UNIVERSITY OF CALIFORNIA,
IRVINEA search for proton decay via p → μ+ K 0 in Super Kamiokande I
DISSERTATION

submitted in partial satisfaction of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
in Physics

byChristopher Regis

Dissertation Committee:
Professor David Casper, Chair
Professor Hank Sobel
Professor Jonas Schultz2011c 2011 Christopher Regis
TABLE OF CONTENTS
Page
List Of Figuresvi

List Of Tablesxii

Acknowledgments

xiv

Curriculum Vitae

xv

Abstract Of The Dissertation

xvi

1 Introduction
1.1 Theoretical Motivation . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Conservation and Symmetries . . . . . . . . . . . . . . . . . .
1.1.2 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Grand Uniﬁed Theories . . . . . . . . . . . . . . . . . . . . . .
1.2 Past Experimental Measurements of p → μ+ K 0 . . . . . . . . . . . .
1.2.1 Soudan 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Irvine Michigan Brookhaven (IMB) . . . . . . . . . . . . . . .
1.2.3 Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Super Kamiokande . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Overview of Experimental Method . . . . . . . . . . . . . . . . . . .

1
1
2
3
5
9
9
9
10
10
10

2 Detector
2.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Super Kamiokande Detector . . . . . . . . . . . . . . . . . . . . . . .
2.3 Photomultiplier Tube . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Electronics & Data Acquisition . . . . . . . . . . . . . . . . . . . . .
2.4.1 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Outer Detector . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Water Puriﬁcation System . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Relative Gain Calibration . . . . . . . . . . . . . . . . . . . .
2.6.3 Absolute Gain Calibration . . . . . . . . . . . . . . . . . . . .
2.6.4 Water Transparency . . . . . . . . . . . . . . . . . . . . . . .

14
14
16
18
18
18
21
21
23
24
24
25
27
28

ii

2.6.5Absolute Energy Calibration . . . . . . . . . . . . . . . . . . .

30

3 Simulation
3.1 Proton Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Fermi Momentum and Nuclear Binding Energy . . . . . . . .
3.1.2 Kaon-Nucleon Interaction in the Oxygen Nucleus . . . . . . .
3.1.3 KL0 →KS0 Regeneration in the Oxygen Nucleus . . . . . . . . .
3.2 Atmospheric Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . .
3.3 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Elastic & Quasi-Elastic Scattering . . . . . . . . . . . . . . . .
3.3.2 Single Meson Production . . . . . . . . . . . . . . . . . . . . .
3.3.3 Deep Inelastic Scattering (DIS) . . . . . . . . . . . . . . . . .
3.3.4 Coherent Pion Production . . . . . . . . . . . . . . . . . . . .
3.3.5 Nuclear Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Photon Propagation . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Hadron Propagation . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 KL0 →KS0 Regeneration in Water . . . . . . . . . . . . . . . . .

38
38
39
40
41
42
44
44
46
48
50
52
54
54
54
54

4 Fully Contained Event Reduction
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Through-going Muon Cut . . . . . . . . . . . . . . . . . . . .
4.4.2 Stopping Muon Cut . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Cable Port Muons . . . . . . . . . . . . . . . . . . . . . . . .
4.4.4 Flasher Event Cut . . . . . . . . . . . . . . . . . . . . . . . .
4.4.5 Accidental Coincidence Cut . . . . . . . . . . . . . . . . . . .
4.4.6 Low Energy Events Cut . . . . . . . . . . . . . . . . . . . . .
4.5 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Stopping Muon Cut . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Invisible Muon Cut . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Coincidence Muon Cut . . . . . . . . . . . . . . . . . . . . . .
4.6.4 Long Tail Flasher Cut . . . . . . . . . . . . . . . . . . . . . .
4.7 Final Fully Contained Fiducial Volume Sample . . . . . . . . . . . . .

56
56
56
57
58
58
59
59
60
60
61
61
63
63
63
64
64
64

5 Event Reconstruction
5.1 Standard Event Reconstruction . . . . . . . . . . . . . . . . . . . . .
5.1.1 Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Particle Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 MS Vertex Fit . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5 Momentum Determination . . . . . . . . . . . . . . . . . . . .

66
66
67
71
73
77
77

iii

5.1.6 Decay Electron Search . . . . . . . . . . . . . . . . . . . . . .
5.1.7 Ring Number Correction . . . . . . . . . . . . . . . . . . . . .
Multiple Vertex Event Reconstruction . . . . . . . . . . . . . . . . . .
5.2.1 Standard Reconstruction Without Timing Cuts . . . . . . . .
5.2.2 PMT Masking Region . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Primary μ-candidate Reconstruction . . . . . . . . . . . . . .
5.2.4 Remaining Particle Reconstruction . . . . . . . . . . . . . . .

82
83
84
85
86
86
92

6 Overview of the p → μ+ K 0 search
6.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Strategy of the Combined p → μ+ K 0 Search . . . . . . . . . . . . . .

95
95
96

7 Search for “KS0 → π 0 π 0 ”
7.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 SK-I Data Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 SK-I Data Event Rate vs. Event Selection . . . . . . . . . . . . . . .
7.4 Breakdown of Remaining Background . . . . . . . . . . . . . . . . . .
7.5 SK-I Data Candidates . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Total Systematic Error of “KS0 → π 0 π 0 ” Search . . . . . . . . . . . .

99
99
106
111
118
120
122

8 Search for “KS0 → π + π − Method #1”
8.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 SK-I Data Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 SK-I Data Event Rate vs. Event Selection . . . . . . . . . . . . . . .
8.4 Breakdown of Remaining Background . . . . . . . . . . . . . . . . . .
8.5 SK-I Data Candidates . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6 Total Systematic Error of “KS0 → π + π − Method #1” Search . . . . .

124
124
130
133
139
140
148

9 Search for “KS0 → π + π − Method #2”
9.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 SK-I Data Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 SK-I Data Event Rate vs. Event Selection . . . . . . . . . . . . . . .
9.4 Breakdown of Remaining Background . . . . . . . . . . . . . . . . . .
9.5 Total Systematic Error of “KS0 → π + π − Method #2” Search . . . . .

150
150
154
157
162
163

10 Search for “KL0 ”
10.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 SK-I Data Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 SK-I Data Event Rate vs. Event Selection . . . . . . . . . . . . . . .
10.4 Breakdown of Remaining Background . . . . . . . . . . . . . . . . . .
10.5 SK-I Data Candidates . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6 Total Systematic Error of “KL0 ” Search . . . . . . . . . . . . . . . . .

165
165
175
180
188
189
191

11 Results

193

12 Comparison With Previous SK p → μ+ K 0 Search

196

5.2

iv

13 Future Prospects

202

14 Conclusion

204

AppendicesA
Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1
Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2
Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . .

205
205
205
206

Bibliography

217v

LIST OF FIGURES
Page
1.1
1.2
1.3
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
3.1
3.2
3.3
3.4
3.5

Feynman diagrams of SU(5) GUT gauge bosons. . . . . . . . . . . .
Feynman diagram of Higgsino exchange from d=5 operator in the
SUSY GUT Lagrangian. . . . . . . . . . . . . . . . . . . . . . . . .
Feynman diagram of p → ν̄K + decay. . . . . . . . . . . . . . . . . .

7

Relative Cherenkov light spectrum in pure water. . . . . . . . . . .
The Super Kamiokande detector. . . . . . . . . . . . . . . . . . . .
The 50 cm PMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The quantum eﬃciency of the 50 cm PMT. . . . . . . . . . . . . . .
The transit time spread of the 50 cm PMT. . . . . . . . . . . . . . .
Schematic of the SK ID DAQ system. . . . . . . . . . . . . . . . . .
Schematic of the SK water puriﬁcation system. . . . . . . . . . . . .
Timing calibration system. . . . . . . . . . . . . . . . . . . . . . . .
Relative gain calibration system using Xe lamp. . . . . . . . . . . .
Absolute gain calibration using a Ni+Cf source. . . . . . . . . . . .
Water attenuation length measurement system. . . . . . . . . . . .
Distribution of corrected p.e. vs. photon travel length. . . . . . . . .
Momentum distribution for decay electrons. . . . . . . . . . . . . .
Invariant mass distribution of neutrino induced π 0 events. . . . . . .
Distribution of reconstructed momentum from observed charge vs.
reconstructed Cherenkov opening angle for cosmic ray stopping μ. .
Ratio of the muon momentum from observed p.e. to momentum from
opening angle as a function of the momentum. . . . . . . . . . . . .
The ratio of momentum/range as a function of range for cosmic ray
stopping μ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time variation of energy scale calibration. . . . . . . . . . . . . . .
The non-uniformity of the detector gain as a function of zenith angle.
Summary of the absolute energy scale calibration. . . . . . . . . . .

15
17
19
19
20
22
24
25
26
27
28
30
31
32

Nucleon momentum distributions of 12 C. . . . . . . . . . . . . . . .
Invariant mass of μ+ K 0 in the p → μ+ K 0 MC simulation in water. .
Primary cosmic ray ﬂux measurements compared with the model usedin the Honda ﬂux calculation. . . . . . . . . . . . . . . . . . . . . .
The predicted atmospheric neutrino ﬂuxes at the SK site. . . . . . .
Quasi-elastic scattering cross-sections of ν and ν̄. . . . . . . . . . . .

vi

9
9

33
34
35
36
37
37
39
40
43
43
46

3.6
3.7
3.8
3.9
3.10
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9

Cross-sections for charged current single pion productions of νμ . . .
Cross-sections for charged current νμ and ν¯μ interactions. . . . . . .
The cross-sections of coherent pion productions oﬀ the carbon nucleus
for CC and NC interactions. . . . . . . . . . . . . . . . . . . . . . .
Cross-sections of π + -16 O scattering as a function of π + momentum.
Wavelength dependence of photon attenuation coeﬃcients used in
MC simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed-true muon momentum of three control samples
described in the text. . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance of the initial vertex ﬁtting of the μ-candidate for p →μ+ KL0 MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ΔV distribution of the initial μ-candidate vertex for atmospheric
neutrino MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The PID likelihood of the true primary muon for p → μ+ KL0 MC. .
Performance of the MS vertex ﬁtting of the μ-candidate for p →μ+ KL0 MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ΔV distribution of the μ-candidate MS vertex for atmospheric
neutrino MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed-true momentum of the true primary muon for p →μ+ KL0 MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance of the remaining particle vertex ﬁtting of the μ-candidate
for p → μ+ KL0 MC. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ΔV− distribution for the remaining particle vertex of the atmospheric neutrino MC. . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1

The p → μ+ K 0 combined search algorithm. . . . . . . . . . . . . . .

7.1

The nring distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . .
The PID likelihood distribution for p → μ+ K 0 and atmospheric neutrino MC along the KS0 → π 0 π 0 search event selection. . . . . . . . .
The number of decay electron distribution for p → μ+ K 0 and atmospheric neutrino MC along the KS0 → π 0 π 0 search event selection. .
The MKS distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . .
The pμ distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . .
The Ptot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . .
The Mtot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . .
The number of decay electron distribution for data and atmospheric
neutrino MC using the KS0 → π 0 π 0 search sideband sample. . . . . .

7.2
7.3
7.4
7.5
7.6
7.7
7.8

vii

48
50
52
53
55
81
88
88
89
90
91
91
93
94
97
102
103
103
104
104
105
105
108

7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
8.1
8.2
8.3

8.4
8.5
8.6

8.7
8.8

The MKS distribution for data and atmospheric neutrino MC using
the KS0 → π 0 π 0 search sideband sample. . . . . . . . . . . . . . . . .
The pμ distribution for data and atmospheric neutrino MC using theKS0 → π 0 π 0 search sideband sample. . . . . . . . . . . . . . . . . . .
The Ptot distribution for data and atmospheric neutrino MC using
the KS0 → π 0 π 0 search sideband sample. . . . . . . . . . . . . . . . .
The Mtot distribution for data and atmospheric neutrino MC using
the KS0 → π 0 π 0 search sideband sample. . . . . . . . . . . . . . . . .
The event rate along the KS0 → π 0 π 0 search event selection. . . . . .
The nring distribution for data and atmospheric neutrino MC along
the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . .
The PID likelihood distribution for data and atmospheric neutrino
MC along the KS0 → π 0 π 0 search event selection. . . . . . . . . . . .
The number of decay electron distribution for data and atmospheric
neutrino MC along the KS0 → π 0 π 0 search event selection. . . . . . .
The MKS distribution for data and atmospheric neutrino MC along
the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . .
The pμ distribution for data and atmospheric neutrino MC along theKS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . . . .
The Ptot distribution for data and atmospheric neutrino MC along
the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . .
The Mtot distribution for data and atmospheric neutrino MC along
the KS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . .
The Mtot vs. Ptot scatter plot for data, atmospheric neutrino MC andp → μ+ K 0 MC along the KS0 → π 0 π 0 search event selection. . . . .
Event display of the candidate for the KS0 → π 0 π 0 search. . . . . . .
The nring distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #1 search event selection. . . . . . .
The PID likelihood distribution for p → μ+ K 0 and atmospheric neutrino MC along the KS0 → π + π − Method #1 search event selection.
The number of decay electron distribution for p → μ+ K 0 and atmospheric neutrino MC along the KS0 → π + π − Method #1 search event
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The pμ distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #1 search event selection. . . . . . .
The Ptot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #1 search event selection. . . . . . .
The number of decay electron distribution for data and atmospheric
neutrino MC using the KS0 → π + π − Method #1 search sideband
sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The pμ distribution for data and atmospheric neutrino MC using theKS0 → π + π − Method #1 search sideband sample. . . . . . . . . . .
The Ptot distribution for data and atmospheric neutrino MC using
the KS0 → π + π − Method #1 search sideband sample. . . . . . . . .
viii

108
109
109
110
113
114
114
115
115
116
116
117
117
121
126
127

128
128
129

131
131
132

8.9
8.10
8.11
8.12
8.13
8.14
8.15

8.16
8.17
8.18
8.19
8.20
8.21
9.1

9.2
9.3
9.4
9.5

9.6
9.7

The event rate along the KS0 → π + π − Method #1 search event selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
The nring distribution for data and atmospheric neutrino MC along
the KS0 → π + π − Method #1 search event selection. . . . . . . . . . 135
The PID likelihood distribution for data and atmospheric neutrino
MC along the KS0 → π + π − Method #1 search event selection. . . . 136
The number of decay electron distribution for data and atmospheric
neutrino MC along the KS0 → π + π − Method #1 search event selection. 136
The pμ distribution for data and atmospheric neutrino MC along theKS0 → π + π − Method #1 search event selection. . . . . . . . . . . . 137
The Ptot distribution for data and atmospheric neutrino MC along
the KS0 → π + π − Method #1 search event selection. . . . . . . . . . 137
The pμ vs. Ptot scatter plot for data, atmospheric neutrino MC andp → μ+ K 0 MC along the KS0 → π + π − Method #1 search event
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Event display of the ﬁrst candidate for the KS0 → π + π − Method #1
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Event display of the second candidate for the KS0 → π + π − Method#1 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Event display of the third candidate for the KS0 → π + π − Method #1
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Event display of the fourth candidate for the KS0 → π + π − Method#1 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Event display of the ﬁfth candidate for the KS0 → π + π − Method #1
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Event display of the sixth candidate for the KS0 → π + π − Method #1
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
The number of decay electron distribution for p → μ+ K 0 and atmospheric neutrino MC along the KS0 → π + π − Method #2 search event
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The MKS distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #2 search event selection. . . . . . .
The Ptot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #2 search event selection. . . . . . .
The Mtot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KS0 → π + π − Method #2 search event selection. . . . . . .
The number of decay electron distribution for data and atmospheric
neutrino MC using the KS0 → π + π − Method #2 search sideband
sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The MKS distribution for data and atmospheric neutrino MC using
the KS0 → π + π − Method #2 search sideband sample. . . . . . . . .
The Ptot distribution for data and atmospheric neutrino MC using
the KS0 → π + π − Method #2 search sideband sample. . . . . . . . .

ix

152
152
153
153

155
155
156

9.8
9.9
9.10
9.11
9.12
9.13
9.14

The Mtot distribution for data and atmospheric neutrino MC using
the KS0 → π + π − Method #2 search sideband sample. . . . . . . . . 156
The event rate along the KS0 → π + π − Method #2 search event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
The number of decay electron distribution for data and atmospheric
neutrino MC along the KS0 → π + π − Method #2 search event selection. 159
The MKS distribution for data and atmospheric neutrino MC along
the KS0 → π + π − Method #2 search event selection. . . . . . . . . . 160
The Ptot distribution for data and atmospheric neutrino MC along
the KS0 → π + π − Method #2 search event selection. . . . . . . . . . 160
The Mtot distribution for data and atmospheric neutrino MC along
the KS0 → π + π − Method #2 search event selection. . . . . . . . . . 161
The Mtot vs. Ptot scatter plot for data, atmospheric neutrino MC
and p → μ+ K 0 MC along the KS0 → π + π − Method #2 search event
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

The potot distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KL0 search event selection. . . . . . . . . . . . . . . . . . .
10.2 The nringt distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KL0 search event selection. . . . . . . . . . . . . . . . . . .
10.3 The PID likelihood distribution for p → μ+ K 0 and atmospheric neutrino MC along the KL0 search event selection. . . . . . . . . . . . .
10.4 The number of decay electron distribution for p → μ+ K 0 and atmospheric neutrino MC along the KL0 search event selection. . . . . . .
10.5 The pμ−cand. distribution for p → μ+ K 0 and atmospheric neutrino
MC along the KL0 search event selection. . . . . . . . . . . . . . . .
10.6 The vsep. distribution for p → μ+ K 0 and atmospheric neutrino MC
along the KL0 search event selection. . . . . . . . . . . . . . . . . . .
10.7 The pattern PID likelihood distribution for p → μ+ K 0 and atmospheric neutrino MC along the KL0 search event selection. . . . . . .
10.8 The μ-candidate Cherenkov angle distribution for p → μ+ K 0 andatmospheric neutrino MC along the KL0 search event selection. . . .
10.9 The proton ID likelihood distribution for p → μ+ K 0 and atmospheric
neutrino MC along the KL0 search event selection. . . . . . . . . . .
10.10 The number of decay electron distribution for data and atmospheric
neutrino MC in the KL0 search sideband sample. . . . . . . . . . . .
10.11 The pμ−cand. distribution for data and atmospheric neutrino MC in
the KL0 search sideband sample. . . . . . . . . . . . . . . . . . . . .
10.12 The vsep. distribution for data and atmospheric neutrino MC in theKL0 search sideband sample. . . . . . . . . . . . . . . . . . . . . . .
10.13 The pattern PID likelihood distribution for data and atmospheric
neutrino MC in the KL0 search sideband sample. . . . . . . . . . . .
10.14 The μ-candidate Cherenkov angle distribution for data and atmospheric neutrino MC in the KL0 search sideband sample. . . . . . . .

10.1

x

169
170
171
172
172
173
173
174
174
176
177
177
178
178

10.15 The proton ID likelihood distribution for data and atmospheric neutrino MC in the KL0 search sideband sample. . . . . . . . . . . . . .
10.16 The event rate along the KL0 search event selection . . . . . . . . . .
10.17 The potot distribution for data and atmospheric neutrino MC along
the KL0 search event selection. . . . . . . . . . . . . . . . . . . . . .
10.18 The nringt distribution for data and atmospheric neutrino MC along
the KL0 search event selection. . . . . . . . . . . . . . . . . . . . . .
10.19 The PID likelihood distribution for data and atmospheric neutrino
MC along the KL0 search event selection. . . . . . . . . . . . . . . .
10.20 The number of decay electron distribution for data and atmospheric
neutrino MC along the KL0 search event selection. . . . . . . . . . .
10.21 The pμ−cand. distribution for data and atmospheric neutrino MC along
the KL0 search event selection. . . . . . . . . . . . . . . . . . . . . .
10.22 The vsep. distribution for data and atmospheric neutrino MC along
the KL0 search event selection. . . . . . . . . . . . . . . . . . . . . .
10.23 The pattern PID likelihood distribution for data and atmospheric
neutrino MC along the KL0 search event selection. . . . . . . . . . .
10.24 The μ-candidate Cherenkov angle distribution for data and atmospheric neutrino MC along the KL0 search event selection. . . . . . .
10.25 The proton ID likelihood distribution for data and atmospheric neutrino MC along the KL0 search event selection. . . . . . . . . . . . .
10.26 Event display of the candidate for the KL0 search. . . . . . . . . . .
12.1
12.2
12.3
12.4

The total momentum vs. μ+ momentum scatter plot. . . . . . . . .
Event display of ﬁrst event selected by this analysis and not thereference data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Event display of second event selected by this analysis and not thereference data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed-true μ-candidate momentum distribution. . . . .

xi

179
182
182
183
184
185
185
186
186
187
187
190
199
200
200
201

LIST OF TABLES
Page
1.1
1.2

KS0 decay branching ratios. . . . . . . . . . . . . . . . . . . . . . . . .
KL0 kinematics in water. . . . . . . . . . . . . . . . . . . . . . . . . .

7.1

Data events, signal detection eﬃciency and background rate along theKS0 → π 0 π 0 search event selection. . . . . . . . . . . . . . . . . . . . .
Breakdown of remaining atmospheric neutrino MC background for the
KS0 → π 0 π 0 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of reconstructed information for the data candidate of theKS0 → π 0 π 0 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic errors on signal detection eﬃciency for the KS0 → π 0 π 0search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic errors on background rate for the KS0 → π 0 π 0 search. . . .

7.2
7.3
7.4
7.5
8.1
8.2
8.3
8.4
8.5
9.1
9.2
9.3
9.4

Data events, signal detection eﬃciency and background rate along theKS0 → π + π − Method #1 search event selection. . . . . . . . . . . . .
Breakdown of remaining atmospheric neutrino MC background for the
KS0 → π + π − Method #1 search. . . . . . . . . . . . . . . . . . . . . .
Summary of reconstructed information for the data candidates of theKS0 → π + π − Method #1 search. . . . . . . . . . . . . . . . . . . . . .
Systematic errors on signal detection eﬃciency for the KS0 → π + π −Method #1 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic errors on background rate for the KS0 → π + π − Method #1
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data events, signal detection eﬃciency and background rate along theKS0 → π + π − Method #2 search event selection. . . . . . . . . . . . .
Breakdown of remaining atmospheric neutrino MC background forKS0 → π + π − Method #2 search. . . . . . . . . . . . . . . . . . . . . .
Systematic errors on signal detection eﬃciency for the KS0 → π + π −Method #2 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic errors on background rate for the KS0 → π + π − Method #2
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12
13
113
119
120
122
123
134
139
141
148
149
158
162
163
164

10.1 Data events, signal detection eﬃciency and background rate along theKL0 search event selection. . . . . . . . . . . . . . . . . . . . . . . . . 181

xii

10.2 Breakdown of remaining atmospheric neutrino MC background for theKL0 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 Summary of reconstructed information for the data candidate of theKL0 search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Systematic errors on signal detection eﬃciency for the KL0 search. . .
10.5 Systematic errors on background rate for the KL0 search. . . . . . . .

188
189
191
192

11.1 Result of the lower lifetime limit calculation. . . . . . . . . . . . . . . 195
12.1 Summary of the p → μ+ KS0 search results from Kobayashi [1] and thisanalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

xiii

ACKNOWLEDGMENTSFirst, 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 forthis 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 andproton 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 towhom 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 thislong 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, IrvineAwards and Honors:
2004-2005

Outstanding Contributions to the Department Award

xv

ABSTRACT OF THE DISSERTATION
A search for proton decay via p → μ+ K 0 in Super Kamiokande I
By
Christopher Regis
Doctor of Philosophy in Physics
University of California, Irvine, 2011
Professor David Casper, Chair

A search for p → μ+ K 0 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 91.2 kt years.
In addition to searching this decay mode via the p → μ+ KS0 channel, previously
performed by Kobayashi using the SK-I data set [1], new event reconstruction wasdeveloped speciﬁcally to search for separated vertices characteristic of the p → μ+ KL0
channel. This new reconstruction takes advantage of the long lifetime of the KL0
which results in a unique event signature in which there are two distinct vertices; onecorresponding to the proton decay point and another at the KL0 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+ K 0 decay. Therefore, a lower limit on the proton partial lifetime, τ /Bp→μ+ K 0 , of 1.1 × 1033 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 universe. It generates electromagnetic, weak and strong interactions via corresponding
gauge symmetries mediated by the corresponding gauge ﬁelds, W ± , Z 0 and photon,
A. Although this model has been very successful in accurately describing results froma 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 typicalfeature 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 theso-called “hierarchy problem”, the inelegant necessity to introduce careful tuning ofparameters 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+ K 0 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 undertranslations 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 aexperimental test of the validity of baryon number conservation.
To describe these symmetries in a mathematical formalism, group theory is used.
An example of this is the SU(2) group used to describe spin- 12 systems in quantum
mechanics. The commutation relation between the generators completely describes
the group.

[Li , Lj ] = iijk Lk(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
matrices, σi , as Li = σ2i . These matrices span the SU(2) space. Any arbitrary unitarymatrix M with determinant = 1 can be expressed in terms of Li as:

M = eiαi ·Li

(1.2)

3

where α is an arbitrary scale vector.
The two physical states of this system are the orthogonal eigenstates up |+ anddown |− 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:
⎤

⎡
L=

1 ⎢ Lz
⎣
2 L

−

L+ ⎥
⎦
−Lz

⎛

⎞

⎜|+⎟
ψ→⎝ ⎠
|−

(1.4)

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

1.1.2

Standard ModelIn the SM of particle physics the fundamental particles and interactions are describedby 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 thiscase the mediators of the strong force are called gluons and are represented as the4generator matrix, Ggluon :⎡⎛⎤⎢grr̄ grḡ grb̄ ⎥⎢⎥⎥Ggluon = ⎢
g
g
g
gr̄
gḡ
⎢
g b̄ ⎥⎣⎦
gbr̄ gbḡ gbb̄⎞⎜ red ⎟⎜⎟⎟
ψc → ⎜
green
⎜
⎟
⎝
⎠
blue

(1.5)

where gbb̄ = grr̄ − ggḡ .
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 , from the U(1)Y symmetry and isassigned 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 massless gauge bosons, W 1 , W 2 , W 3 from SU(2)L and B from U(1)Y . However this isinconsistent with the experimental observation of three massive gauge bosons, W ±and Z 0 that mediate the weak interaction and the massless photon, A, that mediates
the electromagnetic force. One method to resolve this issue is to spontaneously breakthe SU(2)L ⊗ U(1)Y gauge symmetry via the Higgs mechanism by introduction ofa scalar particle known as the Higgs boson. This generates mass for the W ± andZ 0 bosons which are formed from the massless gauge bosons parameterized by the
Weinberg mixing angle θw as:
Z 0 = W 3 cos θw − B sin θw(1.7)

A = W 3 sin θw + B cos θw

(1.8)

5

Although the SM is a very successful theory, it does not represent a complete theoryof 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 interactions 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 theSU(5) group, the smallest gauge group that can contain the SU(3)c ⊗SU(2)L ⊗U(1)Ygroup of the SM [4]. The generators of this group are written as:
⎡
⎢
⎢
⎢
⎢
⎢
VSU (5) = ⎢
⎢
⎢
⎢
⎢
⎣

⎤

grr̄ − √230 B

grḡ

grb̄

X1

Y1

ggr̄

ggḡ − √230 B

ggb̄

X2

Y2

gbr̄

gbḡ

gbb̄ − √230 B

X3

Y3

X̄1

X̄2

X̄3

√1 W 3 + √3 B
2
30

W+

Ȳ1

Ȳ2

Ȳ3

W−

− √12 W 3 + √330 B

⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(1.9)

6

with the fermions contained in 5̄ and 10 representations as:
⎛

d¯r

⎞

⎟
⎜
⎟
⎜
⎜ d¯g ⎟⎟⎜⎟⎜⎟¯
5̄ = ⎜
d
b
⎟
⎜
⎟
⎜
⎜ −⎟
⎜e ⎟
⎠
⎝
−νe

L

⎤

⎡
ūb −ūg
⎢ 0
⎢
⎢ −ū
0
ūr
⎢
b
⎢
⎢
10 = ⎢ ūg −ūr
0
⎢
⎢
⎢ ur
ug
ub
⎢
⎣
dr
dg
db

−ur −dr ⎥⎥−ug −dg ⎥⎥⎥⎥−ub −db ⎥
⎥
⎥
0
e+ ⎥
⎥
⎦
−e+ 0

(1.10)L

The gcc̄ are the gluons of SU(3)c , the W ± , W 3 and B are the gauge bosons of theelectroweak theory of the SM. In this GUT there are twelve new bosons X and Y
with mass MX,Y ∼ 1015 GeV, the GUT energy scale, which do not appear in thestandard model. These bosons have both color and ﬂavor and mediate interactions
between the leptons and quarks. These interactions, whose Feynman diagrams areillustrated 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 newbosons with a lifetime proportional to:
τ∼

MX4
2
αGUT
m5p
1

(1.11)

where αGUT is the value of the coupling constant at the GUT scale.
The favored decay mode for SU(5) is p → e+ π 0 with a calculated partial lifetimeof τ /Bp→eπ0 = 3.7 × 1029±0.7 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
measured by experiment of sin2 θW = 0.23108 ± 0.00005 [7] is inconsistent with thepredicted value of sin2 θW = 0.21020.0037−0.0031 [8].

7

e+ uα

dα

e+ dα

Xα

Yα

ūγ

uβ
Xα

ν̄
Yα

ūγ

dβ
Yα

Figure 1.1: Feynman diagrams representing the interactions mediated by the X α &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-weakHiggs boson of m2H ∼ (250 GeV)2 , the radiative corrections introduce an enormouscorrection ∼ 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 introductionof a symmetry between fermions and bosons known as SUSY. In SUSY every fermionof the SM gets a bosonic partner with the same mass but spin 1/2 diﬀerent and viceversa. 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 theexperimental lifetime limits on p → e+ π 0 . Furthermore, in SUSY GUTs the pre+0.0031
which is consistent withdiction of the weak mixing angle is sin2 θW = 0.2334−0.0027

experimental data [8].
Although the p → e+ π 0 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 theﬁrst family this means that interactions involving this operator require quarks fromthe second or third families. As the strange quark is the only one that is kinematicallyallowed, an anti-strange quark must be in the ﬁnal state. This will bind to a spectatoru or d quark forming a K meson. In minimal SU(5) SUSY, the favored decay modes
are therefore p → ν̄K + shown in Figure 1.3 and n → ν̄K 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
based on the SO(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 → ν̄K + and p → μ+ K 0
of [2]:
Γ(p → μ+ K 0 ) ≈ (20% to 50%) Γ(p → ν̄K + )(1.12)

Given (1.12) and the predicted lifetime of p → ν̄K + of ∼ 1032∼34 years the expected
lifetime of p → μ+ K 0 is:τ /Bp→μ+ K 0 ∼ 1033∼35 years
which is within reach of the SK sensitivity of ∼ 1033 years.

(1.13)

9
q̃
q

l
W̃

H̃

q

q
q̃

Figure 1.2: Feynman diagram representing the exchange of a Higgsino from the d=5
operator in the SUSY GUT Lagrangian.
d̃

u
p

W̃
d

ν̄μ
H̃

ũ

u

s̄
K+
u

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

1.2

Past Experimental Measurements of p → μ+K 0

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 5.9 kt-yr. This
experiment searched both p → μ+ KS0 and p → μ+ KL0 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+ K 0 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 detector 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+ K 0 of

10
1.2 × 1032 years [11] by searching only the p → μ+ KS0 mode.

1.2.3

Kamiokande

The Kamiokande experiment was the precursor to the Super Kamiokande (SK) experiment 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-multipliertubes (PMT) resulting in 20% photocathode coverage. It took data from 1986-1996.
This experiment set a lower lifetime limit on p → μ+ K 0 of 1.2 × 1032 years [12] bysearching only the p → μ+ KS0 mode.

1.2.4

Super Kamiokande

The current best lower lifetime limit on p → μ+ K 0 is 1.3 × 1033 years by Kobayashi
set using the SK-I data set searching the p → μ+ KS0 mode only [1]. Currently, there
is no published result using p → μ+ KL0 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.
The K 0 is a combination of 50% KS0 and 50% KL0 so searches for p → μ+ K 0
typically involve searching for p → μ+ KS0 and p → μ+ KL0 separately.
For this thesis, we search for p → μ+ K 0 in SK-I data by updating the p →μ+ KS0 mode search performed by Kobayashi [1]. We use the latest improved detector
calibration and event reconstruction, use a new combined search analysis strategy

11
described in section 6.2 and introduce a new search of p → μ+ KL0 described in Chapter
10.
The lifetime of the KS0 is 0.9 ns; kinematically in water the KS0 nearly always
decays. The KS0 decay modes along with their respective branching ratios are summarized in Table 1.1 [7].
For the search of p → μ+ KS0 in this thesis, an exclusive search is performed for the
KS0 → π 0 π 0 and KS0 → π + π − decay modes only; the remaining fraction is neglected.
The decay of the proton via p → μ+ KL0 provides a unique event signature dueto the much longer lifetime of the KL0 of 51 ns. Because of this, events from thisproton decay mode are characterized by two vertices that are separated in time andspace within the detector; typically ∼ 20 ns and ∼ 2 m respectively for KL0 decay.
The primary vertex is located at the proton decay point the remaining vertex is thelocation of the KL0 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.
In addition to decaying, the KL0 can hadronically interact in the water in ﬂight.
Additionally, the KL0 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+ K 0 monte-carlo (MC) and SK detector
simulation described in sections 3.1 and 3.4 respectively, the branching fraction wasdetermined for these kinematic processes and summarized in Table 1.2. We perform
an inclusive search of p → μ+ KL0 which is independent of the KL0 kinematic process.
In this thesis we present the results of a proton decay search via p → μ+ K 0 in
the SK detector using the combined results of p → μ+ KS0 and p → μ+ KL0 searches.
The presentation begins in Chapter 2 with a description of the SK detector, dataacquisition 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.
KS0 decay mode

Branching ratio Γ (%)

KS0 → π + π −KS0 → π 0 π 0
KS0 → other

69.2
30.7
0.1
Table 1.1: KS0 decay branching ratios.

13

KL0 kinematic process in water
KL0 N → N, α, 2H, 3H
KL0 N → NK ±KL0 p → π + Λ0
KL0 p → π 0 Σ+
KL0 p → π + Σ0KL0 n → π − Σ+
KL0 n → π + Σ−
KL0 n → π 0 Σ0KL0 n → π 0 Λ0KL0 N → other

16.5
15.7
10.4
5.8
5.8
5.5
5.1
3.6
2.2
1.6

KL0 → π ± e∓ ν
KL0 → π ± μ∓ ν
KL0 → 3π 0
KL0 → π + π − π 0

11.1
7.0
5.7
3.7

KL → KS regeneration

0.1

KL0 → other

0.2

KL0 → interaction
72.2%

KL0 → decay
27.5%

Branching ratio Γ (%)

Table 1.2: KL0 kinematics in water.

Chapter 2
Detector
2.1

Cherenkov Radiation

When a charged particle of mass, m, and momentum, p, travels faster than lightin 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, arerelated by the following:11=
cos θc =
nβ
n

1+

m2
p2

(2.1)

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 :pthresh = √14mn2 − 1(2.2)

15

Figure 2.1: Relative Cherenkov light spectrum in pure water. For comparison thequantum 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:


1
1
d2 N
= 2πα 1 −2dxdλ(nβ) λ2(2.3)

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 acharged particle traveling close to the speed of light (β1) in water (n1.34) 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 kinematicsof 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 41.4 m inheight and 39.3 m in diameter ﬁlled with 50 kt of ultra-puriﬁed water. Within thetank, 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 heightand 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 andremaining tank volume.
The outer-most volume is known as the Outer Detector (OD); it completely surrounds the ID and has a thickness of 1.95 m to 2.2 m. Mounted to the outer wallof 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 ofobservation, a period known as SK-I, the data taking was stopped for maintenanceof the detector. In November, 2001 during the reﬁlling of the detector after the
maintenance work, an accident occurred in which an ID PMT at the bottom region

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 theaccident 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 preparationof the T2K experiment. From the completion of the upgrade in October, 2008 throughthe 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 searchusing 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 creatinga gain of 107 .
The OD PMTs are Hamamatsu R1408 PMTs with a 20 cm diameter photocathode. An acrylic wavelength shifting plate of 60 cm × 60 cm doped with 50 mg l−1 ofbis-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 eﬃciency 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 thatpasses 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

Quantum efficiency

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

0.2

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. equivalentsignals. 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. Withineach 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. PMTSUM 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 to0.25 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 digitization 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 andmerged 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 digitalconversion (TDC) module. This TDC module has a dynamic range of 16 s with aresolution 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 threetriggers: High Energy (HE), Low Energy (LE) and Super Low Energy (SLE) thatare 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 expectedfrom 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 notused 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 PMTSCHATMinterface
Ultra Sparc

x 20
x 240

SMP

ATM

SMP

GONG

online CPU(slave)

SMP
SMP
SMP
SMP

x6

Super Memory Partner

VME
20-inch PMT
SCHUltra Sparc

ATM

online CPU(slave)

x 20
x 240

Ultra Sparc

ATM
GONG

online CPU(host)

Analog Timing Module

online CPU(slave)
TKO

FDDI

Ultra Sparc

Ultra sparc

online CPU(slave)
Ultra Sparc

online CPU(slave)
Ultra Sparc

FDDI

online CPU(slave)
Ultra Sparc

online CPU(slave)

online CPU(slave)interface
Ultra Sparc
SMP
SMP

Ultra Sparc

online CPU(slave)

SMP
SMP
SMP
SMP

interface

Super Memory Partner

VME
VME

interrupt reg.
TRG

20-inch PMT
SCH
TRIGGERATM

TRIGGER

x 20
x 240

PROCESSORHIT INFORMATION
ATM
GONG

Analog Timing ModuleTKO

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 andevent 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 sophisticatedwater system shown schematically in Figure 2.7. The SK water system consists ofeight stages in the order as follows:
1. 1 m 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 numberof particles larger than 0.2 m is reduced to 6 particles/cm3 , the light attenuation
length is ∼ 100 m and the resistivity of the water is increased from about 11 MΩ cm
to an average of 18.2 MΩ cm.

24

VACUUM
DEGASIFIERCARTRIDGE
POLISHERPUMPULTRA MEMBRANEFILTER DEGASIFIERUVSTERILIZERFILTER(1μm Nom.)HEAT
EXCHANGER

PUMP
HEAT
EXCHANGERPUMP

BUFFERTANK

REVERSEOSMOSIS

PUMP
RN-LESS-AIR

RN-LESS-AIR
DISSOLVE TANKREVERSEOSMOSISSK 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 isnecessary 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 thresholdearlier 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 gelmaterial 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 ballto 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
filterSuper Kamiokande
inner tank970

N 2 laser
generator
λ=384nm

960

monitor
PMT

940

sig.

20’PMT

Log Scale930
920

diffuserball
trigger
elec.

910

sig.

900

sig.

diffuser tip(TiO2 )LUDOXLinear Scale

950

T (nsec)

optical fiber

optical fiber

20’PMT

sig.

890
DAQ
elec.

880
1

5

10

100

Q (p.e.)(a)(b)

Figure 2.8: (a) Schematic of the timing calibration system. (b) TQ-map, a timingvs. 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 thedetected 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 isadjusted 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 intoa scintillator ball located within the detector via optical ﬁber. The scintillator ball isUV filter ND filter
Xe Flash Lamp

Photo
Diode

SK TANK

Photo
Diode

Optical fiber

ADC

Scintilator Ball
PMT

1400

1200

σgain = 7.0%
1000

800

600

400

200

Scintilator
Monitor20inchPMT

Number of PMTs in Each Bin

26

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Relative PMT Gain

Trigger(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 peakwavelength 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 , of the i-th PMT is given by:
Qi 2
l exp
Gi =
Q0 f (θ) i

 
li
L

(2.4)

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

5103Ni wire+water

200mm
Cf

2

1

0

0

190mm
(a)

pC

(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 252 Cf 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 theintensity 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 throughgoing 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 thenormal 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 ) of the muon:(A) 50000 < total number of p.e. < 125000(B) rin ≡
2x2in + yin< 15.9 m, zin > 18.1 m(C) rout ≡
(D)





2
x2out + yout
< 15.9 m, zout < −18.1 m(xin − xout )2 + (yin − yout )2 < 5 m

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 thisevent selection, the corrected p.e., qcorr , at each PMT is calculated as:
qcorr = Q × l ×

1
f (θ)

(2.5)

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
qcorr (l) = G × exp −
L

(2.6)

log(Ql/f( θ))

30

500

RUN 3106

P1
P2

5.987
-0.9487E-04

1000

2000

3000

0.4609E-03
0.4444E-06

400
300
200
0

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 detectedin 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 isused:(A) The time interval from the stopping muon event is 1.5 s to 8.0 s.
(B) The number of hit PMT in a 50 ns time window is larger than 60.

Events

31

225
200
175
150
125
100
75
50
25
0

0

10

20

30

40

50

60

70

80

MOMENTUM (MeV/c)

Figure 2.13: Momentum distribution for decay electrons for data (point) and MC(line).
(C) The goodness of the vertex ﬁt is greater than 0.5.
(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 theprediction from the MC. In the MC the measured μ+ /μ− ratio of 1.37 [16] is usedand μ− capture in the oxygen nucleus is also taken into account. The mean values ofthe data agree with the MC within 0.6%.
2.6.5.2

Neutrino Induced π 0 Events

Atmospheric neutrino events that generate π 0 are used to calibrate the energy scalein the few hundred MeV range. A π 0 will immediately decay into two gammas fromwhich the invariant π 0 mass, Mπ0 , can be determined via:Mπ0 =2Pγ1 Pγ2 (1 − cos θ)(2.7)

Where Pγ1 , Pγ2 and θ are the reconstructed momentum and opening angle between the
gammas respectively. To select π 0 events, the following selection criteria is applied:32

Number of E vents

140
120
100
80
60
40
20
0

0

50

100
150
200
250
2
π0 invariant mass (MeV/c )300

Figure 2.14: Invariant mass distribution of neutrino induced π 0 events for data (point)
and MC (box).
(A) Two electron-like rings.
(B) The number of decay electron = 0.
(C) The vertex position is reconstructed more than 2 m away from the ID wall.
Criterion (B) rejects contamination to the sample from π ± π 0 or μ± π 0 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 π 0 , 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 theCherenkov ring opening angle, θ, on the muon momentum, pμ . Because |dθ/dpμ | islarge for small pμ this calibration method is possible in the low momentum region ofpμ  500 MeV/c. The criteria for selecting cosmic ray muons for this calibration are:(A) Total p.e. < 1500.

33

DATA

Monte Carlo500

reconst. momemtum (MeV/c)reconst. momemtum (MeV/c)

500
450
400
350
300
250
200

450
400
350
300
250
200

30

32

34

36

38

40

42

44

30

32

34

36

38

40

opening angle (deg.)

opening angle (deg.)(a) Data(b) MC

42

44

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.
(C) The entrance point is on the top wall.
(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. Criterion (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. fromthe data and MC. The energy scale of the data is compared to the MC using the ratio
Pp.e. /Pθ , where Pp.e. is the momentum estimated from the observed charge and Pθ
is the momentum estimated from the Cherenkov angle. Figure 2.16 shows the averaged 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%.

P(p.e.)/P(θ)

34
1.4
1.3
1.2
1.1
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 fromthe 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 raymuons for the calibration are:(B) The entrance point is on the top wall.
(C) The direction is downward (cos θzenith > 0.94).
(D) One decay electron.
(E) Reconstructed muon range > 7 m.
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 theratio of momentum/range as a function of the range for data and MC. The energyMomentum(MeV/c)/Range(cm)

35
2.6

2.5

2.4

2.3

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 variationof 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 ofdetector uniformity since their vertex and direction are nearly uniform in locationand direction within the ﬁducial volume (FV). To avoid bias from muon polarization,
only electrons whose direction is perpendicular to the parent muon are used. Thisis 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 ofdata 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 angleof 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 uncertainly 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.

(MC - DATA) / DATA (%)

SK-I
8
6
4
2
0
-2

μ rangeμ angle0π massdecaye

-4
-6
-8
10

10

2

10

3

10

4

momentum range (MeV/c)

105Figure 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 anddetector 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 (H2 O) 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+ K 0 decay products can be uniquelydetermined. The direction of the μ+ and K 0 is opposite each other each with amomentum 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 andKL0 →KS0 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 12 C 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-12 C
scattering [17]. Figure 3.1 shows the Fermi momentum distribution of the 1s stateand 1p state for the experimental data. The theoretical calculation shown in theﬁgure is used in our simulation.
Nuclear binding energy is taken into account by modifying the proton mass. The
modiﬁed proton mass, mp , is calculated by mp = mp − Eb where mp is the proton rest
mass and Eb is the nuclear binding energy. The measured nuclear binding energy is
39.0 MeV/c2 and 15.5 MeV/c2 for the 1s and 2p states respectively.
Ten percent of decaying protons have wavefunctions that are correlated with othernucleons 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 16 O used in the p → μ+ K 0 simulation. Correlated decays produce thebroad spectrum below ∼ 850 MeV/c2 shown by the hatched region.

number of events

40

10

4

10

3

10

2

10
0

200

400
+

0

600

μ K invariant mass in

800
16

O

1000
2
MeV/c

Figure 3.2: Invariant mass of μ+ K 0 in the p → μ+ K 0 MC simulation in water (solidline). 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 16 O is calculated according to the Wood-saxon
nuclear density model, ρp (r), which is expressed as [19]:ρp (r) =ρ0Z
A 1 + exp( r−c
)
a

(3.1)

where r is the distance from the center of the nucleus, ρ0 = 0.48m3π is the averagenuclear density, 2a = 0.82 fm is the thickness of the nuclear surface and c = 2.69 fm
is the average nuclear radius for 16 O.
The kaon nucleon interactions that are considered include elastic scattering andinelastic 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
cross-sections using the results of KS0 and K̄ 0 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:pF (r) = 

3π 2
ρ(r)
2


(3.2)

where ρ(r) is the same as (3.1)

3.1.3

KL0 →KS0 Regeneration in the Oxygen Nucleus

Neutral kaons consist of a down quark and strange quark. There are four types ofneutral kaons K 0 (S=+1), K̄ 0 (S=-1) which are the eigenstates of strangeness andKL0 , KS0 which are the weak eigenstates. They are related by the following:
KL0 =K 0 − K̄ 0
√
2

KS0 =

K 0 + K̄ 0
√
2

(3.3)

Since strong interactions conserve strangeness, there are more strong interactions
available for K̄ 0 than for K 0 . Therefore, when a KL0 propagates through a material,
the K 0 and K̄ 0 components interact at diﬀerent rates with the material which introduces a KS0 component in the original KL0 . It is therefore possible to observe a
KS0 after the original KL0 has propagated some distance through a material. This is
known as KL0 →KS0 regeneration.
KL0 →KS0 regeneration in the oxygen nucleus is modeled in the simulation as a
decay channel of the KL0 that is parameterized by a regeneration lifetime in the oxygen
nucleus, τRnucl. ; a tunable parameter that aﬀects the probability of regeneration. We
assume τRnucl. is related to τRH2 O (see section 3.4.3) by:
τRnucl. = τRH2 O

ρnucl.
ρH2 O

(3.4)

Where ρnucl. = 3.7 × 1017 kg m−3 is the density of the oxygen nucleus and ρH2 O =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 ofirreducible background for a search of proton decay. To estimate this background theatmospheric neutrino ﬂux and interactions are simulated. In our simulation of theatmospheric 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 primarycosmic 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 twotheoretical 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 shownin Figure 3.4 with the predictions of G. Battistoni et. al. [27] (Fluka ﬂux) and G. Barret. 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 primarycosmic ray ﬂux and cosmic ray interactions.

43νμ + νμ102νe + νe2−2

Flux*Eν (m sec −1sr −1GeV)

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).

Honda flux

10

Fluka flux
Bartol flux

1 −1
10

1

10

10
Eν (GeV)2

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 aredescribed 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]:
2
M 2 G2F cos2 θC
dσ ν(ν̄)22 s−u
2 (s − u)=+ C(q )A(q ) ∓ B(q )
dq 2
8πEν2
M2
M4

(3.5)

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 − q 2
q2
q2
2
A(q ) =
4 − 2 |FA | − 4 + 2 |FV1 |2
2
4M
M
M


2
2
2 1
q
q
4q FV ξFV2
− 2 |ξFV2 |2 1 +
−
M
4M 2
M2


m2 
− 2 (FV1 + ξFV2 )2 + |FA |2
M
2 

q
B(q 2 ) = 2 FA (FV1 + ξFV2 )
M

1
q2
2
2
1 2
2 2
|ξFV |C(q ) =
|FA | + |FV | −
4
4M 2
2

(3.6)
(3.7)
(3.8)

where m is the charged lepton mass and ξ ≡ μp − μn = 3.71. The vector form factors,
FV1 (q 2 ) and FV2 (q 2 ), and the axial form factor, FA (q 2 ) are determined experimentallyand given by:


−1 
q2
q2
2
2
1−
GM (q )GE (q ) −
4M 2
4M 2
−1



q2
2 2
2
2
G
ξFV (q ) = 1 −
(q
)
−
G
(q
)
E
M
4M 2

−2
q2
2
FA (q ) = − 1.23 1 − 2MA 2 −2q2−1
2
GE (q ) =(1 + ξ) GM (q ) =MV2
FV1 (q 2 ) =(3.9)(3.10)(3.11)(3.12)

where GE and GM are the electric and magnetic form factor, the vector mass MV is
set to be 0.84 GeV/c2 and the axial vector mass MA is set to be 1.21 GeV/c2 , 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 16 O [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, theFermi surface momentum is set to be 225 MeV/c.

ANL
BNL
SKAT

-

Serpukhov
GGM (1977)
GGM (1979)2cm )(a) νμn→μ p

-38

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

σ (10

σ (10-38 cm2)

46

0

2

4

6
8
10
Eν (GeV)

12

14

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

–

GGM (1977)
GGM (1979)
Serpukhov
SKAT+(b) νμp→μ n

0

2

(a) ν

4

6
8
10
Eν (GeV)

1214(b) ν̄

Figure 3.5: Crosssections of (a) ν and (b) ν̄ 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 thefollowing relations [46, 47]:σ(νp → νp) = 0.153 × σ(νn → e− p)(3.13)σ(ν̄p → ν̄p) = 0.218 × σ(ν̄n → e+ n)(3.14)σ(νn → νn) = 1.5 × σ(νp → νp)(3.15)σ(ν̄n → ν̄n) = 1.0 × σ(ν̄p → ν̄p)

(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, and η was simulated based on themodel of Rein & Sehgal [55]. An intermediate baryon resonance is assumed in thismethod: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 ofeach resonance production and the probability of their baryon resonance decay tothe meson. For a baryon resonance with a negligible decay width, the diﬀerential
cross-section is:
1
1 
d2 σ
=
×
|T (νN → lNj∗ )|2 δ(W 2 − Mj2 )22
dq dEν
32πMEν
2 j,spin(3.19)

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 resonanceproduction, which is calculated using the Feynman-Kislinger-Ravndal model [56]. The
invariant mass, W , is restricted to be less than 2 GeV/c2 . For W > 2 GeV/c2 , theinteractions 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 bederived by replacing the δ-function with a Breit-Wigner factor:δ(W 2 − Mj2 ) →Γ
1×
2π (W − MJ )2 + Γ2 /4(3.20)For a single meson production, the axial vector mass MA is also set to be 1.21 GeV/c2 .
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 16 O nuclei, where about 20% of theevents 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

σ(ν μ )(10

−38

cm2)

νμ p → μ− p π+

1.2σ(ν μ )(10

−38

cm2)

48

1
0.8

1
0.9

νμ n → μ− n π+

0.8
0.7
0.6
0.5

0.6

0.4
0.4

0.3
0.2

0.2

0.1
0

1

−

σ(ν μ )(10

−38

cm2)

(a) νµ p → μ pπ
1
0.9

0

10

1

Eν (GeV)+

10−(b) νµ n → μ nπ

νμ n → μ− p π0

Eν (GeV)+ANL Radecky, Phys.Rev.D 25, 1161 (1982)

0.8

ANL Campbell, Phys.Rev.Lett. 30, 225 (1973)

0.7

ANL Barish, Phys.Rev.D 19, 2521 (1979)

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

−

(c) νµ n → μ pπEν (GeV)(d) List of experiments

0

Figure 3.6: Cross-sections for charged current single pion productions of νμ . Solidlines 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 integrating the following equation in the range of the invariant mass W > 1.3 GeV/c2 [58]:yG2F MN Eν
y2d2 σ ν,ν̄
22=(1 − y ++ C1 )F2 (x, q ) ± (1 − + C2 )xF3 (x, q ) (3.21)
dxdy
π
2
2
2
2
2
xyMN
yMl
m
ml
−
(3.22)− l2 −C1 =4MN Eν x
2En
4Eν
2MN Eν x
m2l
C2 = −(3.23)
4MN Eν x

49
where x(= −q 2 /(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 energyof 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
⎪
⎪
⎪
⎨
σ(νN → νX)= 0.26 + 0.04(Eν /3 − 1)σ(νN → μ− X) ⎪
⎪
⎪
⎪
⎪
⎪
⎩0.30
⎧
⎪
⎪
⎪0.39
⎪
⎪
⎪
⎨
σ(ν̄N → ν̄X)
= 0.39 − 0.02(Eν /3 − 1)σ(ν̄N → μ+ X) ⎪
⎪
⎪
⎪
⎪
⎪
⎩0.37

(Eν < 3 GeV)
(3 GeV ≤ Eν < 6 GeV)

(3.24)(Eν ≥ 6 GeV)(Eν < 3 GeV)
(3 GeV ≤ Eν < 6 GeV)

(3.25)(Eν ≥ 6 GeV)

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 isused only for events with W > 2.0 GeV/c2 . This package treats not only π but othermesons such as K, η and ρ. In the region of 1.3 GeV/c2 < W < 2.0 GeV/c2 , only
pions are considered as outgoing mesons. The mean multiplicity of pions is estimatedfrom the result of a Fermilab 15-foot hydrogen bubble chamber experiment [62] :nπ  = 0.09 + 1.83 ln W 2(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

σ/Eν (10-38cm2 GeV-1)

50

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

GRV94LOGRV94LO (w/ B-Y corr.)
GRV98LO
GRV98LO (w/ B-Y corr.)

CCFR 90
CDHSW 87
GGM-PS 79

0

10

CHARM 88
BNL 80
CRS 8020

BEBC-WBB 79
IHEP-JINR 96
IHEP-ITEP 79

CCFRR 84
SKAT

100

200

30 50

150

250

Eν (GeV)Figure 3.7: cross-sections for charged current νμ and ν¯μ interactions. Upper(lower)lines are νμ (ν¯μ )in the hadronic center of mass system is included using the results from the BEBC
experiment [63]:nFπ0.35 + 0.41 ln(W 2 )=nB
0.5 + 0.09 ln(W 2 )π(3.27)

The cross-section of the CC νμ and ν¯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, theangular 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51interactions, and the diﬀerential cross-section is given by:
G2 MN 2 2
d3 σ
1
πN 2
=β
×
(σtotalfπ A Eν (1 − y))22dQ dydt
2π
16π

2
MA2
2
× (1 + r )e−b|t| Fabs
MA2 + Q2
r =Re(fπN (0))/Im(fπN (0))(3.28)(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
is the averaged totaly(= (Eν − El )/Eν ) is the lepton fractional energy loss, σtotal

pion-nucleon cross-section, MA is the axial-vector mass, b = 80 GeV−2 is in the orderof 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 theabsorption of pions in the nucleus and is expressed as:
πN

Fabs = e− x σinel ρ(3.30)

where x is the average path length of the pion in the oxygen, ρ is the nuclear
πN
is the averaged total inelastic pion-nucleon cross-section. However,density and σinel

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σ (10-40cm2/Carbon Nucleous)σ(10-40cm2/Carbon Nucleous)

52

Rein and Sehgal

140

Kartavtsev et al.
120
100
80
60

250
225
200

CHARM(93)MiniBooNE(05)Aachen-Padova(83)Gargamelle(84)

175
150

Rein and Sehgal
Kartavtsev et al.

125
100
75

40

50
20
0

25
1

2

3

4

5

6

7

(a) CC8910Eν(GeV)

0 -1
10

1

10

10

2

Eν(GeV)(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 solidlines 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 16 O nuclei aretracked from their production points until they exit or are absorbed. This is done forπ, 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 > 1 GeV, and thepion-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

+ 16

cross section for π + O (mb)600
inela+abs+cex
inelastic
absorption
charge exchange

500
400

inela+abs+cex

300
200

inelastic

100

absorption

0

charge exchange

0

100

200

300

400

500

600

+

momentum of π (MeV/c)

Figure 3.9: cross-sections of π + -16 O scattering as a function of π + momentum. Solidlines 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 modelof Oset [71]. In the calculation, Fermi motion and Pauli blocking are considered.
In the case of inelastic scattering or charge exchange the direction and momentumof the pion are determined using the results of a phase shift analysis obtained frompion-nucleon scattering experiments [72]. The pion interaction model is tested using
the experimental results from the following interactions: π−12 C scattering, π−16 O
scattering, and pion photo-production (γ +12 C → π − + X) [73, 74] as shown in Figure 3.9. Absorption for η mesons (ηN → N ∗ → π(π)N) is also considered [75] withthe resulting pions tracked using the method described above.
Nucleon re-scattering is also considered using the cascade model. The consideredinteractions 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 througha detector simulation program. The detector simulation simulates the propagationof 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 scattering is dominant due to the λ−4 dependence. Photons are scattered symmetricallyin 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 treatedby a custom simulation program [79] based on experimental data of π-16 O 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.

3.4.3

KL0 →KS0 Regeneration in Water

KL0 →KS0 regeneration is modeled in the simulation as a decay channel of the KL0 thatis parameterized by a regeneration lifetime in water, τRH2 O ; a tunable parameter thataﬀects the probability of regeneration. The probability of regeneration in carbon is

-1

attenuation coefficient (m )

55

-1

10

Dec.-3,4-96
Dec.-17-96
Jan.-18-97

Dec.-14-96
Dec.-27-96
Mar.-6-97

total
absorption-2

10
Mie scattering
Rayleigh scattering-3

10

200 250 300 350 400 450 500 550 600 650 700
wavelength (nm)Figure 3.10: Wavelength dependence of photon attenuation coeﬃcients used in MC
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 theprobability of regeneration in water is the same as in carbon. We generate 400 MeV/cpure KL0 events in the detector simulation and tune τRH2 O such that the fraction
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 fromradioactive 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 ofthese 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(C) TDIFF> 100 s
TDIFF is the time interval from the previous event.
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 whichstop in the ID. Events within 30 s after another event selected by the above criteria
are retained to keep the decay electrons. These retained events are attached to thefully 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 andcosmic 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(C) NHITAin ≥ 10 or NHITAout ≥ 10
NHITAin (NHITAout ) is the number of hit OD PMTs located within 8 m fromthe 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
(ti − Ti )2
goodness = 
×
exp −
1
σi2
2(1.5 × σi )2
i
2
σi
i

(4.1)

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 sameas (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 thisoccurrence, 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 thefollowing criteria is applied:(A) One veto counter hit
AND(B) Lveto < 4 m
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 lightsource. Flashers are characterized by a hit timing distribution that is more broadthan neutrino events. To eliminate these, the following criteria is applied:(A) NMIN100 ≥ 14
OR(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 acosmic 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 andthe 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 andelectrical 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 missedby 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 tolook for these events with a similar pattern and remove them. The algorithm is thefollowing:(A) Divide the ID wall into 1450 patches of 2 m × 2 m square.
(B) Compute the correlation factor, r, by comparing the total charge in each patchof two events, A and B. The correlation is deﬁned as:

r=

A
B
B
1  (QAi − Q ) × (Qi − Q )
N i
σA × σB(4.2)

where N is the number of the patches, and QA(B)  and σA(B) are the averaged
charge and its standard deviation respectively for event A(B).
(C) Calculate the distance, DISTmax , between the PMTs with the maximum pulse
heights in the two compared events.
(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:B
rth = 0.168 × log10 ((PEA
tot + 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 andcount 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 thereconstructed 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(C) NHITACearly + NHITAC500 > 9 if DISTclust < 500 cm
NHITACearly> 9 otherwise

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.
(C) Dwall > 200 cm
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 ± 0.7 events/day.

Chapter 5
Event Reconstruction
After the event reduction steps described in Chapter 4, the event reconstruction isapplied 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 otheranalysis by the SK collaboration. The performance of the standard reconstruction issummarized in other documents [84, 85]. Second, is the multi-vertex reconstruction
algorithm which was developed speciﬁcally for the KL0 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 nonshowering type (from μ± , π ± , p). These showering and non-showering types arealso 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 areconsidered as fake rings.

5.1.1

VertexThere 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 basedon 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 timeof ﬂight subtracted) distribution is most peaked. The timing residual, ti , is calculatedas:ti = t0i −n(qi , li )
× |Pi − O|
c

(5.1)

 are the position of the i-th PMT
where t0i is the timing of the i-th PMT, Pi and O
and estimated vertex respectively. The index of refraction n(qi , li ) is a function of The goodness of thethe detected p.e., qi , and photon travel length, li = |Pi − O|.
point-ﬁt is deﬁned as:1 (ti − t0 )2
Gp =
exp −
N i
2(1.5 × σ)2(5.2)

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 ischosen 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 theparticle direction is determined as the charge weighted average of all PMTs:
d0 =


i

qi ×

0
Pi − O 0|
|Pi − O(5.3)

 0 is the vertex position determined by point
where d0 is the direction of the particle, O
ﬁt, qi and Pi 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

69histogram 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
d2 PE(θ) (B)=0d2 θ θedge

θpeak is the opening angle where PE(θ) is maximum.
the second derivative at θ = θedge should be zero.

If multiple θedge satisfy (A) and (B), then the θedge nearest θpeak is selected.
The ring direction is determined using the following estimator: θedgePE(θ)dθ0Q(θedge ) =sin θedge

×

!2



dPE(θ) (θedge − θexp )2
× exp −dθ θ=θedge
2σθ2

(5.4)

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 d0 found in point ﬁt. The ring directionand edge position are determined which maximize Q(θedge ).
5.1.1.3

TDC FitIn 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 , of the i-th PMT as:

ti =

⎧
⎪
⎪
 i − O| − n × |Pi − X
 i | for PMTs inside the Cherenkov ring⎨t0i − 1 × |X
c
c
⎪
⎪

⎩t0i − n × |Pi − O|cfor PMTs outside the Cherenkov ring(5.5)

 is the vertex position, X
 i is the position at which Cherenkov photons arewhere Oemitted toward the i-th PMT, n is the refractive index of water, Pi is the position
and t0i 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, theestimator GI is deﬁned:

GI =



(ti − t0 )2
exp −
σi2
2(1.5 × σ)2

 1
i

(5.6)

where σi is the timing resolution of the i-th PMT depending on the detected p.e.s, σis 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 
(ti − t0 )2
exp −
×2−1
GO1 =
2
2
σ
2(1.5
×
σ)
i
i

(for ti ≤ t0 )

(5.7)






 1
(ti − t0 )2(for ti > t0 )
GO2 =
max
exp
−
, Gscatt (ti , t0 ) × 2 − 1
σi22(1.5 × σ)2
i
(5.8)
where

 



Rq
(ti − t0 )2Rq
ti − t0
Gscatt (ti , t0 ) =× exp −
+ 1−
× exp −
(5.9)
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:GT =GI + (GO1 or GO2 )
 1
σi2
i

(5.10)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 theevent.
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 thatare 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 andΦ is the azimuthal angle as measured from the reconstructed vertex. The Houghtransform is performed by mapping the detected p.e. corrected for PMT acceptanceand 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 thismapping, 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 ringfound 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:

LN +1 =

i

log probqiobs ,

N
+1


!!
exp
αn · qi,n(5.11)

n=1

where the sum extends over hit PMTs inside N + 1 Cherenkov rings, qiobs is theexp
is the expected p.e.s in the i-th PMT
observed p.e.s in the i-th PMT and αn · qi,nfrom the n-th ring. The LN +1 is maximized by changing the αn scale factors with alower momentum limit constraint. The probability prob is deﬁned as:prob(qiobs , qiexp )⎧⎪(qiobs , qiexp )2⎪
1⎪√(for qiexp > 20 p.e.)
exp −
⎪
2
⎪
2σ
2πσ
⎪
⎪
⎪
⎪
⎪
⎨Probability obtained by the probability density⎪⎪⎪
distribution function based on the convolution of a (for qiexp < 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 , the numberof rings is determined to be N and the ring counting procedure is ﬁnished. For
ring candidates which satisfy LN +1 ≥ LN , the following evaluation functions arecalculated:
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 theCherenkov 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:

FSK−I =4[αi Fi ](5.13)

i=1

where αi are optimized weighting parameters. If FSK−I is positive, then the (N +1)-thring 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 thelower edge of the peak of the TOF subtracted hit timing distribution. This is doneusing 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 (elike) 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. Anotherdistinction 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 andopening 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: 1.5R
1
× f (Θi ) + qiscatt×(5.15)ri
exp(ri /L)⎛⎞
sin2 θxi
1# + qiknock ⎠ ×
qiexp (μ) = ⎝αμ × "× f (Θi ) + qiscattdθ 
exp(ri /L)r sin θ + r ·qiexp (e) = αe × Qexp (pe , θi ) ×

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 waterf (Θi ) : a correction of acceptance to the i-th PMT as a function of thephoton incidence angle Θi
R : radius of the virtual sphere (16.9 m)
Qexp (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.
qiscatt : 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
qiscatt , qiknock : 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 ). Theenergy loss of the muon is taken into account.
In the electron case, the (R/ri )1.5 term corrects for the distance dependence of theCherenkov 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 thearea where Cherenkov photons are emitted when the muon travels a distance dx.
5.1.3.2

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



!
exp
qi,n


(5.17)n =nwhere the product extends over PMTs inside the n-th ring. qiobs is the observedexp(e or μ) is the expected p.e.s from the n-th ring with thep.e.s in the i-th PMT, qi,nexp
assumption of an electron (5.15) or muon (5.16) and qi,n
 are the expected p.e.s fromthe n -th ring without any assumption of particle type. The function prob returns theprobability to detect qiobs in the i-th PMT when qiexp is expected (5.12). By changing
exp
exp
the direction and opening angle of the n-th ring, qi,n
 (e) and qi,n (μ) are optimized togive 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:
χ2n (e or μ) = −2 log Ln (e or μ) + constant(5.18)The probabilities from the ring pattern are:2

(χ2n (e or μ) − min[χ2n (e), χ2n (μ)])
patternPn(e or μ) = exp −2σχ2 2nwhere σχ2 2n =√!
(5.19)

2N and N is the number of PMTs used in the calculation.

The probabilities from Cherenkov opening angle are:
 obs
2 !
exp
θ
−
θ
(e
or
μ)
n
Pnangle (e or μ) = exp − n2(δθn )2

(5.20)

where θnobs and δθn are the reconstructed opening angle of the n-th ring and the ﬁtting
error respectively. θnexp (e or μ) is the expected opening angle of the n-th ring, whichis 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(e, μ) × Psingle(e, μ)
Psingle (e, μ) = Psingle(5.21)

pattern(e, μ)
Pmulti (e, μ) = Pmulti(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-likeand 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 thevertex 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 fromeach 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:
exp
qi,n
obs
obs
qi,n = qi × % expn qi,n(5.23)

obs
where qi,nis the fractional p.e.s assigned to the n-th ring, qiobs is the observed p.e.s
exp
is the expected p.e.s.
in the i-th PMT and qi,nThe 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:⎡
RTOTn =GMC ⎢⎢α ×
Gdata ⎣


θi,n <70◦−50ns<ti <250ns⎤

" r # cos Θ

⎥
i
i
obs
× exp
Si ⎥
qi,n
×
−
⎦
L
f (Θi )
θ <70◦
i,n(5.24)
where
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 waterf (Θi ) : a correction of acceptance to the i-th PMT as a function of thephoton incidence angle Θiri : 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 tothe 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:qiexp (e, μ) = Qexp
e,μ (p, θi ) × exp

R
LMC


×

1
× f (Θi ) + qiscattexp(ri /L)(5.25)

whereri : 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 MCf (Θi ) : a correction of acceptance to the i-th PMT as a function of thephoton incidence angle Θi
R : the radius of the virtual sphere (16.9 m)
Qexpe,μ (p, θi ) : expected p.e. distribution for e and μ on the virutal sphere as afunction of the momentum, p, and opening angle to the i-th PMT,
θiqiscatt : 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:
qiexp (e, μ) → α ×

qiexp (e, μ) +


j=i

!
βij qjexp (e, μ)(5.26)

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 #ij
βij = β × f (Θij ) × exp −L(5.27)

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 isdetermined via MC simulation.
The observed p.e.s for each PMT is estimated by maximizing the likelihood function L:L=θi ,nlog prob qi ,

<70◦



!!
αn · qiexp
 ·n(5.28)n

where qi is the observed p.e.s in the i -th PMT and qiexp
 ·n is the expected p.e.s in
the i -th PMT from the n -th ring, prob(qiobs , qiexp ) is given by (5.12) and αn is the
optimization parameter for each ring which is determined by scaling the expectedcharge pattern to reproduce the observed charge distribution.
The observed p.e.s in the i-th PMT from n-th ring is then:exp
αn · qi,nexp
n αn · qi,nobs= qiobs × %qi,n(5.29)

using the αn which maximizes L.
Typically, the momentum reconstruction for muons has a resolution of ∼ 2.8% [84]however, during this analysis an unknown pathology was found for p → μ+ KS0 MC
events when the muon momentum is ∼ 280 MeV/c. This behavior was investigatedby the use of three control samples consisting of μ+ and π 0 back to back with ﬁxed
vertex and momentum. The three samples are:
1. one μ+ , pμ = 459 MeV/c; one π 0 , pπ0 = 459 MeV/c

81

entries

FCFV, 3≤nring≤5, 1 μ-like
100
75

44.52
Constant
Mean
Sigma

SAMPLE #1

50

/ 36
82.31
4.730
11.29

25

entries

0
-60

-40

-20
0
20
40
60
reconstructed-true μ momentum (MeV/c)
38.65

100

Constant
Mean
Sigma

SAMPLE #2

/ 28
121.6
-16.848.420

50

entries

0
-60

-40

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

100
75

27.13
SAMPLE #3

Constant
Mean
Sigma

50

chisq/ndf=1.6
mean=13.0
sigma=8.7

25
0
-60

/ 21
81.62
-26.69
8.958

-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.
pμ and pπ0 are the same as in p → μ+ π 0 decay.
2. one μ+ , pμ = 280 MeV/c; one π 0 , pπ0 = 274 MeV/c
pπ0 is the same as KS0 → π 0 π 0 decay with pKS0 = 280 MeV/c.
3. one μ+ , pμ = 280 MeV/c; two π 0 , pπ10 = 274 MeV/c, pπ20 = 270 MeV/c
pπ0 is the same as KS0 → π 0 π 0 decay with pKS0 = 280 MeV/c.
The standard event reconstruction was applied to these samples. Figure 5.1 shows thereconstructed-true muon momentum for these three control samples. The resolutionof the ﬁrst sample is ∼ 2% which is consistent with the performance of p → μ+ π 0 [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 difﬁcult 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:Lπ = log





obs 2
1
(Qexp
(θnexp (pπ ) − θnobs )21n (pπ ) − Qn )
exp −
exp −
×
(5.30)
σq
2σq2
σθ
2σθ2

where
pπ : the charged pion momentum
exp
Qexp
n (pπ ), θn (pπ ) : the expected p.e.s and opening angle respectively for the n-th ringas a function of the pion momentum
obs
Qobs
n , θn : the observed p.e.s and opening angle respectively

σq , σθ : the error of the expected p.e.s and opening angle respectively
The function for expected p.e.s, Qexpn (pπ ), was determined by MC simulation.

5.1.6

Decay Electron SearchElectrons 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 subevent.

83

We require the following criteria for sub-event type events:(A) The time interval from the primary event, Δt, is less than 20 s.
(B) Total number of hit PMTs is greater than 50.
(C) The goodness of vertex ﬁt is greater than 0.5.
(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 morethan 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 forprimary-event type and split type(H) 0.1 s < Δt < 0.8 s OR 1.2 s < Δt < 20 s
N50 = 60 corresponds to ∼ 11 MeV/c of electron energy. The gamma emission fromμ− captured on 16 O nuclei is rejected by criteria (A). Events that occur near the endof the primary event timing window are rejected by criteria (H). The eﬃciency ofdetecting 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 toremove mis-reconstructed rings. The criteria to remove the i-th ring are:(A1) pi < pj ; i = j
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
OR(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
reconstructed. However, for a search of p → μ+ KL0 one of the deﬁning characteristics
is that there is a separation between the vertex corresponding to the proton decay
and the KL0 decay or interaction point. Because of this, a new event reconstruction
algorithm is necessary to properly reconstruct these types of events.
The momentum of the primary μ from p → μ+ KL0 is typically monochromaticnear 326.5 MeV/c, well above the Cherenkov threshold. Typically, the KL0 interacts
in the water as it propagates or it may decay via one of the decay modes described inTable 1.2. Depending on whether the KL0 decays or interacts determines the number
and kinematics of the ﬁnal state particles. These particles may be near the Cherenkov
threshold.
Based upon these kinematics of p → μ+ KL0 , 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 describedin section 5.1 modiﬁed by the removal of timing cuts to account for rings withlate timing caused by KL0 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 andother 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 areprocessed, the μ-candidate is deﬁned as the μ-like ring with a momentum nearest
326.5 MeV/c.
The use of timing only for remaining vertex is based on the assumption that the ﬁnal
state particles from the KL0 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 arecaused by KL0 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86existing 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 thelong lifetime of the KL0 which may cause a time diﬀerence of up to ∼ 300 ns between
the PMTs hit from the primary muon and those hit from the KL0 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 usinga PMT masking algorithm. The masking area is deﬁned as the region of PMTs thatsatisfy the following condition:&(P − xi ) · D
θc + 10◦ > arccos
|P − xi ||D|'(5.31)

 is theWhere xi is the coordinate of the i-th PMT, P is the reconstructed vertex, Ddirection 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 tailof 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

VertexThe 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
μ-candidate found in step (G) using both the p → μ+ KL0 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 projectedalong the true μ-candidate direction.
Figure 5.2a shows the ΔV distribution for the p → μ+ KL0 MC sample. The
mean is −77.5 ± 0.7 cm with a resolution (1σ) of 156 cm. Figure 5.2b shows themean (upper ﬁgure) and resolution (lower ﬁgure) of ΔV vs. L, where L is the true
separation between the proton decay point and the point where the KL0 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 themasked 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 andpattern information. The performance of the PID is checked using the p → μ+ KL0
MC sample. Figure 5.4 shows the PID likelihood distribution for the true primaryV|| mean (cm)entries88

3000
p→μKL0 MC
KL→any decay

2500

KL→int.
Other

2000

100
80
60
40
20
0
-20
-40
-60
-80
-100

p→μKL0 MC

0

200

400

600

800

1000

1200

V|| resolution (cm)

1500

1000

500

0
-1000 -750

-500

-250

0

250

500

μ candidate vertex

750 1000
V|| (cm)

200
180
160
140
120
100
80
60
40
20
0

1400
L (cm)

p→μKL0 MC

0

200

400

600

800

1000

μ candidate vertex

(a)

1200

1400
L (cm)(b)entriesFigure 5.2: Performance of the initial vertex ﬁtting of the μ-candidate for p → μ+ KL0
MC. (a) The ΔV distribution. Hatched regions show contribution from KL0 decay
and interaction. (b) The mean and resolution of ΔV vs. L. The statistical error of
the mean is shown.

700

ATM-ν MCCC QE
CC single-π

600

CC multi-π
NC
Other

500

400

300

200

100

0
-1000 -750

-500

-250

0

250

μ candidate vertex

500

750 1000
V|| (cm)

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.

entries

89

14000

p→μKL0 MC
KL→any decay
KL→int.

12000

Other

10000
8000
6000
4000
2000
0

-10

-8

-6

-4

-2

0

2

4

6

PID

8
10
likelihood

Figure 5.4: The PID likelihood distribution of the true primary muon for p → μ+ KL0
MC. The hatched regions show contributions from KL0 decay and interaction.
muon. The mis-PID fraction is 8.3%. PID mis-reconstruction is taken into accountas systematic error in the analysis.
Since there are no timing cuts used in the ring counting algorithm, as describedin section 5.2.1, sometimes true decay-electrons are selected as a ring. When thishappens, 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 theMS 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.
Figure 5.5a shows the ΔV distribution for the p → μ+ KL0 MC sample. The meanis 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.

18000p→μKL0 MC

16000

KL→any decay
KL→int.
Other

14000

V|| mean (cm)entries

90

12000
10000
V|| resolution (cm)

8000
6000
4000
2000
0

50
40
30
20
10
0
-10
-20
-30
-40
-50

-400

-200

0

200

μ candidate MS vertex

400
V|| (cm)

50
45
40
35
30
25
20
15
10
5
0

p→μKL0 MC

0

200

400

600

800

1000

1200

1400
L (cm)

p→μKL0 MC

0

200

(a)

400

600

800

1000

μ candidate MS vertex

1200

1400
L (cm)(b)

Figure 5.5: Performance of the MS vertex ﬁtting of the μ-candidate for p → μ+ KL0
MC. (a) The ΔV distribution. Hatched regions show contribution from KL0 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 istaken 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 momentum reconstruction is checked using the p → μ+ KL0 MC sample. Figure 5.7 shows thereconstructed-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entries

91

4500
ATM-ν MC

4000

CC QE
CC single-π
CC multi-π

3500

NC
Other

3000
2500
2000
1500
1000
500
0

-400

-200

0

200

400
V|| (cm)

μ candidate MS vertex

entriesFigure 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
p→μKL0 MC

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 →μ+ KL0 MC. The hatched regions show contributions from KL0 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 theproton ID algorithm developed by M. Fechner described in [88]. The performance ischecked 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 thevertex, 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 isused. The performance of the ﬁtter is checked in the same way as described in section
5.2.3.1 with the exception that we deﬁne ΔV− , the reconstructed-true KL0 vertex
projected opposite the true μ-candidate direction. The KL0 vertex is the location
where the KL0 disappears via one of the kinematic processes described in Table 1.2.
Figure 5.8a shows the ΔV− distribution for the p → μ+ KL0 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 istaken into account as systematic error in our analysis.

The development of this new reconstruction algorithm now allows us to search
the p → μ+ KL0 decay mode at SK using the unique multi-vertex signature that was
not possible before. Now, both the vertex of the proton decay point and the KL0
disappearance point can be determined independent of the distance between them.
We use this information to separate the p → μ+ KL0 signal from the atmospheric8000

p→μKL0 MC
KL→any decay
KL→int.

7000

Other

V-|| mean (cm)entries

93

6000
5000

V-|| resolution (cm)

4000
3000
2000
1000
0
-1000 -750

-500

-250

0

250

remaining vertex

(a)

500

750 1000
V-|| (cm)

200
150
100
50
0
-50
-100
-150
-200
250
225
200
175
150
125
100
75
50
25
0

p→μKL0 MC

0

200

400

600

800

1000

1200

1400
L (cm)

p→μKL0 MC

0

200

400

600

800

1000

remaining vertex

1200

1400
L (cm)(b)

Figure 5.8: Performance of the remaining particle vertex ﬁtting of the μ-candidate
for p → μ+ KL0 MC. (a) The ΔV− distribution. Hatched regions show contribution
from KL0 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.

entries

94

1200

ATM-ν MCCC QE
CC single-π1000

CC multi-π
NC
Other

800

600

400

200

0
-1000 -750

-500

-250

0

250

remaining vertex

500

750 1000
V-|| (cm)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+K 0 search
6.1

Data Set

We search for the proton decay signal within the SK-I FC data set. The SK-I data wastaken 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+ K 0 MC2 described in section 3.1 and detector simulator3 described in section 3.4
are used to generate MC samples of p → μ+ K 0 . 200,000 events were generated withtrue 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
described in Chapter 4. Pure νμ → ντ oscillation with Δm2 = 2.5 × 10−3 eV2 and1software library version 07d
software library version 09b
3
software version v11p79 with KL0 →KS0 regeneration
2

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+K 0 Search

The previous search of p → μ+ K 0 in SK was performed using only the p → μ+ KS0
MC to estimate the signal detection eﬃciency [1]. In this thesis, we introduce a new
combined method which uses the p → μ+ K 0 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+ K 0 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 isrejected 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 aparticular decay mode of p → μ+ K 0 as well as be independent of each other. Theyare:(I) “KS0 → π 0 π 0 ”
Designed to search for the p → μ+ KS0 ; KS0 → π 0 π 0 decay mode.
(II) “KS0 → π + π − Method #1”
Designed to search for the p → μ+ KS0 ; KS0 → π + π − decay mode with the assumption that one of the charged pions is below the Cherenkov threshold.
4

software library version 09b

97

SK-I Datap → μ+ K 0 MC
atmospheric neutrino MC

goto next
event

no

selected by FCFV?

selected by“KS0 → π 0 π 0 ”?

saveselected
event

yes

no

yes

selected by“KS0 → π + π −Method #1”?

yesnoselected by“KS0 → π + π −Method #2”?

yes

selected by“KL0 ”?

yes

no

no
Figure 6.1: The p → μ+ K 0 combined search algorithm.

(III) “KS0 → π + π − Method #2”
Designed to search for the p → μ+ KS0 ; KS0 → π + π − decay mode with the assumption that both of the charged pions are above the Cherenkov threshold.
(VI) “KL0 ”
Designed to search for the p → μ+ KL0 decay mode.
An event selected by a search is saved. If the event is not selected by any of thesearches the next event is processed.
The event selections for the KS0 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 actuallyused.
The event selections for FCFV and KS0 searches (I-III) use only samples processedwith standard reconstruction. The KL0 search (VI) uses only samples processed withmulti-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 acomparison 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, thesignal candidates if any and ﬁnally a summary of the total systematic error. The ﬁnal
result of the combined p → μ+ K 0 search is described in Chapter 11 .

Chapter 7
Search for “KS0 → π 0π 0”
7.1

Event Selection(D1) 3 ≤ nring ≤ 5(E1) number of μ-like rings = 1(F1) 0 ≤ number of decay electron ≤ 1(G1) 400 MeV/c2 < MKS < 600 MeV/c2(H1) 150 MeV/c < pμ < 400 MeV/c(I1) Ptot < 300 MeV/c(J1) 750 MeV/c2 < Mtot < 1000 MeV/c2
When the free proton decays via p → μ+ KS0 ; KS0 → π 0 π 0 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 s and decays via μ+ →e+ νe ν̄μ . The π 0 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 atleast one gamma from each of the decaying pions as well as the primary muon arereconstructed. Figure 7.1 shows the number of ring (nring) distribution for both thep → μ+ K 0 MC and atmospheric neutrino MC. As expected nearly all, 97.6%, of theKS0 → π 0 π 0 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 thissearch, 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 thetrue muon ring and remaining rings. In the p → μ+ K 0 MC (atmospheric neutrinoMC) 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 thatare within 5◦ of a true electron or gamma are shown for the atmospheric neutrino
MC. For the p → μ+ K 0 MC the mis-PID probability is 2.5% and 3.2% for the truemuon ring and remaining rings respectively. For the atmospheric neutrino MC, themis-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+ K 0 MC and atmospheric
neutrino MC. As expected, there is at most one decay electron detected for the
KS0 → π 0 π 0 sample. The fraction of events with zero detected decay electrons in the
KS0 → π 0 π 0 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:
MKS = EK2 S − PK2 S
nring 
 


pi 
Ptot = 
i=1nring Etot =

|pi |2 + m2i

(7.1)
(7.2)

(7.3)

i=1


2
2
− PtotMtot = Etot

(7.4)

where pi is the momentum of the i-th ring and mi is the mass of the particle associatedwith the ring. The mass of the muon used in the calculation is 105.7 MeV/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-likerings are included in the summation.
Criteria (G1) selects MKS near the expected value of 497.6 MeV/c2 . Figure 7.4
shows the MKS distribution for the p → μ+ K 0 MC and atmospheric neutrino MC.
The main peak is at 461.8 ± 0.8 MeV/c2 in the p → μ+ K 0 MC. The peak is smaller
than the expected value because of the contribution from events with three or fourrings. For these events, all ﬁnal state particles are not reconstructed and therefore
MKS is underestimated. There is a peak at 135.2 ± 0.4 MeV/c2 in the atmospheric
neutrino MC. This results when only two rings are used to calculate MKS and bothare from gammas due to the decay of a single π 0 . This peak is consistent with the
expected π 0 mass of 135.0 MeV/c2 .
Criteria (H1) selects the primary muon momentum, pμ , near the expected valueof 326.5 MeV/c. Figure 7.5 shows the pμ distribution for the p → μ+ K 0 MC andatmospheric 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.

Events/1489.2day

102
9000
ATM-ν MCp→μK0 MC

8000

KS→π0π0
Other

7000
6000
5000
4000
3000
2000
1000
0

1

2

3

4

5

nring

Figure 7.1: The nring distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-C). The hatched region
shows the KS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows 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+ K 0 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 notzero 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
938.3 MeV/c2 corresponding to the invariant proton mass. Figure 7.7 shows the Mtot
distribution for the p → μ+ K 0 MC and atmospheric neutrino MC. The main peak is
at 902.2 ± 0.2 MeV/c2 .

900

μ-likee-likeEvents/1489.2day

Events/1489.2day

103

ATM-ν MCp→μK0 MC800

0 0KS→π πOther

700

μ-likee-likeATM-ν MCp→μK0 MC250

0 0KS→π π
Other

200
600
500

150

400
100

300
200

50
100
0
-10

-8

-6

-4

-2

0

2

4

0
-10

6
8
10
PID likelihood

true μ ring

-8

-6

-4

-2

0

2

remaining rings

4

6
8
10
PID likelihood

Events/1489.2day

Figure 7.2: The PID likelihood distribution for p → μ+ K 0 MC (black solid line) andatmospheric neutrino MC (blue box) after event selections (A-D1) and true particle
selection described in the text. The hatched region shows the KS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 MC is negligible. The box shows thestatistical error of the atmospheric neutrino MC sample. The atmospheric neutrino
MC is normalized to the live-time (1489.2 days). The p → μ+ K 0 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 MCp→μK0 MC400

KS→π0π0
Other

350
300
250
200
150
100
50
0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Figure 7.3: The number of decay electron distribution for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-E1).
The hatched region shows the KS0 → π 0 π 0 contribution. The statistical error of thep → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC byarea. The pink arrows and dash-dot vertical lines indicate the event selection region.

Events/1489.2day

104

45

ATM-ν MC0p→μK MC40

KS→π0π0
Other

35
30
25
20
15
10
5
0

0

200

400

600

800

MKS

1000
2
MeV/c

Events/1489.2day

Figure 7.4: The MKS distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-F1). The hatched region
shows the KS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows and dash-dot vertical lines indicate the event selection region.

10

ATM-ν MCp→μK0 MCKS→π0π0
Other

8

6

4

2

0

0

100

200

300

400
pμ

500

600

700
800
MeV/c

Figure 7.5: The pμ distribution for p → μ+ K 0 MC (black solid line) and atmospheric
neutrino MC (blue box) after event selections (A-G1). The hatched region shows theKS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 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+ K 0
MC is normalized to the atmospheric neutrino MC by area. The pink arrows anddash-dot vertical lines indicate the event selection region.

Events/1489.2day

105

3.5

ATM-ν MCp→μK0 MC0 0KS→π π

3

Other

2.5

2

1.5

1

0.5

0

0

200

400

600

800

1000
MeV/c

Ptot

Events/1489.2day

Figure 7.6: The Ptot distribution for p → μ+ K 0 MC (black solid line) and atmospheric
neutrino MC (blue box) after event selections (A-H1). The hatched region shows theKS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 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+ K 0
MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dashdot vertical line indicate the event selection region.

0.8

ATM-ν MCp→μK0 MCKS→π0π0

0.7

Other

0.6
0.5
0.4
0.3
0.2
0.1
0
500

600

700

800

900
Mtot

1000

1100

1200
2
MeV/c

Figure 7.7: The Mtot distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-I1). The hatched region
shows the KS0 → π 0 π 0 contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows 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 theproton 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 KolomogorovSmirnov test between the data and atmospheric neutrino MC in which the significance, 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 thebest comparison can be made for distributions of parameters that come late in the
proton decay search event selection.
The following event selection is used to deﬁne the sideband sample of the KS0 →π 0 π 0 search:• FCFV• 3 ≤ nring ≤ 5• 1 μ-like ring• exclude events that satisfy:
Ptot < 450 MeV/c

AND

600 MeV/c2 < Mtot < 1150 MeV/c2

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 theminimum 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, multipion 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.
Figure 7.9 shows the MKS distribution. The peak at 136.0 ± 0.4 MeV/c2 in this
distribution corresponds to the π 0 mass of 135.0 MeV/c2 . This reason for this peakis 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.

Events/1489.2day

108

DATA

250

Atm-ν MC

200

150

100

50

0

0

1

2

3

4

5

6

7

8

9

10

number of decay-e (sideband)

Events/1489.2day

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

DATA

120

Atm-ν MC

100

80

60

40

20

0

0

250

500

750

1000

1250

MKS (sideband)

1500

1750 2000
2
MeV/c

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.

Events/1489.2day

109

DATA
Atm-ν MC

70

60

50

40

30

20

10

0

0

500

1000

1500

2000

2500

pμ (sideband)

3000
MeV/c

Events/1489.2day

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

50

40

30

20

10

0

0

500

1000

1500

2000

2500

Ptot (sideband)

3000

3500

4000 4500
MeV/c

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.

Events/1489.2day

110

DATA

70

Atm-ν MC

60

50

40

30

20

10

0

0

500

1000

1500

2000

2500

Mtot (sideband)

3000

3500

4000
2
MeV/c

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 thebasic 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 applied. 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 areobserved. 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, multipion 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 ± 0.4 MeV/c2 seen in this distribution corresponds to the π 0 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 shapeis 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 shapeis 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 andatmospheric neutrino MC agree.
Figure 7.21 shows the Ptot vs. Mtot distribution for p → μ+ K 0 MC, atmospheric
neutrino MC and data respectively. The p → μ+ K 0 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 datais consistent by eye with that of the atmospheric neutrino MC.

113

Event Selection
(A-C)
(D1)
(E1)
(F1)
(G1)
(H1)
(I1)
(J1)

Eﬃciency(%)

Atm-ν MCFC Data

97.6 ± 0.1
37.0 ± 0.1
19.6 ± 0.1
18.0 ± 0.1
10.3 ± 0.1
9.7 ± 0.1
8.9 ± 0.1
8.8 ± 0.111105.8 ± 13.7
1485.6 ± 5.1
527.4 ± 3.0
450.1 ± 2.8
70.5 ± 1.1
21.6 ± 0.6
1.8 ± 0.1
1.1 ± 0.1

12232 ± 110.6
1563 ± 39.5
528 ± 23.0
450 ± 21.2
75 ± 8.7
28 ± 5.3
1 ± 1.0
1 ± 1.0

FCFV
nring
no. μ-likeno. decay-e
MKS
pμ
Ptot
Mtot

Events/1489.2 day

Table 7.1: KS0 → π 0 π 0 search data events, signal detection eﬃciency and backgroundrate along the event selection described in section 7.1. The atmospheric neutrino MC
is normalized to the live-time (1489.2 days).

10

5

10

4

10

3

10

2

DATA
Atm-ν MC

10

1

-1

10

A-C

D1

E1

F1

G1

H1
I1
J1
0 0
KS→π π event selection

Figure 7.13: The event rate along the KS0 → π 0 π 0 search event selection for data (redclosed squares) and atmospheric neutrino MC (blue open triangles). The statisticalerror of both is shown. The atmospheric neutrino MC is normalized to the live-time(1489.2 days).

Events/1489.2day

114

10000

DATA
Atm-ν MC

8000

6000

4000

2000

0

1

2

3

4

5

nring

DATA
Atm-ν MC

-2

0

2

4

Events/1489.2day

μ-likee-like

0
-10

6
8
10
PID likelihood
DATA
Atm-ν MC

100
80
60

-4

-2

0

2

4

nring=3; ring #2

μ-likee-like

-8

-6

-4

-2

0

2

DATA
Atm-ν MC

4nring=3; ring #3

μ-likee-like

-8

-6

-4

-2

0

2

nring=4; ring #1

6
8
10
PID likelihood

68
10
PID likelihood
DATA
Atm-ν MC

4

6
8
10PID likelihood

-6

-4

-2

0

2

4

μ-likee-like

90
80
70
60
50
40
30
20
10
0
-10

20
15

-8

-6

-4

-2

0

2

4

nring=5; ring #2
40

μ-likee-like68
10
PID likelihood
DATA
Atm-ν MC

35
30
25
20
15
10
5

-8

-6

-4

-2

0

2

4

μ-likee-like

-8

-6

-4

-2

0

2

4

μ-likee-like

0
-10

6
8
10
PID likelihood

DATA
Atm-ν MC

nring=4; ring #4
22.5
20
17.5
15
12.5
10
7.5
5
2.5
0
-10

DATA
Atm-ν MC

25

0
-10

6
8
10
PID likelihood
DATA
Atm-ν MC

nring=4; ring #3

Events/1489.2day-6

Events/1489.2day-8

μ-likee-like30

5-8nring=4; ring #2
90
80
70
60
50
40
30
20
10
0
-10

35

10

Events/1489.2day-420

Events/1489.2day

30

6
8
10
PID likelihood
DATA
Atm-ν MC

-8

-6

-4

-2

0

2

4

nring=5; ring #3

Events/1489.2day-640

Events/1489.2day

40

45
40
35
30
25
20
15
10
5
0
-10

μ-likee-like

-8

-6

-4

-2

0

2

40

4

μ-likee-like68
10
PID likelihood

DATA
Atm-ν MC

nring=5; ring #4
Events/1489.2day

-8

120

45
40
35
30
25
20
15
10
5
0
-10

50

10

140

160
140
120
100
80
60
40
20
0
-10

DATA
Atm-ν MC60

20nring=3; ring #1

0-10

μ-likee-like70

Events/1489.2day

μ-likee-likeEvents/1489.2day

90
80
70
60
50
40
30
20
10
0
-10

Events/1489.2day

Events/1489.2day

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.

6
8
10
PID likelihood
DATA
Atm-ν MC

35
30
25
20
15
10
5

-8

-6

-4

-2

0

2

nring=5; ring #1

4

6
8
10
PID likelihood

0
-10

-8

-6

-4

-2

0

2

nring=5; ring #5

4

6
8
10
PID likelihood

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 bothis shown. The atmospheric neutrino MC is normalized to the data by area. The pinkarrows and dash-dot vertical line indicates the event selection threshold.

Events/1489.2day

115

DATA
Atm-ν MC

250

200

150

100

50

0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Events/1489.2day

Figure 7.16: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) after event selections (A-E1). The statisticalerror 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

70

60

50

40

30

20

10

0

0

200

400

600
MKS

800

1000
2
MeV/c

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.

Events/1489.2day

116

14

DATA
Atm-ν MC

12

10

8

6

4

2

0

0

200

400

600

800

1000
MeV/c

pμ

Events/1489.2day

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 anddash-dot vertical lines indicate the event selection region.

DATA
Atm-ν MC

12

10

8

6

4

2

0

0

200

400

600

800

1000
Ptot

1200

1400

1600 1800
MeV/c

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 anddash-dot vertical line indicate the event selection region.

Events/1489.2day

117

1.2
DATA
Atm-ν MC

1

0.8

0.6

0.4

0.2

0
500

600

700

800

900

1000

1100

Mtot

1200
2
MeV/c

Ptot (MeV/c)

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.

0p→μK MCATM-ν MC

DATA

900
800
700
600
500
400
300
200
100
00

500

1000
0
2
Mtot (MeV/c )

500

1000
0
2
Mtot (MeV/c )

500

1000
2
Mtot (MeV/c )Figure 7.21: The Mtot vs. Ptot scatter plot from left to right; p → μ+ K 0 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) areclassiﬁed by true parent neutrino ﬂavor and interaction mode and summarized inTable 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. Thesebackgrounds 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
the KS0 → π 0 π 0 search.
S. Mine [90] estimated the mis-PID fraction of the remaining νμ CC backgroundof the p → μ+ π 0 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 π 0 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 theresult 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].

119Parent ν ﬂavor

ν interaction

SK-I (%)

CC
38.7 ± 6.9%

QE
single meson
multi-meson
DIS

1.9 ± 1.9
19.4 ± 5.5
15.5 ± 5.1
1.9 ± 1.9

NC
13.5 ± 4.8%

QE
single meson
multi-meson
DIS

0.0 ± 1.9
1.9 ± 1.9
7.7 ± 3.7
3.8 ± 2.7

CC
15.0 ± 5.0%

QE
single meson
multi-meson
DIS

0.0 ± 1.9
1.9 ± 1.3
10.6 ± 3.7
2.5 ± 1.8

NC
32.8 ± 6.6%

QE
single meson
multi-meson
DIS

0.0 ± 1.99.7 ± 4.1
9.7 ± 4.1
13.5 ± 4.8

νe52.2 ± 7.1%

νμ47.8 ± 7.1%

Total:

100.0 ± 0.0

Table 7.2: Breakdown of remaining atmospheric neutrino MC background for the
KS0 → π 0 π 0 search. The background is broken down by true neutrino ﬂavor andneutrino interaction. A description of possible neutrino interactions is described in
section 3.3.

120
KS0 → π 0 π 0 candidate
NHITACEvis (MeV/c)
Dwall (cm)nring
PID & momentum (MeV/c)number of decay electron
MKS (MeV/c2 )Ptot (MeV/c)
Mtot (MeV/c2 )

#1
2
645.4
396.9
4
N (μ) 246.2
S (γ) 189.5
S (γ) 185.9
S (γ) 184.2
0
516.9
211.4
800.1

Table 7.3: The reconstructed information of the data candidate for the KS0 → π 0 π 0search. 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

There is one data candidate found for the KS0 → π 0 π 0 search. Figure 7.22 showsthe event display for this candidate. The reconstruction information for this event issummarized 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 describedin 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

1

1

1

1

1

1

1

1

1

1

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/30:;R= 4:NoYet
R :Z : PHI : G
12.93: 5.27:-3.11:0
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:-0 0

1

1

1

RunMODE:NORMALTRG ID :00000111
T diff.:0.101E+0
FEVSK :81002803
nOD YK/LW: 3/ 2
SUB EV : 0/ 1
Dcye: 0( 0/ 0/ 0

Figure 7.22: Event display of the candidate for the KS0 → π 0 π 0 search. The red(cyan) thick solid lines show the reconstructed rings as e-like (μ-like) type.

122

SourceSystematic Error (%)

Physics Simulation
Fermi momentum
Correlated decay
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

2.6
6.2
3.6
4.4

Detector
Water quality (incl. stat. error)
Energy scale

4.1 (3.6)
1.3

Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetry

1.5
1.0
1.2
2.0
0.4

Statistical error

0.8

Total

10.3

Table 7.4: Systematic errors on signal detection eﬃciency for the KS0 → π 0 π 0 search.
The number shown for the uncertainty due to water quality includes the statisticalerror of p → μ+ K 0 MC sample described in section A.2.3 which itself is shown within
the parenthesis.

7.6

Total Systematic Error of “KS0 → π 0π 0” Search

Tables 7.4 and 7.5 summarize the total systematic error on the signal detection eﬃciency and background rate respectively of the KS0 → π 0 π 0 search. The detail of thesystematic error estimation is described in Appendix A.

123

SourceSystematic Error (%)

Physics Simulation
ν FluxAbsoluteν/ν̄νe /νμν cross-section
QE
Single π
MA (QE & single π)
Coherent πMulti πNC/CC ratio
π Nuclear Eﬀect
Elastic
Charge exchange
Absorption
Production
Fermi momentum
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

10.0
1.3
0.2
0.1
4.3
3.9
∼0
1.6
4.8
1.3
1.2
1.8
3.1
1.9
∼0
∼0

Detector
Water quality
Energy scale

15.7
1.5

Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetry

1.2
1.2
5.6
2.0
4.1

Statistical error (250 yr)

11.1

Total

24.7

Table 7.5: Systematic errors on background rate for the KS0 → π 0 π 0 search.

Chapter 8
Search for “KS0 → 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 < pμ < 400 MeV/c
The most energetic ring (ring with largest e-like momentum) is assumed to be
the primary muon. The other ring is assumed to be a charged pion.
(H2) Ptot < 300 MeV/c
When the proton decays via p → μ+ KS0 ; KS0 → π + π − the ﬁnal state particles consistof a primary muon and two charged pions. The kinematics of the muon are thesame 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
KS0 may be asymmetric causing one of the charged pions to be near or below theCherenkov threshold of 159 MeV/c. The decay lifetime of charged pions is 26 ns anddecay 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 thepion decay is 30 MeV/c which is below the Cherenkov threshold. The π − is capturedby 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+ K 0 MC andatmospheric neutrino MC.
Since the ﬁnal state particles consist of muons and pions all rings are μ-like therefore, criteria (E2) is applied. The PID likelihood is calculated using both angle andpattern information. Figure 8.2 shows the PID likelihood distribution of each ringfor both the p → μ+ K 0 and atmospheric neutrino MC. The mis-PID probability ofthe primary muon (ring #1) is 3% in the KS0 → π + π − MC.
We expect no more than two decay electrons in the KS0 → π + π − MC; one fromthe 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+ K 0 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
shows the pμ distribution for the p → μ+ K 0 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 326.5 MeV/c.
Criteria (H2) selects events with Ptot below 300 MeV/c. Ptot is calculated using(7.2). Figure 8.5 shows the Ptot distributions for both the p → μ+ K 0 MC andatmospheric neutrino MC. Since we assume in this method that one of the charged

Events/1489.2day

126
9000
ATM-ν MCp→μK0 MC

8000

KS→π+πOther

7000
6000
5000
4000
3000
2000
1000
0

1

2

3

4

5

Number of rings

Figure 8.1: The nring distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-C). The hatched region
shows the KS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows and dash-dot vertical lines indicate the event selection region.
pions is below the Cherenkov threshold of 159 MeV/c, the momentum carried by thispion is not taken into account in the Ptot calculation. This is the source of the tail in
the Ptot distribution of KS0 → π + π − MC.

μ-likee-like160

ATM-ν MC0p→μK MC
KS→π+π-

140

Other

Events/1489.2day

Events/1489.2day

127

90

μ-likee-likeATM-ν MCp→μK0 MC80

KS→π+πOther

70

120
60
100
50
80
40
60

30

40

20

20

10

0
-10

-8

-6

-4

-2

0

2

nring=2; ring #1

4

6
8
10
PID likelihood

0
-10

-8

-6

-4

-2

0

2

nring=2; ring #2

4

6
8
10
PID likelihood

Figure 8.2: The PID likelihood distribution for p → μ+ K 0 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.
The hatched region shows the KS0 → π + π − contribution. The statistical error of thep → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC
by area. The pink arrows and dash-dot vertical line indicate the event selection
threshold.

Events/1489.2day

128

180
ATM-ν MC160

0p→μK MC
KS→π+πOther

140
120
100
80
60
40
20
0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Events/1489.2day

Figure 8.3: The number of decay electron distribution for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-E2).
The hatched region shows the KS0 → π + π − contribution. The statistical error of thep → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC byarea. The pink arrows and dash-dot vertical lines indicate the event selection region.

ATM-ν MC

140p→μK MC
KS→π+πOther

12

10

8

6

4

2

0

0

100

200

300

400
pμ

500

600

700
800
(MeV/c)Figure 8.4: The pμ distribution for p → μ+ K 0 MC (black solid line) and atmospheric
neutrino MC (blue box) after event selections (A-F2). The hatched region shows theKS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0
MC is normalized to the atmospheric neutrino MC by area. The pink arrows anddash-dot vertical lines indicate the event selection region.

Events/1489.2day

129

1.8
ATM-ν MC0p→μK MC

1.6

KS→π+πOther

1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

200

400

600
Ptot

800

1000
(MeV/c)Figure 8.5: The Ptot distribution for p → μ+ K 0 MC (black solid line) and atmospheric
neutrino MC (blue box) after event selections (A-G2). The hatched region shows theKS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0
MC is normalized to the atmospheric neutrino MC by area. The pink arrow and dashdot 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.
The following event selection are used to deﬁne the sideband sample of the KS0 →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 normalizedby 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 andmulti pion. The distribution shape is as expected considering these kinematics andthe 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/ccorresponds selection criteria of the sideband sample. α = 1.4%; the data and atmospheric neutrino MC agree.

Events/1489.2day

131

120
DATA
Atm-ν MC

100

80

60

40

20

0

0

1

2

3

4

5

6

7

8

9

10

number of decay electron (sideband)

Events/1489.2day

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

40

DATA
Atm-ν MC

35

30

25

20

15

10

5

0

0

500

1000

1500
pμ (sideband)

2000

2500

3000
(MeV/c)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.

Events/1489.2day

132

DATA
Atm-ν MC

60

50

40

30

20

10

0

0

500

1000

1500
Ptot (sideband)

2000

2500

3000
(MeV/c)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 thebackground 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 areobserved. α = 49.2% and α = 6.0% for ring #1 and #2 respectively; the data andatmospheric 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 ofevents 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
(A-C)
(D2)
(E2)
(F2)
(G2)
(H2)

FCFV
nring
no. μ-likeno. decay-epμ
Ptot

Eﬃciency(%)

Atm-ν MCFC Data

97.6 ± 0.1
41.2 ± 0.1
28.6 ± 0.1
15.0 ± 0.1
14.3 ± 0.1
10.5 ± 0.1

11105.8 ± 13.7
1998.3 ± 6.0
287.2 ± 2.1
52.8 ± 0.9
12.6 ± 0.4
3.0 ± 0.2

12232 ± 110.6
2130 ± 46.2
284 ± 16.9
60 ± 7.7
15 ± 3.9
6 ± 2.4

Table 8.1: KS0 → π + π − Method #1 search data events, signal detection eﬃciency andbackground 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.
Figure 8.15 shows the Ptot vs. pμ distributions for p → μ+ K 0 MC, atmospheric
neutrino MC and data respectively after event selections (A-F2). The p → μ+ K 0
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.

Events/1489.2 day

135

10

5

DATA
Atm-ν MC

10

4

10

3

10

2

10

1

-1

10

A-C

D2

E2
F2
G2
H2
+ KS→π π Method #1 event selection

Events/1489.2day

Figure 8.9: The event rate along the KS0 → 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

6000

4000

2000

0

1

2

3

4

5

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.

μ-likee-like225

300

Events/1489.2day

Events/1489.2day

136

DATA
Atm-ν MC200
175

μ-likee-likeDATA
Atm-ν MC

250

200

150
125

150
100
100

75
50

50
25
0
-10

-8

-6

-4

-2

0

2

4

0
-10

6
8
10
PID likelihood

nring=2; ring #1

-8

-6

-4

-2

0

2

nring=2; ring #2

4

6
8
10
PID likelihood

Events/1489.2day

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 themost (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
120
100
80
60
40
20
0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Figure 8.12: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) after event selections (A-E2). The statisticalerror 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.

Events/1489.2day

137

DATA

10

Atm-ν MC

8

6

4

2

0

0

200

400

600

800

1000

1200

pμ

1400
(MeV/c)Events/1489.2day

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 anddash-dot vertical lines indicate the event selection region.

DATA

4.5

Atm-ν MC

4
3.5
3
2.5
2
1.5
1
0.5
0

0

100

200

300

400

500
Ptot

600

700

800

900
(MeV/c)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 anddash-dot vertical lines indicate the event selection region.

Ptot (MeV/c)

1380p→μK MCATM-ν MC

DATA

900
800
700
600
500
400
300
200
100
00

500

0
pμ (MeV/c)

5000pμ (MeV/c)

500pμ (MeV/c)

Figure 8.15: The pμ vs. Ptot scatter plot from left to right; p → μ+ K 0 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 (%)

CC
0.0 ± 0.7%

QE
single meson
multi-meson
DIS

0.0 ± 0.7
0.0 ± 0.7
0.0 ± 0.7
0.0 ± 0.7NC
0.7 ± 0.7%

QE
single meson
multi-meson
DIS

0.0 ± 0.7
0.0 ± 0.7
0.7 ± 0.7
0.0 ± 0.7

CC
94.5 ± 4.7%

QE
single meson
multi-meson
DIS

12.6 ± 2.2
70.0 ± 3.1
11.8 ± 2.3
0.0 ± 0.7NC
4.8 ± 1.8%

QE
single meson
multi-meson
DIS

0.0 ± 0.7
2.8 ± 1.4
0.7 ± 0.7
1.4 ± 1.0νe
0.7 ± 0.7%

νμ99.3 ± 4.6%

Total:

100.0 ± 0.0

Table 8.2: Breakdown of remaining atmospheric neutrino MC background for the
KS0 → 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 inTable 8.2.
The dominant remaining background consist of: νμ CCQE, CC single and multimeson neutrino interactions. These backgrounds are consistent with ﬁnal state kinematics that would be reconstructed as events with two μ-like rings and two decay
electrons that are characteristic of the KS0 → π + π − Method #1 search.

140

8.5

SK-I Data Candidates

There are a total of six candidates found in the data for the KS0 → π + π − Method #1
search. Figures 8.16, 8.17, 8.18, 8.19, 8.20 and 8.21 show the SK event display forthese six candidates. The reconstruction information for these events is summarizedin 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 scatteredgenerating 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 expectedby 22.7% and Ptot is within 20.9% of the event selection threshold.

141

KS0 → π + π − Method #1 candidate
NHITACEvis (MeV/c)
Dwall (cm)nring
PID & momentum (MeV/c)number of decay-e
Ptot (MeV/c)
KS0 → π + π − Method #1 candidate
NHITACEvis (MeV/c)
Dwall (cm)nring
PID & momentum (MeV/c)number of decay-e
Ptot (MeV/c)

#1

#2

#3

1
144.5
493.0
2
N (μ) 281.4
N (π ± ) 243.8
2
295.0

1
192.6
772.9
2
N (μ) 303.5
N (π ± ) 308.4
2
180.7

0
155.5
602.5
2
N (μ) 294.4
N (π ± ) 284.7
2
116.0

#4

#5

#6

1
189.4
698.2
2
N (μ) 333.2
N (π ± ) 287.0
2
143.7

1
203.8
878.5
2
N (μ) 323.5
N (π ± ) 262.8
2
136.0

1
95.6
347.5
2
N (μ) 252.4
N (π ± ) 241.1
2
240.4

Table 8.3: The reconstructed information of the data candidates for the KS0 → 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

NUM
1
RUN
4018
SUBRUN
41
EVENT
289990DATE 1997-May-11
TIME
4:18:53
TOT PE:
1688.
MAX PE:
26.8
NMHIT :
952
ANT-PE:
31.5
ANT-MX:
7.0
NMHITA:
34

45
40
35
30
25
20
15
10
5
0
600

800

1000

0

5

10

1200

1400

1600

1800

1

1

1

1

1

1

1

1

35

1

1

1

1

30

1

1

1

1

25

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/29:;R= 2:NoYet
R :Z : PHI : G
11.97: 1.69: 1.61:0
CANG : RTOT : AMOM : M
35.5:
465:
95:
V=-0.822: 0.199:-0.5
32.0:
269:
55:
V= 0.804: 0.254:-0.5
Comnt;

1

1

1

1

1

1

1

1

RunMODE:NORMALTRG ID :00000011
T diff.:0.128E+0
FEVSK :81002003
nOD YK/LW: 2/ 1
SUB EV : 0/ 2
Dcye: 2( 1/ 1/ 0

20
15
10
5
0
15

20

25

Figure 8.16: The ﬁrst candidate for the KS0 → 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
SUBRUN
226
EVENT
30337267
DATE 1999-Nov-20
TIME
0: 1:55
TOT PE:
1763.
MAX PE:
21.3
NMHIT : 1003
ANT-PE:
23.6
ANT-MX:
3.0
NMHITA:
27

60
50
40
30
20
10
0
600

1

1

1

1

1

1000

1200

1400

1600

1800

30

1

1

800

1

1

1

1

1

1

25

1

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/29:;R= 2:NoYet
R :Z : PHI : G
9.17: -5.06: 0.30:0
CANG : RTOT : AMOM : M
36.2:
567:
115:
V=-0.534: 0.720:-0.4
34.0:
412:
84:
V= 0.731:-0.670:-0.1
Comnt;

RunMODE:NORMALTRG ID :00000111
T diff.:0.189E+0
FEVSK :81002803
nOD YK/LW: 2/ 1
SUB EV : 0/ 1
Dcye: 2( 1/ 1/ 0

1

1

1

1

1

1

1

1

20
15
10
5

1

1

0
0

2.5

5

7.5

10

12.5

15

17.5

20

Figure 8.17: The second candidate for the KS0 → 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 thatis 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 thesource is a decay electron.

144

NUM
2
RUN
8268
SUBRUN66
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

1

1

1

1

1

1

1

1

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/30:;R= 2:NoYet
R :Z : PHI : G
10.87: 5.99: 1.79:0
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;

RunMODE:NORMALTRG ID :00000111
T diff.:0.375E+0
FEVSK :81002803
nOD YK/LW: 0/ 0
SUB EV : 0/ 3
Dcye: 2( 1/ 0/ 0

Figure 8.18: The event display of the third candidate for the KS0 → π + π − Method#1 search. The cyan thick solid lines in the event display show the reconstructedrings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ.

145

NUM
3
RUN
8294
SUBRUN102
EVENT13620274
DATE 2000-Jan-28
TIME
9:17: 0TOT PE:
2228.
MAX PE:
26.7
NMHIT : 1211
ANT-PE:
16.4
ANT-MX:
2.9
NMHITA:
18

60
50
40
30
20
10
0

1

1

1

1

1

1

1

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/30:;R= 2:NoYet
R :Z : PHI : G
9.92: -5.26: 0.89:0
CANG : RTOT : AMOM : M
33.8:
702:
142:
V= 0.687: 0.017:-0.7
36.0:
246:
50:
V=-0.427: 0.177: 0.8
Comnt;

1

RunMODE:NORMALTRG ID :00000111
T diff.:0.642E+0
FEVSK :81002803
nOD YK/LW: 1/ 1
SUB EV : 0/ 1
Dcye: 2( 0/ 2/ 0
1

1

1

1

1

1

1

1

1

1

600

800

0

5

1000

1200

1400

1600

1800

45
40
35
30
25
20
15
10
5
0

1

10

15

20

25

Figure 8.19: The fourth candidate for the KS0 → 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 indicatesthe source is a decay electron.

146

70
1

1

1

1

1

1

1

NUM
4
RUN
8910
SUBRUN
9
EVENT
1290606
DATE 2000-Jun-26
TIME
1:29:25
TOT PE:
2096.4
MAX PE:
20.7
NMHIT : 1114
ANT-PE:
19.5
ANT-MX:
5.3
NMHITA:
22

1

60
50
40
30
20
10

1

1

0

1

1

1

600

1

800

1000

1200

5

7.5

10

1400

1600

1800

1

1

1

1

1

35

1

1

1

1

1

1

1

1

1

30
25
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/07/01:;R= 2:NoYet
R :Z : PHI : G
8.11: 9.31:-2.92:0
CANG : RTOT : AMOM : M
34.0:
673:
137:
V= 0.717:-0.693:-0.0
30.0:
341:
70:
V=-0.733: 0.562:-0.3
Comnt;

RunMODE:NORMALTRG ID :00000111
T diff.:0.108E+0
FEVSK :81002803
nOD YK/LW: 3/ 1
SUB EV : 0/ 3
Dcye: 2( 1/ 1/ 0

20
15
10
5
0
0

2.5

12.5

15

17.5

20

Figure 8.20: The ﬁfth candidate for the KS0 → 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
SUBRUN450
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

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/29:;R= 2:NoYet
R :Z : PHI : G
13.42:-13.17:-0.10:0
CANG : RTOT : AMOM : M
34.7:
364:
74:
V=-0.408: 0.765:-0.4
28.0:
116:
24:
V= 0.823: 0.183: 0.5
Comnt;

1

1

1

RunMODE:NORMALTRG ID :00000111
T diff.:0.833E+0
FEVSK :81002803
nOD YK/LW: 2/ 1
SUB EV : 0/ 5
Dcye: 2( 2/ 0/ 0

1

1

1

1

1

Figure 8.21: The event display of the sixth candidate for the KS0 → π + π − Method#1 search. The cyan thick solid lines in the event display show the reconstructedrings as μ-like type. The “X” denotes the ring that is assumed to be the primary μ.

148

SourceSystematic Error (%)

Physics Simulation
Fermi momentum
Correlated decay
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

4.0
5.9
3.2
4.0

Detector
Water quality (incl. stat. error)
Energy scale

7.0 (3.4)
1.4

Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetry

1.5
1.4
0.6
2.0
1.2

Statistical error

0.7

Total

11.8

Table 8.4: Systematic errors on signal detection eﬃciency for the KS0 → π + π − Method#1 search. The number shown for the uncertainty due to water quality includes thestatistical error of the p → μ+ K 0 MC sample described in section A.2.3 which itself
is shown within the parenthesis.

8.6

Total Systematic Error of “KS0 → π +π − Method#1” Search

Tables 8.4 and 8.5 summarize the total systematic error on the signal detection eﬃciency and background rate respectively of the KS0 → π + π − Method #1 search. The
detail of the systematic error estimation is described in Appendix A.

149

SourceSystematic Error (%)

Physics Simulation
ν FluxAbsoluteν/ν̄νe /νμν cross-section
QE
Single π
MA (QE & single π)
Coherent πMulti πNC/CC ratio
π Nuclear Eﬀect
Elastic
Charge exchange
Absorption
Production
Fermi momentum
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

10.0
1.3
1.1
1.3
14.0
11.7
∼0
0.5
1.9
1.8
1.2
3.2
6.1
0.7
∼0
∼0

Detector
Water quality (incl. stat. error)
Energy scale

8.7 (8.0)
1.2

Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetry

1.2
3.7
∼0
2.0
3.4

Statistical error (200 yr)

6.9

Total

25.5

Table 8.5: Systematic errors on background rate for the KS0 → π + π − Method #1
search.
Systematic errors on background rate for the KS0 → 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
Search for “KS0 → 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(F3) 450 MeV/c2 < MKS < 550 MeV/c2(G3) Ptot < 300 MeV/c(H3) 750 MeV/c2 < Mtot < 1000 MeV/c2
The kinematics of p → μ+ KS0 ; KS0 → π + π − decay is described in section 8.1.
Criteria (D3) is determined with the assumption that both charged pions areabove the Cherenkov threshold. Figure 8.1 shows the nring distribution for both thep → μ+ K 0 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 thenumber of decay electron distribution. As expected, there are no more than two decay
electrons in the KS0 → π + π − MC. This event selection is made with the assumptionthat one may not be detected.
Criteria (F3) chooses events with MKS near the expected value of 497.6 MeV/c2 .
MKS is calculated using (7.1); the mass of the charged pion used in the calculation is139.6 MeV/c2 . Figure 9.2 shows the MKS distribution. There is a peak in KS0 → π + π −MC at 498.0 ± 0.2 MeV/c2 ; within 1% of the expected value. The tail at large MKS
for KS0 → π + π − MC comes from charged pions that strongly interact in the waterproducing π 0 through charge exchange. The gammas from the decay of these π 0
are used in the MKS calculation but assumed to be muons or charged pions. Thisoverestimates 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
938.3 MeV/c2 corresponding to the proton. Figure 9.4 shows the Mtot distribution.
The main peak is at 918.2 ± 0.3 MeV/c2 ; within 2% of the expectation.

Events/1489.2day

152

700
ATM-ν MCp→μK0 MC600

KS→π+πOther

500

400

300

200

100

0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Events/1489.2day

Figure 9.1: The number of decay electron distribution for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-D3).
The hatched region shows the KS0 → π + π − contribution. The statistical error of thep → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC byarea. The pink arrows and dash-dot vertical lines indicate the event selection region.

35

ATM-ν MC0p→μK MC
KS→π+πOther

30

25

20

15

10

5

0

0

200

400

600

800
MKS

1000

1200

1400

1600
2
MeV/c

Figure 9.2: The MKS distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E3). The hatched region
shows the KS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows and dash-dot vertical lines indicate the event selection region.

Events/1489.2day

153

5ATM-ν MC0p→μK MC+ -KS→π π
Other

4

3

2

1

0

0

250

500

750

1000

1250

1500

Ptot

1750 2000
MeV/c

Events/1489.2day

Figure 9.3: The Ptot distribution for p → μ+ K 0 MC (black solid line) and atmospheric
neutrino MC (blue box) after event selections (A-F3). The hatched region shows theKS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0
MC is normalized to the atmospheric neutrino MC by area. The pink arrows anddash-dot vertical lines indicate the event selection region.
0.09
ATM-ν MCp→μK0 MC

0.08

KS→π+πOther

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
500

600

700

800

900
Mtot

1000

1100

1200 1300
2
MeV/c

Figure 9.4: The Mtot distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-G3). The hatched region
shows the KS0 → π + π − contribution. The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized to the atmospheric neutrino MC by area. The pinkarrows 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.
The following criteria are used to deﬁne the sideband sample of the KS0 → π + π −Method #2 search:• FCFV• nring=3• exclude events that satisfy:
600 MeV/c2 < Mtot < 1150 MeV/c2

AND

Ptot < 450 MeV/c

After this event selection, the remaining data events and background rate normalizedby 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 pionand 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. When the atmospheric neutrino MC distribution is changed
within the systematic error described in Appendix A the data and MC agree. Although 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 thethreshold of disagreement however when the atmospheric neutrino MC distribution
is changed within the systematic error described in Appendix A the data and MC
agree.

Events/1489.2day

155

DATA

600

Atm-ν MC

500

400

300

200

100

0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron (sideband)

Events/1489.2day

Figure 9.5: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) in the sideband sample. The statistical error ofboth is shown. The atmospheric neutrino MC is normalized to the data by area.

DATA

180

Atm-ν MC

160
140
120
100
80
60
40
20
0

0

500

1000

1500

2000

2500

MKS (sideband)

3000

3500 4000
2
MeV/c

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.

Events/1489.2day

156

DATA

120

Atm-ν MC

100

80

60

40

20

0

0

1000

2000

3000

4000

Ptot (sideband)

5000
MeV/c

Events/1489.2day

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

120

100

80

60

40

20

0

0

1000

2000

3000

Mtot (sideband)

4000

5000
2
MeV/c

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 thebackground 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 νμCC 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 wereconsidered, 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 shapeis 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
(A-C)
(D3)
(E3)
(F3)
(G3)
(H3)

FCFV
nring
no. decay-e
MKS
Ptot
Mtot

Eﬃciency(%)

Atm-ν MCFC Data

97.6 ± 0.1
19.8 ± 0.1
17.1 ± 0.1
3.5 ± 0.1
2.6 ± 0.1
2.5 ± 0.111105.8 ± 13.7
980.6 ± 4.2
440.0 ± 2.7
33.2 ± 0.7
0.3 ± 0.1
0.1 ± 0.1

12232 ± 110.6
1024 ± 32.0
499 ± 22.3
39 ± 6.2
0 ± 1.00 ± 1.0

Table 9.1: KS0 → π + π − Method #2 search data events, signal detection eﬃciency andbackground 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 shapeis as expected; no discontinuity or abnormal peaks are observed. There is no data
after these event selections are applied.
Figure 9.14 shows Ptot vs. Mtot distributions for p → μ+ K 0 MC, atmospheric
neutrino MC and data respectively after event selections (A-F3). The p → μ+ K 0
MC shows a densely populated region consistent with pμ ∼ 326.5 MeV/c and Ptot
 300 MeV/c as expected. p → μ+ K 0 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.

Events/1489.2 day

159

10

5

DATA
Atm-ν MC

10

4

10

3

10

2

10

1

-1

10

A-C

D3

E3
F3
G3
H3
+ KS→π π Method #2 event selection

Events/1489.2day

Figure 9.9: The event rate along the KS0 → 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).

DATA

600

Atm-ν MC

500

400

300

200

100

0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Figure 9.10: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) after event selections (A-D3). The statisticalerror 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.

Events/1489.2day

160

DATA
Atm-ν MC

35

30

25

20

15

10

5

0

0

200

400

600

800

1000

1200

1400

MKS

1600
2
MeV/c

Events/1489.2day

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

6

4

2

0

0

250

500

750

1000
Ptot

1250

1500

1750

2000
MeV/c

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 anddash-dot vertical lines indicate the event selection region.

Events/1489.2day

161

0.14
DATA
Atm-ν MC

0.12

0.1

0.08

0.06

0.04

0.02

0
500

600

700

800

900
Mtot

1000

1100

1200 1300
2
MeV/c

Ptot (MeV/c)

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 statisticalerror 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.

0p→μK MCATM-ν MC

DATA

900
800
700
600
500
400
300
200
100
00

500

1000
0
2
Mtot (MeV/c )

500

1000
0
2
Mtot (MeV/c )

500

1000
2
Mtot (MeV/c )Figure 9.14: The Mtot vs. Ptot scatter plot from left to right; p → μ+ K 0 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 (%)

CC
0.0 ± 15.9%

QE
single meson
multi-meson
DIS

0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9NC
0.0 ± 15.9%

QE
single meson
multi-meson
DIS

0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9CC100.0 ± 17.1%

QE
single meson
multi-meson
DIS

0.0 ± 15.9
91.3 ± 14.1
8.7 ± 8.0
0.0 ± 15.9NC
0.0 ± 15.9%

QE
single meson
multi-meson
DIS

0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9
0.0 ± 15.9νe
0.0 ± 15.9%νμ100.0 ± 17.1%

Total:

100.0 ± 0.0

Table 9.2: Breakdown of remaining atmospheric neutrino MC background for KS0 →π + π − Method #2 search. The background is broken down by true neutrino ﬂavor
and neutrino interaction. A description of possible neutrino interactions is describedin 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 inTable 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
electrons that are characteristic of the KS0 → π + π − Method #2 search.

163

SourceSystematic Error (%)

Physics Simulation
Fermi momentum
Correlated decay
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

0.6
5.5
3.7
4.4

Detector
Water quality (incl. stat. error)
Energy scale

17.0 (6.6)
0.6

Event Reconstruction
Fiducial volume
Ring counting
Number of decay electrons
Detector response asymmetry

1.5
1.4
2.0
0.2

Statistical error

1.5

Total

19.1

Table 9.3: Systematic errors on signal detection eﬃciency for the KS0 → π + π − Method#2 search. The number shown for the uncertainty due to water quality includes thestatistical error of the p → μ+ K 0 MC sample described in section A.2.3 which itself
is shown within the parenthesis.

9.5

Total Systematic Error of “KS0 → π +π − Method#2” Search

Tables 9.3 and 9.4 summarize the total systematic error on the signal detection eﬃciency and background rate respectively of the KS0 → π + π − Method #2 search. The
detail of the systematic error estimation is described in Appendix A.

164

SourceSystematic Error (%)

Physics Simulation
ν FluxAbsoluteν/ν̄νe /νμν cross-section
QE
Single π
MA (QE & single π)
Coherent πMulti πNC/CC ratio
π Nuclear Eﬀect
Elastic
Charge exchange
Absorption
Production
Fermi momentum
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

10.0
1.3
0.5
0.2
9.7
8.9
0.5
1.0
2.1
2.5
1.2
∼0
4.3
6.3
∼0
∼0

Detector
Water quality
Energy scale

27.7
11.9

Event Reconstruction
Fiducial volume
Ring counting
Number of decay electrons
Detector response asymmetry

1.2
1.1
2.0
4.4

Statistical error (1000 yr)

9.9

Total

37.1

Table 9.4: Systematic errors on background rate for the KS0 → π + π − Method #2
search.

Chapter 10
Search for “KL0 ”
10.1

Event Selection(D4) not selected by KS0 search (I-III) event selections(E4) 500 p.e. < potot < 8000 p.e.
potot is the total charge(F4) nringt ≥ 2nringt 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 < pμ−cand. < 410 MeV/c
The μ-candidate is the μ-like ring with momentum nearest 326.5 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 < 0When the free proton decays via p → μ+ KL0 the ﬁnal state particles consist of a
primary muon and the products from the KL0 interaction in water or KL0 decay. The
kinematics of the muon are the same as described in section 7.1. The kinematics ofthe KL0 are described in section 1.3.
With the assumption of no excess signal beyond the background expectation,
optimization of the event selection thresholds for the KL0 search is determined using
the p → μ+ KL0 and atmospheric neutrino MC and choosing the thresholds which
maximize the p → μ+ KL0 sensitivity.
To ensure the KL0 search is independent of the KS0 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+ K 0 MC and atmospheric neutrino MC.
There are three distinct peaks in the potot distribution of the p → μ+ K 0 MC; eachcorresponding to diﬀerent ﬁnal state kinematics. The ﬁrst peak on the left typicallyconsists of events with the least energetic ﬁnal state kinematics such as KL0 → π ± μ∓ νwith only one or two visible, non-showering remaining particles. The second peaknear the middle of the distribution corresponds to ﬁnal kinematics typically with
one visible, showering remaining particle such as KL0 → π ± e∓ ν and KL0 → π + π − π 0 .
The third peak at larger values of potot corresponds to the most energetic ﬁnal state
kinematics in which all remaining particles are visible such as KL0 → 3π 0 . There aremany diﬀerent types of KL0 interactions in water as summarized in Table 1.2 each with
diﬀerent ﬁnal state kinematics. Because of this, KL0 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+ K 0 MC and atmospheric neutrino MC. As expected,
there are two or three rings found for KL0 → π ± e∓ ν decay where the primary muon

167

and remaining electron are always visible but remaining pion can be near Cherenkov
threshold. As expected, KL0 → 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
threshold respectively. The number of rings for KL0 → π + π − π 0 and KL0 → 3π 0 are
also as expected. Single ring events typically come from KL0 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+ K 0 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 eachring for both the p → μ+ K 0 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+ K 0 event. Figure 10.4 shows the number of decay
electron distribution for both the p → μ+ K 0 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 326.5 MeV/c.
Figure 10.5 shows the pμ−cand. distribution for both the p → μ+ K 0 MC and atmospheric neutrino MC. The p → μ+ K 0 MC distribution is symmetric and peaks at
319.4 ± 0.2 MeV/c; within 2% of the the expected value of 326.5 MeV/c.
The vertex separation, vsep. , is deﬁned as:vsep. ≡ (vμ − vKL ) · dμ(10.1)

168

Where vμ is the MS ﬁt vertex of the μ-candidate found by the algorithm describedin section 5.2.3.3, vKL is the vertex found using the timing ﬁt algorithm describedin section 5.2.4 corresponding to the KL0 decay or interaction point and dμ is a unit
vector of the reconstructed direction of the μ-candidate. Positive (negative) values ofvsep. mean the KL0 decay or interaction point is separated from the proton decay pointin the opposite (same) direction as dμ . With this deﬁnition, criterion (J4) is applied.
Figure 10.6 shows the vsep. distribution for both the p → μ+ K 0 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 aredesigned 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 thesame 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 thepattern PID likelihood described in section 5.1.3 to reject events with rings thatoverlap the μ-candidate since overlapping rings tend to have a charge pattern that issimilar to showering particles. Figure 10.7 shows the the pattern PID likelihood of
the μ-candidate ring for both the p → μ+ K 0 MC and atmospheric neutrino MC.
Criterion (L4) is used to select events in which the μ-candidate Cherenkov angle isconsistent 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+ K 0 MC andatmospheric neutrino MC. For p → μ+ K 0 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 peakat 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.

Events/1489.2day

169

700

ATM-ν MC0p→μK MCKL→e±π±ν600± ±KL→μ π ν
KL→3π0+ - 0KL→π π π500KL→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+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-D4). The hatched regions
show the contributions from KL0 interaction in water and dominant KL0 decay modes.
The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized tothe 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.

Events/1489.2day

170

ATM-ν MC0p→μK MCKL→e±π±ν

5000

KL→μ±π±ν0KL→3πKL→π+π-π04000KL→int.
Other

3000

2000

1000

0

1

2

3

4

5

nringtFigure 10.2: The nringt distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-E4). The hatched regions
show the contributions from KL0 interaction in water and dominant KL0 decay modes.
The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized tothe atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line
indicates the event selection threshold.

ATM-ν MC
p→μK0 MC± ±KL→e π νKL→μ±π±ν
KL→3π080+ - 0KL→π π πKL→int.

70

μ-likee-likeATM-ν MCp→μK0 MC± ±KL→e π ν60KL→μ±π±ν
KL→3π0+ - 0KL→π π π50KL→int.

Other

Events/1489.2day

μ-likee-like100

Events/1489.2day

Events/1489.2day

171

μ-likee-like25

ATM-ν MCp→μK0 MCKL→e±π±ν

KL→μ±π±ν20KL→3π0+ - 0KL→π π πKL→int.

Other

60

Other

15

40

30
10

40
20

5

20
10

-8

-6

-4

-2

0

2

4

6

Events/1489.2day

nringt=2; ring #1 PID

22.5

μ-likee-likeATM-ν MC0p→μK MC20KL→e±π±ν± ±KL→μ π ν
KL→3π0

17.5

+ - 0

KL→π π πKL→int.

15

0

8
10
likelihood

-10

-8

-6

-4

-2

0

2

4

6

nringt=2; ring #2 PID

Other

20

μ-likee-likeATM-ν MC0p→μK MC

17.5

KL→e±π±ν± ±KL→μ π ν
KL→3π015

08
10
likelihood+ - 0

KL→π π πKL→int.

-10

-8

-6

-4

-2

0

2

4

6

nringt=3; ring #1 PID

Events/1489.2day-10

Events/1489.2day

07
μ-likee-likeATM-ν MCp→μK0 MC6KL→e±π±ν± ±KL→μ π ν
KL→3π05KL→π+π-π0
KL→int.

Other

12.5

8
10
likelihood

Other

4
12.5
10
3

10
7.5
7.5

2
5

5

-8

-6

-4

-2

0

2

4

6

Events/1489.2day

nringt=3; ring #2 PID

μ-likee-likeATM-ν MC7p→μK0 MC± ±KL→e π ν± ±KL→μ π ν

6

0

KL→3π

KL→π+π-π0
KL→int.

508
10likelihood

Other

-10

-8

-6

-4

-2

0

2

4

6

nringt=3; ring #3 PID

μ-likee-likeATM-ν MC7p→μK0 MC± ±KL→e π ν± ±KL→μ π ν

6

0

KL→3π

KL→π+π-π0
KL→int.

508
10likelihood

Other

1

1

6

8
10
likelihood

0

-10

-8

-6

-4

-2

0

2

nringt=4; ring #3 PID

4

6

8
10
likelihood

810
likelihood

ATM-ν MCp→μK0 MC± ±KL→3π0KL→int.

1

4μ-like

5

2

2

6

± ±

3

0

4

KL→π+π-π0

2

-2

2

KL→μ π ν3nringt=4; ring #2 PID

0

KL→e π ν

2

-4

-2

6

3

-6

-4

e-like

4

-8

-6

7

4

-10

-8

8

4

0

-10

nringt=4; ring #1 PID

Events/1489.2day-10

Events/1489.2day

0

1

2.5

2.5

0

Other

-10

-8

-6

-4

-2

0

2

nringt=4; ring #4 PID

4

6

8
10
likelihood

Figure 10.3: The PID likelihood distribution of each ring for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-F4). The
hatched regions show the contributions from KL0 interaction in water and dominant
KL0 decay modes. The statistical error of the p → μ+ K 0 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+ K 0 MC isnormalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot
vertical line indicates the event selection threshold.

Events/1489.2day

172

900
ATM-ν MC0p→μK MC800± ±KL→e π νKL→μ±π±ν
0

KL→3π

700

KL→π+π-π0
KL→int.

600

Other

500
400
300
200
100
0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Events/1489.2day

Figure 10.4: The number of decay electron distribution for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-G4). The
hatched regions show the contributions from KL0 interaction in water and dominant
KL0 decay modes. The statistical error of the p → μ+ K 0 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+ K 0 MC isnormalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot
vertical line indicates the event selection threshold.
120
ATM-ν MCp→μK0 MCKL→e±π±ν

100KL→μ±π±ν
KL→3π0KL→π+π-π0
KL→int.

80

Other

60

40

20

0

0

100

200

300

400

500

μ candidate momentum

600

700
800
MeV/c

Figure 10.5: The pμ−cand. distribution for p → μ+ K 0 MC (black solid line) andatmospheric neutrino MC (blue box) after event selections (A-H4). The hatchedregions show the contributions from KL0 interaction in water and dominant KL0 decay
modes. The statistical error of the p → μ+ K 0 MC is negligible. The box shows thestatistical error of the atmospheric neutrino MC sample. The atmospheric neutrino
MC is normalized to the live-time (1489.2 days). The p → μ+ K 0 MC is normalized
to the atmospheric neutrino MC by area. The pink arrows and dash-dot vertical lines
indicate the event selection region.

Events/1489.2day

173

80
ATM-ν MC0p→μK MC70± ±KL→e π ν± ±KL→μ π ν
0

KL→3π

60

KL→π+π-π0
KL→int.
Other

50
40
30
20
10

0
-1000 -800 -600 -400 -2000

200 400 600 800
cm

Vertex separation

Events/1489.2day

Figure 10.6: The vsep. distribution for p → μ+ K 0 MC (black solid line) and atmospheric neutrino MC (blue box) after event selections (A-I4). The hatched regions
show the contributions from KL0 interaction in water and dominant KL0 decay modes.
The statistical error of the p → μ+ K 0 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+ K 0 MC is normalized tothe atmospheric neutrino MC by area. The pink arrow and dash-dot vertical line
indicates the event selection threshold.
6ATM-ν MC0p→μK MCKL→e±π±ν5KL→μ±π±ν
0

KL→3π

+ - 0

KL→π π πKL→int.

4

Other

3

2

1

0

-4

-3

-2

-1

0

1

μ candidate pattern PID

2

3
4
likelihood

Figure 10.7: The pattern PID likelihood distribution for p → μ+ K 0 MC (black solidline) and atmospheric neutrino MC (blue box) after event selections (A-J4). The
hatched regions show the contributions from KL0 interaction in water and dominant
KL0 decay modes. The statistical error of the p → μ+ K 0 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+ K 0 MC isnormalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot
vertical line indicates the event selection threshold.

Events/1489.2day

174

2ATM-ν MC0p→μK MC

1.75

KL→e±π±ν

KL→μ±π±ν
0

KL→3π

1.5

KL→π+π-π0
KL→int.

1.25

Other

1
0.75
0.5
0.25
0

0

10

20

30

40

50

μ candidate Cherekov angle

60
degreeEvents/1489.2day

Figure 10.8: The μ-candidate Cherenkov angle distribution for p → μ+ K 0 MC (blacksolid line) and atmospheric neutrino MC (blue box) after event selections (A-K4). The
hatched regions show the contributions from KL0 interaction in water and dominant
KL0 decay modes. The statistical error of the p → μ+ K 0 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+ K 0 MC isnormalized to the atmospheric neutrino MC by area. The pink arrow and dash-dot
vertical line indicates the event selection threshold.
1

μ-likeproton-like
ATM-ν MCp→μK0 MC± ±KL→e π νKL→μ±π±ν

0.8KL→3π0KL→π+π-π0
KL→int.
Other

0.6

0.4

0.2

0
-2000 -1500 -1000 -5000500

μ candidate proton ID

1000

1500 2000
likelihood

Figure 10.9: The proton ID likelihood distribution for p → μ+ K 0 MC (black solidline) and atmospheric neutrino MC (blue box) after event selections (A-L4). The
hatched regions show the contributions from KL0 interaction in water and dominant
KL0 decay modes. The statistical error of the p → μ+ K 0 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+ K 0 MC isnormalized 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 thissearch.
The following criteria are used to deﬁne the sideband sample of the KL0 search:• FCFV• not selected by KS0 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 normalizedby live-time is 1196 ± 34.6 and 1104.9 ± 4.3 respectively.
Figure 10.10 shows the number of decay electron distribution. The dominantremaining 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 ± 1.9 cm. The negative shift of the vsep. distribution is taken into account as
systematic error. There are no events above 100 cm due to the sideband selection

Events/1489.2day

176

DATA
Atm-ν MC

600

500

400

300

200

100

0

0

1

2

3

4

5

6

7

8

9

10

number of decay electron (sideband)

Figure 10.10: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) in the sideband sample. The statistical error ofboth 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 theatmospheric neutrino MC is 36.5 ± 0.1◦ . This is smaller than the expected angle of38.5◦ from a muon with momentum of 326.5 MeV/c. This shift is taken into accountas 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 andatmospheric 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 andatmospheric neutrino MC is taken into account as systematic error.

Events/1489.2day

177

200
DATA
Atm-ν MC

175
150
125
100
75
50
25
0

0

200

400

600

800

μ candidate momentum (sideband)

1000
MeV/c

Events/1489.2day

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
100
80
60
40
20
0
-600

-400

-200

0

200

vertex separation (sideband)

400

600
cm

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.

Events/1489.2day

178

μ-likee-like200

DATA
Atm-ν MC

175
150
125
100
75
50
25
0

-5

-4

-3
-2
-1
0
1
2
3
4
5
likelihood
μ candidate pattern PID (sideband)

Events/1489.2day

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 ofboth is shown. The atmospheric neutrino MC is normalized to the data by area.

225

DATA
Atm-ν MC

200
175
150
125
100
75
50
25
0

0

10

20

30

40

50

μ candidate Cherenkov angle (sideband)60
degreeFigure 10.14: The μ-candidate Cherenkov angle distribution for data (red points) andatmospheric neutrino MC (blue box) in the sideband sample. The statistical error ofboth is shown. The atmospheric neutrino MC is normalized to the data by area.

Events/1489.2day

179

140

μ-likeproton-like
DATA
Atm-ν MC

120

100

80

60

40

20

0
-2000 -1500 -1000 -500

0

500

1000

μ candidate proton ID (sideband)

1500 2000
likelihood

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 bothis 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 thatare 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 disagreementin 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 mostdominant. 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
(A-C)
(D4)
(E4)
(F4)
(G4)
(H4)
(I4)
(J4)
(K4)
(L4)
(M4)

FCFV
not KS0
potot
nringtno. μ-likeno. decay-e
pμ−cand.
vsep.
pattern PID
Cherenkov angle
proton ID

Eﬃciency(%)

Atm-ν MCFC Data

97.3 ± 0.1
75.7 ± 0.1
75.6 ± 0.1
61.8 ± 0.1
58.5 ± 0.1
51.3 ± 0.1
46.2 ± 0.1
5.5 ± 0.1
4.8 ± 0.1
4.3 ± 0.1
3.7 ± 0.111105.8 ± 13.7
11097.0 ± 13.7
6910.6 ± 10.8
1953.9 ± 5.8
1303.1 ± 4.6
677.1 ± 3.2
339.5 ± 2.3
21.2 ± 0.6
7.4 ± 0.3
3.6 ± 0.2
2.4 ± 0.2

12232 ± 110.6
12225 ± 110.6
7714 ± 87.8
2144 ± 46.3
1399 ± 37.4
790 ± 28.1
385 ± 19.6
22 ± 4.7
4 ± 2.0
2 ± 1.4
1 ± 1.0

Table 10.1: KL0 search data events, signal detection eﬃciency and background rate
along the event selection described in section 10.1. The atmospheric neutrino MC isnormalized to the live-time.
the μ-candidate is selected as the μ-like ring with pμ nearest 326.5 MeV/c we expectpμ−cand. to typically be near this value. The peak of the distribution is 299.5 ± 1.6 MeV/c.
α = 97.9%; the data and atmospheric neutrino MC agree.
Figure 10.22 shows the vsep. distribution after event selections (A-I4). The meanof the atmospheric neutrino MC distribution is −5.0 ± 1.1 cm. 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

Events/1489.2 day

2011/02/10 09.31

10

5

10

4

10

3

10

2

DATA
Atm-nu MC

10

1

-1

10

1

2

3

4

5

6

7

8

9

10

KL event selection

Events/1489.2day

Figure 10.16: The event rate along the KL0 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).

DATA

500

Atm-ν MC

400

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.

Events/1489.2day

183

DATA

6000

Atm-ν MC

5000

4000

3000

2000

1000

0

1

2

3

4

5

nringtFigure 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.

μ-likee-likeDATA
Atm-ν MC

175
150

μ-likee-like

DATA

200

Atm-ν MC

175
150

Events/1489.2day

200

Events/1489.2day

Events/1489.2day

184

70

μ-likee-likeDATA
Atm-ν MC

60

50

125
125

40

100
100
30
75

75
20
50

25

25

0

0

-8

-6

-4

-2

0

2

4

6

Events/1489.2day

nringt=2; ring #1 PID

μ-likee-like90810likelihood

DATA
Atm-ν MC

80
70

-10

-8

-6

-4

-2

0

2

4

6

nringt=2; ring #2 PID

Events/1489.2day

-10

10

60

80

μ-likee-like0810likelihood

DATA
Atm-ν MC

70
60

-10

-8

-6

-4

-2

0

2

4

6

nringt=3; ring #1 PID

Events/1489.2day

50

μ-likee-like22.5

8
10
likelihood

DATA
Atm-ν MC

20
17.5
15

50

12.5

50

40
10

40
30

7.5

30
20

5

20
10

-10

-8

-6

-4

-2

0

2

4

6

Events/1489.2day

nringt=3; ring #2 PID

μ-likee-like

22.5

0

8
10
likelihood

DATA
Atm-ν MC

20
17.5

-10

-8

-6

-4

-2

0

2

4

6

nringt=3; ring #3 PID

Events/1489.2day

0

2.5

μ-likee-like20

DATA
Atm-ν MC

17.5
15

-10

-8

-6

-4

-2

0

2

4

6

nringt=4; ring #1 PID

22.5

μ-likee-like810likelihood

DATA

20

Atm-ν MC

17.5
15

15
12.5

12.5

12.5
10

10

10
7.5

7.5

7.5
5
2.5
0

0

8
10
likelihood

Events/1489.2day

10

-10

-8

-6

-4

-2

0

2

nringt=4; ring #2 PID

4

6

8
10
likelihood

5

5

2.5

2.5

0

-10

-8

-6

-4

-2

0

2

nringt=4; ring #3 PID

4

6

8
10
likelihood

0

-10

-8

-6

-4

-2

0

2

nringt=4; ring #4 PID

4

6

8
10
likelihood

Figure 10.19: The PID likelihood distribution for data (red points) and atmospheric
neutrino MC (blue box) after event selections (A-F4). The statistical error of both isshown. The atmospheric neutrino MC is normalized to the data by area. The pinkarrow and dash-dot vertical line indicates the event selection threshold.

Events/1489.2day

185

800
DATA
Atm-ν MC

700
600
500
400
300
200
100
0

0

1

2

3

4

5

6

7

8

9

10

Number of decay electron

Events/1489.2day

Figure 10.20: The number of decay electron distribution for data (red points) andatmospheric neutrino MC (blue box) after event selections (A-G4). The statisticalerror 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
120
100
80
60
40
20
0

0

200

400

600

μ candidate momentum

800

1000
MeV/c

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.

Events/1489.2day

186

70

DATA
Atm-ν MC

60
50
40
30
20
10
0
-1000 -750

-500

-250

0

250

500

750

Vertex separation

1000
cm

Events/1489.2day

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 arrowand dash-dot vertical line indicates the event selection threshold.

8
DATA
Atm-ν MC

7
6
5
4
3
2
1
0

-4

-3

-2

-1

0

1

μ candidate pattern PID

2

3
4
likelihood

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 errorof 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.

Events/1489.2day

187

1.2
DATA
Atm-ν MC

1

0.8

0.6

0.4

0.2

0

0

10

20

30

40

50

μ candidate Cherekov angle

60
degreeEvents/1489.2day

Figure 10.24: The μ-candidate Cherenkov angle distribution for data (red points) andatmospheric neutrino MC (blue box) after event selections (A-K4). The statisticalerror 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

0.8

0.6

0.4

0.2

0
-1000 -750

-500

-250

0

250

μ candidate proton ID

500

750 1000
likelihood

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 errorof 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 (%)

CC
SK-I: 11.0%

QE
single meson
multi-meson
DIS

3.1 ± 1.6
7.1 ± 2.3
0.8 ± 0.8
0.0 ± 0.8

NC
SK-I: 3.1%

QE
single meson
multi-meson
DIS

0.0 ± 0.8
1.6 ± 1.1
0.8 ± 0.8
0.8 ± 0.8

CC
SK-I: 73.3%

QE
single meson
multi-meson
DIS

30.9 ± 3.2
32.6 ± 3.5
8.9 ± 2.3
1.0 ± 0.7

NC
SK-I: 12.5%

QE
single meson
multi-meson
DIS

0.0 ± 0.8
5.5 ± 2.0
1.6 ± 1.1
5.5 ± 2.0

νeSK-I: 14.2%

νμSK-I: 85.8%

Total:

100.0 ± 0.0

Table 10.2: Breakdown of remaining atmospheric neutrino MC background for theKL0 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) areclassiﬁed by true parent neutrino ﬂavor and interaction mode and summarized inTable 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

KL0 candidate#2

NHITACEvis (MeV/c)
Dwall (cm)
potot (p.e.)
nring

1
589.9
209.8
5007.02
N (μ) 595.1⇒ N (μ) 290.8
1
458.9
0.42
30.6
-230.6

PID & momentum (MeV/c)number of decay electron
vsep. (cm)μ-candidate pattern PID likelihood
μ-candidate Cherenkov angle (◦ )μ-candidate proton ID likelihood

Table 10.3: The reconstructed information of the data candidate for the KL0 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

There is a single candidate found in the data for the KL0 search. Figure 10.26 showsthe event display for this candidate. The reconstruction information is summarizedin 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; thereconstructed ring is aligned with a visible ring edge. pμ is smaller than the expectedvalue by 10.9%. Although this event has large vsep. , the Cherenkov angle of the μcandidate 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 theνμ CCQE interaction with a recoil proton above Cherenkov threshold; one of thedominant 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
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
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;

RunMODE:NORMALTRG ID :00000111
T diff.:0.934E+0
FEVSK :81002803
nOD YK/LW: 2/ 1
SUB EV : 0/ 3
Dcye: 0( 0/ 0/ 0

Figure 10.26: The event display of the candidate for KL0 search. The thick blue solidline shows the reconstructed ring of the μ-candidate. The green (red) triangle shows
the primary (remaining) reconstructed vertex.

191

SourceSystematic Error (%)

Physics Simulation
Fermi momentum
Correlated decay
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

∼0
7.1
1.2
8.3

Detector
Water quality (incl. stat. error)
Energy scale

9.7 (5.9)
0.8

Event Reconstruction
Fiducial volume
Ring counting w/o timing cuts
PID
Number of decay electrons
vsep.
μ-candidate Pattern PID
μ-candidate Cherenkov angle
μ-candidate Proton ID

1.5
1.6
0.5
2.0
7.1
0.5
2.3
4.0

Statistical error

1.3

Total

17.3

Table 10.4: Systematic errors on signal detection eﬃciency for the KL0 search. The
number shown for the uncertainty due to water quality includes the statistical error of
the p → μ+ K 0 MC described in the text which itself is shown within the parenthesis.

10.6

Total Systematic Error of “KL0 ” Search

Tables 10.4 and 10.5 summarize the total systematic error on the signal detection
eﬃciency and background rate respectively of the KL0 search. The detail of the systematic error estimation is described in Appendix A.

192

SourceSystematic Error (%)

Physics Simulation
ν FluxAbsoluteν/ν̄νe /νμν cross-section
QE
Single π
MA (QE & single π)
Coherent πMulti πNC/CC ratio
π Nuclear Eﬀect
Elastic
Charge exchange
Absorption
Production
Fermi momentum
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

10.0
1.3
0.6
3.7
7.1
11.6
0.2
0.4
0.6
1.4
0.1
0.6
3.5
2.0
∼0
∼0

Detector
Water quality (incl. stat. error)
Energy scale

12.1 (11.5)
4.9

Event Reconstruction
Fiducial volume
Ring counting w/o timing cuts
PID
Number of decay electrons
vsep.
μ-candidate Pattern PID
μ-candidate Cherenkov angle
μ-candidate Proton ID

1.2
10.7
1.1
2.0
13.9
1.7
6.0
16.2

Statistical error (200 yr)

8.0

Total

34.2

Table 10.5: Systematic errors on background rate for the KL0 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 theparenthesis.

Chapter 11
Results
In the absence of any excess signal from the background expectation we calculate thelower limit on the proton lifetime using the Bayesian method outlined in [7]. Thismethod 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:  P (Γ|ni ) =e−(Γλi i +bi ) (Γλi i + bi )ni
P (Γ)P (λi )P (i )P (bi )dλi di dbi
ni !

(11.1)

where ni is the number of candidate events in the i-th proton decay search, Γ is thetotal 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
P (i ) = exp −(i − 0,i )2 /2σ,i(0 ≤ i ≤ 1, otherwise 0)(11.2)&'

−(bi Ci − b )2
1 ∞ e−b (b )nb,iexp
P (bi ) =db
(0 ≤ bi , otherwise 0) (11.3)
2
bi 0
nb,i !
2σb,i⎧⎪⎪⎨1 Γ > 0(11.4)
P (Γ) =⎪⎪
⎩0 Γ ≤ 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% conﬁdence level (CL) as:( Γlimit )N

i=1 P (Γ|ni )dΓ
CL = (Γ=0∞ )Ni=1 P (Γ|ni )dΓΓ=0(11.6)

Where N is the number of searches. The lower lifetime limit, τ /Bp→μ+ K 0 , is:τ /Bp→μ+ K 0 =1N[0,i · λ0,i ]

Γlimit i=1(11.7)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+ K 0 search issummarized in Table 11.1.

195

Samplei

Search12
3
4

KS0 → π 0 π 0
KS0 → π + π − Method #1
KS0 → π + π − Method #2
KL0

p → μ+ K 0
0,i (%) σ,i (%)

Atm-ν
nb,i σb,i (%)

8.8
10.5
2.5
3.7

1.1
3.0
0.1
2.4

10.3
11.8
19.1
17.3

Lower
limit
Data
(×1032 yr.)
ni

24.7
25.5
37.1
34.2

1
6
0
1

Combined lower lifetime limit (no systematic error correlation)
Combined lower lifetime limit (full systematic error correlation)
Table 11.1: Result of the lower lifetime limit calculation.

8.1
4.0
3.0
3.4
11
10

Chapter 12
Comparison With Previous SK
p → μ+K 0 Search
Table 12.1 summarizes the results of the p → μ+ K 0 search by Kobayashi [1] and theresults of this analysis (Regis). In Kobayashi’s analysis, the signal detection eﬃciency
is obtained using only the p → μ+ KS0 component of p → μ+ K 0 decay therefore forthis comparison the eﬃciency for this analysis is obtained in the same way.
The eﬃciency, background rate and data are all increased when comparing resultsfrom Kobayashi to this analysis in the KS0 → π 0 π 0 search (I). The reason for thisincrease was found to be a result of an inconsistency in the event selection describedin 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 andused zero or one decay electrons.
The combined lower lifetime limit obtained by Kobayashi is larger than this analysis mainly due to the diﬀerence in the number of data candidates in KS0 → 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 . The box
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 ofthe 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 thereconstructed 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 ofthe 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 ± 4.1 MeV/cwith 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 withthe 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 the12

software library version 02b
software library version 09b

198

SearchEﬃciency(%)

Background(evt./1489.2
day)

Data
(evt./1489.2
day)

Lower
limit
(×1032 yr.)K. [1](I)
5.4 ± 0.6(II)
7.0 ± 0.7(III)
2.8 ± 0.3
Combined lifetime limit

0.4 ± 0.3
3.2 ± 1.3
0.3 ± 0.2

0
3
0

7.0
4.4
3.6
13

Regis

(I)
7.7 ± 0.8†(II)
7.9 ± 0.9†(III)
2.4 ± 0.5†
Combined lifetime limit

1.1 ± 0.3
3.0 ± 0.7
0.12 ± 0.04

1
6
0

7.0
3.0
2.9
8.4

Table 12.1: Summary of the p → μ+ KS0 search results from Kobayashi (K. [1]) and thisanalysis (Regis). For each analysis the signal detection eﬃciency, background rate,
data and lower lifetime limit is summarized for each p → μ+ KS0 search: KS0 → π 0 π 0(I), KS0 → π + π − Method #1 (II) and KS0 → π + π − Method #1 (III). The total error
is shown. † The eﬃciency for Regis is obtained using only p → μ+ KS0 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 alarger statistical sample.

total momentum (MeV/c)

199

900
800
700
600
500
400
300
200
100
0

0

100

200

300

400

500

600

700

800

+

μ momentum (MeV/c)

total momentum (MeV/c)(a) Kobayashi [1](b) Reference data

900
800
700
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
RUN
4018
SUBRUN
41
EVENT
289990DATE 1997-May-11
TIME
4:18:53
TOT PE:
1688.
MAX PE:
26.8
NMHIT :
952
ANT-PE:
31.5
ANT-MX:
7.0
NMHITA:
34

NUM
1
RUN
4018
SUBRUN
41
EVENT
289990DATE 1997-May-11
TIME
4:18:53
TOT PE:
1688.
MAX PE:
26.8
NMHIT :
952
ANT-PE:
31.5
ANT-MX:
7.0
NMHITA:
34

1

1

1

1

1

1

1

1

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
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2003/05/26:;R= 2:NoYet
R :Z : PHI : G
11.98: 1.53: 1.62:0
CANG : RTOT : AMOM : M
33.4:
473:
84:
V=-0.804: 0.159:-0.5
30.0:
282:
51:
V= 0.819: 0.339:-0.4
Comnt;

1

RunMODE:NORMALTRG ID:00000011
Left
ring:
T diff.:0.128E+0:81002003
pFEVSK
:
223
MeV/c
μ
nOD YK/LW:† 2/ 1
SUB EVring:: 0/ 2Right
Dcye: 2( 1/ 1/ 0

1

1

1

1

1

1

1

1

pμ : 235 MeV/c(a) Reference data

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/29:;R= 2:NoYet
R :Z : PHI : G
11.97: 1.69: 1.61:0
CANG : RTOT : AMOM : M
35.5:
465:
95:
V=-0.822: 0.199:-0.5
32.0:
269:
55:
V= 0.804: 0.254:-0.5
Comnt;

1

RunMODE:NORMAL†TRG ID:00000011
Left
ring:
T diff.:0.128E+0:81002003
pFEVSK
:
281
MeV/c
μ
nOD YK/LW: 2/ 1
SUB EVring:: 0/ 2Right
Dcye: 2( 1/ 1/ 0
pμ : 213 MeV/c

1

1

1

1

1

1

1

(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 momentumof each ring is shown. The dagger (†) indicates the ring selected as the μ-candidate.

NUM
25
RUN
10034
SUBRUN450
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

NUM
1
RUN
10034
SUBRUN450
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

1

1

1

1

1

1

1

1

1

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2003/05/26:;R= 2:NoYet
R :Z : PHI : G
13.44:-13.29:-0.10:0
CANG : RTOT : AMOM : M
35.6:
377:
67:
V=-0.400: 0.763:-0.5
28.0:
120:
22:
V= 0.823: 0.183: 0.5
Comnt;

1

1

1

1

1

1

1

1

(a) Reference

RunMODE:NORMAL†TRG ID:00000111
Left
ring:
T diff.:0.833E+0:81002803
pFEVSK
:
233
MeV/c
μ
nOD YK/LW: 2/ 1
SUB EVring:: 0/ 5Right
Dcye: 2( 2/ 0/ 0

pμ : 163 MeV/c

1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
1990/00/00:NoYet:NoYet
2009/06/29:;R= 2:NoYet
R :Z : PHI : G
13.42:-13.17:-0.10:0
CANG : RTOT : AMOM : M
34.7:
364:
74:
V=-0.408: 0.765:-0.4
28.0:
116:
24:
V= 0.823: 0.183: 0.5
Comnt;

1

1

1

RunMODE:NORMAL†TRG ID:00000111
Left
ring:
T diff.:0.833E+0:81002803
pFEVSK
:
252
MeV/c
μ
nOD YK/LW: 2/ 1
SUB EVring:: 0/ 5Right
Dcye: 2( 2/ 0/ 0

pμ : 164 MeV/c

1

1

1

1

1

(b) This analysis

Figure 12.3: Event display of the second event selected by this analysis but notselected using the reference data. The reconstructed momentum of each ring is shown.
The dagger (†) indicates the ring selected as the μ-candidate.

events

events

201

12

10

25

20

8
15
6
10
4
5
2

0

-200

-150

-100

-50

0

50

100

μ candidate rec-true momentum(a) Reference

150

200
(MeV/c)

0

-200

-150

-100

-50

0

50

100

μ candidate rec-true momentum

150

200
(MeV/c)(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 atrue 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 sourcesof 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+ K 0 using a combined analysis
method. Additionally, a new analysis technique using vertex separation is introduced
to search for p → μ+ KL0 . Although substantial eﬀort was made so this vertex separation algorithm is as eﬃcient as possible in distinguishing the p → μ+ KL0 signal fromthe atmospheric neutrino background, there are two modiﬁcations we have in mind
which may improve the vertex separation algorithm. There was insuﬃcient time topursue 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 thefraction of charge in each PMT associated with the μ-candidate and use only thatcharge information in reconstructing the kinematics of the μ-candidate rather thanthe masking area described in section 5.2.2.
Second, the current analysis only considers the physical separation between the

202

203
vertex of the μ-candidate and the remaining particles however in true p → μ+ KL0
decay there is a temporal separation as well. There may be improved ability to
distinguish the p → μ+ KL0 signal from atmospheric neutrino background by using
both the physical separation of the two vertices as well as the timing diﬀerence whichmatches the expected decay time of KL0 .
The proton decay lifetime sensitivity is proportional to the exposure provided thebackground 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, SKIV data sets with exposures respectively of 49.2 kt-yr, 33.8 kt-yr and 32.9 kt-yr as of
September 2010 and achieve a lower lifetime sensitivity of ∼ 2 × 1033 years.

Chapter 14
Conclusion
Proton decay via p → μ+ K 0 was searched in the SK-I data with exposure of 91.7 kt-yr.
This analysis extended upon the work of Kobayashi [1] to include a new combined
analysis method and a search for p → μ+ KL0 .
Although p → μ+ K 0 is one of the dominant modes predicted by SUSY GUT
models, there was no evidence for p → μ+ K 0 decay as a result of this analysis.
The number of candidate events are consistent with the background predicted byatmospheric neutrino MC.
We calculated a combined lower lifetime limit of p → μ+ K 0 to be 1.1 × 1033 years
at 90% conﬁdence level.

204

AppendicesA

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 bycategory according to their source which include: physics simulation, the detector andevent 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+ K 0 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.
A.1.1

“KS0 → π 0 π 0 ” 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 theatmospheric neutrino MC. First, the true vertex is required to be more than 1 mfrom 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 iswithin the FV but the ring-counting reconstruction (section 5.1.2) ﬁnds fewer than 3rings we also stop any further reconstruction. Otherwise, the event reconstruction isunchanged from the procedure described in section 5.1.
A.1.2

“KS0 → 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 estimatedby a comparison of the default model with another model. The default modelof Fermi momentum that is used for the p → μ+ K 0 simulation is measured byelectron-12 C 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]; aFermi gas with a surface momentum of 225 MeV/c.
The largest absolute diﬀerence in signal detection eﬃciency is used as systematic error.

207• Correlated decay: The process of correlated decay and its implementation in
the p → μ+ K 0 simulation is described in section 3.1.1. In the default p → μ+ K 0
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.
• KL0 → KS0 regeneration: The systematic error from regeneration is estimatedseparately within the oxygen nucleus and in the SK tank water. The process ofregeneration 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 determinationof 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/ν̄ ratio: The systematic error on the ν/ν̄ 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 crosssection 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 inbackground rate is used as systematic error.
• Axial Vector Mass (MA ): To estimate the systematic error, QE and singleπ production neutrino events are re-weighted with the assumption of an axial
mass of 1.1 GeV/c2 rather than the default value of 1.2 GeV/c2 . The absolute
diﬀerence in background rate is used as the systematic error.
• NC/CC ratio: The systematic error on the the NC/CC ratio is estimated bychanging the ratio ±20%. The largest absolute diﬀerence in background rate isused 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 systematic 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 modelin 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+ K 0 simulation
measured by electron-12 C scattering [17] described by the distribution shown in
Figure 3.1. The fraction of events with Fermi momentum above 225 MeV/c isneglected.
The absolute diﬀerence in background rate is used as the systematic error.
• KL0 → KS0 regeneration: Regeneration is not taken into account in the atmospheric neutrino MC simulation.
The systematic error for regeneration was estimated as the fraction of eventswith a KL0 generated. This fraction is negligible.
A.2.3

Detector (Signal and Background)• Water quality: The time variation of the attenuation length measured bycosmic 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.
• Water quality of “KS0 → π 0 π 0 ” search: To estimate the systematic
error on signal detection eﬃciency we use a sample of ∼ 10, 000 p → μ+ K 0
MC events generated with random vertex distributed at least 1 m distantfrom the inner detector wall. The systematic error on background rateis 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 scatteringparameters 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) respectively. The event reconstruction of the p → μ+ K 0 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 statisticalerror of the p → μ+ K 0 (atmospheric neutrino) MC sample.
• Water quality of “KS0 → π + π − Method #1” search: To estimate
the systematic error on signal detection eﬃciency and background rate we
generate p → μ+ K 0 and atmospheric neutrino MC respectively in the same
way as described above in “Water quality of ‘KS0 → π 0 π 0 ’ search” withthe 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
in “Water quality of ‘KS0 → π 0 π 0 ’ search”.
• Water quality of “KS0 → π + π − Method #2” search: To estimate
the systematic error on signal detection eﬃciency and background rate we
generate p → μ+ K 0 and atmospheric neutrino MC respectively in the same
way as described above in “Water quality of ‘KS0 → π 0 π 0 ’ search” withthe 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+ K 0
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
in “Water quality of ‘KS0 → π 0 π 0 ’ search”.
• Water quality of “KL0 ” search: To estimate the systematic error on
signal detection eﬃciency and background rate we generate p → μ+ K 0
and atmospheric neutrino MC respectively in the same way as describedabove in “Water quality of ‘KS0 → π 0 π 0 ’ 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
in “Water quality of ‘KS0 → π 0 π 0 ’ 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 thresholdof 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 diﬀerencein the FV deﬁned using the reconstruction vertex and the FV deﬁned using thetrue vertex.
The FV using the true vertex is larger than the FV using the reconstructedvertex 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 neutrino data and MC using the control sample deﬁned by the FCFV (A-C) event
selections.
For the KS0 searches, four distributions are compared, dlfcti {i = 1, 2, 3, 4},
where dlfcti is the ring counting likelihood between i and ≥ i+ 1 rings describedin 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 = 4 the MC
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 andbackground rate from the default likelihood is used.
For the KL0 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 fromthe KS0 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 andthe change in signal detection eﬃciency and background rate from the default
likelihood is used.
• PID: This systematic error is estimated for all searches except KS0 → 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 corresponding to neutral current single π 0 is chosen using the following event selection:

213• FCFV• nring = 2• second ring is e-like (to compare PID likelihood in the ﬁrst ring)• 85 MeV/c2 < Mπ0 < 185 MeV/c2
To compare the PID likelihood distribution in the second ring, the PID of theﬁrst 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 π 0 is chosen using the following event selection:• FCFV• nring = 3• ﬁrst 2 rings contain 1 μ-like and 1 e-like• 85 MeV/c2 < Mπ0 < 185 MeV/c2
For the KS0 searches, we use the PID likelihood obtained only using the charge
pattern, described in section 5.1.3. The PID likelihood distribution from theﬁrst 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.
For the KL0 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 tolarger values than the data by 0.02 for the ﬁrst ring. The MC is shifted tosmaller 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 numberof 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 nonuniformity 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 thresholdof Ptot is changed ±1.2%.
The following sources are estimated only for the KL0 search• Vertex separation: The systematic error of vertex separation is estimated bycomparison of the reconstructed vertex separation and true vertex separation
using p → μ+ K 0 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 using this control sample is +12.8 cm.
To estimate the systematic error, the cut position is changed by ±12.8 cm
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 thethe pattern PID likelihood distribution with all event selections except pattern 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 thefollowing:• 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 momentum 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• FCFVThe (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 thethe μ-candidate Cherenkov angle distribution with all event selections except
μ-candidate Cherenkov angle applied (A-M4, except L4). The largest change insignal detection eﬃciency and background rate is used as the systematic error.
• μ-candidate Proton ID: The systematic error for μ-candidate proton ID isestimated 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+ K 0
for free proton decay.
• no particle decay in the GEANT simulation• aﬁt and proton ID reconstruction is applied• FCFVThe mis-PID probability is 4%. We assume the same mis-PID probability forelectrons, 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

SourceChange in signal detection
Source error eﬃciency for each search (%)
I
II
III
IV

Physics Simulation
Fermi momentum
Correlated decay
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

model
0%
20%
0%
0.2%
0%
0.2%

-2.6
-6.2
+6.2
+3.6
-3.6
+4.4
-4.4

-4.0
-5.9
+5.9
+3.2
-3.2
+4.0
-4.0

-0.6
-5.5
+5.5
+3.7
-3.7
+4.4
-4.4

∼0
-7.1
+7.1
+1.2
-1.2
+8.3
-8.3

+20%
-20%
+1.1%
-1.1%

-1.9
+1.1
+1.3
+1.2

+6.1
-4.7
+1.1
-1.4

-3.0
-16.0
+0.3
-0.6

-3.4
+3.8
-0.8
+0.4

true FV
see text
see text
±2.0%
+1.2%
-1.2%
+12.8 cm
−12.8 cm
+0.03
-0.03
+1◦
−1◦
see text

+1.5
-1.0
+1.2
±2.0
+0.4
-0.3
—
—
—
—
—
—
—

+1.5
+1.4
+0.6
±2.0
+1.1
-1.2
—
—
—
—
—
—
—

+1.5
+1.4
—
±2.0
+0.2
-0.2
—
—
—
—
—
—
—

+1.5
-1.6
-0.5
±2.0
—
—
-6.8
+7.1
-0.4
+0.5
-2.3
+0.9
4.0

Detector
Water quality
Energy scale
Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetryvsep.
μ-candidate Pattern PID
μ-candidate Cherenkov angle
μ-candidate Proton ID

Table A.1: Summary of source errors and change in signal detection eﬃciency foreach systematic error source for each search I-IV (see section 6.2). Entries with ‘—’
are not applicable for that search.

219

SourceSource error

Change in background rate
for each search (%)
I
II
III
IV

Physics Simulation
ν FluxAbsoluteν/ν̄νe /νμ

10.0
pos.
neg.
pos.
neg.

10.0
+1.2
-1.3
+0.2
-0.2

10.0
+1.2
-1.3
+1.1
-1.1

10.0
+1.2
-1.3
-0.5
+0.5

10.0
+1.2
-1.3
-0.6
+0.6

+10%
-10%
+20%
-20%
see text
+30%
-30%
+5%
-5%
+20%
-20%

+0.1
-0.1
+4.3
-4.3
+3.9
∼0
∼0
1.6
-1.6
+4.6
-4.8

+1.3
-1.3
+14.0
-14.0
+11.7
∼0
∼0
+0.5
-0.5
-1.8
+1.9

+0.2
-0.2
+9.7
-9.7
+8.9
+0.5
-0.5
+1.0
-1.0
2.0
-2.1

+3.7
-3.7
+7.1
-7.1
+11.6
+0.2
-0.2
+0.4
-0.4
+0.6
-0.6

+20%
-20%
+30%
-30%
+25%
-25%
+30%
-30%
model
see text
see text

+1.3
-1.3
+1.8
-1.8
+1.2
-1.2
-3.1
+3.1
-1.9

+1.8
-1.8
+1.2
-1.2
+3.2
-3.2
-6.1
+6.1
-0.7

+2.5
-2.5
-1.2
+1.2
∼0
∼0
-4.3
+4.3
-6.3
∼0
∼0

+1.4
-1.4
-0.1
+0.1
+0.6
-0.6
-3.5
+3.5
-5.5

ν cross-section
QE
Single π
MA (QE & single π)
Coherent πMulti πNC/CC ratio
π Nuclear Eﬀect
Elastic
Charge exchange
Absorption
Production
Fermi momentum
KL0 → KS0 regeneration (nucleus)
KL0 → KS0 regeneration (water)

(a)

220

SourceSource error

Change in background rate
for each search (%)
I
II
III
IV

Detector
Water quality
Energy scale

+20%
-20%
+1.1%
-1.1%

-1.0
-15.7
-1.5
+1.5

-3.2
-2.9
+1.1
-1.2

-27.7
-27.1
-2.3
-11.9

+3.9
+0.4
+0.7
-4.9

true FV
see text
see text
±2.0%
+1.2%
-1.2%
+12.8 cm
−12.8 cm
+0.03
-0.03
+1◦
−1◦
see text

+1.2
-1.2
+5.6
±2.0
+4.1
-4.1
—
—
—
—
—
—
—

+1.2
+3.7
∼0
±2.0
+3.0
-3.4
—
—
—
—
—
—
—

+1.2
+1.1
—
±2.0
∼0
-4.4
—
—
—
—
—
—
—

+1.2
-10.7
-1.1
±2.0
—
—
-8.0
+13.9
-1.3
+1.7
-3.6
+6.0
+16.2

Event Reconstruction
Fiducial volume
Ring counting
PID
Number of decay electrons
Detector response asymmetryvsep.
μ-candidate Pattern PID
μ-candidate Cherenkov angle
μ-candidate Proton ID(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 eachsearch 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. Hänssgen 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 Conference, 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 Conference, 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