UNIVERSITY of CALIFORNIA, IRVINE a Search for Proton Decay Via P → Μ +K0 in Super Kamiokande I DISSERTATION Submitted in Part

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UNIVERSITY OF CALIFORNIA, IRVINE

A search for proton decay via p → μ+K0 in Super Kamiokande I

DISSERTATION

submitted in partial satisfaction of the requirements for the degree of

DOCTOR OF PHILOSOPHY

in Physics

Christopher Regis

Dissertation Committee: Professor David Casper, Chair Professor Hank Sobel Professor Jonas Schultz

2011 c 2011 Christopher Regis TABLE OF CONTENTS

Page

List Of Figures vi

List Of Tables xii

Acknowledgments xiv

Curriculum Vitae xv

Abstract Of The Dissertation xvi

1 Introduction 1 1.1TheoreticalMotivation...... 1 1.1.1 ConservationandSymmetries...... 2 1.1.2 StandardModel...... 3 1.1.3 GrandUniﬁedTheories...... 5 1.2 Past Experimental Measurements of p → μ+K0 ...... 9 1.2.1 Soudan2 ...... 9 1.2.2 IrvineMichiganBrookhaven(IMB)...... 9 1.2.3 Kamiokande...... 10 1.2.4 SuperKamiokande...... 10 1.3OverviewofExperimentalMethod...... 10

2 Detector 14 2.1CherenkovRadiation...... 14 2.2SuperKamiokandeDetector...... 16 2.3PhotomultiplierTube...... 18 2.4Electronics&DataAcquisition...... 18 2.4.1 InnerDetector...... 18 2.4.2 OuterDetector...... 21 2.4.3 TriggerSystem...... 21 2.5WaterPuriﬁcationSystem...... 23 2.6Calibration...... 24 2.6.1 TimingCalibration...... 24 2.6.2 RelativeGainCalibration...... 25 2.6.3 AbsoluteGainCalibration...... 27 2.6.4 WaterTransparency...... 28

ii 2.6.5 AbsoluteEnergyCalibration...... 30

3 Simulation 38 3.1ProtonDecay...... 38 3.1.1 FermiMomentumandNuclearBindingEnergy...... 39 3.1.2 Kaon-NucleonInteractionintheOxygenNucleus...... 40 0 → 0 3.1.3 KL KS RegenerationintheOxygenNucleus...... 41 3.2AtmosphericNeutrinoFlux...... 42 3.3NeutrinoInteraction...... 44 3.3.1 Elastic&Quasi-ElasticScattering...... 44 3.3.2 SingleMesonProduction...... 46 3.3.3 DeepInelasticScattering(DIS)...... 48 3.3.4 CoherentPionProduction...... 50 3.3.5 NuclearEﬀects...... 52 3.4DetectorSimulation...... 54 3.4.1 Photon Propagation ...... 54 3.4.2 Hadron Propagation ...... 54 0 → 0 3.4.3 KL KS RegenerationinWater...... 54

4 Fully Contained Event Reduction 56 4.1Overview...... 56 4.2FirstReduction...... 56 4.3SecondReduction...... 57 4.4ThirdReduction...... 58 4.4.1 Through-goingMuonCut...... 58 4.4.2 StoppingMuonCut...... 59 4.4.3 CablePortMuons...... 59 4.4.4 FlasherEventCut...... 60 4.4.5 AccidentalCoincidenceCut...... 60 4.4.6 LowEnergyEventsCut...... 61 4.5FourthReduction...... 61 4.6FifthReduction...... 63 4.6.1 StoppingMuonCut...... 63 4.6.2 InvisibleMuonCut...... 63 4.6.3 CoincidenceMuonCut...... 64 4.6.4 LongTailFlasherCut...... 64 4.7FinalFullyContainedFiducialVolumeSample...... 64

5 Event Reconstruction 66 5.1StandardEventReconstruction...... 66 5.1.1 Vertex...... 67 5.1.2 RingCounting...... 71 5.1.3 ParticleIdentiﬁcation...... 73 5.1.4 MSVertexFit...... 77 5.1.5 MomentumDetermination...... 77

iii 5.1.6 DecayElectronSearch...... 82 5.1.7 RingNumberCorrection...... 83 5.2MultipleVertexEventReconstruction...... 84 5.2.1 StandardReconstructionWithoutTimingCuts...... 85 5.2.2 PMTMaskingRegion...... 86 5.2.3 Primary μ-candidateReconstruction...... 86 5.2.4 RemainingParticleReconstruction...... 92

6 Overview of the p → μ+K0 search 95 6.1DataSet...... 95 6.2 Strategy of the Combined p → μ+K0 Search...... 96

0 → 0 0 7Searchfor“KS π π ”99 7.1EventSelection...... 99 7.2SK-IDataSideband...... 106 7.3SK-IDataEventRatevs.EventSelection...... 111 7.4BreakdownofRemainingBackground...... 118 7.5SK-IDataCandidates...... 120 0 → 0 0 7.6 Total Systematic Error of “KS π π ”Search...... 122

0 → + − 8Searchfor“KS π π Method #1” 124 8.1EventSelection...... 124 8.2SK-IDataSideband...... 130 8.3SK-IDataEventRatevs.EventSelection...... 133 8.4BreakdownofRemainingBackground...... 139 8.5SK-IDataCandidates...... 140 0 → + − 8.6 Total Systematic Error of “KS π π Method#1”Search..... 148 0 → + − 9Searchfor“KS π π Method #2” 150 9.1EventSelection...... 150 9.2SK-IDataSideband...... 154 9.3SK-IDataEventRatevs.EventSelection...... 157 9.4BreakdownofRemainingBackground...... 162 0 → + − 9.5 Total Systematic Error of “KS π π Method#2”Search..... 163

0 10 Search for “KL” 165 10.1EventSelection...... 165 10.2SK-IDataSideband...... 175 10.3SK-IDataEventRatevs.EventSelection...... 180 10.4BreakdownofRemainingBackground...... 188 10.5SK-IDataCandidates...... 189 0 10.6 Total Systematic Error of “KL”Search...... 191

11 Results 193

12 Comparison With Previous SK p → μ+K0 Search 196

iv 13 Future Prospects 202

14 Conclusion 204

Appendices 205 A SystematicErrors...... 205 A.1 DataSet...... 205 A.2 SourcesofError...... 206

Bibliography 217

v LIST OF FIGURES

Page

1.1 FeynmandiagramsofSU(5)GUTgaugebosons...... 7 1.2 Feynman diagram of Higgsino exchange from d=5 operator in the SUSYGUTLagrangian...... 9 1.3 Feynman diagram of p → νK¯ + decay...... 9

2.1 RelativeCherenkovlightspectruminpurewater...... 15 2.2 TheSuperKamiokandedetector...... 17 2.3 The50cmPMT...... 19 2.4 Thequantumeﬃciencyofthe50cmPMT...... 19 2.5 Thetransittimespreadofthe50cmPMT...... 20 2.6 SchematicoftheSKIDDAQsystem...... 22 2.7 SchematicoftheSKwaterpuriﬁcationsystem...... 24 2.8 Timingcalibrationsystem...... 25 2.9 RelativegaincalibrationsystemusingXelamp...... 26 2.10 AbsolutegaincalibrationusingaNi+Cfsource...... 27 2.11 Waterattenuationlengthmeasurementsystem...... 28 2.12 Distributionofcorrectedp.e.vs.photontravellength...... 30 2.13 Momentumdistributionfordecayelectrons...... 31 2.14 Invariant mass distribution of neutrino induced π0 events...... 32 2.15 Distribution of reconstructed momentum from observed charge vs. reconstructed Cherenkov opening angle for cosmic ray stopping μ.. 33 2.16 Ratio of the muon momentum from observed p.e. to momentum from openingangleasafunctionofthemomentum...... 34 2.17 The ratio of momentum/range as a function of range for cosmic ray stopping μ...... 35 2.18 Timevariationofenergyscalecalibration...... 36 2.19 The non-uniformity of the detector gain as a function of zenith angle. 37 2.20 Summaryoftheabsoluteenergyscalecalibration...... 37

3.1 Nucleon momentum distributions of 12C...... 39 3.2 Invariant mass of μ+K0 in the p → μ+K0 MC simulation in water. . 40 3.3 Primary cosmic ray flux measurements compared with the model used intheHondafluxcalculation...... 43 3.4 ThepredictedatmosphericneutrinofluxesattheSKsite...... 43 3.5 Quasi-elastic scattering cross-sections of ν andν ¯...... 46

vi 3.6 Cross-sections for charged current single pion productions of νμ... 48 3.7 Cross-sections for charged current νμ andν ¯μ interactions...... 50 3.8 The cross-sections of coherent pion productions oﬀ the carbon nucleus forCCandNCinteractions...... 52 3.9 Cross-sections of π+-16O scattering as a function of π+ momentum. 53 3.10 Wavelength dependence of photon attenuation coeﬃcients used in MCsimulation...... 55

5.1 The reconstructed-true muon momentum of three control samples describedinthetext...... 81 5.2 Performance of the initial vertex fitting of the μ-candidate for p → + 0 μ KL MC...... 88 5.3 The ΔV distribution of the initial μ-candidate vertex for atmospheric neutrinoMC...... 88 → + 0 5.4 The PID likelihood of the true primary muon for p μ KL MC. . 89 5.5 Performance of the MS vertex fitting of the μ-candidate for p → + 0 μ KL MC...... 90 5.6 The ΔV distribution of the μ-candidate MS vertex for atmospheric neutrinoMC...... 91 5.7 The reconstructed-true momentum of the true primary muon for p → + 0 μ KL MC...... 91 5.8 Performance of the remaining particle vertex fitting of the μ-candidate → + 0 for p μ KL MC...... 93 5.9 The ΔV− distribution for the remaining particle vertex of the atmo- sphericneutrinoMC...... 94

6.1 The p → μ+K0 combinedsearchalgorithm...... 97

7.1 The nring distribution for p → μ+K0 and atmospheric neutrino MC 0 → 0 0 along the KS π π searcheventselection...... 102 7.2 The PID likelihood distribution for p → μ+K0 and atmospheric neu- 0 → 0 0 trino MC along the KS π π searcheventselection...... 103 7.3 The number of decay electron distribution for p → μ+K0 and atmo- 0 → 0 0 spheric neutrino MC along the KS π π search event selection. . 103 → + 0 7.4 The MKS distribution for p μ K and atmospheric neutrino MC 0 → 0 0 along the KS π π searcheventselection...... 104 + 0 7.5 The pμ distribution for p → μ K and atmospheric neutrino MC 0 → 0 0 along the KS π π searcheventselection...... 104 + 0 7.6 The Ptot distribution for p → μ K and atmospheric neutrino MC 0 → 0 0 along the KS π π searcheventselection...... 105 + 0 7.7 The Mtot distribution for p → μ K and atmospheric neutrino MC 0 → 0 0 along the KS π π searcheventselection...... 105 7.8 The number of decay electron distribution for data and atmospheric 0 → 0 0 neutrino MC using the KS π π searchsidebandsample...... 108

vii 7.9 The MKS distribution for data and atmospheric neutrino MC using 0 → 0 0 the KS π π searchsidebandsample...... 108 7.10 The pμ distribution for data and atmospheric neutrino MC using the 0 → 0 0 KS π π searchsidebandsample...... 109 7.11 The Ptot distribution for data and atmospheric neutrino MC using 0 → 0 0 the KS π π searchsidebandsample...... 109 7.12 The Mtot distribution for data and atmospheric neutrino MC using 0 → 0 0 the KS π π searchsidebandsample...... 110 0 → 0 0 7.13 The event rate along the KS π π searcheventselection...... 113 7.14 The nring distribution for data and atmospheric neutrino MC along 0 → 0 0 the KS π π searcheventselection...... 114 7.15 The PID likelihood distribution for data and atmospheric neutrino 0 → 0 0 MC along the KS π π searcheventselection...... 114 7.16 The number of decay electron distribution for data and atmospheric 0 → 0 0 neutrino MC along the KS π π searcheventselection...... 115

7.17 The MKS distribution for data and atmospheric neutrino MC along 0 → 0 0 the KS π π searcheventselection...... 115 7.18 The pμ distribution for data and atmospheric neutrino MC along the 0 → 0 0 KS π π searcheventselection...... 116 7.19 The Ptot distribution for data and atmospheric neutrino MC along 0 → 0 0 the KS π π searcheventselection...... 116 7.20 The Mtot distribution for data and atmospheric neutrino MC along 0 → 0 0 the KS π π searcheventselection...... 117 7.21 The Mtot vs. Ptot scatter plot for data, atmospheric neutrino MC and → + 0 0 → 0 0 p μ K MC along the KS π π searcheventselection..... 117 0 → 0 0 7.22 Event display of the candidate for the KS π π search...... 121 8.1 The nring distribution for p → μ+K0 and atmospheric neutrino MC 0 → + − along the KS π π Method#1searcheventselection...... 126 8.2 The PID likelihood distribution for p → μ+K0 and atmospheric neu- 0 → + − trino MC along the KS π π Method #1 search event selection. 127 8.3 The number of decay electron distribution for p → μ+K0 and atmo- 0 → + − spheric neutrino MC along the KS π π Method #1 search event selection...... 128 + 0 8.4 The pμ distribution for p → μ K and atmospheric neutrino MC 0 → + − along the KS π π Method#1searcheventselection...... 128 + 0 8.5 The Ptot distribution for p → μ K and atmospheric neutrino MC 0 → + − along the KS π π Method#1searcheventselection...... 129 8.6 The number of decay electron distribution for data and atmospheric 0 → + − neutrino MC using the KS π π Method #1 search sideband sample...... 131 8.7 The pμ distribution for data and atmospheric neutrino MC using the 0 → + − KS π π Method#1searchsidebandsample...... 131 8.8 The Ptot distribution for data and atmospheric neutrino MC using 0 → + − the KS π π Method#1searchsidebandsample...... 132

viii 0 → + − 8.9 The event rate along the KS π π Method #1 search event selection...... 135 8.10 The nring distribution for data and atmospheric neutrino MC along 0 → + − the KS π π Method#1searcheventselection...... 135 8.11 The PID likelihood distribution for data and atmospheric neutrino 0 → + − MC along the KS π π Method #1 search event selection. . . . 136 8.12 The number of decay electron distribution for data and atmospheric 0 → + − neutrino MC along the KS π π Method #1 search event selection. 136 8.13 The pμ distribution for data and atmospheric neutrino MC along the 0 → + − KS π π Method#1searcheventselection...... 137 8.14 The Ptot distribution for data and atmospheric neutrino MC along 0 → + − the KS π π Method#1searcheventselection...... 137 8.15 The pμ vs. Ptot scatter plot for data, atmospheric neutrino MC and → + 0 0 → + − p μ K MC along the KS π π Method #1 search event selection...... 138 0 → + − 8.16 Event display of the ﬁrst candidate for the KS π π Method #1 search...... 142 0 → + − 8.17 Event display of the second candidate for the KS π π Method #1search...... 143 0 → + − 8.18 Event display of the third candidate for the KS π π Method #1 search...... 144 0 → + − 8.19 Event display of the fourth candidate for the KS π π Method #1search...... 145 0 → + − 8.20 Event display of the ﬁfth candidate for the KS π π Method #1 search...... 146 0 → + − 8.21 Event display of the sixth candidate for the KS π π Method #1 search...... 147

9.1 The number of decay electron distribution for p → μ+K0 and atmo- 0 → + − spheric neutrino MC along the KS π π Method #2 search event selection...... 152 → + 0 9.2 The MKS distribution for p μ K and atmospheric neutrino MC 0 → + − along the KS π π Method#2searcheventselection...... 152 + 0 9.3 The Ptot distribution for p → μ K and atmospheric neutrino MC 0 → + − along the KS π π Method#2searcheventselection...... 153 + 0 9.4 The Mtot distribution for p → μ K and atmospheric neutrino MC 0 → + − along the KS π π Method#2searcheventselection...... 153 9.5 The number of decay electron distribution for data and atmospheric 0 → + − neutrino MC using the KS π π Method #2 search sideband sample...... 155

9.6 The MKS distribution for data and atmospheric neutrino MC using 0 → + − the KS π π Method#2searchsidebandsample...... 155 9.7 The Ptot distribution for data and atmospheric neutrino MC using 0 → + − the KS π π Method#2searchsidebandsample...... 156

ix 9.8 The Mtot distribution for data and atmospheric neutrino MC using 0 → + − the KS π π Method#2searchsidebandsample...... 156 0 → + − 9.9 The event rate along the KS π π Method #2 search event selection...... 159 9.10 The number of decay electron distribution for data and atmospheric 0 → + − neutrino MC along the KS π π Method #2 search event selection. 159

9.11 The MKS distribution for data and atmospheric neutrino MC along 0 → + − the KS π π Method#2searcheventselection...... 160 9.12 The Ptot distribution for data and atmospheric neutrino MC along 0 → + − the KS π π Method#2searcheventselection...... 160 9.13 The Mtot distribution for data and atmospheric neutrino MC along 0 → + − the KS π π Method#2searcheventselection...... 161 9.14 The Mtot vs. Ptot scatter plot for data, atmospheric neutrino MC → + 0 0 → + − and p μ K MC along the KS π π Method #2 search event selection...... 161

10.1 The potot distribution for p → μ+K0 and atmospheric neutrino MC 0 along the KL searcheventselection...... 169 → + 0 10.2 The nringt distribution for p μ K and atmospheric neutrino MC 0 along the KL searcheventselection...... 170 10.3 The PID likelihood distribution for p → μ+K0 and atmospheric neu- 0 trino MC along the KL searcheventselection...... 171 10.4 The number of decay electron distribution for p → μ+K0 and atmo- 0 spheric neutrino MC along the KL searcheventselection...... 172 + 0 10.5 The pμ−cand. distribution for p → μ K and atmospheric neutrino 0 MC along the KL searcheventselection...... 172 + 0 10.6 The vsep. distribution for p → μ K and atmospheric neutrino MC 0 along the KL searcheventselection...... 173 10.7 The pattern PID likelihood distribution for p → μ+K0 and atmo- 0 spheric neutrino MC along the KL searcheventselection...... 173 10.8 The μ-candidate Cherenkov angle distribution for p → μ+K0 and 0 atmospheric neutrino MC along the KL search event selection. . . . 174 10.9 The proton ID likelihood distribution for p → μ+K0 and atmospheric 0 neutrino MC along the KL searcheventselection...... 174 10.10 The number of decay electron distribution for data and atmospheric 0 neutrino MC in the KL searchsidebandsample...... 176 10.11 The pμ−cand. distribution for data and atmospheric neutrino MC in 0 the KL searchsidebandsample...... 177 10.12 The vsep. distribution for data and atmospheric neutrino MC in the 0 KL searchsidebandsample...... 177 10.13 The pattern PID likelihood distribution for data and atmospheric 0 neutrino MC in the KL searchsidebandsample...... 178 10.14 The μ-candidate Cherenkov angle distribution for data and atmo- 0 spheric neutrino MC in the KL searchsidebandsample...... 178

x 10.15 The proton ID likelihood distribution for data and atmospheric neu- 0 trino MC in the KL searchsidebandsample...... 179 0 10.16 The event rate along the KL searcheventselection...... 182 10.17 The potot distribution for data and atmospheric neutrino MC along 0 the KL searcheventselection...... 182 10.18 The nringt distribution for data and atmospheric neutrino MC along 0 the KL searcheventselection...... 183 10.19 The PID likelihood distribution for data and atmospheric neutrino 0 MC along the KL searcheventselection...... 184 10.20 The number of decay electron distribution for data and atmospheric 0 neutrino MC along the KL searcheventselection...... 185 10.21 The pμ−cand. distribution for data and atmospheric neutrino MC along 0 the KL searcheventselection...... 185 10.22 The vsep. distribution for data and atmospheric neutrino MC along 0 the KL searcheventselection...... 186 10.23 The pattern PID likelihood distribution for data and atmospheric 0 neutrino MC along the KL searcheventselection...... 186 10.24 The μ-candidate Cherenkov angle distribution for data and atmo- 0 spheric neutrino MC along the KL searcheventselection...... 187 10.25 The proton ID likelihood distribution for data and atmospheric neu- 0 trino MC along the KL searcheventselection...... 187 0 10.26 Event display of the candidate for the KL search...... 190 12.1 The total momentum vs. μ+ momentumscatterplot...... 199 12.2 Event display of ﬁrst event selected by this analysis and not the referencedata...... 200 12.3 Event display of second event selected by this analysis and not the referencedata...... 200 12.4 The reconstructed-true μ-candidatemomentumdistribution..... 201

xi LIST OF TABLES

Page

0 1.1 KS decaybranchingratios...... 12 0 1.2 KL kinematicsinwater...... 13 7.1 Data events, signal detection efficiency and background rate along the 0 → 0 0 KS π π searcheventselection...... 113 7.2 Breakdown of remaining atmospheric neutrino MC background for the 0 → 0 0 KS π π search...... 119 7.3 Summary of reconstructed information for the data candidate of the 0 → 0 0 KS π π search...... 120 0 → 0 0 7.4 Systematic errors on signal detection efficiency for the KS π π search...... 122 0 → 0 0 7.5 Systematic errors on background rate for the KS π π search. . . . 123 8.1 Data events, signal detection efficiency and background rate along the 0 → + − KS π π Method#1searcheventselection...... 134 8.2 Breakdown of remaining atmospheric neutrino MC background for the 0 → + − KS π π Method#1search...... 139 8.3 Summary of reconstructed information for the data candidates of the 0 → + − KS π π Method#1search...... 141 0 → + − 8.4 Systematic errors on signal detection efficiency for the KS π π Method#1search...... 148 0 → + − 8.5 Systematic errors on background rate for the KS π π Method #1 search...... 149

9.1 Data events, signal detection eﬃciency and background rate along the 0 → + − KS π π Method#2searcheventselection...... 158 9.2 Breakdown of remaining atmospheric neutrino MC background for 0 → + − KS π π Method#2search...... 162 0 → + − 9.3 Systematic errors on signal detection eﬃciency for the KS π π Method#2search...... 163 0 → + − 9.4 Systematic errors on background rate for the KS π π Method #2 search...... 164

10.1 Data events, signal detection eﬃciency and background rate along the 0 KL searcheventselection...... 181

xii 10.2 Breakdown of remaining atmospheric neutrino MC background for the 0 KL search...... 188 10.3 Summary of reconstructed information for the data candidate of the 0 KL search...... 189 0 10.4 Systematic errors on signal detection eﬃciency for the KL search. . . 191 0 10.5 Systematic errors on background rate for the KL search...... 192 11.1Resultofthelowerlifetimelimitcalculation...... 195

→ + 0 12.1 Summary of the p μ KS search results from Kobayashi [1] and this analysis...... 198

xiii ACKNOWLEDGMENTS

First, I would like to express my deepest gratitude to Dr. Shun’ichi Mine. Without his dedication and very supportive guidance this thesis would not be possible. I also would like to thank my advisor Prof. Dave Casper for providing many suggestions for this analysis as well as Prof. Hank Sobel for his unwavering support of my work. I want to thank Prof. Yoichiro Suzuki, the spokesman of the Super Kamiokande experiment and I would like to thank especially Prof. Masato Shiozawa, Prof. Ed Kearns, Prof. Kenji Kaneyuki, Prof. Takaaki Kajita and Prof. Chris Walter for all of their generous suggestions. I am also grateful to all members of the atmospheric and proton decay analysis group at ICRR including Y. Hayato, C. Ishihara, J. Kameda, M. Miura, S. Moriyama, S. Nakayama, H. Nishino, Y. Obayashi, K. Okumura, N. Tanimoto. Much of the analysis within this thesis would not have been possible without the hard work and dedication of the Super Kamiokande collaboration to whom I am very thankful. I also want to thank Parker Cravens, Mike Litos, Jen Raaf and Roger Wendell for their assistance as well as the many great adventures we had in Japan. I would like to thank my fellow students that I studied with during my graduate career: Shane Curry, Mike Hood, Shiu Liu, Parker Lund, Matt Teig and Erik Trask. I always enjoyed talking over the latest homework problems with you all and enjoying our time together. This work would not be possible without the funding made possible by the US Department of Energy and the cooperation of the Kamioka Mining and Smelting Company. Finally, I’d like to thank my family for always being supportive of me during this long diﬃcult path.

xiv CURRICULUM VITAE

Christopher Regis

Education:

2001 B.S., Physics, University of California, Santa Barbara

2004 M.S., Physics, University of California, Irvine

2011 Ph.D., Physics, University of California, Irvine

Awards and Honors:

2004-2005 Outstanding Contributions to the Department Award

xv ABSTRACT OF THE DISSERTATION

A search for proton decay via p → μ+K0 in Super Kamiokande I

Christopher Regis

Doctor of Philosophy in Physics

University of California, Irvine, 2011

Professor David Casper, Chair

Asearchforp → μ+K0 was performed using the Super Kamiokande I (SK-I) data set with a live-time of 1489.2 days corresponding to a total exposure of 91.2ktyears.

→ + 0 In addition to searching this decay mode via the p μ KS channel, previously performed by Kobayashi using the SK-I data set [1], new event reconstruction was → + 0 developed speciﬁcally to search for separated vertices characteristic of the p μ KL

0 channel. This new reconstruction takes advantage of the long lifetime of the KL which results in a unique event signature in which there are two distinct vertices; one

0 corresponding to the proton decay point and another at the KL disappearance point. These are typically separated by about 2 m in space and 20 ns in time.

We did not observe statistically signiﬁcant evidence for p → μ+K0 decay. There-

33 fore, a lower limit on the proton partial lifetime, τ/Bp→μ+K0 ,of1.1 × 10 years was obtained at 90% conﬁdence level.

xvi Chapter 1

Introduction

1.1 Theoretical Motivation

The Standard Model (SM) of particle physics is a theoretical construct that attempts to explain the interactions between the fundamental particles that make up the uni- verse. It generates electromagnetic, weak and strong interactions via corresponding

gauge symmetries mediated by the corresponding gauge ﬁelds, W ±, Z0 and photon, A. Although this model has been very successful in accurately describing results from a multitude of experiments, there are some limitations to the theory. As one example, the SM does not explain the observation of non-zero neutrino mass.

In an attempt to rectify this situation, as well as motivated by the observation of the apparent merging of the electromagnetic, strong and weak coupling constants at higher energies, Grand Uniﬁed Theories (GUTs) have been developed which attempt to unify these three fundamental forces under a larger gauge symmetry. One typical feature that arises during the construction of these GUTs that is not present in the SM is proton decay. Grand uniﬁcation is not without fault however, particularly the so-called “hierarchy problem”, the inelegant necessity to introduce careful tuning of parameters in the calculation of the Higgs mass. One method to solve this problem

1 2 is known as super-symmetry (SUSY) in which a super-symmetric partner for every particle in the SM is introduced. In some of these SUSY GUT models p → μ+K0 is one of the dominant expected proton decay modes [2]. Details of the SM, GUTs and SUSY GUTs are described sections 1.1.2, 1.1.3 and 1.1.3.2 respectively.

1.1.1 Conservation and Symmetries

In theoretical physics, one of the most useful tools is known as Noether’s theorem which states that there exists a conservation law for every continuous symmetry of the

Lagrangian that describes a physical system [3]. Some examples of this are momentum and energy conservation which are due to the invariance of the Lagrangian under translations in space and time. However, there are other quantities such as baryon number which seem to be conserved but have no underlying symmetry. As baryon

number is not a conserved quantity in proton decay, a search for proton decay is a experimental test of the validity of baryon number conservation. To describe these symmetries in a mathematical formalism, group theory is used.

1 An example of this is the SU(2) group used to describe spin- 2 systems in quantum mechanics. The commutation relation between the generators completely describes the group.

[Li,Lj]=iijkLk (1.1)

where ijk is the completely anti-symmetric tensor and (i, j, k) run over indices 1, 2,

3. The generators, Li, can be expressed in terms of the traceless, unitary Pauli spin

σi matrices, σi,asLi = 2 . These matrices span the SU(2) space. Any arbitrary unitary

matrix M with determinant = 1 can be expressed in terms of Li as:

M = eiαi·L i (1.2) 3 where α is an arbitrary scale vector. The two physical states of this system are the orthogonal eigenstates up |+ and down |− which form a basis of the SU(2) space. In SU(2) there are two important operators:

L± =(L1 ∓ iL2) (1.3)

these represent the mixing between the states L±|∓ = |±. The complete system can now be described in terms of the generator matrix, L, and corresponding doublet,

ψ: ⎡ ⎤ ⎛ ⎞

1 ⎢Lz L+ ⎥ ⎜|+⎟ L = ⎣ ⎦ ψ → ⎝ ⎠ (1.4) 2 L− −Lz |−

The diagonal terms of L represent the projection of ψ and the oﬀ-diagonal terms represent transformations between eigenstates. Now that we have this formalism, we can make an analogy to particle physics. For instance, the doublet can represent a doublet of fermions such as an electron and the νe while the generators, Lz and

0 ± L±, correspond to the gauge bosons (Z and W for example). This gives rise to interactions which allow the states to mix; for instance changing the electron to a νe via the exchange of a W−.

1.1.2 Standard Model

In the SM of particle physics the fundamental particles and interactions are described

by the SU(3)c ⊗ SU(2)L ⊗ U(1)Y gauge symmetry. The SU(3)c gauge symmetry describes strong interactions between quarks. In this group, the quarks have color charge and form a color triplet, ψc, of three states: red, green and blue. In this case the mediators of the strong force are called gluons and are represented as the 4

generator matrix, Ggluon: ⎡ ⎤ ⎛ ⎞

⎢grr¯ grg¯ gr¯b⎥ ⎜ red ⎟ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ → ⎜ ⎟ Ggluon = ⎢g g g ¯⎥ ψc ⎜green⎟ (1.5) ⎣ gr¯ gg¯ gb⎦ ⎝ ⎠

gbr¯ gbg¯ gb¯b blue

− where gb¯b = grr¯ ggg¯.

The SU(2)L ⊗ U(1)Y gauge symmetry describes the uniﬁcation of the electromagnetic and weak interaction into electro-weak theory. Under this symmetry, left handed fermions form SU(2)L doublets with weak isospin, T3, and right-handed fermions are singlets. Each fermion has a weak hypercharge, Y ,fromtheU(1)Y symmetry and is assigned as:

Y =2(Q − T3) (1.6) where Q is the electrical charge of the fermion.

The SU(2)L ⊗ U(1)Y gauge symmetry has four generators expressed as the mass-

1 2 3 less gauge bosons, W ,W ,W from SU(2)L and B from U(1)Y . However this is inconsistent with the experimental observation of three massive gauge bosons, W ±

and Z0 that mediate the weak interaction and the massless photon, A, that mediates the electromagnetic force. One method to resolve this issue is to spontaneously break the SU(2)L ⊗ U(1)Y gauge symmetry via the Higgs mechanism by introduction of a scalar particle known as the Higgs boson. This generates mass for the W ± and

Z0 bosons which are formed from the massless gauge bosons parameterized by the

Weinberg mixing angle θw as:

0 3 Z = W cos θw − B sin θw (1.7)

3 A = W sin θw + B cos θw (1.8) 5

Although the SM is a very successful theory, it does not represent a complete theory of particle physics. Some reasons for this include: the arbitrary assignment of the weak hypercharge to each fermion, the lack of an explanation for the factor of three relationship in charge quantization between quark and leptons, the observation of non-zero neutrino mass and lack of any description of gravity.

1.1.3 Grand Uniﬁed Theories

Grand uniﬁcation is the attempt to unify the strong, weak and electromagnetic in-

teractions under a larger GUT gauge symmetry. One of the earliest indications of this uniﬁcation is the apparent convergence of the running coupling constants that represent the strength of each of these interactions at an energy scale known as the GUT scale. Furthermore, since the SM has been so successful, it suggests that the

SM is a result of spontaneous symmetry breaking of the GUT gauge symmetry at the GUT energy scale.

1.1.3.1 Minimal SU(5)

One of the earliest attempts at a GUT was proposed by Georgi and Glashow using the

SU(5) group, the smallest gauge group that can contain the SU(3)c ⊗SU(2)L ⊗U(1)Y group of the SM [4]. The generators of this group are written as:

⎡ ⎤ 2 g − √ Bg g ¯ X Y ⎢ rr¯ 30 rg¯ rb 1 1 ⎥ ⎢ ⎥ ⎢ − √2 ⎥ ⎢ ggr¯ ggg¯ Bgg¯b X2 Y2 ⎥ ⎢ 30 ⎥ ⎢ 2 ⎥ VSU(5) = ⎢ g g g ¯ − √ BX Y ⎥ ⎢ br¯ bg¯ bb 30 3 3 ⎥ ⎢ ⎥ ⎢ X¯ X¯ X¯ √1 W 3 + √3 BW+ ⎥ ⎣ 1 2 3 2 30 ⎦ Y¯ Y¯ Y¯ W − − √1 W 3 + √3 B 1 2 3 2 30 (1.9) 6 with the fermions contained in 5¯ and 10 representations as:

⎛ ⎞ ⎡ ⎤ ¯ dr ⎢ 0¯ub −u¯g −ur −dr ⎥ ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ ⎜ ¯ ⎟ ⎢ −u¯ 0¯u −u −d ⎥ ⎜ dg ⎟ ⎢ b r g g ⎥ ⎜ ⎟ ⎢ ⎥ 5¯ = ⎜ ¯ ⎟ 10 = ⎢ − − − ⎥ (1.10) ⎜ db ⎟ ⎢ u¯g u¯r 0 ub db ⎥ ⎜ ⎟ ⎢ ⎥ ⎜ − ⎟ ⎢ ⎥ ⎜ e ⎟ ⎢ u u u 0 e+ ⎥ ⎝ ⎠ ⎣ r g b ⎦ + −νe dr dg db −e 0 L L

± 3 The gcc¯ are the gluons of SU(3)c,theW , W and B are the gauge bosons of the electroweak theory of the SM. In this GUT there are twelve new bosons X and Y

15 with mass MX,Y ∼ 10 GeV, the GUT energy scale, which do not appear in the standard model. These bosons have both color and ﬂavor and mediate interactions between the leptons and quarks. These interactions, whose Feynman diagrams are illustrated in Figure 1.1, do not conserve baryon number (B) or lepton number (L) but do conserve (B-L) and lead to nucleon decay via the exchange of one of these new bosons with a lifetime proportional to:

4 ∼ 1 MX τ 2 5 (1.11) αGUT mp

where αGUT is the value of the coupling constant at the GUT scale. The favored decay mode for SU(5) is p → e+π0 with a calculated partial lifetime

29±0.7 of τ/Bp→eπ0 =3.7 × 10 years [5]. However, this GUT model has been ruled out with the most recent lower lifetime limit set for this decay mode at 8.2×1033 years [6]. An additional diﬃculty with the SU(5) model is the value of the weak mixing angle

2 measured by experiment of sin θW =0.23108 ± 0.00005 [7] is inconsistent with the

2 0.0037 predicted value of sin θW =0.2102−0.0031 [8]. 7

dα e+ uα e+ dα ν¯

Xα Y α Y α

uβ u¯γ dβ u¯γ

Xα Y α

Figure 1.1: Feynman diagrams representing the interactions mediated by the Xα & Y α gauge bosons of the SU(5) GUT.

1.1.3.2 Supersymmetric GUTS

Assuming the existence of a GUT, when calculating the mass of the electro-weak

2 ∼ 2 Higgs boson of mH (250 GeV) , the radiative corrections introduce an enormous correction ∼ 1030 GeV2 and so extremely ﬁne tuning of this correction is necessary. This is known as the “hierarchy problem”. One method to solve this is introduction of a symmetry between fermions and bosons known as SUSY. In SUSY every fermion of the SM gets a bosonic partner with the same mass but spin 1/2 diﬀerent and vice versa. In this way, the radiative corrections are canceled by the new SUSY particles.

In addition to solving the hierarchy problem, in a SUSY GUT MX,Y is predicted to be 1016 GeV instead of 1015 GeV in the non-SUSY case thus increasing the proton decay lifetime by four orders of magnitude from (1.11) which is consistent with the experimental lifetime limits on p → e+π0. Furthermore, in SUSY GUTs the pre-

2 +0.0031 diction of the weak mixing angle is sin θW =0.2334−0.0027 which is consistent with experimental data [8]. Although the p → e+π0 decay mode may be suppressed in SUSY GUT models, 8 there are other interactions available in the SUSY GUT Lagrangian which mediate nucleon decay. The most significant contributor is the dimension 5 (d=5) operator via the exchange of a SUSY Higgsino illustrated in the Feynman diagram shown in Figure 1.2. Interactions via this operator require the family of the final state be different than the family of the initial state. Since a proton is composed of quarks from the first family this means that interactions involving this operator require quarks from the second or third families. As the strange quark is the only one that is kinematically allowed, an anti-strange quark must be in the final state. This will bind to a spectator u or d quark forming a K meson. In minimal SU(5) SUSY, the favored decay modes are therefore p → νK¯ + shown in Figure 1.3 and n → νK¯ 0 and the lifetime of these decay modes is calculated to be ∼ 1030±2 years [9].

In addition to SUSY GUT models based on SU(5), others have been proposed basedontheSO(10) group [2]. One feature of these models is the neutrino can obtain mass provided a new set of color triplet ﬁelds is introduced. These ﬁelds generate a new set of d=5 operators which predict comparable rates for p → νK¯ + and p → μ+K0

of [2]:

Γ(p → μ+K0) ≈ (20% to 50%) Γ(p → νK¯ +) (1.12)

Given (1.12) and the predicted lifetime of p → νK¯ + of ∼ 1032∼34 years the expected lifetime of p → μ+K0 is:

33∼35 τ/Bp→μ+K0 ∼ 10 years (1.13) which is within reach of the SK sensitivity of ∼ 1033 years. 9

q˜ q l

W˜ H˜ q q q˜ Figure 1.2: Feynman diagram representing the exchange of a Higgsino from the d=5 operator in the SUSY GUT Lagrangian. d˜ u ν¯μ W˜ H˜ p d s¯ u˜ K+ u u

Figure 1.3: Feynman diagram representing the p → νK¯ + decay mode.

1.2 Past Experimental Measurements of p → μ+K0

1.2.1 Soudan 2

The Soudan 2 experiment was a 963 t (770 t ﬁducial) iron calorimeter experiment

located in the Soudan mine in Minnesota at a depth of 2100 meters water equivalent (m.w.e.). The active portion of the detector consisted of 1 m long 1.5 cm diameter drift tubes encased in a honeycomb matrix of 1.6 mm steel plates. This experiment took data from 1989-2001 corresponding to a ﬁducial mass exposure of 5.9kt-yr. This → + 0 → + 0 experiment searched both p μ KS and p μ KL modes and set a lower lifetime limit on each of 1.5 × 1032 years and 8.3 × 1031 years respectively giving a combined lower lifetime limit on p → μ+K0 of 1.2 × 1032 years [10].

1.2.2 Irvine Michigan Brookhaven (IMB)

The IMB experiment was an 8 kt (3.3 kt ﬁducial), rectangular, water Cherenkov de-

tector located at a depth of 1580 m.w.e. in the Fairpoint Mine in Ohio. It took data from 1982-1991. This experiment set a lower lifetime limit on p → μ+K0 of 10

× 32 → + 0 1.2 10 years [11] by searching only the p μ KS mode.

1.2.3 Kamiokande

The Kamiokande experiment was the precursor to the Super Kamiokande (SK) ex-

periment and also was located in the Mozumi Mine. The experiment was a water Cherenkov detector with a total mass of 3 kt surrounded by 948 50 cm photo-multiplier tubes (PMT) resulting in 20% photocathode coverage. It took data from 1986-1996. This experiment set a lower lifetime limit on p → μ+K0 of 1.2 × 1032 years [12] by → + 0 searching only the p μ KS mode.

1.2.4 Super Kamiokande

The current best lower lifetime limit on p → μ+K0 is 1.3 × 1033 years by Kobayashi

→ + 0 set using the SK-I data set searching the p μ KS mode only [1]. Currently, there → + 0 is no published result using p μ KL with SK data.

1.3 Overview of Experimental Method

The SK detector is the largest water Cherenkov detector in the world with a fiducial mass of 22.5 kt. Assuming the ideal but unrealistic case of 100% signal detection efficiency with 0 background and an exposure of 91.7 kt-yr from SK-I, upper limits on the proton decay lifetime of ∼ 1.3 × 1034 years are possible for decay modes that include final state particles above the Cherenkov threshold.

0 0 0 → + 0 The K is a combination of 50% KS and 50% KL so searches for p μ K → + 0 → + 0 typically involve searching for p μ KS and p μ KL separately. For this thesis, we search for p → μ+K0 in SK-I data by updating the p →

+ 0 μ KS mode search performed by Kobayashi [1]. We use the latest improved detector calibration and event reconstruction, use a new combined search analysis strategy 11

→ + 0 described in section 6.2 and introduce a new search of p μ KL described in Chapter 10.

0 0 The lifetime of the KS is 0.9 ns; kinematically in water the KS nearly always

0 decays. The KS decay modes along with their respective branching ratios are summarized in Table 1.1 [7].

→ + 0 For the search of p μ KS in this thesis, an exclusive search is performed for the 0 → 0 0 0 → + − KS π π and KS π π decay modes only; the remaining fraction is neglected. → + 0 The decay of the proton via p μ KL provides a unique event signature due

0 to the much longer lifetime of the KL of 51 ns. Because of this, events from this proton decay mode are characterized by two vertices that are separated in time and

∼ ∼ 0 space within the detector; typically 20 ns and 2 m respectively for KL decay. The primary vertex is located at the proton decay point the remaining vertex is the

0 location of the KL decay point. For this thesis a new event reconstruction, described in section 5.2, was developed to look for these separated vertices and use this information to help separate the proton decay signal from the atmospheric neutrino background.

0 In addition to decaying, the KL can hadronically interact in the water in ﬂight. 0 → Additionally, the KL can undergo KL KS regeneration a process not previously included in the event simulation and was introduced for this analysis as described in sections 3.1.3 and 3.4.3. Using the p → μ+K0 monte-carlo (MC) and SK detector simulation described in sections 3.1 and 3.4 respectively, the branching fraction was determined for these kinematic processes and summarized in Table 1.2. We perform

→ + 0 0 an inclusive search of p μ KL which is independent of the KL kinematic process. In this thesis we present the results of a proton decay search via p → μ+K0 in

→ + 0 → + 0 the SK detector using the combined results of p μ KS and p μ KL searches. The presentation begins in Chapter 2 with a description of the SK detector, data acquisition and calibration. A description of the simulation of the proton decay, atmospheric neutrino interaction and the detector is given in Chapter 3. The data 12 reduction steps for the fully contained sample is described in Chapter 4. Chapter 5 details the event reconstruction. In Chapter 6 an overview of the proton decay search is presented; the results are shown in Chapters 7-11. A discussion of these results, including a comparison with the previous SK result, future prospects and conclusion are found in Chapters 12, 13 and 14 respectively. Finally, details of systematic error estimation is described in Appendix A.

0 KS decay mode Branching ratio Γ (%) 0 → + − KS π π 69.2 0 → 0 0 KS π π 30.7 0 → KS other 0.1

0 Table 1.1: KS decay branching ratios. 13

0 KL kinematic process in water Branching ratio Γ (%) 0 → 2 3 KL N N,α, H, H 16.5 0 → ± KL N NK 15.7 0 → + 0 KL p π Λ 10.4 K0 p → π0Σ+ 5.8 0 → L KL interaction 0 → + 0 KL p π Σ 5.8 72.2% 0 → − + KL n π Σ 5.5 0 → + − KL n π Σ 5.1 0 → 0 0 KL n π Σ 3.6 0 → 0 0 KL n π Λ 2.2 0 → KL N other 1.6 0 → ± ∓ KL π e ν 11.1 0 → 0 → ± ∓ KL decay KL π μ ν 7.0 0 → 0 27.5% KL 3π 5.7 0 → + − 0 KL π π π 3.7

KL → KS regeneration 0.1 0 → KL other 0.2

0 Table 1.2: KL kinematics in water. Chapter 2

Detector

2.1 Cherenkov Radiation

When a charged particle of mass, m, and momentum, p, travels faster than light in a medium it produces a coherent electromagnetic wavefront known as Cherenkov radiation or Cherenkov light. This wavefront moves outward at an angle with respect

to the particle direction known as the Cherenkov angle, θc. The Cherenkov angle, the index of refraction of the medium, n, and velocity of the particle, β = v/c,are related by the following: 1 1 m2 cos θ = = 1+ (2.1) c nβ n p2

The requirement that the charged particle travel faster than light in the medium for

Cherenkov light to be emitted leads to a minimum momentum threshold, pthresh:

m pthresh = √ (2.2) n2 − 1

14 15

Figure 2.1: Relative Cherenkov light spectrum in pure water. For comparison the quantum eﬃciency of the 50 cm PMT is also shown.

As the particle moves through the medium a unit length, dx, the unit number, dN, of Cherenkov photons emitted with unit wavelength, dλ,is:

d2N 1 1 =2πα 1 − (2.3) dxdλ (nβ)2 λ2 where α ≈ 1/137 is the ﬁne structure constant. As shown in Figure 2.1 the SK detector is sensitive to wavelengths ∼ 300 nm to 600 nm. The number of photons within this wavelength range emitted along the track of a charged particle traveling close to the speed of light (β 1) in water (n 1.34) is

∼ 340 cm−1. The Cherenkov light that is emitted by the particle is projected onto the wall of the SK detector as a ring pattern. From this ring pattern the kinematics of the particle that generated the Cherenkov light are reconstructed. 16

2.2 Super Kamiokande Detector

The SK detector is a water Cherenkov detector located at 2700 m.w.e. in the Mozumi mine beneath Mt. Ikenoyama in Kamioka, Gifu Prefecture, Japan. The detector, diagrammed in Figure 2.2, consists of a stainless steel right cylinder tank 41.4m in height and 39.3 m in diameter filled with 50 kt of ultra-purified water. Within the tank, a stainless steel cylindrical superstructure divides the tank volume into three concentric cylindrical volumes. The inner-most volume is known as the Inner Detector (ID); it is 36.2 m in height and 33.8 m in diameter. Mounted to the inner wall of the superstructure are 11146 50 cm diameter PMTs which face the ID corresponding to 40% photocathode coverage. Lining the inner wall of the superstructure, filling the gaps between the ID PMTs is an opaque black plastic material that serves as an optical barrier between the ID and remaining tank volume. The outer-most volume is known as the Outer Detector (OD); it completely sur- rounds the ID and has a thickness of 1.95 m to 2.2 m. Mounted to the outer wall of the superstructure are 1885 20 cm diameter PMTs with 60 cm square wave-shifter plates that face the OD. This wall is lined with Tyvek bonded to black low density polyethylene which serves as an optical barrier to the ID. The outer-most wall of the OD is lined with DuPont Tyvek; a white reflective material which helps to increase the number of detected photons in the OD. The third volume is the 0.55 m thick dead space region between the ID and OD which is occupied by the superstructure that supports the PMTs as well as the coaxial cables that carry the PMT signals outside the water tank. The detector began taking data in April 1996. In July, 2001 after 5 years of observation, a period known as SK-I, the data taking was stopped for maintenance of the detector. In November, 2001 during the refilling of the detector after the maintenance work, an accident occurredinwhichanIDPMTatthebottomregion 17

Figure 2.2: The Super Kamiokande detector. of the tank imploded. This generated a shockwave in the water that caused a chain reaction which destroyed more than half of the PMTs in the detector. The detector was rebuilt with half the ID PMT density of SK-I and began to take data in October,

2002. This second phase of the detector is known as SK-II. SK-II continued until October, 2005 when work began to replace the PMTs that had been destroyed in the accident and bring the ID PMT density back to the SK-I level. This work completed in June, 2006 and the detector took data in a period known as SK-III. SK-III ended in

September, 2008 with the upgrade of the electronics and online systems in preparation of the T2K experiment. From the completion of the upgrade in October, 2008 through the time of this thesis writing the detector has continued taking data in a period known as SK-IV. In this thesis we present the results of the proton decay search using the SK-I data set. 18

2.3 Photomultiplier Tube

Installed in the ID are Hamamatsu R3600 PMTs with a photocathode 50 cm in diameter as shown in Figure 2.3. The bulbs of the PMTs are hand blown from borosilicate glass to a thickness of about 5 mm. The inner surface of the glass is coated with

Bialkali (Sb-K-Cs) photocathode designed so its quantum eﬃciency (QE) coincides with the peak of the Cherenkov light spectrum as shown in Figure 2.4. Within the PMT, an 11 stage Venetian blind style dynode multiplies the ejected photoelectron (p.e.) from the photocathode across an applied voltage of 1700 V to 2000 V creating a gain of 107. The OD PMTs are Hamamatsu R1408 PMTs with a 20 cm diameter photocathode. An acrylic wavelength shifting plate of 60 cm × 60cmdopedwith50mgl−1 of bis-MSB scintillator is attached to the bulbs of the OD PMTs. The scintillator within the plate absorbs ultraviolet light (UV) then emits scintillation light at a wavelength which matches the peak sensitivity of the PMTs. This improves the collection eﬃ- ciency of the OD PMT by a factor of 1.5. The signals for both ID and OD PMTs are read out via a 70 m coaxial cable that passes through the detector dead space region to exit the top of the detector into one of four electronic huts where they are recorded by the electronics and data acquisition system.

2.4 Electronics & Data Acquisition

2.4.1 Inner Detector

A schematic of the data acquisition system (DAQ) for the ID PMT is shown in Figure 2.6. The ID PMT signals are collected by 12 channel analog timing modules (ATM) [13] that are housed in Tristan KEK Online (TKO) crates [14]. The ATM per- 19

Figure 2.3: The 50 cm diameter PMT Hamamatsu R3600 PMT.

0.2

Quantum efficiency 0.1

0 300 400 500 600 700 Wave length (nm) Figure 2.4: The quantum eﬃciency of the 50 cm PMT. 20

Figure 2.5: The transit time spread of the 50 cm PMT for single p.e. equivalent signals. This spread corresponds to the timing resolution of the PMT. forms an analog to digital conversion of the charge and timing of the PMT signal. The dynamic range for charge and timing for each channel is ∼ 450 pC (picoCoulumbs) with 0.2 pC resolution and ∼ 1300 ns with a resolution of 0.4 ns respectively. Within each channel of the ATM, the analog signal from the PMT is ampliﬁed 100 times then split into four separate signals. The ﬁrst of these split signals is added to the PMTSUM which represents the analog sum of the 12 channels of the ATM. PMT- SUM is used for the FLASH ADC DAQ described elsewhere [15]. The second of the split signals is sent to a discriminator with a threshold of −1 mV corresponding to 0.25 p.e. When this threshold is reached, a 200 ns width 15 mV/channel HITSUM signal is generated which is used to determine the global triggering. The remaining two split signals are sent to a pair of time to analog converters (TAC) and charge to analog converters (QAC). If a global trigger is issued, then the information in the TAC and QAC is digitized. The purpose for two banks of TAC/QAC is to enable the recording of two successive events without dead time introduced by the digitiza- tion process. Events like this occur, for example, by the electron generated from a 21 decaying muon. In total there are 946 ATMs that are read out by 8 online computers via 48 Versa

Module Europe (VME) memory modules called Super-Memory Partner (SMP). The data collected by each SMP is sent to a online host computer where is assembled and merged with the other SMP data to make complete events.

2.4.2 Outer Detector

The electronics system for the OD consists of a charge to timing converter (QTC)

module which takes the OD PMT signal as input and generates a rectangular signal whose width is proportional to the total charge of the input signal. If the signal exceeds the threshold of 0.25 p.e., the QTC also generates a rectangular OD HITSUM signal and the PMT signal is digitized by a Lecroy 1877 multi-hit timing to digital

conversion (TDC) module. This TDC module has a dynamic range of 16 ñswitha resolution of 0.5 ns. This TDC data is then read out by a separate online computer system, transferred to the on-line host computer where it is merged with the ID data.

2.4.3 Trigger System

The HITSUM that is generated by each ATM and QTC is collected and added to

produce a total HITSUM for the ID and OD respectively. For the ID there are three triggers: High Energy (HE), Low Energy (LE) and Super Low Energy (SLE) that are activated if the total ID HITSUM exceeds a speciﬁed threshold. In SK-I the HE trigger threshold is set at −340 mV corresponding to 31 hits within a 200 ns time window. The LE threshold is −320 mV corresponding to 29 hits which is expected from a 5.7 MeV electron assuming 50% trigger eﬃciency. The SLE trigger threshold, implemented in May 1997 is set to 4.7 MeV equivalent. SLE trigger events are not used in this analysis. The OD has only one trigger that is generated when the total OD HITSUM reaches a threshold corresponding to 19 hit PMTs in the OD. 22

20-inch PMT

SCH ATM

x 20 x 240 ATM GONG 20-inch PMT

SCH ATM interface Ultra Sparc x 20 x 240 SMP ATM GONG SMP online CPU(slave) SMP SMP SMP SMP Super Memory Partner x 6

VME 20-inch PMT

SCH Ultra Sparc ATM online CPU(slave) x 20 x 240 ATM Ultra Sparc GONG Analog Timing Module online CPU(host) online CPU(slave) TKO Ultra Sparc FDDI Ultra sparc online CPU(slave)

Ultra Sparc

online CPU(slave)

Ultra Sparc FDDI online CPU(slave)

Ultra Sparc

online CPU(slave)

interface online CPU Ultra Sparc (slave) SMP Ultra Sparc SMP online CPU(slave) SMP SMP SMP SMP Super Memory Partner interface VME VME interrupt reg. 20-inch PMT TRG

SCH ATM TRIGGER

TRIGGER x 20 PROCESSOR x 240 HIT INFORMATION ATM GONG Analog Timing Module

TKO

PMT x 11200 ATM x ~1000 SMP x 48 online CPU(slave) x 9

Figure 2.6: Schematic of the SK ID DAQ system. 23

These four trigger types are sent to the TRG module where the trigger type and event number are recorded and trigger timing is determined with 20 ns accuracy. This information is then sent to the online-host computer where it is merged with the PMT data.

2.5 Water Puriﬁcation System

The origin of the water that ﬁlls the SK detector is spring water from the Mozumi mine. Prior to entering the tank, the water is ultra puriﬁed using a sophisticated

water system shown schematically in Figure 2.7. The SK water system consists of

eight stages in the order as follows: ñ 1. 1 ñm ﬁlter: This rejects relatively larger particles of size > 1 m.

2. Heat exchanger: This maintains the water temperature near 14 ◦C to inhibit growth of bacteria within the water.

3. Ion Exchanger: This removes metal ions from the water.

4. Ultraviolet sterilizer: This kills any live bacteria in the water

5. Vacuum degasiﬁer: This removes any gasses such as oxygen and radon.

6. Cartridge polisher: High performance ion exchanger.

7. Ultra ﬁlter: Removes smaller particles > 10 nm.

8. Reverse Osmosis: Removes organisms up to 100 molecular weight.

To maintain the water quality of the detector, the water in the tank is continuously recirculated at a rate of about 35 t/hour. After the puriﬁcation process, the number

3 of particles larger than 0.2 ñm is reduced to 6 particles/cm , the light attenuation length is ∼ 100 m and the resistivity of the water is increased from about 11 MΩ cm to an average of 18.2MΩcm. 24

VACUUM DEGASIFIER PUMP CARTRIDGE POLISHER ULTRA MEMBRANE FILTER DEGASIFIER UV STERILIZER

HEAT FILTER HEAT PUMP EXCHANGER (1μm Nom.) EXCHANGER

PUMP

BUFFER REVERSE TANK OSMOSIS PUMP RN-LESS-AIR

RN-LESS-AIR REVERSE DISSOLVE TANK OSMOSIS SK TANK SUPER-KAMIOKANDE WATER PURIFICATION SYSTEM Figure 2.7: Schematic of the SK water puriﬁcation system.

2.6 Calibration

2.6.1 Timing Calibration

Timing calibration of the PMTs is crucial to achieve the precision timing that is necessary for accurate vertex reconstruction. There are a two important quantities that must be measured for each PMT to ensure this precision timing is obtained. First, the transit time of the PMT and its ∼ 70 m signal cable. Second, the eﬀect

known as time walk in which a larger signal will trigger the discriminator threshold earlier than a smaller signal. The system used to calibrate the PMT timing is diagrammed in Figure 2.8a. A diﬀuser ball is placed in the water tank. The diﬀuser ball is composed of a silica gel material called LUDOX made from 20 nm glass fragments. Inserted into the ball is

one end of an optical fiber with a TiO2 tip. The optical fiber connects the diffuser ball to a nitrogen dye laser that sends a ∼ 3 ns pulse of light at a wavelength of 384 nm. This wavelength corresponds to the peak quantum efficiency of the ID PMT. The intensity of the light is adjusted using neutral density (ND) optical filters. The TiO2 25

980 variable attenuation filter 970 Linear Scale Log Scale optical fiber N laser 2 generator 960 λ=384nm 950 monitor Super Kamiokande PMT 940 inner tank

optical fiber sig. 930 20’PMT T (nsec) diffuser 920 ball trigger elec. 910

sig. 900

sig. 890 diffuser tip(TiO ) DAQ 2 elec. LUDOX 20’PMT sig. 880 1 5 10 100 Q (p.e.) (a) (b)

Figure 2.8: (a) Schematic of the timing calibration system. (b) TQ-map, a timing vs. charge distribution for a single PMT. tip and LUDOX diﬀuse the light within the ball to create an isotropic light source. By changing the optical ﬁlter, data is taken at a range of intensities and the PMT timing is measured. A distribution of the measured timing as a function of the detected p.e. is made for each PMT. This distribution is known as TQ-map. Figure

2.8b shows an example for one PMT. Each point is data. The open circles represent the average timing for each p.e. bin. The timing of each PMT is then corrected using the TQ-map.

2.6.2 Relative Gain Calibration

Uniform response of the detector is necessary to determine the momentum of a particle without a systematic difference that is dependent on the vertex or direction within the tank. To achieve this, calibration data is taken and the PMT high voltage is adjusted to obtain a uniform gain for all PMTs. A diagram of the relative gain calibration system is shown in Figure 2.9a. Light from a Xe lamp passes through UV and ND optical filters before being injected into a scintillator ball located within the detector via optical fiber. The scintillator ball is 26

UV filter ND filter Xe Flash Lamp 1400 Optical fiber 1200 σ gain = 7.0% 1000

SK TANK 800 Photo Diode Photo Diode

Number of PMTs in Each Bin 600

Scintilator Ball ADC 400

PMT 200

Scintilator 0 Monitor 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 20inch Trigger Relative PMT Gain PMT (a) (b)

Figure 2.9: (a) Schematic of the relative gain calibration system using a Xe lamp. (b) Relative gain distribution of all ID PMTs as measured in 1996.

composed of an acrylic resin doped with MgO powder diﬀuser and BBOT scintillator. The scintillator absorbs the input UV light from the ﬁber and emits light with a peak

wavelength of 440 nm which corresponds to typical Cherenkov light. The intensity of the Xe source is monitored using two photodiodes and a PMT attached to scintillator material.

The relative gain, Gi,ofthei-th PMT is given by: Qi 2 li Gi = li exp (2.4) Q0f(θ) L

where Qi is the charge detected at the i-th PMT, f(θ) is the angular acceptance of the PMT, li is the distance from the scintillator ball to the i-th PMT, L is the water attenuation length and Q0 is a normalization factor. The high voltage of the PMTs are adjusted to give a minimum spread to the relative gain distribution shown in

Figure 2.9b. 27

mean 2.055pC

3 Ni wire +water 200mm

Cf 2

0 0510pC 190mm (a) (b)

Figure 2.10: (a) Diagram of the Ni+Cf gamma-ray calibration source. (b) Charge distribution of a typical ID PMT from the Ni+Cf gamma-ray source.

2.6.3 Absolute Gain Calibration

Absolute gain calibration is done to determine the conversion between charge measured in pC by the PMT and the number of p.e. To do this we use the low energy gamma ray generated from neutron capture on Nickel nucleus to measure the single p.e. distribution. A diagram of the Nickel calibration source is shown in Figure 2.10a. Neutrons

that are produced from the ﬁssion of the 252Cf source thermalize in the water and are captured by Ni nuclei in the surrounding wire generating a 6 MeV to 9 MeV gamma. An example of the single photo electron distribution from this source is shown in Figure 2.10b. The measured conversion is:

2.055 pC = 1 p.e. 28

Figure 2.11: Schematic of the attenuation length measurement system using laser.

2.6.4 Water Transparency

The water transparency measurement is necessary to determine the water attenuation length. This parameter represents the eﬀect of scattering and absorption of light by the water within the tank. There are two methods used to measure the attenuation length, the ﬁrst uses a nitrogen dye laser and the second uses cosmic ray muons.

2.6.4.1 Laser Injection

The system diagrammed in Figure 2.11 shows the the conﬁguration of the laser and CCD camera used to measure water attenuation length. Using a nitrogen laser in

conjunction with a dye, monochromatic light with wavelengths of 337 nm, 365 nm, 400 nm, 420 nm, 460 nm, 500 nm and 580 nm are generated. The light passes via optical fiber to a diffuser ball that is located within the SK tank. The intensity of the light from the diffuser ball as a function of distance is then measured by the CCD

camera located at the top of the detector. The intensity of the light from the laser is also monitored by the PMT. The attenuation length is then determined using the intensity from the diﬀuser ball normalized by the intensity measured at the PMT vs. the separation distance between the diﬀuser ball and the CCD camera. 29

2.6.4.2 Cosmic Ray Muon

Another method to measure the water attenuation length is to use vertical through- going cosmic ray muons which deposit energy at a nearly constant rate along the track. One advantage to this method is cosmic ray muons make up a part of the normal data taking so the water attenuation length can be measured continuously.

To select through-going muons, the following event selection is applied using the ﬁtted entrance point (xin,yin,zin) and exit point (xout,yout,zout)ofthemuon:

(A) 50000 < total number of p.e. < 125000 ≡ 2 2 (B) rin xin + yin < 15.9m,zin > 18.1m ≡ 2 2 − (C) rout xout + yout < 15.9m,zout < 18.1m 2 2 (D) (xin − xout) +(yin − yout) < 5m

Criterion (A) roughly corresponds to the muon track length of 25 m to 63 m. The distance between the top and bottom wall is 39.2 m. This criterion also rejects energetic cosmic ray muons causing hadronic interactions in the detector. By criteria (B) and (C), the entrance and exit points are required on the top and bottom wall, respectively. Criterion (D) selects vertically going muons. For events which pass this event selection, the corrected p.e., qcorr, at each PMT is calculated as:

1 q = Q × l × (2.5) corr f(θ)

Where Q is the detected p.e. at the PMT, l is the travel length of the Cherenkov photon, f(θ) is the PMT acceptance as a function of incident angle θ. This distribution is ﬁtted using the following exponential function:

1 q (l)=G × exp − (2.6) corr L 30 )) θ RUN 3106 P1 5.987 0.4609E-03 500 P2 -0.9487E-04 0.4444E-06

log(Ql/f( 400

300

200

0 1000 2000 3000 4000 5000

Figure 2.12: Distribution of corrected p.e. vs. photon travel length. where G is proportional to the PMT gain and L is the measured attenuation length. Figure 2.12 shows a typical distribution of the corrected p.e. as a function of photon travel length.

2.6.5 Absolute Energy Calibration

The momentum of a particle is determined using the charge information from the PMTs. Since the systematic error in the particle momentum can aﬀect the proton decay search, it is essential to have an accurate measurement of the absolute energy scale. To calibrate the absolute energy, four methods using independent calibration sources with momentum ranges between a few 10 MeV and about 10 GeV are used.

2.6.5.1 Decay Electrons

Many electrons produced by the decay of stopping cosmic ray muons are detected in SK. These electrons have a well understood energy spectrum up to ∼ 53 MeV. The absolute energy scale is determined by comparing the observed data and MC simulation. To select the decay electron sample the following selection criteria is

used: ñ (A) The time interval from the stopping muon event is 1.5 ñsto8.0 s.

(B) The number of hit PMT in a 50 ns time window is larger than 60. 31

225

Events 200

175

150

125

100

0 0 1020304050607080 MOMENTUM (MeV/c)

Figure 2.13: Momentum distribution for decay electrons for data (point) and MC (line).

(D) The vertex position is reconstructed more than 2 m away from the ID wall.

Figure 2.13 shows the momentum spectra of decay electrons as compared to the prediction from the MC. In the MC the measured μ+/μ− ratio of 1.37 [16] is used and μ− capture in the oxygen nucleus is also taken into account. The mean values of the data agree with the MC within 0.6%.

2.6.5.2 Neutrino Induced π0 Events

Atmospheric neutrino events that generate π0 are used to calibrate the energy scale in the few hundred MeV range. A π0 will immediately decay into two gammas from

0 which the invariant π mass, Mπ0 , can be determined via:

Mπ0 = 2Pγ1Pγ2(1 − cos θ) (2.7)

Where Pγ1, Pγ2 and θ are the reconstructed momentum and opening angle between the gammas respectively. To select π0 events, the following selection criteria is applied: 32

140

s 120 t n ve 100 E f o

e 80 b m u N 60

0 0 50 100 150 200 250 300 π0 invariant mass (MeV/c2 ) Figure 2.14: Invariant mass distribution of neutrino induced π0 events for data (point) and MC (box).

(A) Two electron-like rings.

(B) The number of decay electron = 0.

Criterion (B) rejects contamination to the sample from π±π0 or μ±π0 events. Figure

2.14 shows the Mπ0 distribution for the data and MC simulation. There is a clear peak near 135 MeV/c2, the true mass of the π0, the position of the peak in the data is 0.7% higher than the MC.

2.6.5.3 Cosmic Ray Stopping μ Cherenkov Angle

Another calibration method using stopping cosmic ray muons is to utilize the half opening angle of the Cherenkov ring. Equation (2.1) describes the dependence of the

Cherenkov ring opening angle, θ, on the muon momentum, pμ. Because |dθ/dpμ| is large for small pμ this calibration method is possible in the low momentum region of pμ 500 MeV/c. The criteria for selecting cosmic ray muons for this calibration are:

(A) Total p.e. < 1500. 33

DATA Monte Carlo 500 500 ) ) c c V/ V/

e 450 e 450 M M ( (

m 400 m 400 u u t t m m e 350 e 350 m m o o m m

. 300 . 300 t t s s on on 250 250 ec ec r r

200 200 30 32 34 36 38 40 42 44 30 32 34 36 38 40 42 44 opening angle (deg.) opening angle (deg.) (a) Data (b) MC

Figure 2.15: Scatter plots of the reconstructed momentum from observed charge vs. reconstructed Cherenkov opening angle for (a) data and (b) MC.

(B) One cluster of hit PMTs in the OD.

(D) The direction is downward (cos θzenith > 0.9).

(E) There is one decay electron.

Criterion (A) roughly corresponds to the muon momentum of < 380 MeV/c. Crite- rion (B) requires the entrance point of the muon in the OD. Criterion (C) and (D) require the muon is downward going. Figure 2.15 shows the scatter plots of the reconstructed Cherenkov opening angle and the momentum of the observed p.e. from the data and MC. The energy scale of the data is compared to the MC using the ratio

Pp.e./Pθ,wherePp.e. is the momentum estimated from the observed charge and Pθ is the momentum estimated from the Cherenkov angle. Figure 2.16 shows the aver-

aged Pp.e./Pθ for data and MC and the MC/data ratio as a function of the expected momentum Pθ. They agree within 1.1%. 34

) 1.4 θ

1.3

1.2 P(p.e.)/P(

1.1

0.9

0.8

0.7

0.6 200 250 300 350 400 450 500 P(θ) (MeV/c)

Figure 2.16: Ratio of the muon momentum from observed p.e. to momentum from opening angle (Pp.e./Pθ) as a function of the momentum (Pθ) for the data (solid line) and MC (dotted line).

2.6.5.4 Cosmic Ray Stopping μ Track Length

The momentum of high energy muons can be estimated using the track length since the range is approximately proportional to the momentum. We can estimate the range independent of the observed p.e. so we use the measurement of the momentum from the range for checking the energy scale from 1 GeV/c to 10 GeV/c. Higher momentum muons typically do not stop within the detector. The criteria for selecting cosmic ray muons for the calibration are:

(B) The entrance point is on the top wall.

(D) One decay electron.

(E) Reconstructed muon range > 7m.

We determine the muon range as the distance from the entrance point to the reconstructed vertex of the decay electron. Figure 2.17 shows the averaged value of the ratio of momentum/range as a function of the range for data and MC. The energy 35

2.6

2.5

2.4

2.3 Momentum(MeV/c)/Range(cm)

2.2

2.1

2 0 500 1000 1500 2000 2500 3000 3500 Range (cm) Figure 2.17: The ratio of momentum/range as a function of range for data (solid line) and MC (dotted line) loss per cm is about 2.3 MeV/c. The energy scale of the data and MC agree within 0.7%.

2.6.5.5 Time Variation of Energy Scale

Using the stopping muon and decay electron events we can monitor the time variation of the energy scale. Figures 2.18a and 2.18b show the time variation of the decay electron and momentum/range ratio respectively. The RMS of the energy scale variation is 0.83%.

2.6.5.6 Uniformity of Energy Scale

Non-uniformity in the energy scale can lead to inaccuracy in the total momentum reconstruction which is one of the important quantities used for proton decay searches. Decay electrons from stopping cosmic ray muons are a good calibration source of detector uniformity since their vertex and direction are nearly uniform in location and direction within the ﬁducial volume (FV). To avoid bias from muon polarization, only electrons whose direction is perpendicular to the parent muon are used. This is achieved by requiring −0.25 < cos Θeμ < 0.25, where cos Θeμ is the opening angle 36

1.05 1.04 1.03 1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0 500 1000 1500 2000 2500 3000 3500 elapsed days from 1996/Apr./1 (a)

1.05 1.04 1.03 1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0 500 1000 1500 2000 2500 3000 3500 elapsed days from 1996/Apr./1 (b)

Figure 2.18: The time variation of (a) decay electron momentum and (b) ratio of momentum/range of stopping muons. The SK-I run period consists of the block of data points between day 0 and ∼ 2000. between the electron and muon directions. Figure 2.19 shows the momentum of decay electrons for the MC normalized by the observed data as a function of the zenith angle of the electrons. The detector gain is uniform within ±0.6%.

2.6.5.7 Summary of Energy Scale Calibration

Figure 2.20 summarizes the absolute energy scale calibration. The energy scale uncer- tainly is estimated to be less than 0.74% over the momentum range of a few 10 MeV/c to about 10 GeV/c. Combining this result in quadrature with the RMS of the time variation, the systematic error of the energy scale is estimated to be 1.1%. 37

Figure 2.19: The non-uniformity of the detector gain as a function of zenith angle. The vertical axis is the momentum of the decay electron events for the MC normalized by the observed data.

SK-I 8 6 (%) 4 2

/DATA 0 -2 μ range -4 μ angle π0 mass -6 decaye (MC - DATA) - (MC -8 2 3 4 5 10 10 10 10 10 momentum range (MeV/c)

Figure 2.20: Summary of the absolute energy scale calibration. Chapter 3

Simulation

To estimate the detection eﬃciency of proton decays and the number of background events a detailed MC simulation program was developed. Details of the simulation of the proton decay, atmospheric neutrino ﬂux, atmospheric neutrino interactions and

detector simulation are described below in sections 3.1, 3.2, 3.3, 3.4 respectively.

3.1 Proton Decay

The source of protons for the proton decay search is the water (H2O) in the SK detector. A water molecule consists of two free protons and eight protons bound in the oxygen nucleus. We assume equal probability of decay for any of these protons.

For the free protons, the kinematics of the p → μ+K0 decay products can be uniquely determined. The direction of the μ+ and K0 is opposite each other each with a momentum of 326.5 MeV/c. In the case of proton decay in oxygen, Fermi momentum, correlation with other nucleons, nuclear binding energy, kaon-nucleon interaction and 0 → 0 KL KS regeneration must be considered.

38 39

Figure 3.1: Nucleon momentum distributions. The left and right ﬁgures show momenta of 1s state and 1p state in 12C nucleus, respectively. Solid lines show theoretical calculations used in our simulation [17].

3.1.1 Fermi Momentum and Nuclear Binding Energy

We use the Fermi momentum and nuclear binding energy measured by electron-12C scattering [17]. Figure 3.1 shows the Fermi momentum distribution of the 1s state and 1p state for the experimental data. The theoretical calculation shown in the ﬁgure is used in our simulation.

Nuclear binding energy is taken into account by modifying the proton mass. The − modiﬁed proton mass, mp, is calculated by mp = mp Eb where mp is the proton rest mass and Eb is the nuclear binding energy. The measured nuclear binding energy is 39.0MeV/c2 and 15.5MeV/c2 for the 1s and 2p states respectively.

Ten percent of decaying protons have wavefunctions that are correlated with other nucleons within the nucleus [18]. These correlated decays cause the total invariant mass of the decay products to be smaller than the proton mass because of the momentum carried by the correlated nucleons. Figure 3.2 shows the invariant proton mass distribution in 16Ousedinthep → μ+K0 simulation. Correlated decays produce the broad spectrum below ∼ 850 MeV/c2 shown by the hatched region. 40

10 4 number of events

10 3

10 2

0 200 400 600 800 1000 MeV/c2 μ+K0 invariant mass in 16O Figure 3.2: Invariant mass of μ+K0 in the p → μ+K0 MC simulation in water (solid line). The hatched region shows the contribution from nucleon correlated decay. The two peaks near the proton mass in the distribution correspond to the 1s and 1p state which are separated by the diﬀerence in nuclear binding energy.

3.1.2 Kaon-Nucleon Interaction in the Oxygen Nucleus

The position of the decaying proton in 16O is calculated according to the Wood-saxon nuclear density model, ρp(r), which is expressed as [19]:

Z ρ0 ρp(r)= r−c (3.1) A 1+exp( a )

3 where r is the distance from the center of the nucleus, ρ0 =0.48mπ is the average nuclear density, 2a =0.82 fm is the thickness of the nuclear surface and c =2.69 fm is the average nuclear radius for 16O. The kaon nucleon interactions that are considered include elastic scattering and inelastic scattering via charge exchange. The type of interaction is determined using the calculated mean free path. The mean free path is calculated from the diﬀerential

0 ¯0 cross-sections using the results of KS and K scattering experiments [20, 21]. If there is an interaction, the Pauli blocking eﬀect is taken into account by requiring the nucleon momentum after the interaction to be larger than the Fermi surface 41

momentum, pF , deﬁned as: 3π2 p (r)= ρ(r) (3.2) F 2 where ρ(r) is the same as (3.1)

0 0 3.1.3 KL→KS Regeneration in the Oxygen Nucleus

Neutral kaons consist of a down quark and strange quark. There are four types of neutral kaons K0 (S=+1), K¯0 (S=-1) which are the eigenstates of strangeness and

0 0 KL, KS which are the weak eigenstates. They are related by the following:

K0 − K¯0 K0 + K¯0 K0 = √ K0 = √ (3.3) L 2 S 2

Since strong interactions conserve strangeness, there are more strong interactions

¯0 0 0 available for K than for K . Therefore, when a KL propagates through a material, the K0 and K¯0 components interact at diﬀerent rates with the material which in-

0 0 troduces a KS component in the original KL. It is therefore possible to observe a

0 0 KS after the original KL has propagated some distance through a material. This is 0 → 0 known as KL KS regeneration. 0 → 0 KL KS regeneration in the oxygen nucleus is modeled in the simulation as a

0 decay channel of the KL that is parameterized by a regeneration lifetime in the oxygen nucleus, τRnucl. ; a tunable parameter that aﬀects the probability of regeneration. We assume τ is related to τ (see section 3.4.3) by: Rnucl. RH2O

ρ τ = τ nucl. (3.4) Rnucl. RH2O ρH2O

× 17 −3 Where ρnucl. =3.7 10 kg m is the density of the oxygen nucleus and ρH2O = 1000 kg m−3 is the density of water. 42

3.2 Atmospheric Neutrino Flux

Interactions of atmospheric neutrinos in the SK detector are the primary source of irreducible background for a search of proton decay. To estimate this background the atmospheric neutrino ﬂux and interactions are simulated. In our simulation of the

atmospheric neutrino flux we use the calculation of Honda et. al. [22] (Honda Flux) made at the SK site. The BESS [23] and AMS [24] experiments have precisely measured the primary cosmic ray flux up to 100 GeV. In the Honda flux calculation, the model of the

primary flux is a parametrization and fit of experimental data as shown in Figure 3.3. The effect of the solar wind and geomagnetic field of the Earth on the primary flux are considered in the Honda flux calculation. The difference of the flux at solar maximum and solar minimum is more than a factor of two for 1 GeV cosmic rays, while it decreases to ∼ 10% for 10 GeV. The simulation of hadronic interactions in the atmosphere are treated using two theoretical models depending on the primary cosmic ray energy. NUCRIN [25] is used for energies less than 5 GeV and DPMJET-III [26] is used for energies greater than

5 GeV. The neutrino flux is obtained from decays of secondary particles, primarily pions, that are produced in these interactions. The calculated energy spectrum of atmospheric neutrinos at the SK site is shown in Figure 3.4 with the predictions of G. Battistoni et. al. [27] (Fluka flux) and G. Barr et. al. [28] (Bartol flux). Neutrinos with energy on the order of 1 GeV contribute to the background for proton decay searches. The systematic error of the absolute flux was estimated to be 10% [29] stemming from the uncertainties of the absolute primary cosmic ray flux and cosmic ray interactions. 43

Figure 3.3: Primary cosmic ray ﬂux measurements compared with the model used in the Honda ﬂux calculation. The data are taken from Webber [30] (crosses), LEAP [31] (upward triangles), MASS1 [32] (open circles), CAPRICE [33] (vertical diamonds), IMAX [34] (downward triangles), BESS98 [23] (circles), AMS [24](squares), Ryan [35] (horizontal diamonds), JACEE [36] (downward open triangles), Ivanenko [37] (upward open triangles), Kawamura [38] (open squares) and Runjob [39] (open diamonds). GeV)

−1 ν μ + ν μ sr −1

2 10sec ν ν −2 e + e (m 2 ν Honda flux Fluka flux Flux*E 10 Bartol flux

1 10−1 1 10 102 Eν (GeV) Figure 3.4: The predicted atmospheric neutrino fluxes at the SK site. Solid lines show the Honda flux, dashed lines show the Fluka flux [27], and dotted lines show the Bartol flux [28]. 44

3.3 Neutrino Interaction

The atmospheric neutrinos interact with the nucleons and electrons in the SK detector which we simulate using NEUT [40, 41, 42]. The following types of charged current (CC) and neutral current (NC) neutrino interactions are considered in NEUT:

CC/NC (quasi-)elastic scattering: ν + N → l + N

CC/NC single meson production: ν + N → l + N +meson

CC/NC deep inelastic interaction: ν + N → l + N hadrons

CC/NC coherent π production: ν +16 O → l +16 O+π where ν is a neutrino or anti-neutrino, N is a nucleon and l is a lepton. Systematic uncertainties of neutrino interactions are also considered, the details of which are described elsewhere [29].

3.3.1 Elastic & Quasi-Elastic Scattering

The diﬀerential cross-section of the charged current quasi-elastic scattering for free protons is given by [43, 44]:

dσν(¯ν) M 2G2 cos2 θ s − u (s − u)2 F C 2 ∓ 2 2 2 = 2 A(q ) B(q ) 2 + C(q ) 4 (3.5) dq 8πEν M M

where Eν is the neutrino energy, M is the mass of the target nucleon, GF is the Fermi coupling constant, θC is the Cabbibo angle, q is the four-momentum transferred to the lepton and s and u are Mandelstam variables [43]. The factors A, B and C are 45 given by:

m2 − q2 q2 q2 A q2 − |F |2 − |F 1 |2 ( )= 2 4 2 A 4+ 2 V 4M M M q2 q2 4q2F 1 ξF2 − |ξF2 |2 − V V 2 V 1+ 2 2 M 4M M m2 − (F 1 + ξF2 )2 + |F |2 (3.6) M 2 V V A 2 2 q 1 2 B(q )= FA(FV + ξFV ) (3.7) M2 1 q2 C(q2)= |F |2 + |F 1 |2 − |ξF2 |2 (3.8) 4 A V 4M 2 V

where m is the charged lepton mass and ξ ≡ μp −μn =3.71. The vector form factors,

1 2 2 2 2 FV (q )andFV (q ), and the axial form factor, FA(q ) are determined experimentally and given by:

− q2 1 q2 F 1 (q2)= 1 − G (q2) − G (q2) (3.9) V 4M 2 E 4M 2 M − q2 1 ξF2 (q2)= 1 − G (q2) − G (q2) (3.10) V 4M 2 E M − q2 2 F (q2)=− 1.23 1 − (3.11) A M 2 A 2 −2 2 −1 2 q GE(q )=(1+ξ) GM (q )= 2 (3.12) MV

where GE and GM are the electric and magnetic form factor, the vector mass MV is

2 2 set to be 0.84 GeV/c and the axial vector mass MA is set to be 1.21 GeV/c ,which is a common parameter for the single meson production model. The Fermi motion of the nucleons and Pauli exclusion principle must be considered for scattering oﬀ nucleons in 16O [45]. Since nucleons are fermions, the outgoing momentum of the nucleons in the interactions is required to be greater than the Fermi surface momentum to allow quasi-elastic scattering to occur. In NEUT, the Fermi surface momentum is set to be 225 MeV/c. 46

2 2 ANL Serpukhov – GGM (1977) 1.8 (a) ν n→μ-p 1.8 (b) ν p→μ+n μ BNL GGM (1977) μ GGM (1979) 1.6 SKAT GGM (1979) 1.6 Serpukhov

) 1.4 ) 1.4 SKAT 2 2 1.2 1.2 cm cm 1 1 -38 -38 0.8 0.8 (10 (10

σ 0.6 σ 0.6 0.4 0.4 0.2 0.2 0 0 02468101214 02468101214

Eν (GeV) Eν (GeV) (a) ν (b)ν ¯

Figure 3.5: Crosssections of (a) ν and (b)ν ¯ with the experimental data from ANL [48], Gargamelle [49, 50, 51], BNL [52], Serpukhov [53] and SKAT [54].

The cross-section for neutral current elastic scattering are estimated from the following relations [46, 47]:

σ(νp → νp)=0.153 × σ(νn → e−p) (3.13)

σ(¯νp → νp¯ )=0.218 × σ(¯νn → e+n) (3.14)

σ(νn → νn)=1.5 × σ(νp → νp) (3.15)

σ(¯νn → νn¯ )=1.0 × σ(¯νp → νp¯ ) (3.16)

Figure 3.5 shows the cross-section of the quasi-elastic scattering for the experimental data and the calculation by NEUT.

3.3.2 Single Meson Production

The resonant single meson production of π, K,andη was simulated based on the model of Rein & Sehgal [55]. An intermediate baryon resonance is assumed in this method:

ν + N → l + N ∗ (3.17)

N ∗ → N + meson (3.18) 47 where N and N are nucleons, N ∗ is a baryon resonance, and l is a lepton. The diﬀerential cross-section of single meson production is a product of the amplitude of each resonance production and the probability of their baryon resonance decay to the meson. For a baryon resonance with a negligible decay width, the diﬀerential cross-section is:

d2σ 1 1 = × |T (νN → lN∗)|2δ(W 2 − M 2) (3.19) dq2dE 32πME2 2 j j ν ν j,spin

where M is the mass of the target nucleon, Eν is neutrino energy, W is the invariant mass of the hadronic system (or the mass of the intermediate baryon resonance), Mj is the mass of the baryon resonance, and T (νN → lN∗) is the amplitude of resonance production, which is calculated using the Feynman-Kislinger-Ravndal model [56]. The invariant mass, W , is restricted to be less than 2 GeV/c2.ForW>2GeV/c2,the interactions are simulated as deep inelastic scattering as described in section 3.3.3. For a baryon resonance with a ﬁnite decay width, the diﬀerential cross-section can be derived by replacing the δ-function with a Breit-Wigner factor:

1 Γ δ W 2 − M 2 → × ( j ) 2 2 (3.20) 2π (W − MJ ) +Γ /4

2 For a single meson production, the axial vector mass MA is also set to be 1.21 GeV/c . A total of 28 resonances were simulated in our simulation. The eﬀect of the Pauli exclusion principle in the decay of the baryon resonance was considered by requiring the momentum of the scattered nucleon to be greater than the Fermi surface momentum. The pion-less decay of Δ resonance in 16O nuclei, where about 20% of the events do not have a pion in the decay, was also simulated [57]. Figure 3.6 shows the cross-sections of charged current resonant single meson productions for our calculations and the experimental data. Most of the baryon resonances decay to the ﬁnal states including π. The production cross-section for the η meson and K meson are 48 ) ) 2 − 2 1 ν → μ π+ − 1.2 μ p p ν → μ π+ cm cm 0.9 μ n n −38 −38 0.8 )(10 )(10

μ 1 μ ν ν ( (

σ 0.7 σ

0.8 0.6

0.5 0.6 0.4

0.4 0.3

0.2 0.2 0.1

0 0 1 10 1 10 Eν(GeV) Eν(GeV) − + − + (a) νµp → μ pπ (b) νµn → μ nπ )

2 1 ν → μ− π0 cm 0.9 μ n p ANL Radecky, Phys.Rev.D 25, 1161 (1982) −38 0.8 ANL Campbell, Phys.Rev.Lett. 30, 225 (1973) )(10 μ ν ( 0.7 ANL Barish, Phys.Rev.D 19, 2521 (1979) σ

0.6 BEBC Allen Nucl.Phys.B 264, 221 (1986) 0.5 BEBC Allen Nucl.Phys.B 176, 269 (1980) 0.4 BEBC Allasia Nucl.Phys.B 343, 285 (1990) 0.3 BNL Kitagaki Phys.Rev.D 34, 2554 (1986) 0.2 FNAL Bell Phys.Rev.Lett. 41, 1008 (1978) 0.1

0 1 10 Eν(GeV) (d) List of experiments − 0 (c) νµn → μ pπ

Figure 3.6: Cross-sections for charged current single pion productions of νμ. Solid lines indicate our calculations. Experimental data are summarized in the panel (d). much less than that for π. The fractions for the single η meson and the K meson production in the total single meson production events in the atmospheric neutrino MC were approximately 4% and 0.6%, respectively.

3.3.3 Deep Inelastic Scattering (DIS)

The cross-section of charged current deep inelastic scattering is calculated by integrat-

ing the following equation in the range of the invariant mass W>1.3GeV/c2 [58]:

d2σν,ν¯ G2 M E y2 y = F N ν (1 − y + + C )F (x, q2) ± (1 − + C )xF (x, q2) (3.21) dxdy π 2 1 2 2 2 3 yM2 xyM m2 m2 C l − N − l − l 1 = 2 (3.22) 4MN Eν x 2En 4Eν 2MN Eνx 2 ml C2 = − (3.23) 4MN Eνx 49

2 where x(= −q /(2M(Eν − El))) and y(= (Eν − El)/Eν) are Bjorken scaling parameters, MN is the nucleon mass, ml is the outgoing lepton mass, Eν and El are the energy of the incoming neutrino and outgoing lepton in the laboratory frame respectively.

We use the nucleon structure functions F2 and xF3 taken from GRV98 [59]. To obtain the cross-sections for deep inelastic scattering induced by the neutral current, we use the following relations which are estimated from experimental results [60]: ⎧ ⎪ ⎪ ⎪0.26 (Eν < 3GeV) ⎨⎪ σ(νN → νX) = − ≤ (3.24) → − ⎪0.26 + 0.04(Eν/3 1) (3 GeV Eν < 6GeV) σ(νN μ X) ⎪ ⎪ ⎩⎪ 0.30 (Eν ≥ 6GeV) ⎧ ⎪ ⎪ ⎪0.39 (Eν < 3GeV) ⎨⎪ σ(¯νN → νX¯ ) = − − ≤ (3.25) → + ⎪0.39 0.02(Eν/3 1) (3 GeV Eν < 6GeV) σ(¯νN μ X) ⎪ ⎪ ⎩⎪ 0.37 (Eν ≥ 6GeV)

To generate events, a combination of PYTHIA/JETSET [61] and custom software is used. Since PYTHIA/JETSET is intended for simulation at higher energies it is used only for events with W>2.0GeV/c2. This package treats not only π but other mesons such as K, η and ρ. In the region of 1.3GeV/c2

2 nπ =0.09 + 1.83 ln W (3.26)

The number of pions in each event is determined by using KNO (Koba-Nielsen-Olsen) scaling. Since the range of W overlaps with that in single pion production, n ≥ 2 is required in this W region. The forward-backward asymmetry of pion multiplicity 50

) 1

-1 GRV94LO 0.9 GRV94LO (w/ B-Y corr.) GRV98LO 0.8 GRV98LO (w/ B-Y corr.)

GeV 0.7 2 0.6

cm 0.5

-38 0.4 0.3

(10 0.2 ν CCFR 90 CHARM 88 BEBC-WBB 79 CCFRR 84 0.1 CDHSW 87 BNL 80 IHEP-JINR 96 SKAT

/E GGM-PS 79 CRS 80 IHEP-ITEP 79

σ 0 010203050 100 150 200 250 Eν (GeV)

Figure 3.7: cross-sections for charged current νμ andν ¯μ interactions. Upper(lower) lines are νμ(¯νμ) in the hadronic center of mass system is included using the results from the BEBC experiment [63]:

F 2 nπ 0.35 + 0.41 ln(W ) B = 2 (3.27) nπ 0.5+0.09 ln(W )

The cross-section of the CC νμ andν ¯μ interactions are shown in Figure 3.7.

3.3.4 Coherent Pion Production

Coherent pion production occurs when a neutrino interacts with an oxygen nucleus,

which remains intact, and one pion is produced with the same charge as the incoming weak current. Since very little momentum is transferred to the oxygen nucleus, the angular distributions of the outgoing leptons and pions are peaked in the forward direction. The formalism developed by Rein and Sehgal [64] was used to simulate the 51 interactions, and the diﬀerential cross-section is given by:

d3σ G2M 1 =β × N f 2A2E (1 − y) (σπN )2 dQ2dydt 2π2 π ν 16π total M 2 2 × r2 A e−b|t|F (1 + ) 2 2 abs (3.28) MA + Q

r =Re(fπN(0))/Im(fπN(0)) (3.29) where Q2 is the square of the four-momentum transfer of the lepton, β is the axial vector coupling constant with β = 1 for neutral current and β = 2 for charged current,

G is the weak coupling constant, MN is the nucleon mass, fπ =0.93mπ is the pion decay constant, A is the atomic number (=16 for oxygen), Eν is the neutrino energy, − πN y(= (Eν El)/Eν) is the lepton fractional energy loss, σtotal is the averaged total

−2 pion-nucleon cross-section, MA is the axial-vector mass, b =80GeV is in the order of the nucleus transverse dimension, t is the square of the four-momentum transfer to the nucleus, fπN is the pion-nucleon scattering amplitude, Fabs accounts for the absorption of pions in the nucleus and is expressed as:

− x σπN ρ Fabs = e inel (3.30) where x is the average path length of the pion in the oxygen, ρ is the nuclear

πN density and σinel is the averaged total inelastic pion-nucleon cross-section. However, the K2K experiment set an upper limit on the cross-section of coherent CC pion production [65] that is significantly lower than the predicted cross-section by Rein and Sehgal. Therefore, some modification is necessary to the coherent pion production cross-sections used in the MC. The calculated cross-sections of the coherent pion production for the CC and NC interactions by Kartavtsev and Paschos [66] agree better with the several experimental data than that of Rein and Sehgal as shown in Figure 3.8. The difference between the experimental data and the model proposed by 52

250 140 Rein and Sehgal 225 CHARM(93) Kartavtsev et al. MiniBooNE(05) 120 200 Aachen-Padova(83) Gargamelle(84) 175 100 Rein and Sehgal 150 Kartavtsev et al. /Carbon Nucleous) /Carbon Nucleous) 2 2 80

cm 125 cm -40 -40 60 100 (10 (10 σ σ 75 40 50 20 25

0 0 -1 2 12345678910 10 1 10 10 Eν(GeV) Eν(GeV) (a) CC (b) NC

Figure 3.8: The cross-sections of coherent pion productions off the carbon nucleus for CC and NC interactions by two models with the experimental data. The solid lines are calculation by Rein and Sehgal, while the dashed lines are by Kartavtsev and Paschos. On the left figure, the arrow shows the experimental upper limit by K2K [65], and on the right figure. The experimental data are from CHARM [67], MiniBooNE [68], Aachen-Padove [69] and Gargamelle [70].

Kartavtsev and Paschos was taken into account as a systematic uncertainty of 100%.

3.3.5 Nuclear Eﬀects

The secondary mesons produced by the neutrino interactions with the 16Onucleiare tracked from their production points until they exit or are absorbed. This is done for π, K and η by using the same cascade model as that used for kaons in the proton decay simulation described in section 3.1. The interactions of pions are especially important since the cross-section for pion production is large for Eν > 1GeV,andthe pion-nucleon crosssection is also large. The pion-nucleon interactions that are considered in the simulation are: inelastic scattering, charge exchange, and absorption. The pion production point where the neutrino-nucleon interaction occurred is determined by the Woods-Saxon density distribution (3.1). The type of pion interaction is 53

600 inela+abs+cex inelastic 500 absorption charge exchange O (mb)

16 400 + + π inela+abs+cex 300

200 inelastic

absorption

cross section for 100

charge exchange 0 0 100 200 300 400 500 600 momentum of π+ (MeV/c) Figure 3.9: cross-sections of π+-16O scattering as a function of π+ momentum. Solid lines show the calculation from our simulation and points show the experimental data [73]. determined by the calculated mean free path of each interaction based on the model of Oset [71]. In the calculation, Fermi motion and Pauli blocking are considered. In the case of inelastic scattering or charge exchange the direction and momentum of the pion are determined using the results of a phase shift analysis obtained from pion-nucleon scattering experiments [72]. The pion interaction model is tested using the experimental results from the following interactions: π−12C scattering, π−16O scattering, and pion photo-production (γ +12 C → π− + X) [73, 74] as shown in Fig- ure 3.9. Absorption for η mesons (ηN → N ∗ → π(π)N) is also considered [75] with the resulting pions tracked using the method described above. Nucleon re-scattering is also considered using the cascade model. The considered interactions are elastic scattering, a single or two delta(s) production. The diﬀerential cross-sections are obtained from nucleon-nucleon scattering experiments [76]. For delta production, the isobar production model is used [77]. 54

3.4 Detector Simulation

Simulated kinematics of proton decays and neutrino interactions are passed through a detector simulation program. The detector simulation simulates the propagation of particles, Cherenkov radiation, propagation of Cherenkov photons in the detector

water, and the response of the PMTs and electronics. Based on the GEANT package [78], the custom detector simulation program was developed for the SK detector.

3.4.1 Photon Propagation

Absorption, Mie and Rayleigh scattering processes are taken into account in the simulation of photon propagation in the detector. At short wavelengths, Rayleigh scat-

tering is dominant due to the λ−4 dependence. Photons are scattered symmetrically in the forward and backward directions in this process. Absorption is a dominant process for longer wavelengths ( 450 nm). Coeﬃcients for these processes were tuned to reproduce the calibration data as described in section 2.6.4. Figure 3.10 shows the

wavelength dependence of these coeﬃcients and calibration data.

3.4.2 Hadron Propagation

In order to reproduce low energy pion interactions, hadronic interactions are treated by a custom simulation program [79] based on experimental data of π-16O scattering [80] and π-p scattering [81] for charged pions of pπ > 500 MeV/c. The CALOR package [82] is used for propagation of nucleons and charged pions of pπ > 500 MeV/c.

0 0 3.4.3 KL→KS Regeneration in Water

0 → 0 0 KL KS regeneration is modeled in the simulation as a decay channel of the KL that is parameterized by a regeneration lifetime in water, τ ; a tunable parameter that RH2O aﬀects the probability of regeneration. The probability of regeneration in carbon is 55 )

-1 Dec.-3,4-96 Dec.-14-96 Dec.-17-96 Dec.-27-96 -1 Jan.-18-97 Mar.-6-97 10

total absorption -2 10

Mie scattering Rayleigh scattering

attenuation coefficient (m -3 10 200 250 300 350 400 450 500 550 600 650 700 wavelength (nm)

Figure 3.10: Wavelength dependence of photonattenuationcoeﬃcientsusedinMC simulation (solid lines). Measured results from calibration data described in section 2.6.4 is shown (points).

measured to be 0.1% for kaons with momentum of 400 MeV/c [83]. We assume the probability of regeneration in water is the same as in carbon. We generate 400 MeV/c

pure K0 events in the detector simulation and tune τ such that the fraction L RH2O with regeneration in water is ∼ 0.1% of total generated events. Regeneration is not simulated in water for the atmospheric neutrino MC. Chapter 4

Fully Contained Event Reduction

4.1 Overview

Each day, about 106 events are collected by the SK detector not including SLE trigger events. Many of these are due to cosmic ray muons and low energy events from radioactive material such as radon near the detector wall. Also, a non-negligible fraction are PMT flashers from discharges near the dynodes inside the PMT. All of these sources are background to the proton decay search and so we reject these using the fully contained (FC) reduction steps described in this chapter. An FC event by definition only has activity within the ID volume. There are five steps to the FC reduction all of which are automatically applied.

4.2 First Reduction

The selection criteria that comprise the ﬁrst reduction step of the FC event sample are the following:

(A) PE300 ≥ 200 p.e.

PE300 is deﬁned as the maximum number of p.e.s observed by ID PMTs within

56 57

in a sliding 300 ns window.

AND

(B) NHITA800 ≤ 50 or OD trigger is oﬀ

NHITA800 is deﬁned as the total number of hit OD PMTs in a ﬁxed 800 ns window that extends from −400 ns to +400 ns before and after the trigger timing.

AND

Criteria (A) is designed to reject low energy events from radioactive isotopes, (B) rejects cosmic ray muons and (C) rejects decay electrons from cosmic ray muons which

stop in the ID. Events within 30 ñs after another event selected by the above criteria are retained to keep the decay electrons. These retained events are attached to the fully contained candidates as sub-events and not counted as a primary events. The data rate is reduced from 106 events/day to 3000 events/day after the ﬁrst reduction step.

4.3 Second Reduction

The selection criteria that deﬁne the second reduction step of the FC event sample

are the following:

(A) NHITA800 < 25 if PEtot < 100.000 p.e. or OD trigger is oﬀ.

PEtot is the total observed p.e.s in the ID.

AND

(B) PEmax/PE300 < 0.5

PEmax is the maximum number of p.e.s observed by an ID PMT. 58

Criteria (A) is designed to further eliminate cosmic ray muons, (B) rejects low energy and electrical noise events, which have one large hit signal from a single PMT.

The data rate is 200 events/day after the second reduction.

4.4 Third Reduction

After the ﬁrst two reduction steps the remaining background consists of noise and cosmic ray muons with only a few hits in the OD.

4.4.1 Through-going Muon Cut

The following criteria are used to reject through-going muons:

(A) PEmax > 230 p.e.

AND

(B) goodness of through-going muon ﬁt > 0.75

AND

NHITAin (NHITAout) is the number of hit OD PMTs located within 8 m from the entrance (exit) point in a ﬁxed 800 ns time window.

If criteria (A) is satisfied, a muon fitter is applied. The output of the muon fitter is used for criteria (B) and (C). The muon fitter selects an entrance point based on the earliest hit PMT with respect to neighboring PMTs and an exit point defined as the center of the saturated ID PMTs. The fitter then calculates a goodness which is 59 defined as:

1 1 (t − T )2 goodness = × exp − i i (4.1) 1 σ2 2(1.5 × σ )2 i i i σ2 i i

where ti and σi are the observed hit time and resolution of the i-th PMT respectively

and Ti is the hit time expected from the entering time of the muon and its track.

4.4.2 Stopping Muon Cut

To reject stopping muons, a stopping muon fitter is applied which fits the entrance point in a similar fashion as the through-going muon fitter. The following selection

criteria are the used to reject stopping muons:

(A) NHITAin ≥ 10 or

NHITAin ≥ 5 if goodness of stopping muon ﬁt > 0.5

The direction of the muon is reconstructed to maximize the total number of p.e.s inside the cone with a half opening angle of 42◦. The goodness deﬁnition is the same as (4.1).

4.4.3 Cable Port Muons

Located at the top of the detector tank are 12 cable ports that allow the high voltage and signal cables access from the PMTs to the electronics huts. Four of these ports sit above the ID and block the OD. There is a possibility that cosmic ray muons may go through the port and enter the ID without triggering the OD. To eliminate this occurrence, veto counters (2 m × 2.5 m scintillation counters) were installed above 60 the cable ports in April 1997. To eliminate such muons entering the cable ports the following criteria is applied:

(A) One veto counter hit

AND

(B) Lveto < 4m

Lveto is the distance from the cable hole to the the reconstructed vertex.

4.4.4 Flasher Event Cut

Flasher events occur when electrical discharges in a PMT cause it to act as a light source. Flashers are characterized by a hit timing distribution that is more broad than neutrino events. To eliminate these, the following criteria is applied:

(A) NMIN100 ≥ 14

(B) NMIN100 ≥ 10 if the number of hit ID PMTs < 800

NMIN100 is the minimum number of hit ID PMTs in a sliding 100 ns time window from +300 ns to +800 ns after the trigger.

4.4.5 Accidental Coincidence Cut

The accidental coincidence occurs when a low energy event starts the trigger and a cosmic ray muon follows within a single trigger gate. These are not rejected by earlier reduction steps because of the absence of the OD activity on the trigger timing and the large number of total p.e.s in the ID due to the muons. The accidental coincidence events are removed by the following criteria: 61

(A) NHITAoﬀ ≥ 20

NHITAoff is the number of hit OD PMTs in a fixed 500 ns off-timing window from +400 ns to +900 ns after the trigger timing.

AND

(B) PEoﬀ > 5000 p.e.

PEoff is the number of p.e.s observed by ID PMTs in a fixed 500 ns off-timing window from +400 ns to +900 ns.

4.4.6 Low Energy Events Cut

The remaining events are low energy events from the decay of radio isotopes and electrical noise. The following criteria is applied to remove these background:

(A) NHIT50 < 50

NHIT50 is the number of hit ID PMTs in a sliding 50 ns time window.

Where NHIT50 is counted after subtracting the time of flight of each observed photon assuming all photons are generated at a point. The vertex is determined as the position at which the timing residual distribution is peaked. NHIT50 = 50 corresponds to visible energy of 9 MeV/c and is low enough not to lose efficiency for contained neutrino events with Evis > 30 MeV/c where Evis is the total visible energy defined as the sum of the energy of all rings assuming they are produced by electrons. The data rate is 45 events/day after the third reduction.

4.5 Fourth Reduction

This reduction step is designed to remove additional ﬂasher events that are missed by earlier reduction steps. Because ﬂasher events are caused by electrical discharges

in a PMT the event has a characteristic pattern that may repeat over the course of a 62 few hours or days that the ﬂasher is active. A pattern matching algorithm is used to look for these events with a similar pattern and remove them. The algorithm is the following:

(A) Divide the ID wall into 1450 patches of 2 m × 2m square.

(B) Compute the correlation factor, r, by comparing the total charge in each patch of two events, A and B. The correlation is deﬁned as:

1 (QA −QA) × (QB −QB) r = i i (4.2) N σ × σ i A B

A(B) where N is the number of the patches, and Q and σA(B) are the averaged charge and its standard deviation respectively for event A(B).

(D) If DISTmax < 75 cm, an oﬀset value is added to r: r = r +0.15.

(E) If r exceeds the threshold, rth, events A and B are recognized as matched events.

rth is deﬁned as:

× A B rth =0.168 log10((PEtot +PEtot)/2) + 0.130 (4.3)

where PEtot is the total number of p.e.s observed in the ID.

(F) Repeat the above calculation over 10,000 events around the target event and count the number of matched events.

(G) Remove the events with large correlation factor r, or large number of matched events.

The data rate is 18 events/day after the fourth reduction. 63

4.6 Fifth Reduction

4.6.1 Stopping Muon Cut

The remaining stopping muons are rejected by tighter criteria than those in the third reduction stage. Events satisfying the following criteria are rejected:

(A) NHITAin ≥ 5

NHITAin is the number of hit OD PMTs located within 8 m from the entrance point in a sliding 200 ns time window from −400 ns to +400 ns.

The entrance position in the OD is estimated by a backward extrapolation from the reconstructed vertex determined by TDC ﬁt (see section 5.1.1.3).

4.6.2 Invisible Muon Cut

Invisible muons are caused by cosmic ray muons with momenta less than the Cherenkov

threshold and the subsequent decay electrons being observed. These are characterized by a low energy signal from decay electron and a signal in the OD before the trigger timing. Events which satisfy the following cut criteria are rejected as invisible muons:

(A) PEtot < 1000 p.e.

PEtot is the total number of p.e.s observed in the ID.

AND

(B) NHITACearly > 4

NHITACearly is the maximum number of hit PMTs in the OD hit cluster in a sliding 200 ns width time window from −800 ns to −100 ns.

AND

NHITACearly > 9otherwise 64

NHITAC500 is the number of hit PMTs in the OD hit cluster in a ﬁxed 500 ns time window from −100 ns to +400 ns. DISTclust is the distance between the OD hit clusters which are used for NHITACearly and NHITAC500.

4.6.3 Coincidence Muon Cut

The remaining accidental coincidence muons are removed by:

(A) PE500 < 300 p.e.

PE500 is the total number of p.e.s observed in the ID in a ﬁxed 500 ns time window from −100 ns to +400 ns.

AND

(B) PElate ≥ 20 p.e.

PElate is the maximum number of hit OD PMTs in a 200 ns sliding time window from +400 ns to +1600 ns.

4.6.4 Long Tail Flasher Cut

This is a more strict version of the ﬂasher cut in the third FC reduction stage. Events satisfying the following criterion are removed:

(A) NMIN100 > 5 if the goodness of point ﬁt < 0.4

NMIN100 is the minimum number of the hit ID PMTs in a sliding 100 ns time window from +300 ns to +800 ns. Point ﬁt is explained in section 5.1.1.1.

The data rate is 16 events/day after the ﬁfth reduction.

4.7 Final Fully Contained Fiducial Volume Sample

To select the ﬁnal fully contained ﬁducial volume (FCFV) sample the following event

selection is applied: 65

(A) NHITAC < 10 NHITAC is the number of hit PMTs in the highest charge OD cluster.

(B) Evis > 30 MeV/c

Evis is the total visible energy deﬁned as the sum of the energy of all rings assuming they are produced by electrons.

where Dwall is the distance of the reconstructed vertex from the ID PMT surface. This deﬁnes the FV.

This event selection deﬁnes a FV of 22.5 kt. The detection eﬃciency is estimated to be 97.2% with systematic error of 0.2%. The data rate is 8.18 ± 0.7events/day. Chapter 5

Event Reconstruction

After the event reduction steps described in Chapter 4, the event reconstruction is applied to the FC sample. There are two event reconstructions used for this analysis. First, is the standard event reconstruction which is described below in section 5.1.

This is the standard SK reconstruction algorithm that is used for many of the other analysis by the SK collaboration. The performance of the standard reconstruction is summarized in other documents [84, 85]. Second, is the multi-vertex reconstruction

0 algorithm which was developed speciﬁcally for the KL search of this analysis. The algorithm and performance of the multi-vertex reconstruction is described in section 5.2.

5.1 Standard Event Reconstruction

The standard event reconstruction algorithms consist of the following:

(A) Vertex ﬁt

Locates the vertex (origin) of the interaction generating the event as well as the direction of the most dominant (energetic) ring.

(B) Ring counting

66 67

Uses the vertex and direction of the dominant ring found in (A) to search for additional rings.

(C) Particle Identiﬁcation (PID) Determines a particle type for each ring; showering type (from e±,γ) and non- showering type (from μ±,π±, p). These showering and non-showering types are also known as e-like and μ-like respectively.

(D) MS Vertex Fit For single ring events the MS Vertex ﬁt is applied. The PID information from (C) is used to reconstruct the vertex position.

(E) Momentum Reconstruction

The momentum of each ring found in (B) is determined.

(F) Decay electron ﬁnding Searches the event for decay electrons.

(G) Ring number correction Rejects some low energy rings and overlapping rings found in (B) that are

considered as fake rings.

5.1.1 Vertex

There are three steps to the vertex reconstruction algorithm: point fit, ring edge fitting and TDC fit.

5.1.1.1 Point Fit

The first step of vertex reconstruction is appropriately called point fit as it is based on the assumption that the all Cherenkov photons are emitted from a single point. Using this assumption, a rough estimate of the vertex is calculated by searching for 68 the point within the ID volume in which the timing residual (PMT hit time with time of flight subtracted) distribution is most peaked. The timing residual, ti, is calculated as:

n(q ,l) t = t0 − i i ×|P − O | (5.1) i i c i

0 where ti is the timing of the i-th PMT, Pi and O are the position of the i-th PMT and estimated vertex respectively. The index of refraction n(qi,li) is a function of the detected p.e., qi, and photon travel length, li = |Pi − O |. The goodness of the point-ﬁt is deﬁned as:

1 (t − t )2 G = exp − i 0 (5.2) p N 2(1.5 × σ)2 i where N is the number of hit PMTs, t0 is a free parameter chosen to maximize Gp, and σ is the PMT timing resolution taken to be 2.5 ns. The numerical factor 1.5 is chosen to optimize the fitter performance. The fitter searches for the vertex point which gives the maximum value of Gp. Using the estimated vertex from the point fit algorithm a rough estimate of the particle direction is determined as the charge weighted average of all PMTs:

P − O d = q × i 0 (5.3) 0 i | − | i Pi O0

where d0 is the direction of the particle, O0 is the vertex position determined by point

ﬁt, qi and Pi are the charge and position of the i-th PMT respectively.

5.1.1.2 Ring Edge Fitting

The Cherenkov ring edge and direction of the most dominant ring is ﬁt in this step. To determine the Cherenkov ring edge, the p.e. for all PMTs are ﬁlled into a 69 histogram as a function of the Cherenkov opening angle, θ. Here, the p.e. are corrected for attenuation length and PMT acceptance. Using this PE(θ) histogram the criteria to determine the Cherenkov ring edge θedge are:

(A) θedge >θpeak θpeak is the opening angle where PE(θ) is maximum. 2 d PE(θ) (B) = 0 the second derivative at θ = θedge should be zero. d2θ θedge

If multiple θedge satisfy (A) and (B), then the θedge nearest θpeak is selected. The ring direction is determined using the following estimator: θedge 2 PE(θ)dθ − 2 0 dPE(θ) (θedge θexp) Q(θedge)= × × exp − (5.4) sin θ dθ 2σ2 edge θ=θedge θ

where θexp and σθ are the Cherenkov opening angle expected from the charge within the cone and its resolution, respectively. The estimator Q(θedge) is calculated changing the ring direction about the ring direction d0 found in point ﬁt. The ring direction and edge position are determined which maximize Q(θedge).

5.1.1.3 TDC Fit

In this ﬁnal step the vertex position is more precisely determined by now taking into account scattered Cherenkov light and ﬁnite track length.

The track of the particle is considered in the time residual, ti,ofthei-th PMT as: ⎧ ⎪ ⎨ 0 − 1 ×| − |− n ×| − | ti c Xi O c Pi Xi for PMTs inside the Cherenkov ring t = i ⎪ ⎩ 0 − n ×| − | ti c Pi O for PMTs outside the Cherenkov ring (5.5)

where O is the vertex position, X i is the position at which Cherenkov photons are emittedtowardthei-th PMT, n is the refractive index of water, Pi is the position

0 and ti is the hit timing of the i-th PMT. 70

There are three components to the estimator used for TDC ﬁt which are calculated based on PMT location and hit timing. For PMTs inside the Cherenkov ring, the estimator GI is deﬁned: 1 (t − t )2 G = exp − i 0 (5.6) I σ2 2(1.5 × σ)2 i i where σi is the timing resolution of the i-th PMT depending on the detected p.e.s, σ

is the timing resolution for the average p.e.s of all hit PMTs, ti is the time residual of the i-th PMT as calculated by (5.5) and t0 is a free parameter used to maximize GI .

For PMTs outside the Cherenkov ring there are two estimators GO1 and GO2,if the hit timing is later than t0 the contribution from scattered photons is considered. The estimators are deﬁned as:

1 (t − t )2 G = exp − i 0 × 2 − 1 (for t ≤ t ) O1 σ2 2(1.5 × σ)2 i 0 i i (5.7) 1 (t − t )2 G = max exp − i 0 ,G (t ,t ) × 2 − 1 (for t > t ) O2 σ2 2(1.5 × σ)2 scatt i 0 i 0 i i (5.8) where

R (t − t )2 R t − t G (t ,t )= q × exp − i 0 + 1 − q × exp − i 0 (5.9) scatt i 0 1.52 2(1.5 × σ)2 1.52 60 ns

Rq is the fraction of the charge detected inside the Cherenkov ring. The numerical factors in the above equations are determined empirically to give the best reconstruction performance. 71

The total estimator of TDC ﬁt is:

G +(G or G ) G = I O1 O2 (5.10) T 1 σ2 i i

The vertex position and ring direction are selected which maximize GT .

5.1.2 Ring Counting

The ring counting algorithm is used to search for additional Cherenkov rings in the event.

5.1.2.1 Ring Candidate Selection

Ring candidate selection searches for additional Cherenkov rings using an algorithm

know as a Hough transform [86] which is commonly used in pattern recognition. However, before beginning the Hough transform, p.e. contributions from rings that are already regarded as true rings are subtracted to enhance the ring ﬁnding ability. The Hough space is deﬁned as the (Θ, Φ) plane where Θ is the polar angle and Φ is the azimuthal angle as measured from the reconstructed vertex. The Hough transform is performed by mapping the detected p.e. corrected for PMT acceptance and attenuation length from the i-th hit PMT into the (Θi, Φi) pixel in the Hough space for which the opening angle toward the hit PMT is 42◦. As a result of this mapping, the center of ring candidates are observed as peaks in the (Θ, Φ) plane.

5.1.2.2 Ring Candidate Test

In this step, a likelihood method is used to determine whether the candidate ring found by the Hough transform is a true ring or not. When N rings have been found, the likelihood used to check if the (N + 1)-th candidate is probable or not is deﬁned 72 as: N+1 obs · exp LN+1 = log prob qi , αn qi,n (5.11) i n=1

obs where the sum extends over hit PMTs inside N + 1 Cherenkov rings, qi is the · exp observed p.e.s in the i-th PMT and αn qi,n is the expected p.e.s in the i-th PMT from the n-th ring. The LN+1 is maximized by changing the αn scale factors with a lower momentum limit constraint. The probability prob is deﬁned as: ⎧ ⎪ (qobs,qexp)2 ⎪√ 1 − i i exp ⎪ exp (for qi > 20 p.e.) ⎪ 2πσ 2σ2 ⎪ ⎨⎪ obs exp Probability obtained by the probability density prob(qi ,qi ) ⎪ ⎪ exp ⎪distribution function based on the convolution of a (for qi < 20 p.e.) ⎪ ⎪ ⎩⎪single p.e. distribution and a Poisson distribution.

(5.12)

where σ is the resolution for qexp. If no candidate satisﬁes LN+1 ≥ LN ,thenumber ofringsisdeterminedtobeN and the ring counting procedure is ﬁnished. For ring candidates which satisfy LN+1 ≥ LN , the following evaluation functions are calculated:

F1: The diﬀerence LN+1 − LN corrected for the total p.e.s.

F2: The average of the expected p.e.s from the (N + 1)-th ring, near the edge of the Cherenkov ring.

F3: The average of the expected p.e.s outside the (N + 1)-th ring.

F4: The residual p.e.s from the expectation with N rings. 73

The evaluation functions are used to calculate the ﬁnal evaluation function as:

4 FSK−I = [αiFi] (5.13) i=1

where αi are optimized weighting parameters. If FSK−I is positive, then the (N +1)-th ring candidate is considered a true ring. During this process, the eﬀect of muon decay electrons is eliminated by restricting the ring search to PMTs hit within a timing window of width tw starting from the lower edge of the peak of the TOF subtracted hit timing distribution. This is done using the ritofcut routine. tw is given by:

tw =(qtot × 65 + 1400)/(6.4 × 40) + 5 (5.14)

where qtot is the total p.e.s in the ID.

5.1.3 Particle Identiﬁcation

The PID algorithm classiﬁes each Cherenkov ring into two types: showering (e- like) and non-showering (μ-like). Electrons and gamma-rays undergo electromagnetic

showers and multiple scattering which results in Cherenkov rings with diﬀuse edges. The Cherenkov ring edges from muons and charged pions are more sharp. Another distinction is the Cherenkov opening angle. The Cherenkov opening angle for electrons and gamma-rays is 42◦ because they are highly relativistic (β ∼ 1). However, muons and pions can have smaller opening angles if they are not highly relativistic. The PID algorithm uses these diﬀerences between the Cherenkov ring pattern and opening angle to make its determination of ring type. 74

5.1.3.1 Expected Charge Distribution

The ﬁrst necessary step in particle identiﬁcation is the calculation of the expected p.e. distribution for electrons and muons. These distributions are calculated using the following for electrons and muons respectively:

1.5 exp × exp × R × 1 × scatt qi (e)=αe Q (pe,θi) f(Θi)+qi (5.15) ⎛ ri exp(ri/L) ⎞ sin2 θ 1 exp ⎝ × xi knock⎠ × × scatt qi (μ)= αμ + qi f(Θi)+qi r sin θ + r · dθ exp(ri/L) i xi i dx x=xi (5.16) where

αe,αμ : a normalization factor for electrons and muons respectively

ri : is the distance from the vertex to the i-th PMT

θi : is the opening angle between the i-th PMT direction and the ring direction

L : the attenuation length of light in water

f(Θi) : a correction of acceptance to the i-th PMT as a function of the

photon incidence angle Θi

R : radius of the virtual sphere (16.9m)

exp Q (pe,θi) : expected p.e. distribution from an electron as a function of the opening angle and electron momentum. This is obtained by MC simulation.

scatt qi : expected p.e.s for the i-th PMT from scattered photons

x : track length of the muon 75

xi : track length of the muon at which Cherenkov photons are emitted toward the i-th PMT

scatt knock qi ,qi : expected p.e.s for the i-th PMT from scattered photons and knock-on electrons respectively.

θ (θxi ) : Cherenkov opening angle of the muon traversing at x (xi). The energy loss of the muon is taken into account.

1.5 In the electron case, the (R/ri) term corrects for the distance dependence of the Cherenkov intensity. For the muon, the sin2 θ term corrects for the angular dependence of the Cherenkov intensity and the r(sin θ + r(dθ/dx)) term corresponds to the area where Cherenkov photons are emitted when the muon travels a distance dx.

5.1.3.2 Determination of Particle Type

The likelihood used to estimate particle type of the n-th ring is given by: obs exp exp Ln(e or μ)= prob qi ,qi,n (e or μ)+ qi,n (5.17) θi<(1.5×θc) n = n

obs where the product extends over PMTs inside the n-th ring. qi is the observed exp p.e.s in the i-th PMT, qi,n (e or μ) is the expected p.e.s from the n-th ring with the exp assumption of an electron (5.15) or muon (5.16) and qi,n are the expected p.e.s from the n-th ring without any assumption of particle type. The function prob returns the

obs exp probability to detect qi in the i-th PMT when qi is expected (5.12). By changing exp exp the direction and opening angle of the n-th ring, qi,n (e)andqi,n (μ) are optimized to give the maximum likelihood value. To combine this likelihood with another that uses the Cherenkov opening angle, 76 the likelihood is converted into the the following χ2 distribution:

2 − χn(e or μ)= 2logLn(e or μ) + constant (5.18)

The probabilities from the ring pattern are: (χ2 (e or μ) − min[χ2 (e),χ2 (μ)])2 P pattern(e or μ)=exp − n n n (5.19) n 2σ2 χn2 √ 2 where σ 2 = 2N and N is the number of PMTs used in the calculation. χn The probabilities from Cherenkov opening angle are: θobs − θexp(e or μ) 2 angle − n n Pn (e or μ)=exp 2 (5.20) 2(δθn)

obs where θn and δθn are the reconstructed opening angle of the n-th ring and the ﬁtting

exp error respectively. θn (e or μ) is the expected opening angle of the n-th ring, which is estimated from the reconstructed momentum assuming an electron or muon.

For single and multi ring events the probability functions of PID are respectively given by:

pattern × angle Psingle(e, μ)=Psingle (e, μ) Psingle(e, μ) (5.21)

pattern Pmulti(e, μ)=Pmulti (e, μ) (5.22)

With the above probabilities we construct the PID likelihood, PPID ≡ − log P (μ)− − log P (e), used to determine ring type. If PPID < 0 the ring is considered e-like and if PPID ≥ 0 the ring is considered μ-like. This algorithm was tested by a beam test at KEK [87]. 77

5.1.4 MS Vertex Fit

The vertex fitter described in section 5.1.1 mainly uses timing to determine the vertex. However, using only timing for single ring events results in poor resolution of the vertex along the ring direction. The MS vertex fitter attempts to improve the vertex reconstruction by using the Cherenkov ring pattern information to re-fit the vertex

along the ring direction. The fitter acts iteratively, changing both the vertex and ring direction using a likelihood based on the expected p.e. distributions similar to the PID algorithm until changes in vertex position and ring direction are less than 5 cm and 0.5◦ respectively. During the fit the Cherenkov opening angle is fixed.

5.1.5 Momentum Determination

The momentum is estimated from the total number of p.e.s detected within a 70◦ half opening angle towards the reconstructed ring direction. To determine the momentum for each ring, the p.e.s in hit PMTs must be separated based on the contribution from each ring. This separation is carried out based on the expected p.e. distribution which is a function of the opening angle θ and assumes uniformity in azimuthal angle φ. The observed p.e.s of the i-th PMT are then separated as:

qexp obs obs × i,n qi,n = qi exp (5.23) n qi,n

obs obs where qi,n is the fractional p.e.s assigned to the n-th ring, qi is the observed p.e.s exp in the i-th PMT and qi,n is the expected p.e.s. The observed p.e.s for each PMT is corrected for light attenuation in water and

PMT acceptance and summed to obtain the integrated total charge within the 70◦ 78

cone of the n-th ring, RTOTn,as: ⎡ ⎤ G ⎢ r cos Θ ⎥ MC ⎢ × obs × i × i − ⎥ RTOTn = ⎣α qi,n exp Si⎦ Gdata ◦ L f(Θi) ◦ θi,n<70 θi,n<70 −50ns

α : a normalization factor

Gdata,GMC : the relative PMT gain for the data and MC respectively

θi,n : is the opening angle between the i-th PMT direction and the n-th ring direction

ti : the TOF subtracted hit timing of the i-th PMT position

L : the attenuation length of light in water

f(Θi) : a correction of acceptance to the i-th PMT as a function of the

photon incidence angle Θi

ri : the distance from the vertex to the i-th PMT

Si : expected p.e.s for the i-th PMT from scattered photons

To eliminate the eﬀect from muon decay electrons, the summation is restricted to PMTs hit within a time window from −50 ns to +250 ns about the peak of the TOF subtracted hit timing distribution. This is done by the sptofcut routine.

5.1.5.1 Ring Separation

For multi-ring events, it is necessary to separate the observed p.e.s in each PMT to the contribution of each ring so the momentum of each ring can be determined. The 79 expected charge for the i-th PMT used for charge separation is calculated as:

R 1 qexp e, μ Qexp p, θ × × × f qscatt i ( )= e,μ ( i) exp MC (Θi)+ i (5.25) L exp(ri/L) where

ri : the distance from the vertex to the i-th PMT

θi,n : is the opening angle between the i-th PMT direction and the n-th ring direction

L : the attenuation length of light in water

LMC : the attenuation length of light in water in the MC

f(Θi) : a correction of acceptance to the i-th PMT as a function of the

photon incidence angle Θi

R : the radius of the virtual sphere (16.9m)

exp Qe,μ (p, θi) : expected p.e. distribution for e and μ on the virutal sphere as a function of the momentum, p, and opening angle to the i-th PMT,

θi

scatt qi : expected charge for the i-th PMT from scattered photons

For all e-like rings except for the most energetic, the γ conversion length is taken into account in the distance calculation. Reﬂection on the PMT surface is considered as: exp → × exp exp qi (e, μ) α qi (e, μ)+ βijqj (e, μ) (5.26) j= i 80

where α is a normalization factor and βij is the PMT reﬂection factor from the j-th to i-th PMT calculated as:

r β = β × f(Θ ) × exp − ij (5.27) ij ij L

where rij is the distance from the i-th to j-th PMT, Θij is the photon incidence angle to the i-th PMT from the j-th PMT and β is a constant reﬂection factor that is determined via MC simulation. The observed p.e.s for each PMT is estimated by maximizing the likelihood function L: exp · L = log prob qi , αn qi·n (5.28) ◦ θi,n<70 n

exp where qi is the observed p.e.s in the i -th PMT and qi·n is the expected p.e.s in exp obs the i -th PMT from the n -th ring, prob(qi ,qi ) is given by (5.12) and αn is the optimization parameter for each ring which is determined by scaling the expected charge pattern to reproduce the observed charge distribution. The observed p.e.s in the i-th PMT from n-th ring is then:

α · qexp obs obs × n i,n qi,n = qi exp (5.29) · n αn qi,n

using the αn which maximizes L. Typically, the momentum reconstruction for muons has a resolution of ∼ 2.8% [84] → + 0 however, during this analysis an unknown pathology was found for p μ KS MC events when the muon momentum is ∼ 280 MeV/c. This behavior was investigated by the use of three control samples consisting of μ+ and π0 back to back with ﬁxed vertex and momentum. The three samples are:

+ 0 1. one μ , pμ = 459 MeV/c; one π , pπ0 = 459 MeV/c 81

FCFV, 3≤nring≤5, 1 μ-like

100 44.52 / 36 SAMPLE #1 Constant 82.31 75 Mean 4.730

entries Sigma 11.29 50 25 0 -60 -40 -20 0 20 40 60 reconstructed-true μ momentum (MeV/c)

38.65 / 28 SAMPLE #2 Constant 121.6 100 Mean -16.84

entries Sigma 8.420 50

0 -60 -40 -20 0 20 40 60 reconstructed-true μ momentum (MeV/c)

100 27.13 / 21 SAMPLE #3 Constant 81.62 75 Mean -26.69

entries Sigma 8.958 50 chisq/ndf=1.6 mean=13.0 25 sigma=8.7 0 -60 -40 -20 0 20 40 60 reconstructed-true μ momentum (MeV/c) Figure 5.1: The reconstructed-true muon momentum of three control samples described in the text.

+ 0 pμ and pπ0 are the same as in p → μ π decay.

+ 0 2. one μ , pμ = 280 MeV/c; one π , pπ0 = 274 MeV/c

0 0 0 0 → 0 pπ is the same as KS π π decay with pKS = 280 MeV/c.

+ 0 3. one μ , p = 280 MeV/c; two π , p 0 = 274 MeV/c, p 0 = 270 MeV/c μ π1 π2 0 0 0 0 → 0 pπ is the same as KS π π decay with pKS = 280 MeV/c.

The standard event reconstruction was applied to these samples. Figure 5.1 shows the reconstructed-true muon momentum for these three control samples. The resolution of the ﬁrst sample is ∼ 2% which is consistent with the performance of p → μ+π0 [84] however, in sample three there is clearly two peaks in the distribution. The source of this second peak is unknown and this pathology remains in the current analysis.

5.1.5.2 Charged Pion Momentum

A charged pion may interact hadronically with nucleons in the water making it dif- ﬁcult to determine the momentum based on the charge alone. Since a charged pion may not be highly relativistic, we can use the information of the Cherenkov opening 82 angle in addition to the observed p.e.s in the momentum reconstruction. The charged pion momentum is reconstructed by maximizing the likelihood deﬁned as:

1 (Qexp(p ) − Qobs)2 1 (θexp(p ) − θobs)2 L − n π n × − n π n π =log exp 2 exp 2 (5.30) σq 2σq σθ 2σθ where

pπ : the charged pion momentum

exp exp Qn (pπ),θn (pπ) : the expected p.e.s and opening angle respectively for the n-th ring as a function of the pion momentum

obs obs Qn ,θn : the observed p.e.s and opening angle respectively

σq,σθ : the error of the expected p.e.s and opening angle respectively

exp The function for expected p.e.s, Qn (pπ), was determined by MC simulation.

5.1.6 Decay Electron Search

Electrons from the decay of muons are classiﬁed into three types:

• sub-event type These are decay electrons that are observed as a separate event from the primary

event.

• primary-event type These are decay electrons that are observed within the same event as the primary.

• split type These are decay electrons that occur near the end of the primary event timing window. The decay electron event is recorded both in the primary and sub-

event. 83

We require the following criteria for sub-event type events:

(A) The time interval from the primary event, Δt,islessthan20ñs.

(B) Total number of hit PMTs is greater than 50.

(D) The number of hit PMTs within a 50 ns time window, N50, is greater than 30.

(E) The total number of p.e. is less than 2000.

For primary-event type, we search for a second peak with later timing requiring more than 20 hits above the background level within a 30 ns window. For the proton decay search we also require:

(F) N50 > 60

(G) The number of hit PMTs within a 30 ns time window is greater than 40 for

primary-event type and split type

ñ ñ ñ (H) 0.1 ñs < Δt < 0.8 sOR1.2 s < Δt < 20 s

N50 = 60 corresponds to ∼ 11 MeV/c of electron energy. The gamma emission from μ− captured on 16O nuclei is rejected by criteria (A). Events that occur near the end of the primary event timing window are rejected by criteria (H). The eﬃciency of detecting decay electrons is 80% and 63% for μ+ and μ− respectively.

5.1.7 Ring Number Correction

If more than two rings are found in an event, ring number correction is applied to

remove mis-reconstructed rings. The criteria to remove the i-th ring are:

(A1) pi

pi is the momentum of the i-th ring without using the PID information. 84

◦ (A2) θij < 30

θij is the opening angle between the i-th and j-th rings.

(A3) pi cos θij < 60 MeV/c

(B1) pi < 40 MeV/c

(B2) pi/ptot < 0.05

ptot is the total momentum of all the rings without using PID information.

5.2 Multiple Vertex Event Reconstruction

One of the fundamental assumptions made by the standard reconstruction algorithm is that there is a single vertex for the origin of the particles whose kinematics are being

→ + 0 reconstructed. However, for a search of p μ KL one of the deﬁning characteristics is that there is a separation between the vertex corresponding to the proton decay

0 and the KL decay or interaction point. Because of this, a new event reconstruction algorithm is necessary to properly reconstruct these types of events.

→ + 0 The momentum of the primary μ from p μ KL is typically monochromatic

0 near 326.5 MeV/c, well above the Cherenkov threshold. Typically, the KL interacts in the water as it propagates or it may decay via one of the decay modes described in

0 Table 1.2. Depending on whether the KL decays or interacts determines the number and kinematics of the ﬁnal state particles. These particles may be near the Cherenkov threshold.

→ + 0 Based upon these kinematics of p μ KL, the strategy for this new multiple vertex reconstruction algorithm was determined. The algorithm consists of the following procedure: 85

(A) Standard reconstruction without timing cuts: Finds Cherenkov rings using the standard reconstruction algorithm described

in section 5.1 modiﬁed by the removal of timing cuts to account for rings with

0 late timing caused by KL decay.

(B) PMT masking region: Deﬁne a mask of the PMTs inside and outside the ring.

(C) Primary μ-candidate reconstruction: Using only PMTs inside the ring, the primary vertex, PID, momentum and other kinematic parameters are reconstructed.

(D) Remaining particle reconstruction:

Using only PMTs outside the ring, the remaining vertex is reconstructed using timing.

(E) Steps B-D are repeated for each ring in the event.

(G) Final determination of the μ-candidate is done after all rings in an event are processed, the μ-candidate is deﬁned as the μ-like ring with a momentum nearest

326.5MeV/c.

The use of timing only for remaining vertex is based on the assumption that the ﬁnal

0 state particles from the KL may only be near Cherenkov threshold and so there may not be a clear Cherenkov ring but any hit PMTs outside the μ-candidate ring are

0 caused by KL ﬁnal state particles and so should originate from a single vertex.

5.2.1 Standard Reconstruction Without Timing Cuts

To be able to isolate each Cherenkov ring it is first necessary to find the rings using a ring counting algorithm. Rather than develop a new algorithm, we modified the 86 existing standard reconstruction algorithm which includes ring counting by the removal of two timing cut routines ritofcut and sptofcut described in sections 5.1.2

and 5.1.5 respectively. The necessity for the removal of these routines stems from the

0 ∼ long lifetime of the KL which may cause a time diﬀerence of up to 300 ns between

0 the PMTs hit from the primary muon and those hit from the KL ﬁnal state particles. If these routines are included, they may exclude these hit PMTs because of this time diﬀerence. We apply the standard reconstruction algorithm without these timing cut routines.

5.2.2 PMT Masking Region

Each ring found by the standard reconstruction without timing cuts is isolated using a PMT masking algorithm. The masking area is deﬁned as the region of PMTs that satisfy the following condition: ◦ (P − xi) · D θc +10 > arccos (5.31) |P − xi||D |

Where xi is the coordinate of the i-th PMT, P is the reconstructed vertex, D is the

direction of the reconstructed ring, and θc is the reconstructed Cherenkov angle of

◦ the ring. The opening angle of the masking cone is set to θc +10 to include the tail of the charge proﬁle within the mask area.

5.2.3 Primary μ-candidate Reconstruction

To reconstruct the primary μ-candidate, only information from PMTs that satisfy (5.31) are used. The following reconstruction steps are performed: vertex, particle ID, MS vertex ﬁt, momentum determination and proton ID. 87

5.2.3.1 Vertex

The initial vertex fitting uses the vertex fitting algorithm of standard reconstruction described in section 5.1.1. We check the performance of the initial vertex fitter for the

→ + 0 μ-candidate found in step (G) using both the p μ KL and atmospheric neutrino MC samples requiring the μ-candidate to be a true muon. For the atmospheric neutrino MC we also require the true momentum of the muon is between 260 MeV/c and 410 MeV/c. We deﬁne ΔV, the reconstructed-true μ-candidate vertex projected along the true μ-candidate direction.

→ + 0 Figure 5.2a shows the ΔV distribution for the p μ KL MC sample. The mean is −77.5 ± 0.7 cm with a resolution (1σ) of 156 cm. Figure 5.2b shows the mean (upper ﬁgure) and resolution (lower ﬁgure) of ΔV vs. L, where L is the true

0 separation between the proton decay point and the point where the KL disappears through one of the kinematic processes listed in Table 1.2.

Figure 5.3 shows the ΔV distribution for the atmospheric neutrino MC sample.

The mean is −77.4 ± 1.5 cm with a resolution of 146 cm. This vertex ﬁtter assumes the particle type is an electron and relies mainly on timing for reconstruction. When there is only a single ring from a muon within the masked area the reconstructed vertex is shifted signiﬁcantly from the true vertex

opposite the ring direction as seen in these samples. However, this is not the final vertex of the μ-candidate used in our analysis. The vertex found by this initial vertex fitter is later improved by the MS vertex fitter described in section 5.2.3.3.

5.2.3.2 Particle ID

Particle ID is performed using the standard reconstruction algorithm described in

section 5.1.3. The PID likelihood is calculated using both the opening angle and

→ + 0 pattern information. The performance of the PID is checked using the p μ KL MC sample. Figure 5.4 shows the PID likelihood distribution for the true primary 88

100 p→μK 0 MC 3000 80 L 60 p→μK 0 MC L 40 entries K →any decay L 20 mean (cm)

2500 K →int. || L 0 V Other -20 -40 2000 -60 -80 -100 0 200 400 600 800 1000 1200 1400 L (cm) 1500 200 p→μK 0 MC 180 L 160 1000 140 120 100 80 500 resolution (cm) || 60 V 40 20 0 0 -1000 -750 -500 -250 0 250 500 750 1000 0 200 400 600 800 1000 1200 1400 V (cm) L (cm) μ candidate vertex || μ candidate vertex (a) (b)

→ + 0 Figure 5.2: Performance of the initial vertex ﬁtting of the μ-candidate for p μ KL 0 MC. (a) The ΔV distribution. Hatched regions show contribution from KL decay and interaction. (b) The mean and resolution of ΔV vs. L. The statistical error of the mean is shown.

700 ATM-ν MC entries CC QE 600 CC single-π CC multi-π NC 500 Other

400

300

200

100

0 -1000 -750 -500 -250 0 250 500 750 1000 V (cm) μ candidate vertex ||

Figure 5.3: The ΔV distribution of the initial μ-candidate vertex for atmospheric neutrino MC. The hatched regions show contributions from CCQE, CC single-π,CC multi-π and NC. 89

→μ 0 14000 p KL MC entries → KL any decay → KL int. 12000 Other

10000

8000

6000

4000

2000

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 likelihood PID → + 0 Figure 5.4: The PID likelihood distribution of the true primary muon for p μ KL 0 MC. The hatched regions show contributions from KL decay and interaction. muon. The mis-PID fraction is 8.3%. PID mis-reconstruction is taken into account as systematic error in the analysis. Since there are no timing cuts used in the ring counting algorithm, as described in section 5.2.1, sometimes true decay-electrons are selected as a ring. When this happens, the PID likelihood for these rings is near zero since there are very few PMT hits from the decay electron. This can cause a peak near zero in the PID likelihood distribution. An example of this is seen in Figure 10.3.

5.2.3.3 MS Vertex Fit

We assume there is only a single ring located within the masking region therefore the MS vertex fitter described in section 5.1.4 is applied to improve the vertex reconstruction of the primary μ-candidate found in section 5.2.3.1. The performance of the MS vertex fitter is checked in the same way as described in section 5.2.3.1. → + 0 Figure 5.5a shows the ΔV distribution for the p μ KL MC sample. The mean is 23.2 ± 0.3 cm with a resolution of 38 cm. Figure 5.5b shows the mean (upper figure) and resolution (lower figure) of ΔV vs. L.

Figure 5.6 shows the ΔV distribution for the atmospheric neutrino MC sample. 90

50 18000 p→μK 0 MC 40 L →μ 0 p KL MC 30 entries 16000 → KL any decay 20 → KL int. 10 mean (cm) Other || 0 14000 V -10 -20 12000 -30 -40 -50 10000 0 200 400 600 800 1000 1200 1400 L (cm) 8000 50 p→μK 0 MC 45 L 40 6000 35 30 4000 25 20 resolution (cm) || 15 2000 V 10 5 0 0 -400 -200 0 200 400 0 200 400 600 800 1000 1200 1400 V (cm) L (cm) μ candidate MS vertex || μ candidate MS vertex (a) (b)

→ + 0 Figure 5.5: Performance of the MS vertex ﬁtting of the μ-candidate for p μ KL 0 MC. (a) The ΔV distribution. Hatched regions show contribution from KL decay and interaction. (b) The mean and resolution of ΔV vs. L. The statistical error of the mean is shown.

The mean is 18.5 ± 0.6 cm with a resolution of 34 cm.

The shift of ΔV from zero is an unknown feature of the reconstruction which is taken into account as systematic error in our analysis.

5.2.3.4 Momentum Determination

Momentum determination of the primary μ-candidate is done using the standard reconstruction algorithm described in section 5.1.5. The performance of the momen-

→ + 0 tum reconstruction is checked using the p μ KL MC sample. Figure 5.7 shows the reconstructed-true momentum distribution for the true primary muon. The mean is

4.8 ± 0.2 MeV/c with a resolution of 41 MeV/c.

5.2.3.5 Proton ID

The MS vertex ﬁtter used in section 5.2.3.3 is designed for true electron or muon particles. If true particle is a proton, the vertex may be mis-reconstructed since the more massive proton has a smaller Cherenkov angle than a muon of similar 91

4500

ATM-ν MC entries 4000 CC QE CC single-π 3500 CC multi-π NC Other 3000

2500

2000

1500

1000

500

0 -400 -200 0 200 400 V (cm) μ candidate MS vertex ||

Figure 5.6: The ΔV distribution of the μ-candidate MS vertex for atmospheric neutrino MC. The hatched regions show contributions from CCQE, CC single-π,CC multi-π and NC.

18000

→μ 0 p KL MC entries 16000 → KL any decay → KL int. 14000 Other

12000

10000

8000

6000

4000

2000

0 -400 -200 0 200 400 MeV/c reconstructed-true μ-candidate momentum Figure 5.7: The reconstructed-true momentum of the true primary muon for p → + 0 0 μ KL MC. The hatched regions show contributions from KL decay and interaction. 92 momentum which leads to a shift in the reconstructed vertex opposite the proton direction. To identify true muons from true protons as the μ-candidate we use the proton ID algorithm developed by M. Fechner described in [88]. The performance is checked and systematic error is estimated using a true proton and true muon sample described in section A.2.4.

5.2.4 Remaining Particle Reconstruction

Only the vertex is reconstructed for remaining particles. When reconstructing the

vertex, only PMTs that do not satisfy (5.31) are used. To fit the remaining vertex, the TDC fit algorithm described in section 5.1.1.3 is used. The performance of the fitter is checked in the same way as described in section

0 5.2.3.1 with the exception that we deﬁne ΔV−, the reconstructed-true KL vertex

0 projected opposite the true μ-candidate direction. The KL vertex is the location

0 where the KL disappears via one of the kinematic processes described in Table 1.2. → + 0 Figure 5.8a shows the ΔV− distribution for the p μ KL MC sample. The mean is −21.7 ± 0.6 cm with a resolution of 92 cm. Figure 5.8b shows the mean

(upper ﬁgure) and resolution (lower ﬁgure) of ΔV− vs. L.

Figure 5.9 shows the ΔV− distribution for the atmospheric neutrino MC sample. The mean is −46.2 ± 0.9 cm with a resolution of 34 cm.

The shift of ΔV− from zero is an unknown feature of the reconstruction which is taken into account as systematic error in our analysis.

The development of this new reconstruction algorithm now allows us to search

→ + 0 the p μ KL decay mode at SK using the unique multi-vertex signature that was

0 not possible before. Now, both the vertex of the proton decay point and the KL disappearance point can be determined independent of the distance between them.

→ + 0 We use this information to separate the p μ KL signal from the atmospheric 93

200 →μ 0 p KL MC 150

8000 →μ 0 100 p KL MC entries → KL any decay 50 K →int. mean (cm) 7000 L -|| 0 V Other -50 6000 -100 -150 -200 5000 0 200 400 600 800 1000 1200 1400 L (cm) 4000 250 p→μK 0 MC 225 L 3000 200 175 150 2000 125 100 resolution (cm)

-|| 75

1000 V 50 25 0 0 -1000 -750 -500 -250 0 250 500 750 1000 0 200 400 600 800 1000 1200 1400 V (cm) L (cm) remaining vertex -|| remaining vertex (a) (b)

Figure 5.8: Performance of the remaining particle vertex ﬁtting of the μ-candidate → + 0 for p μ KL MC. (a) The ΔV− distribution. Hatched regions show contribution 0 from KL decay and interaction. (b) The mean and resolution of ΔV− vs. L. The statistical error of the mean is shown. neutrino background in the proton decay search described in Chapter 10. 94

1200 ATM-ν MC entries CC QE CC single-π 1000 CC multi-π NC Other 800

600

400

200

0 -1000 -750 -500 -250 0 250 500 750 1000 V (cm) remaining vertex -||

Figure 5.9: The ΔV− distribution for the remaining particle vertex of the atmospheric neutrino MC. The hatched regions show contributions from CCQE, CC single-π,CC multi-π and NC. Chapter 6

Overview of the p → μ+K0 search

6.1 Data Set

We search for the proton decay signal within the SK-I FC data set. The SK-I data was taken from April, 1996 until July, 2001 with a live-time of 1489.2 days corresponding to an exposure of 91.2 kt-yr. The SK-I FC data set is made by applying the FC

reduction1 described in Chapter 4 to this data. To estimate the signal detection eﬃciency of the proton decay search, the p → μ+K0 MC2 described in section 3.1 and detector simulator3 described in section 3.4 are used to generate MC samples of p → μ+K0. 200,000 events were generated with true vertices randomly distributed within the ID volume within 1 m of the ID PMT surface. To estimate the background to the proton decay search, we use the FC atmospheric neutrino MC1 with an equivalent exposure of 200 years for SK-I. The sample is generated using the atmospheric neutrino production, interaction and detector simulations described in sections 3.2, 3.3 and 3.4 respectively and applying the FC reduction

2 −3 2 described in Chapter 4. Pure νμ → ντ oscillation with Δm =2.5 × 10 eV and 1software library version 07d 2software library version 09b 3 0 0 software version v11p79 with KL→KS regeneration

95 96 sin2 2θ =1.0 were assumed. All samples are processed using both the standard reconstruction algorithm4 described in section 5.1 and multi-vertex reconstruction algorithm described in section 5.2.

6.2 Strategy of the Combined p → μ+K0 Search

→ + 0 → + 0 The previous search of p μ K in SK was performed using only the p μ KS MC to estimate the signal detection eﬃciency [1]. In this thesis, we introduce a new

combined method which uses the p → μ+K0 MC to estimate the signal detection efficiency. The algorithm to perform the combined search is illustrated by the flowchart shown in Figure 6.1. The same algorithm is applied event by event to SK-I data, p → μ+K0 MC and atmospheric neutrino MC to obtain the data candidates, signal detection efficiency and expected background respectively. First, the event is tested to see if it is selected by the FCFV event selections (A-C) described in section 4.7. If the event is selected it continues to the next step, if it is rejected then the next event is processed. In the next step, the event is tested to see if it is selected by one of the four searches, each of which is optimized to search for a particular decay mode of p → μ+K0 as well as be independent of each other. They are:

0 → 0 0 (I) “KS π π ” → + 0 0 → 0 0 Designed to search for the p μ KS; KS π π decay mode.

0 → + − (II) “KS π π Method #1” → + 0 0 → + − Designed to search for the p μ KS; KS π π decay mode with the assumption that one of the charged pions is below the Cherenkov threshold.

4software library version 09b 97

SK-I Data goto next p → μ+K0 MC event atmospheric neutrino MC

no selected by FCFV?

save selected by yes selected “K0 → π0π0”? S event no

selected by yes “K0 → π+π− yes S Method #1”? no

selected by yes 0 → + − “KS π π Method #2”? no

selected by yes 0 “KL”? no

Figure 6.1: The p → μ+K0 combined search algorithm.

0 → + − (III) “KS π π Method #2” → + 0 0 → + − Designed to search for the p μ KS; KS π π decay mode with the assumption that both of the charged pions are above the Cherenkov threshold.

0 (VI) “KL” → + 0 Designed to search for the p μ KL decay mode.

An event selected by a search is saved. If the event is not selected by any of the searches the next event is processed.

0 The event selections for the KS searches are the same as described in Kobayashi’s paper [1] except search (I). In this search, we include zero or one decay electron but 98

Kobayashi uses only one decay electron in the event selection. There is a discrepancy in the event selection described in the text of Kobayashi’s paper from what is actually used.

0 The event selections for FCFV and KS searches (I-III) use only samples processed

0 with standard reconstruction. The KL search (VI) uses only samples processed with multi-vertex reconstruction.

In Chapters 7, 8, 9 and 10 searches (I), (II), (III) and (VI) respectively are described. In each of these chapters we describe: the event selection, the results of a comparison of the SK-I data and atmospheric neutrino MC using a sideband sample, the results of the search in SK-I data, a breakdown of the remaining background, the signal candidates if any and ﬁnally a summary of the total systematic error. The ﬁnal result of the combined p → μ+K0 search is described in Chapter 11 . Chapter 7

0 → 0 0 Search for “KS π π ”

7.1 Event Selection

(D1) 3 ≤ nring ≤ 5

(E1) number of μ-like rings = 1

(F1) 0 ≤ number of decay electron ≤ 1

2 2 (G1) 400 MeV/c

(H1) 150 MeV/c

(I1) Ptot < 300 MeV/c

2 2 (J1) 750 MeV/c

→ + 0 0 → 0 0 When the free proton decays via p μ KS; KS π π the ﬁnal state particles consist of a primary muon (μ+) with 326.5 MeV/c momentum and four gammas; two from the decay of each neutral pion. The Cherenkov threshold of the muon is

+ → 120 MeV/c. The primary muon has a decay lifetime of 2.2 ñs and decays via μ

+ 0 e νeν¯μ.Theπ may decay asymmetrically making it diﬃcult to reconstruct one of the gammas if its momentum is very small.

99 100

The limit of 3-5 rings for criteria (D1) is determined with the assumption that at least one gamma from each of the decaying pions as well as the primary muon are reconstructed. Figure 7.1 shows the number of ring (nring) distribution for both the p → μ+K0 MC and atmospheric neutrino MC. As expected nearly all, 97.6%, of the

0 → 0 0 KS π π MC sample is contained within the selected region. Criteria (E1) requires one μ-like ring from the primary muon. All remaining rings

are generated by gammas from the decaying neutral pions and are e-like. For this search, PID likelihood is calculated using both opening angle and pattern information described in section 5.1.3. Figure 7.2 shows the PID likelihood distribution for the true muon ring and remaining rings. In the p → μ+K0 MC (atmospheric neutrino MC) sample the true muon ring is deﬁned as the ring whose reconstructed direction is within 5◦ of the true primary (any true) muon direction. Only remaining rings that are within 5◦ of a true electron or gamma are shown for the atmospheric neutrino MC. For the p → μ+K0 MC the mis-PID probability is 2.5% and 3.2% for the true muon ring and remaining rings respectively. For the atmospheric neutrino MC, the mis-PID probability is 2.3% and 0.9% for the true muon ring and remaining rings respectively. At most, there is one decay electron; it is from the primary muon. Criteria (F1) is determined with the assumption that this decay electron can be missed. Figure 7.3 shows the decay electron distribution for both the p → μ+K0 MC and atmospheric neutrino MC. As expected, there is at most one decay electron detected for the

0 → 0 0 KS π π sample. The fraction of events with zero detected decay electrons in the 0 → 0 0 KS π π sample is 20.5% which is consistent with the decay electron detection eﬃciency of 80% for μ+ described in section 5.1.6.

The invariant kaon mass, MKS , total momentum, Ptot, total energy, Etot and total 101

invariant mass, Mtot, are deﬁned as:

2 2 MK = E − P (7.1) S KS KS nring Ptot = pi (7.2) i=1 nring | |2 2 Etot = pi + mi (7.3) i=1 2 − 2 Mtot = Etot Ptot (7.4)

where pi is the momentum of the i-th ring and mi is the mass of the particle associated with the ring. The mass of the muon used in the calculation is 105.7MeV/c2 while

gammas are considered massless. The calculation of the kaon energy, EKS , and kaon

momentum, PKS , are done in a similar way as Etot and Ptot except only the e-like rings are included in the summation.

2 Criteria (G1) selects MKS near the expected value of 497.6MeV/c . Figure 7.4 → + 0 shows the MKS distribution for the p μ K MC and atmospheric neutrino MC. The main peak is at 461.8 ± 0.8MeV/c2 in the p → μ+K0 MC. The peak is smaller than the expected value because of the contribution from events with three or four rings. For these events, all ﬁnal state particles are not reconstructed and therefore

± 2 MKS is underestimated. There is a peak at 135.2 0.4MeV/c in the atmospheric

neutrino MC. This results when only two rings are used to calculate MKS and both are from gammas due to the decay of a single π0. Thispeakisconsistentwiththe expected π0 mass of 135.0MeV/c2.

Criteria (H1) selects the primary muon momentum, pμ, near the expected value

+ 0 of 326.5 MeV/c. Figure 7.5 shows the pμ distribution for the p → μ K MC and atmospheric neutrino MC. The main peak is at 333.6 ± 0.4 MeV/c; within 2% of the expected value. The source of the second peak near 250 MeV/c is due to a pathology in the momentum reconstruction discussed in section 5.1.5. 102

9000

ATM-ν MC 8000 p→μK0 MC →π0π0 KS Other 7000 Events/1489.2day

6000

5000

4000

3000

2000

1000

0 12345 nring Figure 7.1: The nring distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-C). The hatched region 0 → 0 0 → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

Criteria (I1) selects Ptot below 300 MeV/c. Figure 7.6 shows the Ptot distribution for the p → μ+K0 MC and atmospheric neutrino MC. For free protons, the true total momentum of the decay products should be zero since the proton is at rest. However, for bound protons in the oxygen nucleus, the initial momentum of the proton is not zero due to the Fermi momentum. In this case, the true total momentum of the decay products will equal the initial Fermi momentum of the proton.

Criteria (J1) is used to select events with Mtot near the expected value of

2 938.3MeV/c corresponding to the invariant proton mass. Figure 7.7 shows the Mtot distribution for the p → μ+K0 MC and atmospheric neutrino MC. The main peak is at 902.2 ± 0.2MeV/c2. 103

900 e-like μ-like e-like μ-like ATM-ν MC ATM-ν MC p→μK0 MC p→μK0 MC 800 →π0π0 250 →π0π0 KS KS Other Other 700 Events/1489.2day Events/1489.2day 200 600

500 150

400

100 300

200 50 100

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood true μ ring remaining rings Figure 7.2: The PID likelihood distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-D1) and true particle 0 → 0 0 selection described in the text. The hatched region shows the KS π π contribution. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical line indicate the event selection threshold.

450 ATM-ν MC →μ 0 400 p K MC →π0π0 KS Other 350 Events/1489.2day

300

250

200

150

100

0 012345678910

Number of decay electron Figure 7.3: The number of decay electron distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E1). 0 → 0 0 The hatched region shows the KS π π contribution. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 104

45 ATM-ν MC p→μK0 MC →π0π0 40 KS Other 35 Events/1489.2day

0 0 200 400 600 800 1000 MeV/c2 MKS → + 0 Figure 7.4: The MKS distribution for p μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-F1). The hatched region 0 → 0 0 → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

10 ATM-ν MC p→μK0 MC →π0π0 KS Other 8 Events/1489.2day

0 0 100 200 300 400 500 600 700 800 MeV/c pμ

+ 0 Figure 7.5: The pμ distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-G1). The hatched region shows the 0 → 0 0 → + 0 KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 105

3.5 ATM-ν MC p→μK0 MC →π0π0 KS 3 Other Events/1489.2day

2.5

1.5

0.5

0 0 200 400 600 800 1000 MeV/c Ptot

+ 0 Figure 7.6: The Ptot distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-H1). The hatched region shows the 0 → 0 0 → + 0 KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash- dot vertical line indicate the event selection region.

0.8 ATM-ν MC p→μK0 MC →π0π0 KS 0.7 Other Events/1489.2day 0.6

0.5

0.4

0.3

0.2

0.1

0 500 600 700 800 900 1000 1100 1200 MeV/c2 Mtot

+ 0 Figure 7.7: The Mtot distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-I1). The hatched region 0 → 0 0 → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 106

7.2 SK-I Data Sideband

To ensure there are no obvious problems with the analysis prior to performing the proton decay search, we compare both the absolute shape and the agreement between the data and atmospheric neutrino MC of the basic distributions of parameters used

for the event selection. Comparison of the agreement is quantiﬁed using a two sample Kolomogorov- Smirnov test between the data and atmospheric neutrino MC in which the signif- icance, α, is calculated [89]. The data and atmospheric neutrino MC are considered

to disagree if α ≤ 1%. This threshold for α was determined ad-hoc. The distributions are made using a sideband sample which is deﬁned to satisfy two criteria. The ﬁrst criteria is the proton decay signal kinematics region is well excluded. The second criteria is to maximize the statistics by using minimal selections so the

best comparison can be made for distributions of parameters that come late in the proton decay search event selection.

0 → The following event selection is used to deﬁne the sideband sample of the KS π0π0 search:

• FCFV

• 3 ≤ nring ≤ 5

• 1 μ-like ring

• exclude events that satisfy:

2 2 Ptot < 450 MeV/c AND 600 MeV/c

To satisfy the ﬁrst criteria, the fourth selection excludes events from the signal box

region defined by Ptot and Mtot. The second criteria is satisfied by using only the minimum number of event selections required to define Ptot and Mtot. 107

After this event selection, the remaining data events and background rate normalized by live-time is 498 ± 22.3 and 497.5 ± 2.9 respectively.

Figure 7.8 shows the number of decay electron distribution. The dominant remaining neutrino interactions in the sideband sample are: νμ CC single pion, multi pion and DIS. The distribution shape is as expected considering these kinematics and the decay electron detection eﬃciency. α =85.5%; the data and atmospheric neutrino MC agree.

± 2 Figure 7.9 shows the MKS distribution. The peak at 136.0 0.4MeV/c in this distribution corresponds to the π0 mass of 135.0MeV/c2. This reason for this peak is described in section 7.1. α =90.2%; the data and atmospheric neutrino MC agree.

Figure 7.10 shows the pμ distribution. The distribution falls oﬀ sharply below about 120 MeV/c corresponding to the Cherenkov threshold of the muon. α =10.5%; the data and atmospheric neutrino MC agree.

Figure 7.11 shows the Ptot distribution. The shape is as expected; no discontinuity or abnormal peaks are observed. α =14.9%; the data and atmospheric neutrino MC agree.

Figure 7.12 shows the Mtot distribution. The shape is as expected; no discontinuity or abnormal peaks are observed. α =9.2%; the data and atmospheric neutrino MC agree. 108

250 DATA Atm-ν MC

200 Events/1489.2day

150

100

0 012345678910 number of decay-e (sideband) Figure 7.8: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

120 DATA Atm-ν MC

100 Events/1489.2day

0 0 250 500 750 1000 1250 1500 1750 2000 MeV/c2 MKS (sideband)

Figure 7.9: The MKS distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 109

DATA 70 Atm-ν MC

60 Events/1489.2day

0 0 500 1000 1500 2000 2500 3000 MeV/c pμ (sideband)

Figure 7.10: The pμ distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

DATA 70 Atm-ν MC

60 Events/1489.2day 50

0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 MeV/c Ptot (sideband)

Figure 7.11: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 110

DATA 70 Atm-ν MC

60 Events/1489.2day 50

0 0 500 1000 1500 2000 2500 3000 3500 4000 MeV/c2 Mtot (sideband)

Figure 7.12: The Mtot distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 111

7.3 SK-I Data Event Rate vs. Event Selection

The number of events in the data, the remaining signal detection eﬃciency and expected background obtained from the atmospheric neutrino MC along the event selection described in section 7.1 are summarized in Table 7.1. The Poisson probability

to observe 1 event in data with a background expectation of 1.1 events is 36.7%. This result is consistent with no excess in the data from the background expectation. Therefore, we perform a calculation of the lower limit of the proton decay lifetime in Chapter 11 using this result.

In order to conﬁrm that there is no excess in the data from the background expectation, both the absolute shape and the agreement between the data and atmospheric neutrino MC is checked after each event selection step using the distributions of the basic parameters from the event selection. The comparison of agreement is done using

α in the same way as described in section 7.2. Figure 7.13 shows the event rate after each event selection. The data and atmospheric neutrino MC agree along the event selection. Figure 7.14 shows the nring distribution after event selections (A-C) have been ap-

plied. Single ring events are most common which is expected since CCQE interactions are the most dominant for this event sample. α =8.9%; the data and atmospheric neutrino MC agree. Figure 7.15 shows the PID likelihood distribution for each nring after event selections (A-D1). The shape is as expected; no discontinuity or abnormal peaks are

observed. For all distributions, the value of α is greater than 1%; the smallest value of α is 6.0% for the nring=2; ring#2 distribution. The data and atmospheric neutrino MC agree. Figure 7.16 shows the number of decay electron distribution after event selections

(A-E1). The dominant remaining neutrino interactions are: νμ CC single pion, multi pion and DIS. The distribution shape is as expected considering these kinematics 112 and the decay electron detection eﬃciency. α =70.8%; the data and atmospheric neutrino MC agree.

Figure 7.17 shows the MKS distribution after event selections (A-F1). The peak at 135.2 ± 0.4MeV/c2 seen in this distribution corresponds to the π0 mass as explained in section 7.1. α =90.0%; there is agreement between the data and atmospheric neutrino MC.

Figures 7.18 shows the pμ distribution after event selections (A-G1). The shape is as expected; no discontinuity or abnormal peaks are observed. α =7.3%; the data and atmospheric neutrino MC agree.

Figure 7.19 shows the Ptot distribution after event selections (A-H1). The shape is as expected; no discontinuity or abnormal peaks are observed. α =62.5%; the data and atmospheric neutrino MC agree.

Figure 7.20 shows Mtot distribution after event selections (A-I1). The shape is as expected; no discontinuity or abnormal peaks are observed. α =95.7%; the data and atmospheric neutrino MC agree.

+ 0 Figure 7.21 shows the Ptot vs. Mtot distribution for p → μ K MC, atmospheric neutrino MC and data respectively. The p → μ+K0 MC shows a densely populated region consistent with Ptot 300 MeV/c and Mtot corresponding to the proton mass as expected. Events that are located outside the signal box are mainly a result of having a large Fermi momentum or involve correlated decay. The shape of the data is consistent by eye with that of the atmospheric neutrino MC. 113

Event Selection Eﬃciency(%) Atm-ν MC FC Data (A-C) FCFV 97.6 ± 0.1 11105.8 ± 13.7 12232 ± 110.6 (D1) nring 37.0 ± 0.1 1485.6 ± 5.1 1563 ± 39.5 (E1) no. μ-like 19.6 ± 0.1 527.4 ± 3.0 528 ± 23.0 (F1) no. decay-e 18.0 ± 0.1 450.1 ± 2.8 450 ± 21.2 ± ± ± (G1) MKS 10.3 0.170.5 1.1758.7 (H1) pμ 9.7 ± 0.121.6 ± 0.628± 5.3 (I1) Ptot 8.9 ± 0.11.8 ± 0.11± 1.0 (J1) Mtot 8.8 ± 0.11.1 ± 0.11± 1.0

0 → 0 0 Table 7.1: KS π π search data events, signal detection eﬃciency and background rate along the event selection described in section 7.1. The atmospheric neutrino MC is normalized to the live-time (1489.2 days).

10 5

DATA Atm-ν MC 10 4 Events/1489.2 day 10 3

10 2

-1 10 A-C D1 E1 F1 G1 H1 I1 J1 →π0π0 KS event selection 0 → 0 0 Figure 7.13: The event rate along the KS π π search event selection for data (red closed squares) and atmospheric neutrino MC (blue open triangles). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). 114

10000 DATA Atm-ν MC

8000 Events/1489.2day

6000

4000

2000

0 12345 nring Figure 7.14: The nring distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-C). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

90 e-like μ-like DATA e-like μ-like DATA 35 e-like μ-like DATA Atm-ν MC 70 Atm-ν MC Atm-ν MC 80 30 70 60 25 60 50 20 50 40 40 15

Events/1489.2day Events/1489.2day 30 Events/1489.2day 30 10 20 20 10 10 5 0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood PID likelihood nring=3; ring #1 nring=4; ring #2 nring=5; ring #2 μ DATA 90 μ DATA 40 μ DATA 140 e-like -like e-like -like e-like -like Atm-ν MC 80 Atm-ν MC 35 Atm-ν MC 120 70 30 100 60 25 50 80 20 40

Events/1489.2day 60 Events/1489.2day Events/1489.2day 15 30 40 20 10 20 10 5 0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood PID likelihood nring=3; ring #2 nring=4; ring #3 nring=5; ring #3

μ DATA μ DATA 45 μ DATA 160 e-like -like 90 e-like -like e-like -like Atm-ν MC Atm-ν MC 40 Atm-ν MC 80 140 35 120 70 60 30 100 50 25 80 40 20 Events/1489.2day Events/1489.2day Events/1489.2day 60 30 15 40 20 10 20 10 5 0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood PID likelihood nring=3; ring #3 nring=4; ring #4 nring=5; ring #4 45 e-like μ-like DATA 22.5 e-like μ-like DATA 40 e-like μ-like DATA Atm-ν MC Atm-ν MC Atm-ν MC 40 20 35 35 17.5 30 30 15 25 25 12.5 20 20 10 Events/1489.2day Events/1489.2day Events/1489.2day 15 15 7.5 10 5 10 5 2.5 5 0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood PID likelihood nring=4; ring #1 nring=5; ring #1 nring=5; ring #5 Figure 7.15: The distribution of PID likelihood for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-D1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical line indicates the event selection threshold. 115

DATA Atm-ν MC 250

Events/1489.2day 200

150

100

0 012345678910 Number of decay electron Figure 7.16: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-E1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

80 DATA Atm-ν MC

Events/1489.2day 60

0 0 200 400 600 800 1000 MeV/c2 MKS

Figure 7.17: The MKS distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-F1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 116

14 DATA Atm-ν MC

12 Events/1489.2day 10

0 0 200 400 600 800 1000 MeV/c pμ

Figure 7.18: The pμ distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-G1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

DATA 12 Atm-ν MC

10 Events/1489.2day

0 0 200 400 600 800 1000 1200 1400 1600 1800 MeV/c Ptot

Figure 7.19: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-H1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicate the event selection region. 117

1.2 DATA Atm-ν MC

1 Events/1489.2day 0.8

0.6

0.4

0.2

0 500 600 700 800 900 1000 1100 1200 MeV/c2 Mtot

Figure 7.20: The Mtot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-I1). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

p→μK0 MC ATM-ν MC DATA 900

(MeV/c) 800 tot P 700 600 500 400 300 200 100

0 0 500 1000 0 500 1000 0 500 1000 2 2 2 Mtot (MeV/c ) Mtot (MeV/c ) Mtot (MeV/c ) + 0 Figure 7.21: The Mtot vs. Ptot scatter plot from left to right; p → μ K MC (black), atmospheric neutrino MC (blue) and data (red) after event selections (A-H1). The area inside the pink box indicates the event selection region. 118

7.4 Breakdown of Remaining Background

The atmospheric neutrino MC events remaining after event selections (A-J1) are classiﬁed by true parent neutrino ﬂavor and interaction mode and summarized in Table 7.2.

The dominant remaining backgrounds consist of: νe CC single and multi-meson, νμ

NC DIS single and multi-meson and νμ CC multi-meson neutrino interactions. These backgrounds are consistent with ﬁnal state kinematics that would be reconstructed as events with a single μ-like ring and several e-like rings that are characteristic of 0 → 0 0 the KS π π search.

S. Mine [90] estimated the mis-PID fraction of the remaining νμ CC background of the p → μ+π0 search at 10% where the event is mis-PID if the muon candidate is not a true muon and the remaining rings are not true gammas from π0 decay.

To conﬁrm there is no problem with the analysis tools for this search, we compare the mis-PID fraction obtained using our atmospheric neutrino MC sample with the result of [90]. In our sample, 4 of the 22 νμ CC events remaining were mis-PID resulting in a mis-PID fraction of 18 ± 8%. This is consistent with [90]. 119

Parent ν ﬂavor ν interaction SK-I (%) QE 1.9 ± 1.9 CC single meson 19.4 ± 5.5 38.7 ± 6.9% multi-meson 15.5 ± 5.1 νe DIS 1.9 ± 1.9 52.2 ± 7.1% QE 0.0 ± 1.9 NC single meson 1.9 ± 1.9 13.5 ± 4.8% multi-meson 7.7 ± 3.7 DIS 3.8 ± 2.7 QE 0.0 ± 1.9 CC single meson 1.9 ± 1.3 15.0 ± 5.0% multi-meson 10.6 ± 3.7 νμ DIS 2.5 ± 1.8 47.8 ± 7.1% QE 0.0 ± 1.9 NC single meson 9.7 ± 4.1 32.8 ± 6.6% multi-meson 9.7 ± 4.1 DIS 13.5 ± 4.8

Total: 100.0 ± 0.0

Table 7.2: Breakdown of remaining atmospheric neutrino MC background for the 0 → 0 0 KS π π search. The background is broken down by true neutrino ﬂavor and neutrino interaction. A description of possible neutrino interactions is described in section 3.3. 120

0 → 0 0 KS π π candidate #1 NHITAC 2 Evis (MeV/c) 645.4 Dwall (cm) 396.9 nring 4 N(μ) 246.2 S(γ) 189.5 PID & momentum (MeV/c) S(γ) 185.9 S(γ) 184.2 number of decay electron 0 2 MKS (MeV/c ) 516.9 Ptot (MeV/c) 211.4 2 Mtot (MeV/c ) 800.1

0 → 0 0 Table 7.3: The reconstructed information of the data candidate for the KS π π search. The “S” and “N” refer to showering (e-like) and non-showering (μ-like) PID respectively. The particle listed within the parenthesis for each ring is the assumed particle type used for the momentum reconstruction.

7.5 SK-I Data Candidates

0 → 0 0 There is one data candidate found for the KS π π search. Figure 7.22 shows the event display for this candidate. The reconstruction information for this event is summarized in Table 7.3. Although this event is selected as a candidate, it is not an obvious “golden” proton

decay event. The MKS is larger than the expected kaon mass by 3.8%, Mtot is smaller than the proton mass by 14.7%. The e-like ring near the center of the event display may be fake as it is very near the threshold of rejection by the ring correction described in section 5.1.7. 121

NUM 1 RUN 7787 SUBRUN 217 EVENT 11860097 DATE 1999-Aug-19 TIME 12: 3:29 TOT PE: 6072. MAX PE: 205.7 NMHIT : 2633 ANT-PE: 21.9 ANT-MX: 7.0 NMHITA: 25

1 1

1990/00/00:NoYet:NoYet 1 1990/00/00:NoYet:NoYet 1 RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111 1990/00/00:NoYet:NoYet T diff.:0.101E+0 1990/00/00:NoYet:NoYet FEVSK :81002803 1990/00/00:NoYet:NoYet 2009/06/30:;R= 4:NoYet nOD YK/LW: 3/ 2 R : Z : PHI : G SUB EV : 0/ 1 12.93: 5.27:-3.11:0 Dcye: 0( 0/ 0/ 0 CANG : RTOT : AMOM : M 41.2: 476: 97: V=-0.606:-0.508:-0.6 46.0: 997: 202: - V= 0.703: 0.644: 0.3 46.0: 1047: 212: - Comnt; V= 0.681: 0.624:-0.3 24.0: 655: 133: - V=-0 991:-0 130:-00 0 → 0 0 Figure 7.22: Event display of the candidate for the KS π π search. The red (cyan) thick solid lines show the reconstructed rings as e-like (μ-like) type. 122

Source Systematic Error (%) Physics Simulation Fermi momentum 2.6 Correlated decay 6.2 0 → 0 KL KS regeneration (nucleus) 3.6 0 → 0 KL KS regeneration (water) 4.4 Detector Water quality (incl. stat. error) 4.1 (3.6) Energy scale 1.3 Event Reconstruction Fiducial volume 1.5 Ring counting 1.0 PID 1.2 Number of decay electrons 2.0 Detector response asymmetry 0.4 Statistical error 0.8

Total 10.3

0 → 0 0 Table 7.4: Systematic errors on signal detection eﬃciency for the KS π π search. The number shown for the uncertainty due to water quality includes the statistical error of p → μ+K0 MC sample described in section A.2.3 which itself is shown within the parenthesis.

0 → 0 0 7.6 Total Systematic Error of “KS π π ”Search

Tables 7.4 and 7.5 summarize the total systematic error on the signal detection eﬃ-

0 → 0 0 ciency and background rate respectively of the KS π π search. The detail of the systematic error estimation is described in Appendix A. 123

Source Systematic Error (%) Physics Simulation ν Flux Absolute 10.0 ν/ν¯ 1.3 νe/νμ 0.2 ν cross-section QE 0.1 Single π 4.3 MA(QE & single π)3.9 Coherent π ∼ 0 Multi π 1.6 NC/CC ratio 4.8 π Nuclear Eﬀect Elastic 1.3 Charge exchange 1.2 Absorption 1.8 Production 3.1 Fermi momentum 1.9 0 → 0 ∼ KL KS regeneration (nucleus) 0 0 → 0 ∼ KL KS regeneration (water) 0 Detector Water quality 15.7 Energy scale 1.5 Event Reconstruction Fiducial volume 1.2 Ring counting 1.2 PID 5.6 Number of decay electrons 2.0 Detector response asymmetry 4.1 Statistical error (250 yr) 11.1

Total 24.7

0 → 0 0 Table 7.5: Systematic errors on background rate for the KS π π search. Chapter 8

0 → + − Search for “KS π π Method #1”

8.1 Event Selection

(D2) nring = 2

(E2) number of μ-like rings = 2

(F2) number of decay electron = 2

(G2) 250 MeV/c

(H2) Ptot < 300 MeV/c

→ + 0 0 → + − When the proton decays via p μ KS; KS π π the ﬁnal state particles consist of a primary muon and two charged pions. The kinematics of the muon are the same as described in section 7.1. The momentum of the charged pions is distributed between 50 MeV/c and 500 MeV/c with a mean of 260 MeV/c. The decay of the

124 125

0 KS may be asymmetric causing one of the charged pions to be near or below the Cherenkov threshold of 159 MeV/c. The decay lifetime of charged pions is 26 ns and

± ± decay via π → μ νμ. The pions stop in the water due to energy loss from ionization before they decay. The π+ decays from rest; the momentum of the muon from the pion decay is 30 MeV/c which is below the Cherenkov threshold. The π− is captured by the nucleus before it decays.

Criteria (D2) is determined with the assumption that one of the charged pions is near or below the Cherenkov threshold and not found by the ring counting reconstruction. Figure 8.1 shows the nring distribution for both the p → μ+K0 MC and atmospheric neutrino MC. Since the ﬁnal state particles consist of muons and pions all rings are μ-like there-

fore, criteria (E2) is applied. The PID likelihood is calculated using both angle and pattern information. Figure 8.2 shows the PID likelihood distribution of each ring for both the p → μ+K0 and atmospheric neutrino MC. The mis-PID probability of

0 → + − the primary muon (ring #1) is 3% in the KS π π MC. 0 → + − We expect no more than two decay electrons in the KS π π MC; one from the primary muon and the second from the muon from the decay of the π+. Criteria (F2) is determined with the assumption that both are detected. Figure 8.3 shows the decay electron distribution for both the p → μ+K0 MC and atmospheric neutrino

MC. There are no more than two decay electrons. Criteria (G2) is used to select the momentum of the primary muon. Figure 8.4

+ 0 shows the pμ distribution for the p → μ K MC and atmospheric neutrino MC. The distribution is symmetric and the main peak is at 325.3 ± 0.3 MeV/c; within 1% of the expected value of 326.5MeV/c.

Criteria (H2) selects events with Ptot below 300 MeV/c. Ptot is calculated using

+ 0 (7.2). Figure 8.5 shows the Ptot distributions for both the p → μ K MC and atmospheric neutrino MC. Since we assume in this method that one of the charged 126

9000

ATM-ν MC 8000 p→μK0 MC →π+π- KS Other 7000 Events/1489.2day

6000

5000

4000

3000

2000

1000

0 12345 Number of rings Figure 8.1: The nring distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-C). The hatched region 0 → + − → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. pions is below the Cherenkov threshold of 159 MeV/c, the momentum carried by this pion is not taken into account in the Ptot calculation. This is the source of the tail in 0 → + − the Ptot distribution of KS π π MC. 127

90 e-like μ-like e-like μ-like 160 ATM-ν MC ATM-ν MC →μ 0 →μ 0 p K MC 80 p K MC K →π+π- K →π+π- 140 S S Other Other 70 Events/1489.2day Events/1489.2day 120 60 100 50

80 40

60 30

40 20

20 10

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood nring=2; ring #1 nring=2; ring #2 Figure 8.2: The PID likelihood distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-D2). The left (right) hand ﬁgure shows the PID likelihood distribution of the ﬁrst (second) ring. 0 → + − The hatched region shows the KS π π contribution. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical line indicate the event selection threshold. 128

180

ATM-ν MC 160 p→μK0 MC →π+π- KS 140 Other Events/1489.2day 120

100

0 012345678910 Number of decay electron Figure 8.3: The number of decay electron distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E2). 0 → + − The hatched region shows the KS π π contribution. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

ATM-ν MC 14 p→μK0 MC →π+π- KS Other 12 Events/1489.2day

0 0 100 200 300 400 500 600 700 800 (MeV/c) pμ

+ 0 Figure 8.4: The pμ distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-F2). The hatched region shows the 0 → + − → + 0 KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 129

1.8 ATM-ν MC p→μK0 MC 1.6 →π+π- KS Other 1.4 Events/1489.2day

1.2

0.8

0.6

0.4

0.2

0 0 200 400 600 800 1000 (MeV/c) Ptot

+ 0 Figure 8.5: The Ptot distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-G2). The hatched region shows the 0 → + − → + 0 KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash- dot vertical line indicate the event selection region. 130

8.2 SK-I Data Sideband

We follow the same strategy described in section 7.2 in checking the sideband sample.

0 → The following event selection are used to deﬁne the sideband sample of the KS π+π− Method #1 search:

• FCFV

• nring = 2

• 2 μ-like rings

• Ptot > 450 MeV/c

After this event selection, the remaining data events and background rate normalized by live-time is 199.0 ± 14.1 and 221.1 ± 1.8 respectively. Figure 8.6 shows the number of decay electron distribution. The dominant remaining neutrino interactions in the sideband sample are: νμ CC QE, single and multi pion. The distribution shape is as expected considering these kinematics and the decay electron detection eﬃciency. α =99.0%; the data and atmospheric neutrino MC agree.

Figure 8.7 shows the pμ distribution. The sharp cutoﬀ seen ∼ 120 MeV/c corresponds to the Cherenkov threshold of the muon. α =16.2%; the data and atmospheric neutrino MC agree.

Figures 8.8 shows the Ptot distribution. The sharp cutoﬀ seen below 450 MeV/c corresponds selection criteria of the sideband sample. α =1.4%; the data and atmospheric neutrino MC agree. 131

120 DATA Atm-ν MC

100 Events/1489.2day

0 012345678910 number of decay electron (sideband) Figure 8.6: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

40 DATA Atm-ν MC 35

30 Events/1489.2day

0 0 500 1000 1500 2000 2500 3000 (MeV/c) pμ (sideband)

Figure 8.7: The pμ distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 132

DATA Atm-ν MC 60

Events/1489.2day 50

0 0 500 1000 1500 2000 2500 3000 (MeV/c) Ptot (sideband)

Figure 8.8: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 133

8.3 SK-I Data Event Rate vs. Event Selection

The number of events in the data, the remaining signal detection eﬃciency and expected background obtained from the atmospheric neutrino MC along the event selection described in section 8.1 are summarized in Table 8.1. The Poisson probability

to observe 6 events in the data with an expectation of 3.0 events from atmospheric neutrino MC is 4.9%. This result is consistent with no excess in the data from the background expectation. Therefore, we perform a calculation of the lower limit of the proton decay lifetime in Chapter 11 using this result.

The absolute shape and the agreement between the data and atmospheric neutrino MC is checked in the same way as described in section 7.3. Figure 8.9 shows the event rate after each event selection. The data and atmospheric neutrino MC agree along the event selection.

Figure 8.10 shows the nring distribution after event selections (A-C). α =8.9%; the data and atmospheric neutrino MC agree. Figure 8.11 shows the PID likelihood distribution for each ring after event selections (A-D2). The shape is as expected; no discontinuity or abnormal peaks are observed. α =49.2% and α =6.0% for ring #1 and #2 respectively; the data and atmospheric neutrino MC agree. Figure 8.12 shows the number of decay electron distribution after event selections (A-E2). The dominant neutrino interaction modes contributing to the atmospheric neutrino MC are: νμ CC QE, single and multi pion. The distribution shape is as expected considering these kinematics and the decay electron detection eﬃciency. α =82.8%; the data and atmospheric neutrino MC agree.

Figure 8.13 shows the pμ distribution after event selections (A-F2). The lack of events below ∼ 120 MeV/c is consistent with the Cherenkov threshold of the muon.

α =15.2%; the data and atmospheric neutrino MC agree.

Figure 8.14 shows the Ptot distribution after event selections (A-G2). The shape 134

Event Selection Eﬃciency(%) Atm-ν MC FC Data (A-C) FCFV 97.6 ± 0.1 11105.8 ± 13.7 12232 ± 110.6 (D2) nring 41.2 ± 0.1 1998.3 ± 6.0 2130 ± 46.2 (E2) no. μ-like 28.6 ± 0.1 287.2 ± 2.1 284 ± 16.9 (F2) no. decay-e 15.0 ± 0.152.8 ± 0.960± 7.7 (G2) pμ 14.3 ± 0.112.6 ± 0.415± 3.9 (H2) Ptot 10.5 ± 0.13.0 ± 0.26± 2.4

0 → + − Table 8.1: KS π π Method #1 search data events, signal detection eﬃciency and background rate along the event selection described in section 8.1. The atmospheric neutrino MC is normalized to the live-time. is as expected; no discontinuity or abnormal peaks are observed. α =72.7%; the data and atmospheric neutrino MC agree.

+ 0 Figure 8.15 shows the Ptot vs. pμ distributions for p → μ K MC, atmospheric neutrino MC and data respectively after event selections (A-F2). The p → μ+K0

MC shows a densely populated region consistent with pμ ∼ 326.5 MeV/c and Ptot 300 MeV/c as expected. Events that are located outside the signal box are mainly a result of missing the momentum carried by the charged pion that is below threshold, having a large Fermi momentum or involve correlated decay. The shape of the data points is consistent by eye with that of the atmospheric neutrino MC. 135

10 5

DATA Atm-ν MC 10 4 Events/1489.2 day 10 3

10 2

-1 10 A-C D2 E2 F2 G2 H2 →π+π- # KS Method 1 event selection 0 → + − Figure 8.9: The event rate along the KS π π Method #1 search event selection for data (red closed squares) and atmospheric neutrino MC (blue open triangles). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the live-time (1489.2 days).

10000 DATA Atm-ν MC

8000 Events/1489.2day

6000

4000

2000

0 12345

Number of rings Figure 8.10: The nring distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-C). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 136

300 225 e-like μ-like DATA e-like μ-like DATA Atm-ν MC Atm-ν MC

200 250

175 Events/1489.2day Events/1489.2day

200 150

125 150

100

75 100

50 50 25

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 PID likelihood PID likelihood nring=2; ring #1 nring=2; ring #2 Figure 8.11: The PID likelihood distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-D2). The ﬁrst (second) ring is the most (least) energetic of the two rings. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

DATA 160 Atm-ν MC

140 Events/1489.2day 120

100

0 012345678910

Number of decay electron Figure 8.12: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-E2). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 137

DATA 10 Atm-ν MC

8 Events/1489.2day

0 0 200 400 600 800 1000 1200 1400 (MeV/c) pμ

Figure 8.13: The pμ distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-F2). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

DATA 4.5 Atm-ν MC

Events/1489.2day 3.5

2.5

1.5

0.5

0 0 100 200 300 400 500 600 700 800 900 (MeV/c) Ptot

Figure 8.14: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-G2). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 138

p→μK0 MC ATM-ν MC DATA 900

(MeV/c) 800 tot P 700 600 500 400 300 200 100

0 0 500 0 500 0 500

pμ (MeV/c) pμ (MeV/c) pμ (MeV/c)

+ 0 Figure 8.15: The pμ vs. Ptot scatter plot from left to right; p → μ K MC (black), atmospheric neutrino MC (blue) and data (red) after event selections (A-F2). The pink box indicates the event selection region. 139

Parent ν ﬂavor ν interaction SK-I (%) QE 0.0 ± 0.7 CC single meson 0.0 ± 0.7 0.0 ± 0.7% multi-meson 0.0 ± 0.7 νe DIS 0.0 ± 0.7 0.7 ± 0.7% QE 0.0 ± 0.7 NC single meson 0.0 ± 0.7 0.7 ± 0.7% multi-meson 0.7 ± 0.7 DIS 0.0 ± 0.7 QE 12.6 ± 2.2 CC single meson 70.0 ± 3.1 94.5 ± 4.7% multi-meson 11.8 ± 2.3 νμ DIS 0.0 ± 0.7 99.3 ± 4.6% QE 0.0 ± 0.7 NC single meson 2.8 ± 1.4 4.8 ± 1.8% multi-meson 0.7 ± 0.7 DIS 1.4 ± 1.0 Total: 100.0 ± 0.0

Table 8.2: Breakdown of remaining atmospheric neutrino MC background for the 0 → + − KS π π Method #1 search. The background is broken down by true neutrino ﬂavor and neutrino interaction. A description of possible neutrino interactions is described in section 3.3.

8.4 Breakdown of Remaining Background

The atmospheric neutrino MC events remaining from the after event selections (A-H2) are classiﬁed by true parent neutrino ﬂavor and interaction mode and summarized in Table 8.2.

The dominant remaining background consist of: νμ CCQE, CC single and multi- meson neutrino interactions. These backgrounds are consistent with ﬁnal state kinematics that would be reconstructed as events with two μ-like rings and two decay

0 → + − electrons that are characteristic of the KS π π Method #1 search. 140

8.5 SK-I Data Candidates

0 → + − There are a total of six candidates found in the data for the KS π π Method #1 search. Figures 8.16, 8.17, 8.18, 8.19, 8.20 and 8.21 show the SK event display for these six candidates. The reconstruction information for these events is summarized in Table 8.3. Although these events are selected as candidates they are not obvious “golden” proton decay events. In the ﬁrst event, the primary μ ring edge is correctly reconstructed; the ﬁtted ring matches the visible ring edge. pμ is smaller than expected by 13.8% and Ptot is within 1.6% of the event selection threshold. There is mis-reconstruction of the π± ring, however the true particle seems to be a charged pion which has inelastically scattered generating a second ring. This may be the reason for the mis-reconstruction. In the second event, both the ring edges are correctly reconstructed. Near the π±

ring there is a second ring which by eye is consistent with the characteristics of a true

charged pion that has inelastically scattered. For this event pμ is smaller than the expected value by 7.0%, Ptot is well below the event selection threshold.

Both ring edges in the third event are correctly reconstructed. pμ is smaller than expected by 9.8%, Ptot is well below the event selection threshold.

In the fourth event, both ring edges are correctly reconstructed. pμ is larger than expected by 2.1% and Ptot is well below the event selection threshold.

In the ﬁfth candidate, both ring edges are correctly reconstructed. pμ is smaller than expected by 0.9%, Ptot is well below the event selection threshold.

In the sixth event, both rings are well reconstructed. pμ is smaller than expected by 22.7% and Ptot is within 20.9% of the event selection threshold. 141

0 → + − KS π π Method #1 candidate #1 #2 #3 NHITAC 1 1 0 Evis (MeV/c) 144.5 192.6 155.5 Dwall (cm) 493.0 772.9 602.5 nring 2 2 2 N(μ) 281.4 N (μ) 303.5 N (μ) 294.4 PID & momentum (MeV/c) N(π±) 243.8 N (π±) 308.4 N (π±) 284.7 number of decay-e 2 2 2 Ptot (MeV/c) 295.0 180.7 116.0

0 → + − KS π π Method #1 candidate #4 #5 #6 NHITAC 1 1 1 Evis (MeV/c) 189.4 203.8 95.6 Dwall (cm) 698.2 878.5 347.5 nring 2 2 2 N(μ) 333.2 N (μ) 323.5 N (μ) 252.4 PID & momentum (MeV/c) N(π±) 287.0 N (π±) 262.8 N (π±) 241.1 number of decay-e 2 2 2 Ptot (MeV/c) 143.7 136.0 240.4

0 → + − Table 8.3: The reconstructed information of the data candidates for the KS π π Method #1 search. The “S” and “N” refer to showering (e-like) and non-showering (μ-like) PID respectively. The particle listed within the parenthesis for each ring is the assumed particle type used for the momentum reconstruction. 142

45 NUM 1 40 RUN 4018 SUBRUN 41 35 EVENT 289990 DATE 1997-May-11 30 TIME 4:18:53 TOT PE: 1688. 25 MAX PE: 26.8 20 NMHIT : 952 ANT-PE: 31.5 15 ANT-MX: 7.0 NMHITA: 34 10 5 0 600 800 1000 1200 1400 1600 1800

1 1

1 1 35

1 30

1 1 1 25

1990/00/00:NoYet:NoYet 1 RunMODE:NORMAL 1990/00/00:NoYet:NoYet 1 1 1 TRG ID :00000011 20 1990/00/00:NoYet:NoYet 1 1 1990/00/00:NoYet:NoYet 1 T diff.:0.128E+0 1990/00/00:NoYet:NoYet FEVSK :81002003 15 1990/00/00:NoYet:NoYet 2009/06/29:;R= 2:NoYet nOD YK/LW: 2/ 1 R : Z : PHI : G SUB EV : 0/ 2 10 11.97: 1.69: 1.61:0 Dcye: 2( 1/ 1/ 0 CANG : RTOT : AMOM : M 5 35.5: 465: 95: V=-0.822: 0.199:-0.5 32.0: 269: 55: 0 V= 0.804: 0.254:-0.5 Comnt; 0 5 10 15 20 25 0 → + − Figure 8.16: The ﬁrst candidate for the KS π π Method #1 search. The event display is shown on the left and the raw PMT timing, t (ns), and charge, q (p.e.), distributions are shown on the right. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. The PMTs in the event display that are highlighted green correspond to the late timing peak in the dashed green box which indicates the source is a decay electron. 143

NUM 1 RUN 8112 60 SUBRUN 226 EVENT 30337267 50 DATE 1999-Nov-20 TIME 0: 1:55 40 TOT PE: 1763. MAX PE: 21.3 NMHIT : 1003 30 ANT-PE: 23.6 ANT-MX: 3.0 20 NMHITA: 27 10 0 600 800 1000 1200 1400 1600 1800

1 1 1 1

1 1 1 1 30

1 1

1 1 25

1 1 20 1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet 1 TRG ID :00000111 15 1990/00/00:NoYet:NoYet 1 T diff.:0.189E+0

1990/00/00:NoYet:NoYet 1 FEVSK :81002803

1 1

1990/00/00:NoYet:NoYet 1 nOD YK/LW: 2/ 1 10 2009/06/29:;R= 2:NoYet SUB EV : 0/ 1 1

R : Z : PHI : G 1 9.17: -5.06: 0.30:0 Dcye: 2( 1/ 1/ 0 5 CANG : RTOT : AMOM : M 1 36.2: 567: 115: 1 V=-0.534: 0.720:-0.4 34.0: 412: 84: 0 V= 0.731:-0.670:-0.1 Comnt; 0 2.5 5 7.5 10 12.5 15 17.5 20 0 → + − Figure 8.17: The second candidate for the KS π π Method #1 search. The event display is shown on the left and the raw PMT timing, t (ns), and charge, q (p.e.), distributions are shown on the right. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. The PMTs in the event display that are highlighted green correspond to the late timing peak in the dashed green box which indicates the source is a decay electron. 144

NUM 2 RUN 8268 SUBRUN 66 EVENT 8788469 DATE 2000-Jan-14 TIME 22:22:51 TOT PE: 1403. MAX PE: 30.5 NMHIT : 659 ANT-PE: 26.7 ANT-MX: 2.3 NMHITA: 31

1 1

1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111 1990/00/00:NoYet:NoYet T diff.:0.375E+0 1990/00/00:NoYet:NoYet FEVSK :81002803 1990/00/00:NoYet:NoYet 2009/06/30:;R= 2:NoYet nOD YK/LW: 0/ 0 R : Z : PHI : G SUB EV : 0/ 3 10.87: 5.99: 1.79:0 Dcye: 2( 1/ 0/ 0 CANG : RTOT : AMOM : M 30.1: 518: 105: V=-0.404: 0.739:-0.5 34.0: 266: 54: V= 0.594:-0.775: 0.2 Comnt; 0 → + − Figure 8.18: The event display of the third candidate for the KS π π Method #1 search. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. 145

NUM 3 RUN 8294 SUBRUN 102 60 EVENT 13620274 DATE 2000-Jan-28 50 TIME 9:17: 0 TOT PE: 2228. MAX PE: 26.7 40 NMHIT : 1211 ANT-PE: 16.4 30 ANT-MX: 2.9 NMHITA: 18 20 10 0 600 800 1000 1200 1400 1600 1800

1 1

1 1 40

1 1 35

1 1 1990/00/00:NoYet:NoYet 30 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111 25 1990/00/00:NoYet:NoYet T diff.:0.642E+0 1990/00/00:NoYet:NoYet FEVSK :81002803 20 1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet nOD YK/LW: 1/ 1 15 2009/06/30:;R= 2:NoYet SUB EV : 0/ 1 R : Z : PHI : G Dcye: 2( 0/ 2/ 0 10 9.92: -5.26: 0.89:0

1 1 1 1 5 CANG : RTOT : AMOM : M 1 1 1

33.8: 702: 142: 1 V= 0.687: 0.017:-0.7 0 36.0: 246: 50: 1 Comnt; V=-0.427: 0.177: 0.8 0 5 10 15 20 25 0 → + − Figure 8.19: The fourth candidate for the KS π π Method #1 search. The event display is shown on the left and the raw PMT timing, t (ns), and charge, q (p.e.), distributions are shown on the right. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. The PMTs in the event display that are highlighted green (pink) correspond to the late timing peak in the dashed green (pink) box which indicates the source is a decay electron. 146

70 NUM 4 RUN 8910 60 1 SUBRUN 9 EVENT 1290606 50

1 1 DATE 2000-Jun-26

1 1 TIME 1:29:25 1 TOT PE: 2096.4 40 MAX PE: 20.7 NMHIT : 1114 30 ANT-PE: 19.5 ANT-MX: 5.3 20 NMHITA: 22

1 10

1 0

1 600 800 1000 1200 1400 1600 1800

1 1 1 35 1 1 1

1 30 25 1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet RunMODE:NORMAL 20 1990/00/00:NoYet:NoYet TRG ID :00000111 1990/00/00:NoYet:NoYet T diff.:0.108E+0 1990/00/00:NoYet:NoYet FEVSK :81002803 15 1990/00/00:NoYet:NoYet 2009/07/01:;R= 2:NoYet nOD YK/LW: 3/ 1 R : Z : PHI : G SUB EV : 0/ 3 10 8.11: 9.31:-2.92:0 Dcye: 2( 1/ 1/ 0 CANG : RTOT : AMOM : M 5 34.0: 673: 137: V= 0.717:-0.693:-0.0 30.0: 341: 70: 0 V=-0.733: 0.562:-0.3 Comnt; 0 2.5 5 7.5 10 12.5 15 17.5 20 0 → + − Figure 8.20: The ﬁfth candidate for the KS π π Method #1 search. The event display is shown on the left and the raw PMT timing, t (ns), and charge, q (p.e.), distributions are shown on the right. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. The PMTs in the event display that are highlighted green correspond to the late timing peak in the dashed green box which indicates the source is a decay electron. 147

NUM 1 RUN 10034 SUBRUN 450 EVENT 73887738 DATE 2001-Apr-30 TIME 8:36:44 TOT PE: 928. MAX PE: 23.2 NMHIT : 477 ANT-PE: 24.3 ANT-MX: 2.7 NMHITA: 28

1 1 1 1

1 1 1

1 1

1 1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111 1990/00/00:NoYet:NoYet T diff.:0.833E+0 1990/00/00:NoYet:NoYet FEVSK :81002803

1990/00/00:NoYet:NoYet 1 nOD YK/LW: 2/ 1 2009/06/29:;R= 2:NoYet SUB EV : 0/ 5 R : Z : PHI : G 1

13.42:-13.17:-0.10:0 1 Dcye: 2( 2/ 0/ 0 CANG : RTOT : AMOM : M

34.7: 364: 74: 1

V=-0.408: 0.765:-0.4 1

28.0: 116: 24: 1 1 V= 0.823: 0.183: 0.5 Comnt; 0 → + − Figure 8.21: The event display of the sixth candidate for the KS π π Method #1 search. The cyan thick solid lines in the event display show the reconstructed rings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ. 148

Source Systematic Error (%) Physics Simulation Fermi momentum 4.0 Correlated decay 5.9 0 → 0 KL KS regeneration (nucleus) 3.2 0 → 0 KL KS regeneration (water) 4.0 Detector Water quality (incl. stat. error) 7.0 (3.4) Energy scale 1.4 Event Reconstruction Fiducial volume 1.5 Ring counting 1.4 PID 0.6 Number of decay electrons 2.0 Detector response asymmetry 1.2 Statistical error 0.7

Total 11.8

0 → + − Table 8.4: Systematic errors on signal detection eﬃciency for the KS π π Method #1 search. The number shown for the uncertainty due to water quality includes the statistical error of the p → μ+K0 MC sample described in section A.2.3 which itself is shown within the parenthesis.

0 → + − 8.6 Total Systematic Error of “KS π π Method #1” Search

Tables 8.4 and 8.5 summarize the total systematic error on the signal detection eﬃ-

0 → + − ciency and background rate respectively of the KS π π Method #1 search. The detail of the systematic error estimation is described in Appendix A. 149

Source Systematic Error (%) Physics Simulation ν Flux Absolute 10.0 ν/ν¯ 1.3 νe/νμ 1.1 ν cross-section QE 1.3 Single π 14.0 MA(QE & single π) 11.7 Coherent π ∼ 0 Multi π 0.5 NC/CC ratio 1.9 π Nuclear Eﬀect Elastic 1.8 Charge exchange 1.2 Absorption 3.2 Production 6.1 Fermi momentum 0.7 0 → 0 ∼ KL KS regeneration (nucleus) 0 0 → 0 ∼ KL KS regeneration (water) 0 Detector Water quality (incl. stat. error) 8.7 (8.0) Energy scale 1.2 Event Reconstruction Fiducial volume 1.2 Ring counting 3.7 PID ∼ 0 Number of decay electrons 2.0 Detector response asymmetry 3.4 Statistical error (200 yr) 6.9

Total 25.5

0 → + − Table 8.5: Systematic errors on background rate for the KS π π Method #1 search. 0 → + − Systematic errors on background rate for the KS π π Method #1 search. The number shown for the uncertainty due to water quality includes the statistical error of the atmospheric neutrino MC described in section A.2.3 which itself is shown within the parenthesis. Chapter 9

0 → + − Search for “KS π π Method #2”

9.1 Event Selection

(D3) nring = 3 the most energetic ring is considered as the primary muon the other rings are

considered to be charged pions

(E3) 1 ≤ number of decay electron ≤ 2

2 2 (F3) 450 MeV/c

(G3) Ptot < 300 MeV/c

2 2 (H3) 750 MeV/c

→ + 0 0 → + − The kinematics of p μ KS; KS π π decay is described in section 8.1. Criteria (D3) is determined with the assumption that both charged pions are above the Cherenkov threshold. Figure 8.1 shows the nring distribution for both the p → μ+K0 MC and atmospheric neutrino MC; in this search three rings are selected.

150 151

Criteria (E3) selects events with one or two decay electrons. Figure 9.1 shows the number of decay electron distribution. As expected, there are no more than two decay 0 → + − electrons in the KS π π MC. This event selection is made with the assumption that one may not be detected.

2 Criteria (F3) chooses events with MKS near the expected value of 497.6MeV/c .

MKS is calculated using (7.1); the mass of the charged pion used in the calculation is 2 0 → + − 139.6MeV/c . Figure 9.2 shows the MKS distribution. There is a peak in KS π π ± 2 MC at 498.0 0.2MeV/c ; within 1% of the expected value. The tail at large MKS 0 → + − for KS π π MC comes from charged pions that strongly interact in the water producing π0 through charge exchange. The gammas from the decay of these π0

are used in the MKS calculation but assumed to be muons or charged pions. This overestimates the momentum of the gamma because they are lighter particles which

gives a larger MKS than expected.

Criteria (G3) is used to select events with a Ptot below 300 MeV/c. Figure 9.3 shows the Ptot distribution. The peak near 0 MeV/c corresponds to free protons. The peak near 100 MeV/c is from bound protons.

Criteria (H3) is used to select events with a Mtot near the expected value of

2 938.3MeV/c corresponding to the proton. Figure 9.4 shows the Mtot distribution. The main peak is at 918.2 ± 0.3MeV/c2; within 2% of the expectation. 152

700

ATM-ν MC p→μK0 MC 600 →π+π- KS Other

Events/1489.2day 500

400

300

200

100

0 012345678910 Number of decay electron Figure 9.1: The number of decay electron distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-D3). 0 → + − The hatched region shows the KS π π contribution. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

35 ATM-ν MC p→μK0 MC →π+π- KS 30 Other Events/1489.2day

0 0 200 400 600 800 1000 1200 1400 1600 MeV/c2 MKS → + 0 Figure 9.2: The MKS distribution for p μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E3). The hatched region 0 → + − → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 153

ATM-ν MC p→μK0 MC →π+π- KS 4 Other Events/1489.2day

0 0 250 500 750 1000 1250 1500 1750 2000 MeV/c Ptot

+ 0 Figure 9.3: The Ptot distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-F3). The hatched region shows the 0 → + − → + 0 KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

0.09 ATM-ν MC →μ 0 0.08 p K MC →π+π- KS Other 0.07 Events/1489.2day

0.06

0.05

0.04

0.03

0.02

0.01

0 500 600 700 800 900 1000 1100 1200 1300 MeV/c2 Mtot

+ 0 Figure 9.4: The Mtot distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-G3). The hatched region 0 → + − → + 0 shows the KS π π contribution. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 154

9.2 SK-I Data Sideband

We follow the same strategy described in 7.2 in checking the sideband sample.

0 → + − The following criteria are used to deﬁne the sideband sample of the KS π π Method #2 search:

• FCFV

• nring=3

• exclude events that satisfy:

2 2 600 MeV/c

After this event selection, the remaining data events and background rate normalized by live-time is 1012 ± 31.8 and 971.8 ± 4.2 respectively.

Figure 9.5 shows the number of decay electron distribution. The dominant remaining neutrino interaction in the sideband sample is νμ CC single and multi pion and DIS. The distribution shape is as expected considering these kinematics and the decay electron detection eﬃciency. α =0.5%; the data does not agree with the at-

mospheric neutrino MC. When the atmospheric neutrino MC distribution is changed within the systematic error described in Appendix A the data and MC agree. Al- though all sources of error were considered, the systematic error from NC/CC ratio caused the largest change in the shape of the atmospheric neutrino MC distribution.

Figure 9.6 shows the MKS distribution. α =12.0%; the data and atmospheric neutrino MC agree.

Figure 9.7 shows the Ptot distribution. α =6.4%; the data and atmospheric neutrino MC agree.

Figure 9.8 shows the Mtot distribution. α =0.3%; this is smaller than the threshold of disagreement however when the atmospheric neutrino MC distribution is changed within the systematic error described in Appendix A the data and MC agree. 155

600 DATA Atm-ν MC

500 Events/1489.2day

400

300

200

100

0 012345678910 Number of decay electron (sideband) Figure 9.5: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

DATA 180 Atm-ν MC

160

Events/1489.2day 140

120

100

0 0 500 1000 1500 2000 2500 3000 3500 4000 MeV/c2 MKS (sideband)

Figure 9.6: The MKS distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 156

DATA 120 Atm-ν MC

100 Events/1489.2day

0 0 1000 2000 3000 4000 5000 MeV/c Ptot (sideband)

Figure 9.7: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

160 DATA Atm-ν MC

140

Events/1489.2day 120

100

0 0 1000 2000 3000 4000 5000 MeV/c2 Mtot (sideband)

Figure 9.8: The Mtot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-G3). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 157

9.3 SK-I Data Event Rate vs. Event Selection

The number of events in the data, the remaining signal detection eﬃciency and expected background obtained from the atmospheric neutrino MC along the event selection described in section 9.1 are summarized in Table 9.1. The Poisson probability

to observe 0 events in the data with an expectation of 0.1 events from atmospheric neutrino MC is 88.8%. This result is consistent with no excess in the data from the background expectation. Therefore, we perform a calculation of the lower limit of the proton decay lifetime in Chapter 11 using this result.

The absolute shape and the agreement between the data and atmospheric neutrino MC is checked in the same way as described in section 7.3. Figure 9.9 shows the event rate after each event selection. The data and atmospheric neutrino MC agree along the event selection.

Figure 9.10 shows the number of decay electron distribution after event selections

(A-D3). The dominant remaining neutrino interaction in the sideband sample is νμ CC single and multi pion and DIS. The distribution shape is as expected considering these kinematics and the decay electron detection eﬃciency. α =0.5%; the data does

not agree with the atmospheric neutrino MC. However, when the atmospheric neutrino MC distribution is changed within the systematic error described in Appendix A the data and MC agree. Although all sources described in these chapter were considered, the systematic error from NC/CC ratio caused the largest change in the shape of the atmospheric neutrino MC distribution.

Figure 9.11 shows the MKS distribution after event selections (A-E3). The shape is as expected; no discontinuity or abnormal peaks are observed. α =5.7%; the data and atmospheric neutrino MC agree.

Figure 9.12 shows the Ptot distribution after event selections (A-F3). The shape is as expected; no discontinuity or abnormal peaks are observed. α =45.8%; the data and atmospheric neutrino MC agree. 158

Event Selection Eﬃciency(%) Atm-ν MC FC Data (A-C) FCFV 97.6 ± 0.1 11105.8 ± 13.7 12232 ± 110.6 (D3) nring 19.8 ± 0.1 980.6 ± 4.2 1024 ± 32.0 (E3) no. decay-e 17.1 ± 0.1 440.0 ± 2.7 499 ± 22.3 ± ± ± (F3) MKS 3.5 0.133.2 0.7396.2 (G3) Ptot 2.6 ± 0.10.3 ± 0.10± 1.0 (H3) Mtot 2.5 ± 0.10.1 ± 0.10± 1.0

0 → + − Table 9.1: KS π π Method #2 search data events, signal detection eﬃciency and background rate along the event selection described in section 9.1. The atmospheric neutrino MC is normalized to the live-time.

Figure 9.13 shows the Mtot distribution after event selections (A-G3). The shape is as expected; no discontinuity or abnormal peaks are observed. There is no data after these event selections are applied.

+ 0 Figure 9.14 shows Ptot vs. Mtot distributions for p → μ K MC, atmospheric neutrino MC and data respectively after event selections (A-F3). The p → μ+K0

MC shows a densely populated region consistent with pμ ∼ 326.5 MeV/c and Ptot 300 MeV/c as expected. p → μ+K0 MC events that are located outside the signal box are mainly a result of having a large Fermi momentum or involve correlated decay. The shape of the data points is consistent by eye with that of the atmospheric neutrino MC. 159

10 5

DATA Atm-ν MC 10 4 Events/1489.2 day 10 3

10 2

-1 10 A-C D3 E3 F3 G3 H3 →π+π- # KS Method 2 event selection 0 → + − Figure 9.9: The event rate along the KS π π Method #2 search event selection for data (red closed squares) and atmospheric neutrino MC (blue open triangles). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the live-time (1489.2 days).

600 DATA Atm-ν MC

500 Events/1489.2day

400

300

200

100

0 012345678910

Number of decay electron Figure 9.10: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-D3). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 160

DATA 35 Atm-ν MC

30 Events/1489.2day

0 0 200 400 600 800 1000 1200 1400 1600 MeV/c2 MKS

Figure 9.11: The MKS distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-E3). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

DATA 10 Atm-ν MC

8 Events/1489.2day

0 0 250 500 750 1000 1250 1500 1750 2000 MeV/c Ptot

Figure 9.12: The Ptot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-F3). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 161

0.14

DATA ν 0.12 Atm- MC Events/1489.2day

0.1

0.08

0.06

0.04

0.02

0 500 600 700 800 900 1000 1100 1200 1300 MeV/c2 Mtot

Figure 9.13: The Mtot distribution for atmospheric neutrino MC (blue box) after event selections (A-G3). There is no data after these event selections. The statistical error is shown. The atmospheric neutrino MC is normalized to live-time (1489.2 day). The pink arrows and dash-dot vertical lines indicate the event selection region.

p→μK0 MC ATM-ν MC DATA 900

(MeV/c) 800 tot P 700 600 500 400 300 200 100

0 0 500 1000 0 500 1000 0 500 1000 2 2 2 Mtot (MeV/c ) Mtot (MeV/c ) Mtot (MeV/c ) + 0 Figure 9.14: The Mtot vs. Ptot scatter plot from left to right; p → μ K MC (black), atmospheric neutrino MC (blue) and data (red) after event selections (A-F3). The pink box indicates the event selection region. 162

Parent ν ﬂavor ν interaction SK-I (%) QE 0.0 ± 15.9 CC single meson 0.0 ± 15.9 0.0 ± 15.9% multi-meson 0.0 ± 15.9 νe DIS 0.0 ± 15.9 0.0 ± 15.9% QE 0.0 ± 15.9 NC single meson 0.0 ± 15.9 0.0 ± 15.9% multi-meson 0.0 ± 15.9 DIS 0.0 ± 15.9 QE 0.0 ± 15.9 CC single meson 91.3 ± 14.1 100.0 ± 17.1% multi-meson 8.7 ± 8.0 νμ DIS 0.0 ± 15.9 100.0 ± 17.1% QE 0.0 ± 15.9 NC single meson 0.0 ± 15.9 0.0 ± 15.9% multi-meson 0.0 ± 15.9 DIS 0.0 ± 15.9 Total: 100.0 ± 0.0

0 → Table 9.2: Breakdown of remaining atmospheric neutrino MC background for KS π+π− Method #2 search. The background is broken down by true neutrino ﬂavor and neutrino interaction. A description of possible neutrino interactions is described in section 3.3.

9.4 Breakdown of Remaining Background

The atmospheric neutrino MC events remaining from the after event selections (A-H3) are classiﬁed by true parent neutrino ﬂavor and interaction mode and summarized in Table 9.2.

The dominant remaining background consist of: νμ CC single and multi-meson neutrino interactions. These backgrounds are consistent with ﬁnal state kinematics that would be reconstructed as events with three μ-like rings and one or two decay

0 → + − electrons that are characteristic of the KS π π Method #2 search. 163

Source Systematic Error (%) Physics Simulation Fermi momentum 0.6 Correlated decay 5.5 0 → 0 KL KS regeneration (nucleus) 3.7 0 → 0 KL KS regeneration (water) 4.4 Detector Water quality (incl. stat. error) 17.0 (6.6) Energy scale 0.6 Event Reconstruction Fiducial volume 1.5 Ring counting 1.4 Number of decay electrons 2.0 Detector response asymmetry 0.2 Statistical error 1.5

Total 19.1

0 → + − Table 9.3: Systematic errors on signal detection eﬃciency for the KS π π Method #2 search. The number shown for the uncertainty due to water quality includes the statistical error of the p → μ+K0 MC sample described in section A.2.3 which itself is shown within the parenthesis.

0 → + − 9.5 Total Systematic Error of “KS π π Method #2” Search

Tables 9.3 and 9.4 summarize the total systematic error on the signal detection eﬃ-

0 → + − ciency and background rate respectively of the KS π π Method #2 search. The detail of the systematic error estimation is described in Appendix A. 164

Source Systematic Error (%) Physics Simulation ν Flux Absolute 10.0 ν/ν¯ 1.3 νe/νμ 0.5 ν cross-section QE 0.2 Single π 9.7 MA(QE & single π)8.9 Coherent π 0.5 Multi π 1.0 NC/CC ratio 2.1 π Nuclear Eﬀect Elastic 2.5 Charge exchange 1.2 Absorption ∼ 0 Production 4.3 Fermi momentum 6.3 0 → 0 ∼ KL KS regeneration (nucleus) 0 0 → 0 ∼ KL KS regeneration (water) 0 Detector Water quality 27.7 Energy scale 11.9 Event Reconstruction Fiducial volume 1.2 Ring counting 1.1 Number of decay electrons 2.0 Detector response asymmetry 4.4 Statistical error (1000 yr) 9.9

Total 37.1

0 → + − Table 9.4: Systematic errors on background rate for the KS π π Method #2 search. Chapter 10

0 Search for “KL”

10.1 Event Selection

0 (D4) not selected by KS search (I-III) event selections

(E4) 500 p.e. < potot < 8000 p.e. potot is the total charge

≥ (F4) nringt 2

nringt is the number of rings as determined by the ring counting without timing cuts algorithm described in section 5.2.1.

(G4) number of μ-like rings ≥ 1

(H4) number of decay electron ≥ 1

(I4) 260 MeV/c

(J4) Vertex separation > 230 cm

(K4) μ-candidate pattern PID likelihood > 0.3

165 166

(L4) μ-candidate Cherenkov angle > 30◦

(M4) Proton ID likelihood < 0

→ + 0 When the free proton decays via p μ KL the ﬁnal state particles consist of a

0 0 primary muon and the products from the KL interaction in water or KL decay. The kinematics of the muon are the same as described in section 7.1. The kinematics of

0 the KL are described in section 1.3. With the assumption of no excess signal beyond the background expectation,

0 optimization of the event selection thresholds for the KL search is determined using → + 0 the p μ KL and atmospheric neutrino MC and choosing the thresholds which → + 0 maximize the p μ KL sensitivity.

0 0 To ensure the KL search is independent of the KS searches (D4) is applied. To roughly select the proton decay signal (E4) is applied. Figure 10.1 shows the potot distribution for both the p → μ+K0 MC and atmospheric neutrino MC. There are three distinct peaks in the potot distribution of the p → μ+K0 MC; each corresponding to different final state kinematics. The first peak on the left typically

0 → ± ∓ consists of events with the least energetic ﬁnal state kinematics such as KL π μ ν with only one or two visible, non-showering remaining particles. The second peak near the middle of the distribution corresponds to ﬁnal kinematics typically with

0 → ± ∓ 0 → + − 0 one visible, showering remaining particle such as KL π e ν and KL π π π . The third peak at larger values of potot corresponds to the most energetic ﬁnal state

0 → 0 kinematics in which all remaining particles are visible such as KL 3π .Thereare

0 many diﬀerent types of KL interactions in water as summarized in Table 1.2 each with

0 diﬀerent ﬁnal state kinematics. Because of this, KL interaction in water contributes to each of the three peaks in the potot distribution.

Criterion (F4) is applied to select multi-ring events. Figure 10.2 shows the nringt distribution for both the p → μ+K0 MC and atmospheric neutrino MC. As expected,

0 → ± ∓ there are two or three rings found for KL π e ν decay where the primary muon 167 and remaining electron are always visible but remaining pion can be near Cherenkov

0 → ± ∓ threshold. As expected, KL π μ ν can have three, two or one visible rings depending if both, one, or none of the remaining muon and pion are above Cherenkov

0 → + − 0 0 → 0 threshold respectively. The number of rings for KL π π π and KL 3π are

0 also as expected. Single ring events typically come from KL interactions in water which produce heavy nuclei that are below Cherenkov threshold. For these events, only the primary muon ring is visible. The final state particles of the p → μ+K0 decay always includes at least one muon above the Cherenkov threshold therefore (G4) requires at least one μ-like ring. The PID likelihood is calculated using both the opening angle and pattern information described in section 5.1.3. Figure 10.3 shows the PID likelihood distribution for each ring for both the p → μ+K0 MC and atmospheric neutrino MC. The source of the sharp peak seen near zero likelihood is discussed in section 5.2.3.2. Event selection (H4) requires at least one decay electron since there is at least one final state muon in every p → μ+K0 event. Figure 10.4 shows the number of decay electron distribution for both the p → μ+K0 MC and atmospheric neutrino MC. To select the mono-energetic primary muon that is characteristic of the proton decay signal, event selection (I4) is applied. Among all the rings that are identified as μ-like, the μ-candidate is selected as the ring with momentum nearest 326.5MeV/c.

+ 0 Figure 10.5 shows the pμ−cand. distribution for both the p → μ K MC and atmospheric neutrino MC. The p → μ+K0 MC distribution is symmetric and peaks at 319.4 ± 0.2 MeV/c; within 2% of the the expected value of 326.5MeV/c.

The vertex separation, vsep., is deﬁned as:

≡ − · vsep. (vμ vKL ) dμ (10.1) 168

Where vμ is the MS ﬁt vertex of the μ-candidate found by the algorithm described

in section 5.2.3.3, vKL is the vertex found using the timing ﬁt algorithm described 0 in section 5.2.4 corresponding to the KL decay or interaction point and dμ is a unit vector of the reconstructed direction of the μ-candidate. Positive (negative) values of

0 vsep. mean the KL decay or interaction point is separated from the proton decay point in the opposite (same) direction as dμ. With this deﬁnition, criterion (J4) is applied.

+ 0 Figure 10.6 shows the vsep. distribution for both the p → μ K MC and atmospheric neutrino MC. The background that remains after event selections (A-J4) consists of events without a true single muon for the μ-candidate ring. The following event selections are designed to further reject particles other than a single muon for the μ-candidate ring.

Typically, the ﬁnal state particles of the atmospheric neutrino MC are in the same direction as the parent neutrino. This results in rings that tend to overlap each other as opposed to the proton decay signal where rings tend to be separated since the ﬁnal state particles are typically back to back. Criterion (K4) uses the pattern PID likelihood described in section 5.1.3 to reject events with rings that overlap the μ-candidate since overlapping rings tend to have a charge pattern that is similar to showering particles. Figure 10.7 shows the the pattern PID likelihood of the μ-candidate ring for both the p → μ+K0 MC and atmospheric neutrino MC.

Criterion (L4) is used to select events in which the μ-candidate Cherenkov angle is consistent with the expectation of 38.3◦ from a 326.5 MeV/c muon. Figure 10.8 shows the Cherenkov angle distribution of the μ-candidate for both the p → μ+K0 MC and atmospheric neutrino MC. For p → μ+K0 the peak is at 34.5 ± 0.1◦. Protons which are selected as the μ-candidate typically have a true momentum near 1600 MeV/c which corresponds to a Cherenkov angle of 30.1◦. This is consistent with the peak at 28.7 ± 1.5◦ of the atmospheric neutrino MC distribution which, after selections (A-K4), consists primarily of true protons as the μ-candidate ring. 169

700 ATM-ν MC p→μK0 MC → ±π±ν KL e 600 →μ±π±ν KL → π0 KL 3 →π+π-π0 KL Events/1489.2day → 500 KL int. Other

400

300

200

100

0 0 1000 2000 3000 4000 5000 6000 7000 8000 900010000 p.e. potot Figure 10.1: The potot distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-D4). The hatched regions 0 0 show the contributions from KL interaction in water and dominant KL decay modes. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region.

Criterion (M4) is designed to identify and reject events in which the μ-candidate is consistent with a true proton using the proton ID algorithm described in section 5.2.3.5. Figure 10.9 shows the μ-candidate proton ID likelihood distribution. 170

ATM-ν MC p→μK0 MC → ±π±ν 5000 KL e →μ±π±ν KL → π0 KL 3 →π+π-π0 KL Events/1489.2day → 4000 KL int. Other

3000

2000

1000

0 12345

nringt → + 0 Figure 10.2: The nringt distribution for p μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E4). The hatched regions 0 0 show the contributions from KL interaction in water and dominant KL decay modes. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 171

70 e-like μ-like e-like μ-like 25 e-like μ-like 100 ATM-ν MC ATM-ν MC ATM-ν MC p→μK0 MC p→μK0 MC p→μK0 MC ± ± ± ± ± ± K →e π ν K →e π ν K →e π ν L 60 L L →μ±π±ν →μ±π±ν →μ±π±ν KL KL KL → π0 → π0 → π0 80 KL 3 KL 3 20 KL 3 →π+π-π0 →π+π-π0 →π+π-π0 KL KL KL Events/1489.2day → Events/1489.2day 50 → Events/1489.2day → KL int. KL int. KL int. Other Other Other

60 40 15

30 40 10

20 5 10

0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 ; # likelihood ; # likelihood ; # likelihood nringt=2 ring 1 PID nringt=2 ring 2 PID nringt=3 ring 1 PID

20 7 22.5 e-like μ-like e-like μ-like e-like μ-like ATM-ν MC ATM-ν MC ATM-ν MC p→μK0 MC p→μK0 MC p→μK0 MC 20 → ±π±ν 17.5 → ±π±ν 6 → ±π±ν KL e KL e KL e →μ±π±ν →μ±π±ν →μ±π±ν KL KL KL → π0 → π0 → π0 17.5 KL 3 KL 3 KL 3 →π+π-π0 15 →π+π-π0 →π+π-π0 KL KL 5 KL Events/1489.2day K →int. Events/1489.2day K →int. Events/1489.2day K →int. 15 L L L Other 12.5 Other Other 4 12.5 10 10 3 7.5 7.5 2 5 5 1 2.5 2.5

0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 ; # likelihood ; # likelihood ; # likelihood nringt=3 ring 2 PID nringt=3 ring 3 PID nringt=4 ring 1 PID

8 e-like μ-like e-like μ-like e-like μ-like ATM-ν MC ATM-ν MC ATM-ν MC 7 p→μK0 MC 7 p→μK0 MC 7 p→μK0 MC → ±π±ν → ±π±ν → ±π±ν KL e KL e KL e →μ±π±ν →μ±π±ν →μ±π±ν KL KL KL 6 → π0 → π0 → π0 KL 3 6 KL 3 6 KL 3 →π+π-π0 →π+π-π0 →π+π-π0 KL KL KL Events/1489.2day → Events/1489.2day → Events/1489.2day → KL int. KL int. KL int. 5 Other 5 Other 5 Other

4 4 4

3 3 3

2 2 2

1 1 1

0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 ; # likelihood ; # likelihood ; # likelihood nringt=4 ring 2 PID nringt=4 ring 3 PID nringt=4 ring 4 PID Figure 10.3: The PID likelihood distribution of each ring for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-F4). The 0 hatched regions show the contributions from KL interaction in water and dominant 0 → + 0 KL decay modes. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 172

900 ATM-ν MC p→μK0 MC 800 → ±π±ν KL e →μ±π±ν KL → π0 700 KL 3 →π+π-π0 KL Events/1489.2day → KL int. 600 Other

500

400

300

200

100

0 012345678910 Number of decay electron Figure 10.4: The number of decay electron distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-G4). The 0 hatched regions show the contributions from KL interaction in water and dominant 0 → + 0 KL decay modes. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

120 ATM-ν MC p→μK0 MC → ±π±ν KL e 100 →μ±π±ν KL → π0 KL 3 →π+π-π0 KL Events/1489.2day K →int. 80 L Other

0 0 100 200 300 400 500 600 700 800 MeV/c μ candidate momentum

+ 0 Figure 10.5: The pμ−cand. distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-H4). The hatched 0 0 regions show the contributions from KL interaction in water and dominant KL decay modes. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 173

ATM-ν MC p→μK0 MC 70 → ±π±ν KL e →μ±π±ν KL → π0 KL 3 60 →π+π-π0 KL Events/1489.2day → KL int. 50 Other

0 -1000 -800 -600 -400 -200 0 200 400 600 800 cm Vertex separation

+ 0 Figure 10.6: The vsep. distribution for p → μ K MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-I4). The hatched regions 0 0 show the contributions from KL interaction in water and dominant KL decay modes. The statistical error of the p → μ+K0 MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

ATM-ν MC p→μK0 MC ± ± K →e π ν 5 L →μ±π±ν KL → π0 KL 3 →π+π-π0 KL Events/1489.2day K →int. 4 L Other

0 -4 -3 -2 -1 0 1 2 3 4 likelihood μ candidate pattern PID Figure 10.7: The pattern PID likelihood distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-J4). The 0 hatched regions show the contributions from KL interaction in water and dominant 0 → + 0 KL decay modes. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 174

ATM-ν MC 1.75 p→μK0 MC → ±π±ν KL e →μ±π±ν KL K →3π0 1.5 L →π+π-π0 KL Events/1489.2day → KL int. 1.25 Other

0.75

0.5

0.25

0 0 102030405060 degree μ candidate Cherekov angle Figure 10.8: The μ-candidate Cherenkov angle distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-K4). The 0 hatched regions show the contributions from KL interaction in water and dominant 0 → + 0 KL decay modes. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

1 μ-like proton-like ATM-ν MC p→μK0 MC → ±π±ν KL e →μ±π±ν 0.8 KL → π0 KL 3 →π+π-π0 KL Events/1489.2day → KL int. Other 0.6

0.4

0.2

0 -2000 -1500 -1000 -500 0 500 1000 1500 2000 likelihood μ candidate proton ID Figure 10.9: The proton ID likelihood distribution for p → μ+K0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-L4). The 0 hatched regions show the contributions from KL interaction in water and dominant 0 → + 0 KL decay modes. The statistical error of the p μ K MC is negligible. The box shows the statistical error of the atmospheric neutrino MC sample. The atmospheric neutrino MC is normalized to the live-time (1489.2 days). The p → μ+K0 MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 175

10.2 SK-I Data Sideband

We follow the same strategy described in 7.2 in checking the sideband sample for this search.

0 The following criteria are used to deﬁne the sideband sample of the KL search:

• FCFV

• 0 not selected by KS search event selections

• 500 p.e. < potot < 8000 p.e.

• ≥ nringt 2

• number of μ-like rings ≥ 1

• Vertex separation < 100 cm

After this event selection, the remaining data events and background rate normalized by live-time is 1196 ± 34.6 and 1104.9 ± 4.3 respectively. Figure 10.10 shows the number of decay electron distribution. The dominant remaining neutrino interaction in the sideband sample is νμ CC single charged pion for which two decay electrons are expected. α =10.0%; the data and atmospheric neutrino MC agree.

Figure 10.11 shows the pμ−cand. distribution. The peak of the atmospheric neutrino MC is 331.0 ± 0.2 MeV/c; within 2% of the expected value of 326.5 MeV/c. The sharp drop oﬀ in events below ∼ 120 MeV/c is consistent with the Cherenkov threshold of the muon. α =39.2%; the data and the atmospheric neutrino MC agree.

Figure 10.12 shows the vsep. distribution. The expected vertex separation is 0 cm for atmospheric neutrino MC. The atmospheric neutrino MC distribution peak is at

−11.8 ± 1.9cm.Thenegativeshiftofthevsep. distribution is taken into account as systematic error. There are no events above 100 cm due to the sideband selection 176

DATA 600 Atm-ν MC

500 Events/1489.2day

400

300

200

100

0 012345678910 number of decay electron (sideband) Figure 10.10: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

criteria. α =0.9%; this is smaller than the threshold of disagreement however when the atmospheric neutrino MC distribution is changed within the systematic error described in Appendix A the data and MC agree.

Figure 10.13 shows the μ-candidate pattern PID likelihood distribution. α = 84.5%; the data and the atmospheric neutrino MC agree. Figure 10.14 shows the μ-candidate Cherenkov angle distribution. The peak of the atmospheric neutrino MC is 36.5 ± 0.1◦. This is smaller than the expected angle of 38.5◦ from a muon with momentum of 326.5 MeV/c. This shift is taken into account as systematic error. α =3.9%; the data and the atmospheric neutrino MC agree. Figure 10.15 shows the proton ID likelihood distribution. α ∼ 0%; the data and atmospheric neutrino MC do not agree. The mean of the atmospheric neutrino MC is −302.5 ± 1.6 the mean of the data is −359.1 ± 12.5. The shift between data and atmospheric neutrino MC is taken into account as systematic error. 177

200 DATA Atm-ν MC 175

150 Events/1489.2day

125

100

0 0 200 400 600 800 1000 MeV/c μ candidate momentum (sideband)

Figure 10.11: The pμ−cand. distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

DATA 140 Atm-ν MC

120 Events/1489.2day 100

0 -600 -400 -200 0 200 400 600 cm vertex separation (sideband)

Figure 10.12: The vsep. distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 178

e-like μ-like 200 DATA Atm-ν MC 175

Events/1489.2day 150

125

100

0 -5-4-3-2-1012345 likelihood μ candidate pattern PID (sideband) Figure 10.13: The pattern PID likelihood distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area.

225 DATA Atm-ν MC 200

175 Events/1489.2day 150

125

100

0 0 102030405060 degree μ candidate Cherenkov angle (sideband) Figure 10.14: The μ-candidate Cherenkov angle distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 179

140 μ-like proton-like DATA Atm-ν MC 120

Events/1489.2day 100

0 -2000 -1500 -1000 -500 0 500 1000 1500 2000 likelihood μ candidate proton ID (sideband) Figure 10.15: The proton ID likelihood distribution for data (red points) and atmospheric neutrino MC (blue box) in the sideband sample. The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. 180

10.3 SK-I Data Event Rate vs. Event Selection

The number of events in the data, the remaining signal detection eﬃciency and expected background obtained from the atmospheric neutrino MC along the event selection described in section 7.1 are summarized in Table 10.1. The Poisson probability

to observe 1 event in the data with a background expectation of 2.4 events is 21.3%. This result is consistent with no excess in the data from the background expectation. Therefore, we perform a calculation of the lower limit of the proton decay lifetime in Chapter 11 using this result.

Figure 10.16 shows the event rate after each event selection. The data and atmospheric neutrino MC agree along the event selection. Figure 10.17 shows the potot distribution after event selections (A-D4). α = 0.12%; the data and atmospheric neutrino MC disagree particularly for potot <

500 p.e. This disagreement is due to very low energy events present in the data that

are typically identiﬁed as single ring. These events are rejected by the nringt event selection (F4) and do not remain in the ﬁnal sample. There is no such disagreement in the potot distribution after event selections (A-D4 & F4).

Figure 10.18 shows the nringt distribution after event selections (A-D4). Single ring events are most common which is expected since CCQE interactions are the most dominant. α =92.8%; the data and atmospheric neutrino MC agree.

Figure 10.19 shows the PID likelihood distribution of each ring for each nringt after event selections (A-F4). The shape is as expected; no discontinuity or abnormal

peaks are observed aside from the peak near zero discussed in section 5.2.3.2. For all distributions, the value of α is greater than 1%; the data and atmospheric neutrino MC agree. The smallest value of α is 17.5% for the nring=2; ring#1 distribution. Figure 10.20 shows the number of decay electron distribution after event selections

(A-G4). α =9.6%; the data and atmospheric neutrino MC agree.

Figure 10.21 shows the pμ−cand. distribution after event selections (A-H4). Since 181

Event Selection Eﬃciency(%) Atm-ν MC FC Data (A-C) FCFV 97.3 ± 0.1 11105.8 ± 13.7 12232 ± 110.6 0 ± ± ± (D4) not KS 75.7 0.1 11097.0 13.7 12225 110.6 (E4) potot 75.6 ± 0.1 6910.6 ± 10.8 7714 ± 87.8 ± ± ± (F4) nringt 61.8 0.1 1953.9 5.8 2144 46.3 (G4) no. μ-like 58.5 ± 0.1 1303.1 ± 4.6 1399 ± 37.4 (H4) no. decay-e 51.3 ± 0.1 677.1 ± 3.2 790 ± 28.1 (I4) pμ−cand. 46.2 ± 0.1 339.5 ± 2.3 385 ± 19.6 (J4) vsep. 5.5 ± 0.121.2 ± 0.622± 4.7 (K4) pattern PID 4.8 ± 0.17.4 ± 0.34± 2.0 (L4) Cherenkov angle 4.3 ± 0.13.6 ± 0.22± 1.4 (M4) proton ID 3.7 ± 0.12.4 ± 0.21± 1.0

0 Table 10.1: KL search data events, signal detection eﬃciency and background rate along the event selection described in section 10.1. The atmospheric neutrino MC is normalized to the live-time.

the μ-candidate is selected as the μ-like ring with pμ nearest 326.5 MeV/c we expect pμ−cand. to typically be near this value. The peak of the distribution is 299.5 ± 1.6MeV/c. α =97.9%; the data and atmospheric neutrino MC agree.

Figure 10.22 shows the vsep. distribution after event selections (A-I4). The mean of the atmospheric neutrino MC distribution is −5.0 ± 1.1cm. α =7.3%; the data and atmospheric neutrino MC agree. Figure 10.23 shows the pattern PID likelihood distribution for the μ-candidate after event selections (A-J4). α =55.1%; the data and atmospheric neutrino MC agree.

Figure 10.24 shows the Cherenkov angle distribution for the μ-candidate after event selections (A-K4). α =48.2%; the data and atmospheric neutrino MC agree. Figure 10.25 shows the proton ID likelihood distribution for the μ-candidate after event selections (A-L4). α =81.6%; the data and atmospheric neutrino MC agree. 182

2011/02/10 09.31

10 5

DATA Atm-nu MC 10 4

3 Events/1489.2 day 10

10 2

-1 10 12345678910

KL event selection

0 Figure 10.16: The event rate along the KL search event selection for data (red closed squares) and atmospheric neutrino MC (blue open triangles). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the live-time (1489.2 days).

500 DATA Atm-ν MC

400 Events/1489.2day

300

200

100

0 0 1000 2000 3000 4000 5000 6000 7000 8000 900010000 p.e. potot Figure 10.17: The potot distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-D4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 183

DATA 6000 Atm-ν MC

5000 Events/1489.2day

4000

3000

2000

1000

0 12345

nringt

Figure 10.18: The nringt distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-E4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 184

200 e-like μ-like e-like μ-like 70 e-like μ-like DATA DATA DATA 200 Atm-ν MC Atm-ν MC Atm-ν MC 175 60 175 150

Events/1489.2day Events/1489.2day 150 Events/1489.2day 50 125 125 40 100 100 30 75 75 20 50 50

10 25 25

0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 ; # likelihood ; # likelihood ; # likelihood nringt=2 ring 1 PID nringt=2 ring 2 PID nringt=3 ring 1 PID

μ 80 μ μ e-like -like e-like -like 22.5 e-like -like 90 DATA DATA DATA Atm-ν MC Atm-ν MC Atm-ν MC 70 20 80

70 60 17.5 Events/1489.2day Events/1489.2day Events/1489.2day 15 60 50

50 12.5 40 40 10 30 30 7.5 20 20 5

10 10 2.5

0 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 ; # likelihood ; # likelihood ; # likelihood nringt=3 ring 2 PID nringt=3 ring 3 PID nringt=4 ring 1 PID

22.5 μ μ μ 22.5 e-like -like e-like -like e-like -like DATA 20 DATA DATA Atm-ν MC Atm-ν MC 20 Atm-ν MC 20 17.5 17.5 17.5 15 Events/1489.2day Events/1489.2day Events/1489.2day 15 15 12.5 12.5 12.5 10 10 10 7.5 7.5 7.5

5 5 5

2.5 2.5 2.5

800

DATA 700 Atm-ν MC

600 Events/1489.2day

500

400

300

200

100

0 012345678910 Number of decay electron Figure 10.20: The number of decay electron distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-G4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

180 DATA Atm-ν MC 160

140 Events/1489.2day 120

100

0 0 200 400 600 800 1000 MeV/c μ candidate momentum

Figure 10.21: The pμ−cand. distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-H4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrows and dash-dot vertical lines indicate the event selection region. 186

70 DATA Atm-ν MC

Events/1489.2day 50

0 -1000 -750 -500 -250 0 250 500 750 1000 cm Vertex separation

Figure 10.22: The vsep. distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-I4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

8 DATA Atm-ν MC 7

6 Events/1489.2day

0 -4 -3 -2 -1 0 1 2 3 4 likelihood μ candidate pattern PID Figure 10.23: The pattern PID likelihood distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-J4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 187

1.2

DATA Atm-ν MC 1

Events/1489.2day 0.8

0.6

0.4

0.2

0 0 102030405060 degree μ candidate Cherekov angle Figure 10.24: The μ-candidate Cherenkov angle distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-K4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold.

1.2

DATA Atm-ν MC 1

Events/1489.2day 0.8

0.6

0.4

0.2

0 -1000 -750 -500 -250 0 250 500 750 1000 likelihood μ candidate proton ID Figure 10.25: The proton ID likelihood distribution for data (red points) and atmospheric neutrino MC (blue box) after event selections (A-L4). The statistical error of both is shown. The atmospheric neutrino MC is normalized to the data by area. The pink arrow and dash-dot vertical line indicates the event selection threshold. 188

Parent ν ﬂavor ν interaction SK-I (%) QE 3.1 ± 1.6 CC single meson 7.1 ± 2.3 SK-I: 11.0% multi-meson 0.8 ± 0.8 νe DIS 0.0 ± 0.8 SK-I: 14.2% QE 0.0 ± 0.8 NC single meson 1.6 ± 1.1 SK-I: 3.1% multi-meson 0.8 ± 0.8 DIS 0.8 ± 0.8 QE 30.9 ± 3.2 CC single meson 32.6 ± 3.5 SK-I: 73.3% multi-meson 8.9 ± 2.3 νμ DIS 1.0 ± 0.7 SK-I: 85.8% QE 0.0 ± 0.8 NC single meson 5.5 ± 2.0 SK-I: 12.5% multi-meson 1.6 ± 1.1 DIS 5.5 ± 2.0 Total: 100.0 ± 0.0

Table 10.2: Breakdown of remaining atmospheric neutrino MC background for the 0 KL search. The background is broken down by true neutrino ﬂavor and neutrino interaction. A description of possible neutrino interactions is described in section 3.3.

10.4 Breakdown of Remaining Background

The atmospheric neutrino MC events remaining after event selections (A-M4) are classiﬁed by true parent neutrino ﬂavor and interaction mode and summarized in Table 10.2.

The dominant sources of remaining background are νμ CCQE and νμ CC single meson neutrino interactions. Typically for these background, a recoil proton above Cherenkov threshold is selected as the primary muon candidate. 189

0 KL candidate #2 NHITAC 1 Evis (MeV/c) 589.9 Dwall (cm) 209.8 potot (p.e.) 5007.0 nring 2 N(μ) 595.1 PID & momentum (MeV/c) ⇒ N(μ) 290.8 number of decay electron 1 vsep. (cm) 458.9 μ-candidate pattern PID likelihood 0.42 μ-candidate Cherenkov angle (◦) 30.6 μ-candidate proton ID likelihood -230.6

0 Table 10.3: The reconstructed information of the data candidate for the KL search. The “N” refers to non-showering (μ-like) PID. The particle listed within the parenthesis for each ring is the assumed particle type used for the momentum reconstruction. The arrow (⇒) indicates the ring that is selected as the μ-candidate.

10.5 SK-I Data Candidates

0 There is a single candidate found in the data for the KL search. Figure 10.26 shows the event display for this candidate. The reconstruction information is summarized in Table 10.3. Although this event is selected as a candidate it is not an obvious “golden” proton decay event. The ring edge of the muon candidate is correctly reconstructed; the reconstructed ring is alignedwithavisibleringedge.pμ is smaller than the expected value by 10.9%. Although this event has large vsep., the Cherenkov angle of the μ- candidate is 20.1% smaller than expected and is more consistent with a proton. The second visible ring in this event by eye appears to be from a muon due to its sharp ring edge. Rather than proton decay, this event appears more consistent with the

νμ CCQE interaction with a recoil proton above Cherenkov threshold; one of the dominant remaining backgrounds of this search. 190

NUM 2 RUN 7892 SUBRUN 39 EVENT 5157138 DATE 1999-Oct- 4 TIME 18:58:32 TOT PE: 5007. MAX PE: 43.0 NMHIT : 1320 ANT-PE: 26.2 ANT-MX: 3.2 NMHITA: 31

1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111 1990/00/00:NoYet:NoYet T diff.:0.934E+0 1990/00/00:NoYet:NoYet FEVSK :81002803 1990/00/00:NoYet:NoYet 1990/00/00:NoYet:NoYet nOD YK/LW: 2/ 1 1990/00/00:NoYet:NoYet SUB EV : 0/ 3 1990/00/00:NoYet:NoYet Dcye: 0( 0/ 0/ 0 1990/00/00:NoYet:NoYet 1990/00/00:;R= 0:NoYet R : Z : PHI : G 0.00: 0.00: 0.00:0 CANG : RTOT : AMOM : M Comnt;

0 Figure 10.26: The event display of the candidate for KL search. The thick blue solid line shows the reconstructed ring of the μ-candidate. The green (red) triangle shows the primary (remaining) reconstructed vertex. 191

Source Systematic Error (%) Physics Simulation Fermi momentum ∼ 0 Correlated decay 7.1 0 → 0 KL KS regeneration (nucleus) 1.2 0 → 0 KL KS regeneration (water) 8.3 Detector Water quality (incl. stat. error) 9.7 (5.9) Energy scale 0.8 Event Reconstruction Fiducial volume 1.5 Ring counting w/o timing cuts 1.6 PID 0.5 Number of decay electrons 2.0 vsep. 7.1 μ-candidate Pattern PID 0.5 μ-candidate Cherenkov angle 2.3 μ-candidate Proton ID 4.0 Statistical error 1.3

Total 17.3

0 Table 10.4: Systematic errors on signal detection eﬃciency for the KL search. The number shown for the uncertainty due to water quality includes the statistical error of the p → μ+K0 MC described in the text which itself is shown within the parenthesis.

0 10.6 Total Systematic Error of “KL”Search

Tables 10.4 and 10.5 summarize the total systematic error on the signal detection

0 eﬃciency and background rate respectively of the KL search. The detail of the systematic error estimation is described in Appendix A. 192

Source Systematic Error (%) Physics Simulation ν Flux Absolute 10.0 ν/ν¯ 1.3 νe/νμ 0.6 ν cross-section QE 3.7 Single π 7.1 MA(QE & single π) 11.6 Coherent π 0.2 Multi π 0.4 NC/CC ratio 0.6 π Nuclear Eﬀect Elastic 1.4 Charge exchange 0.1 Absorption 0.6 Production 3.5 Fermi momentum 2.0 0 → 0 ∼ KL KS regeneration (nucleus) 0 0 → 0 ∼ KL KS regeneration (water) 0 Detector Water quality (incl. stat. error) 12.1 (11.5) Energy scale 4.9 Event Reconstruction Fiducial volume 1.2 Ring counting w/o timing cuts 10.7 PID 1.1 Number of decay electrons 2.0 vsep. 13.9 μ-candidate Pattern PID 1.7 μ-candidate Cherenkov angle 6.0 μ-candidate Proton ID 16.2 Statistical error (200 yr) 8.0

Total 34.2

0 Table 10.5: Systematic errors on background rate for the KL search. The number shown for the uncertainty due to water quality includes the statistical error of the atmospheric neutrino MC described in the text which itself is shown within the parenthesis. Chapter 11

Results

In the absence of any excess signal from the background expectation we calculate the lower limit on the proton lifetime using the Bayesian method outlined in [7]. This method is the same used as Kobayashi [1]; assuming no correlation of systematic error

between the proton decay searches. A Poisson distribution is assumed for the proton

decay probability P (Γ|ni) and is expressed as:

−(Γλii+bi) ni e (Γλii + bi) P (Γ|ni)= P (Γ)P (λi)P (i)P (bi)dλididbi (11.1) ni!

where ni is the number of candidate events in the i-th proton decay search, Γ is the

total decay rate, λi is the detector exposure, i is the detection eﬃciency including the meson branching ratio and bi is the expected background. The decay rate probability density P (Γ), and the uncertainties in detector expo-

193 194

sure P (λi), eﬃciency P (i) and background P (bi), are expressed as:

2 2 P (i)=exp −(i − 0,i) /2σ (0 ≤ i ≤ 1, otherwise 0) (11.2) ,i ∞ 1 e−b (b)nb,i −(b C − b)2 P (b )= exp i i db (0 ≤ b , otherwise 0) (11.3) i b n ! 2σ2 i ⎧i 0 b,i b,i ⎪ ⎨1Γ> 0 P (Γ) = (11.4) ⎪ ⎩0Γ≤ 0

P (λi)=δ(λi − λ0,i) (11.5)

where λ0,i is the estimated exposure, Ci is the MC oversampling factor, σ,i and σb,i are the uncertainty in detection eﬃciency and background respectively.

We calculate the lower limit of the nucleon decay rate, Γlimit, using a 90% conﬁ- dence level (CL) as: Γlimit N P (Γ|n )dΓ CL = Γ=0 i=1 i (11.6) ∞ N | Γ=0 i=1 P (Γ ni)dΓ

Where N is the number of searches. The lower lifetime limit, τ/Bp→μ+K0 ,is:

1 N τ/B → + 0 = [ · λ ] (11.7) p μ K Γ 0,i 0,i limit i=1

As reference, we also calculate the combined lower lifetime limit assuming full correlation between systematic errors by the method described in [84]. The result of the lower lifetime limit calculation for the p → μ+K0 search is summarized in Table 11.1. 195

Sample Lower limit i Search p → μ+K0 Atm-ν Data (×1032 yr.) 0,i(%) σ,i(%) nb,i σb,i(%) ni 0 → 0 0 1 KS π π 8.8 10.3 1.1 24.7 1 8.1 0 → + − 2 KS π π Method #1 10.5 11.8 3.0 25.5 6 4.0 0 → + − 3 KS π π Method #2 2.5 19.1 0.1 37.1 0 3.0 0 4 KL 3.7 17.3 2.4 34.2 1 3.4 Combined lower lifetime limit (no systematic error correlation) 11 Combined lower lifetime limit (full systematic error correlation) 10

Table 11.1: Result of the lower lifetime limit calculation. Chapter 12

Comparison With Previous SK p → μ+K0 Search

Table 12.1 summarizes the results of the p → μ+K0 search by Kobayashi [1] and the results of this analysis (Regis). In Kobayashi’s analysis, the signal detection eﬃciency

→ + 0 → + 0 is obtained using only the p μ KS component of p μ K decay therefore for this comparison the eﬃciency for this analysis is obtained in the same way. The eﬃciency, background rate and data are all increased when comparing results

0 → 0 0 from Kobayashi to this analysis in the KS π π search (I). The reason for this increase was found to be a result of an inconsistency in the event selection described in the text of Kobayashi’s paper and the event selection actually used to obtain the results reported in the paper. The text describes using events with either zero or one decay electron but the results are obtained using events with only one decay electron.

In the event selection for this analysis we followed the description in the text and used zero or one decay electrons. The combined lower lifetime limit obtained by Kobayashi is larger than this anal-

0 → + − ysis mainly due to the diﬀerence in the number of data candidates in KS π π Method #1 search (II). We did not have access to the original data and MC ﬁles used

196 197 to obtain Kobayashi’s result so to understand the reason of the difference in the data in search (II) we used available files nearest in time to the published result as reference. Figure 12.1 shows the scatter plot of SK-I data for the total momentum vs. μ+ momentum for (a) Kobayashi [1], (b) the reference1 and (c) this analysis2.Thebox shows the final event selection region. There are three data selected by Kobayashi’s analysis, in the reference data there are four selected events and in this analysis there are six events selected. The four events selected in the reference data are a subset of the six events selected by this analysis. Figures 12.2 and 12.3 show the event displays of the two SK-I data that are selected by this analysis but not by the reference. For both events a change in the reconstructed momentum is the reason the events are included in this analysis but not in the reference. The first event is selected by this analysis because a different μ-candidate is selected than the reference. For the second event the momentum of the μ-candidate is reconstructed within the event selection threshold by this analysis but not for the reference.

The μ-candidate momentum reconstruction was checked using the ﬁnal remaining atmospheric neutrino MC sample of search (II) for this analysis and the reference. Figures 12.4a and 12.4b show the reconstructed-true μ-candidate momentum distribution requiring the μ-candidate be a true muon for the reference and this analysis respectively. The mean value of the distribution for the reference is −16.6 ± 4.1MeV/c with an RMS of 32.1 MeV/c. The mean value of the distribution for this analysis is 4.8 ± 1.9 MeV/c with an RMS of 15.3 MeV/c. There is no obvious problem with the momentum reconstruction for this analysis, there is improvement in momentum reconstruction from the reference.

Generally for all searches, the larger error in the eﬃciency of this analysis is mainly due to the estimation of more sources of systematic error than Kobayashi and the

1software library version 02b 2software library version 09b 198

Search Eﬃciency Background Data Lower (%) (evt./1489.2 (evt./1489.2 limit day) day) (×1032 yr.) (I) 5.4 ± 0.60.4 ± 0.30 7.0 (II) 7.0 ± 0.73.2 ± 1.33 4.4 K. [1] (III) 2.8 ± 0.30.3 ± 0.20 3.6 Combined lifetime limit 13 (I) 7.7 ± 0.8† 1.1 ± 0.31 7.0 (II) 7.9 ± 0.9† 3.0 ± 0.76 3.0 Regis (III) 2.4 ± 0.5† 0.12 ± 0.04 0 2.9 Combined lifetime limit 8.4

→ + 0 Table 12.1: Summary of the p μ KS search results from Kobayashi (K. [1]) and this analysis (Regis). For each analysis the signal detection eﬃciency, background rate, → + 0 0 → 0 0 data and lower lifetime limit is summarized for each p μ KS search: KS π π 0 → + − 0 → + − (I), KS π π Method #1 (II) and KS π π Method #1 (III). The total error † → + 0 is shown. The eﬃciency for Regis is obtained using only p μ KS as described in the text and the total error is assumed the same as Table 11.1. smaller error in the background rate in this analysis is mainly due to the use of a larger statistical sample. 199

900

800

700

total momentum (MeV/c) 600

500

400

300

200

100

0 0 100 200 300 400 500 600 700 800 μ+ momentum (MeV/c) (a) Kobayashi [1] (b) Reference data

900

800

700

total momentum (MeV/c) 600

500

400

300

200

100

0 0 100 200 300 400 500 600 700 800

μ+ momentum (MeV/c) (c) This analysis data

Figure 12.1: The total momentum vs. μ+ momentum scatter plot after event selections (A-F2) for SK-I data. (a) Kobayashi [1], (b) the reference described in the text and (c) this analysis. The box shows the event selection region. 200

NUM 45 NUM 1 RUN 4018 RUN 4018 SUBRUN 41 SUBRUN 41 EVENT 289990 EVENT 289990 DATE 1997-May-11 DATE 1997-May-11 TIME 4:18:53 TIME 4:18:53 TOT PE: 1688. TOT PE: 1688. MAX PE: 26.8 MAX PE: 26.8 NMHIT : 952 NMHIT : 952 ANT-PE: 31.5 ANT-PE: 31.5 ANT-MX: 7.0 ANT-MX: 7.0 NMHITA: 34 NMHITA: 34

1 1 1

1 1

1 1 1

1 1

1 1 1 1

1 1

1 1990/00/00:NoYet:NoYet 1 RunMODE:NORMAL 1990/00/00:NoYet:NoYet 1 RunMODE:NORMAL 1990/00/00:NoYet:NoYet 1 1990/00/00:NoYet:NoYet 1 † 1 1 1

1 TRG ID :00000011 TRG ID :00000011 1990/00/00:NoYet:NoYet 1 1990/00/00:NoYet:NoYet 1 1

1 1 Left ring: 1 1990/00/00:NoYet:NoYet T diff.:0.128E+0 1990/00/00:NoYet:NoYet LeftT diff.:0.128E+0 ring: 1990/00/00:NoYet:NoYet FEVSK :81002003 1990/00/00:NoYet:NoYet FEVSK :81002003 1990/00/00:NoYet:NoYet pμ: 223 MeV/c 1990/00/00:NoYet:NoYet pμ: 281 MeV/c 2003/05/26:;R= 2:NoYet nOD YK/LW:† 2/ 1 2009/06/29:;R= 2:NoYet nOD YK/LW: 2/ 1 R : Z : PHI : G RightSUB EV ring: : 0/ 2 R : Z : PHI : G RightSUB EV ring: : 0/ 2 11.98: 1.53: 1.62:0 Dcye: 2( 1/ 1/ 0 11.97: 1.69: 1.61:0 Dcye: 2( 1/ 1/ 0 CANG : RTOT : AMOM : M CANG : RTOT : AMOM : M 33.4: 473: 84: pμ: 235 MeV/c 35.5: 465: 95: pμ: 213 MeV/c V=-0.804: 0.159:-0.5 V=-0.822: 0.199:-0.5 30.0: 282: 51: 32.0: 269: 55: V= 0.819: 0.339:-0.4 V= 0.804: 0.254:-0.5 Comnt; Comnt;

(a) Reference data (b) This analysis

Figure 12.2: Event display of the ﬁrst SK-I data selected by event selections (A-H3) this analysis but not selected using the reference data. The reconstructed momentum of each ring is shown. The dagger (†) indicates the ring selected as the μ-candidate.

NUM 25 NUM 1 RUN 10034 RUN 10034 SUBRUN 450 SUBRUN 450 EVENT 73887738 EVENT 73887738 DATE 2001-Apr-30 DATE 2001-Apr-30 TIME 8:36:44 TIME 8:36:44 TOT PE: 928. TOT PE: 928. MAX PE: 23.2 MAX PE: 23.2 NMHIT : 477 NMHIT : 477 ANT-PE: 24.3 ANT-PE: 24.3 ANT-MX: 2.7 ANT-MX: 2.7 NMHITA: 28 NMHITA: 28

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1

1 1

1 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet RunMODE:NORMAL 1990/00/00:NoYet:NoYet TRG ID :00000111† 1990/00/00:NoYet:NoYet TRG ID :00000111† 1990/00/00:NoYet:NoYet 1 Left ring: 1990/00/00:NoYet:NoYet Left ring: 1990/00/00:NoYet:NoYet T diff.:0.833E+0 1990/00/00:NoYet:NoYet T diff.:0.833E+0

1990/00/00:NoYet:NoYet 1 FEVSK :81002803 1990/00/00:NoYet:NoYet FEVSK :81002803 1 pμ: 233 MeV/c pμ: 252 MeV/c 1990/00/00:NoYet:NoYet 1 1990/00/00:NoYet:NoYet 1 2003/05/26:;R= 2:NoYet nOD YK/LW: 2/ 1 2009/06/29:;R= 2:NoYet nOD YK/LW: 2/ 1

1 SUB EV : 0/ 5 SUB EV : 0/ 5 R : Z : PHI : G Right ring: R : Z : PHI : G 1 Right ring: 13.44:-13.29:-0.10:0 1 Dcye: 2( 2/ 0/ 0 13.42:-13.17:-0.10:0 1 Dcye: 2( 2/ 0/ 0

1 CANG : RTOT : AMOM : M 1 pμ: 163 MeV/c CANG : RTOT : AMOM : M pμ: 164 MeV/c 35.6: 377: 67: 34.7: 364: 74: 1

V=-0.400: 0.763:-0.5 V=-0.408: 0.765:-0.4 1

28.0: 120: 22: 28.0: 116: 24: 1 1 V= 0.823: 0.183: 0.5 V= 0.823: 0.183: 0.5 Comnt; Comnt;

(a) Reference (b) This analysis

Figure 12.3: Event display of the second event selected by this analysis but not selected using the reference data. The reconstructed momentum of each ring is shown. The dagger (†) indicates the ring selected as the μ-candidate. 201

events 12 events

10 20

8 15

5 2

0 0 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 (MeV/c) (MeV/c) μ candidate rec-true momentum μ candidate rec-true momentum (a) Reference (b) This analysis

Figure 12.4: The reconstructed-true μ-candidate momentum distribution after event selections (A-H2) for atmospheric neutrino MC. The μ-candidate is required to be a true muon. (a) the reference described in the text and (b) this analysis. Chapter 13

Future Prospects

Although there is some understanding of the differences between Kobayashi’s result and this analysis as described in Chapter 12, a detailed understanding of the sources of the difference must be studied. However, this work is incompatible with the completion deadline of this thesis and is left as a future study. This thesis presents the first search at SK for p → μ+K0 using a combined analysis method. Additionally, a new analysis technique using vertex separation is introduced

→ + 0 to search for p μ KL. Although substantial effort was made so this vertex separa- → + 0 tion algorithm is as efficient as possible in distinguishing the p μ KL signal from the atmospheric neutrino background, there are two modifications we have in mind which may improve the vertex separation algorithm. There was insufficient time to pursue these modifications for this thesis and we leave them as a suggestion of further study. They are: First, use the ring separation algorithm described in section 5.1.5.1 to identify the fraction of charge in each PMT associated with the μ-candidate and use only that charge information in reconstructing the kinematics of the μ-candidate rather than the masking area described in section 5.2.2.

Second, the current analysis only considers the physical separation between the

202 203

→ + 0 vertex of the μ-candidate and the remaining particles however in true p μ KL decay there is a temporal separation as well. There may be improved ability to

→ + 0 distinguish the p μ KL signal from atmospheric neutrino background by using both the physical separation of the two vertices as well as the timing diﬀerence which

0 matches the expected decay time of KL. The proton decay lifetime sensitivity is proportional to the exposure provided the background rate and systematic errors are small. Only the SK-I data period with an exposure of 91.7 kt-yr is used for this analysis. In the future we can roughly double the total exposure of the current analysis with the addition of the SK-II, SK-III, SK- IV data sets with exposures respectively of 49.2kt-yr,33.8kt-yrand32.9 kt-yr as of September 2010 and achieve a lower lifetime sensitivity of ∼ 2 × 1033 years. Chapter 14

Conclusion

Proton decay via p → μ+K0 was searched in the SK-I data with exposure of 91.7kt-yr. This analysis extended upon the work of Kobayashi [1] to include a new combined

→ + 0 analysis method and a search for p μ KL. Although p → μ+K0 is one of the dominant modes predicted by SUSY GUT models, there was no evidence for p → μ+K0 decay as a result of this analysis. The number of candidate events are consistent with the background predicted by atmospheric neutrino MC.

We calculated a combined lower lifetime limit of p → μ+K0 to be 1.1 × 1033 years at 90% conﬁdence level.

204 Appendices

A Systematic Errors

Section A.1 describes data set used to estimate the systematic error for each proton decay search in this analysis. Section A.2 describes the various sources of systematic error considered, the error source, how the source error is determined from the error source and how the source

error is used to estimate the systematic errors. The systematic errors are arranged by category according to their source which include: physics simulation, the detector and event reconstruction. A summary of the source, source error and change to the signal detection eﬃciency and background rate is summarized in Tables A.1 and A.2a-A.2b respectively.

A.1 Data Set

All systematic errors on the signal detection eﬃciency and background rate are respectively estimated using the p → μ+K0 MC and atmospheric neutrino MC samples described in section 6.1 unless otherwise speciﬁed in sections A.1.1, A.1.2 or A.2.

0 → 0 0 A.1.1 “KS π π ”Search

To estimate the error in the background rate, a 250 year atmospheric neutrino MC sample is generated using the atmospheric neutrino production, interaction and de-

205 206 tector simulations described in sections 3.2, 3.3 and 3.4. To reduce the computer processing time several pre-selections are applied during the reconstruction of the atmospheric neutrino MC. First, the true vertex is required to be more than 1 m from the ID wall. Second, no further reconstruction is applied after the afit process (section 5.1.1) if the fitted vertex is not within the FV. Finally, if the fitted vertex is within the FV but the ring-counting reconstruction (section 5.1.2) finds fewer than 3 rings we also stop any further reconstruction. Otherwise, the event reconstruction is unchanged from the procedure described in section 5.1.

0 → + − A.1.2 “KS π π Method #2” Search

To estimate the error in the background rate, a 1000 year atmospheric neutrino MC sample is used. The atmospheric neutrino production, interaction and detector simulations described in sections 3.2, 3.3 and 3.4 are used. To reduce computer process time we apply the same pre-selections described in section A.1.1 with the additional requirement that true νe CCQE interactions are not reconstructed at all. Otherwise, the event reconstruction is unchanged from the procedure described in section 5.1.

A.2 Sources of Error

A.2.1 Physics Simulation (Signal)

• Fermi momentum: The systematic error on Fermi momentum is estimated by a comparison of the default model with another model. The default model of Fermi momentum that is used for the p → μ+K0 simulation is measured by

electron-12C scattering [17] described by the distribution shown in Figure 3.1. The model used for comparison is the same as used in NEUT [40, 41, 42]; a Fermi gas with a surface momentum of 225 MeV/c. The largest absolute diﬀerence in signal detection eﬃciency is used as sys-

tematic error. 207

• Correlated decay: The process of correlated decay and its implementation in the p → μ+K0 simulation is described in section 3.1.1. In the default p → μ+K0

MC, 10% of events undergo correlated decay. We use the same same uncertainty in correlated decay probability as [84] of ±100%. The correlated decay probability is changed to 0% and 20% and the largest

absolute diﬀerence in signal detection eﬃciency is used as systematic error.

• 0 → 0 KL KS regeneration: The systematic error from regeneration is estimated separately within the oxygen nucleus and in the SK tank water. The process of regeneration and its implementation in the proton decay and detector simulation is described in sections 3.1.3 and 3.4.3 respectively.

Since this implementation of regeneration is a simplified approximation we use a conservative uncertainty on regeneration probability of ±100%. The probability of regeneration is changed to 0.2% and 0% and the largest absolute difference in signal detection efficiency is used as systematic error.

A.2.2 Physics Simulation (Background)

Nearly all of the same systematic errors as the atmospheric neutrino oscillation analysis in the Super Kamiokande experiment were considered for the systematic error from the neutrino ﬂux and the neutrino interaction. The details of the determination of the source error is not discussed here but can be found in other documents [29, 91]. In this analysis we consider the following:

• Absolute ν ﬂux: A ±10% uncertainty on the absolute neutrino ﬂux is used.

• ν/ν¯ ratio: The systematic error on the ν/ν¯ ratio is estimated by changing

the ratio ±5% for Eν < 10 GeV and linearly increasing with log Eν from ±5%

(10 GeV) to ±10% (100 GeV) where Eν is the total neutrino energy. The largest absolute diﬀerence in background rate is used as systematic error. 208

• νe/νμ ratio: The systematic error on the νe/νμ ratio is estimated by changing

the ratio ±3% for Eν < 5 GeV and linearly increasing with log Eν from ±3%

(5 GeV) to ±10% (100 GeV) where Eν is the total neutrino energy. The largest absolute diﬀerence in background rate is used as systematic error.

• Neutrino interaction cross-section: The systematic error on neutrino cross-

section is estimated by changing independently the fraction of QE, single-π production, coherent-π production and multi-π production generated events by ±10%, ±20%, ±30% and ±5% respectively. The largest absolute diﬀerence in background rate is used as systematic error.

• Axial Vector Mass (MA): To estimate the systematic error, QE and single- π production neutrino events are re-weighted with the assumption of an axial

mass of 1.1GeV/c2 rather than the default value of 1.2GeV/c2.Theabsolute diﬀerence in background rate is used as the systematic error.

• NC/CC ratio: The systematic error on the the NC/CC ratio is estimated by

changing the ratio ±20%. The largest absolute diﬀerence in background rate is used as systematic error.

• π − N interaction: The systematic error from elastic scattering, charge exchange, π absorption and π production is estimated by changing independently the fraction of events for each interaction by ±20%, ±30%, ±25% and ±30% respectively. The largest absolute diﬀerence in background rate is used as sys-

tematic error.

Additionally, the following are considered for this analysis:

• Fermi momentum: The systematic error on Fermi momentum is estimated by a comparison of the default model with another model. The default Fermi model in NEUT is a Fermi gas model with a surface momentum of 225 MeV/c [40, 41,

42]. 209

The model used for comparison is the one used for the p → μ+K0 simulation measured by electron-12C scattering [17] described by the distribution shown in

Figure 3.1. The fraction of events with Fermi momentum above 225 MeV/c is neglected. The absolute diﬀerence in background rate is used as the systematic error.

• 0 → 0 KL KS regeneration: Regeneration is not taken into account in the atmospheric neutrino MC simulation. The systematic error for regeneration was estimated as the fraction of events

0 with a KL generated. This fraction is negligible.

A.2.3 Detector (Signal and Background)

• Water quality: The time variation of the attenuation length measured by cosmic ray muons during the SK-I period is used to estimate the uncertainty on water scattering of ±20%. The data set and method to estimate the systematic error from water quality

for each search is described below.

• 0 → 0 0 Water quality of “KS π π ”search: To estimate the systematic error on signal detection eﬃciency we use a sample of ∼ 10, 000 p → μ+K0 MC events generated with random vertex distributed at least 1 m distant from the inner detector wall. The systematic error on background rate is estimated using a 250 year atmospheric neutrino MC sample with atmospheric neutrino production and interaction simulations described in

sections 3.2 and 3.3 respectively. For both samples, the detector simulation described in section 3.4 is used with the Rayleigh and Mie scattering parameters changed simultaneously from their default value of 0.72 and 0.8 respectively by positive (negative) 20% to 0.864 (0.576) and 0.96 (0.64) re-

spectively. The event reconstruction of the p → μ+K0 MC is the same 210

as described in section 5.1. The event reconstruction of the atmospheric neutrino MC is done using the pre-selections described in section A.1.1.

The systematic error on signal detection efficiency (background rate) is obtained by the quadratic sum of the largest absolute difference in signal detection efficiency (background rate) from the default and the statistical error of the p → μ+K0 (atmospheric neutrino) MC sample.

• 0 → + − Water quality of “KS π π Method #1” search: To estimate the systematic error on signal detection eﬃciency and background rate we generate p → μ+K0 and atmospheric neutrino MC respectively in the same

0 → 0 0 way as described above in “Water quality of ‘KS π π ’ search” with the exception that a 100 year atmospheric neutrino sample is used. The detector simulation with Rayleigh and Mie scattering parameters changed

±20% is used for both samples. The event reconstruction of both samples is same as described in section 5.1. The systematic error is estimated in the same way as described above

0 → 0 0 in “Water quality of ‘KS π π ’search”.

• 0 → + − Water quality of “KS π π Method #2” search: To estimate the systematic error on signal detection eﬃciency and background rate we generate p → μ+K0 and atmospheric neutrino MC respectively in the same

0 → 0 0 way as described above in “Water quality of ‘KS π π ’ search” with the exception that a 1000 year atmospheric neutrino sample is used. The

detector simulation with Rayleigh and Mie scattering parameters changed ±20% is used for both samples. The event reconstruction of the p → μ+K0 MC is the same as described in section 5.1. The event reconstruction of the atmospheric neutrino MC is done using the pre-selections described in section A.1.2.

The systematic error is estimated in the same way as described above 211

0 → 0 0 in “Water quality of ‘KS π π ’search”.

• 0 Water quality of “KL”search: To estimate the systematic error on signal detection eﬃciency and background rate we generate p → μ+K0 and atmospheric neutrino MC respectively in the same way as described

0 → 0 0 above in “Water quality of ‘KS π π ’ search” with the exception that a 75 year atmospheric neutrino sample is used. The detector simulation with Rayleigh and Mie scattering parameters changed ±20% is used for both samples. The event reconstruction of the both MC samples is the same as

described in section 5.2. The systematic error is estimated in the same way as described above

0 → 0 0 in “Water quality of ‘KS π π ’search”.

• Energy scale: As described in section 2.6.5.7 the total systematic uncertainty

on the energy scale is estimated to be 1.1%. The systematic error is estimated by simultaneously changing the threshold of event selections which depend on the energy scale by ±1.1%. The largest absolute diﬀerence from the default is used as the systematic error.

The event selections which depend on the energy scale are: Evis, MKS , pμ,

Mtot and Ptot.

A.2.4 Event Reconstruction (Signal and Background)

• Fiducial Volume: The systematic error in FV is estimated as the difference in the FV defined using the reconstruction vertex and the FV defined using the true vertex. The FV using the true vertex is larger than the FV using the reconstructed

vertex by 1.5% and 1.2% for the signal detection eﬃciency and background rate respectively. This systematic error is common to all searches.

• Ring counting: 212

The systematic error from ring counting is estimated by comparing the difference in the ring counting likelihood distributions between atmospheric neu-

trino data and MC using the control sample deﬁned by the FCFV (A-C) event selections.

0 { } For the KS searches, four distributions are compared, dlfcti i =1, 2, 3, 4 ,

where dlfcti is the ring counting likelihood between i and ≥ i+1 rings described in section 5.1.2. For i =1, 2, 3 the distribution of the MC is shifted to larger values than the data by 0.13, 0.14 and 0.20 respectively. For i =4theMC is shifted to smaller values than the data by 0.31. To estimate the systematic

error, the event selection thresholds of dlfcti {i =1, 2, 3, 4} are simultaneously changed by +0.13, +0.14, +0.20 and +0.31 respectively using the FCFV sample

for both signal and background and the change in signal detection eﬃciency and background rate from the default likelihood is used.

0 For the KL search, the dlfct1 distribution of the MC is shifted to larger

values than the data by 0.8. The reason for the diﬀerence in dlfct1 values from

0 the KS search is the ring counting algorithm is modiﬁed as described in section

5.2.1. To estimate the systematic error, we use the dlfct1 distribution after all event selections are applied except ring counting (A-M4, except F4). The cut value of the likelihood for both signal and background is changed by +0.8 and

the change in signal detection eﬃciency and background rate from the default likelihood is used.

• 0 → + − PID: This systematic error is estimated for all searches except KS π π Method #2 since it does not use PID in the event selection. The systematic error from PID is estimated by comparing the difference in the PID likelihood distribution between atmospheric neutrino data and MC. To compare the difference in the first and second ring a control sample correspond-

ing to neutral current single π0 is chosen using the following event selection: 213

• FCFV

• nring = 2

• second ring is e-like (to compare PID likelihood in the ﬁrst ring)

2 2 • 85 MeV/c < Mπ0 < 185 MeV/c

To compare the PID likelihood distribution in the second ring, the PID of the first ring is fixed as e-like in the event selection. To compare the difference in the third ring a control sample corresponding to charged current single π0 is chosen using the following event selection:

• FCFV

• nring = 3

• ﬁrst 2 rings contain 1 μ-like and 1 e-like

2 2 • 85 MeV/c < Mπ0 < 185 MeV/c

0 For the KS searches, we use the PID likelihood obtained only using the charge pattern, described in section 5.1.3. The PID likelihood distribution from the ﬁrst ring of MC is shifted to larger values than the data by 0.004. The MC is shifted to smaller values than the data by 0.06 and 0.2 for the second and third rings respectively.

0 For the KL search, we use the PID likelihood obtained using both the opening angle and charge pattern, described in section 5.1.3. The MC is shifted to larger values than the data by 0.02 for the first ring. The MC is shifted to smaller values than the data by 0.04 and 0.06 for the second and third rings respectively. For all searches, the difference between atmospheric neutrino data and MC for the fourth and fifth rings are assumed to be the same as the third ring. To estimate the systematic error, the event selection threshold of the PID likelihood is changed in every combination in both the positive and negative directions by 214

the shift value obtained for each ring. The largest diﬀerence in signal detection eﬃciency and background rate from the default event selection is used.

• Number of decay electrons: To estimate the systematic error from number of decay electrons the diﬀerence in the decay electrons between the atmospheric neutrino data and MC using the FCFV, 1 ring, μ-like, sub-GeV sample is used.

This diﬀerence is 2.0% and is the same for all searches.

• Detector response asymmetry: As described in section 2.6.5.6 the non-

uniformity in gain of PMT in the detector is within ±0.6%. This can cause an imbalance in the total momentum reconstruction up to 1.2%. This systematic error is estimated only for searches which make an event

selection using Ptot. The systematic error is estimated using the Ptot distribution

with all event selections except Ptot applied and the event selection threshold

of Ptot is changed ±1.2%.

0 The following sources are estimated only for the KL search

• Vertex separation: The systematic error of vertex separation is estimated by comparison of the reconstructed vertex separation and true vertex separation using p → μ+K0 MC with the event selections up to vertex separation applied (A-I4) as the control sample. The mean value of the reconstructed-true vertex separation distribution us-

ing this control sample is +12.8cm. To estimate the systematic error, the cut position is changed by ±12.8cm on the vertex separation distribution with all event selections applied except vertex separation (A-M4, except J4). The largest change in signal detection

eﬃciency and background rate is used as the systematic error.

• μ-candidate pattern PID: The systematic error for μ-candidate pattern PID

is estimated by comparing the pattern PID likelihood distribution of the μ- 215

candidate between atmospheric neutrino data and MC using a control sample deﬁned with the following event selection:

• FCFV

• 500 p.e. < total p.e. (potot) < 8000 p.e.

•−3 < dlfct1 < 3

Where dlfct1 is the ring counting likelihood described in section 5.2.1. The pattern PID likelihood distribution of the MC is shifted to smaller values than the data by 0.03. To estimate the systematic error, we shift the cut position by ±0.03 on the the pattern PID likelihood distribution with all event selections except pat-

tern PID applied (A-M4, except K4). The largest change in signal detection eﬃciency and background rate is used as the systematic error.

• μ-candidate Cherenkov angle: The systematic error for μ-candidate Cherenkov

angle is estimated by comparing the reconstructed and true Cherenkov angle using three control samples of ﬁxed momentum true single protons with the following:

• True proton

• True vertex is random within the true FV

• True direction is random

• True momentum = 1400 MeV/c, 1600 MeV/c and 2000 MeV/c This corresponds to the minimum, center and maximum of the true mo-

mentum distribution for protons in the atmospheric neutrino MC remaining after event selection up to μ-candidate Cherenkov angle (A-K4).

• aﬁt vertex reconstruction is applied

• no secondary particles generated in the GEANT simulation 216

• FCFV

The (reconstructed Cherenkov angle ﬁtted peak)-(true Cherenkov angle) for each of these control samples are −1.34◦, −0.93◦ and +0.04◦ for true proton momentum of 1400 MeV/c, 1600 MeV/c and 2000 MeV/c respectively.

To estimate the systematic error, we shifted the cut position by ±1◦ on the the μ-candidate Cherenkov angle distribution with all event selections except μ-candidate Cherenkov angle applied (A-M4, except L4). The largest change in signal detection eﬃciency and background rate is used as the systematic error.

• μ-candidate Proton ID: The systematic error for μ-candidate proton ID is estimated using the mis-PID probability.

To estimate the mis-PID probability for protons the same three control samples described above for μ-candidate Cherenkov angle are used. The mis-PID probability is 23%, 29% and 38% for true proton momentum of 1400 MeV/c, 1600 MeV/c and 2000 MeV/c respectively. To estimate the mis-PID probability for muons a control sample is deﬁned with the following:

• True muon

• True vertex is random within the true FV

• True direction is random

• True momentum = 326 MeV/c This corresponds to the expected momentum of the muon from p → μ+K0 for free proton decay.

• no particle decay in the GEANT simulation

• aﬁt and proton ID reconstruction is applied

• FCFV

The mis-PID probability is 4%. We assume the same mis-PID probability for

electrons, gamma and charged pions. 217

The systematic error is estimated by weighting the mis-PID probability by the fraction of true particle type for the μ-candidate after applying event selections up to proton ID (A-L4). For the signal, only a negligible fraction are not true muons so the systematic error on signal detection eﬃciency is 4%. The breakdown of true particle type for the μ-candidate from the atmospheric neutrino MC is 5%, 29%, 19% and 47% for electron or gamma, muon, charged pion and proton respectively. The systematic error on background rate is 30% × 47% + 4%(5% + 29% + 19%) = 16.2% 218

Change in signal detection Source Source error eﬃciency for each search (%) I II III IV Physics Simulation Fermi momentum model -2.6 -4.0 -0.6 ∼0 0% -6.2 -5.9 -5.5 -7.1 Correlated decay 20% +6.2 +5.9 +5.5 +7.1 0% +3.6 +3.2 +3.7 +1.2 K0 → K0 regeneration (nucleus) L S 0.2% -3.6 -3.2 -3.7 -1.2 0% +4.4 +4.0 +4.4 +8.3 K0 → K0 regeneration (water) L S 0.2% -4.4 -4.0 -4.4 -8.3 Detector +20% -1.9 +6.1 -3.0 -3.4 Water quality -20% +1.1 -4.7 -16.0 +3.8 +1.1% +1.3 +1.1 +0.3 -0.8 Energy scale -1.1% +1.2 -1.4 -0.6 +0.4 Event Reconstruction Fiducial volume true FV +1.5 +1.5 +1.5 +1.5 Ring counting see text -1.0 +1.4 +1.4 -1.6 PID see text +1.2 +0.6 — -0.5 Number of decay electrons ±2.0% ±2.0 ±2.0 ±2.0 ±2.0 +1.2% +0.4 +1.1 +0.2 — Detector response asymmetry -1.2% -0.3 -1.2 -0.2 — +12.8cm———-6.8 v sep. −12.8cm———+7.1 +0.03 — — — -0.4 μ-candidate Pattern PID -0.03 — — — +0.5 +1◦ ———-2.3 μ-candidate Cherenkov angle −1◦ ———+0.9 μ-candidate Proton ID see text — — — 4.0

Table A.1: Summary of source errors and change in signal detection eﬃciency for each systematic error source for each search I-IV (see section 6.2). Entries with ‘—’ are not applicable for that search. 219

Change in background rate Source Source error for each search (%) I II III IV Physics Simulation ν Flux Absolute 10.0 10.0 10.0 10.0 10.0 pos. +1.2 +1.2 +1.2 +1.2 ν/ν¯ neg. -1.3 -1.3 -1.3 -1.3 pos. +0.2 +1.1 -0.5 -0.6 ν /ν e μ neg. -0.2 -1.1 +0.5 +0.6 ν cross-section +10% +0.1 +1.3 +0.2 +3.7 QE -10% -0.1 -1.3 -0.2 -3.7 +20% +4.3 +14.0 +9.7 +7.1 Single π -20% -4.3 -14.0 -9.7 -7.1 MA(QE & single π) see text +3.9 +11.7 +8.9 +11.6 +30% ∼ 0 ∼ 0 +0.5 +0.2 Coherent π -30% ∼ 0 ∼ 0 -0.5 -0.2 +5% 1.6 +0.5 +1.0 +0.4 Multi π -5% -1.6 -0.5 -1.0 -0.4 +20% +4.6 -1.8 2.0 +0.6 NC/CC ratio -20% -4.8 +1.9 -2.1 -0.6 π Nuclear Eﬀect +20% +1.3 +1.8 +2.5 +1.4 Elastic -20% -1.3 -1.8 -2.5 -1.4 +30% +1.8 +1.2 -1.2 -0.1 Charge exchange -30% -1.8 -1.2 +1.2 +0.1 +25% +1.2 +3.2 ∼ 0+0.6 Absorption -25% -1.2 -3.2 ∼ 0-0.6 +30% -3.1 -6.1 -4.3 -3.5 Production -30% +3.1 +6.1 +4.3 +3.5 Fermi momentum model -1.9 -0.7 -6.3 -5.5 0 → 0 ∼ KL KS regeneration (nucleus) see text 0 0 → 0 ∼ KL KS regeneration (water) see text 0 (a) 220

Change in background rate Source Source error foreachsearch(%) I II III IV Detector +20% -1.0 -3.2 -27.7 +3.9 Water quality -20% -15.7 -2.9 -27.1 +0.4 +1.1% -1.5 +1.1 -2.3 +0.7 Energy scale -1.1% +1.5 -1.2 -11.9 -4.9 Event Reconstruction Fiducial volume true FV +1.2 +1.2 +1.2 +1.2 Ring counting see text -1.2 +3.7 +1.1 -10.7 PID see text +5.6 ∼ 0—-1.1 Number of decay electrons ±2.0% ±2.0 ±2.0 ±2.0 ±2.0 +1.2% +4.1 +3.0 ∼ 0— Detector response asymmetry -1.2% -4.1 -3.4 -4.4 — +12.8cm — — — -8.0 v sep. −12.8 cm — — — +13.9 +0.03 — — — -1.3 μ-candidate Pattern PID -0.03 — — — +1.7 +1◦ ———-3.6 μ-candidate Cherenkov angle −1◦ ———+6.0 μ-candidate Proton ID see text — — — +16.2 (b)

Table A.2: Summary of the change in background rate from systematic sources from (a) physics simulation, (b) detector and event reconstruction source errors for each search I-IV (see section 6.2). Entries with ‘—’ are not applicable for that search. Bibliography

[1] K. Kobayashi et al., Phys. Rev. D72, 052007 (2005).

[2] K. S. Babu, J. C. Pati, and F. Wilczek, Nucl. Phys. B566, 33 (2000).

[3] E. Noether, Transport Theory and Statistical Physics 1, 186 (1971).

[4] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).

[5] F. Abe et al., Phys. Rev. D50, 2966 (1994).

[6] H. Nishino et al., Phys. Rev. Lett. 102, 141801 (2009).

[7] C. Amsler et al., Phys. Lett. B667, 1 (2008).

[8] P. Langacker and M.-x. Luo, Phys. Rev. D44, 817 (1991).

[9] H. Murayama and A. Pierce, Phys. Rev. D65, 055009 (2002).

[10] D. Wall et al., Phys. Rev. D61, 072004 (2000).

[11] C. McGrew et al., Phys. Rev. D59, 052004 (1999).

[12] K. S. Hirata et al., Phys. Lett. B220, 308 (1989).

[13] H. Ikeda et al., Nucl. Instrum. Meth. A320, 310 (1992).

[14] T. K. Ohsuka et al., (1985), KEK Report 85-10.

[15] H. Nishihama, Master’s thesis, Tokyo Institute of Technology, 2002.

[16] M. Yamada et al., Phys. Rev. D44, 617 (1991).

[17] K. Nakamura et al., Nucl. Phys. A268, 381 (1976).

[18] T. Yamazaki and Y. Akaishi, Phys. Lett. B453, 1 (2000).

[19] R. D. Woods and D. S. Saxon, Phys. Rev. 95, 577 (1954).

[20] B. R. Martin and M. K. Pidcock, Nucl. Phys. B126, 266 (1977).

[21] B. R. Martin and M. K. Pidcock, Nucl. Phys. B126, 285 (1977).

221 BIBLIOGRAPHY 222

[22] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, and T. Sanuki, Phys. Rev. D75, 043006 (2007).

[23] T. Sanuki et al., Astrophys. J. 545, 1135 (2000).

[24] J. Alcaraz et al., Phys. Lett. B490, 27 (2000).

[25] K. H¨anssgen and J. Ranft, Computer Physics Communications 39, 37 (1986).

[26] S. Roesler, R. Engel, and J. Ranft, Phys. Rev. D57, 2889 (1998).

[27] G. Battistoni, A. Ferrari, T. Montaruli, and P. R. Sala, Astropart. Phys. 19, 269 (2003).

[28] G. D. Barr, T. K. Gaisser, P. Lipari, S. Robbins, and T. Stanev, Phys. Rev. D70, 023006 (2004).

[29] Y. Ashie et al., Phys. Rev. D71, 112005 (2005).

[30] W. Webber, R. Golden, and S. Stephens, in Proceedings of the 20th International Cosmic Ray Conference, volume 1, page 325, 1987.

[31] E. S. Seo et al., Astrophys. J. 378, 763 (1991).

[32] P. Pappini et al., in Proceedings of the 23rd International Cosmic Ray Confer- ence, volume 1, page 579, 1993.

[33] M. Boezio et al., Astrophys. J. 518, 457 (1999).

[34] W. Menn et al., Astrophys. J. 533, 281 (2000).

[35] M. J. Ryan, J. F. Ormes, and V. K. Balasubrahmanyan, Phys. Rev. Lett. 28, 985 (1972).

[36] K. Asakimori et al., Astrophys. J. 502, 278 (1998).

[37] I. Ivanenko et al., in Proceedings of the 23rd International Cosmic Ray Confer- ence, volume 2, page 17, 1993.

[38] Y. Kawamura et al., Phys. Rev. D40, 729 (1989).

[39] A. V. Apanasenko et al., Astropart. Phys. 16, 13 (2001).

[40] Y. Hayato, Nucl. Phys. Proc. Suppl. 112, 171 (2002).

[41] G. Mitsuka, AIP Conf. Proc. 967, 208 (2007).

[42] G. Mitsuka, AIP Conf. Proc. 981, 262 (2008).

[43] C. H. Llewellyn Smith, Phys. Rept. 3, 261 (1972).

[44] S. K. Singh and E. Oset, Phys. Rev. C48, 1246 (1993). BIBLIOGRAPHY 223

[45] R. A. Smith and E. J. Moniz, Nucl. Phys. B43, 605 (1972).

[46] C. H. Albright, C. Quigg, R. E. Shrock, and J. Smith, Phys. Rev. D14, 1780 (1976).

[47] L. A. Ahrens et al., Phys. Rev. Lett. 56, 1107 (1986).

[48] S. J. Barish et al., Phys. Rev. D16, 3103 (1977).

[49] S. Bonetti et al., Nuovo Cim. A38, 260 (1977).

[50] M. Pohl et al., Lett. Nuovo Cim. 26, 332 (1979).

[51] N. Armenise et al., Nucl. Phys. B 152, 365 (1979).

[52] A. I. Mukhin et al., Sov. J. Nucl. Phys. 30, 528 (1979).

[53] S. V. Belikov et al., Z. Phys. A320, 625 (1985).

[54] J. Brunner et al., Z. Phys. C45, 551 (1990).

[55] D. Rein and L. M. Sehgal, Phys. Lett. B104, 394 (1981).

[56] R. P. Feynman, M. Kislinger, and F. Ravndal, Phys. Rev. D3, 2706 (1971).

[57] S. K. Singh, M. J. Vicente-Vacas, and E. Oset, Phys. Lett. B416, 23 (1998).

[58] C. H. Albright and C. Jarlskog, Nucl. Phys. B84, 467 (1975).

[59] M. Gluck, E. Reya, and A. Vogt, Eur. Phys. J. C5, 461 (1998).

[60] P. Musset and J. P. Vialle, Phys. Rept. 39, 1 (1978).

[61] T. Sjostrand, CERN-TH-7112-93.

[62] M. Derrick et al., Phys. Rev. D17, 1 (1978).

[63] S. Barlag et al., Z. Phys. C11, 283 (1982).

[64] D. Rein and L. M. Sehgal, Nucl. Phys. B223, 29 (1983).

[65] M. Hasegawa et al., Phys. Rev. Lett. 95, 252301 (2005).

[66] E. Paschos, A. Kartavtsev, and G. Gounaris, Phys. Rev. D74, 054007 (2006).

[67] F. Bergsma et al., Phys. Lett. B157, 458 (1985).

[68] J. L. Raaf, PhD thesis, University of Cincinnati, 2005.

[69] H. Faissner et al., Phys. Lett. B125, 230 (1983).

[70] E. Isiksal, D. Rein, and J. Morﬁn, Phys. Rev. Lett. 52, 1096 (1984). [71] L. Salcedo, E. Oset, M. Vicente-Vacas, and C. Garcia-Recio, Nucl. Phys. A484, 557 (1988).

[72] G. Rowe, M. Salomon, and R. H. Landau, Phys. Rev. C18, 584 (1978).

[73] D. Ashery et al., Phys. Rev. C23, 2173 (1981).

[74] C. Ingram et al., Phys. Rev. C27, 1578 (1983).

[75] D. Sparrow, AIP Conf. Proc. 123, 1019 (1984).

[76] H. Bertini, Phys. Rev. C6, 631 (1972).

[77] S. Lindenbaum and R. Sternheimer, Phys. Rev. 105, 1874 (1957).

[78] R. Brun, F. Carminati, and S. Giani, CERN-W5013.

[79] M. Nakahata et al., J. Phys. Soc. Jap. 55, 3786 (1986).

[80] E. Bracci, J. P. Droulez, V. Flaminio, J. D. Hansen, and D. R. O. Morrison, CERN-HERA-72-01.

[81] A. Carroll et al., Phys. Rev. C14, 635 (1976).

[82] T. Gabriel, J. Brau, and B. Bishop, Nuclear Science, IEEE Transactions on 36, 14 (1989).

[83] P. H. Eberhard and F. Uchiyama, Nucl. Instrum. Meth. A350, 144 (1994).

[84] H. Nishino, PhD thesis, University of Tokyo, 2009.

[85] M. Shiozawa, PhD thesis, University of Tokyo, 1999.

[86] E. R. Davies, Machine Vision: Theory, Algorithms, Practicalities,Academic Press, San Diego, 1997.

[87] S. Kasuga et al., Phys. Lett. B374, 238 (1996).

[88] M. Fechner et al., Phys. Rev. D79, 112010 (2009).

[89] W. Eadie et al., Statistical Methods in Experimental Physics, American Elsevier Pub. Co, Palo Alto, 1971.

[90] S. Mine, Nucl. Phys. Proc. Suppl. 138, 199 (2005).

[91] G. Mitsuka, PhD thesis, University of Tokyo, 2009.

224