Doctoral Dissertation
博士論文

Search for Proton Decay via p → e+π 0 and p → µ+π 0 with an
Enlarged Fiducial Mass of the Super-Kamiokande Detector(スーパーカミオカンデ検出器の拡張有効質量を用いた陽子崩壊 p → e+ π 0 と p → µ+ π 0 の探索)

A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2020
令和 2 年 12 月博士 (理学) 申請

Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科物理学専攻

Akira Takenaka
竹中 彰

Abstract
We have searched for proton decay via p → e+ π 0 and p → µ+ π 0 modes using all SuperKamiokande data until May 2018, in total 450 kton·years exposure. In this analysis, we haveenlarged the Super-Kamiokande fiducial mass from 22.5 kton to 27.2 kton, and the 78 kton·yearsof enlarged fiducial mass region data has been analyzed for the first time. No candidates arefound for p → e+ π 0 with 0.59 of expected atmospheric neutrino backgrounds, and one candidate
is found for p → µ+ π 0 with 0.94 of expected atmospheric neutrino backgrounds. The results
are consistent with the expected number of backgrounds. Lower limits on the proton partial
lifetime are set to be τ /B(p → e+ π 0 ) > 2.4 × 1034 years and τ /B(p → µ+ π 0 ) > 1.6 × 1034 years
at 90% confidence level. They are the wolrd’s most stringent constraints for these decay modes.

Contents
1 Introduction

12 Physics Motivation
2.1 Standard Model (SM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Grand Unified Theories (GUTs) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Minimal SU(5) GUT model . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Extensions of SU(5) GUT model . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Supersymmetric GUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Proton Decay Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
2
4
4
5
5
6

3 The Super-Kamiokande Detector
3.1 Cherenkov Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Inner and Outer Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Water Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Air Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 High-voltage Determination . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Relative Gain Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Absolute Gain Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Relative Quantum Eﬃciency Calibration . . . . . . . . . . . . . . . . . . .
3.3.5 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6 Light Absorption and Scattering in Water . . . . . . . . . . . . . . . . . .
3.3.7 Light Reflection at PMT and Black Sheet . . . . . . . . . . . . . . . . . .

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4 Simulation
4.1 Proton Decay Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Atmospheric Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 (Quasi-)Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Meson Exchange Current . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Single Meson Production . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Coherent Pion Production . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.5 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Hadronic Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Treatment for Neutron Tagging Process . . . . . . . . . . . . . . . . . . .

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CONTENTS

5 Data Set
5.1 Treatment of OD PMT Hits in SK-IV - ID-OD Crosstalk . . . . . . . . . . . . .
5.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Through-going Muon Rejection . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Stopping Muon Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Cable Hole Muon Rejection . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Low Energy Event Rejection . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5 Flasher Event Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.6 Accidental Coincidence Event Rejection . . . . . . . . . . . . . . . . . . .
5.5 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Tight Stopping Muon Rejection . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Tight Cable Hole Muon Rejection . . . . . . . . . . . . . . . . . . . . . .
5.6.3 Invisible Muon Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.4 Further Flasher Event Rejection . . . . . . . . . . . . . . . . . . . . . . .
5.6.5 Tight Accidental Coincidence Event Rejection . . . . . . . . . . . . . . .
5.7 Event Reduction Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1 Event Selection Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Non-neutrino Background Events . . . . . . . . . . . . . . . . . . . . . . .

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6 Event Reconstruction
72
6.1 FC Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1.3 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1.4 Precise Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.5 Ring Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.6 Momentum Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.1.7 Ring Number Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1.8 Michel Electron Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.1.9 Reconstruction Performance on Proton Decay Events . . . . . . . . . . . 89
6.2 Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2.1 Absolute Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . . . . . 90
6.2.2 Evolution of the Energy Scale over Time . . . . . . . . . . . . . . . . . . . 96
6.2.3 Zenith-angle-dependence of the Energy Scale . . . . . . . . . . . . . . . . 96
6.3 Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.1 Time-clustered PMT Dark Noise . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.2 Initial Neutron Candidate Selection . . . . . . . . . . . . . . . . . . . . . 102
6.3.3 Final Neutron Candidate Selection with Neural Network . . . . . . . . . . 102
6.3.4 Am-Be Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7 Proton Decay Search Analysis
114
7.1 Proton Decay Search Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.1 Proton Decay Signal Selection Criteria . . . . . . . . . . . . . . . . . . . . 114
7.1.2 Search Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.1.3 Search Sensitivity Improvement by Enlarging the Fiducial Mass . . . . . . 128
7.2 Search Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.3.1 Physics Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.3.2 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

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CONTENTS

7.4
7.5

7.3.3 Summary of Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . 135
Lifetime Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.5.1 Implications of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.5.2 Future Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

8 Conclusion

141

A Detailed Calibration of 50 cm Diameter PMT Response and Impacts on Event
Reconstruction
143
A.1 Detailed Calibration of SK PMT Response . . . . . . . . . . . . . . . . . . . . . 143
A.1.1 Motivation of the Measurement . . . . . . . . . . . . . . . . . . . . . . . . 143
A.1.2 Measurement Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A.1.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.2 Measurement of PMT Dynode Direction and Residual Magnetic Field in the SK
Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.2.1 PMT Dynode Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A.2.2 Residual Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A.3 Impacts on Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

iii

List of Figures
Proton decay (p → e+ π 0 ) diagram. . . . . . . . . . . . . . . . . . . . . . . . . . .
Inverse of running coupling constants as a function of the logarithm of the energy
scale. Taken from [3, 19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Proton decay (p → νK + ) diagram. In the diagram, H̃C stands for color-triplet
higgs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relation between Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ) and each decay mode’s lifetime.
Diﬀerent gauge group, SU(5), SO(10) and E6 , predictions are plotted in black,
red and blue, respectively. Taken from [25]. . . . . . . . . . . . . . . . . . . . . .
Prediction of Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ) in case of unflipped (standard) SUSY
SU(5) (black line) and flipped SUSY SU(5) with normal (blue histogram) andinverted (green histogram) neutrino mass ordering. Taken from [26]. . . . . . . .

5Super-Kamikoande detector side view. Taken from [28]. . . . . . . . . . . . . . .
Super-Kamikoande detector coordinates. The origin of the coordinates axes is set
at the center of the detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Schematic view of the frame structure (“supermodule”). 12 ID PMTs and 2 OD
PMTs are mounted on one supermodule. Taken from [28]. . . . . . . . . . . . .
3.4 Schematic view of the 50 cm diameter PMT. Taken from [28]. . . . . . . . . . . .
3.5 Quantum eﬃciency as a function of incident photon wavelength. Taken from [28].
3.6 Single photoelectron distribution of the 50 cm diameter PMT. Taken from [28]. .
3.7 Transit time distribution of the 50 cm diameter PMT. Taken from [28]. . . . . .
3.8 Cherenkov ring image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Cherenkov ring image produced by an electron. . . . . . . . . . . . . . . . . . . .
3.10 Cherenkov ring image produced by a muon. . . . . . . . . . . . . . . . . . . . . .
3.11 Schematic view of the compensation coils. They are composed of 26 sets of coils
deployed outside the water tank. Taken from [33]. . . . . . . . . . . . . . . . . .
3.12 Schematic diagram of the water purification system as of SK-IV. Each component
is described in the text. Taken from [35]. . . . . . . . . . . . . . . . . . . . . . .
3.13 Schematic view of the water circulation paths in the SK tank. Taken from [35]. .
3.14 Schematic diagram of the air purification system. Each component is describedin the text. Taken from [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Schematic diagram of the ID data acquisition system for SK-I to -III. The data
flow is described in the text. Taken from [28]. . . . . . . . . . . . . . . . . . . .
3.16 Schematic diagram of the trigger generation for SK-I to -III. When the sum of
HITSUM exceeds the threshold level, a global trigger is issued. Taken from [41].
3.17 Schematic diagram of the OD data acquisition system for SK-I to -III. Taken
from [40]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.18 Schematic diagram of the QBEE electronics. Taken from [29]. . . . . . . . . . . .
3.19 Schematic diagram of the data acquisition system for SK-IV. The data flow is
described in the text. Taken from [30]. . . . . . . . . . . . . . . . . . . . . . . .

11

2.1
2.2
2.3
2.4

2.5

3.1
3.2

iv

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8

8

11
12
13
14
14
14
14
15
15
16
17
17
18
19
20
20
21
22

LIST OF FIGURES

3.20 Net of the ID. Red points denote the locations of 420 “standard PMTs” in the
ID. Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.21 Grouping of the ID PMTs for the HV determination. Taken from [42]. . . . . . . 23
3.22 Uniformity of the observed charge compared to the reference PMT value. Taken
from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.23 Relative gain distribution of the ID PMTs. Values are normalized to their meanvalue. Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.24 Picture of the NiCf source, which is made of 6.5 kg of NiO and 3.5 kg of polyethylene. The Cf source is located inside the ball and provides neutrons. Taken from [42]. 25
3.25 Charge distribution in units of pC obtained in the absolute gain calibration in
SK-III. Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.26 Time variation of the PMT gain. Data points for SK-I to -III are normalized by
the first data point value in each period, and for SK-IV, they are normalzied by
the average value in Apr./2009. In SK-IV, PMTs are divided into five groups
depending on their production year. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.27 Position dependence of the photon detection probability in the detector in therelative QE calibration. The vertical axis values are normalized by the averagevalue of all PMTs. The top plot shows the barrel (side) PMTs, and the horizontal
axis is the Z position of PMTs in cm. The bottom left (right) plot shows the top(bottom) PMTs, and the horizontal axis is the square of the distance from thedetector center in cm2 . Data points are plotted in red, and MC points are plottedin blue. In MC points, the obtained QE of individual PMTs is not reflected.
Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.28 Schematic diagram of the timing calibration system. Taken from [42]. . . . . . . 28
3.29 Cross-section of the diﬀuser ball. Taken from [42]. . . . . . . . . . . . . . . . . . 28
3.30 Typical TQ distribution for one readout channel (PMT No.10). The horizontal
axis corresponds to observed charge and the vertical axis is detection timing.
Larger value in the vertical axis corresponds to earlier hits in this plot. Taken
from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.31 Timing distribution added over all the readout channels (red points) and thefitted asymmetric Gaussian function (solid blue curve). The observed charge
region used in the distribution is about 3 pC (1 photoelectron level). Here again
larger value in the horizontal axis corresponds to earlier hits. Taken from [42]. . 29
3.32 Timing resolution as a function of observed charge. Taken from [42]. . . . . . . . 29
3.33 Schematic view of the water laser system. A typical event display of the “laser”
event is shown in bottom right. The wavelength was changed in 2009; from 365 nm
to 375 nm, from 400 nm to 405 nm, and from 420 nm to 445 nm and 473 nm.
Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.34 Timing distributions after photon time-of-flight (T.O.F.) subtraction (wavelength
at 405 nm). The wavelength was changed in the middle of SK-IV from 400 nm
to 405 nm. Time-of-flight is calculated based on the distance between the target
position of the laser at the detector bottom region and the PMT position. From
top to bottom, the detector top region, and B1 to B5 timing distributions arealigned. Entries in left part in each plot indicate scattered photons, and rightpeaks indicate reflected photons at the detector bottom. Data points are plottedin black dots and MC predictions are plotted in red. Taken from [42]. . . . . . . 31
3.35 Water absorption and scattering coeﬃcients obtained from the water laser data
in 2009 are plotted in dots. Curves are the fitted polynomial functions. Taken
from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32v

LIST OF FIGURES

3.36 Time variation of water transparency (water attenuation length). Absolute values are sensitive to the detector configurations and can not be compared among
diﬀerent detector phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.37 Schematic view of the laser light injector system for the reflectivity measurementof the black sheet. Both the reflected and direct light was measured by ID PMTs.
Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.38 The left plot shows the ratio of the observed charge from reflected light to theobserved charge from direct light without the black sheet as a function of lightincident angle at the black sheet. Data points are plotted in black cross and MC
points are in red circle. The right plot shows the ratio between data and MC.
The top, middle and bottom plots correspond to the wavelength of 337, 400 and
420 nm, respectively. Taken from [42]. . . . . . . . . . . . . . . . . . . . . . . .
Distributions of the Fermi momentum for the P state (left) and S state (right).
Data points show electron-12 C scattering experiment data and solid lines aretheoretical curves. Taken from [44]. . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Proton state distribution during the decay. . . . . . . . . . . . . . . . . . . . . .
4.3 Initial proton momentum distribution. Free proton and bound proton decay
events are stacked. Pion FSI eﬀects are not included. . . . . . . . . . . . . . . .
4.4 Eﬀective proton invariant mass distribution. Free proton and bound proton decay
events are stacked. Pion FSI eﬀects are not included. . . . . . . . . . . . . . . .
4.5 Cross-sections of π ± -12 C scattering (π + in top left and π − in top right) and
π ± -16 O scattering (π + in bottom left and π − in bottom right). Points show experimental data and solid lines are simulation curves. Dashed lines are simulation
curves in previous versions. Taken from [49]. . . . . . . . . . . . . . . . . . . . .
4.6 Fraction of π 0 interactions as a function of π 0 momentum. Taken from [27]. . .
4.7 Typical event display of a p → e+ π 0 event. The ring in the left side is producedby the positron, while the two rings shown in the right side are produced by the
gamma rays from the π 0 decay. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Atmospheric neutrino flux distributions at Kamioka as a function of zenith angle,cos θ. Here θ is the arrival direction of the neutrino, where cos θ = 1 stands forvertically downward going neutrinos. In these distributions, the azimuth component is averaged out. From left to right, neutrino of 0.32 GeV, 1.0 GeV, and
3.2 GeV cases are shown. Taken from [54]. . . . . . . . . . . . . . . . . . . . . .
4.9 Neutrino flux distributions at Kamioka as a function of neutrino energy. The
Honda model prediction is shown in red. The previous Honda model prediction
is shown in blue. Taken from [54]. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 The Fermi momentum distributions. The blue histogram shows the Fermi momentum distribution used in the proton decay MC which is based on the shellmodel [45]. The red histogram shows the one used in the neutrino MC which isbased on the relativistic Fermi gas model [66]. In the neutrino MC (NEUT), theFermi surface momentum is set to 225 MeV/c. . . . . . . . . . . . . . . . . . . .
4.11 Charged current quasi-elastic scattering cross-sections as a function of incoming
neutrino energy. The left plot shows the neutrino case and the right shows theanti-neutrino case. The black line is the model prediction used in this analysis(NEUT version 5.3.6). Experimental data points are from: ANL [69], BNL [70],Gargamelle [71], Serpukhov [72], and SKAT [73]. . . . . . . . . . . . . . . . . . .
4.12 Charged current single π production cross-sections as a function of incoming neutrino energy. The dotted black line corresponds to the model used in previous
SK proton decay searches [27], NEUT 5.1.4, and the solid red line shows that forthe current analysis, NEUT 5.3.6. . . . . . . . . . . . . . . . . . . . . . . . . . .

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40

41

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42

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LIST OF FIGURES

4.13 Four momentum transfer in the charged current single π production interaction. The black histogram corresponds to the model used in previous SK proton
searches [27], NEUT 5.1.4, and the red histogram corresponds that for the current
analysis, NEUT 5.3.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.14 Charged current total cross-sections divided by incoming neutrino energy. The
left plot shows the neutrino case and the right shows the anti-neutrino case. The
black line is the model prediction used in this analysis (NEUT version 5.3.6).
Experimental data points are from: CCFR [82], CDHS [83], Gargamelle [84],
CHARM [85], BEBC [86], SKAT [87], IHEP-JINR [88], IHEP-ITEP [89], and
CCFRR [90]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.15 Treatment of the PMT simulation. The simulated PMT dark noise hits are replaced by the real PMT hits taken from the random trigger event data for thetime region used for neutron tagging, which begins 18 µsec after the primary
trigger. Taken from [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.16 PMT hit rate as a function of time after the primary event trigger. The exponential decay within 10 µsec corresponds to hits produced by Michel electrons frommuon decays. The bump between 12 and 18 µsec corresponds to hits producedby PMT after-pulsing. Taken from [97]. . . . . . . . . . . . . . . . . . . . . . . .
4.17 Average neutron multiplicity (the number of tagged neutrons per primary neutrino event) as a function of detector deposited energy in SK. The black dotsshows the SK-IV data and the red histogram shows the atmospheric neutrino
MC events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1

5.2

5.3

5.4

5.5

5.6

Typical event display in which a large amount of photons are observed in the ID
and fake OD PMT hits are recorded. The main event display is the ID one andthe top left is the OD one. A circle located at each PMT position corresponds to
the PMT hit and the size of its radius is proportional to the number of observed
photoelectrons. In the detector top region, fake OD PMT hits can be found. . .
Typical laser event display in which a large amount of photons are distributed
into the whole ID, and fake OD PMT hits are recorded. In this event, almost all
ID PMTs observed more than 1000 p.e.’s. . . . . . . . . . . . . . . . . . . . . . .
Two-dimensional scatter plots of OD PMT charge and hit timing relative tothe closest ID PMT hit timing. The laser event plot is in left, and the partiallycontained MC event plot is in right. In laser calibration event, no charged particles
exit the ID, while in the partially contained MC events, charged particles actually
exit the ID and emit Cherenkov photons in the OD. Taken from [102]. . . . . .
Reduction variable PEmax /PE300 distributions in SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetime and the twoflavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
“Final Sample” refers to events after all the FC event selection criteria. Verticalerror bars on the data points denote the statistical uncertainty. . . . . . . . . .
Reduction variable NHITA800 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor
oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final
Sample” refers to events after all the FC event selection criteria. Vertical error
bars on the data points denote the statistical uncertainty. . . . . . . . . . . . . .
The top two plots are the two-dimensional NHITAthru
and NHITAthru
out scatterinplots in SK-IV. The bottom two plots show the one-dimensional distributions of
the final sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation
probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars on thedata points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . .

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5.7

Reduction variable NHITAin distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor
oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final
Sample” refers to events after all the FC event selection criteria. Vertical error
bars on the data points denote the statistical uncertainty. . . . . . . . . . . . . .
5.8 Schematic view of the top of the detector. Shaded circles represent the cableholes. Taken from [107]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Schematic view of the veto counter. It is composed of a plastic scintillator plateand 50 cm PMT. Taken from [107]. . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Reduction variable N50 distributions of events with less than 500 ID PMT hits
in SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by
SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). The term “Final Sample” refers to events after all the FC event
selection criteria. Vertical error bars on the data points denote the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.11 Reduction variable NHITmin100 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor
oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final
Sample” refers to events after all the FC event selection criteria. Vertical error
bars on the data points denote the statistical uncertainty. . . . . . . . . . . . . .
5.12 Low energy fit goodness distributions of events with less than 250 ID PMT hits
in SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by
SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). The term “Final Sample” refers to events after all the FC event
selection criteria. Vertical error bars on the data points denote the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.13 The top two plots show the two-dimensional PELATE and NHITALATE scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of
the final sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation
probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars on thedata points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . .
5.14 Typical flasher event displays. They are diﬀerent events but caused by the same
PMT which detects a large amount of photons (the large circle). . . . . . . . . .
5.15 Reduction variable prob distributions in SK-IV. The atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation
probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample”
refers to events after all the FC event selection criteria. Vertical error bars on thedata points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . .
5.16 The top two plots show the two-dimensional stopping muon fit goodness and
NHITAin scatter plots in SK-IV. The bottom two plots show the one-dimensional
distributions of the final sample in SK-IV. In the NHITAin one-dimensional
distribution, events with stopping muon fit goodness of 5 or more are filled.
In the stopping muon fit goodness one-dimensional distribution, events withNHITAin of 5 or more are filled. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars on the data
points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . .

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58
59

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LIST OF FIGURES

5.17 Reduction variable NHITAin200 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor
oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final
Sample” refers to events after all the FC event selection criteria. Vertical error
bars on the data points denote the statistical uncertainty. . . . . . . . . . . . . .
5.18 Reduction variable NHITAin distributions in SK-IV. Events with less than agood <0.77, more than 7000 ID PMT hits and more than 70000 p.e.’s of total observed
charge are plotted. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 =2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after all
the FC event selection criteria. Vertical error bars on the data points denote thestatistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.19 Distributions of the distance between the reconstructed entering point and theclosest cable hole position, dhole , in SK-IV. Events with more than 0.4 of stopping
muon fit goodness, more than 4000 p.e.’s of total charge and cos θz > 0.6 areplotted. The atmospheric neutrino (ATM ν) MC histograms are normalized by
SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). The term “Final Sample” refers to events after all the FC event
selection criteria. Vertical error bars on the data points denote the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 The top two plots show the two-dimensional NHITAearly200 and NHITAsum scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of
the final sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation
probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Only events with less than
1000 p.e.’s of total observed charge are plotted. Vertical error bars on the data
points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . .
5.21 Reduction variable NHITAearly200 distributions without any ID PMT conditions
in SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by
SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). The term “Final Sample” refers to events after all the FC event
selection criteria. Vertical error bars on the data points denote the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.22 The top two plots show the two-dimensional Point-fit goodness and NHITMIN100
scatter plots in SK-IV. The bottom two plots show the one-dimensional distributions of the final sample in SK-IV. In the bottom plots, the atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor
oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars
on the data points denote the statistical uncertainty. . . . . . . . . . . . . . . .
5.23 The top two plots show the two-dimensional PE500 and NHITALATE200 scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of
the final sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation
probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars on thedata points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . .
5.24 Event rate at each reduction step during SK-IV as a function of date. The 1st,
2nd, 3rd, 4th, and 5th reduction output rates are plotted in black, red, green,
blue, and yellow, respectively. The purple (cyan) one corresponds to the event
rate of the final sample with dwall greater than 200 cm (in between 100 and
200 cm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.25 The number of dead OD PMTs as a function of date. . . . . . . . . . . . . . . .

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64

64

65

66

67
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LIST OF FIGURES

5.26 Remaining non-neutrino background distribution as a function of dwall. Cosmicray muons and no Cherenkov ring events are stacked. No Cherenkov ring eventsare dominated by flasher events described in the text. . . . . . . . . . . . . . . .
6.1

6.2

6.3

6.4

6.5
6.6

6.7

6.8

6.9

Typical observed charge distribution as a function of the opening angle (top),
PEcor (θ). The bottom plot is the second derivative distribution of the top plot.
Taken from [108]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distributions of the distance between the reconstructed vertex and true vertex
position on free proton decay MC events. The left plot shows p → e+ π 0 andthe right shows p → µ+ π 0 MC events, and they are livetime-weighted combinedfrom SK-I to -IV. The solid cyan histogram shows events reconstructed in theconventional fiducial mass region, the pink dashed histogram shows that for the
additional fiducial mass region, and the black dotted histogram is for the region
between dwall of 50 cm and 100 cm. Vertex resolution indicates 68 percentile. .
Reconstructed dwall distribution of Sub-GeV multi-ring events in SK-I to -IV.
The black dots show the data and the red histogram shows the atmospheric
neutrino MC (ATM ν MC) events. Atmospheric neutrino MC is normalized bylivetime and includes reweighting to the latest SK oscillation fit [64]. Verticalerror bars denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . .
The Hough transformation. Suppose there are four hit PMTs on in a ring witha radius of r (left). The observed charge is transformed into the Hough space asa circle with a radius of r (right), and the resulting circles are overlapped at thecenter of the original ring, i.e. the original ring center manifests as a peak in the
Hough space. Taken from [108]. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Example of the resulting Hough space for a two-ring event. The peaks correspondto their Cherenkov ring centers. Taken from [108]. . . . . . . . . . . . . . . . . .
Distributions of the number of reconstructed rings of free proton decay MC events.
The left plot shows p → e+ π 0 and the right shows p → µ+ π 0 MC events, andthey are livetime-weighted combined from SK-I to -IV. The solid cyan histogramshows events reconstructed in the conventional fiducial mass region, the pinkdashed histogram shows that for the additional fiducial mass region, and theblack dotted histogram is for the region between dwall of 50 cm and 100 cm. . .
Distributions of the number of reconstructed rings of Sub-GeV events for data
and atmospheric neutrino MC events (SK-I to -IV combined). The left plot corresponds to the conventional fiducial mass region and the right plot to the additional
fiducial mass region. Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK oscillation fit [64]. Vertical error bars on thedata points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . .
Ring counting likelihood distributions of Sub-GeV events for data and atmospheric neutrino MC events (SK-I to -IV combined). The left plot corresponds tothe conventional fiducial mass region and the right plot to the additional fiducial
mass region. Atmospheric neutrino MC is normalized by livetime and includes
reweighting to the latest SK oscillation fit [64]. Vertical error bars on the data
points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . .
PMT charge distributions as a function of the opening angle from the electron
direction. The Black histogram shows MC truth observed charge distribution, andthe blue (red) histogram shows the expected charge distribution before (after) the
update described in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

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74

76

76

77
78

79

80

80

81

LIST OF FIGURES
6.10 Multi-ring PID likelihood distributions of free p → e+ π 0 decay events. The top
three plots correspond to the conventional and the bottom three plots correspondto the additional fiducial mass region. The black (red) distributions are before(after) the expected charge table update described in the text. Here, Mis-PID
rate indicates the fraction of Cherenkov rings which are reconstructed as µ-like.
From left to right, the 1st to 3rd ring distributions are shown. . . . . . . . . . .
6.11 Mis-PID rate as a function of true particle momentum for single-ring events. The
left plot shows the electron case and the right plot shows the muon case. Black andgray (red and magenta) points denote before (after) the updated of the expectedcharge table update described in the text. Vertical error bars denote the MCstatistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Multi-ring PID likelihood distributions of Sub-GeV multi-ring events for data
and atmospheric neutrino MC events (SK-I to -IV combined). The top threeplots correspond to the conventional and the bottom three plots correspond to
the additional fiducial mass region. The black dots show the data and the red
and green histograms show the atmospheric neutrino MC events. Atmospheric
neutrino MC is normalized by livetime and includes reweighting to the latest SK
oscillation fit [64]. From left to right, the 1st to 3rd ring distributions are shown.
Vertical error bars denote the statistical uncertainty. . . . . . . . . . . . . . . .
6.13 Event display of a two-ring event. The left one shows the original event display.
The middle and right one show the separated first and second ring, respectively,
after applying the ring separation algorithm. . . . . . . . . . . . . . . . . . . . .
6.14 Reconstructed total mass distributions for free proton decays via p → e+ π 0 MC
events. The left (right) plot shows two-ring (three-ring) events. In each plot, thesolid cyan histogram shows events reconstructed in the conventional fiducial mass
region, the pink dashed histogram shows that for the additional fiducial mass
region, and the black dotted histogram is for the region between dwall of 50 cm
and 100 cm. The peak position and width of the distributions are obtained using
Gaussian fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.15 Reconstructed total mass distributions for free proton decays via p → µ+ π 0 MC
events. The left (right) plot shows two-ring (three-ring) events. In each plot, thesolid cyan histogram shows events reconstructed in the conventional fiducial mass
region, the pink dashed histogram shows that for the additional fiducial mass
region, and the black dotted histogram is for the region between dwall of 50 cm
and 100 cm. The peak position and width of the distributions are obtained using
Gaussian fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.16 Distributions of the number of tagged Michel electrons for p → µ+ π 0 MC events.
They are livetime-weighted combined from SK-I to -IV The solid cyan histogramshows events reconstructed in the conventional fiducial mass region, the pinkdashed histogram shows that for the additional fiducial mass region, and theblack dotted histogram is for the region between dwall of 50 cm and 100 cm. . .
6.17 Distribution of the number of tagged Michel electrons of Sub-GeV multi-ring
events for atmospheric neutrino MC and data in SK-I to -IV. The left plot corresponds to the conventional fiducial mass region and the right plot to the additional
fiducial mass region. Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK oscillation fit [64]. Vertical error bars denotethe statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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87

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LIST OF FIGURES

6.18 Michel electron momentum distributions. From top to bottom, SK-I to -IV plots
are aligned. The left plots correspond to the conventional and the right plots
correspond to the additional fiducial mass region. In each plot, the number of
entries in the MC histogram is normalized to that of data. Vertical error bars
denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.19 Neutral pion mass distributions. From top to bottom, SK-I to -IV plots arealigned. The left plots correspond to the conventional and the right plots correspond to the additional fiducial mass region. Atmospheric neutrino MC is normalized by livetime and the two-flavor oscillation probability (∆m2 = 2.5×10−3 eV2 ,sin2 2θ = 1.0), here. Vertical error bars denote the statistical uncertainty. . . . . 94
6.20 Cherenkov opening angle as a function of muon momentum. . . . . . . . . . . . 95
6.21 Distribution of the ratio of the momentum derived from the total observed charge(Ppe ) to the momentum derived from the Cherenkov opening angle (Pθ ) for SK-IV.
The left plot corresponds to events with Pθ between 200 and 280 MeV/c. The
middle plot corresponds to events with Pθ between 280 and 360 MeV/c. The
right plot corresponds to events with Pθ between 360 and 440 MeV/c. In eachplot, the blue histogram is data and the red is MC. Taken from [110]. . . . . . . 95
6.22 Muon momentum over range distributions for SK-IV. The Multi-GeV stopping
cosmic-ray muons are divided into six group with their range, Rµ . In each plot,
the number of entries in the MC histogram is normalized to that of data. Verticalerror bars denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . 97
6.23 Absolute energy scale diﬀerence between data and MC control samples. Verticalerror bars denote the statistical uncertainty, and horizontal error bars denotethe momentum range for each control sample. For the Michel electron and π 0samples, points with solid error bars correspond to the conventional fiducial mass
region, and points with dashed error bars correspond to the additional fiducial
mass region. Cosmic-ray muon samples are considered for both the conventional
and additional fiducial mass regions to take the most discrepant control sample.
98
6.24 Time variation of the average momentum of Michel electrons as a function of date.
For each fiducial mass region and SK phase, data points are normalized by theirmean value. The upper (lower) plot corresponds to the conventional (additional)
fiducial mass region. Vertical error bars denote the statistical uncertainty. For
SK-I to -III, each data point corresponds to a one month average and for SK-IV,
each data point corresponds to a 10 day average. . . . . . . . . . . . . . . . . . 99
6.25 Time variation of the average momentum over range of Multi-GeV stopping
cosmic-ray muons as a function of date. For each SK phase, data points arenormalized by their mean value. Vertical error bars denote the statistical uncertainty. Each data point corresponds to a 10 day average. . . . . . . . . . . . . . 99
6.26 Ratio of the average momentum between data and MC as a function of Michelelectron direction, zenith angle, cos θz . From top to bottom, SK-I to -IV plots
are aligned. The left plots correspond to the conventional and the right plots
correspond to the additional fiducial mass region. Vertical error bars denote thestatistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.27 Typical waveform of time-clustered noise hits (1 µsec/div for the horizontal axis
and 5 mV/div for the vertical axis). This sample PMT’s dark noise is measured to
be about 8 kHz in the measurement condition. Therefore, the expected number ofdark noise hits per 10 µsec is about 0.08 if the dark noise is uniformly distributed
in time. Taken from [106]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

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6.28 23 input variable distributions of initial neutron candidates associated with theprimary FC events in the conventional fiducial mass region. The black dots show
the data in SK-IV. The red histograms show the atmospheric neutrino MC eventsand are normalized by livetime and the two-flavor oscillation probability (∆m2 =2.5 × 10−3 eV2 , sin2 2θ = 1.0). True neutron candidates (green) and fake neutron
candidates (blue) are also separately shown. . . . . . . . . . . . . . . . . . . . . 106
6.29 23 input variable distributions of initial neutron candidates associated with theprimary FC events in the additional fiducial mass region. The black dots show
the data in SK-IV. The red histograms show the atmospheric neutrino MC eventsand are normalized by livetime and the two-flavor oscillation probability (∆m2 =2.5 × 10−3 eV2 , sin2 2θ = 1.0). True neutron candidates (green) and fake neutron
candidates (blue) are also separately shown. . . . . . . . . . . . . . . . . . . . . 107
6.30 Neural network output distributions. The black dots show the data in SK-IV.
The red histograms show the atmospheric neutrino MC events and are normalized by livetime and the two-flavor oscillation probability (∆m2 = 2.5×10−3 eV2 ,sin2 2θ = 1.0). True neutron candidates are shown in green. The top (bottom)
three plots correspond to neutron candidates associated with the primary FC
events within the conventional (additional) fiducial mass region. Neutron candidates with N10 = 5 are shown in left, and those with N10 = 6 are shown in
middle, and those with N10 of 7 or more are shown in right. The bold lines andarrows denote the neutron signal selection thresholds. . . . . . . . . . . . . . . . 108
6.31 Neutron capture time (left) and multiplicity (right) distributions. The top (bottom) two plots correspond to tagged neutrons associated with the primary FC
events in the conventional (additional) fiducial mass region. The black points
shows the data in SK-IV, and the red histograms the atmospheric neutrino MC
events and are normalized by livetime and the two-flavor oscillation probability(∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The blue curves in the left plots are
the best fit functions of the data histograms. t = 0 corresponds to the primary
FC event timing. For the multiplicity distributions, only Sub-GeV primary FC
events are used. Vertical error bars denote the statistical uncertainty. . . . . . . 109
6.32 The Am-Be source used for the calibration. The source is embedded in a 5 cm
cube of BGO scintillator and it is held in an acrylic case. Taken from [97]. . . . 110
6.33 N10 distributions of the calibration data, MC, and background data taken with the
Am-Be source at Center. The black dots in the left plot shows the calibration data,
the red histogram shows the generated neutron MC (green) plus the backgrounddata (blue). The black dots in the right plot shows the calibration data after
the subtraction of the background data (blue). Vertical error bars denote thestatistical uncertainty. Entires with N10 of more than 20 are filled in the last bin.
The green histograms are the standard MC outputs (without any QE changes). 111
6.34 Chi-square test results as a function of relative QE change. The red curve is thebest fit quadratic function. The χ2 minimum corresponds to a 0.9% QE change,
and the χ2 + 1 point corresponds to a 2.2% QE change. The discrepancy between
the standard MC prediction and χ2 + 1 point is taken as a systematic uncertainty
on the QE factor in MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.35 Neutron capture time distributions. The top two plots shows events after the
initial selection. The bottom two plots shows events after the neural network
selection. The left plots correspond to the calibration data taken with the AmBe source at Center, while the right plots correspond to the neutron MC plus
the background data. The blue curves are the best fit exponential plus constantfunctions. Vertical error bars denote the statistical uncertainty. . . . . . . . . . 113

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7.1

7.2

7.3

7.4

7.5

Distributions of the number of reconstructed rings after applying C1. They show
the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV are combined). Free
proton decay events (light color) and bound proton events (dark color, hatched)
are stacked. The left plots correspond to the conventional fiducial mass region,and the right plots to the additional. The distributions for the data in SK-I to-IV and atmospheric neutrino MC events are shown in Figure 6.7. . . . . . . . . 116
Multi-ring PID distributions after applying C1 ∼ C2. The top six plots show
the p → e+ π 0 MC events (SK-I to -IV are combined). Free proton decay events(light color) and bound proton events (dark color, hatched) are stacked. The
black dots show the data in SK-I to -IV, and the red and green histograms show
the atmospheric neutrino MC events. Atmospheric neutrino MC is normalized bylivetime and includes reweighting to the latest SK oscillation fit [64]. From left toright, the 1st to 3rd ring distributions are shown. The first and third plots fromtop correspond to the conventional fiducial mass region, and the second from top
and bottom plots correspond to the additional. Vertical error bars on the data
points denote the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . 117
Distributions of the number of tagged Michel electrons after applying C1 ∼ C3.
The top four plots show the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV
are combined). Free proton decay events (light color) and bound proton events(dark color, hatched) are stacked. The black dots show the data in SK-I to -IV,and the red and green histograms show the atmospheric neutrino MC events.
Atmospheric neutrino MC is normalized by livetime and includes reweighting to
the latest SK oscillation fit [64]. Vertical error bars on the data points denotethe statistical uncertainty. The event rate discrepancy between data and MC in
the second bin for p → µ+ π 0 is within the systematic uncertainty associated withthe physics modeling described in Section 7.3.1. The left plots correspond to theconventional fiducial mass region, and the right plots to the additional. . . . . . 118
Neutral pion mass distributions of three-ring events after applying C1 ∼ C4.
The top four plots show the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV
are combined). Free proton decay events (light color) and bound proton events(dark color, hatched) are stacked. Gaussian fits have been used to determine
the π 0 mass peak and width for the signal MC events. The black dots show thedata in SK-I to -IV, and the red and green histograms show the atmospheric
neutrino MC events. Atmospheric neutrino MC is normalized by livetime andincludes reweighting to the latest SK oscillation fit [64]. Vertical error bars on
the data points denote the statistical uncertainty. The left plots correspond tothe conventional fiducial mass region, and the right plots to the additional. . . . 119
Reconstructed total mass and total momentum distributions for p → e+ π 0 (topplot) and p → µ+ π 0 (bottom plot) after all the selection cuts except those on
the plotted variables. In each plot, the top panels show the conventional, andthe bottom panels show the additional fiducial mass region. The left panels show
the reconstructed total mass, and the right panels show the reconstructed total
momentum distributions. The signal MC histograms are stacked, showing free
proton decay events (light color) and bound proton decay events (dark color,hatched), and they are normalized by the 90% C.L. upper limit on the signal
derived in this work. Atmospheric neutrino MC (red and green) is normalizedby livetime and includes reweighting to the latest SK oscillation fit [64]. Verticalerror bars on the data points denote the statistical uncertainty. Bold lines andarrows show the signal region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

xiv

LIST OF FIGURESDistributions of the true number of produced neutrons after applying C1 ∼ C5.
All plots show the enlarged fiducial mass region (100 cm < dwall). The top twoplots show the SK-IV p → e+ π 0 (left) and p → µ+ π 0 (right) MC events. Free
proton decay events (light color) and bound proton events (dark color, hatched)
are stacked. As discussed in Section 4.1, neutrons are emitted only in boundproton decay events. Atmospheric neutrino MC is normalized by livetime andincludes reweighting to the latest SK oscillation fit [64] and is shown in the bottom
two plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.7 Distributions of the number of tagged neutrons after applying C1 ∼ C5. The top
four plots show the SK-IV p → e+ π 0 and p → µ+ π 0 MC events. Free proton decay
events (light color) and bound proton events (dark color, hatched) are stacked.
The black dots show the data in SK-IV, and the red and green histograms show
the atmospheric neutrino MC events. Atmospheric neutrino MC is normalizedby livetime and includes reweighting to the latest SK oscillation fit [64]. Verticalerror bars on the data points denote the statistical uncertainty. The overall event
rate discrepancy between data and MC for p → µ+ π 0 is within the systematic
uncertainty associated with the physics modeling described in Section 7.3.1. The
left plots correspond to the conventional fiducial mass region, and the right plots
to the additional. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.8 The signal selection eﬃciencies (blue and magenta dots) and the expected numberof atmospheric neutrino background events (red and green histograms) and data
candidates (black dots) for p → e+ π 0 (top plot) and p → µ+ π 0 (bottom plot).
Vertical error bars on the data points denote the statistical uncertainty. In eachplot, the left panel corresponds to the conventional fiducial mass region and theright panel to the additional. Atmospheric neutrino MC is normalized by livetime
and includes reweighting to the latest SK oscillation fit [64]. Vertical bands on theatmospheric neutrino MC points denote the sum in quadrature of the systematic
uncertainties associated with the physics modeling described in Section 7.3.1.
The combined data from SK-I to -IV is shown along with the combined signal
and background MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.9 Incoming neutrino energy distributions of the remaining backgrounds (SK-I to-IV are combined). The upper (lower) two plots show the atmospheric neutrino
MC events in the signal region for p → e+ π 0 (p → µ+ π 0 ). These histograms
are normalized by livetime and include reweighting to the latest SK oscillation
fit [64]. The left plots correspond to the conventional fiducial mass region, andthe right plots to the additional. . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.10 Reconstructed total mass shown against the total momentum distributions for
p → e+ π 0 (top) and p → µ+ π 0 (bottom) after all cuts except those on thesevariables. In each plot, the top panels correspond to the conventional and thebottom panels correspond to the additional fiducial mass region. The left panels
show the signal MC (SK-I to -IV are combined), where lighter colors show free
proton decays and dark colors show bound proton decays. The middle panels
show the 2000-year equivalent atmospheric neutrino MC. The right panels show
all the combined data from SK-I to -IV. The black box shows the signal region,and for the middle and right panels, the markers in the signal region have beenenlarged for visibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.11 Run:70690, SubRun:62, Event:15256253. Event display of the p → µ+ π 0 candidate event. Two-ring event. The orange circle denote the µ-like ring and the cyan
circle denote the e-like ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.6

xv

LIST OF FIGURES

7.12 Uncertainty on the absolute flux normalization as a function of neutrino energy.
The black line shows the total uncertainty. The red, purple, green, and blue lines
show the uncertainty associated with the π production modeling, K production
modeling, hadronic interaction cross-sections, and atmospheric density profile,
respectively. Taken from [54]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.13 Schematic view of the HK detector. Taken from [122]. . . . . . . . . . . . . . . . 140
7.14 Proton decay p → e+ π 0 search sensitivity as a function of time. Used signal selection eﬃciency and expected atmospheric neutrino background rate are describedin the text. The black point corresponds to this work. . . . . . . . . . . . . . . . 140
A.1 SK PMT top view and coordinates. The X-axis is parallel to the PMT dynode
major axis, the Y -axis is the perpendicular to X, and the D- (Diagonal) axis isin the middle of the other two. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
A.2 SK PMT cross section and definition of PMT θ. The dotted black line stands for
either the X-, Y -, or D-axis positive direction. . . . . . . . . . . . . . . . . . . . 144
A.3 Schematic view of the PMT measurement setup. The Helmholtz coils are deployed
to control the ambient magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . 145
A.4 Relative gain (top left), relative photon detection eﬃciency (top right), and relative transit time (bottom) distributions at the |B| = 0 condition as a functionof incident photon position on the photocathode (θ) defined in Figure A.2. They
are results for one of the sampled PMTs, EF6453. The black, red, and blue dotsshow the diﬀerent photon incident points along the X-, Y -, and D-axes, respectively. For the relative gain distribution, the vertical axis values are normalized
to the mean of θ = 0 values. For the photon detection eﬃciency distribution, thevertical axis values are normalized to the charge deposition at the monitor PMT.
For the relative transit time distribution, the vertical axis values correspond to
the diﬀerence from the mean of θ = 0 values. Vertical error bars on the data
points shows the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . 147
A.5 Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BX
as a function of incident photon position on the photocathode (θ). They are results for one of the sampled PMTs, EF6453. Diﬀerent colors correspond to thediﬀerent magnetic field conditions. From top to bottom, X, Y , and D direction
scanning results are shown. For the relative gain distribution, the vertical axis
values are normalized to the mean of θ = 0 values at the |B| = 0 condition. For
the photon detection eﬃciency distribution, the vertical axis values are normalized to the charge deposition at the monitor PMT. For the relative transit time
distribution, the vertical axis values correspond to the diﬀerence from the meanof θ = 0 values at the |B| = 0 condition. Vertical error bars on the data points
shows the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
A.6 Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BY
as a function of incident photon position on the photocathode (θ). They are results for one of the sampled PMTs, EF6453. Diﬀerent colors correspond to thediﬀerent magnetic field conditions. From top to bottom, X, Y , and D direction
scanning results are shown. For the relative gain distribution, the vertical axis
values are normalized to the mean of θ = 0 values at the |B| = 0 condition. For
the photon detection eﬃciency distribution, the vertical axis values are normalized to the charge deposition at the monitor PMT. For the relative transit time
distribution, the vertical axis values correspond to the diﬀerence from the meanof θ = 0 values at the |B| = 0 condition. Vertical error bars on the data points
shows the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

xvi

LIST OF FIGURES

A.7 Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BZ asa function of incident photon position on the photocathode (θ). They are resultsfor one of the sampled PMTs, EF6453. Diﬀerent colors correspond to the diﬀerent
magnetic field conditions. From top to bottom, X, Y , and D direction scanning
results are shown. For the relative gain distribution, the vertical axis values arenormalized to the mean of θ = 0 values at the |B| = 0 condition. For the photon
detection eﬃciency distribution, the vertical axis values are normalized to thecharge deposition at the monitor PMT. For the relative transit time distribution,
the vertical axis values correspond to the diﬀerence from the mean of θ = 0
values at the |B| = 0 condition. Vertical error bars on the data points shows thestatistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
A.8 Average distributions of relative gain, relative photon detection eﬃciency, andrelative transit time of the nine sampled PMTs at the |B| = 0 condition as
a function of incident photon position on the photocathode (θ). From top tobottom, X, Y , and D direction scanning results are shown. Vertical bands denotethe statistical uncertainty of the average value at each photon incident position,(standard deviation)√, and correspond to the PMT by PMT individual diﬀerences. . 151
9−1
A.9 Example of the dynode picture taken in the SK detector. The thin while lines correspond to the mesh on the dynode and the dynode direction has been estimatedfrom their tilt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A.10 Dynode angle distributions. The left plot shows the PMTs produced in the 1990s
and the right shows those produced in the 2000s. The dynode angle is definedas the angle from the xy-plane in the SK coordinates for the side PMTs, while
it is defined as the angle from the y-axis in the SK coordinates for the top andbottom PMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
A.11 Distribution of the residual magnetic field strength. The number of entries is3,253 in total, and the number of measurement points in the detector top, side,and bottom region is 321, 2,700, and 232, respectively. The mean value is 33 mG,
and the standard deviation is 16 mG. . . . . . . . . . . . . . . . . . . . . . . . . 154
A.12 Magnetic field maps. Color markers denote the measurement point and magnetic
field strength value in units of mG. The upper plot shows the detector barrel(side) region and the horizontal axis is the azimuth angle from the SK x-axis.
The lower left (right) plot shows the detector top (bottom) region. The highest
magnetic field region is localized in the detector bottom edge, and the markers
are highlighted in green. Due to time constraints, the number of measurement
points in the detector bottom is lower than that in the detector top. Provided
by [124]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
A.13 Distributions of relative gain (left), relative photon detection eﬃciency (middle),
and relative transit time (right) factors. The implemented factors are shown inthe dotted lines. From top to bottom, implemented factors for the X, Y , and D
directions are shown. Bands show the mean ± 1σ region plotted in Fig. A.8. . . 156
A.14 Distributions the distance between the reconstructed vertex and true vertex position and reconstructed momentum. Implemented MC outputs are plotted inred, and standard MC outputs are in black. The top (bottom) four plot show theelectron (muon) 500 MeV/c MC events. The left and right plots correspond tothe conventional and additional fiducial mass regions, respectively. . . . . . . . . 157

xvii

LIST OF FIGURES

A.15 Distributions the distance between the reconstructed vertex and true vertex position and reconstructed momentum. Implemented MC outputs are plotted inred, and standard MC outputs are in black. The top (bottom) four plot show theelectron (muon) 1000 MeV/c MC events. The left and right plots correspond tothe conventional and additional fiducial mass regions, respectively. . . . . . . . . 158

xviii

List of Tables
2.1
2.2
3.1
3.2
3.3
3.4

3.5

4.1

5.1
5.2

5.3

Fermion particles and their gauge group representation and the weak hypercharge(NSU(3) , NSU(2) , Y ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SM particles and SUSY partners. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charged particles often observed in SK and their Cherenkov threshold. . . . . . .
SK data taking phase and detector configuration. . . . . . . . . . . . . . . . . . .
Characteristics of the 50 cm diameter PMT [28, 32]. . . . . . . . . . . . . . . . .
The global trigger threshold value for each trigger type and SK phase. Since theSLE trigger threshold value was changed many times during SK-I and SK-III, theonly initial and last values are shown. . . . . . . . . . . . . . . . . . . . . . . . .
The software trigger threshold value (N200 ) and recorded timing width for eachtrigger. The trigger thresholds for SHE and SLE were changed during SK-IV,
and the only initial and last values are shown. . . . . . . . . . . . . . . . . . . .
Summary of particle emissions from the remaining 15 N nucleus. The residual 15 N
nucleus is at the ground state after proton decays at the P1/2 state, and therefore
no particle emission is predicted. . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
6
9
10
13

21

22

38

Terms representing each fiducial volume (mass region). Exposure is water mass
times livetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Atmospheric neutrino and proton decay event selection eﬃciencies at each reduction step in units of % and the number of events in the final sample in SK-I to -IV.
In the eﬃciency calculation, only events satisfying the final FC criteria presented
in Section 5.7, NHITAC < 16, Evis > 30 MeV, and dwall > 100 cm, are considered for the numerator, while events which are satisfying NHITAC < 16 andEvis > 30 MeV and generated within the enlarged fiducial volume are used for thedenominator. Atmospheric neutrino MC is normalized by livetime and includes
reweighting to the latest SK oscillation fit result [64] described in Section 4.2. . 69
Non-neutrino background contamination rate in each sub-sample in units of %.
Diﬀerent dwall columns show the nun-neutrino background contamination rates
in diﬀerent fiducial volume boundary cases, i.e. numbers in the “dwall Boundary”
column are evaluated using all events with dwall greater than 200, 100, or 50 cm. 71

xix

LIST OF TABLES

6.1

6.2

6.3

6.4
6.5
6.6
7.1

7.2

7.3

7.4

7.5

Summary of reconstruction performance in diﬀerent ID regions using only free
proton decay MC events and weighted by the combined SK-I to -IV livetime.
The particle identification (PID) eﬃciency is the fraction of events which pass the
proton decay signal criterion associated with PID out of all two- and three-ring
signal events. Here Mπ0 (Mtot ) peak is the reconstructed neutral pion (total) mass
distribution’s peak position after applying all selections except the cut associatedwith Mπ0 (Mtot ). The peak is determined using a Gaussian fit. Note that Mπ0peak values are evaluated for only three-ring events. The terms “Conventional”,“Additional” and “Outside” stand for the conventional (200 cm < dwall), additional fiducial volume (100 < dwall ≤ 200 cm) and outside region (50 < dwall ≤100 cm), respectively. The outside region is not used for the present analysis. . 91
Summary of the absolute energy scale uncertainty for both the conventional andadditional fiducial mass regions in units of %. The absolute scale uncertainty istaken to be the value of the most discrepant control sample, and cosmic-ray muon
samples are considered for both fiducial mass regions to take the most discrepant
one. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Summary of the time variation of the energy scale for both the conventional andadditional fiducial mass regions in units of %. The time variation uncertainty istaken to be the larger value among the two control samples, and the cosmic-ray
muon sample is considered for both fiducial mass regions to take the larger one.
97
Summary of the zenith-angle-dependent non-uniformity of the energy scale forboth the conventional and additional fiducial mass regions in units of %. . . . . 100
Summary of the neutron tagging performance. . . . . . . . . . . . . . . . . . . . 108
Summary of relative neutron tagging eﬃciency ϵNN /ϵIS in units of %. . . . . . . 112
Summary of the livetime-weighted total signal selection eﬃciency and the total
expected number of background events. The “Enlarged” row shows results forthe enlarged 27.2 kton fiducial mass region. Detector phase by phase diﬀerenceis shown in Table 7.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Breakdown of interaction modes for background events remaining in the signal
region for the p → e+ π 0 and p → µ+ π 0 searches in units of %. Here, CC
and NC stand for charged-current and neutral-current, respectively, and QE, 1π
and DIS stand for quasi-elastic scattering, single π production and deep inelastic
scattering, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Summary of the signal selection eﬃciencies, the expected number of background
events and the number of data candidates for 92.1 (19.3), 49.1 (10.3), 31.9 (6.7)
and 199.5 (41.8) kton·years exposures from the conventional (additional) fiducial
mass region of SK-I, -II, -III, and -IV, respectively. The “Enlarged” row shows
results for the enlarged 27.2 kton fiducial mass region. Here “Lower” and “Upper”
indicate Ptot < 100 MeV/c and 100 ≤ Ptot < 250 MeV/c, respectively. Errors inthe signal selection eﬃciency and the expected number of background events are
the quadratic sum of MC statistical error and systematic errors. . . . . . . . . . 126
Summary of the search sensitivities (expected lifetime limit at 90% confidence
level). “Conventional” denotes the conventional fiducial mass case (22.5 kton,
372 kton·years exposure), and “Enlarged” denotes the enlarged fiducial mass case(27.2 kton, 450 kton·years exposure). . . . . . . . . . . . . . . . . . . . . . . . . 128
Summary of systematic uncertainties on the expected number of atmospheric
neutrino background events for each fiducial mass region in units of %. They areassociated with the atmospheric neutrino flux model. The “Enlarged” row shows
the result for the combination of the two fiducial mass regions. . . . . . . . . . . 133

xx

LIST OF TABLES

7.6

7.7

7.8

Summary of systematic uncertainties on the expected number of atmospheric
neutrino background events for each fiducial mass region in units of %. They areassociated with the neutrino interaction model (cross-section). The “Enlarged”
row shows the result for the combination of the two fiducial mass regions. . . . . 134
Summary of systematic uncertainties [%] on the signal selection eﬃciency for eachfiducial mass region. SK-I to -IV are livetime-weighted combined. The “Enlarged”
row shows the result for the combination of the two fiducial mass regions. Here,“Lower” and “Upper” show the Ptot < 100 MeV/c and 100 ≤ Ptot < 250 MeV/csignal regions, respectively. Besides, “FV”, “RC”, and “PID” stand for fiducial
volume, ring counting, and particle identification, respectively. . . . . . . . . . . 137
Summary of systematic uncertainties [%] on the expected number of atmospheric
neutrino background events for each fiducial mass region. SK-I to -IV are livetimeweighted combined. They have been evaluated for the combined Ptot < 100 MeV/c
and 100 ≤ Ptot < 250 MeV/c signal regions. Here, the “Enlarged” row shows theresult for the combination of the two fiducial mass regions. Besides, “FV”, “RC”,
and “PID” stand for fiducial volume, ring counting, and particle identification,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xxi

Chapter 1

Introduction
In this thesis, the results of a proton decay search via p → e+ π 0 and p → µ+ π 0 modes with
the Super-Kamokande detector are presented.
A motivation for this study is to test Grand Unified Theories (GUTs) which are briefly
described in Chapter 2. A summary of the Super-Kamiokande detector and its calibration ispresented in Chapter 3. Basic detector components and calibration methods are explained. In
this analysis, an event simulator to produce proton decay Monte Carlo (MC) events and atmospheric neutrino MC events is used. Details of the event simulator are described in Chapter 4.
Chapters 5 and 6 describe an event data set and event reconstruction algorithm used for thisanalysis, respectively. In order to improve the proton decay search sensitivity, it is crucial toaccumulate a larger detector exposure. Therefore, we have enlarged the detector fiducial massfrom 22.5 kton to 27.2 kton and searched for p → e+ π 0 and p → µ+ π 0 using the enlarged
fiducial mass for the first time. In Chapter 5, an external background contamination level inthe 4.7 kton additional fiducial mass region, which we have never used, is discussed. Event
reconstruction performance in the additional fiducial mass region as well as improvements of theparticle identification algorithm are detailed in Chapter 6. One of the most important systematic uncertainties in the proton decay search is the energy scale uncertainty, and it is estimatedfor the 22.5 kton conventional fiducial mass region and 4.7 kton additional fiducial mass region
separately in the same chapter. Proton decay search performances and results are summarizedin Chapter 7. Proton decay signal selection criteria as well as the evaluated signal selection
eﬃciency and expected number of background events are described. The search sensitivity improvement by enlarging the fiducial mass is also mentioned. As no proton decay signal has
been found, calculation of the lifetime limits is presented in this chapter. At last, this thesis isconcluded in Chapter 8. Appendix A describes an additional study to validate PMT responsemodeling in our detector simulation for enlarging the fiducial mass. The main contents of thiswork are summarized in [1].

1Chapter 2

Physics Motivation
The standard model (SM) [2] of particle physics has succeeded in predicting almost all
experimental results; however, it still leaves important questions about the universe, and it
is believed that a new physics paradigm beyond the standard model exists. Grand Unified
Theory (GUT) [3] is one of the most prospective frameworks beyond the SM, and experimental
observation of proton decay would become strong evidence for it. In this Chapter, these theories
and previous proton decay search results are introduced.

2.1

Standard Model (SM)The SM contains quarks, leptons, gauge bosons, and the Higgs boson. It is based on thegauge symmetry:
GSM = SU(3)C × SU(2)L × U(1)Y .
(2.1)
As proved by Noether’s theorem, each of them has a conserved quantity. The group SU(3)C
denotes the color conservation of the strongly-interacting quarks and their gauge particles, gluons. The group SU(2)L is associated with the weak interaction with L indicating that only
left-handed particles participate in this interaction. The third component of weak isospin isconserved in this interaction. At last, U(1)Y conserves the weak hypercharge (Y ), and it has thefollowing relation with the third component of weak isospin (T3 ) and the electric charge (Q):Y = 2Q − 2T3 .

(2.2)

Table 2.1 shows the correspondence between the fermion particles and their gauge group representation.
Table 2.1: Fermion particles and their gauge group representation and the weak hypercharge(NSU(3) , NSU(2) , Y ).
representation andthe weak hypercharge
first generation
second generation
third generation(3,2,1/3)
( )
u
d
( )L
c
s
( )L
t
b L

quarks(3,1,4/3)(3,1,-2/3)

uR

dR

cR

sR

tR

bR

leptons(1,1,-2)((1,2,-1)
)
νe
e−
R
e− L
(
)
νµ
µ−
R
µ− L
(
)
ντ
τR−
τ− L

A complex scalar Higgs doublet, Φ, is added to generate the weak gauge boson mass through2

CHAPTER 2. PHYSICS MOTIVATION

spontaneous symmetry breaking. The Lagrangian for the Higgs field is as follows:
L = |Dµ Φ|2 − V (Φ),(2.3)

V (Φ) = −µ |Φ| + λ|Φ| (µ > 0).

(2.4)

2

2

4

2

This Lagrangian is gauge-invariant for the SU(2)L × U(1)Y transformation. After spontaneous
symmetry breaking, a vacuum expectation value of Φ can be taken as:( )10⟨0|Φ|0⟩ = √
.
(2.5)
2 v
With this vacuum expectation value, the Lagrangian becomes:)
1 (1(∂µ ϕ)2 + g 2 (A1µ )2 + (A2µ )2 (v + ϕ)2
2
8
)
µ2
1( 3
λ
2
+ gAµ − g ′ Bµ (v + ϕ)2 + (v + ϕ)2 − (v + ϕ)4 ,
8
2
4
L=

(2.6)

where ϕ is the perturbation term, A (B) is the SU(2) (U(1)) gauge field, and g (g ′ ) is its coupling
constant. In order to clarify the meaning of the Lagrangian, the following terms are introduced:)
1 (Wµ = √ A1µ − iA2µ ,
2
)
1 ( 1
†
Wµ = √ Aµ + iA2µ ,2) (()( 3 )Aµcos θW − sin θW
Zµ
=
,
Aµ
sin θWcos θWBµg,cos θW = √2
g + g ′2g′sin θW = √,g 2 + g ′2
1
MW = gv,
2
MW
MZ =
,
cos θW√
MH = 2λv,

(2.7)
(2.8)
(2.9)
(2.10)(2.11)(2.12)(2.13)(2.14)

where Wµ (Wµ† ), Zµ , and Aµ correspond to the W + (W − ) gauge boson, Z 0 gauge boson, andphoton, respectively. The mixing angle, θW , is so-called the Weinberg angle. As a consequence,
non-zero gauge boson mass terms (MW , MZ ) and the Higgs mass (MH ) term are derived from
Eq. (2.6):
1 2 † µ 1 2
L = MW
Wµ W + M Z Zµ Z µ
2
2
)
( 2
)(
g 2
1
µ
†
µ
Zµ Z
+
ϕ + gMW ϕ
Wµ W +
4
2 cos2 θW
)
√
1(
λ
1
2 2
+ (∂µ ϕ)2 − MHϕ − √ MH λϕ3 − ϕ4 + const.
2
4
2(2.15)In 2012, the Higgs boson was discovered by the ATLAS and CMS collaborations [4], andthe SM was completed. However, there are several unresolved issues in the SM, which make it
hard to believe that the SM is the ultimate theory of particle physics, and some examples of theunresolved issues are listed as follows:3

CHAPTER 2. PHYSICS MOTIVATION• Neutrino mass is assumed to be zero in the SM, but neutrino oscillations were discoveredby several experiments [5], and non-zero neutrino mass was proved.
• The SM gives no explanations about the gravity [6], a mechanism to generate the baryon
asymmetry of the universe [7], dark matter candidate [8] and strong CP problem [9], etc...
• There are too many free parameters and arbitrarinesses in the SM. This model does notgive any explanations about each coupling constant and complicated assignments of thegauge group representations as well as the quantization of electric charge between quarks
and leptons.
We believe that a new physics paradigm beyond the SM exists, and it solves the above important
open questions.

2.2

Grand Unified Theories (GUTs)

Grand Unified Theories are the extensions of the SM and provide hints of the modern particle
physics problems suggested in the last section. The SM gauge symmetry (GSM ) can be embedded
in some larger gauge symmetry assumed in GUTs, and GUTs predict a single coupling constantfor all three interactions at the super high energy scale, ∼ 1016 GeV, GUT scale. There area variety of proposed GUT models based on diﬀerent gauge symmetries, such as SU(5) [10],SO(10) [11], E6 [12], etc... In GUT models, quarks and leptons are basically incorporated
into common multiplets, and they generically predict proton decay, which is a direct transition
between the quarks and leptons without conserving the baryon number.

2.2.1

Minimal SU(5) GUT model

The minimal choice for unification in a simple group is SU(5). In the SU(5) GUT model, theSM gauge symmetry can be embedded in this larger gauge symmetry, and U(1)Y hypercharge
is automatically quantized. One SM generation particles come from the following 10 and 5̄
representations,
0
ucb −ucg ur dr
 −uc
0
ucr
ug dg 

 cb
c

0
ub db 10 :  ug −ur(2.16)
, −ur −ug −ub
0
ec 



5̄ : 



−dr
dcr
dcg
dcb

e
−νe

−dg


−db

−ec

0



.



(2.17)The top left 3 × 3 and bottom right 2 × 2 blocks in the first matrix correspond to SU(3)C andSU(2)L fermions, respectively. Since in the SU(5) symmetry there are 24 generators, 12 newgauge bosons (X,Y bosons) are introduced in addition to those in the SM. They can be written
in the following matrix form,G11 − √2A
30

G21



G31


X1

Y1

G12
G22 − √2A
30
G32

G13
G23
G33 − √2A
30

X2

X3

Y2

Y3

4

X̄1
X̄2
X̄3

Ȳ1
Ȳ2
Ȳ3

3
W
3A
√ + √
2
30
W−

W+
3

3A
√ + √
−W
2
30





,




(2.18)

CHAPTER 2. PHYSICS MOTIVATION

Figure 2.1: Proton decay (p → e+ π 0 ) diagram.
where G represents the SU(3) gauge field. The top right 3 × 2 and bottom left 2 × 3 blocks
correspond to X and Y bosons, which mediate interactions between quarks and leptons, thus
violating the lepton and baryon number conservations and leading proton decays. The dominant
proton decay mode is predicted to be p → e+ π 0 (Fig. 2.1).
However, the predicted partial lifetime of protons in this model, (τ /B(p → e+ π 0 ) ∼ 1031±1 years [3]),is too short and is already excluded by several experiments [13]. Furthermore, there is still nospace for the right-handed neutrino helicity state, and neutrinos must be massless in this model.

2.2.2

Extensions of SU(5) GUT model

In the SO(10) GUT model [11], an extra singlet, which could represent a right-handed
neutrino helicity state, as well as one SM generation particles can be incorporated into a single
16 representation. From this feature, this model could explain the neutrino mass generation
mechanism through the seesaw model [14].
This gauge symmetry, SO(10), can break directly to the SM gauge symmetry, while there are
two inequivalent breaking patterns into the SM gauge symmetry, SO(10) → SU(5) × U(1) andSO(10) → SU(4) × SU(2) × SU(2). In the first case, U(1)Y hypercharge is a linear combinationof the U(1) charge inside the SU(5) and one outside, leading to a “flipped” relation for the righthanded leptons and quarks relative to the standard SU(5) model. Accordingly, right-handed
quark and lepton assignments in 10 and 5̄ representations are flipped. This model is called theflipped SU(5) model and could enhance p → µ+ π 0 decays [15]. In the latter breaking pattern,
the intermediate gauge symmetry, SU(4) × SU(2) × SU(2), is the historically first proposed GUT
model called the Pati-Salam model [16], and the quantization of electric charge can be also
explained in this model. The predicted proton lifetime in the SO(10) GUT model is at the same
scale or longer than the current lifetime limit (from 1034 to 1039 ) [17].
Further extension of the SO(10) GUT model is also proposed, an exceptional group E6 [12].
In this model, the 16 representation in SO(10) is embedded in the 27 representation in E6 .

2.2.3

Supersymmetric GUT

Supersymmetric (SUSY) models postulate a symmetry between fermions and bosons, requiring each fermion to have a boson partner and vice versa. Table 2.2 shows SM particles and theirSUSY partners. They are expected to exist with a mass of around 1 ∼ 10 TeV and have been
searched for in experiments in the LHC. So far, there is no positive result of the existence of
SUSY particles but this model is still quite prospective.
Originally, SUSY is introduced to solve the fine-tuning problem (or naturalness problem) [18].
In the SM, the Higgs mass correction term (∆mH ) can be in the order of Λ ∼ 1019 GeV, Planckscale, while the observed Higgs mass is about 125 GeV/c2 . It means that the 10−17 order offine-tuning is needed and suggests an underlying mechanism. In SUSY theories, SUSY partners
yield the opposite loop contribution to cancel the mass correction term, and therefore this superprecise tuning is no longer needed.

5

CHAPTER 2. PHYSICS MOTIVATION

Table 2.2: SM particles and SUSY partners.
SM particles Spin SUSY partners Spin
1
q
quark
q̃
squark02
1
˜llleptonslepton02
1g̃
gluino
g
gluon
1
2
1
W W boson
1
W̃
wino
2
1
Z̃
zino
Z
Z boson121γphoton1γ̃photino
2
1
H
higgs
0
H̃
higgsino
2

Figure 2.2: Inverse of running coupling constants as a function of the logarithm of the energy
scale. Taken from [3, 19].
Another interesting feature in SUSY models is that they can realize single point unification of
the coupling constants for the three interactions. Running coupling constants can be calculatedusing renormalization group equations (RGE) with appropriate inputs from experimental results.
In the SM, extrapolated running coupling constants would not meet in a single point, while inthe minimal SUSY standard model (MSSM), coeﬃcients in RGE are modified after the SUSY
breaking scale, and a single unification point can be realized. Figure 2.2 shows the running
coupling constants as a function of the logarithm of the energy scale.
In the MSSM, the predicted partial lifetime of protons via p → e+ π 0 is generically longer thanthat in non-SUSY models because the GUT unification energy scale is shifted to the larger side.
On the other hand, SUSY models favor another decay mode, p → νK + , mediated by SUSY
particles (Fig. 2.3). For this mode, the predicted partial lifetime depends on SUSY particle
parameters, and it is in the order of 1033 years or longer [21].

2.3

Proton Decay Searches

In the last section, GUT models and their proton lifetime predictions are briefly reviewed.
Historically, the first attempt to search for proton decay was conducted in 1954 by F. Reines
et al. before these GUT models were proposed. They searched for proton decays in a plastic
scintillator and set the lower lifetime limit of τp > 1022 years [22]. Thereafter, various proton

6CHAPTER 2. PHYSICS MOTIVATION

Figure 2.3: Proton decay (p → νK + ) diagram. In the diagram, H̃C stands for color-triplet
higgs.
decay searches have been conducted in the past several decades using diﬀerent types of detectors,
such as plastic scintillator detectors [23], fine-grained iron calorimeters [24], and water Cherenkov
detectors [13]. Among such diﬀerent detector types, a water Cherenkov detector is relatively
easy to scale up at a low cost.
This thesis presents proton decay search results via p → e+ π 0 and p → µ+ π 0 using the world’s
largest underground water Cherenkov detector, Super-Kamiokande. Theoretically, the ratio of
the two decay rates, Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ), could be important to identify the GUT model
among SU(5), SO(10), and E6 [25]. Figure 2.4 shows the relation between the ratio of the two
decay rates and each decay mode’s lifetime with varying model parameters. This ratio could bealso used to diﬀerentiate between GUT models, SU(5) and flipped SU(5), through the potential
connection with the neutrino oscillation parameters, the PMNS matrix [5, 26]. Figure 2.5 shows
the prediction of Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ) in case of unflipped (standard) SUSY SU(5) andflipped SUSY SU(5) with normal and inverted neutrino mass ordering assumptions. In the
flipped SU(5) with inverted neutrino mass ordering case, the proton decay mode p → µ+ π 0 isenhanced compared to the p → e+ π 0 mode. In this way, the discovery of the proton decay would
provide not only strong evidence of GUTs but also further physics implications. Therefore, it isquite important to search for these modes comprehensively.
From the experimental point of view, they are the most prospective modes in Super-Kamokande
because all final state particles can be reconstructed, and from their unique (back-to-back) event
topologies, proton decay signal and atmospheric neutrino background events can be clearly discriminated. Moreover, hydrogen nuclei (free protons) in water are suitable targets for thesesearches because they are free from the Fermi motion and other nuclear eﬀects. The previous
most stringent constraints on these partial lifetimes are τ /B(p → e+ π 0 ) > 1.6 × 1034 years
and τ /B(p → µ+ π 0 ) > 7.7 × 1033 years at 90% confidence level using the 306 kton·years ofSuper-Kamiokande data [27].

7CHAPTER 2. PHYSICS MOTIVATION

Figure 2.4: Relation between Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ) and each decay mode’s lifetime.
Diﬀerent gauge group, SU(5), SO(10) and E6 , predictions are plotted in black, red and blue,
respectively. Taken from [25].

Figure 2.5: Prediction of Γ(p → µ+ π 0 )/Γ(p → e+ π 0 ) in case of unflipped (standard) SUSY
SU(5) (black line) and flipped SUSY SU(5) with normal (blue histogram) and inverted (green
histogram) neutrino mass ordering. Taken from [26].

8Chapter 3

The Super-Kamiokande Detector
In this chapter, an overview of the Super-Kamiokande (SK) detector, each detector component, and detector calibration are described.

3.1

Cherenkov Light

Cherenkov light is emitted when a charged particle passes through a dielectric medium at a
speed greater than the light velocity in the medium, and it is emitted in a cone shape with a half
opening angle (Cherenkov angle, θC ) from the particle’s momentum direction. The Cherenkov
angle is given by:1
cos θC =
,
(3.1)
nβ
v
β= ,
(3.2)
c
where n stands for the refractive index of the medium. In water, n is about 1.34, and theCherenkov angle is about 42 degrees for a particle with β ∼ 1. The number of emitted photons
depends on the wavelength of the emitted photon (λ):
(
)
1
1
dN
= 2πα 1 − 2 2
,
(3.3)
dxdλ
n β
λ2
where x stands for the path length of the particle, and α is the fine structure constant. The
number of emitted photons integrated from 300 to 600 nm with respect to λ (SK photomultipliertube (PMT) sensitive wavelength region) is about 340 photons/cm. The momentum threshold(pC ) of the Cherenkov light emission in a medium is given by the refractive index of the medium
and charged particle’s mass (m):
m
.
(3.4)
pC = 2n −1
The momentum thresholds of charged particles in water are summarized in Table 3.1.
Table 3.1: Charged particles often observed in SK and their Cherenkov threshold.
Particle type
Electron Muon Charged Pion Proton
Cherenkov (momentum) threshold [MeV/c]
0.57
118
156
1052

3.2

Detector

3.2.1

Overview

Super-Kamiokande is the world’s largest underground water Cherenkov detector [28]. It
is an upright cylinder in shape, 39.3 m in diameter, and 41.4 m in height, containing a total

9

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

of 50 kton of ultrapure water. The detector is located about 1,000 m (2,700 meters waterequivalent) under Mt. Ikenoyama in Japan. It is optically separated into two regions, an innerdetector (ID) and an outer detector (OD). The ID has a diameter of 33.8 m and a height of
36.2 m. More than 11,000 50 cm diameter photomultiplier tubes (PMTs) are mounted on the
ID wall facing inwards. The photocathode coverage in the ID is about 40%. 1,885 20 cm
diameter PMTs are mounted on the OD behind the ID PMTs facing outwards. The SK datataking period used for the present analysis is divided into four phases with diﬀerent detector
configurations, SK-I, -II, -III, and -IV. The SK-I period began in April 1996 and ended in July
2001. In November 2001, a chain reaction implosion accident destroyed more than half of the
PMTs. Using 5,182 ID PMTs to obtain about 19% of photocathode coverage, SK-II operated
from October 2002 to October 2005. Between SK-II and SK-III, newly manufactured ID PMTs
were installed and SK-III began in July 2006 with recovered 40% of photocathode coverage. In
September 2008, front-end electronics and data acquisition systems were upgraded [29, 30], anda new phase named SK-IV lasted for almost 10 years until May 2018. Table 3.2 summarizes
each detector phase configuration. A detector side view is shown in Fig. 3.1, and the detector
coordinates are defined as shown in Fig. 3.2.
Table 3.2: SK data taking phase and detector configuration.
Phase
SK-I
SK-II
SK-III
SK-IV
Start
Apr./1996 Oct./2002 July/2006 Sep./2008
End
July/2001 Oct./2005 Aug./2008 May/2018
Analysis livetime [days]
1489.2798.6
518.1
3244.4
The number of ID PMTs
11146
5182
11129
11129
The number of OD PMTs
1885
1885
1885
1885
PMT cover
no
yes
yes
yes
ATM
ATM
ATM
QBEE
Front-end electronics

3.2.2

Inner and Outer Detector

The boundary of the ID and OD is a stainless steel frame structure. A unit of the frame
structure is called “supermodule”, and it is 2.1 m in height, 2.8 m in width, and 0.55 m inthickness. 12 ID PMTs and 2 OD PMTs are mounted on each supermodule as shown in Fig. 3.3.
The gaps between the ID PMTs are covered by opaque black sheets on the ID surface. They work
as an optical separation between the ID and OD, and also reduce indirect light contributions,which degrade event reconstruction performance.
A wavelength shifting plate is attached to each OD PMT, and the OD volume is coveredby reflective Tyvek sheets. Both instruments help to enhance the light collection eﬃciency in
the OD, working for rejecting external backgrounds such as cosmic-ray muons and gamma raysfrom radioactive products around the detector.
50 cm Diameter PMT
The 50 cm diameter PMT was originally developed by Hamamatsu Photonics with the cooperation of the Kamiokande collaborators [31]. Based on the original 50 cm diameter PMT,
the bleeder circuit and dynode structure were improved to obtain better charge and timing resolution [32]. Its dynode structure is the venetian-blind type. A schematic view of the 50 cm
diameter PMT is shown in Fig. 3.4, and basic characteristics are summarized in Table 3.3. The
photocathode is coated with Bialkali (Sb-K-Cs), and the sensitive wavelength is from 300 nm
to 600 nm. The peak quantum eﬃciency is about 22% at λ = 390 nm. The quantum eﬃciency
as a function of incident photon wavelength is shown in Fig. 3.5. A typical single photoelectron
distribution and timing distribution are shown in Figures 3.6 and 3.7. Because of the larger

10CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.1: Super-Kamikoande detector side view. Taken from [28].

Figure 3.2: Super-Kamikoande detector coordinates. The origin of the coordinates axes is set
at the center of the detector.

11

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.3: Schematic view of the frame structure (“supermodule”). 12 ID PMTs and 2 OD
PMTs are mounted on one supermodule. Taken from [28].

12CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.4: Schematic view of the 50 cm diameter PMT. Taken from [28].
diameter of the SK PMT, the PMT response depends on the photon incident position on thephotocathode. Such dependence has been measured more detailedly than the previous measurement [32] and is described in Section A.1. From SK-II, the ID PMTs are covered withfiber-reinforced plastic (FRP) and acrylic cases to prevent a chain reaction implosion.
Table 3.3: Characteristics of the 50 cm diameter PMT [28, 32].
Photocathode area
50 cm in diameter
Shape
Hemisherical
Pyrex glass
Window material
Photocathode material Bialkali
DynodeVenetian blind type, 11 stages
Pressure tolerance
6 kg/cm2 water proof
Quantum eﬃciency
22% at λ = 390 nm
Gain
107 at 2000 Volt
200 nA at gain = 107
Dark current
Dark noise rate
∼3 kHz at gain = 107
Transit time
90 nsec typical at gain = 107
Transit time spread
2.2 nsec at single photoelectron

Cherenkov Ring ImageThe ID PMTs detect Cherenkov light emitted from charged particles in the ID, and a
Cherenkov ring image is projected on the ID wall (Fig. 3.8). Events occurring in the ID arereconstructed using ID PMT charge and timing information as well as their Cherenkov ring
image pattern. Figures 3.9 and 3.10 show event displays of an electron and muon generated
by our detector simulation (MC). An electron ring has a fuzzy edge due to overlapping rings
produced by its electromagnetic cascade, while a muon ring has a crisp edge since its mass ismuch larger and it does not make any cascades.
Compensation Coils
Due to the large diameter of the SK PMT and the longer electron trajectory distance inside the PMT bulb, the geomagnetic field (about 450 mG) deteriorates the PMT performance.
Impacts on a single PMT response by an ambient magnetic field have been measured and are

13

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.5: Quantum eﬃciency as a function of incident photon wavelength. Taken from [28].

Figure 3.6: Single photoelectron distributionof the 50 cm diameter PMT. Taken from [28].

Figure 3.7: Transit time distribution of the
50 cm diameter PMT. Taken from [28].

Figure 3.8: Cherenkov ring image.

14

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Super-Kamiokande IV

Super-Kamiokande IV

Run 999999 Sub 0 Event 6

Run 999999 Sub 0 Event 4

19-12-02:16:36:22

19-12-02:16:21:06

Inner: 2267 hits, 4373 pe

Inner: 988 hits, 2683 pe

Outer: 5 hits, 5 pe

Outer: 2 hits, 1 pe

Trigger: 0x07

Trigger: 0x07

D_wall: 1690.0 cm

D_wall: 1690.0 cm

Evis:

Evis:

0.0 MeV

0.0 MeV

Charge(pe)Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
560

1300
0 mu-edecays1040

1 mu-e
decay

448

780

336

520

224
112

260

0

0
0

500

1000

1500

0

2000

Times (ns)

500

1000

1500

2000

Times (ns)Figure 3.9: Cherenkov ring image produced
by an electron.

Figure 3.10: Cherenkov ring image produced
by a muon.

described in Section A.1. To avoid the deterioration of the PMT performance, magnetic fieldcompensation coils are deployed outside the water tank to suppress the magnetic field inside thedetector. A schematic view of the compensation coils is shown in Fig. 3.11. The residual magnetic field inside the ID has been measured. The mean residual magnetic filed strength insidethe detector has been estimated to be less than 40 mG with a standard deviation of 16 mG, andthe details are described in Section A.2.2.

3.2.3

Water Purification System

The detector is filled with ultrapure water, and its origin is spring water in the Kamioka
mine. In order to remove radioactive impurities, dust, and bacteria which produce low energy
background events and degrade the transparency of water, a water purification system nearby
the detector circulates the water with a flow rate of about 60 ton/hour. The PMT dark noise rate
is sensitive to the water temperature, and therefore the system also maintains the water temperature at about 13◦ C. Over the 20 years of operation, the system has been continuously upgraded.
Figure 3.12 shows a schematic diagram of the water purification system as of SK-IV [34, 35].
Specific processes are as follows:
1. 1 µm filter
A 1 µm filter removes dust larger than 1 µm since they often contain radioactive impurities.
2. Heat exchanger
Pumps, which are used to circulate the water, and PMTs generate heat and increase
the water temperature. Under the higher temperature condition, the growth of bacteria
becomes rapid and the PMT dark noise rate becomes higher. To prevent both, a heatexchanger cools the water and keeps it about 13◦ C.
3. Ion exchanger
An ion exchanger removes high molecular and heavy ions including the radioactive contaminations.
4. UV sterilizer
An ultraviolet radiation sterilizer removes bacteria remaining in the water.

15

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.11: Schematic view of the compensation coils. They are composed of 26 sets of coils
deployed outside the water tank. Taken from [33].
5. Radon-less air dissolving system
Radon-less air is dissolved in the water, and it improves the radon removal eﬃciency inthe following vacuum degasifier step.
6. Reverse osmosis filter
A reverse osmosis filter removes particulates in the water.
7. Vacuum degasifier system
Radon and air gases are contained in the water. Dissolved oxygen encourages the growth ofbacteria. A vacuum degasifier removes gases dissolved in the water. The removal eﬃciency
for radon and oxygen gas is estimated to be about 96% and 99%, respectively.
8. Cartridge ion exchanger
Cartridge ion exchanger (polisher) further reduces ions in the water.
9. Ultra filter
An ultrafilter, which consists of hollow fiber membrane filters, removes particulates whose
size is greater than ∼ 10 nm in diameter.
10. Membrane degasifier
A membrane degasifier further reduces radon gas dissolved in the water. The removal
eﬃciency for radon gas at this step is estimated to be about 83%.
After these processes, the radon concentration in the supply water is estimated to be 1.74 ±0.14 mBq/m3 , and in the return water, it is 9.06 ± 0.58 mBq/m3 [35]. Locations of the water
inlets and outlets in the SK tank are shown in Fig. 3.13.

3.2.4

Air Purification System

The radon concentration level in the air in the mine is about 100 times higher than outside.
This “radon rich” air contaminates the water in the detector. Therefore, an air purification
system is located outside the mine, and radon reduced air is sent to the experimental site as16

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.12: Schematic diagram of the water purification system as of SK-IV. Each component
is described in the text. Taken from [35].

Figure 3.13: Schematic view of the water circulation paths in the SK tank. Taken from [35].

17CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.14: Schematic diagram of the air purification system. Each component is described in
the text. Taken from [28].
well as inside the tank. A schematic diagram of the air purification system is shown in Fig. 3.14.
Specific processes are as follows:
1. Air compressor
Air is compressed up to about 8 atm.
2. Air filter
There are three filters, whose mesh size is 0.3 µm, 0.1 µm, and 0.01 µm, and they remove
dust in the air.
3. Air drier
Moisture in the air is removed.
4. Carbon column
Radon gas in the air is absorbed by a carbon column.
5. Cooled charcoal
Radon gas in the air is further removed. To improve the radon removal eﬃciency, thecharcoal is cooled.
After these processes, the radon concentration level in the supply air is less than a few mBq/m3 [36].

3.2.5

Data Acquisition System

Here, data acquisition systems are described. The data acquisition system is diﬀerent between SK-I to -III and SK-IV. During SK-I to -III, ID PMT signals were processed by custom
build TKO (TRISTAN KEK Online) [37] modules called ATM (Analog-Timing-Module) [38, 39].
In 2008, new front-end electronics (QTC-Based Electronics with Ethernet, QBEE [29]) andsoftware trigger system were introduced [30]. There are five electronics huts on the top of thedetector tank, one central hut, and four-quadrant huts. The central hut contains electronics andrelated computers for triggering and GPS. Each quadrant hut contains front-end electronics for
all PMTs in one quadrant of the detector. Each PMT is connected to a high voltage supply
and front-end electronics. A signal from each PMT is sent to the front-end electronics board
through a coaxial cable.
Data Acquisition System for SK-I to -III Inner Detector
A schematic diagram of the ID data acquisition system for SK-I to -III is shown in Fig. 3.15.
When a signal from a PMT is sent to an ATM channel, and its amplitude is greater than18

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.15: Schematic diagram of the ID data acquisition system for SK-I to -III. The data
flow is described in the text. Taken from [28].
1/4 photoelectrons, the ATM channel converts its signal amplitude and detection time to ananalog charge and keeps it. Simultaneously, the ATM board sends an analog signal whose
amplitude is proportional to the number of hit channels (HITSUM signal, a square wave witha width of 200 nsec and height of -15×(number of hit channels) mV) to the trigger module atthe central hut. Here, 200 nsec corresponds to an approximate time duration that a charged
particle takes to pass through the entire detector. All HITSUM signals are summed up, and if
the total amplitude exceeds a threshold, a global trigger is issued. A schematic diagram of thetrigger generation is shown in Fig. 3.16. The global trigger is distributed to all ATMs, and each
ATM digitizes the analog charge, which is kept in the previous step, using an analog-to-digitalconverter (ADC). The digital signals are sent to and stored at SMP (Super Module Partner,a memory module) via SCH (Super Control Head). Finally, these data are sent to the online
computers located at the central hut.
In this system, the impedance matching at the ATM input circuit is not perfect, and reflection
signals from PMTs are observed 700 nsec after the primary PMT signals (the length of thecoaxial cable is about 70 m). Therefore, there is a dead-time not to record these reflectedsignals, degrading the tagging eﬃciency of Michel electrons from muon decays.
Data Acquisition System for SK-I to -III Outer Detector
A schematic diagram of the OD data acquisition system for SK-I to -III is shown in Fig. 3.17.
High-voltage of the OD PMT is supplied through a coaxial cable, and a signal is sent to the
OD electronics through the same cable. A high voltage capacitor picks oﬀ signals from each OD
PMT. A signal from one OD PMT is sent to a charge-to-timing converter (QTC) module, whichconverts it to a rectangular pulse whose width is proportional to the input charge. Similarly to
the ID, a HITSUM signal is generated at the QTC module and sent to the trigger module. If
a global trigger is issued, the leading edge and the width of the rectangular pulse is converted
to the timing and charge information of the OD PMT by the TDC module. Finally, these
digital signals are sent to the online computer through a VME memory module, DPM (DualPort Memory).

19

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.16: Schematic diagram of the trigger generation for SK-I to -III. When the sum of
HITSUM exceeds the threshold level, a global trigger is issued. Taken from [41].

Figure 3.17: Schematic diagram of the OD data acquisition system for SK-I to -III. Taken
from [40].

20CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.18: Schematic diagram of the QBEE electronics. Taken from [29].
Hardware Trigger
There are three types of global triggers for the ID in SK-I to -III, HE (High Energy), LE(Low Energy), and SLE (Super Low Energy). They have diﬀerent threshold values for each, andtheir values are summarized in Table 3.4 including the OD threshold. When the amplitude of thesummed HITSUM signal exceeds one of them, the corresponding type of trigger is issued. The
HE trigger threshold level roughly corresponds to about 6 MeV of electron equivalent energy
deposition in the detector. Among the three, the SLE trigger rate is most sensitive to thedetector ambient background level. Therefore, the SLE trigger threshold value was changed
many times depending on the background level.
Table 3.4: The global trigger threshold value for each trigger type and SK phase. Since the SLE
trigger threshold value was changed many times during SK-I and SK-III, the only initial andlast values are shown.
SK-I
SK-II
SK-III
HE−340 mV−180 mV−320 mV
LE−320 mV−152 mV−302 mVSLE −260 → −186 mV −110 mV −212 → −186 mV
OD−380 mV−380 mV−380 mV

Data Acquisition System for SK-IV
In 2008, the front-end electronics, ATM, was replaced by QBEE. Figures 3.18 and 3.19
show a schematic diagram of the QBEE electronics and a schematic diagram of the entire dataacquisition system for SK-IV, respectively. When a signal is sent to a QBEE channel, and its
amplitude exceeds the threshold, 1/4 photoelectrons, the QTC module integrates the signal
and outputs a rectangular pulse, whose leading-edge represents the signal timing and width
represents the integrated charge. There are three gain ranges, small, medium, and large. The
1gain ratio is set to 1 : 17 : 49
, and the large range channel can record up to about 2500 pC, which
is about five times larger than ATM. The rectangular pulse is sent to the TDC module anddigitized. The digitized charge and timing information is sent to the front-end PC through the
Ethernet cable after being processed by FPGA. The front-end PCs arrange the received data ina timing order and send them to the merger PCs, where a software trigger is issued. Finally,
event information is collected by the organizer PC and recorded on the disk.

21

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.19: Schematic diagram of the data acquisition system for SK-IV. The data flow is
described in the text. Taken from [30].
Software Trigger
In this new system, a software trigger is issued if the number of PMT hits in a sliding
200 nsec timing window, N200 , exceeds the trigger threshold. There are four trigger types for
the ID in SK-IV, SHE (Super High Energy), HE (High Energy), LE (Low Energy), and SLE(Super Low Energy). When a trigger is issued, all hits within -5 µsec to +35 µsec after thetrigger timing are recorded for SHE, HE, and LE. This time width is much longer than that in
ATM and enables us to tag Michel electrons from muon decays more eﬃciently. The thresholdvalue and recorded timing width for each trigger type are summarized in Table 3.5. If an SHE
trigger is issued without an OD trigger, a special trigger, AFT trigger, is issued, and all of
the hits up to 535 µsec after the primary SHE trigger timing are recorded. The AFT trigger
information is used for a search for a 2.2 MeV gamma ray emitted from neutron capture onhydrogen (τcapture ∼200 µsec). The typical event rate in SK-IV for the data set used in thepresent work is described in Chapter 5.
Table 3.5: The software trigger threshold value (N200 ) and recorded timing width for eachtrigger. The trigger thresholds for SHE and SLE were changed during SK-IV, and the only
initial and last values are shown.
N200
Timing Width
SHE 70 → 58
-5 ∼ +35 µsecHE50
-5 ∼ +35 µsec
LE
47
-5 ∼ +35 µsec
SLE 34 → 31 -0.5 ∼ +1.0 µsec
OD
22
-5 ∼ +35 µsec

3.3

Detector Calibration

Using various light and radioactive sources, signal outputs of the ID PMTs are calibrated,
and water quality inside the detector is measured [42]. Here, these calibration methods aredescribed.

22

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.20: Net of the ID. Red points denote the locations of 420 “standard PMTs”
in the ID. Taken from [42].

3.3.1

Figure 3.21: Grouping of the ID PMTs for
the HV determination. Taken from [42].

High-voltage Determination

Each PMT’s applied high-voltage (HV) is set so that all PMTs give the same output charge
for the same incident light intensity. Before installing and calibrating them inside the detector,
applied HVs were determined for 420 “standard PMTs” using an independent calibration setup
to obtain the same output charge among them for the same light intensity. After that “precalibration”, those 420 standard PMTs were mounted as shown by the red points in Fig. 3.20 andserved as “reference PMTs” for other PMTs. PMTs mounted at similar geometrical positions
were grouped as shown in Fig. 3.21. A scintillator ball flashing by Xe lamp was placed at thecenter of the detector (Fig. 3.21), and the HVs of the other PMTs were determined so that theirobserved charges are matched to the average charge of the reference PMTs in the same group.
By doing this, geometrical eﬀects caused by photon absorption and scattering in water can becanceled out. Uniformity of the observed charge compared to the reference PMT value is shownin Fig. 3.22 and its RMS is estimated to be 1.3%.

3.3.2

Relative Gain Calibration

In order to convert the PMT output (observed) charge to the number of photoelectrons(p.e.s), each PMT gain needs to be determined. There were two steps to obtain all PMT gain
values. First, the relative diﬀerence of the PMT gain was measured, and in the next, the overall
average gain was determined. The relative diﬀerence of the PMT gain was extracted in thefollowing two measurements using a nitrogen-laser source placed at the center of the detector:
the first measurement uses high-intensity flashes so that every PMT detects a suﬃcient numberof photoelectrons, and the second uses low-intensity flashes in which only a few PMTs are
fired. Measurement outputs of them, the average charge for the ith PMT, Qobs
i , from the firstmeasurement and the number of hits for the ith PMT, Niobs , from the second measurement canbe parameterized as follows:
Qobs∝ Is × f (Θi ) × ϵqeii × Gi ,(3.5)

Niobs ∝ Iw × f (Θi ) × ϵqe
i ,

(3.6)

23

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.22: Uniformity of the observed charge compared to the reference PMT value. Taken
from [42].

Figure 3.23: Relative gain distribution of the ID PMTs. Values are normalized to their meanvalue. Taken from [42].
where Is and Iw are the average intensities of high- and low-intensity flashes, respectively, f (Θi )is the ith PMT acceptance correction factor as a function of photon incident angle (Θi ), ϵqeiis the ith PMT quantum eﬃciency (QE), and Gi is the ith PMT gain. Then, each relative
PMT gain was extracted by taking the ratio of them. Figure 3.23 shows the distribution of therelative gain of the ID PMTs after being normalized by the overall average gain. The RMSof the distribution is estimated to be 5.9%, and this variation is caused by diﬀerences in QE
among the ID PMTs since each HV was determined so that all PMTs give the same output
charge (“gain” times “QE”) for the same incident light intensity. These relative gain values aretabulated and used to correct each PMT’s observed charge to the number of photoelectrons in
data.

3.3.3

Absolute Gain Calibration

In this calibration, a NiCf source was used (Fig. 3.24) and deployed at the center of thedetector. A gamma ray with an energy of about 9 MeV from thermal neutron capture on
nickel emits Cherenkov photons, and the photon yield is about 0.004 p.e.’s/PMT/event, andthus more than 99% signals are considered to be single photoelectron contributions. Neutrons
are provided by the 252 Cf source inside the “Nickel ball”. The observed charge distribution isshown in Fig. 3.25. The mean value of the distribution corresponds to the absolute gain value

24

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.24: Picture of the NiCf source, which is made of 6.5 kg of NiO and 3.5 kg of polyethylene.
The Cf source is located inside the ball and provides neutrons. Taken from [42].

Figure 3.25: Charge distribution in units of pC obtained in the absolute gain calibration in
SK-III. Taken from [42].
for the ID PMTs, and it is 2.055 in SK-I, 2.297 in SK-II, 2.243 in SK-III, and 2.645 in SK-IV.
The obtained absolute gain factor is also used to convert the observed charge to the numberof photoelectrons. The observed charge distribution in this calibration is considered as a single
photoelectron distribution and implemented in our detector simulation (MC).
The evolution of the PMT absolute gain over time is monitored using oﬀ-timing (dark noise)data. The time variation of the PMT gain is plotted in Fig. 3.26. Since SK-IV, PMTs are divided
into five groups depending on their production year. Although its mechanism is unknown, thePMT gain keeps increasing over time, and it is corrected in the present analysis.

3.3.4

Relative Quantum Eﬃciency Calibration

As pointed out in the previous section, quantum eﬃciency (QE) diﬀers from one PMT toanother. The same NiCf source used in the absolute gain calibration was used for the relative
QE calibration because with this low-intensity light source, the observed hit probability for each
PMT should be proportional to its QE. When this calibration was conducted, the water wasconvected in the entire detector to make its quality uniform and to mitigate the geometricaleﬀects. Since it is diﬃcult to estimate the number of photons arriving at each PMT, MC wasused for predicting it. The position dependence of the photon detection probability in thedetector is shown in Fig. 3.27. In this plot, the number of observed hits is corrected with the
distance between the NiCf source and each PMT position, ri , as well as the PMT eﬀective area,

25

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

1.5

Relative Gain

1.4
1.3

SK-I

SK-II

SK-III

SK-IV

1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

PMT Production Year
1992~1995
1996~1997
2003
2004
2005

2000/01/01 2004/12/31 2009/12/31 2014/12/31

Date
Figure 3.26: Time variation of the PMT gain. Data points for SK-I to -III are normalized by the
first data point value in each period, and for SK-IV, they are normalzied by the average value
in Apr./2009. In SK-IV, PMTs are divided into five groups depending on their production year.
f (Θi ):
Niobs × ri2 /f (Θi ),(3.7)

where f (Θi ) is the PMT acceptance correction factor as a function of photon incident angle,
Θi . When MC models the water quality (photon absorption, scattering) in the detector, as well
as photon reflection on the surfaces of the PMTs and the black sheet, the remaining diﬀerence
between data and MC should correspond to the QE of individual PMTs. By taking the ratioof the number of observed hits in data to MC, the QE of individual PMTs was obtained. Afterbeing tabulated, they are used in MC.

3.3.5

Timing Calibration

The time response of each readout channel is calibrated by taking into account diﬀerencesin the transit time of the PMT, length of the coaxial cable, and the “time-walk” eﬀect. Thiswas calibrated by injecting various intensities of light into PMTs. A schematic diagram of thetiming calibration system is shown in Fig. 3.28. A nitrogen laser light source whose wavelengthis shifted to 398 nm by a dye was used. Considering Cherenkov spectrum, light absorption inwater, and wavelength dependence of the PMT QE, 398 nm is an optimal wavelength. The
pulse width of the nitrogen laser and dye laser is 0.2 nsec and 0.4 nsec in FWHM, respectively.
The laser output was monitored by a fast-response 7.5 cm diameter PMT, and it was used tomeasure the laser light injection time. The laser light intensity to the SK detector was tuned by avariable optical filter so that the dynamic range of the front-end electronics can be covered. The
filtered light was distributed into the whole ID PMTs through a diﬀuser ball (Fig. 3.29). From
this calibration, two-dimensional, timing versus pulse height (charge), correlation distributions
called “TQ-distributions” were obtained. A typical TQ distribution for one readout channel isshown in Fig. 3.30. By fitting this TQ distribution with three polynomial functions for each26

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.27: Position dependence of the photon detection probability in the detector in therelative QE calibration. The vertical axis values are normalized by the average value of all
PMTs. The top plot shows the barrel (side) PMTs, and the horizontal axis is the Z position of
PMTs in cm. The bottom left (right) plot shows the top (bottom) PMTs, and the horizontal
axis is the square of the distance from the detector center in cm2 . Data points are plotted inred, and MC points are plotted in blue. In MC points, the obtained QE of individual PMTs is
not reflected. Taken from [42].

27

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.29: Cross-section of the diﬀuser ball.
Taken from [42].

Figure 3.28: Schematic diagram of the timing
calibration system. Taken from [42].

readout channel, correlation tables between charge and timing, called “TQ-map”, were obtained
for all the ID readout channels and used to correct each readout channel’s detection time indata.
The timing resolution of each readout channel was extracted using the same calibration data.
This was conducted by fitting the timing distribution for each charge region with an asymmetric
Gaussian:()(t − Tpeak )2
f (t) = A1 exp −+ B1 (t > Tpeak ),
(3.8)
σt2
(
)
(t − Tpeak )2
f (t) = A2 exp −+ B2 (t < Tpeak ),
(3.9)
σt′2
where A1,2 , B1,2 , σt , and σt′ are fit parameters. A typical timing distribution for a certain charge
region and fit functions are shown in Fig. 3.31. The obtained timing resolutions (σt and σt′ ) areplotted as a function of observed charge in Fig. 3.32. They are also tabulated and implemented
in MC.

3.3.6

Light Absorption and Scattering in Water

Water absorption and scattering coeﬃcients are also important quantities to be calibrated.
A collimated laser beam injector is installed on the top of the ID as shown in Fig. 3.33. The
detector side region is divided into five regions, B1 to B5, and photons arriving in the side region
are considered as scattered photons. The absorption coeﬃcient was estimated using the numberof observed photons in the detector bottom region. Since these coeﬃcients have wavelength
dependence, four diﬀerent laser light sources with a wavelength of 337 nm, 365 nm, 400 nm,
and 420 nm are prepared. The wavelength was changed in 2009; from 365 nm to 375 nm, from28

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.30: Typical TQ distribution for one readout channel (PMT No.10). The horizontal
axis corresponds to observed charge and the vertical axis is detection timing. Larger value inthe vertical axis corresponds to earlier hits in this plot. Taken from [42].

Figure 3.31: Timing distribution added over
all the readout channels (red points) and thefitted asymmetric Gaussian function (solid
blue curve). The observed charge region usedin the distribution is about 3 pC (1 photoelectron level). Here again larger value in the horizontal axis corresponds to earlier hits. Taken
from [42].

Figure 3.32: Timing resolution as a functionof observed charge. Taken from [42].

29CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.33: Schematic view of the water laser system. A typical event display of the “laser”
event is shown in bottom right. The wavelength was changed in 2009; from 365 nm to 375 nm,
from 400 nm to 405 nm, and from 420 nm to 445 nm and 473 nm. Taken from [42].
400 nm to 405 nm, and from 420 nm to 445 nm and 473 nm. The number of scattered photons
and the shape of the timing distribution were compared between data and MC as shown in
Fig. 3.34. Various MC predictions were produced with diﬀerent coeﬃcients, and the one, which
minimizes the χ2 value for the diﬀerence between data and MC, was selected.
Photon scattering and absorption coeﬃcients are parametrized as follows:()lI(λ) = I0 (λ) exp −,(3.10)
L(λ)1,
L(λ) =(3.11)
aabs (λ) + asym (λ) + aasy (λ)
P1aabs (λ) = P0 × 4 + C,
(3.12)
λ()
P5P4(3.13)
asys (λ) = 4 × 1.0 + 2 ,
λ
λ
(
)
P7
aasy (λ) = P6 × 1.0 + 4 × (λ − P8 )2 ,(3.14)
λwhere l is the travel length of the light, I0 (λ) is the initial light intensity, I(λ) is the lightintensity at l, aabs is the absorption coeﬃcient, asym is the symmetric scattering coeﬃcient, aasy
is the asymmetric scattering coeﬃcient, and P0∼8 is the constant coeﬃcient. Rayleigh scatteringand the symmetric component of Mie scattering contribute to the “symmetric scattering”, andthe asymmetric component of Mie scattering (forward component) corresponds to “asymmetricscattering”. Their wavelength dependence was empirically determined. The obtained coeﬃcientvalues at each wavelength are shown in Fig. 3.35. They are fitted by polynomial functions
written above, and their wavelength dependence is implemented in our MC.
The evolution of the water transparency (“water attenuation length”) over time is monitored
using cosmic-ray muons entering from the top of the detector and going through the detector
bottom. The time variation of water transparency is plotted in Fig. 3.36.

3.3.7

Light Reflection at PMT and Black Sheet

Light reflectivity of the PMT surface was measured using the same laser data as used for thewater parameter calibration. There are four layers (refractive indices) from the surface to the30

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.34: Timing distributions after photon time-of-flight (T.O.F.) subtraction (wavelength
at 405 nm). The wavelength was changed in the middle of SK-IV from 400 nm to 405 nm.
Time-of-flight is calculated based on the distance between the target position of the laser at thedetector bottom region and the PMT position. From top to bottom, the detector top region,
and B1 to B5 timing distributions are aligned. Entries in left part in each plot indicate scatteredphotons, and right peaks indicate reflected photons at the detector bottom. Data points areplotted in black dots and MC predictions are plotted in red. Taken from [42].
inside of the PMT: water (1.34), glass (1.472+ 3670
, where λ is the wavelength in units of nm),λ2
Bialkali (nreal + inimg , where nreal and nimg are the real and imaginary parts of the complex
refractive index, respectively [43]), and vacuum (1.00). Both two parameters, nreal and nimg ,were tuned in the same method as the water parameters, comparison between data and various
MC setups as shown in Fig. 3.34. The best fit values are nimg = 1.667 and nreal = 2.31, 2.69, 3.06,
and 3.24 at λ =337, 365, 400 and 420 nm, respectively. They are also implemented in our MC.
The reflectivity of the black sheet, which covers the gaps between the ID PMTs, was measured
using a laser light injector which is set inside the detector as shown in Fig. 3.37. Both theobserved charge from reflected light at three incident angles, 35, 45, and 60 degrees, with three
wavelengths, 337, 400, 420 nm and the observed charge from direct light without the black sheet
were measured. The results of this measurement are shown in Fig. 3.38 and confirm that thereflection component is less than 5% compared to the direct photons as well as good data andMC agreement (about 1% level).

31

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.35: Water absorption and scattering coeﬃcients obtained from the water laser data in2009 are plotted in dots. Curves are the fitted polynomial functions. Taken from [42].

32CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Water Transparency [m]

140

SK-I

SK-II

SK-III

SK-IV

120
100
80
60
40
20
0

2000/01/01 2004/12/31 2009/12/31 2014/12/31

Date
Figure 3.36: Time variation of water transparency (water attenuation length). Absolute values
are sensitive to the detector configurations and can not be compared among diﬀerent detector
phases.

Figure 3.37: Schematic view of the laser light injector system for the reflectivity measurement of
the black sheet. Both the reflected and direct light was measured by ID PMTs. Taken from [42].

33CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.38: The left plot shows the ratio of the observed charge from reflected light to theobserved charge from direct light without the black sheet as a function of light incident angle
at the black sheet. Data points are plotted in black cross and MC points are in red circle. The
right plot shows the ratio between data and MC. The top, middle and bottom plots correspondto the wavelength of 337, 400 and 420 nm, respectively. Taken from [42].

34Chapter 4

Simulation
In the present work, proton decay simulation (MC) and atmospheric neutrino simulation areused to estimate the signal selection eﬃciency and the expected number of atmospheric neutrino
background events, respectively. In this chapter, the physics models used in the simulation are
described.

4.1

Proton Decay Simulation

In the proton decay MC, the decay is assumed to occur with an equal probability for each
proton in the water molecule (H2 O) when producing proton decay events. Hydrogen nuclei (freeprotons) are stationary and do not interfere with other nucleons, and a positron (anti-muon)
and a neutral pion with a momentum of 459 MeV/c (453 MeV/c) are left after free protonp → e+ π 0 (p → µ+ π 0 ) decay. On the other hand, the eﬀects of the Fermi momentum, nuclear
binding energy, and correlation with other surrounding nucleons influence protons in oxygen
nuclei (bound protons). Furthermore, π nucleon interactions as well as gamma ray and neutron
emissions from the remaining 15 N nuclei are considered in bound proton decays.
Based on the electron-12 C scattering experiment data [44], the Fermi momentum of thenucleon within 16 O is simulated, and its distribution is shown in Fig. 4.1 for both the S state andP state. By changing the eﬀective proton mass, MP′ = MP −Eb , where MP′ is the changed protonmass, MP is the proton rest mass, and Eb is the nuclear binding energy, the eﬀect of the nuclear
binding energy is introduced. The nuclear binding energy, Eb , follows a Gaussian distribution
with a mean of 39.0 MeV (10.2 MeV) and a standard deviation of 10.2 MeV (3.8 MeV) for the S(P ) state. Based on the nuclear shell model [45], the ratio of protons in the S state to those in
the P state is set to be 1:3. Proton decay kinematics can be distorted by continuously occurring
collisions with a surrounding nucleon during the decay, named “correlated decay”, producing
broad invariant mass and total momentum spectra. This mechanism is discussed in [46], and thecorrelated decay probability in bound proton decays is predicted to be about 10%. The proton
state, invariant mass, and proton initial momentum distributions are shown in Figures 4.2, 4.3,
and 4.4, respectively. In the proton kinetic distributions, the initial proton momentum andmass are calculated with the outgoing charged lepton and pion kinetic information, and eﬀects
from pion scattering inside the 16 O nucleus, which are described below, are not included. The
location of protons within the 16 O nucleus is calculated based on the Woods-Saxon nuclear
density model [47],
ρ(0)
(
),
ρ(r) =(4.1)
1 + exp r−abwhere r is the distance from the center of the 16 O nucleus, ρ(0) = 0.48m3π , a = 2.69 fm, and b= 0.41 fm.
Pions produced in bound proton decays often interact with nucleons via π absorption, elastic
scattering, inelastic scattering, and charge exchange. This is so-called final state interaction

35

CHAPTER 4. SIMULATION

Figure 4.1: Distributions of the Fermi momentum for the P state (left) and S state (right).
Data points show electron-12 C scattering experiment data and solid lines are theoretical curves.
Taken from [44].

Number of Events(Normalized to Unity)

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

p

s

Fre

1/2 sta

eP
roto

n

p

3/2 staCor

1/2 sta

te

te

te

rela

ted

Dec

ay

Proton Decay State

10-1

2

Number of Events [/10 MeV/c ](Normalized to Unity)

Number of Events [/10 MeV/c](Normalized to Unity)

Figure 4.2: Proton state distribution during the decay.

Free Proton
S stateP stateCorrelated Decay

10-2

10-3

10-4
0

100 200 300 400 500 600 700 800 900 1000
Proton Momentum [MeV/c]

Figure 4.3: Initial proton momentum distribution. Free proton and bound proton decay
events are stacked. Pion FSI eﬀects are notincluded.

10-1

Free Proton
S stateP stateCorrelated Decay

10-2

10-3

0

100 200 300 400 500 600 700 800 900 1000
Proton Invariant Mass [MeV/c2]

Figure 4.4: Eﬀective proton invariant mass
distribution. Free proton and bound proton
decay events are stacked. Pion FSI eﬀects are
not included.

36

CHAPTER 4. SIMULATION

Figure 4.5: Cross-sections of π ± -12 C scattering (π + in top left and π − in top right) and π ± -16 O
scattering (π + in bottom left and π − in bottom right). Points show experimental data andsolid lines are simulation curves. Dashed lines are simulation curves in previous versions. Taken
from [49].
(FSI) and is simulated based on the NEUT π FSI cascade model (version 5.3.6) [48, 49]. Pionsare propagated classically through a nuclear medium in finite steps in the NEUT π FSI model.
This model is tuned by various π ± -nucleus experimental data such as π ± -C, -O, -Al, and -Fe [50].
The π ± -12 C and π ± -16 O cross-sections obtained from diﬀerent experiments as well as simulated
functions are shown in Fig. 4.5. The fraction of π 0 interactions as a function of π 0 momentum
is shown in Fig. 4.6. The kinematics of the outgoing pion and nucleon after scattering within
the nucleus is simulated based on π ± -p scattering data [51] for pions with a momentum lessthan 500 MeV/c, while it is calculated from the SAID fits [52] for pions with a momentum oflarger than 500 MeV/c. The Pauli exclusion principle is taken into account by requiring the
momentum of the scattered nucleon is larger than the Fermi surface momentum:
)1
(
3
3 2
π ρ(r),(4.2)
pF (r) =2
where ρ(r) is defined in Eq. (4.1). After escaping the nucleus, the neutral pion immediately
decays into two gamma rays.
A gamma ray, neutron, and proton emitted from the remaining 15 N nucleus in the excitedstates after the proton decay are simulated based on [53]. The particle emission probability issummarized in Table 4.1. The probability of neutron emission in proton decay events including
free proton decays is predicted to be less than 10%, and no neutrons are produced in hadronsecondary interactions in water for the p → e+ π 0 and p → µ+ π 0 modes because the remaining
particles are gamma rays and position or anti-muon.
At last, a typical event display of the p → e+ π 0 event is shown in Fig. 4.7. Since free proton
decays are not influenced by any intranuclear eﬀects summarized above, they produce back-to-37

CHAPTER 4. SIMULATION
1
Charge exchange

π production

0.8

Fraction

Scattering

0.6

Absorption

0.4

0.2

0
300

No interaction

350

400

450

500

550

π0 Initial Momentum (MeV/c)

600

Figure 4.6: Fraction of π 0 interactions as a function of π 0 momentum. Taken from [27].
back event topologies as shown in the figure. Besides, in case the π 0 escapes the remaining
nucleus without being aﬀected by π FSI in a bound proton decay, such a event also leaves nearlyback-to-back particle tracks and can pass the proton decay signal selection criteria, which are
introduced in Section 7.1.1.
Table 4.1: Summary of particle emissions from the remaining 15 N nucleus. The residual 15 N
nucleus is at the ground state after proton decays at the P1/2 state, and therefore no particle
emission is predicted.
Proton Decay State Emitted Particle Probability
S1/2
n
1.8%
γ (7.03 MeV), n
1.8%
4.1%
p, n
p
1.8%
γ (7.01 MeV), p
1.8%
γ (3.50 MeV), n4.9%
γ (3.50 MeV)
9.4%
P3/2
γ (6.32 MeV)
43.6%
γ (9.93 MeV)
3.2%
p
3.2%
P1/2
nothing
25.0%

4.2

Atmospheric Neutrino Flux

In this analysis, atmospheric neutrino events mimic proton decay signal events, and therefore
they are considered as background. The atmospheric neutrino flux is simulated based on thecalculation by M. Honda et al., the Honda flux model [54], while other models, the Fluka flux
model [55] and Bartol flux model [56], are used for the systematic uncertainty estimation.
The Honda model is on the basis of AMS [57] and BESS [58] measurements, and the
US-standard atmosphere ’76 [59] is used as the model for the atmospheric density structure.
DPMJET-III [60] is adopted for simulating the generation of secondary cosmic-ray particles,
such as π, µ, in the atmosphere for hadronic interactions above 32 GeV, whereas JAM [61]38CHAPTER 4. SIMULATIONSuper-Kamiokande IV
Run 999999 Sub 0 Event 89
18-11-11:13:21:47
Inner: 3749 hits, 9063 pe
Outer: 4 hits, 4 pe
Trigger: 0x07
D_wall: 600.0 cm
Evis:

0.0 MeV

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7< 0.2
750
0 mu-edecays

600
450
300
150
0
0

500

1000

1500

2000

Times (ns)Figure 4.7: Typical event display of a p → e+ π 0 event. The ring in the left side is produced by
the positron, while the two rings shown in the right side are produced by the gamma rays fromthe π 0 decay.

39

CHAPTER 4. SIMULATION

4x10

3

3x10

2

0.32 GeV

3.2 GeV

1.0 GeV

νµ
10

3

νe

νµ

νµ

10

φν (m−2s−1sr−1GeV−1)φν (m−2s−1sr−1GeV−1)φν (m−2s−1sr−1GeV−1)

10

νµ

2

1

νµ

5x10

νe

νµ

νe

0

νe

νe
2x10

νe
2

4x10
−1.0

0

1

−0.50

0
cos θ

0.50

1.0

3x10
−1.0

−0.50

0

0.50

1.0

cos θ

−1.0

−0.50

0

0.50

1.0

cos θ

Figure 4.8: Atmospheric neutrino flux distributions at Kamioka as a function of zenith angle,cos θ. Here θ is the arrival direction of the neutrino, where cos θ = 1 stands for verticallydownward going neutrinos. In these distributions, the azimuth component is averaged out. Fromleft to right, neutrino of 0.32 GeV, 1.0 GeV, and 3.2 GeV cases are shown. Taken from [54].
is adopted for energy below 32 GeV. These hadronic interactions are fine-tuned using various
experimental data [58, 62, 63]. The curvatures of charged particles in the geomagnetic field aretaken into account when calculating the interaction and propagation of the cosmic-ray particles.
The zenith angle dependence of the atmospheric neutrino flux at Kamioka calculated by the
Honda model is shown in Fig. 4.8. The flux is peaked around the horizon because pions andmuons travel longer in the atmosphere horizontally than those traveling vertically, allowing moretime for the decays. The up-down asymmetry in the lowest energy region in Fig. 4.8 is caused by
the geomagnetic field, which aﬀects the track of the cosmic-ray particles. The neutrino flux andflux ratio distributions at Kamioka as a function of neutrino energy are shown in Fig. 4.9. In
these distributions, all neutrino directional components are averaged out, and the Honda modeland other models are compared.
The atmospheric neutrino MC events have been produced based on the predicted flux at
Kamioka, and the neutrino oscillation eﬀect is not considered in this step. It is assumed that all
neutrinos produced in the atmosphere reach the SK detector in their original flavor. Then, theneutrino oscillation eﬀect is taken into account by varying the MC event weight at the analysis
stage based on the latest oscillation analysis result [64].
The oscillation parameters, which are obtained from [64] and used in this analysis, are as
follows:∆m221 = 7.53 × 10−5 eV2 , (fixed in fit)

(4.3)∆m232 = 2.50 × 10−3 eV2 , (fitted)
sin2 θ12 = 0.304, (fixed in fit)sin2 θ13 = 0.0219, (fixed in fit)sin2 θ23 = 0.588, (fitted)(4.4)

δCP = 4.18. (fitted)

(4.5)
(4.6)
(4.7)
(4.8)

Because of the oscillation eﬀects, at most half of the muon neutrinos of O(1) GeV from thecos θ = −1 direction oscillate into tau neutrinos. In the oscillation fit, flux times cross-sectionsof the atmospheric neutrinos are also fitted using the total number of observed events used in
the oscillation analysis.

40

CHAPTER 4. SIMULATION

10

1.5xν µνe
0.75xν e

10This WorkHKKMS06
Bartol
Fluka

2

1

νµ
This WorkHKKMS06
Bartol
Fluka

0

10

−1

10

0

10
Eν (GeV)10

Neutrino Flux Ratios

φ νx E ν2 (m−2sec −1sr−1GeV)

51

νµ + νµνe + νeνµ2

ν µ ( x1.5)
νe

1

−1

10

0

10
Eν (GeV)

10

νe

1

Figure 4.9: Neutrino flux distributions at Kamioka as a function of neutrino energy. The Honda
model prediction is shown in red. The previous Honda model prediction is shown in blue. Taken
from [54].

4.3

Neutrino Interaction

Atmospheric neutrino interactions inside the detector are simulated based on NEUT [48].
They are classified into two categories, Charged Current (CC) and Neutral Current (NC) interactions. A neutrino exchanges a W ± boson with the target in the CC interaction. After theinteraction, a charged lepton, whose flavor is the same as that of the incoming neutrino, is left
in the final state. By distinguishing the flavor of the charged lepton inside the detector, theincoming neutrino flavor can be identified in this interaction. An event reconstruction algorithm
to identify the flavor of the charged lepton in SK, whether electron or muon, is described in
Section 6.1. In contrast, in the NC interaction, a neutrino interacts with the target mediatedby a Z 0 boson. After this NC interaction, no signs of the neutrino flavor are left within thedetector because the outgoing lepton is also neutrino.
In the NEUT simulation, the following interactions are considered:
1. CC and NC (quasi-)elastic scattering, CCQE (NCQE): ν + N → l(ν) + N ′ ,2. CC meson exchange current, CCMEC: ν + N N ′ → l + N ′′ N ′′′ ,3. CC and NC single meson production: ν + N → l(ν) + N ′ + meson,
4. CC and NC coherent pion production, CCCOH (NCCOH): ν + 16 O → l(ν) + 16 O + π,
5. CC and NC deep inelastic scattering, CCDIS (NCDIS): ν + N → l(ν) + N ′ + hadrons,
where N, N ′ , N ′′ , and N ′′′ stand for nucleons, l stands for a charged lepton, and ν stands for aneutrino.

4.3.1(Quasi-)Elastic Scattering

In the neutral current, NC, elastic scattering process, an incoming neutrino scatters oﬀ anucleon target. In this process, no new particles are produced while some momentum transfer
occurs. On the other hand, in the charged current, CC, quasi-elastic scattering process, anincoming neutrino is converted into a charged lepton, whose flavor is the same as the neutrino,in the final state. The target nucleon is also converted in this interaction, and thus the total
electric charge in the system is conserved.
The Llewellyn-Smith model [65] is adopted in the above two interactions for a hydrogen
nucleus target. For a nucleon target in an oxygen nucleus, eﬀects of the Fermi momentum and41

CHAPTER 4. SIMULATION# of Events [/25 MeV/c]

0.3

Proton Decay MC
Neutrino MC

0.25
0.2

0.15
0.1

0.05
0
0

50
100
150
200
250
The Fermi Momentum [MeV/c]

300

Figure 4.10: The Fermi momentum distributions. The blue histogram shows the Fermi momentum distribution used in the proton decay MC which is based on the shell model [45]. The
red histogram shows the one used in the neutrino MC which is based on the relativistic Fermi
gas model [66]. In the neutrino MC (NEUT), the Fermi surface momentum is set to 225 MeV/c.

NEUT 5.3.6

1.6

ANL
BNL
Gargamelleνµp → µ+n Cross Section

Cross Section [10-38 cm2]

Cross Section [10-38 cm2]

νµn → µ-p Cross Section

2
1.8

Gargamelle
Serpukhov
SKAT

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6

8

10

12

14

Neutrino Energy [GeV]2
1.8

NEUT 5.3.6

Gargamelle
Gargamelle

Serpukhov
SKAT

8

12

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6

10

14

Neutrino Energy [GeV]

Figure 4.11: Charged current quasi-elastic scattering cross-sections as a function of incoming
neutrino energy. The left plot shows the neutrino case and the right shows the anti-neutrino case.
The black line is the model prediction used in this analysis (NEUT version 5.3.6). Experimental
data points are from: ANL [69], BNL [70], Gargamelle [71], Serpukhov [72], and SKAT [73].
the Pauli exclusion principle are considered based on the relativistic Fermi gas model by Smith
and Moniz [66]. The Fermi momentum distribution in the relativistic Fermi gas model is diﬀerent
from the one used in the proton decay simulation described in Section 4.1 and shown in Fig. 4.10.
The diﬀerence between them is taken into account as a systematic uncertainty on the proton
decay signal selection eﬃciency. The Fermi surface momentum in the atmospheric neutrino MC
is set to 225 MeV/c. The diﬀerential cross-section for this interaction is formulated as a functionof four-momentum transfer, vector and axial-vector form factors [65]. These form factors areparametrized by the vector mass (MV ), which is set to 0.84 GeV, and axial mass (MA ), which
is set to 1.21 GeV. They have been determined based on the experimental data from K2K [67]and MiniBooNE [68]. The CCQE cross-sections as a function of incoming neutrino energy in
NEUT and various experimental results are shown in Fig. 4.11.

4.3.2

Meson Exchange Current

In the CCQE interaction described above, a neutrino interacts with a single nucleon only,
and any correlations between the nucleons in the nucleus are neglected. However, MiniBooNE

42

0.6 ν p → µ-p π+

0.4

νµn → µ-p π00.6νµn → µ-nπ+

0.2

0

10-1

Last Analysis, K. Abe et al (2017)
Current Analysis (NEUT 5.3.6)
ANL Data, G. M. Radecky et al (1982)
BNL Data, T. Kitagaki et al (1986)

0.4

0.2

1

1

0.8

0.4

0.2
0

0.8
0.6

µ

10-1

1

Cross Section [10

0.8

1.2
Cross Section [10-38 cm2]

1

-38

1.2

Cross Section [10-38 cm2]

1.2

cm2]

CHAPTER 4. SIMULATION

1

Neutrino Energy [GeV]

0
10-1

1

10

Figure 4.12: Charged current single π production cross-sections as a function of incoming
neutrino energy. The dotted black line corresponds to the model used in previous SK proton
decay searches [27], NEUT 5.1.4, and the solid red line shows that for the current analysis,
NEUT 5.3.6.
data [68] suggests a process in which an incoming neutrino interacts with multiple nucleons in
the target nucleus simultaneously. In order to include this interaction, the Meson Exchange
Current (MEC) model by Nieves et al. [74] has been implemented in NEUT recently.

4.3.3

Single Meson Production

Single meson (such as π, K, and η) production in a neutrino interaction is simulated througha baryon resonance excitation state:ν + N → l(ν) + N ∗ ,∗′N → N + meson,(4.9)(4.10)

where N ∗ is the baryon resonance, and a single meson is produced from N ∗ in the final state.
This interaction is considered for the cases with hadronic invariant mass W < 2.0 GeV/c2 , whichis the mass of the intermediate resonance (N ∗ ).
The charged current single π production (CC1π) process is the dominant background process
for the search for proton decay via p → e+ π 0 and p → µ+ π 0 . In the previous publication about
these searches [27], the Rein-Sehgal model [75] has been used. Since then new form factors(Graczyk and Sobczyk) have been obtained from a simultaneous fit [76] to neutrino scattering
data from bubble chamber experiments [77], and they are currently used in NEUT. A comparisonof the cross-sections as a function of incoming neutrino energy between the previous NEUT
version and the current version is shown in Fig. 4.12. Because the dominant neutrino energy
range contributing to the proton decay background is about from 1 to 3 GeV, this cross-sectionchange reduces the expected number of atmospheric neutrino backgrounds by about 15%. By
this modification, the momentum transfer also becomes smaller as shown in Fig. 4.13, and theoutgoing lepton’s and total reconstructed momentum becomes higher accordingly. Since theevent topology of the proton decay signal event is back-to-back, and only a low total momentum
event is allowed as a proton decay signal as described in Section 7.1.1, this momentum transfer
change further reduces the expected number of backgrounds by about another 15% comparedto the previous version. In total, the reduction of the expected number of backgrounds by the
update of NEUT is about 30%.

4.3.4

Coherent Pion Production

Coherent pion production, in which an incoming neutrino coherently interacts with target
nucleons in an entire oxygen nucleus and leaves a single pion, is simulated based on the Rein-

43

CHAPTER 4. SIMULATION

0.12

Last Analysis, K. Abe et al (2017)
Current Analysis (NEUT 5.3.6)

0.1

a.u.

0.08
0.06
0.04
0.02
0
0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
q2: Four Momentum Transfer [(GeV/c)2]2

Figure 4.13: Four momentum transfer in the charged current single π production interaction.
The black histogram corresponds to the model used in previous SK proton searches [27], NEUT
5.1.4, and the red histogram corresponds that for the current analysis, NEUT 5.3.6.
Sehgal model [75]. Because of the low momentum transfer in this interaction, both the outgoing
lepton and pion tend to have forward-going directions. Therefore, events produced in thisinteraction do not mimic p → e+ π 0 and p → µ+ π 0 events.

4.3.5

Deep Inelastic Scattering

In the deep inelastic scattering process, an incoming neutrino interacts with a constituent
quark in the target nucleon. In this process, multiple hadrons are produced in the final state.
The multiple hadron production is also simulated through a baryon resonance excitation state,
but the mass of the intermediate resonance (W ) is restricted to be higher than 1.3 GeV/c2 .
This interaction becomes dominant in the higher neutrino energy in the NEUT simulation. Forinteractions with W < 2.0 GeV/c2 , only pions are produced as generated hadrons in the final
state. The pion multiplicity is modeled based on experimental data in bubble chamber experiments [78]. Since this hadronic invariant mass region (1.3 < W < 2.0 GeV/c2 ) is overlappedwith the region for the single pion production interaction (W < 2.0 GeV/c2 ), which is describedin Section 4.3.3, only the multiple pion production is simulated as the deep inelastic scattering
process. Other mesons, such as K and η, can be produced in the final state in interactions
with W > 2.0 GeV/c2 , and the hadronic final states are modeled based on PYTHIA and JETSET [79]. The nucleon internal structure is modeled based on the GRV98 parton distributionfunctions [80] with the corrections by Bodek and Yang [81] for the low Q2 region. The total
cross-sections of the charged current interaction including quasi-elastic scattering, single meson
production, and deep inelastic scattering are shown in Fig. 4.14. In the region neutrino energyof more than 10 GeV, the deep inelastic scattering interaction becomes increasingly dominant.

4.4

Hadronic Interaction

Neutrons play an important role to separate between a proton decay signal and atmospheric
neutrino backgrounds because there are several neutron production processes in atmospheric
neutrino events:
1. Primary neutrino interaction, ν̄ + p → l+ + n,
2. Hadron and meson interactions in a nucleus, FSI, p + p → p + n + π + ,3. Hadron secondary interactions in water, SI, n + 16 O → n + n + 15 O∗ .

44

νµ CC Total Cross Section

Cross Section/Eν [10-38 cm2/GeV]

Cross Section/Eν [10-38 cm2/GeV]

CHAPTER 4. SIMULATION

1.2
NEUT 5.3.6

1
0.8
0.6
0.4
0.2
0
1

CCFR
CDHS
Gargamelle

CHARM
BEBC
SKAT

IHEP-JINR
IHEP-ITEP
CCFRR

10

Neutrino Energy [GeV]102

νµ CC Total Cross Section

1.2
NEUT 5.3.6

1
0.8
0.6
0.4
0.2
0
1

10

Neutrino Energy [GeV]102

Figure 4.14: Charged current total cross-sections divided by incoming neutrino energy. The left
plot shows the neutrino case and the right shows the anti-neutrino case. The black line is themodel prediction used in this analysis (NEUT version 5.3.6). Experimental data points are from:CCFR [82], CDHS [83], Gargamelle [84], CHARM [85], BEBC [86], SKAT [87], IHEP-JINR [88],IHEP-ITEP [89], and CCFRR [90].
The dominant neutron production process in atmospheric neutrino events in SK is the hadronsecondary interaction in water and its fraction is about 70% [27].
Hadronic interaction processes are simulated by CALOR package [91], which uses HETC [92]for hadrons below 10 GeV, FLUKA [93] for hadrons above 10 GeV, and MICAP [94] for neutrons
below 20 MeV.

4.5

Detector Simulation

Produced particles from the above physics processes are fed into a GEANT3-based [95]detector simulation called SKDETSIM [96]. Interactions of the particles in water, particle
decays, and production of Cherenkov photons are simulated in SKDETSIM. Detector responses
including the water property, optical modeling as well as PMT and electronics responses to the
produced photons are simulated based on the detector calibration results described in Chapter 3.

4.5.1

Treatment for Neutron Tagging Process

Neutrons emitted from a primary event thermalize in water and are eventually captured byhydrogen nuclei. After a neutron is captured by a hydrogen nucleus with a capture time constantof about 200 µsec, a 2.2 MeV gamma ray is emitted. Low energy background sources, such asa few MeV gamma rays from radioactive decay products, are not simulated in our detector
simulation but they have non-negligible impacts on the 2.2 MeV gamma ray search to countthe number of neutrons. Therefore, in the timing region used for this 2.2 MeV gamma ray
search, which begins 18 µsec after the primary trigger, the simulated PMT dark noise hits are
replaced by the real PMT hit information taken from the random trigger event data (illustrationin Fig. 4.15), which include the low energy background activities. This timing region used forthe 2.2 MeV gamma ray search is defined to avoid eﬀects from PMT after-pulsing which occurs
between 12 and 18 µsec after the primary PMT hit timing as shown in Fig. 4.16. Althoughthe 2.2 MeV gamma ray tagging algorithm is described in Section 6.3 and in [97], the average
neutron multiplicity (the number of tagged neutrons per primary neutrino event) distribution isshown in Fig. 4.17 and confirms that the simulated neutron production processes well reproduce
the neutron multiplicity in the atmospheric neutrino data in SK.

45

CHAPTER 4. SIMULATION

Neutrino Interaction
0μs
Simulated neutrino
interaction

535μs
Simulated neutrons from neutrino interaction
Atmospheric neutrino MC
Real SK dummy trigger data

Simulateddark noise

random low energy background

18μs

Figure 4.15: Treatment of the PMT simulation. The simulated PMT dark noise hits are
replaced by the real PMT hits taken from the random trigger event data for the time regionused for neutron tagging, which begins 18 µsec after the primary trigger. Taken from [97].

Figure 4.16: PMT hit rate as a function of time after the primary event trigger. The exponential
decay within 10 µsec corresponds to hits produced by Michel electrons from muon decays. The
bump between 12 and 18 µsec corresponds to hits produced by PMT after-pulsing. Taken
from [97].

46Number of tagged neutrons

CHAPTER 4. SIMULATION

8

Data
7
6

MC

5
4
3
2
1
0
1.5

2

2.5

3

3.5

4

4.5

Log10(Evis/MeV)

Figure 4.17: Average neutron multiplicity (the number of tagged neutrons per primary neutrino
event) as a function of detector deposited energy in SK. The black dots shows the SK-IV data
and the red histogram shows the atmospheric neutrino MC events.

47

Chapter 5

Data Set
The typical SK event rate for this data set is about tens of Hz, 106 events per day. Most
events are background events such as cosmic-ray muon events, low energy events produced by radioactive products around the detector, and dummy events produced from erroneous discharges
in a PMT’s dynode, “flasher” events. Event selection criteria to extract proton decay candidates
and atmospheric neutrino events are described in this chapter [98].
This analysis uses events termed “fully contained” (FC) whose interaction vertex point isreconstructed within the ID and which have no cluster of hits in the OD. In order to eﬃciently
select FC events from the quite large amount of raw data, the following event selections areapplied, and they are composed of five reduction steps:
1, 2. First and second reductions · · · Loose and simple selection criteria to reject low energy background events and cosmic-ray muons. After the first and second event reduction
steps, the event rate is in the order of 103 and 102 events per day, respectively.
3. Third reduction · · · More complex criteria to mainly reject cosmic-ray muons and flasher
events. The event rate after applying the third reduction is in the order of 10 events perday.
4. Fouth reduction · · · At the fourth reduction step, a dedicated flasher rejection algorithm
is applied.
5. Fifth reduction · · · Miscellaneous criteria are applied to reject remaining backgrounds.
6. Final event selection · · · At the analysis stage, criteria using event reconstruction variables are applied. The typical event rate after these criteria is about 8.2 and 1.5 events per
day in the 22.5 kton conventional and 4.7 kton additional fiducial mass region, respectively.
The definition of the fiducial mass region is introduced in Section 5.7.
An event set passing them, termed “final sample”, is commonly used for proton decay searches,
atmospheric neutrino analyses, and other exotic searches, such as indirect dark matter searches [99],neutron anti-neutron oscillation searches [100], etc... As for other event categories, “partiallycontained” (PC) and “Upward-going muon” (UPMU), their event selection criteria can be foundelsewhere [98, 101].

5.1

Treatment of OD PMT Hits in SK-IV - ID-OD Crosstalk

In very high energetic events during SK-IV, “fake” OD PMT hits are confirmed, induced byneighbor ID PMTs which detect a large amount of photons. A typical event display is shownin Fig. 5.1. This is an up-going electron event with more than 20 GeV of energy depositionin the detector. In the detector top region, several OD PMTs “detect” low charge hits, less48

CHAPTER 5. DATA SET

than 0.2 photoelectrons (p.e.’s), behind the ID PMT hit timing, about 100 nsec late after the
ID trigger timing. The same kind of fake OD PMT hits can be seen in laser calibration events
described in 3.3.5, which also leave a huge amount of photons in the detector and whose event
display is shown in Fig. 5.2. In both events, no particles are thought to exit the ID, and therefore
these OD PMT hits should be treated as noises, ID-OD crosstalk.
Figure 5.3 shows the two-dimensional scatter plots of OD PMT charge and hit timing relative
to the closest ID PMT hit timing for laser calibration events and partially contained MC events,
in which charged particles actually exit the ID and emit Cherenkov photons in the OD. Most
OD PMT hits caused by the ID-OD crosstalk are delayed more than 50 nsec with less than
0.2 p.e.’s. Although the mechanism is not fully understood, to reject these fake hits in the event
selection, OD PMT hits satisfying the following conditions are not counted in the algorithm for
SK-IV:
qODPMT < 0.2 p.e.’s,(5.1)

50 < tODPMT − tIDPMT < 600 nsec,(5.2)

where qODPMT stands for the OD PMT observed charge, tODPMT stands for the OD PMT hit
timing, and tIDPMT for the closest ID PMT hit timing.

5.2

First Reduction

The first event selection criteria are as follows:
FC1-1 PE300 > 200 p.e.’s (100 p.e.’s for SK-II),
where PE300 is the maximum total ID PMT charge in a sliding 300 nsec timing window.
FC1-2 NHITA800 < 50 (55 in SK-IV) or the OD trigger is not issued,
where NHITA800 is the number of OD PMT hits within a fixed 800 nsec timing window,
from -500 nsec to +300 nsec after the trigger timing.
Criterion FC1-1 rejects low energy events produced by radioactive products, several MeV scale
events. 200 p.e.’s corresponds to about 22 MeV of energy deposition in SK. Criterion FC1-2
rejects cosmic-ray muons.

5.3

Second Reduction

Events must satisfy the following criteria to pass the second reduction step:FC2-1 PEmax /PE300 < 0.5,
where PEmax is the maximum charge in any single ID PMT.
FC2-2 NHITA800 < 25 (30 in SK-IV) or PEtotal > 100000 p.e.’s or the OD trigger is not issued,
where PEtotal is the total number of p.e.’s in the ID.
In low energy and flasher events, only a single PMT often detects a large amount of p.e.’s.
They are rejected by FC2-1. Criterion FC2-2 is to further reject cosmic-ray muons. The
PEmax /PE300 and NHITA800 distributions are shown in Figures 5.4 and 5.5, respectively.

5.4

Third Reduction

There are a variety of selection criteria at the third reduction step for each background type.

49

CHAPTER 5. DATA SET

NUM
2357
RUN
70792
SUBRUN470
EVENT
96792018
DATE 2013-Jan- 8
TIME
23:46:45
TOT PE: 273162.0
MAX PE:
891.2
NMHIT : 9632
ANT-PE:
11.7
ANT-MX:
5.6
NMHITA:38

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

RunMODE:NORMALTRG ID :00001111
T diff.: 0.00
us
FEVSK :88010803
nOD YK/LW:20/20
SUB EV : 0/ 0
Dcye: 0( 0/ 0/ 0/ 0)

Comnt;

Figure 5.1: Typical event display in which a large amount of photons are observed in the ID
and fake OD PMT hits are recorded. The main event display is the ID one and the top left is
the OD one. A circle located at each PMT position corresponds to the PMT hit and the size of
its radius is proportional to the number of observed photoelectrons. In the detector top region,
fake OD PMT hits can be found.

50

CHAPTER 5. DATA SET

NUM
35
RUN
71762
SUBRUN
4
EVENT
664730DATE 2013-Aug- 7
TIME
22:36:17
TOT PE:10298942.0
MAX PE: 1794.5
NMHIT : 11123
ANT-PE:
71.4
ANT-MX:
1.8
NMHITA:
931

1990/00/00:NoYet:NoYet
1990/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

RunMODE:NORMALTRG ID :00001111
T diff.: 0.00
us
FEVSK :88010803
nOD YK/LW:**/**SUB EV : 0/ 0
Dcye: 0( 0/ 0/ 0/ 0)

Comnt;

Figure 5.2: Typical laser event display in which a large amount of photons are distributed into
the whole ID, and fake OD PMT hits are recorded. In this event, almost all ID PMTs observed
more than 1000 p.e.’s.

Figure 5.3: Two-dimensional scatter plots of OD PMT charge and hit timing relative to theclosest ID PMT hit timing. The laser event plot is in left, and the partially contained MC event
plot is in right. In laser calibration event, no charged particles exit the ID, while in the partiallycontained MC events, charged particles actually exit the ID and emit Cherenkov photons in the
OD. Taken from [102].

51

CHAPTER 5. DATA SET

106

SK-IV
After 1st Reduction
Data

105
104
3

10

102
10

107
Select

106
105

SK-IV
After 1st Reduction
ATM ν MC

104
3

10

102
10

Number of Events

107
SelectNumber of Events

Number of Events

107

SK-IV
Final Sample
Data
ATM ν MC

106
105
104
103
102
10

1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

PEMAX/PE300

PEMAX/PE300

PEMAX/PE300

Select104

SK-IV
After 1st Reduction
Data

103
102
10
1
0

10

20

30

40

NHITA800 [hit]

50

105

Select104

SK-IV
After 1st Reduction
ATM ν MC

103
102
10
1
0

10

20

30

40

NHITA800 [hit]50

Number of Events [/hit]

105

Number of Events [/hit]

Number of Events [/hit]

Figure 5.4: Reduction variable PEmax /PE300 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after
all the FC event selection criteria. Vertical error bars on the data points denote the statisticaluncertainty.

105

SK-IV
Final Sample
Data
ATM ν MC

104
103
102
10
1
0

10

20

30

40

50

NHITA800 [hit]Figure 5.5: Reduction variable NHITA800 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after
all the FC event selection criteria. Vertical error bars on the data points denote the statisticaluncertainty.

52

CHAPTER 5. DATA SET

5.4.1

Through-going Muon Rejection“Through-going” muons are cosmic-ray muons running through the detector and exiting the
ID. In order to identify their entering and exiting points in the ID, a special through-going muon
fitter is applied to all events which have more than 1000 ID PMT hits with more than 230 p.e.’s
deposited therein. The fitter finds them by maximizing the following goodness:
(
)
∑ 1
1
(t′i − t0 )2
goodness = ∑ 1 ×
exp −
,
(5.3)
2 × (σi × 1.5)2
σi2
i σ2
i

i

where σi is the timing resolution of the ith PMT, t′i is the ith PMT’s time-of-flight corrected
residual time, and t0 is chosen so that the goodness is maximal at each tested entering andexiting point. In the photon time-of-flight calculation, the track length of the muon is taken
into account.
The number of OD PMT hits around the reconstructed entering and exiting points is also
used in the selection. The event rejection criteria are as follows:
FC3-1-1 goodness > 0.75,
FC3-1-2 NHITAthru> 10 or NHITAthru
out > 10,in
thru
where NHITAin (NHITAthru)
is the number of OD PMT hits located within 8 m fromout
the reconstructed entering (exiting) point in a fixed 800 nsec timing window.
Events satisfying the above criteria are removed from the data set as through-going muons.
The two-dimensional NHITAthru
and NHITAthru
out scatter plots after applying FC3-1-1 and onein
dimensional distributions of the final sample are shown in Fig. 5.6.

5.4.2

Stopping Muon Rejection“Stopping” muons are cosmic-ray muons that stop inside the ID and do not have any exiting
points. In a similar manner to through-going muons, a special stopping muon fitter identifies acluster of earliest timing ID PMT hits as a muon entering point from those PMTs’ position, andthe fitting goodness is evaluated using Eq. (5.3). The event rejection criteria to remove stoppingmuons are as follows:
FC3-2-1 The stopping muon fit is succeeded, goodness ≥ 0,
FC3-2-2 NHITAin ≥ 10,
where NHITAin is the number of OD PMT hits located within 8 m from the reconstructed
entering point in a fixed 800 nsec timing window.
Events satisfying both criteria are rejected. In SK-I, events satisfying the following criterion are
additionally rejected.
FC3-2-3 NHITAin ≥ 5 and goodness ≥ 0.5.
The NHITAin distributions are shown in Fig. 5.7.

5.4.3

Cable Hole Muon Rejection“Cable hole” muons are cosmic-ray muons that pass through cable bundles. Because they do
not run in the water, they run through the OD without leaving suﬃcient light. There are twelve
cable holes on the top of the detector through which PMT cables run as shown in Fig. 5.8. Fourcable holes out of the twelve have veto counters with a plastic scintillator plate and 50 cm PMT
because they are located slightly inner than the other eight cable holes. A schematic view ofthe veto counter and a typical cable hole muon is shown in Fig. 5.9. Events with both a veto

53

104

Number of Events [/hit]

Number of Events [/hit]

CHAPTER 5. DATA SET

SK-IVFinal Sample
Data
ATM ν MC

103

102

10

1
0

5 10 15 20 25 30 35 40 45 50
NHITAthru
in [hit]104
SK-IV
Final Sample
Data
ATM ν MC

103

102

10

1
0

5 10 15 20 25 30 35 40 45 50
NHITAthruout [hit]

Reject

SK-IV
After 2nd Reduction
Data

104
103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin [hit]

105

SK-IV
After 2nd Reduction
ATM ν MC

Reject

104
103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin [hit]Number of Events [/hit]

105

Number of Events [/hit]

Number of Events [/hit]

Figure 5.6: The top two plots are the two-dimensional NHITAthru
and NHITAthru
out scatterinplots in SK-IV. The bottom two plots show the one-dimensional distributions of the final
sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATM ν) MC histograms arenormalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). Vertical error bars on the data points denote the statistical uncertainty.

105
104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin [hit]Figure 5.7: Reduction variable NHITAin distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after
all the FC event selection criteria. Vertical error bars on the data points denote the statisticaluncertainty.

54

CHAPTER 5. DATA SET

Figure 5.8: Schematic view of the top of the detector. Shaded circles represent the cable holes.
Taken from [107].
counter hit and an entering point less than 4 m from the corresponding cable hole have beentagged as cable hole muons and rejected from the data set in previous analyses. Here, again the
stopping muon fitter has been used to reconstruct the entering point. In the present analysis,
all events with a veto counter hit in the event trigger timing are additionally rejected regardlessof the reconstructed entering point.

5.4.4

Low Energy Event Rejection

In order to further reject low energy events, the following rejection criteria are applied:FC3-3-1 The number of ID PMT hits is less than 500,
FC3-3-2 N50 ≤ 50 (25 for SK-II),
where N50 is the maximum number of ID PMT hits in a sliding 50 nsec window after
subtracting the photon time-of-flight. The vertex position used for the time-of-flight subtraction is reconstructed with a dedicated low energy event fitter so that the goodness
defined in Eq. (5.3) takes maximum.
Events satisfying both criteria are removed. The N50 distributions after applying FC3-3-1 areshown in Fig. 5.10.

5.4.5

Flasher Event Rejection

Flasher events often have a broad timing distribution compared to events produced bycharged particles. The minimum number of ID PMT hits in a sliding 100 nsec timing window from +300 nsec to +800 nsec after the trigger timing is defined as NHITmin100 . The flasher
event rejection criteria are as follows: For SK-I,
FC3-4-1 NHITmin100 ≥ 15,
orFC3-4-2 The number of ID PMT hits is less than 800 and NHITmin100 ≥ 10.

55

CHAPTER 5. DATA SET

Figure 5.9: Schematic view of the veto counter. It is composed of a plastic scintillator plate and50 cm PMT. Taken from [107].

104
103
102
10
1
0 50 100150200250300350400450500

N50 [hit]

Number of Events [/hit]

Number of Events [/hit]

105

SK-IV
After 2nd Reduction
Data

106

SK-IV
After 2nd Reduction
ATM ν MC

105
104
103
102
10

1
0 50 100150200250300350400450500

N50 [hit]

Number of Events [/hit]

RejectReject

106

106
105
104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0 50 100150200250300350400450500

N50 [hit]

Figure 5.10: Reduction variable N50 distributions of events with less than 500 ID PMT hits in
SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetimeand the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
“Final Sample” refers to events after all the FC event selection criteria. Vertical error bars on
the data points denote the statistical uncertainty.

56

Reject

104

SK-IV
After 2nd Reduction
Data

103
102
10
1
0 10 20 30 40 50 60 70 80 90 100

NHITMIN100 [hit]

105
SK-IV
After 2nd Reduction
ATM ν MC

Reject

104
103
102
10

1
0 10 20 30 40 50 60 70 80 90 100

NHITMIN100 [hit]Number of Events [/hit]

105

Number of Events [/hit]

Number of Events [/hit]

CHAPTER 5. DATA SET

105
104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0 10 20 30 40 50 60 70 80 90 100

NHITMIN100 [hit]Figure 5.11: Reduction variable NHITmin100 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after
all the FC event selection criteria. Vertical error bars on the data points denote the statisticaluncertainty.
For SK-II to -IV,
FC3-4-1′ NHITmin100 ≥ 20.
The NHITmin100 distributions are shown in Fig. 5.11.
Another flasher rejection criterion is applied to events with less than 250 ID PMT hits.
Events whose low energy fit goodness defined in Eq. (5.3) is less than 0.4 are also removed as
flasher events. The low energy fit goodness distributions of events with less than 250 ID PMThits are shown in Fig. 5.12.

5.4.6

Accidental Coincidence Event Rejection

A cosmic-ray muon and low energy activity sometimes accidentally coincide. In case thecosmic-ray muon comes in the detector several hundred nsec after the low energy activity, theevent trigger is issued by the low energy activity, and no obvious OD PMT hits are found aroundthe trigger timing. Since the former event reduction steps search for OD PMT hits around thetrigger timing, such events are not rejected. The event rejection criteria are as follows to prevent
them from contaminating the data set:FC3-5-1 PELATE > 5000 p.e.’s (2500 p.e.’s for SK-II),
where PELATE is the total number of p.e.’s in the ID within a fixed 500 nsec timing window
from +300 nsec to +800 nsec after the trigger timing.
FC3-5-2 NHITALATE ≥ 20,
where NHITALATE is the number of OD PMT hits within a fixed 500 nsec timing window
from +300 nsec to +800 nsec after the trigger timing.
Events satisfying both criteria are removed. The two-dimensional PELATE and NHITALATE
scatter plots and one-dimensional distributions of the final sample are shown in Fig. 5.13.

5.5

Fourth Reduction

At the fourth reduction step, a pattern matching method is used to reject flasher events
because flasher events often occur repeatedly with a similar ID PMT hit profile. Typical flasher

57

CHAPTER 5. DATA SET

SK-IV

Data
3

10

Reject102
10

104 After 2nd Reduction

Number of Events

Number of Events

Number of Events

SK-IV

104 After 2nd Reduction

ATM ν MC
3

10

Reject

102
10

104
103

SK-IV
Final Sample
Data
ATM ν MC

102
10

1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Low-E Fit Goodness

Low-E Fit Goodness

Low-E Fit Goodness

1105

Number of Events [/hit]

Number of Events [/100 p.e.]

Figure 5.12: Low energy fit goodness distributions of events with less than 250 ID PMT hits in
SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetimeand the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
“Final Sample” refers to events after all the FC event selection criteria. Vertical error bars on
the data points denote the statistical uncertainty.

SK-IV
Final Sample
Data
ATM ν MC

104
103
102
10
1
0

2000

4000

6000

8000 10000

PELATE [p.e.]

105
104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITALATE [hit]Figure 5.13: The top two plots show the two-dimensional PELATE and NHITALATE scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of the final
sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATM ν) MC histograms arenormalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). Vertical error bars on the data points denote the statistical uncertainty.

58

CHAPTER 5. DATA SET

1990/00/00:NoYet:NoYet
1990/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

NUM
6
RUN
65939
SUBRUN
5
EVENT
809997
DATE 2009-Nov-17
TIME
5:43:16
TOT PE:
1364.2
MAX PE: 1039.2
NMHIT :
270
ANT-PE:
6.3
ANT-MX:
1.6
NMHITA:
6

NUM
22
RUN
65939
SUBRUN
16
EVENT
2988426
DATE 2009-Nov-17
TIME
5:56: 3
TOT PE:
1994.0MAX PE: 1039.1
NMHIT :
587
ANT-PE:
16.0
ANT-MX:
3.1
NMHITA:15

1990/00/00:NoYet:NoYet
RunMODE:NORMAL
1990/00/00:;R= 0:NoYet
TRG ID :00000111
R :Z : PHI : GOOD
T diff.: 0.00
us
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MSFEVSK :88010803
nOD YK/LW: 2/ 1
SUB EV : 0/ 0
Dcye: 0( 0/ 0/ 0/ 0)

RunMODE:NORMALTRG ID :00000111
T diff.: 0.00
us
FEVSK :88010803
nOD YK/LW: 4/ 2
SUB EV : 0/ 0
Dcye: 0( 0/ 0/ 0/ 0)

Comnt;

Comnt;

Figure 5.14: Typical flasher event displays. They are diﬀerent events but caused by the same
PMT which detects a large amount of photons (the large circle).
event displays are shown in Fig. 5.14. The algorithm tries to find two diﬀerent events in which
PMT hit (charge) patterns are similar. The ID is divided into 2 m × 2 m patches when comparing
the PMT charge profiles in the two diﬀerent events, event A and event B. Each patch has about
8 PMTs, and their charge sum is calculated. The following correlation coeﬃcient, r, is defined:r=B
1 ∑ (QiA − ⟨QA ⟩) × (QBi − ⟨Q ⟩)
,
N
σA σB

(5.4)

i

B
where N is the number of patches, QA
i (Qi ) is the ith patch’s total observed charge in event
AB
A (B), ⟨Q ⟩ (⟨Q ⟩) is the average charge over all patches in event A (B), and σA (σB ) is thestandard deviation of the observed charge in event A (B). For SK-I and -II, this single parameterr is used at this reduction step.
Since SK-III, a Kolmogorov-Smirnov test is performed for the accumulated charge distribution normalized by the total observed charge in each event. The maximum distance between
the two accumulated charge distributions in event A and B, dKS , is introduced. Furthermore,probability density functions are made using atmospheric neutrino MC events and these twoparameters, r and dKS , are combined into a single likelihood parameter. The combined likelihood value, prob, is used to select events at this reduction step. A higher prob value indicates“well-matched” event with another event, and events with more than 3 of prob are rejected. The
prob distributions are shown in Fig. 5.15.

5.6

Fifth Reduction

There are miscellaneous selections at the last step to remove remaining background events.

59

105

105

SK-IV
After 3rd Reduction
104
Data

SK-IV
After 3rd Reduction
104
ATM ν MC

Reject

103
102
10
1
-20 -15 -10 -5

0

5

10

15

20

RejectNumber of Events

105

Number of Events

Number of Events

CHAPTER 5. DATA SET

103
102
10
1
-20 -15 -10 -5

prob

0

5

10

15

20

prob

104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
-20 -15 -10 -5

0

5

10

15

20

prob

Figure 5.15: Reduction variable prob distributions in SK-IV. The atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability(∆m2 = 2.5×10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after all the FC
event selection criteria. Vertical error bars on the data points denote the statistical uncertainty.

5.6.1

Tight Stopping Muon Rejection

In order to further reject stopping muons, events satisfying at least one of the following
criteria are thrown away:
FC5-1-1 Stopping muon fit goodness ≥ 0.5 and NHITAin ≥ 5,
FC5-1-2 NHITAin200 ≥ 4,
where NHITAin200 is the maximum number of OD PMT hits located within 8 m from thereconstructed entering point in a sliding 200 nsec timing window.
FC5-1-3 The vertex reconstruction goodness agood < 0.77, the number of ID PMT hits is morethan 7000 with more than 70000 p.e.’s deposited therein, and NHITAin ≥ 6,
where agood is evaluated in the FC event reconstruction algorithm described in Section 6.1.1.
Criterion FC5-1-1 criterion is the tighter condition of the stopping muon rejection criteria
in the third reduction step (Section 5.4.2). The two-dimensional stopping muon fit goodness
and NHITAin scatter plots and one-dimensional distributions of the final sample are shownin Fig. 5.16. Criterion FC5-1-2 rejects events in which OD PMT hits are localized in termsof time and location. The NHITAin200 distributions are shown in Fig. 5.17. Criterion FC51-3 is introduced in the present analysis to reject high energy cosmic-ray muons which are
mis-reconstructed in the fiducial mass region by the FC event reconstruction algorithm. The
NHITAin distributions after applying agood, the number of ID PMT hits, and total observed
charge criteria are shown in Fig. 5.18.

5.6.2

Tight Cable Hole Muon Rejection

In the third reduction step, only criteria regarding the four cable holes with veto counters
are applied (Section 5.4.3). To reject cosmic-ray muons passing through the other eight cableholes, events satisfying the following conditions are removed:
FC5-2-1 Stopping muon fit goodness ≥ 0.4,
FC5-2-2 PEtot > 4000 p.e.’s,

60

103

104
SK-IV
Final Sample
Data
ATM ν MC103

Number of Events

Number of Events [/hit]

CHAPTER 5. DATA SET

102

10

102

10

1

1
0

SK-IV
Final Sample
Data
ATM ν MC5 10 15 20 25 30 35 40 45 50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NHITAin [hit]Fit Goodness

Reject

SK-IV
After 4th Reduction
Data

103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin200 [hit]

104

SK-IV
After 4th Reduction
ATM ν MC

Reject

103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin200 [hit]Number of Events [/hit]

104

Number of Events [/hit]

Number of Events [/hit]

Figure 5.16: The top two plots show the two-dimensional stopping muon fit goodness and
NHITAin scatter plots in SK-IV. The bottom two plots show the one-dimensional distributionsof the final sample in SK-IV. In the NHITAin one-dimensional distribution, events with stopping
muon fit goodness of 5 or more are filled. In the stopping muon fit goodness one-dimensional
distribution, events with NHITAin of 5 or more are filled. The atmospheric neutrino (ATMν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability(∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). Vertical error bars on the data points denote thestatistical uncertainty.

104
103

SK-IV
Final Sample
Data
ATM ν MC

102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITAin200 [hit]Figure 5.17: Reduction variable NHITAin200 distributions in SK-IV. The atmospheric neutrino(ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers to events after
all the FC event selection criteria. Vertical error bars on the data points denote the statisticaluncertainty.

61

SK-IV
After 4th Reduction
Data

102

10

1
0

5 10 15 20 25 30 35 40 45 50

SK-IV
After 4th Reduction
ATM ν MC

Reject

103

102

10

1
0

5 10 15 20 25 30 35 40 45 50

NHITAin [hit]

NHITAin [hit]Number of Events [/hit]

Reject103

Number of Events [/hit]

Number of Events [/hit]

CHAPTER 5. DATA SET

103

SK-IV
Final Sample
Data
ATM ν MC

102

10

1
0

5 10 15 20 25 30 35 40 45 50

NHITAin [hit]Figure 5.18: Reduction variable NHITAin distributions in SK-IV. Events with less than agood <0.77, more than 7000 ID PMT hits and more than 70000 p.e.’s of total observed charge areplotted. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetimeand the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
“Final Sample” refers to events after all the FC event selection criteria. Vertical error bars on
the data points denote the statistical uncertainty.
FC5-2-3 cos θz > 0.6,
where cos θz is the reconstructed muon direction, and cos θz = 1.0 is vertically downwardgoing.
FC5-2-4 dhole < 250 cm,
where dhole is the distance between the reconstructed entering point and the closest cablehole position.
These criteria have been applied only to the SK-IV data in previous analyses but in the present
work, they are applied to all of the SK data uniformly. The dhole distributions after applying
FC5-2-1, FC5-2-2, and FC5-2-3 are shown in Fig. 5.19.

5.6.3

Invisible Muon Rejection“Invisible muon” events are induced by Michel electrons from cosmic-ray muons which are
below the Cherenkov threshold, invisible, and stop in the ID. A cluster of OD PMT hits, which
are produced earlier than the ID trigger timing and are induced by the muon before its decay,
are often found in such events. The ID event trigger is issued by the Michel electron from themuon decay. Events satisfying at least one of the following criteria are rejected as invisible muon
events:FC5-3-1 For events in which the total ID PMT charge, PEtot , is less than 1000 p.e.’s (500 p.e.’sfor SK-II), NHITAearly200 ≥ 5, and NHITAsum ≥ 10,
where NHITAearly200 is the maximum number of OD PMT hits in a sliding 200 nsec timing
window from -9000 nsec to -200 nsec after the trigger timing, and NHITAsum is:{
NHITAearly200 + NHITA500 , (dOD < 500 cm)
NHITAsum =(5.5)
NHITAearly200 ,(otherwise)
where NHITA500 is the number of OD PMT hits in a fixed 500 nsec timing window from-200 nsec to +300 nsec after the trigger timing, and dOD is the distance between theposition of the OD PMT hit cluster in NHITAearly200 and the position of the OD PMT hit
cluster in NHITA500 .

62

SK-IV
After 4th Reduction
Data

10

102

SK-IV
After 4th Reduction
ATM ν MC

10

1
200

400

600

dhole [cm]

800

1000

10

1
0

SK-IV
Final Sample
Data
ATM ν MC

103

102

102

10

0

Reject3

Number of Events [/50 cm]

Reject3

Number of Events [/50 cm]

Number of Events [/50 cm]

CHAPTER 5. DATA SET

200

400

600

800

1000

10

1
0

dhole [cm]

200

400

600

800

1000

dhole [cm]Figure 5.19: Distributions of the distance between the reconstructed entering point and theclosest cable hole position, dhole , in SK-IV. Events with more than 0.4 of stopping muon fit
goodness, more than 4000 p.e.’s of total charge and cos θz > 0.6 are plotted. The atmospheric
neutrino (ATM ν) MC histograms are normalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term “Final Sample” refers toevents after all the FC event selection criteria. Vertical error bars on the data points denote thestatistical uncertainty.
FC5-3-2 NHITAearly200 ≥ 50 (55 for SK-IV).
Criterion FC5-3-2 is newly implemented in this work and helps to reject remaining invisible
muons. The two-dimensional NHITAearly200 and NHITAsum scatter plots and one-dimensional
distributions of the final sample for events in which the total observed charge in the ID is lessthan 1000 p.e.’s are shown in Fig. 5.20. The NHITAearly200 distributions without any ID PMT
conditions are shown in Fig. 5.21. The agreement between data and MC is not quite good but
the cut point is far from the majority of the expected atmospheric neutrino events, and therefore
the impact of this disagreement is small. This disagreement is caused by accidental OD PMThits produced by uncorrelated low energy activities around the detector, which are not included
in primary event MC.

5.6.4

Further Flasher Event Rejection

In order to further reject flasher events, there are flasher rejection criteria at the fifth reduction step. They use a vertex reconstruction tool, Point-fit, and the algorithm often returns bad
fitting goodness in flasher events because of its broad timing distribution.
FC5-4-1 Point-fit goodness < 0.4 and NHITMIN100 ≥ 6,
where Point-fit goodness is described in Section 6.1.1.
For SK-II to -IV, there is an additional rejection criterion:
FC5-4-2 Point-fit goodness < 0.3 regardless of the NHITMIN100 value.
The two-dimensional Point-fit goodness and NHITMIN100 scatter plots and one-dimensional distributions of the final sample are shown in Fig. 5.22.

5.6.5

Tight Accidental Coincidence Event Rejection

Events satisfying the following criteria are removed from the data set as accidental coincidence events:

63

104

Number of Events [/hit]

Number of Events [/hit]

CHAPTER 5. DATA SET

SK-IVFinal Sample
Data
ATM ν MC

103

102

10

1
0

104
SK-IV
Final Sample
Data
ATM ν MC

103

102

5 10 15 20 25 30 35 40 45 50

10

1
0

5 10 15 20 25 30 35 40 45 50

NHITAearly200 [hit]

NHITAsum [hit]

4

10

SK-IV
After 4th Reduction
Data
Reject

103
102
10
1
0 10 20 30 40 50 60 70 80 90 100

NHITAearly200 [hit]

105
SK-IV
After 4th Reduction
ATM ν MC

4

10

Reject

103
102
10
1
0 10 20 30 40 50 60 70 80 90 100

NHITAearly200 [hit]Number of Events [/hit]

105

Number of Events [/hit]

Number of Events [/hit]

Figure 5.20: The top two plots show the two-dimensional NHITAearly200 and NHITAsum scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of the final
sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATM ν) MC histograms arenormalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). Only events with less than 1000 p.e.’s of total observed charge are plotted.
Vertical error bars on the data points denote the statistical uncertainty.

105
4

10

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0 10 20 30 40 50 60 70 80 90 100

NHITAearly200 [hit]Figure 5.21: Reduction variable NHITAearly200 distributions without any ID PMT conditions in
SK-IV. The atmospheric neutrino (ATM ν) MC histograms are normalized by SK-IV livetimeand the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The term
“Final Sample” refers to events after all the FC event selection criteria. Vertical error bars on
the data points denote the statistical uncertainty.

64

105

104
SK-IV
Final Sample
Data
ATM ν MC104

Number of Events

Number of Events [/hit]

CHAPTER 5. DATA SET

103
2

10

10
1
0

103

SK-IV
Final Sample
Data
ATM ν MC

102

10

1
2

4

6

8 10 12 14 16 18 20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NHITMIN100 [hit]Point-fit Goodness

Figure 5.22: The top two plots show the two-dimensional Point-fit goodness and NHITMIN100
scatter plots in SK-IV. The bottom two plots show the one-dimensional distributions of the final
sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATM ν) MC histograms arenormalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). Vertical error bars on the data points denote the statistical uncertainty.

65

104

Number of Events [/hit]

Number of Events [/10 p.e.]

CHAPTER 5. DATA SET

SK-IVFinal Sample
Data
ATM ν MC

103

102

10

1
0

100

200

300

400

500

600

PE500 [p.e.]

105
104

SK-IV
Final Sample
Data
ATM ν MC

103
102
10
1
0

5 10 15 20 25 30 35 40 45 50

NHITALATE200 [hit]Figure 5.23: The top two plots show the two-dimensional PE500 and NHITALATE200 scatterplots in SK-IV. The bottom two plots show the one-dimensional distributions of the final
sample in SK-IV. In the bottom plots, the atmospheric neutrino (ATM ν) MC histograms arenormalized by SK-IV livetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 ,sin2 2θ = 1.0). Vertical error bars on the data points denote the statistical uncertainty.
FC5-5-1 PE500 < 300 p.e.’s (150 p.e.’s for SK-II),
where PE500 is the total number of p.e.’s in a fixed 500 nsec timing window from -200 nsec
to +300 nsec after the trigger timing.
FC5-5-2 NHITALATE200 ≥ 20 (16 for SK-IV),
where NHITALATE200 is the maximum number of OD PMT hits in a 200 nsec sliding
timing window from +300 nsec to +1500 nsec after the trigger timing.
The two-dimensional PE500 and NHITALATE200 scatter plots and one-dimensional distributionsof the final sample are shown in Fig. 5.23.

5.7

Event Reduction Summary

After the FC event reduction algorithm, the following event selection criteria are applied to
select FC events at the analysis stage:
FCfinal -1 NHITAC < 16 (10 for SK-I),
where NHITAC is the number of OD PMT hits in the highest charge OD cluster.
FCfinal -2 Evis > 30 MeV,
where Evis is the visible (electron equivalent) energy which is defined as the energy of anelectromagnetic shower producing the same amount of Cherenkov photons.

66CHAPTER 5. DATA SET

Figure 5.24: Event rate at each reduction step during SK-IV as a function of date. The 1st,
2nd, 3rd, 4th, and 5th reduction output rates are plotted in black, red, green, blue, and yellow,
respectively. The purple (cyan) one corresponds to the event rate of the final sample with dwall
greater than 200 cm (in between 100 and 200 cm).
FCfinal -3 dwall > 100 cm,
where dwall is the distance between the reconstructed event vertex position and the closest
ID wall.
As for FCfinal -3, called fiducial volume cut, in the previous analysis [27], the cut boundary was
200 cm, giving a 22.5 kton of water fiducial mass. However, the fiducial volume in this analysis
is enlarged up to 100 cm from the ID wall, which gives an additional 4.7 kton of water fiducial
mass. The non-neutrino background contamination level around the fiducial volume boundary
is discussed in Section 5.7.2. The event reconstruction performance inside the new fiducial mass
region is presented in Chapter 6. In the following, the term “conventional” fiducial volume(or fiducial mass region) refers to the region with dwall greater than 200 cm, and “additional”
fiducial volume (or fiducial mass region) refers to the region in between dwall 100 cm and200 cm. Terms representing each fiducial volume (mass region) are summarized in Table 5.1.
The “Outside” region is not used in the proton decay analysis but it is used to evaluate thenon-neutrino background contamination level and event reconstruction performance. Moving
the fiducial mass boundary from 200 cm to 100 cm from the ID wall increases the total detector
exposure from 372 kton·years to 450 kton·years.
Table 5.1: Terms representing each fiducial volume (mass region). Exposure is water mass
times livetime.
Term
dwall
Water mass
Exposure
Conventional
200 cm < dwall
22.5 kton
372 kton·years
Additional
100 < dwall ≤ 200 cm
4.7 kton
78 kton·years
Enlarged
100 cm < dwall
27.2 kton
450 kton·years
Outside50 < dwall ≤ 100 cm
2.6 kton
43 kton·years
The event rate during SK-IV kept increasing as shown in Fig. 5.24 because of the increased
ID PMT gain, which is shown in Fig. 3.26, and the increased number of dead OD PMTs asshown in Fig. 5.25. However, the event rate of the final sample is stable in both fiducial mass
regions, and it is 8.2 (1.5) events per day in the conventional (additional) fiducial mass region
in SK-IV. In SK-I, -II, and -III, it is 8.2 (1.4), 8.3 (1.4), and 8.4 (1.6) events per day in theconventional (additional) fiducial mass region, respectively.
There are several new event reduction criteria as presented in Sections 5.4.3, 5.6.1, 5.6.2,

67

CHAPTER 5. DATA SET

Figure 5.25: The number of dead OD PMTs as a function of date.
and 5.6.3. The SK-IV data has been reprocessed with the updated event selection algorithm
from the raw data. On the other hand, the data in the other phases have been processed by justapplying the new criteria to the final sample to save processing time. Although overall signal
selection eﬃciencies for atmospheric neutrino MC and proton decay MC events are discussed
in the next section, an additional signal selection eﬃciency loss for them by adopting the newcriteria is estimated to be less than 0.01% in the enlarged fiducial mass region and is therefore
negligible.

5.7.1

Event Selection Eﬃciency

Atmospheric neutrino and proton decay event selection eﬃciencies are evaluated using theirMC events. Their value at each reduction step and the number of events in the final sample ofthe experimental data are summarized in Table 5.2. The reduction ineﬃciencies are estimatedto be a few % level.

5.7.2

Non-neutrino Background Events

Non-neutrino backgrounds, which are not atmospheric neutrinos nor proton decay candidates, such as cosmic-ray muons and flasher events generically deteriorate SK physics analyses.
For example, cosmic-ray muons may mimic proton decay signals in which a single non-showering
track is left in the detector (p → ν̄K + [103], p → ν̄π + [104]), and also may bias atmospheric
neutrino up-down ratios [64] because all of them are down-going. Flasher events may also contaminate proton decay search analyses but it is hard to estimate quantitatively. Furthermore,
flasher events tend to produce similar topological events as shown in Fig. 5.14 and have similar
event reconstruction results, such as reconstructed “particle direction”. Thus, they may become
unexpected backgrounds in atmospheric neutrino analyses and some exotic searches, e.g. search
for neutrinos from WIMPs in the Earth’s core [105]. Therefore, they must be minimized in the
final sample.
They typically have a reconstructed vertex on the ID wall, dwall ∼ 0 cm, but some of them
are reconstructed inside the fiducial volume due to the limited vertex reconstruction resolution,and more of them were anticipated to exist in the region closer to the ID wall. Therefore,
all events in the final sample with dwall greater than 50 cm were eye-scanned to evaluate thebackground contamination level around the fiducial volume boundary using a graphical event
display as shown in Figures 5.1, 5.2, or 5.14. No events are rejected based on the scanning
results. The remaining background distribution as a function of dwall is shown in Fig. 5.26. As
predicted, more backgrounds have been found in the region closer to the ID wall. The fractionof the non-neutrino backgrounds to the total number of events in the final sample is about 0.5%
(0.1%) in the additional (conventional) fiducial mass region, and it is tolerably worse than thatin the conventional fiducial mass region. However, in the region between dwall of 50 cm and100 cm, it increases to about 2.0% and restricts further expansion of the fiducial mass. The
main component of the remaining non-neutrino backgrounds is flasher event that occurred during
detector initial phases. When a flashing PMT is identified in daily event reduction processes,
its HV is turned oﬀ and such flasher event rate decreases over time.
Events in the final sample are divided into the following sub-samples in SK standard analyses:

68CHAPTER 5. DATA SET

Table 5.2: Atmospheric neutrino and proton decay event selection eﬃciencies at each reduction
step in units of % and the number of events in the final sample in SK-I to -IV. In the eﬃciency
calculation, only events satisfying the final FC criteria presented in Section 5.7, NHITAC < 16,
Evis > 30 MeV, and dwall > 100 cm, are considered for the numerator, while events which aresatisfying NHITAC < 16 and Evis > 30 MeV and generated within the enlarged fiducial volume
are used for the denominator. Atmospheric neutrino MC is normalized by livetime and includes
reweighting to the latest SK oscillation fit result [64] described in Section 4.2.
Atmospheric neutrino MC
SK phase
SK-I SK-II SK-III SK-IV
1st reduction
99.1
99.1
99.4
99.3
2nd reduction 99.0
99.0
99.4
99.3
3rd reduction 98.5
98.7
99.1
99.0
4th reduction 97.8
98.3
97.7
98.0
98.0
97.5
97.8
5th reduction 97.4+
0p → e π MC
SK phase
SK-I SK-II SK-III SK-IV
1st reduction
99.3
99.3
99.6
99.6
2nd reduction 99.3
99.2
99.5
99.5
3rd reduction 99.0
98.9
99.1
99.2
4th reduction 98.7
98.6
97.2
97.6
5th reduction 97.7
97.9
96.2
96.9
p → µ+ π 0 MC
SK phase
SK-I SK-II SK-III SK-IV
1st reduction
99.5
99.4
99.6
99.5
2nd reduction 99.5
99.3
99.6
99.5
3rd reduction 99.2
99.1
99.4
99.3
4th reduction 98.9
98.9
98.8
98.8
5th reduction 98.5
98.6
98.4
98.6
Number of events in the final sample
SK phase
SK-I
SK-II SK-III SK-IV
Data
14286
7740
5182
31317
Atmospheric neutrino MC 14164.7 7655.3 5035.2 30907.3

80
70
60
50
40
30
20
10
0
0

SK-I to -IV
Cosmic-Ray Muon
No Cherenkov Ring

Not Scanned

Number of External
Background Events [/10 cm]

100
90

Additional
RegionConventional
Region50
100 150 200 250 300 350
Distance to the nearest ID Wall (dwall ) [cm]Figure 5.26: Remaining non-neutrino background distribution as a function of dwall. Cosmicray muons and no Cherenkov ring events are stacked. No Cherenkov ring events are dominatedby flasher events described in the text.

69

CHAPTER 5. DATA SET• Sub-GeV single-ring e-like,• Sub-GeV single-ring µ-like,• Multi-GeV single-ring e-like,• Multi-GeV single-ring µ-like,• Multi-ring e-like,• Multi-ring µ-like,
where Sub-GeV (Multi-GeV) stands for Evis less (more) than 1.33 GeV, e-like (µ-like) stands
for the reconstructed particle type of the most energetic particle is electron (muon). The “contamination rate” for each sub-sample is conservatively evaluated as follows:{√(NnonνBG + NnonνBG )/Nall , (NnonνBG > 0)
(5.6)
contamination rate =1/Nall ,(NnonνBG = 0)
where NnonνBG is the number of non-neutrino background events, and Nall is the total number of
events in each sub-sample. The contamination rates in diﬀerent fiducial volume boundary cases,
dwall = 200, 100, and 50 cm for reference, are summarized in Table 5.3. In the case of the dwall
boundary at 100 cm, they are kept within the consistent level with the conventional fiducial
mass analysis for every detector phase and sub-sample. Therefore, in terms of the event quality,
enlarging the fiducial mass up to 100 cm from the ID wall does not significantly deteriorate
physics analyses in which this FC data set is used. The numbers in SK-IV are relatively small
because of the stable data taking, longest live days, and reduced flasher event rate as describedabove.

70

CHAPTER 5. DATA SET

Table 5.3: Non-neutrino background contamination rate in each sub-sample in units of %.
Diﬀerent dwall columns show the nun-neutrino background contamination rates in diﬀerent
fiducial volume boundary cases, i.e. numbers in the “dwall Boundary” column are evaluatedusing all events with dwall greater than 200, 100, or 50 cm.
dwall Boundary
Phase Sub-sample
200 cm 100 cm 50 cm
Sub-GeV single-ring e-like
0.1
0.2
0.2
Sub-GeV single-ring µ-like
0.6
0.7
1.2
Multi-GeV single-ring e-like
0.2
0.2
0.2
SK-I
Multi-GeV single-ring µ-like
0.1
0.1
0.5
Multi-ring e-like
0.2
0.4
1.0
Multi-ring µ-like
0.2
0.1
0.2
Sub-GeV single-ring e-like
0.2
0.3
0.3
Sub-GeV single-ring µ-like
0.3
0.4
0.4
Multi-GeV single-ring e-like
0.3
0.2
0.2
SK-II
Multi-GeV single-ring µ-like
0.3
0.2
0.2
Multi-ring e-like
0.4
0.4
2.8
Multi-ring µ-like
0.3
0.5
1.4
Sub-GeV single-ring e-like
0.2
0.4
0.5
Sub-GeV single-ring µ-like
0.3
0.4
0.7
Multi-GeV single-ring e-like
0.4
0.3
0.3
SK-III
Multi-GeV single-ring µ-like
0.4
0.7
1.1
Multi-ring e-like
0.6
0.5
0.5
Multi-ring µ-like
0.4
0.4
0.4
Sub-GeV single-ring e-like
< 0.1
< 0.1
< 0.1
Sub-GeV single-ring µ-like
< 0.1
< 0.1
< 0.1
Multi-GeV single-ring e-like
0.1
0.1
0.1
SK-IV
Multi-GeV single-ring µ-like
0.1
0.1
0.1
Multi-ring e-like
0.1
0.1
0.1
Multi-ring µ-like
0.1
0.1
0.1

71

Chapter 6

Event Reconstruction
For events passing the FC event selection algorithm described in Chapter 5, charged particles above the Cherenkov threshold inside the ID are reconstructed with ID PMT timing andcharge information to extract physics quantities, such as interaction (production) vertex position, number of Cherenkov rings (charged particles), particle type, and particle momentum.
To tag neutrons emitted in a primary FC event, there is also an independent neutron tagging
algorithm, which searches for a faint signature of 2.2 MeV gamma ray from neutron capture onhydrogen. In this Chapter, the FC event reconstruction algorithm and neutron tagging algorithm are described [108, 97, 106]. One of the most important reconstruction items in this study
is the energy reconstruction, and the energy scale uncertainty is also discussed in this Chapter.

6.1

FC Event Reconstruction

The FC event reconstruction algorithm is divided into the following steps:
1. Vertex Reconstruction · · · The charged particle production vertex point is reconstructed
mainly using PMT timing information.
2. Ring Counting · · · The number of Cherenkov rings projected on the ID wall is countedwith a ring pattern recognition technique.
3. Particle Identification (PID) · · · Each Cherenkov ring is identified as either a showering(e-like) particle (e± , γ) or non-showering (µ-like) particle (µ± , π ± ) based on the patternof PMT hits.
4. Precise Vertex Reconstruction · · · The event vertex position is redetermined using PMT
charge information. This is applied only to single-ring events.
5. Ring Separation · · · For multi-ring events such as p → e+ π 0 and p → µ+ π 0 signal events,
the observed charge at each PMT is separated into the contribution from each Cherenkov
ring.
6. Momentum Determination · · · Each ring momentum is determined using the total observed
charge associated with the ring taking into account the water attenuation length, PMT
acceptance as well as indirect light eﬀects.
7. Ring Number Correction · · · If the momentum of one of the reconstructed rings is too
small, or if the ring direction is too close to another, that ring is discarded as a fake ring.
8. Michel Electron Search · · · Clusters of PMT hits produced by subsequent Michel electrons from muon decays are searched for in the time-of-flight subtracted residual time
distribution.

72

CHAPTER 6. EVENT RECONSTRUCTION

The algorithm proceeds step by step, and the later reconstruction steps use results obtained in
the former steps.

6.1.1

Vertex Reconstruction

The vertex reconstruction algorithm consists of three steps, Point-fit, ring edge finding, andTDC-fit. Since this step is prior to the ring counting algorithm described later, the following
calculation assumes a single-ring event and focuses on the most energetic ring.
Point-fit
An initial vertex position is estimated by maximizing the following estimator (G), assuming
all photons are emitted at the same time and position:()
1 ∑(t′i − t0 )2
G=
exp −
,
(6.1)
N
2 × (⟨σ⟩ × 1.5)2i

where N is the number of hit PMTs, ⟨σ⟩ is fixed to 2.5 nsec here, and t′i is the ith PMT’stime-of-flight subtracted residual time for an assumed vertex position:t′i = ti −n|Pi − vtx|,
c

(6.2)

where ti is the ith PMT’s photon detection time, Pi is the ith PMT position vector, and vtx
is the vertex position vector. The factor of 1.5 in Eq. (6.1) has been determined to optimize
performance, and t0 is chosen so that G is maximized at each test vertex position. The vertex
position is searched for by changing the assumed vertex position. The reconstructed vertex
position in this step is the point with the highest G value, i.e. the residual time distribution
becomes most peaked.
Using the reconstructed vertex position, the Cherenkov ring (particle) direction of the mostenergetic one is also estimated by taking the following vector sum:
dir =

∑

qiobs ×i

Pi − vtx,|Pi − vtx|

(6.3)

where dir is the ring direction vector, and qiobs is the ith PMT’s observed charge.
Ring Edge Finding
The edge position (opening angle) and direction of the most energetic Cherenkov ring areredetermined using the following estimator, Q(θedge ):∫ θedgeQ(θedge ) =0

PEcor (θ)dθ×sin θedge(

dPEcor (θ)dθ)2θ=θedge)((θedge − θexp )2,
× exp −
2σθ2

(6.4)

where θedge is the tested Cherenkov opening angle from the particle direction, and θexp and σθ are
the expected Cherenkov opening angle and its resolution estimated by the total observed charge
within a cone whose half opening angle is 70 degrees from the particle direction, respectively.
Here, PEcor (θ) is the observed charge distribution as a function of the angle from the particle
direction, where the observed charge is corrected with the water attenuation length and PMT
acceptance. A typical corrected charge distribution, PEcor (θ), is shown in Fig. 6.1. The ring
direction of the most energetic Cherenkov ring is reconstructed by searching for the direction
which gives the highest Q(θedge ).
Using the reconstructed ring direction, the ring edge (Cherenkov opening) angle of the ring(θedge ) which satisfies the following conditions is determined:73

CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.1: Typical observed charge distribution as a function of the opening angle (top),
PEcor (θ). The bottom plot is the second derivative distribution of the top plot. Taken from [108].
1. θedge > θpeak ,2cor

2. d PEdθ2= 0,
θ=θedgewhere θpeak is the peak position of the PEcor (θ) distribution. If multiple angles satisfy the above
conditions, the angle closest to the peak angle (θpeak ) is chosen. Some PMTs around the edge
position are tagged, and they are used in the following TDC-fit step.
For events with dwall less than 400 cm, the opening angle and direction of the most energetic
Cherenkov ring are determined using the same algorithm for particle identification described in
Section 6.1.3. In the calculation for particle identification, the ring direction and Cherenkov
opening are optimized using observed charge information.
TDC-fit
In TDC-fit, the track length of the particle and eﬀects from scattered photons are taken into
account.
First, the most energetic ring direction is tuned using the tagged PMTs, which are definedat the last step, so that the following estimator (χ(dir)) is minimized:χ(dir) =∑√qiobs ×i

(θi − ⟨θ⟩)2,(70 cm/|Pi − vtx|)2(6.5)

where qiobs is the ith tagged PMT’s observed charge, θi is the opening angle of the ith tagged
PMT position from an assumed ring direction, ⟨θ⟩ is the average of θi for the tagged PMTs,
and 70 cm corresponds to the size of the gaps between individual ID PMTs. The summation is
performed for all of the tagged PMTs, and the ring direction which gives the minimum χ(dir)is used in the later steps. At the same time, the Cherenkov opening angle (θC ) is determined asfollows:
θC = ⟨θ⟩,
(6.6)

74

CHAPTER 6. EVENT RECONSTRUCTION

with the determined ring direction.
The total track length of the particle is estimated with the total observed charge within acone whose half opening angle is 70 degrees from the particle direction and an assumed particle
energy loss, dE/dx = 3 MeV/cm. This value is chosen to optimize performance. Time-offlight subtracted residual time for PMTs located inside the reconstructed Cherenkov edge isrecalculated as follows:1nt′i = ti − × Xi − vtx − × Pi − vtx ,
c
c

(6.7)

where Xi is the position where Cherenkov photons detected by the ith PMT are emitted, and
it is deduced with the total track length, ring direction, and Cherenkov opening angle.
In TDC-fit, a vertex fitting estimator, agood, is calculated for PMTs inside the Cherenkov
edge and for those outside separately. For PMTs inside the Cherenkov edge, the estimator (GI )is defined as follows:)(∑
1(t′i − t0 )2
GI =
exp −
,
(6.8)
2 × (⟨σ ′ ⟩ × 1.5)2σ 2 (qiobs )iwhere σ(qiobs ) is the ith PMT timing resolution which is tabulated as a function of observed
charge, ⟨σ ′ ⟩ is the average timing resolution for hit PMTs. For PMTs outside the Cherenkov
edge, t0 is modified to take into account the late timing PMT hits:
t′0 = t0 + σi × (0.8 − 1.5 × Rout ),(6.9)

where the factors of 0.8 and 1.5 have been empirically determined, and Rout is the fractionalcharge outside the Cherenkov edge,∑obs
θ<θ +3 qi
Rout = 1 − ∑ C obs .
(6.10)
θ<70◦ qi
For PMTs outside the Cherenkov edge with t′i < t′0 , the fitting estimator (GO1 ) is revised as:
(
(
)
)
∑
(t′i − t′0 )21GO1 =2 × exp −−1 ,(6.11)
2 × (⟨σ ′ ⟩ × 1.5)2σ 2 (qiobs )iand for PMTs outside the Cherenkov edge with t′i > t′0 , the fitting estimator (GO2 ) is corrected
to consider eﬀects from scattered photons:
)
))
(
(
(
∑
1
(t′i − t′0 )
−1 ,
GO2 =
(6.12)
2 × max GO1 , CA × GO1 + CB × exp −60 nsec
σ 2 (qiobs )iCA = 1 − CB ,(6.13)

CB = (0.8 − 1.5 × Rout ) + (0.2 + 1.5 × Rout ) × (1 − 1/1.5 ).
2(6.14)

Finally, agood is defined by summing up these three estimators:
agood =

GI + GO1 + GO2
∑
.
2 obs
i 1/σ (qi )(6.15)

At each tested vertex position, t0 is chosen so that agood becomes maximal, and the reconstructed vertex position is the point with the highest agood. The vertex position reconstructedhere is used for multi-ring events but for single-ring events, the vertex position is redeterminedat the later step, Section 6.1.4.

75

CHAPTER 6. EVENT RECONSTRUCTION

Free p→µ+π0 MC

0.18
0.16

200 cm<dwall

Vertex Resolution
17.1 cm0.14

100<dwall ≤200 cm

0.12

24.1 cm

0.1
0.08

25.9 cm

50<dwall ≤100 cm

0.06
0.04
0.02
0
0

20

40

60

80

100

120

Number of Events [/3 cm](Normalized to Unity)

Number of Events [/3 cm](Normalized to Unity)

Free p→e+π0 MC
0.14Distance between True and Recon. Vertex [cm]100<dwall ≤200 cm

0.1

24.8 cm
50<dwall ≤100 cm

0.08

26.7 cm

0.06
0.04
0.02
0
0

140

200 cm<dwall

Vertex Resolution
20.6 cm

0.12

20

40

60

80

100

120

140

Distance between True and Recon. Vertex [cm]Figure 6.2: Distributions of the distance between the reconstructed vertex and true vertex
position on free proton decay MC events. The left plot shows p → e+ π 0 and the right showsp → µ+ π 0 MC events, and they are livetime-weighted combined from SK-I to -IV. The solid cyan
histogram shows events reconstructed in the conventional fiducial mass region, the pink dashedhistogram shows that for the additional fiducial mass region, and the black dotted histogram isfor the region between dwall of 50 cm and 100 cm. Vertex resolution indicates 68 percentile.

Number of Events

1400
1200
1000
800
Data SKI~IV
ATM ν MC

600
400
200
0
0

200 400 600 800 1000 1200 1400 1600

Distance to the Closest Wall (dwall ) [cm]Figure 6.3: Reconstructed dwall distribution of Sub-GeV multi-ring events in SK-I to -IV. The
black dots show the data and the red histogram shows the atmospheric neutrino MC (ATM νMC) events. Atmospheric neutrino MC is normalized by livetime and includes reweighting to
the latest SK oscillation fit [64]. Vertical error bars denote the statistical uncertainty.
Performance of Vertex Reconstruction
Figure 6.2 shows the distributions of the distance between the reconstructed vertex and true
vertex position on free proton decay MC events. Only free proton decay events are used toremove the influence of nuclear eﬀects. In the additional fiducial mass region, the number of
PMT hits tends to be smaller when the charged particle travels toward the ID wall. In p → e+ π 0
and p → µ+ π 0 decay events in which they produce back-to-back event topologies, at least oneof the particles in the final state often has a small distance to the wall, and the number of PMT
hits associated with its Cherenkov ring also becomes small. Since the vertex reconstruction
performance depends on the number of hit PMTs associated with the most energetic ring, theperformance is degraded outside the conventional fiducial mass region when the most energetic
ring travels toward the wall. The vertex resolution for the p → e+ π 0 (p → µ+ π 0 ) mode is17.1 cm (20.6 cm) in the conventional fiducial mass region, and it is 24.1 cm (24.8 cm) in the
additional fiducial mass region. Figure 6.3 shows the distributions of the distance between thereconstructed vertex and the closest ID wall (dwall) of Sub-GeV multi-ring events for data andatmospheric neutrino MC events.

76

CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.4: The Hough transformation. Suppose there are four hit PMTs on in a ring with aradius of r (left). The observed charge is transformed into the Hough space as a circle with aradius of r (right), and the resulting circles are overlapped at the center of the original ring, i.e.
the original ring center manifests as a peak in the Hough space. Taken from [108].

6.1.2

Ring Counting

After reconstructing the vertex position with the most energetic ring, the total number of
Cherenkov rings projected on the ID wall is counted. This process is divided into two steps,
ring candidate selection and ring candidate test using a likelihood method.
Ring Candidate Selection
Cherenkov rings other than the one used for the previous vertex estimation are searched
for using a ring pattern recognition algorithm based on the Hough transformation [109]. The
principle of the Hough transformation is illustrated in Fig. 6.4. Suppose there are four hit PMTs
in a ring with a radius of r as shown in the left figure, each PMT’s observed charge is transformed
into the Hough space as a circle with a radius of r. The amplitude of the circle in the Hough
space is weighted by the observed charge which is corrected with the water attenuation lengthand PMT acceptance. The resulting circles in the Hough space are overlapped at the center ofthe original ring as shown in the right figure, and the original ring center manifests as a peak in
the Hough space. Before this transformation, contributions from other Cherenkov rings, which
are already identified, are subtracted to make the algorithm find a potential ring more easily.
The Hough space is defined as two-dimensional polar coordinates (Θ, Φ), which are calculated
from the reconstructed vertex position. An actual Cherenkov image does not have sharp ringedges as shown in Fig. 6.4, and therefore a charge distribution template as a function of opening
angle, which has been obtained using 500 MeV/c electron MC events in advance, is used as aweight in the transformation to diﬀuse the resulting circle edges in the Hough space. An exampleof the resulting Hough space is shown in Fig. 6.5, and peaks are identified as Cherenkov ringcandidates. However, if the direction of the ring candidate is too close (less than 15 degrees) toanother ring, which is already identified, that ring is not selected.
Ring Candidate Test
The ring candidates identified in the previous candidate selection are tested if they are real
Cherenkov rings or not using a likelihood method. Given that N rings are already identified
as real Cherenkov rings, and there is an (N + 1)th ring candidate, the following likelihood for77CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.5: Example of the resulting Hough space for a two-ring event. The peaks correspondto their Cherenkov ring centers. Taken from [108].
either the (N + 1) ring or N ring assumption is defined:( ())∃ n∈N +1,θi,n <1.2×θC,n
N
+1
∑
∑
exp
N +1
obs
L
=
log P qi ,αn × qi,ni( (∃ n∈N +1,θLN =i,n <1.2×θC,n
∑

log P

qiobs ,

nN∑

(6.16)))
exp
αn × qi,n(6.17)ni

exp
where θC,n is the Cherenkov opening angle of the nth ring, αn × qi,nis the ith PMT expected
)
(
∑
exp
+1(N )
αn × qi,nis the probability density function
charge given by the nth ring, and P qiobs , Nn∑exp+1(N )
αn × qi,n. The probability density functionof observing qiobs with an expectation of Nnis tabulated based on the convolution of the single p.e. distribution and a Poisson distribution
for the low charge region, and it is obtained from a Gaussian distribution for the high charge
region. The summation is performed for all PMTs whose angle to the direction of one of the(N + 1) rings (θi,n ) is within 1.2 times its Cherenkov opening angle (θC,n ), and the same PMTs
are used for both likelihoods. The expected charge given by the (N + 1)th ring in each PMT,
exp
αN +1 × qi,N
+1 , is deduced by the total observed charge within a cone whose half opening angle
is 70 degrees from the (N + 1)th ring direction. The expected charge given by the other alreadyidentified N rings is obtained by the ring separation algorithm detailed in [108]. Both likelihoods
are maximized by tuning αn . For the (N + 1)th ring candidate which satisfies LN +1 ≥ LN , thelikelihood formula is modified by incorporating the following components:• The average observed charge deposited around the edge of the (N + 1)th ring candidate,
Qedge . If it is large, the (N + 1)th ring candidate is regarded as a more probable ringcandidate.
• The average observed charge deposited around outside the edge of the (N + 1)th ringcandidate. If it is smaller than Qedge , the (N + 1)th ring candidate is regarded as a moreprobable ring candidate.
• The residual observed charge, which is the sum of the observed charge associated withnone of the identified N rings, in the N ring assumption. If it is large, the (N + 1)th ringcandidate is regarded as a more probable ring candidate.

78

CHAPTER 6. EVENT RECONSTRUCTION

Free p→µ+π0 MC

Free p→e+π0 MC
0.6

0.6

3-ring58.7%

100<dwall ≤200 cm

0.4

51.9%

44.5%

50<dwall ≤100 cm

0.3

55.9%

37.6%

0.2
0.1
0
0

1

2

3

4

5

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

200 cm<dwall

2-ring
39.3%

0.5

0.5
0.4

49.1%

Number of Reconstructed Rings

3-ring62.0%

100<dwall ≤200 cm

48.4%

50<dwall ≤100 cm

0.3

55.3%

39.8%

0.2
0.1
0
0

6

200 cm<dwall

2-ring
36.8%

1

2

3

4

5

6

Number of Reconstructed Rings

Figure 6.6: Distributions of the number of reconstructed rings of free proton decay MC events.
The left plot shows p → e+ π 0 and the right shows p → µ+ π 0 MC events, and they are livetimeweighted combined from SK-I to -IV. The solid cyan histogram shows events reconstructed in
the conventional fiducial mass region, the pink dashed histogram shows that for the additional
fiducial mass region, and the black dotted histogram is for the region between dwall of 50 cm
and 100 cm.
Weights used to combine the above components into a final ring counting likelihood are optimized
using atmospheric neutrino MC events.
Once the (N + 1)th ring is judged as a real Cherenkov ring, the algorithm goes back to thering candidate selection step to find another ring candidate. This procedure continues until nomore candidates are found or the 5th ring is found.
Performance of Ring Counting
The distributions of the number of reconstructed rings of free proton decay MC events
are shown in Fig. 6.6. Ideally, they should be reconstructed as three-ring events for both the
p → e+ π 0 and p → µ+ π 0 modes but a Cherenkov ring associated with one of the gamma raysfrom the π 0 decay sometimes overlaps with other rings, and thus such events are reconstructed
as two-ring events. Although the full proton decay event selection criteria are discussed in
Section 7.1.1, two-ring events are allowed as signal events. Besides, since hit PMTs in eventsin the additional fiducial mass region are more localized than those in the conventional fiducial
mass region, the fraction of two-ring events becomes higher. Figures 6.7 and 6.8 show the
distributions of the number of reconstructed rings and ring counting likelihood distributions,
respectively, of Sub-GeV events for data and atmospheric neutrino MC events.

6.1.3

Particle Identification

The particle type of each identified Cherenkov ring is determined using the pattern of hit
PMTs in the ring. As shown in Figures 3.9 and 3.10, the diﬀerence between showering (e-like)and non-showering (µ-like) particles manifests in their PMT hit (charge) profile. The following
algorithm calculates the expected charge distribution for each particle assumption and comparesit to the observed charge distribution. Therefore, the calculation of the expected PMT charge
is essential. Furthermore, the reconstructed Cherenkov opening angle is also useful information
to separate between the two particle types, especially in single-ring events.
Expected charge table for each particle type assumption
Expected charge distributions in the showering (electron) assumption have been tabulatedusing electron MC events. However, because some discrepancies between the old expected charge

79CHAPTER 6. EVENT RECONSTRUCTION

6000

Number of Events

Number of Events

30000
Conventional Region
Data SKI~IV
ATM ν MC

25000
20000
15000
10000
5000
0
0

1

2

3

4

5

5000
4000
3000
2000
1000
0
0

6

Additional Region
Data SKI~IV
ATM ν MC

Number of Reconstructed Rings

1

2

3

4

5

6

Number of Reconstructed Rings

Figure 6.7: Distributions of the number of reconstructed rings of Sub-GeV events for data
and atmospheric neutrino MC events (SK-I to -IV combined). The left plot corresponds tothe conventional fiducial mass region and the right plot to the additional fiducial mass region.
Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK
oscillation fit [64]. Vertical error bars on the data points denote the statistical uncertainty.

Multi-ring

5000
Conventional Region
Data SKI~IV
ATM ν MC

4000
3000
2000
1000
0
-15

-10

-5

0

5

10

Additional Region
Data SKI~IV
ATM ν MC

800
600
400
200
0
-15

15

Ring Counting Likelihood

Multi-ringSingle-ring

1000

Number of Events

Number of Events

Single-ring

-10

-5

0

5

10

15

Ring Counting Likelihood

Figure 6.8: Ring counting likelihood distributions of Sub-GeV events for data and atmospheric
neutrino MC events (SK-I to -IV combined). The left plot corresponds to the conventional
fiducial mass region and the right plot to the additional fiducial mass region. Atmospheric
neutrino MC is normalized by livetime and includes reweighting to the latest SK oscillation
fit [64]. Vertical error bars on the data points denote the statistical uncertainty.

80CHAPTER 6. EVENT RECONSTRUCTION

Number of p.e.'s
Normalized to Unity

0.06
MC True
OLD Table
NEW Table

0.05

0.04
0.03
0.02
0.01
0
0

10

20

30

40

50

60

70

80

90

Opening Angle [Degree]

Figure 6.9: PMT charge distributions as a function of the opening angle from the electron
direction. The Black histogram shows MC truth observed charge distribution, and the blue(red) histogram shows the expected charge distribution before (after) the update described in
the text.
tables and MC expectations have been found, new expected charge tables have been made using
the latest detector simulation (SKDETSIM) and introduced in this work. Electron particle gun
MC events with a momentum of 30, 100, 200, 300, 500, 700, 1000, 1500, 2000, 5000, 10000 MeV/chave been generated. In the generation, eﬀects from water scattering and absorption were turned
oﬀ. The new expected charge distributions, Qexp (p, θ, r), are tabulated as a function of particle
momentum (p), the distance between the event vertex and PMT position (r), and the opening
angle from the particle direction (θ). Necessary linear interpolations and extrapolations weremade to cover the entire electron event phase space. Using them, the expected charge given
direct (e), is calculated as follows to correct with the waterby the nth ring at the ith PMT, qi,nattenuation length and PMT acceptance:( r )idirectqi,n(e) = αn (e) × Qexp (pn , θi,n , ri ) × exp −× f (Θi ),(6.18)
L
where αn (e) is the normalization factor, pn is the nth ring momentum deduced from the total
observed charge in the nth ring, θi,n is the opening angle to the ith PMT position from thenth ring particle direction, ri is the distance between the event vertex and ith PMT position, L
is the water attenuation length introduced in Section 3.3.6, and f (Θi ) is the PMT acceptancecorrection factor as a function of photon incident angle (Θi ). Figure 6.9 compares the obtained
direct (e) distributions as a function of opening angle with the updated Qexp (p , θ , r ) andqi,nn i,n ithe old one for 500 MeV/c electron events. The MC output is also shown, and the updated
expected charge distribution well reproduces the MC expectation. The impacts of this update
are discussed later in this section.
On the other hand, the expected charge given by the nth ring at the ith PMT for the muon
direct (µ), is analytically calculated as:assumption, qi,n
directqi,n(µ) = αn (µ) ×

(
ri ×

(
sin θxi,n + ri ×

dθ
dx

))−1
x=xi,n( r )i
× sin2 θxi,n ×exp −×f (Θi ),L(6.19)
where αn (µ) is the normalization factor, x is the distance between the event vertex and particle
position on its track, xi,n is the distance between the event vertex and point where Cherenkov
photons to the ith PMT from the nth ring are emitted, θxi,n is the opening angle from the nth
ring direction at x = xi,n . The change of θxi,n on its track due to the particle energy loss is taken
into account. The factor of sin2 θxi,n corresponds to the number of emitted Cherenkov photons

81CHAPTER 6. EVENT RECONSTRUCTION
(

(

ri ×

between x and x + dx, and the factor of))dθ
sin θxi,n + ri × dx

corresponds to thex=xi,ncross-section to which they are emitted.
In this algorithm, direct photons and indirect (scattered and reflected) photons are separately
treated. They are separated using ith PMT’s time-of-flight subtracted time, t′i :direct photons · · · − 30 < t′i − t0 < 2σi (qiobs ) + 5 nsec,
indirect photons · · · 2σi (qiobs ) + 5 nsec < t′i − t0 ,(6.20)(6.21)

where t0 is the peak of the time-of-flight subtracted time distribution. Then, the expected chargeexp
at each PMT, qi,n(e, µ), is revised:exp
directindirectqi,n(e, µ) = qi,n(e, µ) + qi,n,(6.22)

indirect is the indirect light (scattered and reflected photons) contribution at the ith
where qi,nPMT from the nth ring and is deduced from the total observed charge in the nth ring withan assumption that scattered photons and reflected photons are distributed isotropically fromthe scattered and reflected points, respectively. Photon scattering points are estimated using
the water attenuation length and scattering coeﬃcients described in Section 3.3.6, while photon
reflection points are assumed to be on the PMT surfaces.

Particle Identification Likelihood
The following likelihood, Ln , is defined to determine the particle type of the nth ring:
)
(

∑
exp
obs , q exp (e, µ) +, (direct photons)PqΠ′ ̸=n qi,n′θ<1.5×θ

i,n
i
C,n
n
i,n

 





(
)

∑
exp
exp
obs 
obs
indirect qi,n+ qi,n− qi,n′ − qiLn (e, µ) = Πθi,n <1.5×θC,n P 0, qi,n (e, µ) +(6.23)

′ ̸=n

n


(
)


 × P q obs , q indirect + q obs − q obs , (indirect photons)
i

where

(∑

n′ ̸=n

exp
qi,n
′

i,n

i

i,n

)
is the expected contributions from other rings (except for the nth ring),

P (qiobs , qiexp ) is the probability density function of observing qiobs with an expectation of qiexp ,obs is the separated observed charge at the ith PMT from the nth ring. The product isand qi,nperformed for all PMTs whose angle from the nth ring direction (θi,n ) is within 1.5 times the
Cherenkov opening angle of the nth ring (θC,n ). In each assumption, Ln (e, µ) is maximized
by changing the nth ring direction and Cherenkov opening angle. For multi-ring events, such
+ 0
+ 0
as
√ those from p →√e π and p → µ π decays, the diﬀerence in the two likelihood values,− log10 Ln (e) − − log10 Ln (µ), is defined as “PID Likelihood” and used for particle identification. The optimized ring directions and opening angles in this step are also used in theanalysis.
In order to combine with another likelihood evaluated with the Cherenkov opening angle,
Ln (e, µ) is transformed into a χ2 parameter:χ2n (e, µ) = (− log10 Ln (e, µ)) + const..
The probability from the PMT hit pattern, Pnpattern (e, µ), is defined as:
(
( 2
) )
2 (e), χ2 (µ)) 2
1
χ
(e,
µ)
−
min(χ
n
n
n
√
Pnpattern (e, µ) = const. × −,2
2Nnwhere Nn is the number of PMTs used in Eq. (6.23).

82(6.24)(6.25)

CHAPTER 6. EVENT RECONSTRUCTION
The probability from the Cherenkov opening angle, Pnangle (e, µ), is defined as:
(
(
)2 )
exp
θ
(e,
µ)
−
θ
(e,
µ))
1
n
C,n
Pnangle (e, µ) = const. × −,2
σθ2(6.26)

where θC,n (e, µ) is the optimized Cherenkov opening angle in each assumption, σθ is its uncertainty, and θnexp (e, µ) is the expected opening angle estimated from the total observed charge in
the nth ring. Finally, the two probabilities are combined as follows:
Pntotal (e, µ) = Pnpattern (e, µ) + Pnangle (e, µ).

(6.27)√totalFor√ single-ring events, the diﬀerence in the total probability in each assumption, − log Pn (e)−total
− log Pn (µ), is used for particle identification. However, because of the gamma ray conversion length, about 50 cm in water, including Pnangle (e, µ) degrades the performance of theCherenkov opening angle reconstruction in p → e+ π 0 and p → µ+ π 0 signal events, resulting in
the worse PID capability. Therefore, only the probability from the PMT hit pattern is used inthis analysis as described above.
Performance of Particle Identification
Figure 6.10 shows the multi-ring PID likelihood distributions of free p → e+ π 0 decay eventsin both the conventional and additional fiducial mass regions. From the 1st to 3rd ring, each PID
distribution is shown. In every distribution, more rings are correctly reconstructed as e-like after
introducing the update of the expected charge calculation. Since the number of hit PMTs tends
to be smaller in the additional fiducial mass region, giving a more precise expected charge toeach PMT is more important. Therefore, the update results in a more significant improvementin the additional fiducial mass region than in the conventional fiducial mass region. The signal
selection eﬃciencies for p → e+ π 0 and p → µ+ π 0 events are improved by about 20% in the
additional fiducial mass region compared to the previous reconstruction version. After adopting
the update, the correct PID fraction of events which pass one of the proton decay signal criteria
associated with PID out of all two- and three-ring events is 95.8% (87.7%) for p → e+ π 0 and
96.2% (90.7%) for p → µ+ π 0 in the conventional (additional) region.
Figure 6.11 shows the mis-PID rate as a function of particle momentum for single-ring events.
They are estimated with electron and muon particle gun MC events. For single-ring events, themis-PID rates are reduced by 35% in the additional fiducial mass region by adopting the update.
The data and MC comparison for Sub-GeV multi-ring events is shown in Figure 6.12.

6.1.4

Precise Vertex Reconstruction

Using not only timing information but also charge information, the precise vertex reconstruction algorithm improves the vertex reconstruction performance only for single-ring events.
In this step, the Cherenkov opening angle and particle type determined in the former step areused.
First, the vertex position is scanned so that the estimator defined in Eq. (6.15) is maximized.
Here, the scanning direction is limited to the perpendicular direction to the ring direction.
Then, the vertex position along the ring direction is searched for by maximizing the pattern
PID estimator of the identified particle type assumption, Eq. (6.23). At the end of this step,
the ring direction is also redetermined using the vertex position fixed in this step by maximizing
the same estimator again, Eq. (6.23).

6.1.5

Ring Separation

Since a PMT detects the total number of photoelectrons from all Cherenkov rings observedin the ID, it needs to be separated into the contribution from each ring. In order to determine83CHAPTER 6. EVENT RECONSTRUCTION

Conventional Region
1st Ring
Before Update
Mis-PID rate
3.0%
After Update
2.0%

0.12
0.1
0.08
0.06

e-like

0.16

0.04
0.02

0.14

Conventional Region
2nd Ring
Before Update
Mis-PID rate
2.9%
After Update
1.4%

0.12
0.1
0.08
0.06

-4

-2
0
2
Multi-ring PID Likelihood

4

0.04
0
-6

6

-4

Free p→e+π0 MC

0.1

0.06
0.04

e-like0.14

Additional Region
1st Ring
Before Update
Mis-PID rate
9.9%
After Update
7.2%

0.08

-2
0
2
Multi-ring PID Likelihood

4

0.02
-4

-2
0
2
Multi-ring PID Likelihood

0.1
0.05
0
-6

6

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-6

-4

Additional Region
2nd Ring
Before Update
Mis-PID rate
12.9%
After Update
2.9%

0.1
0.08
0.06

4

6

0.04

0
-6

-4

-2
0
2
Multi-ring PID Likelihood

46Free p→e+π0 MC

0.02

0
-6

0.2
0.15

6

µ -like

0.12µ -like
Conventional Region
3rd Ring
Before Update
Mis-PID rate
2.5%
After Update
1.3%

0.25

Free p→e+π0 MCµ -like

Number of Events(Normalized to Unity)e-like0.12

e-like

0.3

0.02

0
-6

Number of Events(Normalized to Unity)

Free p→e+π0 MCµ -like

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

0.14

Free p→e+π0 MCµ -like

Number of Events(Normalized to Unity)e-likeNumber of Events(Normalized to Unity)

Free p→e+π0 MC
0.16

-2
0
2
Multi-ring PID Likelihood

4e-likeµ -like
Additional Region
3rd Ring
Before Update
Mis-PID rate
7.4%
After Update
3.7%

-4

-2
0
2
Multi-ring PID Likelihood

4

6

Figure 6.10: Multi-ring PID likelihood distributions of free p → e+ π 0 decay events. The
top three plots correspond to the conventional and the bottom three plots correspond to theadditional fiducial mass region. The black (red) distributions are before (after) the expectedcharge table update described in the text. Here, Mis-PID rate indicates the fraction of Cherenkov
rings which are reconstructed as µ-like. From left to right, the 1st to 3rd ring distributions areshown.

14

14

Before: Conventional Region

1210

Before: Conventional Region
After: Conventional Region

Mis-PID Rate [%]Mis-PID Rate [%]After: Conventional Region
Before: Additional Region
After: Additional Region

8
6
4

12
10

Before: Additional Region
After: Additional Region

8
6
4

2

2

0
100 200 300 400 500 600 700 800 900 1000

0100 200 300 400 500 600 700 800 900 1000

True Electron Momentum [MeV/c]

True Muon Momentum [MeV/c]

Figure 6.11: Mis-PID rate as a function of true particle momentum for single-ring events. The
left plot shows the electron case and the right plot shows the muon case. Black and gray (redand magenta) points denote before (after) the updated of the expected charge table update
described in the text. Vertical error bars denote the MC statistical uncertainty.

84

CHAPTER 6. EVENT RECONSTRUCTION

Conventional Region
1st ring
Data SKI~IV
ATM ν MC

800
600
400
200
0
-6

-4

-2

0

2

4

6

Multi-ring PID Likelihoodµ -likee-like

250

150
100
50
0
-6

-2

0

2

4

-2

0

2

500
400
300
200

120

Additional Region
2nd ring
Data SKI~IV
ATM ν MC

250
200
150
100

4

6

Multi-ring PID Likelihood

-4

-2

0

2

Multi-ring PID Likelihood

-4

-2

0

2

4

6

Multi-ring PID Likelihoodµ -likee-like300

0-6Conventional Region
3rd ring
Data SKI~IV
ATM ν MC

600

0
-6

6

50
-4

700

100
-4

350

Additional Region
1st ring
Data SKI~IV
ATM ν MC

200

Conventional Region
2nd ring
Data SKI~IV
ATM ν MCµ -likee-like800

Multi-ring PID Likelihood

Number of Events

Number of Events

300µ -likee-likeNumber of Events

1000

2000
1800
1600
1400
1200
1000
800
600
400
200
0
-6

Number of Events

Number of Events

Number of Eventsµ -likee-like1200

46µ -likee-like100

Additional Region
3rd ring
Data SKI~IV
ATM ν MC

80
60
40
20
0
-6

-4

-2

0

2

4

6

Multi-ring PID Likelihood

Figure 6.12: Multi-ring PID likelihood distributions of Sub-GeV multi-ring events for data andatmospheric neutrino MC events (SK-I to -IV combined). The top three plots correspond tothe conventional and the bottom three plots correspond to the additional fiducial mass region.
The black dots show the data and the red and green histograms show the atmospheric neutrino
MC events. Atmospheric neutrino MC is normalized by livetime and includes reweighting to
the latest SK oscillation fit [64]. From left to right, the 1st to 3rd ring distributions are shown.
Vertical error bars denote the statistical uncertainty.
each ring’s momentum in multi-ring events, this procedure is necessary. The separation of theobserved charge is done using the expected charge distribution. The calculation of the expectedcharge for each PMT is almost the same as Equations (6.18) and (6.19). This calculation isdone based on the identified particle type. Indirect light contributions, such as scattered andreflected photons, are also taken into account.
The following likelihood, Ln , is defined:
( (
))
∑
∑
exp
Ln =
log P qiobs ,αn′ × qi,n,(6.28)′
θi,n <70◦n′exp
where αn′ is the normalization factor to be optimized, and αn′ × qi,n
′ is the expected charge′
given by the n th ring at the ith PMT. The summation is performed for all PMTs inside the
70 degree half opening angle cone from the nth ring direction. The optimal αn′ ’s are searched
for by maximizing Ln .
obs ) is calculatedThen, the observed charge contribution from the nth ring at the ith PMT (qi,nas:exp
αn × qi,nobs
qi,n= qiobs × ∑(6.29)
exp ,n′ αn′ × qi,n′where αn′ ’s are optimized ones in the former likelihood calculation. This ring separation algorithm is also processed before identifying the particle types of the rings, such as in the ringcounting and particle identification algorithms. In such cases, all rings are assumed to be e-likeparticles and the algorithm separates the observed charge at each PMT in a similar manner [108].
Figure 6.13 shows a two-ring event’s event display. From left to right, the original event
display, the separated first ring, and the second ring are shown as a result of the ring separation
algorithm.

85

CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.13: Event display of a two-ring event. The left one shows the original event display.
The middle and right one show the separated first and second ring, respectively, after applying
the ring separation algorithm.

6.1.6

Momentum Determination

The momentum of each Cherenkov ring is calculated with the total observed charge withina cone whose half opening angle is 70 degrees from the ring direction. When summing up
the observed charge inside the cone, the following correction is applied to convert it to RT OTntaking into account eﬀects from water scattering, absorption, PMT acceptance as well as reflected
photons:


)
(
)
(
MC
∑
∑
G
cos Θiri
obs
RT OTn = data α ××−
(Si + Ri ) ,
qi,n
× exp
L
f (Θi )
G◦◦
θi,n <70 ,t1 <ti <t2

θi,n <70(6.30)
where GMC is the gain factor in MC, Gdata is the gain factor in data including its evolution over
obs is the observed charge at thetime discussed in Section 3.3.3, α is the normalization factor, qi,nith PMT from the nth ring, ri is the distance between the event vertex and ith PMT position, L
is the water attenuation length discussed in Section 3.3.6, cos Θi is the PMT density correction
factor, f (Θi ) is the PMT acceptance correction factor, and Si and Ri are the contributions
from scattered photons and reflected photons, respectively. The timing range (t1 , t2 ) starts
from t0 − 50 nsec (= t1 ) and ends at t0 + 250 nsec (= t2 ), where t0 is the peak of the timeof-flight subtracted timing distribution. The relation between RT OTn and particle momentum
has been tabulated in advance using MC for both the electron and muon assumptions, and thering momentum is determined using it.
In the proton decay event selection, the total (invariant) mass (Mtot ) and total momentumof the multi-ring kinematics (Ptot ) are used, and they are defined as:

Ptot =∑

p⃗n ,(6.31)∑√
Etot =|pn |2 + m2n ,(6.32)nn√
2 − P2 ,Mtot = Etot
tot

(6.33)

where pn is the nth ring momentum, mn is the electron (muon) mass in case the nth ring isreconstructed as an e-like (µ-like) ring, and Etot is the total deposited energy.

86CHAPTER 6. EVENT RECONSTRUCTION

0.12

200 cm<dwall

0.1

Fitted Peak, Sigma
910 MeV/c2 30.1 MeV/c2

0.08

898 MeV/c2 54.1 MeV/c2

0.06

828 MeV/c 72.0 MeV/c

Free p→e+π0 MC
Number of Events [/10 (MeV/c2)](Normalized to Unity)

Number of Events [/10 MeV/c2](Normalized to Unity)

Free p→e+π0 MC

100<dwall ≤200 cm
50<dwall ≤100 cm
2

2

0.04
0.02
0

700

800

900

1000

1100
2

0.14
0.12
0.1
0.08
0.06

200 cm<dwall

Fitted Peak, Sigma
933 MeV/c2, 27.6 MeV/c2
100<dwall ≤200 cm

927 MeV/c2, 41.9 MeV/c2
50<dwall ≤100 cm

852 MeV/c2, 68.4 MeV/c2

0.04
0.02
0

700

800

900

1000

1100

Reconstructed Total Mass [MeV/c2]

Reconstructed Total Mass [MeV/c ]Figure 6.14: Reconstructed total mass distributions for free proton decays via p → e+ π 0 MC
events. The left (right) plot shows two-ring (three-ring) events. In each plot, the solid cyan
histogram shows events reconstructed in the conventional fiducial mass region, the pink dashedhistogram shows that for the additional fiducial mass region, and the black dotted histogram
is for the region between dwall of 50 cm and 100 cm. The peak position and width of the
distributions are obtained using Gaussian fits.
Performance of Momentum Reconstruction
The reconstructed total mass distributions of free proton decay MC events are shown in
Figures 6.14 and 6.15. The distributions outside the conventional fiducial mass region have
longer tails in the low mass region. This is because of the worse momentum resolution resulting
from the lower number of hit PMTs in events occurring closer to the wall. Furthermore, particles
generated in the region closer to the wall more often escape the ID and disable us to fullyreconstruct their momenta. The data and MC agreement on the momentum reconstruction, theenergy scale uncertainty, is discussed in Section 6.2.

6.1.7

Ring Number Correction

In this step, each reconstructed ring is tested if it is a real Cherenkov ring or not. There are
two types of ring rejection criteria, and the first criteria are as follows:
Ringcorr 1-1 EvisA < EvisB ,where EvisA(B) is the visible (electron equivalent) energy of ring-A(B).
Ringcorr 1-2 θA−B < 30◦ ,where θA−B is the angle between the ring-A and ring-B directions.
Ringcorr 1-3 EvisA × sin θA−B < 60 MeV.
If ring-A satisfies the above conditions, it is discarded as a fake ring. The second criteria are as
follows:
visA
Ringcorr 2-1 EEvistot< 0.05,where Evistot is the total visible energy in the event.

Ringcorr 2-2 EvisA < 40 MeV
If ring-A satisfies the above conditions, it is also discarded as a fake ring. This process is applied
only to multi-ring events. When at least one of the reconstructed rings is judged as a fake ring,the momenta of the remaining rings are redetermined.

87CHAPTER 6. EVENT RECONSTRUCTION

Free p→µ+π0 MC
Number of Events [/10 (MeV/c2)](Normalized to Unity)

Number of Events [/10 MeV/c2](Normalized to Unity)

Free p→µ+π0 MC
0.14
200 cm<dwall

0.12
0.1
0.08

Fitted Peak, Sigma
917 MeV/c2 27.6 MeV/c2
100<dwall ≤200 cm

917 MeV/c2 36.8 MeV/c2
50<dwall ≤100 cm
2

0.06

2

905 MeV/c 33.2 MeV/c

0.04
0.02
0

700

800

900

1000

1100
2

0.16
200 cm<dwall

0.14
0.12

Fitted Peak, Sigma
936 MeV/c2, 24.2 MeV/c2
100<dwall ≤200 cm

0.1

941 MeV/c2, 27.5 MeV/c2

0.08

925 MeV/c2, 35.6 MeV/c2

50<dwall ≤100 cm

0.06
0.04
0.02
0

700

800

900

1000

1100

Reconstructed Total Mass [MeV/c2]

Reconstructed Total Mass [MeV/c ]Figure 6.15: Reconstructed total mass distributions for free proton decays via p → µ+ π 0 MC
events. The left (right) plot shows two-ring (three-ring) events. In each plot, the solid cyan
histogram shows events reconstructed in the conventional fiducial mass region, the pink dashedhistogram shows that for the additional fiducial mass region, and the black dotted histogram
is for the region between dwall of 50 cm and 100 cm. The peak position and width of the
distributions are obtained using Gaussian fits.

6.1.8

Michel Electron Search

Subsequent Michel electrons after muon decays are searched for using an independent low
energy fitter, the same one used in Section 5.4.4. If a PMT hit cluster occurring after the
primary event trigger timing satisfies the following criteria, it is tagged as a Michel electron:
Michel-etag 1 The time diﬀerence from the primary event is less than 20 µsec.
Michel-etag 2 The number of ID PMT hits in a fixed 1.3 µsec timing window around the hit
cluster timing is greater than 50 (25 in SK-II).
Michel-etag 3 The total observed charge in a fixed 1.3 µsec timing window around the hit cluster
timing is less than 2000 (1000 in SK-II) p.e.’s.
Michel-etag 4 Low energy fit goodness defined in Eq. (5.3) is greater than 0.5.
Michel-etag 5 The maximum number of ID PMT hits in a sliding 50 nsec timing window, N50
which is defined in Section 5.4.4, is greater than 30 (16 in SK-II).
For SK-I to -III, there are additional criteria:
Michel-etag 6 The time diﬀerence from the primary event (∆t) must satisfy, 0.1 < ∆t < 0.8 µsec
or 1.2 < ∆t < 20 µsec.
Michel-etag 7 N30 − NBG > 50 (25 in SK-II).
where N30 is the number of ID PMT hits in a 30 nsec timing window around the hit cluster
timing, and NBG is the estimated number of ID PMT hits induced by other than the Michelelectron in the same timing window. The value of NBG is estimated with the number of ID PMThits before the hit cluster timing. In this calculation, the time-of-flight subtracted residual timing
is used with the primary vertex position. Due to eﬀects from the PMT signal reflection in thecable, the time region between 800 and 1200 nsec after the primary event trigger is not used in
the Michel electron search in SK-I to -III by applying Michel-etag 6 as discussed in Section 3.2.5.

88

CHAPTER 6. EVENT RECONSTRUCTION

Free p→µ+π0 MC
Number of Events(Normalized to Unity)

0.9
200 cm<dwall

0.8

0 Michel-e 1 Michel-e

0.7

11.4%

88.6%

100<dwall ≤200 cm

0.6

21.1%

0.5

78.9%

50<dwall ≤100 cm

35.2%

0.4

64.8%

0.3
0.2
0.1
0
0

1

2

3

4

5

6

7

8

9

10

Number of Tagged Michel Electrons

Figure 6.16: Distributions of the number of tagged Michel electrons for p → µ+ π 0 MC events.
They are livetime-weighted combined from SK-I to -IV The solid cyan histogram shows eventsreconstructed in the conventional fiducial mass region, the pink dashed histogram shows thatfor the additional fiducial mass region, and the black dotted histogram is for the region between
dwall of 50 cm and 100 cm.

1200

5000

Number of Events

Number of Events

6000
Conventional Region
Data SKI~IV
ATM ν MC

4000
3000
2000
1000
0
0

1

2

3

4

5

6

7

8

9

800
600
400
200
0
0

10

Number of Tagged Michel Electrons

Additional Region
Data SKI~IV
ATM ν MC

1000

1

2

3

4

5

6

7

8

9

10

Number of Tagged Michel Electrons

Figure 6.17: Distribution of the number of tagged Michel electrons of Sub-GeV multi-ring
events for atmospheric neutrino MC and data in SK-I to -IV. The left plot corresponds tothe conventional fiducial mass region and the right plot to the additional fiducial mass region.
Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK
oscillation fit [64]. Vertical error bars denote the statistical uncertainty.
Michel Electron Tagging Eﬃciency
The Michel electron tagging eﬃciency in cosmic-ray muon events is estimated to be about
73% in SK-I to -III. Because of the electronics upgrade described in Section 3.2.5, it improved
to about 90% in SK-IV. The number of tagged Michel electron distribution of p → µ+ π 0 MC
events is shown in Fig. 6.16. In the p → µ+ π 0 mode, an eﬀect from muons escaping the ID
manifests in the Michel electron tagging performance. A muon escaping from the ID disables
us to tag the subsequent Michel electron, and therefore the tagging eﬃciency in the additional
fiducial mass region (78.9%) is lower than that in the conventional fiducial mass region (88.6%).
The data MC agreement is shown in Fig. 6.17 using Sub-GeV multi-ring events.

6.1.9

Reconstruction Performance on Proton Decay Events

The reconstruction performance on free p → e+ π 0 and p → µ+ π 0 events is summarizedin Table 6.1 among diﬀerent ID regions. As described in each section, in events outside theconventional fiducial mass region, the number of hit PMTs tends to be small and they are more

89

CHAPTER 6. EVENT RECONSTRUCTION
localized than those inside. It is especially true for p → e+ π 0 and p → µ+ π 0 decays because
they produce back-to-back event topologies and one of the reconstructed rings generally has asmall distance to the wall along its direction. These eﬀects result in more two-ring events, worse
particle identification, wider total mass distribution with longer tails on the low mass side, andlower Michel electron tagging eﬃciency. Although they are unavoidable and the signal selection
eﬃciencies in the additional fiducial mass region are not as good as those in the conventional
fiducial mass region due to them, the search sensitivity improvement by enlarging the fiducial
mass is confirmed. It is discussed in Chapter 7, together with the concrete signal selection
eﬃciencies and the expected number of atmospheric neutrino background events.

6.2

Energy Scale Uncertainty

In this section, the energy scale uncertainty used in this analysis is described. The obtainedenergy scale uncertainty is used as the source of the systematic uncertainty for the proton decay
searches described in Chapter 7. The following three items are evaluated:• Absolute energy scale uncertainty.
• Evolution of the energy scale over time.
• Zenith-angle-dependence of the energy scale.
For all items, the uncertainty is separately estimated in the conventional and additional fiducial
mass region.

6.2.1

Absolute Energy Scale Uncertainty

The following control samples are used to evaluate the absolute energy scale uncertainty.
• Michel electrons from cosmic-ray muons.
• Neutral pions induced by atmospheric neutrinos.
• Sub-GeV stopping cosmic-ray muons.
• Multi-GeV stopping cosmic-ray muons.
The absolute energy scale uncertainty is estimated with the diﬀerence in reconstructed momenta
or masses between data and MC for the above control samples in each SK phase. Among them,the event vertices of Michel electron and neutral pion events are almost uniformly distributed
inside the ID and used to estimate the diﬀerence between data and MC for each fiducial massof the detector separately. In the following, the uncertainty evaluation method for each control
sample is described, and results are summarized at the end of this sub-Section.
Michel Electron Momentum
The Michel electron momentum spectrum from stopping cosmic-ray muons is used. The
Michel electron event selection criteria are as follows:
Michel-eEscale 1 The time diﬀerence from the primary cosmic-ray event must be between 2 (1.2for SK-IV) and 8 µsec.
Michel-eEscale 2 The maximum number of ID PMT hits in a sliding 50 nsec window for theMichel electron: N50 > 60 (30 for SK-II).
Michel-eEscale 3 The low energy fit goodness, the same one used in Section 6.1.8, > 0.5.

90

Table 6.1: Summary of reconstruction performance in diﬀerent ID regions using only free proton decay MC events and weighted by the combined
SK-I to -IV livetime. The particle identification (PID) eﬃciency is the fraction of events which pass the proton decay signal criterion associated with
PID out of all two- and three-ring signal events. Here Mπ0 (Mtot ) peak is the reconstructed neutral pion (total) mass distribution’s peak position
after applying all selections except the cut associated with Mπ0 (Mtot ). The peak is determined using a Gaussian fit. Note that Mπ0 peak values
are evaluated for only three-ring events. The terms “Conventional”, “Additional” and “Outside” stand for the conventional (200 cm < dwall),additional fiducial volume (100 < dwall ≤ 200 cm) and outside region (50 < dwall ≤ 100 cm), respectively. The outside region is not used for thepresent analysis.
Decay Mode
Vertex2-ring3-ringPID
Michel electron
Mπ0 peakMtot peak
Mtot peak
Regionresolution fraction fraction eﬃciency tagging eﬃciency(3-ring)(2-ring)(3-ring)p → e+ π 0
Conventional
17.1 cm
39.3%
58.7%
95.8%
N.A.
135 MeV/c2
910 MeV/c2
933 MeV/c222Additional
24.1 cm
51.9%
44.5%
87.7%
N.A.
134 MeV/c
898 MeV/c
927 MeV/c222
Outside25.9 cm
55.9%
37.6%
89.6%
N.A.
125 MeV/c
828 MeV/c
852 MeV/c2
p → µ+ π 0
Conventional
20.6 cm
36.8%
62.0%
96.2%
88.6%
135 MeV/c2
917 MeV/c2
936 MeV/c2
Additional
24.8 cm
49.1%
48.1%
90.7%
78.9%
132 MeV/c2
917 MeV/c2
941 MeV/c222
Outside64.8%
905 MeV/c
925 MeV/c2
26.7 cm
55.3%
39.8%
82.6%
125 MeV/c

CHAPTER 6. EVENT RECONSTRUCTION

91

CHAPTER 6. EVENT RECONSTRUCTION

Michel-eEscale 4 Fiducial volume cut using the reconstructed Michel electron vertex.
The Michel electron momentum spectra of data and MC are shown in Figure 6.18. The diﬀerencein the mean values between data and MC in each detector phase and fiducial mass region isused for the absolute energy scale uncertainty estimation.
Neutral Pion Mass
The neutral pion mass spectrum in atmospheric neutrino events is used. Neutral pions aremainly induced via NC meson production. Two-ring both e-like events are selected from the FC
final sample, and the neutral pion mass is obtained based on Equations (6.31), (6.32), and (6.33).
The π 0 mass distributions are shown in Figure 6.19. The diﬀerence in the peak values obtained
by Gaussian fits between data and MC in each detector phase and fiducial mass region is used
for the uncertainty estimation.
Sub-GeV Stopping Cosmic-ray Muon Momentum and Cherenkov Opening Angle
For this item, the following relation between particle momentum (p) and Cherenkov opening
angle (θC ) is utilized:√cos θC =

1
1
=
nβ
n

1+

m2
.
p2

(6.34)As shown in Fig. 6.20, a Cherenkov opening angle depends on the muon momentum. Conversely,
the muon momentum is calculated from the observed Cherenkov ring shape. Using Sub-GeV
stopping cosmic-ray muon data and MC, the momentum derived from the total observed charge
associated with the muon Cherenkov ring (Ppe ) and the momentum derived from the Cherenkov
opening angle (Pθ ) are compared.
The Sub-GeV stopping cosmic-ray muon selection criteria are as follows:
STMUEscale 1-1 The reconstructed muon Z position must be greater than 1720 cm.
STMUEscale 1-2 The reconstructed muon direction cos θz must be greater than 0.87, wherecos θz = 1.0 is vertically downward-going.
STMUEscale 1-3 The muon fit goodness must be greater than 0.6.
STMUEscale 1-4 The total observed charge, PEtot , in the ID must be 500 < PEtot < 5000 p.e.’s(250 < PEtot < 2500 p.e.’s in SK-II).
STMUEscale 1-5 The reconstructed muon momentum derived from the Cherenkov opening angle
must be 200 < Pθ < 440 MeV/c.
STMUEscale 1-6 There must be exactly one tagged Michel electron, and the time diﬀerence
between the muon and Michel electron must be longer than 1.2 µsec.
The selected samples are divided into three groups with Pθ : 200 < Pθ < 280, 280 < Pθ < 360,
and 360 < Pθ < 440 MeV/c. The Ppe /Pθ distributions in each Pθ region in SK-IV are shown in
Fig. 6.21. The diﬀerence in the mean values between data and MC is assigned as the uncertainty
for this control sample.
Multi-GeV Stopping Cosmic-ray Muon Momentum over Range
Multi-GeV stopping cosmic-ray muons are used for the highest energy region. The momentum divided by the range (track length) of muons (Rµ ) is compared between data and MC. The
following selection criteria are applied to select Multi-GeV stopping cosmic-ray muons:

92

800
700
600

Number of Events [/4 MeV/c]

Number of Events [/4 MeV/c]

CHAPTER 6. EVENT RECONSTRUCTION

SK-I
Conventional Region
Data
MC

500
400
300
200
100
0
0

10 20 30 40 50 60 70 80 90 100

180
160
140
120
100
80
60
40
20
0
0

700
600

SK-II
Conventional Region
Data
MC

500
400
300
200
100
0
0

10 20 30 40 50 60 70 80 90 100

160
140
120
80
60
40
20
0
0

SK-III
Conventional Region
Data
MC

800
600
400
200
0
0

10 20 30 40 50 60 70 80 90 100

220
200
180
160
140
120
100
80
60
40
20
0
0

7000
6000

SK-IV
Conventional Region
Data
MC

5000
4000
3000
2000
1000
0
0

SK-III
Additional RegionDataMC

10 20 30 40 50 60 70 80 90 100

Momentum [MeV/c]

Number of Events [/4 MeV/c]

Number of Events [/4 MeV/c]

Momentum [MeV/c]

8000

10 20 30 40 50 60 70 80 90 100

Momentum [MeV/c]

Number of Events [/4 MeV/c]

Number of Events [/4 MeV/c]

1000

SK-II
Additional Region
Data
MC

100

Momentum [MeV/c]

1200

10 20 30 40 50 60 70 80 90 100

Momentum [MeV/c]

Number of Events [/4 MeV/c]

Number of Events [/4 MeV/c]

Momentum [MeV/c]

800

SK-I
Additional RegionDataMC

10 20 30 40 50 60 70 80 90 100

Momentum [MeV/c]

1400
1200
1000

SK-IV
Additional Region
Data
MC

800
600
400
200
0
0

10 20 30 40 50 60 70 80 90 100

Momentum [MeV/c]

Figure 6.18: Michel electron momentum distributions. From top to bottom, SK-I to -IV plots
are aligned. The left plots correspond to the conventional and the right plots correspond to
the additional fiducial mass region. In each plot, the number of entries in the MC histogram isnormalized to that of data. Vertical error bars denote the statistical uncertainty.

93

80
60
40
20
0
0

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

SK-II

50

Data
MC

40
30
20
10
0
0

50

100

150

200

250

300

45

SK-III

40

Data
MC

35
30
25
20
15
10
5
0
0

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

SK-IV

250
Data
MC

200
150
100
50
0
0

50

100

150

200

250

10
9
8
7
6
5
4
3
2
1
0
0

Number of Events [/10 (MeV/c2)]

Reconstructed π0 Mass [MeV/c2]

Number of Events [/10 (MeV/c2)]

Data
MC

100

20
18
16
14
12
10
8
6
4
2

Number of Events [/10 (MeV/c2)]

SK-I

120

Number of Events [/10 (MeV/c2)]

Number of Events [/10 (MeV/c2)]

Number of Events [/10 (MeV/c2)]

Number of Events [/10 (MeV/c2)]

Number of Events [/10 (MeV/c2)]

CHAPTER 6. EVENT RECONSTRUCTION

300

Reconstructed π0 Mass [MeV/c ]
2

0

SK-I
Data
MC

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

SK-II
Data
MC

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

SK-III

6

Data
MC

5
4
3
2
1
0

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

60

SK-IV

50

Data
MC

40
30
20
10
0
0

50

100

150

200

250

300

Reconstructed π0 Mass [MeV/c2]

Figure 6.19: Neutral pion mass distributions. From top to bottom, SK-I to -IV plots arealigned. The left plots correspond to the conventional and the right plots correspond to theadditional fiducial mass region. Atmospheric neutrino MC is normalized by livetime and thetwo-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0), here. Vertical error
bars denote the statistical uncertainty.

94

Cherenkov Opening Angle [Degree]

CHAPTER 6. EVENT RECONSTRUCTION

50
45
40
35
30
25
20
15
10
5
0
0 100 200 300 400 500 600 700 800 9001000

Muon Momentum [MeV/c]

Figure 6.20: Cherenkov opening angle as a function of muon momentum.

Figure 6.21: Distribution of the ratio of the momentum derived from the total observed charge(Ppe ) to the momentum derived from the Cherenkov opening angle (Pθ ) for SK-IV. The left
plot corresponds to events with Pθ between 200 and 280 MeV/c. The middle plot corresponds
to events with Pθ between 280 and 360 MeV/c. The right plot corresponds to events with Pθ
between 360 and 440 MeV/c. In each plot, the blue histogram is data and the red is MC. Taken
from [110].

95

CHAPTER 6. EVENT RECONSTRUCTION

Table 6.2: Summary of the absolute energy scale uncertainty for both the conventional andadditional fiducial mass regions in units of %. The absolute scale uncertainty is taken to be thevalue of the most discrepant control sample, and cosmic-ray muon samples are considered forboth fiducial mass regions to take the most discrepant one.
Absolute energy scale uncertainty
Region
SK-I
SK-II
SK-III
SK-IV
Conventional
3.1
2.0
1.6
2.1
Additional
3.1
3.9
1.6
2.1
STMUEscale 2-1 The reconstructed muon entering point must be on the top of the detector.
STMUEscale 2-2 The muon fit is succeeded, fit goodness > 0 (0.5 in SK-IV).
STMUEscale 2-3 The reconstructed muon direction cos θz must be greater than 0.94.
STMUEscale 2-4 There must be exactly one tagged Michel electron, and the time diﬀerence
between the muon and the Michel electron must be longer than 1.2 µsec.
The selected samples are divided into five (six in SK-IV) groups with Rµ : 700 (500 in SK-IV) <Rµ < 1000, 1000 < Rµ < 1500, 1500 < Rµ < 2000, 2000 < Rµ < 2500, and 2500 < Rµ <3000 cm(, and 3000 < Rµ < 3500 cm only in SK-IV). The muon momentum over range
distributions for SK-IV are shown in Fig. 6.22. The diﬀerence in the peak values obtained by
Gaussian fits between data and MC is taken as the uncertainty for this sample.
Summary of the Absolute Energy Scale Uncertainty
Figure 6.23 shows the absolute energy scale diﬀerence between data and MC for each of
the control samples discussed above. Michel electrons and π 0 events are used to estimate thediﬀerence between data and MC for each fiducial mass region of the detector separately. The
absolute scale uncertainty is taken to be the value of the most discrepant control sample in each
SK phase and fiducial mass region and is summarized in Table 6.2. To take the most discrepant
control sample, cosmic-ray muon samples are considered for both fiducial mass regions.

6.2.2

Evolution of the Energy Scale over TimeThe evolution of the energy scale over time is estimated using the variation in the averagereconstructed momentum of Michel electrons and the variation in the reconstructed momentum
over range of Multi-GeV stopping cosmic-ray muons. The selection criteria for both two samples
are the same as those described above. All Multi-GeV stopping cosmic-ray muons with Rµ
between 700 (500 in SK-IV) and 3000 (3500 in SK-IV) cm are used. Figures 6.24 and 6.25
show the time variation of Michel electron momentum and momentum over range of Multi-GeV
stopping cosmic-ray muons, respectively. As mentioned in Section 6.1.6, the evolution of the
PMT gain and water attenuation length is corrected in the momentum reconstruction precess.
The time variation is defined as the sample standard deviation of the data value over the runtime in each SK phase and fiducial mass region. The larger value is taken as the uncertainty
between the two samples. To take the larger value, the cosmic-ray muon sample is considered
for both fiducial mass regions. The uncertainty due to the time variation of the energy scale issummarized in Table 6.3.

6.2.3

Zenith-angle-dependence of the Energy Scale

Particle directional dependence of the energy scale is estimated using Michel electrons because vertices and directions of Michel electrons are almost uniformly and isotropically dis-96

Number of events [0.05 MeV/c/cm]

180
160
140
120
100
80
60
40
20
0

SK-IV
500 < Rµ < 1000 cm
DataMC

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

180
160
140
120
100
80
60
40
20
0

Number of events [0.05 MeV/c/cm]

Momentum over Range [MeV/c/cm]

SK-IV
1500 < Rµ < 2000 cm
DataMC

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

Momentum over Range [MeV/c/cm]

Number of events [0.05 MeV/c/cm]

Number of events [0.05 MeV/c/cm]

Number of events [0.05 MeV/c/cm]

Number of events [0.05 MeV/c/cm]

CHAPTER 6. EVENT RECONSTRUCTION

120
SK-IV
2500 < Rµ < 3000 cm

100

Data
MC

80
60
40
20
0

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

Momentum over Range [MeV/c/cm]

180

SK-IV
1000 < Rµ < 1500 cm

160
140
120

Data
MC

100
80
60
40
20
0

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

Momentum over Range [MeV/c/cm]

140

SK-IV
2000 < Rµ < 2500 cm

120

Data
MC

100
80
60
40
20
0

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

Momentum over Range [MeV/c/cm]

120

SK-IV
3000 < Rµ < 3500 cm

100

Data
MC

80
60
40
20
0

1.6 1.82

2.2 2.4 2.6 2.83

3.2 3.4

Momentum over Range [MeV/c/cm]

Figure 6.22: Muon momentum over range distributions for SK-IV. The Multi-GeV stopping
cosmic-ray muons are divided into six group with their range, Rµ . In each plot, the numberof entries in the MC histogram is normalized to that of data. Vertical error bars denote thestatistical uncertainty.

Table 6.3: Summary of the time variation of the energy scale for both the conventional andadditional fiducial mass regions in units of %. The time variation uncertainty is taken to be thelarger value among the two control samples, and the cosmic-ray muon sample is considered forboth fiducial mass regions to take the larger one.
Time variation of the energy scale
Region
SK-I
SK-II
SK-III
SK-IV
Conventional
0.9
0.6
1.8
0.4
Additional
0.9
0.6
1.8
0.6

97

CHAPTER 6. EVENT RECONSTRUCTION

642(MC - Data) / Data [%]

SK-I

0

SK-II

Michel Electron
Conventional Region
Additional Region-2

Neutral Pion π 0 Mass
Conventional Region
Additional Region-4

Sub-GeV Stopping µ
Multi-GeV Stopping µ-642
SK-III

SK-IV

0
-2
-4
-6

102

103

104
102
Momentum [MeV/c]

103

104

Figure 6.23: Absolute energy scale diﬀerence between data and MC control samples. Verticalerror bars denote the statistical uncertainty, and horizontal error bars denote the momentum
range for each control sample. For the Michel electron and π 0 samples, points with solid error
bars correspond to the conventional fiducial mass region, and points with dashed error bars
correspond to the additional fiducial mass region. Cosmic-ray muon samples are considered forboth the conventional and additional fiducial mass regions to take the most discrepant control
sample.

98

CHAPTER 6. EVENT RECONSTRUCTION

Deviation from Mean [%]Conventional Region
SK-I

SK-II

SK-III

SK-IV

2
0
-2
-4
2000/01/01

4

Additional Region

2004/12/31

2009/12/31

2014/12/31

Date

2
0
-2
-4

2000/01/01

2004/12/31
2009/12/31
Date

2014/12/31

Figure 6.24: Time variation of the average momentum of Michel electrons as a function of date.
For each fiducial mass region and SK phase, data points are normalized by their mean value. The
upper (lower) plot corresponds to the conventional (additional) fiducial mass region. Verticalerror bars denote the statistical uncertainty. For SK-I to -III, each data point corresponds to a
one month average and for SK-IV, each data point corresponds to a 10 day average.

Deviation from Mean [%]Deviation from Mean

Deviation from Mean

4

4

SK-I

SK-II

SK-III

2000/01/01

2004/12/31 2009/12/31
Date

SK-IV

2
0
-2
-4
2014/12/31

Figure 6.25: Time variation of the average momentum over range of Multi-GeV stopping
cosmic-ray muons as a function of date. For each SK phase, data points are normalized by theirmean value. Vertical error bars denote the statistical uncertainty. Each data point corresponds
to a 10 day average.

99

CHAPTER 6. EVENT RECONSTRUCTION

Table 6.4: Summary of the zenith-angle-dependent non-uniformity of the energy scale for boththe conventional and additional fiducial mass regions in units of %.
Zenith-angle-dependent non-uniformity
Region
SK-I
SK-II
SK-III
SK-IV
Conventional
0.6
1.1
0.6
0.5
Additional
1.4
1.5
1.3
0.4

tributed in the ID. The Michel electron events are divided into five bins with their direction,cos θz . In each bin, the average Michel electron momentum is compared between data and MC.
Figure 6.26 shows the ratio of the average momentum of MC to that of data as a function ofparticle direction (zenith angle), cos θz , in each SK phase and fiducial mass region. The MC overdata ratio is normalized by the absolute diﬀerence derived in Section 6.2.1 using the Michel electron sample. The five bins’ standard deviation is assigned as the uncertainty for SK-I to -III, andthe most discrepant point is assigned as the uncertainty for SK-IV. The zenith-angle-dependent
non-uniformity of the energy scale is summarized in Table 6.4.
Summarizing the above, data and MC agree within a few % level in both the conventional
and additional fiducial mass regions for all items, the absolute energy scale (Table 6.2), time
variation of the energy scale (Table 6.3), and zenith-angle-dependent non-uniformity of theenergy scale (Table 6.4).

6.3

Neutron Tagging

Because of the data taking system upgrade presented in Section 3.2.5, neutrons emitted ina primary FC event can be counted in SK-IV by tagging 2.2 MeV gamma rays from neutron
capture on hydrogen:n + p → d + γ (2.2 MeV).
(6.35)In order to tag this faint gamma ray (Compton-scattered electron), an independent neutron
tagging algorithm has been developed [97, 106]. The algorithm is composed of the following two
steps:
1. Initial neutron candidate selection.
2. Final neutron candidate selection with Neural Network.
First, PMT hit clusters produced by such faint gamma rays are searched for as the initial
selection. Then, 23 input variables associated with each initial neutron candidate are calculated
and used as input variables to a dedicated neural network to identify it as either a neutron signal
or background (fake signal).

6.3.1

Time-clustered PMT Dark Noise

About the SK PMT dark noise, besides random dark noise, which is uniformly distributed
in time, another type of dark noise has been found recently [106]. That one clusters in time,and a typical waveform of such time-clustered noise hits is shown in Fig. 6.27. The source of
these time-clustered noise hits has been identified to be the scintillation light in the SK PMT
glass. Since a typical number of PMT hits induced by 2.2 MeV gamma ray (Compton-scatteredelectron) is less than 10, it is beneficial to identify a PMT hit as either a photon detection hit
or dark noise hit and to eﬀectively reduce the dark noise hits, which mimic a faint gamma ray
signal. Therefore, a dedicated time-clustered noise cut is introduced in the initial selection andinput variable calculations.

100

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

SK-I
Conventional Region
Standard Deviation 0.62

MC/Data Ratio

MC/Data Ratio

CHAPTER 6. EVENT RECONSTRUCTION

+/-1%

-1

-0.5

0

0.5

1

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

SK-I
Additional Region
Standard Deviation 1.44
+/-1%

-1

-0.5

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

SK-II
Conventional Region
Standard Deviation 1.07
+/-1%

-1

-0.5

0

0.5

1

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

MC/Data Ratio

MC/Data Ratio

+/-1%

-0.5

0

+/-1%

-1

-0.5

0.5

1

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

0

0.5

MC/Data Ratio

MC/Data Ratio

+/-1%

-0.5

0.5

1

+/-1%

-1

-0.5

0

0.5

1

Zenith Angle

SK-IV
Conventional Region
Max Deviation 0.51

-10SK-III
Additional Region
Standard Deviation 1.33

Zenith Angle

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

1

Zenith Angle

SK-III
Conventional Region
Standard Deviation 0.60

-1

0.5

SK-II
Additional Region
Standard Deviation 1.45

Zenith Angle

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

0

Zenith Angle

MC/Data Ratio

MC/Data Ratio

Zenith Angle

1

Zenith Angle

1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95

SK-IV
Additional Region
Max Deviation 0.44
+/-1%

-1

-0.5

0

0.5

1

Zenith Angle

Figure 6.26: Ratio of the average momentum between data and MC as a function of Michelelectron direction, zenith angle, cos θz . From top to bottom, SK-I to -IV plots are aligned. The
left plots correspond to the conventional and the right plots correspond to the additional fiducial
mass region. Vertical error bars denote the statistical uncertainty.

101

CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.27: Typical waveform of time-clustered noise hits (1 µsec/div for the horizontal axis
and 5 mV/div for the vertical axis). This sample PMT’s dark noise is measured to be about
8 kHz in the measurement condition. Therefore, the expected number of dark noise hits per
10 µsec is about 0.08 if the dark noise is uniformly distributed in time. Taken from [106].

6.3.2

Initial Neutron Candidate Selection

As the initial selection, the number of PMT hits in a sliding 10 nsec timing window iscounted, and PMT hit clusters produced by faint gamma rays are searched for. Each PMT hit
timing is corrected with time-of-flight using the primary FC event vertex position (describedin Section 6.1.1, and 6.1.4) in this calculation. The number of PMT hits in the sliding timing
RAW . If a cluster with N RAW of more than four is found, that cluster
window is defined as N10
10
RAW is more than 50, or the number of PMT
is identified as a possible neutron candidate. If N10
hits in a 200 nsec timing window around the cluster timing (N200 ) is more than 200, that cluster
is rejected as a background.
RAW is redefined to be N . If there
The time-clustered noise cut is introduced here, and N10
10
are multiple hits in the same PMT within X µsec, these hits are removed. The value of X
RAW . For hit clusters with N RAW of less than 7, X is set to 12 µsec,
depends on the value of N10
10
RAW of 7 or more, X is set to 6 µsec. They have been determined towhile for hit clusters with N10
optimize performance, and hit clusters with the remaining number of PMT hits (N10 ) of morethan four are selected as initial neutron candidates.

6.3.3

Final Neutron Candidate Selection with Neural Network

Before calculating the input variables to the neural network used in this analysis, the vertex
position of the initial neutron candidate (Compton-scattered electron) is reconstructed using
Neut-Fit. Neut-Fit searches for the vertex position so that the RMS of the time-of-flight subtracted residual timing distribution of the initial candidate is minimized. The RMS of theresidual timing distribution is defined as follows:√∑N10n ′
(ti − t′mean )2′i,trms =(6.36)
N10nt′mean =

N
10n
∑
i

t′i
,
N10n

(6.37)

where t′i is the ith PMT’s time-of-flight corrected residual time for an assumed vertex position,
and N10n is the number of PMT hits in a 10 nsec timing window in residual timing for anassumed vertex position. Neut-Fit is executed twice: first, the reconstructed vertex position isforced to be within 200 cm from the primary FC event vertex position, and second, the vertex
position is reconstructed without any constraints. In the following, the Neut-Fit vertex position
denotes the result from the first attempt unless otherwise noted.

102

CHAPTER 6. EVENT RECONSTRUCTION

Input Variables to Neural Network
For each initial neutron candidate, the following 23 input variables are defined:
1. Number of hits in 10 nsec, N10 :The same variable used in the initial selection. Initial neutron candidates with larger N10
are regarded as more signal-like candidates.
2. Mean opening angle, θmean :The direction of each initial candidate is reconstructed by calculating the vector sum of
the hit PMT directions from the Neut-Fit vertex position. Then, an opening angle to each
hit PMT in the 10 nsec window is calculated from the obtained direction. The mean valueof the opening angles is defined as θmean . Initial neutron candidates with θmean around42 degrees are regarded as more signal-like candidates.
3. Hit vector RMS, ϕrms :An azimuthal angle to each hit PMT is also calculated using the reconstructed direction
and Neut-Fit vertex position. The azimuthal angle diﬀerences between two consecutive
hits in azimuth are calculated. Then, the RMS of the diﬀerences is used as an input
variable, ϕrms . Initial neutron candidates with small ϕrms are regarded as more signallike candidates because Cherenkov photons are expected to be distributed uniformly inazimuth.
4. Number of spatially clustered hits, Nc :PMT hits induced by radioactive products (background) are often spatially localized.
Multiple hits within an opening angle of 14.1 degrees are counted as clustered-hits, Nc . If
there are three spatially clustered hits or more, Nc is set to the number of these spatiallyclustered hits, otherwise 0. The diﬀerence between N10n and Nc , N10n − Nc , is used.
Backgrounds are expected to have lower N10n − Nc .
5. Number of hits in 300 nsec, N300 :In order to reject other possible higher energy backgrounds, the number of PMT hits in a
300 nsec timing window around the initial neutron candidate timing is calculated, N300 .
The diﬀerence between N300 and N10n , N300 − N10n , is used, and initial neutron candidates
with larger N300 − N10n are regarded as more background-like candidates.
6. Root-Mean-Square of hit timing, t′rmsFC :Initial neutron candidates from true neutrons should have a narrower peak in the residual
timing distribution. In order to separate a gamma ray signal from backgrounds with thisfeature, the RMS of the residual timing distribution is used as an input variable. Here,the primary FC event vertex position is used for the calculation of the RMS of the residual
timing distribution, t′rmsFC :√∑N10 ′(ti − t′meanFC )2′i,(6.38)
trmsFC =N10
t′meanFC =

N10
∑
t′i
.
N10

(6.39)

i

Initial neutron candidates with smaller t′rmsFC are regarded as more signal-like candidates.
7, 8. Minimum RMS of hit timing, min(t3rms ) and min(t6rms ):The minimum RMS of hit timing for 3 and 6 consecutive hits in time is defined as min(t3rms )and min(t6rms ), respectively, using Equations (6.36) and (6.37). In a similar manner tot′rmsFC , initial neutron candidates with smaller min(t3rms ) and min(t6rms ) are regarded as
more signal-like.

103CHAPTER 6. EVENT RECONSTRUCTION

9, 10. BONSAI fit variables, BSwall and BSenergy :The low energy reconstruction tool developed for solar neutrino analyses in SK, BONSAI [111], is used to reconstruct the Compton-scattered electron vertex position and energy. Vertex positions for backgrounds from radioactive products in the PMT components,
such as PMT cases, and PMT cables, are localized in the edge of the detector. The distance between the BONSAI vertex position and the closest ID wall is defined as BSwall ,and backgrounds are expected to have smaller BSwall . The reconstructed energy withBONSAI, BSenergy , is expected to be around 2 MeV for true neutron candidates.
11, 12, 13. Neut-Fit variables, ∆t′rms , ∆N10 , and NFwall :The diﬀerence between t′rms and t′rmsFC is defined as ∆t′rms . The former one is derived
from the Neut-Fit vertex position, while the latter one is from the primary FC event
vertex position. Similarly, N10n − N10 is defined as ∆N10 .
The distance between the Neut-Fit vertex position and the closest ID wall is defined as
NFwall . Here, the second Neut-Fit result is used. Vertex positions for backgrounds are
expected to be localized in the small NFwall region.
14, 15. Fit agreement variables: (NF − BS)dis , and (NF − FC)dis :The distance between the two vertex positions from Neut-Fit and BONSAI is defined as(NF − BS)dis . Furthermore, the diﬀerence between Neut-Fit and the primary FC event
vertex positions, (NF − FC)dis , is also used. True neutron candidates are more likely tobe reconstructed consistently among the diﬀerent tools. Initial neutron candidates withsmaller (NF − BS)dis and (NF − FC)dis are regarded as more signal-like candidates.
16. Acceptance parameter, PAcceptance :The probability to detect photons from a Compton-scattered electron at each PMT depends on the distance between the PMT and electron position as well as the PMT acceptance (eﬀective coverage). On the other hand, it is not the case for dark noise hits.
To diﬀerentiate neutron signals and backgrounds using this feature, the photon detection
probability of each PMT (Pi ) and the final acceptance parameter (PAcceptance ) are defined
as follows:( r )f (Θi )
i
Ai =
×
exp
−
,
(6.40)
L
ri2∑
Atotal =Ai ,(6.41)
i

Pi =

Ai
,
Atotal
∑N10n

PAcceptance =i(6.42)
log PiN10n,(6.43)

where f (Θi ) is the PMT acceptance correction factor as a function of photon incident angle(Θi ), ri is the distance between the ith PMT and Neut-Fit vertex position, and L is thewater attenuation length. Initial neutron candidates with larger PAcceptance are regarded
as more signal-like candidates.
17. Cherenkov angle likelihood parameter, LCherenkov :Cherenkov photons are distributed around 42 degrees of opening angle from the Comptonscattered electron direction. This variable uses that feature. First, a cone is defined using
three hit PMTs in N10n to define the base, and the Neut-Fit vertex position is considered as
the apex. There are N10n C3 of combinations to select three hit PMTs. The opening angleof the cone for the jth three PMT combination is defined as θj . The probability density
functions for the signal and background assumptions, Pbkg , and Psig , are tabulated as a104

CHAPTER 6. EVENT RECONSTRUCTION

function of θj , N10n , and products of photon detection probabilities defined in Eq. (6.42)
for three hits using a 150-year equivalent exposure of atmospheric neutrino MC events.
Then, the Cherenkov angle likelihood parameter, LCherenkov , is defined as follows:
N10n C3

LCherenkov =∑(log Pbkg (N10n , θj ,j3∏Pk ) − log Psig (N10n , θj ,

k=1

3
∏

)
Pk )

(6.44)

k=1

Initial neutron candidates with negative LCherenkov are regarded as more signal-like candidates.
18∼22. Isotropy parameters, β1∼5 :Isotropy parameters, β’s, are defined to further utilize the spatial distribution of hit PMTs:
N10n10n∑−1 N∑2βl =Pl (cos θij ),N10n (N10n − 1)i=1

(6.45)

j=i+1

where l is the index (l = 1 ∼ 5), θij is the opening angle diﬀerence between the ith andjth hit PMTs, and Pl is lth Legendre polynomial.
23. Distance to the ID wall along Compton-scattered electron direction, towall:
The distance between the Neut-Fit vertex position and the ID wall along the reconstructed
direction is defined as towall. Spatial parameters introduced above have towall dependence, and in order to eﬃciently train the neural network including such dependence,
towall is included as an input variable.
Figure 6.28 (6.29) shows the 23 input variable distributions of initial neutron candidates
associated with the primary FC events in the conventional (additional) fiducial mass region.
All 23 variables are fed into a neural network, which is a machine-learning-based tool usedin various particle physics experiments. The ROOT class TMLP is employed to implement afeed-forward Multi-Layer Perceptron [112]. The neural network has been trained on a 250-year
equivalent exposure of atmospheric neutrino MC events, and another 250-year atmospheric
neutrino MC events have been used for testing the trained neural network.
Neutron Tagging Performance
The resultant distributions of the neural network output are shown in Figures 6.30 for neutron
candidates associated with the primary FC events. Because the separation performance depends
on the value of N10 , the threshold values on the neural network output to select a signal candidate
have been also determined depending on the value of N10 . The threshold value is set to 0.920 for
initial neutron candidates with N10 = 5, 0.908 for initial neutron candidates with N10 = 6, and0.874 with N10 of 7 or more. The final neutron tagging eﬃciency and fake neutron tagging (falsepositive) probability for the primary FC events in the conventional (additional) fiducial mass
region are estimated using a 500-year equivalent exposure of atmospheric neutrino MC events,
and they are 25.9% (22.7%) and 0.016 (0.029) per primary FC event, respectively (Table 6.5).
The reason for the lower neutron tagging eﬃciency in the additional fiducial mass region is similar
to the case in the particle momentum reconstruction. Because neutrons produced by primary
FC events often travel more than 100 cm before thermalizing (the mean value of the neutron
travel distance is about 160 cm), about 5% of neutrons produced in the additional fiducial mass
region escape the ID, resulting in the lower tagging eﬃciency. Furthermore, as shown in the
BSwall and NFwall distributions in Figure 6.29, backgrounds from radioactive products in thedetector components are localized in the region closer to the ID wall. It results in the higher
fake neutron tagging probability in the additional fiducial mass region.

105

400
350

Total MC300

Signal MC
Bckg MC

200
150
100
50
10

15

20000
10000
0
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50

40000
35000
30000
25000
20000
15000
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5000
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20

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60

25000
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1

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1000

1500

8000
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0
0

2

200
150
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20000
18000
16000
14000
12000
10000
8000
6000
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0

(NF-BS)

140
120
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80
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20
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0

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400

20000
15000
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β

4

10000
5000
1

50000
40000
30000
20000
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β

1

30000
25000
20000
15000
10000
5000
0
-4

-2

20000
15000
10000
5000
0.5

β

0

2

4

∆t'rms [nsec]

25000
20000
15000
10000
5000
0
0

500

1000

1500

2000

50000
40000
30000
20000
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Number of Neutron Candidates

Number of Neutron Candidates

CHAPTER 6. EVENT RECONSTRUCTION

40000
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towall [cm]5

Figure 6.28: 23 input variable distributions of initial neutron candidates associated with theprimary FC events in the conventional fiducial mass region. The black dots show the data in
SK-IV. The red histograms show the atmospheric neutrino MC events and are normalized bylivetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). True
neutron candidates (green) and fake neutron candidates (blue) are also separately shown.
10660000Signal MC
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CHAPTER 6. EVENT RECONSTRUCTION

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Figure 6.29: 23 input variable distributions of initial neutron candidates associated with theprimary FC events in the additional fiducial mass region. The black dots show the data in
SK-IV. The red histograms show the atmospheric neutrino MC events and are normalized bylivetime and the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). True
neutron candidates (green) and fake neutron candidates (blue) are also separately shown.
107

CHAPTER 6. EVENT RECONSTRUCTION

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Figure 6.30: Neural network output distributions. The black dots show the data in SK-IV.
The red histograms show the atmospheric neutrino MC events and are normalized by livetimeand the two-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). True neutron
candidates are shown in green. The top (bottom) three plots correspond to neutron candidates
associated with the primary FC events within the conventional (additional) fiducial mass region.
Neutron candidates with N10 = 5 are shown in left, and those with N10 = 6 are shown in middle,
and those with N10 of 7 or more are shown in right. The bold lines and arrows denote the neutron
signal selection thresholds.
Table 6.5: Summary of the neutron tagging performance.
RegionNeutron Tagging Eﬃciency
False-positive Rate
Conventional
25.9%
0.016 per primary event
Additional
22.7%
0.029 per primary event

The neutron capture time and multiplicity distributions are shown in Fig. 6.31. A neutron
capture time constant has been obtained by fitting the neutron capture time distribution toan exponential plus a constant. It is 217.5 ± 8.6 µsec (214.5 ± 23.5 µsec) in the conventional(additional) fiducial mass region for data, while it is 205.7 ± 7.6 µsec (205.0 ± 22.3 µsec) for
MC. They are consistent with the previous result of 204.8 ± 0.5 µsec [113]. The neural network
performance is validated in the following americium-beryllium (Am-Be) source calibration.

6.3.4

Am-Be Calibration

Calibration Setup
An americium-beryllium source is used to take neutron tagging calibration data. An 241 Am
emits an α particle, and it interacts with 9 Be, and eventually emits a neutron as follows:
α + 9 Be → 12 C∗ + n,
12

∗

C →

12

C + γ (4.43 MeV),(6.46)(6.47)

orα + Be → 12 C (ground state) + n.
9108

(6.48)

1600
1400

Data

14000

MC

12000

Number of Events

Number of Tagged Neutrons

CHAPTER 6. EVENT RECONSTRUCTION

1200

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Figure 6.31: Neutron capture time (left) and multiplicity (right) distributions. The top (bottom) two plots correspond to tagged neutrons associated with the primary FC events in theconventional (additional) fiducial mass region. The black points shows the data in SK-IV, andthe red histograms the atmospheric neutrino MC events and are normalized by livetime and thetwo-flavor oscillation probability (∆m2 = 2.5 × 10−3 eV2 , sin2 2θ = 1.0). The blue curves in theleft plots are the best fit functions of the data histograms. t = 0 corresponds to the primary
FC event timing. For the multiplicity distributions, only Sub-GeV primary FC events are used.
Vertical error bars denote the statistical uncertainty.

109

CHAPTER 6. EVENT RECONSTRUCTION

Figure 6.32: The Am-Be source used for the calibration. The source is embedded in a 5 cm
cube of BGO scintillator and it is held in an acrylic case. Taken from [97].
The Am-Be source is embedded in a 5 cm cube of bismuth germanium oxide (BGO) scintillator
as shown in Fig. 6.32. The scintillation light induced by the 4.43 MeV gamma ray in the BGO
scintillator is used for triggering as “a primary FC event”. In this calibration, the recorded
timing width is extended from 535 µsec to 835 µsec. The Am-Be source was placed at three
diﬀerent points in the detector: (35.3, -70.7, 0.0) cm (Center), (35.3, -1201.9, 0.0) cm (Y12),
and (35.3, -70.7, 1500.0) cm (Z15). The selection criteria for the primary event induced by the
scintillation light are diﬀerent depending on the source position, and they are as follows:
Center : 750 < PEtot < 1050 p.e.’s,(6.49)

Y12 : 850 < PEtot < 1150 p.e.’s,(6.50)

Z15 : 900 < PEtot < 1150 p.e.’s,(6.51)

where PEtot is the total deposited charge in the detector in a 1.3 µsec timing window aroundthe trigger timing.
Am-Be Data Analysis
The same neural network algorithm trained on the atmospheric neutrino MC events is applied
to both calibration data and MC. The diﬀerence in the neutron tagging eﬃciencies obtained inthis calibration between data and MC is taken as a systematic uncertainty.
Neutron particle gun MC events have been generated as Am-Be calibration MC using theenergy spectrum of the neutron from the α-Be reaction [114]. After combining with the random
trigger data taken with the Am-Be source inside the detector (as background data), the sameneural network is applied to the generated MC events.
The systematic uncertainties on the initial selection and final neural network selection are
estimated separately. First, the systematic uncertainty on the initial selection is estimated bycomparing the N10 distributions between calibration data and MC. In order to extract N10
distributions of true neutron candidates, the background component is statistically subtracted
from the calibration data. The background component is obtained from the random trigger
data. Figure 6.33 shows the N10 distributions of the calibration data, MC, and background datataken with the Am-Be source at Center. They are after the application of the initial selection(N10 ≥ 5). Since the value of N10 has strong dependence on the photon detection eﬃciency(QE), various neutron MC predictions have been generated by varying the overall QE factor in
SKDETSIM. For each MC prediction, a χ2 test has been conducted on the N10 distribution of
the calibration MC against the N10 distribution of the calibration data after the backgroundsubtraction, which is shown in the right plot in Figure 6.33. Figure 6.34 shows the χ2 vs. relative
QE change distribution. From the fitting result using a quadratic function, the 1 sigma error
on the QE factor is estimated to be a 2.2% change. The 2.2% QE change corresponds to a 1.7%
change in the number of initial neutron candidates. Therefore, the systematic uncertainty of
1.7% is assigned to the initial selection.

110

Number of Neutron Candidates

Number of Neutron Candidates

CHAPTER 6. EVENT RECONSTRUCTION

106
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Figure 6.33: N10 distributions of the calibration data, MC, and background data taken with
the Am-Be source at Center. The black dots in the left plot shows the calibration data, the redhistogram shows the generated neutron MC (green) plus the background data (blue). The black
dots in the right plot shows the calibration data after the subtraction of the background data
(blue). Vertical error bars denote the statistical uncertainty. Entires with N10 of more than 20
are filled in the last bin. The green histograms are the standard MC outputs (without any QEchanges).

300
250

χ2

200

χ2min+1

150
χ2min

100
50
0

0.8 0.85 0.9 0.95

1 1.05 1.1 1.15 1.2

Relative QE Change

Figure 6.34: Chi-square test results as a function of relative QE change. The red curve is thebest fit quadratic function. The χ2 minimum corresponds to a 0.9% QE change, and the χ2 + 1
point corresponds to a 2.2% QE change. The discrepancy between the standard MC predictionand χ2 + 1 point is taken as a systematic uncertainty on the QE factor in MC.

111

CHAPTER 6. EVENT RECONSTRUCTION

Table 6.6: Summary of relative neutron tagging eﬃciency ϵNN /ϵIS in units of %.
Am-Be Position Data MC (MC-Data)/Data
Center
62.7 60.0-4.5
Z15
62.5 67.0
8.8
Y12
68.1 65.9-3.2

As for the neural network selection, the neural network neutron tagging eﬃciencies relative tothe initial selection eﬃciencies are compared between data and MC for all three Am-Be source
points. The neutron capture time distributions after applying the initial selection and after
applying the neural network selection are fitted with an exponential plus a constant. Figure 6.35
shows neutron capture time distributions for Center data and MC. The obtained capture timevalues (τ ’s) are shown in Equations (6.54) ∼ (6.57). The relative neutron tagging eﬃciency(ϵNN /ϵIS ) has been calculated by integrating the best fit exponential functions:∫ t=835 µsec

t=18 µsec fNN (t)ϵNN /ϵIS = ∫ t=835 µsec
,
f
(t)
IS
t=18 µsec()
tfIS,NN (t) = AIS,NN × exp −,τIS,NN

(6.52)(6.53)

τIS,Data = 204.8 ± 4.0 µsec,(6.54)

τIS,MC = 204.7 ± 4.0 µsec,(6.55)

τNN,Data = 209.8 ± 2.8 µsec,(6.56)

τNN,MC = 198.3 ± 2.6 µsec,(6.57)

where A’s are obtained by the fit, IS stands for the initial selection, and NN stands for theneural network selection. The estimated relative neutron tagging eﬃciencies are summarized inTable 6.6. The most discrepant value of 8.8% (Z15) is taken as the uncertainty on the neutral
network selection. The combined systematic uncertainty on the neutron tagging eﬃciency isestimated to be 9.0%. This is used as the source of the systematic uncertainty for the proton
decay searches described in Chapter 7.

112

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CHAPTER 6. EVENT RECONSTRUCTION

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Figure 6.35: Neutron capture time distributions. The top two plots shows events after the
initial selection. The bottom two plots shows events after the neural network selection. The leftplots correspond to the calibration data taken with the Am-Be source at Center, while the rightplots correspond to the neutron MC plus the background data. The blue curves are the best fit
exponential plus constant functions. Vertical error bars denote the statistical uncertainty.

113

Chapter 7

Proton Decay Search Analysis
An analysis of the proton decay search via p → e+ π 0 and p → µ+ π 0 with all SK-I to -IV enlarged fiducial mass FC data, which is described in Chapter 5 and corresponds to 450 kton·years
exposure, is presented in this Chapter. First, the event selection criteria for the search for thesemodes as well as plots of variables used in the analysis are presented. The signal selection
eﬃciency and the expected number of atmospheric neutrino background events for each modeare obtained by applying the same event selection criteria to the signal MC and atmospheric
neutrino MC events, respectively, introduced in Chapter 4. Then, the unblinded data results
are presented. As no proton decay signal has been found, lifetime limits together with the systematic uncertainties on the signal selection eﬃciency and the expected number of atmospheric
neutrino background events are discussed. At last, the implications of the results and future
prospects are discussed.

7.1

Proton Decay Search Performance

7.1.1

Proton Decay Signal Selection Criteria

The event selection criteria for the search for p → e+ π 0 and p → µ+ π 0 are as follows:
C1 Events must pass the FC event selection criteria with a vertex within the fiducial mass
region.
C2 Events must have two or three reconstructed Cherenkov rings.
C3 All rings must be reconstructed as showering (e-like) for p → e+ π 0 , and exactly one ringmust be a non-showering (µ-like) for p → µ+ π 0 .
C4 There must be no tagged Michel electrons for p → e+ π 0 and exactly one for p → µ+ π 0 .
C5 For events with three rings, the reconstructed π 0 mass must be 85 < Mπ0 < 185 MeV/c2 .
C6 The total reconstructed mass must be 800 < Mtot < 1050 MeV/c2 .
C7 The total momentum must be Ptot < 250 MeV/c.
C8 For the SK-IV data, there must be no tagged neutrons.
The vertex resolution for the p → e+ π 0 (p → µ+ π 0 ) MC events including proton decays
within 16 O nuclei (bound proton decays) is 20.1 cm (22.5 cm) in the conventional fiducial mass
region, and it is 26.3 cm (26.6 cm) in the additional.
The distributions of the number of reconstructed rings after applying C1 are shown in
Fig. 7.1. The π FSI eﬀects discussed in Section 4.1 manifest in the number of reconstructedrings. When a neutral pion from the proton decay is absorbed or changes to a charged pion

114

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

with a momentum below the Cherenkov threshold, only a charged lepton from the proton decay
is visible in the detector, and that event is reconstructed as a single-ring event. Since hit PMTs
are more spatially localized in events closer to the ID wall, the two-ring event fraction in the
additional fiducial mass region is higher than that in the conventional fiducial mass region.
The multi-ring PID distributions of the p → e+ π 0 MC, atmospheric neutrino MC events, anddata after applying C1 ∼ C2 are shown in Fig. 7.2. Although the signal selection eﬃciency forboth modes has been improved by about 20% using the updated particle identification algorithm
as described in Section 6.1.3, the PID performance in the additional fiducial mass region is stillinferior to that in the conventional due to fewer PMT hits. As for the data and MC comparison,
good agreement is confirmed with the new expected charge table.
Since there are no particles which decay to a Michel electron in p → e+ π 0 decay events,
events with at least one Michel electron are rejected in the p → e+ π 0 selection. On the other
hand, one Michel electron is expected from the muon decay for the p → µ+ π 0 mode. The
distributions of the number of tagged Michel electrons after applying C1 ∼ C3 are shown in
Fig. 7.3. Since it is easier for muons from the p → µ+ π 0 decays in the additional fiducial mass
region to escape the ID, the Michel electron tagging eﬃciency in the additional fiducial mass
region is lower than that in the conventional.
Criterion C5 is applied to only three-ring events. The π 0 mass is calculated with every pairof rings for the p → e+ π 0 mode. The pair giving the π 0 mass closest to 135 MeV/c2 is considered
to be two gamma rays from the π 0 decay. The π 0 mass distributions of three-ring events for thesignal MC, atmospheric neutrino MC events, and data after applying C1 ∼ C4 are shown in
Fig. 7.4.
The total reconstructed mass and total momentum distributions after applying all the selection cuts except cuts on the plotted variables are shown in Fig. 7.5. The kinematics of boundproton decays which experience π FSI scattering or correlated decay is distorted and is often
reconstructed out of C6 and C7. Furthermore, because of fewer PMT hits and particles escaping the ID, the total mass and total momentum distributions of the proton decay MC events inthe additional fiducial mass region are wider than those in the conventional.
As presented in Section 6.3, the neutron tagging technique is applicable to only SK-IV data.
The neutron emission probability in the proton decay MC events is expected to be less than
10%, while atmospheric neutrino events are often accompanied by neutrons. Figure 7.6 shows
the distributions of the true number of produced neutrons per primary event after applying
C1 ∼ C5. No tagged neutrons are required at C8, and this criterion reduces the atmospheric
neutrino backgrounds by about 50%. The distributions of the number of tagged neutrons after
applying C1 ∼ C5 are shown in Fig. 7.7.

7.1.2

Search Performance

The signal selection eﬃciencies and the expected number of atmospheric neutrino background
events for both the conventional and additional fiducial mass regions are estimated by applying
the same selection criteria to the signal and atmospheric neutrino MC events. Their values
at each event selection step are shown in Figure 7.8. The expected number of atmospheric
neutrino background events is estimated using a 500-year equivalent exposure of atmospheric
neutrino MC events for each SK phase (2000 years in total) and is normalized to detector livetimeand the latest oscillation fit result [64] (oscillation parameters are mentioned in Section 4.2).
The signal selection eﬃciency for both modes in the additional fiducial mass region has been
improved by about 20% by the improvement of the event reconstruction algorithm as mentioned
in Section 6.1.3. However, because of fewer ID PMT hits and escaping particles from the ID,
signal selection eﬃciencies in the additional fiducial mass region are still lower than those in
the conventional, especially in C3 (PID) and C6 (energy leakage due to escaping particles) forp → e+ π 0 , and C3 (PID) and C4 (muon escaping the ID) for p → µ+ π 0 . For the p → e+ π 0(p → µ+ π 0 ) mode, the livetime-weighted total signal selection eﬃciency and the total expected

115

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→e+π0 MC

0.45

0.4

Conventional Region

Free Proton
Bound Proton

0.3

2-ring Fraction
32.5%
3-ring Fraction
37.5%

0.25
0.2
0.15
0.1

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

0.4
0.35

0.05
0
0

Free Proton
Bound Proton

0.3

2-ring Fraction
39.1%
3-ring Fraction
28.2%

0.25
0.2
0.15
0.1
0.05

1

2

3

4

5

0
0

6

1

2

0.4

0.4

Free Proton
Bound Proton

0.3

2-ring Fraction
30.4%
3-ring Fraction
40.4%

0.2
0.15
0.1

Number of Events(Normalized to Unity)

Conventional Region

0.25

4

5

6

p→µ+π0 MC

0.45

0.35

3

Number of Reconstructed Rings

p→µ+π0 MC

0.45
Number of Events(Normalized to Unity)

Additional Region

0.35

Number of Reconstructed Rings

0.05
0
0

p→e+π0 MC

0.45

Additional Region

Free Proton
Bound Proton

0.35
0.3

2-ring Fraction
37.2%
3-ring Fraction
30.9%

0.25
0.2
0.15
0.1
0.05

1

2

3

4

5

0
0

6

Number of Reconstructed Rings

1

2

3

4

5

6

Number of Reconstructed Rings

Figure 7.1: Distributions of the number of reconstructed rings after applying C1. They show
the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV are combined). Free proton decay
events (light color) and bound proton events (dark color, hatched) are stacked. The left plots
correspond to the conventional fiducial mass region, and the right plots to the additional. The
distributions for the data in SK-I to -IV and atmospheric neutrino MC events are shown in
Figure 6.7.

116

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→e+π0 MC
Free Proton
Bound Proton
1st ring
e-like Fraction
97.8%µ -like Fraction
2.2%

0.08
0.06
0.04
0.02

Free Proton
Bound Proton

0.12

2nd ring
e-like Fraction
94.4%µ -like Fraction
5.6%

0.1
0.08
0.06
0.04
0.02

-2

0

2

4

0
-6

6

-4

-2

p→e+π0 MC
0.16
Additional Region

Free Proton
Bound Proton

0.1

1st ring
e-like Fraction
94.1%µ -like Fraction
5.9%

0.08
0.06
0.04
0.02

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

2

4

-2

0

0.1
0.05
-4

-2

2

4

0.14

Free Proton
Bound Proton

0.12

2nd ring
e-like Fraction
91.5%µ -like Fraction
8.5%

0.1
0.08
0.06
0.04

0
-6

6

-4

-2

0

2

4

3rd ring
e-like Fraction
95.5%µ -like Fraction
4.5%

0.15
0.1
0.05
0
-6

6

Free Proton
Bound Proton

0.2

-4

-2

600
400
200
0
-6

-4

-2

0

2

4

6

Data
ATM ν MC
2nd ring

Data
ATM ν MC600

3rd ring

500
400
300
200
100

-4

-2

0

2

4

0
-6

6

-4

-2

150
100

250

150
100
50

0
-6

0
-6

-2

0

2

PID Likelihood

4

6

2nd ring

200

50
-4

100

Data
ATM ν MC

300

Number of Events

1st ring

46µ -likee-likeAdditional Region

Number of Events

Number of Events

200

2p→e+π0µ -like

Additional Region

Data
ATM ν MC0PID Likelihood

p→e+π0e-like

350

250

6

Conventional Region

700

PID Likelihoodµ likee like4µ -likee-like800

Conventional Region

PID Likelihood

3002p→e+π0µ -likee-likeNumber of Events

800

1st ring

Number of Events

Number of Events

1000

Data
ATM ν MC

2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
-6

0

PID Likelihood

p→e+π0Conventional Region

6

Additional Region

PID Likelihoodµ likee like1200

4µ -likee-like0.25

Additional Region

PID Likelihood2p→e+π0 MCµ -likee-like0

PID Likelihood

0.02
-4

3rd ring
e-like Fraction
98.6%µ -like Fraction
1.4%

0.15

0
-6

6

Free Proton
Bound Proton

p→e+π0 MCµ -likee-like0.12

0Conventional Region

0.2

PID Likelihood

Number of Events(Normalized to Unity)-4µ -likee-like0.25

Conventional Region

0.14

PID Likelihood

0-6µ -likee-likeNumber of Events(Normalized to Unity)

Conventional Region

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

0.16

0.1

0
-6

p→e+π0 MC

p→e+π0 MCµ -likee-like0.12

Additional Region

Data
ATM ν MC80

3rd ring

60
40
20

-4

-2

0

2

PID Likelihood

4

6

0
-6

-4

-2

0

2

4

6

PID Likelihood

Figure 7.2: Multi-ring PID distributions after applying C1 ∼ C2. The top six plots show thep → e+ π 0 MC events (SK-I to -IV are combined). Free proton decay events (light color) andbound proton events (dark color, hatched) are stacked. The black dots show the data in SK-I to-IV, and the red and green histograms show the atmospheric neutrino MC events. Atmospheric
neutrino MC is normalized by livetime and includes reweighting to the latest SK oscillation
fit [64]. From left to right, the 1st to 3rd ring distributions are shown. The first and thirdplots from top correspond to the conventional fiducial mass region, and the second from top andbottom plots correspond to the additional. Vertical error bars on the data points denote thestatistical uncertainty.

117

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→e+π0 MC

p→e+π0 MC

1

1
Additional Region

Free Proton
Bound Proton

0.8

0 Michel-e Fraction
99.1%
1 Michel-e Fraction
0.9%

0.6
0.4
0.2
0
0

1

2

3

4

5

6

7

8

9

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

Conventional Region

0 Michel-e Fraction
98.7%
1 Michel-e Fraction
1.3%

0.6
0.4
0.2
0
0

10

Free Proton
Bound Proton

0.8

Number of Tagged Michel Electrons

1

2

3

p→µ+π0 MC
Conventional Region

0.8

Free Proton
Bound Proton

0.7
0.6

0 Michel-e Fraction
11.2%
1 Michel-e Fraction
88.2%

0.5
0.4
0.3
0.2

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

6

7

8

9

Additional Region

0.8

Free Proton
Bound Proton

0.7
0.6

0 Michel-e Fraction
20.8%
1 Michel-e Fraction
78.5%

0.5
0.4
0.3
0.2
0.1

1

2

3

4

5

6

7

8

9

0
0

10

1

2

3

4

5

6

7

8

9

Number of Tagged Michel Electrons

Number of Tagged Michel Electrons

p→e+π0p→e+π0Conventional Region

800

Additional Region

3500

Data
ATM ν MC700

Data
ATM ν MC

Number of Events

4000
3000
2500
2000
1500
1000
500
0
0

10

0.9

0.1

Number of Events

5p→µ+π0 MC

0.9

0
0

4

Number of Tagged Michel Electrons

10

600
500
400
300
200
100

1

2

3

4

5

6

7

8

9

0
0

10

Number of Tagged Michel Electrons

1

2

3

4

5

6

7

8

9

10

Number of Tagged Michel Electrons

p→µ+π0p→µ+π0300
Conventional Region

Additional Region

Data
ATM ν MC

1200

Number of Events

Number of Events

1400

1000
800
600
400

Data
ATM ν MC

200
150
100
50

200
0
0

250

1

2

3

4

5

6

7

8

9

Number of Tagged Michel Electrons

10

0
0

1

2

3

4

5

6

7

8

9

10

Number of Tagged Michel Electrons

Figure 7.3: Distributions of the number of tagged Michel electrons after applying C1 ∼ C3.
The top four plots show the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV are combined). Free
proton decay events (light color) and bound proton events (dark color, hatched) are stacked.
The black dots show the data in SK-I to -IV, and the red and green histograms show theatmospheric neutrino MC events. Atmospheric neutrino MC is normalized by livetime andincludes reweighting to the latest SK oscillation fit [64]. Vertical error bars on the data points
denote the statistical uncertainty. The event rate discrepancy between data and MC in thesecond bin for p → µ+ π 0 is within the systematic uncertainty associated with the physics
modeling described in Section 7.3.1. The left plots correspond to the conventional fiducial mass
region, and the right plots to the additional. 118

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Fitted Peak
135.4 MeV/c2
Fitted Sigma
17.5 MeV/c2

50

100

150

200

250

300

Additional Region

Free Proton
Bound Proton
Fitted Peak
134.9 MeV/c2
Fitted Sigma
21.8 MeV/c2

50

100

150

200

250

Reconstrcued π0 Mass [MeV/c2]

p→µ+π0 MC

p→µ+π0 MC
Conventional Region

Free Proton
Bound Proton
Fitted Peak
134.1 MeV/c2
Fitted Sigma
17.9 MeV/c2

50

100

150

200

250

300

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

Free Proton
Bound Proton
Fitted Peak131.9 MeV/c2
Fitted Sigma
21.2 MeV/c2

50

100

150

200

250

Reconstrcued π0 Mass [MeV/c2]

p→e+π0p→e+π0140

Data
ATM ν MC

120
100
80
60
40
20
50

100

150

200

250

300

25

Additional Region

20

Data
ATM ν MC

10
5
0
0

50

100

150

200

250

Reconstrcued π0 Mass [MeV/c2]

p→µ+π0p→µ+π0Conventional Region

70

Data
ATM ν MC

60
50
40
30
20
10
50

100

150

200

250

Reconstrcued π0 Mass [MeV/c ]
2

300

300

15

Reconstrcued π0 Mass [MeV/c2]

80

300

Additional Region

Reconstrcued π0 Mass [MeV/c2]

Conventional Region

0
0

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

Reconstrcued π0 Mass [MeV/c2]

160

0
0

Number of Events [/10 MeV/c2](Normalized to Unity)

Free Proton
Bound Proton

Number of Events [/10 MeV/c2](Normalized to Unity)

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

Conventional Region

Number of Events [/10 MeV/c2]

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

p→e+π0 MC

Number of Events [/10 MeV/c2]

Number of Events [/10 MeV/c2]

Number of Events [/10 MeV/c2]

Number of Events [/10 MeV/c2](Normalized to Unity)

Number of Events [/10 MeV/c2](Normalized to Unity)p→e+π0 MC

300

Additional Region

12

Data
ATM ν MC

10
8
6
4
2
0
0

50

100

150

200

250

300

Reconstrcued π0 Mass [MeV/c2]

Figure 7.4: Neutral pion mass distributions of three-ring events after applying C1 ∼ C4. The
top four plots show the p → e+ π 0 and p → µ+ π 0 MC events (SK-I to -IV are combined). Free
proton decay events (light color) and bound proton events (dark color, hatched) are stacked.
Gaussian fits have been used to determine the π 0 mass peak and width for the signal MC
events. The black dots show the data in SK-I to -IV, and the red and green histograms show
the atmospheric neutrino MC events. Atmospheric neutrino MC is normalized by livetime andincludes reweighting to the latest SK oscillation fit [64]. Vertical error bars on the data points
denote the statistical uncertainty. The left plots correspond to the conventional fiducial mass
region, and the right plots to the additional.
119CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→e+π0
103

102

102

10

10

1

1

10-1

10-1

10-2

10-2

Number of Events

103

102

0

200

400

600

800

1000
2

Total Mass [MeV/c ]

10-3
1200
0
102

10

10

1

1

10-1

10-1

10-2

10-2

10-30

200

400

600

800

1000

10-3

0

2

Conventional Region

DATA SKI~IV
ATM ν MCFree Proton
Bound Proton
200

400

600
800
1000
Additional
RegionTotal Momentum [MeV/c]

DATA SKI~IV
ATM ν MCFree Proton
Bound Proton

200

400

600

800

1000

Total Momentum [MeV/c]

Total Mass [MeV/c ]p→µ+π0
103

102

102

10

10

1

1

10-1

10-1

10-2

10-2

Number of Events

103

102

0

200

400

600

800

1000
2

Total Mass [MeV/c ]

10-3
1200
0
102

10

10

1

1

10-1

10-1

10-2

10-2

10-30

200

400

600

800

1000

10-3

0

2

Conventional Region

DATA SKI~IV
ATM ν MCFree Proton
Bound Proton
200

400

600
800
1000
Additional
RegionTotal Momentum [MeV/c]

DATA SKI~IV
ATM ν MCFree Proton
Bound Proton

200

400

600

800

1000

Total Momentum [MeV/c]

Total Mass [MeV/c ]Figure 7.5: Reconstructed total mass and total momentum distributions for p → e+ π 0 (topplot) and p → µ+ π 0 (bottom plot) after all the selection cuts except those on the plottedvariables. In each plot, the top panels show the conventional, and the bottom panels show theadditional fiducial mass region. The left panels show the reconstructed total mass, and the rightpanels show the reconstructed total momentum distributions. The signal MC histograms arestacked, showing free proton decay events (light color) and bound proton decay events (darkcolor, hatched), and they are normalized by the 90% C.L. upper limit on the signal derived inthis work. Atmospheric neutrino MC (red and green) is normalized by livetime and includes
reweighting to the latest SK oscillation fit [64]. Vertical error bars on the data points denotethe statistical uncertainty. Bold lines and arrows show the signal region.
120

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→µ+π0 MC

p→e+π0 MC
0.9

0.9
Enlarged Region

Free Proton
Bound Proton

0.7
0.6
0.5
0.4
0.3
0.2

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

Enlarged Region

0.8

0.1
0
0

1

2

3

4

5

6

7

8

9

0.6
0.5
0.4
0.3
0.2
0
0

10

1

2

3

4

5

6

7

8

9

True Number of Produced Neutrons

True Number of Produced Neutrons

p→e+π0p→µ+π0250

Enlarged Region

ATM ν MC

Number of Events

Number of Events

Free Proton
Bound Proton

0.7

0.1

1000
800
600
400

10

Enlarged Region

ATM ν MC

200
150
100
50

200
0
0

0.8

2

4

6

8

0
0

10

True Number of Produced Neutrons

2

4

6

8

10

True Number of Produced Neutrons

Figure 7.6: Distributions of the true number of produced neutrons after applying C1 ∼ C5.
All plots show the enlarged fiducial mass region (100 cm < dwall). The top two plots show the
SK-IV p → e+ π 0 (left) and p → µ+ π 0 (right) MC events. Free proton decay events (light color)and bound proton events (dark color, hatched) are stacked. As discussed in Section 4.1, neutrons
are emitted only in bound proton decay events. Atmospheric neutrino MC is normalized bylivetime and includes reweighting to the latest SK oscillation fit [64] and is shown in the bottom
two plots.

121

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

p→e+π0 MC
0.9

Conventional Region

Free Proton
Bound Proton

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

1

2

3

4

5

6

7

8

9

Number of Events(Normalized to Unity)

Number of Events(Normalized to Unity)

0.9

p→e+π0 MC

10Additional Region

Free Proton
Bound Proton

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

1

Number of Tagged Neutrons
p→µ+π0 MC

1

2

3

4

5

6

7

0.4
0.2

2

3

4

5

6

8

9

0.4
0.2

1

2

3

4

5

6

p→e+π0Conventional Region

Data
ATM ν MC

800
600
400

9

300

Additional Region

250

Data
ATM ν MC

10

200
150
100
50

200
1

2

3

4

5

6

7

8

9

0
0

10

1

2

3

4

5

6

7

8

Number of Tagged Neutrons

Number of Tagged Neutrons

p→µ+π0p→µ+π0

500

9

10

100
Conventional Region

Additional Region

Data
ATM ν MC

400

Number of Events

Number of Events

8p→e+π0

1000

300
200
100
0
0

7

Number of Tagged Neutrons

1200

0
0

0.6

0
0

10

Free Proton
Bound Proton

0.8

Number of Tagged Neutrons

1400

Number of Events

7

Number of Events(Normalized to Unity)

0.6

1

10

Additional Region

Free Proton
Bound Proton

Number of Events

Number of Events(Normalized to Unity)

Conventional Region009p→µ+π0 MC

1

0.8

8

Number of Tagged Neutrons

Data
ATM ν MC

80
60
40
20

1

2

3

4

5

6

7

8

Number of Tagged Neutrons

9

10

0
0

1

2

3

4

5

6

7

8

9

10

Number of Tagged Neutrons

Figure 7.7: Distributions of the number of tagged neutrons after applying C1 ∼ C5. The top
four plots show the SK-IV p → e+ π 0 and p → µ+ π 0 MC events. Free proton decay events (lightcolor) and bound proton events (dark color, hatched) are stacked. The black dots show thedata in SK-IV, and the red and green histograms show the atmospheric neutrino MC events.
Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK
oscillation fit [64]. Vertical error bars on the data points denote the statistical uncertainty. The
overall event rate discrepancy between data and MC for p → µ+ π 0 is within the systematic
uncertainty associated with the physics modeling described in Section 7.3.1. The left plots
correspond to the conventional fiducial mass region, and the right plots to the additional.
122

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Table 7.1: Summary of the livetime-weighted total signal selection eﬃciency and the total
expected number of background events. The “Enlarged” row shows results for the enlarged
27.2 kton fiducial mass region. Detector phase by phase diﬀerence is shown in Table 7.3.
Livetime-weighted total
Total expected number ofRegionsignal selection eﬃciency (%)
background events (events)p → e+ π 0
Conventional
39.8
0.49
Additional
25.8
0.10
Enlargedp → µ+ π 0
Conventional
Additional

37.6

0.59

36.3
25.2

0.74
0.19

Enlarged

34.5

0.94

Table 7.2: Breakdown of interaction modes for background events remaining in the signal
region for the p → e+ π 0 and p → µ+ π 0 searches in units of %. Here, CC and NC stand forcharged-current and neutral-current, respectively, and QE, 1π and DIS stand for quasi-elastic
scattering, single π production and deep inelastic scattering, respectively.
Region
CCQE
CC1π
CCDIS
NC1π
NCDIS
+
0
p→e π
Conventional
18
63
10
1
8
Additional
21
62
14
0
3
p → µ+ π 0
Conventional
13
65
18
0
4
Additional
7
60
17
0
16

number of background events in the additional fiducial mass region are 25.8% (25.2%) and 0.10
(0.19), respectively, while in the conventional fiducial mass region, they are 39.8% (36.3%) and
0.49 (0.74). They are summarized in Table 7.3 including the performance in the combined(enlarged) fiducial mass region.
The incoming neutrino energy distributions of the remaining backgrounds are shown in
Fig. 7.9. Atmospheric neutrinos of about 1 to 3 GeV are the main background component inboth fiducial mass regions. A breakdown of the remaining atmospheric neutrino background
events by neutrino interaction mode is shown in Table 7.2. As mentioned in Section 4.2, thedominant interaction mode is the charged current single π production interaction, and there areno significant diﬀerences between the two fiducial mass regions. The expected background rate
for p → e+ π 0 without C8 is 1.83 /Mt·years and is consistent with previous estimations by the+0.45
K2K 1 kton water Cherenkov detector of 1.63+0.42−0.33 (stat)−0.51 (sys) /Mt·years [115].
In order to improve the search sensitivity, the signal region is further divided into two
regions: a lower total momentum region (Ptot < 100 MeV/c) and a higher total momentum
region (100 ≤ Ptot < 250 MeV/c). The final signal selection eﬃciencies and expected numberof atmospheric neutrino background events for each SK phase are summarized in Table 7.3.
Figure 7.10 shows the reconstructed total mass vs. total momentum distributions for the signal
MC, atmospheric neutrino MC and all data from SK-I to -IV after all the selection cuts except
the cuts on the plotted variables. In the lower Ptot signal region, most free proton decay events
are reconstructed, and a nearly background-free search can be performed in both fiducial mass
regions. Bound proton decays reconstructed outside the signal region in Fig. 7.10 are mainly
due to the eﬀects of π FSI scattering in the remaining nucleus and correlated decay.

123CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

50

Conventional Region
p→e+π0 MC

20
FCF

V

4

102

Additional Region
p→e+π0 MC

Num

p
N
P
Mic
T
T
F
hel- i0 Mas otal M otal M eutron CFV
ber ID
s
e
ass
om
of R
Tag
e nt
ing
um
s

Num

P
ber ID
of R
in

Mic
he

l-e

gs

4

10
Number of Events

Signal Selection Efficiency [%]

102

pi0

N
Mas Total M Total M eutro
n Ta
s
ass
om
e nt
g
um

10

103

Number of Events

Signal Selection Efficiency [%]p→e+π0

103

102

102

10

DATA SKI~IV
ATM ν MC

1

10-1

10

DATA SKI~IV
ATM ν MC

1

10-1

-2
10-2 C1 C2 C3 C4 C5 C6 C7 10
C8 C1 C2 C3 C4 C5 C6 C7 C8Event Selection

50

Conventional Regionp→µ +π0 MC

20
FCF

V

Number of Events

104

1

10

Additional Regionp→µ +π0 MC

p
N
P
Mic
T
T
F
hel- i0 Mas otal M otal M eutron CFV
ber ID
s
e
ass
om
of R
Tag
e nt
ing
um
s

104

Num

p
N
P
Mic
T
T
hel- i0 Mas otal M otal M eutron
ber ID
s
e
ass
om
of R
Tag
e nt
ing
um
s

103

102

-1

102

Num

103

10

Signal Selection Efficiency [%]102

Number of Events

Signal Selection Efficiency [%]p→µ+π0102

DATA SKI~IV
ATM ν MC10
1DATA SKI~IV
ATM ν MC

-1

10

-2
10-2 C1 C2 C3 C4 C5 C6 C7 10
C8 C1 C2 C3 C4 C5 C6 C7 C8Event Selection
Figure 7.8: The signal selection eﬃciencies (blue and magenta dots) and the expected numberof atmospheric neutrino background events (red and green histograms) and data candidates(black dots) for p → e+ π 0 (top plot) and p → µ+ π 0 (bottom plot). Vertical error bars on thedata points denote the statistical uncertainty. In each plot, the left panel corresponds to theconventional fiducial mass region and the right panel to the additional. Atmospheric neutrino
MC is normalized by livetime and includes reweighting to the latest SK oscillation fit [64].
Vertical bands on the atmospheric neutrino MC points denote the sum in quadrature of thesystematic uncertainties associated with the physics modeling described in Section 7.3.1. The
combined data from SK-I to -IV is shown along with the combined signal and background MC.
124

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Conventional Region

ATM ν MC

2000

4000

6000

8000

Additional Region

0.05

ATM ν MC

0.04
0.03
0.02
0.01
0
0

10000

p→e+π0

0.06

2000

4000

6000

8000

True Neutrino Energy [MeV]True Neutrino Energy [MeV]p→µ+π0p→µ+π00.3

Conventional Region

ATM ν MC

0.25
0.2
0.15
0.1
0.05
0
0

Number of Events [/400 MeV]

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

2000

4000

6000

8000

Number of Events [/400 MeV]

Number of Events [/400 MeV]

Number of Events [/400 MeV]

p→e+π0Additional Region

0.1

ATM ν MC

0.08
0.06
0.04
0.02
0
0

10000

True Neutrino Energy [MeV]

10000

2000

4000

6000

8000

10000

True Neutrino Energy [MeV]

Figure 7.9: Incoming neutrino energy distributions of the remaining backgrounds (SK-I to-IV are combined). The upper (lower) two plots show the atmospheric neutrino MC eventsin the signal region for p → e+ π 0 (p → µ+ π 0 ). These histograms are normalized by livetime
and include reweighting to the latest SK oscillation fit [64]. The left plots correspond to theconventional fiducial mass region, and the right plots to the additional.

125

18.3±1.7
20.0±3.3(Lower)(Upper)Enlarged126

16.0±1.5
16.0±2.9(Lower)(Upper)Enlarged

Additional17.0±1.6
16.7±3.1
11.1±1.5
12.0±2.3(Lower)(Upper)(Lower)(Upper)Conventionalp → µ+ π 0

Additional19.9±1.921.0±3.5
9.6±1.514.5±2.9(Lower)(Upper)(Lower)(Upper)14.9±1.415.8±2.7

16.2±1.5
16.5±2.88.8±1.2
12.6±2.3

16.6±1.719.4±3.0

18.1±1.8
20.2±3.2
8.8±1.4
14.9±2.7

16.4±1.5
16.1±2.917.5±1.6
16.8±3.0
11.0±1.4
12.5±2.2

18.7±1.7
20.3±3.3

20.3±1.8
21.1±3.5
9.9±1.7
16.4±2.818.7±1.718.2±3.4

19.9±1.918.9±3.712.7±1.2
14.7±2.6

18.2±1.519.2±3.1

19.6±1.6
19.8±3.3
11.0±1.515.9±2.6

Signal Selection Eﬃciency (%)
I
II
III
IV

Conventional

Search Mode
Regionp → e+ π 00.03±0.02
0.21±0.07

0.03±0.02
0.19±0.06< 0.010.02±0.02

0.01±0.01
0.15±0.06< 0.010.13±0.05
0.01±0.01
0.02±0.01I

0.01±0.01
0.14±0.04< 0.010.10±0.04< 0.010.03±0.01

0.01±0.01
0.11±0.04

0.01±0.01
0.11±0.04< 0.01< 0.010.01±0.01
0.08±0.03

0.01±0.01
0.06±0.02< 0.010.02±0.01< 0.010.07±0.03< 0.010.05±0.02< 0.010.02±0.01< 0.010.46±0.15< 0.010.34±0.12< 0.010.12±0.06< 0.010.25±0.11< 0.010.20±0.09< 0.010.05±0.04

Atmospheric ν Background (events)
II
III
IV

0.05±0.03
0.89±0.29

0.04±0.03
0.70±0.24
0.01±0.01
0.19±0.08

0.02±0.02
0.57±0.23

0.01±0.01
0.48±0.21
0.01±0.01
0.09±0.05

I to IV

0
0

0
0
0
0

0
0

0
0
0
0

0
0

0
0
0
0

0
0

0
0
0
0

0
0

0
0
0
0

0
0

0
0
0
0

0
1

0
1
0
0

0
0

0
0
0
0

Candidate (events)
I II IIIIV

Table 7.3: Summary of the signal selection eﬃciencies, the expected number of background events and the number of data candidates for 92.1
(19.3), 49.1 (10.3), 31.9 (6.7) and 199.5 (41.8) kton·years exposures from the conventional (additional) fiducial mass region of SK-I, -II, -III,and -IV, respectively. The “Enlarged” row shows results for the enlarged 27.2 kton fiducial mass region. Here “Lower” and “Upper” indicate
Ptot < 100 MeV/c and 100 ≤ Ptot < 250 MeV/c, respectively. Errors in the signal selection eﬃciency and the expected number of background
events are the quadratic sum of MC statistical error and systematic errors.

CHAPTER 7. PROTON DECAY SEARCH ANALYSISCHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Figure 7.10: Reconstructed total mass shown against the total momentum distributions for
p → e+ π 0 (top) and p → µ+ π 0 (bottom) after all cuts except those on these variables. In eachplot, the top panels correspond to the conventional and the bottom panels correspond to theadditional fiducial mass region. The left panels show the signal MC (SK-I to -IV are combined),
where lighter colors show free proton decays and dark colors show bound proton decays. The
middle panels show the 2000-year equivalent atmospheric neutrino MC. The right panels show
all the combined data from SK-I to -IV. The black box shows the signal region, and for the
middle and right panels, the markers in the signal region have been enlarged for visibility.

127

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Table 7.4: Summary of the search sensitivities (expected lifetime limit at 90% confidence level).
“Conventional” denotes the conventional fiducial mass case (22.5 kton, 372 kton·years exposure),and “Enlarged” denotes the enlarged fiducial mass case (27.2 kton, 450 kton·years exposure).
Regionp → e+ π 0
p → µ+ π 0
Conventional 1.7 × 1034 years
1.4 × 1034 years
34
Enlarged
1.9 × 10 years
1.6 × 1034 years

7.1.3

Search Sensitivity Improvement by Enlarging the Fiducial Mass

The search sensitivity (expected lifetime limit at 90% confidence level, τexp ) is calculated asfollows:
Γexp =∞ −b n
∑
e b

n!

n=0

τexp /B =

1
Γexp

,

× Γlimit (b, n),

(7.1)
(7.2)

where Γexp is the expected decay rate, b is the expected number of background events, n is thenumber of candidate events, and B is the branching ratio of a particular decay mode. Here,Γlimit (b, n) is an upper limit of the decay rate with a candidate of n and a background of b, and thederivation of Γlimit (b, n) is detailed in Section 7.4. Using the signal selection eﬃciencies, expected
number of backgrounds, exposure in Table 7.3, and their systematic uncertainties described in
Section 7.3, the search sensitivity is calculated for both the conventional fiducial mass (22.5 kton,
372 kton·years exposure) case and enlarged (27.2 kton, 450 kton·years exposure) case. Although
the signal selection eﬃciencies in the additional fiducial mass region are lower than those in theconventional fiducial mass region, the search sensitivity for p → e+ π 0 (p → µ+ π 0 ) is improved
from 1.7 × 1034 years (1.4 × 1034 years) to 1.9 × 1034 years (1.6 × 1034 years) at 90% confidence
level by enlarging the fiducial mass. For both modes, the search sensitivity improves by about
12% (Table 7.4).

7.2

Search Results

By applying the same proton decay selection criteria to a 450 kton·years exposure of the
SK-I to -IV enlarged fiducial mass data, proton decay search results have been obtained. In the
p → e+ π 0 mode, no signal candidates have been observed in either the conventional or additional
fiducial mass region. On the other hand, a single candidate is found for the p → µ+ π 0 mode,
which is the same candidate event reported in the last published analysis [27]. The one candidate
is in the higher Ptot signal region and the conventional fiducial mass region. No new candidates
have been observed in the updated dataset. The number of observed candidates is consistent
with the total atmospheric neutrino backgrounds, 0.59 events for p → e+ π 0 , and 0.94 events
for p → µ+ π 0 . For p → µ+ π 0 , the Poisson probability to observe 1 event or more with a meanvalue of 0.94 is 61%. The data distributions are consistent with the atmospheric neutrino MC
predictions. The event rate discrepancy between data and MC for the p → µ+ π 0 mode is coveredby the systematic uncertainties associated with the physics modeling described in Section 7.3.1.
The event display of the single candidate event for the p → µ+ π 0 mode is shown in Fig. 7.11.
It is a two-ring event, and there is one µ-like ring with a momentum of 559 MeV/c and one
e-like ring with a momentum of 377 MeV/c. The distance between the vertex position and theclosest ID wall is 458 cm, in the conventional fiducial mass region. The reconstructed total massis 917 MeV/c2 , and the reconstructed total momentum is 233 MeV/c, in the higher Ptot signal
region.

128

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Super-Kamiokande IV
Run 70690 Sub 62 Event 15256253
12-11-30:09:40:13
Inner: 2504 hits, 7418 pe
Outer: 1 hits, 1 pe
Trigger: 0x10000007
D_wall: 458.2 cm
Evis: 769.7 MeVCharge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7< 0.2
350
1 mu-e
decay

280
210
140
70
0
0

500

1000

1500

2000

Times (ns)Figure 7.11: Run:70690, SubRun:62, Event:15256253. Event display of the p → µ+ π 0 candidate
event. Two-ring event. The orange circle denote the µ-like ring and the cyan circle denote the
e-like ring.

129

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

7.3

Systematic Uncertainty

Systematic uncertainties for the signal selection eﬃciencies and the expected number ofatmospheric neutrino events have been estimated. Uncertainties on the expected number ofatmospheric neutrino events have been evaluated combining the higher and lower Ptot signal
regions because there are only a few events remaining in the lower Ptot signal region.
Uncertainties of the physics modeling as well as the reconstruction performance are considered. As systematic uncertainties associated with the physics modeling, the following three
items are taken into account for the signal selection eﬃciency:• correlated decay,• the Fermi momentum,• π FSI,and the following three are for the expected number of atmospheric neutrino events:• neutrino flux,• neutrino interaction,• π FSI and SI.
Since particles in the final state of proton decay p → e+ π 0 and p → µ+ π 0 events are gamma
rays and a charged lepton, the hadron secondary interaction in water (SI) is not considered forthe signal selection eﬃciency. For the reconstruction part, systematic uncertainties associatedwith the following items are commonly considered for both the signal selection eﬃciencies andexpected number of atmospheric neutrino events:• fiducial volume,• vertex position,• number of identified Cherenkov rings,• identified particle type,• number of tagged Michel electrons,• energy scale,• non-uniformity of the energy scale,• number of tagged neutrons.
Unless otherwise noted, the systematic uncertainty for each item is evaluated as follows:{ ϵ −ϵsys
def,(signal selection eﬃciency)
systematic uncertainty = Bkgϵdefsys −Bkgdef, (expected number of atmospheric neutrino events)
Bkgdef(7.3)
where ϵdef (Bkgdef ) is the central value of the signal selection eﬃciency (expected number of atmospheric neutrino events) shown in Table 7.3, and ϵsys (Bkgsys ) is the changed signal selection
eﬃciency (expected number of atmospheric neutrino events) by introducing the source uncertainty of each item. The systematic uncertainties are estimated in each (either conventional,
additional, or enlarged) fiducial mass region separately. In the following, the evaluation method
for each item is described, and a summary of the evaluated systematic uncertainties is presented
in Section 7.3.3.

130

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

7.3.1

Physics ModelingFirst, the systematic uncertainties associated with the physics modeling, which is introducedin Chapter 4, for the signal selection eﬃciency are discussed, and then those for the atmospheric
neutrino events are described.
Correlated Decay
The probability of the correlated decay in proton decays within 16 O is predicted to be about
10% [46]. The changed signal selection eﬃciency is estimated by reweighting the correlated
decay probability to 0% or 20%:ϵsys =

nfree (NS + NP ∓ αNcorr ) (nS + nP )
ncorr
+
×
+ (1 ± α) ×,
Ntot
(NS + NP )
Ntot
Ntot

(7.4)

where n is the number of signal MC events passing the signal selection criteria, N is the numberof generated proton decay MC events in the fiducial volume, “free” stands for free proton decays,
S (P ) stands for proton decays in the S (P ) state in 16 O, and “corr” stands for correlated decays.
Using this notation, the central value of the signal selection eﬃciency is expressed as:
ϵdef =(nfree + nS + nP + ncorr )
.
Ntot

(7.5)

A factor of α is taken to be 1 (the correlated decay probability is twice) or −1 (no correlated
P ∓αNcorr )decays), and a factor of (NS +N
is introduced to conserve the total number of generated(NS +NP )events. The more discrepant ϵsys between the α = 1 and α = −1 cases is used for the uncertainty
estimation.
The Fermi Momentum
The diﬀerence in the initial proton momentum distributions between the proton decay MC
and atmospheric neutrino (NEUT) MC is considered to be the source of this item. The twoplots are shown in Fig. 4.10. The changed signal selection eﬃciency is calculated by reweighting
to fit the initial proton momentum distribution to that in NEUT:
NNEUT,infree ∑ ni
+
×
,
Ntot
Ntot
NPDK,i11

ϵsys =(7.6)

i=1

where i is the index of each initial momentum bin, NPDK,i (NNEUT,i ) is the number of generated
events with an initial proton momentum of between (25 × (i − 1)) MeV/c and (25 × i) MeV/cin the proton decay (NEUT) MC. In order to conserve the total number of generated events,
NNEUT,i is normalized to NPDK,i :
11
∑
i=1

NPDK,i =11∑

NNEUT,i .

(7.7)

i=1

Pion FSI and SI
The π FSI and SI probabilities in MC are calculated with six internal parameters, and they
are determined based on π scattering experiment results as described in Section 4.1. For thesix internal parameters, 16 diﬀerent parameter sets are prepared so that the possible parameter
space, which is suggested by the π scattering experiments, can be covered [49]. The signal
selection eﬃciency (ϵsys ) and expected number of atmospheric neutrino backgrounds (Bkgsys )are recalculated based on diﬀerent π FSI and SI probabilities using the 16 parameter sets. For
this item, the standard deviation of 16 ϵsys ’s and Bkgsys ’s over each mean value is assigned as
the uncertainty.

131

Relative Uncertainty

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS
0.30

δ tot
δπ
δK
δσ
δ air

0.25
0.20
0.15
0.10
0.05
0

0

10

10

1

10

2

10
E ν (GeV)

3

Figure 7.12: Uncertainty on the absolute flux normalization as a function of neutrino energy.
The black line shows the total uncertainty. The red, purple, green, and blue lines show the uncertainty associated with the π production modeling, K production modeling, hadronic interaction
cross-sections, and atmospheric density profile, respectively. Taken from [54].
Neutrino Flux
The uncertainty on the atmospheric neutrino flux is divided into various components and issummarized in Table 7.5. The dominant uncertainty source is the absolute flux normalization.
It is provided by [54] and is the sum of the uncertainties on the π, K production modeling(δπ , δK ), hadronic interaction cross-sections (δσ ), and atmospheric density profile (δair ). The
absolute normalization uncertainty as a function of neutrino energy is shown in Fig. 7.12.
Neutrino Interaction
The uncertainty on the atmospheric neutrino interaction (cross-section) is also divided into
diﬀerent items depending on the interaction mode. The estimated uncertainties are summarizedin Table 7.6.
The dominant uncertainty source is the single meson production interaction as is expectedfrom the interaction mode breakdown of the remaining backgrounds shown in Table 7.2. This isestimated by varying the new form factors, which are introduced in Section 4.3.3, by their error
size. Furthermore, the cross-section ratios ν̄/ν and (π 0 production)/(π ± production) are taken
into account by comparing the NEUT model and another model by E. Hernández et al. [116].
The sub-dominant component is the quasi-elastic scattering. The uncertainties on the absolute total cross-section as well as the cross-section ratios ν̄/ν and (νµ + ν̄µ )/(νe + ν̄e ) are
estimated from the diﬀerence between the NEUT prediction and another model prediction by
J. Nieves et al. [117]. Besides, an uncertainty of 20% is assigned to the axial vector mass.

7.3.2

Reconstruction

Fiducial Volume
The uncertainty associated with the fiducial volume is estimated to be 1.2% by comparing
the number of events between data and MC. For this item, FC Sub-GeV multi-ring events areused. The number of atmospheric neutrino MC events within the conventional fiducial volume(200 cm < dwall) is normalized to that of data for this calculation. The systematic uncertainty
for this item is defined to be the diﬀerence in the number of events between data and normalized132

Table 7.5: Summary of systematic uncertainties on the expected number of atmospheric neutrino background events for each fiducial mass regionin units of %. They are associated with the atmospheric neutrino flux model. The “Enlarged” row shows the result for the combination of the two
fiducial mass regions.
Absolute
ν and ν̄Up-down K-π
Neutrino
Solar
Relative Normalization Matter
Total
RegionNormalization Flux Ratios
Ratio
Ratio Path Length Activity
in Multi-GeV Region
Eﬀect
p → e+ π 0
Conventional
7.0
2.2
0.1
0.2
< 0.1
0.5
< 0.1
< 0.1
7.3
Additional
7.0
1.7
0.4
0.3
< 0.1
0.3
< 0.1
< 0.1
7.2
Enlarged
7.0
2.2
0.2
0.2
< 0.1
0.4
< 0.1
< 0.1
7.3
p → µ+ π 0
Conventional
6.8
1.9
0.1
0.4
0.4
0.4
1.5
0.1
7.2
Additional
7.0
2.2
0.3
0.4
0.5
0.4
1.2
0.1
7.3
Enlarged
6.9
1.9
0.1
0.4
0.4
0.4
1.5
0.1
7.3

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

133

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Table 7.6: Summary of systematic uncertainties on the expected number of atmospheric neutrino background events for each fiducial mass region in units of %. They are associated with
the neutrino interaction model (cross-section). The “Enlarged” row shows the result for the
combination of the two fiducial mass regions.
Quasi-elastic Single Meson Deep Inelastic CC and NC
Total
RegionScattering
Production
Scattering
Ratio
p → e+ π 0
Conventional
11.7
16.7
5.2
1.9
21.2
17.3
Additional
10.4
12.6
5.8
0.6
Enlarged
11.6
15.1
5.3
1.6
19.8
p → µ+ π 0
Conventional
6.7
16.9
5.6
0.9
19.0
16.8
Additional
3.6
13.7
8.5
3.2
Enlarged
6.1
16.1
6.0
1.3
18.3

MC within the enlarged fiducial volume (100 cm < dwall):systematic uncertantiyfiducail volume =NNormalized MC − NData
,
NData

(7.8)

where N is the number of events within the enlarged fiducial volume. The evaluated systematic
uncertainty is 1.2%, and Figure 6.3 confirms good agreement between data and MC.
Vertex Position
A systematic vertex reconstruction bias between data and MC does not manifest in theoverall vertex distribution such as Fig. 6.3. Since the vertex reconstruction step is the firstreconstruction step (Section 6.1), this possible fitting bias aﬀects later reconstruction results.
In order to estimate impacts of the vertex fit bias, an alternative reconstruction tool, in which
an artificial vertex shift of ±20 cm along the most energetic ring direction is introduced after the vertex reconstruction calculation, has been applied to the same proton decay MC andatmospheric neutrino MC events. 20 cm is a comparable size to the accuracy of the timing
calibration (Section 3.3.5) and vertex resolution for proton decay events. Then, ϵsys and Bkgsys
are estimated by applying the same proton decay event selection criteria, which are presented
in Section 7.1.1. The more discrepant ϵsys (Bkgsys ) between the +20 cm shift and −20 cm shiftcases is taken as the uncertainty.
Ring Counting and Particle Identification
The source uncertainties for ring counting and particle identification are evaluated by comparing their likelihood distributions between data and MC such as shown in Figures 6.8 and 7.2.
FC Sub-GeV multi-ring events are used for these items again. The likelihood distribution of
MC (L) is fitted to that of data by shifting and smearing as:
L′ = a × L + b,

(7.9)

where a is a scale parameter, b is a shift parameter, and L (L′ ) stands for either ring counting
likelihood or multi-ring PID likelihood. A log-likelihood shape test [118] has been conducted
to search for the best-fit parameter pair, (abest , bbest ), for each SK phase and fiducial mass
region. By artificially shifting and smearing the likelihood values with (abest , bbest ), ϵsys andBkgsys are estimated. As for the uncertainty associated with ring counting, similarly to theuncertainty associated with the vertex position, the best-fit two parameters are introduced in134CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

the reconstruction tool, and the same proton decay MC and atmospheric neutrino MC events
have been reprocessed because the ring counting result also aﬀects later reconstruction outputs.
When propagating the best-fit parameters, those obtained in the conventional and additional
fiducial mass region are applied to the proton decay and atmospheric neutrino MC events within
the conventional and additional fiducial mass region, respectively. Then, combining the two
results gives the systematic uncertainty in the enlarged fiducial mass region.
Michel Electron Tagging
Atmospheric neutrino MC and FC data events passing C1 ∼ C3 are used (shown in Figure 7.3). After normalizing the number of MC events to that of data, the number of events inthe no (one) Michel electron bin is compared between data and normalized MC for p → e+ π 0(p → µ+ π 0 ). This is done for each fiducial mass region separately, and the discrepancy between
data and normalized MC is assigned as the uncertainty. Furthermore, the uncertainties for (SK-I
to -III) and SK-IV are separately estimated because the Michel electron tagging performance is
diﬀerent among the SK phases.
Energy Scale
As the source uncertainty (δE), the sum in quadrature of the absolute energy scale (Table 6.2)
and the time variation of the energy scale (Table 6.3) is used. By scaling the reconstructed
π 0 mass (Mπ0 ), total mass (Mtot ), and total momentum (Ptot ) by ±δE, ϵsys and Bkgsys are
estimated for each SK phase and fiducial mass region, where the value of ±δE depends on the
SK phase and fiducial mass region as shown in Tables 6.2 and 6.3. In a similar manner to theuncertainty associated with ring counting and particle identification, combining the two fiducial
mass results gives the systematic uncertainty in the enlarged fiducial mass region. The more
discrepant ϵsys (Bkgsys ) between the +δE scale and −δE scale cases is taken as the uncertainty.
Non-uniformity of the Energy Scale
The source uncertainty (δEnonuni ) for this item is the zenith-angle-dependent non-uniformityof the energy scale (Table 6.4). Since the target proton decays produce back-to-back event
topologies, the non-uniformity of the energy scale aﬀects the reconstructed total momentum(Ptot ). By scaling it by ±2δEnonuni , ϵsys and Bkgsys are estimated for each SK phase and fiducial
mass region, where the value of ±δEnonuni depends on the SK phase and fiducial mass region
as shown in Table 6.4. The uncertainty in the enlarged fiducial mass region is obtained by the
combination of the two fiducial mass results. The more discrepant ϵsys (Bkgsys ) between the+2δEnonuni scale and −2δEnonuni scale cases is taken as the uncertainty.
Neutron Tagging
The uncertainty on the neutron tagging eﬃciency is estimated to be 9.0% in Section 6.3.4.
The 9.0% change of the neutron tagging eﬃciency corresponds to a 5.4% change of the numberof remaining atmospheric neutrino backgrounds, and it is assigned to the expected number ofatmospheric neutrino events in SK-IV as an additional uncertainty. This is deduced from thetrue number of produced neutrons in the remaining background MC events.

7.3.3

Summary of Systematic Uncertainties

Tables 7.7 and 7.8 show the summary of the evaluated systematic uncertainties on the signal
selection eﬃciency and expected number of atmospheric neutrino background events, respectively. As for the signal selection eﬃciency, basically, the dominant uncertainty originates from135

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

the physics modeling part. However, for the additional fiducial mass region, some of the uncertainties in the reconstruction part become comparable. Due to the degraded momentum
resolution and the eﬀects of escaping particles, more signal MC events in the additional fiducial
mass region are reconstructed near the total mass and total momentum cut boundaries thanin the conventional one as shown in Fig. 7.5. This has the eﬀect of making the selection eﬃciency in the additional fiducial mass region more sensitive to uncertainties in the energy scale.
The reconstructed momentum is also sensitive to the vertex position since in the momentum
calculation, the observed PMT charge is corrected using the reconstructed vertex position as
described in Section 6.1.6. Therefore, the eﬀects from the vertex shift manifest more obviously
in the additional fiducial mass region.
Systematic uncertainties associated with the neutrino interaction modeling and the energy
scale are dominant for the expected number of atmospheric neutrino background events. As
shown in the interaction mode breakdown table (Table 7.2) and kinetic distributions (Fig. 7.5),
there are no major diﬀerences between the two fiducial mass regions, resulting in a similar size of
uncertainties. For some of the items, the systematic uncertainty partially anticorrelates between
the conventional and additional fiducial mass regions, and it leads to the smallest uncertainty
after combining the two fiducial mass regions. The systematic uncertainties in the “Enlarged”
rows are used in the following lifetime limit calculation. At last, the systematic uncertainty on
the detector exposure is conservatively set to 1%.

7.4

Lifetime Limit

Since no significant data excess has been found in either decay mode, lower limits on the
proton partial lifetime have been calculated using a Bayesian method [119]. In this calculation,
numbers in the “Enlarged” rows in Tables 7.3, 7.7, and 7.8 and 450 kton·years have beenused as the signal selection eﬃciency, expected number of background events, their systematic
uncertainties, and exposure. Since the search performance varies depending on the SK phase,
separate exposures from SK-I to -IV are taken into account. The expected number of background
events is also diﬀerent between the two Ptot signal regions, and therefore they are consideredseparately in the following calculation. The probability to detect ni candidate events is calculated
by Poisson statistics:
Pi (ni |Γλi ϵi bi ) =e−(Γλi ϵi +bi ) (Γλi ϵi + bi )ni,
ni !

(7.10)

where i is the index of each signal region (SK-I to -IV, “Lower” and “Upper”), Γ is the true
decay rate, λi is the true detector exposure, ϵi is the true signal selection eﬃciency, and bi is thetrue number of backgrounds. According to Bayes’ theorem, it is transformed as follows:
Pi (Γλi ϵi bi |ni )Pi (ni ) = Pi (ni |Γλi ϵi bi )P (Γλi ϵi bi )= Pi (ni |Γλi ϵi bi )P (Γ)P (λi )P (ϵi )P (bi ),(7.11)(7.12)

where P (X) stands for the prior probability of X. The second equality holds because thedecay rate, detector exposure, signal selection eﬃciency, and the number of backgrounds are
independent.
In the eight signal regions (SK-I to -IV, “Lower” and “Upper”), each probability density
function of the decay rate is defined as follows:∫∫∫
Pi (Γ|ni ) =Pi (Γλi ϵi bi |ni )dϵi dλi dbi ,(7.13)∫ ∫ ∫ −(Γλi ϵi +bi )1e(Γλi ϵi + bi )ni=
P (Γ)P (λi )P (ϵi )P (bi )dϵi dλi dbi ,(7.14)
Ai
ni !

136

1.9
9.2

(Lower)(Upper)Enlarged

137
7.2
7.7

7.3
8.3
6.8
4.0

7.2
5.7

2.7
13.0

2.7
13.3
2.9
11.3

2.9
11.7

1.2
1.2

1.2
1.2
1.2
1.2

1.2
1.2

1.7
1.1

1.5
0.3
3.8
6.4

1.8
0.4

0.2
0.3

0.1
0.2
0.7
0.6

0.3
0.5

0.4
0.4

0.2
0.2
1.2
1.2

0.3
0.4

3.5
3.5

3.3
3.3
4.5
4.5

1.5
1.5

2.3
2.3

2.3
1.8
2.8
5.0

2.5
2.7

1.0
0.2

0.9
0.2
2.0
0.6

1.1
0.1

9.3
18.2

9.2
18.7
10.4
17.5

8.8
16.1

19.0
16.8

7.2
7.3

7.3

Enlarged

18.3

19.8

7.3

Enlargedp → µ+ π 0
Conventional
Additional
8.0

9.3
11.3

12.7

1.2

1.2
1.2

1.2

7.1

8.4
18.7

8.3

0.8

1.0
1.2

2.4

2.3

3.2
1.3

1.7

3.5

3.3
4.5

1.5

10.1

11.0
6.5

15.5

5.8

6.2
4.1

6.4

5.4

5.4
5.4

5.4

26.3

27.8
30.3

32.0

Table 7.8: Summary of systematic uncertainties [%] on the expected number of atmospheric neutrino background events for each fiducial mass
region. SK-I to -IV are livetime-weighted combined. They have been evaluated for the combined Ptot < 100 MeV/c and 100 ≤ Ptot < 250 MeV/csignal regions. Here, the “Enlarged” row shows the result for the combination of the two fiducial mass regions. Besides, “FV”, “RC”, and “PID”
stand for fiducial volume, ring counting, and particle identification, respectively.
π FSI
VertexMichel-e Energy
EnergyNeutronν Flux ν Interaction
FV
RC PID
Total
Regionand SI
Position
Tagging
Scale
Non-uniformity Tagging
p → e+ π 0
Conventional
7.3
21.2
12.8
1.2
12.0
2.5 1.4
1.5
16.4
4.2
5.4
33.5
34.3
Additional
7.2
17.3
13.9
1.2
9.1
1.8 2.9
1.4
15.2
17.1
5.4

Additional

1.9
9.3
2.0
8.4

1.9
8.9

(Lower)(Upper)(Lower)(Upper)(Lower)(Upper)Conventionalp → µ+ π 0

Enlarged

Table 7.7: Summary of systematic uncertainties [%] on the signal selection eﬃciency for each fiducial mass region. SK-I to -IV are livetimeweighted combined. The “Enlarged” row shows the result for the combination of the two fiducial mass regions. Here, “Lower” and “Upper” show
the Ptot < 100 MeV/c and 100 ≤ Ptot < 250 MeV/c signal regions, respectively. Besides, “FV”, “RC”, and “PID” stand for fiducial volume, ringcounting, and particle identification, respectively.
Correlated
Fermi
VertexMichel-e Energy
Energyπ FSI FVRC PID
Total
RegionDecay
Momentum
Position
Tagging
Scale
Non-uniformity
p → e+ π 0
8.6(Lower)
1.7
7.2
2.8
1.2
1.1
0.3 0.4
1.5
2.5
1.0
Conventional(Upper)
9.0
6.7
11.9
1.2
0.1
0.4 0.5
1.5
1.9
0.2
16.6
(Lower)
2.7
7.8
3.8
1.2
8.9
2.4 1.6
1.4
2.9
2.3
13.7
Additional(Upper)
8.4
1.0
10.6
1.2
4.4
2.5 1.3
1.4
8.3
0.3
16.8

CHAPTER 7. PROTON DECAY SEARCH ANALYSISCHAPTER 7. PROTON DECAY SEARCH ANALYSIS

where Ai is the normalization factor representing the total integral of Pi (Γ|ni ). The probability
density function P (Γ) is the prior probability of the decay rate and is assumed to be uniform,
and P (λi ) and P (ϵi ) stand for the prior probability of the exposure and the signal selection
eﬃciency, respectively, defined by a Gaussian function:)(
exp −(λi −λ0i )2 , (λ > 0)i
22σλP (λi ) ∝(7.15)i
0,(otherwise)()
exp −(ϵi −ϵ0i )2 , (ϵ > 0)i
22σϵi
P (ϵi ) ∝(7.16)
0,(otherwise)
where λ0i (σλi ) and ϵ0i (σϵi ) are the estimations (systematic uncertainties) of the exposureand signal selection eﬃciency, respectively. The prior probability of the expected number ofbackground events, P (bi ), is defined by the convolution of a Gaussian and Poisson distribution:()
∫ ∞ e−B B nbi exp −(Ci bi −B)2 dB, (b > 0)
i
nbi !
0
2σb2
P (bi ) ∝(7.17)i
0,(otherwise)
where nbi is the expected number of backgrounds in each 500 years atmospheric neutrino MC (notnormalized by livetime), Ci is a constant factor to normalize MC livetime to the data livetime,and σbi is the systematic uncertainty of the expected number of backgrounds. The systematic
uncertainties described in Section 7.3 are considered as a standard deviation of each Gaussianfunction. With these prior probability distributions, confidence level (C.L.) is calculated asfollows:∫ Γ=Γlimit ∏8
C.L. =Pi (Γ|ni )dΓ.
(7.18)
Γ=0

i=1

As a consequence, the lower limits on the proton partial lifetime are obtained by calculating:1
τlimit=,BΓlimit(7.19)

where B is the branching ratio of each proton decay mode. From the above formulas, 90%
confidence limits of the proton partial lifetime have been calculated, and they are:
τ /B(p → e+ π 0 ) > 2.4 × 1034 years,(7.20)andτ /B(p → µ π ) > 1.6 × 1034 years.
+ 0

7.5

Discussion

7.5.1

Implications of the Results(7.21)

Compared to the previous results [27], the lifetime limit for the p → e+ π 0 mode has improved by a factor of 1.5 as is expected from the increased exposure, from 306 kton·years to
450 kton·years. On the other hand, for the p → µ+ π 0 mode, the lifetime limit has improvedby a factor of two because one of the two candidates reported in the last results moved out of
the signal region after introducing a new gain correction method. In the new method, the PMT
gain correction factor depends on the PMT production year as described in Section 3.3.3.
In comparison with theoretical predictions, the obtained lifetime limits are in the middle of
the SO(10) GUT and SUSY GUT predictions, which are in the order of ∼ 1034 years or longer

138

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

and discussed in Chapter 2. Although the updated lifetime limits can not completely exclude
them, they give the world’s most stringent constraints for these decay modes.
According to [3], the proton lifetime and the mass of the mediator particle (GUT scale, MX )is approximately connected as follows:
τp ∼

4
1 MX
αG m5p(7.22)

1
Assuming that αG , the coupling constant at the unification scale (Figure 2.2), is about 40
, the
+
0
34
obtained lifetime limit (τ /B(p → e π ) > 2.4 × 10 years) gives a constraint on the value ofMX :MX ≳ 5 × 1015 GeV.

7.5.2

(7.23)

Future Prospect

In order to further enhance the proton decay search sensitivity, a larger detector exposureand further atmospheric neutrino background reduction are essential. Because the update anddata set presented in this thesis are generically applicable to every nucleon decay mode search(as well as atmospheric neutrino analysis), the search sensitivities for other decay modes will
also improve using the enlarged fiducial mass. In the following, future proton decay searches, inwhich the neutron tagging technique becomes more important to reduce atmospheric neutrino
backgrounds, are discussed.
In summer 2020, about 0.02% of Gadolinium (Gd) sulfate, Gd2 (SO4 )3 , by mass, i.e. about
0.01% of Gd has been dissolved in water of SK. After neutron capture on Gd, gamma rays
with a total energy of about 8 MeV are emitted. Because of the higher energy deposition in
the detector than neutron capture on hydrogen (2.2 MeV gamma ray), the neutron tagging
eﬃciency is expected to increase from 25% to about 50%. The original goal of the “SKGd”
project [120, 121] is to detect diﬀuse neutrinos from supernova explosions in the universe, but
the higher neutron tagging eﬃciency is also beneficial to the proton decay search because more
atmospheric neutrino backgrounds can be rejected with neutron information. By requiring
no tagged neutrons for a proton decay signal, the expected number of atmospheric neutrino
background rate is expected to be reduced by 65% (50%) in SKGd (SK-IV).
As a future project, the Hyper-Kamiokande (HK) detector [122] is being constructed, and
it is expected to start its data taking in 2027. A schematic view of the HK detector is shownin Fig. 7.13. It is an upright cylinder in shape as SK, 68.0 m in diameter and 72.0 m in height,
containing a total of 258 kton of water. The nominal fiducial volume is defined as the region
more than 150 cm from the inner detector wall, and it gives a 188 kton of water fiducial mass.
Suppose the fiducial volume boundary is extended to be 100 cm from the inner detector wall, thefiducial mass increases to 198 kton accordingly. Furthermore, a higher neutron tagging eﬃciency
is expected to be achieved because of the new PMT with a higher photon detection eﬃciency.
The expected neutron tagging eﬃciency in HK is estimated to be 70%. The expected number ofatmospheric neutrino background rate in HK is reduced by 75% by requiring no tagged neutrons
as a proton decay signal.
For both prospects, the proton decay p → e+ π 0 search sensitivity is calculated using Equations (7.1) and (7.2), and it is plotted in Fig. 7.14. For both experiments, the fiducial volume isassumed to be defined as the region more than 100 cm from the inner detector wall, 27.2 kton
for SKGd and 198 kton for HK, and the signal selection eﬃciency is assumed to be the same as
the SK-IV performance in Table 7.3. As for the expected atmospheric neutrino background rate,
it is assumed to be reduced to 23 Mt·years in SKGd from that in SK-IV (about 1 /Mt·year) and
it is assumed to be reduced by half in HK compared to that in SK-IV. The search sensitivity is
expected to reach in the order of 1035 years after the HK detector accumulates about 15 yearsof livetime.

139

CHAPTER 7. PROTON DECAY SEARCH ANALYSIS

Figure 7.13: Schematic view of the HK detector. Taken from [122].

Search Sensitivity(90% C.L.) [years]

p→e+π0

1035

SKGd

1034

HK

2020 2025 2030 2035 2040 2045 2050

Year
Figure 7.14: Proton decay p → e+ π 0 search sensitivity as a function of time. Used signal
selection eﬃciency and expected atmospheric neutrino background rate are described in the
text. The black point corresponds to this work.

140

Chapter 8

Conclusion
We have performed searches for proton decay via p → e+ π 0 and p → µ+ π 0 with the SuperKamiokande enlarged fiducial mass data. In order to enlarge the fiducial mass from 22.5 kton to27.2 kton for nucleon decay searches as well as atmospheric neutrino analyses, we have conducted
the following comprehensive studies. First, we have introduced several tighter criteria in theevent selection algorithm and quantified the non-neutrino background contamination rate in the
additional fiducial mass region by event scanning. As a result of adopting the new selection
criteria and the event scanning, we have demonstrated that the contamination rate is kept
within 1%, tolerable level for SK analyses, while the selection eﬃciency for proton decay andatmospheric neutrino events is kept more than 96%. As for the event reconstruction performance,
the particle identification algorithm has been improved by introducing new expected charge
tables, resulting in the 20% higher signal selection eﬃciency in the additional fiducial mass
region for both search modes. Furthermore, we have evaluated systematic uncertainties in the
additional fiducial mass region and proved that the energy scale uncertainty, one of the mostimportant error sources, is kept within a few percent level. Combining with the newly estimatedsystematic uncertainties, we confirm that enlarging the fiducial mass increases the proton decay
search sensitivity by 12% for both modes.
Since the last publication [27], the detector has accumulated 25% more livetime and its
fiducial mass has been enlarged by about 20%, resulting in a 50% larger exposure of SK-I to-IV full data, 450 kton·years. Using that updated data set, we have searched for proton decay
via p → e+ π 0 and p → µ+ π 0 . No candidates have been found for the p → e+ π 0 mode andone candidate has been found for the p → µ+ π 0 mode. They are not significant event excesses
compared to the atmospheric neutrino background predictions, 0.59 for p → e+ π 0 , and 0.94 forp → µ+ π 0 . Lower limits on the proton partial lifetime of τ /B(p → e+ π 0 ) > 2.4 × 1034 years
and τ /B(p → µ+ π 0 ) > 1.6 × 1034 years are set at 90% confidence level. These limits are a 1.5
times longer lifetime limit for the p → e+ π 0 mode and two times longer for the p → µ+ π 0 mode
than the previous results [27]. They do not completely rule out any prospective and remaining
major GUT models such as SO(10) and SUSY GUT, but they are the world’s most stringent
constraints for these decay modes and should be referred to in building GUT models.
The analysis improvements and data set described above are applicable to other nucleon
decay searches in Super-Kamiokande, and the search sensitivities for them are expected to
improve using the enlarged fiducial mass.

141

Acknowledgments
I am grateful to all of the people who have contributed to this work. I express my sincere
thanks to Prof. Masato Shiozawa for giving me this great opportunity to work on the SuperKamiokande experiment. Without his many important suggestions and tireless support, thisthesis could not have been completed. I would like to thank to Dr. Hidekazu Tanaka for hiskind support throughout my master and Ph.D. courses, especially in the PMT calibration workand dataset preparation. I am grateful to Prof. Masayuki Nakahata, spokesperson of the SuperKamiokande collaboration, for his helpful advice. I also thank all analysis group members,
especially Ed Kearns, Yoshinari Hayato, Roger Wendell, Shunichi Mine, Makoto Miura, Kimihiro Okumura, Masahiro Kuze, Yosuke Kataoka, Mahdi Taani, and Yutaro Sonoda, for their
many useful suggestions about the proton decay search analysis as well as FC data management.
I would also like to take this opportunity to thank all calibration group members, especially
Shigetaka Moriyama, Akira Konaka, Jun Kameda, Yasuhiro Nishimura, Motoyasu Ikeda, Yasuhiro Nakajima, Rika Sugimoto, Gianmaria Collazuol, Ali Ajmi, and Fabio Iacob. Thanks to
all Kamioka staﬀ and students, I could have a very enjoyable time in Kamioka.
This work is partially supported by Grant-in-Aid for JSPS Fellows. I also thank to the ALPS
program in the University of Tokyo for its educational and financial support.
Finally, I would like to sincerely thank my family for their continuous support.

142

Appendix A

Detailed Calibration of 50 cm
Diameter PMT Response andImpacts on Event Reconstruction
In this appendix, first, measurements of the photon incident position and ambient magnetic
field dependence of the SK PMT response are described in Section A.1. Their impacts on theevent reconstruction performance are estimated by implementing the obtained PMT response
into SKDETSIM. The implementation and results are covered in Section A.3. Since it has beenfound in the PMT measurement that there is anisotropy of the PMT response with respect to
the PMT dynode direction and a 100 mG level of the magnetic field has a sizable impact on
the PMT response, the dynode directions of all of the PMTs and the residual magnetic fieldin the SK detector have been measured during the tank refurbishment work in 2018. These
measurement results are described in Section A.2.

A.1

Detailed Calibration of SK PMT Response

A.1.1

Motivation of the Measurement

It has been demonstrated using SKDETSIM that Cherenkov photon incident positions on
the SK PMT photocathode generically depend on the primary event topology, such as vertex
position and particle direction. However, the photon incident position dependence of the SK
PMT response was not fully understood in the previous measurement [32], and thus the PMT
response in SKDETSIM is approximated to be uniform across the entire photocathode. Since
events in the additional fiducial mass region have a smaller distance to the ID wall than those in
the conventional and have not been actually used in SK analyses before, the size of the impact
on the event reconstruction induced by this dependence needs to be understood in advance.

A.1.2

Measurement Method

Nine PMTs (R3600) were sampled from the SK detector, and their serial numbers are as
follows:• CE5817,• CE5852,• EF6453,• FH5947,

143

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Figure A.1: SK PMT top view and coordinates.
The X-axis is parallel to the PMT dynode majoraxis, the Y -axis is the perpendicular to X, andthe D- (Diagonal) axis is in the middle of theother two.

Figure A.2: SK PMT cross section and definition of PMT θ. The dotted black line stands for
either the X-, Y -, or D-axis positive direction.

• FH5993,• GH5655,• GH5656,• JM3213,• LM7806.
The following items’ position and magnetic field dependence has been measured:• gain,• photon detection eﬃciency,• transit time.
Since the venetian blind dynode structure does not have rotational symmetry, the measurement
point on the photocathode is defined along three diﬀerent axes. The PMT coordinates aredefined and are shown in Fig. A.1: the X-axis is parallel to the PMT dynode major axis, theY -axis is perpendicular to X, and the D- (Diagonal) axis is in the middle of the other two. A
photoelectron trajectory inside the PMT bulb depends on the photon incident position, and it
produces a variation of the PMT response. Therefore, 11 optical fibers were put on the PMT
photocathode to evaluate the variation: the PMT zenith angle θ = 0, 20, 40, 45, 50, 55, 60, 65,
70, 75, and 80 degrees. The definition of the PMT zenith angle θ is shown in Fig. A.2.
Figure A.3 shows the measurement setup. The PMT was placed at the center of Helmholtz
coils, which are deployed to control the ambient magnetic field, and the room temperature wasabout 30◦ C. In order to measure magnetic field dependence of the PMT response, this PMT
measurement has been conducted under the following magnetic field conditions in units of mG:• (BX, BY, BZ) = (0, 0, 0),• (BX, BY, BZ) = (50, 0, 0),• (BX, BY, BZ) = (−50, 0, 0),• (BX, BY, BZ) = (−100, 0, 0),144

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Figure A.3: Schematic view of the PMT measurement setup. The Helmholtz coils are deployed
to control the ambient magnetic field.
• (BX, BY, BZ) = (0, 50, 0),• (BX, BY, BZ) = (0, −50, 0),• (BX, BY, BZ) = (0, −100, 0),• (BX, BY, BZ) = (0, 0, 50),
• (BX, BY, BZ) = (0, 0, 100),• (BX, BY, BZ) = (0, 0, −50),• (BX, BY, BZ) = (0, 0, −100),
where BX, BY , and BZ are defined as the magnetic field coordinates as shown in Fig. A.3, andthe BX- and BY -axes are parallel to the X- and Y -axes in the PMT coordinate, respectively. A
7.5 cm diameter PMT was deployed a few meters away from the Helmholtz coils and split lightfrom a light source is fed into the 7.5 cm PMT to monitor the light intensity variation during
the measurement.
As a laser light source, a laser diode device produced by Hamamatsu Photonics, PLP-10,
was used. Its laser pulse wavelength is 405.6 nm, and pulse width is 63.0 psec. Using a lightattenuator (AQ-3105A), the incident light intensity was tuned so that the SK PMT counting
rate was about 1%. PMT charge and timing information has been recorded with ADC (Lecroy:1182) and TDC (CAEN: V1290) modules.

145

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

A.1.3

Measurement Results

The PMT gain value at each photon incident position was obtained by fitting a Gaussianfunction to the ADC single photoelectron distribution. The photon detection eﬃciency wascalculated using the number of pulses whose height exceeds a certain threshold level. In thismeasurement, the threshold value was set to -1 mV, which is comparable to the SK configuration, and the photon detection eﬃciency at each incident position is normalized to the charge
deposition at the 7.5 cm monitor PMT.
The signal transit time was calculated by fitting an asymmetric Gaussian function to the TDC
distribution. A correction for the “time walk” eﬀect has been applied to the TDC distributionin advance.
Figure A.4 shows the relative gain, relative photon detection eﬃciency, and relative transit
time distributions at the |B| = 0 condition as a function of incident photon position on thephotocathode for one of the sampled PMTs, EF6453. The black, red, and blue dots show thediﬀerent photon incident points along the X-, Y -, and D-axes, respectively. These plots confirm
that there is a ±30% variation in gain, a ±25% variation in detection eﬃciency, and a ±3 nsec
variation in transit time across the entire photocathode. An electron trajectory simulation
by Hamamatsu Photonics suggests that the fall of the PMT gain seen around θ = ±60◦ in
the Y and D directions is caused by photoelectrons which pass through the gaps of the firstdynode. The systematic uncertainty of this measurement is estimated from the measurement
reproducibility. The same PMT was measured twice, and the reproducibility including fiber
positioning is estimated to be better than 5% for the PMT gain and detection eﬃciency, 0.2 nsec
for the PMT transit time measurement.
Figures A.5, A.6, and A.7 show the relative gain, relative photon detection eﬃciency, andrelative transit time distributions of the same PMT at diﬀerent magnetic field conditions along
BX, BY , and BZ, respectively. The impact by applying the magnetic field along BX is mostsignificant, and under the BX = −100 mG condition, the size of the deviation from the |B| = 0
condition is comparable to the size of the photon incident position dependence eﬀect. Basically,
these behaviors are also consistent with the electron trajectory simulation results by Hamamatsu
Photonics.
Figure A.8 shows the average distributions of relative gain, relative photon detection eﬃciency, and relative transit time for the nine sampled PMTs at the |B| = 0 condition. Verticalbands denote the statistical uncertainty of the average value at each photon incident position,(standard deviation)√, and correspond to the PMT by PMT individual diﬀerences. The PMT by
9−1
PMT individual diﬀerence of relative gain, relative photon detection eﬃciency, and relativetransit time is estimated to be less than 5%, 3%, and 0.5 nsec, respectively. The nine PMTs’
average results are consistent with an assumption that the non-uniform PMT response is symmetric with respect to θ = 0.

A.2

Measurement of PMT Dynode Direction and Residual Magnetic Field in the SK Detector

From the PMT response measurement, it has been found that there is anisotropy of the PMT
response with respect to the PMT dynode direction, and about 100 mG level of the magnetic
field also has a sizable impact on the PMT response. In order to estimate impacts on theevent reconstruction by these detailed PMT responses, dynode directions of the PMTs and themagnetic field in the SK detector have been measured during the tank refurbishment work in
2018.

146

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

EF6453 Efficiency vs. Position (Angle) BX=0, BY=0, BZ=0 in mG

EF6453 Gain vs. Position (Angle) BX=0, BY=0, BZ=0 in mG

1.6

Relative Efficiency

1.6

Relative Gain

1.4
1.2
1
0.8
0.6
0.4

X direction

0.2

Y direction

0

0

20

40

Angle θ [Degree]

60

1.2
1
0.8
0.6
0.4
0.2

D direction-80 -60 -40 -20

1.4

0

80

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

Relative Transit Time [nsec]

EF6453 Transit Time vs. Position (Angle) BX=0, BY=0, BZ=0 in mG

6
4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

Figure A.4: Relative gain (top left), relative photon detection eﬃciency (top right), and relativetransit time (bottom) distributions at the |B| = 0 condition as a function of incident photon
position on the photocathode (θ) defined in Figure A.2. They are results for one of the sampled
PMTs, EF6453. The black, red, and blue dots show the diﬀerent photon incident points along
the X-, Y -, and D-axes, respectively. For the relative gain distribution, the vertical axis values
are normalized to the mean of θ = 0 values. For the photon detection eﬃciency distribution,
the vertical axis values are normalized to the charge deposition at the monitor PMT. For the
relative transit time distribution, the vertical axis values correspond to the diﬀerence from themean of θ = 0 values. Vertical error bars on the data points shows the statistical uncertainty.

147

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

1.6

0.8
0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=-50 mG,BY=0 mG,BZ=0 mG

BX=50 mG,BY=0 mG,BZ=0 mG

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0.2

BX=100 mG,BY=0 mG,BZ=0 mG-80 -60 -40 -20

0

80

20

40

60

0.8
0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=-50 mG,BY=0 mG,BZ=0 mG

BX=50 mG,BY=0 mG,BZ=0 mG

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0

80

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=-50 mG,BY=0 mG,BZ=0 mG

BX=50 mG,BY=0 mG,BZ=0 mG
BX=100 mG,BY=0 mG,BZ=0 mG-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

20

40

60

80

2
0
-2
-4
-6
-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

EF6453 D Direction Scan Transit Time vs. Position (Angle) with BX Change

6

1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

4

-8

80

Relative Transit Time

0.8

Relative Efficiency

1-80 -60 -40 -20

EF6453 Y Direction Scan Transit Time vs. Position (Angle) with BX Change

1.6

1.2

-6

EF6453 D Direction Scan Efficiency vs. Position (Angle) with BX Change

EF6453 D Direction Scan Gain vs. Position (Angle) with BX Change

1.4

-4

6

0.2

BX=100 mG,BY=0 mG,BZ=0 mG-80 -60 -40 -20

0-2

Angle θ [Degree]

Relative Transit Time1

Relative Efficiency

1.2

2

-8

80

1.6

1.4

Relative Gain

04EF6453 Y Direction Scan Efficiency vs. Position (Angle) with BX Change

1.6

Relative Gain

-80 -60 -40 -20

Angle θ [Degree]

EF6453 Y Direction Scan Gain vs. Position (Angle) with BX Change

0

Relative Transit Time1

Relative Efficiency

Relative Gain

1.2

0

6

1.6

1.4

0

EF6453 X Direction Scan Transit Time vs. Position (Angle) with BX Change

EF6453 X Direction Scan Efficiency vs. Position (Angle) with BX Change

EF6453 X Direction Scan Gain vs. Position (Angle) with BX Change-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

Figure A.5: Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BX as a functionof incident photon position on the photocathode (θ). They are results for one of the sampled
PMTs, EF6453. Diﬀerent colors correspond to the diﬀerent magnetic field conditions. From top
to bottom, X, Y , and D direction scanning results are shown. For the relative gain distribution,
the vertical axis values are normalized to the mean of θ = 0 values at the |B| = 0 condition.
For the photon detection eﬃciency distribution, the vertical axis values are normalized to thecharge deposition at the monitor PMT. For the relative transit time distribution, the verticalaxis values correspond to the diﬀerence from the mean of θ = 0 values at the |B| = 0 condition.
Vertical error bars on the data points shows the statistical uncertainty.

148

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

1.6

0.8
0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=0 mG,BY=-50 mG,BZ=0 mG

BX=0 mG,BY=50 mG,BZ=0 mG

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0.2

BX=0 mG,BY=100 mG,BZ=0 mG-80 -60 -40 -20

0

80

20

40

60

0.8
0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=0 mG,BY=-50 mG,BZ=0 mG

BX=0 mG,BY=50 mG,BZ=0 mG

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0

80

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

0.6
0.4

BX=0 mG,BY=0 mG,BZ=0 mG

0.2

BX=0 mG,BY=-50 mG,BZ=0 mG

BX=0 mG,BY=50 mG,BZ=0 mG
BX=0 mG,BY=100 mG,BZ=0 mG-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

20

40

60

80

2
0
-2
-4
-6
-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

EF6453 D Direction Scan Transit Time vs. Position (Angle) with BY Change

6

1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

4

-8

80

Relative Transit Time

0.8

Relative Efficiency

1-80 -60 -40 -20

EF6453 Y Direction Scan Transit Time vs. Position (Angle) with BY Change

1.6

1.2

-6

EF6453 D Direction Scan Efficiency vs. Position (Angle) with BY Change

EF6453 D Direction Scan Gain vs. Position (Angle) with BY Change

1.4

-4

6

0.2

BX=0 mG,BY=100 mG,BZ=0 mG-80 -60 -40 -20

0-2

Angle θ [Degree]

Relative Transit Time1

Relative Efficiency

1.2

2

-8

80

1.6

1.4

Relative Gain

04EF6453 Y Direction Scan Efficiency vs. Position (Angle) with BY Change

1.6

Relative Gain

-80 -60 -40 -20

Angle θ [Degree]

EF6453 Y Direction Scan Gain vs. Position (Angle) with BY Change

0

Relative Transit Time1

Relative Efficiency

Relative Gain

1.2

0

6

1.6

1.4

0

EF6453 X Direction Scan Transit Time vs. Position (Angle) with BY Change

EF6453 X Direction Scan Efficiency vs. Position (Angle) with BY Change

EF6453 X Direction Scan Gain vs. Position (Angle) with BY Change-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

Figure A.6: Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BY as a functionof incident photon position on the photocathode (θ). They are results for one of the sampled
PMTs, EF6453. Diﬀerent colors correspond to the diﬀerent magnetic field conditions. From top
to bottom, X, Y , and D direction scanning results are shown. For the relative gain distribution,
the vertical axis values are normalized to the mean of θ = 0 values at the |B| = 0 condition.
For the photon detection eﬃciency distribution, the vertical axis values are normalized to thecharge deposition at the monitor PMT. For the relative transit time distribution, the verticalaxis values correspond to the diﬀerence from the mean of θ = 0 values at the |B| = 0 condition.
Vertical error bars on the data points shows the statistical uncertainty.

149

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

1.6

0.8
0.6
BX=0 mG,BY=0 mG,BZ=0 mG
BX=0 mG,BY=0 mG,BZ=50 mG
BX=0 mG,BY=0 mG,BZ=-50 mG
BX=0 mG,BY=0 mG,BZ=100 mG
BX=0 mG,BY=0 mG,BZ=-100 mG

0.4
0.2-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0.2
0

80

20

40

60

0.8
0.6
BX=0 mG,BY=0 mG,BZ=0 mG
BX=0 mG,BY=0 mG,BZ=50 mG
BX=0 mG,BY=0 mG,BZ=-50 mG
BX=0 mG,BY=0 mG,BZ=100 mG
BX=0 mG,BY=0 mG,BZ=-100 mG

0.4
0.2-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

1.4
1.2
1
0.8
0.6
0.4
0

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

BX=0 mG,BY=0 mG,BZ=0 mG
BX=0 mG,BY=0 mG,BZ=50 mG
BX=0 mG,BY=0 mG,BZ=-50 mG
BX=0 mG,BY=0 mG,BZ=100 mG
BX=0 mG,BY=0 mG,BZ=-100 mG

0.4
0.2-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

20

40

60

80

2
0
-2
-4
-6
-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

EF6453 D Direction Scan Transit Time vs. Position (Angle) with BZ Change

6

1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

4

-8

80

Relative Transit Time

0.6

Relative Efficiency

0.8-80 -60 -40 -20

EF6453 Y Direction Scan Transit Time vs. Position (Angle) with BZ Change

1.6

1

-6

EF6453 D Direction Scan Efficiency vs. Position (Angle) with BZ Change

EF6453 D Direction Scan Gain vs. Position (Angle) with BZ Change

1.2

-4

6

0.2

80

1.4

0
-2

Angle θ [Degree]

Relative Transit Time1

Relative Efficiency

1.2

2

-8

80

1.6

1.4

Relative Gain

04EF6453 Y Direction Scan Efficiency vs. Position (Angle) with BZ Change

1.6

Relative Gain

-80 -60 -40 -20

Angle θ [Degree]

EF6453 Y Direction Scan Gain vs. Position (Angle) with BZ Change

0

Relative Transit Time1

Relative Efficiency

Relative Gain

1.2

0

6

1.6

1.4

0

EF6453 X Direction Scan Transit Time vs. Position (Angle) with BZ Change

EF6453 X Direction Scan Efficiency vs. Position (Angle) with BZ Change

EF6453 X Direction Scan Gain vs. Position (Angle) with BZ Change-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

Figure A.7: Relative gain (left), relative photon detection eﬃciency (middle), and relativetransit time (right) distributions at diﬀerent magnetic field conditions along BZ as a functionof incident photon position on the photocathode (θ). They are results for one of the sampled
PMTs, EF6453. Diﬀerent colors correspond to the diﬀerent magnetic field conditions. From top
to bottom, X, Y , and D direction scanning results are shown. For the relative gain distribution,
the vertical axis values are normalized to the mean of θ = 0 values at the |B| = 0 condition.
For the photon detection eﬃciency distribution, the vertical axis values are normalized to thecharge deposition at the monitor PMT. For the relative transit time distribution, the verticalaxis values correspond to the diﬀerence from the mean of θ = 0 values at the |B| = 0 condition.
Vertical error bars on the data points shows the statistical uncertainty.

150

Relative Efficiency

Relative Gain

1.2
1
0.8
0.6
0.4

1
0.8
0.6
0.4
0.2

0

0

-80 -60 -40 -20

0

20

40

60

80

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

80

1.6

Relative Efficiency

Y direction

1.4

Relative Gain

1.2

0.2

Angle θ [Degree]

1.2
1
0.8
0.6
0.4

1.4
1.2
1
0.8
0.6
0.4

0.2

0.2

0

0

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

80

1.6

Relative Efficiency

D direction

1.4

Relative Gain

1.4

1.2
1
0.8
0.6
0.4

1.4
1.2
1
0.8
0.6
0.4

0.2

0.2

0

0

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

6
4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

60

80

-80 -60 -40 -20

0

20

40

60

80

-80 -60 -40 -20

0

20

40

60

80

Angle θ [Degree]

Relative Transit Time [nsec]

1.6

X direction

1.4

6
4
2
0
-2
-4
-6
-8

Angle θ [Degree]

Relative Transit Time [nsec]

1.6

Relative Transit Time [nsec]

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

6
4
2
0
-2
-4
-6
-8

Angle θ [Degree]

Figure A.8: Average distributions of relative gain, relative photon detection eﬃciency, andrelative transit time of the nine sampled PMTs at the |B| = 0 condition as a function ofincident photon position on the photocathode (θ). From top to bottom, X, Y , and D direction
scanning results are shown. Vertical bands denote the statistical uncertainty of the average
deviation)√
value at each photon incident position, (standard, and correspond to the PMT by PMT
9−1
individual diﬀerences.

151

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Figure A.9: Example of the dynode picture taken in the SK detector. The thin while lines
correspond to the mesh on the dynode and the dynode direction has been estimated from their
tilt.

A.2.1

PMT Dynode Direction

The dynode direction inside the PMT can be seen in front of the PMT photocathode byeye. Therefore, a digital camera, OLYMPUS TG-5, has been deployed in front of the PMTs andhas recorded the dynode directions. An example of the dynode picture is shown in Fig. A.9. A
mesh (thin white lines in the figure), which is deployed for fine-tuning the electric field inside
the bulb, is tagged as a mark to estimate the dynode direction. A picture processing tool basedon OpenCV [123] has been developed, and it calculates the mesh angle from the picture horizon
with both ends of the mesh. The mesh end positions on the display were pointed out by workers.
Pictures of the dynode directions have been taken from the top to bottom of the detector.
For the top, side, and bottom PMTs, the camera was placed so that the picture horizon isaligned with the y-axis, xy-plane, and x-axis in the SK coordinates, respectively. For the top
PMTs, the camera was handled by hand, while for the side and bottom PMTs, the camera was
fixed on a selfie stick as necessary. Some PMTs’ dynode directions have been taken twice, andthe measurement reproducibility is estimated to be 3 degrees.
Figure A.10 shows the dynode angle distributions. The left plot shows the PMTs producedin the 1990s, and the right shows those produced in the 2000s. The dynode angle is definedas the angle from the xy-plane in the SK coordinates for the side PMTs, while it is defined as
the angle from the y-axis in the SK coordinates for the top and bottom PMTs. The dynodedirections of PMTs produced in the 2000s were intended to distribute randomly. On the other
hand, those produced in the 1990s were basically manufactured in almost the same manner.

A.2.2

Residual Magnetic Field

A magnetometer with a user interface functionality has been developed based on a nineaxes sensor module, LSM9DS0, in which an accelerometer, gyroscope, and magnetometer are
integrated. Using the magnetometer, the residual magnetic field at more than 3,000 points inthe entire detector has been measured while the compensation coils, which are described in152Production Year 1990s
300
250
200
150
100
50
0
0

20

40

60

80 100 120 140 160 180

Number of PMTs [/3 Degree]

Number of PMTs [/3 Degree]

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION
Production Year 2000s
300
250
200
150
100
50
0
0

20

Dynode Direction [Degree]

40

60

80 100 120 140 160 180

Dynode Direction [Degree]

Figure A.10: Dynode angle distributions. The left plot shows the PMTs produced in the 1990s
and the right shows those produced in the 2000s. The dynode angle is defined as the angle fromthe xy-plane in the SK coordinates for the side PMTs, while it is defined as the angle from they-axis in the SK coordinates for the top and bottom PMTs.
Section 3.2.2, were on to reproduce the SK operation condition. The number of measurement
points is more than six times larger than the previous measurement [42]. The magnetometer
was handled by hand, and the tilt of the sensor is corrected with the accelerometer data. The
measurement reproducibility is estimated to be better than 4 mG.
Figure A.11 shows the distribution of the residual magnetic field strength in the SK detector.
In Figure A.11, the number of entries is 3,253 in total, and the number of measurement points
in the detector top, side, and bottom region is 321, 2,700, and 232, respectively. Although themeasurement points are not distributed uniformly inside the detector due to time constraints,
the magnetic field strength has been measured to be less than 100 mG for more than 99% of
the measurement points. The mean value is 33 mG, and the standard deviation is 16 mG.
Figure A.12 shows the magnetic field maps. Color markers denote the measurement point andmagnetic field strength value. The highest magnetic field region is localized in the detector
bottom edge, where the dominant component is along the SK y-axis, and the highest value is
122 mG.

A.3

Impacts on Event Reconstruction

The results of the PMT response calibration and detector inspection confirm that an impact
on a single PMT response by the photon incident position dependence is larger than that by
the residual magnetic field eﬀect for almost all the detector parts. Therefore, only the photon
incident position dependence has been implemented into SKDETSIM to estimate impacts on
the event reconstruction as a first-order approximation. Assuming that the PMT response issymmetric with respect to the center of the PMT photocathode, relative gain, photon detection
eﬃciency, and transit time factors are calculated based on the PMT measurement results described in Section A.1. Figure A.13 shows the distributions of the implemented relative gain,
relative photon detection eﬃciency, and relative transit time factors. The implemented factors
are shown in the dotted lines, which are calculated by averaging the measurement results in theθ ≥ 0 and θ ≤ 0 regions. Bands show the mean±1σ regions plotted in Fig. A.8. The same factors
have been implemented for all the ID PMTs in SKDETSIM uniformly. The dynode directionsof the PMTs have been also implemented based on the measurement results. In the following,“implemented MC” refers to MC described above, and “standard MC” refers to conventional
SKDETSIM MC.
After necessary parameter tuning to reproduce the calibration results presented in Sec-153

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

400

Entries [/5 mG]

350
300
250
200
150
100
50
0
0

20 40 60 80 100 120 140 160 180 200

Magnetic Field Strength [mG]
Figure A.11: Distribution of the residual magnetic field strength. The number of entries is 3,253
in total, and the number of measurement points in the detector top, side, and bottom regionis 321, 2,700, and 232, respectively. The mean value is 33 mG, and the standard deviation is
16 mG.
tion 3.3, several types of MC events have been generated using implemented MC in the SK-IV
detector configuration:• 500 MeV/c electron,• 500 MeV/c muon,• 1000 MeV/c electron,• 1000 MeV/c muon.
These events have been generated inside the entire detector with randomly distributed particle
directions. The same reconstruction algorithm described in Section 6.1 has been applied to thegenerated events. Figures A.14 and A.15 show the distributions of the distance between thereconstructed vertex and true vertex position as well as reconstructed momentum distributions.
The 500 MeV/c and 1000 MeV/c particle gun MC events are plotted in Fig. A.14 and A.15,
respectively. The size of the vertex and momentum shifts between implemented MC and standard MC in the additional fiducial mass region is less than 1 cm and less than 0.3% and ismuch smaller than the vertex resolution (20 ∼ 30 cm) and energy scale uncertainty discussed in
Section 6.2 (2 ∼ 3%), respectively. No significant diﬀerences are observed in the ring counting
and particle identification performances. Furthermore, proton decay p → e+ π 0 MC events havebeen also generated using implemented MC. Applying the same event reconstruction and same
signal selection criteria results in a 1% of signal selection eﬃciency change in the additional
fiducial mass region, which is also smaller than the estimated systematic uncertainty associatedwith the detector (reconstruction) performance described in Section 7.3.2. These results confirm
that the average impacts by the photon incident position dependence of the SK PMT response
is limited on the event reconstruction performance, and the approximation in standard MC istolerable for enlarging the fiducial mass. Since outputs of standard MC are well understood andcalibrated with various control samples, standard MC is used in the analysis presented in thisthesis, and implemented MC is not used.

154

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Figure A.12: Magnetic field maps. Color markers denote the measurement point and magnetic
field strength value in units of mG. The upper plot shows the detector barrel (side) region andthe horizontal axis is the azimuth angle from the SK x-axis. The lower left (right) plot shows
the detector top (bottom) region. The highest magnetic field region is localized in the detector
bottom edge, and the markers are highlighted in green. Due to time constraints, the numberof measurement points in the detector bottom is lower than that in the detector top. Provided
by [124].

155

Relative Efficiency

Relative Gain

1.2
1
0.8
0.6
0.4
0.2
0

-80 -60 -40 -20

0

20

40

60

1
0.8
0.6
0.4
0

80

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

1.6

60

80

1.6

Relative Efficiency

Y direction

1.4

Relative Gain

1.2

0.2

Angle θ [Degree]

1.2
1
0.8
0.6
0.4

1.2
1
0.8
0.6
0.4
0.2

0

0

-80 -60 -40 -20

0

20

40

60

80

Y direction

1.4

0.2

Angle θ [Degree]-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

1.6

1.6

Relative Efficiency

D direction

1.4

Relative Gain

X direction

1.4

1.2
1
0.8
0.6
0.4

1.2
1
0.8
0.6
0.4

0.2

0.2

0

0

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

D direction

1.4-80 -60 -40 -20

0

20

40

Angle θ [Degree]

60

80

6

X direction

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

Relative Transit Time [nsec]

1.6

X direction

1.4

60

80

6

Y direction

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]

Relative Transit Time [nsec]

1.6

Relative Transit Time [nsec]

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

60

80

6
D direction

4
2
0
-2
-4
-6
-8

-80 -60 -40 -20

0

20

40

Angle θ [Degree]60

80

Figure A.13: Distributions of relative gain (left), relative photon detection eﬃciency (middle),
and relative transit time (right) factors. The implemented factors are shown in the dotted lines.
From top to bottom, implemented factors for the X, Y , and D directions are shown. Bands
show the mean ± 1σ region plotted in Fig. A.8.

156

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Number of Events [/3 cm](Normalized to Unity)

0.1
0.08

Conventional Region
Standard MC
Resolution 27.6 cm
Impelement MC
Resolution 27.0 cm

0.06
0.04
0.02
0
0

Electron 500 MeV/c
Number of Events [/3 cm](Normalized to Unity)

Electron 500 MeV/c
0.12

0.12
0.1
0.08
0.06
0.04
0.02
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Conventional Region
Standard MCMean 497.7+/-0.1 MeV/c
RMS 24.3+/-0.1 MeV/c
Impelement MC
Mean 497.1+/-0.1 MeV/c
RMS 24.2+/-0.1 MeV/c

0.16
0.14
0.12
0.1
0.08

0.04
0.02
0
0

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

0.14
0.12

Conventional Region
Standard MC
Resolution 18.3 cm
Impelement MC
Resolution 18.6 cm

0.1
0.08
0.06
0.04
0.02
0
0

Muon 500 MeV/c
0.14
0.12
0.1

0.06
0.04
0.02
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]

0.25
0.2
0.15
0.1
0.05
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Muon 500 MeV/c
Number of Events [/10 MeV/c](Normalized to Unity)

Number of Events [/10 MeV/c](Normalized to Unity)

0.3

Conventional Region
Standard MCMean 500.2+/-0.0 MeV/c
RMS 12.6+/-0.0 MeV/c
Impelement MC
Mean 499.9+/-0.0 MeV/c
RMS 12.5+/-0.0 MeV/c

Additional Region
Standard MC
Resolution 20.7 cm
Impelement MC
Resolution 21.5 cm

0.08

Muon 500 MeV/c
0.35

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

0.16
Number of Events [/3 cm](Normalized to Unity)

Number of Events [/3 cm](Normalized to Unity)

0.16

Additional Region
Standard MCMean 489.5+/-0.5 MeV/c
RMS 51.3+/-0.3 MeV/c
Impelement MC
Mean 488.9+/-0.5 MeV/c
RMS 50.4+/-0.3 MeV/c

0.06

Muon 500 MeV/c
0.18

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Electron 500 MeV/c
Number of Events [/10 MeV/c](Normalized to Unity)

Number of Events [/10 MeV/c](Normalized to Unity)

Electron 500 MeV/c
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

Additional Region
Standard MC
Resolution 28.5 cm
Impelement MC
Resolution 27.7 cm

0.3
0.25
0.2
0.15
0.1
0.05
0
0

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

Additional Region
Standard MCMean 505.6+/-0.2 MeV/c
RMS 20.4+/-0.1 MeV/c
Impelement MC
Mean 504.9+/-0.2 MeV/c
RMS 20.3+/-0.1 MeV/c

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

Figure A.14: Distributions the distance between the reconstructed vertex and true vertex position and reconstructed momentum. Implemented MC outputs are plotted in red, and standard
MC outputs are in black. The top (bottom) four plot show the electron (muon) 500 MeV/c
MC events. The left and right plots correspond to the conventional and additional fiducial mass
regions, respectively.

157

APPENDIX A. DETAILED CALIBRATION OF 50 CM DIAMETER PMT RESPONSE
AND IMPACTS ON EVENT RECONSTRUCTION

Conventional Region
Standard MC
Resolution 25.1 cm
Impelement MC
Resolution 24.8 cm

0.12
0.1
0.08
0.06
0.04
0.02
0
0

Electron 1000 MeV/c
Number of Events [/3 cm](Normalized to Unity)

Number of Events [/3 cm](Normalized to Unity)

Electron 1000 MeV/c
0.1
0.08
0.06
0.04
0.02
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Conventional Region
Standard MCMean 998.8+/-0.2 MeV/c
0.1 RMS 39.8+/-0.1 MeV/c
Impelement MC
0.08 Mean 997.9+/-0.2 MeV/c
RMS 38.7+/-0.1 MeV/c

0.06
0.04

0.02
0
0

Number of Events [/3 cm](Normalized to Unity)

Number of Events [/3 cm](Normalized to Unity)

Conventional Region
Standard MC
Resolution 17.6 cm
Impelement MC
Resolution 17.0 cm

0.1

Additional Region
Standard MC
0.08 Mean 975.6+/-1.0 MeV/c
RMS 108.8+/-0.7 MeV/c
Impelement MC
0.06 Mean 973.3+/-1.1 MeV/c
RMS 109.4+/-0.7 MeV/c

0.04
0.02
0
0

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

Muon 1000 MeV/c
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]

0.2
0.18

0.04
0.02
0
0

Muon 1000 MeV/c
Additional Region
Standard MC
Resolution 20.7 cm
Impelement MC
Resolution 19.7 cm

0.12
0.1
0.08
0.06
0.04
0.02
0
0

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Muon 1000 MeV/c
Number of Events [/10 MeV/c](Normalized to Unity)

Number of Events [/10 MeV/c](Normalized to Unity)

0.08
0.06

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

0.16
0.14

Muon 1000 MeV/c
0.18 Conventional Region
Standard MC
0.16 Mean 998.1+/-0.1 MeV/c
0.14 RMS 29.1+/-0.1 MeV/c
Impelement MC
0.12
Mean 997.1+/-0.1 MeV/c
0.1 RMS 29.1+/-0.1 MeV/c

50
100
150
200
250
300
Distance b/w True & Recon. Vertex [cm]Electron 1000 MeV/c
Number of Events [/10 MeV/c](Normalized to Unity)

Number of Events [/10 MeV/c](Normalized to Unity)

Electron 1000 MeV/c
0.12

Additional Region
Standard MC
Resolution 28.6 cm
Impelement MC
Resolution 28.1 cm

0.12

0.14

Additional Region
Standard MC
0.12 Mean 1006.3+/-0.6 MeV/c
RMS 60.7+/-0.4 MeV/c
0.1
Impelement MC
0.08 Mean 1004.8+/-0.6 MeV/c
RMS 57.9+/-0.4 MeV/c

0.06
0.04
0.02
0
0

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

200 400 600 800 1000 1200 1400
Reconstructed Momentum [MeV/c]

Figure A.15: Distributions the distance between the reconstructed vertex and true vertex position and reconstructed momentum. Implemented MC outputs are plotted in red, and standard
MC outputs are in black. The top (bottom) four plot show the electron (muon) 1000 MeV/c
MC events. The left and right plots correspond to the conventional and additional fiducial mass
regions, respectively.

158

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