 17.5$\\sim$20~MeV and 90\\% (54\\%) for 20$\\sim$26~MeV, for the same (5 times larger) amount of the cosmic muons.\nBecause the amount of spallation backgrounds decreases exponentially at the higher energies, no spallation background is expected above 26\\,MeV.\nThe results are shown in Table~\\ref{tab:spacut_solar} and Table~\\ref{tab:spacut_relic}.\n\n\\begin{table}\n\\begin{center}\n\t\\caption{The expected spallation background reduction efficiency for solar neutrino analysis.\n\tThe signal efficiency of 80\\% is kept for the event selection.}\n\\label{tab:spacut_solar}\n\\begin{tabular}{lcccc}\n\\hline \\hline\nCosmic muons rate, comparing to Super-K && $\\times 1$ & $\\times 5$ (Tochibora site) \\\\\n\\hline \nSignal Efficiency && 80\\% & 80\\% \\\\\nSpallation Reduction Efficiency && 1.2\\% & 3.9\\% \\\\\n\\hline \\hline \n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n\t\\caption{The expected spallation background reduction efficiency for supernova relic neutrino searches.\n\tThe spallation background is reduced to the level of less than 1 event for the each energy range.}\n\\label{tab:spacut_relic}\n\\begin{tabular}{lcccc}\n\\hline \\hline\nCosmic muons rate, comparing to Super-K && $\\times 1$ & $\\times 5$ (Tochibora site) \\\\\n\\hline \nSignal Efficiency ( - 20\\,MeV) && 79\\% & 29\\% \\\\\nSignal Efficiency (20 - 26\\,MeV) && 90\\% & 54\\% \\\\\n\\hline \\hline \n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\subsection{Neutron background estimation for atmospheric neutrino\/proton decay study \\label{sec:neutron_bg}}\n\nThis subsection will discuss the possible cosmic-ray\nbackgrounds for the atmospheric neutrino and proton decay analyses,\nwhich visible energy is greater than 30~MeV. In this energy range the\nspallation background caused by cosmic muons, which is described in\nSection~\\ref{sec:lowe_bg}, can be neglected.\n\nIn the Super-K detector case, thanks to the double structure of the\ninner and outer detector, cosmic muons entering the detector can be\neasily rejected by looking at hit clusters around the entering and\nexiting points of muons. According to Super-K's experience, the\nestimated background of the cosmic muons are negligible ($\\sim$0.1\\%\nin the final atmospheric neutrino fully-contained sample).\nConsidering that Hyper-K design is basically same structure, similar\nlevel of the background rejection performance for cosmic muons by the\nouter detector is expected even if the cosmic muon rate is increased\nby several factor due to the shallower site of Hyper-K.\n\n\nOne possible concern about the background due to neutral particle,\nsuch as neutrons and neutral kaons, which are produced by hadronic\ninteraction of cosmic muons near the detector, and enter the detector\nwithout being detected by the outer detector. Such particles may\npenetrate deep into the detector and produce hadrons, such as $\\pi^0$,\nby interacting with water, which could become electron-like\nbackgrounds. Figure~\\ref{fig:neutron_pi0_event} shows a Super-K event\ndisplay of the simulated neutron background events which produced\n$\\pi^0$ particle in the detector.\n\n\\begin{figure}[htb]\n\\includegraphics[width=0.6\\textwidth]{background\/neutron_bg_display-crop.pdf}\n\\caption{Event display of a neutron background simulation. $\\pi^0$ is produced by the interaction of $n + X \\to X' + \\pi^0$. A neutron is simulated with an energy of 1~GeV of the center of the detector.}\n\\label{fig:neutron_pi0_event}\n\\end{figure}\n\nFor the study of neutron backgrounds, the flux of cosmic neutron at the detector site are estimated \nbased on \\cite{PhysRevD.73.053004} and shown in Table~\\ref{tab:neutron_flux}. \nAccording to this table, the neutron flux of $E>100$~MeV at Hyper-K site will increase by a factor of $\\sim$8 \nthan that of Super-K site.\n\n\n\\begin{table}\n\\begin{center}\n\\caption{Comparison of various parameters related to neutron background estimation between Super-K and Hyper-K.\n The estimation of these values are based on \\cite{PhysRevD.73.053004}. }\n\\label{tab:neutron_flux}\n\\begin{tabular}{lccc}\n\\hline \\hline\n && Super-K site & Hyper-K site \\\\\n\\hline \nSite depth (m.w.e.) && 2700 & 1750 \\\\\nCosmic muon rate (10$^{-6}$\/cm$^2$\/sec) && 0.13$\\sim$0.14 & 1.0$\\sim$2.3 \\\\\nEffective depth (m.w.e.) && 2050 & 1170 \\\\\n$$ (GeV) && 219 & 146 \\\\\n$\\Phi_n$ (10$^{-9}$\/cm$^2$\/sec) && 12.3 & 101 \\\\\n~~~~~~~ ($>$100~MeV) && 0.81 & 6.7 \\\\\n$$ (MeV) && 76 & 53 \\\\\n\\hline \\hline \n\\end{tabular}\n\\end{center}\n\\end{table}\n\nThough detecting neutron is difficult, their backgrounds can be reduced by two ways; \n\n\\begin{itemize}\n\\item Self-shielding effects due to surrounding water around fiducial volume. In Super-K case, \na water volume of $\\sim$ 4.6~m thick (2.0~m in the inner detector and\n2.6$\\sim$2.8~m in the outer detector) is surrounded around fiducial\nvolume. Since the neutron is reduced by hadronic interactions in\nwater in a scale of several 10~cm, neutrons is expected to be reduced\nsignificantly before reaching the fiducial volume.\n\\item By detection of the accompanying cosmic muon. As seen in Fig~\\ref{fig:neutron_lateral},\ncosmic neutron and its parent muon are correlated spatially. This means that neutrons are reduced after traveling in several meter from muon track in the rock. Considering the detector size of the Hyper-K, when neutrons comes into the detector, \nit is supposed that accompanying muons go through the detector also in most case, and rejected by the signal in\nthe outer detector.\n\\end{itemize}\n\n\n\\begin{figure}[htb]\n\\includegraphics[width=0.6\\textwidth]{background\/neutron_lateral_dist-crop.pdf}\n\\caption{Lateral distribution of cosmic neutron from parent muon track. Figure was taken from \\cite{PhysRevD.73.053004} }\n\\label{fig:neutron_lateral}\n\\end{figure}\n\nIn order to estimate the neutron background in Hyper-K,\nneutron background simulations that took into account \nthe effect of the accompanying muons were performed.\nThe detector simulation of Super-K was used. \nSince most of the neutrons are expected to be rejected by\ntaking the coincidence with muon signal, as described above, simple\ntoy Monte Carlo simulation considering the detector geometry are\nperformed, and then events in which only neutron is entering are\nsimulated with the Super-K simulator. The detail procedure of the\nsimulation is described as follows:\n\n\\begin{enumerate}\n\\item Determine muon track. The starting position of muon track is in the plane about 20~meter above the top of Super-K detector \nand the vertex is randomly determined within the region of 200~meter from the detector center. \n\\item Determine the point at which neutron enters the detector according to the neutron lateral distribution from muon track. \n If there is no neutron which track does not hit the detector, this event is not counted. \n\\item Rejection by muon track. If muon track goes through the detector region, this event is discarded. \n\\item For the events which pass the previous step, neutron vector information, such as vertex, energy, direction, are fed into Super-K detector simulator and simulate neutron interactions.\n\\item Apply simple fully-contained (FC) reduction cut to simulated neutron events. Criterion that the number of hits in the outer detector ($nhitac$) is less than 16 and the visible energy in the inner detector ($E_{vis}$) is greater than 30~MeV are required. \n\\end{enumerate}\n\nThe energy and directional angle distributions of neutrons are determined based on \\cite{PhysRevD.73.053004}. \nAccording to the toy simulation, 97\\% of events are rejected by the criteria of muon coincidence with neutron in step 3. \n\nFig~\\ref{fig:neutron_reduction} shows the distributions of the reduction parameters, $nhitac$ and $E_{vis}$. \nFig~\\ref{fig:neutron_energy} shows the distribution of neutron kinetic energy for all simulated events and the \nremaining events after FC and fiducial volume (FCFV) cut.\nFig~\\ref{fig:neutron_vertex} shows the vertex distribution in Z (height) vs R (radius) of the detector, $D_{wall}$ distribution, which \nis the distance to the wall. \nIn the vertex distribution events are gathering around the side wall and fewer events around top, \nsuggesting the vertical muons passing nearby the detector produced neutrons entering the detector. \n\n\\begin{figure}[htb]\n\\includegraphics[width=0.8\\textwidth]{background\/neutron_reduction_dist_new.pdf}\n\\caption{Distributions of number of hits in the outer detector ($nhitac$) (left) and visible energy in the inner detector ($E_{vis}$) (right) for simulated neutron background events. }\n\\label{fig:neutron_reduction}\n\\end{figure}\n\n\\begin{figure}[htb]\n\\includegraphics[width=0.6\\textwidth]{background\/neutron_energy-crop.pdf}\n\\caption{Distributions of true neutron kinetic energy for all simulated events (black) and remaining events after FCFV cut (red).}\n\\label{fig:neutron_energy}\n\\end{figure}\n \n\n\\begin{figure}[htb]\n\\includegraphics[width=0.8\\textwidth]{background\/neutron_vertex-crop.pdf}\n\\caption{Reconstructed vertex distributions of neutron background events which pass after fully-contained reduction (left),\nand $D_{wall}$ distribution ,which corresponds to the distance between reconstructed vertex to the detector wall, \nfor same event (right).}\n\\label{fig:neutron_vertex}\n\\end{figure}\n\n\nTable~\\ref{tab:neutron_MC_summary} shows the summary of the neutron\nbackground MC events in each reduction step. Normalizing to the\nnumber of events per one year at Super-K detector condition, 2.1 and\n0.2 events are expected for fully-contained (FC) and fully-contained\nfiducial volume (FCFV) event, respectively. Considering the event\nrate of $\\sim$3000 atmospheric neutrinos, this corresponds to\n$0.2\/3000=7\\times10^{-3}$\\% background rate in FCFV sample. As for\nthe case of Hyper-K site, neutron flux is increased by about factor of\neight according to Table~\\ref{tab:neutron_flux} due to the shallower\noverburden of detector site condition.\nWhen the background rate is simply scaled by the factor of eight according to the increase of the muon flux,\n$7\\times10^{-2}$~$\\times$~8~$=$~$5\\times10^{-2}$\\% \nof the neutron background rate is estimated for Hyper-K case, which\nseems to be negligible level for physics study.\n\n\n\n\\begin{table}\n\\begin{center}\n\\caption{ Summary of the number of events in neutron background using Super-K detector simulation.}\n\\label{tab:neutron_MC_summary}\n\\begin{tabular}{lccc}\n\\hline \\hline\n && All simulation & Event\/1year at Super-K \\\\\n\\hline \nentering neutrons && 4.5$\\times$10$^8$ & 8.9$\\times$10$^6$ \\\\\nw\/o muon coincidence && 1.1$\\times$10$^7$ & 2.1$\\times$10$^5$ \\\\\npassed fully-contained cut (FC) && 105 & 2.1 \\\\\nvertex is in FV (FCFV) && 11 & 0.2 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nAnother possible neutral particle which could be the background is\nneutral kaon. According to the calculation of neutral kaon flux in\nunderground~\\cite{JHEP04.041}, neutral flux is estimated to be\nsignificantly smaller; 0.3\\% of neutron flux at 3~km m.w.e.. \n\nThe neutral kaon background is also estimated by the same simulation \nmethod as in the neutron case with the estimated flux and energy spectrum \ndescribed in \\cite{JHEP04.041}. The simulation data corresponding to \n50~years livetime in Hyper-K are produced. After applying\nFCFV selection, no background events are remained in the fiducial volume,\nconcluding that the background from neutral kaon is negligible for the \natmospheric neutrino analysis.\n\nIt would plausible to consider that the impact of the neutron and \nkaon backgrounds on the proton decay analysis\nis negligible as in the atmospheric neutrino case since \nthe there is no reason that those backgrounds have the same event topologies\nas proton decay. These backgrounds will be also reduced similarly as \natmospheric neutrino background by the proton decay selection cuts. \n\n\n\n\n\n\\subsection{Detector calibrations \\label{sec:calibration}}\n\n\\input{design-calibration\/introduction.tex}\n\n\\subsubsection{Inner Detector Calibration}\n\n\\input{design-calibration\/ID_calib_preface.tex}\n\n\\input{design-calibration\/system.tex}\n\n\\input{design-calibration\/ptf.tex}\n\n\n\\input{design-calibration\/monitoring.tex}\n\n\\subsubsection{Calibrations dedicated for physics analyses}\n\n\\input{design-calibration\/LowE_phys.tex}\n\n\\input{design-calibration\/HighE_phys.tex}\n\n\\input{design-calibration\/OD_calib.tex}\n\n\n\n\n\n\n\n\n\\subsubsection{OD calibration system}\n\\label{sec:hk_od_calibration}\n\n\nThe major task of the OD part of the Hyper-K detector is not to\nobtain the exact energy deposited but to identify\nthe neutrino events out of the cosmic-ray muons.\nFor example, ``fully contained'' events are identified by requiring no\nenergy deposition in OD, and ``partially contained'' events and\n``upward-going muon'' events, which are important sub-samples in\natmospheric neutrino analyses, are identified with OD hits\ncoinciding with ID hits.\nFor these physics analyses, an `inter-calibrations' between OD and ID,\ne.g. timing calibrations between OD and ID, is also important in\naddition to the calibrations of OD itself.\n\nCompared the ID part, the OD has various disadvantages in having a\ncalibration system. They are: 1) many light injection points are\nnecessary to illuminate all the light sensors in the OD area to an\nintensity level of a few 100 PE's, 2) there are sensor support\nstructures which can hinder the delivery of calibration light, and 3)\nthere is no easy way to deploy additional light injection points to\nreplace non-functional ones once the detector is filled with\nwater. The latter 2 points can be mitigated by having redundant light\ninjectors, but this will certainly increase the total cost of the\nsystem.\n\nIn the case of Super-Kamiokande experiment, the OD calibration system\nconsists of a $N_2$ and a dye laser, monitoring PMT's, a variable\nattenuation wheel, optical switches, and 52 fibers. Each fiber is\nequipped with a light diffusing tip at the end. Of these fibers, 24\nare placed in wall section and 14 each are placed in top and bottom\nsections. They are 72\\,m long, except for those placed in the bottom\nsection which is 110\\,m long. In average, each wall fiber covers\n160\\,m$^2$ of OD sensor area and about 2.5\\,m away from the OD PMT\nplane. Top and bottom fibers cover 64\\,m$^2$ per fiber and about 1.6~m\naway. These fibers are reasonably redundant and a little over a half\nof them are actually used to calibrate all the OD PMT's.\n\nFor the SK OD calibration system to be adopted to the Hyper-K detector, 79\nfibers are required to achieve the same fiber density as the SK for\nthe Hyper-K wall section. For top and bottom, 61 each is necessary. In\ntotal, 201 fibers are needed for the entire Hyper-K detector. In terms of\nlength, 200~m fibers for bottom and 120~m ones for other sections are\nnecessary to compensate the linear dimension difference between the SK\nand Hyper-K detectors.\n\n\n\n\n\n\\subsection{Cavern}\\label{section:cavern}\n\n\\subsubsection{Cavern shape}\n\nThe Hyper-K cavern has \na cylindrically shaped, barrel region 76\\,meters in diameter and\n62\\,meters in height with a 16\\,meter high dome above it.\nFigure~\\ref{fig:cavern_dimension} shows the cavern dimension.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{cavern_dimension.pdf}\n \\caption{Cavern shape and dimension. The dimensions in the figure are in meter.\n The shape of the dome section (top portion of the cavern) is defined with \n two different curvatures divided in 24.305\\,degree and 65.695\\,degree sections\n denoted in top-right of the figure.}\n \\label{fig:cavern_dimension}\n \\end{center}\n\\end{figure}\nThe excavation volume of the cavern is approximately 0.34 Million m$^3$.\nIt should be noted that the dimension of the excavation volume will be\nslightly larger than the detector dimension since the water\ncontainment system, e.g. a concrete lining, is constructed inside of\nthe excavated cavern surface.\n\n\\subsubsection{Cavern stability and support\\label{sec:cavern_stability_support}}\nThe excavated rock wall is supported by rock-bolts, pre-stressed (PS)\nanchors and shotcrete. A cavern structural stability analysis has been\ncarried out based on the geological condition obtained from the\ngeological surveys.\nThe vertical profile of rock quality is\nassumed to have the uniform distribution of the CH-class, which is the\nmajor component in the rock quality measurement. The initial rock\nstress for this analysis is based on the measured stress at 553\\,m\na.s.l. as shown in Fig.~\\ref{fig:ini-stress} and the rock stress at\neach depth is corrected by taking into account the depth, overburden.\nThe FLAC3D analysis software, which uses a finete difference method,\nis adopted to perform a three-dimensional stability analysis. The\nHoek-Brown model \\cite{Hoek-1,Hoek-2,Hoek-3} is applied as a dynamic\nmodel. The Hoek-Brown model is the method to estimate physical\nproperties of rock by using results obtained from examinations of\nsampled rock, and is widely used in the world.\n\nFigure~\\ref{fig:cavern_plastic_region_CH} shows the plastic region at\n45\\,degree and 105\\,degree slices in the case of no support (i.e., no\nrock-bolts, no PS-anchors, and no shotcrete).\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.38\\textwidth]{cavern_CH_plastic_region_045deg.pdf}\n \\includegraphics[width=0.38\\textwidth]{cavern_CH_plastic_region_105deg.pdf}\n \\includegraphics[width=0.18\\textwidth]{view.pdf}\n \\caption{The plastic region at 45\\,degree (left) and 105\\,degree (middle)\n slices with assumption of uniform CH distribution. The right figure shows definition of the view angle.}\n \\label{fig:cavern_plastic_region_CH}\n \\end{center}\n\\end{figure}\nThe plastic region depth is estimated to be $\\sim$2.5\\,m to $12$\\,m.\nThe variation of the plastic region depth is due to the geological\ncondition, e.g. initial stress direction.\nBased on the plastic region obtained, the respective cavern support\n(PS-anchors) patterns are considered as shown in\nFig.~\\ref{fig:cavern_anchor_pattern_CH}.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.48\\textwidth]{cavern_CH_psanchors_045deg.pdf}\n \\includegraphics[width=0.48\\textwidth]{cavern_CH_psanchors_105deg.pdf}\n \\includegraphics[width=0.27\\textwidth]{cavern_CH_anchor_pattern_dorm.pdf}\n \\includegraphics[width=0.68\\textwidth]{cavern_CH_anchor_pattern_barrel.pdf}\n \\caption{PS-anchors pattern at 45\\,degree (top-left) and 105\\,degree (top-right)\n slices with uniform CH distribution. \n Colored lines indicate PS-anchors with different setting of initial force applied to\n PS-anchors. Bottom figures show developed figures of PS-anchors pattern for dome (bottom-left)\n and barrel (bottom-right) sections. Initial force and length of PS-anchors\n are indicated by colored circles.}\n \\label{fig:cavern_anchor_pattern_CH}\n \\end{center}\n\\end{figure}\nThe number of PS-anchors and the total length for the cavern construction are\nsummarized in Table~\\ref{tab:PS_anchor_summary_CH}.\nThe total length of PS-anchors is estimated to be approximately\n45\\,km.\n\n\\begin{table\n\\caption{Summary of total number of PS-anchors and total length for the cavern\nexcavation in case of uniform CH distribution.\n\\label{tab:PS_anchor_summary_CH}}\n\\begin{tabular}{c|r|r}\n\\hline\\hline\nSection & \\# of anchors & Total length (m) \\\\ \\hline\\hline\nDome & 1,537 & 26,539 \\\\\nBarrel & 1,307 & 18,823 \\\\ \\hline\nTotal & 2,844 & 45,362 \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{table}\n\nAnother analysis is performed with a different vertical profile of\nrock quality, as shown in Fig.~\\ref{fig:rock_qual_assum}.\n\\begin{figure\n\\centering\n \\includegraphics[width=0.5\\textwidth]{rock_qual_assum.pdf}\n \\caption{Assumed rock quality distribution in vertical direction.\n Rock quality in horizontal plane is assumed to be uniform.\n Two classes of the rock quality, CH and CM classes, are used for this analysis.}\n \\label{fig:rock_qual_assum}\n\\end{figure}\nIn Fig.~\\ref{fig:rock_qual_assum}, the fraction of rock quality is\nbased on the measurements of rock quality and CM-class is arranged to\nthe dome and bottom sections, which are structurally weaker due to its\nshape, so as to perform an analysis with a severe condition.\nFigure~\\ref{fig:cavern_plastic_region_CMCH} shows the plastic region at\n45\\,degree and 105\\,degree slices with the CH-CM mixed assumption in\nthe case of no support.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.38\\textwidth]{cavern_CMCH_plastic_region_045deg.pdf}\n \\includegraphics[width=0.38\\textwidth]{cavern_CMCH_plastic_region_105deg.pdf}\n \\caption{The plastic region at 45\\,degree (left) and 105\\,degree (right)\n slices with assumption of CH-CM mixed distribution.}\n \\label{fig:cavern_plastic_region_CMCH}\n \\end{center}\n\\end{figure}\nThe plastic region depth is estimated to be $\\sim$10\\,m to $24$\\,m.\nIn the plastic region at 105\\,degree slice, two spikes in the plastic region\ncan be seen at the boundary between CH and CM classes. These sharp\nspikes are due to the discontinuity of rock quality, which corresponds\nto a discontinuous change in physical strength, and it is difficult to\ncorrectly analyze the plastic region in such a discontinuous\ncondition. PS-anchor pattern is also considered for this case, as\nshown in Fig.~\\ref{fig:cavern_anchor_pattern_CMCH}.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.48\\textwidth]{cavern_CMCH_psanchors_045deg.pdf}\n \\includegraphics[width=0.48\\textwidth]{cavern_CMCH_psanchors_105deg.pdf}\n \\includegraphics[width=0.27\\textwidth]{cavern_CMCH_anchor_pattern_dorm.pdf}\n \\includegraphics[width=0.68\\textwidth]{cavern_CMCH_anchor_pattern_barrel.pdf}\n \\caption{PS-anchors pattern at 45\\,degree (top-left) and 105\\,degree (top-right)\n slices with assumption of CH-CM mixed distribution.\n Colored lines indicate PS-anchors with different setting of initial force applied to\n PS-anchors. Bottom figures show developed figures of PS-anchors pattern for dome (bottom-left)\n and barrel (bottom-right) sections. Initial force and length of PS-anchors\n are indicated by colored circles.}\n \\label{fig:cavern_anchor_pattern_CMCH}\n \\end{center}\n\\end{figure}\nThe number of PS-anchors and the total length for the cavern excavation are\nsummarized in Table~\\ref{tab:PS_anchor_summary_CHCM}.\nThe total length of PS anchors is estimated to be approximately\n81\\,km \nin this assumption. The difference in the total length\nbetween two cases can be considered as an uncertainty on the\nPS-anchors estimation.\n\n\\begin{table\n\\caption{Summary of total number of PS-anchors and total length for the cavern excavation\nin case of CH-CM mixed distribution.\n\\label{tab:PS_anchor_summary_CHCM}}\n\\begin{tabular}{c|r|r}\n\\hline\\hline\nSection & \\# of anchors & Total length (m) \\\\ \\hline\\hline\nDome & 1,962 & 44,479 \\\\\nBarrel & 2,020 & 36,392 \\\\\\hline\nTotal & 3,982 & 80,871 \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{table}\n\nWhile the geological surveys that have been completed already show the\nfeasibility of the required cavern construction, further detailed\nsurveys in the vicinity of the candidate site must be conducted for\nthe final determination of the cavern allocation and \nPS-anchors pattern before starting cavern excavation.\nIt should be stressed that structural stability of the detector cavern with the proposed\nshape can be achieved by using existing cavern construction technologies.\n\nA detailed plan for the additional geological surveys, which need to be done before actual\nconstruction begins, has been established.\nThe surveys are divided into three steps:\n{\\it Step-1} begins with drilling boreholes in the vertical direction from\nthe existing tunnels at 653\\,m a.s.l. to the cavern location where is defined\nin Fig.\\ref{fig:seismic_results},\n{\\it Step-2} carries out an `{\\it in-situ} testing' to measure the physical properties\nof the rock at around the cavern construction site using the existing tunnels,\n{\\it Step-3} is the final step of making the detailed cavern design (e.g. PS-anchor pattern)\nfor the actual cavern excavation, based on the geological survey results in {\\it Step-1} and\n{\\it Step-2}.\n\n\\subsubsection{Cavern construction\\label{sec:cavern_construction}}\n\nThis section describes the cavern construction\nmethod and procedure.\n\nThe cavern excavation begins with construction of access tunnels and\napproach tunnels. The tunnels and cavern are excavated with a\nblasting technique. \n\nThe tunnels leading from the mine entrance into the detector site\nvicinity are called ``access tunnels,'' and the tunnels leading from\nthe access tunnels into the group of tunnels connected to the cavern\nare collectively called ``approach tunnels.''\nFigure~\\ref{fig:tunnels_overview} shows overview of the access tunnels.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.98\\textwidth]{cavern_access_tunnel_layout_1cav.pdf}\n \\caption{Overview of the access tunnels. For details of Hyper-K site, one can refer\n to Fig.~\\ref{fig:approach_tunnels}.}\n \\label{fig:tunnels_overview}\n \\end{center}\n\\end{figure}\nThe access tunnel, named as `Wasabo' access tunnel, is also used to transport the excavated\nrock to the Wasabo site where excavated rock is temporarily stored (described\nin later section). \n\nThe cavern is excavated from top to bottom, and there are two\ngeneral phases in the cavern construction -- excavation of ``dome''\nand ``barrel'' sections. The dome section is top portion of the\ncavern, and the barrel section is vertical straight wall section of the cavern\n(see Fig.~\\ref{fig:cavern_dimension}). The barrel section is further\ndivided into four stages.\nEach stage has 15.5\\,m height, and the barrel section is excavated in\nstage by stage basis. Top and bottom of each stage are connected to\napproach tunnels, and excavation of each stage proceed from the top\napproach tunnel to the bottom approach tunnel.\nFigures~\\ref{fig:approach_tunnels} and \\ref{fig:approach_tunnels2}\nillustrate the layout of the approach tunnels.\nAs shown in the figure, ``outer incline tunnel'' is helicoidally or spirally arranged around\nthe cavern and the outer incline tunnel works as an interface between access tunnels and\napproach tunnels.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{cavern_approach_tunnel_layout1_3D_1cav.pdf}\n \\includegraphics[width=0.9\\textwidth]{cavern_approach_tunnel_layout2_3D_1cav.pdf}\n \\caption{Layout of approach tunnels (see also Fig.~\\ref{fig:approach_tunnels2}).\n The figure shows the `water rooms' as well,\n where the water purification systems are located.\n The ``electronics huts,'' (a.k.a. counting room) which stores the readout electronics\n and DAQ computers etc. (not shown in the figure), \n will be built in the approach tunnel.}\n \\label{fig:approach_tunnels}\n \\end{center}\n\\end{figure}\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{cavern_approach_tunnel_layout2.pdf}\n \\caption{Layout of approach tunnels.} \n \\label{fig:approach_tunnels2}\n \\end{center}\n\\end{figure}\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth]{cavern_excavation_step_dome.pdf}\n \\includegraphics[width=0.7\\textwidth]{cavern_excavation_step_barrel.pdf}\n \\caption{Illustration of the excavation steps for dome section (upper figure) and\n barrel section (lower figure).}\n \\label{fig:excavation_step}\n \\end{center}\n\\end{figure}\nFigure~\\ref{fig:excavation_step} shows schematic of the excavation steps\nof the cavern construction. The dome section is excavated with\nthirteen steps (from section ``A-1'' through section ``A-6''). The barrel\nsection is divided into four stages and each stage has three\n``benches.'' The excavation of barrel section proceeds from ``bench\n1-1'' through ``bench 4-3''.\n\n\n\n\\subsubsubsection{Excavated rock handling and disposal}\n\nFor the excavated rock handling and disposal, two sites are used for different purposes:\n\\begin{itemize}\n\\item{\\bf Wasabo-site}\\\\\n Wasabo-site is an intermediate (temporary) excavated rock deposition site.\n All the excavated rock from cavern and tunnels excavation is transported and temporary\n stored at Wasabo-site.\n\\item{\\bf Maruyama-site}\\\\\n Maruyama-site is the main rock disposal site for all the excavated rock\n from tunnels and cavern excavation.\n Capacity of the site is more than two Million-m$^3$.\n The total distance from Wasabo-site to Maruyama-site is about 14\\,km.\n\\end{itemize}\n\n\nThe excavated rock will be transported with dump-trucks\nfrom the detector site to Wasabo-site and from Wasabo-site to\nthe Maruyama-site.\nFigure~\\ref{fig:cavern_waste_rock_transportation} shows the route of\nexcavated rock transportation from the detector site vicinity through to\nMaruyama-site.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{cavern_waste_rock_transport_routing.pdf}\n \\caption{Overview of the excavated rock transportation routing from Hyper-K site to\n Maruyama-site.\n Magenta line denotes the transportation routing from Wasabo-site to Maruyama-site.\n }\n \\label{fig:cavern_waste_rock_transportation}\n \\end{center}\n\\end{figure}\nThere are the existing roads from Wasabo-site to Maruyama-site, that\ncan be used for the transportation of the excavated rock. Some part of the\nexisting roads, however, need to be improved, e.g. widening the roads\nor allocating turnouts (passing-places), in order to get a large\nnumber of dump-trucks pass through.\n\n\n\\begin{figure}\n \\centering \n \\includegraphics[width=1.0\\textwidth]{maruyama_photo_wide.pdf}\n \\caption{The rock disposal site at Maruyama.\n Its capacity is more than two Million-m$^3$.}\n \\label{fig:maruyama_photo}\n\\end{figure}\nThe rock disposal site at Maruyama has a large sinkhole (see FIG.~\\ref{fig:maruyama_photo})\ninduced by the past underground block caving.\nThe excavated rock with a soil volume of 570,000\\,m$^3$ produced by the Hyper-K\ncavern construction will be piled up on top of this sinkhole.\nThe base of such a sinkhole induced by block caving is mainly filled with caved waste.\nTo investigate the geological condition of the rock disposal place,\ntwo vertical boring holes, No.1 and No.2, were excavated.\n\nThe No.1 borehole with a length of 24\\,m was excavated near the edge of the sinkhole\nto understand physical properties of the surface soil layer and its thickness.\nFirst, the standard penetration test has shown that the thickness of\nthe surface layer (i.e. the depth to bedrock) was about 21\\,m.\nThen, core samples were subjected to various laboratory testings,\nsuch as uniaxial compression test and consolidated-undrained triaxial compression test,\nto measure their physical properties,\nnamely the wet bulk density, the uniaxial compression strength,\nthe deformation coefficient, the cohesion, and the internal friction angle.\n\nThe No.2 borehole with a length of 100\\,m was excavated at the midpoint of the sinkhole\nto understand the geological condition of the caved waste.\nFirst, the core inspection has shown that\na gravel bed ($0.0\\sim9.4$\\,m) overlay a sandy clay layer ($9.4\\sim100$\\,m),\nand no cavity was found in the surveyed range.\nThe laboratory testings of the core samples obtained by the No.2 borehole drilling\nhave indicated that the filling state and relative density of the sandy clay\nwere higher at a deeper position.\nA suspension P-S velocity logging was also performed by using the No.2 borehole.\nA several meters long probe, containing a source and two receivers\nspaced 1\\,m apart, was lowered into the borehole to a specific depth,\nwhere the source generated seismic waves.\nThe elapsed time between arrivals of the waves at the receivers was used\nto determine the average velocity of a 1\\,m column of the ground around the borehole.\nIt was confirmed by the P-S logging that no cavity existed in the surveyed range\nand the filling state of the ground were higher at a deeper position.\n\n\\begin{figure}\n \\centering \n \\includegraphics[width=0.85\\textwidth]{maruyama_vertical_displacement2.pdf}\n \\caption{Ground subsidence which might arise by piling up the excavated rock\n on the Maruyama sinkhole. The figure shows a vertical section of the rock disposal place,\n and the colored region above the gray line represents the piled rock produced by\n the Hyper-K cavern excavation.\n The white line show the boundary between the region filled with the caved waste\n by past block caving and the surrounding bedrock.}\n \\label{fig:maruyama_vertical_displacement2}\n\\end{figure}\nBy using geological information obtained by the boring survey,\nwe have performed two types of stability analyses.\nOne is a standard slope stability analysis considering circular slip surfaces.\nIn the analysis, safety factors during a normal period and those during earthquakes\nwere calculated both for the slope made of the piled excavated rock\nand for the existing slope around the sinkhole.\nThe design horizontal seismic coefficient was set at 0.15\naccording to the technical guideline established by METI\n(Ministry of Economy, Trade and Industry in Japan).\nThe safety factors were found to be above 1.20,\nwhich is the reference value described in the guideline,\nboth for the slope of the piled rock and for the existing slope.\n\nThe other is an elasto-plastic analysis using the finite element method (FEM) of the sinkhole ground.\nDistributions of stress, plastic region, and displacement were calculated\nfor both the situations before and after piling up the excavated rock\non top of the sinkhole, and were compared for estimating influences of the piling up.\nIn the analysis, physical properties of the excavated rock were set\naccording to results from the past boring survey at Tochibora\n(i.e. Hyper-K tank construction site), and those of the caved waste and surrounding bedrock\nwere set based on the boring survey results at the Maruyama sinkhole.\nAs a result of the analysis,\nFIG.~\\ref{fig:maruyama_vertical_displacement2} shows the distribution of\nthe expected ground subsidence which might arise by piling up the Hyper-K excavated rock\non the Maruyama sinkhole.\nThe size of possible subsidence is expected to be at most about 1.7\\,m,\nwhich would not be difficult to deal with.\nMonitoring subsidences during the rock piling work will be important for safety.\n\nIn the undergound of the sinkhole exist many mine tunnels, which were excavated\nto extract ores in the past block caving.\nDead ends of such tunnels are located near the boundary between\nthe caved waste region and the surrounding bedrock.\nCurrently the caved waste including broken ores stay at the dead ends by an arch effect\nand don't flow into the mine tunnels,\nbut it might be possible that they will start to move and flow in\ndue to the pressure from the excavated rock piled on the ground.\nAccording to the FEM stability analysis mentioned above,\nadditional horizontal compression stresses at dead ends of existing mine tunnels,\nwhich might cause such an inflow of rocks,\nwere calculated to be 0.8\\,MN at most.\nBy constructing concrete plugs with a length of about 3\\,m in front of dead ends,\nsuch an inflow of rocks into existing tunnels can be prevented.\n\nAll the stability analyses of the Maruyama rock disposal site described in this section\nwere performed by assuming that\nthe volume of the piled excavated rock was 2,600,000\\,m$^3$,\nwhich was an estimation from the old 1 mega-ton Hyper-K design\nand was much larger than 570,000\\,m$^3$ from the current design.\nTherefore, in the current rock disposal plan,\nthe safety factors of the slope stability during a normal period and during earthquakes\nmust be even higher,\nthe expected ground subsidence must be even smaller,\nand the length of concrete plugs necessary to prevent possible inflow of caved wastes\nto existing tunnels must be even shorter\nthan those described above.\n\n\n\n\\subsubsubsection{Cavern construction time}\n\nThe construction sequence has been established by making every effort\nto minimize the total construction time and construction cost, for\nexample, \nthe approach tunnels construction and cavern construction run in\nparallel at different elevations, {\\it etc}.\n\nAs described in the previous section, the cavern construction begins\nwith\nWasabo access tunnel constructions, and the\ncavern constructions will follow.\nThe construction of the access\ntunnels takes $\\sim$17\\,months, and the cavern\nexcavation takes $\\sim$30\\,months.\nThe total duration of cavern construction is estimated to be $\\sim$4 years.\n\nIt should be noted that additional $\\sim$10\\,months will be required in the cavern\nconstruction time if the cavern excavation volume\nand\/or PS-anchor supporting region is near a weak layer, such as a\nfracture zone, that requires additional construction work.\nFurther detailed surveys in the vicinity of the candidate site is important\nto minimize such slippage of the cavern construction,\n\n\n\n\\subsection{Computing}\nHyper-K adopts a Tiered computing model where Kamioka and KEK sites form the\nTier-0 due to the distributed nature of the experiment. A general overview of a future \nHyper-K tiered system is shown in Fig.~\\ref{fig:computing_tiers}.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[scale=0.4]{design-computation\/figures\/hk-comp.pdf}\n \\end{center}\n\\caption {General overview of a possible Hyper-K tiered system.}\n \\label{fig:computing_tiers}\n\\end{figure}\n\nThe Tier0 sites will hold the raw experiment data as well as the processed data. The KEK\nTier0 will also contain a \nThe Tier1 centres (such as RAL, TRIUMF, ccin2p3) would hold portions of the raw, processed\nand simulated data and provide computational resources for the\nsimulation, processing and reprocessing. The Tier2 sites which\ntypically consist of universities will provide computational and\nstorage resources (the storage is usually used to hold specific\nsubsets of the data or simulation). The model makes efficient use the\navailable computing resources that exist at collaborating sites. The\nmodel will be regularly reviewed as changes to the computing landscape\ntake place.\n\n\n\nA current estimate of the rate of raw data to be stored is ~20\\,TB\/day. \nAbout 80\\,PB of the disk space\nis necessary to store the raw data for the 10 years operation. \n\nReduction and reconstruction software will be\napplied to all the data in the Kamioka Tier0 as soon as the data are\ntaken to provide different samples for different energy regions or\ndifferent analysis groups, i.e. low energy region mainly for the study\nof solar neutrinos, higher energy for the study of nucleon decay and\natmospheric neutrinos, downward going muons for the background study\nof solar neutrinos, the data during the beam timing from the\naccelerator for the beam neutrino analyses. These data sets also\nprovide timely feedback to the experiment and beam operations groups\non the quality of the beam and performance of the detector. Also,\nearly detection of a supernova burst is crucial and dedicated realtime\nanalysis has to be performed in the independent system. The required\ncomputing power for data reduction and reconstruction at this level,\ntogether with the supernova detection system, is not so huge and 1000\ncores of the current Intel IA64 CPUs will be sufficient.\n\n\\subsubsection{Simulation production}\n\nMass production of the simulation data sets and their analyses are\nexpected to be performed in the Tier-1 centres because the required\nCPU resource for the huge amount of simulation data is expected to be\nat least a few tens of times larger than the ones necessary for the\nreal time data processing. On the other hand, the simulated data set\nis not extremely large and the cost of the storage could be less than\n10\\% of the storage for the real data sets. All the data sets after\nreduction and the processed simulation data sets are shared among the\ngeographically distributed analysis working groups. The Tiered model\nensures results in a more scalable architecture capable of meeting the\ncomputational and storage demands of the experiment.\n\nThe Monte Carlo simulation production currently makes use of existing\nHEP computational Grid resources to produce sufficient quantities of\nphysics events necessary to optimise the detector design for maximum\nefficiency. The data are managed by the iRODS data management system\n(\\url{http:\/\/irods.org\/}) that enables distributed storage to be\nmanaged and accessed in an uniform manner. Collaborators access the\nstored data using the intuitive and simple iRODS client API.\n\n\n\n\n\n\\subsection{Data acquisition system }\\label{section:daq}\n\\subsubsection{Data acquisition and triggering}\n\nAll PMT hits from the detector (above a threshold of $\\sim\n0.25$\\,p.e.) will be delivered to the data readout and processing\nsystem where they will be formed into events and recorded on disk for\nfurther processing offline. The overall rate of hits (mostly from\ndark noise) from the inner detector will be about\n460\\,MHz, \nleading to a total input data rate of 5GB\/s including additional data,\nin the absense of waveform information.\nThe OD adds less than 10\\% to this data load. To reduce the data\nrecorded, trigger decisions will be made using real-time processing of\nthe hits in the detector. Events will be formed from all hits within\na time-window surrounding the trigger and recorded to disk for offline\nstudy.\n\nThe main trigger will be the same as that used in SK-IV; a trigger\nwill be generated when the total number of hits seen (NHITS) in a\nsliding time-window exceeds a certain threshold (e.g. 27\\,hits). This\ntrigger will accept all the necessary data for studies of proton\ndecay, atmospheric neutrinos, beam neutrinos and cosmic ray muon\nevents. It is important that there is no dead time in the triggering\nor data collection so that delayed energy depositions following a\ntriggered event, such as from a Michel electron or neutron capture,\nare recorded, either as part of the same event or separately. More\nsophisticated trigger algorithms, which can be added into the\narchitecture, are being studied to increase sensitivity to lower\nenergy events (by distinguishing events with fewer hits from random\ncombinations of dark-noise hits) and detection of supernova bursts (by\nobserving elevated trigger rates). As in Super-K, an additional\ntrigger input will be derived from the J-PARC beam-spill gate to\ndefine readout windows around the beam spill time, independent of the\nnumber of hits observed. Triggers will be defined to receive\ncalibration events. Also, external trigger inputs are necessary to\ntake the calibration data with synchronized timing. The estimated\nrate of events is shown in Table~\\ref{event_rates:daq} for readout\nwith the hit-only electronics, which require 12\\,bytes per hit (the\nwaveform option needs a factor four higher bandwidth, $\\sim 50$\\,bytes\nof information per hit).\n\n\n\n\\begin{table}[htbp]\n\\begin{center}\n \\caption{Estimates of data rates. The ``pre-trigger'' data rates for each physics process\n is given: (a) for events without dark noise and (b) for events including dark noise. \n In these calculations, 12 Bytes per PMT hit is assumed. Event rates and event windows for background, muon, beam calibration and pedestal events are based on those from Super-Kamiokande.}\n \\label{event_rates:daq}\n \\begin{tabular}{l|l|r|r|r|r}\n\\hline\\hline\nData source & Event rate & Hits\/event & Data rate & Data rate & Data rate per\\\\\n & & (event window) & pre-trigger(a)& pre-trigger(b)& event window\\\\\n\\hline\nDark noise & 10\\,kHz each in 46,700\\,PMT & 1 & 5.6\\,GB\/s & -- & -- \\\\\nVery low energy background & 10\\,kHz (1.5\\,$\\mu$s) & 25 & 3\\,MB\/s & 84\\,MB\/s & 200\\,MB\/s \\\\\nLow energy background & 35\\,Hz (40\\,$\\mu$s) & 50 &21\\,kB\/s & 7.8\\,MB\/s & 15\\,MB\/s\\\\\nCosmic muons & 100\\,Hz (40\\,$\\mu$s) & 46,700 &56\\,MB\/s & 78\\,MB\/s & 15\\,GB\/s\\\\\nBeam events & 1\\,Hz (1\\,ms) & 0 & 0\\,MB\/s & 5.6\\,MB\/s &5.6\\,kB\\\\\nCalibration & 2\\,Hz & 46,700 & 2\\,MB\/s & 2\\,MB\/s & -- \\\\\nPedestal & 1\\,Hz & 46,700 & 2\\,MB\/s & 2MB\/s & -- \\\\\n\n\\hline\nTotal rate & & & 5.6GB\/s & 180MB\/s & \\\\\n\\hline\\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\n\nA requirement of the data acquisition system is to reliably trigger\nand collect information from a supernova burst. This is one of the\nmore challenging design aspects and benefits from the large memory\nbuffers available in modern commodity hardware, sufficient to retain\nall raw hit information for around 100\\,s of detector operation. In \nthe event of a supernova, the detector will self-trigger on a supernova \nburst by searching for an elevated rate of\nindividual triggers in a sliding time-window e.g.~0.1\\,s. If such a\ntrigger occurs, all raw hit information in a large time window around\nthe supernova trigger would be saved in the local hardware and then\nslowly written to disk. Note that even a close supernova burst\nyielding 100,000~events per second of 50~PMT hits each (5~million\nhits\/s) will not overwhelm the readout which is designed to\ncontinuously read 460\\,MHz of dark noise hits. A large storage buffer \non hard disk drives is used to save\nall the hit data, overwriting the oldest data. An external\nobservation may reveal up to a few hours after the event that a\nsupernova signature was seen, perhaps in a neighbouring galaxy, in\nwhich only a few events are expected to be observed in Hyper-K.\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[width=0.8\\textwidth]{design-daq\/figures\/HKDAQ1.pdf}\n \\caption{Simplified block diagram of the readout showing the\n sequence of data transfers.}\n\\label{online_schematics:daq}\n\\end{center}\n\\end{figure}\nFigure~\\ref{online_schematics:daq} is a schematic diagram of the data\nreadout and processing system showing the five steps in the sequence\nof readout operations. The main components are readout buffer units\n(RBU) that receive PMT hit (and possibly waveform) data from the\nfront-end boards, trigger processing units (TPU) and event building\nunits (EBU). The sequence of operation is indicated by the numbers\n1-5 on Figure~\\ref{online_schematics:daq}: (1) Data on hits in a group\nof channels are streamed into buffers in the RBUs, where they are\nretained for the duration of the trigger decision. (2) A summary\nblock of information for triggering is sent to the TPUs. (3) Trigger\ndecisions are delivered back to the RBUs to extract event data from\nthe buffer. (4) The event data are sent to the EBUs. (5) Built\nevents are written to disk for later processing offline. A description\nof each of the blocks shown is given in the following sections. The\nDAQ system will be designed to be homogeneous, flexible and scalable.\n\nParameters of the readout system, including data rates at each point\nin the sequence of readout operation are shown in\nTable~\\ref{data_rates:daq}. Since the architecture is flexible, the\nadditional data generated by the waveform option is easily\naccommodated, although a larger number of Readout buffer units (RBUs) would be required.\n\n\\begin{table}[htbp]\n\\begin{center}\n \\caption{Parameters of the readout design.}\n \\label{data_rates:daq}\n \\begin{tabular}{l|r|r}\n\\hline\\hline\n Parameter & Hit-only option & Waveform option \\\\\n\\hline\n Pre-trigger input data rate & 5,600 MB\/s & 23,400 MB\/s \\\\\n Number of RBUs & 38 & 122 \\\\\n Input rate to each RBU & 150 MB\/s & 188 MB\/s \\\\\n Latency provided by RBU (pre-trigger buffer length)& 109 s & 87 s \\\\\n Trigger info output rate per RBU & 50 MB\/s & 15 MB\/s \\\\\n TPU data input rate (for 16 TPUs in detector) & 117 MB\/s & 117 MB\/s \\\\\n\\hline\\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\n \n\\subsubsection{Readout buffer unit (RBUs)}\n\nThe RBUs receive continuous streams of data from the front-end cards\nand perform three main tasks. First they store incoming data in\nbuffer storage. A short-term store of the most recent data is\nretained whilst trigger decisions are made and a long-term storage\narea is reserved in case of a supernova event until it can be read\nout. Second, it forms a compressed block of data which is handed to\nthe TPU for trigger decision making. Finally, the RBU handles trigger\nrequests to dispatch complete event data to the event builder unit,\nand supernova trigger requests to move data to the long term storage\narea. Since the detector is large, and to allow scalability, there\nare many RBUs working in parallel, each responsible for processing\ndata from a designated region of the detector. In the current design\nof 45,000~PMTs, between about 40~and 120~RBUs will be required\ndepending on the amount of data received per hit, and each will use\n16\\,GB of memory to provide the necessary storage. The RBU design is\nscalable and thus largely independent of the detector size.\n\nThe final design of the RBUs depends on the layout and interface of\nthe upstream electronics. Possible implementations use either\ncommodity computers with commodity network switches to direct the\ndata, or hardware receiver cards in a communication-crate such as \nAdvanced Telecommunications Computing Architecture (ATCA)\nwith a commodity computer as a controller. The RBU may also include an\ninterface to the upstream link for monitoring information.\n\n\\subsubsection{Trigger processing unit}\n\nThe Trigger Processing Units (TPUs) will accept compressed trigger\ndata blocks from the RBUs and use these to form trigger decisions,\nsuch as the simple, robust NHITS trigger. Hooks will be provided to\nallow for more sophisticated triggering. The trigger will also search\nfor large collections of individual events, which may indicate a burst\nof neutrinos from a supernova explosion in the galaxy.\n\nThe trigger will operate using windows of fixed time duration\n(e.g.~60\\,per second) in order to allow the trigger processing to be\nparallelized. The parallelisation allows for a scalable design that \ncan be extended easily if workloads change due to increased darknoise, \nas well as handling any reprocessing due to errors or data corruption. \nOne TPU is\nallocated for a given time window and will process all the data in\nthat time window. The TPUs are connected to the RBUs by a switched\nEthernet network to allow the data from the different RBUs (one for\neach section of the detector) to be routed to the correct TPU. The\ndata is transferred asynchronously and the TPU starts processing when\nall data packets have arrived.\n\nThe trigger information can be compressed into a 32-bit word per hit\nto identify the channel number within the RBU (10\\,bits) and the time\nwithin the window (21\\,bits) to 10\\,ns accuracy (better time\nresolution is not needed in the trigger) and one spare status bit.\nThe trigger information can be truncated if it is clear that the NHITS\ntrigger will be satisfied from the data in that one RBU alone, as in\nthis case, the event is guaranteed to be collected without further\ntransfer or processing of trigger data. For this level of packing,\nthe output rate per RBU will be about 30\\,MB\/s and if a farm of\n16\\,TPUs is used, the input rate to each will be around 100\\,MB\/s.\nThe final design of the TPUs is largely independent of the choice of \nfront-end electronics, because the RBUs provide the trigger data in the same \nformat regardless. The TPU design depends on the type of processing required \nfor the sophisticated triggers. The base line design is to use commodity \ncomputer componets, where data packets would be received by the computer \nand complex trigger processing would occur in FPGAs or GPUs that read the \ndata over PCIe links and deliver the trigger verdict for a given time \nblock back to the main memory. \n\n\\subsubsection{Event Building Unit}\n\nOnce the trigger decision has been made for a time-window, the\ndecision is reported back to a central trigger control process, from\nwhere it is delivered to the RBUs. The request contains an event\nnumber, and the definition of the position and width of the trigger\nwindow. The central trigger control process also looks for an\nincreased rate of positive triggers, which would be indicative of a\nsupernova burst, and in such case sends the RBUs an instruction to\nsave the relevant data in the long-term part of the buffer memory. \n\nOn receipt of a normal trigger, the RBUs send all the hits in the\ntrigger window to a designated event-building node, which puts the\nevent together and writes it to the output file. Once the file\nreaches a certain size, it is closed and released for offline\nprocessing, and new events are recorded in a new output file without\ninterruption. The event builders also allow events to be read by\nmonitoring and event display programs. Once a supernova trigger has\noccurred, a separate event-building stream is used to gather the data\nin the long-term part of the RBU memory and output it to a separate\nfile. There will be one file per supernova trigger. A\nstraightforward implementation of the event builders is to use\ncommodity computers.\n\n\\subsubsection{Triggering}\nA trigger will be issued if any event exceeds a pre-determined threshold \nof hits (NHITS) in a sliding time window. This trigger will accept with \nhigh efficiency, all events for studies of proton decay, atmospheric \nneutrinos, beam neutrinos and cosmic ray interactions. Aside from the \nNHITS requirement, the trigger must have no dead time as this could lead \nto the loss of information from associated delayed energy deposition events \nsuch as Michel electrons or neutron captures.\n\nThe low energy threshold limited by the dark noise rate of the PMTs, which \nprevents the use of such a simple NHITs trigger for low energy physics events \nsuch as solar neutrinos, supernova and neutron capture. To allow sensitivity \nto low energy physics, the Hyper-K DAQ system must incorporate intelligent, \nfast trigger algorithms that can reject noise events but retain the low energy \nphysics events of interest. Any event that fails the NHITS threshold will be \npassed to the low energy trigger. \n\nThe base line low energy trigger design uses a grid of test vertex positions \nwith 5 m spacing inside the detector. The distance between each test-vertex \nand PMT position is used to produce a look up table of time of flight \ninformation for each test-vertex PMT pair. For an event, the ID and TDC \ninformation for each tube are recorded and \npassed to the test-vertices algortihm. The algorithm loops over the test-vertices \nand corrects the measured TDC by the time of flight for each test-vertex PMT pair. \nThis corrected value represents the time at which the photon was emitted by the \ntest vertex to produce the observed PMT hit. A one dimensional histogram of photon \nemission times is produced with a carefully chosen bin width corresponding to half \nof the time resolution. The best vertex is found by selecting the histogram bin \nwith the highest number of entries and if this number of entries is greater than \na pre-determined threshold, the trigger is accepted. Due to the computational \nintensity of this process, it will be executed using high performance Graphical \nProcessing Units (GPUs). Results from Monte Carlo simulations show high noise \nrejection and good low energy acceptance.\n\nA second trigger that uses convolution neural nets and GPUs to perform real-time \nimage recognition for triggering is also being investigated. Initial studies have proven \nvery promising, with good performance even at very low energies. Other specialist \ntriggers will be developed for calibration sources and supernova detection. \n\nAdaptations will be made to trigger algorithms for the use in the intermediate detector. \nAs the low energy physics reach of the intermediate detector is less than that of \nthe far detector, the triggering scheme can be simplified. However, low energy \ntriggers will be required to accept gadolinium gamma cascades. Work in this area \nis continuing. \n\n\\subsection{Frontend electronics }\\label{section:electronics}\n\\subsubsection{ General concept of the baseline design }\\label{section:electronics-general}\n\n It is not possible to tell when and where a natural neutrino \ninteracts in the detector. Therefore, the front-end electronics \nmodules for the detectors, which are used to study neutrino from nature, \nare required to digitize all signals from photo-sensors that are above a certain\nthreshold -- i.e. the acquisition needs to be self-triggered. The digitized information \nis then either recorded or discarded, depending on the design of the detector-wide trigger system.\n\nCurrent design of the HK detector is quite similar to the SK\ndetector, in terms of the required specifications and the number of\nphoto-sensors in one detector. Therefore, it is reasonable to \nstart with the system used in the SK detector.\n\n The photo-sensor for the inner detector of HK is newly developed.\nBased on the baseline option, around 40,000 20inch PMT R12860-HQE \nis used. The R12860-HQE PMT has better timing and charge resolution \ncompared to the same diameter PMT (R3600), which has been used in SK.\nThe dark (noise) rate is required not to exceed 4~kHz, which is a \nsimilar requirement to the R3600 PMT. \nBased on these information, we have\nestimated the total data rate and concluded that it is possible to\ndesign the data acquisition system, which has similar to the concept \nof the SK-IV DAQ.\n\n As already realized in the SK-IV DAQ system, it is possible to \nread out all the hit information from the photo-sensors, including \nthe dark noise hits. There is no technical problem in selecting \nthe actual events to be recorded for the analyses by software.\n\n One difference is the size of the detector. The total amount of\nphoto-sensors in one entire detector is expected to be up to $\\sim$\n47,000, including the sensors for OD. If we locate the front-end \nelectronics modules on the top of the detector, it is necessary \nto run the cable from the PMT to the roof and the detector structure \nhas to support the weight of the cables, which is expected to be 800~tons. \nThus, it would be possible\nto simplify the detector structure if we can reduce the weight\nof the cables. Also, the maximum length of the cable is $\\sim$ \n30\\% longer than in the SK case. This not only reduces the signal amplitude,\nbut also degrades the quality of the signal -- the leading edge is smoothed out due\nto higher attenuation of the cable in the high frequency region.\nTherefore, we plan to place the modules with the front-end \nelectronics and power supplies for the photo-sensors\nin the water, close to the photo-sensors. This configuration\nmakes it possible to have shorter signal cables from the photo-sensors \nand also allows for significant reduction of the weight that needs to be supported by the photo-sensor \nsupport structure. Of course, it is necessary to place the front-end module and\npower supply for the photo-sensors in a pressure tolerant enclosure, and also to \nuse water-tight connectors. This kind of ``water-tight'' casing \nhas been studied in other experiments and there are several \npossible options. One concern is the cost of the special cables\nand connectors -- consequently, we are developing special cables and connectors\ndedicated for HK.\n\n The other issue we have to keep in mind is an inability to do any repairs \n to a broken module that will be submerged in water. Furthermore, a failure of\none module could affect the data transmission from other modules, resulting in a much\nlarger region of the detector that could be lost. Therefore, the system\nmust be redundant and care must be taken to avoid a single\npoint of failure. Also, careful design of the data\ntransport connections and the timing distribution system are\nessential.\n \n The current baseline design of the front-end module is prepared\nconsidering these requirements. The schematic diagram of the front-end\nmodule is shown in Fig.~\\ref{schematic_frontend:daq}.\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[width=0.7\\textwidth]{design-electronics\/figures\/daq_schematics.pdf}\n \\caption{Schematic diagram of the front-end module.}\n\\label{schematic_frontend:daq}\n\\end{center}\n\\end{figure}\n\n There are 4 main function blocks in the front-end board. The signal\ndigitization block, the photo-sensor power supply block, the slow\ncontrol block and the communication block. In the current baseline design, \none module accepts signals from 24 photo-sensors, digitizes them and \nsends out the data.\n\n In the following sections, details of each component of the\nfront-end module are described, along with the data readout and processing parts.\n\n\\subsubsection{ Signal digitization block }\n\n The signal digitization block accepts the signals from the photo-sensors \nand converts them to the digital timing and charge data. As\nmentioned in the previous section, there is no way to tell when a\nneutrino or a nucleon decay event happens. Therefore, the front-end\nelectronics module is required to have self-triggered analog to\ndigital conversion mechanism and to be dead-time free. The actual\nevent rate is expected to be smaller than a tens of kHz, even with the\nbackground events from gamma-rays from the surrounding wall or\nfrom cosmic-rays. Also, the number of photo-sensors, which detect\nsufficient charge in case of gamma-ray events is quite small, much \nless than 1\\% of the photo-sensors in the detector.\nTherefore, the time interval between photons hitting a single photo-sensor \nis rather long, much longer than the dark rate of the sensor.\nHowever, muons decay into electrons in the detector and photons from\nboth of them may hit a single photo-sensor. Therefore, it is necessary \nto have the capability to detect both photons, generated by the parent \nmuons and the decay electrons. The lifetime of muons are rather long, \n$\\sim$ 2\\,$\\mu$ sec and thus, it it not necessary to be completely \ndead-time free but the dead-time should be as short as possible.\n\n One possible way to satisfy these requirements is to employ the \ncharge-to-time conversion (QTC) chips. The QTC chip receives\nthe signal from the photo-sensor and produces the digital signal, \nwhose width is linearly dependent on the amount of the input charge. Also, \nthe leading edge of the output digital signal corresponds to the \ntime when the input signal exceeded the pre-defined threshold to produce the\noutput digital signal. The digital output signal from the QTC chip\nis read out by a TDC. Usually, the maximum width of the output \nsignal may be slightly longer than the charge integration gate \nwidth. Therefore, there is a small dead-time after the first \nsignal but it is no larger than several hundreds of ns and \nis acceptable for use in the water Cherenkov detector.\n\n The requirements of the charge and timing resolution are summarized\nin Table~\\ref{requirements1:daq}.\n\n\\begin{table}[htb]\n\\begin{tabular}{l|l}\n\\hline\\hline\nitems & required values \\\\\n\\hline\nBuilt-in discriminator threshold & 1\/4 p.e ( $\\sim$ 0.3 mV )\\\\\nProcessing speed & $\\sim$ 1$\\mu$sec. \/ hit \\\\\nCharge resolution & $\\sim$ 0.05 p.e. ( RMS ) for $<$ 5 p.e. \\\\\nCharge dynamic range & 0.2 $\\sim$ 2500 pC ( 0.1 $\\sim$ 1250 pe. )\\\\\nTiming response & 0.3 ns RMS ( 1 p.e. )\\\\\n & 0.3 ns RMS ( $\\geq$ 5 p.e. )\\\\\nLeast time count & 0.52 ns \\\\\nTime resolution & 0.25 ns \\\\\nDynamic range & $\\geq$ 15 bits \\\\\n\\hline\\hline\n\\end{tabular}\n\\caption{ Specification of the signal digitization block. }\n\\label{requirements1:daq}\n\\end{table}\n\n The QTC chips ( CLC101 ) used in the front-end module of SK-IV, \ncalled the QBEE, are a good reference and satisfy all the requirements. \nThe design rule of these chips is 0.35$\\mu$m and it is possible to\nproduce them again. As for the TDC, the chips used in the QBEE, called AMT3,\nhave been discontinued. However, there are several implementations\nof a `TDC in an FPGA' and some of them seem to have sufficient performance.\nOne candidate is the `wave union TDC' developed at FNAL. The performance \nof this TDC is expected to be better than that of the AMT3 and we are currently\nevaluating this TDC design.\n\n Even though the current baseline design is to utilize the QTC-TDC \napproach, we are also investigating possibility of adopting Flash-ADC \n(FADC) type digitization. In this case, the FADC chip would run all \nthe time and digitize the input signal. Afterwards, FPGA-based \non-the-fly digital signal processing would be utilized to find the PMT \npulse and determine its charge and time of arrival. An advantage of \nthis approach is that it is completely dead-time free -- we would be \nable to detect photons both from prompt muons and from decay electrons, \neven if the latter happen only 100 ns after the initial interaction. \nWe may also be able to distinguish photons from direct and reflected light.\n Another potential advantage is an ability to remove deterministic \ninterference that may be present in the PMT signal. Example sources of \nsuch an interference are switching power supplies and high voltage \nsupplies. The disadvantage is potentially larger power consumption and\nhigher cost.\n\n Since both the power consumption and the cost are highly dependent on \nthe speed and precision of the FADC ICs, it is advisable is to use the \nslowest possible configuration that will `do the job'. As such, a study \nhas been performed in order to understand the performance of the system \nas a function of both the resolution and the sampling frequency of the \nFADC. Furthermore, models of the system were developed and validated, \nso that further studies can be streamlined. Finally, various signal \nprocessing methods were tested for determining timing of the pulse -- \namong them the digital constant fraction discriminator \\cite{Huber:2011dt}, \noptimal filters \\cite{Gatti:2004lms,Abbiati:2006tim} and matched filters. \nThe results of the study are presented in \nFig.~\\ref{electronics:fadc:shaper_study}. It is relatively easy to \nachieve the timing resolution that is below 10\\% of the sampling period \n($T_S$). With sufficiently high SNR it is also possible to reach even \nbetter timing accuracy, well below 1\\% of $T_S$. Based on these results,\nwe decided to use a 100 MSPS\/14 bit FADC as the current baseline design for \nthis digitization scheme. Two FADC channels will be used per single PMT (high-gain and low-gain channels), \nso that the dynamic range requirements are fulfilled. Current studies concentrate \non optimizing an anti-aliasing filter, in order to achieve best possible \ntiming resolution.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=0.49\\textwidth,trim={12mm 74mm 22mm 74mm},clip]{design-electronics\/figures\/fadc_sigma_time_cfd.pdf}\n\\includegraphics[width=0.49\\textwidth,trim={12mm 74mm 22mm 74mm},clip]{design-electronics\/figures\/fadc_sigma_time_fir.pdf}\n\\caption{Results of the study of the timing performance of FADC-type digitization, with pulse timing using digital constant fraction algorithm (left) and optimal filter (right). The precision of the ADC is expressed as signal-to-noise ratio -- $SNR = 6.02N + 1.76$~[dB], with $N$ being the effective number of bits.}\n \\label{electronics:fadc:shaper_study}\n\\end{figure}\n \n Another solution, which allows for savings in power consumption and still \nmaintains high sampling frequency, is to use switched capacitor \narrays (SCA). The biggest advantage of this approach is that no \nbandwidth-limiting anti-aliasing filter is necessary. The price to pay \nis dead-time introduced due to `freezing' of the capacitor, which \nis necessary for its readout. One possibility of alleviating this problem is \nto utilize multiple SCA channels per photo-sensor. This way a dead-time free readout\ncan be provided up to a certain trigger frequency. A better option is to use SCAs\nwith segmented memory, so that one can avoid potentially expensive increase of the number\nof SCA chips. Unfortunately, we are currently not aware of an existence of such an IC, with sufficiently \nlarge memory buffer. Therefore, we are considering possibility of a development of a new IC. The goal would be\nto allow both a dead-time less readout, typical for pure FADC-type digitization,\n as well as high sampling speeds and low power consumption, provided by the SCAs.\n \n The basic assumption of the new design is that the chip would consist \nof both an SCA-type analog memory, a flash-ADC and a discriminator. The \nsampling speed of both the SCA and the flash-ADC would be equal. The\nflash-ADC, which is the most `power hungry' part, would be kept off \nmost of the time -- it would be activated only once a sufficiently high \npulse is detected at the input. Since some time is required for resuming\nthe flash-ADC operation, the analog memory would be used to store the \npulse -- sampled, but not yet quantized. Once the ADC is fully active, \nthe analog memory would act as a first-in first-out buffer, without any freezing \nof its content. Thus, the system would be able to work as long as there \nis any useful signal, without any dead-time.\n\n In either case, it is necessary to be prepared for a failure of the\ndigitization component. We are therefore considering to have a set of spare\ndigitizer channels and to insert analog switches between the signal \ninputs and the digitization block. With this configuration, we have \nsome flexibility to change the assignment of input signals to \ndigitizer channels. This also provides us with an additional way to\ncalibrate the digitization blocks. Of course, analog switch is known\nto degrade the quality of the signal. Thus, we are going to study\ncarefully prior to implementing this solution. Furthermore, the photo-sensors, \nwhich are currently considered, produce faster pulses and, consequently, higher maximum\nvoltage, which is expected to exceed 6 volts. This is larger than\nthe maximum allowable voltage of the digitizer chips. Therefore, we need to\ndesign the protection circuit, which will\nnot degrade the timing and charge resolutions. \n\n Because the relative timing is used to reconstruct the event vertex \nin the detector, all the modules have to be synchronized. Therefore, \nit is necessary to drive the TDC or FADC by a clock synchronized to \nthe reference clock fed externally. Also, the system-wide counter \nis attached to the data to combine the data from different modules \nat a later stage.\n\n\\subsubsection{ The timing synchronization block }\n\n Synchronization of the timing of each TDC or FADC is crucial for precise \nmeasurement of the timing of photon arrival. In Hyper-Kamiokande,\ntiming resolution of the photo-sensor is expected to be largely\nimproved. Therefore, we have to be careful with the\nsynchronization of the modules -- the design should minimize the clock jitter, so that\nthe timing resolution of the whole system is as good as possible. We are planning to distribute the\ncommon system clock and the reference counter to all the modules. We\nhave not yet started the actual design of this system, but there are\nseveral existing examples. The first method is to send the clock and\nserialized 32 bit counter information using special STP cable, called the\nnano-skew cable, whose skew is less than a few nanoseconds for a 100\\,m long\ncable. This system has been used in current SK DAQ system and the\nskew is measured to be much smaller than 100\\,ps. It requires\nintermediate timing distributor and therefore needs to be modified for\nuse in Hyper-Kamiokande, but it is not difficult. The other\npossibility is to use the idea of White Rabbit. The White Rabbit\nsystem is designed for the synchronization in the accelerator complex\nand corrects the timing differences with measured delay in each node.\nIt is not necessary to implement entire functionality of White Rabbit\nfor our case but employ the main part of the timing synchronization\nand stabilization.\n\n\\subsubsection{ The photo-sensor power supply block }\n\n If HPDs are used as the photo-sensor, the high voltage supplies for the \n acceleration voltage and the avalanche photodiode bias voltage will\n be put on the HPD base. In this case, the front-end module will control \n both power supplies via control signals.\n\nIf the normal PMTs are used as the photo-sensors, we are considering to\nput the high voltage module in the same enclosure as the front-end\nmodule. In this case, the control signal would be fed internally between \nthe two modules.\n\nThe control signals to the HPD base or to the internal high \nvoltage modules will be controlled remotely through the communication \nblock.\n\n\\subsubsection{ The slow control and monitor block }\n\n It is important to control and monitor the status of the power supply\nfor the photo-sensors. Also, the voltage, the current and the\ntemperature of the front-end module has to be monitored. This slow\ncontrol and monitor block is prepared for this purpose. It\naccepts the commands from the communication block and also keeps the\ncurrent status, which is available for read-back. All communication with the\n`external world' is done through the communication block.\n\n\\subsubsection{ The communication block }\n\nIn order\nto reduce the amount of cables, we are planning to connect the modules\nin a mesh topology, with each module connected to its neighbors -- Fig.~\\ref{connections:daq}. \nOnly the top modules would be connected to the readout computers. Each module will have\nseveral communication ports, so that a single point of failure would be avoided. \nIn case of failure of one of the modules, the data would simply be re-routed to one of the neighbors, \nthus ensuring that communication path will be secured.\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[width=0.4\\textwidth]{design-electronics\/figures\/daq_connections.pdf}\n \\caption{Schematic diagram of the connections between front-end modules.}\n\\label{connections:daq}\n\\end{center}\n\\end{figure}\n\n There are several possibilities for the connection, but one of\nthe promising ones is the SiTCP, an FPGA based TCP\/IP stack. This TCP\/IP\nstack does not require a CPU core in the FPGA and is accessible like a simple\nFIFO buffer. SiTCP acts as either a TCP\/IP server or a client, so it is \npossible both to receive data from the other module and to add own data\n and later to send everything to the next module. Also, SiTCP has\nregisters, which can be accessed via UDP commands. With this \nfunctionality, it is possible to realize the slow control and\nmonitor system, such as setting the high voltage or monitoring\nthe status, for example read-back of voltages of the power supply.\nRecently, CPU cores are embedded in the FPGA chip. With this kind\nof chips, TCP\/IP communication part is also possible to be handled\nwith the embedded CPU. We will investigate this possibility.\nApart from TCP\/IP, there are several other industry standard\ncommunication protocols available. One example is the Rocket-I\/O.\nRocket I\/O is the standard interface supported in Xilinx FPGA.\nThis allows us to transfer data at speeds exceeding gigabit per second.\nWe are also investigating this possibility for a faster \ncommunication between the modules.\n\n\\subsubsection{ Pressure tolerant cable and Water tight connectors }\n In order to connect the front-end electronics module with other modules, the photo-sensors\nand the clock modules, we need to have water tight connectors and\npressure tolerant cables. It is known that normal Ethernet\ncables are not capable of transmitting the data at full rate\nunder the pressure, because the characteristics of the cable\nare changed when the cable is squeezed under the pressure.\nTherefore, we have started the R\\&D of the pressure-tolerant,\nwater tight Ethernet cable. This cable will use the similar sheath\nmaterial to the one used as the photo-sensor signal cable\nnot to affect the water quality of the detector.\nWe have also started designing the water tight connectors\nfor the PMT connection and the Ethernet connection. Both of the \nconnectors are using screws and are easy to connect. This will \nreduce the time to connect cables during the construction.\nThe mock-up connectors have been designed and we are going\nto produce samples and evaluate them in the coming years.\n\n\\subsubsection{ Timeline }\n Current plan from the finalization of the design to the completion\nof the production and tests is shown in Table \\ref{timeline1:daq}\n\\begin{table}[h]\n\\begin{tabular}{l l}\n Spring 2020 & Final design review of the system \\\\\n Autumn 2020 & Start the design of the system based on the design review \\\\\n Autumn 2021 & Start bidding procedure \\\\\n Autumn 2022 & Start mass production \\\\\n Autumn 2023 & Start final system test \\\\\n Autumn 2024 & Complete mass production \\\\\n Autumn 2025 & Complete system test and get ready for install\n\\end{tabular}\n\\caption{Timeline to complete the production for the installation.}\n\\label{timeline1:daq}\n\\end{table}\n\n In order to complete the design by Spring 2020, R\\&D and evaluation\nof each component have to be finished by then. Table \\ref{timeline2:daq}\nshows the deadlines for each component.\n\\begin{table}[h]\n\\begin{tabular}{l l}\n Digitizer & Autumn 2018 based on the decision of the photo sensors \\\\\n Timing and synchronization & Select technology by Autumn 2018 \\\\\n Communication block & Fix specification by Autumn 2018 \\\\\n & Design by Spring 2019 \\\\\n High voltage system & Product selection and design by Autumn 2019 \\\\\n Water tight components & Technology choice by Spring 2019\n\\end{tabular} \n\\caption{Deadlines for each components.}\n\\label{timeline2:daq}\n\\end{table}\n\n Considering the schedule, we need good coordination with the other\ngroups, including not only the photo-sensor groups but also the construction\ngroups. The allocated time for each item is not much but still achievable.\n\n\n\n\n\n\n\\subsection{Introduction of the Hyper-Kamiokande detector}\n\\graphicspath{{design-introduction\/figures\/}}\n\nThe 1TankHD{} design, i.e. one cylindrical vertical tank with\n40\\% phoocoverage as shown in Fig.\\ref{fig:hk-perspective-1TankHD}, corresponds to the optimized configuration studied\nby the proto-collaboration. It is referred as 1TankHD{} in this report.\n\nThe strategy considers also a staged second tank (2TankHK-staged)\ncurrenlty being investigated (see appendix~\\ref{sec:hakamagoshi}).\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.69\\textwidth]{HK1TankHD_schematic.pdf}\n \\caption{Schematic view for the configuration of single cylindrical tank instrumented with high density (40\\% photocoverage) PMTs.\nIt is referred as 1TankHD{} in this report.}\n \\label{fig:hk-perspective-1TankHD}\n \\end{center}\n\\end{figure}\n\nThe Hyper-K experiment employs a ring-imaging water Cherenkov detector\ntechnique to detect rare interactions of neutrinos and the possible\nspontaneous decay of protons and bound neutrons.\nTable~\\ref{Table:detectorparameters} summarizes the key parameters of\nthe Hyper-K detector compared with other previous and currently\noperating water Cherenkov detectors. These types of detectors are\nlocated deep underground in order to be shielded from cosmic rays and\ntheir corresponding daughter particles and thereby to achieve a very\nlow background environment.\n\nThe detector mass -- or equivalently the underground detector cavern\nsize or water tank size -- is one of the key detector parameters that\ndetermines the event statistics in neutrino observations and nucleon\n(proton or bound neutron) decay searches. The detector water plays\ntwo roles: a target material for incoming neutrinos and source of\nnucleons to decay. We need a detector mass of at least $O(10^2)$\nkton. in order to accumulate $O(10^3)$ electron neutrino signal\nevents (as shown in Table~\\ref{Tab:sens-selection-nue}) from the\nJ-PARC neutrino beam. This is necessary to measure the $CP$ violation\neffect with a few \\% accuracy. This mass of water contains\n$O(10^{35})$ nucleons (protons and nucleons) which would give an\nunprecedented sensitivity to nucleon lifetime at the level of\n$10^{35}$ years. The location and detailed designs of the Hyper-K\ncavern and tank are presented in Section~\\ref{section:location},\n\\ref{section:cavern}, and \\ref{section:tank}.\n\nThe detector is filled with highly transparent purified water, as\nshown in Section~\\ref{section:water}. A light attenuation length above\n100\\,m can be achieved which allows us to detect a large fraction of\nthe emitted Cherenkov light around the periphery of the water volume.\nRadon concentration in the supplied water is kept below 1\\,mBq\/m$^3$\nto control the radioactive background event rate in solar neutrino and\nother low energy observation. An option being investigated is the\nGd-doping of the water. This option, in addition to the nominal water\none, is presented in Section~\\ref{section:water}.\n\n\\begin{table}[!tbp]\n \\centering\n \\caption{Parameters of past\n (KAM~\\cite{Suzuki:1992as,Fukugita:1994wx}), running\n (SK~\\cite{Fukuda:2002uc,Abe:2013gga}), and future\n HK-1TankHD{}) water Cherenkov\n detectors.\n The KAM and SK have undergone several configuration changes\n and parameters for KAM-II and SK-IV are referred \n in the table.\n The single-photon detection efficiencies are products of\n the quantum efficiency at peak ($\\sim 400$\\,nm), \n photo-electron collection efficiency,\n and threshold efficiency.\n }\\label{Table:detectorparameters}\n \\begin{tabular}{lccc}\n \\hline\n \\hline\n & KAM & SK & HK-1TankHD{} \\ \\\\\n \\hline\n Depth & 1,000 m & 1,000 m & 650 m \\\\\n Dimensions of water tank & & & \\\\\n ~~~~diameter & 15.6 m $\\phi$ & 39 m $\\phi$ & 74 m $\\phi$ \\\\\n ~~~~height & 16 m & 42 m & 60 m \\\\\n Total volume & 4.5 kton & 50 kton & 258 kton \\\\\n Fiducial volume & 0.68 kton & 22.5 kton & 187 kton \\\\\n Outer detector thickness & $\\sim$ 1.5 m & $\\sim$ 2 m & $1 \\sim 2$ m \\\\\n Number of PMTs & & & \\\\\n ~~~~inner detector (ID) & ~~948 (50 cm $\\phi$)~~ & ~~11,129 (50 cm $\\phi$)~~ & ~~40,000 (50 cm $\\phi$)~~ \\\\\n ~~~~outer detector (OD) & 123 (50 cm $\\phi$) & 1,885 (20 cm $\\phi$) & 6,700 (20 cm $\\phi$) \\\\\n Photo-sensitive coverage & 20\\% & 40\\% & 40\\% \\\\\n Single-photon detection & unknown & 12\\% & 24\\%\\\\\n efficiency of ID PMT & & & \\\\\n Single-photon timing & $\\sim 4$ nsec & 2-3 nsec & 1 nsec \\\\\n resolution of ID PMT & & & \\\\\n \\hline\n \\hline\n \\end{tabular}\n \\label{table:example}\n \\end{table}\n\nThe detector is instrumented with an array of sensors with\nsingle-photon sensitivity in order to enable reconstruction of the\nspatial and timing distributions of the Cherenkov photons which are\nemitted by secondary particles from neutrino interactions and nucleon\ndecays. The dimension of the photo-sensors and their density are\nsubject to an optimization that takes into account the required signal\nidentification efficiencies, background rejection power, and cost. As\na reference, the Super-K detector shown in\nTable~\\ref{Table:detectorparameters} covers $40\\%$ of the detector\nwall with Hamamatsu R3600 50\\,cm diameter hemispherical\nphotomultiplier tubes (PMTs) with the original goal to measure the\nsolar neutrino energy spectrum above $\\sim$5\\,MeV.\n\nThe Hyper-K detector is designed to employ newly developed\nhigh-efficiency and high-resolution PMTs (Hamamatsu R12860) which\nwould amplify faint signatures such as neutron signatures associated\nwith neutrino interactions, nuclear de-excitation gammas and $\\pi^+$\nin proton decays into Kaons, and so on. This increased sensitivity\ngreatly benefit the major goals of the Hyper-K experiment such as\nclean proton decay searches via $p\\rightarrow e^+ + \\pi^0$ and\n$p\\rightarrow \\bar{\\nu} + K^+$ decay modes and observation of\nsupernova electron anti-neutrinos. The characteristics of the R12860\ntubes are shown in Section~\\ref{section:photosensors}. The\nphoto-sensors have vacuum glass bulbs and will be located as much as\n60\\,m underwater in the Hyper-K cavern. At this depth, the applied\npressure is close to the manufacturers upper specification of the\nSuper-K R3600 PMT (0.65\\,MPa). Therefore, we need to develop a new\nbulb design and a quality controlled production method to ensure that\nthe sensors can withstand this pressure. Furthermore, PMT cases\nwill envelop each photo-sensors to avoid a potential chain reaction\naccident due to the implosion of a glass bulb in the water. The\ndesigns of the bulb and case are also described in\nSection~\\ref{section:photosensors}.\n\nThe detector is instrumented with front-end electronics and a readout\nnetwork\/computer system as shown in Section~\\ref{section:electronics}\nand \\ref{section:daq}. The system is capable of high-efficient data\nacquisition for two successive events in which Michel electron events\nfollow muon events with a mean interval of 2\\,$\\mu$sec. It is also\nable to collect the vast amount of neutrinos, which would come from\nnearby supernova in a nominal time period of 10\\,sec.\n\nSimilar to Super-K, an outer detector (OD) is being envisaged that, in\naddition to enabling additional physics, would help to constrain the\nexternal background. Sparser photo-coverage and smaller PMTs than\nthat for the ID is also planned.\n\n\n\\subsection{Detector site}\\label{section:location}\n\n\\subsubsection{Detector location}\nThe Hyper-K detector candidate site, located 8\\,km south of Super-K,\nis in the Tochibora mine of the Kamioka Mining and Smelting Company,\nnear Kamioka town in Gifu Prefecture, Japan, as shown in\nFig.~\\ref{fig:map}.\n\\begin{figure}[tb]\n \\includegraphics[width=1.0\\textwidth]{HKlocation.pdf} \n \\caption{The candidate site map. Broad area map (left) and detailed map\n (right).} \\label{fig:map}\n\\end{figure}\nThe J-PARC neutrino beamline is designed so that the existing\nSuper-Kamiokande detector and the Hyper-K candidate site in Tochibora\nmine have the same off-axis angle. The experiment site is accessible\nvia a drive-in, $\\sim$2.5\\,km long, (nominally) horizontal mine tunnel.\nThe detector will lie under the peak of Nijuugo-yama, with an\noverburden of 650\\,meters of rock or 1,750\\,meters-water-equivalent\n(m.w.e.), at geographic coordinates Lat. 36$^{\\circ}$21'20.105''N,\nLong. 137$^{\\circ}$18'49.137''E (world geographical coordinate\nsystem), and\nan altitude of 514\\,m above sea level (a.s.l.). The candidate site is\nsurrounded by several faults as shown in Fig.~\\ref{fig:fault} and the\ncaverns and their support structure are placed to avoid a conflict\nwith the known faults.\n\\begin{figure}[tb]\n\\centering\n \\includegraphics[width=0.95\\textwidth]{fault-side.pdf} \\caption{Location\n of faults and existing tunnels around the candidate site. The\n existing tunnels are located at 423, 483, and 553\\,m\n a.s.l.} \\label{fig:fault}\n\\end{figure}\nThe site has a neighboring mountain, Maruyama, just 2.3\\,km away,\nwhose collapsed peak enables us to dispose of more than one million\nm$^3$ of the excavated rock from the detector cavern excavation.\n\n\\subsubsection{Geological condition at the site vicinity}\nRock quality is investigated in the existing tunnels and in sampled\nborehole cores near the candidate site.\nFig.~\\ref{fig:rock_qual_meas} summarizes the geological surveys.\n\\begin{figure}[tb]\n\\centering\n \\includegraphics[width=1.0\\textwidth]{rock_qual_meas_1tank.pdf} \\caption{Location\n of rock quality measurements in existing tunnels and bore-hole cores\n at 423\\,m, 483\\,m, and 553\\,m a.s.l. The red rectangulars show the\n surveyed regions in the measurements. \n The black dashed circle indicates the Hyper-K cavern construction candidate site\n and size of the cavern.\n } \\label{fig:rock_qual_meas}\n\\end{figure}\nThe rock wall in the existing tunnels and sampled borehole cores are\ndominated by Hornblende Biotite Gneiss and Migmatite in the state of\nsound, intact rock mass. This is desirable for constructing such\nunprecedented large underground cavities. A rock mass classification\nsytem developed by Central Research Institute of Electric Power\nIndustry (CRIEPI)~\\cite{rock_class}, which is widely used for dams and\nunderground cavities construction for the electric power plants in\nJapan,\nis utilized to classify rock quality. The CRIEPI system categorizes\nrock quality in six groups as A, B, CH, CM, CL, and D (in order of\ngood quality), among which the A, B, and CH classes are suitable for\ncavern construction. Fraction of rock quality at the measured sites\nis summarized in Table~\\ref{tab:rock_qual_dist}.\n\\begin{table}[htbp]\n\\caption{Summary of measured rock quality fraction. Sum of rock quality fraction\nin some Bore-holes is not 100\\% since a small fraction of sampled rock cores was broken\nduring the survey due to a sampling failure.\n \\label{tab:rock_qual_dist}}\n\\begin{tabular}{l|c|c|c|c|c|c}\n\\hline\\hline\nPlace & \\multicolumn{6}{c}{Rock quality fraction (\\%)} \\\\ \\cline{2-7}\n & A & B & CH & CM & CL & D \\\\\\hline\\hline\nTunnel No.1 & 0.0 & 51.6 & 43.6 & 3.0 & 1.8 & 0.0 \\\\\\cline{2-7}\n(553 m a.s.l.) & \\multicolumn{3}{c|}{95.2} & \\multicolumn{3}{c}{4.8} \\\\\\hline\nBore-hole No.1 & 0.0 & 67.9 & 27.7 & 4.0 & 0.4 & 0.0 \\\\\\cline{2-7}\n(553 m a.s.l.) & \\multicolumn{3}{c|}{95.6} & \\multicolumn{3}{c}{4.4} \\\\\\hline\nTunnel No.2 & 0.0 & 11.4 & 45.4 & 39.8 & 3.4 & 0.0 \\\\\\cline{2-7}\n(483 m a.s.l.) & \\multicolumn{3}{c|}{56.8} & \\multicolumn{3}{c}{43.2}\\\\\\hline\nTunnel No.3 & 0.0 & 4.9 & 55.7 & 25.0 & 14.4 & 0.0 \\\\\\cline{2-7}\n(483 m a.s.l.) & \\multicolumn{3}{c|}{60.6} & \\multicolumn{3}{c}{39.4}\\\\\\hline\nBore-hole No.2 & 2.4 & 10.5 & 49.2 & 29.7 & 5.7 & 0.2 \\\\\\cline{2-7}\n(483 m a.s.l.) & \\multicolumn{3}{c|}{62.1} & \\multicolumn{3}{c}{35.6}\\\\\\hline\nBore-hole No.3 & 0.0 & 19.2 & 59.2 & 16.5 & 3.8 & 0.3 \\\\\\cline{2-7}\n(483 m a.s.l.) & \\multicolumn{3}{c|}{78.4} & \\multicolumn{3}{c}{20.6}\\\\\\hline\nBore-hole No.4 & 6.6 & 20.5 & 36.4 & 22.6 & 7.1 & 3.1 \\\\\\cline{2-7}\n(483 m a.s.l.) & \\multicolumn{3}{c|}{63.5} & \\multicolumn{3}{c}{32.8}\\\\\\hline\nTunnel No.4 & 0.0 & 18.1 & 39.0 & 38.1 & 1.9 & 2.9 \\\\\\cline{2-7}\n(423 m a.s.l.) & \\multicolumn{3}{c|}{57.1} & \\multicolumn{3}{c}{42.9}\\\\\\hline\\hline\n\\end{tabular}\n\\end{table}\nThe geological surveys are performed at three different altitudes\n(423\\,m, 483\\,m and 553\\,m a.s.l.) and better fraction of B and CH\nclasses is observed at higher altitude. The measured fraction of rock\nquality is used for an assumption of rock quality distribution in\ncavern stability analyses.\n \nThe initial stress of the rock is also measured at three points, two\nof which are located at the bottom of the detector cavern (483\\,m\na.s.l.) and one at top (553\\,m a.s.l.).\nIt was found that the two measurements at 483\\,m a.s.l. are strongly\ninfluenced by existing faults.\nWe aim to build our detector at a place where there is no interference\nwith any faults or fracture zone, and the inputs, like initial stress,\nto the cavern stability analysis should not be influenced with faults.\nThus, the two measurements at 483\\,m a.s.l. are eliminated and the one at\n553\\,m a.s.l. is used for a cavern stability analysis described later.\nThe measured rock stress at 553\\,m a.s.l. is shown in\nFig~\\ref{fig:ini-stress}.\n\\begin{figure}[tb]\n\\centering\n \\includegraphics[width=0.9\\textwidth]{initial_stress.pdf}\n \\caption{Results of initial rock stress measurement at 553\\,m a.s.l.}\n \\label{fig:ini-stress}\n\\end{figure}\nBased on the {\\it in-situ} measurements of the rock quality and the\nrock stress, it is confirmed that the Hyper-K caverns can be\nconstructed with the existing excavation techniques (described in\nsection~\\ref{section:cavern}).\n\n\n\n\\input{design-location\/seismic_prospecting.tex}\n\n\\subsubsection{Refining the cavern construction candidate site\\label{sec:seismic}}\n\nAs shown in previous section, the candidate site\nfor cavern construction has area of approximately 300\\,m$\\times$300\\,m\n(see Fig.~\\ref{fig:rock_qual_meas}).\nIn order to further refine and narrow the candidate area where has the best geological condition\nfor the cavern construction,\na geological survey in wide-range, called ``seismic prospecting,'' has been carried out.\n\nSeismic prospecting uses an artificially generated elastic wave that\ntransmits underground bedrock, and identifies physical properties\nof bedrock and geological structure underground, based on the classical physics\nprinciple of transmission, reflection, and refraction of the elastic wave.\nFor example, the speed of elastic wave transmission is varied\nif the elastic wave propagates in a bedrock with different physical\nproperties, e.g. elastic modulus.\n\n\nThe target area of seismic prospecting is defined as\n423$\\sim$703\\,m a.s.l., 400 meters from east to west and 400 meters\nfrom south to north, that covers the entire Hyper-K candidate site\nshown in Fig.~\\ref{fig:rock_qual_meas}.\nThere are six existing tunnels around the target area and they locate\nat different elevations between 423$\\sim$723\\,m a.s.l.\nFor the seismic prospecting, receivers or sensors, called `geophones,'\nwhich detect the elastic wave, were installed in all the six tunnels at interval of 20\\,m \n-- 111 locations in total and each location has three geophones to\ncapture triaxial components of the elastic wave.\nA seismic source is set in the tunnels and generated the elastic wave\nat all the six tunnels with interval of 2.5\\,m in order -- 738 seismic source points in total.\n\nFigure~\\ref{fig:seismic_waveform} shows a waveform data obtained with all geophones\nwhen an elastic wave generated at a location in the tunnel at 723\\,m a.s.l.\nOne can find that an elastic wave transmitted from the seismic source point\nthrough the tunnels in lower altitude.\n\\begin{figure\n \\begin{center}\n \\includegraphics[width=0.88\\textwidth]{seismic_waveform.pdf}\n \\caption{Seismic prospecting waveform data obtained with geophones\n when an elastic wave generated at a location in the tunnel at 723\\,m a.s.l., as an example.\n Vertical axis is a time in millisecond and the origin of vertical axis is when\n an elastic wave is generated.\n Each line runs in vertical direction is a waveform data obtained with a geophone,\n and figure shows waveform data for all the 333 geophones, which are arranged in the\n lateral direction.\n In the figure, pulse heights of the waveform are shown with different colors,\n and the waveform in darker color corresponds to a time when geophones captured an elastic wave.}\n \\label{fig:seismic_waveform}\n \\end{center}\n\\end{figure}\n\nThe data obtained in the seismic survey were analyzed with two methods, seismic\ntomography and reflection imaging.\nSeismic tomography uses the speed of transmission of the elastic wave.\nThe speed of elastic wave transmission varies depending on the physical properties,\ne.g. elastic modulus, density,\nand seismic tomography identifies the physical properties of rock in the\ntarget region, the entire Hyper-K candidate site.\nReflection imaging identifies fault, fracture zone and open cracks in rock\nusing a nature that an elastic\nwave is reflected if there is a discontinuous or uneven structure, like a fault, in the bedrock.\nLeft figure in Fig.~\\ref{fig:seismic_results} shows the results of reflection imaging.\nIn the figure, blue dashed lines indicate the known faults location.\nAs shown in the figure, the reflection imaging identified the known faults, and\nconfirmed that there is no major fault, fracture zone nor open cracks in the\nHyper-K cavern construction candidate site.\nRight figure in Fig.~\\ref{fig:seismic_results} is rock class distribution obtained by\ncombining the results of seismic tomography, reflection imaging and by comparing\nthose results with the geological survey results shown in Fig.~\\ref{fig:rock_qual_meas}, \nwhich are obtained with borehole coring and investigation of the existing tunnels.\nThe red dashed rectangles in the figures denote a region where has the best rock\nquality and the least uneven rock over the entire Hyper-K candidate site.\nFrom the seismic prospecting results, the location for Hyper-K cavern\nconstruction is narrowed down to approximately $200$\\,m$\\times150$\\,m region\n(red dashed rectangle in Fig.~\\ref{fig:rock_qual_meas}).\n\n\nIn conclusion, the risk associated with insufficient geological information,\nespecially regarding geological discontinuities, e.g. faults, and low quality\nrock mass with CM or lower classes, has been largely reduced by the seismic surveys.\n\n\\begin{figure}[p\n \\begin{center}\n \\includegraphics[width=0.45\\textwidth]{seismic_reflection_imaging_Eng.pdf}\n \\includegraphics[width=0.45\\textwidth]{seismic_rock_class_Eng.pdf}\n \\includegraphics[width=0.45\\textwidth]{seismic_reflection_imaging_vertical_slice_Eng.pdf}\n \\includegraphics[width=0.47\\textwidth]{seismic_rock_class_vertical_slice_Eng.pdf}\n \\caption{Results of seismic prospecting at Hyper-K candidate site.\n Top two figures are the results at altitude of 483\\,m a.s.l.\n and lower two figures are results in vertical slice from south to north direction\n as an example.\n Top-left and lower-left plots show the results of reflection imaging,\n and asterisk (*) indicate the identified locations where have fault,\n fracture zone or open cracks in the bedrock.\n In the top-left figure, blue dashed lines indicates the location of known faults which\n are shown in Fig.~\\ref{fig:rock_qual_meas}.\n Top-right and lower-right figures are rock class distribution obtained by combining the results of\n seismic tomography, reflection imaging and the geological survey results\n with borehole and the existing tunnels as shown in Fig.~\\ref{fig:rock_qual_meas}.\n The red dashed rectangles in the figures denotes a region where has best rock\n quality and least uneven rock structure over the entire Hyper-K candidate site.\n Dashed circle indicates the size of Hyper-K cavern.}\n \\label{fig:seismic_results}\n \\end{center}\n\\end{figure}\n\n\\subsection{Photosensors}\\label{section:photosensors}\n\n \\subsubsection{Introduction}\\label{section:photosensors:intro} \n\nThe Hyper-K photosensors detect the\nCherenkov ring pattern created in particle interactions. Photosensors\nview the ID, as well as the OD where they are used to tag particles\nentering or exiting the detector. \n\nThe ID photosensor was newly developed for Hyper-K to meet the\nrequirements listed in Table~\\ref{photosensorrequirement}. The new\nphotosensor is based on the well established and reliable design of\nthe 50\\,cm R3600 PMT by Hamamatsu Photonics K.K. with a Venetian blind\ndynode type, which is used for Super-K, and the 43\\,cm PMT with a\nbox-and-line dynode (Hamamatsu R7250), which is used for the KamLAND\nexperiment. Further improvements include a higher quantum\nefficiency photocathode and an optimized box-and-line dynode, resulting in the new\nphotosensor, a Hamamatsu R12860-HQE PMT (Figure~\\ref{fig:R12860pic}).\n\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{R12860HQEpic.jpg}%\n \\caption{Picture of the HQE 50\\,cm box-and-line R12860 PMT.}\n \\label{fig:R12860pic}\n \\end{center}\n\\end{figure}\n\n\n\\begin{table}[htbp]\n \\begin{center}\n \\begin{tabular}{l|l|l|l}\n \\hline \\hline\n Requirements & Value & & Conditions \\\\ \n \\hline\n Photon detection efficiency & 26\\% & Typ. & Quantum Efficiency $\\times$ Collection Efficiency\\\\ \n & & & ~around 400\\,nm wavelength \\\\ %\n & (10\\%) & & (including Photo-Coverage on the inner detection area)\\\\ \n Timing resolution & 5.2\\,nsec & FWHM, Typ. & Single Photoelectron (PE) \\\\ \n Charge resolution & 50\\% & $\\sigma$, Typ. & Single PE \\\\ \n Signal window & 200\\,nsec & Max. & Time window covering more than 95\\% \\\\ \n & & & ~of total integrated charge\\\\\n Dynamic range & 2 photons\/cm$^{2}$ & Min. & Per detection area on wall\\\\ \n Gain & $10^{7} \\sim 10^{8}$ & Typ. & \\\\ \n Afterpulse rate & 5\\% & Max. & For single PE, relative to the primary pulse\\\\ \n Rate tolerance & 10\\,MHz & Min. & Single PE pulse, within 10\\% change of gain \\\\ \n Magnetic field tolerance & 100\\,mG & Min. & Within 10\\% degradation \\\\ \n Life time & 20\\,years & Min. & Less than 10\\% dead rate \\\\ \n Pressure rating & 0.8\\,MPa & Min. & Static, load in water \\\\ \n \\hline \\hline\n \\end{tabular}\n \\caption{Minimum requirements of the Hyper-K ID photosensors.\n The dark rate is also an important parameter, but its\n minimum required value depends on the photosensor\n specification and is specific to each physics topic.\n It will be explored in the future using the Hyper-K simulation.\n }\n \\label{photosensorrequirement}\n \\end{center}\n\\end{table}\n\nThe OD photosensor design is based on the Super-K OD photosensor, the\n20\\,cm Hamamatsu R5912 PMT, with an improved high quantum efficiency photocathod and a hard waterproofing cover to stand the 60\\,m deep water pressure in Hyper-K.\n\nThis section describes the characteristics of\nthese photosensors. In addition, we present prospects for alternative\noptions, which may be adopted in future.\n\n \\subsubsection{Photosensor for Inner Detector}\\label{section:photosensors:ID} \n\n \\subsubsubsection{Performance}\\label{section:photosensors:IDperformance} \nA newly developed 50 \\,cm R12860-HQE PMT (HQE, high quantum efficiency) for\nHyper-K by Hamamatsu (hereafter referred to as the HQE B\\&L PMT), has a faster time response, better\ncharge resolution and a higher detection efficiency with a stable\nmechanical structure, compared to the existing large aperture PMTs.\nThis section describes the specifications of the HQE B\\&L PMT, as well\nas the safety design that ensures longevity of operation.\n\n\n \\subsubsubsubsection{Design and\nSpecifications}\\label{section:photosensors:IDperformance:design} \nFigure~\\ref{fig:R12860} shows a side view of the HQE B\\&L PMT, whose\nshape is similar to the PMT used in Super-K. Hence, the support structure\ndeveloped in Super-K to attach the PMT is also appropriate for\nthe HQE B\\&L PMT in Hyper-K. The dynode structure and the\nsurface curvature were improved. A typical bias voltage of 2,000\\,V is\ndivided to each dynode by a PMT base circuit such the one shown in\nFigure~\\ref{fig:R12860bleeder}. The specifications for a typical HQE\nB\\&L PMT is listed in Table~\\ref{pmtspec}.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{photosensor_R12860design.pdf}%\n \\caption{Outline of the HQE 50\\,cm box-and-line R12860 PMT.}\n \\label{fig:R12860}\n \\end{center}\n\n\\end{figure}\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{photosensor_VD12860-4.pdf}%\n \\caption{PMT base circuit of the HQE box-and-line R12860 PMT.}\n \\label{fig:R12860bleeder}\n \\end{center}\n\\end{figure}\n\n\n\\begin{table}[htbp]\n \\begin{center}\n \\begin{tabular}{l|l}\n \\hline \\hline\n Shape & Hemispherical \\\\\n Photocathode area & 50\\,cm diameter (20 inches)\\\\\n Bulb material & Borosilicate glass ($\\sim3$\\,mm) \\\\\n Photocathode material & Bialkali (Sb-K-Cs) \\\\\n Quantum efficiency & 30\\,\\% typical at $\\lambda=390$\\,nm \\\\\n Collection efficiency & 95\\,\\% at $10^7$ gain \\\\\n Dynodes & 10\\,stage box-and-line type\\\\\n Gain & 10$^7$ at $\\sim2000$\\,V \\\\\n Dark pulse rate & $\\sim8$\\,kHz at $10^7$ gain (13 Celsius degrees, after stabilization for a long period) \\\\\n Weight & 9\\,kg (without cable) \\\\ \n Volume & 61,000\\,cm$^3$ \\\\\n Pressure tolerance & 1.25\\,MPa water proof \\\\\n \\hline \\hline\n \\end{tabular}\n \\caption{Specifications of the 50\\,cm R12860-HQE PMT by Hamamatsu.}\n \\label{pmtspec}\n \\end{center}\n\\end{table}\n\n\n\\subsubsubsubsection{Detection\n Efficiency}\\label{section:photosensors:IDperformance:efficiency} \nThe single photon detection efficiency of the HQE B\\&L PMT is a factor of two\nbetter than the conventional R3600 in Super-K (Super-K PMT).\nFigure~\\ref{fig:HQE} shows the measured quantum efficiency (QE) of\nseveral HQE B\\&L PMTs as a function of wavelength compared with a\ntypical QE curve of the Super-K PMT (dotted line). \nThe QE of the R12860-HQE PMT is typically 30\\% at peak wavelength around 390\\,nm, while the peak QE of the Super-K PMT is about 22\\%.\n\n \\begin{figure}[htbp]\n \\includegraphics[width=0.4\\textwidth]{HQEspectra-eps-converted-to.pdf}%\n \\caption{Measured QE for six high-QE R12860 (solid lines) and a R3600 (dashed line).\\label{fig:HQE}}\n \\end{figure}\n\n The HQE B\\&L PMT has a high collection efficiency and large sensitive photocathode area. The\n photocathode area with a collection efficiency (CE) of 50\\% or better\n is 49.2\\,cm for the HQE B\\&L PMT, compared to 46\\,cm in case of the\n Super-K PMT and 43.2\\,cm in the KamLAND PMT. Compared with 73\\% CE\n of the Super-K PMT within the 46\\,cm area, the HQE B\\&L PMT reaches\n 95\\% in the same area and still keeps a high efficiency of 87\\% even\n in the full 50\\,cm area. This high CE was achieved by optimizing the\n glass curvature and the focusing electrode, in addition to the use of a\n box-and-line dynode. In the Super-K Venetian blind dynode, the\n photoelectron sometimes misses the first dynode while the wide first\n box dynode of the box-and-line accepts almost all the photoelectrons.\n This also helps improving the single photoelectron (PE) charge\n resolution, which then improves the hit efficiency at a single PE\n level. By measuring the single PE level, we confirmed the CE\n improvement by a factor of 1.4 compared with the Super-K PMT, and 1.9\n in the total efficiency including HQE.\n Figure~\\ref{fig:EffUniformity} shows that the CE response is quite\n uniform over the whole PMT surface despite the asymmetric dynode\n structure.\n\nA relative CE loss in case of a 100\\,mG residual Earth magnetic field is at most 2\\% in the worst direction, or negligible when the PMT is aligned to avoid this direction on the tank wall.\nThe reduction of geomagnetism up to 100\\,mG can be achieved by active shielding by coils.\n\n \\begin{figure}[htbp]\n \\includegraphics[width=0.7\\textwidth]{photosensor_EffUniformityRel.pdf}%\n \\caption{Relative single photon detection efficiency as a function of the position in the photocathode, where a position angle is zero at the PMT center and $\\pm 90^{\\circ}$ at the edges.\n The dashed line is the scan along the symmetric line of the box-and-line dynode whereas the solid line is along the perpendicular direction of the symmetric line.\n The detection efficiency represents QE, CE and cut efficiency of the single photoelectron at 0.25 PE.\n A HQE B\\&L PMT with a 31\\% QE sample shows a high detection efficiency by a factor of two compared with normal QE Super-K PMTs (QE = 22\\%, based on an average of four samples).\\label{fig:EffUniformity}}\n \\end{figure}\n\n\n \\subsubsubsubsection{Performance of Single Photoelectron\nDetection}\\label{section:photosensors:IDperformance:1pe} \nThe single photoelectron pulse in a HQE B\\&L PMT has a 6.7\\,nsec rise\ntime (10\\% -- 90\\%) and 13.0\\,nsec FWHM without ringing, which is faster\nthan the 10.6\\,nsec rise time and 18.5\\,nsec FWHM in the Super-K PMT. The\ntime resolution for single PE signals is 1.1\\,nsec in $\\sigma$ for the fast\nleft side of the transit time peak in Figure~\\ref{fig:PMTTTS} and 4.1\\,nsec\nat FWHM, which is about half of the Super-K PMTs. This would be an\nimportant factor to improve the reconstruction performance of events\nin Hyper-K.\n\nThe nominal gain is $10^7$ and can be adjusted for several factors in\na range between 1500\\,V to 2200\\,V.\nFigure~\\ref{fig:PMT1PE} shows the charge distribution, where the 35\\%\nresolution in $\\sigma$ of the single PE is better for the HQE B\\&L PMT compared to the 50\\%\nof the Super-K PMT. The peak-to-valley ratio is about 4, defined by\nthe ratio of the height of the single PE peak to that of the valley\nbetween peaks.\n\n\\begin{figure}[htbp]\n \\begin{tabular}{c}\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_1petts.pdf}\n \\caption{Transit time distribution at single photoelectron, compared with the Super-K PMT in dotted line. \\label{fig:PMTTTS}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{1cm}\n\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_1pecharge.pdf}\n \\caption{Single photoelectron distribution with pedestal, compared with the Super-K PMT in dotted line. \\label{fig:PMT1PE}}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\n\n \\subsubsubsubsection{Gain Stability}\\label{section:photosensors:IDperformance:gainstability} \nBecause the Hyper-K detector aims for various physics subjects in a wide energy range, the PMT is required to have a wide dynamic range. \nThe Super-K PMTs have an output linearity up to 250 PEs in\ncharge according to the specifications and up to about 700 PEs as measured in Super-K\n(with up to 5\\% distortion)~\\cite{Abe:2013gga}, while the linearity of\nthe HQE B\\&L PMT was measured to be within 5\\% up to 470 PEs as seen\nin Figure~\\ref{fig:pmtlinearity}. Even with more than 1,000 PEs, the\noutput is not saturated and the number of PEs can be calculated by\ncorrecting the non-linear response.\nThe linearity range depends on the dynode current, and\ncan be optimized by changing the resistor values in the PMT base \ncircuit. This result demonstrates sufficient detection capabilities\nin the wide MeV -- GeV region as in Super-K, as long as it is\ncorrected according to the response curve.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{photosensor_linearity_log.pdf}\n \\caption{Output linearity of the HQE B\\&L PMT in charge, where a dotted line shows an ideal linear response.\n It is derived by measurements of a coincident emission by two light sources compared with an expectation by sum of individual detections. }\n \\label{fig:pmtlinearity}\n \\end{center}\n\\end{figure}\n\nA fast recovery of gain for high signal rate is needed for supernova\nobservation, decay electrons from muons, and any accidental pileup\nevents. On the other hand, separation of individual signals in time is limited by the charge integration range,\nthat is 200\\,nsec (equivalent to 5\\,MHz) or more depending on the electronics.\n\nThe rate dependence of the output charge was measured at several light\nintensities while varying the constant interval time of light pulses\n(as shown in Figure~\\ref{fig:pmtratetolerance}). A 5\\% drop is\nobserved at the output current of 170 $\\mu$A. It corresponds to 78\nMHz in the single PE intensity or 1\\,MHz in most of detected\nintensities like at the level of few tens of PE. This is sufficient\nto detect possible burst physics events \n(Section~\\ref{sec:supernova}).\n\n\\begin{figure}[htbp]\n \\begin{tabular}{c}\n\n \\begin{minipage}{0.46\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_rate_tolerance_log.pdf}\n \\caption{Measured charge as a function of the pulse rate in three light intensities of 25, 50 and 100 photoelectrons, relative to outputs at 100\\,Hz.\n Each charge is calculated using the baseline just before the pulse. \\label{fig:pmtratetolerance}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{0.5cm}\n\n \\begin{minipage}{0.46\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_gainrecovery.pdf}\n \\caption{Output charge fidelity of a delayed pulse after a primary pulse, compared with no primary pulse.\n The charge set is about 150 PEs at 10$^{7}$ gain for both primary and delayed pulses in various delayed time. }\n \\label{fig:pmtgainrecovery}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\n\nEven when two near continuous events are detected, like in the case of\nan event with a\ndecay particle, no loss of charge was observed for the\nsecond delayed pulse. By measuring two continuous pulses of about 150\nPEs in both, the observed loss of gain is stable within 0.5\\% as shown\nin Figure~\\ref{fig:pmtgainrecovery}. \nTherefore, the output charge fidelity for a delayed signal is sufficient with the HQE B\\&L PMT.\n\nA long term stability test was performed on three HQE B\\&L PMTs\nin a 200\\,ton water Cherenkov detector at the Kamioka mine, which was\nconstructed to evaluate the feasibility of anti-neutrino tagging via gadolinium doping\nin water. All the HQE B\\&L PMTs functioned over two years, and\nthe gain measured using the charge peak resulting from a pulsed calibration source was stable\nwithin 1\\% RMS (Figure~\\ref{fig:pmtstability}).\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.5\\textwidth]{photosensor_BLPMTpeakhistory.pdf}\n \\caption{Relative charge of three HQE B\\&L PMTs for two months in a 200\\,ton water Cherenkov detector.\n Signals of several tens photoelectrons from a xenon light pulse were monitored. }\n \\label{fig:pmtstability}\n \\end{center}\n\\end{figure}\n\n\n \\subsubsubsubsection{Backgrounds}\\label{section:photosensors:IDperformance:BG} \nThe dark hit rate originates from a thermionic emission on the\nphotocathode, and depends on the environmental temperature, the bias\nhigh voltage and the accumulated operating time for stabilization.\nFor Hyper-K, the energy threshold for low energy physics studies depends largely on the PMT \ndark hit rate, because the sum of the PMT dark hits create fake event triggers.\n\nThe dark hit rates of several HQE B\\&L PMTs were measured to be\n8.3\\,kHz at a temperature of 15\\,$^\\circ$C in air after a month-long\nstabilization period. \nThe adequacy of this dark hit rate on the physics sensitivities will be discussed in Section \\ref{section:physics}.\nSince the detection efficiency is doubled for the HQE B\\&L PMTs, the obtained current dark hit rate is relatively high compared to the Super-K PMT (4.2\\,kHz). \nA lower dark rate results in a better sensitivity to low energy events, thus\nthe HQE B\\&L PMT production is being optimized to achieve a lower dark\nhit rate. We expect further improvements within the next year.\n\nThe afterpulse has a long delay of several microseconds order after\nthe primary PE, and can result in mis-reconstruction for tagging delayed\nparticles. Afterpulsing is caused by a feedback of the ionized residual gas to\nthe photocathode, and several timing peaks appear due to the different gas\nmolecular masses.\nAs shown in Figure~\\ref{fig:pmtafterpulse}, hit timing distribution of the HQE B\\&L PMT has several peaks of afterpulses.\nThe afterpulse rate is, in total, less than 5\\% relative to the main\npulse at single PE observation. It is comparable to the Super-K PMT.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.85\\textwidth]{photosensor_afterpulse.pdf}\n \\caption{Time distribution of hits, where the primary single PE signal comes at zero and others are afterpulses.\n The dotted line represents the level of the dark hit which is set to zero.\n The expected value of the number of afterpulses is measured to be 0.05 for one primary pulse in this sample. }\n \\label{fig:pmtafterpulse}\n \\end{center}\n\\end{figure}\n\nThe radioactive contamination in the surface glass was measured by a\ngermanium semiconductor detector. It is listed\nin Table~\\ref{pmtglassri} by Uranium series, Thorium series and\nPotassium-40. The contamination of Potassium-40 was reduced by an\norder of magnitude compared to the glass used in the Super-K PMT. \n\n\\begin{table}[htbp]\n \\begin{center}\n \\begin{tabular}{l|lll}\n \\hline \\hline\n & U-chain & Th-chain & K$^{40}$ \\\\\n \\hline\n Bq\/kg & 5.4 & 1.8 & 1.6 \\\\\n Bq\/PMT & 34.5 & 11.3 & 10.5 \\\\\n \\hline \\hline\n \\end{tabular}\n \\caption{Radioactive contamination in glass for the HQE B\\&L PMT (Hamamatsu R12860-HQE).}\n \\label{pmtglassri}\n \\end{center}\n\\end{table}\n\n\n \\subsubsubsection{Mechanical Characteristics}\\label{section:photosensors:Mechanical}\nThe HQE B\\&L PMT bulb has been improved and proven to survive under\n60\\,meter water for Hyper-K as described in this section. It is\nsufficiently better than the Super-K PMT, which is only specified for 40\\,meter deep water. \n\nHowever, with the large number of photosensors in Hyper-K we expect\nthat even with a pre-selection (using a quick pressure test, etc.)\nbefore installation, it is difficult to\nensure that there is no glass failure.\nIn 2001, a chain implosion of 6,779 PMTs out of 11,146 took place at Super-K. \nIt was triggered by an accidental implosion which was transmitted to other PMTs as pressure pulse. \nIn order to avert a similar accident, a protective cover made of a ultraviolet (UV) transparent acrylic cover for the detection area and a Fiber Reinforced Plastics (FRP) for the rear was introduced in Super-K.\n\nSuch a protective cover is needed to avoid any cascade implosion of the photosensors, making up for the difficult control of the glass quality in the production.\nThe cover was re-designed to further reduce the impact of pressure pulse, because a 60\\,meter water depth boosts the peak pressure caused by the implosion by a factor of 1.6 from Super-K, corresponding to 6--7\\,MPa.\nThe new design of the ID photosensor cover and its validation are explained in this section.\n\n\n \\subsubsubsubsection{Design and Confirmation Test}\\label{section:photosensors:Mechanical:Design} \nThe weakest point of the Super-K PMT, which is around the largest reverse curvature\n(Neck in Figure~\\ref{fig:pmtcurvature}), was improved for the HQE B\\&L\nPMT.\nBased on a stress analysis, the first bulb shape, R12860-A, was designed to reduce the stress concentration around the neck. \nFurther improvement was achieved in R12860-B by optimizing the\ncurvature because there was a crack observed on the photocathode\nsurface of R12860-A (in Figure~\\ref{fig:pmtcurvature}) after a high pressure water test. \n\n\\begin{figure}[h]\n \\centering\n \\includegraphics[width=4.8cm]{photosensor_R12860_curvature.pdf}\n \\caption{Comparison of the glass bulb curvature between R3600 and R12860 PMTs. }\n \\label{fig:pmtcurvature}\n\\end{figure}\n\nTo validate the degree of improvement, a dedicated test of the PMT in\nwater under high pressure was performed. In a high pressure vessel\nfilled with water, one PMT was tested by increasing the pressure in\nsteps of 0.1\\,MPa above 0.5\\,MPa and waiting for 7 minutes in each\nstep.\n\nAt first, we tested 35 samples of the initial prototypes\n(R12860-A), and the depth range of implosion or crack was between 70\nand 155\\,meters pressure water (Figure~\\ref{fig:PMTdepth}).\nAccording to a survey of the glass thickness before the test, samples that\nimploded around a shallow depth of 70--100\\,meters were found to have a\nrelatively thin thickness of around 2.0--2.5\\,mm at the thinnest point as in\nFigure~\\ref{fig:PMTthickness}. \nTo mitigate this, a quality control step will be introduced whereby we\nmeasure the glass thickness and reject bulbs with thin thicknesses.\nThe glass quality, in regards to bubbles, foreign matter, cracks and\nthickness, is expected to be enhanced after improved training in bulb blowing\nover the year prior to mass production.\n\nThe R12860-B PMT improved with the new shape was also tested. 21\nR12860-B PMTs out of the total 25 did not implode up to 1.5\\,MPa (150\\,m equivalent) as shown in Figure~\\ref{fig:PMTdepth}.\nAll tested PMTs had sufficient high pressure resistance\nfor the 60\\,meter water depth of Hyper-K.\nIt should be noted that the test performed this time was in several\ndifferent conditions of PMT length or waterproofing, in order to find\nthe best design with high pressure bearing.\n\nOne of the two PMTs that imploded did so between 1.2 and 1.3\\,MPa\n(120\\,m and 130\\,m equivalent). This PMT had the smallest measured\nglass thickness around the neck out of all of the 25 tested R12860-B\nPMTs. Another PMT formed crack around the metal pins in the back,\nwhich the stress analysis determined to be the weakest part in the\nR12860. This PMT had a waterproofed guard cover around the pins with\nthe same design as the R3600's, and its Polyethylene material is not\nsufficiently hard to guard the glass against the high pressure water\nthat exists above 1\\,MPa level. Thus, the guard cover was improved\nwith a new hemisphere design made of PPS (Poly Phenylene Sulfide)\nresin and adopted for a subsequent test of fifty PMTs. \n\n\n\\begin{figure}[htbp]\n \\begin{tabular}{c}\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_depth.pdf}\n \\caption{\nBroken pressure in tested R12860-A and R12860-B samples up to 1.5\\,MPa.\n\\label{fig:PMTdepth}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{0.5cm}\n\n \\begin{minipage}{0.5\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_glassthickness.pdf}\n \\caption{\nRelation between a broken pressure in water depth and the minimum\nglass thickness of the R12860-A tested samples. The minimum glass\nthickness was estimated from several points around the neck of the\nbulb and the photocathode glass.\nSeveral PMTs that cracked, but did not implode, are shown in a blank\ncircle. \\label{fig:PMTthickness}}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\n \\subsubsubsubsection{Quality Control of the PMT Glass Bulb}\n\\label{section:photosensors:Mechanical:Test} \nThe glass bulb is manufactured by hand; therefore it is difficult to expect uniform thickness throughout the mass production. \nIn order to find an indication of a possible failure, the glass\nthickness was checked by an ultrasonic thickness gauge at various measurement points. \nAs indicated in Figure~\\ref{fig:PMTthickness} there exists a relation\nbetween the glass thickness and failure pressure, and therefore\nscreening PMTs based on glass thickness would be effective to minimize the failure. \nAlso the bulb was inspected by eye to find unexpected cracks, foam and foreign matter. \n\nEventually after the production, individual PMTs will be tested before installation.\nIt is planned to load a high pressure in water over a few minutes before the installation to the Hyper-K tank, in order to reject a bad bulb.\nIn case of Super-K, 4,727 PMTs were checked with 0.65\\,MPa high pressure water to be safely used up to 40\\,m water depth for the reconstruction after the accident.\nSixteen PMTs of 4,727 were rejected using the test, that is 0.3\\% fraction.\n\nBefore the mass production of photosensors starts, we aim to establish\nthe quality control criteria.\nWe performed a screening test using fifty of the R12860 PMTs, in order\nto set the best criteria that we will use for the mass production. \n\n\\begin{itemize}\n \\item Remarkable failures such as bubbles, foreign matter and striae\n were recorded and photographed during the quality check to measure\n the size and to count the number of occurances.\n \\item The glass thickness was measured at 57 points.\n\\end{itemize}\n\nIt is noted that the photocathode and dynode are absent, but it does not matter because we only investigated the mechanical characteristics without measuring the detection performance.\nSimilar to the screening performed in Super-K, we tested all fifty PMTs in a high pressure water vessel. \nAt this time, the load pressure is assumed to be 0.95\\,MPa for the use in 60 meter water corresponding to 0.65\\,MPa for 40 meter in Super-K.\nSo far, fifty PMTs were tested after the production and there was no damage at 0.95\\,MPa.\nAll of the fifty PMTs were also tested up to 1.25\\,MPa for further\ninvestigation, but here we also found no damage in all PMTs.\n\nAccording to this test, the selection criteria and condition is optimized. \nIn the 2017 fiscal year, we will test 140 functional PMTs \nand will apply the criteria that will be used in Hyper-K. \nAlthough the bulb design of the R12860 PMT is same as the previous test, the production will be improved as below.\n\\begin{itemize}\n \\item The metal mold is renewed. \n \\item The amount of glass is controlled by an automated machine to\n reduce variations in glass thickness.\n \\item The automated measurement system of glass thickness is available for the precise and quick screening.\n\\end{itemize}\n\n\n \\subsubsubsubsection{Degradation of the PMT Glass Bulb}\n\\label{section:photosensors:Mechanical:Degradation} \nAs for a degradation of the glass material, the HQE B\\&L PMT uses stable\nglass made of borosilicate like Super-K, which is highly resistant to\nan aqueous corrosion.\nA general pressure cooker test for the glass plate, in 100\\% humidity air at 121$^{\\circ}$C and\n0.2\\,MPa for 17 hours, showed almost no optical degradation, where the\nlargest degradation is about 1\\% only seen at around 350\\,nm wavelength\nand negligibly small. A test to immerse a glass powder in\n98$^{\\circ}$C boiled pure water for an hour showed a small 0.03\\%\ndissolution in weight, which is very low compared to existing glass.\n\nMechanical characteristics were evaluated at\nfour different points on the PMT using PMT sampling glass taken from the bottom of the Super-K\ntank after 5-years of running. A composition ratio of material and\nbending strength are surveyed, and found to be comparable with other\nSuper-K PMTs stored in air at atmospheric pressure. The high pressure\ntest was also performed on nine sample PMTs from Super-K -- three each\nfrom the top, bottom and barrel sections after 5-years in water -- and\nthere was no implosion with a 0.65\\,MPa load.\n\nTo examine the possibility of degradation by glass crystallization, the\nglass surface was surveyed using X-ray diffraction at the four\ndifferent points as well. There was no diffraction peak originating\nfrom the crystallized glass, in either of the two samples;\none stored in air and the other from the bottom of\nSuper-K.\n\nThe number of dead channels of the ID photosensors is 0.4\\% after\nseven years of Super-K operation, including the ones with wrong\ncable connections. It might also include PMTs with an unknown crack\nor implosion, and therefore we would expect a similar rate of glass\ndamage in Hyper-K, 1\\% at maximum for twenty years.\n\nIt is concluded that the borosilicate glass used in the HQE B\\&L PMT\nis expected to have stable material characteristics over twenty years, and\nseveral mechanical tests using the Super-K PMTs could\nfind no degradation in the long run.\nThe mass production and selection should be well managed such that the\nphysical damage rate is suppressed to the 1\\% level. This level of \nfailure is acceptable because the protective cover will avoid a chain implosion.\n\n\n \\subsubsubsubsection{Shockwave Prevention Covers for PMTs}\\label{section:photosensors:cover} \n\n\\paragraph*{\\underline{Necessity of PMT covers}}\nAs described in previous sections, every effort has been and will be\nmade to avoid a PMT implosion inside the Hyper-K water tank. Based on\nthe knowledge of the mechanical characteristics of the Super-K PMT,\nthe new 50\\,cm PMT has been designed to have enough strength for the\nsafe use at a water depth of 60\\,m, and its performance has been\ndemonstrated by hydrostatic pressure tests. The production of the\nforty thousand PMTs for Hyper-K will be carried out under a strict\nquality control, and the total inspection of the products including a\npressure test will get rid of any individual PMTs having a higher risk\nof an implosion before their installation.\n\nHowever, the possibility of a single PMT implosion cannot be zero. To\nprevent a chain reaction of imploding PMTs caused by the failure of a\nsingle one, all PMTs in Hyper-K are housed in the shockwave prevention\ncovers, similar to those installed on the 50\\,cm PMTs in Super-K after the catastrophic\naccident.\n\n\\paragraph*{\\underline{Basic design concept}}\nThe PMT cover for Hyper-K is designed on the same basic concept as\nthat for the Super-K PMT cover design. In both detectors, the PMT\ncover has several small holes, and the gap between the PMT surface and\nthe cover is filled with the tank water. Since the covers themselves\nare not usually exposed to the water pressure, there is no need to\ncare about any deformations caused by a long-term exposure to the high\nwater pressure. On the other hand, the PMTs are constantly exposed to\nthe water pressure. In the unlikely event of an imploding PMT, the\nwater pressure is immediately applied to the cover housing the broken PMT. \nThe tank water slowly flows in through the small holes on the cover and fills up the vacuum region made by the PMT implosion.\nThe PMT cover is designed to have enough strength so that it can keep its shape even in such a case. \nTherefore, the peak amplitude of the pressure shockwave is significantly\nreduced outside the PMT cover and thus cannot cause a chain reaction.\n\n\n\\paragraph*{\\underline{Super-K PMT covers}}\nIn developing the Super-K PMT cover, there were strict restrictions on\nits weight and shape, since the PMT supporting framework constructed\nin the tank had originally been designed to support the bare PMTs.\nAmong three major candidate designs, the PMT cover formed by combining\nan acrylic front window and a backside cover made of fiber-glass\nreinforced plastic (FRP) was selected in Super-K, since it had been\ndemonstrated by a hydrostatic test and a PMT implosion test that the\ncover would not be crushed even if the PMT inside would implode.\nThus, the Super-K group decided that the combination of the acrylic and FRP parts\nwith flange coupling bolts was suitable for a possible future PMT\nreplacement work and that the components can be readily produced.\n\nA cover formed by combining two half bodies of a molded acrylic\nproduct was another candidate. This full-acrylic cover also was found\nto have enough mechanical strength for withstanding the water pressure\nin the case of a PMT implosion, but it was not adopted due to its mass\nproduction difficulty, a higher manufacturing cost and uncertainty of\nthe strength when combining two bodies.\n\nA cover composed of an acrylic front cover and a stainless steel (SUS)\nbackside cover was also a candidate. \nThe reproducibility of its shape and thickness is better than those of FRP cases. \nThe SUS cover with a thickness of 2\\,mm could not pass a PMT implosion test, \nwhile PMT covers with a thicker SUS component were not possible \ndue to the restriction on the cover weight in Super-K, \n\n\\paragraph*{\\underline{Cover design selection for Hyper-K}}\nSince the depth of the Hyper-K water tank (60\\,m) is about 1.5 times\nlarger than that of the Super-K water tank (41.4\\,m), the Hyper-K PMT\ncovers have to withstand a higher pressure in the case of an implosion\nof the PMT inside. The three cover designs which had been studied for\nSuper-K (i.e. acrylic+FRP, full acrylic, and acrylic+SUS covers) can\nbe also candidates for the Hyper-K PMT cover.\n\nHowever, it is now known that FRP does not just contain much more\nradioisotopes than those in the PMT glass but FRP itself also emits\nlight via chemiluminescence, as observed in Super-K.\nSince these unwelcome things can produce more background events for\nlow energy physics, we have decided not to use any FRP-made covers in\nHyper-K. As for the PMT cover formed by a molded acrylic product,\nthere are still the problems such as a higher cost for an initial prototype.\nIf these problems could be solved\nwithin a reasonable time scale, the full-resin cover can be an\nalternative design for Hyper-K.\n\nThe cover made of the stainless steel contains less radioisotopes and\nis suitable for mass production. Unlike the Super-K case, in which\nSUS-made PMT covers were not adopted due to the weight limit coming\nfrom the existing tank framework specification, the Hyper-K tank\nframework can be designed so that it can support the PMT system\nincluding the SUS covers of a sufficient strength. Therefore, we have\nadopted the PMT cover design of a combination of acrylic and SUS\ncomponents for Hyper-K.\n\n\\paragraph*{\\underline{Hyper-K cover design}}\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{protective_cover_shape.pdf}\n \\caption{A schematic view of the shockwave prevention cover\nfor the Hyper-K ID PMTs.}\n \\label{fig:protective_cover_shape}\n \\end{center}\n\\end{figure}\n\nFigure~\\ref{fig:protective_cover_shape} shows the shape of the Hyper-K\nPMT cover. The front-side cover with a partial spherical shape is\nmade of a UV transparent acrylic with thicknesses of 11\\,mm at the\ncenter position and 15\\,mm at the flange part\n(Figure~\\ref{fig:acrylic_cover_photo}), which is about 1.2 times\nthicker than the acrylic part of the Super-K PMT cover. The light\ntransmittance of the acrylic cover measured in water is more than 95\\%\nfor a wavelength longer than 350\\,nm, which is reasonably good\nconsidering the quantum efficiency of the 50\\,cm Hyper-K PMT. Since\nthe section modulus is proportional to the square of the thickness,\nthe Hyper-K acrylic cover could have about twice the strength of the\nSuper-K one, though this is just a crude estimation. The backside\ncover with a combination of ring and circular truncated cone shapes is\nmade of stainless steel with a thickness of 3\\,mm. The front acrylic\npart and the backside SUS part are connected to each other by flange\ncoupling bolts.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{acrylic_cover_photo.jpg}\n \\caption{Acrylic window part of the PMT cover.}\n \\label{fig:acrylic_cover_photo}\n \\end{center}\n\\end{figure}\n\nThe detailed design of the cover, such as a thickness of each part,\nhas been determined based on a dynamic behavior analysis, simulating\nthe situation after a PMT implosion. The analysis has shown that the\nPMT cover of the design mentioned above \nwill not be crushed even if the PMT inside would implode at a\nwater depth of 100\\,m. The PMT implosion simulation should have some\nuncertainties, but we think they cannot change the conclusion that the\ncover will be functioning well at the depth of 60\\,m. This was\nconfirmed by the performance demonstration tests described later. \n\nOn the acrylic cover, five holes with a diameter of 10\\,mm are formed;\none at the center and four near the flange. These number, diameter\nand position of the holes on the acrylic cover are the same as those\nfor the Super-K PMT cover. In developing the Super-K PMT cover, the\nsoundness of the holes on the acrylic cover against the water stream\ncaused by a PMT implosion had been checked. The test had shown that\nthe holes were not affected when exposed to a water stream with a\nhydraulic pressure of 0.65\\,MPa. Therefore, the hole design should be\nsufficient for the Hyper-K PMT cover.\n\nIt is measured that acrylic is degraded to 77\\% by water absorption. \nTherefore, if it is confirmed by the PMT implosion test at 80\\,m that the covers have enough performance\nto prevent a chain implosion of PMTs, they are expected to be\nfunctioning for the duration of the Hyper-K lifetime.\n\n\n\n \\subsubsubsubsection{Demonstration Test of Shockwave Prevention Covers}\n\\label{section:photosensors:implosiontest}\n\nThe Hyper-K PMT cover has been designed so that it will not be crushed in the unlikely event of a PMT implosion and will prevent the occurrence of the shockwave causing a chain reaction of imploding PMTs.\nTo measure the performance of our PMT cover, we carried out two tests.\nFirst, we carried out a hydrostatic pressure test of the PMT cover in Kamioka Mine to ensure the mechanical strength.\nIn this test, PMT cover was wrapped by a waterproof plastic bag and set in a high pressure vessel filled with water.\nWe pressurized the water surrounding the PMT cover, and the test showed that our PMT cover stood up to 1.1 to 1.5\\,MPa as it was designed.\n\nNext we carried out a prevention of the chain reaction of implosion with a mock-up of the PMT array of Hyper-K.\nWe utilized a test site formally used by Japan Microgravity Center (JAMIC), in Kami-Sunagawa, Hokkaido, Japan, for our chain implosion test.\nThe site has a vertical shaft depth of about 700\\,m with about 4\\,m diameter, filled with spring water.\n\nIn the test, nine PMTs were aligned 3 $\\times$ 3 and mounted on a framework with same 70\\,cm spacing in the Hyper-K inner detector.\nFigure~\\ref{fig:mock_implosion_test} shows the photograph of the mock-up just before sinking to deep water.\nThe central PMT was housed in the PMT cover, and implosion of the central PMT in the cover was induced by the apparatus which was designed to hit and crash the PMT remotely.\nThe others were bare to confirm there is no damage by a shockwave of the implosion at the center.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{cover_test.pdf}\n \\caption{Mock of the chain implosion test. PMT encased in the cover was surrounded with bare PMTs to test the effect of the shockwave.\n Four pressure sensors were set in front of the PMT array to measure the pressure of the shockwaves.\n High-speed camera and lights are also set to investigate the crush visually.}\n \\label{fig:mock_implosion_test}\n \\end{center}\n\\end{figure}\n\nThis mockup was sunk into the deep water (60\\,m or 80\\,m) with pressure gauges and high-speed camera.\nThree trials for each depth were done, and we found that the pressure was reduced to less than 1\/100 and the cover was not crushed.\nFigure~\\ref{fig:shockwave_measurement} shows the measured pressure at the front of the central PMTs for each test at 60\\,m water depth.\nThe PMTs surrounding the center one were used in the second and third tests, but no damage was incurred due to a sufficient suppression of the shockwave by the central cover.\nWe conclude that our PMT cover works to prevent the chain implosion in both 60\\,m and 80\\,m water depths.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{woCover60mWater.pdf}\n \\includegraphics[width=0.4\\textwidth]{wCover60mWater.pdf}\n \\caption{Measured pressure at 70\\,cm ahead of the imploded PMT center at the 60\\,m water depth.\n (Left panel) Shock wave without PMT cover. (Right panel) Shock wave with PMT cover. Three trials are shown in different colors.}\n \\label{fig:shockwave_measurement}\n \\end{center}\n\\end{figure}\n\nWe successfully established the cover design for Hyper-K using these tests.\nIn order to reduce cost and weight, improvement of the cover is on-going and several alternative ideas are under study.\n\n \\subsubsubsubsection{Summary}\\label{section:photosensors:prospect} \n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=1.\\textwidth]{photosensor_productionflow.pdf}\n \\caption{Flow from the bulb manufacture to the operation in Hyper-K. }\n \\label{fig:pmtproduction}\n \\end{center}\n\\end{figure}\n\nThe strength of the PMT bulb was enhanced by the improved bulb design,\nquality check and pre-test in the high pressure vessel before the\ninstallation. A schematic flow diagram of various measures to avoid a\nchain reaction of imploding PMTs is summarized in\nFigure~\\ref{fig:pmtproduction}. In general, it is hard to expect\nthere will be no implosion in Hyper-K over the decades-long operation.\nThus, the protective cover is conservatively designed to avoid any\nchain implosion by suppressing the shockwave, and this design will be\ntested in advance of final production.\n\n \\subsubsection{Photosensor for the Outer Detector}\\label{section:photosensors:OD} \n\n The primary function of the Outer Detector is to reject the\n incident cosmic ray muons that make up part of the background\n in the measurement of nucleon decays and neutrino interactions\n occurring in the Inner Detector. The photosensor design for\n the Hyper-K Outer Detector will be similar to that of the\n successful Super-K Outer Detector using 20\\,cm Hamamatsu R5912\n PMTs. The OD PMT array is sparse relative to the ID PMT\n array, resulting in a 1\\% photocathode coverage on the inner\n wall of the OD. To improve the light collection efficiency by\n about a factor of 1.5, an acrylic wavelength shifting plate of\n a 60\\,cm $\\times$ 60\\,cm square shape is placed around the\n glass bulb of each of the 20\\,cm OD PMTs.\n\nThe pressure tolerance tests have demonstrated that R5912 PMTs could withstand the water pressure at a depth of 60\\,m.\nFor Hyper-K, the R5912 was improved using PPS resin for the guard cover like the R12860 PMT, as shown in Figures~\\ref{fig:R5912} and \\ref{fig:R5912pic}.\nIt also has improved high quantum efficiency of 30\\%\n\n\\begin{figure}[htbp]\n \\begin{tabular}{c}\n \\begin{minipage}{0.5\\hsize}\n \\begin{center}\n \\includegraphics[width=1.0\\textwidth]{photosensor_8pmtassy2.png}\n \\caption{Design of the HQE 20\\,cm box-and-line R5912 PMT.}\n \\label{fig:R5912}\n \\end{center}\n \\end{minipage}\n \\begin{minipage}{0.3\\hsize}\n \\begin{center}\n \\includegraphics[width=1.0\\textwidth]{R5912HQEpic.jpg}\n \\caption{Picture of the HQE 20\\,cm box-and-line R5912 PMT.}\n \\label{fig:R5912pic}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\nIn Super-K, there is no cover attached to the 20\\,cm OD PMTs. \nIt is noted that the volume of the 20\\,cm PMT bulb is 6\\% of the 50\\,cm one, with the similar glass thickness and far distance among OD PMTs. \nBecause of the 60\\,m deep water level compared with Super-K, we would reconsider a safety use of the PMT and cover with appropriate evaluation and tests such as implosion. \n\n \\subsubsection{Alternative Designs}\\label{section:photosensors:Alternative} \nThere is still room to improve the Hyper-K performance with new possible\nphotosensors which are under development. The key of the alternative\noptions is to show sufficient or superior physics sensitivities\nwhile demonstrating safe use in the water tank over a long period of\ntime at a reasonable cost.\nAll the listed alternative candidates are expected to be ready before\nthe Hyper-K construction period, but are currently shown as options\nbecause the product design is not finalized.\n\n \\subsubsubsection{50\\,cm High-QE Hybrid Photodetector}\\label{section:photosensors:HPD} \nAnother new 50\\,cm photosensor with the better time and charge\nresolution than the\nexisting 50\\,cm photosensors is a combination semiconductor\ndevice, called a hybrid photodetector (HPD), and is made by Hamamatsu\n(R12850-HQE).\n\nThe HPD uses an avalanche diode (AD) instead of a metal dynode for the\nmultiplication of PEs emitted from a photocathode. \nA simple AD structure will have good quality\ncontrol in mass production, and a lower production cost than the\ncomplex of metal dynodes. In order to collect PEs in a small 20\\,mm\ndiameter area of the AD, a high 8\\,kV is applied. Related items such\nas the cable, connector and power supply were also developed.\n\nFigure~\\ref{fig:HPDamplification} shows that electrons are multiplied\nby a factor of $10^{5}$ with a combination of a bombardment gain and\nthen avalanche gain. The gain is adjusted by the bias voltage applied\non the AD, around a few hundred volt, while the 8\\,kV is fixed. The\nHPD is equipped with a pre-amplifier, so the resulting gain is\nequivalent to PMTs.\nThe size and surface material are almost the same as those of the 50\\,cm\nPMT as shown in Figure~\\ref{fig:HPDdesign}, thus the same support\nstructure and protective cover can be used.\n\n\\begin{figure}[htbp]\n \\begin{tabular}{cc}\n \\begin{minipage}{0.5\\hsize}\n \\begin{center}\n \\includegraphics[width=1.\\textwidth]{photosensor_HPDprinciple20inch.pdf}\n \\caption{Schematic view of amplification system on the HQE 50\\,cm HPD.\\label{fig:HPDamplification}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{0.5cm}\n\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.6\\textwidth]{photosensor_R12850HQE-10.pdf}\n \\caption{Design of the HQE 50\\,cm HPD (before waterproofing).\\label{fig:HPDdesign}}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\nThe single PE detection is significantly better, though it is still limited by the pre-amplifier because of a large junction capacitance of the AD (400\\,nF).\nThe transit time spread at single PE is 3.6\\,nsec in FWHM measured at the fixed threshold, as drawn by the red line in Figure~\\ref{fig:HPDTTS}.\nIt is superior to 7.3 and 4.1\\,nsec for the Super-K PMT (black) and B\\&L PMT (blue), respectively.\nWith the time walk correction using measured charge, the HPD resolution reached 3.2\\,nsec in FWHM as shown by the dotted magenta line.\n\nFigure~\\ref{fig:HPD1PE} shows the 15\\% charge resolution of the HPD as\nthe standard deviation at the single photoelectron peak as in the red line.\nIt is superior to both the 53\\% and 35\\% for the Super-K PMT (black) and B\\&L PMT (blue).\nIf the AD is segmented into two channels as a test, individual readout of HPD showed better resolution of 10\\% as shown by a dotted line due to a half junction capacitance.\nFurther five segmentation into a center channel and surrounding four channels brings a position sensitive detection with considering a hit probability in five channels\nby a slight focusing shift by different arrival points of photons on the glass.\nIt might help a good event reconstruction and background rejection.\n\n\n\\begin{figure}[htbp]\n \\begin{tabular}{cc}\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_HPDSPETTS.pdf}\n \\caption{Transit time distribution at single photoelectron, compared with the Super-K PMT in dotted line. (HPD is added in Figure~\\ref{fig:PMTTTS}.) \\label{fig:HPDTTS}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{1cm}\n\n \\begin{minipage}{0.45\\hsize}\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{photosensor_HPDPMTSPE_1ch.pdf}\n \\caption{Single photoelectron distribution with pedestal, compared with the Super-K PMT in dotted line. (HPD is added in Figure~\\ref{fig:PMT1PE}.) \\label{fig:HPD1PE}}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\nThe waterproof HPD was successfully operated for 20 days in a dark box filled with water as shown in Figure~\\ref{fig:HPDwater}.\nIn very near future, the HPD would be a superior option to the PMTs, after successful long-term tests of all\nperformance and usability criteria.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.4\\textwidth]{photosensor_HPDwaterproof.pdf}\n \\caption{The HQE 50\\,cm HPD (R12850) testing in water. \\label{fig:HPDwater}}\n \\end{center}\n\\end{figure}\n\n\n \\subsubsubsection{Smaller Photosensors}\\label{section:photosensors:SmallPD} \nPhotosensors with a 20--30\\,cm aperture\ncan also be an alternative option.\nThese are available with the HQE and by another manufacturer.\nUsing two small photosensors are comparable to a single 50\\,cm photosensor as for the detection efficiency, or a little larger aperture size than the 20\\,cm photosensor can be considered as the OD photosensor.\nA smaller 7.7\\,cm PMT with a large photo-collection plate is also a possible alternative option with a low cost for the OD photosensor system.\n\n\n\n\n \\subsubsubsubsection{20--30\\,cm High-QE PMTs}\\label{section:photosensors:HQEODPMT} \nBased on the successful development of the 50\\,cm HQE B\\&L PMT, 20\\,cm\nor 30\\,cm PMTs can obtain superior performance compared to the existing small PMTs.\nBy applying the same techniques, the 20\\,cm and 30\\,cm PMTs with a high\nQE box-and-line dynode and improved performance will be available\neasily by scaling the 50\\,cm PMT down with a similar design. The\nperformance is expected to be equivalent or better compared with the\n50\\,cm HQE B\\&L PMT.\n\nPrior to that, the HQE 30\\,cm PMT, R11780-HQE by Hamamatsu, was\ndeveloped aimed at a large water Cherenkov detector planned in US for\nthe LBNE project. It reached a QE of 30\\% and pressure rating over 1\nMPa. Further improvement was tried, and a new bulb design of the HQE\n30\\,cm PMT based on the R12860-HQE and R11780-HQE was made. In order\nto validate the high pressure tolerance, a test in a high pressure\nwater was performed on three samples at Kamioka. As a result, all the\nsamples got no implosion up to 150\\,meter water equivalently. \n\nUntil recently, photomultiplier tubes with an aperture over 25\\,cm have\nbeen almost exclusively supplied to the market by Hamamatsu. It is\nimportant that additional vendors come in the marketplace for price\ncompetition and for additional supply capacity.\n\nET Enterprises Limited ADIT, now a US-based PMT manufacturer in Texas,\nhas been developing a large area PMT, financially supported by NSF.\nTesting of the operational first generation 28\\,cm HQE PMTs have been\nperformed at Pennsylvania, UC Davis, etc. showing comparable\nefficiency and charge measurement performance to those of\nsimilarly-sized Hamamatsu HQE PMTs.\n\nIf successfully produced, the PMTs can be a cost-effective\nalternative to Hamamatsu for Hyper-K OD PMTs.\n\n\n \\subsubsubsubsection{7.7\\,cm Photodetector Tube}\n\\label{section:photosensors:OD3inchPMT} \n\n\\par\nIn this section we will focus on an alternative design of the\nouter-detector using the 7.7\\,cm photosensors. It is expected that the\ncosts will be lower than the nominal configuration as well as also\nproviding an extended market and production capacity. At the moment\nthe nominal configuration of the outer-detector consists of an array\nof 20\\,cm hemispherical photosensors placed on a grid to reach a\nphoto-coverage of 1\\%, as represented in\nFig.~\\ref{fig:pmt_arrangement}. These photosensors are mounted on\nwavelength shifting plates, to improve the light collection.\n\nBy using 7.7\\,cm photosensors instead of the 20\\,cm, the number of\nphotosensors is multiplied by six to keep the same coverage. The\nphotosensors are therefore closer to each other thus increasing the\nnumber of hits collected, and improving the coincidence accuracy.\nMoreover, the outer-detector water thickness is about 1\\,m, and\nparticles will produce less light and in a narrower region ---\ncompared to the Super-Kamiokande detector where the outer-detector\nwater thickness is about 2\\,m. Thus, a setup with more photosensors\ncloser to each other should allow a better sensitivity, especially\nwith the configuration of Hyper-Kamiokande with a reduced water\nthickness.\n\nWe are currently testing candidate 7.7\\,cm photosensors to be used in\nthe outer-detector, see Fig.~\\ref{fig:QMSetup} for the teststand, as\nwell as implementing the outer detector in that simulation and\nreconstruction, which is needed for optimizing the configuration.\n\n\\begin{figure}[!htb]\n \\centering \\includegraphics[width=0.5\\linewidth]{setup.png} \\caption{Setup\n for photosensors testing at Queen Mary University of London. This\n picture was taken with a 20\\,cm ET9354KB (on the left) and a\n 7.7\\,cm ET9302B (on the right) photosensors. One can see the XY\n stage above the photosensors (blue) which moves the optical fibre\n (in yellow) along the X-Y axis. The optical fibre guides the light\n out from the LED driver to the blackbox.} \\label{fig:QMSetup}\n\\end{figure}\n\nOur tests have been performed using the ET9302KB and other\nphotosensors. The ET9302KB was extensively tested and many of its\nparameters measured. It has a QE of 30\\% and a small dark current\nrate which has been measured at 400\\,Hz --- about ten times less than\ntypical rates for 20\\,cm photosensors --- and a small after-pulse rate\nwith respect to the gain.\n\n\n\nThe ET9302KB would fit perfectly in a configuration with several\nphotosensors like the outer detector, since the number of accidental\ncoincidences inherently raised by the amount of photosensors used will\nbe reduced thanks to its low-noises properties.\n\nFurthermore, these photosensors also showed excellent linearity and\nresolution, allowing an accurate reconstruction of the energy of the\nparticles inside the outer-detector.\nFigure~\\ref{fig:lin:ET9302KB} shows the linearity of the photosensor,\nwhere deviation was measured to be of the order of 1\\%.\nThe resolution at 1000 photoelectrons collected\n--- which is what is expected for a few-MeV gamma event for example ---\nis measured to be 2\\%.\n\n \\begin{figure}[!htb]\n \\begin{minipage}[t]{1.\\linewidth}\n \\includegraphics[width=0.6\\linewidth]{lin}\n \\caption{Linearity for the 7.7\\,cm photosensor ET9302KB,\n measured with an LED driver ranged from few to several thousands\n photons.}\n \\label{fig:lin:ET9302KB}\n \\end{minipage}\n \\end{figure}\n\n\nThe newly improved photosensor from ET Enterprises Ltd., D793KFLB, with a transit time spread of 1.6\\,nsec, a nominal gain $6 \\times 10^{6}$ at 850--1100\\,V and nominal dark rate 1000\\,Hz at 800\\,V is currently under test. \nPreliminary results showed excellent linearity and resolution.\n\nThe photosensors are hemi-spherical and will also be mounted on\nwavelength shifting plates, which allow an easy way to enhance the\nlight collection. Wavelength shifting plates will reemit the absorbed\nphotons in the direction of the photo-cathode of the photosensors at a\nwavelength around 400\\,nm, where the quantum efficiency of the\nET9302KB is maximum.\n\nOuter detector alternative configurations with 7.7\\,cm photosensors\nwill be evaluated in simulation and the best setting will be selected\naccordingly, using realistic cosmic flux files from the Super-K\ncollaboration to test the performance.\n\nThe chosen configuration should achieve at least the minimum detection\nefficiency to have sufficient ability to veto cosmic rays or catch\nthrough-going particles.\n\nFinally, also another alternative of using 12.7\\,cm photosensors,\ni.e. an intermediate solution between 7.7\\,cm and 20\\,cm photosensors,\nis planned to be addressed in both the optimization in simulation of\nthe configurations and in testing the photosensors.\n\n \\subsubsubsection{Multi-PMT Optical Module }\\label{section:photosensors:MultiPMT}\n\\par The concept of an optical module with a 20 to 40\\,cm PMT housed in a glass pressure vessel\n has been developed the past decades for neutrino telescopes in\n water and ice (DUMAND~\\cite{DUMAND}, Baikal~\\cite{Baikal},\n NESTOR@~\\cite{NESTOR,NESTOR-PMT}, ANTARES~\\cite{Antares,\n Antares-PMT}, AMANDA~\\cite{AMANDA} and IceCube~\\cite{IceCube}).\n For KM3NeT~\\cite{KM3NetDR}, the km$^3$ neutrino observatory under\n construction in the Mediterranean, a single large area phototube\n has been replaced by 31 7.7\\,cm PMTs packed in the same glass\n pressure vessel. This new fly's eye photosensor concept, in which small PMTs replace a\n single PMT, has been dubbed the ``multi-PMT Optical Module (mPMT)''.\n The mPMT has several advantages as a photosensor module:\n \\begin{itemize}\n \\item Increased granularity\\\\\n The increased granularity of mPMT provides enhanced event reconstruction, in particular for\n multi-ring events, such as in proton decays and multi-GeV neutrinos which is important for mass hierarchy studies,\n and for events near the wall where fiducial volume is defined.\n Since each of the PMTs have different orientations with limited field of views,\n the mPMT carries information on the direction of each detected photon.\n This directional information effectively reduces the dark hit rate since the dark hits only applies to the field of view\n of the PMT. As a result, it improves signal-to-noise separation for low energy events such as solar\/supernova\n neutrinos and the neutron tagging as discussed in Section~\\ref{section:pdecay-coverage}.\n \\item Mechanically safe pressure vessel with readout and calibration integrated\\\\\n The pressure vessel protect against implosion. Since the vessel is filled with\n small PMTs, electronics and the support structure without large void,\n shock waves would be suppressed even when implosion takes place.\n The pressure vessel contains digitization electronics and calibration sources,\n providing natural solutions for readout and calibrations.\n \\item Cost, geomagnetic field tolerance, and fast timing for 7.7\\,cm PMT's\\\\\n Economical mass-production of 7.7\\,cm PMT's in particular for medical use\n provides almost the same cost per photocathode area for 7.7\\,cm PMT compared\n to larger PMTs. For example, KM3NeT claims the cost per photocathode\n area is cheaper than for the 20 to 40\\,cm PMTs.\n Additional advantages of small PMTs are their much lower sensitivity to the Earth's magnetic field,\n which makes magnetic shielding unnecessary~\\cite{KM3Net:VLVnT15.1}, and potentially better\n timing resolution, which could further reduce the dark hit background and event reconstruction.\n The failure rate of small PMTs is of the order of 10$^{-4}$\/year. Any\n loss of a single PMT would affect the detector performance\n minimally compared to the loss of one large area PMT.\n \\item Complex structure, an opportunity for international contributions\\\\\n A potential draw back of mPMT compared to off-the-shelf 50\\,cm PMT is its complicated structure\n with multiple components. This could be regarded as an advantage for international contributions\n where each partner can take on mPMT module parts and\/or assembly and testing procedures,\n as is successfully done for the KM3NeT mPMT and IceCube mDOM (Digital Optical Module) constructions.\n \\end{itemize}\n\n\n\n\n \n \n\n\n\n\\begin{figure}[htbp]\n \\begin{tabular}{c}\n \\begin{minipage}{0.55\\hsize} \n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{mPMT_NuPRISM.png}\n \\caption{Multi-PMT conceptual drawing with 19 7.7\\,cm PMTs as ID detectors and the OD detectors on the other half. Each small PMT has\n a reflector cone. An 50-cm acrylic covers on a cylindrical support is used as pressure vessel. Readout electronics and calibration\n sources are imbedded inside the vessel.\n \\label{fig:mPMT}}\n \\end{center}\n \\end{minipage}\n\\hspace{0.5cm}\n \\begin{minipage}{0.38\\hsize} \n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{3inchPMT.jpg}\n \\caption{A Hamamatsu R12199-02 7.7\\,cm PMT that is currently used in KM3NeT and considered for\n IceCube-Gen2 modules. As this passed the Hyper-K PMT requirements, it is also a good candidate\nfor a Hyper-K mPMT. \\label{fig:3inchPMT}} \n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\n\n\n\\subsubsubsubsection{The Multi-PMT Reference Design} \\label{multiPMT reference design}\nAs a reference design for Hyper-K, we consider 50\\,cm size vessel, the same size as the baseline\n50\\,cm PMT so that the same mechanical support structure can be used. This would allow part\nof the photocathode coverage to be replaced by an mPMT without major change in the support structure.\nFig.~\\ref{fig:mPMT} shows the 50\\,cm diameter mPMT design originally developed for the NuPRISM detector.\nThere are 19 7.7\\,cm PMTs looking inner detector side and 6 7.7\\,cm PMTs looking outer detector side.\nThe 7.7\\,cm PMTs will be supported by a 3D printed foam structure and\noptically and mechanically coupled by Silicon Gel to an acrylic pressure sphere.\nWhen reflector cones are added to each 7.7\\,cm PMT to increase the effective photocathode area\nby about 30\\%, we get about half of the effective photocathode area as a single 50\\,cm PMT.\nFor the low energy events such as neutron tagging, the number of detected photons will be reduced\nby a factor of two, which can be compensated by the reduction of the effective dark hit rate with the\nlimited field of view. A back-of-the-envelope calculation shows that the neutron tagging efficiency\nwould be similar or better than all 50\\,cm PMT, although more detailed simulation studies are required.\n\n\n\n\\par Currently, there are two main candidate 7.7\\,cm PMTs that have\n been developed specifically for KM3NeT, the Hamamatsu R12199-02\n (see Fig.~\\ref{fig:3inchPMT}) and the ET Enterprises\n D792KFL\/9320KFL. They have been measured in\n detail~\\cite{VLVnT13.1,VLVnT13.2,VLVnT13.3} and would be adequate\n for Hyper-K. Both PMTs have a high peak QE of $\\sim$ 27\\% at\n 404\\,nm. Their collection efficiency is more than 90\\%. The\n transit time spread is about 4\\,nsec at FWHM and the dark rate is\n 200--300\\,Hz. \n \nRecently, improved photosensors from both Hamamatsu and ET Enterprises have been made available, and are currently under test to fully characterize their performances.\nPreliminary measurements of the newly developed Hamamatsu R14374 7.7\\,cm PMT showed an improved TTS and dark rate respect to Hamamatsu R12199 PMT, finding a gain $\\sim 5 \\times 10^{6}$ at $\\sim$ 1.2\\,V with negative HV ($\\sim$ 1.1\\,V with positive HV) and a TTS of 1.35\\,ns with negative HV ($\\sim$ 1.58\\,ns with positive HV) at gain $\\sim 5 \\times 10^{6}$. \nThe dark hit rates were measured to be $\\sim$ 0.3\\,kHz at the 25\\,$^\\circ$C temperature in air. \nAn improved photosensor from ET Enterprises Ltd., D793KFLB, which has been recently made available, and is currently under test. \nPreliminary results are given in Section \\ref{section:photosensors:OD3inchPMT}.\nIn addition to Hamamatsu and ET Enterprises PMT's, HZC XP72B20 is currently reducing the TTS and dark rate and becomes a candidate.\nHZC has a mass production capacity and potential to provide significantly lower cost. \nMELZ PMT, that is considered for the JUNO experiment, is another potential candidate.\n\n\n\n\n\\par The price for $\\sim$19 7.7\\,cm PMTs is comparable or cheaper than\none large area 50\\,cm HQE B\\&L PMT. In addition, the cost could be reduced\ndue to the competition between several companies like\nHamamatsu, ET Enterprises and HZC in the next couple of years.\nThe front-end electronics\nwill be situated in modules in the water near the PMTs which need to\nbe pressure tolerant, water-tight and use water-tight connectors (see\nSection~\\ref{section:electronics-general}). This cost may be reduced\nby encasing the front-end electronics inside the same pressure vessel\nas the ID and OD PMTs. The HV generation for each ID PMT can be done\non a board attached to the PMT base. Only one water-proof cable for\nboth communication, LV and signal can then be connected to the whole\nmodule through a penetrator, as done in previous deep water neutrino\nexperiments.\n\n\n\\par A flexible implementation in the simulation software WCSim (see Section~\\ref{software:WCSim}) makes\n optimization of the reference design possible and will be the\n main topic for further study together with further improvement of\n small photosensors. Based on the results of the optimization\n studies \n facilities a prototype mPMT will be built and tested.\n Figure~\\ref{fig:mPMT_display} shows an event display of mPMT for NuPRISM\n which assumes mPMT for all the photosensors. The event shows an improved\n ring pattern recognition by mPMT for an event.\n\n\\begin{figure}[htbp]\n \\begin{center}\n\\includegraphics[width=0.95\\textwidth]{Electron_Unrolled_Zoom.png}\n\\caption{An event display of mPMT for NuPRISM which assumes mPMT for all the photosensors. }\n\\label{fig:mPMT_display}\n \\end{center}\n\\end{figure}\n\n\n\\subsubsubsubsection{The mPMT Prototype}\n\n\\par The design of a KM3NeT mPMT module is restricted by the size of\n commercially available transparent pressure vessels: borosilicate\n glass spheres with a diameter of 33.3\\,cm and 43.5\\,cm.\n The glass sphere also contains radioactive contaminants that emit Rn into the water,\n which is not a problem for KM3NeT where the radioactive background rate is limited\n by $^{40}$K in the sea water.\n Pure glass could be used for the vessel in Hyper-K, but the cost\n should increase, therefore a good alternative is given by\n acrylics. A first prototype of an mPMT of the future Hyper-K\n experiment is under construction mainly to demonstrate the\n effectiveness of a vessel system based on acrylic and to study a\n better solution for the PMT Read-out system. Other prototypes\n will be built and tested when the final design of the mPMT will\n be defined on the basis of the optimization studies. Several\n comparative tests are ongoing to identify the best acrylic for\n the experimental requirements, including optical tests, stress\n and compression mechanical tests and thermal tests. The water\n absorption tests are based on Nuclear Reaction Analysis (NRA),\n whereas radioactivity contamination measurements are based on\n gamma spectroscopy. The UV transparency has\n been measured for several commercial acrylics. For some sample,\n the light transmittance of the acrylic cover measured in water is\n greater than 95\\% for a wavelength longer than 350\\,nm. The\n pressure vessel will be realized starting from two acrylic\n hemispheres. The hemisphere fabrication processes starts by blowing the\n flat sheet onto a positive mold. A mold made from two parts\n (i.e., positive and negative) could be used to have\n a more uniform thickness. The final design of the vessel will be\n defined on the basis of the simulation studies for the mPMT\n optimization.\n\n\\par For the pressure vessel closure system, the two acrylic\nhemispheres might be glued by using a specific glue for\nacrylics. However, glue itself could emit light, producing more\nbackground events for low-energy physics. A mechanical system has been\nevaluated, both to avoid fluorescence emissions, and to guarantee a\nlonger endurance, and to simplify the anchorage to the tank frame and\nthe implementation of the cooling system of the mPMT. Thus a metallic\nring is being evaluated, modifying the spherical final shape by\nextending the equatorial zone with a cylinder.\nThe acrylic vessel in the mPMT is similar in price to the protective cover required for the single large PMTs.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth]{.\/design-photosensor\/figures\/VesselDesign.png}\n \\caption{Preliminary\n design of the mPMT vessel with its cooling system in the equator of\n the sphere.}\n \\label{fig:VesselDesign}\n \\end{center}\n\\end{figure}\n\n\n\n\n\nThe first mPMT prototype will have an acrylic vessel with a diameter of 17 inches\n(432\\,mm, as in KM3NeT). Several commercial acrylics have been studied\nand tested. EVONIK UV transmitting PLEXIGLAS GS \\footnote{\\href{http:\/\/www.plexiglas.net}{http:\/\/www.plexiglas.net}} has been\nchosen for the construction of the first prototype.\nThe thickness of the vessel has been studied on the basis of\nsimulation and three vessel prototype with thickness of 12, 15 and 18\\,mm\nwill undergo to preliminary pressure tests. The sphere will house\n26 PMTs with a photocathode diameter of 7.7\\,cm.\n\n19 PMTs will view the inner detector side and 7 PMTs\nwill view the outer detector side. The final number of PMTs in the\nmPMT will be defined on the basis of simulation studies.\nThe PMTs will be placed into a 3D printed structure and will be\noptically and mechanically coupled by Silicon Gel to an acrylic\npressure sphere.\nThe optical gel used for this prototype will be the same as in\nKM3NeT. The compatibility between optical gel and acrylic has been\nchecked and the transparency of acrylic+optical gel has been measured.\nFor the final mPMT design, other options for the optical gel are under\nstudy.\n\nFor the present prototype module, Hamamatsu R12199 PMTs are used. They\nare arranged in 3 rings of PMTs in the hemisphere looking at the inner\ndetector with zenith angles of 33$^\\circ$, 56$^\\circ$, 72$^\\circ$,\nrespectively. In each ring 6 PMTs are spaced at 60$^\\circ$ in azimuth\nand successive rings are staggered by 30$^\\circ$. The central PMT in\nthe hemisphere point at a zenith angle of 0$^\\circ$, looking at the\ninner detector axis. Seven PMTs are arranged in the hemisphere looking at\nthe outer detector. Six of them are arranged in one ring which opens a\nhalf angle of 33$^\\circ$ with respect to the nadir.\n\nA basic Cockcroft-Walton voltage multiplier circuit design developed\nby KM3NeT Collaboration~\\cite{Timmer2010GF} is used to generate multiple\nvoltages to drive the dynodes of the photomultiplier tube. The system\ndraws less than 1.5\\,mA of supply current at a voltage of 3.3\\,V with\noutputs up to -1400\\,V$_{dc}$ cathode voltage.\nA passive cooling system, based on the heat conduction mechanism,\naimed at keeping the temperature of the electronic components as low\nas possible, thus maximizing their lifetime has been designed in order\nto optimize the transfer of the heat generated by the electronics.\nIn KM3NeT the time over threshold (ToT) strategy is exploited; this is\nnot a good solution for Hyper-K project in which charge measurement is\nimportant.\nTo fulfill the requirements of low consumption and charge and time\nresolution, a solution based on a Sample\\&Hold plus ADC has been\ninvestigated. Several commercial low power and highly versatile ASIC\nfrom Weeroc \\footnote{\\href{http:\/\/www.weeroc.com}{http:\/\/www.weeroc.com}} are under study.\n\nFor this prototype, the module was developed as a complete stand-alone\ndetector and it will fully test both in air and in water.\n\n \\subsubsubsection{Alternative Cover Design}\n\\label{section:photosensors:coveralternatives}\n\nAn alternative design of the shockwave prevention cover is a cheap stainless steel tube with the acrylic window, instead of the conical shape cover, as shown in Figure~\\ref{fig:AcrSUStubecover}.\nBenefit of the mass production and installation is expected due to the simple outer shape.\n\nFigure~\\ref{fig:AcrPPScover} shows another possible idea to use a resin instead of stainless steel.\nIt can give a cheap and light weight option.\nOne of the possible material is PPS resin mixed with a reinforced filler.\n\n\\begin{figure}[h!]\n \\begin{tabular}{cc}\n \\begin{minipage}{0.35\\hsize}\n \\begin{center}\n \\includegraphics[width=1.\\textwidth]{photosensor_AcrSUStubeCover_outside.pdf}\n \\caption{Alternative cover design comprised of a stainless steel tube and the acrylic window.\\label{fig:AcrSUStubecover}}\n \\end{center}\n \\end{minipage}\n\n\\hspace{1.0cm}\n\n \\begin{minipage}{0.4\\hsize}\n \\begin{center}\n \\includegraphics[width=1.\\textwidth]{photosensor_AcrPPSCover_outside.pdf}\n \\caption{Alternative cover design comprised of a resin cover and the acrylic window.\\label{fig:AcrPPScover}}\n \\end{center}\n \\end{minipage}\n \\end{tabular}\n\\end{figure}\n\nThe light weight of the cover allows for a lower cost of the tank structure because the current cover weight is much heavier than the PMT and dominant in overall weight of the photosensor system.\nFast production and installation are also cost effective.\nIn both alternative cases, the design was evaluated by a simulation assuming a high pressure load outside, but it is still preliminary.\nThe hydrostatic test and demonstration test with implosion are necessary to ensure that the alternative covers are feasible for Hyper-K.\n\n\\subsubsection{Schedule}\\label{section:photosensors:schedule} \n\nBefore the photosensor mass production, it takes 0.5 years to complete\na design of a production line, and 1--1.5 years for the setup and\nstartup of the equipment in the factory. The capacity of the factory\nproduction is expected to be 11k 50\\,cm and 4k 20\\,cm photosensors per\nyear.\n\n\nA test in Super-K using about a hundred of the B\\&L PMTs starts\nfrom 2018 to demonstrate the Hyper-K photosensor system.\nMoreover, criteria for the quality control including a\nselection with high pressure load will be established by the production.\n\nTable~\\ref{photosensoroption} summarizes the default design and\nalternatives for photosensors described in this section.\nEven without the alternatives, Hyper-K has sufficient\nperformance with a realistic time line using the default options.\nFurther improvements could be achieved and could be available in\ntime for Hyper-K tank construction.\n\n\\clearpage\n\n\\begin{table}[!h]\n \\begin{center}\n \\begin{tabular}{ll|ll|l}\n \\hline \\hline\n Items & & Type & & Remaining studies \\\\\n \\hline\n \\hline\n \n \\multicolumn{2}{l|}{{\\bf ID photosensor}} &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n {\\bf HQE 50\\,cm\\\\\n \\ B\\&L PMT}\\\\\n {\\bf \\small (Hamamatsu\\\\\n \\ R12860-HQE)} \\\\\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{3.cm}\n \\includegraphics[width=\\textwidth]{photosensor_R12860design.pdf}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Mass test using about 100 PMTs \\\\\n \\ with reduced dark hit rate\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n \n & (Alternative) &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n HQE 50\\,cm HPD \\\\\n (Hamamatsu R12850-HQE)\\\\\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.4cm}\n \\includegraphics[width=\\textwidth]{photosensor_HPDwaterproof.pdf}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Electronics tuning,\\\\\n Confirmation of pressure resistance,\\\\\n Long-term proof test in water,\\\\\n Cost estimation\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n \\hline\n \n \\multicolumn{2}{l|}{ {\\bf OD photosensor }} &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n {\\bf HQE 20\\,cm\\\\\n \\ B\\&L PMT}\\\\\n {\\bf \\small (Hamamatsu\\\\\n \\ R5912)}\\\\\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.5cm}\n \\includegraphics[width=\\textwidth]{photosensor_8pmtassy2.png}\n \\end{minipage}\n &\n Test in high pressure water\\\\\n \\hline\n & (Alternative) & HQE 20--30\\,cm PMT & & HQE study using prototype, \\\\\n & & & & Trial manufacture and necessary test \\\\\n \\hline\n & (Alternative) &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n 7.7\\,cm PMT\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.cm}\n \\includegraphics[width=\\textwidth]{3inchPMT.jpg}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Performance simulation in Hyper-K,\\\\\n Detection efficiency measured with prototype,\\\\\n Selection between design\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n \\hline\n \\multicolumn{2}{l|}{\n \\begin{minipage}{3.cm}\n \\begin{flushleft}\n {\\bf (ID and OD \\\\\n \\ photosensor\\\\\n \\ alternative) }\n \\end{flushleft}\n \\end{minipage}\n }\n &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n Multi-PMT \\\\ optical module\\\\\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.cm}\n \\includegraphics[width=\\textwidth]{mPMT_NuPRISM.png}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Performance simulation in Hyper-K,\\\\\n Cost estimation,\\\\\n Selection of 7.7\\,cm photosensor,\\\\\n Trial manufacture and necessary test\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n \\hline\n \\multicolumn{2}{l|}{ {\\bf ID cover }} &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n {\\bf Acrylic and \\\\\n \\ stainless steel\\\\\n \\ cone}\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.8cm}\n \\includegraphics[width=\\textwidth]{protective_cover_shape.pdf}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Improved with light weight,\\\\\n Test of the improved design\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n & (Alternative) &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n Acrylic and \\\\\n \\ stainless steel\\\\\n \\ tube\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{1.7cm}\n \\includegraphics[width=\\textwidth]{photosensor_AcrSUStubeCover_outside.pdf}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Design and simulation,\\\\\n Implosion test\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline\n & (Alternative) &\n \\begin{minipage}{3.6cm}\n \\begin{flushleft}\n Acrylic and \\\\\n \\ full resin\n \\end{flushleft}\n \\end{minipage}\n &\n \\begin{minipage}{2.cm}\n \\includegraphics[width=\\textwidth]{photosensor_AcrPPSCover_outside.pdf}\n \\end{minipage}\n &\n \\begin{minipage}{7.cm}\n \\begin{flushleft}\n Design and simulation,\\\\\n Prototype production,\\\\\n Implosion test\n \\end{flushleft}\n \\end{minipage}\n \\\\\n \\hline \\hline\n \\end{tabular}\n \\caption{ Summary of the current base design in bold type and alternative options related with photosensors.\n The remained studies of the baseline photosensors and cover will be finalized in fiscal year 2017.\n }\n \\label{photosensoroption}\n \\end{center}\n\\end{table}\n\n\n\\subsection{Summary of the Hyper-Kamiokande detector timeline}\n\\graphicspath{{design-summary\/figures\/}}\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=1.0\\textwidth]{HK_timeline_NamatameCheck_v2_Eng.pdf}\n \\caption{Construction period for the 1TankHD{}}\n \\label{fig:construction-perod-1TankHD}\n \\end{center}\n\\end{figure}\n\nFigure~\\ref{fig:construction-perod-1TankHD} shows the estimated construction\nperiod of the Hyper-K detector for 1TankHD{}.\nThe construction is estimated to take about 10 years \nincluding the geological survey and final design making.\n\n\nFor the operation of the 1TankHD{} detector, \nnecessary manpower is estimated to be\nabout 20 full-time equivalent (FTE) by taking into account\nmanagement and detector calibration\nin addition to the operation and maintenance of water system, electronics,\nDAQ system, and computer system. \nIn the case of three tank case, the necessary FTE would be as twice as\nthe single tank case.\n\n\n\n\n\n\\subsubsection{Tank Liner}\nThe lining covers inner surface of the Hyper-Kamiokande tank. It is to\ncontain ultra purified water (UPW) or gadolinium sulfate\n(Gd$_2$(SO$_4$)$_3$) water solution inside of the tank ideally without\nany leakage and without any dissolution of impurities into the\nmedium. Durability should be $\\sim$30 years.\nThe lining structure is to be constructed inside of the cavern bedrock\ncoated with shotcrete. Between the shotcrete and the lining, a\nbackfill concrete is to be employed. As a former example, a\n4\\,mm-thick stainless steel membrane, backfilled with a reinforced\nconcrete, was adopted as the lining material for the Super-Kamiokande\ntank~\\cite{Fukuda:2002uc}.\nIn designing a similar lining structure for Hyper-K, we assume the\nfollowing conditions:\n\\begin{itemize}\n\\item Physical properties of the bedrock surrounding the tank are the same as those used for the Super-Kamiokande designing. For example, elastic modulus of the bedrock is 51 (20)\\,GPa for non-damaged (damaged) region, respectively.\n\\item Physical properties of the backfill concrete are taken from {\\it Standard Specification for Concrete Structure}\\cite{liner:spec-concrete}.\n\\item The surrounding bedrock will not be displaced during\/after tank construction.\n\\item The backwater is controlled so that there is no water pressure on the lining structure from the bedrock side. To satisfy this critical condition, location of the entire detector cavern(s) is to be chosen at the -370\\,mL above the main water drainage level of the candidate mine site (-430\\,mL).\n\\end{itemize} \n\n\\paragraph{Liner sheet characteristics} \nAs a lining material for the gigantic Hyper-K, firm adhesion to the\nbackfill concrete wall and enough elongation to follow possible\ndeficits and cracks of the concrete wall are both desirable\ncharacteristics. To fulfill these functionalities, concrete embedment\nliner, or the Concrete Protective Liner (CPL), made of High Density\nPolyEthylene (HDPE), has been chosen as the baseline candidate lining\nmaterial. Figure~\\ref{fig:liner-concept} shows schematic views of the\ncandidate CPL (Studliner, GSE Environmental). It has a\n2.0$\\sim$5.0\\,mm thick section of HDPE with a number of studs\nprotruding from one side, that lock the liner into the surface of\nconcrete to prolong the service life of concrete structures.\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-concept.pdf}\n\\caption{Concrete Protective Liner made of High Density PolyEthylene, considered as the baseline tank lining material of Hyper-Kamiokande (Studliner, GSE Environmental).}\n \\label{fig:liner-concept}\n \\end{center}\n\\end {figure}\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-examples.pdf}\n\\caption{Former examples of the HDPE lining. (a) IMB detector's 8\\,kt water tank lined with HDPE geomembrane sheets (product of Schlegel Lining Technology, a precursor of GSE Environmental). (b) The CPL (GSE Studliner) applied to water-sealing walls of a large industrial waste processing trench.}\n \\label{fig:liner-examples}\n \\end{center}\n\\end {figure}\n\nHDPE is a thermoplastic resin, a linear polymer prepared from ethylene\n(C$_2$H$_4$) by a catalytic process. The absence of branching results in\na more closely packed structure with a higher density (greater than\n0.94), and somewhat higher chemical resistance than Low Density\nPolyethylene (LDPE). HDPE is also harder and more opaque, and it can\nwithstand higher temperatures (120$^\\circ$\\,Celsius for short periods,\n110$^\\circ$\\,Celsius continuously). HDPE is known to maintain pure water\nquality as shown later. Advantages of HDPE as the lining\nmaterial are: impact\/wear resistance, flexibility (very high\nelongation before breaking), good chemical resistance, very low water\npermeability, good plasticity (particularly well to blow molding), and\nlow price. On the contrary, disadvantages of HDPE are: it may have\nvoids, bubbles or sink in the thick sections, poor dimensional\naccuracy, and low mechanical and thermal properties.\n\nA former example to apply HDPE liner to large water tank can be found\nin the IMB detector\\cite{BeckerSzendy:1992hr} as shown in\nFig.\\ref{fig:liner-examples}(a). The 8\\,kt water tank\n(22.5$\\times$17$\\times$18\\,m$^3$) utilized 2.5\\,mm -thick double\nlayered non-reflective black HDPE liners, separated by a plastic\ndrainage grid allowing water to flow between the liners. They were\nproduced and installed by Schlegel Lining Technology, one of the\nprecursors of GSE Environmental. Figure~\\ref{fig:liner-examples}(b)\nshows an application of the CPL as the water-sealing walls of a large\nindustrial waste processing trench. Table~\\ref{tab:liner-spec} shows\nmaterial parameters of the candidate CPL, GSE Studliner. It is also to\nbe noted that the original design for the far-site LBNE Water Cherenkov Detector (WCD) with\n200\\,kt volume adopted the water containment system option with\nuse of 1.5$\\sim$2.5\\,mm-thick Linear Low-Density PolyEthylene\n(LLDPE) geomembrane.\\cite{liner:LBNE-WCD-Golder}\n\n\\begin{table}[htbp]\n\\begin{center}\n\\caption{Material parameters, taken from specification of the candidate CPL (Studliner, GSE Environmental).} \n\\label{tab:liner-spec}\n\\footnotesize\n\\begin{tabular}{lll}\n\\hline\\hline\n\\multicolumn{2}{l}{Material property} & Nominal Value \\\\\n\\hline\nThickess\t& (mm)\t\t& 5.00 \\\\\nDensity\t& (g\/cm$^3$)\t& 0.94 \\\\\nYield strength & (MPa)\t& 15.2 \\\\\nElongation at break & (\\%)\t& 500 \\\\\nCarbon black content & (\\%) & 2$-$3 \\\\\nPigment content\t& (\\%) & 1.5$-$2.5 \\\\\nNotched constant tensile load & (hours) & 400 \\\\\nThermal Expansion Coefficient & (C$^\\circ$) & 1.20E-04 \\\\\nLow temperature brittleness & (C$^\\circ$) & -77 \\\\\nDimensional stability in each direction & (\\%) & $\\pm$1.0 \\\\\nWater vapor transmission & (g\/m$^2$\/day) & $<$ 0.01 \\\\\nTypical roll dimension & (m) & 2.44(W)$\\times$59.73(L) \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-install.pdf}\n\\caption{Schematics of the planned procedures for CPL installation into the cavern \n with shotcrete surface.}\n \\label{fig:liner-install}\n \\end{center}\n\\end {figure}\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-welding.pdf}\n\\caption{(a) The extrusion welding and a welded seam. (b) The high-voltage pin-hole test.}\n \\label{fig:liner-welding}\n \\end{center}\n\\end {figure}\n\nThe planned procedures of the CPL installation into cavern are\nillustrated in Fig.\\ref{fig:liner-install}: At first CPL is fastened\nto the inside of molds before concrete is poured to create a surface\nlined with HDPE. The backfill concrete flows around the studs\nanchoring CPL firmly in place, and fastens it securely to the surface\nof the concrete. The waterproof sheet between bedrock-covering\nshotcrete and backfill concrete aims conveyance of water, coming from\ntiny leakage of water through the CPL and backfill concrete structure,\nif any, and\/or penetrating underground backwater from bedrock.\n\nThe adjacent CPLs are welded by the extrusion welding of\nthermoplastics, which is used typically for assembly of large\nfabrications (such as chemical storage vessels and tanks) with wall\nthicknesses up to 50\\,mm. Figure~\\ref{fig:liner-welding}(a) shows\nan extrusion welding work and close-up to the welded seam. In this\nmethod, molten thermoplastic filler material is fed into the joint\npreparation from the barrel of a mini hand-held extruder based on an\nelectric drill. For the CPL welding the same HDPE is used as the\nfiller material. The molten material emerges from a PTFE shoe shaped\nto match the profile being welded. At the leading edge of the shoe a\nstream of hot gas is used to pre-heat the substrate prior to the\nmolten material being deposited, ensuring sufficient heat is available\nto form a weld.\n\nFor the quality control of the lining, the holes in the CPL sheets\nwith size of $>$0.5\\,mm, including those on the welded seams, can\nbe identified by a high-voltage pin-hole testing\nmethod~\\cite{liner:industrialwaste}, as illustrated in\nFig.~\\ref{fig:liner-welding}(b): It utilizes a charged metal or\nneoprene-rubber broom above the liner. The power source is grounded to\nthe conductive deck and creates a high potential difference ($\\sim$30\nkV at maximum) with tiny current. When the metallic broom head is\nswept over a breach or a hole in the insulating membrane surface,\ncurrent is detected by the test unit which turns off the power to the\nbroom and emits a beep sound to alert the test operator. The area is\nthen carefully swept again at $\\sim$90 degrees to the original\nsweeping direction to pinpoint the exact location of the\nbreach\/hole. This process is continued until all areas of the CPL have\nbeen tested. Occasionally negative pressure tests with a vacuum box\ncan be applied on the possible breaches and the welded seams. The\nleakage water through the holes less than 0.5\\,mm diameter, if\nany, can be collected and controlled by a leakage detection and drain\nsystem, as described later.\n\n\\paragraph{Liner sheet tests}\nVarious material tests were carried out for the candidate CPL, as are\ndescribed in Appendix~\\ref{sec:linertests}.\nTo see the change of light absorbance and elusion of impurities,\nspecimens of the lining sheet were soaked both into ultra-purified\nwater and into 1\\% gadolinium sulfate solution: increase of the light\nabsorbance were observed at the wavelength lower than 300\\,nm, and\ncertain amount of material elution, i.e. total organic carbon, anions\nand metals, were observed. The relation between material elusion and\nchange of light absorbance should be studied carefully. Meanwhile,\nsince PMT is sensitive for higher wavelength, the effect to the\nexperiment can be limited.\n\nMeasurements on material strength, i.e. tension test and creep\ntest, were performed: the candidate CPL sheet has basically enough\nstrength. If cracks or rough holes happen in the backfill concrete,\nthe liner should locally stand for water pressure. To simulate the\nsituation, tests to apply localized water pressure on the lining were\nperformed with variety of slits and holes: For all cases, the liner\nsurvived without breaking.\nAnother concern is that tensile or shear stress may be applied to the\nliner sheet if deformation in the backfill concrete occurs after installation.\nA crack elongation of the liner sheet was tested in the following way: \nA liner sheet was attached to a concrete block and a crack or a step\nwas created in the concrete as shown in Figure~\\ref{fig:liner_elongation_test_fig},\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner_elongation_test_fig.pdf}\n \\caption{Two possible situations in deformation of backfill concrete, which\n can introduce tensile or shear stress in the liner sheet. Left:\n a crack is created. Right: a step is created.}\n \\label{fig:liner_elongation_test_fig}\n \\end{center}\n\\end{figure}\nthen strain on surface of the liner sheet was measured. The surface of the liner sheet\nwas pressurized with 0.8~MPa during the measurement to simulate a water pressure.\nFigure~\\ref{fig:liner_elongation_test_pic} shows the actual setup of the crack\nelongation test.\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner_elongation_test_pic.pdf}\n \\caption{Picture of setup for crack elongation test. A HDPE sheet was\n attached to a concrete block and a crack or a step was intentionally\n produced in the concrete block. Strain on the liner sheet was then measured.}\n \\label{fig:liner_elongation_test_pic}\n \\end{center}\n\\end{figure} \nFrom the experience of Super-K operation\\footnote{During Super-K operation, \nobserved deformation was at most $O(0.01)$\\%. Cracks in concrete tend to be created\nin an even pitch. Assuming deformation of 0.1~\\% (with a safety factor of 10) and\ncrack pitch of 600~mm, a gap of crack can be estimated to be 0.6~mm.},\na gap or a step of 1~mm was applied to the concrete block as shown in\nFigure~\\ref{fig:liner_elongation_test_fig}. \nIn this test, the concrete was moved by 1~mm for 6 miniutes,\nheld for 30 minutes, and then moved back to the original position. This procedure was\nrepeated 10 times. \nThe measured strain with 1~mm gap\/step was at most 1.4\\%\/0.9\\%, respectively.\nThese values were consistent with the simulated ones based on the test condition.\nFrom the simulation results, it was found that strain of approximately 6\\% at maximum could be\napplied on the back (concrete) side of the liner sheet.\nAfter this test, no damage was observed on the liner sheet by visual inspection.\nFurthermore, water leak test with 0.8~MPa was also performed and no leakage was\nobserved. From the crack elongation test, it was concluded that the HDPE liner sheet\nhad enough strength against deformation and water tightness could be proved even in case that\ndeformation of the backfill concrete occured after installation.\n\nThe water leak can happen around components which penetrate the water\ntank lining, such as anchors and water pipes. A possible design of the\npenetration structure was developed. Its prototype was exposed to\nseries of pressure tests, which showed no leaks.\n\n\\paragraph{Long term stability}\nLong term stability of the liner sheet is one of big concerns on a water tank.\nPolyethylene materials have been used for sheeth of PMT cables and PMT endcap inside SK\nfor 20 years, and no obvious problem is observed. \nPossible sources of degradation of HDPE material are physical stress,\nand some other effects (materials attached to the liner, oxidization, temperature, \netc.)\\footnote{Generally, a UV light is one of the big concern on long term stability of \nHDPE material, but this is not the case for underground area.}.\nEffect of oxidization on lifetime of a HDPE material was reported in \\cite{liner:HDPE_lifetime}.\nLifetime of HDPE liner can be strongly affected by temperature. At 20~$^{\\circ}$C its lifetime\nis predicted to be 446 years, however it reduces to 69 years at 40~$^{\\circ}$C.\nSince water temperature in HK tank will be controlled below 15~$^{\\circ}$C,\nlifetime can be expected to be more than 500 years. To estimate long term stability, \nan accelerating test to measure strength of a HDPE liner sheet after long-term soak \nin ultra pure water is being considered.\n\n\\paragraph{Leakage detection and drain system}\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{liner-leakdrain.pdf}\n\\caption{Conceptual diagram of water leak detection\/drain system.}\n \\label{fig:liner-leakdrain}\n \\end{center}\n\\end {figure}\nThe water leakage, if it happens, will be not through the sheets\nthemselves, but through small holes, which are undetectable by the\npin-hole\/vacuum tests, or breaches, which are caused unavoidably by\nworks after the tests. To be prepared for these possible failures, a\nleak detection\/drainage system is to be\ndeveloped. Figure~\\ref{fig:liner-leakdrain} shows preliminary concept\nof the system. HDPE plastic moldings are embedded together with the\nCPL in the backfill concrete, to work as partition at a pitch of about\n10\\,m in the direction of circumference of the tank. Water leaks\nfrom the CPL(s) or seam(s) in each partition are to be collected\nindividually, so that leak detector installed at the bottom can\nidentify the partition with the problem. Occasionally, water leak\nthrough the CPL can flow into bedrock side through cracks of the\nbackfill concrete. Water-proof sheets (high panel signal sheet),\ninstalled between bedrock and backfill concrete, can separate leakage\nof inside (tank) water and sump water coming from outside\nbedrock. These water will be drained separately, and tank water will\nbe treated with care especially for the case with gadolinium sulfate\nsolution is used in the tank.\n\n\n\n\\subsection{Water Tank}\\label{section:tank}\n\n\n\\input{design-tank\/overview.tex}\n\n\n\\subsubsection{Tank-Cavern Interface} \n\\input{design-tank\/interface.tex}\n\n\n\\subsubsection{Tank Liner} \n\\label{section:tank-liner}\n\\input{design-tank\/liner.tex}\n\n\n\\subsubsection{Photosensor Support Framework} \n\\input{design-tank\/framework.tex}\n\n\n\\subsubsection{Geomagnetic Field Compensation Coils} \n\\label{section:tank-coil}\n\\input{design-tank\/coil.tex}\n\n\n\\subsubsection{Construction} \n\\input{design-tank\/construction.tex}\n\n\n\n\n\n\\subsection{Water purification and circulation system }\\label{section:water}\n\n\\subsubsection{Introduction}\nWater is the target material and signal-sensitive medium of the\ndetector, and thus its quality directly affects the sensitivity. In\norder to realize such a huge Cherenkov detector, achieving good water\ntransparency is the highest priority. In addition, as radon emanating\nfrom the photosensors and detector structure materials is the main\nbackground source for low energy neutrino studies, an efficient radon\nremoval system is indispensable.\n\nIn Super-Kamiokande the water purification system has been continually\nmodified and improved over the course of SK-I to SK-IV. As a result,\nthe transparency is now kept above 100 m and is very stable, and the\nradon concentration in the tank is held below 1\\,mBq\/m$^3$. Following\nthis success, the Hyper-Kamiokande water system design will be based\non the current Super-Kamiokande water system.\n\nNaturally, ever-faster water circulation is generally more effective\nwhen trying to keep huge amounts of water clean and clear, but\nincreasing costs limit this straightforward approach so a compromise\nbetween transparency and re-circulation rate must be found. In\nSuper-Kamiokande, 50\\,ktons of water is processed at the rate of\n 60\\,tons\/hour in order to keep the water transparency (the attenuation\nlength for 400\\,nm-500\\,nm photons) above 100\\,m, and 20\\,Nm$^3$\/hour of\nradon free air is generated for use as a purge gas in degas modules,\nand as gas blankets for both buffer tanks and the Super-Kamiokande\ntank itself. For the 258\\,ktons of water in\nthe tank of Hyper-Kamiokande, these process speeds will need to be scaled-up to\n310\\,tons\/hour for water circulation and 50\\,Nm$^3$\/hour for radon free\nair generation.\n\n\\subsubsection{Source water}\nThe rate of initial water filling is restricted by the amount of available source water.\n In Mt.~Nijuugo-yama, the baseline location of Hyper-Kamiokande, the total\namount of the spring water is about 600\\,tons\/hour. (It varies\nseasonally between 300\\,tons\/hour and 800\\,tons\/hour and it is above\n600\\,tons\/hour except in Winter (December-March).) However, as the mine\ncompany uses all the water for their smelting factory, the available\nspring water for Hyper-Kamiokande is limited and cannot be allocated at this point. \nTherefore, the baseline plan is getting 105\\,tons\/hour of source water from the outside of the mine, making 78\\,tons\/hour of\nultra-pure water and filling the 258\\,ktons for 180\\,days.\nThe source water site is the well for snow-melting system in the Kamioka town at Oshima public hall which is\nabout 5\\,km away from the tank position. \nHida city is supportive in our use of the well and Gifu prefecture is also helping to\ndecide the route from the well to the entrance of the Tochibora mine.\nSerious investigations and negotiations are ongoing with these local governments.\n\nThe water quality of the snow melt water and Tochibora spring\nwater are compared with that of Mozumi spring water in Table~\\ref{tab:source}.\nIn the Mozumi mine, the location of Super-Kamiokande, there is sufficient mine water and no mining\/smelting activities.\n\\begin{table}[htb]\n\\begin{center}\n\\scalebox{0.8}[0.8]{\n\\begin{tabular}{lr|rrr}\n\\hline\\hline\n & & The well for Kamioka snow melt & Tochibora spring water & Mozumi spring water \\\\\n & & as of 21 Jun. 2016 & as of 1 Mar. 2011 & as of 16 Mar. 2011 \\\\\n\\hline \\hline \nTemperature(Typical) & $^{\\circ}$C & 11.9 & 11 & 12 \\\\\npH (25$^{\\circ}$C) & & 7.1 & 7.8 & 7.8 \\\\\nConductivity & $\\mu$S\/cm & 101 & 170 & 221 \\\\\nTurbidity °ree(Kaolin) & $<1$ & $<1$ & $<1$ \\\\\nAcid consumption (pH 4.8) & mg CaCO$_3$\/L & 27.9 & 40.0 & 75.8 \\\\\nTOC & mg\/L & $<0.1$ & $<1$ & $<1$ \\\\\nPhosphate & mg\/L & $<0.1$ & $<0.1$ & $<0.1$ \\\\\nNitrate & mg\/L & 3.0 & 1.0 & 1.6 \\\\\nSulfate & mg\/L & 4.4 & 36.4 & 30.2 \\\\\nFluoride & mg\/L & $<0.1$ & 0.3 & 0.4 \\\\ \nChloride & mg\/L & 8.6 & 1.6 & 1.8 \\\\\nSodium & mg\/L & 4.6 & 4.9 & 6.2 \\\\\nPotassium & mg\/L & 0.8 & 0.5 & 0.5 \\\\ \nCalcium & mg\/L & 12.3 & 25.2 & 32.0 \\\\ \nMagnesium & mg\/L & 1.5 & 1.5 & 2.9 \\\\\nAmmonium & mg\/L & $<0.1$ & $<0.1$ & $<0.1$ \\\\\nIonic silicon dioxide & mg\/L & 12.8 & 17.1 & 11.8 \\\\\nIron & mg\/L & $<0.01$ & $<0.01$ & $<0.01$ \\\\\nCopper & mg\/L & $<0.01$ & $<0.01$ & $<0.01$ \\\\\nZinc & mg\/L & - & 0.09 & $<0.01$ \\\\\nLead & mg\/L & $<0.1$ & $<0.1$ & $<0.1$ \\\\\nAluminum & mg\/L & $<0.01$ & $<0.01$ & $<0.01$ \\\\\nBoron & mg\/L & $<0.01$ & $<0.01$ & 0.2 \\\\\nStrontium & mg\/L & - & 0.18 & 0.52 \\\\\nBarium & mg\/L & $<0.01$ & $<0.01$ & 0.03 \\\\\n\\hline\\hline\n\\end{tabular}\n}\n\\caption{Source water quality.}\n\\label{tab:source}\n\\end{center}\n\\end{table}\n\n\n\\subsubsection{Main system flows and layouts}\nThe HK main water purification system consists of a 1st stage system\n(filling) and a 2nd stage (re-circulation) system for the 258,000\\,m$^3$ tank \nas shown in Figure~\\ref{fig:1st2ndsys}.\nFigure~\\ref{fig:LO} shows their layouts.\n\\begin{figure}[htb]\n\\includegraphics[width=0.95\\textwidth]{design-water\/1stand2nd.pdf}\n\\caption{1st stage and 2nd stage water systems.}\n\\label{fig:1st2ndsys}\n\\end{figure}\n\\begin{figure}[htb]\n\\includegraphics[width=1.0\\textwidth]{design-water\/Layouts.pdf}\n\\caption{Necessary space for the main systems.}\n\\label{fig:LO}\n\\end{figure}\nThe process power of the 1st stage system is 78\\,m$^3$\/h, and accordingly, it takes\n138 days to fill the tank without consideration of any maintenance.\nIt may take about 180 days in the realistic case.\nPreferably, an additional, same amount, of 11 $^{\\circ}$C cooling water is required for the heat\nexchangers.\n\nThe process power of the 2nd stage system for the recirculation is \n310\\,m$^3$\/h.\n\n\\subsubsection{Water flow simulation in the tank}\nWater flow in the tank directly affects the water quality and the\nphysics results, therefore water flow simulations for the baseline\ndesign tank were conducted. Water flow is determined not only by the\ntotal water flow rate but also by detector geometry, the configuration\nof water inlets and outlets, supply water temperature, heat sources in\nthe tank, surrounding rock temperature and so on. The input parameters\nare summarized in Table~\\ref{tab:simpara}, and the main results are\nshown in Figure~\\ref{fig:flowsim}. \nWhen cold water is supplied from the bottom of the tank, convection in the tank is suppressed\nand the flow becomes laminar, resulting in effective water replacement. When cold\nwater is supplied from the top of the tank, large convection is evoked and the water quality in the\ntank becomes uniform, spoiling effective water replacement. Actually this behavior was\nconfirrmed in Super-Kamiokande's 50 kton tank and seem to be common to cylindrical tanks; \nthus the water flow in Hyper-Kamiokande should be controlled as in Super-Kamiokande.\n\n\n\\begin{table}[htb]\n\\begin{center}\n\\scalebox{1}[1]{\n\\begin{tabular}{l|r}\n\\hline\\hline\nID flow rate & 271.8 m$^3$\/h \\\\ \nOD flow rate & 37.9 m$^3$\/h \\\\ \nInlets\/Outlets & 65A$\\times$37\/65A$\\times$37 \\\\\nID boundary condition & Inlet: 0.61 m\/s, 286K Outlet: 0Pa \\\\\nOD boundary condition & Inlet: 0.67 m\/s, 286K Outlet: 0Pa \\\\\nSupply water temperature & 13.0 $^{\\circ}$C \\\\\nTop level rock temperature & 16.7 $^{\\circ}$C \\\\\nBottom level rock temperature & 17.7 $^{\\circ}$C \\\\\nHeat flux from the PMT\/electronics\/coil & 3.2W\/m$^2$\\\\\nTotal heat form ID top and bottom & 2100W and 2100W \\\\\nTotal heat from ID wall & 6502W \\\\\nTotal heat from OD wall(rock) & 5384W \\\\\nWater density & 999.4 kg\/m$^2$ @286 K, 998.4 kg\/m$^2$ @292 K \\\\\nWater heat conductivity & 0.587 W\/m\/K @286 K, 0.597 W\/m\/K @292 K \\\\\nWater viscosity & 0.0012 kg\/m\/s @286 K, 0.0010 kg\/m\/s @292 K \\\\\n\\hline\\hline\n\\end{tabular}\n}\n\\caption{Input parameters for the water flow simulations.}\n\\label{tab:simpara}\n\\end{center}\n\\end{table}\n\n\\begin{figure}[htb]\n\\begin{center}\n\\includegraphics[width=0.85\\textwidth]{design-water\/Flowtemp.pdf}\n\\includegraphics[width=0.95\\textwidth]{design-water\/FlowSim.pdf}\n\\caption{Water temperature distributions (top 2 figures) \n and water replacement efficiencies \n as the result of water flow simulations. As the tank is in cylindrical shape and the \n water inlets and outlets are distributed symmetrically, \n only 1\/6 of the tank was simulated with symmetric boundary condition and shown here.\n (a) The case for supplying water from the bottom of the\n tank and draining water from the top of the tank. (b) The case for\n supplying water from the top of the tank and draining water from the\n bottom of the tank. The elapsed days since the recirculation starts\n are indicated. In this simulation, at first the tank was filled with\n old water ($= 0$, blue), then new water ($= 1$, red) was supplied to the tank,\n therefore the color scale in the figures corresponds to the water\n replacement efficiency. After 40 days case (a) is more reddish, while case (b) is more uniform.}\n\\label{fig:flowsim}\n\\end{center}\n\\end{figure}\n\n\\subsubsection{Radon in the water}\n\\label{sec:radon-in-water}\nThe dominant low energy background is expected to be radon and \nthe dominant radon source in the tank is expected to be the PMTs\nthemselves. The radon emanation from Hyper-Kamiokande photon sensors have \nnot been measured yet, but each Super-Kamiokande ID PMT emanates about 10 mBq \nand the measured radon concentration in the Super-Kamiokande water is 2 mBq\/$m^3$.\nSuper-Kamiokande has 11129 ID PMTs and 50\\,ktons of water, therefore\nthe average radon concentration should be around\n10 mBq\/PMT $\\times$ 11129 PMTs \/ 50000 tons = 2.2 mBq\/$m^3$.\nAccordingly, the radon concentration expected in one Hyper-Kamiokande HD tank is\n10 mBq\/PMT $\\times$ 40000 PMTs \/ 258000 tons = 1.6 mBq\/$m^3$.\n\nRegarding radon suppression, the Hyper-Kamiokande water system includes Super-Kamiokande-based vacuum\ndegasifiers which reduce radon by about one order of magnitude as shown\nin Figure~\\ref{fig:1st2ndsys}. That being said, in the experience of Super-Kamiokande the best way to reduce\nradon is by inducing a gentle laminar flow in the fiducial volume, \nallowing the radon to primarily decay close to the PMTs (i.e., not in\nthe fiducial volume) where it can do the least harm.\n\n\n\\subsubsection{Gd option}\nIn order to realize the many physics benefits provided by efficient\ntagging of neutrons in water, it has been proposed (and recently approved) \nto add dissolved gadolinium sulfate to Super-Kamiokande. As a result, \nover a period of\nyears much effort has gone into the design and demonstration of a\nspecialized water system capable of maintaining the exceptional water\ntransparency discussed above, while at the same time maintaining the\ndesired level of dissolved gadolinium in solution. In other words,\nsomehow the water must be continuously recirculated and cleaned of\neverything {\\em except} gadolinium sulfate.\n\nBuilt in 2007, a 0.2 tons\/hour prototype selective filtration system at \nthe University of California, Irvine, led in 2010 to the 3 tons\/hour \nsystem at the heart of the Kamioka-based EGADS (Evaluating Gadolinium's \nAction on Detector Systems) project. EGADS has now shown that this novel \nselective water filtration technology --- known as a \"molecular band-pass \nfilter\" --- is both feasible and scalable.\nIt continuously improves and then maintains the transparency of water loaded with\n\\mbox{Gd$_2$(SO$_4$)$_3$} to SK ultrapure water levels, removing\nunwanted impurities while simultaneously and indefinitely retaining\nthe desired levels of both the gadolinium and sulfate ions.\n\nSince EGADS was built specifically to show that gadolinium loading\nwould be feasible in Super-K, scalability was always an important\ndesign criterion. Therefore, from the beginning the EGADS band-pass\nsystem was conceived of as a modularized design. It uses\ncost-effective, readily available components operating in parallel to\nachieve the desired throughput and assure serviceability.\n\nAs the band-pass design is modular and uses off-the-shelf equipment,\nalbeit in novel ways, scaling it up from the current 3~tons\/hour to\n60~tons\/hour for Super-Kamiokande, or 310\\,tons\/hour for \nHyper-Kamiokande, is straightforward. Figure~\\ref{fig:rack} indicates\nhow one rack of filtration membrane housings, the modular unit around\nwhich the Hyper-K band-pass system is designed, is derived from the\noperating EGADS selective filtration system.\n\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{design-water\/rack.pdf}\n \\caption[Scaling the EGADS Band-Pass to Hyper-Kamiokande]\n {Scaling the modular EGADS selective filtration\n band-pass for Hyper-Kamiokande. One rack of filtration\n membrane housings is shown here;\n Figure~\\ref{fig:Gd_WS} shows many of them arranged\n into a functional selective filtration system.}\n \\label{fig:rack}\n \\end{center}\n\\end{figure}\n\n\nFigure~\\ref{fig:Gd_WS} depicts how the modular rack from\nFigure~\\ref{fig:rack} may be duplicated and operated in parallel to\nprovide the needed throughput. Further design simplification and cost\nsavings are achieved by using this standardized membrane housing array\nand filling the housings with a variety of filter membranes, each of\nwhich handles a different cleaning task. These components include\nnanofilters (NF), ultrafilters (UF), and reverse osmosis (RO)\nmembranes; in each case there are two stages. Note that the layout\nshown in Figure~\\ref{fig:Gd_WS} is schematic in nature. Due to space\nconstraints underground the illustrated system would likely be split\ninto two levels, one atop the other.\n\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{design-water\/HK_Gd_WS.pdf}\n \\caption[Gadolinium-capable water system for Hyper-Kamiokande.]\n {Gadolinium-capable water system for\n Hyper-Kamiokande. Two stages each of nanofilters (NF),\n ultrafilters (UF), and reverse osmosis (RO) membrane\n racks are shown, sufficient to provide selectively\n filtered water for Hyper-K.} \n \\label{fig:Gd_WS}\n \\end{center}\n\\end{figure}\n\nUsing the baseline Hyper-K design, the system shown in\nFigure~\\ref{fig:Gd_WS} represents what is needed for selective\nfiltration following the addition of\ngadolinium sulfate to the Hyper-K water. It is assumed that pure water\nfor filling the detector will be provided by the main, non-Gd-capable\nwater system described above. The Gd-specific ``molecular band-pass''\nsystem described here will be augmented with additional Gd-capable water \nhandling equipment -- also demonstrated by and scaled up from a working \nEGADS version -- known as a ``fast recirculation'' system. The Hyper-K \nfast recirculation system will be used in conjunction with HK's \nband-pass to maintain the Gd-loaded water's quality.\n\n\nDue to gadolinium sulfate's benign nature with regards to the usual\ndetector components (materials compatibility was another component of\nthe EGADS study), retaining the ability to add gadolinium to\nHyper-Kamiokande primarily means retaining the option of adding\ngadolinium filtration capability to the Hyper-K water system. Indeed,\nif gadolinium works as well as expected in Super-Kamiokande over the\nnext few years, it is hard to imagine that a next-generation detector\nlike Hyper-K would not also want to enjoy the physics advantages a\ngadolinium-loaded Super-K would already have. Therefore, we have been\ncareful to keep the possibility of gadolinium loading in mind when\ndesigning the overall Hyper-Kamiokande water system.\n\n\n\n\\part{Introduction}\n\\input{introduction\/introduction.tex}\n\n\n\\clearpage\n\\color{black}\n\\part{Experimental Configuration} \\label{part:experimentalconfiguration}\n\\input{jparc\/jparc.tex}\n\n\n\\clearpage\n\\color{black}\n\\section{Hyper-Kamiokande detector} \\label{section:design}\n\n\\input{design-introduction\/introduction.tex}\n\\newpage\n\\input{design-location\/location.tex}\n\\newpage\n\\input{design-cavern\/cavern.tex}\n\n\\newpage\n\\input{design-tank\/tank.tex}\n\n\\newpage\n\\input{design-water\/water.tex}\n\n\n\\clearpage\n\\input{design-photosensor\/photosensor.tex}\n\\clearpage\n\\input{design-electronics\/electronics.tex}\n\\newpage\n\\input{design-daq\/daq.tex}\n\n\\newpage\n\\input{design-calibration\/calibration.tex}\n\n\\newpage\n\\input{design-computation\/computation.tex}\n\n\\clearpage\n\\input{software\/software.tex}\n\n\\clearpage\n\\input{background\/background.tex}\n\n\n\\clearpage\n\\part{Physics Potential}\n\\label{section:physics}\n\n\\section{Neutrino Oscillation}\n\n\\input{physics-lbl\/lbl.tex}\n\\newpage\n\\input{physics-atmnu\/atmnu.tex}\n\\newpage\n\\input{physics-solarnu\/solarnu.tex}\n\n\\newpage\n\\section{Nucleon Decays}\n\\input{physics-pdecay\/pdecay.tex}\n\n\\section{Neutrino Astrophysics and Geophysics}\n\n\\input{physics-supernova\/supernova.tex}\n\\newpage\n\\input{physics-darkmatter\/dm.tex}\n\\newpage\n\\input{physics-astronu\/astronu.tex}\n\\newpage\n\\input{physics-geophys\/geophys.tex}\n\\newpage\n\n\\clearpage\n\\part{Second Detector in Korea}\n\\label{section:secon-detector-korea}\n\\section{Second Detector in Korea}\n\\input{second-tank-korea\/overview.tex}\n\\clearpage\n\n\\section{Introduction}\n\\label{section:intro}\n\nRecent advances in experimental particle physics have yielded\nfascinating insights into the inner workings of the smallest-scale\nphenomena. In 2012, the last missing piece of the standard model (SM)\nof elementary particles, the Higgs boson, was finally observed by the\nATLAS and CMS experiments at the Large Hadron Collider (LHC) in\nCERN~\\cite{Aad:2012tfa,Chatrchyan:2012xdj}. The SM is highly\nsuccessful in explaining experimental data, however our current\nability to describe nature from a fundamental physics point of view is\nfar from satisfactory, most significantly the fact that neutrino mass\ncannot be incorporated, and so we need beyond the standard model (BSM)\nphysics. \n\nThe Nobel Prize in 2002 was awarded for the detection of cosmic\nneutrinos (in particular the ones coming from supernova) in Kamiokande\nand for the pioneering solar neutrino experiment at the Homestake\nmine. More recently, the 2015 Nobel Prize was awarded for the\ndiscovery of neutrino oscillations using data taken by the\nSuper-Kamiokande (Super-K) and the Sudbury Neutrino Observatory collaborations,\nwhich has the very profound implication that neutrinos have non-zero\nbut very tiny masses.\n\nBuilding on the expertise gained from the past and current\nexperiments, Kamiokande and Super-Kamiokande, Hyper-Kamiokande\n(Hyper-K) is a natural progression for the highly successful\nJapanese-hosted neutrino program.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\begin{tabular}{cc}\n \\includegraphics[width=0.8\\textwidth]{introduction\/figs\/HKmain-170509-web.jpg}\n \\end{tabular}\n \\caption{Illustration of the Hyper-Kamiokande first cylindrical tank in Japan.}\n \\label{fig:hk-perspective-JTank}\n \\end{center}\n\\end{figure}\n\nHyper-Kamiokande is a next-generation, large-scale water Cherenkov\nneutrino detector. A dedicated task force determined the optimal tank\ndesign to be two cylindrical detectors that are 60\\,m in height and\n74\\,m in diameter with 40\\% photocoverage, where a staging between the\nfirst and second tank is considered. We first focus on building the\nfirst tank in Japan, see Fig.~\\ref{fig:hk-perspective-JTank} for the\ndrawing.\n\n\n\nCandidate sites for the Hyper-K experiment were selected such that\nneutrinos generated in the J-PARC accelerator facility in Tokai, Japan\ncan be measured in the detector. J-PARC will operate a 750\\,kW beam in\nthe near future, and has a long-term projection to operate with 1300\\,kW\nof beam power. Near detectors placed close to the J-PARC beam line\nwill determine the information about the neutrinos coming from the\nbeam, thus allowing for the extraction of oscillation parameters from\nthe Hyper-K detector. The ND280 detector suite, which has been used\nsuccessfully by the T2K experiment, could be upgraded to further\nimprove the measurement of neutrino cross section and flux. The\nWAGASCI detector is a new concept under development that would have a\nlarger angular acceptance and a larger mass ratio of water (and thus\nmaking the properties more similar to the Hyper-K detector) than the\nND280 design. Intermediate detectors, placed 1-2 km from the J-PARC\nbeam line, would measure the beam properties directly on a water\ntarget. Details of the beam, as well as the near and intermediate\ndetectors, can be found in Section~\\ref{section:jparc}.\n\nHyper-K is a truly international proto-collaboration with over 70\nparticipating institutions from Armenia, Brazil, Canada, France,\nItaly, Korea, Poland, Russia, Spain, Sweden, Switzerland, Ukraine, the United\nKingdom and the United States, in addition to Japan.\n\nHyper-K will be a multipurpose neutrino detector with a rich physics\nprogram that aims to address some of the most significant questions\nfacing particle physicists today. Oscillation studies from\naccelerator, atmospheric and solar neutrinos will refine the neutrino\nmixing angles and mass squared difference parameters and will aim to\nmake the first observation of asymmetries in neutrino and antineutrino\noscillations arising from a CP-violating phase, shedding light on\none of the most promising explanations for the matter-antimatter\nasymmetry in the Universe. The search for nucleon decays will probe\none of the key tenets of Grand Unified Theories. In the case of a\nnearby supernova, Hyper-K will observe an unprecedented number of\nneutrino events, providing much needed experimental results to\nresearchers seeking to understand the mechanism of the\nexplosion. Finally, the detection of astrophysical neutrinos from\nsources such as dark matter annihilation, gamma ray burst jets, and\npulsar winds could further our understanding of some of the most\nspectacular, and least understood, phenomena in the Universe. These\ntopics will be discussed further in Section~\\ref{section:physics}.\n\nThis design report is organized as follows. There are a total of five\nparts. The remainder of this Part~\\ref{section:intro} outlines the\ntheoretical framework for the physics topics contained in this report\nand discusses the relationships between Hyper-K and other large-scale\nneutrino experiments. Part~\\ref{part:experimentalconfiguration}\ndescribes the experimental configuration where\nSection~\\ref{section:jparc} describes the J-PARC neutrino beam line\nand near detector facility; Section~\\ref{section:design} discusses the\ntechnical details of the experimental design and\nSection~\\ref{section:software} details the software packages that will\nbe utilized by the Hyper-K experiment. A discussion of pertinent\nradioactive backgrounds is contained in\nSection~\\ref{section:background}. Part~\\ref{section:physics} explains\nthe physics capabilities for\nHyper-K. Part~\\ref{section:secon-detector-korea} introduces a possible\nsecond tank in Korea. \nThe last part, Part~\\ref{section:appendices}, is the Appendix with\ndetails on the liner sheet tests (A) and a\ndescription of a possible second tank in Japan at Hakamagoshi (B).\n\n\\subsection{Neutrino oscillations}\n\nNeutrino oscillations, discovered by the Super-Kamiokande (Super-K)\nexperiment in 1998~\\cite{Fukuda:1998mi}, implies that neutrinos have\nnonzero masses and flavor mixing, providing one of the most convincing\nexperimental proofs known today for the existence of physics beyond\nthe Standard Model (BSM).\nIndeed neutrino oscillation has been established as a very powerful\ntool to probe extremely small neutrino masses (or their differences)\nas well as lepton flavor mixing.\n\nThroughout this design report, unless stated otherwise, we consider\nthe standard three flavor neutrino framework. The 3$\\times3$ unitary\nmatrix $U$ which describes the mixing of neutrinos~\\cite{Maki:1962mu}\n(that is often referred to as the Pontecorvo-Maki-Nakagawa-Sakata\n(PMNS) or Maki-Nakagawa-Sakata\n(MNS)~\\cite{Pontecorvo:1967fh,Maki:1962mu} matrix) relates the flavor\nand mass eigenstates of neutrinos as\n\\begin{eqnarray} \n\\nu_\\alpha = \\sum_{i=1}^3 U_{\\alpha i} \\nu_i\n\\ \\ (\\alpha = e, \\mu, \\tau),\n\\end{eqnarray} \nwhere $\\nu_\\alpha (\\alpha = e, \\mu, \\tau)$ \nand $\\nu_i (i = 1,2,3)$ \ndenote neutrino fields with definite flavor and mass, respectively. \n\nUsing the standard parameterization, found, e.g. in\nRef.~\\cite{Agashe:2014kda}, $U$ can be expressed as,\n\\begin{eqnarray}\n\\hskip -0.5cm\nU \n& = &\n\\left(\n\\begin{array}{ccc}\n1 & 0 & 0 \\\\\n0 & c_{23} & s_{23} \\\\\n0 & -s_{23} & c_{23} \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{ccc}\nc_{13} & 0 & s_{13}e^{-i\\ensuremath{\\delta_{CP}} } \\\\\n0 & 1 & 0 \\\\\n-s_{13}e^{i\\ensuremath{\\delta_{CP}} } & 0 & c_{13} \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{ccc}\nc_{12} & s_{12} & 0 \\\\\n-s_{12} & c_{12} & 0 \\\\\n0 & 0 & 1 \\\\\n\\end{array}\n\\right) \n\\left(\n\\begin{array}{ccc}\n1 & 0 & 0 \\\\\n0 & e^{i\\frac{\\alpha_{21}}{2}} & 0 \\\\\n0 & 0 & e^{i\\frac{\\alpha_{31}}{2}} \\\\\n\\end{array}\n\\right)\n\\label{eq:mixing}\n\\end{eqnarray}\nwhere $c_{ij} \\equiv \\cos\\theta_{ij}$, $s_{ij} \\equiv \\sin\\theta_{ij}$, \nand $\\ensuremath{\\delta_{CP}} $ --- often called the Dirac $CP$ phase ---, \nis the Kobayashi-Maskawa type $CP$ phase~\\cite{Kobayashi:1973fv} \nin the lepton sector. \nOn the other hand, the two phases, $\\alpha_{21}$ and $\\alpha_{31}$,\n--- often called Majorana $CP$ phases --- exist only if neutrinos are\nof Majorana type~\\cite{Schechter:1980gr, Bilenky:1980cx,Doi:1980yb}.\nWhile the Majorana $CP$ phases can not be observed in neutrino\noscillation, they can be probed by lepton number violating processes\nsuch as neutrinoless double beta ($0\\nu \\beta\\beta$) decay.\n\nIn the standard three neutrino flavor framework, only two mass squared\ndifferences, $\\Delta m^2_{21}$ and $\\Delta m^2_{31}$, for example, are\nindependent. Here, the definition of mass squared differences is\n$\\Delta m^2_{ij}$ $\\equiv$ $m^2_i - m^2_j$. Therefore, for a given\nenergy and baseline, there are six independent parameters that\ndescribe neutrino oscillations: three mixing angles, one $CP$ phase,\nand two mass squared differences.\nAmong these six parameters, $\\theta_{12}$ and $\\Delta m^2_{21}$ have\nbeen measured by solar~\\cite{Ahmad:2002jz,Ahmad:2001an,Abe:2010hy} and\nreactor~\\cite{Eguchi:2002dm,Araki:2004mb,Abe:2008aa} neutrino\nexperiments. The parameters $\\theta_{23}$ and $|\\Delta m^2_{32}|$\n(only its absolute value) have been measured by\natmospheric~\\cite{Ashie:2005ik,Ashie:2004mr} and\naccelerator~\\cite{Ahn:2006zza,Adamson:2011ig,Abe:2012gx,Abe:2014ugx}\nneutrino experiments.\nIn the last few years, \\(\\theta_{13}\\) has also been measured by\naccelerator~\\cite{Abe:2011sj,Adamson:2011qu,Abe:2013xua,Abe:2013hdq}\nand reactor experiments~\\cite{Abe:2011fz,Ahn:2012nd,An:2012eh,\n An:2013zwz,Abe:2014lus}.\nRemarkably, the Super-K detector has successfully measured all of\nthese mixing parameters, apart from the $CP$ phase and the sign of\n$\\Delta m^2_{32}$.\nThe current best-measured values of the mixing parameters are listed\nin ~\\cite{Agashe:2014kda}, where the mass hierarchy and $CP$ phase are still unknown \nthough there are some weak preferences by the current \nneutrino data as will be mentioned later in this section. \n\nBy studying neutrino oscillation behaviour, Hyper-K is expected to\nimprove the current bounds obtained by Super-K for various\nnon-standard neutrino properties, such as the possible presence of\nsterile neutrinos~\\cite{Abe:2014gda}, non-standard interactions of\nneutrinos with matter~\\cite{Mitsuka:2011ty}, or violation of Lorentz\ninvariance~\\cite{Abe:2014wla}.\n\n\\subsubsection{Mass Hierarchy}\n\nThe positive or negative sign of $\\Delta m^2_{32}$ (or equivalently\nthat of $\\Delta m^2_{31}$) corresponds, respectively, to the case of\nnormal ($m_2 < m_3$) or inverted ($m_3 < m_2$) mass hierarchy\n(ordering). From a theoretical point of view, it is of great interest\nto know the mass hierarchy to understand or obtain clues about how the\nneutrino masses and mixing are generated (see\ne.g. \\cite{Mohapatra:2006gs} for a review). Also the mass hierarchy\nhas a significant impact on the observation of the $0\\nu \\beta \\beta $\ndecay for the case where neutrinos are Majorana particles. If the\nmass hierarchy is inverted, a positive signal of $0\\nu\\beta\\beta$\nis expected in future experiments if the current sensitivity on the effective\nMajorana mass can be improved by about one order of magnitude beyond\nthe current limit.\n\nIn the $\\nu_\\mu \\to \\nu_e$ appearance channel, its oscillation\nprobability at around the first oscillation maximum, $O(L\/E_\\nu) \\sim\n1$, tends to be enhanced (suppressed) if the mass hierarchy is normal\n(inverted) due to the matter effect or the so called\nMikheev-Smirnov-Wolfenstein (MSW)\neffect~\\cite{Mikheev:1986gs,Wolfenstein:1977ue} as we will see in Part\n\\ref{section:physics}. For the antineutrino channel, $\\bar{\\nu}_\\mu\n\\to \\bar{\\nu}_e$, the effect become opposite, namely, the normal\n(inverted) mass hierarchy tends to suppress (enhance) the appearance\nprobability. The longer the baseline ($L$), larger the effect of such\nenhancement or suppression. Therefore, in principle, the mass\nhierarchy can be determined by measuring the oscillation probability\nprovided that the matter effect is sufficiently large. This is the\nmost familiar way to determine the mass hierarchy in neutrino\noscillation which can be done using accelerator or atmospheric\nneutrinos.\n\nIndependently from this method, it is also possible to determine the\nmass hierarchy by observing the small interference effects caused by\n$\\Delta m^2_{31}$ and $\\Delta m^2_{32}$ in the medium baseline ($L\n\\sim 50$ km) reactor neutrino oscillation experiment as first\ndiscussed in \\cite{Petcov:2001sy}. The proposed projects such as\nJUNO~\\cite{An:2015jdp} and RENO-50~\\cite{Kim:2014rfa} aim to determine\nthe mass hierarchy by this method.\nFurthermore, in principle, it is possible to determine the mass\nhierarchy by comparing the absolute values of the effective mass\nsquared differences determined by reactor ($\\bar{\\nu}_e$\ndisappearance) and accelerator ($\\nu_\\mu$ disappearance) with high\nprecision ~\\cite{deGouvea:2005hk,Nunokawa:2005nx}.\n\nIt is expected by the time Hyper-K will start its operation,\naround the year 2025, the mass hierarchy could be determined at $\\sim$\n(3-4)$\\sigma$ or more by combining the future data coming from the\nongoing experiments such as NOvA, T2K and reactor experiments, Daya\nBay~\\cite{Guo:2007ug}, RENO~\\cite{Ahn:2010vy}, Double\nChooz~\\cite{Ardellier:2006mn}, and proposed future experiments such as\nJUNO~\\cite{An:2015jdp}, RENO-50~\\cite{Kim:2014rfa},\nICAL~\\cite{Ahmed:2015jtv}, PINGU~\\cite{Aartsen:2014oha}, and\nORCA~\\cite{Katz:2014tta} where the last three projects will use\natmospheric neutrinos to determine the mass hierarchy.\n\n\\subsubsection{CP Violation}\n\nThe magnitude of the charge-parity ($CP$) violation in neutrino\noscillation can be characterized by the difference of neutrino\noscillation probabilities between neutrino and anti-neutrino channels\n~\\cite{Barger:1980jm,Pakvasa:1980bz}.\n\nThe current data coming from T2K~\\cite{Abe:2015awa} and\nNOvA~\\cite{NOvA-talk-nufact15}, when combined with the result of the\nreactor $\\theta_{13}$ measurement, prefer the value around\n$\\delta_{CP} \\sim - \\pi\/2$ (or equivalently, $\\delta_{CP} \\sim\n3\\pi\/2$) for both mass hierarchies though the statistical significance\nis still small.\nInterestingly, the Super-K atmospheric neutrino data also prefers\nsimilar $\\delta_{CP}$ values with a similar statistical\nsignificance~\\cite{Wendell:2014dka}.\n\nIf $CP$ is maximally violated ($|\\sin \\delta_{CP} | \\sim 1$), $CP$\nviolation ($\\sin \\delta_{CP} \\ne 0$) could be established at $\\sim$\n(2-3)$\\sigma$ CL by combining the future data coming from T2K and NOvA\nas well as with data coming from the reactor $\\theta_{13}$\nmeasurements.\n\nIn Hyper-K the neutrino oscillation parameters will be measured using\ntwo neutrino sources which can provide complementary information.\nBoth atmospheric neutrinos, where neutrino oscillations were first\nconfirmed by Super-K, and a long baseline neutrino beam, where\nelectron neutrino appearance was first observed by T2K, will be\nemployed.\n\nWith a total exposure of 1.3~MW $\\times$ 10$^8$ sec integrated proton\nbeam power (corresponding to $2.7\\times10^{22}$ protons on target\nwith a 30~GeV proton beam) to a $2.5$-degree off-axis neutrino beam,\nit is expected that the leptonic $CP$ phase $\\ensuremath{\\delta_{CP}} $ can be\ndetermined to better than 23 degrees for all possible values of\n$\\ensuremath{\\delta_{CP}} $, and $CP$ violation can be established with a statistical\nsignificance of more than $3\\sigma$ ($5\\sigma$) for $76\\%$\n($57\\%$) of the $\\ensuremath{\\delta_{CP}} $ parameter space.\n\nFigure~\\ref{fig:hierarchy_CP} shows how both CP-violation and mass\nhierarchy affect the difference between $\\nu_\\mu \\to \\nu_e$ detection\nprobability relative to $\\bar{\\nu}_\\mu \\to \\bar{\\nu}_e$ detection\nprobability for a given set of\nneutrino parameters. \n\n\\begin{figure}\n \\centering\n \\includegraphics[width=0.9\\textwidth]\n {introduction\/figs\/Asym-Pmue-295km-test.pdf} \n \\caption{The effect of neutrino mass hierarchy and $CP$-violation ($\\delta_{CP}$) on\n the neutrino\/antineutrino detection probability, for a specific\n set of neutrino mixing parameters, neutrino energy(E$_\\nu$), and\n propagation length (L).}\n \\label{fig:hierarchy_CP}\n\\end{figure}\n\n\\subsection{Astrophysical neutrino observations \\label{subsection:intro\/astrophysics}}\n\n Hyper-K is also capable of observing neutrinos from various\n astrophysical objects. One main advantage of the detector is that\n its energy threshold can be set as low as several MeV; this enables\n us to reconstruct neutrinos from the Sun and supernovae on an\n event-by-event basis.\n\nThe Sun is an abundant and nearby source of neutrinos. Recently,\nSuper-K showed the first indication of the terrestrial matter effects\non $^8$B solar neutrino oscillations ~\\cite{sk4-daynight}. This was a\ndirect confirmation of the MSW model\n\\cite{Wolfenstein:1977ue,Mikheyev:1985zz,Mikheyev:1986zz} predictions\nfor neutrino interactions with matter, which is also used to describe\nneutrino behaviour as it travels through the Sun. Furthermore,\nterrestrial matter effects hint at an intriguing possibility of using\natmospheric and long baseline neutrinos to measure mass hierarchy and\n$CP$ phase as both these parameters affect how neutrinos interact with\nmatter. Hyper-K hopes to measure terrestrial matter effects with\nhigher precision to better understand neutrino oscillation behaviour\nin the presence of matter. This also might resolve the $\\sim 2 \\sigma$\ntension between the current best fit values of $\\Delta m^2_{21}$ from\nsolar and reactor neutrino experiments, which is thought to be due to\nsolar neutrino interactions in matter. Additionally, there are several\nphysics goals for the solar neutrino observations in Hyper-K, such as\nlong and short time variation of the $^8$B flux, the first measurement\nof $hep$ neutrinos, and precise measurement of solar neutrino energy\nspectrum.\n\nComputational simulations of core-collapse supernovae (CCSN) have\nfailed to successfully reproduce explosions for more than 40 years.\nHowever, thanks to the recent advances in modeling techniques and the\ngrowth of available computation power, multi-dimensional (2D and 3D)\nsimulations can now produce successful explosions \\cite{Bruenn:13,\n Melson:15a, Lentz:15, Takiwaki:14}. Nevertheless, there are still\nsome puzzles, such as the finding that the total explosion energy of\nthe available multi-dimensional models is small compared to the\nSN1987A observation. Furthermore, the available 3D models are\ngenerally less energetic (or unsuccessful) compared with the more\nextensively simulated 2D models \\cite{Couch:14, Tamborra:13,\n Lentz:15,Takiwaki:14}. Clearly, details of the supernova explosion\nmechanism are still lacking. High statistics observations of\nneutrinos from a CCSN (along with gravitational waves) are the only\nway to obtain precious inside information on the dynamics of the CCSN\ncentral engine and the explosion mechanism\n\\cite{OConnor:13,Tamborra:13}. If a CCSN explosion were to take place\nnear the center of our Galaxy, Hyper-K would observe as many as\ntens of thousands of neutrino interactions (see Section~\\ref{sec:supernova}).\nFurthermore, Hyper-K will have the ability to precisely determine the\narrival time of supernova neutrinos, which will help contribute to the\nunderstandings of both neutrino and CCSN properties. For example, by\ncomparing of the number of $\\nu_e$ and $\\bar{\\nu}_e$ during the CCSN\nneutronization burst (first $\\sim$10\\,msec) we will be able to\ndetermine the neutrino mass hierarchy (see\nSection~\\ref{sec:supernova}). High frequency timing will also provide\nexperimental evidence of the multidimensional dynamics thought to be\ncrucial in the CCSN explosion mechanism \\cite{Tamborra:13}. A large\ntarget volume like that of Hyper-K is also required to observe\nneutrinos from CCSN explosions in nearby ($\\sim$ few Mpc) galaxies.\nIn this volume, CCSNe occur every few years \\cite{Ando:2005ka}.\nMeanwhile, while waiting for a nearby explosion to occur, the\ncontinuous flux of relic supernova neutrinos from all past CCSN\nexplosions in the observable universe will guarantee a steady\naccumulation of valuable astrophysical data.\n\nThanks to its good low energy performance for upward-going muons,\nHyper-K has a larger effective area for upward-going muons below 30\nGeV than do cubic kilometer-scale neutrino telescopes. Additionally,\nfully contained events in Hyper-K have energy, direction, and flavor\nreconstruction and resolutions as good as those in Super-K. This high\nperformance will be useful for further background suppression or\nstudies of source properties. For example, the detector is extremely\nsensitive to the energy range of neutrinos from annihilations of light\n(below 100 GeV) WIMP dark matter, a region which is suggested by\nrecent direct dark matter search experiments. Hyper-K can search for\ndark matter WIMPs by looking for neutrinos created in pair\nannihilation from trapped dark matter in the Galactic centre or the\ncentre of the Sun. Atmospheric neutrinos are a background to this WIMP\nsearch, so spacial cuts are made to determine if there is an excess of\nneutrinos coming from the Galactic centre or the Sun. Hyper-K will\nhave the ability to detect both $\\nu_{e}$ and $\\nu_{\\mu}$ components\nof the signal, making it more sensitive to this type of analysis.\n\nThe detection of neutrinos from solar flares is another astrophysics\ngoal for Hyper-K. This will give us important information about the\nmechanism of the particle acceleration at work in solar flares. There\nhave been some estimations of the number of expected\nneutrinos. Although it has large uncertainties, about 20 neutrinos\nwill be observed at Hyper-K during a solar flare as large as the one\nin 20 January 2005.\nHyper-K also has the potential to see neutrinos from astrophysical\nsources such as magnetars, pulsar wind nebulae, active galactic\nnuclei, and gamma ray bursts. The large target volume of Hyper-K,\ncombined with the potential for these sources to emit neutrinos with\nenergy at the GeV-TeV scale, could make Hyper-K an interesting\nexperiment for observing these neutrinos. As with dark matter\nsearches, the most significant background for detecting neutrinos for\nthese astrophysical sources are atmospheric neutrinos. Spacial, and in\nsome cases temporal, cuts need to be utilized to disentangle the\nastrophysical neutrino signal from the atmospheric neutrino\nbackground.\n\n\\subsection{Nucleon decay searches\\label{subsection:intro\/nucleondecay}}\n\nThe stability of everyday matter motivated Weyl, Stueckelberg, Wigner,\nand other early quantum physicists to introduce a conserved quantity,\nbaryon number, to explain the observed and unobserved particle\nreactions. Baryon number violation is believed to have played an\nimportant role during the formation of the universe, and comprises one\nof the famous Sakharov Conditions to explain the baryon asymmetry of\nthe universe. Proton decay and the decay of bound neutrons are\nobservable consequences of the violation of baryon number.\n\nThe Standard Model Lagrangian explicitly conserves baryon number,\nalthough anomalous quantum effects do violate baryon number at an\nunobservably tiny level. Nevertheless, there are reasons to believe\nthat the Standard Model is part of a more expansive theory. Baryon\nnumber violation is a generic prediction of Grand Unified Theories\n(GUTs) that combine quarks and leptons and include interactions that\nallow their transition from one to the other. These theories are well\nmotivated by observations such as the equality of the sum of quark and\nlepton charges, the convergence of the running gauge couplings at an\nenergy scale of about $10^{16}$ GeV, and frequently have mechanisms to\ngenerate neutrino mass. If new forces carrying particles have masses\nat this GUT scale, the lifetime of the proton will be in excess of\n$10^{30}$ years, where past, present, and future proton decay\nexperiments must search.\n\nBaryon number violation has never been experimentally observed and\nlifetime limits, mainly by Super-Kamiokande, greatly restrict\nallowable Grand Unified theories and other interactions of interest to\nmodel building theorists. In Fig.~\\ref{fig:limits-compared-theory}, we\nshow 90\\% CL lifetime limits by Super-Kamiokande and earlier\nexperiments compared with representative lifetime ranges predicted by\nvarious GUTs. We also show the improvement in lifetime limits expected\nfor 10 years of Hyper-Kamiokande exposure. The complementary\nexperiment DUNE, assumed to be a 40 kt liquid argon time projection\nchamber (LArTPC) is also a sensitive to nucleon decay. Due to its\nsmaller mass compared to Hyper-K, it is competitive mainly in modes\nwith distinctive final state tracks such as those involving kaons.\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=0.9\\textwidth]\n {introduction\/figs\/sklimits_compare_theory_2015_KamLAND.pdf} \n \\caption{A comparison of historical experimental limits on the rate\n of nucleon decay for several key modes to indicative ranges of\n theoretical prediction. Included in the\n figure are projected limits for Hyper-Kamiokande and DUNE based\n on 10 years of exposure.}\n \\label{fig:limits-compared-theory}\n\\end{figure}\n\nThe message the reader should conclude from this figure is that 10\nyears of Hyper-K exposure is sensitive to lifetimes that are commonly\npredicted by modern grand unified theories. The key decay channel $p\n\\rightarrow e^+\\pi^0$ has been emphasized, because it is dominant in a\nnumber of models, and represents a nearly model independent reaction\nmediated by the exchange of a new heavy gauge boson with a mass at the\nGUT scale. The other key channels involve kaons, wherein a final state\ncontaining second generation quarks are generic predictions of GUTs\nthat include supersymmetry. Example Feynman diagrams are shown in\nFig.~\\ref{fig:diagrams-ek}.\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=0.9\\textwidth]\n {introduction\/figs\/diagrams-ek.pdf} \n \\caption{Two sample Feynman diagrams that could be responsible for\n proton decay. The left diagram is a $d = 6$ interaction mediated\n by a heavy gauge boson, $X$, with mass at the GUT scale. The\n right diagram contains superymmetric particles and a $d = 5$\n operator that is predicted in many SUSY GUTs.}\n \\label{fig:diagrams-ek}\n\\end{figure}\n\nGenerally, nucleon decay may occur through multiple channels and\nideally, experiments would reveal information about the underlying GUT\nby measuring branching ratios. It is a strength of Hyper-K that it is\nsensitive to a wide range of nucleon decay channels, however the few\nshown here are sufficient to discuss the details of the search for\nnucleon decay by Hyper-Kamiokande later in this document.\n\nPractically, because of the stringent limits from more than\n300\\,kt$\\cdot$y of Super-K running, the next generation experiments\nwill have to concentrate on the discovery of nucleon decay, perhaps by\none or a small number of events. The predictions are uncertain to two\nor three orders of magnitude, and one should not expect a negative\nsearch to definitively rule out the idea of GUTs. To excel in the\nsearch for proton decay, Hyper-Kamiokande requires the largest mass\nthat is affordable in combination with sufficient instrumentation to\nminimize experimental background.\n\n\\subsection{Synergies between Hyper-K and other neutrino experiments}\n\nThis section will focus on understanding how Hyper-K will fit into the\ncontext of the global neutrino community. This includes currently\noperating experiments such as T2K and Super-K, as well as future\nexperiments like DUNE.\n\n\\subsubsection{T2K}\n\nT2K \\cite{Abe:2011sj} is a currently-operating experiment which uses\nSuper-K to measure neutrinos produced in the J-PARC beam line. Hyper-K\nwill use much of the existing infrastructure used by T2K, particularly\nthe beam line and near detectors. Hyper-K will also benefit from any\nimproved data analysis techniques developed for T2K. Several important\nT2K upgrades and improvements are planned for the coming years, and\nthis will have a direct impact on improved Hyper-K performance.\n\n\\begin{itemize}\n\t\\item\n \\textbf{Near detector improvements}: The T2K experiment uses\n the ND280 near detector suite. Future analysis improvements\n in the ND280 detector aim to reduce the cross section and\n flux uncertainties. Hardware upgrades, particularly to the\n time projection chamber component has also been\n proposed. The reader should refer to\n Section~\\ref{subsection:nd280} for the full details of the\n current and future status of the ND280 detector.\n\t\\item\n \\textbf{Increased beam power}: J-PARC is planning an upgrade\n of the proton drivers in the neutrino beam. The near-term\n goal is to improve the beam power from 365\\,kW to\n 750\\,kW. After the proton driver upgrade, beam power is\n projected to reach 1300\\,kW. See Section~\\ref{section:jparc}\n for more details.\n\t\\item\n \\textbf{Better data analysis techniques}: T2K demonstrated\n in its publications about $\\nu_e$ appearance that\n aspects of the data analysis such $\\pi^0$ rejection can be\n improved. Other improvements to the data analysis technique\n are under development, including $\\nu_e$ detection\n efficiency, precision of the vertex\n determination (which could allow for an increased fiducial\n volume), and an improvement in $\\pi\/\\mu$ separation.\n\\end{itemize}\n\nIn addition to benefiting directly from the upgraded hardware and\nanalysis techniques, Hyper-K will also benefit from the expertise\ngained through implementing these upgrades. Furthermore, these\nupgrades can serve as a test bed for new near detector designs that\nhave been proposed for Hyper-K (see Section~\\ref{section:jparc}).\n\n\\subsubsection{Super-K}\n\n\n\n\nIn June 2015, the Super-Kamiokande Collaboration approved the SK-Gd\nproject. This project is an upgrade of the detector's capabilities,\nachieved by dissolving 0.2\\% gadolinium sulfate into Super-K's water\nin order to enhance detection efficiency of neutrons from neutrino\ninteractions. One of the main motivations of SK-Gd is to discover\nsupernova relic neutrinos (SRN), the diffuse flux of neutrinos emitted\nby all supernovae since the beginning of the universe. SRN primarily\ninteract in Super-K via inverse beta decay (IBD). Therefore,\nfollowing the prompt detection of a positron, the accompanying IBD\nneutron can be identified in SK-Gd by a delayed gamma cascade, the\nresult of the neutron's capture on gadolinium. As a result of this\npositive identification of true IBD events, a much improved separation\nbetween signal and background can be achieved.\n\nAs Super-K will be the first example of gadolinium loading in a\nlarge-scale water Cherenkov detector, this will be a template for any\nfuture possibility of loading gadolinium into Hyper-K. In addition to\ndetermining the physics performance of gadolinium-loaded water,\nHyper-K will also benefit from the extensive research done to optimize\nthe water purification system, as well as the tests for material\ncompatibility that was required to upgrade the Super-K detector.\n\n\\subsubsection{DUNE}\nThe Deep Underground Neutrino Experiment (DUNE), formerly LBNE\n\\cite{LBNE}, is a 40 kilotonne liquid argon neutrino experiment that\nis projected to begin taking data around the same time as\nHyper-K. Because DUNE will use a different target material than\nHyper-K (liquid argon rather than water), many complementary\nmeasurements can be made, including nucleon decay measurements (as\ndescribed in Section~\\ref{subsection:intro\/nucleondecay}) and\nsupernova neutrino detection.\n\nAs mentioned in Section~\\ref{subsection:intro\/astrophysics},\ninformation about the neutrino signature from supernovae is much\nsought after, and Hyper-K and DUNE will each add to the overall\npicture. The primary reaction channel for these neutrinos in Hyper-K\nis the inverse beta decay channel, in which only electron\nantineutrinos will take part. In DUNE, the reaction channel will be\nthe charged-current reaction on $^{40}$Ar, which measures electron\nneutrinos. Taken together, these measurements will be able to\ndetermine the relative abundance of neutrinos to\nantineutrinos. Furthermore, DUNE will be able to better determine some\nfeatures of the neutrino spectrum which are dominated by the electron neutrino\nsignal, such as the neutronization burst that occurs during early\ntimes, while Hyper-K will better measure features where there is an\nantineutrino signal, such as the accretion and cooling phases that\noccur at late times.\n\nDue to the fact that the baseline between the accelerator facility and Hyper-K will be\nshorter than the proposed baseline for the DUNE experiment, the two\nexperiments will have some complementarity in the information they can\nextract from their accelerator programs. The longer baseline to the\nDUNE experiment\nmeans their measurement will be more affected by matter effects, which\nwill give them more sensitivity to the mass\nhierarchy. The shorter baseline of Hyper-K experiment means less\nsensitivity to matter effects, which should lead to an increased\nsensitivity to the measurement of the CP-violation phase. This is further\ndescribed in Section~\\ref{sec:cp}. \n\n\n\\subsubsection{Off-axis angle spanning configuration \\label{sec:nuprism}}\nThe intermediate WC detector can be oriented with the polar axis of\nthe cylinder in the vertical direction and the detector extending from\nthe ground level downward. This configuration was originally \nproposed as the NuPRISM detector~\\cite{Bhadra:2014oma}, located at a\nbaseline of 1\\,km filling a 10\\,m diameter, 50\\,m deep pit. \nFig.~\\ref{fig:nuprism_offaxis} shows the conceptual drawing for the\nNuPRISM detector and the $\\nu_{\\mu}$ spectra for the\n$1^{\\circ}-4^{\\circ}$ off-axis angle range spanned by the detector.\nThe baseline design for the detector is an instrumented structure with\na 10\\,m tall inner-detector containing 3215 8 inch inward facing\nphotomultiplier tubes to detect the Cherenkov light, giving 40\\%\nphoto-coverage. A crane system will move the detector structure\nvertically in the 50\\,m pit to make measurements at different off-axis\nangles. By orienting the long axis of the detector perpendicular to the beam\ndirection, the detector covers a range of angles relative to the beam\ndirection. Hence, each vertical slice of the detector samples a\ndifferent neutrino spectrum due to the decay kinematics of the pions\nand kaons producing the neutrinos, the so-called off-axis beam effect.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=0.25\\textwidth]{jparc\/figs\/nuprism-middlecut.png}\n\\includegraphics[width=0.40\\textwidth]{jparc\/figs\/off_axis_spectrum.pdf}\n\\caption{Left: A conceptual drawing of the nuPRISM detector. Right: the $\\nu_{\\mu}$ flux energy dependence for the\n$1^{\\circ}-4^{\\circ}$ off-axis angle range.\n\\label{fig:nuprism_offaxis}}\n\\end{figure}\n\nThere are three primary motivations for making neutrino measurements\nover a range of off-axis angles. First, the change in the neutrino\nspectrum with off-axis angle is well known from the flux model, so the\npredicted off-axis spectra can be combined in a linear combination to\nproduce almost arbitrary neutrino spectra. Measured distributions at\ndifferent off-axis angles can be combined in the linear combination to\nproduce the predicted measured quantity for the neutrino spectrum of\ninterest. In this way, it is possible to measure the muon spectrum\nfor a nearly mono-chromatic neutrino spectrum, or a spectrum that\nclosely matches the oscillated spectrum that is expected at the far\ndetector. This approach can nearly eliminate the main model dependent\nuncertainty in near to far extrapolations, which arises from the\ncombination of two factors: the near and far detector do not see the\nsame flux due to oscillations, and the relationship between the true\nneutrino energy and final state lepton kinematics strongly depends on\nnuclear effects, which are not well modelled~\\cite{Bhadra:2014oma}.\n\nThe second physics motivation is the measurement of the electron\nneutrino cross section relative to the muon neutrino cross section.\nAt further off-axis positions, the fraction of intrinsic\n$\\nu_{e},\\bar{\\nu}_{e}$ in the beam becomes large, making the\nselection of pure candidate samples possible. By taking advantage of\nthe enhanced purity at large off-axis angles, a measurement of the\ncross section ratio, $\\sigma_{\\nu_{e}}\/\\sigma_{\\nu_{\\mu}}$ with 3\\%\nprecision or better may be possible. A measurement of the\n$\\sigma_{\\bar{\\nu}_{e}}\/\\sigma_{\\bar{\\nu}_{\\mu}}$ ratio is also\npossible, although the precision is expected to be degraded due to the\nlarger neutral current background rate for electron antineutrino\ncandidates and the presence of a larger wrong-sign background for both\nmuon and electron antineutrino charge current interactions.\n\nThe third physics motivation is the search for sterile neutrino\ninduced oscillations that are consistent with the\nLSND~\\cite{Aguilar:2001ty} and\nMiniBooNE~\\cite{Aguilar-Arevalo:2013pmq} $\\bar{\\nu}_{e}$ and $\\nu_{e}$\nappearance anomalies. At a 1\\,km baseline, the $L\/E$ of the neutrino\nspectrum peak varies between 1.1\\,km\/GeV at $1^{\\circ}$ off-axis to\n2.5\\,km\/GeV at $4^{\\circ}$ off-axis. Since the neutrino spectrum\nvaries with off-axis angle, it is possible to search for the\noscillation pattern not only through the reconstructed energy of the\nneutrino candidate events, but also through the reconstructed off-axis\nangle. This method provides a significant improvement in the electron\nneutrino appearance search sensitivity, and preliminary studies with a\nnon-optimal detector configuration already show that much of the LSND\nallowed region can be excluded at 5$\\sigma$~\\cite{NUPRISMProposal}.\n\n\\subsubsection{Gadolinium Loading}\n\nRecent developments in the addition of gadolinium\n(Gd)~\\cite{Watanabe:2008ru} and Water-based Liquid Scintillator (WbLS)\ncompounds~\\cite{Alonso:2014fwf} to water raise the possibility to\nseparate neutrino and antineutrino interactions by detecting the\npresence of neutrons or protons in the final state.\n\nFinal state proton tagging has been studied intensively for an\napplication for LArTPC detectors~\\cite{Acciarri:2014gev}, where final\nstate protons can be counted to further purify the sample to improve\nthe oscillation sensitivity~\\cite{Mosel:2013fxa}. An analogous\napproach is possible for the larger WC detectors.\nNamely, Gd-doped WC detectors possess neutron tagging\nability on top of the 4$\\pi$ detector coverage~\\cite{Abe:2014oxa},\nwhich allows statistical separation of primary interaction modes,\notherwise impossible. \nIn particular, the ability to tag neutrons provides charge separation\ninformation due to the enhanced presence of neutrons in the final\nstate for $\\bar{\\nu}$ charged current interactions. This will allow\nstudies of neutrino:anti-neutrino cross-section ratios on water and constraints on wrong-sign backgrounds, thus\nreducing a critical systematic uncertainty in both the beam\n$\\delta_{CP}$ and atmospheric neutrino oscillation analyses. Neutron\ntagging also allows more detailed studies of the interaction modes,\nand in particular final state interaction effects, for the main\nbackgrounds to proton decay. \n\nThe TITUS detector was originally proposed to provide an intermediate detector with neutron tagging capabilities for Hyper-K as described in Ref.~\\cite{TITUSpreprint}. \nFigure~\\ref{fig:neutrontaggingresolution} shows an example of a WC near detector simulation study for TITUS in which selecting ``neutron$\\ge$1'' increases the selection purity for $\\bar{\\nu}$CCQE\ninteractions and hence improves the energy resolution. This technique\nwill be also applied to the ANNIE experiment~\\cite{Anghel:2015xxt} in\nthe next years.\n\n\\begin{figure}[!tbp]\\centering\n\n\\includegraphics[width=0.32\\textwidth]{jparc\/figs\/resolution_titus_muon_rhc.pdf}\n\\includegraphics[width=0.32\\textwidth]{jparc\/figs\/resolution_titus_muon_rhc_noneutron.pdf}\n\\includegraphics[width=0.32\\textwidth]{jparc\/figs\/resolution_titus_muon_rhc_hasneutron.pdf}\n\\caption{The neutrino energy resolution due to the QE assumption in water Cherenkov near detector simulation \nfor the TITUS detector~\\cite{TITUSpreprint} during anti-neutrino mode running. \nThe effect of different neutron selections is shown. From left to right, no neutron tagging, neutron number =0, \nand neutron number $>$ 0.\\label{fig:neutrontaggingresolution}}\n\\end{figure}\n\nOne aspect of the intermediate detector's design that needs to be\ncarefully considered with Gd-doped water is how to veto incoming\nneutrons from beam-induced interactions in the material surrounding\nthe detector which will be the dominant contributor for the number of\nparticles entering the detector. Vetoing most of these particles\nrequires at least 1\\,m of water to reduce the low energy tail, plus a\nfiducial cut on the reconstructed capture vertex. Preliminary studies\nusing spallation rates induced by muons~\\cite{Galbiati:2005ft} and\ninteractions in the material surrounding the detector show this veto\ncan reduce the number of neutrons entering the detector's ID to just\n10\\% of all the events entering the tank and the fiducial region\nfurther reduces this to approximately 7\\% of the entering particles.\n\nIn principle, Gd loading is compatible with the off-axis spanning\ndetector configuration described in the previous section. The\noff-axis spanning detector should be as near as possible to the beam\norigin to reduce the depth of the excavated volume, while the Gd\nloaded detector should be far enough away to limit the beam induced\nentering neutron background to the necessary level. Preliminary\nstudies suggest that the entering neutron rate is sufficiently low for\nthe off-axis spanning detector located at 1\\,km from the neutrino\nproduction point.\n\n \n\n\n\\section{J-PARC neutrino beam facility} \\label{section:jparc}\nThe accelerator neutrinos detected by Hyper-K are produced at the\nJapan Proton Accelerator Research Complex (J-PARC)~\\cite{JPARCTDR}.\nThe proton accelerator chain, neutrino beamline and near detectors are\nlocated within J-PARC. Proposed intermediate detectors would be\nlocated near the J-PARC site at a distance of 1-2\\,km from the\nproduction target. This section describes the proton accelerator\nchain, neutrino beamline, near detectors and proposed intermediate\ndetectors. In each case, the current configuration and future\nupgrades are described.\n\n\\subsection{Neutrino beam and near detectors in long baseline oscillation measurements \\label{sec:beam_and_nd}}\nThe neutrino beam is produced by colliding 30\\,GeV protons\nextracted from the J-PARC accelerator chain with a 91\\,cm long graphite\ntarget. Three magnetic horns focus secondary charged particles that\nare produced in the proton-target collisions. The polarity of the\nhorns' currents determine which charge is focused and defocused,\nallowing for the creation of neutrino or antineutrino enhanced beams.\nThe secondary particles are allowed to decay in a 96\\,m long decay\nvolume. The dominant source of neutrinos is the decay of $\\pi^{\\pm}$.\nMost $\\mu^{\\pm}$ are stopped in the absorber located at the end of the\ndecay volume before they decay, and $\\nu_{e}(\\bar{\\nu_{e}})$ from\n$\\mu^{\\pm}$ decays contribute less than 1\\% to the total neutrino flux\nat at the peak energy.\n\nThe J-PARC beam is aimed 2.5$^{\\circ}$ away from the Super-K and\nHyper-K detectors to take advantage of the pion decay kinematics to\nproduce a narrow band beam~\\cite{Beavis-BNL-52459} with a spectrum\npeaked at 600\\,MeV, at the first oscillation maximum for a baseline of\n295\\,km. Fig.~\\ref{fig:hk_fluxes} shows the calculated energy dependent\nneutrino fluxes in the absence of neutrino oscillations impinging on\nHyper-K for 320\\,kA horn currents in both horn polarities. Neglecting\noscillations, neutrino detectors located near the neutrino source\nobserve a similar neutrino spectrum to the far detector spectrum, but\nthe peak of the spectrum is broader since the beam appears as a line\nsource for near detectors, compared to a point source for far\ndetectors.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=0.45\\textwidth]{physics-lbl\/figures\/hk_numode_flux.pdf}\n\\includegraphics[width=0.45\\textwidth]{physics-lbl\/figures\/hk_anumode_flux.pdf}\n\\caption{The neutrino spectra at Hyper-K for the neutrino enhanced\n (left) and antineutrino enhanced (right) horn current polarities\n with the absolute horn current set to 320\\,kA.\n\\label{fig:hk_fluxes}}\n\\end{figure}\n\n\nThe neutrino flux is calculated using a data-driven simulation that\nemploys primary proton beam measurements, hadron production\nmeasurements, beamline element alignment measurements and horn current\nand field measurements~\\cite{Abe:2012av}. The dominant uncertainty on\nthe flux calculation arises from modeling of hadron production in the\ngraphite target and surrounding material. To minimize the hadron\nproduction uncertainties, the NA61\/SHINE\nexperiment~\\cite{Abgrall:2014xwa} has measured particle production\nwith 30\\,GeV protons incident on a thin (4\\% of an interaction length)\ntarget~\\cite{Abgrall:2011ae,Abgrall:2011ts}, and a replica T2K\ntarget~\\cite{Abgrall:2012pp}. The thin target data have been used in\nthe T2K flux calculation, and a 10\\% uncertainty on the flux\ncalculation has been achieved, as shown in\nFig.~\\ref{fig:t2k_flux_errors}. Much of the remaining uncertainty\narises from the modeling of secondary particle re-interactions inside\nthe target. Preliminary work suggests that the hadron production\nuncertainty can be reduced to $\\sim5\\%$ by using the NA61\/SHINE\nmeasurement of the particle multiplicities exiting the T2K replica\ntarget~\\cite{Hasler:2039148}. In the context of Hyper-K, the thin\ntarget data from NA61\/SHINE are applicable to the flux calculation,\nand the replica target data may also be used if the target geometry\ndoes not change significantly. If the target geometry or material \nare changed for Hyper-K, then new hadron production measurements will\nbe necessary. \n\n\\begin{figure}\n\\centering\n\\includegraphics[width=0.45\\textwidth]{jparc\/figs\/total_err_sk_numode_numu.pdf}\n\\includegraphics[width=0.45\\textwidth]{jparc\/figs\/total_err_sk_anumode_numub.pdf}\n\\caption{The uncertainties on the T2K flux calculation at Super-K for neutrino enhanced (left) and \nantineutrino enhanced (right) beams.\n\\label{fig:t2k_flux_errors}}\n\\end{figure}\n\nThe near neutrino detectors of T2K are located 280\\,m from the pion\nproduction target and they include the INGRID on-axis\ndetector~\\cite{Otani:2010zza} and the ND280 off-axis\ndetector~\\cite{Assylbekov:2011sh,Allan:2013ofa,Aoki:2012mf,Amaudruz:2012agx,Abgrall:2010hi}.\nThe INGRID detector is used primarily to measure the beam direction and neutrino yield,\nwhile ND280 measurements provide constraints on the neutrino flux and\ninteraction models that are used to predicted the event rate at the\nfar detector after oscillations. Measurements with the ND280 detector\nare used for both dedicated neutrino cross-section measurements and\nevent rate constraints that are used directly in neutrino oscillation\nmeasurements. For neutrino cross-section measurements, the neutrino\nflux is derived from the previously described flux calculation and the\nneutrino cross-section is inferred from the event rate and particle\nkinematics measured with the ND280 detector. The cross-section\nmeasurements provide constraints on the building of models of\nneutrino-nucleus interactions that are ultimately used in oscillation\nmeasurements. For the oscillation measurements themselves, nuisance\nparameters are introduced to describe the uncertainty on the neutrino\nflux and interaction models. A fit to a subset of the ND280 data\nsimultaneously constrains the flux and interaction model nuisance\nparameters, and the predicted event rate and uncertainty at the far\ndetector are updated~\\cite{Abe:2015awa}. The beam direction\nmeasurement, neutrino cross section measurements and direct\nconstraints on the neutrino event rate for oscillation measurements\nare all necessary for long baseline oscillations measurements at\nHyper-K.\n\n\n\\subsection{The J-PARC accelerator chain }\nThe J-PARC accelerator cascade~\\cite{JPARCTDR} \nconsists of a normal-conducting LINAC as an injection \nsystem, a Rapid Cycling Synchrotron (RCS), and a Main Ring synchrotron (MR). \nH$^-$ ion beams, with a peak current of 50 mA and pulse width of 500 $\\mu$s, \nare accelerated to 400 MeV by the LINAC. \nConversion into a proton beam is achieved by charge-stripping foils at\ninjection into the RCS ring, which accumulates and accelerates two\nproton beam bunches up to 3 GeV at a repetition rate of 25 Hz. Most of\nthe bunches are extracted to the Materials and Life science Facility\n(MLF) to generate intense neutron\/muon beams. The beam power of RCS\nextraction is rated at 1\\,MW. With a prescribed repetition cycle, four\nsuccessive beam pulses are injected from the RCS into the MR at 40 ms\n(= 25 Hz) intervals to form eight bunches in a cycle, and\naccelerated up to 30 GeV. In fast extraction (FX) mode operation, the\ncirculating proton beam bunches are extracted within a single turn\ninto the neutrino primary beamline by a kicker\/septum magnet system.\n\n\n\\begin{table}[t]\n \\caption{Main Ring rated parameters for fast extraction, with numbers\n achieved as of December 2017. The columns show (left to right): the\n currently achieved operation parameters, the original design\n parameters, the projected parameters after the MR RF and magnet\n power supply upgrade, and the projected parameters for the maximum\n beam power achievable after the upgrade. }\n \\label{jparc:MRFXpara}\n \\begin{center}\n \\begin{tabular}{lcccc}\n \\hline \\hline\n Parameter & Achieved & Original & Doubled rep-rate & Long-term Projection \\\\\n \\hline\n Circumference & \\multicolumn{4}{c}{1,567.5\\,m } \\\\\n Beam kinetic energy & 30\\,GeV & 50\\,GeV & 30\\,GeV & 30\\,GeV \\\\\n Beam intensity & $2.45\\times 10^{14}$\\,ppp\n & $3.3\\times 10^{14}$\\,ppp & $2.0\\times 10^{14}$\\,ppp & $3.2\\times 10^{14}$\\,ppp \\\\\n ~ & $3.1\\times 10^{13}$\\,ppb\n & $4.1\\times 10^{13}$\\,ppb & $2.5\\times 10^{13}$\\,ppb & $4.0\\times 10^{13}$\\,ppb \\\\\n $[$ RCS equivalent power $]$ & $[$ 575\\,kW $]$\n & $[$ 1\\,MW $]$ & $[$ 610\\,kW $]$ & $[$ 1\\,MW $]$ \\\\\n Harmonic number & \\multicolumn{4}{c}{9} \\\\\n Bunch number & \\multicolumn{4}{c}{8~\/~spill} \\\\\n Spill width & \\multicolumn{4}{c}{$\\sim$~5\\,$\\mu$s} \\\\\n Bunch full width at extraction & $\\sim$50\\,ns & -- & $\\sim$50\\,ns & $\\sim$50\\,ns \\\\\n Maximum RF voltage & 280\\,kV & 280\\,kV & 560\\,kV & 560\\,kV \\\\\n Repetition period & 2.48\\,sec & 3.52\\,sec & 1.32\\,sec & 1.16\\,sec \\\\\n \\hline\n Beam power & 485\\,kW\\footnote{As of 2018} & 750\\,kW & 750\\,kW & 1340\\,kW \\\\\n \\hline\n \\hline\n \\end{tabular}\n \\end{center}\n\\end{table}\n\nIn the MR FX mode operation, a beam intensity of 2.45$\\times$10$^{14}$ proton-per-pulse (ppp) \nhas been achieved, corresponding to $\\sim$485\\,kW beam power (as of 2018).\nThe accelerator team is following \na concrete upgrade scenario~\\cite{jparc-midterm-new}\nto reach the design power of 750\\,kW in forthcoming years, \nwith a typical planned parameter set as listed in Table~\\ref{jparc:MRFXpara}.\nThis will double the current repetition rate by \n(i) replacing the magnet power supplies, \n(ii) replacing the RF system, and \n(iii) upgrading injection\/extraction devices. \nBased on high intensity studies of the current accelerator performance,\nit is expected that 1-1.3\\,MW beam power can be achieved after these upgrades~\\cite{jparc-status-upgrade,jparc-plan-2026}.\nThe projected beam performance up to 2028 is shown in Fig.~\\ref{fig:power_proj}.\nFor operation larger than 2\\,MW beam power, conceptual design studies are now\nunderway~\\cite{jparc-longterm-new}, and they include approaches such as raising the RCS top energy, enlarging the MR\naperture, or inserting an \"emittance-damping\" ring between the RCS and MR.\n\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]\n {jparc\/figs\/jparc_mr_power_projection_2017_labelled.pdf}\n \\caption{The projected Main Ring fast extraction performance up to 2028, including the beam power, the protons per pulse, and the repitition rate.}\n \\label{fig:power_proj}\n \\end{center}\n\\end {figure}\n\n\n\\subsection{Neutrino beamline}\n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]\n {jparc\/figs\/jparc-beamline-overview_v2.pdf}\n \\caption{The neutrino experimental facility \n (neutrino beamline) at J-PARC.}\n \\label{fig:beamline}\n \\end{center}\n\\end {figure}\nFig.~\\ref{fig:beamline} shows an overview of the neutrino experimental\nfacility~\\cite{Abe:2011ks}. The primary beamline guides the extracted\nproton beam to a production target\/pion-focusing horn system in a\ntarget station (TS). The pions decay into muons and neutrinos during\ntheir flight in a 96 m-long decay volume. A graphite beam dump is\ninstalled at the end of the decay volume, and muon monitors downstream\nof the beam dump monitor the muon profile. The beam is aimed\n2.5$^{\\circ}$ off-axis~\\cite{OffAxisBeam} from the direction to\nSuper-K and the beamline has the capability to vary the off-axis angle\nbetween 2.0$^\\circ$ to 2.5$^\\circ$.\nThe centreline of the beamline extends 295 km to the west, \npassing midway between Tochibora and Mozumi, so that both \nsites have identical off-axis angles. \n\\begin {figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]\n {jparc\/figs\/jparc-nu-secondary-beamline-v2.pdf}\n \\caption{(Left) Side view of the secondary beamline, \n with a close up of the target station helium vessel.\n (Right) A schematic view of a support module and shield blocks \n for horn-3. If a horn fails, the horn together with its \n support module is transferred remotely to a purpose-built \n maintenance area, disconnected from the support module \n and replaced. \n }\n \\label{fig:secondaryBL}\n \\end{center}\n\\end {figure}\n\n\\subsubsection{Secondary beamline}\nThe secondary beamline consists of the beamline from the TS entrance\nto the muon monitors. Fig.~\\ref{fig:secondaryBL} shows a cross\nsection of the secondary beamline, and a close-up of the TS helium\nvessel. The secondary beamline components and their capability to\naccept high power beam are reviewed here.\n\nA helium cooled, double skin titanium alloy beam window separates the\nhelium environment in the TS vessel ($\\sim$1 atm pressure) from the\nvacuum of the primary beamline. The proton beam collides with a\nhelium-cooled graphite production target that is inserted within the\nbore of the first of a three-horn pion-focusing system. At 750\\,kW\noperation, a $\\sim$20\\,kW heat load is generated in the target. The\nneutrino production target and the beam window are designed for 750\\,kW\noperation with 3.3$\\times$10$^{14}$ ppp (equivalent to RCS 1\\,MW\noperation) and 2.1\\,sec cycle. In the target, the pulsed beam generates\nan instantaneous temperature rise per pulse of 200 C$^\\circ$ and a\nthermal stress wave of magnitude 7 MPa. Given the tensile strength,\nthe safety factor is $\\sim$5. Although the tensile strength and\nsafety factor will be reduced by cyclic fatigue, radiation damage and\noxidization of the graphite, a lifetime of 2$-$5 years is expected.\n\nThe horns are suspended from the lid of the TS helium vessel. Each\nhorn comprises two co-axial cylindrical conductors which carry up to a\n320 kA pulsed current. This generates a peak toroidal magnetic field\nof 2.1\\,Tesla which focuses one sign of pions. The heat load generated\nin the inner conductors by secondary particles and by joule heating is\nremoved by water spray cooling. So far the horns were operated with a\n250 kA pulsed current and a minimum repetition cycle of 2.48 sec. To\noperate the horns at a doubled repetition rate of $\\sim$1 Hz requires\nnew individual power supplies for each horn utilizing an energy\nrecovery scheme and low inductance\/resistance striplines. These\nupgrades will reduce the charging voltage\/risk of failure, and, as\nanother benefit, increase the pulsed current to 320 kA. The horn-1\nwater-spray cooling system has sufficient capacity to keep the\nconductor below the required 80$^\\circ$C at up to 2\\,MW.\n\nAll secondary beamline components become highly radioactive during\noperation and replacements require handling by a remotely controlled\noverhead crane in the target station. Failed targets can be replaced\nwithin horn-1 using a bespoke target installation and exchange\nmechanism.\n\nBoth the decay volume and the beam dump dissipate $\\sim$1\/3 of the\ntotal beam power, respectively. The steel walls of the decay volume\nand the graphite blocks of the hadron absorber (core of the beam dump)\nare water cooled and both are designed to accept 3$\\sim$4\\,MW beam\npower since neither can be upgraded nor maintained after irradiation\nby the beam.\n\nConsiderable experience has been gained on the path to achieving\n475\\,kW beam power operation, and the beamline group is promoting\nupgrades to realize 750\\,kW operation and to expand the facilities for the\ntreatment of activated water. Table~\\ref{jparc:BLupgrade} gives a\nsummary of acceptable beam power and\/or achievable parameters for each\nbeamline component~\\cite{IFW-nu750kW,IFW-numultiMW}, for both the\ncurrent configuration and after the proposed upgrades in forthcoming\nyears.\n\n\n\\begin{table}[t]\n \\caption{Acceptable beam power and achievable parameters\n for each beamline component after proposed upgrades.\n Limitations as of December 2017 are also given in\n parentheses.}\n \\label{jparc:BLupgrade}\n \\begin{center}\n \\begin{tabular}{lcc}\n \\hline \\hline\n Component & \\multicolumn{2}{c}\n {Acceptable beam power or achievable parameter} \\\\\n \\hline\n Target & \\multicolumn{2}{c}{3.3$\\times$10$^{14}$ ppp } \\\\\n Beam window & \\multicolumn{2}{c}{3.3$\\times$10$^{14}$ ppp } \\\\\n Horn & ~ & ~ \\\\\n \\multicolumn{1}{c}{cooling for conductors} &\n \\multicolumn{2}{c}{2 MW} \\\\\n \\multicolumn{1}{c}{stripline cooling}\n & ( 750 kW $\\rightarrow$) & $\\sim$3 MW \\\\\n \\multicolumn{1}{c}{hydrogen production}\n & ( 1 MW $\\rightarrow$) & $\\sim$2 MW \\\\\n \\multicolumn{1}{c}{power supply} & ( 250 kA $\\rightarrow$) & 320\nkA \\\\\n ~ & ( 0.4 Hz $\\rightarrow$) & 1 Hz \\\\\n Decay volume & \\multicolumn{2}{c}{4 MW} \\\\\n Hadron absorber (beam dump) & \\multicolumn{2}{c}{3 MW} \\\\\n \\multicolumn{1}{c}{water-cooling facilities}\n & ( 750 kW $\\rightarrow$) & $\\sim$2 MW \\\\\n Radiation shielding & ( 750 kW $\\rightarrow$) & 4 MW \\\\\n Radioactive cooling water treatment\n & ( 600 kW $\\rightarrow$) & $\\sim$1.3 MW \\\\\n \\hline \\hline\n \\end{tabular}\n \\end{center}\n\\end{table}\n\\subsection{Near detector complex\\label{sec:NDcomplex}}\nThe accelerator neutrino event rate observed at Hyper-K depends on the\noscillation probability, neutrino flux, neutrino interaction\ncross-section, detection efficiency, and the detector fiducial mass of\nHyper-K. To extract estimates of the oscillation parameters from\ndata, one must model the neutrino flux, cross-section and detection\nefficiency with sufficient precision. In the case of the neutrino\ncross-section, the model must describe the exclusive differential\ncross-section that includes the dependence on the incident neutrino\nenergy, $E_{\\nu}$, the kinematics of the outgoing lepton, momentum\n$p_{l}$ and scattering angle $\\theta_{l}$, and the kinematics of final\nstate hadrons and photons. In our case, the neutrino energy is\ninferred from the lepton kinematics, while the reconstruction\nefficiencies depend on the hadronic final state as well.\n\nThe near detectors measure the neutrino interaction rates close enough to the neutrino\nproduction point so that oscillation effects are negligible. The prediction of \nevent rates at Hyper-K for a given set of oscillation parmeters will be precisely\nconstrained by event rates measured in the near detector and the flux simulation\nbased on hadron production data from NA61\/SHINE and other hadron production experiments.\nOur approach to using near detector data will build on the experience of\nT2K while considering new near detectors that address\nlimitations in reducing neutrino cross section modelling uncertainties\nwith the current T2K near detector suite.\n\nThe near detectors should be capable of measuring the signal and\nbackground processes relevant for neutrino oscillation measurements\nmade using the accelerator produced neutrinos. The processes include:\n\\begin{itemize}\n\\item The charged current interactions with no detected final state\n pion (CC0$\\pi$) that are the signal channel for the oscillation\n measurements in Hyper-K.\n\\item The intrinsic electron neutrino component of the beam from muon\n and kaon decays, which is a background for the electron\n (anti)neutrino appearance signal.\n\\item The neutral current interactions with $\\pi^{0}$ production\n (NC$\\pi^{0}$) that are a background for the electron (anti)neutrino\n appearance signal.\n\\item The wrong-sign charged current processes (neutrinos in the\n antineutrino beam and vise versa) which are a background in the CP\n violation measurement.\n\\end{itemize}\nIn addition to measuring these processes, the near detectors should be\ndesigned to maximize the cancellation of systematic uncertainties when\nextrapolating from measured event rates in the near detector to\npredict the event rate at Hyper-K. Hence, the near detector should be\nable to make measurements with the same angular acceptance (4$\\pi$)\nand target nuclei (H$_2$O) as Hyper-K. Another source of uncertainty\nin the extrapolation is the difference between the near and far\ndetector neutrino spectra due to oscillations, which can amplify\nsystematic errors related to the modeling of the relationship between\nthe final state lepton kinematics and the incident neutrino\nenergy~\\cite{Martini:2012fa,Lalakulich:2012hs,Martini:2012uc}. The\nnear detectors should be able to sufficiently constrain the modeling\nof the dependence of lepton kinematics on neutrino energy over the\nrelevant neutrino energy range.\n\nThe near detectors can also be used to constrain important neutrino\ninteraction modes for atmospheric neutrino and nucleon decay\nmeasurements at Hyper-K. For example, Hyper-K may use neutron\ncaptures on Gd or H to statistically separate neutrinos and\nantineutrinos in the atmospheric measurements, or to reject\natmospheric neutrino backgrounds in the nucleon decay measurements.\nThe neutron multiplicities produced in the interactions of neutrinos\nand antineutrinos with energy of $\\mathcal{O}($1 GeV$)$ can be\nmeasured in the near detectors. The dominant sources of uncertainty\nin the determination of the mass hierarchy and $\\theta_{23}$ quadrant\nwith atmospheric neutrinos are uncertainties in the neutrino to\nanti-neutrino cross section ratio for both CCQE and single pion\nproduction modes, the axial vector nucleon form factor, the\nneutrino-tau cross section, and the DIS cross section model.\nNear detector measurements that would constrain these uncertainties\nfor interactions on water, have the potential to significantly improve\nthe sensitivity of these atmospheric neutrino measurements.\nThe near detectors can also be used to measure the interaction modes for nucleon decay\nbackgrounds, including the CC$\\pi^{0}$ background to the $e^{+}(\\mu^{+})\\pi^{0}$ mode and the kaon production background to the $K^{+}\\nu$ mode.\n\nTo summarize, the near and intermediate detectors for Hyper-K should cover the full momentum and angular acceptance of the far detector, include homogenous H$_2$O targets to make precision measurements on H$_2$O, have sign selection capability to measure wrong sign backgrounds, be capable of directly measuring intrinsic $\\nu_e,\\bar{\\nu_e}$ and NC$\\pi^0$ backgrounds, be capable of reconstructing exclusive final states with low particle thresholds, be capable of measuring the $\\nu_e,\\bar{\\nu_e}$ cross sections, be capable of measuring the final state neutron multiplicities and be capable of measurements at multiple off-axis angles with varying peak neutrino energies. We have not identified a single detector technology that can achieve all of these capabilities. In the minimum configuration, it is necessary to have both a magnetized tracking detector and kiloton scale water Cherenkov detector. The magnetized tracking detector may provide full momentum and angular acceptance, sign selection, reconstruction of exclusive final states with low particle thresholds, measurement of the $\\nu_e,\\bar{\\nu_e}$ rates and off-axis spanning measurements. The water Cherenkov detector may provide full angular acceptance, a homogenous water target, direct measurement of the intrinsic $\\nu_e,\\bar{\\nu_e}$ and NC$\\pi^0$ backgrounds, measurement of the $\\nu_e,\\bar{\\nu_e}$ cross sections, measurements of final state neutron multiplicities and the off-axis spanning measurements. Hence, in the following text we present the upgrade for the current ND280 magnetized tracking detector, new tracking detector technologies, and intermediate water Cherenkov detectors as potential components of the Hyper-K near and intermediate detector suite.\n\n\n \\subsubsection{The ND280 Detector Suite}\n \\input{jparc\/nd280.tex} \\label{subsection:nd280}\n\n \n \\subsubsection{Intermediate detector}\n \\input{jparc\/intermediate.tex}\n\n\n\\subsection{Summary}\nThis section has outlined the performance and requirements of the\naccelerator complex, neutrino beamline and near detectors at J-PARC\nthat will be required for the Hyper-K physics program. The J-PARC\naccelerator chain has achieved 475 kW beam power extracted to the\nneutrino beamline. The accelerator upgrade plan, which includes the\nupgrade of the MR magnet powers supplies and RF, is expected to achieve\n1.3\\,MW beam operation with $3.2\\times10^{14}$ protons per pulse, as\nearly as 2026.\n\nThe neutrino beamline components require some upgrades to accept the\nrepetition rate, proton intensity and total beam power necessary to\nachieve 1.3\\,MW at $3.2\\times10^{14}$ protons per pulse. To achieve\nthe 1.16 Hz operation, each magnetic horn requires an individual power\nsupply utilizing an energy recovery scheme and low\ninductance\/resistance striplines. \nThe treatment facilities for activated cooling water will be expanded to accept up to 2 MW operation as well. \nThe current beam window and\ntarget are rated to $3.3\\times10^{14}$ ppp, however their lifetime at\n$3.2\\times10^{14}$ ppp and 1.16 Hz will be studied and upgrades may be\nnecessary.\n\nThe current T2K near detectors, including ND280 and INGRID, are used\nto control neutrino flux and cross-section systematic errors at the\n$\\sim$5--6\\% level. Further upgrades to the ND280 data analyses with\nwater target measurements and large angle tracks will reduce the\nsystematic error, although the ultimate performance may be limited by\nthe relatively low water fraction and low efficiency for large angle\ntrack reconstruction. Upgrades to ND280 are being considered by T2K\nand these include a high pressure TPC, the WAGASCI water\/scintillator\n3D grid detector and emulsion detectors. A reconfiguration of the TPC\ngeometry is also being considered to give better reconstruction at\nhigh angles. It is expected that some of these upgrades may be\ncarried out during the T2K experiment and Hyper-K may benefit from\ntheir continued use. If they are not implemented during T2K, these\nND280 upgrades as well as the continued operation of ND280 are an\nexpected area for international contributions to Hyper-K.\n\nAn intermediate water Cherenkov detector provides a necessary\ncomplement to the ND280 magnetized tracking detector in order to\nconstrain all the dominant systematics at the precision required. The\nWC detector requires a new facility off of the J-PARC site and the\nexcavation of a new pit to house the detector. \n\n\n\\subsubsection*{#1}}\n\n\\pagestyle{headings}\n\\markright{Reference sheet: \\texttt{natbib}}\n\n\\usepackage{shortvrb}\n\\MakeShortVerb{\\|}\n\n\\begin{document}\n\\thispagestyle{plain}\n\n\\newcommand{\\textsc{Bib}\\TeX}{\\textsc{Bib}\\TeX}\n\\newcommand{\\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}}{\\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}}\n\\begin{center}{\\bfseries\\Large\n Reference sheet for \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ usage}\\\\\n \\large(Describing version \\fileversion\\ from \\filedate)\n\\end{center}\n\n\\begin{quote}\\slshape\nFor a more detailed description of the \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ package, \\LaTeX\\ the\nsource file \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\texttt{.dtx}.\n\\end{quote}\n\\head{Overview}\nThe \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ package is a reimplementation of the \\LaTeX\\ |\\cite| command,\nto work with both author--year and numerical citations. It is compatible with\nthe standard bibliographic style files, such as \\texttt{plain.bst}, as well as\nwith those for \\texttt{harvard}, \\texttt{apalike}, \\texttt{chicago},\n\\texttt{astron}, \\texttt{authordate}, and of course \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}.\n\n\\head{Loading}\nLoad with |\\usepackage[|\\emph{options}|]{|\\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}|}|. See list of\n\\emph{options} at the end.\n\n\\head{Replacement bibliography styles}\nI provide three new \\texttt{.bst} files to replace the standard \\LaTeX\\\nnumerical ones:\n\\begin{quote}\\ttfamily\n plainnat.bst \\qquad abbrvnat.bst \\qquad unsrtnat.bst\n\\end{quote}\n\\head{Basic commands}\nThe \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ package has two basic citation commands, |\\citet| and\n|\\citep| for \\emph{textual} and \\emph{parenthetical} citations, respectively.\nThere also exist the starred versions |\\citet*| and |\\citep*| that print\nthe full author list, and not just the abbreviated one.\nAll of these may take one or two optional arguments to add some text before\nand after the citation.\n\\begin{quote}\n\\begin{tabular}{l@{\\quad$\\Rightarrow$\\quad}l}\n |\\citet{jon90}| & Jones et al. (1990)\\\\\n |\\citet[chap.~2]{jon90}| & Jones et al. (1990, chap.~2)\\\\[0.5ex]\n |\\citep{jon90}| & (Jones et al., 1990)\\\\\n |\\citep[chap.~2]{jon90}| & (Jones et al., 1990, chap.~2)\\\\\n |\\citep[see][]{jon90}| & (see Jones et al., 1990)\\\\\n |\\citep[see][chap.~2]{jon90}| & (see Jones et al., 1990, chap.~2)\\\\[0.5ex]\n |\\citet*{jon90}| & Jones, Baker, and Williams (1990)\\\\\n |\\citep*{jon90}| & (Jones, Baker, and Williams, 1990)\n\\end{tabular}\n\\end{quote}\n\\head{Multiple citations}\nMultiple citations may be made by including more than one\ncitation key in the |\\cite| command argument.\n\\begin{quote}\n\\begin{tabular}{l@{\\quad$\\Rightarrow$\\quad}l}\n |\\citet{jon90,jam91}| & Jones et al. (1990); James et al. (1991)\\\\\n |\\citep{jon90,jam91}| & (Jones et al., 1990; James et al. 1991)\\\\\n |\\citep{jon90,jon91}| & (Jones et al., 1990, 1991)\\\\\n |\\citep{jon90a,jon90b}| & (Jones et al., 1990a,b)\n\\end{tabular}\n\\end{quote}\n\n\\head{Numerical mode}\nThese examples are for author--year citation mode. In numerical mode, the\nresults are different.\n\\begin{quote}\n\\begin{tabular}{l@{\\quad$\\Rightarrow$\\quad}l}\n |\\citet{jon90}| & Jones et al. [21]\\\\\n |\\citet[chap.~2]{jon90}| & Jones et al. [21, chap.~2]\\\\[0.5ex]\n |\\citep{jon90}| & [21]\\\\\n |\\citep[chap.~2]{jon90}| & [21, chap.~2]\\\\\n |\\citep[see][]{jon90}| & [see 21]\\\\\n |\\citep[see][chap.~2]{jon90}| & [see 21, chap.~2]\\\\[0.5ex]\n |\\citep{jon90a,jon90b}| & [21, 32]\n\\end{tabular}\n\\end{quote}\n\\head{Suppressed parentheses}\nAs an alternative form of citation, |\\citealt| is the same as |\\citet| but\n\\emph{without parentheses}. Similarly, |\\citealp| is |\\citep| without\nparentheses.\n\nThe |\\citenum| command prints the citation number, without parentheses, even\nin author--year mode, and without raising it in superscript mode. This is\nintended to be able to refer to citation numbers without superscripting them.\n\n\\begin{quote}\n\\begin{tabular}{l@{\\quad$\\Rightarrow$\\quad}l}\n |\\citealt{jon90}| & Jones et al.\\ 1990\\\\\n |\\citealt*{jon90}| & Jones, Baker, and Williams 1990\\\\\n |\\citealp{jon90}| & Jones et al., 1990\\\\\n |\\citealp*{jon90}| & Jones, Baker, and Williams, 1990\\\\\n |\\citealp{jon90,jam91}| & Jones et al., 1990; James et al., 1991\\\\\n |\\citealp[pg.~32]{jon90}| & Jones et al., 1990, pg.~32\\\\\n |\\citenum{jon90}| & 11\\\\\n |\\citetext{priv.\\ comm.}| & (priv.\\ comm.)\n\\end{tabular}\n\\end{quote}\nThe |\\citetext| command\nallows arbitrary text to be placed in the current citation parentheses.\nThis may be used in combination with |\\citealp|.\n\\head{Partial citations}\nIn author--year schemes, it is sometimes desirable to be able to refer to\nthe authors without the year, or vice versa. This is provided with the\nextra commands\n\\begin{quote}\n\\begin{tabular}{l@{\\quad$\\Rightarrow$\\quad}l}\n |\\citeauthor{jon90}| & Jones et al.\\\\\n |\\citeauthor*{jon90}| & Jones, Baker, and Williams\\\\\n |\\citeyear{jon90}| & 1990\\\\\n |\\citeyearpar{jon90}| & (1990)\n\\end{tabular}\n\\end{quote}\n\\head{Forcing upper cased names}\nIf the first author's name contains a \\textsl{von} part, such as ``della\nRobbia'', then |\\citet{dRob98}| produces ``della Robbia (1998)'', even at the\nbeginning of a sentence. One can force the first letter to be in upper case\nwith the command |\\Citet| instead. Other upper case commands also exist.\n\\begin{quote}\n\\begin{tabular}{rl@{\\quad$\\Rightarrow$\\quad}l}\n when & |\\citet{dRob98}| & della Robbia (1998) \\\\\n then & |\\Citet{dRob98}| & Della Robbia (1998) \\\\\n & |\\Citep{dRob98}| & (Della Robbia, 1998) \\\\\n & |\\Citealt{dRob98}| & Della Robbia 1998 \\\\\n & |\\Citealp{dRob98}| & Della Robbia, 1998 \\\\\n & |\\Citeauthor{dRob98}| & Della Robbia\n\\end{tabular}\n\\end{quote}\nThese commands also exist in starred versions for full author names.\n\n\\head{Citation aliasing}\nSometimes one wants to refer to a reference with a special designation,\nrather than by the authors, i.e. as Paper~I, Paper~II. Such aliases can be\ndefined and used, textual and\/or parenthetical with:\n\\begin{quote}\n\\begin{tabular}{lcl}\n |\\defcitealias{jon90}{Paper~I}|\\\\\n |\\citetalias{jon90}| & $\\Rightarrow$ & Paper~I\\\\\n |\\citepalias{jon90}| & $\\Rightarrow$ & (Paper~I)\n\\end{tabular}\n\\end{quote}\nThese citation commands function much like |\\citet| and |\\citep|: they may\ntake multiple keys in the argument, may contain notes, and are marked as\nhyperlinks.\n\\head{Selecting citation style and punctuation}\nUse the command |\\setcitestyle| with a list of comma-separated\nkeywords (without spaces) as argument.\n\\begin{itemize}\n\\item\n Citation mode: |authoryear| or |numbers| or |super|\n \n\\item\n Braces: |round| or |square| or |open={|\\emph{char}|},close={|\\emph{char}|}|\n \n\\item\n Between citations: |semicolon| or |comma| or |citesep={|\\emph{char}|}|\n \n\\item\n Between author and year: |aysep={|\\emph{char}|}|\n \n\\item\n Between years with common author: |yysep={|\\emph{char}|}|\n \n\\item\n Text before post-note: |notesep={|\\emph{text}|}|\n \n\\end{itemize}\nDefaults are |authoryear|, |round|, |comma|, |aysep={;}|, |yysep={,}|,\n|notesep={, }|\n\nExample~1, |\\setcitestyle{square,aysep={},yysep={;}}| changes the author--year\noutput of\n\\begin{quote}\n |\\citep{jon90,jon91,jam92}|\n\\end{quote}\ninto [Jones et al. 1990; 1991, James et al. 1992].\n\nExample~2, |\\setcitestyle{notesep={; },round,aysep={},yysep={;}}| changes the output of\n\\begin{quote}\n |\\citep[and references therein]{jon90}|\n\\end{quote}\ninto (Jones et al. 1990; and references therein).\n\n\\head{Other formatting options}\nRedefine |\\bibsection| to the desired sectioning command for introducing\nthe list of references. This is normally |\\section*| or |\\chapter*|.\n\nRedefine |\\bibpreamble| to be any text that is to be printed after the heading but\nbefore the actual list of references.\n\nRedefine |\\bibfont| to be a font declaration, e.g.\\ |\\small| to apply to\nthe list of references.\n\nRedefine |\\citenumfont| to be a font declaration or command like |\\itshape|\nor |\\textit|.\n\nRedefine |\\bibnumfmt| as a command with an argument to format the numbers in\nthe list of references. The default definition is |[#1]|.\n\nThe indentation after the first line of each reference is given by\n|\\bibhang|; change this with the |\\setlength| command.\n\nThe vertical spacing between references is set by |\\bibsep|; change this with\nthe |\\setlength| command.\n\n\\head{Automatic indexing of citations}\nIf one wishes to have the citations entered in the \\texttt{.idx} indexing\nfile, it is only necessary to issue |\\citeindextrue| at any point in the\ndocument. All following |\\cite| commands, of all variations, then insert\nthe corresponding entry to that file. With |\\citeindexfalse|, these\nentries will no longer be made.\n\n\\head{Use with \\texttt{chapterbib} package}\n\nThe \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ package is compatible with the \\texttt{chapterbib} package\nwhich makes it possible to have several bibliographies in one document.\n\nThe package makes use of the |\\include| command, and each |\\include|d file\nhas its own bibliography.\n\nThe order in which the \\texttt{chapterbib} and \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ packages are loaded\nis unimportant.\n\nThe \\texttt{chapterbib} package provides an option \\texttt{sectionbib}\nthat puts the bibliography in a |\\section*| instead of |\\chapter*|,\nsomething that makes sense if there is a bibliography in each chapter.\nThis option will not work when \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\ is also loaded; instead, add\nthe option to \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}.\n\nEvery |\\include|d file must contain its own\n|\\bibliography| command where the bibliography is to appear. The database\nfiles listed as arguments to this command can be different in each file,\nof course. However, what is not so obvious, is that each file must also\ncontain a |\\bibliographystyle| command, with possibly differing arguments.\n\nAs of version~8.0, the citation style, including mode (author--year or\nnumerical) may also differ between chapters. The |\\setcitestyle| command\ncan be issued at any point in the document, in particular in different\nchapters.\n\\head{Sorting and compressing citations}\nDo not use the \\texttt{cite} package with \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}; rather use one of the\noptions \\texttt{sort}, \\texttt{compress}, or \\texttt{sort\\&compress}.\n\nThese also work with author--year citations, making multiple citations appear\nin their order in the reference list.\n\n\n\\head{Merged Numerical References}\nDo not use the \\texttt{mcite} package with \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}; rather use the package option \\texttt{merge}.\n\n\nWith this option in effect, citation keys within a multiple |\\citep| command\nmay contain a leading * that causes them to be merged in the bibliography\ntogether with the previous citation as a single entry with a single reference\nnumber. For example, |\\citep{feynmann,*salam,*epr}| produces a single number,\nand all three references are listed in the bibliography under one entry with\nthat number.\n\nThe \\texttt{elide} option also activates the merging features, but also sees\nto it that common parts of the merged references (e.g., authors) are not\nrepeated but are written only once in the single bibliography entry.\n\nThe \\texttt{mcite} option turns off the merging and eliding features, but\nallows the special syntax (the * and optional inserted texts) to be ignored.\n\nThese functions are available only to numerical-mode citations, and only when\nused parenthetically, similar to the restrictions on \\texttt{sort} and\n\\texttt{compress}.\n\nThey also require special \\texttt{.bst} files, as provided for example by the\nAmerican Physical Society for their REV\\TeX\\ class.\n\\head{Long author list on first citation}\nUse option \\texttt{longnamesfirst} to have first citation automatically give\nthe full list of authors.\n\nSuppress this for certain citations with |\\shortcites{|\\emph{key-list}|}|,\ngiven before the first citation.\n\n\\head{Local configuration}\nAny local recoding or definitions can be put in \\texttt{#1}\\def\\filedate{#2}\\def\\fileversion{#3}}\\texttt{.cfg} which\nis read in after the main package file.\n\n\\head{Options that can be added to \\texttt{\\char`\\\\ usepackage}}\n\\begin{description}\n\\item[\\ttfamily round] (default) for round parentheses;\n\\item[\\ttfamily square] for square brackets;\n\\item[\\ttfamily curly] for curly braces;\n\\item[\\ttfamily angle] for angle brackets;\n\\item[\\ttfamily semicolon] (default) to separate multiple citations with\n semi-colons;\n\\item[\\ttfamily colon] the same as \\texttt{semicolon}, an earlier mistake in\n terminology;\n\\item[\\ttfamily comma] to use commas as separators;\n\\item[\\ttfamily authoryear] (default) for author--year citations;\n\\item[\\ttfamily numbers] for numerical citations;\n\\item[\\ttfamily super] for superscripted numerical citations, as in\n \\textsl{Nature};\n\\item[\\ttfamily sort] orders multiple citations into the sequence in\n which they appear in the list of references;\n\\item[\\ttfamily sort\\&compress] as \\texttt{sort} but in addition multiple\n numerical citations are compressed if possible (as 3--6, 15);\n\\item[\\ttfamily compress] to compress without sorting, so compression only\n occurs when the given citations would produce an ascending sequence of\n numbers;\n\\item[\\ttfamily longnamesfirst] makes the first citation of any reference\n the equivalent of the starred variant (full author list) and subsequent\n citations normal (abbreviated list);\n\\item[\\ttfamily sectionbib] redefines |\\thebibliography| to issue\n |\\section*| instead of |\\chapter*|; valid only for classes with a\n |\\chapter| command; to be used with the \\texttt{chapterbib} package;\n\\item[\\ttfamily nonamebreak] keeps all the authors' names in a citation on\n one line; causes overfull hboxes but helps with some \\texttt{hyperref}\n problems;\n\\item[\\ttfamily merge] to allow the * prefix to the citation key,\n and to merge such a citation's reference with that of the previous\n citation;\n\\item[\\ttfamily elide] to elide common elements of merged references, like\n the authors or year;\n\\item[\\ttfamily mcite] to recognize (and ignore) the merging syntax.\n\\end{description}\n\\end{document}\n\n\\subsection{Other astrophysical neutrino sources}\\label{section:astro}\n \n\\subsubsection{Solar flare}\nSolar flares are the most energetic bursts which occur in the solar\nsurface. Explosive release of energy stored in solar magnetic fields\nis caused by magnetic reconnections, resulting in plasma heating,\nparticle accelerations, and emission of synchrotron X-rays or charged\nparticles from the solar surface. In a large flare, an energy of\n10$^{33}$ ergs is emitted over 10's of minutes, and the accelerated\nprotons can reach energies greater than 10 GeV. Such high energy\nprotons can produce pions by nuclear interactions in the solar\natmosphere. Evidence of such nuclear interactions in the solar\natmosphere are obtained via observations of solar neutrons, 2.2 MeV\ngamma rays from neutron captures on protons, nuclear de-excitation\ngamma rays, and possible $>100$ MeV gamma rays from neutral pion\ndecays. Thus, it is likely that neutrinos are also emitted by the\ndecay of mesons following interactions of accelerated particles.\nDetection of neutrinos from a solar flare was first discussed in\n1970's by R.Davis~\\cite{dav, bacall_sf}, but no significant signal has\nyet been found~\\cite{aglietta,hirata}. There have been some estimates\nof the number of neutrinos which could be observed by large water\nCherenkov detectors~\\cite{fargion,kocharov}. According\nto \\cite{fargion}, about 6-7 neutrinos per tank will be observed at\nHyper-Kamiokande during a solar flare as large as the one in 20\nJanuary 2005, although the expected numbers have large uncertainties.\nTherefore, regarding solar flares our first astrophysics goal is to\ndiscover solar flare neutrinos with Hyper-K. This will give us\nimportant information about the mechanism of the particle acceleration\nat work in solar flares.\n\n\n\\subsubsection{Gamma-Ray Burst Jets and Newborn Pulsar Winds}\nGamma-ray bursts (GRBs) are the most luminous astrophysical phenomena\nwith the isotropically-equivalent gamma-ray luminosity,\n$L_\\gamma\\sim{10}^{52}~{\\rm erg}~{\\rm s}^{-1}$, which typically occur\nat cosmological distance. Prompt gamma rays are observed in the MeV\nrange, and their spectra can be fitted by a smoothened broken power\nlaw~\\cite{grbrev}. The prompt emission comes from a relativistic jet\nwith the Lorentz factor of $\\Gamma\\sim{10}^{2}-{10}^{3}$, which is\npresumably caused by a blackhole with an accretion disk or\na fast-spinning, strongly-magnetized neutron star. Observed gamma-ray\nlight curves are highly variable down to $\\sim1$~ms, suggesting\nunsteady outflows. However, GRB central engines and their radiation\nmechanism are still unknown, and GRBs have been one of the biggest\nmysteries in high-energy astrophysics.\n\nInternal shocks are naturally expected for such unsteady jets, and the\njet kinetic energy can be converted into radiation via shock\ndissipation. In the ``classical'' internal shock\nscenario~\\cite{rm94}, observed gamma rays are attributed to\nsynchrotron emission from non-thermal electrons accelerated at\ninternal shocks. It has been suggested that GRBs may also be\nresponsible for ultrahigh-energy cosmic rays (CRs), and TeV-PeV\nneutrinos have been predicted as a smoking gun of CR acceleration in\nGRBs~\\cite{grbnu1}. One of the key advantages in GRB neutrino\nsearches is that atmospheric backgrounds can significantly be reduced\nthanks to space- and time-coincidence, but no high-energy neutrino\nsignals correlated with GRBs have been found in any neutrino detector\nincluding Super-K~\\cite{skgrb} and IceCube~\\cite{icecubegrb}.\n\nOn the other hand, the recent theoretical and observational progress\nhas suggested that the above classical scenario has troubles in\nexplaining observational features such as the low-energy photon\nspectrum. Alternatively, the photospheric scenario, where prompt\ngamma rays are generated around or under the ``photosphere'' (where\nthe Compton scattering optical depth is unity), has become more\npopular~\\cite{photosphere1,photosphere2,photosphere3}. Indeed,\nobservations have indicated a thermal-like component in GRB\nspectra~\\cite{fermigrb,fermigrb2}. Energy dissipation may be caused\nby inelastic nucleon-neutron\ncollisions~\\cite{neutron1,neutron2,neutron3}, and neutrons can\nnaturally be loaded by GRB central engines either\nblackhole-accretion-disk system or strongly-magnetized neutron star.\nThen, quasi-thermal GeV-TeV neutrino emission is an inevitable consequence of such inelastic nucleon-neutron collisions~\\cite{mur+13}. Since neutrinos easily leave the flow, predictions for these neutrinos are insensitive to details of gamma-ray spectra. \nHyper-K will enable us to search these quasi-thermal GeV-TeV neutrinos\nfrom GRB jets, and it also has an advantage over \nIceCube (that is suitable for higher-energy $>10$-$100$~GeV\nneutrinos). The GeV-TeV neutrino detection is feasible if a GRB\nhappens at $\\lesssim100$~Mpc, and successful detections should allow\nus to discriminate among prompt emission mechanisms and probe the jet\ncomposition, leading to a breakthrough in understanding GRB physics.\nHowever, GRBs are rare astrophysical phenomena, so we have little\nchance to expect such a nearby bright burst in the next 10-100 years.\nMuch more promising targets as high-energy neutrino sources would be\nenergetic supernovae driven by relativistic\noutflows~\\cite{mw01,rmw04,ab05,mi13}. A significant fraction of GRB\njets may fail to puncture their progenitor star, and photon emission\nfrom the jets can easily be hidden. Indeed, theoretical studies\nrevealed the existence of conditions for a jet to make a successful\nGRB. ``Choked jets'' or ``failed GRBs'' are naturally predicted when\nthe jet luminosity is not sufficient or the jet duration is too short\nor the progenitor is too big. The choked jets can explain\ntrans-relativistic supernovae or low-luminosity GRBs, which show\nintermediate features between GRBs and supernovae~\\cite{sod+06}.\n\nThe neutrino event rate expected in Hyper-K depends on the\nisotropically-equivalent dissipation energy ${\\mathcal E}_{\\rm\ndiss}^{\\rm iso}$, Lorentz factor $\\Gamma$, and distance $d$. For\n${\\mathcal E}_{\\rm diss}^{\\rm iso}={10}^{53}~{\\rm erg}~{\\rm s}^{-1}$,\n$\\Gamma=10$ and $d=10$~Mpc, the characteristic energy of quasi-thermal\nGeV-TeV neutrinos is $E_\\nu^{\\rm qt}\\sim3$~GeV~\\cite{mur+13}. The\nneutrino-nucleon cross section for the charged-current interaction at\n1~GeV is $\\sim0.6\\times {10}^{-38}~{\\rm cm}^2$ (averaged over $\\nu$\nand $\\bar{\\nu}$), so the effective area of Hyper-K is\n$\\sim2\\times{10}^{-3}~{\\rm cm}^2$ at 1~GeV. Then, Hyper-K will be\nable to detect $\\sim5$ signal events from such a jet-driven supernova.\nSuccessful detections enable us to probe jet physics that cannot be\ndirectly studied by electromagnetic observations. Neutrinos enable us\nto understand how jets are accelerated and what the jet composition\nis, and will give us crucial keys to the mysterious connection between\nGRBs and energetic supernovae~\\cite{tho+04}. Also, in principle,\nmatter effects in neutrino oscillation could be\ninvestigated~\\cite{fs08,rs10}. Moreover, we will able to study how CR\nacceleration operates in dense radiation environments inside a GRB\nprogenitor star. Whether CRs are accelerated or not depends on\nproperties of shocks. The conventional shock acceleration mechanism\ncan effectively operate only if the shock is radiation-unmediated\ncollisionless~\\cite{mi13}. On the other hand, when the shock is\nmediated by radiation, the so-called neutron-proton-converter\nacceleration mechanism can work efficiently~\\cite{npc,kas+13}, which\nboosts the energy of quasi-thermal neutrinos produced by\nnucleon-neutron collisions~\\cite{mur+13}.\n\nAs discussed above, relativistic outflows containing neutrons should\nnaturally lead to GeV-TeV neutrino production, but the outflows do not\nhave to be jets. Another interesting case may be realized when a\nsupernova explosion leaves a fast-spinning neutron star. Neutrons are\nloaded in the proto-neutron star wind via neutrino heating. Around\nthe base of the outflow, the particle density is so high that neutrons\nand ions are tightly coupled via elastic collisions. Neutrons should\nbe accelerated together with ions as the Poynting-dominated pulsar\nwind is accelerated.\nOnce the outflow becomes relativistic enough to exceed the pion-production threshold, inelastic collisions naturally occur as the main dissipation process of relativistic neutrons. \nThe neutrons then interact with the material decelerated by the shock\nand possibly with the overlying stellar material, producing 0.1-1~GeV\nneutrinos~\\cite{mur+14}. Detecting this signal would probe the\notherwise completely obscured process of jet acceleration and the\nphysics of rotating and magnetized proto-neutron star birth during the\ncore collapse of massive stars. Hyper-K may expect $\\sim20-30~({\\mathcal\nE}_{\\nu}^{\\rm iso}\/{10}^{48}~{\\rm erg})$ events for a core-collapse\nsupernova at 10~kpc. In addition, Hyper-K could also allow us to see\n$\\sim10-100$~MeV neutrinos through the $\\bar{\\nu}_ep\\rightarrow e^+n$\nchannel. However, detection of these lower energy neutrinos would be\nmore difficult because of the smaller cross sections at lower energies\nand because the signal may be buried in the exponential tail of\nthermal MeV neutrinos from the proto-neutron star.\n\nTo detect high-energy neutrino signals from hidden GRB jets or newborn\npulsar winds embedded in supernovae, it is crucial to reduce\natmospheric backgrounds using space and time coincidence, so\ninformation at other wavelengths is relevant. The atmospheric\nneutrino background at GeV energies is $\\approx1.3\\times{10}^{-2}~{\\rm\nGeV}~{\\rm cm}^{-2}~{\\rm s}^{-1}~{\\rm sr}^{-1}$ for $\\nu_e+\\bar{\\nu}_e$\nand $\\approx2.6\\times{10}^{-2}~{\\rm GeV}~{\\rm cm}^{-2}~{\\rm\ns}^{-1}~{\\rm sr}^{-1}$ for $\\nu_\\mu+\\bar{\\nu}_\\mu$,\nrespectively~\\cite{hon+11}. We may take the time window of $t_{\\rm\nthin}\\sim10-100$~s after the explosion time that is measurable with\nMeV neutrinos or possibly gravitational waves. The localization is\npossible by follow-up observations at x-ray, optical, and infrared\nbands. The atmospheric background flux in the typical angular and\ntime window is $\\sim2\\times{10}^{-3}~{\\rm erg}~{\\rm cm}^{-2}$, which\ncan be low enough for a nearby supernova.\n\nNote that it is critical to have large volume detectors for the\npurpose of detecting GeV-TeV neutrinos. The present Super-K and\nliquid scintillator detectors such as JUNO and RENO-50 are too small\nto detect high-energy signals from astrophysical objects especially if\nextragalactic, and much bigger detectors such as Hyper-K and PINGU are\nnecessary to have a good chance to hunt high-energy neutrinos from\nGRBs and energetic supernovae. Because of the atmospheric background,\nsensitivities above GeV energies are typically essential but searches\nfor neutrinos below $\\sim1$~GeV could also be useful for nearby\nevents.\n\n\\subsubsection{Neutrinos from gravitational-wave sources}\n\n100 years after the prediction by Einstein, gravitational waves (GWs)\nhave been detected by advanced-LIGO in 2015~\\cite{YS-ref1}. This\nhas allowed us to conduct multi-messenger observations of astrophysical\nobjects via multiple signals, i.e., electromagnetic (EM) waves (from\nradio to gamma-rays), neutrinos (from MeV to PeV) and GWs\n(kHz). Some strong GW emitters are also expected to be strong sources of\nneutrinos, e.g. supernovae and gamma-ray bursts. The searches\nfor neutrino counterparts to GW sources have been\nperformed~\\cite{YS-ref2}, including a search done by Super-Kamiokande\ncollaboration~\\cite{YS-ref3}, but there has been no clear counterpart\nfound.\nThis is consistent with the theoretical prediction because these GW\nsources (GW150914 and GW151226) are binary black-hole mergers.\nAlthough binary black-hole mergers as GW sources are not expected to\ngenerate other detectable signals, the mergers that contain at least\none neutron star (i.e. black hole-neutron star binary or neutron\nstar-neutron star binary) could emit other signals, includeing $\\sim\n10^{53}$ erg of neutrinos~\\cite{YS-ref4}. Indeed, a number of EM\ncounterparts associated with GW170817 (neutron-star binary merger)\nwere detected, including GRB170817A~\\cite{YS-ref5,YS-ref6}. A search\nfor neutrinos by Super-Kamiokande was also reported~\\cite{YS-ref7}, which did\nnot detect any coincident neutrino. Hyper-Kamiokande has the potential to\ndetect thermal neutrinos from nearby ($\\lesssim 10$Mpc) neutron\nstar meger events.\n\nDepending on the event rates, these objects would contribute to the\nrelic neutrino spectrum. The central engine of gamma-ray bursts are\nalso candidates of strong emitters of neutrinos and GWs. It is\nevident that there are ultra-relativistic jets which are driven by the\ncentral engine. However, the mechanism that generates the jet is\nstill unclear. If this jet is driven by neutrino annihilation, which\nis one of the promising scenarios, concurrent observations of\nneutrinos and GWs will be important probe of the very central part of\nthe violent cosmic explosions at Hyper-Kamiokande era~\\cite{YS-ref8}.\n\n\\subsection{Atmospheric neutrinos}\\label{section:atmnu}\n\n \\input{physics-atmnu\/intro.tex}\n\n \\subsubsection{Neutrino oscillation studies (MH, \\(\\theta_{23}\\) octant, $CP$ phase)}\n \n \\input{physics-atmnu\/atmospheric_study.tex}\n\n \\subsubsection{Combination with Beam Neutrinos}\n\n \\input{physics-atmnu\/with_beam.tex}\n\n \\subsubsection{Exotic Oscillations And Other Topics}\n\n \\input{physics-atmnu\/exotic.tex}\n\n\n\n\n\n\n\\subsection{Dark matter searches}\\label{section:darkmatter}\n \n \\input{physics-darkmatter\/intro.tex}\n\n \\input{physics-darkmatter\/wimp.tex}\n\n\n\n\n\\subsubsection{Search for WIMPs at the Galactic Center}\n\nDark matter trapped in the gravitational potential of galaxies is said\nto form a halo. Halo models predict dark matter density distributions\nthat peak sharply near the center of a given galaxy and drop with\nradial distance. For example, for the Milky Way galaxy the expected\ndensity distribution at the position of our solar system, $r =\n8.5$~kpc, is roughly 1000 times smaller than that at the galactic\ncenter in the NFW model~\\cite{Navarro:1995iw}. When simulating the\nexpected signal distribution expected at Hyper-Kamiokande a diffuse\ndark matter profile following the full NFW density distribution is\nassumed and accordingly the signal is expected to arise primarily from\nthe galactic center.\n\n\\begin{figure}[thb]\n \\begin{center}\n \\includegraphics[scale=0.55]{physics-darkmatter\/figures\/gc_signal_demo_bbar_beta_1pc_5_20GeV_cos.pdf}\n \\end{center}\n \\caption{Signal and background (blue) distributions used in the Hyper-K sensitivity study of dark matter \n annihilating via $\\chi\\chi \\rightarrow b \\bar b$ at the galactic center. \n Analysis samples are binned in $\\mbox{cos}\\theta_{gc}$, the direction to the galactic \n center.\n Two WIMP hypotheses are shown: $m_{\\chi} = 5 \\mbox{GeV\/c}^{2}$ in green and $m_{\\chi} = 20 \\mbox{GeV\/c}^{2}$\n in red. \n All distributions have been area normalized with the WIMP normalization taken to 5\\% of the \n background MC.\n }\n\\label{fig:gc_signal_demo}\n\\end{figure}\n\n\nThe differential neutrino flux arising from WIMP annihilation into the\nstandard model particles listed above is simulated using the DarkSUSY\npackage~\\cite{Gondolo:2005we}, and the resulting spectrum adjusted to account for\noscillations on the way to the detector. An independent set of\natmospheric neutrino MC is reweighted to this distribution to give a\nreconstructed signal MC at Hyper-Kamiokande. In computing the\nsensitivity to an additional neutrino source, the analysis samples are\nrebinned in momentum and $\\mbox{cos}\\theta_{gc}$, where $\\theta_{gc}$\nis the angle between the galactic center position (RA = 266$^{\\circ}$,\nDec = -28$^{\\circ}$) and the reconstructed direction.\nFigure~\\ref{fig:gc_signal_demo} shows the $\\mbox{cos}\\theta_{gc}$\ndistributions of the atmospheric neutrino background and\ntwo WIMP hypotheses for each of the analysis samples. During the fit\nMC data sets without a WIMP signal are fit against a PDF built from\nthe atmospheric background MC plus a WIMP signal modified by a\nnormalization parameter, $\\beta$. Here the maximum value of $\\beta$\nthat is consistent with the background-only model within errors is\nused to compute the upper limit on the amount of additional neutrinos\nfrom the galactic center allowed after a 3.8~Mton$\\cdot$year exposure\nof Hyper-K.\n\n\n\\begin{figure}[thb]\n \\begin{center}\n \\includegraphics[width=0.90\\linewidth]{physics-darkmatter\/figures\/sigmaV-all-SKdata-HKsens-IceCube79-90CL-may2017.png}\n \\end{center}\n \\caption{Hyper-K's expected 90\\% C.L. limit on the WIMP velocity averaged \n annihilation cross section for several annihilation modes after \n a 3.8~Mton$\\cdot$year exposure overlaid with \n limits from several experiments. \n Limits are shown as a function of the dark matter mass. }\n\\label{fig:gc_wimps}\n\\end{figure}\n\nUnlike direct detection experiments this search method is insensitive\nto the WIMP-nucleon interaction cross section. Instead limits can be\nplaced on the velocity averaged self-annihilation cross section,\n$< \\sigma \\times v > $, where $v$ is the assumed velocity distribution\nof WIMPs in the halo. Figure~\\ref{fig:gc_wimps} shows the expected\nsensitivity of Hyper-K to WIMP annihilations at the galactic center.\nThe analysis makes use of potential signals\nin both $\\nu_{e}$- and $\\nu_{\\mu}$-enriched samples across the entire\nenergy range of atmospheric neutrinos and their energy and directional distributions\ncontribute to the sensitivity. \nHyper-Kamiokande's sensitivity to the WIMP velocity\naveraged self-annihilation cross section is expected to exceed that of\nSuper-Kamiokande's limits by factors of three to ten, depending on \nthe assumed WIMP mass and annihilation channel.\nUnlike other experiments,\nHyper-K's ability to reconstruct down to $O(100)$~MeV neutrino\ninteractions gives it unparalleled sensitivity to WIMPs with masses\nless than $\\sim$ 100 GeV\/$c^{2}$.\n\n\\subsubsection{Search for WIMPs from the Earth}\n\n\\begin{figure}[thb]\n \\begin{center}\n \\includegraphics[width=0.9\\textwidth]{physics-darkmatter\/figures\/earth-wimp-spin-independent.png}\n \\end{center}\n \\caption{The 90\\% C.L. upper limits on the\n spin-independent WIMP-nucleon scattering cross section based on a search from\nWIMP-induced neutrinos coming from the center of the earth for several annihilation channels.\nLimits (lines) and allowed regions (hatched regions) from other experiments are also shown.\nResults from Super-Kamiokande assuming annihilations in the sun are taken from~\\cite{Choi:2015ara}.}\n\\label{fig:earth_wimps}\n\\end{figure}\n\nWIMPs bound in the halo of the galaxy may also become gravitationally\ntrapped within the Earth (or sun) after losing energy via scattering processes\nwith nuclei in its interior. If these then pair annihilate and\nproduce neutrinos, they will escape the core of the Earth and be detectable at\nHyper-Kamiokande. Assuming that the rate of WIMP capture within the\nsun is in equilibrium with the annihilation rate, measurements of the\nWIMP-induced neutrino flux can be directly translated into\nmeasurements of the WIMP-nucleon scattering cross section without the\nneed to measure the self-annihilation cross section. \nSince the Earth is composed of heavy nuclei (relative to hydrogen) \nit is further possible to study WIMP interactions that are \nnot coupled to the nuclear spin (spin independent, SI).\n\n\n\nIn the analysis below the local dark matter density is assumed to be\n0.3 GeV\/$\\mbox{cm}^{3}$ with an RMS velocity of 270~km\/s. The\nrotation of the solar system through the halo is taken to be 220~km\/s.\nSignal MC has been generated by reweighting atmospheric neutrino MC\nevents to spectra produced by the WIMPSIM package~\\cite{Blennow:2007tw}, which accounts for\nthe passage of particles through terrestrial matter. Oscillation between\nflavors as the neutrinos travel from the Earth core to the detector are\nincluded. An independent set of atmospheric neutrino MC is used to\nmodel the background.\n\nThe search for WIMPs bound and annihilating at the center of the Earth \nproceeds along similar lines as the search for events from the\ngalactic center, though events are now binned in momentum and\n$\\mbox{cos}\\theta_{zenith}$, the zenith angle of the reconstructed \nlepton direction relative to Hyper-K. \nIn these coordinates the atmospheric neutrino background takes its \ncharacteristic shape while the WIMP signal MC is peaked sharply in the direction \nof the Earth core; the most upward-going bin.\nLimits on the WIMP-induced neutrino flux are translated into\nlimits on the WIMP-nucleon SI cross sections using the DarkSUSY\nsimulation. Hyper-K's sensitivity with a 1.9 Mton$\\cdot$year exposure\nshown in Figure~\\ref{fig:earth_wimps}. \nThe plot shows the sensitivity to the WIMP-nucleon SI cross section\nfor masses $m_{\\chi} > 4 \\mbox{GeV\/c}^{2}$ compared to allowed regions\n(shown as hatched spaces) and limits (shown as lines) from current\nexperiments. These limits have been produced assuming WIMPs have only\nSI interactions and have been estimated for\n$\\chi\\chi \\rightarrow W^{+}W^{-}, b \\bar b,$ and $\\tau^{+}\\tau^{-}.$\nHyper-K's is expected to produce limits a factor of $3\\sim 4$ times\nstringent than Super-K if no WIMP signal is seen.\nFurther, current hints for a positive SI\ndark matter signal~\\cite{Bernabei:2008yi,Savage:2009mk,Agnese:2013rvf,Angloher:2011uu,Aalseth:2010vx}, \ncan be probed completely by Hyper-K's $\\tau\\tau$ channel.\n\nIt is worth noting that in both the Earth and galactic center analyses\nno improvement in systematic errors beyond Super-K's current\nunderstanding has been assumed. At Hyper-K the statistical\nuncertainty in the data is small enough that increases in sensitivity\nrelative to Super-K is limited by systematic errors in the atmospheric\nneutrino flux and cross section model. Due to the relatively high energy\nof the signal events and the expected directional resolution of the\ndetector, systematic errors in the detector response, while currently\nless well known, are expected to be less significant. While it is\nuncertain how the flux and cross section model will evolve in the\nfuture, improved modeling will translate directly into better\nsensitivity to WIMP-induced neutrinos at Hyper-K.\n\n\n\n\n\n\n\n\n\\subsection{Neutrino geophysics}\\label{section:radiography}\n\nThe chemical composition of the Earth's core is one of the most\nimportant properties of the planet's interior, because it is deeply\nconnected to not only the formation and evolution of the\nEarth~\\cite{Allegre1995} itself but also to the origin of the\ngeomagnetic field~\\cite{Fearn1981}. While paleomagnetic evidence\nsuggests that the geomagnetic field has existed for roughly three\nbillion years, it is known that a core composed of iron alone could\nnot sustain this magnetic field for more than 20,000 years.\nExplaining the continued generation of the geomagnetic field as well\nas its other properties requires knowledge of composition of the core\nmatter. Based on seismic wave velocity measurements and the\ncomposition of primordial meteorites the composition of the core is\npresumed to be an iron-nickel alloy that additionally includes light\nelements, such as oxygen, sulfur, or silicon~\\cite{McDonough1995}.\nHowever, since no sample of the Earth's mantle has even been acquired,\nlet alone a sample of the core, the composition of the latter,\nparticularly its light element a abundance, remains highly uncertain.\nSince the deepest wellbore to date has a depth of\n14~km~\\cite{Popov1999}, and the depth to the outer core is 2900~km it\nis unlikely that a core sample can be obtained within this century.\nAs a result, addition methods of determining the chemical composition\nof the core are essential to understanding the Earth and its magnetic\nfield.\n\n\\begin{figure}[thb]\n \\begin{center}\n \\includegraphics{physics-geophys\/geochemical_sensitivity.pdf}\n \\end{center}\n \\caption{Constraints on the proton to nucleon ratio of the Earth's outer core \n for a 10 Mton year exposure of Hyper-K to atmospheric neutrinos. \n Colored bands indicate the effect of present uncertainties in the \n neutrino mixing parameters.}\n\\label{fig:geophys_za}\n\\end{figure}\n\n\nAs discussed in Section~\\ref{section:atmnu}, the oscillation\nprobability of atmospheric neutrinos depends on not only the various\nmixing angles, the neutrino mass differences, and CP-violating phase,\n$\\delta_{CP}$, but also on the electron density of the media they\ntraverse. This last property makes atmospheric neutrinos an ideal\nprobe for measuring the electron density distribution of the Earth\npresuming the other oscillation parameters are well measured. Since\naccelerator neutrino measurements at Hyper-K itself are expected to\ndramatically improve on the precision of these parameters\n(c.f. Section~\\ref{sec:cp}), Hyper-K may be able to make the first\nmeasurement of the core's chemical composition using its atmospheric\nneutrino sample.\n\nHyper-K's sensitivity in this regard has been studied in the context\nof atmospheric neutrino spectrum's dependence upon the ratio of the\nproton to nucleon ratio (Z\/A) of material in the outer core.\nConstraints from the combination of measurements of the Earth's\ngeodetic-astronomical parameters, such as its precession and nutation,\nwith its low frequency seismic oscillation modes (free oscillations),\nand seismic wave velocity measurements have yielded precise knowledge\nof the planet's density profile~\\cite{Dziewonski1981}. Using this\ninformation the inner core and mantle layers of the Earth are fixed to\npure iron (Z\/A = 0.467) and pyrolite (Z\/A = 0.496) and the Z\/A value\nof the outer core is varied. The analysis uses the same analysis\nsamples presented in Section~\\ref{section:atmnu} and focuses on\nupward-going events between 1 and 10 GeV. Assuming the outer and\ninner core chemical compositions are the same,\nfigure~\\ref{fig:geophys_za} shows the expected constraint on the Z\/A\nparameter. After a 10 Mton year exposure Hyper-K can exclude lead and\nwater (pyrolite) outer core hypotheses by approximately $\\sim 3\\sigma\n(1\\sigma)$. \nWhile geophysics models will ultimately require even\ngreater precision in such measurements, Hyper-K has the potential to\nmake the spectroscopic measurements of the Earth's core.\nIt is worth noting that other proposed experiments with the ability \nto make similar geochemical measurements, such as the next generation of neutrino \ntelescopes, rely primarily on the muon disappearance channel. \nHyper-Kamiokande's, on the other hand, is unique in that its sensitivity \nis derived from the electron appearance channel. \n\n\n\n\n\n\\subsubsection{J-PARC to Hyper-Kamiokande long baseline experiment}\n\nThe neutrino energy spectrum of J-PARC neutrino beam is tuned to the\nfirst oscillation maximum with the off-axis technique, which enhances the\nflux at the peak energy while reducing the higher energy component\nthat produces background events. The peak energy, around 600~MeV, is\nwell matched to the water Cherenkov detector technology, which has an excellent\n$e$\/$\\mu$ separation capability, high background rejection efficiency\nand high signal efficiency for sub-GeV neutrino events.\nDue to the relatively short baseline of 295~km and thus lower neutrino\nenergy at the oscillation maximum, the contribution of the matter\neffect is smaller for the J-PARC to Hyper-Kamiokande experiment\ncompared to other proposed experiments like DUNE \nin the United States~\\cite{Acciarri:2015uup}.\nThus the $CP$ asymmetry measurement with the J-PARC to Hyper-K long\nbaseline experiment has less uncertainty related to the matter effect,\nwhile other experiments with $>1000$~km baseline have much better\nsensitivity to the mass hierarchy (the sign of $\\Delta m^2_{32}$) \nwith accelerator neutrino beams.\nNevertheless, Hyper-K can determine the mass hierarchy using atmospheric \nneutrinos as described in Section~\\ref{section:atmnu}. The sensitivities for\n$CP$ violation and mass hierarchy can be further enhanced by combining\naccelerator and atmospheric neutrino measurements.\n\nThe focus of the J-PARC to Hyper-K experiment is the measurements of $|\\Delta\nm^2_{32}|$, $\\sin^2\\theta_{23}$, $\\sin^2\\theta_{13}$ and $\\ensuremath{\\delta_{CP}} $.\nThe standard flavor mixing scenario is assumed in the following as a baseline study, although it is possible that new physics is involved in neutrino oscillation and will be revealed by Hyper-K.\nThe analysis presented in this report is based on \\cite{Abe:2015zbg} but with an updated treatment of systematic uncertainties.\n\n\\subsubsection{Oscillation probabilities and measurement channels}\nIn what follows, the oscillation probabilities and sensitivities to\noscillation parameters with $\\nue$ appearance and $\\numu$\ndisappearance measurements are discussed. The analysis will be\nperformed by a combination of these two channels.\n\n\\paragraph{$\\numu \\to \\nue$ appearance channel}\nThe oscillation probability from $\\nu_\\mu$ to $\\nu_e$\nis expressed, to the first order of the matter effect, as follows~\\cite{Arafune:1997hd}:\n\\begin{eqnarray}\nP(\\numu \\to \\nue) & = & 4 c_{13}^2s_{13}^2s_{23}^2 \\cdot \\sin^2\\Delta_{31} \\nonumber \\\\\n& & +8 c_{13}^2s_{12}s_{13}s_{23} (c_{12}c_{23}\\cos\\ensuremath{\\delta_{CP}} - s_{12}s_{13}s_{23})\\cdot \\cos\\Delta_{32} \\cdot \\sin\\Delta_{31}\\cdot \\sin\\Delta_{21} \\nonumber \\\\\n& & -8 c_{13}^2c_{12}c_{23}s_{12}s_{13}s_{23}\\sin\\ensuremath{\\delta_{CP}} \\cdot \\sin\\Delta_{32} \\cdot \\sin\\Delta_{31}\\cdot \\sin\\Delta_{21} \\nonumber \\\\\n& & +4s_{12}^2c_{13}^2(c_{12}^2c_{23}^2 + s_{12}^2s_{23}^2s_{13}^2-2c_{12}c_{23}s_{12}s_{23}s_{13}\\cos\\ensuremath{\\delta_{CP}} )\\cdot \\sin^2\\Delta_{21} \\nonumber \\\\\n& & -8c_{13}^2s_{13}^2s_{23}^2\\cdot \\frac{aL}{4E_\\nu} (1-2s_{13}^2)\\cdot \\cos\\Delta_{32}\\cdot \\sin\\Delta_{31} \\nonumber \\\\\n& & +8 c_{13}^2s_{13}^2s_{23}^2 \\frac{a}{\\Delta m^2_{31}}(1-2s_{13}^2)\\cdot\\sin^2\\Delta_{31}, \\label{Eq:cpv-oscprob}\n\\end{eqnarray}\n\\noindent where $s_{ij} = \\sin\\theta_{ij}$, $c_{ij}=\\cos\\theta_{ij}$, $\\Delta_{ij} = \\Delta m^2_{ij}\\, L\/4E_\\nu$, \nand $a =2\\sqrt{2}G_Fn_eE_\\nu= 7.56\\times 10^{-5}\\mathrm{[eV^2]} \\times \\rho \\mathrm{[g\/cm^3]} \\times E_\\nu[\\mathrm{GeV}].$\n$L$, $E_\\nu$, $G_F$ and $n_e$ are the baseline, the neutrino energy, the Fermi coupling constant and the electron density, respectively. \nThe corresponding probability for a $\\numubar \\to \\nuebar$ transition is obtained by replacing $\\ensuremath{\\delta_{CP}} \\rightarrow -\\ensuremath{\\delta_{CP}} $\nand $a \\rightarrow -a$.\nThe third term, containing $\\sin\\ensuremath{\\delta_{CP}} $, is the $CP$ violating term\nwhich flips sign between $\\nu$ and $\\bar{\\nu}$ and thus introduces\n$CP$ asymmetry if $\\sin\\ensuremath{\\delta_{CP}} $ is non-zero. The last two terms are\ndue to the matter effect. Those terms which contain $a$ change their\nsign depending on the mass hierarchy. As seen from the definition of\n$a$, the amount of asymmetry due to the matter effect is proportional\nto the neutrino energy at a fixed value of $L\/E_\\nu$.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{cpv-oscprob-nu.pdf}\n\\includegraphics[width=0.48\\textwidth]{cpv-oscprob-anti.pdf}\n\\caption{Oscillation probabilities as a function of the neutrino energy for $\\numu \\to \\nue$ (left) and $\\numubar \\to \\nuebar$ (right) transitions with L=295~km and $\\sin^22\\theta_{13}=0.1$. \nBlack, red, green, and blue lines correspond to $\\ensuremath{\\delta_{CP}} = 0^\\circ$,\n90$^\\circ$, 180$^\\circ$ and $-90^\\circ$, respectively. Solid (dashed)\nline represents the case for a normal (inverted) mass hierarchy.\n\\label{fig:cp-oscpob}}\n\\end{figure}\n\nFigure~\\ref{fig:cp-oscpob} shows the $\\numu \\to \\nue$ and\n$\\numubar \\to \\nuebar$ oscillation probabilities as a function of the\ntrue neutrino energy for a baseline of 295~km. The Earth matter\ndensity is assumed to be 2.6\\,$g$\/cm$^3$. The cases for $0^\\circ$,\n90$^\\circ$, 180$^\\circ$ and $-90^\\circ$, are shown together. One can\nsee the effect of different $\\ensuremath{\\delta_{CP}} $ values on the oscillation\nprobabilities. For example, if $\\ensuremath{\\delta_{CP}} = -90^\\circ$, the appearance\nprobability will be enhanced for neutrino but suppressed for\nanti-neutrino. By comparing the oscillation probabilities of\nneutrinos and anti-neutrinos, one can measure the $CP$ asymmetry. \nThe information on the $CP$ phase can be derived from not only the total\nnumber of events but also the energy spectrum of the oscillated events. \nFor example, for both $\\ensuremath{\\delta_{CP}} = 0^\\circ$ and $180^\\circ$, $CP$ is conserved\n($\\sin\\ensuremath{\\delta_{CP}} =0$) and the oscillation probabilities in vacuum are the\nsame for neutrino and anti-neutrino, however those two cases can be\ndistinguished using spectrum information as seen in\nFig.~\\ref{fig:cp-oscpob}.\n\nAlso shown in Fig.~\\ref{fig:cp-oscpob} are the case of normal mass\nhierarchy ($\\Delta m^2_{32}>0$) with solid lines and inverted mass\nhierarchy ($\\Delta m^2_{32}<0$) with dashed lines.\nThere are sets of different mass hierarchy and values of $\\ensuremath{\\delta_{CP}} $\nwhich give similar oscillation probabilities, resulting in a potential\ndegeneracy if the mass hierarchy is unknown. By combining information\nfrom experiments currently ongoing~\\cite{Abe:2011ks,Ayres:2004js,\nGuo:2007ug,Ahn:2010vy,Ardellier:2006mn} and\/or planned in the near\nfuture~\\cite{Aartsen:2014oha,Katz:2014tta,Ahmed:2015jtv,An:2015jdp,Kim:2014rfa},\nit is expected that the mass hierarchy will be determined by the time\nHyper-K starts to take data. If not, Hyper-K itself has a sensitivity\nto the mass hierarchy by the atmospheric neutrino measurements as\ndescribed in the next section. Thus, the mass hierarchy is assumed to\nbe known in this analysis, unless otherwise stated.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.45\\textwidth]{cpv-oscprob-breakdown-m90deg.pdf}\n\\includegraphics[width=0.45\\textwidth]{cpv-oscprob-breakdown-anti-m90deg.pdf}\n\\caption{Oscillation probabilities of $\\numu \\to \\nue$ (left) and $\\numubar \\to \\nuebar$ (right) as a function of the neutrino energy with a baseline of 295~km. $\\sin^22\\theta_{13}=0.1$,\n$\\ensuremath{\\delta_{CP}} = -90^\\circ$, and normal hierarchy are assumed.\nContribution from each term of the oscillation probability formula is shown separately.\n\\label{fig:cp-oscpob-bd}}\n\\end{figure}\n\nFigure~\\ref{fig:cp-oscpob-bd} shows the contribution from each term of the $\\numu \\to \\nue$ and $\\numubar \\to \\nuebar$ oscillation probability formula, Eq.(\\ref{Eq:cpv-oscprob}),\nfor $L=295$\\,km, $\\sin^22\\theta_{13}=0.1$, $\\sin^22\\theta_{23}=1.0$, $\\ensuremath{\\delta_{CP}} = -90^\\circ$, and normal mass hierarchy.\nFor $E_\\nu\\simeq 0.6$\\,GeV which gives $\\sin\\Delta_{32} \\simeq \\sin\\Delta_{31} \\simeq 1$,\n\\begin{eqnarray}\n\\frac{P(\\nu_\\mu \\to \\nu_e) - P(\\bar\\nu_\\mu \\to \\bar\\nu_e)}{P(\\nu_\\mu \\to \\nu_e) + P(\\bar\\nu_\\mu \\to \\bar\\nu_e)} &\\simeq& \n\\frac{-16J_{CP}\\sin \\Delta_{21} + 16 c_{13}^2s_{13}^2s_{23}^2 \\frac{a}{\\Delta m^2_{31}}(1-2s_{13}^2) }{8c_{13}^2s_{13}^2s_{23}^2}\\\\\n&\\simeq& -0.28 \\sin\\delta + 0.09,\n\\end{eqnarray}\nwhere $J_{CP} = c_{12}c_{13}^{2}c_{23}s_{12}s_{13}s_{23}\\sin\\delta$ is called Jarlskog invariant.\nThe effect of $CP$ violating term can be as large as 28\\%, while that of the matter effect is 9\\%.\nThe first term will be $-0.31 \\sin\\delta$ with $\\sin^{2}2\\theta_{13}=0.082$~\\cite{Olive:2016xmw}.\n\nThe uncertainty of the Earth's density between Tokai and Kamioka is estimated to be at most 6\\%~\\cite{Hagiwara:2011kw}. Because the matter effect contribution to the total $\\numu \\to \\nue$ appearance probability is less than 10\\% for 295km baseline, the uncertainty from the matter density is estimated to be less than 0.6\\% and neglected in the following analysis.\n\n\\paragraph{$\\numu$ disappearance channel}\nThe currently measured value of $\\theta_{23}$ is consistent with maximal mixing, $\\theta_{23} \\approx \\pi\/4$~\\cite{Abe:2014ugx, Adamson:2014vgd, Himmel:2013jva},\nwhile NOvA collaboration recently reported a possible hint of non-maximal mixing~\\cite{Adamson:2017qqn}.\nIt is of great interest to determine if $\\sin^22\\theta_{23}$ is maximal or not, and if not, whether $\\theta_{23}$ is less or greater than $\\pi\/4$, as \nit could constrain models of neutrino mass generation and quark-lepton unification~\\cite{King:2013eh,Albright:2010ap,Altarelli:2010gt,Ishimori:2010au,Albright:2006cw,Mohapatra:2006gs}.\nWhen we measure $\\theta_{23}$ with the survival probability $P(\\numu \\to \\numu)$ which is proportional to $\\sin^22\\theta_{23}$ to first order, \n\\begin{eqnarray}\nP(\\nu_\\mu \\rightarrow \\nu_\\mu) &\\simeq& 1-4c^2_{13}s^2_{23} [1-c^2_{13}s^2_{23}]\\sin^2(\\Delta m^2_{32}\\, L\/4E_\\nu) \\\\\n&\\simeq & 1-\\sin^22\\theta_{23}\\sin^2(\\Delta m^2_{32}\\, L\/4E_\\nu), \\hspace{2cm} \\textrm{(for $c_{13}\\simeq1$)}\n\\end{eqnarray}\nthere is an octant ambiguity, as for each value of $\\theta_{23} \\le\n45^\\circ $ (in the first octant), there is a value in the second\noctant ($\\theta_{23} > 45^\\circ$) that gives rise to the same\noscillation probability. As seen from Eq.~\\ref{Eq:cpv-oscprob},\n$\\nu_e$ appearance measurement can determine\n$\\sin^2\\theta_{23}\\sin^22\\theta_{13}$. In addition, the reactor\nexperiments provide an almost pure measurement of $\\sin^22\\theta_{13}$.\nThus, the combination of those complementary measurements will be able\nto resolve this degeneracy if $\\theta_{23}$ is sufficiently away from\n$\\frac{\\pi}{4}$~\\cite{Fogli:1996pv,Minakata:2002jv,Hiraide:2006vh}.\n\nMeasurement of $\\nuebar$ disappearance by reactor neutrino experiments\nprovides a constraint on the following combination of mass-squared\ndifferences,\n\\begin{equation}\n\\Delta m^2_{ee} = \\cos^2\\theta_{12}\\Delta m^2_{31}+\\sin^2\\theta_{12}\\Delta m^2_{32}.\n\\end{equation}\nwhile $\\numu$ disappearance measurement with Hyper-K provides a different combination~\\cite{Nunokawa:2005nx, deGouvea:2005hk}\n\\begin{equation}\n\\Delta m^2_{\\mu\\mu} = \\sin^2\\theta_{12}\\Delta m^2_{31}+\\cos^2\\theta_{12} \\Delta m^2_{32}\n+ \\cos\\ensuremath{\\delta_{CP}} \\sin\\theta_{13} \\sin2\\theta_{12}\\tan\\theta_{23} \\Delta m^2_{21}.\n\\end{equation}\nBecause the mass squared difference measurements by Hyper-K and by\nreactor experiments give independent information, by comparing them\none can check the consistency of the mixing matrix framework, and\nobtain information on the neutrino mass hierarchy. In order to have\nsensitivity to the mass hierarchy, uncertainties of both measurements\nmust be smaller than 1\\%. Future medium baseline reactor experiments,\nJUNO~\\cite{An:2015jdp} and RENO-50~\\cite{Kim:2014rfa}, plan to measure\n$\\Delta m^2_{ee}$ with precision better than 1\\%. Thus, precision\nmeasurement of $\\Delta m^2$ by Hyper-K will provide important\ninformation on the consistency of three generation mixing framework\nand mass hierarchy.\n\n\\subsubsection{Analysis method}\nAs described earlier, a binned likelihood analysis based on the\nreconstructed neutrino energy distribution is performed to extract the oscillation parameters. \nBoth \\nue\\ appearance and \\numu\\ disappearance samples, in both neutrino and\nantineutrino mode data, are simultaneously fitted.\n\nThe $\\chi^2$ used in this study is defined as \n\\begin{equation} \\label{eq:sens:chi2}\n\\chi^2 = -2 \\ln \\mathcal{L} + P,\n\\end{equation}\nwhere $\\ln \\mathcal{L}$ is the log likelihood for a Poisson distribution,\n\\begin{equation}\n-2\\ln \\mathcal{L} = \\sum_k \\left\\{ -{N_k^\\mathrm{test}(1+f_i)} + N_k^\\mathrm{hyp} \\ln \\left[ N_k^\\mathrm{test}(1+f_i) \\right] \\right\\}.\n\\end{equation}\nHere, $N_k^\\mathrm{hyp}$ and $N_k^\\mathrm{test}$ are the number of\nevents in $k$-th reconstructed energy bin for the hypothesis and test oscillation parameters, respectively.\nThe index $k$ runs over all reconstructed energy bins for muon and electron neutrino samples and for neutrino and anti-neutrino mode data. \nThe parameters $f_i$ represent fractional variations of the bin entries due to systematic uncertainties.\n\nThe penalty term $P$ in Eq.~\\ref{eq:sens:chi2} constrains the systematic parameters $f_i$ with the normalized covariance matrix $C$,\n\\begin{equation}\nP = \\sum_{i,j} f_i (C^{-1})_{i,j} f_j.\n\\end{equation}\nIn order to reduce the number of the systematic parameters, several\nreconstructed energy bins that have similar covariance values are\nmerged for $f_i$.\n\nA robust estimate of the uncertainties is possible based on the T2K experience.\nFor each of three main categories of systematic uncertainties, we have made the following assumptions taking into account improvements expected with future T2K data and analysis improvements.\n\\begin{description}\n\\item[i) Flux and cross section uncertainties constrained by the fit to near detector data] \nData from near detectors will be used in conjunction with models for\nthe neutrino beam, neutrino interactions, and the detector performance\nto improve our predictions of the flux at SK and some cross-section\nparameters. The understanding of the neutrino beam, interaction, and\ndetector is expected to improve in the future, which will result in\nreduction of uncertainties in this category.\nOn the other hand, the near detector analysis is expected to include\nmore samples to reduce the uncertainty for category ii), which will\nresult in migration of some errors into this category. This category\nof uncertainties is assumed to stay at the same level as currently\nestimated by T2K.\n\\item[ii) Cross section uncertainties not constrained by the fit to near detector data ]\nThis category of error stems from the cross-section parameters which are independent between \nthe near and far detectors because of their different elemental composition and the cross-section \nparameters for which the near detector is insensitive.\nIn T2K, an intensive effort has been made to include more samples into analysis, such as data \nfrom FGD2 containing a water target~\\cite{Abe:2017uxa} and large scattering angle events, to \nprovide more constraints on the cross section models.\nFurther improvement is expected in future analysis as T2K accumulates and analyze more data.\nIn addition, the intermediate detector will significantly reduce the uncertainty due to \nthe neutrino interaction models.\n\\item[iii) Uncertainties on the far detector efficiency and reconstruction modeling]\nBecause most of the uncertainties related to far detector performance\nare estimated by using atmospheric neutrinos as a control sample and\nthe current error is limited by statistics, errors in this category\nare expected to decrease with much larger statistics available with \nHyper-K than currently used for T2K.\nUncertainties arising from the energy scale are kept the same because\nthey are not estimated by the atmospheric neutrino sample, although it\ncould be also reduced with a larger statistics control sample and\nbetter calibration of the detector.\n\\end{description}\nCompared to the systematic uncertainty used for the past \npublication~\\cite{Abe:2015zbg}, the uncertainties for anti-neutrino beam \nmode have been reduced to a similar level as those for neutrino beam mode, \nbased on the experience with T2K anti-neutrino oscillation analysis.\nThe flux and cross section uncertainties are assumed to be\nuncorrelated between the neutrino and anti-neutrino data, except for\nthe uncertainty of \\nue\/\\numu\\ cross section ratio which is treated to\nbe anti-correlated considering the theoretical uncertainties studied\nin~\\cite{Day:2012gb}. Because some of the uncertainties, such as\nthose from the cross section modeling or near detector systematics,\nare expected to be correlated and give more of a constraint, this is a\nconservative assumption. The far detector uncertainty is treated to\nbe fully correlated between the neutrino and anti-neutrino data.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{SystNue2.pdf}\n\\includegraphics[width=0.48\\textwidth]{SystNumu2.pdf}\n\\caption{\nFractional and total systematic error size for the appearance (left) and the disappearance\n(right) samples in the neutrino mode. Black: total uncertainty, red:\nthe flux and cross-section constrained by the near detector, magenta:\nthe near detector non-constrained cross section, blue: the far\ndetector error.\n\\label{Fig:systerror}\n}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{SystAntiNue2.pdf}\n\\includegraphics[width=0.48\\textwidth]{SystAntiNumu2.pdf}\n\\caption{\nFractional and total systematic error size for the appearance (left) and the disappearance\n(right) samples in the anti-neutrino mode. Black: total uncertainty,\nred: the flux and cross-section constrained by the near detector,\nmagenta: the near detector non-constrained cross section, blue: the\nfar detector error.\n\\label{Fig:systerror-anti}\n}\n\\end{figure}\n\nFigures~\\ref{Fig:systerror} and \\ref{Fig:systerror-anti} show the\nfractional and total systematic uncertainties for the appearance and\ndisappearance reconstructed energy spectra in neutrino and\nanti-neutrino mode, respectively. Black lines represent the prior\nuncertainties and bin widths of the systematic parameters $f_i$, while\ncolored lines show the contribution from each uncertainty source. It\nshould be noted that because some uncertainties are correlated between\nbins, the uncertainty on the total number of events is not a simple\nflux-weighted sum of these errors. For example, the energy scale\nuncertainty of the far detector has a large contribution around the\nflux peak, but it does not change the total number of events.\nFigure~\\ref{Fig:correlationmatrix} shows the correlation matrix of the\nsystematic uncertainties between the reconstructed neutrino energy\nbins of the four samples. The systematic uncertainties of the number\nof expected events at the far detector are summarized in\nTable~\\ref{tab:sens:systsummary}.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{CorrelationMatrix2.pdf}\n\\caption{\nCorrelation matrix between reconstructed energy bins of the four samples due to the systematic uncertainties.\nBins 1--8, 9--20, 21--28, and 29--40 correspond to \nthe neutrino mode single ring $e$-like,\nthe neutrino mode single ring $\\mu$-like,\nthe anti-neutrino mode single ring $e$-like, and\nthe anti-neutrino mode single ring $\\mu$-like samples, respectively.\n\\label{Fig:correlationmatrix}\n}\n\\end{figure}\n\n\n\\begin{table}[htbp]\n\\caption{Uncertainties for the expected number of events at Hyper-K from the systematic uncertainties assumed in this study.}\n\\centering\n\\begin{tabular}{cccccc} \\hline \\hline\n& & ~~Flux \\& ND-constrained~~ & ~~ND-independent~~ & \\multirow{2}{*}{~~Far detector~~} & \\multirow{2}{*}{Total} \\\\\n & & cross section & cross section \\\\ \\hline\n\\multirow{2}{*}{$\\nu$ mode~~} \t\t\t& Appearance \t& 3.0\\% & 0.5\\% & 0.7\\% & 3.2\\% \\\\\n\t\t\t\t\t\t\t\t\t& Disappearance \t& 3.3\\% & 0.9\\% & 1.0\\% & 3.6\\% \\\\ \\hline\n\\multirow{2}{*}{$\\overline{\\nu}$ mode~~}\t& Appearance \t& 3.2\\% & 1.5\\% & 1.5\\% & 3.9\\% \\\\\n\t\t\t\t\t\t\t\t\t& Disappearance \t& 3.3\\% & 0.9\\% & 1.1\\% & 3.6\\% \\\\\n\\hline \\hline\n\\end{tabular}\n\n\\label{tab:sens:systsummary}\n\\end{table}%\n\n\\subsubsection{Searches for new physics}\nIn addition to the study of standard neutrino oscillation, the\ncombination of intense beam and high performance detectors enables us\nto search for new physics in various ways. Examples of possible\nsearches for new physics with Hyper-K and accelerator beam are listed\nbelow.\n\n\\paragraph{Search for sterile neutrinos}\nSterile neutrinos can be searched for in both disappearance and\nappearance channels in near and intermediate detectors. With neutrino\nenergy of 0.1--few~GeV and baseline of 0.3~km and 1--2~km, it will be\nsensitive to $\\Delta m^2$ of $\\mathcal{O}(1)$~eV$^2$, which is\nthe interesting region in light of several anomalies reported by recent\nexperiments. T2K has searched for sterile neutrino in $\\nue$\nappearance and $\\numu$ disappearance with near\ndetectors~\\cite{Abe:2014nuo, Dewhurst:2015aba}. With more statistics,\nimproved detectors, and possible two detector configuration with near\nand intermediate detectors, Hyper-K near detectors will have chance to\nimprove the sensitivity for sterile neutrino searches.\n\nNeutral current measurements at the far detector will be also sensitive to the sterile neutrino,\nbecause the neutral current channel measures the total active flavor content.\nBy selecting two electron-like ring events with no decay electron and invariant mass consistent with $\\pi^0$, neutral current events with 96\\% purity can be obtained.\nWith $1.56\\times10^{22}$ protons on target and 560~kton fiducial mass, more than 4,000 \nNC $\\pi^0$ events are expected after selection.\nNormalization of the NC $\\pi^{0}$ production can be strongly\nconstrained by the high statistics data at the intermediate detector\nas shown in Table~\\ref{tab:lbl-ndcross}.\n\n\\paragraph{Test of Lorentz and CPT invariance}\nLorentz Violation arises when the behavior of a particle depends on\nits direction or boost velocity and is predicted to occur at the\nPlanck scale (10$^{19}$~GeV). Searches for Lorentz Violation have\nbeen performed by various experiments, including T2K, by looking for a\nsidereal time dependence of the neutrino event rate. Similar searches\ncan be carried out with larger statistics and improved detectors.\n\n\\paragraph{Heavy neutrino search}\nThe existence of heavy neutral leptons (heavy neutrinos) is predicted\nin many extensions of the Standard Model. Such heavy neutrinos may be\nproduced in decays of kaons and pions from the target. Then, decays\nof heavy neutrinos can be detected in the near detector. The\nfeasibility of search for heavy neutrinos in accelerator neutrino\nexperiment, in particular with T2K, is studied in \\cite{Asaka:2012bb}\nand the sensitivity is expected to be better than previous searches.\nBecause interactions of ordinary neutrinos produce background to this\nsearch, having a low density detector such as a gas TPC inside a\nmagnetic field like ND280 is an advantage for this search. The\nsensitivity will be further enhanced if a larger volume of gas\ndetector is employed.\n\n\n\\subsubsection{Analysis overview}\nThe analysis used in this report is based on a framework developed for\nthe sensitivity study by T2K presented in~\\cite{Abe:2014tzr}. A\nbinned likelihood analysis based on the reconstructed neutrino energy\ndistribution is performed using both \\nue\\ (\\nuebar) appearance\nand \\numu\\ (\\numubar) disappearance samples simultaneously. A full\noscillation probability formula, not the approximation shown in\nEq.~\\ref{Eq:cpv-oscprob}, is used in the analysis.\nTable~\\ref{Tab:oscparam} shows the nominal oscillation parameters used\nin the study presented in this report, and the treatment during the\nfitting. Parameters to be determined with the fit are\n$\\sin^2\\theta_{13}$, $\\sin^2\\theta_{23}$, $\\Delta m^2_{32}$ and\n$\\ensuremath{\\delta_{CP}} $.\n\n\n\nAn integrated beam power of 13~MW$\\times$10$^7$~sec is assumed in\nthis study, corresponding to $2.7\\times10^{22}$ protons on target\nwith 30\\,GeV J-PARC beam.\nIt corresponds to about ten Snowmass years with 1.3~MW.\nWe have studied the sensitivity to $CP$\nviolation with various assumptions of neutrino mode and anti-neutrino\nmode beam running time ratio for both normal and inverted mass\nhierarchy cases. The dependence of the sensitivity on the\n$\\nu$:$\\overline{\\nu}$ ratio is found not to be significant between\n$\\nu$:$\\overline{\\nu}$=1:1 to 1:5. In this report,\n$\\nu$:$\\overline{\\nu}$ ratio is set to be 1:3 so that the expected\nnumber of events are approximately the same for neutrino and\nanti-neutrino modes.\n\n\n\\begin{table}[htbp]\n\\caption{Oscillation parameters used for the sensitivity analysis and treatment in the fitting. The \\textit{nominal} values are used for figures and numbers in this section, unless otherwise stated.}\n\\centering\n\\begin{tabular}{cccccccc} \\hline \\hline\nParameter & $\\sin^22\\theta_{13}$ & $\\ensuremath{\\delta_{CP}} $ & $\\sin^2\\theta_{23}$ &\n$\\Delta m^2_{32}$ & mass hierarchy & $\\sin^22\\theta_{12}$ & $\\Delta\nm^2_{21}$ \\\\ \\hline Nominal & 0.10 & 0 & 0.50 &\n$2.4\\times10^{-3}~\\mathrm{eV}^2$ & Normal & $0.8704$ &\n$7.6\\times10^{-5}~\\mathrm{eV}^2$ \\\\ Treatment & Fitted & Fitted &\nFitted & Fitted & Fixed & Fixed & Fixed \\\\ \\hline \\hline\n\\end{tabular}\n\\label{Tab:oscparam}\n\\end{table}%\n\nInteractions of neutrinos in the Hyper-K detector are simulated with\nthe NEUT program\nlibrary~\\cite{hayato:neut,Mitsuka:2007zz,Mitsuka:2008zz}, which is\nused in both Super-K and T2K. The response of the detector is\nsimulated using the Super-K full Monte Carlo simulation based on the\nGEANT3 package~\\cite{Brun:1994zzo}, although some improvements are expected\nwith new photo-sensors with higher photon detection efficiency and timing\nresolution (see Section~\\ref{section:photosensors}). \nThe simulation is based on the SK-IV configuration, which has an upgraded electronics and DAQ system compared to SK-III.\nEvents are reconstructed with the Super-K reconstruction software, which\ngives a realistic estimate of the Hyper-K performance.\n\n\nBased on the experience with the SK-II period when the number of PMT\nwas about half compared to other periods (corresponding to 20\\%\nphotocoverage with the Super-K PMT R3600), the reconstruction\nperformance for beam neutrino events with around 1~GeV energy is known\nnot to degrade significantly with reduced photocathode coverage down to 20\\% (with\nR3600). \nThus, the performance for the beam neutrino interactions is comparable within the range of \nthe photocathode coverage considered for Hyper-K.\nThere will be additional capabilities such as neutron tagging with higher coverage, \nbut they are not yet taken into account in the current study.\n\nIn what follows, results are presented assuming ten years of running with a single tank detector with 187\\,kton fiducial volume unless otherwise noticed.\nAlso shown for comparison are results from the staging approach with ten years of running, with a single tank for the first six years, and two tanks starting in the seventh year.\n\n\\subsubsection{Expected observables at the far detector}\nThe criteria to select \\nue\\ and \\numu\\ candidate events are based on\nthose developed for and established with the Super-K and T2K\nexperiments. Fully contained (FC) events with a reconstructed vertex\ninside the fiducial volume (FV), which is defined as the region more than 1.5\\,m away from inner detector wall, and visible energy ($E_\\mathrm{vis}$)\ngreater than 30\\,MeV are selected as FCFV neutrino event candidates.\nIn order to enhance charged current quasielastic (CCQE, $\\nu_l +\nn \\rightarrow l^- + p$ or $\\overline{\\nu}_l + p \\rightarrow l^+ + n$)\ninteraction, a single Cherenkov ring is required.\n\nAssuming a CCQE interaction, the neutrino energy ($E_\\nu ^{\\rm rec}$)\nis reconstructed from the energy of the final state charged lepton\n($E_\\ell$) and the angle between the neutrino beam and the charged\nlepton directions ($\\theta_\\ell$) as\n\\begin{eqnarray}\nE_\\nu ^{\\rm rec}=\\frac {2(m_n-V) E_\\ell +m_p^2 - (m_n-V)^2 - m_\\ell^2} {2(m_n-V-E_\\ell+p_\\ell\\cos\\theta_\\ell)},\n\\label{eq:Enurec}\n\\end{eqnarray}\nwhere $m_n, m_p, m_\\ell$ are the mass of neutron, proton, and charged\nlepton, respectively, $p_\\ell$ is the charged lepton momentum, and $V$\nis the mean nuclear potential energy (27\\,MeV).\nIt was shown in T2K analysis that the sensitivity can be slightly improved\nby using two-dimentional information of $(p_\\ell, \\theta)$ in oscillation fit.\n\n\nThen, to select \\nue\/\\nuebar\\ candidate events the following criteria are applied;\nthe reconstructed ring is identified as electron-like ($e$-like),\n$E_\\mathrm{vis}$ is greater than 100 MeV, there is no decay electron\nassociated to the event, and $E_\\nu^\\mathrm{rec}$ is less than\n1.25~GeV. Finally, in order to reduce the background from\nmis-reconstructed $\\pi^0$ events, additional criteria using the\nreconstructed $\\pi^0$ mass and the ratio of the best-fit likelihoods\nof the $\\pi^0$ and electron fits~\\cite{Abe:2013hdq} are applied.\n\n\\begin{figure}[tbp]%\n\\includegraphics[width=0.48\\textwidth]{Numode_Appearance_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{AntiNumode_Appearance_1tank.pdf}\\\\\n\\caption{\nReconstructed neutrino energy distribution of the $\\nue$ candidate events.\nLeft: neutrino beam mode, right: anti-neutrino beam mode. Normal mass\nhierarchy with $\\sin^22\\theta_{13}=0.1$ and $\\ensuremath{\\delta_{CP}} =0^\\circ$ is\nassumed.\nCompositions of appearance signal, $\\numu \\to \\nue$ and $\\numubar \\to \\nuebar$,\nand background events originating from ($\\numu + \\numubar$) and ($\\nue + \\nuebar$) are shown separately.\n\\label{Fig:sens-enurec-nue}\n}\n\\end{figure}\n\n\\begin{table}[tbp]%\n\\caption{\\label{Tab:sens-selection-nue}%\nThe expected number of $\\nue\/\\nuebar$ candidate events and\nefficiencies with respect to FCFV events.\nNormal mass hierarchy with\n$\\sin^22\\theta_{13}=0.1$ and $\\ensuremath{\\delta_{CP}} =0$ are assumed. Background is\ncategorized by the flavor before oscillation.}\n\\begin{center}%\n\\begin{tabular}{cc|cc|ccccc|c|c} \\hline \\hline\n&\t& \\multicolumn{2}{c|}{signal} & \\multicolumn{6}{c|}{BG} & \\multirow{2}{*}{Total} \\\\ \n&\t&~$\\numu \\to \\nue$~\t& ~$\\numubar \\to \\nuebar$~ \t&~$\\numu$ CC~\t&~$\\numubar$ CC~\t&~$\\nue$ CC~& ~$\\nuebar$ CC~ & ~NC~ & ~BG Total~\t& \\\\ \\hline \n\\multirow{2}{*}{$\\nu$ mode~~} & Events\t& 1643\t&\t15& 7 \t& 0\t & 248\t&11\t& 134\t&\t400 & 2058 \\\\ \n & Eff.(\\%) & 63.6 & 47.3 & 0.1 & 0.0 & 24.5 & 12.6 & 1.4 & 1.6 & --- \\\\\n \\hline\n\\multirow{2}{*}{$\\bar{\\nu}$ mode~~} & Events\t& 206\t&\t1183& 2\t& 2\t& 101\t& 216\t& 196&\t517 & 1906 \\\\ \n & Eff. (\\%) & 45.0 & 70.8 & 0.03 & 0.02 & 13.5 & 30.8 & 1.6 & 1.6 & --- \\\\\n\\hline \\hline\n\\end{tabular}%\n\\end{center}\n\\end{table}%\n\nFigure~\\ref{Fig:sens-enurec-nue} shows the reconstructed neutrino\nenergy distributions of $\\nue\/\\nuebar$ events after all the\nselections. \nThe expected number of\n$\\nue\/\\nuebar$ candidate events is shown in\nTable~\\ref{Tab:sens-selection-nue} for each signal and background\ncomponent. The efficiencies of selection with respect to FCFV events\nare also shown in Table~\\ref{Tab:sens-selection-nue}. In the neutrino\nmode, the dominant background component is intrinsic $\\nue$\ncontamination in the beam. The mis-identified neutral current $\\pi^0$\nproduction events are suppressed thanks to the improved $\\pi^0$\nreconstruction. The total rejection factor, including FCFV selection,\nfor NC $\\pi^0$ interactions is $>99.5$\\%. In the anti-neutrino mode,\nin addition to $\\nuebar$ and $\\numubar$, $\\nue$ and $\\numu$ components\nhave non-negligible contributions due to larger fluxes and\ncross-sections compared to their counterparts in the neutrino mode.\n\n\\begin{figure}[tbp]%\n\\includegraphics[width=0.48\\textwidth]{Numode_Disappearance_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{AntiNumode_Disappearance_1tank.pdf}\n\\caption{%\nReconstructed neutrino energy distribution of the $\\numu\/\\numubar$ candidate events after oscillation.\nLeft: neutrino beam mode, right: anti-neutrino beam mode.\n\\label{Fig:sens-enurec-numu}\n}\n\\end{figure}\n\n\\begin{table}[tbp]%\n\\begin{center}%\n\\caption{\\label{Tab:sens-selection-numu}%\nThe expected number of $\\numu\/\\numubar$ candidate events and efficiencies (with respect to FCFV events) for each flavor and interaction type.\n}\n\\begin{tabular}{lcccccccccc} \\hline \\hline\n\t\t\t&\t&~$\\numu$CCQE\t& ~$\\numu$CC non-QE & ~$\\numubar$CCQE\t& ~$\\numubar$CC non-QE &~$\\nue+\\nuebar$ CC \t&~NC~ \t& ~$\\numu \\to \\nue$\t\t& ~total~ \t\t\\\\ \\hline \n\\multirow{2}{*}{$\\nu$ mode}\t& Events\t& 6043 & 2981\t &\t348 & \t\t194\t& 6\t\t\t\t& 480 \t\t& 29\t\t\t& 10080\t\t \\\\ \n & Eff. (\\%) & 91.0 & 20.7 & 95.6 & 53.5 & 0.5 & 8.8 & 1.1& --- \\\\ \\hline\n\\multirow{2}{*}{$\\bar{\\nu}$ mode} & Events\t& 2699 & \t2354\t&\t6099 &\t 1961 & 7\t\t& 603\t\t& 4 \t\t\t& 13726\t\t \\\\ \n & Eff. (\\%) & 88.0 & 20.1 & 95.4 & 54.8 & 0.4 & 8.8 & 0.7 & ---\\\\\n\\hline \\hline\n\\end{tabular}%\n\\end{center}\n\\end{table}%\n\nFor the \\numu\/\\numubar\\ candidate events the following criteria are applied;\nthe reconstructed ring is identified as muon-like ($\\mu$-like),\nthe reconstructed muon momentum is greater than 200 MeV\/$c$, and\nthere is at most one decay electron associated to the event.\n\nFigure~\\ref{Fig:sens-enurec-numu} shows the reconstructed neutrino\nenergy distributions of the selected $\\numu$\/$\\numubar$ events.\nTable~\\ref{Tab:sens-selection-numu} shows the number of\n$\\numu\/\\numubar$ candidate events for each signal and background\ncomponent. In the neutrino beam mode, the purity of $\\numu$ CC\nevents, after oscillation and for $E_{rec}<1.5$~GeV, is 89\\%. For the\nanti-neutrino mode data, the contribution of wrong-sign $\\numu$ CC\nevents is significant because the cross section for neutrino interactions is about\nthree times larger than anti-neutrino interactions in this energy range. The\nfractions of $\\numubar$ and $\\numu$ CC events in anti-neutrino beam\nmode data after selection, for $E_{rec}<1.5$~GeV, are 66\\% and 26\\%,\nrespectively.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{DeltaCP_Energy_numode_Appearence_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{DeltaCP_Energy_antinumode_Appearence_1tank.pdf} \\\\\n\\caption{\nTop: Reconstructed neutrino energy distribution for several values of\n$\\ensuremath{\\delta_{CP}} $. $\\sin^22\\theta_{13}=0.1$ and normal hierarchy is assumed.\nBottom: Difference of the reconstructed neutrino energy distribution\nfrom the case with $\\ensuremath{\\delta_{CP}} =0^\\circ$. The error bars represent the\nstatistical uncertainties of each bin.\n}\n\\label{enurecdiff-nue}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{Numode_Disappearance_nonOsc_comp_total_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{AntiNumode_Disappearance_nonOsc_comp_total_1tank.pdf}\n\\caption{\nReconstructed neutrino energy distributions of $\\numu$ candidates.\nDotted black lines are for no oscillation case,\nwhile solid red lines represent prediction with oscillation.\nLeft: for neutrino beam mode. Right: for anti-neutrino beam mode.\n}\n\\label{enurecdiff-numu}\n\\end{figure}\n\nThe reconstructed neutrino energy distributions of $\\nue$ events for\nseveral values of $\\ensuremath{\\delta_{CP}} $ are shown in the top plots of\nFig.~\\ref{enurecdiff-nue}. The effect of $\\ensuremath{\\delta_{CP}} $ is clearly seen\nusing the reconstructed neutrino energy. The bottom plots show the\ndifference of reconstructed energy spectrum from $\\ensuremath{\\delta_{CP}} =0^\\circ$\nfor the cases $\\ensuremath{\\delta_{CP}} = 90^\\circ, -90^\\circ$ and $180^\\circ$. The\nerror bars correspond to the statistical uncertainty.\nBy using not only the total number of events but also the reconstructed energy\ndistribution, the sensitivity to $\\ensuremath{\\delta_{CP}} $ can be improved and one\ncan discriminate all the values of $\\ensuremath{\\delta_{CP}} $, including the\ndifference between $\\ensuremath{\\delta_{CP}} = 0^\\circ$ and $180^\\circ$ for which CP\nsymmetry is conserved.\n\nFigure~\\ref{enurecdiff-numu} shows the reconstructed neutrino energy\ndistributions of the $\\numu$ sample, for the cases with\n$\\sin^2\\theta_{23}=0.5$ and without oscillation. Thanks to the narrow\nenergy spectrum tuned to the oscillation maximum with off-axis beam,\nthe effect of oscillation is clearly visible.\n\n\\subsubsection{Measurement of $CP$ asymmetry}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{2Dmap13_reactor_constraint_NH_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{2Dmap13_reactor_constraint_IH_1tank.pdf}\n\\caption{The expected 90\\% CL allowed regions in the $\\sin^22\\theta_{13}$-$\\ensuremath{\\delta_{CP}} $ plane.\nThe results for the true values of $\\ensuremath{\\delta_{CP}} = (-90^\\circ, 0, 90^\\circ, 180^\\circ)$ are shown.\nLeft: normal hierarchy case. Right: inverted hierarchy case.\nRed (blue) lines show the result with Hyper-K only (with $\\sin^22\\theta_{13}$ constraint from reactor experiments). \n\\label{fig:CP-contour}}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.5\\textwidth]{CPresolvedSigmaVStruedCP_NH-1tank.pdf}\n\\caption{Expected significance to exclude $\\sin\\ensuremath{\\delta_{CP}} = 0$ in case of normal hierarchy. Mass hierarchy is assumed to be known.\n\\label{fig:CP-chi2}}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{Delta3Sigma_POT-1tank.pdf}\n\\caption{Fraction of $\\ensuremath{\\delta_{CP}} $ for which $\\sin\\ensuremath{\\delta_{CP}} = 0$ can be excluded with more than 3\\,$\\sigma$ (red) and 5\\,$\\sigma$ (blue) significance as a function of the running time. \nFor the normal hierarchy case, and mass hierarchy is assumed to be known.\nThe ratio of neutrino and anti-neutrino mode is fixed to 1:3. \n\\label{fig:delta-sens-time}}\n\\end{figure}\n\nFigure~\\ref{fig:CP-contour} shows examples of the 90\\% CL allowed\nregions on the $\\sin^22\\theta_{13}$--$\\ensuremath{\\delta_{CP}} $ plane resulting from\nthe true values of $\\ensuremath{\\delta_{CP}} = (-90^\\circ, 0, 90^\\circ, 180^\\circ)$.\nThe left (right) plot shows the case for the normal (inverted) mass\nhierarchy. Also shown are the allowed regions when we include a\nconstraint from the reactor experiments,\n$\\sin^22\\theta_{13}=0.100 \\pm0.005$. With reactor constraints,\nalthough the contour becomes narrower in the direction of\n$\\sin^22\\theta_{13}$, the sensitivity to $\\ensuremath{\\delta_{CP}} $ does not\nsignificantly change because $\\delta_{CP}$ is constrained by the\ncomparison of neutrino and anti-neutrino oscillation probabilities by\nHyper-K and not limited by the uncertainty of $\\theta_{13}$.\n\nFigure~\\ref{fig:CP-chi2} shows the expected significance to exclude\n$\\sin\\ensuremath{\\delta_{CP}} = 0$ (the $CP$ conserved case). The significance is\ncalculated as $\\sqrt{\\Delta \\chi^2}$, where $\\Delta \\chi^2$ is the\ndifference of $\\chi^2$ for the \\textit{trial} value of \\ensuremath{\\delta_{CP}} \\ and\nfor $\\ensuremath{\\delta_{CP}} = 0^\\circ$ or 180$^\\circ$ (the smaller value of\ndifference is taken). We have also studied the case with a reactor\nconstraint, but the result changes only slightly.\nFigure~\\ref{fig:delta-sens-time} shows the fraction of $\\ensuremath{\\delta_{CP}} $ for\nwhich $\\sin\\ensuremath{\\delta_{CP}} = 0$ is excluded with more than 3\\,$\\sigma$ and\n5\\,$\\sigma$ of significance as a function of the integrated beam\npower. The ratio of integrated beam power for the neutrino and\nanti-neutrino mode is fixed to 1:3. The normal mass hierarchy is\nassumed. The results for the inverted hierarchy are almost the same.\n$CP$ violation in the lepton sector can be observed with more than\n3(5)\\,$\\sigma$ significance for 76(57)\\% of the possible values of $\\ensuremath{\\delta_{CP}} $.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{DeltaErr_POT-1tank.pdf}\n\\caption{Expected 68\\% CL uncertainty of $\\ensuremath{\\delta_{CP}} $ as a function of running time. \nFor the normal hierarchy case, and mass hierarchy is assumed to be known. \n\\label{fig:delta-error-time}}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{Delta3Sigma_theta23_1tank.pdf}\n\\caption{Fraction of $\\ensuremath{\\delta_{CP}} $ for which $\\sin\\ensuremath{\\delta_{CP}} = 0$ can be excluded with more than 3\\,$\\sigma$ (red) and 5\\,$\\sigma$ (blue) significance as a function of the true value of $\\sin^2\\theta_{23}$, for the normal hierarchy case.\n\\label{fig:delta-theta23}}\n\\end{figure}\n\nFigure~\\ref{fig:delta-error-time} shows the 68\\% CL uncertainty of\n$\\ensuremath{\\delta_{CP}} $ as a function of the integrated beam power.\nThe value of $\\ensuremath{\\delta_{CP}} $ can be determined with an\nuncertainty of 7.2$^\\circ$ for $\\ensuremath{\\delta_{CP}} =0^\\circ$ or $180^\\circ$, and\n23$^\\circ$ for $\\ensuremath{\\delta_{CP}} =\\pm90^\\circ$.\n\nAs the nominal value we use $\\sin^2\\theta_{23}=0.5$, but the\nsensitivity to $CP$ violation depends on the value of $\\theta_{23}$.\nFigure~\\ref{fig:delta-theta23} shows the fraction of $\\ensuremath{\\delta_{CP}} $ for\nwhich $\\sin\\ensuremath{\\delta_{CP}} = 0$ is excluded with more than 3\\,$\\sigma$ and\n5\\,$\\sigma$ of significance as a function of the true value of\n$\\sin^2\\theta_{23}$.\nT2K collaboration reported $\\sin^{2}\\theta_{23}=0.55^{+0.05}_{-0.09}$ \nin case of the normal hierarchy~\\cite{Abe:2017vif}.\n\n\\begin{table}[htbp]\n\\caption{Comparison of CP sensitivity with different configurations. As a reference, the former results published in PTEP~\\cite{Abe:2015zbg} are also shown, where 560kton fiducial volume, 7.5~MW$\\times 10^7$s integrated beam power, and an old estimate of systematic uncertainty with larger anti-neutrino errors are assumed.}\n\\begin{center}\n\\begin{tabular}{l|cc|cc}\n & \\multicolumn{2}{c|}{($\\sin\\ensuremath{\\delta_{CP}} =0$) exclusion} & \\multicolumn{2}{c}{68\\% uncertainty of $\\ensuremath{\\delta_{CP}} $}\\\\\nConfiguration & ~~$>3\\sigma$~~ & ~~$>5\\sigma$~~ & ~~$\\ensuremath{\\delta_{CP}} =0^\\circ$~~ & ~~$\\ensuremath{\\delta_{CP}} =90^\\circ$~~\\\\ \\hline \\hline\n1 tank & 76\\% & 57\\% & 7.2$^\\circ$ & 23$^\\circ$\\\\ \\hline\nStaging & 78\\% & 62\\% & 7.2$^\\circ$ & 21$^\\circ$ \\\\ \\hline\nPTEP~\\cite{Abe:2015zbg} & 76\\% & 58\\% & 7$^\\circ$ & 19$^\\circ$\\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:cp-tank-comparison}\n\\end{table}%\n\n\nTable~\\ref{tab:cp-tank-comparison} shows a comparison of several configurations for CP violation sensitivities.\n\n\\subsubsection{Precise measurements of $\\Delta m^2_{32}$ and $\\sin^2\\theta_{23}$}\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{2Dmap_Dis_050_s2th23_err_1tank.pdf}\n\\caption{ The 90\\% CL allowed regions in the $\\sin^2\\theta_{23}$--$\\Delta m^2_{32}$ plane.\nThe true values are $\\sin^2\\theta_{23}=0.5$ and $\\Delta m^2_{32} = 2.4 \\times 10^{-3}$~eV$^2$.\nEffect of systematic uncertainties is included. The red (blue) line corresponds to the result with Hyper-K alone (with a reactor constraint on $\\sin^22\\theta_{13}$).\n\\label{fig:theta23-0.50}}\n\\end{figure}\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.48\\textwidth]{2Dmap_Dis_045_s2th23_err_1tank.pdf}\n\\includegraphics[width=0.48\\textwidth]{2Dmap_Dis_045_s2th23_withDB_err_1tank.pdf}\n\\caption{ 90\\% CL allowed regions in the $\\sin^2\\theta_{23}$--$\\Delta m^2_{32}$ plane.\nThe true values are $\\sin^2\\theta_{23}=0.45$ and $\\Delta m^2_{32} = 2.4 \\times 10^{-3}$~eV$^2$.\nEffect of systematic uncertainties is included.\nLeft: Hyper-K only. Right: With a reactor constraint. \n\\label{fig:theta23-0.45}}\n\\end{figure}\n\n\\begin{table}[tbp]\n\\caption{Expected 1$\\sigma$ uncertainty of $\\Delta m^2_{32}$ and $\\sin^2\\theta_{23}$ for true $\\sin^2\\theta_{23}=0.45, 0.50, 0.55$. \nReactor constraint on $\\sin^22\\theta_{13}=0.1\\pm 0.005$ is imposed.}\n\\begin{center}\n\\begin{tabular}{ccccccc} \\hline \\hline\nTrue $\\sin^2\\theta_{23}$\t& \\multicolumn{2}{c}{$0.45$} \t\t& \\multicolumn{2}{c}{$0.50$} \t\t& \\multicolumn{2}{c}{$0.55$}\\\\ \nParameter \t\t\t\t& $\\Delta m^2_{32}$ (eV$^2$) \t& $\\sin^2\\theta_{23}$ & $\\Delta m^2_{32}$\t(eV$^2$)\t& $\\sin^2\\theta_{23}$ \t& $\\Delta m^2_{32}$ (eV$^2$)\t& $\\sin^2\\theta_{23}$\\\\ \\hline\n NH\t& $1.4\\times10^{-5}$\t\t& 0.006 \t\t\t& $1.4\\times10^{-5}$\t\t& 0.017\t\t\t\t& $1.5\\times10^{-5}$\t\t\t& 0.009\\\\\n IH & $1.5\\times10^{-5}$\t\t& 0.006 \t\t\t& $1.4\\times10^{-5}$\t\t& 0.017\t\t\t\t& $1.5\\times10^{-5}$\t\t\t& 0.009\\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:23sensitivity}\n\\end{table}%\n\nA joint fit of the $\\numu$ and $\\nue$ samples enables us to also precisely measure $\\sin^2\\theta_{23}$ and $\\Delta m^2_{32}$.\nFigure~\\ref{fig:theta23-0.50} shows the 90\\% CL allowed regions for the true value of $\\sin^2\\theta_{23}=0.5$.\nThe expected precision of $\\Delta m^2_{32}$ and $\\sin^2\\theta_{23}$ for true $\\sin^2\\theta_{23}=0.45, 0.50, 0.55$ with reactor constraint on $\\sin^22\\theta_{13}$ is summarized in Table~\\ref{tab:23sensitivity}.\n\n\\begin{figure}[tbp]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{DeltaChiOCTANTvsSin2theta23_1tank.pdf}\n\\caption{The expected significance $(\\sigma \\equiv \\sqrt{\\Delta \\chi^2})$ for wrong octant rejection, by beam neutrino measurement with reactor constraint, as a function of true $\\sin^2\\theta_{23}$ in the normal hierarchy case.\n\\label{fig:lbl-octant}}\n\\end{figure}\n\nFigure~\\ref{fig:theta23-0.45} shows the 90\\% CL allowed regions on the\n$\\sin^2\\theta_{23}$--$\\Delta m^2_{32}$ plane, for the true values of\n$\\sin^2\\theta_{23}=0.45$ and $\\Delta m^2_{32} = 2.4 \\times\n10^{-3}$~eV$^2$. With a constraint on $\\sin^22\\theta_{13}$ from the\nreactor experiments, Hyper-K measurements can resolve the octant\ndegeneracy and precisely determine $\\sin^2\\theta_{23}$.\nFigure~\\ref{fig:lbl-octant} shows the expected significance $(\\sigma \\equiv \\sqrt{\\Delta \\chi^2})$ for wrong octant rejection with beam neutrino measurement alone as a function of true value of $\\sin^2\\theta_{23}$ in the normal hierarchy case.\n\n\n\nAs discussed earlier, a precision measurement of $\\Delta m^2_{32}$,\ncompared with reactor measurements of $\\Delta m^2_{ee}$, will enable a\nconsistency check of the mixing matrix framework. The difference\nexpected from the current knowledge of oscillation parameters is a\nfew \\%. The uncertainty of $\\Delta m^2_{32}$ by Hyper-K is expected\nto reach $0.6\\%$, while measurements by future reactor experiments are\nexpected to achieve $<1\\%$ precision. Thus, the comparison will yield\na significant consistency check.\n\n\\subsubsection{Summary}\nThe sensitivity to leptonic $CP$ asymmetry of a long baseline\nexperiment using a neutrino beam directed from J-PARC to the\nHyper-Kamiokande detector has been studied based on a full simulation\nof beamline and detector. \nWith $1\\times$10$^8$~sec of running time with 1.3~MW beam power,\nthe value of $\\ensuremath{\\delta_{CP}} $ can be determined with 7.2$^\\circ$ for $\\ensuremath{\\delta_{CP}} =0^\\circ$ \nor $180^\\circ$, and 23$^\\circ$ for $\\ensuremath{\\delta_{CP}} =\\pm90^\\circ$. \n$CP$ violation in the lepton sector can be observed with more than\n3~$\\sigma$(5~$\\sigma$) significance for 76\\%(57\\%) of the possible\nvalues of $\\ensuremath{\\delta_{CP}} $.\nUsing both $\\nu_e$ appearance and $\\nu_\\mu$ disappearance data,\nprecise measurements of $\\sin^2\\theta_{23}$ and $\\Delta m^2_{32}$ will\nbe possible. The expected 1$\\sigma$ uncertainty of\n$\\sin^2\\theta_{23}$ is 0.017 (0.006) for $\\sin^2\\theta_{23}=0.5 (0.45)$.\nThe uncertainty of $\\Delta m^2_{32}$ is expected to reach $<1\\%$.\n\nThere will be also a variety of measurements possible with both near\nand far detectors, such as neutrino-nucleus interaction cross section\nmeasurements and search for exotic physics, using the well-understood\nneutrino beam.\n\n\\subsubsection{Neutrino cross section measurements}\n\nWith a set of highly capable neutrino detectors envisioned for Hyper-K\nproject, a variety of neutrino interaction cross section measurements\nwill become possible. The near detector suite offers a range of\ncapabilities to probe different theoretical models for neutrino\ninteractions: in particular data across different momenta ranges and a\nrange of lepton emission angles. Figure~\\ref{fig:lbl-ndcrosseff} shows\nthe efficiency of different detectors as a function of angle and muon\nmomentum. The ability to measure exclusive hadronic final states,\nusing techniques such as high pressure gas TPCs or emulsion detectors,\nprovides valuable additional information for exclusive\ncross-sections. In table\n\\ref{tab:lbl-ndcross} we estimate the sensitivity of each proposed near detector for key selections \nbased on a flux of $10^{21}$POT.\n\n \\begin{table}[htbp]\n\\begin{center}\n\\begin{tabular}{|c|c|c|p{5.5cm}|} \\hline\nDetector\t& Selection & Nevents & Selection Characteristics \\\\ \\hline\\hline\nND280 detector, 280m\t& $\\nu_{\\mu}$CC0$\\pi$ & 20k\t& FGD1 (1--3\\,GeV), $P\\approx $72\\% \\cite{Abe:2015awa}\t \\\\ \\hline\nND280 detector, 280m\t& $\\nu_{\\mu}$CC1$\\pi$ & 6k\t& FGD1 (1--3\\,GeV), $P\\approx $50\\%\\ \\cite{Abe:2015awa}\t \\\\ \\hline\nND280 detector, 280m\t& $\\nu_{\\mu}$CC inclusive & 40k\t& FGD1 (1--3\\,GeV), $P\\approx $90\\%\\cite{Abe:2015awa}\t \\\\ \\hline\n\\hline\nINGRID & $\\nu_{\\mu}$CC inclusive & 17.6$\\times 10^6$ & $\\epsilon>$70\\% (1--3\\,GeV), $P = $ 97\\% \\cite{Abe:2015biq}\\\\ \\hline\n\\hline\nHPTPC, 8\\,m$^3$, 10\\,bar Ne (CF$_4$) & $\\nu_{\\mu}$CC inclusive & 4.2k (18.4k) & $\\epsilon \\approx $70\\%, protons $>$ 5\\,MeV detected \\\\ \\hline\nHPTPC, 8\\,m$^3$, 10\\,bar Ne (CF$_4$) & $\\nu_{e}$CC inclusive & 80 (450) & $\\epsilon \\approx $70\\%, protons $>$ 5\\,MeV detected \\\\ \\hline\n\\hline\nWAGASCI\t & $\\nu_{\\mu}$CC0$\\pi$ & 63k &P=75\\%, proton reconstruction: $\\epsilon \\approx 15$\\% at p=500\\,MeV\/c, water in; $\\epsilon \\approx 27$\\% at p=250\\,MeV\/c, water out (15\\% @ 150MeV\/c) \\\\ \\hline\nWAGASCI\t & $\\nu_{\\mu}$CC1$\\pi$ & 10k &P=50\\% (protons as above)\\\\ \\hline\nWAGASCI\t & $\\nu_{\\mu}$CC inclusive & 75k &P=96\\% (protons as above)\\\\ \\hline\n\n\\hline\n200kg Water target \t\t& $\\nu_\\mu$ CC+NC inclusive & 10k-20k & 4$\\pi$ automated readout \\\\\nemulsion off-axis, 280m & & & proton $>$ 10-30\\,MeV detected \\\\ \\hline\n200kg Water target \t& $\\nu_e$ CC inclusive & 1k & 4$\\pi$ automated readout \\\\\nemulsion off-axis, 280m & & & proton $>$ 10-30\\,MeV detected \\\\ \\hline\n\n\\hline\n1kton WC \\@ 1\\,km & $\\nu_{\\mu}$CC0$\\pi$ (1-2$^{\\circ}$,2-3$^{\\circ}$,3-4$^{\\circ}$) & 1682k,1060k,519k & $P\\approx$92\\%,95\\%,95\\% \\\\ \\hline \n1kton WC \\@ 1\\,km & $\\bar{\\nu}_{\\mu}$CC0$\\pi$ (1-2$^{\\circ}$,2-3$^{\\circ}$,3-4$^{\\circ}$) & 519k,331k,186k & $P\\approx$74\\%,77\\%,76\\% \\\\ \\hline \n1kton WC \\@ 1\\,km & $\\nu_{\\mu}$CC1$\\pi$ (1-2$^{\\circ}$,2-3$^{\\circ}$,3-4$^{\\circ}$) & 208k,65k,27k & $P\\approx$46\\%,44\\%,31\\% \\\\ \\hline \n1kton WC \\@ 1\\,km & $\\nu_{e}$CC0$\\pi$ (1-2$^{\\circ}$,2-3$^{\\circ}$,3-4$^{\\circ}$) & 11.2k,6.9k,4.6k & $P\\approx$54\\%,71\\%,80\\% \\\\ \\hline \n1kton WC \\@ 1\\,km & $\\nu$NC$\\pi^{0}$ (1-2$^{\\circ}$,2-3$^{\\circ}$,3-4$^{\\circ}$) & 300k,111k,45k & $P\\approx$58\\%,63\\%,60\\% \\\\ \\hline \n\\end{tabular}\n\n\\caption{\nSome of the primary cross-section measurements accessible with\ndifferent elements of the Near Detector Suite (see chapter 2 for\ndetails). The predicted number of events or measurement precision have\nbeen evaluated for $10^{21}$POT. $\\epsilon$ = efficiency = number\nselected \/ total events for given topology, $P$ = purity = number of\ngiven topology \/ total events selected. For the ND280 measurements\nonly events for a single fine grained detector (FGD1) are projected,\nthe second FGD plus the use of other detector components as targets\nincreases the statistics. Numbers are obtained either from independent\nMonte Carlo studies, or extrapolated from the cited references.}\n\n\\label{tab:lbl-ndcross}\n\\end{center}\n\\end{table}%\n\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[width=0.85\\textwidth]{NDeffPlot.pdf}\n\\caption{\nExample detector efficiency in muon momentum and direction. a) A\nhorizontally oriented 2\\,kton cylindrical intermediate WC detector at\n2km, b) the same detector vertically oriented with respect to the\nbeam, c) the current ND280 near detector and d) the WAGASCI\ndetector. Good coverage of this phase space helps to constrain\nuncertainties in cross-section models. }\n\\label{fig:lbl-ndcrosseff}\n\\end{center}\n\\end{figure}\n\n\\subsection{Accelerator based neutrinos \\label{sec:cp}}\n\n\\input{physics-lbl\/lbl-intro.tex}\n\\input{physics-lbl\/lbl-observable.tex}\n\\input{physics-lbl\/lbl-method.tex}\n\\input{physics-lbl\/lbl-resuts.tex}\n\\input{physics-lbl\/lbl-xsec.tex}\n\\input{physics-lbl\/lbl-newphysics.tex}\n\\input{physics-lbl\/lbl-summary.tex}\n\n\\subsection{Impact of Photocathode Coverage and Improved Photosensors}\\label{section:pdecay-coverage}\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/hit_neutron_gamma_3tanks.pdf}\n \\end{center}\n \\caption{Number of hit PMTs for a toy MC simulation of the 2.2\\,MeV $\\gamma$ rays \n emitted following neutron capture on hydrogen. \n Cutting at more than nine hits in the Super-K distribution yields an \n estimated 18\\% tagging efficiency.}\n \\label{fig:n_dg_p_nhit}\n\\end{figure} \n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/pdk_ntag_70pc.pdf}\n \\end{center}\n \\caption{Neutron multiplicity distribution for background events in the $p \\rightarrow e^{+}\\pi^{0}$\n search at Hyper-K. The red histogram shows the distribution prior to \n neutron tagging and the green histogram shows the result of \n applying a tagging algorithm with 70\\% efficiency. }\n \\label{fig:ep0_n_mult}\n\\end{figure} \n\nImproved photon collection with larger photocathode coverages, higher\nquantum efficiency photosensors, and their combination have\na dramatic effect on the physics sensitivity of Hyper-K. \nNucleon decay searches, in particular, are expected to benefit significantly\nfrom enhanced ability to detect low levels of Cherenkov light. With\nthe large exposures Hyper-K will provide, the atmospheric neutrino\nbackground to these searches becomes sizable and\ncan inhibit the discovery potential of the experiment. However, these\nsame backgrounds are often expected to produce neutrons either\ndirectly through the CC interaction of antineutrinos or indirectly via\nthe secondary interaction of hadrons in the interaction. Proton decay\nevents, in contrast, are only rarely expected to be accompanied by\nneutrons. Though such neutrons are ordinarily transparent to water\nCherenkov detectors, Super-Kamiokande has demonstrated the ability to\ntag the 2.2\\,MeV photon emerging from neutron capture on hydrogen,\n$n(p,d)\\gamma$. Naturally this channel will be available to\nHyper-K.\nIn this section we compare the performance of Hyper-K 1TankHD\\, configuration with its 40\\% photocathode \ncoverage and high quantum efficiency photosensors\nagainst a design with 20\\% coverage and the same PMTs used in Super-K.\n\nSince 2.2\\,MeV is only barely visible in Super-K, their tagging algorithm\nmakes use of a neural network to isolate signal neutrons, which are\ncorrelated spatially and temporally with the primary neutrino\ninteraction, from background sources. Though the method achieved\n20.5\\% tagging efficiency with a 1.8\\% false tag\nprobability~\\cite{Wendell:2014dka} it is worth noting that so far it\nhas only been successful during the SK-IV phase of the experiment.\nDespite 40\\% photocathode coverage with Hamamatsu R3600 50~cm PMTs, on\naverage the neutron capture signal produces only 7~hits in the\ndetector~\\cite{Wendell:2014dka}. Since the average photon travel\nlength in Hyper-K will be larger than that of SK-IV, in order to take\nadvantage of the neutron signal it is essential to augment Hyper-K's\nphoton yield wherever possible.\n\nWhile a full analysis of Hyper-K's neutron tagging capability is in\ndevelopment a rough estimation for the 1TankHD\\, design \n(c.f. Section~\\ref{section:photosensors}) has been determined via\nsimulation. Figure~\\ref{fig:n_dg_p_nhit} shows the number of hit\nphotosensors for a simulated sample of the 2.2\\,MeV $\\gamma$ ray\nemitted when a neutron captures on a proton for three water Cherenkov\ndetector configurations. The green distribution shows the response of\na Super-K-sized detector with 40\\% photocathode coverage by Hamamatsu\nR3600 PMTs, while the blue line shows the effect of implementing the HQE\nBox and Line photosensors. \nUsing the same photocathode coverage and the\nlatter photosensors but with an enlarged tank representative of a\nthe Hyper-K design (60~m diameter and 74~m height results)\nresults in the red curve. Using these distributions the number of hit\nphotosensors which reproduces the tagging efficiency realized in the\nSuper-K analysis is chosen as the metric to represent the expected\ntagging efficiency at Hyper-K. For the Super-K distribution gamma\nevents with more than nine PMT hits result in an 18\\% tagging efficiency.\nAssuming the same 10 hit threshold can be used at Hyper-K, the\nequivalent distribution (red curve in the figure) suggests 73\\%\nefficiency can be achieved. The sensitivity studies presented in this \ndocument assume this number for Hyper-K when neutron tagging is employed. \nIn what follows sensitivity estimates are\npresented assuming both this and the Super-K tagging efficiency for comparison.\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/epi0_bkg_reduction_exposure.pdf}\n\\end{center}\n\\caption {Hyper-K sensitivity to proton decay for the $p \\rightarrow e^{+}\\pi^{0}$ mode \n as a function of exposure. The black curve illustrates the sensitivity \n assuming equivalent performance to Super-K.\n Improved sensitivity curves as a result of a finer binned signal region \n (red) in conjunction with a 50\\% reduction in background (green) \n or a 70\\% reduction (blue) are also shown.\n The latter is the analysis presented in Section~\\ref{section:pdecay}. }\n\\label{fig:ep0_bkg_exp}\n\\end{figure} \n\n\nBased on MC studies, the fraction of atmospheric neutrino backgrounds\nto the $p \\rightarrow e^{+}\\pi^{0}$ search which are accompanied by at\nleast one final state neutron is $> 80\\%$. At the same time, only 4\\%\nof signal MC events have such a neutron. The multiplicity\ndistribution for the background sample is shown in\nFigure~\\ref{fig:ep0_n_mult}. Due to the presence of high multiplicity\nevents, assuming 70\\% neutron tagging efficiency, the\nneutron background can be reduced by approximately 70\\% (green\nhistogram) by rejecting events with one or more neutron tags.\nReducing the background in this manner will have a large impact on the\nsensitivity to this decay mode, as shown in\nFigure~\\ref{fig:ep0_bkg_exp}. In the figure the black curve represents\nthe sensitivity of the analysis without neutron tagging and cuts defining \nonly a single signal region.\nIf that signal region is divided into a piece where free proton\ndecays are enhanced ($p_{tot} < 100 \\mbox{MeV\/c}^{2}$) and a region\nwith predominantly bound decays ($p_{tot} > 100 \\mbox{MeV\/c}^{2}$), as is assumed \nin the analysis above, the\nresulting sensitivity is shown by the red line. Further, if the total\nbackground is then reduced by 50\\% (70\\%), by the introduction of\nneutron tagging, the sensitivity improves as shown in\nthe green (blue) lines. \nWith these background reductions Hyper-K will require exposures of \n3.0 and 2.4 Mton $\\cdot$years to reach lifetime limits of $10^{35}$ years if no signal is observed.\nWithout any background reduction 7.0~Mton$\\cdot$years are required.\n\n\nIt should be noted that $p \\rightarrow e^{+}\\pi^{0}$ is not the only\nmode that is expected to benefit from a higher photon yield; Most\nmodes are similarly expected to have reduced atmospheric neutrino\nbackgrounds with neutron tagging. However, the $p\n\\rightarrow \\bar \\nu K^{+}$ search can also benefit from enhanced\nlight collection to improve the signal efficiency. Its two lowest\nefficiency, but most sensitive search modes, one in which the decay is\naccompanied by a prompt 6.3 MeV de-excitation $\\gamma$ from the\nrecoiling nucleus and the other in which the $K^{+}$ decays into\n$\\pi^{+}\\pi^{0}$, both have components that are looking for small\namounts of light. Higher photon yields are thus connected directly to\nefficiency improvements in these channels.\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/ngam-bl.pdf}\n\\end{center}\n\\caption {Distribution of the number of hits within a 12~nsec timing window used to search for the 6.3 MeV $\\gamma$ \n from $p \\rightarrow \\bar \\nu K^{+}$ events. \n The upper panel corresponds to a Hyper-K design with 20\\% photocathode coverage \n and the same PMTs used in SK (Hamamatsu R3600).\n In the lower panel the result for the 1TankHD\\, design is shown. \n Red (blue) lines show the proton decay signal (atmospheric neutrino background) distribution. \n The proton decay signal region is defined as $4 < N_{\\gamma} < 30$ hits and $8 < N_{\\gamma} < 120$ \n for the 20\\% coverage and 1TankHD\\, coverage designs, respectively.\n Vertical lines in the plots show the lower bound of these signal regions. }\n\\label{fig:ngam-bl}\n\\end{figure} \n\nAs discussed above, the search for the prompt $\\gamma$ ray is done\nusing the number of hit PMTs within a 12~nsec wide timing widow prior\nto the muon candidate from the $K^{+} \\rightarrow \\mu^{+} \\nu$\n(c.f. Figure~\\ref{fig:prompt-gamma}). Figure~\\ref{fig:ngam-bl} shows\nthis distribution for the proton decay signal (red) and background\nfrom atmospheric neutrinos (blue) for a Hyper-K design with\n20\\% photocathode coverage (upper panel) and the 1TankHD\\, design. \nIn the latter study the photon yield is assumed to be 1.9\ntimes greater than that of the PMT used in the 20\\% coverage design and\nwith half the intrinsic timing resolution of the photosensor\n(1~nsec at 1~p.e.). Additionally, these sensors are assumed to have a\nhigher dark rate of 8.4~kHz. For both detector configurations the peak\nnear zero corresponds to events in which a $\\gamma$ was not found; \nthese hits are dominated by dark noise. Though\nthis peak is not well separated from the feature at higher hits in the\n20\\% coverage configuration, with improved photosensors and 40\\% coverage a clear distinction\nbetween the two can be seen. Further, since the $\\gamma$ search is\ndesigned to avoid hit contamination from the $\\mu^{+}$, the narrower\ntiming resolution of the improved sensors means that the search can\noccur closer in time to the muon. Practically speaking, this means $K^{+}$\nwith earlier decay times can be used in the analysis as shown in\nFigure~\\ref{fig:gam-eff}. Both of these effects lead to an overall\nincrease in the signal efficiency of the $p \\rightarrow \\bar \\nu K^{+}$\nmode. Based on this distribution the proton decay signal region is\ndefined as $4 < N_{\\gamma} < 30$ hits for the 20\\% coverage design \nand $8 < N_{\\gamma} < 120$ for the 1TankHD\\, case.\n\n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/eff-gam.pdf}\n\\end{center}\n\\caption {Prompt $\\gamma$ tagging efficiency as a function of the \n $K^{+}$ decay time for the $p \\rightarrow \\bar \\nu K^{+}$ decay mode. \n A Hyper-K design with only 20\\% photocathode coverage is shown in black and \n the design with 40\\% photocathode coverage and photosensors with 1.9 times \n higher photon yield (1TankHD\\, ) is shown in red. \n }\n\\label{fig:gam-eff}\n\\end{figure} \n\nAccordingly, the signal efficiency for the prompt $\\gamma$ tag method\nto search for $p \\rightarrow \\bar \\nu K^{+}$ increases from 6.7\\% in\nthe design with 20\\% photocathode coverage to 12.7\\% in the 1TankHD\\, configuration.\nThough not detailed here, improved tagging of the $\\pi^{+}$ from the\n$K \\rightarrow \\pi^{+} \\pi^{0}$ component of this search yields 10.2\\%\nsignal efficiency in the 1TankHD\\, design compared to 6.7\\% in the\n20\\% coverage case.\nAs in the $p \\rightarrow e^{+} \\pi^{0}$ study\nabove, if neutron tagging with 70\\% efficiency is assumed\n(c.f. Figure~\\ref{fig:ep0_bkg_exp}) the background to these $p\n\\rightarrow \\bar \\nu K^{+}$ search methods can be reduced to 0.87 and\n0.71~events\/Mton$\\cdot$year, respectively. For comparison the\nbackground rates are 2.8 and\n3.4~events\/Mton$\\cdot$year without neutron tagging. \nFigure~\\ref{fig:bl-sens} shows the\ncorresponding sensitivity curves for both the design with 20\\% coverage (black) and\nfor the 1TankHD\\, design (red). Two vertical lines at exposures of 1.9 and\n5.6~Mton$\\cdot$year in the figure denote positions of comparable\nsensitivity between the two designs. \n\n\\begin{figure}[htbp]\n\\begin{center}\n \\includegraphics[scale=0.35]{physics-pdecay\/figures\/nuk-sens-bl.pdf}\n\\end{center}\n\\caption {Sensitivity to $p \\rightarrow \\bar \\nu K^{+}$ at 90\\% C.L. for the 1TankHD\\, design is shown in red. \n The black curve shows the corresponding sensitivity for a design with 20\\% coverage and Super-K PMTs. }\n\\label{fig:bl-sens}\n\\end{figure} \n\nIt should be noted that since backgrounds for the Super-K neutron\ntagging algorithm are taken from its data, it is difficult to provide\na realistic estimate of the potential of a similar algorithm at\nHyper-K at this time. \nHowever assuming similar performance, Hyper-K's dramatic\nimprovement in proton decay sensitivity makes this topic among the\nmost fundamental to the development of its future program. It is clear\nthat the potential for a discovery is connected to\nHyper-K's background reduction and efficiency enhancement\ncapabilities, both of which are realizable with higher photon yields.\n\n\n\n\n\\subsection{Nucleon decays }\\label{section:pdecay}\nOptimizing Hyper-Kamiokande for the observation and discovery of a\nnucleon decay signal is one if its primary design drivers. In order\nto significantly extend sensitivity beyond existing limits, many of\nwhich have been set by Super-Kamiokande, Hyper-K needs both a much\nlarger number of nucleons than its predecessor and sufficient\nreconstruction ability to extract signals and suppress backgrounds.\nWhile it is possible to target specific decay channels, one of the\nstrengths of water Cherenkov technology is its sensitivity to a wide variety\nof modes. Using MC and analysis techniques originally developed for\nSuper-Kamiokande, this section details Hyper-K's expected sensitivity\nto both the flagship proton decay modes, $p \\rightarrow e^{+} \\pi^{0}$\nand $p \\rightarrow \\overline{\\nu} K^{+}$, as well as other $\\Delta\n(B-L)$ conserving, $\\Delta B =2$ dinucleon, and $\\Delta (B-L)=2$ decays. \n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[scale=0.4]{physics-pdecay\/figures\/epi0_massmom_pdk_corr.pdf}\n \\includegraphics[scale=0.4]{physics-pdecay\/figures\/epi0_massmom_atmc.pdf}\n \\end{center}\n\\caption {Reconstructed invariant mass and total momentum distributions for the $p \\rightarrow e^{+} \\pi^{0}$ \n MC (left) and atmospheric neutrino MC (right) after all\n event selections except the cuts on these variables. The\n final signal regions are shown by two black boxes in the\n plane. In the signal plot decays from bound and free\n protons have been separated by color, dark blue and cyan\n respectively. Background events have been generated for a\n 45~Mton$\\cdot$year exposure and those falling in the signal\n regions have been enlarged for\n visibility. } \\label{fig:epi0_plane}\n\\end{figure} \n\n\n\n\n\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.47\\textwidth,trim={0 4.5cm 0 4cm},clip]{physics-pdecay\/figures\/totmom-1hd.pdf}\n \\includegraphics[width=0.45\\textwidth]{physics-pdecay\/figures\/totmass-1tank.pdf}\n \\end{center}\n\\caption { Total momentum distribution of events passing all steps of the $p \\rightarrow e^{+} \\pi^{0}$ event selection \n except the momentum cut after a 10 year exposure of a single Hyper-K tank (left).\n Reconstructed invariant mass distribution of events passing all steps of the $p \\rightarrow e^{+} \\pi^{0}$ event selection \n except the invariant mass cut after a 10 year exposure of a single Hyper-K tank (right).\n The hatched histograms show\n the atmospheric neutrino background and the solid crosses\n denote the sum of the background and proton decay\n signal. Here the proton lifetime is assumed to be,\n $1.7 \\times 10^{34}$\\,years, just beyond current Super-K\n limits. \n The free and bound proton-enhanced bins are shown by the lines in the left plot, \n and are the upper and lower panels of the right plot. } \\label{fig:pmass_epi0}\n\\end{figure} \n\n\n\n\n\\subsubsection{Sensitivity to $p \\rightarrow e^{+} + \\pi^{0}$ Decay}\nProton decay into a positron and neutral pion is a favored mode of\nmany GUT models.\nExperimentally this decay has a very clean\nevent topology, with no invisible particles in the final state. As a\nresult it is possible fully reconstruct the proton's mass from its\ndecay products and as a two body process the total momentum of\nthe recoiling system should be small. The event selection focuses on\nidentifying fully contained events within the Hyper-K fiducial volume\nwith two or three electron-like Cherenkov rings. Though the decay of\nthe pion is expected to produce two visible gamma rays, for\nforward-boosted decays the two photons may be close enough in space to\nbe reconstructed as a single ring. Atmospheric neutrino events with\na muon below threshold are removed by requiring there are no Michel\nelectrons in the event. For those events with three rings, the two\nrings whose invariant mass is closest to the $\\pi^{0}$ mass are\nlabeled the $\\pi^{0}$ candidate. An additional cut on the mass of\nthose candidates, $ 85 < m_{\\pi} < 185$~MeV\/$c^{2}$, is applied.\nThe signal sample is selected by requiring the total invariant mass of\nthe event be near the proton mass, $800 < m_{inv} <\n1050$~MeV\/$c^{2}$ and that the total momentum, $p_{tot}$, be less\nthan 250~MeV\/$c$. Water is an excellent molecule for studying proton\ndecay because in addition to providing 10 protons per molecule, two of\nthose are unbound free protons. Decays from those protons are not\nsubject to nuclear effects and result in final state particles with\nvery low total momentum. At the same time, very few atmospheric\nneutrino interactions are reconstructed with both a proton-like invariant\nmass and low total momentum. To optimize the analysis sensitivity,\nproton-decay candidates are divided into two signal regions after the\ninvariant mass cut, a free proton decay enriched region ($0 < p_{tot}\n< 100$~MeV\/$c$) and a bound proton decay region ($100 < p_{tot}\n< 250$~MeV\/$c$). \nFinally, neutron tagging (described in a later section)\nis used to reject background events by requiring events have no neutron candidates\nin the final state.\nFigure~\\ref{fig:epi0_plane} shows the signal\nand background MC in the invariant mass and total momentum plane\nbefore the final signal region is defined. Signal efficiencies and\nbackground rates with corresponding systematic errors after all\nselections are listed in Table~\\ref{tbl:pdkepi0}.\n\n\\begin{table}[htb]\n \\begin{center}\n \\begin{tabular}{c|c||c|c}\n\\hline\n\\hline\n\\multicolumn{2}{c||}{ $0 < p_{tot} < 100$~MeV\/$c$ } & \\multicolumn{2}{c}{ $100 < p_{tot} < 250$~MeV\/$c$ } \\\\\n$\\epsilon_{sig}$ [\\%] & Bkg [\/Mton$\\cdot$yr] & $\\epsilon_{sig}$ [\\%] & Bkg [\/Mton$\\cdot$yr] \\\\\n\\hline\n\\hline\n$18.7 \\pm 1.2$ & $0.06 \\pm 0.02$ & $19.4 \\pm 2.9$ & $0.62 \\pm 0.20$ \\\\\n\\hline\n\\hline\n \\end{tabular}\n \\end{center}\n \\caption{Signal efficiency and background rates as well as estimated systematic uncertainties \n for the $p \\rightarrow e^{+} \\pi^{0}$ analysis at Hyper-K. }\n \\label{tbl:pdkepi0}\n\\end{table}\n\n\n\n\\begin{figure}[p]\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth,trim={0 0.5cm 0 0},clip]{physics-pdecay\/figures\/hk_epi0_disco_overlay_exposure_1and2HD_DUNE_JUNO_SK3s_C_year.pdf}\n \\end{center}\n \\caption{Comparison of the 3~$\\sigma$ $p \\rightarrow e^{+}\\pi^{0}$ discovery potential as a function of year\n Hyper-K (red solid) assuming a single tank \n as well as that of the 40~kton liquid argon detector DUNE (cyan solid) following~\\cite{Acciarri:2015uup}. \n In the orange dashed line an additional Hyper-K tank is assumed to\n come online six years after the start of the experiment.\n Super-K's discovery potential in 2026 assuming 23 years of data is also shown.\n }\n \\label{fig:epi_discovery}\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth,trim={0 0.5cm 0 0},clip]{physics-pdecay\/figures\/hk_epi0_limit_overlay_exposure_1and2HD_DUNE_JUNO_SK90pc_L_year.pdf}\n \\end{center}\n\\caption {Hyper-K's sensitivity to the $p \\rightarrow e^{+} \\pi^{0}$ decay mode \n at 90\\% C.L. as a function of run time appears in red assuming one detector in comparison with other experiments (see caption of Figure~\\ref{fig:epi_discovery}).\n Super-K's current limit is shown by a horizontal line.\n }\n \\label{fig:sens_epi0}\n\\end{figure}\n\nMonte Carlo simulation of these decays includes the effects of the\nnucleon binding energy, Fermi motion, and interactions within the\n$^{16}O$ nucleus. The latter represents a significant, but\nunavoidable, source of inefficiency as the signal $\\pi^{0}$ may be\nlost to absorption or charge exchange prior to exiting the nucleus.\nAlthough the signal efficiency of free proton decays is roughly 87\\% \nthese nuclear effects reduce the\nefficiency of bound proton decays such that the overall efficiency is\nonly $\\sim$ 40\\% when all decays are considered.\n\n\nAtmospheric neutrino interactions are the main background to proton\ndecay searches. Not only can CC $\\nu_{e}$ single-pion production\nprocesses produce the same event topology expected in the\n$p \\rightarrow e^{+} \\pi^{0}$ decay, but recoiling nucleons from\nquasi-elastic processes can produce pion final states through hadronic\nscatters that mimic the signal. After the event selection above the\nexpected background rate is 0.06 events in the free proton\nenhanced bin and 0.62 events in the bound proton enhanced bin\nper Mton$\\cdot$year.\nThese background expectations have been experimentally verified using\nbeam neutrino measurements with the K2K experiment's one kiloton water\nCherenkov detector, which found an expected atmospheric neutrino\nbackground contamination to $p \\rightarrow e^{+} \\pi^{0}$ searches of\n$1.63^{+0.42}_{-0.33}(stat)^{+0.45}_{-0.51}(sys)$ events per\nMegaton$\\cdot$year~\\cite{Mine:2008rt} without neutron tagging.\n\n\nThe ability to reconstruct the proton's invariant mass is a powerful\nfeature of this decay mode. The left panel of Figure~\\ref{fig:pmass_epi0} shows the\nexpected distribution of this variable for both signal events and\natmospheric neutrino backgrounds after a 10 year exposure assuming the\nproton lifetime is $\\tau_{x} = 1.7 \\times 10^{34}$ years. \nSimilarly, the left panel shows the total momentum distribution\nof candidate events prior to the momentum selection.\nBoth plots illustrate \nthe marked difference in the signal and background expectations \nfor the free proton and bound proton analysis bins.\n\nHyper-Kamiokande's proton decay discovery potential has been estimated \nbased on a likelihood ratio method. \nA likelihood function is constructed from a Poisson probability density \nfunction for the event rate in each total momentum bin of the $p \\rightarrow e^{+} \\pi^{0}$\nanalysis with systematic errors on the selection efficiency and background \nrate represented by Gaussian nuisance parameters.\nThe experiment's expected sensitivity to a proton decay signal at a given \nconfidence level, $\\alpha$, is calculated as the fastest proton decay rate, $\\Gamma$, \nwhose median likelihood ratio value assuming a proton decay signal\nyields a p-value not larger than $\\alpha$ from the likelihood ratio distribution\nunder the background-only hypothesis.\nThat is, \n\\begin{equation}\n\\Gamma_{disc} = \\max_{\\Gamma} \\left[ \\alpha = \\int_{ M(\\Gamma) }^{\\infty} f( q_{0} | b ) d q_{0} \\right], \n\\end{equation}\n\\noindent where $f$ is the distribution function of the likelihood ratio, $q_{\\Gamma}$, and \n$ M(\\Gamma) = \\mbox{median}[ f( q_{\\Gamma} | \\Gamma \\epsilon \\lambda + b ) ]$. \nHere $\\epsilon$ is the selection efficiency, $\\lambda$ the detector exposure, \nand $b$ is the expected number of background events.\nFor the calculated significance the corresponding proton lifetime is then $\\tau_{disc} = 1\/\\Gamma_{disc}$.\nUnder this definition Hyper-K's $3 \\sigma$ (one-sided) discovery potential as a function of run\ntime is shown in Figure~\\ref{fig:epi_discovery}. Note that if the\nproton lifetime is as short as $\\tau_{x}$ its decay into\n$e^{+}\\pi^{0}$ will be seen at this significance within two years of\nHyper-K running. \n\nEven in the absence of a signal Hyper-K is expected\nto extend existing limits considerably.\nHyper-K's sensitivity to this decay mode is computed as\n\\begin{equation}\n\\tau_{limit} = \\sum_{n=0}^{\\infty} O(n|b) \/ \\Gamma_{n},\n\\end{equation}\n\\noindent where\n\\begin{equation}\n\\Gamma_{n} = \\left[ \\Gamma_{l} : 1 - \\alpha = \\int_{0}^{\\Gamma_{l}} P( \\Gamma | n ) d\\Gamma \\right]\n\\end{equation}\n\\noindent and $P( \\Gamma | n )$ is the probability that the proton decay rate is $\\Gamma$ given \nan observation of $n$ events. \nSimilarly, $O(n|b)$ is the Poisson probability to observe $n$ events given a mean of $b$.\nThe function $P( \\Gamma | n )$ is obtained using Bayes' theorem and the likelihood function \noutlined above. \nHyper-K's expected sensitivity to $p \\rightarrow e^{+} \\pi^{0}$ using this metric is shown \nin Figure~\\ref{fig:sens_epi0}.\nIn both this and the discovery potential figure, systematic errors on the signal and background have been\nincluded based on the Super-K analysis; The errors are listed in Table~\\ref{tbl:pdkepi0}. \nA detailed description of the systematic error estimation and the limit calculation may be found\nin~\\cite{Nishino:2012bnw}.\n\n\n\n\\subsubsection{Sensitivity study for the $p \\rightarrow \\overline{\\nu} K^{+}$ mode} \n\nProton decays into a lepton and a kaon are a feature of supersymmetric grand unified theories, of\nwhich $p \\rightarrow \\overline{\\nu} K^{+}$ is among the most\nprominent. Searching for the $K^{+}$ in a water Cherenkov detector is\ncomplicated by the fact it emerges from the decay with a momentum of\nonly 340\\,MeV\/$c$, well below the threshold for light production,\n749\\,MeV\/$c$. As a result the $K^{+}$ must be identified by its decay\nproducts: $K^+ \\to \\mu^{+}+\\nu$ (64\\% branching fraction) and\n$K^+ \\to \\pi^{+}+\\pi^{0}$ (21\\% branching fraction). Since both of\nthese modes are two body decays the outgoing particles have\nmonochromatic momenta. Furthermore, the 12~ns lifetime of the kaon\nmakes it possible to observe prompt $\\gamma$ ray emission produced\nwhen the proton hole leftover from a bound proton decay is filled by the\nde-excitation of another proton. For $^{16}O$ nuclei the probability\nof producing a 6\\,MeV $\\gamma$ from such a hole is roughly 40\\%, making\nthis a powerful tool for identifying the $K^{+}$ decay products and rejecting \natmospheric neutrino backgrounds.\n\nThree methods, each targeting different aspects of the $K{+}$ decay,\nare used to search for $p \\rightarrow \\overline{\\nu} K^{+}$\nevents~\\cite{Abe:2014mwa}. The ``prompt $\\gamma$'' method searches\nfor a prompt nuclear de-excitation $\\gamma$ ray (6.3\\,MeV) occurring\nprior to and separated in time from a 236\\,MeV\/$c$ muon. A schematic\nof this process appears in Figure~\\ref{fig:prompt-gamma}. In the\nsecond method the same monochromatic muon is searched for but without\nthe $\\gamma$ tag. Finally, the third method, or ``$\\pi^{+}\\pi^{0}$\nmethod'', searches for a monochromatic $\\pi^{0}$ with light from a\nbackward $\\pi^{+}$. Here the charged pion is only slightly above\nCherenkov threshold, making it difficult to reconstruct a full \nring.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[height=19pc]{physics-pdecay\/figures\/t-sample.pdf}\n \\end{center}\n\\caption {Schematic view of the expected timing distribution of events in the \n prompt $\\gamma$ search method for $p \\rightarrow \\overline{\\nu} K^{+}$ decays.\n The upper panel shows the full event time window with the $\\mu$, Michel, \n and $\\gamma$ candidate clusters. The bottom panel shows the time of flight \n subtracted timing distribution around the $\\mu$ candidate.\n }\n \\label{fig:prompt-gamma}\n\\end{figure}\n\n\\begin{table}[htb]\n \\begin{center}\n \\begin{tabular}{c|c||c|c||c|c||c}\n\\hline\n\\hline\n\\multicolumn{2}{c||}{ Prompt $\\gamma$ } & \\multicolumn{2}{c||}{ $\\pi^{+}\\pi^{0}$ } & \\multicolumn{3}{c}{ $p_{\\mu}$ Spectrum } \\\\\n$\\epsilon_{sig}$ [\\%] & Bkg [\/Mton$\\cdot$yr] & $\\epsilon_{sig}$ [\\%] & Bkg [\/Mton$\\cdot$yr] & $\\epsilon_{sig}$ [\\%] & Bkg [\/Mton$\\cdot$yr] & $\\sigma_{fit}$ [\\%] \\\\\n\\hline\n\\hline\n$12.7 \\pm 2.4$ & $0.9 \\pm 0.2$ & $10.8 \\pm 1.1$ & $0.7 \\pm 0.2$ & 31.0 & 1916.0 & 8.0 \\\\\n\\hline\n\\hline\n \\end{tabular}\n \\end{center}\n \\caption{Signal efficiency and background rates as well as estimated systematic uncertainties \n for the $p \\rightarrow \\bar \\nu K^{+}$ analysis at Hyper-K.}\n \\label{tbl:pdknuk}\n\\end{table}\n\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.48\\textwidth,trim={0 4.5cm 0 4cm},clip,trim={0 4.5cm 0 4cm},clip]{physics-pdecay\/figures\/mumom-1hd.pdf}\n \\includegraphics[width=0.48\\textwidth,trim={0 4.5cm 0 4cm},clip]{physics-pdecay\/figures\/kmass-pipi-1hd.pdf}\n \\end{center}\n\\caption { Reconstructed muon momentum distribution for muons found in the prompt $\\gamma$ search \n of the $p \\rightarrow \\bar \\nu K^{+}$ analysis after a 10 year exposure of a single Hyper-K tank (left).\n The right figure shows the reconstructed kaon mass based on the reconstructed final state in candidates from the \n $\\pi^{+}\\pi^{0}$. \n The hatched histograms show the atmospheric neutrino background and the solid crosses\n denote the sum of the background and proton decay signal. \n Here the proton lifetime is assumed to be,\n $6.6 \\times 10^{33}$ years, just beyond current Super-K limits.\n All cuts except for the cut on visible energy opposite the $\\pi^{0}$ candidate have been applied in the right plot. }\n \\label{fig:nuk_pmu}\n\\end{figure} \n\n\n\nThe prompt $\\gamma$ search method proceeds by identifying fully\ncontained fiducial volume interactions with a single $\\mu$-like ring\naccompanied by a Michel electron. In order to suppress atmospheric\nneutrino backgrounds, particularly those with an invisible muon, the\nmuon momentum is required to be $215< p_{\\mu} < 260$\\,MeV\/$c$ and the\ndistance between its vertex and that of the Michel electron cannot\nexceed 200~cm. Events with high momentum protons that create a\n$\\mu$-like Cherenkov ring are rejected using a dedicated likelihood\ndesigned to select in favor of genuine muons based on the PMT hit\npattern and the Cherenkov opening angle. Searching backward in time\nfrom the muon candidate, de-excitation $\\gamma$ ray candidates are\nidentified as the largest cluster of PMT hits within a 12~ns sliding\nwindow around the time-of-flight-subtracted time distribution. \nThe time difference between the center of the time window\ncontaining the $\\gamma$ candidate, $t_{\\gamma}$, and the muon time,\n$t_{\\mu}$ is then required be consistent with decay of a kaon,\n$t_{\\mu}- t_{\\gamma} < 75$~ns ($\\sim 6\\tau_{K^+}$). Finally, only\nevents whose number of hits in this window, $N_{\\gamma}$, is\nconsistent with 6\\,MeV of energy deposition ($8 < N_{\\gamma} < 120$) are\nkept. The left panel of Figure~\\ref{fig:nuk_pmu} shows the expected $p_{\\mu}$\ndistribution after all selection cuts have been applied assuming a\nproton lifetime of $6.6\\times 10^{33}$ years, which is slightly less than the current \nSuper-K limit. \n\n\nThe second search ($p_{\\mu}$ spectrum) method also focuses on\nidentifying the monochromatic muon but with relaxed search criterion.\nOnly those cuts applied before the proton likelihood cut\nare used. A fit is then applied to the resulting muon momentum\ndistribution to identify any proton decay-induced excess of muon\nevents over the considerable atmospheric neutrino background.\n\n\\begin{figure}[p]\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth,trim={0 0.5cm 0 0},clip]{physics-pdecay\/figures\/hk_nuk_disco_overlay_exposure_1and2HD_DUNE_JUNO3s_C_year.pdf}\n \\end{center}\n \\caption{Comparison of the 3~$\\sigma$ $p \\rightarrow \\bar \\nu K^{+}$ discovery potential as a function of year for \n the Hyper-K as well as that of the 40~kton DUNE detector (cyan solid) based on~\\cite{Acciarri:2015uup} and \n the 20~kton JUNO detector based on~\\cite{An:2015jdp}. \n The red line denotes a single Hyper-K tank, while the orange line shows the expectation when a second \n tank comes online after six years.\n The expected discovery potential for Super-K by 2026 assuming 23 years of data is also shown.\n }\n \\label{fig:nuK_discovery}\n \\begin{center}\n \\includegraphics[width=0.7\\textwidth,trim={0 0.5cm 0 0},clip]{physics-pdecay\/figures\/hk_nuk_limit_overlay_exposure_1and2HD_DUNE_JUNO_SK90pc_L_year.pdf}\n \\end{center}\n\\caption {Hyper-K's sensitivity to the $p \\rightarrow \\bar \\nu K^{+}$ decay mode \n at 90\\% C.L. as a function of run time is shown in red against other experiments (see caption of Figure~\\ref{fig:nuK_discovery}).\n Super-K's current limit is also shown.\n }\n \\label{fig:sens_nuk}\n\\end{figure}\n\nLike the prompt $\\gamma$ search, the $\\pi^{+}\\pi^{0}$ search relies on\nmore sophisticated event selections to identify the signal. While the\nmomentum of both the $\\pi^{+}$ and $\\pi^{0}$ from the $K^{+}$ decay\nwill be 205\\,MeV\/$c$, the former does not deposit enough light to be\nreconstructed fully. To compensate for this the search method focuses\non PMT hits opposite the direction of a $\\pi^{0}$ at the correct\nmomentum. Fully contained events with one or two reconstructed rings,\nall of which are $e$-like, are selected. In addition there should be\none Michel electron from the charged pion decay chain. For two-ring\nevents the invariant mass is required to be consistent with that of a\nneutral pion, $ 85 < m_{\\pi^{0}} < 185$\\,MeV\/$c^2$. Further, the total\nmomentum should be between 175 and 250\\,MeV\/$c$. At this stage the\n$\\pi^{+}$ light is identified as electron-equivalent visible energy between 7 and 17\\,MeV\nlocated at an angular separation between 140 and 180\\,degrees from the\n$\\pi^{0}$ candidate's direction. Finally a likelihood method is used\nto evaluate the consistency of this light pattern with that produced\nby a $\\pi^{+}$. Details of the full search method are documented\nelsewhere~\\cite{Abe:2014mwa}.\nIn addition, as in the $p\\rightarrow e^{+}\\pi^{0}$ search, the number \nof tagged neutron candidates is required to be zero.\n\n\nTable~\\ref{tbl:pdknuk} summarizes the expected signal efficiency and background rates \nfor each of the search methods. \nAccompanying systematic errors have been calculated based on Super-K methods~\\cite{Abe:2014mwa} and are included in \nthe table. \nAssuming a proton lifetime close to current Super-K limits, \nFigures~\\ref{fig:nuk_pmu} show the reconstructed muon momentum from \nthe prompt gamma search and the reconstructed kaon mass spectrum from the $\\pi^{+}\\pi^{0}$ search.\nNote that while the latter is unused in the analysis itself it provides a demonstration \nof the signal reconstruction since the proton mass for this decay mode cannot be reconstructed. \nThe expected discovery potential and sensitivity of Hyper-K in comparison with other experiments \nappears in Figures~\\ref{fig:nuK_discovery} and~\\ref{fig:sens_nuk}.\n\n\n\n\\subsubsection{Sensitivity study for other nucleon decay modes}\nAlthough the $p \\rightarrow e^{+} \\pi^{0}$ decay mode is predicted to be dominant \nin many GUT models, a variety of other decay modes are possible, each with a sizable \nbranching ratio.\nTable~\\ref{tab:branch} shows the branching ratio distribution and ratio of neutron to proton \nlifetimes as predicted by several GUT models.\nThe diversity in these predictions suggests that in order to make a discovery and to subsequently \nconstrain proton decay models, it is critical to probe as many nucleon decay modes as possible.\nFortunately, Hyper-Kamiokande is expected to be sensitive \nto many decay modes beyond the two standard decays discussed above. \n\n\\begin{table}[htb]\n\\caption{Branching ratios for various proton decay modes together with the\nratio of the neutron to proton lifetimes as predicted by SU(5) and SO(10) models.\n.\\label{tab:branch}}\n\\vspace{0.4cm}\n\\begin{center}\n\\begin{tabular}{l|rrrrr}\n\\hline\\hline\n & \\multicolumn{5}{c}{Br.($\\%$)} \\\\ \n\\hline\n & \\multicolumn{4}{c}{SU(5)}& SO(10) \\\\ \n\\hline\nReferences& ~\\cite{mach} & ~\\cite{gav} & ~\\cite{dono} & ~\\cite{bucc} & ~\\cite{bucc} \\\\ \n\\hline\n$p \\rightarrow e^{+} \\pi^{0}$ & 33 & 37 & 9 & 35 & 30 \\\\ \n\\hline\n$p \\rightarrow e^{+} \\eta^{0}$ & 12 & 7 & 3 & 15 & 13 \\\\\n\\hline \n$p \\rightarrow e^{+} \\rho^{0}$ & 17 & 2 & 21 & 2 & 2 \\\\ \n\\hline\n$p \\rightarrow e^{+} \\omega^{0}$ & 22 & 18 & 56 & 17 & 14 \\\\\n\\hline \nOthers & 17 & 35 & 11 & 31 & 31 \\\\ \n\\hline\n\\hline\n$\\tau_{p}\/\\tau_{n}$ & 0.8 &1.0 & 1.3 & & \\\\\n\\hline \\hline \n\\end{tabular}\n\\end{center}\n\\end{table}\n\nHyper-Kamiokande's sensitivity to other nucleon decay modes has been \nestimated based in part on efficiencies and background rates\nfrom Super-Kamiokande~\\cite{:2009gd}. \nTable~\\ref{tab:other_mode} shows the 90~$\\%$ CL\nsensitivities with a 1.9\\,Megaton$\\cdot$year exposure in the 1TankHD\\ configuration. \nUnder these conditions Table~\\ref{tab:disc_other} shows the $3\\sigma$ discovery potential of Hyper-K \nfor a selected number of decay modes after a 1.9~Mton$\\cdot$year exposure.\n\n\n\\begin{table}[htp]\n\\caption{Summary of Hyper-K's sensitivity to various $|B-L|$ conserving nucleon decay modes after a 1.9\\,Megaton$\\cdot$year exposure of the 1TankHD\\ design compared in comparison with existing lifetime limits. The current limits for $p \\rightarrow e^{+} \\pi^{0}$, $p \\rightarrow \\mu^{+} \\pi^{0}$ are from a 0.316\\'Megaton$\\cdot$year exposure of Super-Kamiokande~\\cite{Miura:2016krn}, $p \\rightarrow \\overline{\\nu} K^{+}$ is from a 0.26\\,Megaton$\\cdot$year exposure~\\cite{Abe:2014mwa}, and the other modes are from a 0.316\\,Megaton$\\cdot$year exposure~\\cite{TheSuper-Kamiokande:2017tit}.\n\\label{tab:other_mode}}\n\\vspace{0.4cm}\n\\begin{center}\n\\begin{tabular}{l|c|c}\n\\hline\nMode & Sensitivity (90$\\%$ CL) [years] & Current limit [years] \\\\\n\\hline\n\\hline\n\\textcolor{blue}{$p \\rightarrow e^{+} \\pi^{0}$} & 7.8 $\\times 10^{34}$ & 1.6$\\times 10^{34}$ \\\\\n\\textcolor{blue}{$p \\rightarrow \\overline{\\nu} K^{+}$} & 3.2 $\\times 10^{34}$ & 0.7$\\times 10^{34}$ \\\\\n\\hline\n\\hline\n$p \\rightarrow \\mu^{+} \\pi^{0}$ & 7.7$\\times 10^{34}$ & 0.77$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow e^{+} \\eta^{0}$& 4.3$\\times 10^{34}$ & 1.0$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow \\mu^{+} \\eta^{0}$& 4.9$\\times 10^{34}$ & 0.47$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow e^{+} \\rho^{0}$& 0.63$\\times 10^{34}$ & 0.07$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow \\mu^{+} \\rho^{0}$& 0.22$\\times 10^{34}$ & 0.06$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow e^{+} \\omega^{0}$& 0.86$\\times 10^{34}$ & 0.16$\\times 10^{34}$ \\\\\n\\hline\n$p \\rightarrow \\mu^{+} \\omega^{0}$& 1.3$\\times 10^{34}$ & 0.28$\\times 10^{34}$ \\\\\n\\hline\n$n \\rightarrow e^{+} \\pi^{-}$ & 2.0$\\times 10^{34}$ & 0.53$\\times 10^{34}$ \\\\\n\\hline\n$n \\rightarrow \\mu^{+} \\pi^{-}$ & 1.8$\\times 10^{34}$ & 0.35$\\times 10^{34}$ \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nThe decay modes in Table~\\ref{tab:other_mode} all conserve baryon\nnumber minus lepton number, $(B-L)$. \nHowever, the $(B+L)$\nconserving mode, $n \\rightarrow e^{-} K^{+}$, was also given attention\nand searched for by Super-Kamiokande. In $n \\rightarrow e^{-} K^{+}$,\nthe $K^{+}$ stops in the water and decays into $\\mu^{+} + \\nu$. The\nfinal state particles observed in $n \\rightarrow e^{-} K^{+},K^+ \\to \\mu^+ \\nu$ are $e^{-}$ and $\\mu^{+}$.\n Both $e^{-}$ and\n$\\mu^{+}$ have monochromatic momenta as a result of originating from\ntwo-body decays. Furthermore, the timing of the $\\mu^{+}$ rings are \ndelayed with respect to the $e^{-}$ rings because of the $K^{+}$\nlifetime. In SK-II, the estimated efficiencies and the background\nrate are 8.4\\% and 1.1\\,events\/Megaton$\\cdot$year, respectively. From\nthose numbers, the sensitivity to the $n \\rightarrow e^{-} K^{+}$ mode\nwith a 1.9\\,Megaton$\\cdot$year exposure is estimated to be 1.0$\\times\n10^{34}$ years.\n\nThe possibility of $n \\overline{n}$ oscillation is another interesting\nphenomenon; it violates baryon number $(B)$ by $|\\Delta B|$ = 2.\nThese $n \\overline{n}$ oscillations have been searched for in\nSuper-Kamiokande with an exposure of 0.09\\,Megaton$\\cdot$year~\\cite{jang}. \nFurther improvement of the $n \\overline{n}$\noscillation search is expected in Hyper-Kamiokande.\n\n\\begin{table}[htp]\n\\caption{Summary of Hyper-K's $3 \\sigma$ discovery potential for several nucleon decay modes in the 1TankHD\\ configuration.\n A 10 year exposure of a single detector \n has been assumed. Numbers in brackets denote the potential assuming a second detector comes online six years \n after the start of the experiment. Current limits are summarized in Table~\\ref{tab:other_mode}. }\n\\label{tab:disc_other}\n\\vspace{0.4cm}\n\\begin{center}\n\\begin{minipage}[b][][b]{.45\\linewidth}\n\\begin{tabular}{>{\\raggedright}p{3cm}|>{\\centering}p{3cm}}\n\\hline\nMode & $\\tau_{disc}$ $3\\sigma$ [years] \\tabularnewline\n\\hline\n\\hline\n\\textcolor{blue}{$p \\rightarrow e^{+} \\pi^{0}$} & 6.3 (8.0)$\\times 10^{34}$ \\tabularnewline\n\\textcolor{blue}{$p \\rightarrow \\overline{\\nu} K^{+}$} & 2.0 (2.5)$\\times 10^{34}$ \\tabularnewline\n\\hline\n\\hline\n$p \\rightarrow \\mu^{+} \\pi^{0}$ & 6.9 (8.7)$\\times 10^{34}$ \\tabularnewline\n\\hline\n$p \\rightarrow e^{+} \\eta^{0}$ & 3.0 (3.9)$\\times 10^{34}$ \\tabularnewline \n\\hline\n$p \\rightarrow \\mu^{+} \\eta^{0}$ & 3.4 (4.7)$\\times 10^{34}$ \\tabularnewline \n\\hline\n$p \\rightarrow e^{+} \\rho^{0} $ & 3.4 (5.0)$\\times 10^{33}$ \\tabularnewline \n\\hline\n$p \\rightarrow \\mu^{+} \\rho^{0}$ & 1.3 (1.6) $\\times 10^{33}$ \\tabularnewline \n\\hline\n$p \\rightarrow e^{+} \\omega $ & 5.4 (6.9)$\\times 10^{33}$ \\tabularnewline\n\\hline\n$p \\rightarrow \\mu^{+} \\omega $ & 0.78 (1.0)$\\times 10^{34}$ \\tabularnewline\n\\hline\n\\hline\n\\end{tabular}\n\\end{minipage}\n\\begin{minipage}[b][][b]{.45\\linewidth}\n\\begin{tabular}{>{\\raggedright}p{3cm}|>{\\centering}p{3cm}}\n\\hline\nMode & $\\tau_{disc}$ $3\\sigma$ [years] \\tabularnewline\n\\hline\n\\hline\n$n \\rightarrow e^{+} \\pi^{-}$ & 1.3 (1.6)$\\times 10^{34}$ \\tabularnewline\n\\hline\n$n \\rightarrow \\mu^{+} \\pi^{-}$ & 1.1 (1.5)$\\times 10^{34}$ \\tabularnewline\n\\hline\n$n \\rightarrow e^{+} \\rho^{-}$ & 1.1 (1.5)$\\times 10^{33}$ \\tabularnewline\n\\hline\n$n \\rightarrow \\mu^{+} \\rho^{-}$ & 6.2 (8.1)$\\times 10^{32}$ \\tabularnewline\n\\hline\n\\hline\n\\end{tabular}\n\\end{minipage}\n\\end{center}\n\\end{table}\n\n\n\n\n\n\n\\begin{table}[htp]\n\\caption{Summary of Hyper-K's sensitivity to various $| \\Delta (B-L) | = 2 $ and $| \\Delta B | = 2$ proton and dinucleon decay modes after a 5.6\\,Megaton$\\cdot$year exposure compared with existing lifetime limits. \nThe current limits are taken from a 0.273~Mton$\\cdot$year exposure of Super-K.\nLimits on the dinucleon decay modes are reported per $^{16}O$ nucleus, whereas the single nucleon decays are displayed \nas limits per nucleon.\n}\n\\label{tab:dbl_eq_2}\n\\begin{center}\n\\begin{tabular}{l|c|c}\n\\hline\nMode & Sensitivity (90$\\%$ CL) [years] & Current limit [years] \\\\\n\\hline\n$p \\rightarrow e^{+} \\nu\\nu$ & 10.2 $\\times 10^{32}$ & 1.7 $\\times 10^{32}$ \\\\\n$p \\rightarrow \\mu^{+} \\nu\\nu$ & 10.7 $\\times 10^{32}$ & 2.2 $\\times 10^{32}$ \\\\\n\\hline\n\\hline\n$p \\rightarrow e{+} X $ & 31.1 $\\times 10^{32}$ & 7.9 $\\times 10^{32}$ \\\\\n\\hline\n$p \\rightarrow \\mu^{+} X $ & 33.8 $\\times 10^{32}$ & 4.1 $\\times 10^{32}$ \\\\\n\\hline\n$n \\rightarrow \\nu \\gamma $ & 23.4 $\\times 10^{32}$ & 5.5 $\\times 10^{32}$ \\\\\n\\hline\n\\hline\n$np \\rightarrow e^{+} \\nu $ & 6.2 $\\times 10^{32}$ & 2.6 $\\times 10^{32}$ \\\\\n\\hline\n$np \\rightarrow \\mu^{+} \\nu $ & 4.2 $\\times 10^{32}$ & 2.0 $\\times 10^{32}$ \\\\\n\\hline\n$np \\rightarrow \\tau^{+} \\nu $ & 6.0 $\\times 10^{32}$ & 3.0 $\\times 10^{32}$ \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nIn addition to $(B-L)$ conserving modes several other nucleon channels\nare available. Unification schemes invoking left-right symmetry\n(c.f.~\\cite{Pati:1974yy}) predict trilepton decays such as\n$p \\rightarrow e^{+} (\\mu^{+}) \\nu\\nu$, which violate $(B-L)$ by two units\n($| \\Delta (B-L) |= 2 $).\nThough there are two particles in the final state that are invisible to Hyper-Kamiokande,\nthe presence of a positron or muon from such decays can, in principal, be detected.\nWhile this type of single charged lepton signature would naturally be subject to large \natmospheric backgrounds, with a sufficiently large decay rate, spectral information can be \nused to separate the two. \nGoing one step farther, then, spectral analysis makes it possible to search for generic decay \nmodes as well, such as $p \\rightarrow e^{+} (\\mu^{+}) X$, where $X$ is an unknown and unseen particle.\n\nThough only single nucleon decays have been considered up until this\npoint, it is worth noting that dinucleon processes, in which a\nneutron-proton (or proton-proton) pair decays into a pair of leptons,\ncan also be studied at Hyper-Kamiokande.\nModes where $\\Delta B =2$ , such as $np \\rightarrow l^{+}\\nu$,\nappear in models with extended Higgs sectors~\\cite{Perez:2013osa} and\nhave connections to Baryogenesis. Interestingly, these models have the\nadditional property that the single nucleon decay modes are suppressed\nrelative to the dinucleon decays. This wealth of predictions for\npossible channels further emphasizes the need to search for as many\nnucleon decay signatures as possible in the quest for grand\nunification. Table~\\ref{tab:dbl_eq_2} lists Hyper-K's expected\nsensitivity to both $| \\Delta (B-L) | =2 $ and $\\Delta B =2$ decays\nfor a 5.6~Mton$\\cdot$year exposure. While searches for these modes\nare dominated by the atmospheric neutrino background, Hyper-K can be\nexpected to extend existing limits by a factor of three to ten if \nno signal is observed.\n\n\\input{physics-pdecay\/coverage.tex}\n\n\n\\subsection{Solar neutrinos}\n\n\\label{section:solar}\n\nThe solar neutrino measurements are capable of determining the neutrino\noscillation parameters between mass eigenstate $\\nu_1$ and $\\nu_2$ in\nthe equation (\\ref{eq:mixing}). Figure~\\ref{fig:sol-osc} shows the\nlatest combined results of the allowed neutrino oscillation\nparameters, $\\theta_{12}$ and $\\Delta m^2_{21}$ from all the solar\nneutrino experiments, as well as the reactor neutrino experiment\nKamLAND~\\cite{sol-neutrino2014}. The mixing angle is consistent between\nsolar and reactor neutrinos, while there is about 2$\\sigma$ tension in\n$\\Delta m^2_{21}$. This mainly comes from the recent result of the solar\nneutrino day-night asymmetry and energy spectrum shape observed in Super-K.\nIn solar neutrino oscillations, regeneration of the electron neutrinos through the MSW\nmatter effect in the Earth is expected. According to the MSW model,\nthe observed solar neutrino event rate in water Cherenkov detectors in\nthe nighttime is expected to be higher -- by about a few percent in\nthe current solar neutrino oscillation parameter region -- than that\nin the daytime as shown in the Figure~\\ref{fig:sol-osc}. Super-K\nfound the first indication of this day-night flux asymmetry at the\n3$\\sigma$ level~\\cite{sk4-daynight}, but conclusive evidence is\nexpected in Hyper-K. If the 2$\\sigma$ tension of $\\Delta m^2_{21}$\nbetween solar ($\\nu_e$) and reactor ($\\bar{\\nu_e}$) neutrinos is a\nreal effect, new physics must be introduced.\n\nIn addition to that, the observation of the upturn in the solar\nneutrino survival probability might be possible. The spectrum upturn is produced by\nthe transition of the survival probability in $\\nu_e$ from the matter\ndominant energy region to the vacuum dominant energy region in the\nsolar neutrino oscillation, and has been observed by the comparison\nbetween $^8$B solar neutrino flux in Super-K and SNO and $^7$Be solar\nneutrino flux in BOREXINO~\\cite{borexino-7be}. However, the precise\nmeasurement of the spectrum shape can distinguish the usual neutrino\noscillation scenario from several exotic models such as non standard\ninteraction~\\cite{sol-nsi}, MaVaN~\\cite{sol-mavan}, and sterile\nneutrino~\\cite{sol-sterile}, for example. \nDue to the high photo-coverage of 40~\\%, the\nlower energy threshold required to measure the upturn is possible because of better energy\nresolution and reduction of the radio active background.~\\footnote{\nThough the energy of the radioactive events are lower than the energy\nthreshold, they can be misreconstructed such that they contaminate the\nregion above the energy threshold. \nIf the energy resolution is better, the background will be reduced more.\nSee more in Section~\\ref{sec:lowe_bg}.\n}\n\nIn the following sections, the sensitivity of the day-night flux\nasymmetry and spectrum upturn in Hyper-K are described.\n\n\\if 0\nIn solar neutrino oscillations, regeneration of the electron neutrinos\nthrough the Mikheyev-Smirnov-Wolfenstein (MSW) matter effect\n\\cite{Wolfenstein:1977ue,Mikheyev:1985zz,Mikheyev:1986zz} \nin the Earth is expected. \nRegeneration of the solar electron neutrinos in the Earth would constitute \nconcrete evidence of the MSW matter effect, and so it is important \nto experimentally observe this phenomenon.\nHowever, the matter effect acting on solar neutrinos passing through the Earth has not been \ndirectly confirmed yet, since the sensitivities of the current \nsolar neutrino experiments are not sufficient.\nAccording to the MSW model, the observed solar neutrino event rate \nin water Cherenkov detectors in the nighttime is expected to be higher \n-- by about a few percent in the current solar\nneutrino oscillation parameter region --\nthan that in the daytime. \nWe would like to measure this difference in Hyper-Kamiokande. \n\\fi\n\nHyper-K also could be used for variability analyses of the Sun. For\nexample, the $^8$B solar neutrino flux highly depends on the Sun's\npresent core temperature~\\cite{1996PhRvD..53.4202B}.\nUnlike multiply scattered, random-walking\nphotons or slow-moving helioseismic waves, free streaming solar\nneutrinos are the only available messengers with which to precisely\ninvestigate ongoing conditions in the core region of the Sun.\nHyper-K, with its unprecedented statistical power, could measure the\nsolar neutrino flux over short time periods. Therefore, short time\nvariability of the temperature in the solar core could be monitored by\nthe solar neutrinos in Hyper-K.\n\n\\if 0\nIn order to achieve these precision measurements, background event\nlevels must be sufficiently small. Here, we have estimated the basic\nperformance of Hyper-K for low energy events assuming some typical\nbackground levels. In this study, the current analysis tools and the\ndetector simulation for the low energy analysis~\\cite{Abe:2011xx} in\nSuper-K were used. The dark rate of the PMTs and the water\ntransparency were assumed to be similar to those in the current\nSuper-K detector. A brief summary of the low energy event\nreconstruction performance in Hyper-K is listed in\nTable~\\ref{tab:performance}.\n\nThe analysis threshold of the total energy of the recoil electrons in\nHyper-K will be 7.0\\,MeV or lower, since a 7.0\\,MeV threshold was\npreviously achieved in the SK-II solar neutrino\nanalysis~\\cite{sk2-solar}. The current analysis tools will work all\nthe way down to 4.5\\,MeV in Hyper-K with a vertex resolution of 3.0~m.\nNot surprisingly, higher energy events will be reconstructed with even\nbetter vertex resolution.\n\\fi\n\n\\begin{figure}[htb]\n \\begin{center} \\includegraphics[height=9.5cm]{physics-solarnu\/plot_skosc.pdf} \\\\ \\end{center} \\caption{Allowed\n neutrino oscillation parameter region from all the solar neutrino\n experiments (green), reactor neutrino from KamLAND (blue) and\n combined (red) from one to five sigma lines and three sigma filled\n area. The star shows the best fit parameter from the solar\n neutrinos. The contour of the expected day-night asymmetry with\n 6.5\\,MeV (in kinetic energy) energy threshold is overlaid.} \\label{fig:sol-osc}\n\\end{figure}\n\n\\subsubsection{Background estimation}\n\\label{section:solar_bg}\nThe major background sources for the $^8$B solar neutrino measurements\nare the radioactive spallation products created by cosmic-ray muons~\\cite{sk-spa} and\nthe radioactive daughter isotopes of ${}^{222}\\mbox{Rn}$ in water.\nThe spallation products is discussed in detail in the paragraph~\\ref{par:spallation_reduction},\nand the rate of spallation which result in relevant backgrounds is 2.7 times higher in Hyper-K compared to Super-K\nbecause of its shallow depth.\n\\if 0\n${}^{222}\\mbox{Rn}$ will be reduced to a similar (or lower) level as that currently\nin the Super-K detector, since Hyper-K will employ a similar water\npurification system and design improvements may well occur over the\nnext several years. However, the spallation products will be\nincreased in Hyper-K.\n\\fi\nAs the radioactive daughter isotopes, ${}^{222}\\mbox{Rn}$ is an important background source for the spectrum upturn\nmeasurement. First of all, the water purification system must achieve ${}^{222}\\mbox{Rn}$ levels similar to that achieved at Super-K.\nFurthermore, this background level must be achieved across the full fiducial volume, unlike at Super-K, where only a limited volume can be used for events with less than 5\\,MeV of energy.\nIt is a challenging task but we believe that this should be\npossible by design improvements over the next several years.\nTherefore, the same ${}^{222}\\mbox{Rn}$ background level as Super-K in full fiducial volume is assumed in the following calculation.\n\n\\if 0\n While\nthe spallation products will be definitely increased in Hyper-K\nbecause of shallow cavern. In the current design, the cosmic-ray muon\nrate is expected to be increased by a factor of 4.9 $\\pm$ 1.0 in equal\nvolumes, as discussed in Sec.~\\ref{sec:lowe_bg}.\n\nThe spallation products will not simply be increased by the same\nfactor. This is because high energy cosmic-ray muons tend to produce\nthe spallation products, while the average energy of the cosmic-ray\nmuons at the shallower Hyper-K site is expected to be lower than that\nat the deeper Super-K site; greater overburden means less muons, but\nit also means those that do get through are more energetic. We have\nestimated the average energies of the cosmic-ray muons to be $\\sim\n258$\\,GeV at the Super-K site and $\\sim 200$\\,GeV at the Hyper-K site.\nConsidering the discussion with FLUKA simulation in\nSec.~\\ref{sec:lowe_bg}, the density of spallation products will be\nincreased by a factor of 4. We found the remaining spallation\nproducts will be decreased by a factor of 0.75 at the above condition,\ncomparing with current Super-K analysis, after the spallation\nreduction discussed in Sec.~\\ref{sec:lowe_bg}.\nIn summary, the density of the remaining spallation products will be increased \nby a factor of 2.7 in Hyper-K.\n\nIn Super-K, angular information is used to extract the solar neutrino\nsignal events~\\cite{full-solar}. \nWe have estimated the possible effect of the background level in the\nsignal extraction after considering angular information.\n\nIn this study, we used 9.0--9.5\\,MeV Super-K-I data as a reference.\nThe extracted solar neutrino signal events and background events in\nthis energy region over the entire run period\n(0.09~Megaton$\\cdot$years) were 1350 events and 7700 events,\nrespectively. So, the Signal-to-Noise (S\/N) ratio is 18\\%. We made\nartificial data samples with reduced S\/N ratios, then applied the\nsignal extraction. As a result, we found the expected statistical\nerror is almost the square root of 2 $\\sim$ 15 times the number of\nsignal events for 1 $\\sim$ 20 times the Super-K-I background level,\nrespectively. Table~\\ref{tab:sol-bgtest} shows a summary of the\nexpected statistical errors in a Super-K-I type detector with\nincreased backgrounds, as well as that of Hyper-K.\n\\begin{table}[htb]\n \\caption{Expected statistical uncertainties for 10000 signal events with increased background \n levels. The Super-K-I solar neutrino data sample between 9.0--9.5\\,MeV was used as a reference \n The 3rd column is the Hyper-K factor relative to Super-K given the same observation time.\n To estimate the 3rd column, the same detector resolution\n and 0.56~Mton fiducial volume are assumed in Hyper-K. }\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline \\hline\nBackground level & Stat. err. in SK & & Stat. err. in HK\\\\\n\\hline\nSK-I BG $\\times 20$ & 3.6\\% & & $\\times 1\/2.0$ \\\\ \nSK-I BG $\\times 10$ & 2.7\\% & & $\\times 1\/2.7$ \\\\ \nSK-I BG $\\times 7$ & 2.4\\% & & $\\times 1\/3.1$ \\\\ \nSK-I BG $\\times 5$ & 2.1\\% & & $\\times 1\/3.5$ \\\\ \nSK-I BG & 1.4\\% & & $\\times 1\/5.2$ \\\\ \n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:sol-bgtest}\n\\end{table}\nOnce the angular distribution is used to extract the solar signal, \nthe statistical error on this signal would be reduced by a factor of 2.0 in Hyper-K, \neven though the background level is increased by a factor of 20, \nfor the same observation time assuming both detectors have identical resolution.\n\nIn summary, Hyper-K will provide higher statistical measurements of\nsolar neutrinos than Super-K, even though there will be more spallation\nbackgrounds.\n\\fi\n\n\\subsubsection{Oscillation studies}\n\nIn order to calculate the neutrino oscillation sensitivity, the signal\nand background rates in each option have to be estimated. As for the\nday-night asymmetry analysis, the energy threshold is set to 6.5\\,MeV\n(in kinetic energy)\nsince its effect is larger at higher energy region. In this\nenergy region, only spallation backgrounds should be considered. The\nremaining spallation background rate in Super-K phase IV (40\\%\nphoto-coverage) has been reduced by a factor three comparing to Super-K\nphase II (20\\% photo-coverage) because of the better energy resolution\nand better vertex resolution.\nFrom this experience in Super-K, the spallation background in Hyper-K\nwill be reduced by a factor three because of the higher photon detection\nefficiency than Super-K.\n\nFigure~\\ref{fig:sol-dn} shows the sensitivity of the day-night asymmetry\nas a function of the observation time.\nThe $\\Delta m^2_{21}$ separation ability between solar neutrino (HK) and\nreactor anti-electron neutrino (KamLAND) is expected 4$\\sim$5$\\sigma$ level in ten years observation, though it depends on the systematic uncertainty.\n\nIn the measurement of the spectrum upturn, the ${}^{222}\\mbox{Rn}$ background is\ncritical because the $^{214}$Bi beta decay events (3.27\\,MeV end point\nenergy) will come above the energy threshold due to the energy\nresolution. The Hyper-K detector, which has better energy resolution\nbecause of the higher photon detection efficiency than Super-K,\nis strong to reduce such kind of radioactive background.\nFurthermore, the precise energy calibration has to be considered.\nHere, it is assumed that the same background level with full fiducial\nvolume and the same precision of the energy calibration as Super-K are\nachieved in Hyper-K.\nFigure~\\ref{fig:sol-upturn} shows the sensitivity of the spectrum upturn\ndiscovery as a function of the observation time.\nIt is about 3$\\sigma$ level in ten years observation with 4.5\\,MeV energy threshold.\n\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=9.5cm]{physics-solarnu\/plot_dn_year.pdf} \\\\\n \\end{center}\n \\caption{Day-night asymmetry observation sensitivity as a function of observation time. The red line shows the sensitivity from the no asymmetry, while the blue line shows from the asymmetry expected by the reactor neutrino oscillation. The solid line shows that the systematic uncertainty which comes from the remaining background direction is 0.3\\%, while the dotted line shows the 0.1\\% case.}\n \\label{fig:sol-dn}\n\\end{figure}\n\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=9.5cm]{physics-solarnu\/plot_upturn_year.pdf} \\\\\n \\end{center}\n \\caption{Spectrum upturn discovery sensitivity as a function of observation time. The solid line shows that the energy threshold is 4.5MeV, while the dotted line shows the 3.5MeV}\n \\label{fig:sol-upturn}\n\\end{figure}\n\n\\if 0\nIn solar neutrino oscillations, a difference in the solar neutrino\nevent rates during the daytime and the nighttime is expected from the\nMSW effect in the Earth. This is called the day\/night asymmetry; it\nhas not yet been observed. In Hyper-K, a precise measurement of the\nday\/night asymmetry will be performed using higher statistics than\nthose available in Super-K.\n\nThe upper plots in Fig.~\\ref{fig:sol-dn1} show the expected day\/night\nasymmetries with different lower energy thresholds. \n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=9.5cm]{physics-solarnu\/plot_map3-new.pdf} \\\\\n \\end{center}\n \\caption{Expected day\/night asymmetry in a megaton water Cherenkov\n detector. 40\\% photo-coverage, 0.5~Megaton$\\cdot$years daytime data \n and 0.5~Megaton$\\cdot$years nighttime data are assumed. \n The effect of background events and reduction efficiencies are not considered. \n Upper left: expected day\/night asymmetry in the 5.0--20\\,MeV electron \n total energy region. \n Upper right: expected day\/night asymmetry in the 8.0--20\\,MeV region.\n Lower left: expected day\/night asymmetry with uncertainties as a\n function of the lower energy threshold at \n $(\\tan^2 \\theta_{12}, \\Delta \\rm{m}^2_{21}) = (0.40, 7.9 \\times 10^{-5} {\\rm eV}^2)$. \n The upper energy threshold is 20\\,MeV.\n The meaning of the different colors are defined in the lower right plot.\n Lower right: expected day\/night significance as a function of the\n energy threshold.}\n \\label{fig:sol-dn1}\n\\end{figure}\nThe expected day\/night asymmetry is at about the 1\\% level around the current\nsolar global oscillation parameters. \nIn order to observe the day\/night asymmetry in Hyper-K, \nwe must reduce the up-down systematic uncertainty below that level.\n\nThe expected day\/night asymmetry in the high energy region is larger \nthan that in the low energy region, as shown in the lower left plot in\nFig.~\\ref{fig:sol-dn1}.\nSo, high statistics data in this higher energy region would be desirable. \nWe have studied two typical values of systematic uncertainty, where the one at \n1.3\\% corresponds to the up-down systematic uncertainty of Super-K.\nFrom the lower right plot in Fig.~\\ref{fig:sol-dn1}, \nthe most sensitive lower energy threshold would be 6\\,MeV and 8\\,MeV for the\n0.5\\% and 1.3\\% up-down systematic uncertainties, respectively.\nFigure~\\ref{fig:sol-dn2} shows expected day\/night significance \nas a function of the observation time.\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=6.5cm]{physics-solarnu\/plot_map3_all1.pdf} \\\\\n \\end{center}\n \\caption{Expected day\/night significance as a function of the\n observation time near the solar global oscillation best-fit parameters.\n The Super-K-I value of S\/N is assumed. \n The total electron energy region is 5.0--20\\,MeV.}\n \\label{fig:sol-dn2}\n\\end{figure}\nSince the expected day\/night asymmetry is small, it will be important to\nreduce the systematic uncertainties in order to observe the day\/night\nasymmetry with high precision.\nWe believe that this should be possible, especially if we design and prepare \nthe necessary calibration devices during detector construction.\n\\fi\n\n\\if 0\n\\subsubsection{Time variation}\n\nSolar neutrinos could be used as a direct probe of the nuclear \nreactions taking place in the solar core.\nIn particular, the $^8$B solar neutrino flux has a remarkable $T^{18}$ dependence \naccording to the Standard Solar Model (SSM)~\\cite{bahcall-textbook}. \nHere, $T$ is the solar core temperature, and with such a high-order dependence\nit is possible that even modest changes in the solar core temperature \ncould be amplified into something detectable via measurements of the $^8$B solar neutrino flux.\n\nAssuming the statistical uncertainties estimated in \nSec.~\\ref{section:solar_bg} can be used for Hyper-K,\nthe expected uncertainty on the solar core temperature \nwhen the background level is increased by a factor of 20 \nwould be the following:\n\\[\n \\frac{\\sigma_T}{T} \n = \\frac{1}{18} \\frac{\\sigma_N}{N} \n = \\frac{\\sqrt{15 \\cdot N}}{18 \\cdot N}\n\\]\nHere $N$, $\\sigma_{\\rm T}$, and $\\sigma_{\\rm N}$ are the number of\nobserved $^8$B solar neutrinos, error in $T$, and error in $N$,\nrespectively. The expected number of observed $^8$B solar neutrinos\nin Hyper-K is 200 events per day above 7.0\\,MeV, as shown in\nTable~\\ref{tab:targets}. When $N$ is $200$, $\\sigma_T\/T$ will be\n$0.015$. Therefore, the solar core temperature could be monitored\nwithin a few percent accuracy day by day. Naturally, by integrating\nover longer periods, more subtle temperature changes - potentially\ndown to the 0.1\\% level - could be monitored.\n\\fi\n\n\\subsubsection{Hep solar neutrino}\n\nHep solar neutrino produced by the $^{3}$He + $p$ fusion reaction \nhas the highest energy in solar neutrinos.\nBut, most of the hep energy spectrum is overlapped with $^8$B solar neutrinos.\nThe expected $^8$B solar neutrino flux is more than 100 times larger than that of hep solar\nneutrino in Standard Solar Model (SSM). \nSo far, only upper limits were reported from SNO and SK group~\\cite{hep-sno,hep-sk}, \nbut a recent improved analysis of the SNO charged-current data shows hints of \na hep solar neutrino signal~\\cite{hep-sno-2016}, and indicates a higher hep \nflux than the SSM prediction.\n \nThe measurement of the hep solar neutrino could provide new\ninformation on solar physics. The production regions of the $^8$B and\nhep neutrinos are different in the Sun. \nThe energy production peak of hep neutrinos is located at the outermost \nradius in the solar core region\namong all the solar neutrinos in pp-chain~\\cite{bahcall-textbook}.\nSo, they could be used as a new probe of the solar interior around core region.\nNon-standard solar models, originally motivated by the solar neutrino problem, \npredict the potential enhancement of the hep neutrino flux~\\cite{Bahcall:1988}.\nThis is realized through the mixing of $^{3}$He into the inner core on a time scale \nshorter than the $^{3}$He burning time. Significant mixing is \nalready ruled out by helioseismology, however, the hep neutrino observation\ncan be a sensitive probe of the degree of the mixing in the solar core.\nThere is also the solar abundance problem. $^8$B and hep solar neutrino\nfluxes show different behavior with GS98 and AGSS09 chemical\ncompositions~\\cite{solar-abundance}.\nTheoretical calculation of hep solar neutrinos is a difficult \nchallenge~\\cite{solar-fusion}. The measurement of the hep solar neutrino\nflux will provide a better understanding of SSM.\nHep solar neutrinos could be also used to test non-standard neutrino physics\nin the energy range ($\\sim 18$~MeV)~\\cite{kubodera-hep}. \n\nIn Hyper-K, a high sensitivity measurements of hep solar neutrino flux\nwould be possible, since the detector has a good energy resolution.\nFigure~\\ref{fig:sol-hep} shows the expected solar neutrino fluxes\nin 1.9 Mton year in Hyper-K detector.\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=9.5cm]{physics-solarnu\/plot_b8hep5.pdf} \\\\\n \\end{center}\n \\caption{Expected solar neutrino fluxes with neutrino oscillation \n in Hyper-K. \n The horizontal axis is the energy threshold in electron total energy \n and the vertical axis is expected event rate in the energy range \n from the threshold up to 25\\,MeV in 10-year observation in Hyper-K.\n BP2004 SSM fluxes are assumed. \n The effect of background events, reduction efficiencies, systematic\n uncertainties are not considered.}\n \\label{fig:sol-hep}\n\\end{figure}\nThe separation between $^8$B and hep solar neutrinos highly depends\non the energy resolution of the detector. \nTable~\\ref{tab:sol-hep} shows a list of expected numbers of solar\nneutrino events in typical energy regions.\n\\begin{table}[htb]\n \\caption{Expected solar neutrino event rates in water Cherenkov detectors. \nThe assumptions are same as Fig.~\\ref{fig:sol-hep}.}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline \\hline\nEnergy resolution & Energy range & $^8$B & hep & hep \/ $^8$B \\\\\n & [MeV] & [\/1.9 Mton\/year] & [\/1.9 Mton\/year] & \\\\\n\\hline\n\\hline\n \n SK-III\/IV & 19.5--25.0 & 0.77 & 3.03 & 3.9 \\\\\n Hyper-K & 18.0--25.0 & 0.56 & 6.04 & 10.6 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:sol-hep}\n\\end{table}\nHyper-K has a better separation between hep and $^8$B solar neutrinos\ncomparing to SK-III\/IV.\\par\n\nFigure~\\ref{fig:sol-hep-sensitivity} shows an estimation of hep neutrino detection sensitivity.\nA spectrum fit analysis is performed here,\nconsidering the spallation background, detection efficiency and systematic uncertainties of the energy scale and resolution.\nThe statistical error due to remaining spallation background is the dominant source of ambiguity.\nWhen we simply scale the current remaining spallation background level in SK-IV solar analysis, with the cosmic muon rate at Tochibora,\nthe uncertainty of the hep neutrino flux will be $\\sim$60\\% ($\\sim$40\\%) and the non-zero significance will be 1.8$\\sigma$ (2.3$\\sigma$) in ten (twenty) years observation in Hyper-K.\nDue to the higher energy resolution of Hyper-K, there is still chance to improve the sensitivity.\nIf we can reduce the remaining spallation background to the SK-IV level, the uncertainty of hep neutrino flux will be $\\sim$40\\% ($\\sim$30\\%) and non-zero significance will be improved to 2.5$\\sigma$ (3.2$\\sigma$) in ten (twenty) years observation.\nHere the same systematic uncertainties of detector energy scale (0.5~\\%) and resolution (0.6~\\%) as SK-IV are considered.\n\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[height=6.5cm]{physics-solarnu\/plot_hep_sensitivity.pdf} \\\\\n \\end{center}\n \\caption{\n\t Expected soler hep neutrino sensitivity with 187\\,kt fiducial volume.\n The horizontal axis is the observation time and the vertical axis is non-zero significance of hep neutrino signal expected from a energy spectrum analysis.\n BP2004 SSM fluxes are assumed. \n The effects of remaining spallation background, detection efficiency and systematic uncertainties of the energy scale and resolution estimated from SK-IV data are considered.\n The black solid line shows the expected sensitivity in Tochibora site.\n The red solid and dashed lines show the cases in Mozumi site and no spallation background, respectively.\n }\n \\label{fig:sol-hep-sensitivity}\n\\end{figure}\n\n\n\\subsubsection{Summary}\n\nIn this section, estimates of potential solar neutrino measurements\nare reported. The solar neutrino analysis is sensitive to the\ndetector resolutions and background levels. We have estimated\nexpected sensitivities in 10 years of Hyper-K observation based on the\ncurrent Super-K knowledge.\n\nAs a result of its shallower site, the increase of the spallation\nbackground level in Hyper-K will be up to a factor of 2.7 larger as compared\nto Super-K. However -- due to its much greater size and high energy\nresolution-- the statistical uncertainties on solar\nneutrino measurements would actually be reduced in Hyper-K as compared\nto Super-K on an equal time basis.\n\nThe sensitivity to the difference in neutrino oscillation\nparameters between solar and reactor neutrinos due to the day-night asymmetry\nis estimated to be 4$\\sim$5$\\sigma$.\nThe possibility of spectrum upturn observation is estimated to be at\nthe 3$\\sigma$ level.\n\nThe solar hep neutrino could be measured in \nHyper-K \nwith a few Mton year data at the level of $2\\sim3 \\sigma$.\n\n\\if 0\nIn this section, rough estimates of potential solar neutrino\nmeasurements are reported. The solar neutrino analysis is sensitive\nto the detector resolutions and background levels. We have estimated\nthe expected sensitivities based on the current Super-K analysis tools.\n\nAs a result of its shallower site, the increase of the background\nlevel in Hyper-K will be up to a factor of 20 as compared to Super-K.\nHowever -- due to its much greater size -- the statistical\nuncertainties on solar neutrino measurements would actually be reduced\nby a factor of at least two in Hyper-K as compared to Super-K on an\nequal time basis, assuming similar detector resolutions.\n\nThe day\/night asymmetry of the solar neutrino flux -- concrete\nevidence of the matter effect on oscillations -- could be discovered\nand then precisely measured in Hyper-K, given that the detector\nup-down response is understood to better than about 1\\%. Good\ncalibration tools will be a must for this physics.\n\nHyper-K will provide short time and high precision variability\nanalyses of the solar core activity. The solar core temperature could\nbe monitored within a few percent accuracy day by day, and to a tenth\nof a percent over the period of several months.\n\nThe solar hep neutrino could be measured in a 1TankHD{} \ndetector with a few Mton year data.\n\\fi\n\n\n\\subsection{Supernova}\\label{sec:supernova}\n\\subsubsection{Supernova burst neutrinos}\\label{sec:supernova-burst}\n\\paragraph{Introduction}\n\nCore-collapse supernova explosions are the last process in the\nevolution of massive ($>8$M$_{\\rm sun}$) stars. Working their way\nsuccessively through periods of predominantly hydrogen fusion, helium\nfusion, and so on, eventually silicon fusion starts making iron. Once\nan iron core has formed, no more energy can be released via its fusion\ninto still-heavier elements, and the hydrodynamic balance between\ngravity and stellar burning is finally and catastrophically disrupted.\nThe sudden gravitational collapse of their iron cores --\nwhich will go on to form either a neutron star or a black hole -- is\nthe main source of energy from this type of supernova explosion. The\nenergy released by a supernova is estimated to be $\\sim 3 \\times\n10^{53}$\\,ergs, making it one of the most energetic phenomena in the\nuniverse. Since neutrinos interact weakly with matter, almost 99\\% of\nthe released energy from the exploding star is carried out by\nneutrinos. As a result, the detection of supernova neutrinos gives\ndirect information of energy flow during the explosion. The neutrino\nemission from a core collapse supernova starts with a short\n($\\sim$10\\,millisecond) burst phase of electron captures ($p +\ne^- \\rightarrow n + \\nu_e$) called the neutronization burst, which\nreleases about $10^{51}$\\,ergs. Following that, the majority of the\nburst energy is released by an accretion phase ($< \\sim$1\\,second) and\na cooling phase (several seconds) in which all three flavours of\nneutrinos (as well as anti-neutrinos) are created.\\par\nThe observation of a handful (25 in total) of supernova burst\nneutrinos from SN1987a by the Kamiokande, IMB, and Baksan experiments\nproved that the basic scenario of the supernova explosion was correct.\nHowever, more than three decades later the detailed mechanism of\nexplosions is still not known.\nAchieving the necessary conditions\nfor a supernova explosion in computer simulations has been a\nlong-standing challenge.\nRecently, successful supernova explosions in two-dimensional and\nthree-dimensional simulations have been reported, the details of which will be\ndescribed later\\cite{Tamborra:13,SASIBlondin,SASIScheck,Takiwaki:2017tpe}.\nThough several models have produced successful\nsupernova explosions in simulations,\ndetecting supernova neutrinos will provide further input to improve the physics accuracy of the models.\nHyper-K can detect neutrinos with energy down to $\\sim$3\\,MeV and can point the supernova, due to its event-by-event directional sensitivity.\nBecause the supernova neutrinos are detected as a burst in a short time period, we can neglect the low energy radioactive backgrounds.\nThe localization in time also makes it possible to utilize most of full inner volume for our analysis, $i.e.$ 220\\,kt for each tanks.\nCompared with the current or planned experiments, $e.g.$ Super-K, the ice Cherenkov detector IceCube\/PINGU~\\cite{Aartsen:2014oha} and large liquid Ar TPC detectors like DUNE,\nHyper-K has several advantages for the supernova measurement.\nThe first advantage is the large volume and statistics. \nHyper-K will have a FV of 8\\,times to 16\\,times larger than the Super-K detector, resulting in a commensurate increase in the number of detected supernova neutrinos and sensitivity to supernovae occurring in nearby galaxies.\nLikewise, Hyper-K will be significantly larger than DUNE\nwith mass in the tens of kt scale.\nFurthermore, Hyper-K primarily detects anti-electron-neutrino from the\nsupernova explosion using the inverse beta decay reaction\n($\\bar{\\nu}_e + p \\rightarrow e^+ + n$), unlike LArTPC detectors which\nprimarily detect electron neutrinos.\nLarge neutrino telescopes like IceCube\/PINGU has capability of huge\nstatistics detection, however, they would detect only single PMT hits from such low energy neutrino events, allowing them to separate supernova neutrinos from their dark noise only on a statistical basis.\nIn contrast, every single event will be reconstructable with Hyper-K down to an energy analysis threshold of $\\sim$3\\,MeV.\nOur precise event-by-event measurement will be essential for the comprehensive study of supernova neutrinos, especially with the detailed and time-dependent energy spectrum.\nWith these advantages, Hyper-K is able to perform unique measurements to reveal the mechanism of supernova explosions.\\\\\n\n\\paragraph{Expected observation in Hyper-Kamiokande}\n\nIn order to correctly estimate the expected number of neutrino events detected\nin Hyper-K, we must consider the neutrino oscillation due to the MSW matter\neffect through the stellar medium.\nThe flux of each neutrino type emitted from a supernova is related to the originally produced fluxes ($F^0_{\\nu_e}$, $F^0_{\\bar{\\nu}_e}$ and $F^0_{\\nu_x}$, where $\\nu_x$ is $\\nu_{\\mu,\\tau}$ and $\\bar{\\nu}_{\\mu,\\tau}$) by the following formulas~\\cite{Dighe:1999id, Fogli:2004ff} :\n\n\\noindent\nFor normal hierarchy,\n\\begin{eqnarray}\nF_{\\bar{\\nu}_e} &\\simeq& \\cos^2\\theta_{12} F^0_{\\bar{\\nu}_e} + \\sin^2\\theta_{12}F^0_{\\nu_x}\\ , \\nonumber \\\\\nF_{\\nu_e} &\\simeq& \\sin^2\\theta_{12} P_{H} F^0_{\\nu_e} + (1-\\sin^2\\theta_{12} P_{H}) F^0_{\\nu_x}, \\nonumber \\\\\nF_{\\nu_\\mu} + F_{\\nu_\\tau} &\\simeq& (1-\\sin^2\\theta_{12} P_{H}) F^0_{\\nu_e} + (1 + \\sin^2\\theta_{12} P_{H}) F^0_{\\nu_x}, \\nonumber \\\\\nF_{\\bar{\\nu}_\\mu} + F_{\\bar{\\nu}_\\tau} &\\simeq& (1-\\cos^2\\theta_{12}) F^0_{\\bar{\\nu}_e} + (1 + \\cos^2\\theta_{12}) F^0_{\\nu_x} , \\nonumber\n\\end{eqnarray}\n\n\\noindent\nand, for inverted hierarchy,\n\\begin{eqnarray}\nF_{\\bar{\\nu}_e} &\\simeq& \\cos^2\\theta_{12} P_{H} F^0_{\\bar{\\nu}_e} + (1-\\cos^2\\theta_{12} P_{H}) F^0_{\\nu_x}\\ , \\nonumber \\\\\nF_{\\nu_e} &\\simeq& \\sin^2\\theta_{12} F^0_{\\nu_e}+ \\cos^2\\theta_{12}F^0_{\\nu_x} , \\nonumber \\\\\nF_{\\nu_\\mu} + F_{\\nu_\\tau} &\\simeq& (1-\\sin^2\\theta_{12}) F^0_{\\nu_e} + (1 + \\sin^2\\theta_{12}) F^0_{\\nu_x} , \\nonumber \\\\\nF_{\\bar{\\nu}_\\mu} + F_{\\bar{\\nu}_\\tau} &\\simeq& (1-\\cos^2\\theta_{12}P_H) F^0_{\\bar{\\nu}_e} + (1 + \\sin^2\\theta_{12} P_H) F^0_{\\nu_x} , \\nonumber\n\\end{eqnarray}\n\n\\noindent\nwhere $P_H$ is the crossing probability through the matter resonant\nlayer corresponding to $\\Delta m^2_{32}$. $P_H = 0$ ($P_H = 1$) for\nadiabatic (non-adiabatic) transition.\nRecent measurement of $\\theta_{13}$ indicates the adiabatic transition ($P_H=0$) for the matter transition in the supernova envelope.\nThe supernova neutrino spectrum is\naffected not only by stellar matter but also by other neutrinos and\nanti-neutrinos at the high density core (so-called collective\neffects). These collective effects, which swap the $\\nu_{e}$ and\n$\\bar{\\nu}_e$ spectra with those of $\\nu_x$ in certain energy\nintervals bounded by sharp spectral splits, were first discussed\nin~\\cite{Duan:2006an,Duan:2006jv}. This has become an active field of\nstudy whose recent investigations include taking into account the\npossibility of multiple splits~\\cite{Dasgupta:2009dd}, computation with\nthree neutrino flavors~\\cite{Friedland:2010sc}, and utilizing the full\nmulti-angle framework~\\cite{Duan:2010bf}.\nSo, in the following description of the performance of the\nHyper-Kamiokande detector, three cases are considered in order to\nfully cover the possible variation of expectations: (1)\nno~oscillations, (2) normal~hierarchy (N.H.) with $P_H=0$, and (3)\ninverted~hierarchy (I.H.) with $P_H=0$. The process depends critically on\n$\\theta_{12}$; in what follows we assume $\\sin^2\\theta_{12}=0.31$.\nConcerning the neutrino fluxes and energy spectra at the production\nsite, we used results obtained by the Livermore\nsimulation~\\cite{Totani:1997vj}.\n\nFigure~\\ref{fig:sn-rate} shows time profiles for various interactions\nexpected at the Hyper-Kamiokande detector for a supernova at a\ndistance of 10\\,kiloparsecs~(kpc). This distance is a bit farther than\nthe center of the Milky Way galaxy at 8.5\\,kpc; it is chosen as being\nrepresentative of what we might expect since a volume with a radius of\n10\\,kpc centered at Earth includes about half the stars in the galaxy.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=16cm]{physics-supernova\/pdf_1tank\/eventrate_persec_hk_1tank-crop_upto_100MeV.pdf}\n \\end{center}\n\\vspace{-1cm}\n\\caption{Expected time profile of a supernova at 10\\,kpc with 1 tank. \nLeft, center, and right figures show profiles for no oscillation, normal \nhierarchy, and inverted hierarchy, respectively.\nBlack, red, purple, and light blue curves show event rates for\ninteractions of inverse beta decay ($\\bar{\\nu}_e + p \\rightarrow e^+ + n$), \n$\\nu e$-scattering ($\\nu + e^- \\rightarrow \\nu + e^-$), \n$\\nu_e~^{16}$O CC ($\\nu_e + {\\rm ^{16}O} \\rightarrow e^- + {\\rm^{16}F^{(*)}}$),\nand \n$\\bar{\\nu}_e~^{16}$O CC\n($\\bar{\\nu}_e + {\\rm ^{16}O} \\rightarrow e^+ + {\\rm ^{16}N^{(*)}}$), respectively.\nThe numbers in parentheses are integrated\nnumber of events over the burst. \nThe fluxes and energy spectra are from the Livermore \nsimulation~\\cite{Totani:1997vj}\n \\label{fig:sn-rate}\n }\n\\end{figure}\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/sn-neutronization_1tank.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Expected event rate at the time of neutronization burst for\n\t a supernova at 10\\,kpc with 1 tank. Red and green\n\t show event rates for $\\nu e$-scattering events originated with neutronization neutrino and inverse beta\n\t events, respectively. Solid, dotted, and dashed curved\n\t indicate the neutrino oscillation scenarios of no\n\t oscillation, N.H., and I.H.,\n\t respectively.\n \\label{fig:sn-neutronization}\n }\n\\end{figure}\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/all_spectrum_hk_osc_resol.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Total energy spectrum for each interaction\n\t for a supernova at 10\\,kpc with 1 tank. \nBlack, red, purple, and light blue curves show event rates for\ninteractions of inverse beta decay, $\\nu e$-scattering, \n$\\nu_e+^{16}$O CC, and $\\bar{\\nu}_e+^{16}$O CC, respectively.\nSolid, dashed, and dotted curves correspond to no oscillation, N.H., and\nI.H., respectively.\n \\label{fig:sn-spec}\n}\n\\end{figure}\nThe three graphs in the figure show the cases of no oscillation, normal hierarchy and inverted hierarchy, respectively.\nColored curves in the figure show event rates for inverse beta decay\n($\\bar{\\nu}_e + p \\rightarrow e^+ + n$), \n$\\nu e$-scattering($\\nu + e^- \\rightarrow \\nu + e^-$), \n$\\nu_e+^{16}$O CC($\\nu_e + {\\rm ^{16}O} \\rightarrow e^- + {\\rm ^{16}F^{(*)}}$),\nand \n$\\bar{\\nu}_e+^{16}$O CC\n($\\bar{\\nu}_e + {\\rm ^{16}O} \\rightarrow e^+ + {\\rm ^{16}N^{(*)}}$).\nThe burst time period is about 10\\,s and the peak event rate of inverse beta decay events reaches about 50\\,kHz at 10 kpc.\nThe DAQ and its buffering system of Hyper-K will be designed to accept the broad range of rates, for a galactic SN closer than 10 kpc.\nA sharp timing spike is expected for $\\nu e$-scattering events at the time of neutronization.\nFig.~\\ref{fig:sn-neutronization} shows the expanded plot around the neutronization burst peak region.\nWe expect $\\sim$9, $\\sim$23 and $\\sim$55 $\\nu e$-scattering events in this region for a supernova at 10\\,kpc, for N.H., I.H., and no oscillation respectively.\nAlthough the number of inverse beta events is $\\sim$100 (N.H.), $\\sim$210 (I.H.), and $\\sim$60 (no oscillation) in the 10\\,ms bin of the neutronization burst, \nthe number of events in the direction of the supernova is typically 1\/10 of the total events. \nSo, the ratio of signal events ($\\nu e$-scattering) to other events (inverse beta) is expected to be about 9\/10~(N.H.),\n23\/21~(I.H.) and 55\/6~(no oscillation).\n\n\nThe energy distributions of each interaction are shown in Fig.~\\ref{fig:sn-spec}, where the energy is the electron-equivalent total energy measured by a Cherenkov detector.\nThe energy spectrum of $\\bar{\\nu}_e$ can be extracted from the distribution.\n\nFigure~\\ref{fig:sn-evtvsdist} shows the expected number of supernova neutrino events at Hyper-K versus the distance to a supernova.\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/evtvsdist-hk-oscrange-1tank-upto-100MeV-crop.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Expected number of supernova burst events for each\n\t interaction as a function of the distance to a supernova with 1 tank.\nThe band of each line shows the possible variation due to the assumption\nof neutrino oscillations.\n \\label{fig:sn-evtvsdist}\n}\n\\end{figure}\nAt the Hyper-Kamiokande detector, we expect to see about 50,000 to 75,000 inverse beta decay events, 3,400 to 3,600 $\\nu e$-scattering events, 80 to 7,900 $\\nu_e+^{16}$O CC events, and 660 to 5,900 $\\bar{\\nu}_e+~^{16}$O CC events, in total 54,000 to 90,000 events, for a 10\\,kpc supernova.\nThe range of each of these numbers covers possible variations due to the neutrino oscillation scenario (no oscillation, N.H., or I.H.).\nEven for a supernova at M31 (Andromeda Galaxy), about 10 to 16 events are expected at Hyper-K.\nIn the case of the Large Magellanic Cloud (LMC) where SN1987a was located, about 2,200 to 3,600 events are expected.\n\nThe observation of supernova burst neutrino and the directional\ninformation can provide an early warning for electromagnetic observation\nexperiments, e.g. optical and x-ray telescopes. \nFigure~\\ref{fig:sn-cossn} shows expected angular\ndistributions with respect to the direction of the supernova for four\nvisible energy ranges. The inverse beta decay events have a nearly\nisotropic angular distribution. On the other hand, $\\nu e$-scattering\nevents have a strong peak in the direction coming from the supernova.\nSince the visible energy of $\\nu e$-scattering events are lower than\nthe inverse beta decay events, the angular distributions for lower energy\nevents show more enhanced peaks. The direction of a supernova at\n10\\,kpc can be reconstructed with an accuracy of about 1 to 1.3 degrees with Hyper-K,\nassuming the performance of event direction reconstruction similar to Super-K~\\cite{Abe:2016waf}.\nThis pointing accuracy will be precise enough for the multi-messenger measurement of supernova at the center of our galaxy,\nwith the world's largest class telescopes, $i.e.$ Subaru HSC and future LSST telescope~\\cite{Nakamura:2016kkl}.\\\\\n\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=10cm]{physics-supernova\/pdf_1tank\/sn-cossn_1tank.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Angular distributions of a simulation of\n\t a 10\\,kpc supernova with 1 tank. The plots show a visible energy range of \n5-10\\,MeV (left-top), \n10-20\\,MeV (right-top), 20-30\\,MeV (left-bottom), and 30-40\\,MeV (right-bottom).\nThe black dotted line and the red solid histogram (above the black dotted line)\nare fitted contributions of inverse beta decay and $\\nu e$-scattering events.\nConcerning the neutrino oscillation scenario, the $no~oscillation$ case is shown\nhere.\n \\label{fig:sn-cossn}\n}\n\\end{figure}\n\n\\paragraph{Physics impacts}\n\nThe shape of the rising time of supernova neutrino flux and energy strongly depends on the model.\nFigure~\\ref{fig:sn-model} shows inverse beta decay event rates and mean $\\bar{\\nu}_e$ energy distributions predicted by various models\n\\cite{Totani:1997vj,Takiwaki:2013cqa,Tamborra:2014hga,Dolence:2014rwa,Pan:2015sga,Nakazato:2015rya,Bruenn:2014qea} for the first 0.3\\,sec after the onset of a burst.\nThe statistical error is much smaller than the difference between the models, and so Hyper-K should give crucial data for comparing model predictions.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_1tank\/model_obsevents_nuebar_2016-crop.pdf}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_1tank\/model_obsenergy_nuebar_2016-crop.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t Time profiles of the observed inverse beta decay event rate (left) and mean energy of these events, \npredicted by supernova simulations~\\cite{Totani:1997vj,Takiwaki:2013cqa,Tamborra:2014hga,Dolence:2014rwa,Pan:2015sga,Nakazato:2015rya,Bruenn:2014qea} for the first 0.3\\,seconds after the onset \nof a 10\\,kpc distant burst with Hyper-K 1 tank.\n \\label{fig:sn-model} \n}\n\\end{figure}\nThe left plot in Fig.~\\ref{fig:sn-model} shows that about 150-500\nevents are expected in the first 20 millisecond bin. This means that\nthe onset time can be determined with an accuracy of about 1 ms. This\nis precise enough to allow examination of the infall of the core in\nconjunction with the signals of neutronization as well as\npossible data from future gravitational wave detectors.\nOur measurement will also provide an opportunity to observe black hole formation directly, as a sharp drop of the neutrino flux~\\cite{Sekiguchi:2010ja}.\n\nWe can use the sharp rise of the burst to make a measurement of\nthe absolute mass of neutrinos. Because of the finite mass of\nneutrinos, their arrival times will depend on their energies. This\nrelation is expressed as \\\\\n\\begin{eqnarray}\n\t\\Delta t = 5.15~{\\rm msec} (\\frac{D}{10~{\\rm kpc}})\n\t(\\frac{m}{1~{\\rm eV}})^2 (\\frac{E_\\nu}{10~{\\rm MeV}}) ^{-2}\n\\end{eqnarray}\nwhere $\\Delta t$ is the time delay with respect to that assuming zero\nneutrino mass, $D$ is the distance to the supernova, $m$ is the\nabsolute mass of a neutrino, and $E_\\nu$ is the neutrino energy.\nTotani~\\cite{Totani:1998nf} discussed Super-Kamiokande's sensitivity\nto neutrino mass using the energy dependence of the rise time; scaling\nthese results to the much larger statistics provided by Hyper-K, we\nexpect a sensitivity of 0.5 to 1.3\\,eV for the absolute neutrino\nmass~\\cite{Totani:2005pv}. Note that this measurement of the absolute\nneutrino mass does not depend on whether the neutrino is a Dirac or\nMajorana particle.\n\nHyper-K can also statistically extract an energy distribution of\n$\\nu_e + \\nu_X (X = \\mu, \\tau)$ events using the angular distributions\nin much the same way as solar neutrino signals are separated from\nbackground in Super-K. Although the effect of neutrino oscillations\nmust be taken into account, the $\\nu_e + \\nu_X$ spectrum gives another\nhandle on the temperature of neutrinos.\nHyper-K will be able to evaluate the temperature\ndifference between $\\bar{\\nu}_e$ and $\\nu_e + \\nu_X$. This would be a\nvaluable input to model builders. For example, the prediction from\nmany of the \nmodels that the energy of $\\nu_e$ is less than $\\nu_X$ can be confirmed.\nThe temperature is also critical for the nucleosynthesis via supernova explosion~\\cite{2016inpc.confE.249H}.\n\nFrom recent computer simulation studies, new characteristic\nmodulations of the supernova neutrino flux are proposed.\nThese modulations are due to the dynamic motions in the supernovae such as convection.\nThe stall of shock wave after core bounce has been an issue in supernova computer simulations, which was not able to achieve successful explosions.\nThese dynamic motions enable the inner materials to be heated more efficiently by the neutrinos from collapsed core, and realize the shock wave revival.\nSuch modulations can be detected as a variance of the neutrino event rate in Hyper-K.\nIt will be the clear evidence that neutrino is the driver of supernova burst process.\nOne source of such modulation is the Standing Accretion Shock\nInstability (SASI)~\\cite{Tamborra:13,SASIBlondin,SASIScheck}.\nFigure~\\ref{fig:sn_tamborra_sasi} shows the detection rate modulation\nin Hyper-K, induced by SASI.\nThe modulation can be observed as a variance of $\\sim$10\\% of the number of supernova events in Hyper-K detector\n\\cite{Tamborra:13}.\nThis flux variance caused by SASI has a characteristic peak in the frequency space.\nWhen we assume a 3\\% flux modulation on the total supernova flux,\nthough the amount of the flux modulation depends on several variables, e.g. progenitor mass or equation of states,\nit is possible to see the existence of SASI for the supernovae within about 15\\,kpc distance.\\cite{Migenda:16}\nUnder this assumption of a 3\\% flux modulation, we will have chances to prove SASI effects for $\\sim$90\\% of galactic supernovae with Hyper-K, compared with only $\\sim$15\\% with Super-K.\n\\\\\nAnother source of modulation is the rotation of supernova~\\cite{Takiwaki2014,Takiwaki:2017tpe}.\nThe size of variation depends on the angle between the direction of\nearth and the rotational axis of supernova. When the supernova\nrotational axis is orthogonal with the direction to the earth, the\ndetectable variance will be the maximum. In that case, Hyper-K will\ndetect a variance of $\\sim$50\\% in the number of observed signals\nas shown in Figure~\\ref{fig:sn_tamborra_sasi}.\nThe observation of these modulation with Hyper-K\nwill be a good test of such simulations and also provide important\ninformation for understanding the dynamics in supernovae.\n\n\\if0\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/sn_sasi_tamborra.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t Detection rate modulation induced by SASI in 5\\,ms bins (0.56 Mt).\n\t The SN progenitor mass is 27 solar mass.\n\t The direction to the detector is chosen for strong signal modulation.\n\t This figure is adopted from~\\cite{Tamborra:13}.\n \\label{fig:sn_tamborra_sasi}\n }\n\\end{figure}\n\\fi\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/SASI_2msBin_220kt.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t Detection rate modulation induced by SASI in Hyper-K 1 tank.\n\t Red line shows the theoretical event rate estimation for the inverse beta decay reaction.\n\t Gray line shows a simulated event rate taking into account statistical fluctuation.\n\t The SN progenitor mass is 27 solar mass.\n\t The direction to the detector is chosen for strong signal modulation.\n\t This neutrino flux is adopted from~\\cite{Tamborra:13}.\n \\label{fig:sn_tamborra_sasi}\n }\n\\end{figure}\n\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=10cm]{physics-supernova\/pdf_1tank\/time-Rev-HK1tank.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t Detection rate modulation produced by a rotating SN model in Hyper-K 1 tank.\n\t The SN progenitor mass is 27 solar mass.\n\t The supernova rotational axis is orthogonal (red) and parallel (green) with the direction to the earth.\n\t This figure is adopted from~\\cite{Takiwaki:2017tpe}.\n \\label{fig:sn_tatewaki_rotation}\n }\n\\end{figure}\n\nNeutrino oscillations could be studied using supernova neutrino events.\nThere are many papers which discuss the possibility of extracting signatures of neutrino oscillations free from uncertainties of supernova models \\cite{Totani:1997vj,Takiwaki:2013cqa,Tamborra:2014hga,Dolence:2014rwa,Pan:2015sga,Nakazato:2015rya,Bruenn:2014qea}.\nOne big advantage of supernova neutrinos over other neutrino sources (solar, atmospheric, accelerator neutrinos) is that they inevitably pass through very high density matter on their way to the detector.\nThis gives a sizeable effect in the time variation of the energy spectrum~\\cite{Schirato:2002tg, Fogli:2004ff, Tomas:2004gr}.\nThough the combination of MSW stellar matter effects and collective effects makes the prediction quite difficult~\\cite{Duan:2006an,Duan:2006jv,Dasgupta:2009dd,Friedland:2010sc,Duan:2010bf},\nwe will still have opportunities to determine the neutrino mass hierarchy from the supernova burst.\nThe first chance is the neutronization burst, where mostly pure $\\nu_e$ will be emitted from the proto-neutron star.\nSince, the collective effect through $\\nu_e\\bar{\\nu}_e\\rightarrow\\nu_X\\bar{\\nu}_X$ interaction can be negligible.\nThe multi-angle effect can also be ignored, because these neutrinos are emitted only from the very center of the supernova.\nThe flux is well predicted and hardly affected by the physics\nmodelling of the EOS or the progenitor mass~\\cite{Kachelriess:2004ds, Mirizzi:2015eza}.\nThe number of event will be about 50\\% larger in IH case comparing to NH, after 20\\,ms from the core bounce.\nIn the succeeding accretion phase, we will have another chance by observing the rise-time of neutrino event rate.\nThe mixing of $\\bar{\\nu}_X$ to $\\bar{\\nu}_e$, will result in a 100\\,ms faster rise time for the inverted hierarchy compared to the normal hierarchy case~\\cite{Serpico:2011ir}.\nWe will have fair chance to investigate it for a supernova at the galactic center, see Fig.~\\ref{fig:sn-model}.\n\n\\if0\nAn example is shown in Figure~\\ref{fig:sn-nuosc}~\\cite{Fogli:2004ff}.\nThe propagation of the supernova shock wave causes time variations in\nthe matter density profile through which the neutrinos must travel.\nBecause of neutrino conversion by matter, there may be a bump in the\ntime variation of the inverse beta event rate for a particular energy\nrange ($i.e.$, 45$\\pm$5\\,MeV as shown in\nFig.~\\ref{fig:sn-nuosc}(right)) while no change is observed in the\nevent rate near the spectrum peak ($i.e.$, 20$\\pm$5\\,MeV as shown in\nFig.~\\ref{fig:sn-nuosc}(left)). This effect is observed only in the\ncase of inverted mass hierarchy; this is one way in which the mass\nhierarchy could be determined by a supernova burst.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=16cm]{physics-supernova\/sn-fp2-Fogli0412046.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Time variation of the neutrino event rate affected by\n\t neutrino conversion by matter due to shock wave propagation\n\t (reproduced from~\\cite{Fogli:2004ff}).\n\t Left (right) plot shows the time variation of inverse beta\n\t events for the energy range of 20$\\pm$5\\,MeV (45$\\pm$5\\,MeV).\n\t Solid black, dashed red, and blue dotted histograms show the\n\t event rates for I.H. with shock wave propagation, I.H. with\n\t static matter density profile, and N.H., respectively. It\n\t has been assumed that\n\t $\\sin^2\\theta_{13}=10^{-2}$. \\label{fig:sn-nuosc}}\n\\end{figure}\n\\fi\n\nIn Hyper-K, it could be possible to detect burst neutrinos from\nsupernovae in nearby galaxies. As described above, we expect to\nobserve a very large number of neutrino events from a galactic\nsupernova. However, galactic supernovae are expected to happen once\nper 30\\,-\\,50 years. So, we cannot count on seeing many galactic\nsupernova bursts. In order to examine a variety of supernova bursts,\nsupernovae from nearby galaxies are useful even though the expected\nnumber of detected events from any single such burst is small.\nFurthermore, the merged energy spectrum from these supernovae will be highly useful for understanding that of supernova relic neutrinos (see next sub-section) for the absence of red-shift.\nThe supernova events from nearby galaxies provide a reference energy spectrum for this purpose.\nThe supernovae rate in nearby galaxies was discussed in~\\cite{Ando:2005ka} and a figure from the\npaper is shown in Fig.~\\ref{fig:sn-nearby}.\nIt shows the cumulative supernova rate versus distance and indicates that if Hyper-K can see signals out to 4\\,Mpc then we could expect a supernova about every three years.\nIt should be noted that recent astronomical observations indicate about 3 times higher nearby supernova rate~\\cite{Horiuchi:2013}, compared to the conservative calculation.\nIt is also valuable to mention that two strange supernovae have been found at $\\sim$2\\,Mpc distance in the past 11 years observation, which are called dim supernovae~\\cite{Horiuchi:2013}.\nThe detections of supernova neutrinos from these dim supernovae will prove their explosion mechanism is core-collapse.\nFigure~\\ref{fig:sn-nearbyprob} shows detection probability versus distance for the Hyper-K detector 1 tank (left) and 2 tanks configuration (right).\nIn this estimate, we required the neutrino energy be greater than 10\nMeV in order to reduce background.\nRequiring the number of neutrino events to be more than or or equal to two\\,(one), the detection probability is 27 to 48\\% (64 to 80\\%) with 1 tank, for a supernova at 2\\,Mpc.\nThe probability will be 3 to 6\\% (22 to 33\\%) for the supernovae at 4\\,Mpc.\nWith 2 tank configuration and 375 kt fiducial volume, the detection probability will be increased to 10 to 18\\% (40 to 57\\%) for a supernova at 4\\,Mpc.\nIf we can use a tight timing coincidence with other types of supernova sensors (e.g. future gravitational wave detectors), we should be able to identify even single supernova neutrinos.\nWe expect to observe 2.4 to 4.6 or 0.6 to 1.4 supernovae with and without dim supernovae within 10\\,Mpc respectively, during 20 years of Hyper-K one tank operation.\nHere we required two or more neutrino events for each supernovae, and referred to the nearby galactic supernova rate given by CCSNe counting in ref.~\\cite{Horiuchi:2013}.\nThe number of observations can be increased to 5.0 to 8.2 and 1.6 to 3.3 supernovae with and without dim supernova respectively, with Hyper-K staging two tank scenario.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=7cm]{physics-supernova\/sn-nearbyrate.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Cumulative calculated supernova rate versus distance for \n\t supernovae in nearby galaxies. The dashed line is core-collapse supernova rate expectation, using the $z = 0$ limit of star formation rate measured by GALEX. The figure is reproduced from ref.~\\cite{Ando:2005ka}.\n \\label{fig:sn-nearby}\n}\n\\end{figure}\n\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_1tank\/sn-nearbyprob_1tank-crop.pdf}\n\\hspace{3mm}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_2tank\/sn-nearbyprob_2tank-crop.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{(Left) Detection probability of supernova neutrinos versus distance at Hyper-K assuming a 187\\,kiloton fiducial volume and 10\\,MeV threshold for this analysis.\nBlack, green, and blue curves show the detection efficiency resulting in requiring more than or equal to one, two, and three events per burst, respectively.\nSolid, dotted, and dashed curves are for neutrino oscillation scenarios of no oscillation, N.H., and I.H., respectively.\n\t(Right) Detection probability of supernova neutrinos with Hyper-K 2 tanks.\n \\label{fig:sn-nearbyprob}\n}\n\\end{figure}\n\n\\paragraph{Summary}\n\nThe expected number of supernova neutrino events in the Hyper-Kamiokande detector is summarized in Table~\\ref{tab:phys_supernova_summary}.\nThese events will be enough to provide detailed information about the time profile and the energy spectrum for inspecting supernova explosion mechanism, including black hole formation.\nThey will also provide an opportunity for further physics topics, $i.e.$ the neutrino mass, the mass hierarchy and the neutrino oscillations in the supernova.\nPhysics beyond the standard model also can be tested, $e.g.$\nsterile neutrinos~\\cite{Hidaka:2006sg, Loveridge:2003fy, Hidaka:2007se, Tamborra:2011is},\nthe neutrino magnetic moment~\\cite{Lattimer:1988mf, Barbieri:1988nh}\nthe neutrino non-standard interaction~\\cite{EstebanPretel:2007yu, Ohlsson:2012kf} and\nthe axion~\\cite{Turner:1987by, Burrows:1988ah, Keil:1996ju, Raffelt:2006cw, Fischer:2016cyd}.\nThe better energy resolution from high photo-coverage will help these analyses.\nThe lower energy threshold will also help to understand the whole picture of supernova explosion.\nThe detection of supernovae in nearby galaxies will be possible even with a single tank, though the number of events will be small.\nThe energy spectrum of these events will still be useful to understand the nature of the supernova explosion.\n\\if0\nAxion \\cite{Turner:1987by, Burrows:1988ah, Keil:1996ju, Raffelt:2006cw, Fischer:2016cyd}\nSterile \\cite{Hidaka:2006sg, Loveridge:2003fy, Hidaka:2007se, Tamborra:2011is}\nNSI \\cite{EstebanPretel:2007yu, Ohlsson:2012kf}\nMagnetic Moment \\cite{Lattimer:1988mf, Barbieri:1988nh}\n\\fi\n\n\\if0\n\\begin{table}[t]\n\t\t\\caption{Summary table of expected supernova neutrino events in the Hyper-Kamiokande detector (E$_\\nu=$4 - 60\\,MeV). A supernova at Galactic center (10\\,kpc) is assumed. Our references for each cross-section are also shown.\n\t\t\\label{tab:phys_supernova_summary_old}\n\t\t}\n\t\\begin{ruledtabular}\n\t\t\\begin{tabular}{lccc}\n\t\t\tNeutrino source & \\hkthreetank{} (660\\,kt Full Volume) & 1TankHD{} (220\\,kt Full Volume) & Ref. \\\\\n\t\t\t\\hline\n\t\t\t$\\bar{\\nu}_e + p$ & 147,000$\\sim$204,000\\,events& 49,000$\\sim$68,000\\,events &\\cite{Vogel:1999zy}\\\\\n\t\t\t${\\nu} + e^-$& 6,400$\\sim$7,500~events& 2,100$\\sim$2,500~events& \\cite{tHooft:1971ucy} \\\\\n\t\t\t${\\nu}_e + ^{16}O$ CC & 250$\\sim$12,000~events& 80$\\sim$4,100~events& \\cite{Tomas:2003xn}\\\\\n\t\t\t$\\bar{\\nu}_e + ^{16}O$ CC & 1,900$\\sim$12,000~events& 650$\\sim$3,900~events& \\cite{Kolbe:2002gk}\\\\\n\t\t\t${\\nu}_e + e^-$ (Neutronization) & 18$\\sim$120~events& 6$\\sim$40~events& \\cite{tHooft:1971ucy}\\\\\n\t\t\t\\hline\n\t\t\tTotal & 160,000$\\sim$240,000~events& 52,000$\\sim$79,000~events &\\\\\n\t\t\\end{tabular}\n\t\\end{ruledtabular}\n\\end{table}\n\\fi\n\\if0\n\\begin{table}[t]\n\t\t\\caption{Summary table of expected supernova neutrino events in the Hyper-Kamiokande detector. A supernova at Galactic center (10\\,kpc) is assumed.\n\t\t\\label{tab:phys_supernova_summary}\n\t\t}\n\t\\begin{ruledtabular}\n\t\t\\begin{tabular}{lcc}\n\t\t\tNeutrino source & 2 Tanks (440\\,kt Full Volume) & Single Tank (220\\,kt Full Volume) \\\\\n\t\t\t\\hline\n\t\t\t$\\bar{\\nu}_e + p$ & 98,000$\\sim$136,000\\,events& 49,000$\\sim$68,000\\,events \\\\\n\t\t\t${\\nu} + e^-$ & 4,200$\\sim$5,000~events& 2,100$\\sim$2,500~events \\\\\n\t\t\t${\\nu}_e + ^{16}O$ CC & 160$\\sim$8,200~events& 80$\\sim$4,100~events \\\\\n\t\t\t$\\bar{\\nu}_e + ^{16}O$ CC & 1,300$\\sim$7,800~events& 650$\\sim$3,900~events \\\\\n\t\t\t${\\nu}_e + e^-$ (Neutronization) & 12$\\sim$80~events& 6$\\sim$40~events \\\\\n\t\t\t\\hline\n\t\t\tTotal & 104,000$\\sim$158,000~events& 52,000$\\sim$79,000~events \\\\\n\t\t\\end{tabular}\n\t\\end{ruledtabular}\n\\end{table}\n\\fi\n\\begin{table}[t]\n\t\t\\caption{Summary table of expected supernova neutrino events in the Hyper-Kamiokande detector, with E$_\\nu$ upto 100\\,MeV and the detection threshold of 3\\,MeV. A supernova at Galactic center (10\\,kpc) is assumed. Our references for each cross-section are also shown.\n\t\t\\label{tab:phys_supernova_summary}\n\t\t}\n\t\\begin{ruledtabular}\n\t\t\\begin{tabular}{lccc}\n\t\t\tNeutrino source & Single Tank (220\\,kt Full Volume) & 2 Tanks (440\\,kt Full Volume) & Ref.\\\\\n\t\t\t\\hline\n\t\t\t$\\bar{\\nu}_e + p$ & 50,000 - 75,000\\,events& 100,000 - 150,000\\,events&\\cite{Vogel:1999zy}\\\\\n\t\t\t${\\nu} + e^-$ & 3,400 - 3,600~events& 6,800 - 7,200~events&\\cite{tHooft:1971ucy} \\\\\n\t\t\t${\\nu}_e + ^{16}O$ CC & 80 - 7,900~events& 160 - 11,000~events&\\cite{Tomas:2003xn} \\\\\n\t\t\t$\\bar{\\nu}_e + ^{16}O$ CC & 660 - 5,900~events& 1,300 - 12,000~events& \\cite{Kolbe:2002gk}\\\\\n\t\t\t${\\nu} + e^-$ (Neutronization) & 9 - 55~events& 17 - 110~events &\\cite{tHooft:1971ucy}\\\\\n\t\t\t\\hline\n\t\t\tTotal & 54,000 - 90,000~events& 109,000 - 180,000~events \\\\\n\t\t\\end{tabular}\n\t\\end{ruledtabular}\n\\end{table}\n\n\\subsubsection{High-energy neutrinos from supernovae with interactions with circumstellar material}\nCore-collapse supernovae are promising sources of high-energy ($\\gtrsim$ GeV) neutrinos as well as multi-MeV neutrinos.\nThe supernova shock\npropagates in the stellar material and experiences a shock breakout,\nwhich can be observed at ultraviolet or X-ray wavelengths. Before the\nshock breakout, the supernova shock is mediated by radiation since the\nphoton diffusion time is longer than the expansion time. During this\ntime, the conventional cosmic-ray (CR) acceleration is inefficient, so\nassociated neutrino production is not promising. However, as the\nshock becomes collisionless after the breakout, the CR acceleration\nstarts to be effective~\\cite{wl01,mur+11}. The situation is expected\nto be analogous to supernova remnants, which are almost established as\nCR accelerators and widely believed as the origin of Galactic CRs.\n\nIn the early phase just after the breakout, the matter density is still high, so that accelerated CRs are efficiently used for neutrino production via inelastic $pp$ scatterings.\nFor type II supernovae, which are associated with red\nsuper-giants, the released energy of high-energy neutrinos is\ntypically ${\\mathcal E}_{\\nu}\\sim{10}^{47}$\\,erg~\\cite{wl01}.\nOne to two events of GeV neutrinos are expected in a timescale of hours after the core-collapse for a Galactic supernova at 10kpc in Hyper-K 1 tank.\n\nAbout 10\\% of core-collapse supernovae show strong interactions with\nambient circumstellar material, which are often called\ninteraction-powered supernovae. If the circumstellar material mass is\n$\\sim0.1$-$1~M_\\odot$, the released high-energy neutrino energy\nreaches ${\\mathcal\nE}_{\\nu}\\sim{10}^{49}$-${10}^{50}$~erg~\\cite{mur+11}. For example,\nEta Carinae at 2.3\\,kpc is an interesting candidate that showed violent\nmass eruptions in the past. If a real supernova occurs and the ejecta\ncollides with the circumstellar material shell with $\\sim10\\,M_\\odot$,\none may expect $\\sim300$ events with Hyper-K. However, because of\nthe long duration (from months to years), the signal can overwhelm the\nbackground only at early times and sufficiently high energies.\n\nHigh-energy neutrinos from supernovae are detectable hours to months\nafter the core-collapse, and detecting the signals will give us new\ninsights into supernova physics, such as how collisionless shocks are\nformed and CR acceleration starts, as well as the connection to\nsupernova remnants as the origin of Galactic CRs. We may be able to\nsee the time evolution of multi-energy neutrino emission from the\ncore-collapse to shock breakout and following interactions with the\ncircumstellar material.\n \n\\subsubsection{Supernova relic neutrinos}\\label{sec:supernova-relic}\nThe neutrinos produced by all of the\nsupernova explosions since the beginning of the universe are called\nsupernova relic neutrinos (SRN) or diffuse supernova neutrino background (DSNB). They must fill the present universe\nand their flux is estimated to be a few tens\/cm$^2$\/sec. If we can\ndetect these neutrinos, it is possible to explore the history of how\nheavy elements have been synthesized since the onset of stellar\nformation.\n\\par\n\\if0\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/srn-prediction.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Predictions of the supernova relic neutrino (SRN) spectrum.\nFluxes of reactor neutrinos and atmospheric neutrinos are also shown.\n\t\\cite{Totani:1995rg,Totani:1995dw,Hartmann:1997qe,Malaney:1996ar,Kaplinghat:1999xi,Ando:2002ky,Lunardini:2006pd,Fukugita:2002qw}\n \\label{fig:sn-srn-prediction} }\n\\end{figure}\n\\fi\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/relic_fluxplot_hbd-crop.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Predictions of the supernova relic neutrino (SRN) spectrum.\nFluxes of reactor neutrinos and atmospheric neutrinos are also shown\n\t\\cite{Horiuchi:2008jz}.\n \\label{fig:sn-srn-prediction} }\n\\end{figure}\nFigure~\\ref{fig:sn-srn-prediction} shows the SRN spectra predicted by\nvarious models. Although searches for SRN have been conducted at\nlarge underground detectors, no evidence of SRN signals has yet been\nobtained because of the small flux of SRN. The expected inverse beta\n($\\bar{\\nu}_e+p \\rightarrow e^++n$) event rate at Super-Kamiokande is\n0.8-5 events\/year above 10\\,MeV, but because of the large number of\nspallation products and the low energy atmospheric neutrino background\n(decay electrons from muons below Cherenkov threshold produced by\natmospheric muon neutrinos, the so-called invisible muon background),\nSRN signals have not yet been observed at Super-Kamiokande. In order\nto reduce background, lower the energy threshold, individually\nidentify true inverse beta events by tagging their neutrons, and\nthereby positively detect SRN signals at Super-Kamiokande, a project\nto add 0.1\\% gadolinium (Gd) to tank (the SK-Gd project, called\nGADZOOKS! project previously) was proposed by J.F. Beacom and\nM.R. Vagins~\\cite{Beacom:2003nk}.\nAs the result of very active R\\&D works, the detector upgrade to SK-Gd is planned in 2018.\nThe first observation of the SRN could be made by the SK-Gd project.\nHowever, a megaton-scale detector is still desired to measure the spectrum of the SRN and to investigate the history of the universe because of its huge statistics as shown in Fig.~\\ref{fig:srn-comp}.\nFurthermore, Hyper-K could measure the SRN neutrinos at E =\n16-30\\,MeV, while the SK-Gd project concentrates on the energy of 10-20\\,MeV.\nThese observation at a different energy region can measure the contribution of extraordinary supernova bursts on the SRN, e.g. black hole formation~\\cite{Lunardini:2009,Horiuchi:2015HK}.\nFigure~\\ref{fig:srn-BH} shows the SRN signals in Hyper-K fiducial volume, with a different fraction of black hole formations.\nBecause the successful formation of black hole depends on the initial mass and metallicity of the progenitor,\nthe rate will provide information of the history about the formation of stars and their metallicity.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/Comparison_Fill_col2_v3.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Expected number of inverse beta decay reactions due to supernova relic neutrinos in several experiments as a function of year.\nRed, gray and purple line shows Hyper-Kamiokande, SK-Gd, and JUNO, respectively.\nThe sizes of their fiducial volume and analysis energy thresholds were considered.\nThe neutrino temperature is assumed to be 6MeV.\nSolid line corresponds to the case, in which all the core-collapse supernovae emits neutrinos with the particular energy.\nDashed line corresponds to the case, in which 30\\% of the supernovae form black hole and emits higher energy neutrinos corresponding to the neutrino temperature of 8\\,MeV. \\label{fig:srn-comp} }\n\\end{figure}\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/calc_SRN-crop.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t The SRN signal expectations in Hyper-K 1 tank fiducial volume and 10 years measurement.\n\t Black line shows the case of neutrino temperature in supernova of 6\\,MeV, and red shows the case of 4\\,MeV~\\cite{Horiuchi:2008jz,Horiuchi:2017pv}.\n\t Solid line corresponds to the case, in which all the core-collapse supernovae emits neutrinos with the particular energy.\n\t Dashed line corresponds to the case, in which 30\\% of the supernovae form black hole and emits higher energy neutrinos corresponding to the neutrino temperature of 8\\,MeV.\n\t Shaded energy region shows the range out of SRN search window at Hyper-K.\n \\label{fig:srn-BH} }\n\\end{figure}\n\nFigure~\\ref{fig:srn-no-n-tag} shows expected SRN signals at Hyper-K with 10\\,years' livetime.\nBecause of the high background rate below 20\\,MeV from spallation products, the detection of SRN signals is limited to above $\\sim$16\\,MeV,\nwhile above 30\\,MeV the atmospheric neutrino backgrounds completely overwhelm the signal.\nConsidering the event selection efficiency after spallation product background reduction,\nthe expected number of SRN events in E = 16 to 30\\,MeV is about 70 (140) after 10 (20) years observation with Hyper-K 1 tank.\nThe statistical error will be 17 (25) events, corresponding to an observation of SRN in the energy range 16 to 30\\,MeV with 4.2 (5.7) $\\sigma$ significance (fig.~\\ref{fig:srn-det}). \nHere, we assumed the flux prediction described in ref.~\\cite{Ando:2003aa} and neutron tagging using $n + p \\rightarrow d + \\gamma\\,(2.2\\,$MeV$)$ with the tagging efficiency of 70\\%.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_1tank\/srn-hyperk-10years-notag.pdf}\n\t \\hspace{3mm}\n \\includegraphics[width=7cm]{physics-supernova\/pdf_1tank\/srn-hyperk-10years.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{\n\t Expected spectrum of SRN signals at Hyper-K with 10 years of livetime without tagging neutrons.\n\t Left figure shows the case without tagging neutrons, assuming a signal selection efficiency of 90\\%.\n\t Neutron tagging were applied for right figure, with the tagging efficiency of 67\\% and the pre-gamma cut for invisible muon background reduction.\n\tThe black dots show the sum of the signal and the total background, while the red shows the total background.\nGreen and blue show background contributions from the invisible muon and \n$\\nu_e$ components of atmospheric neutrinos.\nThe SRN flux prediction in~\\cite{Ando:2003aa} is applied.\n \\label{fig:srn-no-n-tag} }\n\\end{figure}\n\n\\begin{figure}[tbp]\n\t \\begin{center}\n\t\t \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/plot_SRN_candidates.pdf}\n\t\t\t \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/plot_SRN_sigma.pdf}\n\t\t\t\t \\end{center}\n\t\t\t\t\t\\vspace{-1cm}\n\t\t\t\t\t \\caption{The left (right) plot shows the number of observed SRN events (the discovery sensitivity) as a function of observation period.\n\t\t\t\t\t\t Red solid line shows the continuous measurement with 1 tank and red dashed line shows the staging scenario, respectively.\n\t\t\t\t\t\t \\label{fig:srn-det} }\n\t\t\t\t\t\t\\end{figure}\n\n\n\nIt is still important to measure the SRN spectrum down to $\\sim$ 10\\,MeV in order to explore the history of supernova bursts back to the epoch of red shift (z) $\\sim$1.\nTherefore, in the following discussion of the expected SRN signal with\ngadolinium neutron tagging, we assume that an\nanalysis with a lower energy threshold of $\\sim$ 10\\.MeV is possible.\nInverse beta reactions can be identified by coincident detection of both positron and delayed neutron signals, and requiring tight spatial and temporal correlations between them.\nWith 0.1\\% by mass of gadolinium dissolved in the water, neutrons are captured on gadolinium with about 90\\% capture efficiency; the excited Gd nuclei then de-excite by emitting 8\\,MeV gamma cascades.\nThe time correlation of about 30\\,$\\mu$sec between the positron and the Gd(n,$\\gamma$)Gd cascade signals, and the vertex correlation within about 50\\,cm are strong indicators of a real inverse beta event.\nRequiring both correlations (as well as requiring the prompt event to be Cherenkov-like and the delayed event to be isotropic) can be used to reduce background of spallation products by many orders of magnitude while also reducing invisible muon backgrounds by about a factor of 5.\nThe expected number of SRN events in the energy range of 10-30\\,MeV is about 280 (390) with 10 years of live time with Gd-loaded Hyper-K 1 tank (staging 2 tanks).\n\\if0\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_2tank\/srn-hyperk-10years_2tank.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Expected spectrum of the SRN signals at Hyper-K with 10 years\nof livetime. The black dots show signal+background (red component).\nGreen and blue show background contributions from the invisible muon and \n$\\nu_e$ components of atmospheric neutrinos.\nA SRN flux prediction~\\cite{Ando:2003aa} was used, and \na 67\\% detection efficiency of 8\\,MeV gamma cascades and\na factor of 5 reduction in the invisible muon background were assumed.\n\\label{fig:srn-megaton}}\n\\end{figure}\n\\fi\nIn addition, by comparing the\ntotal SRN flux with optical supernova rate observations, a\ndetermination of the fraction of failed (optically dark) supernova\nexplosions, currently unknown but thought to occur in not less than\n5\\% and perhaps as many as 50\\% of all explosions, will be possible.\nPossible backgrounds to the SRN search down to $\\sim$ 10\\,MeV are (1) accidental\ncoincidences with the spallation event, (2) spallation products with accompanying neutrons, and\n(3) the resolution tail of the reactor neutrinos. For (1) accidental\ncoincidences, the possible source of the prompt event is the\nspallation products. By requiring time coincidence, vertex correlation\nand energy and pattern of the delayed event, the accidental\ncoincidence rate can be reduced by a factor about 5 and can be below\nthe level of the expected SRN signal.\nFor (2) spallation products with accompanying neutrons, the only\npossible spallation product is $^9$Li and an estimation by a Geant4\nsimulation is shown in Fig.~\\ref{fig:srn-bg}. Because of the short\nhalf-life of $^9$Li ($\\tau_{\\frac{1}{2}}=0.18$~sec), a high rejection\nefficiency of $\\sim$99.5\\% is expected. With this expectation, the\n$^9$Li background is less than the signal level above 12~MeV; this\ncould be lowered by further development of the background reduction\ntechnique. For (3) the resolution tail of the reactor neutrinos, the\nestimated background rate is about 100(20)\/10\\,years above 10\\,MeV\n(11\\,MeV) as shown in Fig.~\\ref{fig:srn-bg} with full reactor\nintensity.\n\\begin{figure}[tbp]\n \\begin{center}\n \\includegraphics[width=8cm]{physics-supernova\/pdf_1tank\/srn-hk10yr-li9bg.pdf}\n \\end{center}\n\\vspace{-1cm}\n \\caption{Green (red) curve shows the estimated $^9$Li production rate\nbefore (after) applying cuts based on a correlation with cosmic ray muons.\nBlue shows estimated background from reactor neutrinos at full intensity.\nBlack data points show expected SRN signal based on the\nflux prediction in~\\cite{Ando:2003aa}.\n\\label{fig:srn-bg}}\n\\end{figure}\n\n\n\n\n\n\\subsection{Motivations}\\label{sec:secondtankkorea-motivations}\n\nStrategy of the future Hyper-K experiment is to build two identical water-Cherenkov detectors in stage with 260 kton of purified water per detector.\nThe first detector will be built at Tochibora mine in Japan, and this Hyper-K design report is dedicated to describe the design of the first detector in Japan.\nLocations in Korea are currently investigated for the second detector where the J-PARC neutrino beam passes through, and this section focuses on the benefits of building the second detector in Korea. \nFigure~\\ref{f:OAB} shows the J-PARC neutrino beam aiming at the Japanese site with 2.5 degree off-axis angle (OAA) and also passing through Korea\nwith an 1$\\sim$3 degree OAA range.\n\nIn fact, having a 2$^\\text{nd}$ detector regardless of its location, will improve sensitivities of all areas of physics covered by the Hyper-K 1$^\\text{st}$ detector.\nHowever, building a 2$^\\text{nd}$ detector in Korea rather than in Japan further enhances physics capabilities on neutrino oscillation physics\n(leptonic CP violation, determination of neutrino mass ordering, non-standard neutrino interaction etc.)\nusing beam neutrinos thanks to the longer baseline ($\\sim$1,100~km). \n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=1.0\\textwidth]{second-tank-korea\/figures\/Beam_Japan_to_Korea.pdf}\n\\end{center}\n\\caption{ Contour map of the J-PARC off-axis angle beam to Korea~\\cite{Hagiwara2006,Hagiwara2006e,Hagiwara2007}. }\n\\label{f:OAB}\n\\end{figure}\n\n\nThe benefits of Korean site for beam neutrino physics are well expressed by an appearance bi-probability plot: \n$P(\\nu_{\\mu}\\rightarrow\\nu_{e})$ vs. $P(\\bar{\\nu}_{\\mu}\\rightarrow\\bar{\\nu}_{e})$. \nFigure~\\ref{f:bp} shows appearance bi-probability plots at Hyper-K sites in Tochibora, Japan (left) and in Mt. Bisul, Korea (right). \nEach point in colored ellipses represents different $\\delta_{CP}$ value for normal (inverted) neutrino mass ordering \nin solid (dotted) lines.\nThree different colors correspond to three representing neutrino energies for each site.\nThe blue ellipses correspond to the peak energy at each OAA and the green and red ones represent median\nenergy after splitting the events into two parts below and above the peak. \nNote that there are high energy ($>$ 1.25 GeV) appearance events observed in Korean site due to the longer baseline,\nand this results in an important difference in physics sensitivities between Japan and Korean sites. \nThe gray ellipses indicates the sizes of the statistical\nuncertainties given by $\\sqrt N$ from the number of events around peak energy in $\\nu_{e}$ and $\\overline{\\nu_{e}}$ appearance signals. \nIt is clear from the bi-probability plots that the ellipses in Mt. Bisul site are well separated compare to those at Tochibora site\nalthough the statistics is lower with the longer distance. \nThis will allow us to resolve degeneracies (overlaps of ellipses) in neutrino mass ordering and $\\delta_{CP}$ parameters.\n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[width=1.0\\textwidth]{second-tank-korea\/figures\/bp_double_fig.pdf}\n\\caption{Appearance bi-probability plots at Hyper-K sites in Tochibora (left) at $2.5^{\\circ}$ OAA and in Mt. Bisul (right) at $1.3^{\\circ}$ OAA. \nThese plots show the principle by which Hyper-K determines the mass ordering and measures the CP phase in three representing energies\ndrawn with green, blue and red colors. \nNormal (inverted) ordering for different $\\delta_{CP}$ values is represented by a solid (dotted) curves. \nGrey ellipses represent the sizes of statistical error for a ten-year exposure on one Hyper-K detector. \nThe $\\Phi_{32}$ is defined as $\\frac{2}{\\pi}\\frac{\\left|\\Delta m^2_{32}\\right|L}{E}$ \nand is close to odd-integer values for oscillation maxima, and close to even-integer values for oscillation minima.\n}\n\\label{f:bp}\n\\end{figure}\n\nThanks to the longer baselines in Korean sites the 1$^\\text{st}$ and 2$^\\text{nd}$ oscillation maxima of the appearance probability are reachable\nwith higher ($>$ 1.25 GeV) neutrino energy, and this allows much better sensitivities especially on the neutrino mass ordering determination and non-standard neutrino interaction (NSI) in matter. \nBy having the 2$^\\text{nd}$ detector in Korea the fraction of $\\delta_{CP}$ coverage is also increased and more precise measurement of $\\delta_{CP}$ is achieved. \nAccording to the sensitivity studies performed, described later, smaller OAA in Korean site gives best sensitivities in most physics cases with beam neutrinos. \nReaching higher energy with smaller OAA, however, introduces more $\\pi^{\\circ}$ background but a good news is that T2K has recently reduced \nthe $\\pi^{\\circ}$ background and its systematic uncertainty~\\cite{Abe:2015awa}. \nThanks to the larger overburdens in Korean sites the sensitivities on solar neutrino and Supernova relic neutrinos (SRN) are also further improved. \n\n\n\\subsection{Location and Detector}\\label{sec:secondtankkorea-location}\n\n\nThere are several candidate sites to locate the 2$^\\text{nd}$ detector in Korea and they are listed in Table~\\ref{t:six_sites}.\nAmong the six candidate sites Mt. Bisul with the smallest OAA seems to be the most favorite ones according to our sensitivity study described later. \n\n\\begin{table}[hbt]\n\\captionsetup{justification=raggedright,singlelinecheck=false}\n\\small\n \\caption{Candidate sites with the off-axis angles between 1 and 2.5 degrees for the 2$^\\text{nd}$ Hyper-K detector in Korea. The baseline is the distance from the production point of the J-PARC\\\n neutrino beam~\\cite{Abe:2016t2hkk}.}\n \\centering\n \\begin{tabular*}{0.95\\textwidth}{@{\\extracolsep{\\fill}} l c c c l}\n\n \\hline \\hline\nSite & Height & Baseline & Off-axis angle & Composition of rock \\\\[-1.4ex]\n & (m) & (km) & (degree) & \\\\\n\\hline\n Mt. Bisul & 1084 & 1088 & 1.3$^{\\circ}$ & Granite porphyry,\\\\[-1.4ex]\n & & & & andesitic breccia \\\\[0.4ex]\n Mt. Hwangmae & 1113 & 1141 & 1.9$^{\\circ}$ & Flake granite, \\\\[-1.4ex]\n& & & & porphyritic gneiss \\\\[0.4ex]\n Mt. Sambong & 1186 & 1169 & 2.1$^{\\circ}$ & Porphyritic granite, \\\\[-1.4ex]\n & & & & biotite gneiss \\\\[0.4ex]\n Mt. Bohyun & 1124 & 1043 & 2.3$^{\\circ}$ & Granite, volcanic rocks, \\\\[-1.4ex]\n & & & & volcanic breccia \\\\[0.4ex]\n Mt. Minjuji & 1242 & 1145 & 2.4$^{\\circ}$ & Granite, biotite gneiss \\\\[0.4ex]\n Mt. Unjang & 1125 & 1190 & 2.2$^{\\circ}$ & Rhyolite, granite porphyry, \\\\[-1.4ex]\n & & & & quartz porphyry \\\\\n \\hline \\hline\n \\end{tabular*}\n \\label{t:six_sites}\n \\end{table}\n\n\nThe larger overburdens of the Korean candidate sites allow much less muon flux and spallation isotopes. \nWith a flat tunnel the overburden is $\\sim$820~m for both Mt. Bisul and Mt. Bohyun, the two favorable sites in a more favorable order.\nBy making a sloped tunnel the overburden becomes $\\sim$1000~m for both mountains, and this is the default tunnel construction plan.\nFigure~\\ref{fig:muon-direction} shows muon flux as a function of zenith (top) and azimuth (bottom) angles\nfor Mt. Bisul and Mt. Bohyun as well as Super-K and Hyper-K (Tochibora) sites for comparison.\nThe muon flux at the two Korean sites with $\\sim$1,000~m overburden are similar to that of Super-K site\nand about four times smaller than Hyper-K Tochibora site. \n\n\\begin{figure}[tb]\n\\centering\n\\includegraphics[width=0.7\\textwidth]{second-tank-korea\/figures\/muon-theta.pdf}\n\\includegraphics[width=0.7\\textwidth]{second-tank-korea\/figures\/muon-phi.pdf}\n\\caption{Muon flux as a function of cosine of zenith angle $\\cos\\theta$ (upper) and azimuth angle $\\phi$ (lower) for Hyper-K (Tochibora), \nMt.\\ Bisul (1,000~m overburden), Mt.\\ Bohyun (1,000~m overburden), and Super-K.\nThe east corresponds to the azimuth angle of zero degree.\nThe blue lines show the data for Super-K, and the red lines show the MC predictions based on the \\texttt{MUSIC} simulation. }\n\\label{fig:muon-direction}\n\\end{figure}\n\n\\subsection{Physics Sensitivities}\\label{sec:secondtankkorea-physics}\n\nPhysics sensitivity studies are performed \nfor three different off-axis angles (1.5$^{\\circ}$, 2.0$^{\\circ}$, and 2.5$^{\\circ}$) at a baseline distance of $L=1,000$~km.\nSensitivity study results are obtained for the determination of the mass ordering, the discovery of CP violation by excluding of the sin($\\delta_{cp}$) = 0\nhypothesis, the precision measurement of $\\delta_{cp}$, fraction of $\\delta_{cp}$ as a function of CPV significance and exposure, $\\theta_{23}$ octant, \natmospheric parameters and NSI.\nOnly part of these studies are shown here due to a limited space, but the full studies will be published in a separate paper. \nThe results are obtained by assuming 2.7$\\times$10$^{22}$ proton-on-target with $\\nu : \\bar{\\nu} = 1 : 3$\nwhich corresponds to 10-year operation with 1.3 MW beam power for 187 kton fiducial volume mass per detector. \nIn this section relatively simplistic systematic uncertainty model~\\cite{Abe:2016t2hkk} is used in the sensitivity studies \nwhile the size of the systematic uncertainties are mostly based on the current T2K analyses. \nNote that the same simplistic systematic uncertainty model is used for the Japanese detector, \nwhich is a little different from the systematic uncertainties used in other sections of this document. \nIn sensitivity studies other oscillation parameter values are from the Particle Data Group (PDG) 2015 Review of Particle Physics~\\cite{Olive:2016xmw}\nexcept for $\\theta_{23}$ and $\\Delta m^{2}_{32}$, where $\\sin^{2}\\theta_{23}=0.5$ and $\\Delta m^{2}_{32} = 2.5 \\times 10^{-3}$ eV$^{2}$ are used \ndue to their large uncertainties in their absolute values, and no CP violation ($\\delta$ = 0) is assumed unless it is specified.\nTwo detector configuration, either JD (Japanese Detector) + KD (Korean Detector) or JD $\\times$ 2, assumes no staging in the sensitivity studies shown in this section. \n\nFigure~\\ref{fig:cp_precision} shows the sensitivity on the 1$\\sigma$ precision of the $\\delta_{cp}$ measurement assuming no prior knowledge on neutrino mass ordering. \nFor most of the true $\\delta_{cp}$ the best sensitivity is from JD + KD with 1.5$^{\\circ}$ OAA. \nEspecially when the CP is maximally violated the sensitivity difference is largest between the JD + KD with 1.5$^{\\circ}$ OAA and JD $\\times$ 2 or JD $\\times$ 1. \n\\begin {figure}[htbp]\n\\captionsetup{justification=raggedright,singlelinecheck=false}\n \\begin{center}\n \\includegraphics[width=0.80\\textwidth]{second-tank-korea\/figures\/cp_precision_true_nh_jdx1.pdf}\\\\\n \\includegraphics[width=0.80\\textwidth]{second-tank-korea\/figures\/cp_precision_true_ih_jdx1.pdf}\n \\caption{The 1$\\sigma$ precision of the $\\delta_{cp}$ measurement as a function of the true $\\delta_{cp}$ value. Here, it is assumed there is no prior knowledge of the\nmass ordering.}\n \\label{fig:cp_precision}\n \\end{center}\n\\end {figure}\nFigure~\\ref{fig:cp_prec_cp_frac} shows the sensitivity on the fraction of $\\delta_{cp}$ for the 1$\\sigma$ precision of the $\\delta_{cp}$ measurement. \nThe results with JD + KD with any off-axis angle are always better than JD $\\times$ 2 and JD $\\times$ 1. \nThe sensitivity with 2.0$^{\\circ}$ OAA is slightly better than that of 1.5$^{\\circ}$ OAA if the $\\delta_{cp}$ precision is less than 10 degree\nbut otherwise the 1.5$^{\\circ}$ OAA gives the best sensitivity. \nMore details on the physics sensitivity studies are found in Ref~\\cite{Abe:2016t2hkk}.\n\\begin {figure}[htbp]\n\\captionsetup{justification=raggedright,singlelinecheck=false}\n \\begin{center}\n \\includegraphics[width=0.8\\textwidth]{second-tank-korea\/figures\/cp_prec_frac_dcp_jdx1.pdf}\n \\caption{The fraction of $\\delta_{cp}$ values (averaging over the true mass ordering) for which a given precision or better on $\\delta_{cp}$ can be achieved.}\n \\label{fig:cp_prec_cp_frac}\n \\end{center}\n\\end {figure}\nAccording to our sensitivity study CP violation sensitivity improves a little in JD + KD compared to JD $\\times$ 2. \nThe $\\theta_{23}$ octant sensitivity and atmospheric parameter sensitivities get slightly worse in JD + KD configuration compared to JD $\\times$ 2. \n\nThe sensitivity on NSI of neutrinos in matter (not in production nor in detection) \nis also greatly enhanced by having an additional 2$^\\text{nd}$ detector in Korea,\nand the details on NSI sensitivity studies are found in Ref~\\cite{Fukasawa:2016lew,Liao2017}. \n\n\nThanks to the similar overburden to Super-K in Korean candidate sites (see Fig.~\\ref{fig:muon-direction}) \nbut with a larger detection volume, \nlow energy astrophysics such as solar neutrinos and SRN sensitivities are expected to be good. \nAccording to our sensitivity study on the SRN we expect about 5 (4) sigma sensitivity for 10 years of data taking \nin Mt. Bisul or Mt. Bohyun (Tochibora) sites~\\cite{Yeom2017_SRN_sens}. \nMoreover we expect to observe spectral distribution of SRN due to large statistics from 8.4 times larger detection volume than Super-K,\nand this might lead to solving SN burst rate problem. \n\n\\subsection{Conclusion}\\label{sec:secondtankkorea-conclusion}\n\nHaving a 2$^\\text{nd}$ Hyper-K detector in addition to the 1$^\\text{st}$ one will enhance physics sensitivities\nfrom beam neutrino physics to astroparticle physics due to the increased detection volume.\nAccording to our sensitivity studies, physics capabilities of the Hyper-K project are further improved by locating the 2$^\\text{nd}$ detector in Korea, \nsuch as determination of neutrino mass ordering, precision of $\\delta_{CP}$ measurement and test of NSI.\nWith the longer baseline in Korean site both the 1$^\\text{st}$ and the 2$^\\text{nd}$ oscillation maximum of the appearance neutrino probability are reachable,\nand this is a unique opportunity since no other past and current experiment (MINOS, T2K, NOvA) can reach the 2$^\\text{nd}$ oscillation maxima. \nThe longer baseline to the detector in Korea allows to resolve the degeneracy between the mass ordering and the value of delta CP that would happen \nfor only certain values of the parameters with a detector(s) in Japan. The bi-probability plots can intuitively show this feature even before \nperforming any sensitivity studies.\nNSI sensitivities are also improved especially with the smaller OAA site in Korea. \nAccording to our sensitivity studies the best Korean candidate site seems to be the Mt. Bisul. \nWith $\\sim$1000~m overburden sensitivities on solar neutrino and SRN physics are further enhanced in the Korean candidate sites\nthan those in the Tochibora mine ($\\sim$650~m overburden). \n\n\\section{Hyper-Kamiokande software} \\label{section:software}\n\nThe Hyper-K software system is designed around the following\nprinciples:\n\\begin{itemize} \\itemsep0em\n\\item Adaptable. The Hyper-K experiment is expected to run for more\n than a decade. This period typically spans more than one\ngeneration of software and infrastructure. The Hyper-K offline system\nis being designed to be flexible enough to accommodate changes in\ntools or infrastructures.\n\\item Reliable. Each component needs to demonstrate it's reliability\nby exhibiting well defined behaviour on control samples.\n\\item Understandable. Documentation on what the component does, what\nit's dependencies are as well as test samples and outputs are\nessential in being able to use it successfully.\n\\item Low overhead. The management and maintenance should be as\nautomated as possible to free collaborators to focus on the challenge\nof extracting the high-quality physics measurements.\n\\end{itemize}\n\nThe software consists of a collection of loosely-coupled packages,\nsome of which are open-source and some of which are specific to\nHyper-K. The distributed code management system Git \\cite{git} is used to manage\nthe software. Each package is hosted on a third-party central\nrepository (\\url{https:\/\/github.com\/}) that provides distributed\naccess to the packages. The distributed nature of the code management\nallows researchers the possibility to develop the software independently without\nimpacting other researchers. The loose-coupling between packages\nallows those that reach their end of life to be replaced by better\nalternatives with minimal impact on the rest of the system. Where\npossible standard particle physics software libraries are used to\nreduce the burden of support of experiment-specific code. The working\nlanguage for the Hyper-K software packages is C++, with the output\nfiles being written in ROOT \\cite{Brun97} format.\n\nThe flow for the simulation is as follows: The event topologies are\ngenerated by a neutrino interaction package(GENIE\n\\cite{Andreopoulos:2009rq} and NEUT \\cite{Hayato:2009zz}, for\nexample), and modeled by a Monte Carlo detector response code called\nWCSim \\cite{WCSim}. The event information is reconstructed using\neither BONSAI \\cite{icrc0213smy} (for low energy events) or fiTQun\n(for high energy events) \\cite{Tobayama_2016}. This is shown\nschematically in Figure~\\ref{fig:software_flow}. These packages will\nbe described in more detail in the next Sections.\n\nAn online workbook is also maintained to provide higher-level\ndocumentation on overall procedures and information for new users of\nthe software and developers. An overall software control package\nallows for the fully automated download, compilation and running of\nthe software, based on user requests.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[scale=0.4]{software\/figures\/Software_flow_fig.pdf}\n \\end{center}\n\\caption {Flowchart of the simulation process.}\n \\label{fig:software_flow}\n\\end{figure}\n\n\\subsection{WCSim}\\label{software:WCSim}\n\nThe Water Cherenkov Simulation (WCSim) package is a flexible,\nGeant4-based code that is designed to simulate the geometry and\nphysics response of user-defined water Cherenkov detector\nconfigurations. WCSim is an open-source code and is available for\ndownload at \\url{https:\/\/github.com\/WCSim\/WCSim}.\n\nThe final performance of the Hyper-Kamiokande detector depends on the\ndetector geometry, the type of photodetectors, and the photocoverage\nthat will be used. WCSim takes these variables as inputs and simulates\nthe detector response, which can then be used to determine the physics\npotential. WCSim users specify the type of photodetectors, the number\nof photodetectors, the detector diameter and radius, and whether the\nwater should be doped with gadolinium. The outer detector volume is\ncurrently not implemented in WCSim, though it is actively being\ndeveloped for a future release.\n\nFor this report, the relevant photodetectors in WCSim are the R3600\n20'' diameter PMTs, as well as the R12850 20'' and 12'' diameter box\nand line photodetectors. Photodetector parameters in the simulation\ninclude the timing resolution, dark noise rate, and the overall\nefficiency for a photon to register a charge (including the quantum\nefficiency, collection efficiency, and hit efficiency as described in\nSection \\ref{section:photosensors}). For the R3600 PMTs, the\nparameters were taken from the Super-Kamiokande simulation code\nSKDETSIM. The parameters for the R12850 are taken from measurements as\ndescribed in Section \\ref{section:photosensors}. Some higher-level photodetector effects\nsuch as after-pulsing are not currently simulated in WCSim, though\nthis is a planned upgrade for a future releases.\n\nGeant4 \\cite{Agostinelli:2002hh} is used to track\nthe particles as they pass through the detector and compute the\nfinal deposited energy. Particles that reach the photodetector glass\nand pass the quantum efficiency and collection efficiency cuts are\nregistered as a hit. The hits are then digitized based on the SK-I\nelectronics scheme, though the code has the flexibility for users to\ninclude their own custom electronics configurations. \n\nThe output for the WCSim code includes both the raw hit and the\ndigitized information. The raw hit information includes which tubes\nwere hit and how many times each tube was hit. The digitized\ninformation includes the number of hits in a trigger window, as well\nas the charge and time of the hit tubes. WCSim output files can be\nused for event reconstruction by fiTQun or BONSAI, which are described in the\nfollowing subsections. Geant4 visualization tools can be used to display the\ndetector geometry and particle tracks. Figure~\\ref{fig:HK-WCSim} is a\nrendering of one of the proposed Hyper-K\ntanks. Figure~\\ref{fig:HK-WCSim-eventdisplay} shows an example of an\nevent display for an electron and for a muon, each with 1 GeV kinetic energy. \n\n\\begin{figure}[tbp]\n\n \\includegraphics[scale=0.4]{software\/figures\/HK-WCSim.pdf}\n \n\\caption {Geant4 visualization of the Hyper-Kamiokande detector\nconfiguration. The top cap of the detector has\nbeen removed for visualization purposes. Phototubes are shown in\nblack, while the walls of the detector are shown in grey.}\n \\label{fig:HK-WCSim}\n\\end{figure}\n\n \\begin{figure}[tbp]\n \\centering\n \\begin{tabular}{cc}\n \\centering\n \\includegraphics[scale=0.4]{software\/figures\/HK-WCSim-EDe-.pdf}\n &\n \\centering\n \\includegraphics[scale=0.4]{software\/figures\/HK-WCSim-EDmu-.pdf}\n \\end{tabular}\n \\caption {Event displays in the HK detector for a 1 GeV electron\n (left) and a 1 GeV muon (right).}\n \\label{fig:HK-WCSim-eventdisplay}\n \\end{figure}\nFigure~\\ref{fig:total-charge} shows how the flexibility of WCSim can\nbe used to explore different detector configurations. Here, the total\ncharge distribution for electrons and muons at several momenta in\nthe Hyper-Kamiokande detector with two different photocoverage options\nare shown. RMS divided by mean charge\nis plotted in Figure~\\ref{fig:rms-mom} indicating better resolution\nwith 40\\% photocoverage than with\n14\\% photocoverage. For lower energy particles, the resolution can be\napproximated using nhits (the number of phototubes that register a\nhit). The nhit distribution for both 14\\% photocoverage and\n40 \\% photocoverage are shown in Figure~\\ref{fig:nhits}. \n\n \\begin{figure}[tbp]\n \\begin{tabular}{cc}\n \n \\centering\n \\includegraphics[trim=0cm 7.0cm 2.5cm 7.0cm, clip=true, scale=0.4]{software\/figures\/QMean_60m_inner_e.pdf}\n \n&\n \\centering\n \\includegraphics[trim=0cm 7.0cm 2.5cm 7.0cm, clip=true, scale=0.4]{software\/figures\/QMean_60m_inner_mu.pdf}\n\n \\end{tabular}\n \\caption {Total charge distributions for electrons (left) and muons (right)\n with several momenta in the Hyper-K detector. The red line\n corresponds to 14\\% photocoverage, while the blue line corresponds\n to 40 \\% photocoverage.}\n \\label{fig:total-charge}\n \\end{figure}\n \\begin{figure}[htbp]\n \\begin{tabular}{cc}\n\n \\centering\n \\includegraphics[trim=0cm 7.0cm 2.5cm 7.0cm, clip=true, scale=0.4]{software\/figures\/ChargeRMS_inner_electron.pdf}\n\n& \n \\centering\n \\includegraphics[trim=0cm 7.0cm 2.5cm 7.0cm, clip=true, scale=0.4]{software\/figures\/ChargeRMS_inner_muon.pdf}\n\n \\end{tabular}\n \\caption {RMS\/Total charge distributions for electrons (left) and muons (right)\n with several momenta. The red line corresponds to the configuration\n with 14\\% photocoverage, while the blue line corresponds to the\n configuration with 40\\% photocoverage.}\n \\label{fig:rms-mom}\n \\end{figure}\n \\begin{figure}[htbp]\n \\begin{tabular}{cc}\n \n \\centering\n \\includegraphics[scale=0.47]{software\/figures\/Nhits_3TankLD.pdf}\n \n&\n \n \\centering\n \\includegraphics[scale=0.47]{software\/figures\/Resolution_3TankLD.pdf}\n \n \\end{tabular}\n \\caption{ Expected number of PMT hits (N$_{PMT hits}$) and the RMS of\n the N$_{PMT hit}$ distributions. \nWCsim is used for simulating the injection of electrons with several\nvalues of kinetic energy (E$_{kin}$).\nThe initial position is uniformly distributed inside the fiducial\nvolume ($>$2~m from inner detector wall). The red line corresponds to\nthe 14\\% photocoverage configuration, while the blue line corresponds to\nthe configuration with 40\\% photocoverage.}\n \\label{fig:nhits}\n \\end{figure}\n\n\\subsection{FiTQun} FiTQun is an event reconstruction\npackage initially developed for the Super-K detector based on the\nformalism used by the MiniBooNE experiment\n\\cite{Patterson:2009ki}. The reconstruction algorithm allows for\nsingle- and multiple-ring event hypotheses to be tested against\nobserved data. For a given event hypothesis, a prediction is made for\nthe complete set of observables at each PMT. This includes whether or\n not the PMT was hit, and for hit PMTs, the hit time and integrated \ncharge. The hypothesis and associated kinematic parameters that best \ndescribe a given event are found by maximizing a likelihood function \nof the prediction with respect to the observed data.\n\nFiTQun has been shown to perform well on Super-K data, with\nsignificant improvements on vertex, angle and momentum resolutions, as\nwell as particle identification when compared to previous\nreconstruction algorithms. In particular, fiTQun was successfully\ndeployed to reject $\\pi^0$ events from the Super-K $\\nu_{e}$ sample in\nthe T2K $\\nu_{e}$ appearance analysis (Figure~\\ref{fig:pi0plot}) \\cite{Abe:2013hdq,Abe:2015awa}.\n\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.6\\textwidth]{software\/figures\/sigbkg_pi0cut.pdf}\n \\end{center}\n \\caption {FiTQun used for $\\pi^0$ rejection in the $\\nu_{e}$\n selection for the T2K $\\nu_{e}$ appearance\n analysis\\cite{Abe:2013hdq}. The red line represents the cut, with\n events above the line being rejected as $\\pi^0$ background.}\n \\label{fig:pi0plot}\n\\end{figure}\n\n\\subsubsection{Reconstruction algorithm} \nAt the core of fiTQun lies a likelihood function, which is evaluated\nover all the PMTs in the detector:\n\\begin{equation} \nL \\left( {\\bf x} \\right)= \\prod_j^{unhit} P_j\\left(unhit | {\\bf x} \\right) \\prod_i^{ ihit} P_i \\left(hit | {\\bf x}\\right) f_q\\left(q_i|{\\bf x}\\right) f_t \\left(t_i | {\\bf x} \\right) \\,.\n\\end{equation} \n\nEvent hypotheses are characterized by ${\\bf x}$, which\nincludes the time and position of the interaction vertex, momentum and\ndirection of the charged particle tracks, and any other relevant\nkinematic parameters such as the distance or time interval between\ntracks, or the energy lost between track segments. For a given ${\\bf\nx}$, a prediction of the amount of charge at each PMT, $\\mu_i$, is\nmade and the time at which the light is expected to arrive each PMT is\ncalculated.\n\nThe detector response is folded into these predictions to give the\nprobabilities $P$ of a PMT being hit and the read-out time and charge\nprobability distribution functions $f_t$ and $f_q$, respectively. The\nnegative log-likelihood ($-log\\left( L \\right)$) is maximised to\nobtain the ${\\bf x}$ that best describe the event according to some\nevent topology (\\emph{e.g.}, single electron-like ring).\n\nOnce the best-fit parameters have been obtained for several\ntopologies, the ratio between their likelihoods is used to determine\nwhich topology gives the best match to the event. This can be used as\na particle identification tool if simple one-particle hypotheses are\nused, or as a more complex selection criterion if multiple final-state\nparticles are included in the hypothesis (\\emph{e.g.}, a nuclear\nde-excitation photon followed by a $K^+$ decay muon for the selection\nof $p\\rightarrow K^+ \\nu$ events).\n\n\n\n\n\n\n\\subsubsection{Integration with WCSim and tuning} FiTQun has been\nadapted to reconstruct events simulated with WCSim, in the various\ndetector configurations implemented in the simulation software. A\nC++ class was written (WCSimWrapper) that reads in both detector \ngeometry (positions and radius of PMTs) and event data from the WCSim\nROOT output files. A preprocessor flag allows fiTQun to be compiled \nagainst WCSim libraries, removing its dependence on Super-K software.\n\nIn the context of WCSim, events can be generated in an arbitrary\nnumber of detector configurations. For fiTQun to adequately\nreconstruct events in any given configuration, some of its components\nhave to be re-evaluated. For example, the charge and time response of\nPMTs must be accurately known in order to obtain unbiased estimates of\nparticle momentum and vertex position. The tuning procedure developed\nfor Super-K and SKDETSIM was adapted to be used with WCSim and with\ngeneralized cylindrical geometries.\n\nThe tunes produced for each simulated detector consist of ROOT files\nand run-time parameters. A configuration file (that contains the \ninformation needed by fiTQun to load the appropriate files and \nparameters) is given for each tune. These configuration files are \npackaged with fiTQun, such that any tune available can be selected\nin a single step.\n\n\\subsection{BONSAI} \nFor event reconstruction at low\nenergy, i.e. few MeV - few tens MeV, a reconstruction algorithm BONSAI\n(Branch Optimization Navigating Successive Annealing Iterations) is\nsupplied for Hyper-Kamiokande. BONSAI was originally developed for\nSuper-Kamiokande \\cite{icrc0213smy} and written in C++. It has been used for the low\nenergy physics analysis of SK-I to SK-IV. In the low energy region,\nmost of the photosensor signals are single photon hits. BONSAI uses\nthis relative hit time information to reconstruct the position of the\nCherenkov light source, i.e. the position of low energy event.\nFor Hyper-K analysis, a wrapper library (libWCsimBonsai) is supplied for ROOT environment.\n\n\\subsubsection{Vertex reconstruction} \nFor the vertex reconstruction, BONSAI performs a maximum likelihood fit using the\nphotosensor hit timing residuals. This likelihood fit is done for the\nCherenkov signal as well as the dark noise background for each vertex\nhypothesis. The likelihood of the selected hypothesis is compared\nto the likelihood of a hypothesis in an area nearby. Highly ranked\nhypotheses and new points in the likelihood will survive this step.\nFinally, after several iterations, the hypothesis with the largest\nlikelihood is chosen as the reconstructed vertex.\n\nThe vertex goodness criterion testing the time residual distribution\nis defined as follows:\\\\\n\\begin{equation} g\n\t(\\vec{v})=\\sum_{i=1}^{N}w_{i}\\exp{-0.5(t_i-|\\vec{x_i}-\\vec{v}|\/c_{wat})\/\\sigma)^2}\n\\end{equation} where $t_i$ are the measured PMT hit times, $\\vec{x_i}$\nthe photosensor locations, $\\vec{v}$ is reconstructed event vertex,\n$\\sigma$ is the effective timing resolution expected for Cherenkov events (total of photosensor and DAQ resolution).\n$c_{wat}$ is the group speed of light in the water, i.e. $c\/n$ with the speed of light in vacuum $c$ and refractive index $n$.\n$\\omega_i$ are Gaussian hit weights also based on the hit time residuals, but with a much wider effective time resolution.\nThe weights reduces the dark noise contamination of the Cherenkov light.\nA result of vertex reconstruction performance study with BONSAI and WCSim can be found in the figure \\ref{fig:bonsaivtx}.\nMore Cherenkov photons could be detected with new photosensors for Hyper-K and it improves the reconstruction results, comparing to those of Super-K\nThough, at same time, the random photosensor signals caused by their dark pulse can spoil the merit.\nSo reducing dark pulse is a crucial factor to improve the low energy event detection.\nMany efforts for the dark pulse reduction (\\ref{section:photosensors:IDperformance:BG}) and improvements of the softwares are being continued.\n\\begin{figure}[htbp]\n \\begin{center}\n \\includegraphics[width=0.6\\textwidth]{software\/figures\/VtxResolution-crop.pdf}\n \\end{center}\n \\caption {\n\t Vertex reconstruction resolution for electrons with BONSAI for Hyper-K and Super-K detectors.\n\t Here, WCSim is used for Hyper-K detector simulation.\n\t Red line shows the resolution with the PMT dark pulse rate of 8.4\\,kHz, as seen in \\ref{section:photosensors}.\n\t Blue is for the case of PMT dark pulse rate of 4.2\\,kHz, which is same as the rate of Super-K photosensors.\n\t Black line shows the performance with Super-K detector, simulated with SKDETSIM.\n \\label{fig:bonsaivtx}\n }\n\\end{figure}\n\n\\subsubsection{Energy and direction reconstruction}\nBONSAI and its related subroutines also determine the energy and the\nevent direction reconstruction.\nBecause most of the photosensor signals consist of single photon hits at low energy below few tens MeV,\nthe total number of photosensor hits is the leading parameter for\nreconstructing the energy of events. First, time-of-flight values are\nsubtracted from each of the hit timing values based on the position of\neach photosensor and the result of the BONSAI vertex reconstruction.\nNext, the number of photosensor hits around the expected event timing\nis calculated, considering its cross-section and the local\nphotocoverage with neighboring photosensors. Finally, the number of\nhits are scaled to energy using the information from detector\nsimulations and calibrations.\\\\\nThe direction reconstruction is also performed on the photosensor hit\npatterns using a circular KS test that checks the azimuthal symmetry\naround the Cherenkov cone.\nAs the result, the vertex position, direction and energy of low-energy\nevents are available after BONSAI reconstruction.\n\nSeveral likelihoods to test mis-reconstruction are also available\nduring the reconstruction. Likelihoods calculated using photosensor\nhit patterns are also used in particle identification, e.g. to\ndifferentiate between electron and gamma events.\n\n\\section*{Executive summary}\n\nOn the strength of a double Nobel prize winning experiment\n(Super)Kamiokande and an extremely successful long baseline neutrino\nprogramme, the third generation Water Cherenkov detector,\nHyper-Kamiokande, is being developed by an international collaboration\nas a leading worldwide experiment based in Japan.\n\nIt will address the biggest unsolved questions in physics through a\nmulti-decade physics programme that will start in the middle of the\nnext decade.\n\nThe Hyper-Kamiokande detector will be hosted in the Tochibora mine,\nabout 295\\,km away from the J-PARC proton accelerator research complex\nin Tokai, Japan.\n\nThe currently existing accelerator will be steadily upgraded to reach\na MW beam by the start of the experiment.\nA suite of near detectors will be vital to constrain the beam for\nneutrino oscillation measurements. They will be a combination of\nupgraded and new detectors at a distance ranging from 280\\,m to\n1-2\\,km from the neutrino target.\n\nA new cavern will be excavated at the Tochibora mine to host the\ndetector. The corresponding infrastructure will be built. The\nexperiment will be the largest underground water Cherenkov detector in\nthe world and will be instrumented with new technology photosensors,\nfaster and with higher quantum efficiency than the ones in\nSuper-Kamiokande. Pressure tests demonstrate that they will be able to\nsupport the pressure due to the massive tank.\n\nThe science that will be developed will be able to shape the future\ntheoretical framework and generations of experiments.\nHyper-Kamiokande will be able to measure with the highest precision\nthe leptonic CP violation that could explain the baryon asymmetry in\nthe Universe. The experiment also has a demonstrated excellent capability to\nsearch for proton decay, providing a significant improvement in\ndiscovery sensitivity over current searches for the proton lifetime.\nThe atmospheric neutrinos will allow to determine the neutrino mass\nordering and, together with the beam, able to precisely test the\nthree-flavour neutrino oscillation paradigm and search for new\nphenomena. A strong astrophysical programme will be carried out at the\nexperiment that will also allow to measure precisely solar neutrino\noscillation. A set of other main physics searches is planned, like\nindirect dark matter.\n\nIn summary, a new experiment, based on the experience and facilities of\nthe already existing Super-Kamiokande and long baseline neutrino\nexperiment as T2K, is being developed by the international physics\ncommunity to provide a wide and groundbreaking multi-decade physics\nprogramme from the middle of the next decade (see Table~\\ref{tab:intro:phys}).\n\n\n\\begin{table}[hbtp]\n \\caption{Expected sensitivities of the Hyper-Kamiokande experiment assuming 1 tank for 10 years.} \t\n \\label{tab:intro:phys}\n \\begin{center}\n \\begin{tabular}{lll} \\hline \\hline\n Physics Target & Sensitivity & Conditions \\\\\n \\hline \\hline\n Neutrino study w\/ J-PARC $\\nu$~~ && 1.3\\,MW $\\times$ $10^8$ sec\\\\\n $-$ $CP$ phase precision & $<23^\\circ$ & @ $\\sin^22\\theta_{13}=0.1$, mass hierarchy known \\\\\n $-$ $CPV$ discovery coverage & 76\\% (3\\,$\\sigma$), 57\\% ($5\\,\\sigma$) & @ $\\sin^22\\theta_{13}=0.1$, mass hierarchy known \\\\\n $-$ $\\sin^2\\theta_{23}$ & $\\pm 0.017$ & 1$\\sigma$ @ $\\sin^2\\theta_{23}=0.5$ \\\\\n \\hline\n Atmospheric neutrino study && 10 years observation\\\\\n $-$ MH determination & $> 2.2\\,\\sigma$ CL & @ $\\sin^2\\theta_{23}>0.4$ \\\\\n $-$ $\\theta_{23}$ octant determination & $> 3\\,\\sigma$ CL & @ $|\\theta_{23} - 45^{\\circ}| > 4^{\\circ}$ \\\\\\hline\n \\hline\n Atmospheric and Beam Combination && 10 years observation\\\\\n $-$ MH determination & $> 3.8\\,\\sigma$ CL & @ $\\sin^2\\theta_{23}>0.4$ \\\\\n $-$ $\\theta_{23}$ octant determination & $> 3\\,\\sigma$ CL & @ $|\\theta_{23} - 45^{\\circ}| > 2.3^{\\circ}$ \\\\\\hline\n %\n Nucleon Decay Searches && 1.9 Mton$\\cdot$year exposure \\\\\n $-$ $p\\rightarrow e^+ + \\pi^0$ & $7.8 \\times 10^{34}$ yrs (90\\% CL UL) &\\\\\n & $6.3 \\times 10^{34}$ yrs ($3\\,\\sigma$ discovery) &\\\\\n $-$ $p\\rightarrow \\bar{\\nu} + K^+$ & $3.2 \\times 10^{34}$ yrs (90\\% CL UL) &\\\\\n & $2.0 \\times 10^{34}$ yrs ($3\\,\\sigma$ discovery) &\\\\ \n \\hline\n Astrophysical neutrino sources && \\\\\n $-$ $^8$B $\\nu$ from Sun & 130 $\\nu$'s \/ day & 4.5\\,MeV threshold (visible\n energy) w\/ osc.\\\\\n $-$ Supernova burst $\\nu$ & 54,000$-$90,000 $\\nu$'s & @ Galactic center (10 kpc)\\\\ \n & $\\sim$10 $\\nu$'s & @ M31 (Andromeda galaxy) \\\\ \n $-$ Supernova relic $\\nu$ & 70 $\\nu$'s \/ 10 years & 10$-$30\\,MeV, 4.2$\\sigma$ non-zero significance \\\\\n $-$ WIMP annihilation in the Earth & & 10 years observation\\\\\n ~~($\\sigma_{SD}$: WIMP-proton spin & $\\sigma_{SD}=10^{-40}$cm$^2$ & @ $M_{\\rm WIMP}=10$\\,GeV, $\\chi\\chi\\rightarrow b\\bar b$ dominant\\\\\n ~~~~dependent cross section)& $\\sigma_{SD}=10^{-44}$cm$^2$ & @ $M_{\\rm WIMP}=50$\\,GeV, $\\chi\\chi\\rightarrow \\tau^+ \\tau^-$ dominant\\\\\n \\hline \\hline\n \\end{tabular}\n \\end{center}\n\\end{table}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\nThere is strong observational evidence \\cite{observation_dm} that approximately $22\\%$ of the total energy density of the universe is in the form of dark matter. Up until now it is unclear what this dark matter should be made of. One of the favourite candidates are Weakly Interacting Massive Particles (WIMPs) which\narise in extensions of the Standard Model.\nRecently, new theoretical models of the dark matter sector have been proposed \\cite{dark}, in which\nthe Standard Model is coupled to the dark sector via an attractive interaction term.\nThese models have been motivated by new astrophysical observations \\cite{observation_ee} which show an excess \nin electronic production in the galaxy. Depending on the experiment, the energy of these\nexcess electrons is between a few GeV and a few TeV.\nOne possible explanation for these observations is the annihilation of dark matter \ninto electrons. Below the GeV scale, the interaction term in these models is basically of the form of a direct\ncoupling between the U(1) field strength tensor of the dark matter sector and the U(1) field strength tensor of\nelectromagnetism. The U(1) symmetry of the dark sector has to be spontaneously broken, otherwise a ``dark photon'' background leading to observable consequences would exist.\n\nConsequently, it has been shown that the dark sector can have string-like solutions, denominated ``dark strings'' \nand the observational consequences of the interaction of these dark strings with the Standard Model\nhave been discussed \\cite{vachaspati}.\n\nTopological defects are believed to have formed in the numerous phase transitions in the early\nuniverse due to the Kibble mechanism \\cite{topological_defects}.\nWhile magnetic monopoles and domain walls, which result from the spontaneous\nsymmetry breaking of a spherical and parity symmetry, respectively, \nare catastrophic for the universe since they would overclose it, cosmic strings\nare an acceptable remnant from the early universe. These objects \nform whenever an axial symmetry gets spontaneously broken and (due to topological arguments)\nare either infinitely long or exist in the form of cosmic string loops. Numerical\nsimulations of the evolution of cosmic string networks have shown that\nthese reach a scaling solution, i.e. their contribution to the total energy density\nof the universe becomes constant at some stage. The main mechanism that allows\ncosmic string networks to reach this scaling solution is the formation\nof cosmic string loops due to self-intersection and the consequent decay of these loops\nunder the emission of gravitational radiation.\n\nFor some time, cosmic strings were believed to be responsible for the structure\nformation in the universe. New Cosmic Microwave background (CMB) data, however, clearly\nshows that the theoretical power spectrum associated to Cosmic strings\nis in stark contrast to the observed power spectrum. However, there has been\na recent revival of cosmic strings since it is now believed that cosmic strings\nmight be linked to the fundamental strings of string theory \\cite{polchinski}.\n\nWhile perturbative fundamental strings were excluded to be observable on cosmic scales\nfor many reasons \\cite{witten}, there are now new theories containing\nextra dimensions, so-called brane world model, that allow to lower the fundamental\nPlanck scale down to the TeV scale. This and the observation that\ncosmic strings generically form at the end of inflation in inflationary models\nresulting from String Theory \\cite{braneinflation} and Supersymmetric Grand Unified Theories \\cite{susyguts}\nhas boosted the interest in comic string solutions again.\n\nDifferent field theoretical models describing cosmic strings have been investigated.\nThe $U(1)$ Abelian--Higgs model possesses string--like solutions \\cite{no}. This is a simple toy\nmodel that is frequently used to describe cosmic strings. However, the symmetry breaking\npattern $U(1)\\rightarrow 1$ has very likely never occurred in the evolution of the universe.\nConsequently, more realistic models with gauge group $SU(2)\\times U(1)$ and symmetry\n breaking $SU(2)\\times U(1)\\rightarrow U(1)$ have been considered and it has been\nshown that these models have string--like solutions \\cite{semilocal,gors}. Semilocal strings\nare solutions of a $SU(2)_{global}\\times U(1)_{local}$ model which -- in fact --\ncorresponds to the Standard Model of Particle physics in the limit $\\sin^2\\theta_{\\rm w}=1$, where\n$\\theta_{\\rm w}$ is the Weinberg angle. The simplest semilocal string solution is an\nembedded Abelian--Higgs solution \\cite{semilocal}. A detailed analysis of the stability\nof these embedded solutions has shown \\cite{hindmarsh} that they are unstable (stable)\nif the Higgs boson mass is larger (smaller) than the gauge boson mass. In the case\nof equality of the two masses, the solutions fulfill a Bogomolny--Prasad--Sommerfield (BPS) \\cite{bogo}\nbound such that their energy per unit length is directly proportional to the winding number.\nInterestingly, it has been observed \\cite{hindmarsh} that in this BPS limit, a one-parameter\nfamily of solutions exists: the Goldstone field can form a non-vanishing condensate\ninside the string core and the energy per unit length is independent of the value of this condensate.\nThese solutions are also sometimes denominated ``skyrmions'' and have been related to the zero-mode present\nin the BPS limit.\n\nIn this paper, we consider the interaction of dark strings with string--like solutions\nof the Standard Model in the specific limit $\\sin^2\\theta_{\\rm W}=1$. The two sectors\ninteract via an attractive interaction that couples the two $U(1)$ field strength tensors to each other.\nThis type of interaction has been studied before in \\cite{ha}, where the interaction\nbetween Abelian--Higgs strings and dark strings has been investigated. It has been \nfound that a BPS bound exists that depends on the interaction paramater and that Abelian--Higgs strings\nand dark strings can form bound states.\n\n\nOur paper is organized as follows: in Section 2, we give the model, the equations of motion, the boundary\nconditions and the asymptotics. In Section 3, we present our numerical results and Section 4 contains\nour conclusions.\n\n\n\n\\section{The model}\nWe study the interaction of a $SU(2)_{global}\\times U(1)_{local}$ model, which\nhas semilocal strings solutions \\cite{semilocal}\nwith the low energy dark sector, which is a $U(1)$ Abelian-Higgs model.\n\n\nThe matter Lagrangian\n${\\cal L}_{m}$ reads:\n\\begin{equation}\n{\\cal L}_{m}=(D_{\\mu} \\Phi)^{\\dagger} D^{\\mu} \\Phi-\\frac{1}{4} F_{\\mu\\nu} F^{\\mu\\nu}\n-\\frac{\\lambda_1}{2}(\\Phi^{\\dagger}\\Phi-\\eta_1^2)^2\n+(D_{\\mu} \\xi)^* D^{\\mu} \\xi-\\frac{1}{4} H_{\\mu\\nu} H^{\\mu\\nu}\n- \\frac{\\lambda_2}{2}(\\xi^*\\xi-\\eta_2^2)^2 + \\frac{\\varepsilon}{2} F_{\\mu\\nu}H^{\\mu\\nu}\n\\end{equation} \nwith the covariant derivatives $D_\\mu\\Phi=\\nabla_{\\mu}\\Phi-ie_1 A_{\\mu}\\Phi$,\n$D_\\mu\\xi=\\nabla_{\\mu}\\xi-ie_2 a_{\\mu}\\xi$\nand the\nfield strength tensors $F_{\\mu\\nu}=\\partial_\\mu A_\\nu-\\partial_\\nu A_\\mu$, \n$H_{\\mu\\nu}=\\partial_\\mu a_\\nu-\\partial_\\nu a_\\mu$ of the two U(1) gauge potential $A_{\\mu}$, $a_{\\mu}$ with coupling constants $e_1$\nand $e_2$.\n$\\Phi=(\\phi_1,\\phi_2)^T$ is a complex scalar doublet, while $\\xi$ is a complex scalar field.\nThe gauge fields have masses $M_{W,i}=\\sqrt{2}e_i \\eta_i$, $i=1,2$, while the Higgs fields\nhave masses $M_{H,i}=\\sqrt{2\\lambda_i} \\eta_i$, $i=1,2$.\nThe term proportional to $\\varepsilon$ is the interaction term \\cite{vachaspati}.\nTo be compatible with observations, $\\varepsilon$ should be on the order of $10^{-3}$. \n\n\\subsection{The Ansatz}\n\nFor the matter and gauge fields, we have \\cite{semilocal,hindmarsh,no}:\n\\begin{equation}\n\\phi_1(\\rho,\\varphi)=\\eta_1 h_1(\\rho)e^{i n\\varphi} \\ \\ , \\ \\ \\phi_2(\\rho)=\\eta_1 h_2(\\rho) \\ \\ , \\ \\\n\\xi(\\rho,\\varphi)=\\eta_2 f(\\rho)e^{i m\\varphi} \n\\end{equation}\n\\begin{equation}\nA_{\\mu}dx^{\\mu}=\\frac {1}{e_1}(n-P(\\rho)) d\\varphi \\ \\ , \\ \\ a_{\\mu}dx^{\\mu}=\\frac {1}{e_2}(m-R(\\rho)) d\\varphi \\ .\n\\end{equation}\n$n$ and $m$ are integers indexing the vorticity of the two Higgs fields around the $z-$axis.\nIn the following, we will refer to solutions with $h_2(\\rho)\\equiv 0$ as ``embedded Abelian--Higgs solutions'', while solutions with $h_2(\\rho)\\neq 0$ will be referred to as ``semilocal solutions''.\nNote that in the case $\\varepsilon=0$, the solutions of the semilocal sector of\nour model are often also denominated ``skyrmions''.\n\n\n\\subsection{Equations of motion}\nWe define the following dimensionless variable $x=e_1\\eta_1 \\rho$, which measures the radial\ndistance in units of $M_{W,1}\/\\sqrt{2}$. \n\nThen, the total Lagrangian ${\\cal L}_m \\rightarrow {\\cal L}_m\/(\\eta_1^4 e_1^2)$ depends only on the following dimensionless coupling constants\n\n\\begin{equation}\n\\beta_i=\\frac{\\lambda_i}{e_1^2}=\\frac{M^2_{H,i}}{M^2_{W,1}}\\frac{\\eta_1^2}{\\eta_i^2} \\ , \\ i=1,2 \\ , \\ \\ g=\\frac{e_2}{e_1} \\ \\ , \\ \\ \\\nq=\\frac{\\eta_2}{\\eta_1} \\ \\ . \\ \\ \n\\end{equation}\n Varying the action with respect to the matter fields we\nobtain a system of five non-linear differential equations. The Euler-Lagrange equations for the matter field functions read:\n\\begin{equation}\n\\label{eq1}\n(xh_1')'=\\frac{P^2 h_1}{x}+\\beta_1x(h_1^2+h_2^2-1)h_1\n\\end{equation}\n\\begin{equation}\n\\label{eq2}\n(xh_2')'=\\frac{(n-P)^2 h_2}{x}+\\beta_1x(h_1^2+h_2^2-1)h_2\n\\end{equation}\n\\begin{equation}\n\\label{eq3}\n(xf')'=\\frac{R^2f}{x}+\\beta_2x(f^2-q^2)f\n\\end{equation}\n\\begin{equation}\n\\label{eq4}\n(1-\\varepsilon^2)\\left(\\frac{P'}{x}\\right)'=2 \\frac{h_1^2 P}{x} -2\\frac{(n-P)h_2^2}{x} + 2\\varepsilon g \\frac{R f^2}{x} \\ ,\n\\end{equation}\n\\begin{equation}\n\\label{eq5}\n(1-\\varepsilon^2)\\left(\\frac{R'}{x}\\right)'=2 g^2 \\frac{f^2 R}{x} + 2\\varepsilon g \\left(\\frac{P h_1^2}{x}-\\frac{(n-P)h_2^2}{x}\\right) \\ ,\n\\end{equation}\nwhere the prime now and in the following denotes the derivative with respect to $x$.\n\n\\subsection{Energy per unit length and magnetic fields}\n\nThe non-vanishing components of the energy-momentum tensor are (we use the notation\nof \\cite{clv}):\n\\begin{eqnarray}\nT_0^0 &=& e_s + e_v + e_w + u \\ \\ , \\ \\ \nT_x^x = -e_s - e_v + e_w + u \\nonumber \\\\\nT_{\\varphi}^{\\varphi} &=&e_s - e_v - e_w + u \\ \\ , \\ \\ T_z^z = T_0^0 \n\\end{eqnarray}\nwhere\n\\begin{equation}\n\\label{contributions}\ne_s= (h_1')^2 + (h_2')^2 + (f')^2 \\ \\ \\ , \\ \\ \\ e_v = \\frac{(P')^2}{2 x^2} + \\frac{(R')^2}{2 g^2 x^2} -\\frac{\\varepsilon}{g}\\frac{R'P'}{x^2} \\ \\ \\ , \\ \\ \\ e_w = \\frac{h_1^2 P^2}{x^2} + \\frac{h_2^2 (n-P)^2}{x^2} + \\frac{R^2 f^2}{x^2} \\end{equation}\nand\n\\begin{eqnarray}\nu & = & \\frac{\\beta_1}{2}\\left(h_1^2+h_2^2-1\\right)^2 + \\frac{\\beta_2}{2} \\left(f^2-q^2\\right)^2 \\ . \n\\end{eqnarray}\n\nWe define as inertial energy per unit length of a solution describing the interaction of a semilocal\nstring with winding $n$ and a dark string with winding $m$:\n\\begin{equation}\n \\mu^{(n,m)}=\\int \\sqrt{-g_3} T^0_0 dx d\\varphi\n\\end{equation}\nwhere $g_3$ is the determinant of the $2+1$-dimensional space-time given by $(t,x,\\varphi)$.\nThis then reads:\n\\begin{equation}\n \\mu^{(n,m)}=2\\pi\\int_{0}^{\\infty} x \\left(\\varepsilon_s + \\varepsilon_v + \\varepsilon_w + u\\right) \\ dx\n\\end{equation}\nNote that the string tension $T=\\int \\sqrt{-g_3} \\ T^z_z dx d\\varphi$ is equal to the energy per unit length. There are a few special case, in which energy bounds can be given:\n\\begin{enumerate}\n \\item\nFor $h_2(x)\\equiv 0$, the energy per unit length of the solution is\ngiven by:\n\\begin{equation}\n\\mu^{(n,m)}=2\\pi n \\eta_1^2 g_1(\\beta_1) + 2\\pi m \\eta_1^2 g_2(\\beta_2) \n\\end{equation}\nwhere $g_1$ and $g_2$ are functions that depend only weakly on $\\beta_1$ and $\\beta_2$, respectively.\nThe energy bound is fulfilled, when the functions $g_1$ and $g_2$ become equal to unity.\nThis happens at $\\beta_1=\\beta_2=1\/(1-\\varepsilon)$ and $n=m$ \\cite{ha}.\n\n\\item For $\\varepsilon=0$ and $h_2(x)\\neq 0$, the energy per unit length of the solution is\ngiven by\n\\begin{equation}\n\\mu^{(n,m)}=2\\pi n \\eta_1^2 + 2\\pi m \\eta_2^2 g_2(\\beta_2) \n\\end{equation}\nwhere $g_2$ is a function that depends only weakly on $\\beta_2$ with $g_2(1)=1$.\nNote that the solution of the semilocal sector exists only for $\\beta_1=1$ and fulfills the BPS bound\nfor all choices of $h_2(0)$.\n\n\\end{enumerate}\n\nThe magnetic fields associated to the solutions are given by \\cite{ha}~:\n\\begin{equation}\n\\label{magnetic}\n B_z(x)=\\frac{-P'(x)+\\frac{\\varepsilon}{g} R'(x)}{e_1 x} \\ \\ \\ {\\rm and} \\ \\ \\ b_z(x)=-\\sqrt{1-\\varepsilon^2}\\frac{R'(x)}{e_2 x} \\ , \n\\end{equation}\nrespectively, where we have used the fact that the part of the Lagrangian containing\nthe field strength tensors can be rewritten as \\cite{vachaspati}~:\n\\begin{equation}\n -\\frac{1}{4} F_{\\mu\\nu} F^{\\mu\\nu}-\\frac{1}{4} H_{\\mu\\nu} H^{\\mu\\nu}+ \\frac{\\varepsilon}{2} F_{\\mu\\nu}H^{\\mu\\nu} \\Rightarrow -\\frac{1}{4} G_{\\mu\\nu} G^{\\mu\\nu} -\\frac{1}{4}(1-\\varepsilon^2) H_{\\mu\\nu} H^{\\mu\\nu}\n\\end{equation}\nwith $G_{\\mu\\nu}=\\partial_{\\mu} \\tilde{A}_{\\nu}- \\partial_{\\nu} \\tilde{A}_{\\mu}$\nwhere $\\tilde{A}_{\\mu}=A_{\\mu}-\\varepsilon a_{\\mu}$.\nThe corresponding magnetic fluxes $\\int d^2x \\ B$ are\n\\begin{equation}\n \\Psi= \\frac{2\\pi}{e_1}\\left(n-\\frac{\\varepsilon}{g} m\\right) \\ \\ {\\rm and} \\ \\ \n\\psi=\\sqrt{1-\\varepsilon^2} \\ \\frac{2\\pi m}{e_2} \\ ,\n\\end{equation}\nrespectively. Obviously, these magnetic fluxes are not quantized for generic $\\varepsilon$.\n\n\n\\subsection{Boundary conditions and asymptotics}\nThe requirement of regularity at the origin leads to the following boundary \nconditions:\n\\begin{equation}\nh_1(0)=0 \\ , \\ h_2'(0)=0 \\ , \\ f(0)=0 \\ , \\ P(0)=n \\ , \\ R(0)=m\n\\label{bc1}\n\\end{equation}\nFor $h_2(0)=0$, the semilocal strings correspond to embedded Abelian--Higgs \nstrings. Here, we are mainly interested in constructing solutions that are truly semilocal, i.e. we require $h_2(0)\\neq 0$.\nThe finiteness of the energy per unit length requires:\n\\begin{equation}\nh_1(\\infty)=1 \\ , \\ h_2(\\infty)=0 \\ , \\ f(\\infty)=q \\ , \\ P(\\infty)=0 \\ , \\ R(\\infty)=0 \\ .\n\\end{equation}\n\nThe asymptotic behaviour for $x\\rightarrow \\infty$ depends crucially on whether the function $h_2(x)\\equiv 0$ or\n$h_2(x)\\neq 0$. \n\\begin{enumerate}\n \\item For $h_2(x)\\equiv 0$ we find:\n\\begin{eqnarray}\n P (x\\rightarrow \\infty) &=& - \\sqrt{x} \\ m_{12} \\ \\left[C_1 \\exp\\left(-x\\beta_+\\right) + C_2 \\exp\\left(-x \\beta_-\\right) \\right] + .... \\\\\n R(x\\rightarrow \\infty) &=& \\sqrt{x} \\ \n \\left[C_1 \\ m_{11}(\\beta_+) \\exp\\left(-x\\beta_+\\right) + C_2 \\ m_{11}(\\beta_-) \\exp\\left(-x \\beta_-\\right) \\right]+ ...\n\\end{eqnarray}\nwhere $C_1$ and $C_2$ are constants, $m_{11}(\\beta_{\\pm})= (1-\\varepsilon^2)\\beta_{\\pm}^2 - 2$ and $m_{12} = -2 \\varepsilon q^2 g$. The $\\beta_{\\pm}$ are positive and are given by\n\\begin{equation}\n \\beta^2_{\\pm} = \\frac{1+q^2 g^2 \\pm \\sqrt{(1-q^2 g^2)+ 4 \\varepsilon q^2 g^2}}{1-\\varepsilon^2}\n\\end{equation}\nThe numerical evaluation (see below) shows that for specific values of the coupling constants the constants $C_1$ and $C_2$\nhave opposite sign. Hence, the function $R(x)$ can possess a node asymptotically which we have confirmed\nnumerically. However, the numerics has shown that these type of solutions exist only\nfor values of $\\varepsilon$ of order one. Hence, we don't present them here since we believe that\nthey are unphysical.\n\nFor the scalar fields, we find \n\\begin{eqnarray}\nh_1 (x\\rightarrow \\infty) &=& 1 + \\frac{C_3}{\\sqrt{x}} \\exp\\left(-x\\sqrt{2\\beta_1}\\right) \n+ \\frac{c_+}{x} \\exp\\left(-2x \\beta_+\\right) + \\frac{c_-}{x} \\exp\\left(-2x \\beta_-\\right) + ...\\\\\nf(x\\rightarrow \\infty) &=& q + \\frac{C_4}{\\sqrt{x}} \\exp\\left(-x\\sqrt{2\\beta_2}\\right) \n+ \\frac{d_+}{x} \\exp\\left(-2x \\beta_+\\right) + \\frac{d_-}{x} \\exp\\left(-2x \\beta_-\\right) + ...\n\\end{eqnarray}\n$C_3$ and $C_4$ are two constants, while $c_{\\pm}$, $d_{\\pm}$ depend on \nthe constants $C_1, \\dots, C_4$ and on $\\beta_1$ and $\\beta_2$.\n\n\\item For $h_2(x)\\neq 0$ we find~:\n\\begin{equation}\n\\label{as_gauge}\nP(x\\rightarrow \\infty)= \\frac{n c^2}{x^{2n}} + ... \\ \\ , \\ \\ R(x\\rightarrow \\infty)= \\frac{c_R}{x^{2n+2}} + ...\n \\end{equation}\nfor the gauge field functions. Here $c$, $c_R$ are constants that depend on the values of the coupling constants.\nFor the scalar and Higgs field functions we have\n\\begin{equation}\n\\label{as_scalar}\nh_1(x\\rightarrow \\infty) = 1 - \\frac{c^2}{2} \\frac{1}{x^{2n}} + ... \\ \\ , \\ \\ h_2(x) = \\frac{c}{x^n} + ... \\ \\ , \\ \\ \nf(x\\rightarrow \\infty)= q - \\frac{c_R^2}{2 q \\beta_2} \\frac{1}{x^{4n+6}} + ....\n\\end{equation}\n\n\\end{enumerate}\nObviously, the presence of the scalar field $h_2(x)$ changes the asymptotics drastically.\nWhile for $h_2(x)\\equiv 0$, the gauge and Higgs fields decay exponentially, they have power-law \ndecay for $h_2(x)\\neq 0$. \n\n\\subsection{Stability}\n\nFollowing the investigation in the case $\\varepsilon=0$ \\cite{hindmarsh}, we are interested\nin the stability of the embedded Abelian--Higgs string coupled to a dark string.\nIn order to do that we will study\nthe normal mode along a very specific (but standard) direction\nin perturbation space about the embedded Abelian--Higgs string coupled to a dark string. We consider the perturbation\n\\begin{equation}\n h_1(x)=\\tilde{h}_1(x) \\ , \\ h_2(x)= {\\rm e}^{i\\omega t}\\eta(x) \\ , \\ \n P(x) = \\tilde{P}(x) \\ , \\ R(x) = \\tilde{R}(x) \\ , \\ f(x) = \\tilde{f}(x)\n\\end{equation}\nwhere the tilded functions denote the profiles of an embedded Abelian--Higgs string\ncoupled to a dark string, i.e. solutions to the equations (\\ref{eq1}),(\\ref{eq3}), (\\ref{eq4}) and (\\ref{eq5}) for $h_2(x)\\equiv 0$. The perturbation is denoted by $\\eta$\nand the parameter $\\omega$ is real. \nInserting this perturbation into (\\ref{eq2}) and keeping only the linear terms in $\\eta$ leads to the\n linear eigenvalue equation~:\n\\begin{equation}\n\\label{sta}\n \\left(-\\frac{d^2}{dx^2} - \\frac{1}{x} \\frac{d}{dx} + V_{eff}\\right)\\eta(x) = \\omega^2 \\eta(x) \\ \\ , \n \\ \\ V_{eff} = \\frac{(n-\\tilde{P}(x))^2}{x^2} + \\beta_1 (\\tilde{h}_1(x)^2-1)\n\\end{equation}\nThe spectrum of the linear operator entering in (\\ref{sta}) consists of a continuum for $\\omega^2 > 0$ \nand of a finite number of bound states (or normalisable solutions) for $\\omega^2 < 0$.\nIn the latter case, the solutions fulfill\n\\begin{equation}\n \\eta(0) = 1 \\ , \\ \\eta'(0) = 0 \\ \\ \\ {\\rm with} \\ \\ \\ \\eta(x) \\to e^{-|\\omega| x} \\ {\\rm for} \\ x \\to \\infty\n\\end{equation} \nwhere we have fixed the arbitrary normalisation by choosing $\\eta(0)=1$.\n\n\nOnly bound states are of interest to us since they signal the presence of an instability. \n It should be pointed out that the functions $\\tilde{P}(x)$, $\\tilde{h}_1(x)$ entering in the\n effective potential feel the effect of the\ndark sector since the corresponding equations are directly coupled.\n\n\n\n\n\n\n\n\\section{Numerical results}\nFor all our numerical calculations, we have chosen $q=g=1$.\n\n\\subsection{Stability of the embedded Abelian--Higgs--dark strings}\nWe have first studied the stability of the embedded Abelian--Higgs strings coupled\nto dark strings by investigating the bound states of (\\ref{sta}) for different\nvalues of $\\varepsilon$. Our results for $n=m=1$ and $\\beta_2=1$ are shown in Fig.\\ref{fignew}.\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=12.0cm\n\\epsfbox{eigenvalue.eps}\\\\\n\\caption{\\label{fignew} We give the value of $\\omega^2$ (see (\\ref{sta}) in dependence\non $\\beta_1$ for three different choices of $\\varepsilon$ including the non--interacting\ncase $\\varepsilon=0$. Here $n=m=1$ and $\\beta_2=1$. }\n\\end{figure}\n\nFor $\\varepsilon=0$ we recover the result of \\cite{hindmarsh} that the\nembedded--Abelian-Higgs strings are unstable for $\\beta_1 >1$. \nFor $\\varepsilon \\neq 0$, we observe that the larger $\\varepsilon$, the larger the\nratio of Higgs to gauge boson mass $\\beta_1$ at which the embedded Abelian--Higgs strings\ncoupled to dark strings become unstable. In the following, we will denote the value of $\\beta_1$ at which\n$\\omega^2=0$ $\\beta_1^{cr}$. \nWith view to the observations for the $\\varepsilon=0$ case, we would thus expect additional\nsolutions with $h_2(x)\\neq 0$ for $\\beta_1 > \\beta_1^{cr}$. \nIn section 3.2, we will discuss the properties of these solutions.\n \nLet us also remark that our analysis does not reveal the occurence of additional unstable modes in the sector explored.\n\n\n\n\\subsection{Properties of semilocal--dark strings}\nIn the case $\\varepsilon=0$, the two sector do not interact and for the semilocal sector\ntwo different types of solutions are possible: (a) embedded Abelian--Higgs solutions with\n$h_2(x)\\equiv 0$ which exist for generic choices of $\\beta_1$ \\cite{semilocal} and \n(b) semilocal strings (``skyrmions'') with $h_2(x)\\neq 0$ which exist only for $\\beta_1=1$ \\cite{hindmarsh}.\nIn the latter case, it was shown that \nthere is a zero mode associated to the fact that the energy of the ``skyrmions''\ndoes not depend on the value of $h_2(0)$. \n\nThe case with $\\varepsilon\\neq 0$ and $h_2(x)\\equiv 0$ corresponds hence to the case\nof an embedded Abelian--Higgs string interacting with a dark string. The equations\nof motion that describe this case are exactly those studied in \\cite{ha}.\nIn \\cite{ha}, the interaction of a dark string with an Abelian--Higgs string has been studied\nin detail. Since the only difference between an Abelian--Higgs string and\nan embedded Abelian--Higgs string is the stability -- see section 3.1 -- we do not discuss this case in detail in this paper and focus on the\ncase of semilocal strings interacting with dark strings. We have solved the\ndifferential equations subject to the boundary conditions numerically using the\nODE solver COLSYS \\cite{colsys}.\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=12.0cm\n\\epsfbox{ener_dens.eps}\\\\\n\\caption{\\label{fig0} We give the profiles of the energy density $T_0^0$, the effective energy density $x\\cdot T^0_0$ as well as the\nmagnetic field $B_z$ (see (\\ref{magnetic})) for\n$\\varepsilon=1\/6$, $\\beta_1=3$ and $\\beta_2=(1-\\varepsilon)^{-1}=1.2$. We compare semilocal--dark string\nsolutions with $h_2(0) > 0$ (black) and embedded Abelian--Higgs--dark string solutions with $h_2(0)=0$ (red).}\n\\end{figure}\n\nTo see the difference between embedded Abelian--Higgs--dark string solutions\nand semilocal--dark string solutions, we present the energy density $T_0^0$, the effective\nenergy density $xT_0^0$ as well as the magnetic field $B_z$ (see (\\ref{magnetic}))\nin Fig.\\ref{fig0} for $\\varepsilon=1\/6$, $\\beta_1=3$ and $\\beta_2=(1-\\varepsilon)^{-1}=1.2$. Clearly, the effective energy density tends to zero very quickly for the\nembedded--Abelian--Higgs--dark string, while for the semilocal--dark string is has a long tail which\nresults from the power--law fall off of the functions. Moreover, the magnetic field $B_z$\ntends to zero exponentially for the embedded Abelian--Higgs--dark strings, while it falls\noff power--like for the semilocal--dark strings. Hence, the core of the\nmagnetic flux tube of the latter solution is not well defined.\n\n\n\nWhile for $\\varepsilon=0$ solutions with $h_2(x)\\neq 0$ exist only for\n$\\beta_1=1$, the situation is different here.\nFor $\\varepsilon\\neq 0$, we find solutions for generic values of $\\beta_1$, i.e. different from\nunity. In fact, the solutions exist only for $\\beta_1$ larger than a critical \nvalue, $\\beta_1^{cr}$, which depends on the choice of the winding numbers\nand other coupling constants, in particular $\\varepsilon$. Moreover, we observe that\nthe $\\beta_1$ at which semilocal--dark strings exist is a function of $h_2(0)$.\nWhile for $\\varepsilon=0$, $\\beta_1=1$ for all choices of $h_2(0)$, we find that for $\\varepsilon\\neq 0$\nthe choice of $h_2(0)$ fixes the value of $\\beta_1$.\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=12.0cm\n\\epsfbox{data_eps_01.eps}\\\\\n\\caption{\\label{fig1} The energy per unit length $\\mu^{(1,1)}$ (in units of $2\\pi\\eta_1^2$) as well as the value of $h_2(0)$ and the asymptotic constants $c$ and $c_R$ (see (\\ref{as_gauge}), \n(\\ref{as_scalar})) of the semilocal--dark string solutions are shown in dependence on $\\beta_1$ for $\\varepsilon=0.1$, $\\beta_2=1$ and $n=m=1$ (dashed).\nFor comparison, we also give the energy per unit length of the embedded Abelian--Higgs--dark string solution (solid).}\n\\end{figure}\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=12.0cm\n\\epsfbox{data_eps_05.eps}\\\\\n\\caption{\\label{fig2}The energy per unit length $\\mu^{(1,1)}$ (in units of $2\\pi\\eta_1^2$) as well as the value of $h_2(0)$ and the asymptotic constants $c$ and $c_R$ (see (\\ref{as_gauge}), (\\ref{as_scalar})) of the semilocal--dark string solution are shown in dependence on $\\beta_1$ for $\\varepsilon=0.5$, $\\beta_2=1$ and $n=m=1$ (dashed). For comparison, we also give the energy per unit length of the embedded Abelian--Higgs--dark string solution (solid). }\n\\end{figure}\n\nAt $\\beta_1^{cr}$ the branch of solutions describing a semilocal string in\ninteraction with a dark string bifurcates with the branch of solutions describing\nthe interaction of an embedded Abelian--Higgs string with a dark string. \nThis is shown in Fig.s \\ref{fig1},\\ref{fig2} for $\\varepsilon=0.1$ and $\\varepsilon=0.5$, respectively. Note that $\\beta_1^{cr}$ is exactly the value at which the\nembedded Abelian--Higgs--dark strings become unstable.\n\nHere, we give the value of $h_2(0)$ in dependence on $\\beta_1$ for $n=m=1$ and $\\beta_2=1.0$.\nClearly at some $\\beta_1^{cr}$, $h_2(0)$ tends to zero which means that $h_2(x)\\equiv 0$.\nHere the semilocal--dark string solutions bifurcate with the embedded Abelian--Higgs--dark string solutions.\nWe also compare the energy per unit length of the two types of solutions. Clearly,\nwhenever semilocal--dark string solutions exist, they have lower energy than \nthe corresponding embedded Abelian--Higgs--dark string solutions. Moreover, the larger $\\beta_1$, the bigger\nis the difference between the two energies per unit length.\nWe would thus expect the semilocal solutions to be stable with respect to the decay into the\nembedded Abelian solutions when coupled to dark strings. \nWe also present the values of the asymptotic constants $c$ and $c_R$ (see (\\ref{as_gauge}), (\\ref{as_scalar})). These vanish identically at $\\beta_1=\\beta_1^{cr}$.\n\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=14.0cm\n\\epsfbox{self_dual.eps}\\\\\n\\caption{\\label{fig4} The energy per unit length $\\mu^{(1,1)}$ (in units\nof $2\\pi\\eta_1^2$) is shown for semilocal strings interacting with dark strings as function of $\\beta_1$ for $\\beta_2=(1-\\varepsilon)^{-1}$ with $\\varepsilon=0.5$ and $\\varepsilon=1\/6$, respectively (dashed). \nFor comparison, we also give the energy per unit length of the corresponding embedded Abelian--Higgs\nsolutions interacting with dark strings (solid).}\n\\end{figure}\n\n\n\\begin{figure}[!htb]\n\\centering\n\\leavevmode\\epsfxsize=14.0cm\n\\epsfbox{ep_betacr.eps}\\\\\n\\caption{\\label{fig3} The value of $\\beta_1^{cr}$ at which the branch of semilocal\nsolutions bifurcates with the branch of embedded Abelian--Higgs solutions is shown as function\nof $\\varepsilon$ for $m=1$, $m=2$, respectively and $\\beta_2=1.0$, $\\beta_2=2.0$, respectively. }\n\\end{figure}\n\nIn general, $\\beta_1^{cr}$ will depend on the choice of $\\beta_2$, $n$ and $m$: $\\beta_1^{cr}(\\beta_2,n,m)$.\nAs shown in \\cite{ha} in the limit $h_2(x)\\equiv 0$ a BPS bound exists for $\\beta_1=\\beta_2=(1-\\varepsilon)^{-1}$ and $n=m$. In this limit, the energy per unit length (in units\nof $2\\pi\\eta_1^2$) is just $n+m=2n$. We have studied the dependence of the energy per unit length\non $\\beta_1$ for $\\beta_2=(1-\\varepsilon)^{-1}$ where $\\varepsilon=1\/6$\nand $\\varepsilon=0.5$, respectively. We have chosen $n=m=1$. Our results are given in Fig.\\ref{fig4}.\nInterestingly, we find that the branch of semilocal--dark string solutions\nbifurcates with the branch of embedded Abelian--Higgs--dark string solutions\nexactly at $\\beta_1=\\beta_2=(1-\\varepsilon)^{-1}$. For $\\beta_1 > (1-\\varepsilon)^{-1}$, the energy per unit length\nof the semilocal--dark string solutions is always smaller than that of the corresponding\nembedded Abelian--Higgs--dark string solutions, for $\\beta_1 < (1-\\varepsilon)^{-1}$ no semilocal--dark string\nsolutions exist at all. Hence, we find that \n\\begin{equation}\n \\beta_1^{cr}(\\beta_2=(1-\\varepsilon)^{-1},1,1)=(1-\\varepsilon)^{-1}\n\\end{equation}\n\n\nWe have also studied the dependence of $\\beta_1^{cr}$ on the winding of the dark string\nand the Higgs to gauge boson ratio $\\beta_2$ of the U(1) model describing the dark string in more detail.\nOur results are shown in Fig.\\ref{fig3}. Obviously, $\\beta_1^{cr}$ increases with increasing\n$\\varepsilon$. This is related to the fact that the core width of the strings decreases with increasing\n$\\varepsilon$. This means more gradient energy and hence we have to choose larger values\nof $\\beta_1$ to be able to compensate for this increase by decrease in potential energy.\n \nFor $\\beta_1=1.0$, which in fact corresponds to the BPS limit of the U(1) dark string model \nfor $\\varepsilon=0$, the value of $\\beta_1^{cr}$ increases for increasing winding $m$ of the\ndark string. Again increasing $m$ increases gradient energy such that we have to choose\nlarger value of $\\beta_1$ to compensate the increase by decrease in potential energy.\nThis is also true when increasing $\\beta_2$. Increasing $\\beta_2$ decreases the core size of\nthe dark string, this increases gradient energy and we again have to compensate by increasing\nthe value of $\\beta_1$.\n\n\n\n\n\\section{Conclusions}\nIn this paper we have shown that the interaction of semilocal strings with dark strings\nhas important effects on the properties of the former. While embedded Abelian--Higgs strings\nexist for all values of the Higgs to gauge boson ratio when interacting with dark strings, semilocal\nstrings with a condensate inside their core exist only above a critical value of the\nHiggs to gauge boson ratio. At this critical value, the embedded\nAbelian--Higgs--dark strings become unstable. The critical value of the ratio \ndepends on the choice of the Higgs to\ngauge boson ratio of the dark string and the windings. In the limit where the\nratio tends to the critical ratio, the condensate vanishes identically and the branch of\nsemilocal--dark string solutions bifurcates with the branch of embedded Abelian--Higgs--dark string\nsolutions. Apparently, the presence of the condensate lowers the energy in such a way\nthat whenever semilocal--dark strings exist, they are lower in energy than their\nembedded Abelian--Higgs-dark string counterparts. The value of the Higgs to gauge boson ratio\nfor which semilocal--dark strings exist depends on the value of the condensate\non the string axis and increases for increasing values of the condensate.\nAll these results are quite different from what is observed in the non--interacting case.\nIn the non--interacting case, semilocal strings exist only for Higgs to gauge boson\nratio equal to unity and in this limit, the energy per unit length is independent of the value\nof the condensate and in addition fulfills a BPS bound. To state it differently~: when not interacting\nwith dark strings, semilocal strings and embedded Abelian--Higgs strings are degenerate\nin energy, while the former are lower in energy as soon as they interact with dark strings.\nSince the branch of semilocal--dark string solutions bifurcates with the branch of\nembedded Abelian--Higgs--dark strings at the self--dual point of the embedded Abelian--Higgs-dark strings\n-- at which these fulfill an energy bound \\cite{ha} -- we expect that semilocal--dark strings\nare stable. Moreover, they are stable for all choices of the Higgs to gauge boson ratio for which they exist and not just -- as in the non--interacting case -- for Higgs to gauge boson ratio smaller\nor equal to unity. Since all current observations point to the fact that the Higgs boson\nmass is larger than the gauge boson masses, semilocal strings could still be stable\nwhen interacting with dark strings.\nInterestingly -- as mentioned above -- semilocal strings can lower their energy by \nforming a non--vanishing condensate inside their core. This could be important\nfor the evolution of cosmic string networks since next to the formation of bound states \\cite{wyman}\nthis would be a further mechanism for the network to loose energy.\n\nWe didn't study the gravitational properties of the solutions since we believe that the qualitative\nfeatures are similar to the case studied in \\cite{ha}. Since semilocal--dark strings\nhave lower energy per unit length than their embedded Ablian--Higgs--dark string\ncounterparts, we would expect the deficit angle created by the former to be smaller than that of the latter. Furthermore, the critical value of the gravitational coupling at which the solutions\nbecome singular is larger for the semilocal--dark strings than for the\nembedded Abelian--Higgs--dark strings.\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\subsection{Introduction}\n\\ac{ML} is a set of models which can automatically identify the hidden patterns\nin the data and can then utilize hidden patterns to make decisions in condition\nof uncertainty. \\ac{ML} has been progressively implemented in several areas\nincluding chemistry, biomedical science and robotics. \\ac{ML} falls into three\ncategories, i.e. supervised learning (e.g. classification), unsupervised\nlearning (e.g. clustering) and reinforcement learning. In this paper we focus on\nclassification, which is the way to represent and allocate objects into different\ncategories.\n\n\\ac{QT} is the probabilistic approach to representing and predicting properties\nof microscopic phenomena. Given an observable and an arbitrary state\nof a microscopic particle, \\ac{QT} computes a probability distribution of the\nvalues of the observable. The quantum formalism is explicitly acceptable to\nexplain distinct types of stochastic processes. Several nonstandard\nimplementations of the quantum formalism has emerged. For instance, the quantum\nformalism have been utilized vastly in the economic processes, game theory and cognitive\nscience as well.\n\nSince the data is growing exponentially, current state-of-the-art models are\nstill not effective. In particular, \\emph{recall} is still unsatisfactory\nbecause most classification models aim to maximize precision especially when the\nitems of a class can be ranked by a certain measure of membership to the class;\na glaring example is the search of the Internet. In contrast, recall is crucial\nin many daily tasks aiming to find all the pertinent items of a class such as patent search and biomedical image classification.\n\nOur approach is to develop a new theoretical approach inspired by \\ac{QM} in\norder to dig into the quantum world and come up with new and effective models\nwhich are capable of increasing recall. Our hypothesis is that, since \\ac{QM} has\nalready shown its effectiveness in several fields, it may also be effective in\n\\ac{ML}. To this end we will exploit Quantum Probability theory, which is the quantum\ngeneralization of classical probability theory and was developed by Von\nNeumann. While classical probability theory provides that a system can be in\neither state 0 or 1, quantum probability comes into existence to go beyond\nclassical theory and describes states which can be anything in-between 0 and 1. In\nthis paper, we propose the \\ac{BCIQT} model which is a step towards shifting\nfrom classical models to quantum models.\n\\section{Proposed Methodology}\n\n\\subsection{Classical and Quantum Signal Detection Theory}\n\\label{sec:quant-detect-fram}\n\n\\ac{BCIQT} is based on the overlap between \\ac{SDT} and \\ac{QM}. The main\ndifference between the classical framework and the quantum framework of signal\ndetection regards what encoders encode and what decoders decode\n\\cite{helstrom1969quantum}.\n\nIn the classical framework,\nthere is c-c (classical-classical) mapping from a symbol to the wave to the\ncorrupted channel; then the decoder produce c-c (classical-classical) mapping\nfrom the corrupted channel wave to a symbol. In the quantum framework, there is a coder between the source and\nthe channel; the classical symbol is transmitted through the quantum\nstate. Initial encoding starts like c-q (classical-quantum) mapping from the\nsymbol to the quantum state selected from a finite set of possible states. More\ndetails about classical and quantum \\ac{SDT} can be found in\n\\cite{helstrom1969quantum}.\n\n\n\n\\subsection{Binary Classifier Inspired by Quantum Theory}\n\nA novel \\ac{BCIQT} that is inspired by quantum detection theory is described in\nthis section. For each category we supposed that each training sample was about\nthe category or not. For a given category and the set of training samples, we\nused the projector $\\Delta$ for each category to identify whether the test\nsample was about the category or not. To determine whether the test sample was\nabout the category, $\\Delta$ was examined against a vectorial representation of\nthe test samples.\n\nConsider a set of distinct features calculated from the whole sample collection.\nEach sample could be represented as a vector of features; each element in the\nfeature vector was a non-negative number such as frequency. Each sample in the\ntraining set had a binary label in $\\{0,1\\}$. The main goal of \\ac{BCIQT} was\nto obtain one binary label for each sample in the test set.\n\nThe \\ac{BCIQT} estimated two density operators $\\rho_{0}$ and $\\rho_{1}$, one\noperator for each category or class and its complement, by using the training\nsamples; in particular, for each class, the negative training samples were\nutilized to estimate $\\rho_{0}$ and the positive training samples were utilized\nto estimate $\\rho_{1}$.\n\nIn order to achieve these density operators $\\rho_{0}$ and $\\rho_{1}$, we first\ncalculated the total number of samples with non-zero values for each particular\nfeature. In such a way, one vector $\\ket{v}$ was obtained for each class. Since\nwe were considering the binary case, two vectors $\\ket{v_{0}}$ and $\\ket{v_{1}}$\nwere obtained; the former referred to the negative training samples and the\nlatter referred to the positive training samples; these vectors may be\nconsidered as statistics of the features in a class. We normalized the vectors\nto obtain $|\\braket{v|v}|^2=1$. Then, we calculated the outer product in order\nto obtain the density operators $\\rho_{0}$ and $\\rho_{1}$ as follows:\n\\begin{equation}\n \\label{eq:rhos}\n \\rho_0 = \\frac{\\ket{v_0} {\\bra{v_0}} }{tr(\\ket{v_0} {\\bra{v_0}})}\n \\qquad\n \\rho_1 = \\frac{\\ket{v_1} {\\bra{v_1}} }{tr(\\ket{v_1} {\\bra{v_1}})}\n\\end{equation}\nWe computed the projection operator $\\Delta$ according to\n\\cite{melucci2016relevance}, that is,\n\\begin{equation}\n \\label{eq:decomposition}\n \\rho_1 - \\lambda \\rho_0 = \\eta\\,\\Delta + \\beta\\,\\Delta^\\perp \\qquad \\eta > 0\n \\qquad \\beta < 0 \\qquad \\Delta\\,\\Delta^\\perp = 0\n\\end{equation}\nwhere $\\xi$ is the prior probability of the negative class and\n$ \\lambda = {\\xi}\\,\/\\,(1-\\xi) $; moreover, $\\eta$ is the positive eigenvalue\ncorresponding to $\\Delta$ which represents the subspaces of the vectors\nrepresenting the sample to be accepted in the target class.\n\nWe set $\\lambda = 1$ to simply mean that both classes had the same prior\nprobability ($\\xi=0.5$); moreover, there was no cost for wrong detection\n$C_{00}=C_{11}=0$; finally, the costs of false alarm and miss were constant\n($C_{01}=C_{10}$). Eventually, we determined the binary label for the given test\nsample $S_{j}$ by inspecting the value of\n$ \\langle w_{S_j} \\vert \\Delta \\vert w_{S_j} \\rangle$: If\n$\\langle w_{S_j} \\vert \\Delta \\vert w_{S_j}\\rangle \\geq 0.5$, then $C(S_j) = 1$;\notherwise $C(S_j) = 0$.\n\n\\section{Experiment}\n\nThe MNIST database \\footnote{\\url{http:\/\/yann.lecun.com\/exdb\/mnist\/}} of\nhandwritten digits has a training set of 60,000 examples, and a test set of\n10,000 examples. There are 9 categories from 0 to 9 but excluded 9. It is a subset of a larger set\navailable from the National Institute of Standards and Technology (NIST). The\ndigits have been size-normalized and centered in a fixed-size image.\n\nThe four models i.e. \\ac{NB}, \\ac{SVM}, \\ac{KNN} and \\ac{DT} were used as baselines. Prior to training the models,\nthe top 100 features were selected as the best features for all the models in terms of recall. The chi-square feature selection model was used.\n\nWe used one-vs-all strategy: for each category, the training samples labeled as\npertinent to the category are considered positive examples, while the rest are\nconsidered negative examples. While training the model, five fold cross\nvalidation was used. As it can be seen from Table \\ref{tab:1}, our proposed\nmodel performs better than any state-of-art-model in terms of recall for every\ncategory. By changing number of features, evaluation measures(i.e. accuracy, precision, recall and f-measure) also change and provide comparable results to the baselines.\n\n\n\\begin{table}[h!]\n\\large\n\\caption{Comparison of Recall among k-nearest neighbors(KNN), Decision Tree(DT), Naive Bayes (NB), Support Vector Machine (SVM) and Binary Classifier Inspired by Quantum Theory (BCIQT)}\n\n\\begin{tabular}{cccccc}\n\t\\hline\n Category\t&\tKNN\t& DT\t&\tNB\t&\tSVM\t& BCIQT\t\\\\\n\t\\hline\n \t\t0\t&0.959\t&0.884\t&0.889\t&0.292&\t\\textbf{1}\n\n\t\\\\\n \t\t1\t& 0.699&\t0.710&\t0.582&\t0.390&\t\\textbf{0.996}\n\n\t\\\\\n \t\t2\t&0.704&\t0.652&\t0.709&\t0.474&\t\\textbf{1}\n\n\t\\\\\n \t\t3\t&0.623&\t0.508&\t0.792&\t0.346&\t\\textbf{0.997}\n\n\t\\\\\n \t\t4\t&0.643&\t0.621&\t0.666&\t0.259&\t\\textbf{0.999}\n\n\t\\\\\n \t\t5\t&0.892&\t0.855&\t0.872&\t0.621&\t\\textbf{1}\n\n\t\\\\\n \t\t6\t&0.743&\t0.755&\t0.873&\t0.454&\t\\textbf{0.999}\n\n\t\\\\\n \t\t7\t&0.753&\t0.728&\t0.779&\t0.332&\t\\textbf{1}\n\n\t\\\\\n \t\t8\t&0.749&\t0.677&\t0.817&\t0.209&\t\\textbf{1}\n\n\t\\\\\n\t\\hline\n\\end{tabular}\n\\label{tab:1}\n\\end{table}\n\n\\section{Conclusion and Future Works}\n\nWe found out that our proposed model outperforms the state-of-the-art models in terms of\n\\emph{recall}; therefore, this model can be safely implemented if someone is\nlooking for high recall. We believe that this is an encouraging result and\nopens a gateway towards quantum inspired \\ac{ML} approaches. As for future\nwork, we would like to develop multi-class classifiers (i.e. how to assign an\nitem to more than one class) and multi-label classifiers (i.e. how to deal with\nnon-binary labels), and re-rank the test items of a class by increasing precision as well.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{ Acknowledgments}\n\"This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 721321\".\n\n\\bigskip\n\\noindent \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\nAll modern supersymmetric models are derived from a fundamental general scalar superfield. The application of the covariant superfield derivatives $D_\\alpha$ and $\\bar{D}_{\\dot{\\alpha}}$ allows then a systematic derivation of various chiral and anti-chiral superfields, see e.g. \\cite{sohnius85, dine07}. If the discussion is restricted to the supersymmetric description of bosonic fields with integer-valued mass dimension and fermionic fields with half-integer-valued mass dimension this approach is sufficient and leads to the Minimal Supersymmetric Standard Model. This changes, however, if the previous assumption on the mass dimensions of fermionic and bosonic fields is dropped.\n\nAn investigation of this matter is of special interest due to the recent proposal of fermionic fields with mass dimension one -- eigenspinors of the charge conjugation operator (ELKO) -- by Ahluwalia-Khalilova and Grumiller \\cite{ahluwaliakhalilova05a,ahluwaliakhalilova05b}. In their publications they use the field theory formalism to formulate a nonlocal theory of fermionic fields with mass dimension one. Ahluwalia et al. then modify this formalism by introducing a preferred direction along which the fermionic field with mass diemension one satisfies a local theory \\cite{ahluwalia10}. Subsequently da Rocha and Hoff da Silva construct a Lagrangian for ELKO spinors motivated from supergravity using mass dimension transmuting operators \\cite{darocha09}. Therfore, the question arises how to formulate a supersymmetric model from a fundamental superfield that is able to describe fermionic fields with mass dimension one.\n\nThe article is structured as follows. Section \\ref{CLSUSY} discusses the construction of a supersymmetric Lagrangian. It is shown that the straightforward approach using a general scalar superfield with redefined mass dimensions fails while the construction of a model based on a general spinor superfield is successful. Then, the corresponding supercurrent is calculated in Section \\ref{CJonshell}. In Section \\ref{CHposition} the Hamiltonian is derived using the supersymmetry algebra. This approach ensures that the resulting Hamiltonian is positive definite. Finally, the results are summarised in Section \\ref{Csummary}.\n\n\\section{A Supersymmetric Lagrangian}\n\\label{CLSUSY}\nIn this section a supersymmetric Lagrangian for fermionic fields with mass dimension one is derived. It is shown that a construction based on the general scalar superfield with redefined mass dimension of the component fields is impossible. This is due to problems generating a kinetic contribution for the fermionic fields with mass dimension one as well as constructing a consistent second quantisation. Afterwards the general spinor superfield is presented and all chiral and anti chiral superfields up to third order in covariant derivatives are derived systematically. This general spinor superfield is then used to construct a supersymmetric on-shell Lagrangian for fermionic fields with mass dimension one.\n\\subsection{Constructing a Model Based on the General Scalar Superfield}\n\\label{SLnot}\nThe most straightforward approach to formulate a supersymmetric model for fermionic fields with integer-valued mass dimension is to formulate a model in analogy to the commonly used formalism where fermionic fields have half-integer-valued mass dimension. This is done by starting from the general scalar superfield\n\\begin{align}\nV\n\t&= C\n\t- i \\theta \\chi\n\t+ i \\bar{\\chi}' \\bar{\\theta}\n\t- \\frac{i}{2} \\theta^2 \\left( M - i N \\right)\n\t+ \\frac{i}{2} \\left( M + i N \\right)\n\t- \\theta \\sigma^\\mu \\bar{\\theta} A_\\mu +\\notag \\\\\n\t&\\quad + i \\bar{\\theta}^2 \\theta \\left( \\lambda - \\frac{i}{2} \\dslash{\\partial} \\bar{\\chi}' \\right)\n\t- i \\theta^2 \\bar{\\theta} \\left( \\bar{\\lambda}' - \\frac{i}{2} \\bar{\\dslash{\\partial}} \\chi \\right)\n\t- \\frac{1}{2} \\theta^2 \\bar{\\theta}^2 \\left( D + \\frac{1}{2} \\Box C \\right) ,\n\\end{align}\nand redefining the mass dimensions of the component fields appropriately, e.g. $\\mathrm{dim}{\\left( C \\right)} = 1\/2$, $\\mathrm{dim}{\\left( \\chi \\right)} = 1$, etc. . The chiral superfields $X$ and $W_\\alpha$ are then defined as\n\\begin{align}\nX\n\t&= \\frac{i}{2} \\bar{D}^2 X \\, ,\\\\\nW_\\alpha\n\t&= \\frac{i}{4} \\bar{D}^2 D_\\alpha V \\, .\n\\end{align}\nwhere the covariant derivatives are given by\n\\begin{align}\nD_\\alpha\n\t&= \\partial_\\alpha - i \\dslash{\\partial}_{\\alpha \\dot{\\beta}} \\bar{\\theta}^{\\dot{\\beta}} \\, , \\label{covariantD}\\\\\n\\bar{D}_{\\dot{\\alpha}}\n\t&= - \\bar{\\partial}_{\\dot{\\alpha}} + i \\theta^\\beta \\dslash{\\partial}_{\\beta \\dot{\\alpha}} \\, . \\label{covariantDbar}\n\\end{align}\nThis choice of conventions differs by a factor of $- i$ from the conventions used in \\cite{wess82}.\n\nHowever, there are two fundamental problems that prevent a feasible theory using this approach. The first problem is that all possible contributions to the Lagrangian fail to produce a nonvanishing kinetic term for the fermionic fields. The second problem is encountered during second quantisation of the Lagrangian. It can be shown that already the simplest possible Lagrangian leads to negative energy solutions. In the following subsections these two problems will be discussed in detail.\n\n\\subsubsection{A Non-kinetic Supersymmetric Lagrangian}\n\\label{SSnonkinSUSYL}\n\\begin{TABLE}[t]{\n\\begin{tabular}{r|c|l}\nContribution & Mass Dimension & Possible Contributions \\\\\n\\hline\n$V V$ & $\\mathrm{dim}{\\left( V V \\right)} = 1$ & $\\left( m V V \\right)_D$ \\\\\n\\hline\n$X V$ & $\\mathrm{dim}{\\left( X V\\right)} = 2$ & $\\left( X V \\right)_D$ \\\\\n$D V D V$ & $\\mathrm{dim}{\\left( D V D V\\right)} = 2$ & $\\left( D V D V \\right)_D$ \\\\\n$V X$ & $\\mathrm{dim}{\\left( V X \\right)} = 2$ & $\\left( V X \\right)_D$ \\\\\n\\hline\n$D W V$ & $\\mathrm{dim}{\\left( D W V \\right)} = 3$ & mass dimension too big for D-component \\\\\n$W D V$ & $\\mathrm{dim}{\\left( W D V \\right)} = 3$ & mass dimension too big for D-component \\\\\n$X X$ & $\\mathrm{dim}{\\left( X X \\right)} = 3$ & $\\left( X X \\right)_F$ \\\\\n$D V W$ & $\\mathrm{dim}{\\left( D V W \\right)} = 3$ & mass dimension too big for D-component \\\\\n$V D W$ & $\\mathrm{dim}{\\left( V D W \\right)} = 3$ & mass dimension too big for D-component \n\\end{tabular}\n\\caption{Contributions to the Lagrangian based on the general scalar superfield if $\\chi$ is identified with the fermionic field of mass dimension one. In addition to the contributions built from products of unbarred superfields, the hermitian conjugates are permitted as well.}\n\\label{TChiDMnot}}\n\\end{TABLE}\nThe general scalar superfield has two possible candidates for a fermionic field with mass dimension one, $\\chi$ and $\\lambda$. For simplicity, the discussion is restricted to the case for $\\chi$ as fermionic field with mass dimension one. Similar calculations can be repeated for $\\lambda$. Due to the shift in mass dimension of the component fields the maximum number of covariant derivatives that needs to be considered is then increased by two and the discussion becomes more involved.\n\nIf $\\chi$ is identified with the fermionic field with mass dimension one it can be shown that the mass dimensions of the general superfield $V$ and the chiral superfields $X$ and $W_\\alpha$ are\n\\begin{align}\n\\mathrm{dim}{\\left( V \\right)}\n\t&= \\frac{1}{2} \\, , \\quad\n\\mathrm{dim}{\\left( X \\right)}\n\t= \\frac{3}{2} \\, , \\quad \n\\mathrm{dim}{\\left( W_\\alpha \\right)}\n\t= 2 \\, . \\quad\n\\end{align}\nThese results for the building blocks of the Lagrangian can be utilised to work out all possible contributions to the Lagrangian which have to satisfy three basic requirements. First, all contributions to the Lagrangian have to be Lorentz scalars and thus cannot contain any uncontracted indices. Second, all structure constants must have positive mass dimension for the theory to be renormalizable. Third, the contributions must have the appropriate mass dimension to contribute either via the $F$-component or the $D$-component.\n\nAll possible terms that satisfy the requirements are summarised in table \\ref{TChiDMnot}. It groups the contributions into three groups depending on the mass dimension of the superfield product without structure constants. It is possible to conceive terms with higher mass dimension, however, those terms cannot contribute to the Lagrangian and are irrelevant for the following discussion. For simplicity the discussion is restricted to the unbarred fields while the hermitian conjugated components have to be considered for the Lagrangian as well.\n\nThe first group of terms with mass dimension one consists of one single term which is the product of two general superfields. As the general superfield is neither chiral nor antichiral the only possible contribution to the Lagrangian is a mass term via the D-component.\n\nThe second group containing all terms with mass dimension two then encompasses all terms that can be constructed using two general superfields and two covariant derivatives. This results in three possible contributions to the kinetic term via the D-component. There can be no contributions to the mass term via the F-component as neither $V$ nor $D V$ are chiral or anti-chiral.\n\nFinally, the third group summarises all terms with mass dimension three which contain two general superfields as well as four covariant derivatives. Due to the mass dimension only contributions via the F-component are possible. The only term that satisfies the necessary symmetry requirements is $X X$ which contributes to the kinetic term.\n\nAltogether, there is one contribution to the mass term as well as four contributions to the kinetic term. On the first glance this seems to ensure the existence of a valid model. However, explicit calculations reveal that neither of the four kinetic terms in question is able to produce a kinetic term for $\\chi$ which was originally identified with the fermionic field with mass dimension one. A similar discussion can be repeated for the case where $\\lambda$ is identified with the fermionic field with mass dimension one. Although the discussion for $\\lambda$ produces an even larger number of potential contributions to the kinetic term neither of these terms produces a kinetic term for $\\lambda$. Therefore, it can be concluded that it is impossible to construct a Lagrangian -- other than the trivial solution for a constant background spinor field -- based on the general scalar superfield that is able to describe fermionic fields with mass dimension one.\n\n\\subsubsection{Problems with Second Quantisation}\n\\label{SSProblemSQ}\nThe second major problem arises from the second quantisation of the component fields. A simple way to demonstrate this is to start with the simplest possible Lagrangian for a fermionic field with mass dimension one\n\\begin{align}\n\\mathcal{L}\n\t&= \\partial_\\mu \\bar{\\psi} \\partial^\\mu \\psi\n\t- m^2 \\bar{\\psi} \\psi \\, .\n\\end{align}\nThe corresponding Hamiltonian is then found to be\n\\begin{align}\nH\n\t&= \\vec{\\mathbf{\\nabla}} \\mathbf{\\bar{\\psi}} \\vec{\\mathbf{\\nabla}} \\mathbf{\\psi}\n\t+ m^2 \\bar{\\psi} \\psi \\, .\n\\end{align}\nInserting the quantised Dirac field\n\\begin{align}\n\\psi\n\t&= \\int \\frac{\\mathrm{d}^3 \\mathbf{p}}{\\left( 2 \\pi \\right)^3} \\frac{1}{\\sqrt{2 E_\\mathbf{p}}} \\sum\\limits_s \\left( a^s_\\mathbf{p} u^s{\\left( \\mathbf{p} \\right)} e^{-i p \\cdot x} + {b^s_\\mathbf{p}}^\\dagger v^s{\\left( \\mathbf{p} \\right)} e^{i p \\cdot x} \\right) \\, , \\\\\n\\bar{\\psi}\n\t&= \\int \\frac{\\mathrm{d}^3 \\mathbf{p}}{\\left( 2 \\pi \\right)^3} \\frac{1}{\\sqrt{2 E_\\mathbf{p}}} \\sum\\limits_s \\left( b^s_\\mathbf{p} \\bar{v}^s{\\left( \\mathbf{p} \\right)} e^{- i p \\cdot x} + {a^s_\\mathbf{p}}^\\dagger \\bar{u}^s{\\left( \\mathbf{p} \\right)} e^{i p \\cdot x} \\right) \\, ,\n\\end{align}\ninto the Hamiltonian and removing the zero-point energy leads to\n\\begin{align}\nH\n\t&= \\int \\frac{\\mathrm{d}^3 \\mathbf{p}}{\\left( 2 \\pi \\right)^3} m E_\\mathbf{p} \\sum\\limits_s \\left( {a^s_\\mathbf{p}}^\\dagger a^s_\\mathbf{p} - {b^s_\\mathbf{p}}^\\dagger b^s_\\mathbf{p} \\right) .\n\\end{align}\nThe creation operator $b^\\dagger$ can be used to lower the energy arbitrarily and obtain negative energy solutions.\n\n\\subsection{The General Superfield with one Spinor Index}\n\\label{SVgeneral}\nIn the previous section it was shown that a theory based on the general scalar superfield cannot be viable. This motivated an ansatz based on the general spinor superfield. So far only few references to the general spinor superfield exist in the literature. One exception being the article by Gates \\cite{gates77} that contains an expansion of a spinor superfield in Grassmann variables. In addition, an expansion of the chiral spinor superfield was given by Siegel \\cite{siegel79}. Their results are also included in the book by Gates, Grisaru, Ro\\v{c}ek, and Siegel \\cite{gates01}. As our notation differs from previous publications and is based on spinor superfields with different mass dimension the spinor superfield is introduced in detail and all chiral and anti-chiral superfields up to third order in covariant derivatives are derived.\n\nIn analogy to the general scalar superfield , the general spinor superfield can immediately be written down as expansion in $\\theta$ and $\\bar{\\theta}$\n\\begin{align}\nV_\\alpha\n\t&= \\kappa_\\alpha\n\t+ \\theta^\\beta M_{\\beta \\alpha}\n\t+ \\bar{\\theta}^{\\dot{\\beta}} N_{\\dot{\\beta} \\alpha}\n\t+ \\theta^\\beta \\theta^\\gamma \\psi_{\\alpha \\beta \\gamma}\n\t+ \\bar{\\theta}^{\\dot{\\beta}} \\bar{\\theta}^{\\dot{\\gamma}} \\chi_{\\alpha \\dot{\\beta} \\dot{\\gamma}}\n\t+ \\theta^\\beta \\bar{\\theta}^{\\dot{\\gamma}} \\omega_{\\alpha \\beta \\dot{\\gamma}} + \\notag \\\\\n\t&\\quad + \\theta^\\beta \\theta^\\gamma \\bar{\\theta}^{\\dot{\\delta}} R_{\\dot{\\delta} \\alpha \\beta \\gamma}\n\t+ \\theta^\\beta \\bar{\\theta}^{\\dot{\\gamma}} \\bar{\\theta}^{\\dot{\\delta}} S_{\\alpha \\beta \\dot{\\gamma} \\dot{\\delta}}\n\t+ \\theta^\\beta \\theta^\\gamma \\bar{\\theta}^{\\dot{\\delta}} \\bar{\\theta}^{\\dot{\\epsilon}} \\lambda_{\\alpha \\beta \\gamma \\dot{\\delta} \\dot{\\epsilon}} \\, .\n\\end{align}\nTo bring this ansatz into a more convenient form the Grassmann variables need to be contracted over the respective indices. After absorbing some of the prefactors into the component fields, the general superfield is found to be\n\\begin{align}\nV_\\alpha\n\t&= \\kappa_\\alpha\n\t+ \\theta^\\beta M_{\\beta \\alpha}\n\t- \\bar{\\theta}^{\\dot{\\beta}} N_{\\dot{\\beta} \\alpha}\n\t+ \\theta^2 \\psi_\\alpha\n\t+ \\bar{\\theta}^2 \\chi_\\alpha\n\t+ \\theta \\sigma^\\mu \\bar{\\theta} \\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\omega_{\\alpha \\beta \\dot{\\gamma}} - \\notag \\\\\n\t&\\quad - \\theta^2 \\bar{\\theta}^{\\dot{\\delta}} R_{\\dot{\\delta} \\alpha}\n\t+ \\bar{\\theta}^2 \\theta^\\beta S_{\\beta \\alpha}\n\t+ \\theta^2 \\bar{\\theta}^2 \\lambda_\\alpha \\, ,\n\\end{align}\nwhere $\\kappa$, $\\psi$, $\\chi$, and $\\lambda$ are Majorana spinors, $M$, $N$, $R$, and $S$ are complex second-rank spinors, and $\\omega$ is a complex third-rank spinor. The four complex second-rank spinors contain 32 bosonic degrees of freedom while the four Majorana spinors contain 16 fermionic degrees of freedom. As the number of bosonic and fermionic degrees of freedom must be the same for a supersymmetric theory, the 3-rd rank spinor must also have 16 fermionic degrees of freedom. It is then tempting to rewrite the third-rank spinor as a vector of majorana spinors\n\\begin{align}\n\\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\omega_{\\alpha \\beta \\dot{\\gamma}}\n\t&= \\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\left( \\sigma^\\nu \\right)_{\\beta \\dot{\\gamma}} \\omega_{\\nu \\alpha}\n\t= 2 \\omega_{\\mu \\alpha} \\, ,\n\\end{align}\nwhich has 16 degrees of freedom as well. In the following discussion it will be referred to as a spinor-vector field. After appropriate rescaling of the component fields the most general spinor superfield is given by\n\\begin{align}\nV_\\alpha\n\t&= \\kappa_\\alpha\n\t+ \\theta^\\beta M_{\\beta \\alpha}\n\t- \\bar{\\theta}^{\\dot{\\beta}} N_{\\dot{\\beta}\\alpha}\n\t+ \\theta^2 \\psi_\\alpha\n\t+ \\bar{\\theta}^2 \\chi_\\alpha\n\t+ \\theta \\sigma^\\mu \\bar{\\theta} \\omega_{\\mu \\alpha} - \\notag \\\\\n\t&\\quad - \\theta^2 \\bar{\\theta}^{\\dot{\\beta}} R_{\\dot{\\beta} \\alpha}\n\t+ \\bar{\\theta}^2 \\theta^\\beta S_{\\beta \\alpha}\n\t+ \\theta^2 \\bar{\\theta}^2 \\lambda_\\alpha \\, .\n\\label{Valpha}\n\\end{align}\n\n\\subsubsection{The Chiral Superfields}\n\\label{SSChiralFields}\nFor the general scalar superfield the chiral and anti-chiral fields are derived by repeated operation of the covariant derivatives $D$ and $\\bar{D}$. By definition the chiral and anti-chiral superfields satisfy the following relations\n\\begin{align}\n\\bar{D}_{\\dot{\\alpha}} X\n\t&= 0 \\, , \\\\\nD_\\alpha Y\n\t&= 0 \\, ,\n\\end{align}\nwhere it is assumed that $X$ is a chiral superfield and $Y$ is an anti-chiral superfield which can have an arbitrary number of spinor indices. The chiral and anti-chiral superfields up to third order in covariant derivatives are then derived systematically by calculating $\\bar{D}^2 V$ and $D^2 V$, as well as $\\bar{D}^2 D V$ and $D^2 \\bar{D} V$.\n\nThe chiral spinor field is found by repeated operation of the covariant derivative $\\bar{D}$ onto the general superfield\n\\begin{align}\nX_\\alpha\n\t&= - \\frac{1}{4} \\bar{D}^2 V_\\alpha \\notag \\\\\n\t&= \\chi_\\alpha\n\t+ \\theta^\\beta \\left( S_{\\beta \\alpha} + \\frac{i}{2} \\dslash{\\partial}_\\beta{}^{\\dot{\\delta}} N_{\\dot{\\delta} \\alpha} \\right)\n\t+ \\theta^2 \\left( \\lambda_\\alpha + \\frac{i}{2} \\partial^\\mu \\omega_{\\mu \\alpha} - \\frac{1}{4} \\Box \\kappa_\\alpha \\right)\n\t- i \\theta \\dslash{\\partial} \\bar{\\theta} \\chi_\\alpha + \\notag \\\\\n\t&\\quad + \\frac{i}{2} \\theta^2 \\bar{\\theta}^{\\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma}}{}^\\beta \\left( S_{\\beta \\alpha} + \\frac{i}{2} \\dslash{\\partial}_\\beta{}^{\\dot{\\delta}} N_{\\dot{\\delta} \\alpha} \\right)\n\t- \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\chi_\\alpha \\, .\n\\label{Xchiral}\n\\end{align}\nComparison with the general expansion of a chiral field with one spinor index leads to the very elegant expression\n\\begin{align}\nX_\\alpha\n\t&= \\exp{\\left( - i \\theta \\dslash{\\partial} \\bar{\\theta} \\right)} \\left( \\chi_\\alpha + \\theta^\\beta \\left( S_{\\beta \\alpha} + \\frac{i}{2} \\dslash{\\partial}_\\beta{}^{\\dot{\\delta}} N_{\\dot{\\delta} \\alpha} \\right) + \\theta^2 \\left( \\lambda_\\alpha + \\frac{i}{2} \\partial^\\mu \\omega_{\\mu \\alpha} - \\frac{1}{4} \\Box \\kappa_\\alpha \\right) \\right) \\, .\n\\end{align}\nAs this notation is not used in the further discussion an explicit notation in exponential form is not given for $Y$, $Z$, $Z_0$, and $Z'$ but can be derived in a similar way.\n\nThe calculations for the anti-chiral spinor field can be performed in perfect analogy where the operation of the covariant derivatives $D$ on the general superfield replaces the operation of $\\bar{D}$\n\\begin{align}\nY_\\alpha\n\t&= - \\frac{1}{4} D^2 V_\\alpha \\notag \\\\\n\t&= \\psi_\\alpha\n\t- \\bar{\\theta}^{\\dot{\\beta}} \\left( R_{\\dot{\\beta} \\alpha} + \\frac{i}{2} \\bar{\\dslash{\\partial}}_{\\dot{\\beta}}{}^\\gamma M_{\\gamma \\alpha} \\right)\n\t+ \\bar{\\theta}^2 \\left( \\lambda_\\alpha + \\frac{i}{2} \\partial^\\mu \\omega_{\\mu \\alpha} - \\frac{1}{4}\\Box \\kappa_\\alpha \\right)\n\t- i \\theta \\dslash{\\partial} \\bar{\\theta} \\psi_\\alpha - \\notag \\\\\n\t&\\quad - \\frac{i}{2} \\theta^\\gamma \\bar{\\theta}^2 \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} \\left( R_{\\dot{\\beta} \\alpha} + \\frac{i}{2} \\bar{\\dslash{\\partial}}_{\\dot{\\beta}}{}^\\delta M_{\\delta \\alpha} \\right)\n\t- \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\psi_\\alpha \\, .\n\\label{Yantichiral}\n\\end{align}\n\nTo third order in covariant derivatives there is again one chiral and one anti-chiral superfield which are now second-rank spinor fields. The chiral second-rank spinor field is found to be\n\\begin{align}\nZ_{\\gamma \\alpha}\n\t&= - \\frac{1}{4} \\bar{D}^2 D_\\gamma V_\\alpha \\notag \\\\\n\t&= \\left( S_{\\gamma \\alpha} - \\frac{i}{2} \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} N_{\\dot{\\beta} \\alpha} \\right)\n\t+ \\theta^\\beta \\left( 2 \\epsilon_{\\beta \\gamma} \\lambda_\\alpha + \\left( \\sigma^{\\nu \\mu} \\right)_{\\beta \\gamma} \\partial_\\nu \\omega_{\\mu \\alpha} + \\frac{1}{2} \\epsilon_{\\beta \\gamma} \\Box \\kappa_\\alpha \\right) - \\notag \\\\\n\t&\\quad - i \\theta^2 \\left( \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} R_{\\dot{\\beta} \\alpha} - \\frac{i}{2} \\Box M_{\\gamma \\alpha} \\right)\n\t- i \\theta \\dslash{\\partial} \\bar{\\theta} \\left( S_{\\gamma \\alpha} - \\frac{i}{2} \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} N_{\\dot{\\beta} \\alpha} \\right) + \\notag \\\\\n\t&\\quad + \\frac{i}{2} \\theta^2 \\bar{\\theta}^{\\dot{\\delta}} \\dslash{\\partial}^\\beta{}_{\\dot{\\delta}} \\left( 2 \\epsilon_{\\beta \\gamma} \\lambda_\\alpha + \\left( \\sigma^{\\nu \\mu} \\right)_{\\beta \\gamma} \\partial_\\nu \\omega_{\\mu \\alpha} + \\frac{1}{2} \\epsilon_{\\beta \\gamma} \\Box \\kappa_\\alpha \\right) - \\notag \\\\\n\t&\\quad - \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\left( S_{\\gamma \\alpha} - \\frac{i}{2} \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} N_{\\dot{\\beta} \\alpha} \\right) \\, .\n\\label{Zchiral}\n\\end{align}\nA special case arises if the two undotted indices of the second-rank spinor field are contracted. It is then reduced to a scalar superfield\n\\begin{align}\nZ_0\n\t&= \\mathrm{Tr}{\\left( S + \\frac{i}{2} \\dslash{\\partial} N \\right)}\n\t- \\theta^\\beta \\left( 2 \\lambda_\\beta + \\sigma^{\\nu \\mu} \\partial_\\nu \\omega_\\mu + \\frac{1}{2} \\Box \\kappa_\\beta \\right) \n\t+ i \\theta^2 \\mathrm{Tr}{\\left( \\dslash{\\partial} R + \\frac{i}{2} \\Box M \\right)} - \\notag \\\\\n\t&\\quad - i \\theta \\dslash{\\partial} \\bar{\\theta} \\mathrm{Tr}{\\left( S + \\frac{i}{2} \\dslash{\\partial} N \\right)}\n\t- \\frac{i}{2} \\theta^2 \\bar{\\theta}^{\\dot{\\delta}} \\dslash{\\partial}^\\beta{}_{\\dot{\\delta}} \\left( 2 \\lambda_\\beta + \\sigma^{\\nu \\mu} \\partial_\\nu \\omega_\\mu + \\frac{1}{2} \\Box \\kappa_\\beta \\right) - \\notag \\\\\n\t&\\quad - \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\mathrm{Tr}{\\left( S + \\frac{i}{2} \\dslash{\\partial} N \\right)} \\, .\n\\label{Z0chiral}\n\\end{align}\nThe calculations for the anti-chiral second-rank spinor field are nearly identical and it is found to be\n\\begin{align}\nZ'\n\t&= - \\frac{1}{4} D^2 \\bar{D}_{\\dot{\\gamma}} V_\\alpha \\notag \\\\\n\t&= \\left( R_{\\dot{\\gamma} \\alpha} + \\frac{i}{2} \\dslash{\\partial}^\\beta{}_{\\dot{\\gamma}} M_{\\beta \\alpha} \\right)\n\t- \\bar{\\theta}^{\\dot{\\beta}} \\left( 2 \\epsilon_{\\dot{\\beta} \\dot{\\gamma}} \\lambda_\\alpha - \\left( \\bar{\\sigma}^{\\nu \\mu} \\right)_{\\dot{\\beta} \\dot{\\gamma}} \\partial_\\nu \\omega_{\\mu \\alpha} + \\frac{1}{2} \\epsilon_{\\dot{\\beta} \\dot{\\gamma}} \\Box \\kappa_\\alpha \\right) + \\notag \\\\\n\t&\\quad + \\bar{\\theta}^2 \\left( i \\bar{\\dslash{\\partial}}_{\\dot{\\gamma}}{}^\\beta S_{\\beta \\alpha} - \\frac{1}{2} \\Box N_{\\dot{\\gamma} \\alpha} \\right)\n\t+ i \\theta \\dslash{\\partial} \\bar{\\theta} \\left( R_{\\dot{\\gamma} \\alpha} + \\frac{i}{2} \\dslash{\\partial}^\\beta{}_{\\dot{\\gamma}} M_{\\beta \\alpha} \\right) + \\notag \\\\\n\t&\\quad + \\frac{i}{2} \\theta^\\delta \\bar{\\theta}^2 \\dslash{\\partial}_\\delta{}^{\\dot{\\beta}} \\left( 2 \\epsilon_{ \\dot{\\beta} \\dot{\\gamma}}\\lambda_\\alpha - \\left( \\bar{\\sigma}^{\\nu \\mu} \\right)_{\\dot{\\beta} \\dot{\\gamma}} \\partial_\\nu \\omega_{\\mu \\alpha} + \\frac{1}{2} \\epsilon_{\\dot{\\beta} \\dot{\\gamma}} \\Box \\kappa_\\alpha \\right) - \\notag \\\\\n\t&\\quad - \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\left( R_{\\dot{\\gamma} \\alpha} + \\frac{i}{2} \\dslash{\\partial}^\\beta{}_{\\dot{\\gamma}} M_{\\beta \\alpha} \\right) \\, .\n\\label{Zprimeantichiral}\n\\end{align}\nUnlike for the chiral second-rank spinor field, no special case exists for the anti-chiral second-rank spinor field. This is due to the odd number of dotted and undotted indices which makes it impossible to contract the indices to achieve a scalar superfield. At most it can be written as a product of a Pauli-matrix and a vector field.\n\n\\subsubsection{Unitary Supertranslations}\n\\label{SSSUSYtranslation}\nFor the later discussion of the supercurrent and the derivation of the second quantisation of the component fields the superfield variation of the general spinor superfield must be derived. The calculation follows the discussion for the general scalar superfield in \\cite{dick09} and was adapted accordingly to compensate for the additional spinor index.\n\nThe starting point for the derivation of the behaviour of a superfield under unitary supertranslations is the definition of a superspace eigenstate\n\\begin{align}\n\\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, ,\n\\end{align}\nwhich has the eigenvalues\n\\begin{align}\nx^\\mu \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle\n\t&= x_0 \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, , \\\\\n\\theta_\\alpha \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle\n\t&= \\theta_{0 \\alpha} \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, , \\\\\n\\bar{\\theta}_{\\dot{\\alpha}} \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle\n\t&= \\bar{\\theta}_{0 \\dot{\\alpha}} \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, .\n\\end{align}\nHere $\\theta_\\alpha$, $\\bar{\\theta}_{\\dot{\\alpha}}$, and $x^\\mu$ are operators acting on the superspace eigenstate while the eigenvalues are denoted by a subscript $0$ for the original eigenstate and with a prime for the translated state. Therefore, a state that is shifted under unitary supertranslations can be written as\n\\begin{align}\n\\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, ,\n\\end{align}\nwhere the prefactors $a$, $b$, and $c$ still need to be determined. An arbitrary operator $\\mathcal{O}$ acting on the shifted state can be expressend as\n\\begin{align}\n\\mathcal{O} \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\exp{\\left( - i a y \\cdot P - i b \\zeta Q - i c \\bar{Q} \\bar{\\zeta} \\right)} \\times \\notag \\\\\n\t& \\quad \\times \\mathcal{O} \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, .\n\\end{align}\nUsing the Cambell-Baker-Hausdorff formula\n\\begin{align}\ne^{- i G \\lambda} \\mathcal{O} e^{i G \\lambda}\n\t&= \\sum\\limits_{j} \\left( - i \\lambda \\right)^j \\stackrel{j}{\\left[ \\right.} \\!\\!\\! \\left. G , \\mathcal{O} \\right]\n\\end{align}\nthis product of operators can be decomposed into an infinite sum of commutators\n\\begin{align}\n\\mathcal{O} \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\times \\notag \\\\\n\t&\\quad \\times \\sum\\limits_{j} \\left( - i \\lambda \\right)^j \\stackrel{j}{\\left[ \\right.} \\!\\!\\! \\left. a y \\cdot P + b \\zeta Q + c \\bar{Q} \\bar{\\zeta} , \\mathcal{O} \\right] \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, .\n\\end{align}\nTo evaluate the commutators it proves useful to utilise the following three commutators and anticommutators\n\\begin{align}\n\\left\\{ \\partial_\\beta , \\theta_\\alpha \\right\\}\n\t&= \\epsilon_{\\beta \\alpha} \\, , \\\\\n\\left\\{ \\partial_{\\dot{\\beta}} , \\bar{\\theta}_{\\dot{\\alpha}} \\right\\}\n\t&= \\epsilon_{\\dot{\\alpha} \\dot{\\beta}} \\, , \\\\\n\\left[ P_\\nu , x_\\mu \\right]\n\t&= i \\eta_{\\nu \\mu} \\, .\n\\end{align}\n\nFor the operator $\\theta$ acting on the translated eigenstate it is found that\n\\begin{align}\n\\theta_\\alpha \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\times \\notag \\\\\n\t&\\quad \\times \\sum\\limits_{j} \\left( - i \\lambda \\right)^j \\stackrel{j}{\\left[ \\right.} \\!\\!\\! \\left. a y \\cdot P + b \\zeta Q + c \\bar{Q} \\bar{\\zeta} , \\theta \\right] \\left| x , \\theta , \\bar{\\theta} \\right\\rangle \\, ,\n\\end{align}\nwhere the $j$-th commutator has to be derived recursively. Conveniently, the first commutator is given by\n\\begin{align}\n\\left[ a y^\\mu P_\\mu + b \\zeta^\\beta Q_\\beta + c \\bar{Q}_{\\dot{\\beta}} \\bar{\\zeta}^{\\dot{\\beta}} , \\theta_\\alpha \\right]\n\t&= i b \\zeta_\\alpha \\, .\n\\end{align}\nThis implies that the second commutator vanishes. Therefore, all higher order contributions to the infinite sum must vanish identically as well and the eigenvalue of the shifted state is\n\\begin{align}\n\\theta'_\\alpha \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\left( \\theta_{0 \\alpha} + b \\zeta_\\alpha \\right) \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle \\, .\n\\end{align}\n\nA similar calculation can be repeated for the operator $\\bar{\\theta}$. It is found that\n\\begin{align}\n\\bar{\\theta}_{\\dot{\\alpha}} \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\times \\notag \\\\\n\t&\\quad \\times \\sum\\limits_{j} \\left( - i \\lambda \\right)^j \\stackrel{j}{\\left[ \\right.} \\!\\!\\! \\left. a y \\cdot P + b \\zeta Q + c \\bar{Q} \\bar{\\zeta} , \\bar{\\theta}_{\\dot{\\alpha}} \\right] \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, .\n\\end{align}\nAgain, the $j$-th commutator must be calculated recursively starting with the first order commutator\n\\begin{align}\n\\left[ a y \\cdot P + b \\zeta^\\beta Q_\\beta + c \\bar{Q}_{\\dot{\\beta}} \\bar{\\zeta}^{\\dot{\\beta}} , \\bar{\\theta}_{\\dot{\\alpha}} \\right]\n\t&= i c \\bar{\\zeta}_{\\dot{\\alpha}} \\, .\n\\end{align}\nLike in the previous case this result implies that the second commutator vanishes identically and the eigenvalue of the shifted state is \n\\begin{align}\n\\bar{\\theta}'_{\\dot{\\alpha}} \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\left( \\bar{\\theta}_{0 \\dot{\\alpha}} + c \\bar{\\zeta}_{\\dot{\\alpha}} \\right) \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle \\, .\n\\end{align}\n\nFinally, the behaviour of the eigenvalue of the operator $x^\\mu$ is analysed\n\\begin{align}\nx^\\mu \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\exp{\\left( i a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} \\right)} \\times \\notag \\\\\n\t&\\quad \\times \\sum\\limits_{j} \\left( - i \\lambda \\right)^j \\stackrel{j}{\\left[ \\right.} \\!\\!\\! \\left. a y \\cdot P + i b \\zeta Q + i c \\bar{Q} \\bar{\\zeta} , x^\\mu \\right] \\left| x_0 , \\theta_0 , \\bar{\\theta}_0 \\right\\rangle \\, .\n\\end{align}\nThe first commutator is found to be\n\\begin{align}\n\\left[ a y^\\nu P_\\nu + b \\zeta^\\alpha Q_\\alpha + c \\bar{Q}_{\\dot{\\alpha}} \\bar{\\zeta}^{\\dot{\\alpha}} , x^\\mu \\right]\n\t&= i a y^\\mu\n\t- b \\zeta \\sigma^\\mu \\bar{\\theta}\n\t+ c \\theta \\sigma^\\mu \\bar{\\zeta} \\, .\n\\end{align}\nOn the first glance it seems as if the series expansion doesn't terminate after the first commutator. However, the explicit calculation of the second commutator reveals that it vanishes identically\n\\begin{align}\n\\stackrel{2}{\\left[ \\right.} \\!\\!\\! \\left. a y^\\nu P_\\nu + b \\zeta^\\alpha Q_\\alpha + c \\bar{Q}_{\\dot{\\alpha}} \\bar{\\zeta}^{\\dot{\\alpha}} , x^\\mu \\right]\n\t&= 0 \\, .\n\\end{align}\nThis terminates the infinite series and the eigenvalue for the operator $x^\\mu$ acting on the translated state is given by\n\\begin{align}\nx^\\mu \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\left( x_0^\\mu + a y^\\mu + i \\left( b \\zeta \\sigma^\\mu \\bar{\\theta}_0 - c \\theta_0 \\sigma^\\mu \\bar{\\zeta} \\right) \\right) \\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle \\, .\n\\end{align}\n\nCombining the results for the operators $\\theta$, $\\bar{\\theta}$, and $x^\\mu$ yields a translated superspace eigenstate of\n\\begin{align}\n\\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\left| x_0 + a y_0 + i \\left( b \\zeta \\sigma \\bar{\\theta}_0 - c \\theta_0 \\sigma \\bar{\\zeta} \\right) , \\theta_0 + b \\zeta , \\bar{\\theta}_0 + c \\bar{\\zeta} \\right\\rangle \\, ,\n\\end{align}\nwhere the prefactors $a$, $b$, and $c$ are still arbitrary. As a convention it is assumed that the discussion is restricted to pure superspace translations for which the spatial translation vanishes and thus $a y_0 =0$. Furthermore, the translations of the superspace coordinates $\\theta$ and $\\bar{\\theta}$ are chosen to be positive which results in $b = c = 1$. This results in a relation between the original and shifted state of the following form\n\\begin{align}\n\\left| x' , \\theta' , \\bar{\\theta}' \\right\\rangle\n\t&= \\left| x + i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) , \\theta + \\zeta , \\bar{\\theta} + \\bar{\\zeta} \\right\\rangle\n\t= \\exp{\\left( i \\zeta Q + i \\bar{Q} \\bar{\\zeta} \\right)} \\left| x , \\theta , \\bar{\\theta} \\right\\rangle \\, ,\n\\end{align}\nwhere the subscript $0$ was dropped as it is no longer necessary to distinguish between operators and eigenvalues. The eigenstate at the shifted superspace coordinates is expressed in terms of the superspace coordinates of the original superspace eigenstate. It can be seen that a superspace translation, unlike a translation of normal fields, not only induces a spatial translation, but also results in a shift of the superspace coordinates $\\theta$ and $\\bar{\\theta}$.\n\nNow that the behaviour of a superspace eigenstate under unitary supertranslation is known, the calculation of the translated general spinor superfield is straightforward\n\\begin{align}\nV'_\\alpha{\\left( x , \\theta , \\bar{\\theta} \\right)}\n\t&= \\left\\langle x , \\theta , \\bar{\\theta} \\right| \\exp{\\left( i \\zeta Q + i \\bar{Q} \\bar{\\zeta} \\right)} \\left| V_\\alpha \\right\\rangle \\notag \\\\\n\t&= \\left\\langle x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) , \\theta - \\zeta , \\bar{\\theta} - \\bar{\\zeta} \\right| \\left. V_\\alpha \\right\\rangle \\notag \\\\\n\t&= V_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) , \\theta - \\zeta , \\bar{\\theta} - \\bar{\\zeta} \\right)} \\, .\n\\end{align}\nAs for the superspace eigenstate, a unitary supertranslation acting on a general superfield induces a spatial translation as well as a shift of superspace coordinates. In terms of the component fields the translated superfield can then be written as\n\\begin{align}\nV'_\\alpha{\\left( x , \\theta , \\bar{\\theta} \\right)}\n\t&= \\kappa_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)}\n\t+ \\left( \\theta^\\beta - \\zeta^\\beta \\right) M_{\\beta \\alpha}{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} - \\notag \\\\\n\t&\\quad - \\left( \\bar{\\theta}^{\\dot{\\beta}} - \\bar{\\zeta}^{\\dot{\\beta}} \\right) N_{\\dot{\\beta}\\alpha}{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)}\n\t+ \\left( \\theta - \\zeta \\right)^2 \\psi_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\left( \\bar{\\theta} - \\bar{\\zeta} \\right)^2 \\chi_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\left( \\theta - \\zeta \\right) \\sigma^\\mu \\left( \\bar{\\theta} - \\bar{\\zeta} \\right) \\omega_{\\mu \\alpha}{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} - \\notag \\displaybreak[3] \\\\\n\t&\\quad - \\left( \\theta - \\zeta \\right)^2 \\left( \\bar{\\theta}^{\\dot{\\beta}} - \\bar{\\zeta}^{\\dot{\\beta}} \\right) R_{\\dot{\\beta} \\alpha}{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\left( \\bar{\\theta} - \\bar{\\zeta} \\right)^2 \\left( \\theta^\\beta - \\zeta^\\beta \\right) S_{\\beta \\alpha}{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} + \\notag \\\\\n\t&\\quad + \\left( \\theta - \\zeta \\right)^2 \\left( \\bar{\\theta} - \\bar{\\zeta} \\right)^2 \\lambda_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)} \\, .\n\\label{SUSYvariationTaylor}\n\\end{align}\nTo express the translated component fields in terms of the component fields at the original superspace coordinates a Taylor expansion of the component fields can be used. In the present case an expansion up to first order in the transformation parameters $\\zeta$ and $\\bar{\\zeta}$ of the form\n\\begin{align}\n\\kappa_\\alpha{\\left( x - i \\left( \\zeta \\sigma \\bar{\\theta} - \\theta \\sigma \\bar{\\zeta} \\right) \\right)}\n\t&\\approx \\kappa_\\alpha{\\left( x \\right)}\n\t- i \\left( \\zeta \\sigma^\\nu \\bar{\\theta} - \\theta \\sigma^\\nu \\bar{\\zeta} \\right) \\partial_\\nu \\kappa_\\alpha{\\left( x \\right)}\n\\end{align}\nis sufficient. After appropriately rewriting equation (\\ref{SUSYvariationTaylor}), neglecting all terms of second or higher order in the transformation parameters $\\zeta$ and $\\bar{\\zeta}$, and collecting the terms with corresponding orders in the Grassmann variables $\\theta$ and $\\bar{\\theta}$ the shifted superfield is given by\n\\begin{align}\nV'_\\alpha{\\left( x , \\theta , \\bar{\\theta} \\right)}\n\t&= \\kappa_\\alpha{\\left( x \\right)}\n\t- \\zeta^\\beta M_{\\beta \\alpha}{\\left( x \\right)}\n\t+ \\bar{\\zeta}^{\\dot{\\beta}} N_{\\dot{\\beta}\\alpha}{\\left( x \\right)} + \\notag \\\\\n\t&\\quad + \\theta^\\beta \\left( M_{\\beta \\alpha}{\\left( x \\right)}\n\t+ i \\left( \\sigma^\\mu \\right)_{\\beta \\dot{\\gamma}} \\bar{\\zeta}^{\\dot{\\gamma}} \\partial_\\mu \\kappa_\\alpha{\\left( x \\right)} \n\t- 2 \\zeta_\\beta \\psi_\\alpha{\\left( x \\right)}\n\t- \\left( \\sigma^\\mu \\right)_{\\beta \\dot{\\gamma}} \\bar{\\zeta}^{\\dot{\\gamma}} \\omega_{\\mu \\alpha}{\\left( x \\right)} \\right) - \\notag \\displaybreak[3] \\\\\n\t&\\quad - \\bar{\\theta}^{\\dot{\\beta}} \\left( N_{\\dot{\\beta}\\alpha}{\\left( x \\right)}\n\t- i \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\beta} \\gamma} \\zeta^\\gamma \\partial_\\mu \\kappa_\\alpha{\\left( x \\right)}\n\t- 2 \\bar{\\zeta}_{\\dot{\\beta}} \\chi_\\alpha{\\left( x \\right)}\n\t- \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\beta} \\gamma} \\zeta^\\gamma \\omega_{\\mu \\alpha}{\\left( x \\right)} \\right) + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\theta^2 \\left( \\psi_\\alpha{\\left( x \\right)}\n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\delta}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\delta}}{}^\\beta \\partial_\\mu M_{\\beta \\alpha}{\\left( x \\right)} \n\t+ \\bar{\\zeta}^{\\dot{\\beta}} R_{\\dot{\\beta} \\alpha}{\\left( x \\right)} \\right) + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\bar{\\theta}^2 \\left( \\chi_\\alpha{\\left( x \\right)}\n\t- \\frac{i}{2} \\zeta^\\delta \\left( \\sigma^\\mu \\right)_\\delta{}^{\\dot{\\beta}} \\partial_\\mu N_{\\dot{\\beta}\\alpha}{\\left( x \\right)} \n\t- \\zeta^\\beta S_{\\beta \\alpha}{\\left( x \\right)} \\right) + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\theta \\sigma^\\mu \\bar{\\theta} \\left( \\omega_{\\mu \\alpha}{\\left( x \\right)}\n\t+ \\frac{i}{2} \\zeta^\\delta \\left( \\sigma^\\nu \\bar{\\sigma}_\\mu \\right)_\\delta{}^\\beta \\partial_\\nu M_{\\beta \\alpha}{\\left( x \\right)}\n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\delta}} \\left( \\bar{\\sigma}^\\nu \\sigma_\\mu \\right)_{\\dot{\\delta}}{}^{\\dot{\\beta}} \\partial_\\nu N_{\\dot{\\beta}\\alpha}{\\left( x \\right)} - \\right. \\notag \\displaybreak[3] \\\\\n\t&\\qquad \\left. - \\zeta_\\gamma \\left( \\sigma_\\mu \\right)^{\\gamma \\dot{\\beta}} R_{\\dot{\\beta} \\alpha}{\\left( x \\right)}\n\t+ \\bar{\\zeta}_{\\dot{\\gamma}} \\left( \\bar{\\sigma}_\\mu \\right)^{\\dot{\\gamma} \\beta} S_{\\beta \\alpha}{\\left( x \\right)} \\right) - \\notag \\displaybreak[3] \\\\\n\t&\\quad - \\theta^2 \\bar{\\theta}^{\\dot{\\beta}} \\! \\left( \\! R_{\\dot{\\beta} \\alpha}{\\left( x \\right)} \n\t- i \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\beta} \\gamma} \\zeta^\\gamma \\partial_\\mu \\psi_\\alpha{\\left( x \\right)}\n\t+ \\frac{i}{2} \\left( \\bar{\\sigma}^\\mu \\sigma^\\nu \\right)_{\\dot{\\beta} \\dot{\\epsilon}} \\bar{\\zeta}^{\\dot{\\epsilon}} \\partial_\\nu \\omega_{\\mu \\alpha}{\\left( x \\right)}\n\t- 2 \\bar{\\zeta}_{\\dot{\\beta}} \\lambda_\\alpha{\\left( x \\right)} \\! \\right) \\! + \\notag \\displaybreak[3] \\\\\n\t&\\quad + \\bar{\\theta}^2 \\theta^\\beta \\! \\left( \\! S_{\\beta \\alpha}{\\left( x \\right)}\n\t+ i \\left( \\sigma^\\mu \\right)_{\\beta \\dot{\\gamma}} \\bar{\\zeta}^{\\dot{\\gamma}} \\partial_\\mu \\chi_\\alpha{\\left( x \\right)}\n\t+ \\frac{i}{2} \\left( \\sigma^\\mu \\bar{\\sigma}^\\nu \\right)_{\\beta \\delta} \\zeta^\\delta \\partial_\\nu \\omega_{\\mu \\alpha}{\\left( x \\right)}\n\t- 2 \\zeta_\\beta \\lambda_\\alpha{\\left( x \\right)} \\! \\right) \\! + \\notag \\\\\n\t&\\quad + \\theta^2 \\bar{\\theta}^2 \\left( \\lambda_\\alpha{\\left( x \\right)}\n\t- \\frac{i}{2} \\zeta^\\gamma \\left( \\sigma^\\mu \\right)_{\\gamma}{}^{\\dot{\\beta}} \\partial_\\mu R_{\\dot{\\beta} \\alpha}{\\left( x \\right)}\n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\delta}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\delta}}{}^\\beta \\partial_\\mu S_{\\beta \\alpha}{\\left( x \\right)} \\right) \\, .\n\\label{SUSYvariation}\n\\end{align}\nThe variation of the general spinor superfield is then defined as the difference between the translated superfield and the superfield at the original superspace coordinates\n\\begin{align}\n\\delta V_\\alpha{\\left( x , \\theta , \\bar{ \\theta} \\right)}\n\t&= V'_\\alpha{\\left( x , \\theta , \\bar{ \\theta} \\right)} - V_\\alpha{\\left( x , \\theta , \\bar{ \\theta} \\right)} \\, .\n\\end{align}\nTherefore, the variation of the component fields can be extracted immediately from equation (\\ref{SUSYvariation})\n\\begin{align}\n\\delta \\kappa_\\alpha\n\t&= - \\zeta^\\beta M_{\\beta \\alpha}{\\left( x \\right)}\n\t+ \\bar{\\zeta}^{\\dot{\\beta}} N_{\\dot{\\beta}\\alpha}{\\left( x \\right)} \\, , \\label{deltakappa} \\displaybreak[3] \\\\\n\\delta M_{\\beta \\alpha}\n\t&= - 2 \\zeta_\\beta \\psi_\\alpha{\\left( x \\right)}\n\t+ i \\bar{\\zeta}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\gamma} \\beta} \\partial_\\mu \\kappa_\\alpha{\\left( x \\right)} \n\t- \\bar{\\zeta}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\gamma} \\beta} \\omega_{\\mu \\alpha}{\\left( x \\right)} \\, , \\label{deltaM} \\displaybreak[3] \\\\\n\\delta N_{\\dot{\\beta}\\alpha}\n\t&= - 2 \\bar{\\zeta}_{\\dot{\\beta}} \\chi_\\alpha{\\left( x \\right)}\n\t- i \\zeta^\\gamma \\left( \\sigma^\\mu \\right)_{\\gamma \\dot{\\beta}} \\partial_\\mu \\kappa_\\alpha{\\left( x \\right)}\n\t- \\zeta^\\gamma \\left( \\sigma^\\mu \\right)_{\\gamma \\dot{\\beta}} \\omega_{\\mu \\alpha}{\\left( x \\right)} \\, , \\label{deltaN} \\displaybreak[3] \\\\\n\\delta \\psi_\\alpha\n\t&= \\bar{\\zeta}^{\\dot{\\beta}} R_{\\dot{\\beta} \\alpha}{\\left( x \\right)} \n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\beta}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\beta}}{}^\\gamma \\partial_\\mu M_{\\gamma \\alpha}{\\left( x \\right)} \\, , \\label{deltapsi} \\displaybreak[3] \\\\\n\\delta \\chi_\\alpha\n\t&= - \\zeta^\\beta S_{\\beta \\alpha}{\\left( x \\right)}\n\t- \\frac{i}{2} \\zeta^\\beta \\left( \\sigma^\\mu \\right)_\\beta{}^{\\dot{\\gamma}} \\partial_\\mu N_{\\dot{\\gamma} \\alpha}{\\left( x \\right)} \\, , \\label{deltachi} \\displaybreak[3] \\\\\n\\delta \\omega_{\\mu \\alpha}\n\t&= \\zeta^\\beta \\left( \\sigma_\\mu \\right)_\\beta{}^{\\dot{\\gamma}} R_{\\dot{\\gamma} \\alpha}{\\left( x \\right)}\n\t+ \\frac{i}{2} \\zeta^\\beta \\left( \\sigma^\\nu \\bar{\\sigma}_\\mu \\right)_\\beta{}^\\gamma \\partial_\\nu M_{\\gamma \\alpha}{\\left( x \\right)} - \\notag \\\\\n\t&\\quad - \\bar{\\zeta}^{\\dot{\\beta}} \\left( \\bar{\\sigma}_\\mu \\right)_{\\dot{\\beta}}{}^\\gamma S_{\\gamma \\alpha}{\\left( x \\right)} \n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\beta}} \\left( \\bar{\\sigma}^\\nu \\sigma_\\mu \\right)_{\\dot{\\beta}}{}^{\\dot{\\gamma}} \\partial_\\nu N_{\\dot{\\gamma}\\alpha}{\\left( x \\right)} \\label{deltaomega} \\, , \\displaybreak[3] \\\\\n\\delta R_{\\dot{\\beta} \\alpha}\n\t&= - 2 \\bar{\\zeta}_{\\dot{\\beta}} \\lambda_\\alpha{\\left( x \\right)}\n\t- i \\zeta^\\gamma \\left( \\sigma^\\mu \\right)_{\\gamma \\dot{\\beta}} \\partial_\\mu \\psi_\\alpha{\\left( x \\right)}\n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}^\\nu \\sigma^\\mu \\right)_{\\dot{\\gamma} \\dot{\\beta}} \\partial_\\nu \\omega_{\\mu \\alpha}{\\left( x \\right)} \\, , \\label{deltaR} \\displaybreak[3] \\\\\n\\delta S_{\\beta \\alpha}\n\t&= - 2 \\zeta_\\beta \\lambda_\\alpha{\\left( x \\right)} \n\t+ i \\bar{\\zeta}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\gamma} \\beta} \\partial_\\mu \\chi_\\alpha{\\left( x \\right)}\n\t- \\frac{i}{2} \\zeta^\\gamma \\left( \\sigma^\\nu \\bar{\\sigma}^\\mu \\right)_{\\gamma \\beta} \\partial_\\nu \\omega_{\\mu \\alpha}{\\left( x \\right)} \\, , \\label{deltaS} \\displaybreak[3] \\\\\n\\delta \\lambda_\\alpha\n\t&= - \\frac{i}{2} \\zeta^\\beta \\left( \\sigma^\\mu \\right)_{\\beta}{}^{\\dot{\\gamma}} \\partial_\\mu R_{\\dot{\\gamma} \\alpha}{\\left( x \\right)}\n\t- \\frac{i}{2} \\bar{\\zeta}^{\\dot{\\beta}} \\left( \\bar{\\sigma}^\\mu \\right)_{\\dot{\\beta}}{}^\\gamma \\partial_\\mu S_{\\gamma \\alpha}{\\left( x \\right)} \\, . \\label{deltalambda}\n\\end{align}\nThese results then imply the variation of the on-shell component fields. After eliminating the auxiliary fields and using the definition of the component fields $\\tilde{R}$ and $\\tilde{S}$ from equations (\\ref{tildeS}) and (\\ref{tildeR}) in section \\ref{SSLmassiveonshell} the variation of the component field of the on-shell Lagrangian are found to be\n\\begin{align}\n\\delta \\psi_\\alpha\n\t&= \\bar{\\zeta}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha} \\, , \\displaybreak[3] \\label{deltapsionshell}\\\\\n\\delta \\chi_\\alpha\n\t&= - \\zeta^\\beta \\tilde{S}_{\\beta \\alpha} \\, , \\displaybreak[3] \\label{deltachionshell}\\\\\n\\delta \\tilde{R}_{\\dot{\\beta} \\alpha}\n\t&= m \\bar{\\zeta}_{\\dot{\\beta}} \\chi_\\alpha\n\t- 2 i \\zeta^\\gamma \\dslash{\\partial}_{\\gamma \\dot{\\beta}} \\psi_\\alpha \\, , \\displaybreak[3] \\label{deltaRonshell}\\\\\n\\delta \\tilde{S}_{\\beta \\alpha}\n\t&= m \\zeta_\\beta \\psi_\\alpha\n\t+ 2 i \\bar{\\zeta}^{\\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma} \\beta} \\chi_\\alpha \\, . \\label{deltaSonshell}\n\\end{align}\n\n\\subsection{Constructing a Model Based on the General Spinor Superfield}\n\\label{SSLchi}\n\\begin{TABLE}[t]{\n\\begin{tabular}{r|c|l}\nProduct & Mass Dimension & Contributions \\\\\n\\hline\n$V V$ & $\\mathrm{dim}{\\left( V V \\right)} = 0$ & $\\left( m^2 V V \\right)_D$ \\\\\n\\hline\n$X V$ & $\\mathrm{dim}{\\left( X V \\right)} = 1$ & $\\left( m X V \\right)_D$ , $\\left( m Y V \\right)_D$\\\\\n$D V D V$ & $\\mathrm{dim}{\\left( D V D V \\right)} = 1$ & $\\left( m D V D V \\right)_D$ , $\\left( m \\bar{D} V \\bar{D} V \\right)_D$ \\\\\n$V X$ & $\\mathrm{dim}{\\left( V X \\right)} = 1$ & $\\left( m V X \\right)_D$ , $\\left( m V Y \\right)_D$ \\\\\n\\hline\n$D Z V$ & $\\mathrm{dim}{\\left( D Z V \\right)} = 2$ & $\\left( D Z V \\right)_D$ , $\\left( \\bar{D} Z' V \\right)_D$\\\\\n$Z D V$ & $\\mathrm{dim}{\\left( Z D V \\right)} = 2$ & $\\left( Z D V \\right)_D$ , $\\left( Z' \\bar{D} V \\right)_D$\\\\\n$X X$ & $\\mathrm{dim}{\\left( X X \\right)} = 2$ & $\\left( m X X \\right)_F$ , $\\left( m Y Y \\right)_F$ , $\\left( X Y \\right)_D$ , $\\left( Y X \\right)_D$ \\\\\n$D V Z$ & $\\mathrm{dim}{\\left( D V Z \\right)} = 2$ & $\\left( D V Z \\right)_D$ , $\\left( \\bar{D} V Z' \\right)_D$ \\\\\n$V D Z$ & $\\mathrm{dim}{\\left( V D Z \\right)} = 2$ & $\\left( V D Z \\right)_D$ , $\\left( V \\bar{D} Z' \\right)_D$ \\\\\n\\hline\n$D Z X$ & $\\mathrm{dim}{\\left( D Z X \\right)} = 3$ & mass dimension too big for D-component \\\\\n$Z Z$ & $\\mathrm{dim}{\\left( Z Z \\right)} = 3$ & $\\left( Z Z \\right)_F$ , $\\left( Z' Z' \\right)_F$ \\\\\n$X D Z$ & $\\mathrm{dim}{\\left( X D Z \\right)} = 3$ & mass dimension too big for D-component\n\\end{tabular}\n\\caption{Possible contributions to the Lagrangian for $\\chi$ as fermionic field with mass dimension one based on the general spinor superfield. The first two columns specify the product and mass dimensionality using the general superfield and chiral superfields only. The third column then summarises all possible contributions corresponding to the product outlined in the first column including the contributions that arise from the antichiral superfields.}\n\\label{TChiDM}}\n\\end{TABLE}\nIf $\\chi$ is identified with the fermionic field with mass dimension one it can be shown that\n\\begin{align}\n\\mathrm{dim}{\\left( V_\\alpha \\right)}\n\t&= 0 \\, , \\quad\n\\mathrm{dim}{\\left( X_\\alpha \\right)}\n\t= \\mathrm{dim}{\\left( Y_\\alpha \\right)}\n\t= 1 \\, , \\quad\n\\mathrm{dim}{\\left( Z_{\\gamma \\alpha} \\right)}\n\t= \\mathrm{dim}{\\left( Z'_{\\dot{\\gamma} \\alpha} \\right)}\n\t= \\frac{3}{2} \\, .\n\\end{align}\nIt is interesting to note that for $\\chi$ as fermionic field with mass dimension one the mass dimension of the general spinor superfield is $1\/2$ lower than for the previous approach based on the the general scalar superfield. This indicates that the structure of this model is richer as there are more allowed contributions to the Lagrangian. For convenience the discussion is resticted to the unbarred superfields while the hermitian conjugates contribute to the Lagrangian as well.\n\nThe contributions to the Lagrangian have to satisfy the same basic requirements as outlined in Section \\ref{SSnonkinSUSYL} -- no uncontracted spinor indices, positive mass dimension for structure constants, and appropriate mass dimension for contribution via $D$- or $F$-component. All conceivable terms that are in agreement with these conditions are then summarised in table \\ref{TChiDM}. It contains more possible contributions to the Lagrangian which are now divided into four groups. The additional group is due to the lower mass dimensionality of the general spinor superfield which allows a spectrum for the mass dimension ranging from 0 and 3.\n\nThe first group which contains only one term, the product of two general spinor superfields without additional covariant derivatives, has mass dimension 0. For symmetry reasons the only possible contribution to the Lagrangian is a mass term via the D-component.\n\nThe second group containing all terms with mass dimension 1 has 6 possible terms. As $V$ and $D V$ are neither chiral nor anti-chiral all six terms are contributions to the mass term via the D-component.\n\nIn the third group all terms with mass dimension 2 are grouped together. It contains 12 terms of which 10 are contributions to the kinetic term via the D-component while 2 are contributions to the mass term via the F-component. It is worth mentioning that this is the only group that contains contributions to the kinetic term as well as contributions to the mass term. Even more intriguing is the fact that a superfield product of the form $X_1 X_2$ where $X_1$ and $X_2$ can be either chiral or antichiral is able to produce both kind of contributions.\n\nFinally, the fourth group which contains all terms with mass dimension 3 has two entries. Due to the mass dimension only contributions via the F-component are possible which means that both terms can only contribute to the kinetic term.\n\nIt is interesting to note that some of the terms contained in table \\ref{TChiDM}, namely $D V D V$ and $X V$ were previously considered by Gates and Siegel \\cite{gates80,gates81}. However, in these articles the authors assume the commonly used mass dimensinos for fermionic and bosonic fields. This has two consequences. First, all kinetic terms in \\cite{gates80,gates81} become mass terms in the present scenario due to the change of mass dimensionality. Second, all contributions summarised in groups three and four of table \\ref{TChiDM}, and therefore the products of chiral superfields $X X$ and $Y Y$ do not exist without redefinition of mass dimensions to accommodate fermionic fields with mass dimension one and thus were not considered before.\n\n\\subsection{The On-shell Lagrangian}\n\\label{SSLmassiveonshell}\nA supersymmetric Lagrangian can be constructed by combining contributions that were found in the dimensional analysis of the previous section. It was mentioned earlier that the first two groups of table \\ref{TChiDM} with mass dimension 0 and 1 respectively contain only contributions to the mass term while the group with mass dimension 3 only produces contributions to the kinetic term. Therefore, the following discussion for the construction of a supersymmetric Lagrangian will be resticted to the third group which is the only one containing kinetic as well as mass terms. This limits the number of superfield products that need to be calculated to 12. Explicit calculations reveal that this number can be narrowed down even further. It can be shown that the terms $\\left( D Z V \\right)_D$, $\\left( Z D V \\right)_D$, $\\left( X Y \\right)_D$, $\\left( D V Z \\right)_D$, $\\left( V D Z \\right)_D$ are identical up to a prefactor. Therefore, only the D-component of the terms $X Y$ and $Y X$ will be considered for the kinetic term. The Lagrangian can then be written in a very compact form\n\\begin{align}\n\\mathcal{L}\n\t&= \\left( X Y \\right)_D + \\left( Y X \\right)_D + \\frac{m}{2} \\left( X X \\right)_F + \\frac{m}{2} \\left( Y Y \\right)_F + h.c. \\, .\n\\label{Lcompact}\n\\end{align}\nFrom the previous derivation of the chiral superfield $X$ in equation (\\ref{Xchiral}) and the anti-chiral superfield $Y$ in equation (\\ref{Yantichiral}) it can be seen that the component fields $N$, $M$, $S$, $R$, $\\lambda$, and $\\kappa$ are not independent. Therefore, it is convenient to introduce the new component fields\n\\begin{align}\n\\tilde{S}_{\\beta \\alpha}\n\t&= S_{\\beta \\alpha} + \\frac{i}{2} \\dslash{\\partial}_\\beta{}^{\\dot{\\gamma}} N_{\\dot{\\gamma} \\alpha} \\, , \\label{tildeS} \\\\\n\\tilde{R}_{\\dot{\\beta} \\alpha} \n\t&= R_{\\dot{\\beta} \\alpha} - \\frac{i}{2} \\bar{\\dslash{\\partial}}_{\\dot{\\beta}}{}^\\tau M_{\\tau \\alpha} \\, , \\label{tildeR} \\\\\n\\tilde{\\lambda}_\\alpha\n\t&= \\lambda_\\alpha - \\frac{1}{4} \\Box \\kappa_\\alpha \\, . \\label{tildelambda}\n\\end{align}\nFurthermore, it can be seen that the spinor-vector field $\\omega^\\mu_\\alpha$ is always contracted with a four derivative which is simplified by defining\n\\begin{align}\n\\tilde{\\omega}_\\alpha \n\t&= \\partial^\\mu \\omega_{\\mu \\alpha} \\, . \\label{tildeomega}\n\\end{align}\nThe chiral and anti-chiral superfields can then be written as\n\\begin{align}\nX_\\alpha\n\t&= \\chi_\\alpha\n\t+ \\theta^\\beta \\tilde{S}_{\\beta \\alpha}\n\t+ \\theta^2 \\left( \\tilde{\\lambda}_\\alpha + \\frac{i}{2} \\tilde{\\omega}_\\alpha \\right)\n\t- i \\theta \\dslash{\\partial} \\bar{\\theta} \\chi_\\alpha\n\t+ \\frac{i}{2} \\theta^2 \\bar{\\theta}^{\\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma}}{}^\\beta \\tilde{S}_{\\beta \\alpha}\n\t- \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\chi_\\alpha \\, , \\\\\nY_\\alpha\n\t&= \\psi_\\alpha\n\t- \\bar{\\theta}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha}\n\t+ \\bar{\\theta}^2 \\left( \\tilde{\\lambda}_\\alpha - \\frac{i}{2} \\tilde{\\omega}_\\alpha \\right)\n\t+ i \\theta \\dslash{\\partial} \\bar{\\theta} \\psi_\\alpha\n\t+ \\frac{i}{2} \\theta^\\gamma \\bar{\\theta}^2 \\dslash{\\partial}_\\gamma{}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha}\n\t- \\frac{1}{4} \\theta^2 \\bar{\\theta}^2 \\Box \\psi_\\alpha \\, .\n\\end{align}\nThis can be used to calculate the contributions to the Lagrangian outlined in equation (\\ref{Lcompact})\n\\begin{align}\n\\left( X^\\alpha X_\\alpha \\right)_F\n\t&= \\chi \\tilde{\\lambda}\n\t+ \\frac{i}{2} \\chi \\tilde{\\omega}\n\t- \\frac{1}{2} \\mathrm{Tr}{\\left( \\tilde{S}^T \\tilde{S} \\right)}\n\t+ \\tilde{\\lambda} \\chi\n\t+ \\frac{i}{2} \\tilde{\\omega} \\chi \\, , \\displaybreak[3] \\\\\n\\left( Y^\\alpha Y_\\alpha \\right)_F\n\t&= \\psi \\tilde{\\lambda}\n\t- \\frac{i}{2} \\psi \\tilde{\\omega}\n\t- \\frac{1}{2} \\mathrm{Tr}{\\left( \\tilde{R}^T \\tilde{R} \\right)}\n\t+ \\tilde{\\lambda} \\psi\n\t- \\frac{i}{2} \\tilde{\\omega} \\psi \\, , \\displaybreak[3] \\\\\n\\left( X^\\alpha Y_\\alpha \\right)_D\n\t&= \\partial_\\mu \\chi \\partial^\\mu \\psi\n\t+ \\tilde{\\lambda} \\tilde{\\lambda}\n\t- \\frac{i}{2} \\tilde{\\lambda} \\tilde{\\omega}\n\t+ \\frac{i}{2} \\tilde{\\omega} \\tilde{\\lambda}\n\t+ \\frac{1}{4} \\tilde{\\omega} \\tilde{\\omega}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{S}^T \\dslash{\\partial} \\tilde{R} \\right)} \\, , \\\\\n\\left( Y^\\alpha X_\\alpha \\right)_D\n\t&= \\partial_\\mu \\psi \\partial^\\mu \\chi\n\t+ \\tilde{\\lambda} \\tilde{\\lambda}\n\t+ \\frac{i}{2} \\tilde{\\lambda} \\tilde{\\omega}\n\t- \\frac{i}{2} \\tilde{\\omega} \\tilde{\\lambda}\n\t+ \\frac{1}{4} \\tilde{\\omega} \\tilde{\\omega}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{R}^T \\bar{\\dslash{\\partial}} \\tilde{S} \\right)} \\, .\n\\end{align}\nTherefore, the Lagrangian is given by\n\\begin{align}\n\\mathcal{L}\n\t&= \\partial_\\mu \\chi \\partial^\\mu \\psi\n\t+ \\partial_\\mu \\psi \\partial^\\mu \\chi\n\t+ 2 \\tilde{\\lambda} \\tilde{\\lambda}\n\t+ \\frac{1}{2} \\tilde{\\omega} \\tilde{\\omega}\n\t+ \\frac{m}{2} \\chi \\tilde{\\lambda}\n\t+ \\frac{i m}{4} \\chi \\tilde{\\omega}\n\t+ \\frac{m}{2} \\tilde{\\lambda} \\chi\n\t+ \\frac{i m}{4} \\tilde{\\omega} \\chi + \\notag \\\\\n\t&\\quad + \\frac{m}{2} \\psi \\tilde{\\lambda}\n\t- \\frac{i m}{4} \\psi \\tilde{\\omega}\n\t+ \\frac{m}{2} \\tilde{\\lambda} \\psi\n\t- \\frac{i m}{4} \\tilde{\\omega} \\psi\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{S}^T \\dslash{\\partial} \\tilde{R} \\right)}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{R}^T \\bar{\\dslash{\\partial}} \\tilde{S} \\right)} - \\notag \\\\\n\t&\\quad - \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{S}^T \\tilde{S} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{R}^T \\tilde{R} \\right)} \n\t+ h.c. \\, .\n\\label{Lmdimone}\n\\end{align}\nIt can be seen that this Lagrangian still contains the auxiliary fields $\\tilde{\\lambda}$ and $\\tilde{\\omega}$. They can be eliminated from the Lagrangian using their equations of motion\n\\begin{align}\n\\tilde{\\omega}_\\tau\n\t&= - \\frac{i m}{2} \\left( \\chi_\\tau - \\psi_\\tau \\right) \\, , \\label{Mdimoneeqmomega} \\\\\n\\tilde{\\lambda}_\\tau\n\t&= - \\frac{m}{4} \\left( \\chi_\\tau + \\psi_\\tau \\right)\\, . \\label{Mdimoneeqmlambda}\n\\end{align}\nThis process is also referred to as going \"on-shell\". The resulting on-shell Lagrangian is then found to be\n\\begin{align}\n\\mathcal{L}\n\t&= \\partial_\\mu \\chi \\partial^\\mu \\psi\n\t+ \\partial_\\mu \\psi \\partial^\\mu \\chi\n\t- \\frac{m^2}{4} \\psi \\chi\n\t- \\frac{m^2}{4} \\chi \\psi + \\notag \\\\\n\t&\\quad + \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{S}^T \\dslash{\\partial} \\tilde{R} \\right)}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{R}^T \\bar{\\dslash{\\partial}} \\tilde{S} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{S}^T \\tilde{S} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{R}^T \\tilde{R} \\right)} \\, .\n\\label{Lonshell}\n\\end{align}\nIt is solely dependent on the on-shell component fields $\\chi$, $\\psi$, $\\tilde{S}$, and $\\tilde{R}$. On the first glance it seems that there are twice as many bosonic degrees of freedom as fermionic ones, because each of the second-rank spinor fields has in general 8 degrees of freedom while each of the complex spinor fields only encompasses four degrees of freedom. However, on-shell the bosonic second-rank spinor fields satisfy a Weyl type equation which reduces the number of bosonic on-shell degrees of freedom by a factor of 2. This means that the Lagrangian indeed has 8 fermionic and 8 bosonic degrees of freedom.\n\n\\section{The Supercurrent}\n\\label{CJonshell}\nIn classical field theory the Noether theorem describes the connection between symmetry transformations that leave the Lagrangian invariant and the corresponding conserved quantities. It states that every symmetry results in a conserved current which can alternatively be expressed as a conserved charge. Even though supersymmetry is not a symmetry in the classical sense the on-shell Lagrangian is invariant under the variation of the component fields as defined in equations (\\ref{deltapsionshell}) to (\\ref{deltaSonshell}). Therefore, according to Noether's theorem, a conserved supercurrent exists.\n\nThe general equation for the supercurrent is given by\n\\begin{align}\nJ_{\\mu \\kappa}\n\t&= \\frac{\\partial}{\\partial \\zeta^\\kappa} \\left( \\sum\\limits_\\phi \\delta \\phi \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\phi}\n\t- \\mathcal{K}_\\mu \\right) \\, ,\n\\end{align}\nwhere the summation runs over all component fields of the Lagrangian. It has to be emphasised that this compact general equation for the supercurrent suppresses any indices of the component fields and also includes all hermitian conjugate component fields as well. The term $\\mathcal{K}_\\mu$ in this equation is related to the variation of the Lagrangian by\n\\begin{align}\n\\partial^\\mu \\mathcal{K}_\\mu\n\t&= \\delta \\mathcal{L} \\, .\n\\end{align}\n\nAs the full supercurrent $J_\\mu$ is hermitian it is possible to restrict the discussion to the on-shell Lagrangian without hermitian conjugate part and to calculate both $J_\\mu^{1\/2}$ as well as $\\bar{J}_\\mu^{1\/2}$. The complete supercurrent can then be constructed from the two contributions $J_\\mu^{1\/2}$ and $\\bar{J}_\\mu^{1\/2}$.\n\nThe general equation for $J^{1\/2}_\\mu$ can be written as\n\\begin{align}\nJ^{1\/2}_{\\mu \\kappa}\n\t&= \\frac{\\partial}{\\partial \\zeta^\\kappa} \\left( \\delta \\chi^\\tau \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\chi^\\tau}\n\t+ \\delta \\psi^\\tau \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\psi^\\tau}\n\t+ \\delta \\tilde{S}^{\\tau \\omega} \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\tilde{S}^{\\tau \\omega}}\n\t+ \\delta \\tilde{R}^{\\dot{\\tau} \\omega} \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\tilde{R}^{\\dot{\\tau} \\omega}}\n\t- \\mathcal{K}_\\mu \\right) \\, .\n\\end{align}\nInserting the on-shell Lagrangian from equation (\\ref{Lonshell}) into the equation for the supercurrent yields\n\\begin{align}\nJ_{\\mu \\kappa}\n\t&= - 3 \\tilde{S}_\\kappa{}^\\alpha \\partial_\\mu \\psi_\\alpha\n\t- \\frac{i m}{2} \\psi^\\alpha \\left( \\sigma_\\mu \\right)_\\kappa{}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha}\n\t- i \\partial_\\nu \\psi^\\alpha \\left( \\sigma^\\nu{}_\\mu \\right)_\\kappa{}^\\beta \\tilde{S}_{\\beta \\alpha}\n\t- \\frac{\\partial}{\\partial \\zeta^\\kappa} \\mathcal{K}_\\mu \\, .\n\\end{align}\nThe explicit form of $\\mathcal{K}_\\mu$ is derived from the variation of the Lagrangian without hermitian conjugate part\n\\begin{align}\n\\delta \\mathcal{L}\n\t&= \\partial_\\mu \\delta \\chi \\partial^\\mu \\psi\n\t+ \\partial_\\mu \\chi \\partial^\\mu \\delta \\psi\n\t+ \\partial_\\mu \\delta \\psi \\partial^\\mu \\chi\n\t+ \\partial_\\mu \\psi \\partial^\\mu \\delta \\chi\n\t- \\frac{m^2}{4} \\delta \\psi \\chi\n\t- \\frac{m^2}{4} \\psi \\delta \\chi\n\t- \\frac{m^2}{4} \\delta \\chi \\psi - \\notag \\\\\n\t&\\quad - \\frac{m^2}{4} \\chi \\psi \\delta + \\frac{i}{2} \\mathrm{Tr}{\\left( \\delta \\tilde{S}^T \\dslash{\\partial} \\tilde{R} \\right)}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{S}^T \\dslash{\\partial} \\delta \\tilde{R} \\right)}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\delta \\tilde{R}^T \\bar{\\dslash{\\partial}} \\tilde{S} \\right)}\n\t+ \\frac{i}{2} \\mathrm{Tr}{\\left( \\tilde{R}^T \\bar{\\dslash{\\partial}} \\delta \\tilde{S} \\right)} - \\notag \\\\\n\t&\\quad - \\frac{m}{4} \\mathrm{Tr}{\\left( \\delta \\tilde{S}^T \\tilde{S} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{S}^T \\delta \\tilde{S} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\delta \\tilde{R}^T \\tilde{R} \\right)}\n\t- \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{R}^T \\delta \\tilde{R} \\right)} \\, .\n\\end{align}\t\nIt can be shown that the variation of the Lagrangian is a four divergence as expected which implies that\n\\begin{align}\n\\mathcal{K}_\\mu\n\t&= \\zeta^\\beta \\tilde{S}_{\\beta \\alpha} \\partial_\\mu \\psi^\\alpha\n\t- \\bar{\\zeta}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha} \\partial_\\mu \\chi^\\alpha\n\t+ \\frac{i m}{2} \\left( \\bar{\\sigma}_\\mu \\right)_{\\dot{\\beta}}{}^\\gamma \\bar{\\zeta}^{\\dot{\\beta}} \\chi^\\alpha \\tilde{S}_{\\gamma \\alpha}\n\t+ \\frac{i m}{2} \\left( \\sigma_\\mu \\right)_\\beta{}^{\\dot{\\gamma}} \\zeta^\\beta \\psi^\\alpha \\tilde{R}_{\\dot{\\gamma} \\alpha} + \\notag \\\\\n\t&\\quad + i \\bar{\\zeta}^{\\dot{\\delta}} \\left( \\bar{\\sigma}_\\mu{}^\\nu \\right)_{\\dot{\\delta}}{}^{\\dot{\\gamma}} \\chi^\\alpha \\partial_\\nu \\tilde{R}_{\\dot{\\gamma} \\alpha}\n\t+ i \\zeta^\\delta \\left( \\sigma_\\mu{}^\\nu \\right)_\\delta{}^\\gamma \\psi^\\alpha \\partial_\\nu \\tilde{S}_{\\gamma \\alpha} \\, .\n\\label{Kmu}\n\\end{align}\nThis result can then be inserted into the equation for the supercurrent. After differentiating with respect to the transformation parameter $\\zeta$ the supercurrent is found to be\n\\begin{align}\nJ^{1\/2}_{\\mu \\kappa}\n\t&= - i m \\left( \\sigma_\\mu \\right)_\\kappa{}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha} \\psi^\\alpha\n\t+ 2 \\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma} \\kappa} \\psi^\\alpha \\tilde{S}_{\\beta \\alpha} \\, .\n\\label{Jhalf}\n\\end{align}\n\nThe contribution to the full supercurrent $\\bar{J}_\\mu^{1\/2}$ is defined in perfect analogy to $J_\\mu^{1\/2}$ by replacing the derivative with respect to the Grassmann variable $\\zeta$ with a derivative with respect to $\\bar{\\zeta}$. It has to be noted that the behaviour of the Grassmann derivative is rather subtle and depends on the conventions chosen. In the present scenario where by convention all derivatives are written as right derivatives the change from left to right derivative introduces an additional overall minus sign\n\\begin{align}\n\\bar{J}^{1\/2}_{\\mu \\dot{\\kappa}}\n\t&= - \\frac{\\partial}{\\partial \\bar{\\zeta}^{\\dot{\\kappa}}} \\left( \\delta \\chi^\\tau \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\chi^\\tau}\n\t+ \\delta \\psi^\\tau \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\psi^\\tau}\n\t+ \\delta \\tilde{S}^{\\tau \\omega} \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\tilde{S}^{\\tau \\omega}}\n\t+ \\delta \\tilde{R}^{\\dot{\\tau} \\omega} \\frac{\\partial \\mathcal{L}}{\\partial \\partial^\\mu \\tilde{R}^{\\dot{\\tau} \\omega}}\n\t- \\mathcal{K}_\\mu \\right) \\, .\n\\end{align}\nThe supercurrent $\\bar{J}_\\mu^{1\/2}$ for the Lagrangian without the complex conjugate part is then given by\n\\begin{align}\n\\bar{J}^{1\/2}_{\\mu \\dot{\\kappa}}\n\t&= 3 \\tilde{R}_{\\dot{\\kappa} \\alpha} \\partial_\\mu \\chi^\\alpha\n\t+ i \\left( \\sigma^\\nu{}_\\mu \\right)_{\\dot{\\kappa}}{}^{\\dot{\\beta}} \\partial_\\nu \\chi^\\alpha \\tilde{R}_{\\dot{\\beta} \\alpha}\n\t+ \\frac{i m}{2} \\left( \\bar{\\sigma}_\\mu \\right)_{\\dot{\\kappa}}{}^\\beta \\tilde{S}_{\\beta \\alpha} \\chi^\\alpha\n\t+ \\frac{\\partial}{\\partial \\bar{\\zeta}^{\\dot{\\kappa}}} \\mathcal{K}_\\mu \\, ,\n\\end{align}\nwhere the term $\\mathcal{K}_\\mu$ is already known from equation (\\ref{Kmu}). After differentiation with respect to the Grassmann variable the final result is\n\\begin{align}\n\\bar{J}^{1\/2}_{\\mu \\dot{\\kappa}}\n\t&= i m \\left( \\bar{\\sigma}_\\mu \\right)_{\\dot{\\kappa}}{}^\\beta \\tilde{S}_{\\beta \\alpha} \\chi^\\alpha\n\t+ 2 \\left( \\bar{\\sigma}_\\mu \\right)^{\\dot{\\beta} \\gamma} \\dslash{\\partial}_{\\gamma \\dot{\\kappa}} \\chi^\\alpha \\tilde{R}_{\\dot{\\beta} \\alpha} \\, .\n\\label{Jbarhalf}\n\\end{align}\nTogether with the previous result for $J^{1\/2}_\\mu$ from equation (\\ref{Jhalf}) the construction of the full supercurrent is straightforward\n\\begin{align}\nJ_{\\mu \\kappa}\n\t&= - i m \\left( \\sigma_\\mu \\right)_\\kappa{}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\alpha} \\psi^\\alpha\n\t+ 2 \\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma} \\kappa} \\psi^\\alpha \\tilde{S}_{\\beta \\alpha} - \\notag \\\\\n\t&\\quad - i m \\left( \\sigma_\\mu \\right)_{\\kappa}{}^{\\dot{\\beta}} \\bar{\\tilde{S}}_{\\dot{\\beta} \\dot{\\alpha}} \\bar{\\chi}^{\\dot{\\alpha}}\n\t+ 2 \\left( \\sigma_\\mu \\right)^{\\beta \\dot{\\gamma}} \\bar{\\dslash{\\partial}}_{\\dot{\\gamma} \\kappa} \\bar{\\chi}^{\\dot{\\alpha}} \\bar{\\tilde{R}}_{\\beta \\dot{\\alpha}} \\, .\n\\label{Jfull}\n\\end{align}\n\n\\section{The Hamiltonian in Position Space}\n\\label{CHposition}\nThe Hamiltonian in position space is usually derived from the Lagrangian by canonical quantisation. However, it is not immediately clear whether this approach is still valid for the present scenario that is based on a general spinor superfield instead of a scalar superfield. Therefore, a more conservative approach based on the supersymmetry algebra was chosen. It utilises the anticommutation relation between the barred and unbarred supersymmetry generator of the $N = 1$ supersymmetry algebra\n\\begin{align}\n2 \\left( \\sigma^\\mu \\right)_{\\alpha \\dot{\\beta}} P_\\mu\n\t&= \n\t\\left\\{ Q_\\alpha , \\bar{Q}_{\\dot{\\beta}} \\right\\} .\n\\label{PSUSYalgebra}\n\\end{align}\n\nAt this point it can already be seen that a successful derivation of the Hamiltonian from the supersymmetry algebra requires the knowledge of the commutation and anticommutation relations of the component fields in position space. Therefore, the second quantisation of the component fields in position space will be discussed in Section \\ref{SQuantCompFields}. Afterwards in Section \\ref{CHSUSYalgebra}, these results will be used to derive an expression for the Hamiltonian in position space which is founded in the supersymmetry algebra. Finally, in Section \\ref{CHcanonicalquant} it will be shown that canonical quantisation yields the same Hamiltonian in position space as the approach based on the supersymmetry algebra.\n\n\\subsection{Second Quantisation in Position Space}\n\\label{SQuantCompFields}\nA viable supersymmetric model of fermionic fields with mass dimension one requires a second quantisation that is in agreement with the superfield transformations of the component fields as derived in Section \\ref{SSSUSYtranslation}. This can be achieved by calculating the commutator between the component fields and the generators of the superspace translations\n\\begin{align}\n\\delta \\phi\n\t&= - i \\left[ \\phi , \\zeta^\\alpha Q_\\alpha + \\zeta_{\\dot{\\alpha}} Q^{\\dot{\\alpha}} \\right] \\, .\n\\label{compfieldvarcommutator}\n\\end{align}\nTo generalise the notation the spinor indices of the field $\\phi$ are suppressed and it can represent a scalar field as well as first, second, or higher rank spinor fields. Subsequently, the commutation and anticommutation relations of the barred component fields are derived from the results for the unbarred component fields.\n\nThe supersymmetry generators that appear in this equation are proportional to the supercurrent\n\\begin{align}\nQ_\\alpha\n\t&= \\int \\mathrm{d} \\mathbf{x} J_{0 \\alpha} \\, , \\label{QproptoJ}\\\\\n\\bar{Q}_{\\dot{\\alpha}} \n\t&= \\int \\mathrm{d} \\mathbf{x} \\bar{J}_{0 \\dot{\\alpha}} \\, . \\label{QbarproptoJbar}\n\\end{align}\nIn general the supersymmetry generators must contain the full supercurrent. However, the previous results for the superfield translations, equations (\\ref{deltapsionshell}) to (\\ref{deltaSonshell}), imply that no mixing between barred and unbarred component fields occurs. Therefore, it is sufficient to restrict the discussion in this section to the supercurrent arising from the Lagrangian without hermitian conjugate contribution, as any cross terms vanish identically and define the constrained generators\n\\begin{align}\nQ^{1\/2}_\\alpha\n\t&= \\int \\mathrm{d} \\mathbf{x} J^{1\/2}_{0 \\alpha} \\, , \\\\\n\\bar{Q}^{1\/2}_{\\dot{\\alpha}} \n\t&= \\int \\mathrm{d} \\mathbf{x} \\bar{J}^{1\/2}_{0 \\dot{\\alpha}} \\, .\n\\end{align}\nTo distinguish the constrained generators from the full generators as outlined in equations (\\ref{QproptoJ}) and (\\ref{QbarproptoJbar}) an additional superscript $1\/2$ was incorporated into the notation in analogy to the notation for the supercurrent in Chapter \\ref{CJonshell}. Inserting the results for the supercurrent from equations (\\ref{Jhalf}) and (\\ref{Jbarhalf}) then yields the following expression for the constrained supersymmetry generators\n\\begin{align}\nQ^{1\/2}_\\alpha\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left( - i m \\left( \\sigma_\\mu \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{R}_{\\dot{\\gamma} \\beta}{\\left( x \\right)} \\psi^\\beta{\\left( x \\right)}\n\t+ 2 \\left( \\sigma_\\mu \\right)^{\\gamma \\dot{\\delta}} \\tilde{S}_{\\gamma \\beta}{\\left( x \\right)} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\psi^\\beta{\\left( x \\right)} \\right) \\, , \\label{generatorQ}\\\\\n\\bar{Q}^{1\/2}_{\\dot{\\alpha}}\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left( i m \\left( \\bar{\\sigma}_\\mu \\right)_{\\dot{\\alpha}}{}^\\gamma \\tilde{S}_{\\gamma \\beta}{\\left( x \\right)} \\chi^\\beta{\\left( x \\right)}\n\t+ 2 \\left( \\bar{\\sigma}_\\mu \\right)^{\\dot{\\gamma} \\delta} \\tilde{R}_{\\dot{\\gamma} \\beta}{\\left( x \\right)} \\dslash{\\partial}_{\\delta \\dot{\\alpha}} \\chi^\\beta{\\left( x \\right)} \\right) \\, . \\label{generatorQbar}\n\\end{align}\n\n\\subsubsection{Superfield Transformation of the Fermionic Component Fields}\nInserting the constrained supersymmetry generators as defined in equations (\\ref{generatorQ}) and (\\ref{generatorQbar}) into equation (\\ref{compfieldvarcommutator}) for the commutator between component field $\\chi$ and the generators of superspace translations yields a variation of $\\chi$ of\n\\begin{align}\n\\delta \\chi_\\alpha{\\left( x \\right)}\n\t&= \\int \\mathrm{d} \\mathbf{x}' \\left( m \\zeta^\\beta \\left( \\sigma_0 \\right)_\\beta{}^{\\dot{\\gamma}} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\tilde{R}_{\\dot{\\gamma} \\delta}{\\left( x' \\right)} \\psi^\\delta{\\left( x' \\right)} \\right\\} + \\right. \\notag \\\\\n\t&\\qquad + 2 i \\zeta^\\beta \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\tilde{S}_{\\gamma \\epsilon}{\\left( x' \\right)} \\bar{\\dslash{\\partial}}'_{\\dot{\\delta} \\beta} \\psi^\\epsilon{\\left( x' \\right)} \\right\\} - \\notag \\\\\n\t&\\qquad - m \\bar{\\zeta}_{\\dot{\\beta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\beta} \\gamma} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\tilde{S}_{\\gamma \\delta}{\\left( x' \\right)} \\chi^\\delta{\\left( x' \\right)} \\right\\} + \\notag \\\\\n\t&\\qquad \\left. + 2 i \\bar{\\zeta}_{\\dot{\\beta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\delta} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\tilde{R}_{\\dot{\\gamma} \\epsilon}{\\left( x' \\right)} \\dslash{\\partial}'_\\delta{}^{\\dot{\\beta}} \\chi^\\epsilon{\\left( x' \\right)} \\right\\} \\right) \\, .\n\\end{align}\nEach of the contributions to the variation of the component field $\\chi$ contains an anticommutator involving two fermionic fields and one bosonic field. They can be rewritten using the anticommutator relation\n\\begin{align}\n\\left\\{ F_1 , B_2 F_2 \\right\\}\n\t&= B_2 \\left\\{ F_1 , F_2 \\right\\} \\, .\n\\end{align}\nIn addition, it can be seen that the second and fourth term contain a four derivative $\\dslash{\\partial}$ acting on one of the component fields in the anticommutator. These terms can be rewritten by splitting the four derivative into its time and spatial components\n\\begin{align}\n\\dslash{\\partial}_{\\alpha \\dot{\\beta}}\n\t&= \\left( \\sigma^\\mu \\right)_{\\alpha \\dot{\\beta}} \\partial_\\mu\n\t= \\left( \\sigma^0 \\right)_{\\alpha \\dot{\\beta}} \\partial_0\n\t+ \\boldsymbol{\\sigma}_{\\alpha \\dot{\\beta}} \\cdot \\boldsymbol{\\nabla} \\, .\n\\end{align}\nIt is important to recall that there is a plus sign between the time and spatial components and not a minus sign as the derivative is a covariant three vector $\\boldsymbol{\\nabla} = \\left( \\partial_1 , \\partial_2 , \\partial_3 \\right)$ while all standard vectors, e.g. $\\mathbf{p} = \\left( p^1, p^2 , p^3 \\right)$, are contravariant three vectors. After partial integration over the spatial components each term involving a four-derivative is replaced by two terms -- one containing a time derivative acting on one of the fields in the commutator and one simply containing the commutator of component fields. Furthermore, the boundary terms from the partial integration which are 3-divergences vanish identically and are ignored. This results in\n\\begin{align}\n\\delta \\chi_\\alpha{\\left( x \\right)}\n\t&= \\int \\mathrm{d} \\mathbf{x}' \\left( m \\zeta^\\beta \\left( \\sigma_0 \\right)_\\beta{}^{\\dot{\\gamma}} \\tilde{R}_{\\dot{\\gamma} \\delta}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\psi^\\delta{\\left( x' \\right)} \\right\\}\n\t+ 2 i \\zeta^\\beta \\tilde{S}_{\\beta \\epsilon}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\dot{\\psi}^\\epsilon{\\left( x' \\right)} \\right\\} + \\right. \\notag \\\\\n\t&\\qquad + 2 i \\zeta^\\beta \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\boldsymbol{\\sigma}_{\\dot{\\delta} \\beta} \\cdot \\boldsymbol{\\nabla}' \\tilde{S}_{\\gamma \\epsilon}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\psi^\\epsilon{\\left( x' \\right)} \\right\\} - \\notag \\\\\n\t&\\qquad - m \\bar{\\zeta}_{\\dot{\\beta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\beta} \\gamma} \\tilde{S}_{\\gamma \\delta}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\chi^\\delta{\\left( x' \\right)} \\right\\} \n\t- 2 i \\bar{\\zeta}^{\\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\epsilon}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\dot{\\chi}^\\epsilon{\\left( x' \\right)} \\right\\} + \\notag \\\\\n\t&\\qquad \\left. + 2 i \\bar{\\zeta}_{\\dot{\\beta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\delta} \\boldsymbol{\\sigma}_\\delta{}^{\\dot{\\beta}} \\cdot \\boldsymbol{\\nabla}' \\tilde{R}_{\\dot{\\gamma} \\epsilon}{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\chi^\\epsilon{\\left( x' \\right)} \\right\\} \\right) \\, .\n\\label{deltachisecondquant}\n\\end{align}\nBy comparison with the previously derived superspace translation of $\\chi$ in equation (\\ref{deltachionshell}) it can be seen that the only nonvanishing contribution comes from the term proportional to $\\zeta \\tilde{S}$ while all other contributions have to vanish identically. This implies that three of the anticommutators vanish identically\n\\begin{align}\n\\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\psi_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0 \\, ,\\\\\n\\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\dot{\\chi}_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0 \\, , \\\\\n\\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\chi_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0 \\, .\n\\end{align}\nThe only nonvanishing anticommutator satisfies\n\\begin{align}\n- \\zeta^\\beta \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)}\n\t&= - 2 i \\zeta^\\beta \\int \\mathrm{d} \\mathbf{x}' \\tilde{S}_\\beta{}^\\gamma{\\left( x' \\right)} \\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\dot{\\psi}_\\gamma{\\left( x' \\right)} \\right\\} \\, ,\n\\label{quantrelchi}\n\\end{align}\nwhich has the solution\n\\begin{align}\n\\left\\{ \\chi_\\alpha{\\left( x \\right)} , \\dot{\\psi}_\\gamma{\\left( x' \\right)} \\right\\}\n\t&= \\frac{i}{2} \\epsilon_{\\alpha \\gamma} \\delta{\\left( x - x' \\right)} \\, .\n\\end{align}\n\nAs the Lagrangian is symmetric with respect to the exchange of $\\chi$ and $\\psi$ there is no difference between the calculation of $\\delta \\chi$ and $\\delta \\psi$. Again, three of the anticommutators have to vanish identically\n\\begin{align}\n\\left\\{ \\psi_\\alpha{\\left( x \\right)} , \\dot{\\psi}_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0 \\, , \\\\\n\\left\\{ \\psi_\\alpha{\\left( x \\right)} , \\psi_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0 \\, , \\\\\n\\left\\{ \\psi_\\alpha{\\left( x \\right)} , \\chi_\\beta{\\left( x' \\right)} \\right\\}\n\t&= 0\\, ,\n\\end{align}\nwhile the only nonvanishing anticommutator is the one involving $\\psi$ and $\\dot{\\chi}$\n\\begin{align}\n\\left\\{ \\psi_\\alpha{\\left( x \\right)} , \\dot{\\chi}_\\gamma{\\left( x' \\right)} \\right\\}\n\t&= \\frac{i}{2} \\epsilon_{\\alpha \\gamma} \\delta{\\left( \\mathbf{x} - \\mathbf{x'} \\right)} \\, .\n\\end{align}\n\n\\subsubsection{Superfield Transformation of the Bosonic Component Fields}\nThe discussion for the superfield transformation of the bosonic component fields is in perfect analogy to those for the fermionic component fields. The change from a fermionic to a bosonic field results in an exchange of all anticommutators with commutators\n\\begin{align}\n\\delta \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)}\n\t&= \\int \\mathrm{d} \\mathbf{x}' \\left( - m \\zeta^\\gamma \\left( \\sigma_0 \\right)_\\gamma{}^{\\dot{\\epsilon}} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\delta}{\\left( x' \\right)} \\psi^\\delta{\\left( x' \\right)} \\right] - \\right. \\notag \\\\\n\t&\\qquad- 2 i \\zeta^\\gamma \\left( \\sigma_0 \\right)^{\\epsilon \\dot{\\delta}} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{S}_{\\epsilon \\kappa}{\\left( x' \\right)} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\gamma} \\psi^\\kappa{\\left( x' \\right)} \\right] + \\notag \\\\\n\t&\\qquad + m \\bar{\\zeta}_{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\epsilon} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{S}_{\\epsilon \\delta}{\\left( x' \\right)} \\chi^\\delta{\\left( x' \\right)} \\right] - \\notag \\\\\n\t&\\qquad \\left. - 2 i \\bar{\\zeta}_{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\epsilon} \\delta} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\kappa}{\\left( x' \\right)} \\dslash{\\partial}_\\delta{}^{\\dot{\\gamma}} \\chi^\\kappa{\\left( x' \\right)} \\right] \\right) \\, .\n\\end{align}\nThe commutators involved in this expression each contain two bosonic and one fermionic component field and can be simplified using the commutator relation\n\\begin{align}\n\\left[ B_1 , B_2 F_2 \\right]\n\t&= F_2 \\left[ B_1 , B_2 \\right] \\, .\n\\end{align}\nTherefore, the variation of the bosonic second-rank spinor field $\\tilde{S}$ takes the form\n\\begin{align}\n\\delta \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)}\n\t&= \\int \\mathrm{d} \\mathbf{x}' \\left( - m \\zeta^\\gamma \\left( \\sigma_0 \\right)_\\gamma{}^{\\dot{\\epsilon}} \\psi^\\delta{\\left( x' \\right)} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\delta}{\\left( x' \\right)} \\right] - \\right. \\notag \\\\\n\t&\\qquad - 2 i \\zeta^\\gamma \\left( \\sigma_0 \\right)^{\\epsilon \\dot{\\delta}} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\gamma} \\psi^\\kappa{\\left( x' \\right)} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{S}_{\\epsilon \\kappa}{\\left( x' \\right)} \\right] + \\notag \\\\\n\t&\\qquad + m \\bar{\\zeta}_{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\epsilon} \\chi^\\delta{\\left( x' \\right)} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{S}_{\\epsilon \\delta}{\\left( x' \\right)} \\right] - \\notag \\\\\n\t&\\qquad \\left. - 2 i \\bar{\\zeta}_{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\epsilon} \\delta} \\dslash{\\partial}_\\delta{}^{\\dot{\\gamma}} \\chi^\\kappa{\\left( x' \\right)} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\kappa}{\\left( x' \\right)} \\right] \\right) \\, .\n\\label{deltaSsecondquant}\n\\end{align}\nIf this result is compared to the superspace translation of $\\tilde{S}$ in equation (\\ref{deltaSonshell}) it can be immediately read off that\n\\begin{align}\n\\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{S}_{\\gamma \\delta}{\\left( x' \\right)} \\right]\n\t&= 0 \\, .\n\\end{align}\nThe remaining two relations for the commutator between $\\tilde{S}$ and $\\tilde{R}$ should yield the same result. Using the first relation \n\\begin{align}\nm \\zeta_\\beta \\psi_\\alpha\n\t&= - m \\zeta^\\gamma \\left( \\sigma_0 \\right)_\\gamma{}^{\\dot{\\epsilon}} \\int \\mathrm{d} \\mathbf{x}' \\psi^\\delta{\\left( x' \\right)} \\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\delta}{\\left( x' \\right)} \\right]\n\\label{quantrelS}\n\\end{align}\nit is found that $\\tilde{S}$ and $\\tilde{R}$ satisfy the commutation relation\n\\begin{align}\n\\left[ \\tilde{S}_{\\beta \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\epsilon} \\delta}{\\left( x' \\right)} \\right]\n\t&= - \\epsilon_{\\alpha \\delta} \\delta{\\left( x - x' \\right)}\\left( \\sigma^0 \\right)_{\\beta \\dot{\\epsilon}} \\, .\n\\label{commutatorSR}\n\\end{align}\nInserting this result into the second relation then provides a consistency check as it satisfies the relation identically.\n\nAgain, the calculations for the superfield transformation of $\\tilde{R}$ are in perfect analogy to those for $\\tilde{S}$. It is found that the commutator of $\\tilde{R}$ with itself vanishes\n\\begin{align}\n\\left[ \\tilde{R}_{\\dot{\\beta} \\alpha}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\gamma} \\delta}{\\left( x' \\right)} \\right]\n\t&= 0 \\, .\n\\end{align}\nFinally, the remaining commutator between $\\tilde{R}$ and $\\tilde{S}$ can be derived from equation (\\ref{commutatorSR}) by commuting the component fields and renaming the spinor indices appropriately\n\\begin{align}\n\\left[ R_{\\dot{\\beta} \\alpha}{\\left( x \\right)} , S'_{\\epsilon \\delta}{\\left( x' \\right)} \\right]\n\t&= - \\epsilon_{\\alpha \\delta} \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\beta} \\epsilon} \\delta{\\left( x - x' \\right)} \\, .\n\\label{commutatorRS}\n\\end{align}\n\n\\subsubsection{Transformation of the Conjugate Component Fields}\nGenerally it is possible to repeat the calculations outlined in the previous sections for the hermitian conjugate component fields. However, it is much easier to calculate the hermitian conjugate of the previously derived commutation and anticommutation relations.\n\nFor the anticommutation relations between the spinor fields hermitian conjugation is straightforward and the two nonvanishing anticommutation relations between the barred component fields are\n\\begin{align}\n\\left\\{ \\bar{\\chi}_{\\dot{\\alpha}}{\\left( x \\right)} , \\dot{\\bar{\\psi}}_{\\dot{\\gamma}}{\\left( x' \\right)} \\right\\}\n\t&= \\frac{i}{2} \\epsilon_{\\dot{\\alpha} \\dot{\\gamma}} \\delta{\\left( \\mathbf{x} - \\mathbf{x}' \\right)} \\, , \\\\\n\\left\\{ \\bar{\\psi}_{\\dot{\\alpha}}{\\left( x \\right)} , \\dot{\\bar{\\chi}}_{\\dot{\\gamma}}{\\left( x' \\right)} \\right\\}\n\t&= \\frac{i}{2} \\epsilon_{\\dot{\\alpha} \\dot{\\gamma}} \\delta{\\left( \\mathbf{x} - \\mathbf{x'} \\right)} \\, .\n\\end{align}\nThe only difficulty that arises is the sign change of the second-rank $\\epsilon$-tensor under hermitian conjugation.\n\nFor the commutation relations of the bosonic second-rank spinor fields the discussion is only slightly more involved as the hermitian conjugation inverts the ordering of the component fields which induces an additional sign flip for the commutators that didn't occur for the spinor fields. Therefore, the commutation relations for the barred component fields are given by\n\\begin{align}\n\\left[ \\tilde{\\bar{S}}_{\\dot{\\beta} \\dot{\\alpha}}{\\left( x \\right)} , \\tilde{\\bar{R}}_{\\epsilon \\dot{\\delta}}{\\left( x' \\right)} \\right]\n\t&= - \\epsilon_{\\dot{\\alpha} \\dot{\\delta}} \\delta{\\left( \\mathbf{x} - \\mathbf{x}' \\right)} \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\beta} \\epsilon} \\, , \\\\\n\\left[ \\tilde{\\bar{R}}_{\\beta \\dot{\\alpha}}{\\left( x \\right)} , \\tilde{\\bar{S}}_{\\dot{\\epsilon} \\dot{\\delta}}{\\left( x' \\right)} \\right]\n\t&= - \\epsilon_{\\dot{\\alpha} \\dot{\\delta}} \\left( \\sigma^0 \\right)_{\\beta \\dot{\\epsilon}} \\delta{\\left( \\mathbf{x} - \\mathbf{x}' \\right)} \\, .\n\\end{align}\n\n\\subsection{The Hamiltonian from the Supersymmetry Algebra}\n\\label{CHSUSYalgebra}\nTo derive an explicit equation for the Hamiltonian the supersymmetry generators in equation (\\ref{PSUSYalgebra}) have to be expressed in terms of the component fields. This can be achieved using the relations between the supersymmetry generators which are the conserved Noether charges of the system and the supercurrents which were defined in equations (\\ref{QproptoJ}) and (\\ref{QbarproptoJbar}). Inserting the result for the supercurrent from equations (\\ref{Jfull}) and its hermitian conjugate leads to the following expression of the supersymmetry generators in terms of the component fields\n\\begin{align}\nQ_\\alpha\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left( - i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{R}_{\\dot{\\gamma} \\beta}{\\left( x \\right)} \\psi^\\beta{\\left( x \\right)}\n\t+ 2 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{S}_{\\gamma \\beta}{\\left( x \\right)} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\psi^\\beta{\\left( x \\right)} - \\right. \\notag \\\\\n\t&\\qquad \\left. - i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{\\bar{S}}_{\\dot{\\gamma} \\dot{\\beta}}{\\left( x \\right)} \\bar{\\chi}^{\\dot{\\beta}}{\\left( x \\right)}\n\t+ 2 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{\\bar{R}}_{\\gamma \\dot{\\beta}}{\\left( x \\right)} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\bar{\\chi}^{\\dot{\\beta}}{\\left( x \\right)} \\right) \\, , \\displaybreak[3] \\\\\n\\bar{Q}_{\\dot{\\alpha}}\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left( i m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\alpha}}{}^\\gamma \\tilde{S}_{\\gamma \\beta}{\\left( x \\right)} \\chi^\\beta{\\left( x \\right)}\n\t+ 2 \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\delta} \\tilde{R}_{\\dot{\\gamma} \\beta}{\\left( x \\right)} \\dslash{\\partial}_{\\delta \\dot{\\alpha}} \\chi^\\beta{\\left( x \\right)} + \\right. \\notag \\\\\n\t&\\qquad \\left. + i m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\alpha}}{}^\\gamma \\tilde{\\bar{R}}_{\\gamma \\dot{\\beta}}{\\left( x \\right)} \\bar{\\psi}^{\\dot{\\beta}}{\\left( x \\right)}\n\t+ 2 \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\gamma} \\delta} \\tilde{\\bar{S}}_{\\dot{\\gamma} \\dot{\\beta}}{\\left( x \\right)} \\dslash{\\partial}_{\\delta \\dot{\\alpha}} \\bar{\\psi}^{\\dot{\\beta}}{\\left( x \\right)} \\right) \\, .\n\\end{align}\nTo streamline the notation it proves useful to introduce the short notation\n\\begin{align}\n\\dslash{P}_{\\alpha \\dot{\\beta}}\n\t&= \\left( \\sigma^\\mu \\right)_{\\alpha \\dot{\\beta}} P_\\mu \\, ,\n\\end{align}\nwhich is defined in analogy to the commonly used contraction with Dirac matrices. The momentum operator is then given by\n\\begin{align}\n2 \\dslash{P}_{\\alpha \\dot{\\beta}}\n\t&= \\left\\{ \\int \\mathrm{d} \\mathbf{x} \\left( - i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{R}_{\\dot{\\gamma} \\omega}{\\left( x \\right)} \\psi^\\omega{\\left( x \\right)}\n\t+ 2 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{S}_{\\gamma \\omega}{\\left( x \\right)} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\psi^\\omega{\\left( x \\right)} - \\right. \\right. \\notag \\\\\n\t&\\qquad \\left. - i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{\\bar{S}}_{\\dot{\\gamma} \\dot{\\omega}}{\\left( x \\right)} \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)}\n\t+ 2 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{\\bar{R}}_{\\gamma \\dot{\\omega}}{\\left( x \\right)} \\bar{\\dslash{\\partial}}'_{\\dot{\\delta} \\alpha} \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)} \\right) , \\notag \\\\\n\t&\\quad \\int \\mathrm{d} \\mathbf{x}' \\left( i m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\tilde{S}_{\\kappa \\epsilon}{\\left( x' \\right)} \\chi^\\epsilon{\\left( x' \\right)}\n\t+ 2 \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\tilde{R}_{\\dot{\\kappa} \\epsilon}{\\left( x' \\right)} \\dslash{\\partial}'_{\\tau \\dot{\\beta}} \\chi^\\epsilon{\\left( x' \\right)} + \\right. \\notag \\\\\n\t&\\qquad \\left. \\left. + i m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\tilde{\\bar{R}}_{\\kappa \\dot{\\epsilon}}{\\left( x' \\right)} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)}\n\t+ 2 \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\tilde{\\bar{S}}_{\\dot{\\kappa} \\dot{\\epsilon}}{\\left( x' \\right)} \\dslash{\\partial}_{\\tau \\dot{\\beta}} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)} \\right) \\right\\} \\, .\n\\end{align}\nThe anticommutators containing two fermionic and two bosonic component fields can now be rewritten using the commutator relation\n\\begin{align}\n\\left\\{ B_1 F_1 , B_2 F_2 \\right\\}\n\t&= \\left[ B_1 , B_2 \\right] F_1 F_2 + B_2 B_1 \\left\\{ F_1 , F_2 \\right\\} \\, ,\n\\end{align}\nwhere it was assumed that the fermionic and bosonic fields commute. This assumption is justified by the previous derivation of the commutation and anticommutation relations of the component fields as well as the results of the superfield translations.\n\nAfter separation of the time and spatial derivatives as well as partial spatial integration the momentum operator is given by\n\\begin{align}\n2 \\dslash{P}_{\\alpha \\dot{\\beta}}\n\t&= \\int \\mathrm{d} \\mathbf{x} \\mathrm{d} \\mathbf{x}' \\left(\n\tm^2 \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\psi^\\omega{\\left( x \\right)} \\chi^\\epsilon{\\left( x' \\right)} \\left[ \\tilde{R}_{\\dot{\\gamma} \\omega}{\\left( x \\right)} , \\tilde{S}_{\\kappa \\epsilon}{\\left( x' \\right)} \\right] - \\right. \\notag \\\\\n\t&\\qquad - 2 i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\sigma^0 \\right)_{\\tau \\dot{\\beta}} \\tilde{R}_{\\dot{\\kappa} \\epsilon}{\\left( x' \\right)} \\tilde{R}_{\\dot{\\gamma} \\omega}{\\left( x \\right)} \\left\\{ \\psi^\\omega{\\left( x \\right)} , \\dot{\\chi}^\\epsilon{\\left( x' \\right)} \\right\\} + \\notag \\displaybreak[3] \\\\\n\t&\\qquad + 2 i m \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\delta} \\alpha} \\tilde{S}_{\\kappa \\epsilon}{\\left( x' \\right)} \\tilde{S}_{\\gamma \\omega}{\\left( x \\right)} \\left\\{ \\chi^\\epsilon{\\left( x' \\right)} , \\dot{\\psi}^\\omega{\\left( x \\right)} \\right\\} + \\notag \\displaybreak[3] \\\\\n\t&\\qquad + 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\psi^\\omega{\\left( x \\right)} \\dslash{\\partial}'_{\\tau \\dot{\\beta}} \\chi^\\epsilon{\\left( x' \\right)} \\left[ \\tilde{S}_{\\gamma \\omega}{\\left( x \\right)} , \\tilde{R}_{\\dot{\\kappa} \\epsilon}{\\left( x' \\right)} \\right] - \\notag \\displaybreak[3] \\\\\n\t&\\qquad - 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\delta} \\alpha} \\boldsymbol{\\sigma}_{\\tau \\dot{\\beta}} \\cdot \\boldsymbol{\\nabla}' \\tilde{R}_{\\dot{\\kappa} \\epsilon}{\\left( x' \\right)} \\tilde{S}_{\\gamma \\omega}{\\left( x \\right)} \\left\\{ \\chi^\\epsilon{\\left( x' \\right)} , \\dot{\\psi}^\\omega{\\left( x \\right)} \\right\\} - \\notag \\\\\n\t&\\qquad - 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\sigma^0 \\right)_{\\tau \\dot{\\beta}} \\tilde{R}_{\\dot{\\kappa} \\epsilon}{\\left( x' \\right)} \\boldsymbol{\\bar{\\sigma}}_{\\dot{\\delta} \\alpha} \\cdot \\boldsymbol{\\nabla} \\tilde{S}_{\\gamma \\omega}{\\left( x \\right)} \\left\\{ \\psi^\\omega{\\left( x \\right)} , \\dot{\\chi}^\\epsilon{\\left( x' \\right)} \\right\\} + \\notag \\\\\n\t&\\qquad + m^2 \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)} \\left[ \\tilde{\\bar{S}}_{\\dot{\\gamma} \\dot{\\omega}}{\\left( x \\right)} , \\tilde{\\bar{R}}_{\\kappa \\dot{\\epsilon}}{\\left( x' \\right)} \\right] - \\notag \\\\\n\t&\\qquad - 2 i m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\sigma^0 \\right)_{\\tau \\dot{\\beta}} \\tilde{\\bar{S}}_{\\dot{\\kappa} \\dot{\\epsilon}}{\\left( x' \\right)} \\tilde{\\bar{S}}_{\\dot{\\gamma} \\dot{\\omega}}{\\left( x \\right)} \\left\\{ \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)} , \\dot{\\bar{\\psi}}^{\\dot{\\epsilon}}{\\left( x' \\right)} \\right\\} + \\notag \\\\\n\t&\\qquad + 2 i m \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\delta} \\alpha} \\tilde{\\bar{R}}_{\\kappa \\dot{\\epsilon}}{\\left( x' \\right)} \\tilde{\\bar{R}}_{\\gamma \\dot{\\omega}}{\\left( x \\right)} \\left\\{ \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)} , \\dot{\\bar{\\chi}}^{\\dot{\\omega}}{\\left( x \\right)} \\right\\} + \\notag \\\\\n\t&\\qquad + 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)} \\dslash{\\partial}'_{\\tau \\dot{\\beta}} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)} \\left[ \\tilde{\\bar{R}}_{\\gamma \\dot{\\omega}}{\\left( x \\right)} , \\tilde{\\bar{S}}_{\\dot{\\kappa} \\dot{\\epsilon}}{\\left( x' \\right)} \\right] - \\notag \\\\\n\t&\\qquad - 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\bar{\\sigma}^0 \\right)_{\\dot{\\delta} \\alpha} \\boldsymbol{\\sigma}_{\\tau \\dot{\\beta}} \\cdot \\boldsymbol{\\nabla}' \\tilde{\\bar{S}}_{\\dot{\\kappa} \\dot{\\epsilon}}{\\left( x' \\right)} \\tilde{\\bar{R}}_{\\gamma \\dot{\\omega}}{\\left( x \\right)} \\left\\{ \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x' \\right)} , \\dot{\\bar{\\chi}}^{\\dot{\\omega}}{\\left( x \\right)} \\right\\} - \\notag \\\\\n\t&\\qquad \\left. - 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\left( \\sigma^0 \\right)_{\\tau \\dot{\\beta}} \\tilde{\\bar{S}}_{\\dot{\\kappa} \\dot{\\epsilon}}{\\left( x' \\right)} \\boldsymbol{\\bar{\\sigma}}_{\\dot{\\delta} \\alpha} \\cdot \\boldsymbol{\\nabla} \\tilde{\\bar{R}}_{\\gamma \\dot{\\omega}}{\\left( x \\right)} \\left\\{ \\bar{\\chi}^{\\dot{\\omega}}{\\left( x \\right)} , \\dot{\\bar{\\psi}}^{\\dot{\\epsilon}}{\\left( x' \\right)} \\right\\} \\right) \\, .\n\\end{align}\nInserting the previously derived results for the commutation and anticommutation relations between the component fields in position space then yields\n\\begin{align}\n2 \\dslash{P}_{\\alpha \\dot{\\beta}}\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left(\n\t- m^2 \\left( \\sigma_0 \\right)_{\\alpha \\dot{\\beta}} \\psi_\\epsilon{\\left( x \\right)} \\chi^\\epsilon{\\left( x \\right)}\n\t- m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{R}_{\\dot{\\beta} \\epsilon}{\\left( x \\right)} \\tilde{R}_{\\dot{\\gamma}}{}^\\epsilon{\\left( x \\right)} + \\right. \\notag \\\\\n\t&\\qquad + m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\tilde{S}_\\kappa{}^\\omega{\\left( x \\right)} \\tilde{S}_{\\alpha \\omega}{\\left( x \\right)}\n\t- 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\psi_\\epsilon{\\left( x \\right)} \\dslash{\\partial}_{\\gamma \\dot{\\beta}} \\chi^\\epsilon{\\left( x \\right)} + \\notag \\\\\n\t&\\qquad + 2 i \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\boldsymbol{\\sigma}_{\\tau \\dot{\\beta}} \\cdot \\boldsymbol{\\nabla} \\tilde{R}_{\\dot{\\kappa}}{}^\\omega{\\left( x \\right)} \\tilde{S}_{\\alpha \\omega}{\\left( x \\right)}\n\t+ 2 i \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{R}_{\\dot{\\beta} \\epsilon}{\\left( x \\right)} \\boldsymbol{\\bar{\\sigma}}_{\\dot{\\delta} \\alpha} \\cdot \\boldsymbol{\\nabla} \\tilde{S}_\\gamma{}^\\epsilon{\\left( x \\right)} + \\notag \\\\\n\t&\\qquad + m^2 \\left( \\sigma_0 \\right)_{\\alpha \\dot{\\beta}} \\bar{\\chi}_{\\dot{\\epsilon}}{\\left( x \\right)} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x \\right)}\n\t+ m \\left( \\sigma_0 \\right)_\\alpha{}^{\\dot{\\gamma}} \\tilde{\\bar{S}}_{\\dot{\\beta} \\dot{\\epsilon}}{\\left( x \\right)} \\tilde{\\bar{S}}_{\\dot{\\gamma}}{}^{\\dot{\\epsilon}}{\\left( x \\right)} - \\notag \\\\\n\t&\\qquad - m \\left( \\bar{\\sigma}_0 \\right)_{\\dot{\\beta}}{}^\\kappa \\tilde{\\bar{R}}_\\kappa{}^{\\dot{\\omega}}{\\left( x \\right)} \\tilde{\\bar{R}}_{\\alpha \\dot{\\omega}}{\\left( x \\right)}\n\t+ 4 \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\bar{\\dslash{\\partial}}_{\\dot{\\delta} \\alpha} \\bar{\\chi}_{\\dot{\\epsilon}}{\\left( x \\right)} \\dslash{\\partial}_{\\gamma \\dot{\\beta}} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x \\right)} - \\notag \\\\\n\t&\\qquad \\left. - 2 i \\left( \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\tau} \\boldsymbol{\\sigma}_{\\tau \\dot{\\beta}} \\cdot \\boldsymbol{\\nabla} \\tilde{\\bar{S}}_{\\dot{\\kappa}}{}^{\\dot{\\omega}}{\\left( x \\right)} \\tilde{\\bar{R}}_{\\alpha \\dot{\\omega}}{\\left( x \\right)}\n\t- 2 i \\left( \\sigma_0 \\right)^{\\gamma \\dot{\\delta}} \\tilde{\\bar{S}}_{\\dot{\\beta} \\dot{\\epsilon}}{\\left( x \\right)} \\boldsymbol{\\bar{\\sigma}}_{\\dot{\\delta} \\alpha} \\cdot \\boldsymbol{\\nabla} \\tilde{\\bar{R}}_\\gamma{}^{\\dot{\\epsilon}}{\\left( x \\right)} \\right) \\, .\n\\end{align}\nTo extract the Hamiltonian from the momentum operator it has to be contracted with the appropriate Pauli matrix\n\\begin{align}\n\\mathcal{H}\n\t&= \\frac{1}{2} \\left( \\sigma_0 \\right)^{\\alpha \\dot{\\beta}} \\dslash{P}_{\\alpha \\dot{\\beta}} \\, .\n\\end{align}\nThe Hamiltonian is therefore given by\n\\begin{align}\n\\mathcal{H}\n\t&= \\frac{1}{4} \\int \\mathrm{d} \\mathbf{x} \\left(\n\t2 m^2 \\psi{\\left( x \\right)} \\chi{\\left( x \\right)}\n\t+ m \\tilde{R}_{\\dot{\\beta} \\epsilon}{\\left( x \\right)} \\tilde{R}^{\\dot{\\beta} \\epsilon}{\\left( x \\right)}\n\t- m \\tilde{S}^{\\alpha \\omega}{\\left( x \\right)} \\tilde{S}_{\\alpha \\omega}{\\left( x \\right)} - \\right. \\notag \\\\\n\t&\\qquad - 4 \\left( \\sigma_0 \\bar{\\sigma}^\\mu \\sigma_0 \\right)^{\\gamma \\dot{\\beta}} \\partial_\\mu \\psi_\\epsilon{\\left( x \\right)} \\dslash{\\partial}_{\\gamma \\dot{\\beta}} \\chi^\\epsilon{\\left( x \\right)} \n\t+ 2 i \\left( \\bar{\\sigma}_0 \\sigma^i \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\alpha} \\partial_i \\tilde{R}_{\\dot{\\kappa}}{}^\\omega{\\left( x \\right)} \\tilde{S}_{\\alpha \\omega}{\\left( x \\right)} + \\notag \\\\\n\t&\\qquad + 2 i \\left( \\sigma_0 \\bar{\\sigma}^i \\sigma_0 \\right)^{\\gamma \\dot{\\beta}} \\tilde{R}_{\\dot{\\beta} \\epsilon}{\\left( x \\right)} \\partial_i \\tilde{S}_\\gamma{}^\\epsilon{\\left( x \\right)}\n\t+ 2 m^2 \\bar{\\chi}{\\left( x \\right)} \\bar{\\psi}{\\left( x \\right)}\n\t- m \\tilde{\\bar{S}}_{\\dot{\\beta} \\dot{\\epsilon}}{\\left( x \\right)} \\tilde{\\bar{S}}_{\\dot{\\gamma}}{}^{\\dot{\\beta} \\dot{\\epsilon}}{\\left( x \\right)} + \\notag \\\\\n\t&\\qquad + m \\tilde{\\bar{R}}^{\\alpha \\dot{\\omega}}{\\left( x \\right)} \\tilde{\\bar{R}}_{\\alpha \\dot{\\omega}}{\\left( x \\right)}\n\t+ 4 \\left( \\sigma_0 \\bar{\\sigma}^\\mu \\sigma_0 \\right)^{\\gamma \\dot{\\beta}} \\partial_\\mu \\bar{\\chi}_{\\dot{\\epsilon}}{\\left( x \\right)} \\dslash{\\partial}_{\\gamma \\dot{\\beta}} \\bar{\\psi}^{\\dot{\\epsilon}}{\\left( x \\right)} - \\notag \\\\\n\t&\\qquad \\left. - 2 i \\left( \\bar{\\sigma}_0 \\sigma^i \\bar{\\sigma}_0 \\right)^{\\dot{\\kappa} \\alpha} \\partial_i \\tilde{\\bar{S}}_{\\dot{\\kappa}}{}^{\\dot{\\omega}}{\\left( x \\right)} \\tilde{\\bar{R}}_{\\alpha \\dot{\\omega}}{\\left( x \\right)}\n\t- 2 i \\left( \\sigma_0 \\bar{\\sigma}^i \\sigma_0 \\right)^{\\gamma \\dot{\\beta}} \\tilde{\\bar{S}}_{\\dot{\\beta} \\dot{\\epsilon}}{\\left( x \\right)} \\partial_i \\tilde{\\bar{R}}_\\gamma{}^{\\dot{\\epsilon}}{\\left( x \\right)} \\right) \\, .\n\\end{align}\nThis expression for the Hamiltonian can be further simplified using relations (\\ref{threesigplusthreesig}) and (\\ref{threebarsigplusthreebarsig}) in Appendix \\ref{Asigmarelations} for the special case where the first and last index are 0\n\\begin{align}\n\\sigma^0 \\bar{\\sigma}^\\mu \\sigma^0\n\t&= 2 \\eta^{\\mu 0} \\sigma^0 - \\sigma^\\mu \\, , \\\\\n\\bar{\\sigma}^0 \\sigma^\\mu \\bar{\\sigma}^0\n\t&= 2 \\eta^{\\mu 0} \\bar{\\sigma}^0 - \\bar{\\sigma}^\\mu \\, .\n\\end{align}\nThe Hamiltonian is then reduced to \n\\begin{align}\n\\mathcal{H}\n\t&= \\int \\mathrm{d} \\mathbf{x} \\left(\n\t2 \\dot{\\psi}{\\left( x \\right)} \\dot{\\chi}{\\left( x \\right)}\n\t+ 2 \\boldsymbol{\\nabla} \\psi{\\left( x \\right)} \\cdot \\boldsymbol{\\nabla} \\chi{\\left( x \\right)}\n\t+ \\frac{m^2}{2} \\psi{\\left( x \\right)} \\chi{\\left( x \\right)}\n\t+ 2 \\dot{\\bar{\\chi}}{\\left( x \\right)} \\dot{\\bar{\\psi}}{\\left( x \\right)} + \\right. \\notag \\\\\n\t&\\qquad + 2 \\boldsymbol{\\nabla} \\bar{\\chi}{\\left( x \\right)} \\cdot \\boldsymbol{\\nabla} \\bar{\\psi}{\\left( x \\right)}\n\t+ \\frac{m^2}{2} \\bar{\\chi}{\\left( x \\right)} \\bar{\\psi}{\\left( x \\right)}\n\t+ \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{R}^T{\\left( x \\right)} \\tilde{R}{\\left( x \\right)} \\right)}\n\t+ \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{S}^T{\\left( x \\right)} \\tilde{S}{\\left( x \\right)} \\right)} - \\notag \\\\\n\t&\\qquad - i \\mathrm{Tr}{\\left( \\tilde{R}^T{\\left( x \\right)} \\boldsymbol{\\bar{\\sigma}} \\cdot \\boldsymbol{\\nabla} \\tilde{S}{\\left( x \\right)} \\right)}\n\t+ \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{\\bar{R}}^T{\\left( x \\right)} \\tilde{\\bar{R}}{\\left( x \\right)} \\right)}\n\t+ \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{\\bar{S}}^T{\\left( x \\right)} \\tilde{\\bar{S}}{\\left( x \\right)} \\right)} - \\notag \\\\\n\t&\\qquad \\left. - i \\mathrm{Tr}{\\left( \\tilde{\\bar{S}}^T{\\left( x \\right)} \\boldsymbol{\\bar{\\sigma}} \\cdot \\boldsymbol{\\nabla} \\tilde{\\bar{R}}{\\left( x \\right)} \\right)} \\right) \\, .\n\\label{Hxspace}\n\\end{align}\nIt contains the sum of unbarred spinor products and their barred counterparts which is only restricted to be real but could, at least in principle, be either positive or negative. Therefore, on the first glance it seems that this Hamiltonian could have negative eigenvalues. However, as the Lagrangian is by construction supersymmetric and in addition the Hamiltonian was derived using the supersymmetry algebra the eigenvalues of the Hamiltonian must be positive definite. This can also be shown by deriving the momentum space expansion of the component fields in position space, calculating the commutation and anticommutation relations of the momentum space operators, and determining the normal ordered Hamiltonian in momentum space.\n\n\\subsection{The Hamiltonian from Canonical Quantisation}\n\\label{CHcanonicalquant}\nThe derivation of the Hamiltonian using the supersymmetry algebra is by construction positive definite and is founded in the fundamental properties of the algebra. However, it immediately raises the question whether this approach is equivalent to a construction of the Hamiltonian from canonical quantisation which doesn't require the Lagrangian to be supersymmetric.\n\nFor brevity the discussion is restricted to the Lagrangian without hermitian conjugate contribution. The Hamiltonian from canonical quantisation is then defined as \n\\begin{align}\n\\mathcal{H}_{c.q.}\n\t&= \\int \\mathrm{d}^3 \\mathbf{x} \\left( - \\frac{\\partial \\mathcal{L}}{\\partial \\dot{\\chi}^\\tau} \\dot{\\chi}^\\tau\n\t- \\frac{\\partial \\mathcal{L}}{\\partial \\dot{\\psi}^\\tau} \\dot{\\psi}^\\tau\n\t+ \\frac{\\partial \\mathcal{L}}{\\partial \\dot{\\tilde{S}}^{\\tau \\omega}} \\dot{\\tilde{S}}^{\\tau \\omega}\n\t+ \\frac{\\partial \\mathcal{L}}{\\partial \\dot{\\tilde{R}}^{\\dot{\\tau} \\omega}} \\dot{\\tilde{R}}^{\\dot{\\tau} \\omega}\n\t- \\mathcal{L} \\right) \\, .\n\\end{align}\nInserting the Lagrangian into this definition of the Hamiltonian results in\n\\begin{align}\n\\mathcal{H}_{c.q.}\n\t&= \\int \\mathrm{d}^3 \\mathbf{x} \\left( 2 \\dot{\\chi}{\\left( x \\right)} \\dot{\\psi}{\\left( x \\right)}\n\t+ 2 \\boldsymbol{\\nabla} \\chi{\\left( x \\right)} \\boldsymbol{\\nabla} \\psi{\\left( x \\right)}\n\t+ \\frac{m^2}{2} \\psi{\\left( x \\right)} \\chi{\\left( x \\right)} \n\t- i \\mathrm{Tr}{\\left( \\tilde{R}^T{\\left( x \\right)} \\boldsymbol{\\bar{\\sigma}} \\cdot \\boldsymbol{\\nabla} \\tilde{S}{\\left( x \\right)} \\right)} \\right. \\notag \\\\\n\t&\\qquad \\left. + \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{S}^T{\\left( x \\right)} \\tilde{S}{\\left( x \\right)} \\right)}\n\t+ \\frac{m}{4} \\mathrm{Tr}{\\left( \\tilde{R}^T{\\left( x \\right)} \\tilde{R}{\\left( x \\right)} \\right)} \\right) \\, .\n\\end{align}\nIt turns out that the Hamiltonian derived from canonical quantisation after normal ordering is identical to the one derived using the supersymmetry algebra. This is intriguing as it paves the way for a significantly simplified derivation of the Hamiltonian in position space involving fermionic fields with mass dimension one. It represents an extension of the commonly used formalism of canonical quantisation to component fields with non-standard mass dimensions.\n\n\\section{Summary}\n\\label{Csummary}\nThe primary objective of this article was to construct a supersymmetric model for fermionic fields with mass dimension one.\n\nTo achieve this goal it was investigated whether it is possible to obtain a model based on the general scalar superfield commonly used in supersymmetric models. It has been shown that such a model cannot be formulated due to problems constructing a Lagrangian containing kinetic terms for the fermionic fields with mass dimension one. This eliminated all but the trivial solution which corresponds to a constant non-dynamic background spinor field and is not appealing. In addition no consistent second quantisation for the component fields can be constructed.\n\nThis motivated the formulation of a model for fermionic fields with mass dimension one based on a general spinor superfield. Up to now no explicit calculations for the general spinor superfield exist in the literature, therefore, necessitating the derivation of the model from the ground up. This included the calculation of all chiral and anti-chiral superfields up to third order in covariant derivatives. To second oder in covariant derivatives there is one chiral and one anti-chiral spinor field while to third order there is one chiral and one anti-chiral second rank spinor field. Interestingly, the chiral second-rank spinor field admits a special case that leads to a scalar superfield while the anti-chiral second-rank spinor field can at most be written as a vector superfield.\n\nDimensional analysis revealed that there is a large number of possible contributions to the mass and kintic terms. Therefore, the discussion was restricted to terms built from chiral and anti-chiral superfields. The resulting on-shell Lagrangian depends solely on two spinor fields and two second-rank spinor fields which corresponds to 8 fermionic and 8 bosonic degrees of freedom.\n\nAs it was not ad hoc clear that the Hamiltonian can be derived from the Lagrangian by canonical quantisation a conservative approach based on the supersymmetry algebra was utilised. It provides an anticommutation relation between the supersymmetry generators which is proportional to the momentum operator that contains the Hamiltonian as 0-th component. This is then related to the Lagrangin via the position space representation of the generators that are proportional to the spacetime integral of the supercurrent which itself can be derived from the Lagrangian. This process ensures a Hamiltonian that is consistent with the initial on-shell Lagrangian as well as the supersymmetry algebra. Therefore, the resulting Hamiltonian is positive definite. \n\nSubsequently it was shown that the Hamiltonian derived by canonical quantisation is identical to the one calculated using the supersymmetry algebra. This shows that it is possible to extend the commonly used formalism of canonical quantisation to component fields with non-standard mass dimensions.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\n\nM87 is a nearby dominant elliptical galaxy in the Virgo Cluster with the first discovered extragalactic jet \\citep{Curtis1918}. It is one of the closest radio galaxies, with a distance of only about 16~Mpc \\citep{BlakesleeEtal2009}. It is generally believed that the observed relativistic jet is powered by a supermassive black hole with a mass of $(3-6)\\times10^9\\text{ M}_\\odot$ \\citep{MacchettoEtal1997,GebhardtEtal2011,WalshEtal2013}, which corresponds to an active galactic nucleus (AGN). The proximity of M87 facilitates detailed investigation of the activity, which manifests itself throughout the spectrum from radio to very-high-energy $\\gamma$-ray emission \\citep{WilsonYang2002,PerlmanWilson2005,MadridEtal2007,AcciariEtal2009,BaesEtal2010,PerlmanEtal2011,HadaEtal2014}, and makes it a good candidate for broadening our knowledge of physical processes occurring in the central engine of the AGN.\n\nAn interest in theoretical studies of relativistic jets, arisen after the first pioneering works on the energy extraction from a black hole and the jet origin \\citep{Penrose1969,Blandford1976,Lovelace1976,BlandfordZnajek1977,BlandfordPayne1982}, is yet more growing nowadays because of the necessity to firmly establish the nature of the jet and the exact mechanism of its launching, collimation, stabilization and propagation in the external medium \\citep{ChiuehEtal1991,ApplCamenzind1993,IstominPariev1996,Fendt1997,LyndenBell2003,BeskinNokhrina2009,porthFendt2010,PorthEtal2011,Cao2012,ColgateEtal2015,TchekhovskoyBromberg2016,FengEtal2016,YangReynolds2016,EnglishEtal2016,BritzenEtal2017,SobacchiEtal2017}. For the same reason, a significant role is given to high-resolution observational research \\citep{JunorEtal1999,KovalevEtal2007,HadaEtal2011,HadaEtal2012,HadaEtal2014,DoelemanEtal2012,AkiyamaEtal2015}, which can clarify some key features of the internal jet structure. The brightness and closeness of the M87 jet allowed one to reach an unprecedented ultra-high resolution down to $50\\text{ }\\mu$arcsec in Very Long Baseline Interferometer (VLBI) radio observations, which corresponds to only $6-10$ Schwarzschild radii \\citep{HadaEtal2016,KimM87Etal2016}.\n\nAll previous studies showed that the M87 jet is almost parabolic at relatively small ($<10^5$ Schwarzschild radii) distances from the base \\citep{AsadaNakamura2012}, characterized by a limb-brightened transverse profile of radio intensity at various frequencies, and then can be considered e.g. in the model of a magnetohydrodynamic nozzle \\citep{NakamuraAsada2013}. However, new radio observations of M87 at 15~GHz (2~cm) using the NRAO Very Long Baseline Array in concert with the phased Y27 Very Large Array clearly indicate the existence of a persistent triple-ridge structure across the jet \\citep{Hada2017}. Moreover, detection of an ultra-narrow central radio ridge in these observations sets up problems in explaining the effect with the standard spine-sheath jet model usually used when explaining the appearance of the limb brightness \\citep{GhiselliniEtal2005} and poses a question whether we really observe a single jet with some decaying radial velocity profile. In this paper, I study the possibility that observing the above structure in the radio image, we can in fact deal with a pure jet-in-jet structure in M87: the inner jet is placed inside the outer annular jet. This circumstance can be evidence of simultaneous operation of two different jet-launching mechanisms, one relating to the black hole and the other to the accretion disc.\n\n\\section{Jet in jet}\n\nThe whole jet is governed by the Maxwell equations\n\\begin{gather}\n\\label{divE}\n\\operatorname{div}\\mathbf{E}=4\\pi\\rho_e,\n\\\\\n\\label{divB}\n\\operatorname{div}\\mathbf{B}=0,\n\\\\\n\\label{rotE}\n\\operatorname{curl}\\mathbf{E}=-\\frac{\\partial\\mathbf{B}}{\\partial t},\n\\\\\n\\label{rotB}\n\\operatorname{curl}\\mathbf{B}=4\\pi\\mathbf{j}+\\frac{\\partial\\mathbf{E}}{\\partial t},\n\\end{gather}\nthe condition of infinite conductivity\n\\begin{equation}\n\\label{forceFree}\n\\mathbf{E}=-\\mathbf{v}\\times\\mathbf{B},\n\\end{equation}\nand the laws of conservation of matter\n\\begin{equation}\n\\label{matterConservation}\n\\frac{\\partial\\gamma\\rho}{\\partial t}+\\operatorname{div}\\gamma\\rho\\mathbf{v}=0,\n\\end{equation}\nenergy\n\\begin{equation}\n\\label{energyConservation}\n\\frac{\\partial}{\\partial t}\\biggl(\\gamma^2 \\rho h-p+\\frac{E^2+B^2}{8\\pi}\\biggr)+\\operatorname{div}\\biggl(\\gamma^2 \\rho h\\mathbf{v}+\\frac{\\mathbf{E}\\times\\mathbf{B}}{4\\pi}\\biggr)=0,\n\\end{equation}\nand momentum\n\\begin{align}\n\\label{momentumConservation}\n&\\frac{\\partial}{\\partial t}\\biggl(\\gamma^2 \\rho h\\mathbf{v}+\\frac{\\mathbf{E}\\times\\mathbf{B}}{4\\pi}\\biggr)\\nonumber\\\\\n&+\\operatorname{div}\\biggl[\\biggl(p+\\frac{E^2+B^2}{8\\pi}\\biggr)\\mathbf{I}+\\gamma^2 \\rho h\\mathbf{v}\\mathbf{v}-\\frac{\\mathbf{E}\\mathbf{E}+\\mathbf{B}\\mathbf{B}}{4\\pi}\\biggr]=0.\n\\end{align}\nIn the above equations, we put the speed of light $c=1$, and the electric and magnetic fields are denoted by $\\mathbf{E}$ and $\\mathbf{B}$, respectively, $\\rho_e$ and $\\mathbf{j}$ are the volume charge and current densities, respectively, $\\mathbf{v}$ is the velocity of the jet plasma at a given point, $\\gamma=(1-v^2)^{-1\/2}$ is the corresponding Lorentz factor, $h=1+\\varepsilon+p\/\\rho$ is the specific relativistic enthalpy, $\\varepsilon$ is the specific internal energy, $p$ is the pressure and $\\rho$ is the mass density in the comoving reference frame. We also use notations $\\mathbf{a}\\mathbf{b}=||a_ib_j||$ for a dyad, $\\mathbf{I}=||\\delta_{ij}||$ for the unit tensor, and $\\operatorname{div}\\mathbf{T}=\\nabla\\cdot\\mathbf{T}=||\\partial T_{ji}\/\\partial x_j||$ for the divergence of a tensor $\\mathbf{T}=||T_{ij}||$. The system is complemented by an equation of state $p=p(\\rho,\\varepsilon)$.\n\nWe will consider the case of stationarity and pure cylindrical symmetry. We may write in the cylindrical coordinates the velocity\n\\begin{equation}\n\\label{velocity}\n\\mathbf{v}=v_\\phi\\mathbf{e}_\\phi+v_z\\mathbf{e}_z\n\\end{equation}\nand electromagnetic fields\n\\begin{gather}\n\\label{electricField}\n\\mathbf{E}=E_r\\mathbf{e}_r=(v_z B_\\phi-v_\\phi B_z)\\,\\mathbf{e}_r,\n\\\\\n\\label{magneticField}\n\\mathbf{B}=B_\\phi\\mathbf{e}_\\phi+B_z\\mathbf{e}_z.\n\\end{gather}\nThe components $v_\\phi$, $v_z$, $B_\\phi$, $B_z$ as well as the other scalar quantities depend on $r$ only, the distance from the symmetry axis to a given point. Equations \\eqref{velocity}--\\eqref{magneticField} mean that the lines of the matter flow and the magnetic field lines are helices lying on a cylindrical tube, and the electric field lines are orthogonal to the lateral tube surface and radially diverge from (or converge to) the symmetry axis. In the stationary case, equations \\eqref{divB}, \\eqref{rotE} and \\eqref{forceFree}--\\eqref{energyConservation} are then automatically satisfied, while equations \\eqref{divE} and \\eqref{rotB} simply determine the charge and current densities\n\\begin{gather}\n\\label{charge}\n\\rho_e=\\frac{(r E_r)'}{4\\pi r},\n\\\\\n\\label{current}\n\\mathbf{j}=-\\frac{B'_z}{4\\pi}\\,\\mathbf{e}_\\phi+\\frac{(r B_\\phi)'}{4\\pi r}\\,\\mathbf{e}_z,\n\\end{gather}\nwhere prime denotes the $r$ derivative. Consequently, the momentum conservation law \\eqref{momentumConservation}, which now takes the form\n\\begin{equation}\n\\label{momentumConservation2}\n\\biggl(p+\\frac{B_z^2+B_\\phi^2-E_r^2}{8\\pi}\\biggr)'+\\frac{B_\\phi^2-E_r^2}{4\\pi r}-\\gamma^2 \\rho h\\frac{v_\\phi^2}{r}=0,\n\\end{equation}\nplays the major role in determining the jet equilibrium.\n\nAn equivalent approach to stationary axisymmetric plasma systems is based on the Grad-Shafranov equation \\citep{Fendt1997,BeskinNokhrina2009} and earlier allowed one to study jet collimation with the help of a steady-state trans-field force-balance equation \\citep{ChiuehEtal1991,ApplCamenzind1993}, consider differential rotation in the force-free approximation \\citep{Fendt1997}, and then extend the results to the full time-dependent two-dimensional solution for the collimated jet structure close to the disc and central object \\citep{porthFendt2010,PorthEtal2011}. The equivalence of the two approaches is evident as in the stationary axisymmetric case, when the radius of a magnetic tube may change with the distance from the jet base, we have the same integrals of motion as in the Grad-Shafranov approach that follow from conservation of the magnetic flux in the tube and, respectively, matter conservation \\eqref{matterConservation},\n\\begin{equation}\n\\label{GSeta}\n\\eta=\\frac{\\gamma\\rho v_\\text{p}}{B_\\text{p}},\n\\end{equation}\nenergy conservation \\eqref{energyConservation},\n\\begin{equation}\n\\label{GSE}\n\\mathcal{E}=\\gamma h\\eta-\\frac{\\Omega_\\text{F}I}{2\\pi},\n\\end{equation}\nand momentum conservation \\eqref{momentumConservation},\n\\begin{equation}\n\\label{GSL}\n\\mathcal{L}=\\gamma h\\eta r v_\\phi-\\frac{I}{2\\pi},\n\\end{equation}\nwhere $\\Omega_\\text{F}=(v_\\phi-v_\\text{p}B_\\phi\/B_\\text{p})\/r$ is the so-called Ferraro isorotation frequency, which is also conserved along the magnetic tube, $v_\\text{p}$ and $B_\\text{p}$ are the poloidal components of the velocity and magnetic field, and $I$ is the electric current in the tube.\n\nThe intensity of radio emission increases with the number of emitting particles, so the radio-emitting areas may simply reflect the areas with an active dense plasma. In this case, the observed three-peaked transverse radio profile (fig.~2 in \\cite{Hada2017}) can directly show up the intrinsic structure of the M87 jet and be naturally interpreted thus: the jet as a whole can represent a pinch-like inner jet that is placed in an outer jet, and both jets are coaxial. The inner jet is a solid plasma cylinder of a radius $r_0$, the outer jet is a hollow plasma cylinder of an inner radius $r_1>r_0$ and thickness $d$, so that the radius of the whole jet is $R=r_1+d$.\n\nEquation \\eqref{momentumConservation2} implies the following condition at an interface between plasmas with different pressures and electromagnetic fields in the absence of singular density distribution at the interface:\n\\begin{equation}\n\\label{boundaryRelation}\n\\Delta\\biggl(p+\\frac{B_z^2+B_\\phi^2-E_r^2}{8\\pi}\\biggr)=0,\n\\end{equation}\nwhere $\\Delta$ denotes the difference between the quantities on different sides from the interface.\n\nThe basic equations allow singular charge and current densities, such as current sheets, and if a jump in the electromagnetic fields takes place as one passes through the outer boundary of the inner jet or the inner or outer boundary of the outer jet, the corresponding surface charges and currents are non-zero and can readily be found in the standard way. However, the absence of discontinuities and surface charges and currents is beneficial to proper numerical simulations of jets \\citep{GourgouliatosEtal2012,KimEtal2017}. On this basis, we may consider surface charges and currents as a potential source of instability and assume their absence. This implies zero jump in electromagnetic fields and, hence, in pressure on the boundaries,\n\\begin{equation}\n\\label{boundaryContinuity}\n\\Delta p=\\Delta E_r=\\Delta B_\\phi=\\Delta B_z=0.\n\\end{equation}\nThus, the electromagnetic field and pressure are continuous everywhere in the case of zero surface charges and currents.\n\nThe inner jet bears a total axial electric current $I$ and charge per unit length $Q$. Both the jets may rotate and some toroidal currents are allowed in the plasma, so the electromagnetic field between the jets is\n\\begin{equation}\n\\label{electricFieldBetweenJets}\nE_r=\\frac{2Q}{r},\\text{ }B_\\phi=\\frac{2I}{r},\\text{ }B_z=\\frac{\\alpha}{r}+\\beta,\\text{ }r_0R$.\n\nIn principle, the fields outside could have the same structure as those between the jets, so that the external field could be determined by some non-zero charge and current of the jet as a whole, while the axial magnetic field could be generated by some toroidal currents placed far away from the jet. In this case, the energy of the external electromagnetic field goes to infinity, but this fact itself cannot exclude the possibility of non-zero external field as it is largely an artefact of an idealized cylindrical consideration, seeing that the same situation is with an ordinary straight wire with current. Meanwhile, the absence of external field corresponds to full concentration of electromagnetic energy in the jet (which is in a certain sense `energetically profitable' when the internal field remains unchanged) and, as we will discuss below, favours the jet stability.\n\nThe quantities $Q$, $I$ and $B_z$ are not independent. We may relate the fields \\eqref{electricFieldBetweenJets} by equation \\eqref{electricField} to the toroidal and axial velocities $v_\\phi$ and $v_z$ of the intermediate plasma:\n\\begin{equation}\n\\label{chargeCurrentRelation}\nQ=v_zI-\\frac{r v_\\phi B_z}{2}.\n\\end{equation}\nWe may go to the outer boundary of the inner jet or to the inner boundary of the outer jet and relate the above three quantities to the corresponding boundary velocities $v_{0\\phi}$ and $v_{0z}$ at $r=r_0$ or $v_{1\\phi}$ and $v_{1z}$ at $r=r_1$. On the one hand, the axial magnetic field and velocities of the outer jet are related to the charge and current of the inner jet and, on the other hand, the axial magnetic field of the inner jet is determined by the toroidal current in the intermediate plasma and outer jet, so the jets are not independent but electromagnetically connected.\n\nEquation \\eqref{chargeCurrentRelation} implies the relation $v_{0z}-v_{1z}=(r_0 v_{0\\phi}B_{0z}-r_1 v_{1\\phi}B_{1z})\/2I$. When the axial velocities and magnetic fields coincide, $v_{0z}=v_{1z}$ and $B_{0z}=B_{1z}$, the ratio of the azimuthal velocities for the inner and outer jets is the inverse of the ratio for the corresponding radii, $v_{1\\phi}\/v_{0\\phi}=r_0\/r_1<1$. In this case, the outer jet rotates slower than the inner and the ratio of angular velocities of the boundaries is $\\Omega_1\/\\Omega_0=(r_0\/r_1)^2<1$.\n\nNow notice that for the electromagnetic fields of the form \\eqref{electricFieldBetweenJets} we have $(B_\\phi^2-E_r^2)'=-2(B_\\phi^2-E_r^2)\/r$. Substituting these in the momentum conservation law \\eqref{momentumConservation2} yields a balance of the relativistic centrifugal force and the gradient of hydrodynamic plus axial magnetic pressure,\n\\begin{equation}\n\\label{intermediateMomentumConservation}\n\\biggl(p+\\frac{B_z^2}{8\\pi}\\biggr)'=\\gamma^2 \\rho h\\frac{v_\\phi^2}{r}.\n\\end{equation}\nFor a constant axial magnetic field, we would have a hydrodynamic balance of the pressure gradient and centrifugal force,\n\\begin{equation}\n\\label{hydrodynamicMomentumConservation}\np'=\\gamma^2 \\rho h\\frac{v_\\phi^2}{r}.\n\\end{equation}\nSince the total momentum conservation in fact signifies the balance of hydrodynamic and electromagnetic forces, the vanishing of electromagnetic fields from the force balance means that the fields so chosen generate zero Lorentz forces and hence the hydrodynamic forces have to balance themselves. Differently speaking, the plasma can bear significant electromagnetic fields but nevertheless flow in a purely hydrodynamic way.\n\nWe expect that the plasma density between the jets is significantly lower than in the jets, and hence neglect the centrifugal term in equation~\\eqref{intermediateMomentumConservation},\n\\begin{equation}\n\\label{intermediatePressureBalance}\np+\\frac{B^2_z}{8\\pi}=\\text{const},\\text{ }r_0