UNIVERSITY OF CALIFORNIA,
IRVINE

Search for the Diffuse Supernova Neutrino Backgroundat Super-Kamiokande
DISSERTATION

submitted in partial satisfaction of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
in Physics

byKirk Ryan Bays

Dissertation Committee:
Professor Henry W. Sobel, Chair
Professor Jonas Schultz
Professor Guarang Yodh2012

c 2012 Kirk Ryan BaysTABLE OF CONTENTS
Page
LIST OF FIGURESv

LIST OF TABLES

viii

ACKNOWLEDGMENTS

ix

CURRICULUM VITAEx

ABSTRACT OF THE DISSERTATION

xiii

1 Introduction
1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 SN1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 The DSNB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 The First SK Study . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Other searches for the DSNB . . . . . . . . . . . . . . . . . . . . . .

1
1
2
8
9
12
13

2 The Super-Kamiokande Detector
2.1 Introduction to the Detector . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Timeline of the Detector . . . . . . . . . . . . . . . . . . . . .
2.1.3 Detector Details . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Physics in the Detector . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The Water System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Radon Free Air System . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 The DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 ID DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 OD DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14
14
14
16
17
19
23
25
26
26
29
30

3 Detector Calibration
3.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 DT Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32
32
34
35

ii

3.4

Water Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Laser Measurements . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Decay Electrons . . . . . . . . . . . . . . . . . . . . . . . . . .

38
38
39

4 Software Tools
4.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Muon Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Multiple Coulomb Scattering Estimation . . . . . . . . . . . . . . . .
4.6 Cherenkov Angle Reconstruction . . . . . . . . . . . . . . . . . . . .
4.7 dE/dx reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Alternate Muon Fitting . . . . . . . . . . . . . . . . . . . . . . . . . .

43
43
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46
47
51
51
52
54

5 Modeling
5.1 The Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Atmospheric Neutrino Backgrounds . . . . . . . . . . . . . . . . . . .
5.3 DSNB Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57
57
58
62

6 Analysis: Event Reduction
6.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
OD triggered events . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charge cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fiducial volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50 µs cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calibration events . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noise cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 2-peak cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Incoming Event Cut . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Solar Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Spallation Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1 Spallation Likelihood Variables . . . . . . . . . . . . . . . . .
6.5.2 Method of Determining Spallation . . . . . . . . . . . . . . . .
6.5.3 Multiple Muons . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.4 Spallation Summary . . . . . . . . . . . . . . . . . . . . . . .
6.6 Pion Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Multi Ring Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 OD-Correlated Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 ‘Sub-event Cut’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Cherenkov Angle Distribution . . . . . . . . . . . . . . . . . . . . . .
6.11 Reduction Efficiency Summary . . . . . . . . . . . . . . . . . . . . . .

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70
72
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80
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88
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7 Analysis: Limit Extraction
92
7.1 Cherenkov Angle Regions . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2 Extended Maximum Likelihood Fit . . . . . . . . . . . . . . . . . . . 94
7.3 Inclusion of Systematic Errors . . . . . . . . . . . . . . . . . . . . . . 96
7.3.1 Energy Scale and Resolution Uncertainty . . . . . . . . . . . . 96
7.3.2 Atmospheric ν Background Systematic Errors . . . . . . . . . 97
7.3.3 Energy Independent Efficiency Systematic Error . . . . . . . . 100
8 Results
102
8.1 Basic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8.2 Comparison to 2003 Result . . . . . . . . . . . . . . . . . . . . . . . . 106
9 Limit on SN Emission Spectrum
108
9.1 Making a General Relic Model . . . . . . . . . . . . . . . . . . . . . . 108
9.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
10 Conclusion and Future

114

Bibliography

116

AppendicesA
Appendix A - Spallation . . . . . . . . . . . . . . . . . . . . . . . . .
A.1
Spallation: SK-I/III Combined Likelihoods . . . . . . . . . . .
A.2
SK-II likelihoods . . . . . . . . . . . . . . . . . . . . . . . . .
A.3
Spallation: Algorithm . . . . . . . . . . . . . . . . . . . . . .
BAppendix B - spectral PDFs . . . . . . . . . . . . . . . . . . . . . . .
B.1
SRN PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2
SK-I remaining background fits . . . . . . . . . . . . . . . . .
B.3
SK-II remaining background fits . . . . . . . . . . . . . . . . .
B.4
SK-III remaining background fits . . . . . . . . . . . . . . . .
CAppendix C - NC . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DAppendix D - Expanded fit results . . . . . . . . . . . . . . . . . . .

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144
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151
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159
163
168

iv

LIST OF FIGURES
Page
1.1
1.2
1.3

Expected events from galactic SN . . . . . . . . . . . . . . . . . . . .
Examples of theoretical DSNB spectra . . . . . . . . . . . . . . . . .
2003 final data sample . . . . . . . . . . . . . . . . . . . . . . . . . .

10
11
13

2.1 A schematic of the SK detector. . . . . . . . . . . . . . . . . . . . . .
2.2 Schematic of the Hamamatsu R3600 PMT . . . . . . . . . . . . . . .
2.3 Quantum efficiency of the Hamamatsu R3600 PMT . . . . . . . . . .
2.4 Event rate predictions for different SRN interaction modes . . . . . .
2.5 Interaction cross sections . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Example event display . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Schematic of the SK Water Purification System. . . . . . . . . . . . .
2.8 Schematic of the radon free air system. . . . . . . . . . . . . . . . . .
2.9 Schematic of the SK ID DAQ. . . . . . . . . . . . . . . . . . . . . . .
2.10 Schematic of the SK OD DAQ. . . . . . . . . . . . . . . . . . . . . .

16
18
19
21
22
23
24
25
28
29

3.1
3.2
3.3
3.4
3.5

LINAC information . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical TQ map . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Light intensity vs. distance distribution . . . . . . . . . . . . . . . . .
SK-III water transparency . . . . . . . . . . . . . . . . . . . . . . . .
Nef f vs water transparency . . . . . . . . . . . . . . . . . . . . . . .

34
37
40
41
42

4.1
4.2

Example distribution of 3-hit combinations . . . . . . . . . . . . . . .
Example dE/dx distribution for a typical muon. . . . . . . . . . . . .

52
54

5.1

Spectra of the four remaining backgrounds. . . . . . . . . . . . . . . .

62

6.1 Distribution of deposited charge . . . . . . . . . . . . . . . . . . . . .
6.2 2-peak event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Max number of hits outside main timing peak . . . . . . . . . . . . .
6.4 SK-I def f vs energy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 def f of final sample . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 cos(θsun ) distribution . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 SK-I solar cut background fit . . . . . . . . . . . . . . . . . . . . . .
6.8 Spallation half-life vs energy . . . . . . . . . . . . . . . . . . . . . . .
6.9 Schematic showing spallation distance variables. . . . . . . . . . . . .
6.10 SK-I/III LT RAN S . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66
68
69
71
72
73
75
77
78
81

v

6.11 SK-I/III LLON G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Multiple ring event display . . . . . . . . . . . . . . . . . . . . . . . .
6.13 SN relic Cherenkov angle distribution . . . . . . . . . . . . . . . . . .
6.14 Signal efficiency now compared to 2003 . . . . . . . . . . . . . . . . .

81
86
89
90

7.1
7.2

Final data Cherenkov angle distribution showing backgrounds . . . .
Asymmetric Gaussian normalization . . . . . . . . . . . . . . . . . .

94
99

8.1
8.2
8.3
8.4

SK-I LMA fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-II LMA fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-III LMA fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LMA fit likelihoods . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103
103
104
105

9.1
9.2
9.3

Positron spectra in SK from MC . . . . . . . . . . . . . . . . . . . . . 110
Limit contour event rate vs ν temperature . . . . . . . . . . . . . . . 111
Limit contour luminosity vs ν temperature . . . . . . . . . . . . . . . 112

A.1 Single muon SK-I/III spallation likelihoods . . . . . . . . . . . . . . .
A.2 Stopping muon SK-I/III spallation likelihoods . . . . . . . . . . . . .
A.3 Multiple muon (type 1) SK-I/III spallation likelihoods . . . . . . . .
A.4 Multiple muon (type 2) SK-I/III spallation likelihoods . . . . . . . .
A.5 Single muon SK-I/III random likelihoods . . . . . . . . . . . . . . . .
A.6 Stopping muon SK-I/III random likelihoods . . . . . . . . . . . . . .
A.7 Multiple muon (type 1) SK-I/III random likelihoods . . . . . . . . . .
A.8 Multiple muon (type 2) SK-I/III random likelihoods . . . . . . . . . .
A.9 Multiple track SK-I/III likelihoods . . . . . . . . . . . . . . . . . . .
A.10 Single muon SK-II spallation likelihoods . . . . . . . . . . . . . . . .
A.11 Stopping muon SK-II spallation likelihoods . . . . . . . . . . . . . . .
A.12 Multiple muon (type 1) SK-II spallation likelihoods . . . . . . . . . .
A.13 Multiple muon (type 2) SK-II spallation likelihoods . . . . . . . . . .
A.14 Single muon SK-II random likelihoods . . . . . . . . . . . . . . . . .
A.15 Stopping muon SK-II random likelihoods . . . . . . . . . . . . . . . .
A.16 Multiple muon (type 1) SK-II random likelihoods . . . . . . . . . . .
A.17 Multiple muon (type 2) SK-II random likelihoods . . . . . . . . . . .
A.18 Multiple track SK-II likelihoods . . . . . . . . . . . . . . . . . . . . .
B.19 SK-I SRN PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.20 SK-II SRN PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.21 SK-III SRN PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.22 SK-I SRN PDFs II . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.23 SK-II SRN PDFs II . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.24 SK-III SRN PDFs II . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.25 SK-I νµ CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.26 SK-I νe CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.27 SK-I NC elastic fit . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.28 SK-I µ/π CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.29 SK-II νµ CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi

122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
145
146
147
148
149
150
151
152
153
154
155

B.30 SK-II νe CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.31 SK-II NC elastic fit . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.32 SK-II µ/π CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.33 SK-III νµ CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.34 SK-III νe CC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.35 SK-III NC elastic fit . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.36 SK-III µ/π fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.37 NC MC background 1 . . . . . . . . . . . . . . . . . . . . . . . . . .
C.38 NC MC background 2 . . . . . . . . . . . . . . . . . . . . . . . . . .
C.39 NC MC background 3 . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

156
157
158
159
160
161
162
164
166
167

LIST OF TABLES
Page
2.1

Trigger summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

4.1

Alternate muon fitter entry position thresholds . . . . . . . . . . . . .

56

6.1
6.2
6.3

SK-I/III solar cut inefficiency summary . . . . . . . . . . . . . . . . .
Spallation Cut Signal Efficiencies . . . . . . . . . . . . . . . . . . . .
Cut Signal Efficiency (Systematic Error) Summary . . . . . . . . . .

76
84
91

7.1

Total Efficiency Systematic Error . . . . . . . . . . . . . . . . . . . . 100

8.1

90% CL flux limit (ν̄e cm−2 s−1 ), Eν > 17.3 MeV . . . . . . . . . . . 102

9.1

Summary of limit values. . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.1
D.2
D.3
D.4

Spallation products . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-I complete fit results . . . . . . . . . . . . . . . . . . . . . . . . .
SK-II complete fit results . . . . . . . . . . . . . . . . . . . . . . . . .
SK-III complete fit results . . . . . . . . . . . . . . . . . . . . . . . .

viii

121
169
169
170

ACKNOWLEDGMENTS
I would like to thank Michael Smy for his kind and unfailing mentorship. He wasalways available, always helpful, and always had my best interests in mind. I learned
more from him than anyone else in my academic career, and without him, I would
have accomplished much less.
I would like to thank Hank Sobel for his friendly advisorship. He was always there
when I needed him, always kind, and opened all the doors to allow me to participate
in world class science and enter the scientific community.
I would like to thank Masayuki Nakahata for his friendly genius, overseeing my work in
the low energy group, and always being willing to take some time out of his incredibly
busy schedule to answer a question or examine my progress.
I would like to acknowledge the rest of the UCI group - Mark Vagins, Bill Kropp, Jeff
Griskevich - for their friendliness and helpfulness. Thanks for making work a goodplace to be.
To my colleagues in the low energy group and Super-K: it’s been a pleasure doing
science with you.
Thanks to my thesis committee and professors, for their work at helping me be abetter scientist.
And to my fellow graduate students who I’ve known for all or part of the last sevenyears - it was a good time; best of luck and hope to see you out there!

ix

CURRICULUM VITAE
Kirk Ryan Bays
Research Interests:
Particle physics, especially neutrinos and cosmic rays. Participating in new experimental techniques and discoveries.
Education:
University of California, Irvine
Ph.D., Physics, 2012
• Thesis Topic: Search for the Diffuse Supernova Neutrino Background at SuperKamiokande• Adviser: Professor Henry W. Sobel• Area of Study: Experimental Neutrino Physics
Oregon State University
B.S., Physics and Computational Physics, June 2004
• Minor in Mathematics
Publications:
K. Abe et al. (Super-Kamiokande Collaboration). Solar neutrino results in SuperKamiokande-III. Phys. Rev. D 83, 052010 (2011).
doi:10.1103/PhysRevD.83.052010

R. Wendell et al. (The Super-Kamiokande Collaboration). Atmospheric neutrino
oscillation analysis with subleading effects in Super-Kamiokande I, II, and III. Phys.
Rev. D 81, 092004 (2010).
doi:10.1103/PhysRevD.81.092004

E. Thrane et al. (The Super-Kamiokande Collaboration). Search for astrophysicalneutrino point sources at Super-Kamiokande. ApJ 704 503 (2009).
doi:10.1088/0004-637X/704/1/503

x

E. Thrane et al. (The Super-Kamiokande Collaboration). Search for neutrinos from
GRB 080319B at Super-Kamiokande. ApJ 697 730 (2009).
doi:10.1088/0004-637X/697/1/730

M. Fechner et al. (The Super-Kamiokande Collaboration). Kinematic reconstructionof atmospheric neutrino events in a large water Cherenkov detector with proton identification. Phys. Rev. D 79 112010 (2009).
doi:10.1103/PhysRevD.79.112010

H. Nishino et al. (The Super-Kamiokande Collaboration). Search for Proton Decay
via p → e+ π 0 and p → µ+ π 0 in a Large Water Cherenkov Detector. Phys. Rev. Lett.
102, 141801 (2009).
doi:10.1103/PhysRevLett.102.141801

H. Watanabe et al. (The Super-Kamiokande Collaboration). First study of neutron
tagging with a water Cherenkov detector . Astroparticle Physics 31 4 (2009).
doi:10.1016/j.astropartphys.2009.03.002

Conference Proceedings:
K. Bays and T. Iida for the Super-Kamiokande Collaboration. Supernova Relic Neutrino Studies at Super-Kamiokande. ICRC 2009, Lodz, Poland (presentation)

K. Bays for the Super-Kamiokande collaboration. Search for Supernova Relic Neutrinos at Super-Kamiokande. Neutrino 2010, Athens, Greece (poster)
Teaching Experience:
University of California, Irvine
September 2005 to August 2007

Teaching Assistant• TA for multiple classes. Helped develop TA curricula for other TA’s. Private
tutoring in physics tutoring center.

xiOregon State University
September 2002 to January 2004

Teaching Assistant• TA for multiple classes.

2003 to 2004

Special Student Assistant• Special student assistant to a blind physics undergraduate. Acted as lab partner in electronics lab. Three classes total.
Professional Experience:Super-Kamiokande
2006-2011

Graduate Student Researcher• Responsible for water transparency calibration via decay electrons for low energy group (2006-2007)• Participated in many on-site calibrations, using both a linear accelerator anda custom deuterium-tritium generator• Carried out reactor neutrino feasability study, including coding and creating
custom MC (2007-2008)• Processed and implemented 16 N cut for official SK-III solar analysis (20082009)• Major improvements to supernova relic neutrino analysis (thesis work), including new techniques for determining cosmic ray spallation• PRD paper submitted Nov. 2011, preprint: http://arxiv.org/abs/1111.5031
Indiana University Cyclotron Facility
Research Experience for Undergraduates

Summer 2002

• Worked on the final physics experiment at the IUCF
doi:10.1103/PhysRevLett.91.142302.
• Responsible for measuring the exact geometry of a lead glass detector arrayfor entry into GEANT.
Hardware and Software Skills:• Experience with water Cherenkov techniques, machine shop tools, a magnet steered
linear accelerator, computers and electronics• Familiarity with Fortran, C, PAW, Root, ZBS, UNIX, shell scripts, GNU make,Mathematica, GEANT, NQS, and morexii

ABSTRACT OF THE DISSERTATION
Search for the Diffuse Supernova Neutrino Backgroundat Super-Kamiokande
By
Kirk Ryan Bays
Doctor of Philosophy in Physics
University of California, Irvine, 2012
Professor Henry W. Sobel, Chair

A search for the SN relic neutrino signal (also known as the diffuse supernova neutrino background) was carried out at Super-Kamiokande (SK), using SK-I, II, and III
data (176 kton-years total data, over 2853 live days). The search improved over theprevious SK search by a multitude of improvements to the cuts, improving average
efficiency from 52% to about 75%, further reducing backgrounds in the final sample,
and lowering the analysis energy threshold from 18 MeV (total positron energy) to
16 MeV (except for SK-II). The spallation cut was especially improved, by means ofa new longitudinal tracking technique, better tuning, and a better muon fitter thatallows muon categorization. The study also utilizes a new unbinned likelihood fit,with two new remaining backgrounds considered, and many new systematic errors.
These improvements make this study the most sensitive search for SN relic neutrinos
to date. No signal was found, although a positive indication of a relic component in
the SK-II and SK-III data set is interesting, if not significant. New limits were placedon many models, and a limit as a function of emitted neutrino spectrum is presented.

xiii

Chapter 1
Introduction
1.1

Neutrinos

In 1930, Pauli theorized a new particle in order to conserve momentum in beta decay
reactions. Termed the neutrino, its existence wasn’t experimentally verified until 1956
by Reines and Cowan (for which Reines received the Nobel prize in 1995). Originallybelieved to be massless, we know now that neutrinos indeed have mass, and thatthey come in three flavors, each associated with a lepton, and that the neutrino canundergo flavor change (‘oscillation’), as the mass eigenstates differ from the flavor
eigenstates.
In the standard model of physics, the neutrino is considered a fundamental
particle. Since we know it has mass, it interacts gravitationally, but the mass is
so small that this effect is negligible. As it is electromagnetically neutral, and does
not interact via the strong force, this leaves the weak nuclear force as the only realmeans the neutrino has of interacting with the rest of reality. Because of this, it isvirtually ghostlike, traveling through large quantities of matter as if it didn’t exist,
and is very difficult to study experimentally, typically requiring very large detectors
and sophisticated detection techniques.

1

Neutrinos are generated by nuclear reactions, such as fusion in the sun, fission in
the Earth’s crust and mantle, and man made nuclear reactors. Neutrinos are created
when cosmic rays interact with nuclei in the Earth’s atmosphere, creating showers ofoften unstable particles, whose decays produce neutrinos (termed atmospheric neutrinos). Man made neutrino beams now exist. A large amount of neutrinos remainfrom the big bang as well, termed big bang relic neutrinos, not to be confused withsupernova relic neutrinos. Many experiments exist that attempt to study neutrinos
from the various sources.
One use of neutrinos still in its infancy is the field of neutrino astronomy. Many
astrophysical phenomena should produce copious amounts of neutrinos, which can be
useful and distinct from studies of extraterrestrial objects through electromagnetic
radiation. Not only do neutrinos sometimes carry information not contained in electromagnetic radiation, but neutrinos are not blocked, scattered, or otherwise affectedby matter that may be encountered on the trip to Earth.
As of the time of this writing, the only extraterrestrial neutrinos definitively seen
on Earth are from the sun and from supernova SN1987A. As our understanding of
the properties of the neutrino advance along with the sophistication of our neutrino
detectors, it is expected that more sources will be detected, allowing us to learn new
and important things about the universe around us.
This thesis is the result of a search for a never before seen extraterrestrial neutrino signal.

1.2

Supernovae

The universe is full of stars, and they live interesting and varied lives. Stars heavier
then about eight solar masses tend to end their lives in an incredible explosion ofenergy we call a core collapse supernova, where for a brief time the star releases so2much electromagnetic radiation, it often outshines the entire rest of the galaxy it lives
in. Although there are other types of supernovae, core collapse supernovae are what
we are most interested in for the purpose of this thesis, and I will now attempt tosummarize our current understanding of them.
When a collection of matter in space (a nebula, for instance) becomes sufficiently
dense, it gathers all the matter in a region tightly in on itself, forming a star. Thismatter is all pulled towards the center of mass of the system. The temperature of
the matter increases with the density; once the temperature becomes high enough,fusion commences, and a star is born.
Most stars begin life comprised of mostly hydrogen, and spend the majorityof their life fusing that hydrogen into helium. The heat produced by this reaction
radiates out, creating an outwards pressure that counters the gravitational forces
seeking to pull the star towards its own center. The size of the star is determined by
the equilibrium of these forces.
When a star runs out of hydrogen to burn in its core, there is not a sufficient
force left to counter gravity, and the star collapses upon itself. If the star’s mass issmall (like our sun), electron degeneracy pressure will slow the collapse of the core,
but the contracting outer layers of the star will heat up and begin fusing remaininghydrogen. Since the outer layer is less confined then the core, the star will expand insize and become a red giant, and then eventually a white dwarf.
For stars with greater then about eight solar masses, however, the electron degeneracy pressure is not sufficient to slow the collapse of the star completely, and thecore’s density continues to increase. Just as with the star’s original birth, the temperature increases with density and pressure, until it is hot enough for helium fusion
to occur. As some hydrogen still exists in the outer portions of the star, hydrogento helium fusion can still takes place there, but in the core helium to carbon fusion
dominates, and the star becomes layered. When the core’s helium is exhausted, the3star collapses again, until the core temperature and pressure becomes high enoughfor the next most massive nuclei to fuse; again, a helium burning layer still exists, as
does a hydrogen burning layer.
As the core moves on to increasingly dense elements to burn, the star becomeslayered like an onion. Each phase of burning takes successively less time to finish,
and the star quickly cycles towards its inevitable demise. Silicon burning in thecore signals the final stage before complete collapse; once silicon starts to fuse into
nickel-56, the star’s life is measured in days [1].
Once the silicon in the core is exhausted, the star begins to collapse again, but
this time no further fusion processes exist to stop it. Some of the nickel in the core
will decay to iron, and the core at this stage will be a combination of nickel and iron.
For stars that begin with more then around eight solar masses, the remaining coreat this point will be heavier then the Chandrasekhar limit, and electron degeneracypressure will be overcome. In this case, the matter in the star accelerates towards thecenter, achieving velocities of up to .2 c, and the density increases rapidly, causing
the temperature to climb as well.
The high temperature in the core makes electron capture processes favorable,
and electrons and protons are quickly converted into neutrinos and neutrons. As
electrons disappear, the electron degeneracy pressure becomes smaller, which causes
the collapse to occur more quickly, causing higher temperatures, which makes theelectron capture processes occur even more quickly. This positive feedback effectincreases the rate of supernova collapse, and also turns many of the electrons into
electron neutrinos, and many of the protons into neutrons, such that the mass becomescomprised mostly of neutrons. Many heavy elements remain however, especially inthe outer layers of the star, and it is believed that most of the heavy elements in theuniverse are created in core collapse supernovae, and spread into the universe by the
resulting explosion, where they can collect and mix with other matter, and eventually4form galaxies and solar systems like ours. The quick transformation of most of the
protons to neutrons is called a neutronization burst (or deleptonization burst). The
neutrinos created in this burst are inside the core, which is reaching densities large
enough to slow or even trap the neutrinos from escaping; generally the neutronization
burst neutrinos escape the star in a ∼10 ms window.
At some point in the collapse, the density in the core will reach a point where
neutrinos are largely trapped; the boundary of the mass from which neutrinos cannot
easily escape is called the neutrinosphere. Neutrinos created in the core will diffuse
outwards and finally escape from the surface of the neutrinosphere; inside it is so densethat neutrino-neutrino interactions become very important and cannot be neglected.
The collapse continues until nuclear densities are achieved, where neutron degeneracy pressure and neutron-neutron interactions form the final barrier to continued
collapse. For stars starting with less then about 20 solar masses this barrier will not
be overcome, and the rapidly collapsing matter hits it like the proverbial brick wall.
So abruptly is it reached, in fact, that the collapsing matter rebounds, and what wasa collapse becomes an explosion, as the energy of the collapse is transformed into an
expanding shock wave.
The expanding super-sonic shock wave will interact with the still infalling matter,
where it can break heavy nuclei into radioactive elements, which decay and emit light.
It can also free protons, which are quickly neutronized via electron capture, producing
neutrinos.
As the supersonic shock wave expands, the super-heated neutron core (around100 billion K) releases neutrinos in pairs of neutrinos and anti-neutrinos of all flavors.
This neutrino ‘thermal burst’ releases almost a hundred times as many neutrinos
as were created by the neutronization burst. This thermal burst releases ∼1046 J
of energy, and cools the core to more stable levels. The thermal neutrinos diffuse
out of the neutrinosphere as the core expands; it takes ∼10 seconds for all of the5thermal neutrinos to escape. Thus, the energy of a supernova comes originally fromgravitational potential; is converted to heat; then finally released mostly as neutrinos(∼ 99%), kinetic energy of the accelerated particles (∼1%) and light (∼ 0.1%). As theneutronization burst neutrinos are created earlier and not trapped, and the thermal
neutrinos are created later and are trapped in the expanding neutrinosphere, the twoshould be separated in time when reaching Earth.
Those who model supernovae often find that the rebound shock is not sufficient
to explain the full supernova explosion, and that on its own, the shock wave would
likely stall, losing all its energy to interactions with infalling matter. It is generally
supposed that the thermal neutrinos provide the rest of the energy necessary to
explain the explosion; calculations indicate that if the thermal neutrinos can transfer
as much as 1% of their energy to the infalling matter, the explosion can be well
explained [2]. There is still some confusion as to how exactly this energy transfer
occurs, however.
Neutrinos and anti-neutrinos of all flavors are created in roughly equal proportions during the thermal burst, though there are slightly more electron type neutrinos
created overall if we include those from the neutronization burst. However, the neutrinos do not all interact in the same way. As time passes, neutrinos are created in
the thermal burst, and the shock wave causes the star to expand, all of which rapidly
causes cooling. The tau and muon flavor neutrinos will only interact with the mattervia neutral current interactions, as they are not energetic enough to create muons ortaus via charged current interactions, and thus find themselves the least restricted.
They are able to escape the neutrinosphere most easily, and can escape from deeper
in the core, where the temperature is still much hotter than the surface. On theother hand, electron neutrinos can interact on neutrons, and electron anti-neutrinos
on protons in charge current reactions. Since there are more neutrons than protons
in the core, electron neutrinos will be most restricted, can only escape from the most6

shallow depths, and will thus on average be cooler. In general, hEνe i < hEν̄e i <hEνµ ,ν̄µ i ≈ hEντ ,ν̄τ i.
Neutrinos stuck inside of or passing through the dense matter in the neutrinosphere will undergo oscillation via the MSW effect [3]. This can have a variety ofimportant effects on the spectrum shape of the emitted neutrinos and must be taken
into account for proper modeling. Oscillation and neutrino-neutrino interaction effects also may help explain how the neutrino burst transfers energy to the infalling
matter.
After the explosion, which blows off most of the light elements and outer layersof the star and leaves only the dense neutron core, stars beginning with mass less thanaround 20 solar masses are left as neutron stars. For stars beginning with between
about 20 to 50 solar masses, it is believed that the star’s core collapse will produce
a supernova explosion, but not all the mass will escape, and a black hole will be
produced. For stars above around 50 solar masses, it is thought that the collapse willlead directly to black hole formation, with no supernova explosion.
Supernovae are classified by their spectral properties. If the supernova spectrum
contains a hydrogen line (Balmer series) is it classified as Type II; if not, it is Type I.
These are further subdivided. However, most classifications are simply different typesof core collapse supernovae. An exception is Type Ia supernovae, which generally
occurs when a white dwarf in a binary star system accretes matter until it reaches
the Chandrasekhar limit of around 1.38 solar masses. There are some theories thatthe explosion occurs due to carbon fusion before a collapse is initiated; regardless ofthe cause, Type Ia supernovae are unique in that they all share an almost identicallight profile, as they all come from the same physical process finally reaching the same
threshold. This feature of a shared light profile - that is both readily identifiable andnearly identical to all Type Ia supernovae - makes Type Ia’s particularly useful to theastronomical community as a so called ‘standard candle’, allowing nearby objects to7

be calibrated in comparison.
Thus in general, all supernovae can be classified as either Type Ia, or core collapse; a main difference being the light profile, which is less transparent for the morecompact Type Ia supernovae. For Type Ia’s, most of the light ultimately comes fromthe decay of radionuclides, especially Ni-56 and Co-56, as opposed to the light froma core collapse supernova, which produces most of its light from energy originatingfrom the collapse shock wave. Type Ia supernovae are less common, produce lessneutrinos, and are generally not considered in the scope of this thesis.

1.3

SN1987A

On February 23, 1987, the light from a core collapse supernova in the Large Magellanic
Cloud, a nearby galaxy that is considered a satellite galaxy to our own, was seen on
Earth. The supernova is thought to have occurred approximately 51.4 kiloparsecs
away [4], and is the first nearby supernova seen by modern astronomy apparatus.
A small burst of neutrinos was detected approximately 3 hours prior to the arrival of the first light by three terrestrial detectors. The first two detectors, IMB
and KamiokaNDE (the predecessor to the current Super-Kamiokande), were water
Cherenkov detectors designed to study proton decay. KamiokaNDE detected 11 neutrino events, and IMB 8 neutrino events, coincident within seconds [5, 6]. Baksan,
a neutrino observatory in Russia, saw 5 events. These events were highly significant
compared to background, and constituted the first ever certain detection of neutrinos
from farther away then our sun.
The 1987A supernova neutrino burst verified the fundamental model of corecollapse, and generated a tremendous amount of interest and excitement in the scientific community. Literally thousands of scientific papers have been written about
the 24 neutrinos events detected, studying them in every manner imaginable. It can

8be argued that the scientific excitement of this event begat what we now know of as
modern neutrino astronomy.

1.4

The DSNB

With supernovae releasing on the order of 1046 J of energy, 99% as neutrinos, theneutrino flux from each supernova event is enormous. In a galaxy such as the MilkyWay, it is estimated a supernova will occur around 2 or 3 times a century [7]. Current
terrestial neutrino detectors are patiently waiting for another galactic supernova,
which would give us invaluable scientific data, and next generation detectors arebeing built with the hopes that a galactic supernova will occur soon. SK is currently
the world’s premiere detector for SN neutrino burst detection, and would see on theorder of thousands of events (see Fig. 1.1), allowing a precision measurement of thespectrum shape.
However, the wait could be decades, and there is an alternative to patience.
Although we would not see a significant neutrino burst from a supernova farther
away than our galaxy and its satellites, all of the supernovae that have exploded
throughout the history of the universe have released neutrinos, most of which havenever interacted and are still in existence. In fact, it is theorized that a backgroundof supernova neutrinos exists everywhere, from supernovae throughout all of time.
This signal is called the Diffuse Supernova Neutrino Background (DSNB), or alsofrequently referred to as the Supernova Relic Neutrino background. Although still
often called ‘relics’, this terminology is disfavored due to confusion with big bang
relic neutrinos. For convenience, I may refer to them as relics or SN relics during thecourse of this thesis, however.
Many cosmologists have considered the DSNB signal, constructing models thatpredict both the flux and the spectrum. The first models were crafted even before

9Figure 1.1: Expected number of events in SK (right axis) as a function of supernova
distance, for different interaction modes, from [8].
SN1987A [9, 10, 11], then after SN1987A with increasing interest and sophistication[12, 13, 14, 15, 16, 17, 18]. Some examples of theoretical spectra are shown in Fig. 1.2.
The models shown are those considered in our analysis: Malaney’s cosmic gas infall

102

Flux /cm /sec/MeV

10

1

-1

10

-2

10
LMA 03-3

10

6 MeV 09
Failed SN 09
Cosmic Gas 97-4

10
Heavy Metal 00
Chemical Evolution 97
-5

10

5

10

15

20

25

30

35

40

45

50

Neutrino energy (MeV)
MeV6bandFigure 1.2: Examples of theoretical DSNB spectra. The 6 MeV (from [19]) is shown
as a band, as the authors estimated exact total errors on their calculation. The yearof each model’s publication is also listed.
model [14]; Woosley and Hartmann’s chemical evolution model [13]; Kaplinghat etal.’s heavy metal abundance model [16]; Ando et al.’s LMA model [17] 1 ; Lunardini’s
failed supernova model [15] 2 ; and the variable neutrino temperature formulation of
Horiuchi et al. (6 MeV considered) [19]. Although the normalizations vary, the general shape and slope of the predicted spectra are relatively constant, which simplifies
the experimental analysis.
The DSNB has never been seen. The current world limit on DSNB flux is from1

The flux of the LMA model is increased by a factor of 2.56 from the paper, a revision introduced
at NNN05
2
Assumed parameters are: Failed SN rate = 22%, EoS = Lattimer-Swesty, and survival probability = 68%

11

a previous SK analysis (see next section). Even without accurate measurements ofthe spectra, placing limits on the flux (or seeing a signal) helps modelers constrain
theories, and can reveal important information about related quantities, such as supernova rates of stars, or star formation rates in galaxies, which go into the DSNB
models. As scientific models of supernovae themselves have advanced, cosmologists
have been able to more accurately understand the details of the neutrino oscillations
that occur inside a supernova, which should lead to more accurate DSNB predictions.
Recent models predict a DSNB flux that is on the cusp of discovery [18]. Theysuggest that a slightly improved sensitivity over the published SK analysis could resultin discovery of a signal, and have helped motivate the research that led to this thesis.

1.5

The First SK Study

A paper was published in 2003 detailing the first search for the DSNB at SK [20].
This paper was the culmination of the thesis research of a student [21]. Although a
DSNB signal was not seen, a flux limit was established that was ∼100 times more
stringent then the previous limit [22].
The basic method was to eliminate all conceivable backgrounds, then attempt
to model the spectrum of the remaining backgrounds. A χ2 fit was performed on theenergy spectrum of the data sample, with two background components and one signal
component. This method is benefited by how most DSNB models have very similar
spectrum shapes. From this fit (Fig. 1.3), a final limit was extracted of 1.2 ν̄ cm−2
s−1 for Eν̄ > 17.3 MeV, which has remained the most stringent limit on DSNB flux
until the research reported in this thesis.

12Event Rate / year / 22.5 kton / 4 MeV

14
12
10
8
6
4
2
0

20

30

40

50

60

70

80

Energy (MeV)
Figure 1.3: χ2 fit of final data sample in published 2003 analysis. Overlaid on theblack real data are dotted and dot-dashed red lines indicating the best fit νe and νµcharged current modeled backgrounds. Solid red is the sum of the two backgrounds,
and dashed blue is with the DSNB 90% CL flux limit added.

1.6

Other searches for the DSNB

Although SK currently has the best sensitivity for seeing the DSNB signal in theworld, other collaborations have performed searches that deserve to be recognized.
A non-comprehensive list includes Kamiokande (1991, [23]), Mont Blanc (1992, [24]),
SNO (2006, [25]), and KamLAND (2011, [26]).

13

Chapter 2
The Super-Kamiokande Detector
2.1

Introduction to the Detector

2.1.1

Detector Overview

After the success of the IMB and Kamiokande experiments, scientists were eager tobuild the next generation of detector. Although previously competitors, Americans
joined forces with Japanese scientists on their new detector, and a new international
collaboration was formed.
Originally KamiokaNDE meant Kamioka Nucleon Decay Experiment, as it was
designed as a proton decay experiment. However, due to the exciting advances in neutrino physics, the primary focus of the new detector was changed, and the Kamiokande
part of the new name, Super-Kamiokande, was chosen to be Kamioka Neutrino Detection Experiment.
The site of the detector is the same mine as that of the old Kamiokande experiment, the Kamioka mine in Japan. The mine, located precisely at Lat. 36◦ 25′ 32.5862
N., Long. 137◦ 18′ 37.1241 E., was once one of the world’s largest Zinc mines, but now
is used exclusively for physics experiments. The detector has an average of a 1 km
rock overburden (2700 m.w.e.), which largely shields the detector from cosmic rays.
14

Cosmic ray muons of energy less than ∼1.3 TeV cannot penetrate to the detector.
Super-Kamiokande (SK) is a giant 50 kton water Cherenkov detector in a stainless steel tank. The tank is a right cylinder 41.6 m high and 39.3 m in diameter. The
detector is divided into two sections, the inner detector (ID) and outer detector (OD).
The inner surface of the ID (32.5 kton) is lined with many (11146 for SK-I) inward
facing 20 inch Hamamatsu R3600 Photo-Multiplier Tubes (PMTs). The PMTs give
∼40% cathode coverage (except for SK-II). The rest of the ID surface is covered in
opaque black sheet, which is a dense polyethylene telephthalate fabric. This reduces
photon reflection and optically separates the ID and OD.
The surface of the OD is lined with 1885 outward facing 8 inch PMTs, allowing
the OD to operate as a veto for events entering from the outside. The rest of the OD
surface is covered in white Tyvek, to maximize photon reflection and improve the OD
light sensitivity.
As of the time of this writing (2011), SK is the largest water Cherenkov detector
tank ever built. The water within is kept ultra pure by continuous recirculation
through an extensive water purification system (section 2.3). Due to the size of SK,
it takes as long as two months to fill the tank with water when empty.
Above the tank is a research dome, which houses the control room, 5 electronics
huts (which hold the DAQ [section 2.5]), the LINAC (a linear accelerator used for
detector calibration [section 3.1]), and various instrumentation and storage.

15

Figure 2.1: A schematic of the SK detector.

2.1.2

Timeline of the Detector

SK began operating in April 1996 with 40% ID cathode coverage and 11146 ID PMTs.
In July, 2001, it was shut down for routine maintanance and upgrades. The period
from April 1996 to July 2001 is referred to as the SK-I period. During this period, in
1998, the SK collaboration released the first highly significant experimental evidence
for neutrino oscillations [27], and also confirmed the solar deficit [28].
On November 12, 2001, after the maintenance was completed and the tank
was being refilled with water, a catastrophic accident occurred. One of the PMTs
imploded when the tank was ∼75% full, causing a chain reaction resulting in the
implosion of almost all the underwater PMTs [29]. The chain reaction was violent
enough that it registered as a seismological event to a seismological recorder 8.8 km
distant.
6665 out of 11146 ID tubes were found to be destroyed. The water was drained
again, and the broken glass cleaned. Unfortunately remaking so many PMTs is a16

time consuming process, and it was decided to run the detector in the meantime.
The surviving tubes were redistributed throughout the detector, after being fittedwith new acrylic coverings (tube front) and ‘FRPs’ (fiberglass reinforced plastic, tubeback), to prevent the shock wave of any future tube implosions from causing anotherchain reaction. The detector was turned back on with 19% cathode coverage (47%that of SK-I), and ran until the new PMTs were ready in July 2005. This period ofdata is referred to as SK-II.
In 2002, due to the success of the experiment, the head of the KamiokaNDE
experiment, and SK collaborator, Masatoshi Koshiba, was awarded the Nobel Prizein physics (25%), along with Ray Davis Jr. (25%), “for pioneering contributions toastrophysics, in particular for the detection of cosmic neutrinos”.
The refitting of the PMTs took almost a year, and the detector was operational
again in June 2006. In August 2008, the SK electronics system was completely overhauled and a new upgraded system was put in place. The data period from June 2006
to August 2008 is called SK-III. Since September 2008, after the electronics upgrade
was completed, data taking has continued, and this period is referred to as SK-IV.

2.1.3

Detector Details

The SK tank is surrounded by 26 sets of vertical and horizontal Helmholtz coils tocompensate for the Earth’s magnetic field, which can cause PMT response to be
non-uniform. The coils reduce the ambient magnetic field from 450 mG to about 50
mG.
The PMTs used in SK are all hand blown borosilicate glass made by the Hamamatsu corporation. The 20 inch ID tubes (Fig. 2.2) were constructed specifically for
SK. Originally all of the 8 inch OD tubes were Hamamatsu R1408 model, originallyused in IMB, and then reused for SK. Unfortunately, the OD was also affected by the17Figure 2.2: Schematic of the Hamamatsu R3600 PMT
2001 accident, and most of the OD tubes in the lower two thirds of the detector had
to be replaced with new tubes. As of October 2010, 591 of the original IMB R1408
tubes remained, while 1253 of the tubes were the new, Hamamatsu R5912 model.
PMTs operate by releasing a photo-electron (p.e.) when struck by a photon (itdoesn’t always work; the success rate is measured by the tube’s quantum efficiency).
This photon is accelerated by a high voltage (about 2kV), then strikes a dynode.
When an accelerated electron strikes a dynode, more electrons are released, which
are all accelerated again to the next dynode. By the time the initial signal has madeit through the series of dynodes, 1 p.e. will have turned into about ten million p.e.
(gain of 107 ), which is output as an electronic signal to the DAQ. The downside tothis design is that it is highly susceptible to false signals, where a thermally excitedelectron in the PMT itself starts the chain reaction without any photon causing it.
PMTs show false positive low energy signals, or ‘dark noise’, at a rate of a few KHz.

18

Figure 2.3: Quantum efficiency of the Hamamatsu R3600 PMT
The naturally cool temperature of the SK water helps keep the dark noise rate frombeing even higher.
The quantum efficiency (QE) of a PMT is defined as the percentage of time thatan impinging photon will cause the PMT to fire. The QE is wavelength dependent,
and the QE for the Hamamatsu R3600 model PMT used in the ID is shown in Fig.
2.3.

2.2

Physics in the Detector

As a water Cherenkov detector, SK operates by observing Cherenkov light. Cherenkov
light is a ‘shock wave’ of light that occurs when something with charge travels fasterthan the speed of light inside a medium (never faster then the speed of light invacuum), much akin to the sonic boom of sound that occurs when a physical object
19

travels faster then the speed of sound in air. The condition for a charged object toradiate Cherenkov light is often written in terms of the index of refraction of themedium, n, as β > 1/n, where β = v/c. Some example Cherenkov energy thresholds
for charged particles are: e+/− .767 MeV; µ+/− 157.4 MeV; π + 207.9 MeV.
The Cherenkov light will be emitted at an angle θc with respect to the particle
track direction, where cosθc = 1/nβ.
For pure water, the index of refraction is about 4/3 (it’s wavelength dependent).
Highly energetic particles have a value of β very close to 1, which means they emit
Cherenkov light at an angle θc of 42◦ . Electrons in the detector, being so light, tend
to always be traveling at the speed of light, and emit light at this angle, while heavier
particles often travel slower and emit light at smaller angles.
When a neutrino interacts in the SK detector, it can produce a charged particle
such as an electron or muon with enough energy to create Cherenkov radiation. An
electron will only travel a short distance in the detector (10’s of cm) before becoming
sub-Cherenkov due to energy loss, and can be considered point like. Even during theshort distance it travels, however, it can produce enough light to be seen. The coneof light created will travel through the pure water and shine on the inner detector
wall as a shape such as an ellipse, where the light intensity is recorded by the PMTs.
Using the charge and timing of the light, critical information about the particle canbe reconstructed, such as location, direction, and energy. An example event is shownin Fig. 2.6.
Muons can be more complicated due to the continuous emission of light as it
travels in the detector, usually for the whole length of the detector before exiting.
Some muons are created by neutrino interactions, but many more (∼2 Hz) are cosmic
ray muons that penetrate the rock overburden and enter the detector. These eventsare easily distinguishable from muons created in the detector by use of the OD, andthe entire muon track can usually be reconstructed. Other charged particles, such as

20

Figure 2.4: Interaction modes of DSNB neutrinos in SK as calculated by [30].

21Figure 2.5: Neutrino interaction cross sections in a large water Cherenkov detector,
including resolution and threshold effects, from [8].
pions, are also seen.
SK can see neutrinos from the sun, from atmospheric cosmic ray interactions,from supernovae, from neutrino beams, and most likely from nuclear reactors, thoughthese are incredibly hard to isolate. Due to SK’s large size, the detector is also
useful for proton decay and dark matter searches. As this thesis is dedicated to SN
relic neutrinos, little detail will be given about the solar [31, 32], atmospheric [33],beamline, proton decay [34], or dark matter analyses [35], but information can easily
be found in the given references.
DSNB events would interact in SK mostly by means of inverse beta decay (ν¯e +p → e+ + n), about 100 times more then the next most likely interaction mode (seeFigures 2.4 and 2.5). Because this is the dominant reaction, SK is almost exclusively
sensitive to electron type anti-neutrino DSNB events. Furthermore, a free neutronis created in the reaction. In pure water, this neutron is captured by hydrogen,producing a 2.2 MeV gamma ray that is usually not detectable, but could possibly

22

Figure 2.6: A muon neutrino event interacting in the SK detector and making amuon, the Cherenkov light from which shines on the inner wall of the detector in aring (or conic section).
be seen in rare occasions or if the detector energy threshold can be lowered. This
neutron however opens up the possibility for possible neutron tagging physics in futurewater Cherenkov experiments with the addition of a doping material (for example,
gadolinium [36]).

2.3

The Water System

Water purity in the detector is of primary importance. The water needs to be clear,so the Cherenkov light can travel through it and reach the tubes without obstruction.
Furthermore, the water needs to be kept clean of radioactive particles that can cause
background.
23

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

PUMP
HEAT
EXCHANGER

PUMPREVERSEOSMOSISBUFFERTANK
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.
The SK water supply is a small river that runs through the mine. This watermust be filtered to meet the detector standards. The SK water is continuously recirculated through the filtration system, at a rate of 30-60 metric tons per hour (usuallyaround 50). This is also the fill rate when the detector is emptied.
The water system is pictured in Fig. 2.7. It starts with 1 µm mesh filtration
to remove larger particles and contaminants. A heat exchanger keeps the water cool(around 13◦ C) in order to curb bacterial growth. An ion exchanger removes ions,and UV radiation kills bacteria. It is further filtered through reverse osmosis, anda vacuum degasifier removes dissolved oxygen and radon gas (∼96% effective). An
ultrafilter removes particulates down to a size of 10 nm, and a membrane degasifier
further reduces radon and other dissolved gases.
Water entering the detector from the filtration system has a resistivity of around18.2 MΩ·cm, near the chemical limit, and radon in the water passing through the24

COMPRESSORCARBONCOLUMNBUFFERTANK

AIR FILTER(0.3mm)AIR DRIERCARBONCOLUMNHEATEXCHANGER

AIR FILTER(0.01mm)
AIR FILTER(0.1mm)

COOLEDCHARCOAL(-40 oC)

SUPER-KAMIOKANDE AIR PURIFICATION SYSTEM

Figure 2.8: Schematic of the radon free air system.
system is reduced by about seven orders of magnitude.

2.4

Radon Free Air System

The water isn’t the only thing that needs to be kept clean. Being a deep mine, there
are radioactive elements present in the rock and air that can not only cause background in the detector, but can also be harmful to the health of workers in the mine.
Most important of these contaminants is radon. In the mine, radon levels are seasonal
due to varying temperature differences and airflow. In the winter, radon concentrations tend to be a few hundred Bq/m3 , while in the summer the concentration ismuch higher, usually a few thousand Bq/m3 . Two special systems were developed,
one to keep the air in the detector area (dome and water purification system areas)clean of radon, the other to reduce radon in the detector itself.
The detector system (pictured in Fig. 2.8) supplies purified air to the gap between the top of the water and the lid of the tank. The system for the dome andsurrounding area starts at a hut outside the mine entrance. Here, fresh outside air
is collected, pressurized, and passed through a serious of carbon filters and cooled
charcoal, which remove the radon. The fresh air is then pumped into the SK work
area in the mine at a rate of about 10 m3 /min. The system removes more than 99.9%of the radon in the air that passes through it, and keeps radon concentrations in the25detector area to 10-40 Bq/m3 , which is safe for a sustained human environment.

2.5

The DAQ

This is just an overview of the pertinent information regarding the DAQ; more detailed
information on the DAQ hardware and structure can be found in reference [37].

2.5.1

ID DAQIn 2008, the SK ID DAQ was overhauled and replaced with new, custom hardware.
As this thesis focuses solely on data prior to this renovation, the new DAQ will not
be described. Detail on the new DAQ can be found in references [38, 39].
The ID and OD data acquisition systems (DAQs) are separate, and were designed
independently for different purposes.
Each PMT in the ID is connected via cable to an Analog Timing Module (ATM).
These modules are located in the periphial electronics huts in the dome above thetank. The ATM modules take the analog timing and charge information from a PMT
and digitize it using a 12 bit ADC. Each ATM module can handle up to 12 PMTs.
The ATM modules are grouped physically inside of what are called TKO (Tristan
KEK Online) crates [40]. There are 48 TKO crates, each holding up to 20 ATM
modules.
Each PMT has 2 channels on an ATM module, so that when reading out anddigitizing the data from one channel, data can be collected on the secondary channel,
reducing dead time. Each PMT signal is amplified and split 4 ways: the two digitizer
channels, a discriminator, and one to the flash ADC DAQ. The discriminator channel
checks if the signal passes a threshold of 0.25 p.e., and if this threshold is reached, thePMT triggers. The ADC starts to digitize the information from one of the 2 signal
channels and store it in its first in first out (FIFO) internal memory, and a 200 ns, -15

26

mV square wave pulse is sent to a global trigger (HITSUM). 200 ns is approximately
the longest time it could take for a Cherenkov photon to travel through the detector.
The ID-HITSUM signal is passed through an AC coupled discriminator to subtract out dark noise. After this process, the signal is reduced to approximately -11
mV/PMT.
The global trigger HITSUM is the analog sum of all self triggers, and any time
the square waves add up to more then a certain threshold, a global trigger is issued.
Information for each hit ID PMT is stored for 400 ns before and 900 ns after anytime
a global trigger is issued, for an event window of 1.3 µs. In the case of a global trigger,
the digitized timing and charge information is sent to and stored in Super Memory
Partner (SMP) boards, one per TKO crate, from which the data is eventually readout by server computers in the central electronics hut via an optical network called
the Fiber Distributed Data Interface (FDDI), and saved to permanent storage. If a
global trigger is not issued within sufficient time, the PMT information stored in theinternal FIFO memory of the ATM module is discarded.

27

20-inch PMT
TKO CHATM

x 240
20-inch PMT

x 20
ATM

TKO CHATM
interface
SUN classic
x 20
x 240

MP
ATM

MP
MP

online CPU(slave)

MP
MP
MP

x6

Memory Partner

VME

20-inch PMT
TKO CHSUN classic
ATM

online CPU(slave)
x 20
x 240

SUN classic
ATM

online CPU(host)

Analog Timing Module

online CPU(slave)TKO
SUN classic

FDDI

SUN sparc10

online CPU(slave)
SUN classic

online CPU(slave)
SUN classic

FDDI

online CPU(slave)
SUN classic

online CPU(slave)interface
SUN classic

online CPU(slave)MPMP

SUN classic

online CPU(slave)

MP
MP
MP
MP

interface

Memory Partner

VME
VME

20-inch PMT

TRG

TKO CHATM

TRIGGER
TRIGGERx 20
HIT INFORMATION

x 240
ATM

Analog Timing Module

TKO

Figure 2.9: Schematic of the SK ID DAQ.
28

PROCESSER

Figure 2.10: Schematic of the SK OD DAQ.

2.5.2

OD DAQThe OD DAQ is similar in design to the ID DAQ. Although the actual hardware
is different (custom paddle cards are used instead of TKO crates, LeCroy branddigitizers are utilized, and the PMTs are different models), the idea is the same: self
triggered PMTs (also with a self trigger threshold of 0.25 p.e.) send out a squarewave that combine into an OD-HITSUM signal, which issues an OD trigger when athreshold is surpassed. One notable difference is the length of time the informationis stored - when a global trigger is issued, a 1.3 µs window of ID TQ informationis stored, but 16 µs of OD TQ information is stored (10 µs before and 6 µs after
the global trigger is issued). Furthermore, a circular buffer exists for each channel
allowing up to 8 PMT pulses within the 16 µs time window, as the elongated timing29

window means separate but overlapping events occur more frequently.

2.5.3

Triggers

The detector has multiple triggers useful for different analyses. There are four main
trigger types: the ID triggers (high energy [HE], low energy [LE], and super low energy[SLE]), each of which have a different HITSUM threshold, and the OD trigger. Anyof the four triggers will result in a global trigger which stores the event information
into permanent storage.
The HE trigger is mostly used for atmospheric neutrino studies. The LE trigger
is good for SN relic events and solar neutrino events. The SLE trigger was introduced
to look for low energy solar neutrino events. The lower threshold of the SLE trigger
causes a much higher trigger rate (roughly an order of magnitude more triggers per
MeV the threshold is lowered). Much of the increase comes from background, suchas gammas from the rock walls and radioactivity from the PMT glass itself. In order
to effectively lower the low energy threshold and not be swamped by background,a prefilter was introduced for SLE events called the intelligent trigger (IT). The
IT does a quick vertex fit to SLE events and only saves those within the fiducial
volume (inner 22.5 ktons), eliminating much of the background. As computing powerincreased throughout SK-I, the IT system was upgraded to handle a higher event
rate, and the SLE threshold was lowered multiple times as SK-I progressed. During
SK-II, all thresholds were lowered to reflect the decreased cathode coverage. Trigger
thresholds are summarized in Table 2.1. The OD trigger has remained constant at
19 OD hits.

30Table 2.1: ID Trigger thresholds for SK-I through SK-III.
Name
HE
LE
SLE1
SLE2
SLE3
SLE4

SK-I Threshold-340 mV (31 hits, about 6 Hz)-320 mV (29 hits, about 16 Hz)-260 mV (May 1997 to May 1999)-250 mV (May 1999 to Sep 1999)-222 mV (Sep 1999 to Sep 2000)-186 mV (Sep 2000 to July 2001)

31

SK-II
-180 mV-152 mV-110 mV

SK-III-320 mV-302 mV-186 mVChapter 3
Detector Calibration
Herein I will summarize relevant detector calibrations; more details on many of thecalibrations can be found in [37].

3.1

LINAC

A medical LINear ACcelerator (LINAC) was acquired from a hospital and converted
into a calibration tool for SK in 1996 (described in depth in [41]). Permanently
housed in the dome area above the tank, the variable energy (roughly 5-18 MeV)
mono-energetic electron beam can be controlled (through bends and around corners)
with a series of steering magnets. Beam intensity is tunable, and the beam can becollimated such that electrons are injected into the tank at a low enough rate (downto around 0.1 per 2 µs microwave pulsed ‘bunch’) to allow single electron events(multiple electron events can still rarely occur, and are identified during the offline
analysis). The exact beam energy is measured with a germanium detector with anenergy resolution of 1.92 keV.
Multiple calibration port holes exist on the top of the detector, and the beampipe
can be lowered to a variable depth in the detector. In this fashion, many different
areas in the detector are accessible and can be calibrated (for example, to check the32

center of the detector compared to the sides, or the top compared to the bottom).
LINAC calibration data is taken after any major change to the detector to ensure
MC and data quality.
The LINAC was developed for the solar neutrino analysis, for which the energy
scale was measured to better than 1%. The energy scale can be extrapolated to higher
energies, however, and this calibration is also relevant for the DSNB analysis.
Knowing the location of the injection point also allows the data to be used tocheck the accuracy of vertex and direction reconstruction software. For example, in
SK-I, the LINAC data shows the energy resolution to be between 21% at 5 MeV to
13% at 16 MeV; the vertex resolution to vary from 180 cm at 5 MeV to 50 cm at 16
MeV; and the angular resolution to go from 37 degrees at 5 MeV to 21 degrees at 16
MeV, as can be seen in Fig. 3.1. SK-II energy resolution is about 18% at 16 MeV,
and vertex resolution is about 80 cm at 14 MeV [32]; for SK-III all resolutions areslightly slightly better than SK-I [42].
The LINAC has one major drawback: the beam pipe must always be directed infrom the top of the detector, thus only allowing a beam with a downwards direction.
Just as energy and position can be varied, it would be ideal if direction could bevaried as well to check all combinations of parameters.

33

LINAC (%)

TOWER FOR INSERTING BEAM PIPE
D2 MAGNET

D3 MAGNET

24

(a)
A
B
C
D
E
F
G
H

22

D1 MAGNET
LINAC

20
18

1300 cm
E C

A
4200 cm

16
BEAM PIPE
F D

B

H

G

14
12

Z

10

X
Y

4000 cm

4

6

8

10

12

14

16

18

total energy (MeV)

250

LINAC (degree)

LINAC (cm)(a) Schematic of the LINAC system. Various (b) Energy resolution in SK-I as measured bycalibration points in the detector are shown. the LINAC at various energies and beam injection position.

(a)

225
200

A
B
C
D
E
F
G
H

175
150
125

45
(a)

40
A
B
C
D
E
F
G
H

35
30
25

100
75

20

50
15
25
0

4

6

8

10

12

14

16

10

18

4

6

8

total energy (MeV)

10

12

14

16

18

total energy (MeV)(c) Vertex resolution in SK-I as measured by (d) Angular resolution in SK-I as measured by
the LINAC at various energies and beam injec- the LINAC at various energies and beam injection position.
tion position.

Figure 3.1: LINAC information

3.2

DT Generator

A deuterium-tritium (DT) generator is used to check the absolute energy scale forlow energy events [43]. It operates in conjunction with the LINAC, providing a crosscheck on the energy calibration. It is less time consuming to use then the LINAC
and better for monitoring long term stability with frequent checks. Furthermore, the34device output is isotropic, and isn’t limited to only downward going events like the
LINAC, thus allowing study of direction dependent effects.
The device is a custom built calibration tool consisting of a computer operated
crane that lowers the DT generator itself into the detector, and can raise and lower
it to specific depths. The accelerator isotropically produces 14.2 MeV neutrons via
the reaction 2 H +3 H →4 H + n, and the neutrons can then interact with 16 O in
the SK water to produce 16 N. The 16 N isotropically beta decays, with the primarymode (66%) having a half-life of 7.13 seconds and being accompanied by a 6.13 MeV
gamma. The second most likely mode (28%) has no accompanying gamma ray.
DT data is taken every few months, and the energy scale as determined by the
DT agrees with the results of the LINAC calibration to better than 1%. Various
positions in the tank are monitored to assure the energy scale at all regions are
consistent.

3.3

PMT Calibration

The detector PMTs need to be calibrated in order to understand the data properly.
The PMT timing and gain are especially critical; the PMT hit timing is the fundamental quantity that underlies all SK data, and the recorded charge, which is affectedby the gain, is also critical (for muon reconstruction, even if not for SN relic events,
which make a 1 p.e. per PMT assumption).
The PMT gain is approximately 107 , but needs to be calibrated for each PMT(by adjusting the PMT voltage), as a uniform detector response is desired to minimize
systematic errors. In order to achieve uniform response, the relative gain of each PMT
in SK is measured using a Xe lamp which is capable of producing light flashes of very
consistent (within 5%) intensity. Briefly described, the light from the Xe lamp is split,
and fed to a reference, as well as a scintillator ball which produces almost uniform light35

similar in wavelength to Cherenkov light (peaking at 440 nm). The light recordedby each PMT is then corrected to take into account distance traveled by the lightin water (water transparency effects), PMT acceptance (geometry), and scintillatorball non-uniformities. After corrections, the light is compared to the reference todetermine the PMT gain, which can be tweaked by adjusting PMT voltages. For
SK-I, the spread in the PMT gain was about 7%. For SK-II and SK-III, a method of
pre-calibrating some PMTs before mounting them in the tank, which the surrounding
PMTs could then be compared to, allowed improved measurements, and the SK-II
and SK-III gain spreads were within 2%.
PMT absolute gain is also measured. Even if the gain of each PMT is the same,
it is important that amount be carefully understood. This number is expressed asa conversion between ADC charge and number of photo-electrons. To measure this,a Ni-Cf source was used. The Cf source emits neutrons which are captured on Ni
wire, causing the emission of 6-9 MeV gamma rays. This source causes events witharound 50 hit PMTs, >99% of which are only 1 photo-electron hits. The resultant
conversion factors were as follows: 2.055 pC/p.e. for SK-I; 2.297 for SK-II; and 2.243
for SK-III. The Ni-Cf source is also used to measure the quantum efficiency (QE) of
each PMT on an individual basis. Not only can the QE for a PMT differ slightly fromthe manufacturer’s specifications, but the tubes installed in SK-III to replace those
destroyed in the accident are newer than the others and somewhat different (higher
quality in general).
Furthermore, in SK-II the Ni-Cf calibration found that in general the hit rates of
PMTs in the top of the detector were lower than those on the bottom by 3-5%. This
leads to a ‘top-bottom asymmetry’, which was carefully measured and modeled in the
MC by means of adding a z dependent term to the light absorption parameter. As theNi-Cf source releases gammas isotropically it can also be used to calculate any vertex
shift in the reconstruction software, which could cause events actually in the fiducial

36

980
970

Linear Scale

Log Scale960

T (nsec)

950
940
930
920
910
900
890
880
1

5

10

100

Q (p.e.)Figure 3.2: Example TQ map. Larger timings (vertical axis) represent earlier hits.
volume to reconstruct outside the fiducial volume or vice-versa. Any systematic bias
in the fitter could cause an error in the number of events in the fiducial volume; thiserror is measured to be on the order of 1%.
PMT timing must also be checked. Due to slewing, or the ‘time walk’ effect(where larger charge hits exceed the TDC threshold more quickly, causing different
response even if the hit time is the same) PMT response can vary as a function of
the amount of charge seen, which must be understood. Scatter plots of PMT timing
vs. pulse heights (called ‘TQ maps’) are constructed using a N2 laser connected toa diffuser ball, which is capable of creating diffuse light with a very small timing
spread. A typical TQ map is shown in Fig. 3.2. The light intensity can be varied
to measure the PMT timing response for different light inputs. The PMTs typicallyhave a measured timing resolution of around 3 ns for a single photo-electron pulse
height.
The PMT timing resolution is fine enough that for proper accuracy, the lengthof the cables connecting the tube (in the tank) to the electronics system (in the dome37

on top of the tank) must be measured and taken into account as well. In SK-I and
SK-II, to find the ‘time’ of the event for N2 laser calibration data, the average of the
TOF-subtracted timing distribution for the event (after noise hits are cleaned fromthe event) is used. However, this average can be affected by late or scattered hits,
which can be a position dependent effect. For events closer to the walls, for instance,
reflected hits are more likely, leading to systematic errors in this calibration. For
SK-III, the method was improved by using the timing peak rather than the average,
which led to greater timing accuracy.

3.4

Water Transparency

3.4.1

Laser Measurements

Lasers are used to directly measure light scattering and absorption parameters in avariety of wavelengths. SK-I and SK-II mostly used a titanium sapphire laser (tunable
to output light between 350 and 500 nm), a diffuser ball, and a CCD camera. Laserlight is directed through the diffuser ball via optical fiber and recorded by the CCD atdifferent distances; the change in intensity over distance allows determination of thewater transparency. Data must be taken at regular intervals as the water transparencychanges over time. For SK-III, Nitrogen and dye lasers were used, at 337 nm, 365
nm, 400, and 420 nm. The light attenuation length from laser measurements tends
to be about 90 meters and agrees well with separate measurements using cosmic raymuons. However, for the SN relic study, this data was only used as a cross check,and the water transparency parameters were obtained by the decay electron method
described below.
The SK MC utilizes a model with one water absorption parameter, and twowater scattering parameters (for Mie and Rayleigh scattering). The MC parameters
are obtained from the laser measurements as well.
38

3.4.2

Decay Electrons

Cosmic ray muons enter the detector at a rate of about 2 Hz, and about one in 20
will stop in the detector. These stopping muons decay into electrons with the wellknown Michel spectrum. These decay electrons can be identified by associating theevent with a muon that closely precedes it in time, and whose reconstructed muon
stopping point is near (< 5 m) in space to the location of the decay electron vertex.
With about 2850 live days of data from SK-I through SK-III, a very large sample ofthe events accumulate, and they can be used as an independent means of monitoring
detector stability.
Water transparency can be calculated from the decay electrons recorded during
the time in question. While maintaining the water transparency table for the SK low
energy group for SK-III (particulars of the SK-I and SK-II methods vary only slightly,
and are detailed in [37]), I used six day bins. During six days, many thousands of
decay electrons would be recorded.
A few simple cuts were required to ensure the decay electron quality, including
requiring that the decay electron follow the parent muon by between three and eightmicroseconds, in order to prevent contamination by events from the hardware aftertriggers (forced triggers that occur set times after HE triggers in order to try andcatch decay electrons, but often are empty; sufficient statistics exist that carefully
selecting the true decay electron events from this sample is not necessary). The
standard fiducial volume cut (where any event within 2 meters of the inner detector
wall is cut out) is also applied.
After cuts, the light recorded by the PMTs during each event were binned bydistance from the event vertex to the PMT. For each event only information insideof a 50 ns time window was used. The amount of contribution from each PMT was
corrected for occupancy and geometry, in the same way as these terms are corrected
for in the energy reconstruction (see section 4.2). When fitting each decay electron,
39

average log(intensity) seen by a PMT (p.e.)

P1
P2

1.4

1.424
-0.1140E-03

1.3

1.2

1.1

1

0.9

0.8

1000

1500

2000
2500
3000
3500
distance traveled by light (cm)Figure 3.3: The light intensity vs. distance distribution used to determine watertransparency from decay electrons, for a example 6 day period. The first bins exhibit
strange effects, and are neglected.
and when reconstructing the energy, both of which occur at the beginning of the
decay electron event selection, a water transparency must be assumed, so the processof determining the water transparency from decay electrons is iterative. Once a
distribution of light intensity vs distance the light has traveled is obtained (see Fig.
3.3), a simple line is fit to the data, and the water transparency is simply the inverseof the fit slope. The first bins of the distribution are not used in the fit, due to strange
effects for light traveling shorter distances, which were never fully understood. The
fit was found to be more accurate if the y-intercept of the fit line was fixed to an
average value, as opposed to a free-floating y-intercept. An error on the fit is also
recorded.
The water transparency is not constant (Fig. 3.4). Changes in temperature,
alterations to the water system, introduction of contaminants, and more can all affectthe water transparency, making constant monitoring of the water transparency critical40

Water transparency (cm)

18000

16000

14000

12000

10000

8000
100

200

300 400 500 600 700
elapsed days since July 12, 2006

Figure 3.4: Water transparency of SK-III, from the decay electron method. The bin
to bin variation in some cases exceeds the statistical error; this effect was not wellunderstood.
for accurate data analysis. A water transparency is used in the fitting process as acorrection to the light intensity recorded by each event. This correction, along withoccupancy and geometry effects, is used to convert the number of hits seen in theevent (within 50 ns) into an ‘effective’ number of hits, a number which is directly
proportional to the energy of the event.
Because of this, the accuracy of the water transparency measurement can beverified by monitoring the stability of the average value of this ‘effective’ number ofhits over time. Fig. 3.5 shows the average value of this parameter over time, as
opposed to assuming a constant water transparency of 90 meters. We can see that byusing the final values of the water transparency from decay electrons, the most stable
distribution is obtained. In fact, the average effective number of hits was stable towithin 1% over all SK-III.

41

average effective number of hits

295
290
285
280
275
270
265
260
255

wt from decay electrons

250
245

constant 90 meter wt

100

200

300

400 500 600 700
days since July 12, 2006

Figure 3.5: The difference in the stability of effective number of hits (see Eq. 4.1),
depending on water transparency assumed. Assuming a constant 90 meter watertransparency causes the Nef f to vary greatly, tracking the true water transparency.
The variation of Nef f assuming the water transparency from decay electrons is stable
to within 1%.

42Chapter 4
Software Tools
4.1

Vertex Reconstruction

Electrons and positrons resulting from an interaction will only travel a short distance(∼10 cm at 20 MeV, and ∼20 cm at 50 MeV) before stopping in the detector, and areconsidered point sources (an assumption that may come close to being inaccurate at
the highest energies, but is still reasonable considering the small distances comparedto the size of the detector). Reconstructing the vertex of these events is of primary
importance. Numerous vertex fitters were developed for the solar analysis. The
one with the best vertex resolution is BONSAI (Branch Optimization Navigating
Successive Annealing Iterations, with a vertex resolution of better then 50 cm > 16
MeV), which fits events based almost entirely on PMT hit timing.
In BONSAI, many possible starting points are constructed out of combinationsof four hit PMTs, for which a likelihood is calculated by matching timing residuals
to a timing residual likelihood shape determined from LINAC calibration data. The
likelihood is maximized by checking against 12 nearby points on a grid of successively
smaller sizes, down to 1 cm. A flat dark noise component is assumed. Bonsai wasused for all low energy (< 100 MeV) non-muon fits in the DSNB study. BONSAI

43

was introduced in the SK-II solar analysis, and is described there in more detail [32].
One nice feature of BONSAI is that it is least likely of all the SK low energy vertex
fitters to misfit an event. The fitter also returns a fit goodness value which can beused to evaluate the quality of the fit, and identify misfits.

4.2

Energy Reconstruction

First, it should be noted that all particle energies considered in this thesis are quoted
in terms of total energy, not visible energy. Secondly, the energy reconstruction always
assumes that the base particle is an electron (or positron). Other events (such as apion or muon) for whom this reconstruction algorithm is applied will be assigned anenergy that will be inappropriate; for instance a pion with a total energy of some
hundreds of MeV could conceivably be reconstructed as having an energy of 40 MeV
total energy, which is less than the pion rest mass and unphysical. However, all events
have a reconstructed energy using the following algorithm (since in many cases it is
not certain what the particle that caused the event really is), and all energy values
should be considered as a ‘total electron equivalent energy’. Ultimately this search
looks for inverse beta decay positrons, and we can can hope to remove all events thataren’t electrons or positrons through our cuts.
The energy reconstruction algorithm used was originally developed for the SK
solar neutrino analysis. However, events up to 100 MeV are considered ‘low energy’ in
SK, and the energy reconstruction can be applied to events at these higher energies.
For very low energy events (electrons and positrons < 5 MeV or so), PMTs are
typically hit by only one photon, and event energy can be reconstructed from thenumber of hit PMTs, ignoring the amount of light seen by each PMT. The higher theenergy of the event, the more the one photon per PMT assumption breaks down; acorrection is applied for accurate energy reconstruction.

44

To reconstruct the energy, first most of the dark noise is filtered out, by only
considering hit PMTs with time residuals in a 50 ns window. Then the number of
PMT hits is converted into an ‘effective’ number of hits, Nef f , by applying a few
corrections. Nef f represents the number of photoelects. The formula is as follows(from [31]):Nhit 
ri

X
RcoverNallλ(run)
×e
×
Nef f =× Gi (t) (4.1)(Xi + ǫtail − ǫdark ) ×
Nnorm S(θi , φi )i=1
Where Xi is the occupancy correction (described shortly), ǫtail and ǫdark arecorrections for dark noise and late time hits (generally there is a measurable tailof late time hits due to multiple Coulomb scattering); Nall is the total number of
PMTs in the experiment phase (11146 for SK-I), and Nnorm are the number properly
operating, thus making the second factor a correction for bad (broken or hot) PMTs;
the third factor is for PMT photo-coverage, with Rcover being the ratio of area on thewalls covered by PMTs to full inner detector area (0.4041 in SK-I), and S(θi , φi ) taking
into account how the PMT coverage changes with incidence angle (PMT shadowing
effects); fourth is the water transparency (λ) correction, with ri being the distancefrom reconstructed event vertex to hit PMT; and lastly Gi (t) is a single photon timedependent gain factor.
The occupancy is the correction that allows reconstruction of higher energy
events that break the single photon per PMT assumption. The basic idea is that theCherenkov ring doesn’t only strike one PMT in isolation. If a PMT is going to detect
multiple photo-electrons, it is likely that the PMT is located in the center of a ‘brightspot’. If this is true, then it is likely that the neighboring PMTs also detected light;
in fact the brighter the spot, the more likely multiple photo-electrons were detected,
and the more likely that the neighboring PMTs detected light.
Since the algorithm doesn’t use the information of the intensity of light detectedby the PMT, each PMT to start is simply assigned a value of 0 (not hit) or 1 (hit).
45

So for every hit PMT, the 8 neighboring PMTs (the PMTs are aligned on a grid) aresearched. If none, or just a few are hit, then it is likely that the PMT is in a dim regionof the Cherenkov ring (the entire ring may be dim for low energy events), or saw light
simply because of a scattered photon, or a coincidental dark noise fluctuation, andlittle or no correction is applied (Xi ∼ 1). If many of the neighboring PMTs are
struck however, it is likely that the PMT is in the middle of a bright spot of light,
and the PMT is given a value larger than one. If all eight neighboring PMTs are also
hit, then the hit PMT under consideration is assigned a value of 3, which basicallymeans it should be treated as if it saw three photo-electrons.
Formally, if we define the fraction of the nine PMTs in the 3x3 patch that are hit
as xi (the center tube is always hit by construction), then if all 8 neighboring PMTs
are hit (xi = 1), then Xi = 3; otherwise, from Poisson statistics,

Xi =1
log 1−x
i

(4.2)

xi

The energy calculation is described in more detail in the SK-I solar paper [31].
The energy resolution for an 18 MeV event is about 10%.

4.3

Direction Reconstruction

Incoming neutrinos that interact through elastic scattering create recoil electrons
that retain the directionality of the neutrino to within about 15 degrees (in general,
positrons formed through inverse beta decay do not retain a significant correlation to
the incoming neutrino, although a very weak backwards bias exists below 15 MeV, andslight forward bias exists that grows with energy above 15 MeV [44]). The direction
is important for identifying solar neutrinos, as well as for background reduction (suchas eliminating radioactivity events).
46

The direction reconstruction is also copied from the SK solar neutrino analysis [31]. Only hit PMTs with timing residuals within 30 ns are considered when
determining the direction. Starting at the already reconstructed vertex, many direction vectors are considered, and the angle between each direction vector and the hit
PMTs is compared to an angular likelihood function extracted from MC. This likelihood function broadly peaks around 42 degrees, which is the Cherenkov angle of an
ultra-relativistic particle in pure water. The contribution of each hit to the total likelihood is a combination of the angular likelihood value and a factor that corrects forthe varying quantum efficiency of the PMT due to the incidence angle. The directionthat returns the maximum likelihood is the final reconstructed direction.
As with most reconstructed quantities, the directional resolution improves with
event energy, although the increased hit statistics of a higher energy event is offset by
the increased likelihood of multiple Coulomb scattering, which is the limiting factor in
the direction resolution; a 16 MeV event in SK-I has an angular resolution of around22 degrees. In SK-II the lower photo-cathode coverage reduced angular resolution
by about 10% compared to SK-I; in SK-III the likelihood function was modified bytuning it to be a function of the total event energy, allowing an improvement inangular resolution over SK-I by about 10%.

4.4

Muon Fitting

Muons in the detector were fit using software called Muboy; these muon fits wereused for the spallation cut, and are critical to the analysis. Muboy is described indetail in [45, 46].
The Muboy algorithm starts with PMT selection. ID tubes are required to passa charge threshold to be considered by Muboy; the cut is dependent on the numberof hit ID tubes. For less than 8000 hit tubes, the charge threshold is 2 p.e.; from 8000

47

to 10,000 tubes it is 2.5 p.e.; and it is 3 p.e. for more than 10,000 hit tubes.
Next, Muboy takes the center tube of the patch of nine tubes with the highest
total charge as a first guess for a likely exit point for the muon. Typically, the exit
point of a through-going muon is the region of highest charge in the event, as the
Cherenkov light emitted from each point on the track is directed into progressively
smaller rings (or conic sections) centered on the exit position.
Thirdly, Muboy introduces another selection criteria for which hit PMTs are
considered by counting the number of nearest neighbor hit PMTs within 10 ns foreach hit PMT. If the number of nearest neighbor hit PMTs within 10 ns is below acertain threshold, the tube is disregarded. This threshold depends on the number oftubes left after the charge threshold cut, and goes between 1 (< 500 hit tubes left)
and 5 (> 7500 tubes remaining).
The first guess of an entry position is the earliest time hit PMT with at least
3 hit neighbors within 10 ns. If no such PMT exists the number of required nearest
neighbors within 10 ns is relaxed until a PMT is found. An entry and exit position
gives an initial guess of the track.
Causality arguments are used to gain further information. For a single throughgoing muon, if the entry position is known, then it is physically impossible for lightfrom the same muon to strike a PMT if not enough time has passed for an object
traveling at velocity c to traverse the distance to the PMT from the entry position.
Any such hit PMT is either a noise hit, or many may be an indication of a multiple
muon event (where many muons from the same parent interaction all are travelingparallel and enter the detector simultaneously).
Muboy is unique among the muon fitters available at SK as it not only fits simple
single through-going muons with a single entry and exit position, but actually looks fordifferent types of muon events as it fits, and categorizes the event accordingly. Muboy
will categorize each event as being one of the following: single through-going muon48

(∼82% of events), stopping muons (muon enters from outside but stops in detector,
usually decaying into electron ∼7%), multiple muon bundles (found two different
ways, described later ∼7%), and so called ‘corner clippers’ (where the track length isvery short, ∼4%). There are a small fraction of events that Muboy completely fails
to fit as well.
If Muboy finds more than 45 hit tubes (after previously described charge threshold and nearest neighbor timing cuts) that have a PMT time such that to traverse
the distance to the PMT from the entrance position would require traveling at morethan 33 cm/ns, then the event is tagged as a multiple muon (type 1). For otherevents, PMT hits that would require travel of more than 34 cm/ns (early time) or
less than 18 cm/ns (late time) hits are rejected as noise. For those tagged as multiple
muons (type 1) this requirement is tightened to only keeping hit PMTs where thetimes indicate direct travel from the entrance position would mean a travel speed of
between 19.5 cm/ns and 32 cm/ns. Muboy determines final tracks by maximizing a
goodness. The information used in this goodness include the fraction of hits inside
the Cherenkov cone, and the timing residuals of the tubes. The full form can befound in [46].
The goodness is maximized by fixing the entrance position and moving the exit
position on a grid. For events that are not thought to be multiple muons, a second
iteration allows the entrance time to change slightly; a third iteration allows the
Cherenkov angle to change slightly. If, after this new goodness maximization, thenumber of early time hits has risen above 35, the event is classified as multiple muon
(type 2).
For non-multiple muon type events, the event is then checked to see if it qualifies
as a corner clipper. If the event is near the top of the detector, the direction ischecked; if near the bottom, the track length is checked (<3 m indicates a cornerclipper). Corner clipper muons were not found to cause any measurable amount of49

spallation.
The remaining events are checked to see if they stop in the inner detector. If
the amount of charge in the patch of events surrounding the exit position by 2 m isabnormally small (< 300 p.e. if no OD data exists; otherwise combinations of OD
and ID tubes are tested) then the event is classified as a stopping muon, and thestopping position is guessed by looking for a fall off in the dE/dx information.
Events that have made it this far without being classified as anything else aredetermined to be single through-going muons.
If the event was classified as a multiple muon, then the fit track has all thecorrelated hits removed, and another fit is performed on the remaining hit tubes.
The full procedure is actually a bit more complicated and can be seen at [46]. If
another reasonable fit is found, the procedure is repeated. Up to 10 tracks can befit; or, in some cases, only 1 track is ever fit, even though the event is considered amultiple muon.
All events have a quality of fit goodness number calculated. For multiple muon
type events, a quality of fit goodness is calculated for each track, and are typicallyincreasingly poor for each additional track. In general, fit tracks above the second or
third are not very trustworthy.
Studies were carried out to determine Muboy accuracy. Taking a sample ofabout 2000 muons, the events were fit with Muboy and also scanned by eye. Out of
1728 events judged by Muboy to be single through-going muons, only 9 were thought
to be something else by eye scan. Of 74 events Muboy judged as corner clippers, one
was a stopping muon by eye scan. Of 129 thought by Muboy to be multiple muon
events, 17 were thought to be through-going by eye scan; of 113 found by Muboy to
be stopping muons, almost a third were considered through-going by eye scan, leading
to the largest discrepancy. Overall, the agreement was very good.
Resolutions studies found that the entry point resolution was around 100 cm for50

all muon types, excluding multiple muons with more than 3 tracks. The direction
resolution in all cases was around 6 degrees.
All in all, Muboy is ideal as it can fit a muon more quickly than the precisionmuon fitters available to SK, but still fits the track well. Furthermore, its ability tocategorize muons is highly valuable for determining spallation.

4.5

Multiple Coulomb Scattering Estimation

Electrons and positrons traveling in the detector multiple Coulomb scatter more as
their energy increases. A measure of the amount of multiple scattering is especially
important for increasing the efficiency of cutting solar neutrino events, as the amountof multiple scattering is correlated to how much the direction of the event is changed
from the solar direction.
Multiple Coulomb scattering is estimated by software that utilizes a Hough transform to each event to calculate a goodness. Specifically, for each of a pair of two hit
PMTs, a cone (with opening angle equal to the Cherenkov angle) is constructed, starting at the reconstructed vertex position, and pointed directly at the PMT. These twocones should intersect, usually in two places. The unit vectors from the reconstructed
event vertex to these cone intersection points are recorded. They won’t line up exactly. The goodness is the vector sum of all these unit vectors divided by the longest
possible path (all vectors exactly aligned). The higher the goodness value, the lessmultiple scattering should have occurred. This theory is born out by MC studies;plots can be seen in the discussion of solar neutrino background (Fig. 6.6).

4.6

Cherenkov Angle Reconstruction

Reconstructing the opening angle of the Cherenkov cone of events is especially important for the DSNB analysis. This is accomplished by use of ‘three hit combinations’51

22500
20000
17500
15000
12500
10000
7500
5000
2500
0

0

10 20 30 40 50 60 70 80
Opening Angle from 3-PMT combinations

90

Figure 4.1: Example of distributions of 3-hit combinations used for calculating theCherenkov angle. The Cherenkov angle (in degrees) is determined by a fit to the peak(shown). Electron-like events have a broader distribution then pion-like events. Oneof each type is shown.
or ‘triplets’. Every combination of three different hit PMTs in an event can be used
to form a cone with a particular opening angle. A distribution is made of the opening
angle formed by each three hit combination (see Fig. 4.1). The peak of this distribution is used as the Cherenkov angle of the event. The width of this distribution canhelp differentiate pions from electrons and positrons, as well.

4.7

dE/dx reconstruction

For muons, it can be useful to know not just the total amount of light deposited in thedetector from the event, but also the emission profile along the track. To determine
this dE/dx information, the amount of light seen by each PMT was assigned a location
along the muon track it probably originated from. This emission point was determined52

using timing information. First, Muboy reconstructs the time and place the muonentered the detector. We also have the very precise timing information of each PMT.
By assuming the muon is traveling with a velocity c, and that the Cherenkov photon
is traveling at a velocity c/n (with n being the index of refraction of pure water), I
determine where along the muon track the light originated in order to satisfy all thetiming requirements. The equation is as follows:h1hic2 (t − t0 )2c(t − t0 ) i
2
X
+
−
r
+
2
~
r
·
µ̂
−
−
1
X2 = 0
n2
n2
n2

(4.3)

Where t0 is the time the muon entered the detector, as fit by Muboy; t is the
PMT time; ~r is the vector from the muon entry point to the hit PMT; µ̂ is the muon
direction (as reconstructed by Muboy); and X stands for c(te − t0 ), with te being theemission time of the Cherenkov photon from the muon track, which is the quantity
we need to solve for. As a quadratic equation is involved, there are two possible
solutions; if neither is unphysical, both are kept.
The information from all PMTs can then be combined into a dE/dx profile. The
amount of light seen by a PMT may be different than the amount of light actuallyemitted, and therefore water transparency and PMT coverage effects (light travelingin certain directions from a particular point may be more or less likely to be seen
by a PMT on average due to the geometric PMT coverage in that direction and theincidence angle the photon would strike those PMTs) are corrected for. An example
of a resultant dE/dx profile can be seen in Fig. 4.2.

53

Light deposited in ID, with corrections (p.e.)

5000

4000

3000

2000

1000

0

0

5

10

15
20
25
30
35
40
Distance along muon track in ID (m)Figure 4.2: Example dE/dx distribution for a typical muon.

4.8

Alternate Muon Fitting

In rare cases, Muboy will have trouble correctly fitting the muon. This is indicatedby a poor goodness value being returned by the fit. There are enough single muonsthat this can be a problem, as the fit is used to search for spallation. If a muoncauses spallation, the spallation product should be close in space and time to themuon track. If the track is incorrectly fit, the track may mistakenly seem far awayfrom the spallation product, possibly causing important spallation events to not berejected by our spallation cut.
To help deal with this problem, an alternate muon fitter was developed forthe rare cases when Muboy was unreliable. This fitter was quite crude and slow,
and simply projected a grid onto the inner surface of the detector. Many possiblecombination of muon entry and exit points were then tested (the single muon case wasassumed). This slow method was termed the Brute Force Fitter (BFF). To improve54

computation speed, the total charge in the surrounding PMTs within 2 m of the exit
position was required to be at least 70 photo-electrons, and the total charge of the
PMTs within 2 m of the entry position was also required to exceed a threshold, as
described in Table 4.1. For each combination of entry and exit point, a goodness
was calculated; the combination that maximized the goodness was then used as thefit, and the goodness value itself was recorded as an indication of quality of fit. The
goodness used is defined as follows:
n
t2
hits
X
− i2
Nall
2σ
×
e i
G=
Ncone
i=1

(4.4)

where nhits is the number of hit PMTs with a time residual within +/- 100 ns
of zero; t is the timing residual of the PMT; σ is the time resolution of PMT i (andis a function of charge); Nall is the total number of hits above the charge threshold;and Ncone is the number of hits above charge threshold inside the Cherenkov cone
for the considered fit. In order to calculate timing residuals and the location of theCherenkov cone, a Cherenkov angle of 42 degrees was assumed. The PMT charge
threshold is a function of the total charge Qtotal :Qthresh = C ×

Qtotal
+1
1000

(4.5)

where C is 1.6 if Qtotal ≤50,000 and 1.8 for Qtotal >50,000.
The BFF was able to correctly refit about 75% of the muons Muboy had trouble
with (Muboy goodness < 0.4).

55

Table 4.1: Charge requirement of total number of photo-electrons seen by PMTs
within 2 m of the considered entry position, as a function of total light seen in theevent.
Event total light (p.e.)≤100,000>100,000>250,000>400,000

Entry position threshold (p.e.)
12
20
26
33

56

Chapter 5
Modeling
5.1

The Monte Carlo

Backgrounds were modeled using SKDETSIM, which is the official SK MC, using
GEANT 3.21 for particle tracking and NEUT [47] to model neutrino interactions(mostly inside the nucleus). Hadronic interactions are simulated using a combinationof CALOR and custom SK code ([48, 49]). The SKDETSIM MC has been welltested and verified at most energies. Rayleigh and Mie scattering and absorption are
considered, as is the varying transparency of the water.
For tuning the solar neutrino cut, we made use of the detailed and well studied
solar neutrino MC which already exists for the SK solar analysis, and models 8 B and
hep neutrinos [31].
The physics occurring in NEUT is tracked by a code, which is especially usefulfor understanding the complicated NC background. Particles created in NEUT (notGEANT) are each listed, as is their created position and momentum, which allows
us to track the MC in detail.

57

5.2

Atmospheric Neutrino Backgrounds

The main remaining backgrounds left in the analysis after all of the cuts are applied
are from atmospheric neutrino interactions. Carefully modeling these remaining backgrounds are critical to accurately understanding the final sample. To achieve this,500 years of MC was used for each SK experimental phase, and the entire analysis
reduction was applied. A recent effort, largely due to this analysis, has been madeat SK to check and revise the MC at the lowest energies, as a few bugs were found.
This has led to new, corrected MC with revised cross sections for certain processes(especially NC processes). The MC used here for SK-I/II/III does not have these
corrections applied. Instead we had to take careful steps to prevent the bugs fromharming the analysis. We believe the resulting MC is mostly correct, and that any
inaccuracies are within our highly conservative systematic errors.
The first bug noted was that 15.1 MeV gamma rays appeared in elastic scatteringinteractions far more frequently than they should. This was traced to a typo inbranching ratios causing these events to appear orders of magnitude more often than
was appropriate. In order to prevent this from affecting the analysis, all 15.1 MeV
gamma events were suppressed. Although this also removes any few 15.1 MeV gamma
events that should be in the sample, these are estimated to be quite few, and we believe
this small issue is well covered by the highly conservative systematics.
The types of events seen can be sorted into 3 categories:1) νe CC events. Atmospheric ν̄e ’s are indistinguishable from DSNB ν̄e ’s on
an individual basis, but have a very different energy spectrum. Atmospheric νe ’s canin principle be distinguished from DSNB ν̄e ’s, but SK cannot distinguish between
electron and positron events. Sometimes νe events can emit low energy pre-activity
gammas, which, if detected, allows the event to be rejected; in practice, however, onlya small portion of events can be caught with this method. For simplicity, both the ν̄eand νe CC events are combined under the label ‘νe CC’.
582) νµ CC events. This is the largest remaining background in the sample.
Atmospheric νµ ’s and ν̄µ ’s interact in the water of the detector and create a muon
via a charged current (CC) reaction. This muon can be very low energy, often below Cherenkov threshold, in which case its decay electron cannot be removed likeother decay electrons (by correlation to the preceding muon), since the muon is invisible. This background’s energy spectrum is the well known Michel spectrum, slightly
modified by resolution effects, and is quite different from the SN relic spectrum.
Furthermore, the muons themselves that are created, when low energy, can bemistaken for positrons. Most of these events are cut in our event reduction, especiallythrough Cherenkov angle considerations. A few, however, survive in our final sample
in our signal region.
When a sub-Cherenkov muon is created, a low energy (around 6 MeV) prompt
gamma can be created. Seeing this gamma and correlating it to the decay electron
allows reduction of this background. The new SK-IV electronics, as well as proposed
improvements that could allow further lowering of the SK energy threshold, may
allow improved effectiveness of detecting this pre-activity. Again, both the νµ and ν̄µsignals are combined as ‘νµ CC’.
3) NC events. This category is especially complicated, and can be subdivided
as follows (with spectral plots for each subdivision available in Appendix C), where
the percentages listed represent the proportion of events in the MC sample after cuts:a) Pion absorption (36%): These events were mistakenly high in energy in theMC, reconstructing at energies > 16 MeV and therefore entering the final sample.
An independent study 1 concluded that this was due to outdated code, and was notcorrect; >99% of pion absorption events in our MC should instead result in a gamma
ray of < 7.6 MeV, which cannot reconstruct > 16 MeV. Therefore events from thismode were neglected.
1

Private communication with M. Sakuda

59b) NC elastic scattering (25%): Neutral current (NC) elastic events (meaningelastic scattering on a nucleon, which then becomes excited, and can give off deexcitation gammas, or cause other nuclear reactions) have an energy spectrum thatrises sharply at our lower energy bound, similar to SN relics. Most are removed by
Cherenkov angle reconstruction, but some still leak into our final sample and must
be modeled. With the lowering of the energy threshold from 18 MeV to 16 MeV, thisbackground has become especially relevant.
c) Single π − events (all energies), and single π + events (> 200 MeV/C only)(19%): The pion events >200 MeV mostly deposit energy in the detector throughCherenkov radiation from the accelerated pion. As the energy reconstruction assumes
these are electrons, the reconstructed energy varies largely and is roughly flat. π −events below 200 MeV generally capture on an oxygen, leading to an excited nucleus
which gives off de-excitation gammas.
d) Single π + events < 200 MeV/C (7%): Lower energy π + events cannot capture on an oxygen like their negatively charged counterparts, as their charge is wrong.
However they are less relativistic, create less Cherenkov light, and decay faster, generally into a muon, which then decays into an electron, giving these events a Michel
spectrum.
e) Single unabsorbed π 0 events (7%): The spectrum of these single particle events
fall slowly as energy increases.
f) Multiple pion production (5%): The spectrum is roughly flat in energy.
g) Other (for instance, deep inelastic scattering) (<1%): So few events we neglect.
Of all these modes, the NC elastic is the most important. This is because of the
sharp spectrum increase at low energy, similar to the behavior of real relic events, aswell as the large amounts of them. Also important is c), as there are quite a few ofthese events.

60

Treating each of these modes as a separate channel to model is prohibitively
difficult, both in terms of manpower and computing power, and is unnecessary. Modea) is neglected; b) must be modeled; and c) is important. Modes d), e) and f) not
only have a small number of events, and relatively flat spectra that won’t greatlychange our results, but furthermore it was discovered that the spectrum of each ofthese modes can be well described as a linear combination of the spectra of modes we
do consider. In other words, if we consider νe CC events, νµ CC events, NC elastic
events, and single π − events with single π + events > 200 MeV/C, then when we
perform our maximum likelihood search on our final sample in an attempt to fit thedata to these spectra, modes d), e), and f) will be absorbed into the other modes in
the fit. This means we don’t have to worry about them.
Also, both the charged pions (mode c) and the muons from νµ CC events thatare confused as positrons have Cherenkov angle distributions that tend to be smaller
than relics. They are also both quite a bit less important than the other modes. To
simplify the analysis, it was deemed prudent to merge these two categories into one
channel, referred to as ‘µ/π’.
Thus, the remaining atmospheric backgrounds are grouped into four categories:
1) Atmospheric νµ CC events. Specifically, decay electrons from sub-Cherenkov
muons. This background was considered in the 2003 study.
2) νe CC events. This background was considered in the 2003 study.
3) Atmospheric ν NC elastic events. This background was not consideredin the 2003 study.
4) Heavy particle production from atmospheric ν events, or µ/π. This
last category is a grouping of two different things, both heavier particles. First,
NC reactions produce charged pions (only π + events > 200 MeV/C are included
here), some of which survive the pion cut. Included with them, since the spectrum
and Cherenkov angle distribution are relatively similar, are surviving muons (from61Number of events in SK-I final sample

6
Decay-eνe CC

5NC Elastic
µ/π

4

3

2

1

0

20

30

40

50

60

70
80
90
Energy (MeV)

Figure 5.1: Spectra of the four remaining backgrounds.
muon neutrino interactions) above Cherenkov threshold. This background was notconsidered in the 2003 study.
The background spectra of the four backgrounds are shown in Fig. 5.1. Anotherimportant handle is their Cherenkov angle distributions, which are shown in Fig. 7.1.

5.3

DSNB Modeling

MC was made for the following DSNB models: Malaney’s cosmic gas infall model [14];Woosley and Hartmann’s chemical evolution model [13]; Kaplinghat et al.’s heavy
metal abundance model [16]; Ando et al.’s LMA model [17] [NNN05 ref]; Lunardinis
failed supernova model [15]; and many cases of the formulation by Horiuchi et al. [19](see Chapter 9), of which the 6 MeV case is featured. Although many more excellent
models exist, I have worked towards a new, model independent method of presenting
our results (Chapter 9), and therefore did not feel it was necessary to perform a62

comprehensive survey of all existing models.
The MC was created using SKDETSIM, with the energy spectrum of the events
matched to the energy spectrum of the particular model, from 10 to 90 MeV. MC
was simulated for each model, for SK-I, SK-II, and SK-III separately, and events wereassumed to occur uniformly in the detector, up to a distance of 50 cm from the PMTs(a comfortably larger volume than the fiducial volume, which discards all events up
to 2 m from the PMTs).

63

Chapter 6
Analysis: Event Reduction
There are many types of events in the SK data set, many of which are backgrounds
to the SN relic analysis. Each PMT fires thousands of times a second due to darknoise fluctuations; cosmic ray muons enter the detector at a rate of approximately
2 Hz, lighting up the detector and often breaking apart oxygen nuclei (spallation),resulting in radioactive isotopes; radioactivity in the rock walls or PMT glass itself
can cause events, and more. From this enormous rate of data it is our job to search
for a signal that we expect to see only see a few times a year. The first step in thisdifficult task is to filter out as best we can anything that is probably not a supernova
relic neutrino event, followed by the second task of understanding everything thatis left. This chapter describes the series of cuts that were implemented in order togenerate our final data samples.

6.1

First Reduction

The first reduction is a series of loose cuts that eliminates noise, muons, calibration
events, and other things that are clearly not SN relics. It is the first set of cuts
applied, and greatly reduces the data volume, giving us an easily manageable sample
to study. Events that survive the first reduction we consider to be ‘relic candidates’,64although most if not all will be further background events. These cuts are largely thesame for the relic analysis as they are for the long established SK solar analysis, fromwhence the name ‘first reduction’ carries over. With the exception of the fiducial
volume cut, the first reduction is estimated to be more than 99% efficient. The first
reduction is comprised of the following cut criteria:

OD triggered events
We search for SN relic events that are fully contained inside the ID. If both the ID
and OD have triggered it generally means that a charged particle has entered thedetector from the outside, depositing light in the OD along the way. These eventsin general will not be SN relics, as the incoming neutrino has no charge, and thepositron resulting from the inverse beta decay reaction only travels a short distance(10 - 20 cm). Thus, any event with an OD trigger is removed from the sample.

Charge cut
One basic variable is the total light deposited in the detector. In general, cosmic raymuons create much more light in the detector than a SN relic event would, as only
high energy muons can penetrate the rock overburden. Although most muons arecaught by the OD cut, some may escape it, and fully contained muon events (wherean atmospheric muon neutrino creates a muon in the ID) are possible. A simple
charge cut will eliminate most of them (Fig. 6.1).
In SK-I and SK-III, events with more then 2,000 p.e., or that cause more then800 PMTs to see light within the event, are eliminated from the data sample. For
SK-II, the criteria is halved, due to the reduction of PMT coverage by approximately
a factor of 2.

65

number of eventsx 10 2

6000

5000

4000

3000

2000

1000

0

0

1

2
3
4
5
6
7
Log10 of the number of photo-electrons

Figure 6.1: Photo-electron distribution of amount of light deposited in the detector by
events in SK for over a 24 hour period. The line is at 2000 p.e.; the red histogram to
the right of the line shows the distribution of rejected events that are mostly muons.

Fiducial volume
The entire ID volume is not used. First, there is an excess of low energy eventsnear the boundary of the ID, due largely to radioactive events (some from the PMT
glass itself, or their shielding installed after SK-I). Secondly, our reconstruction tools,
especially the energy reconstruction, begin to fail near the ID boundary. By removing
the outer 2 m of the ID, we eliminate almost all of this extra background, and restrict
ourselves to the volume in which our tools work well. The ID contains 32.5 ktons ofwater; when we remove the volume within 2 meters of any wall, we are left with theFV, which contains 22.5 ktons. Only events in the FV are used in the DSNB analysis.

66

50 µs cut
Events close in time can be evidence for background. For instance, after a high energymuon, electronic noise and pulse reflections may cause the illusion of another event
shortly afterwards. Also, many muons stop in the detector (∼0.15 Hz) and decay
into electrons which can mimic the relic signal. The muon lifetime is 2.2 µs, although
in water, it is not the same for positive and negative muons due to the possibility ofµ− capture, and averages to about 2.08 µs. Since a real SN relic event should nothave any correlation with any other event occurring in the detector, we can eliminate
electronic noise and decay electrons by rejecting all events for a short time after every
event (LE trigger or higher). 50 µs is used, which adds an almost negligible amountof inefficiency as the LE rate is less than 20 Hz.

Calibration events
Calibrations occur periodically even during normal data taking. These are tagged as
calibration events and are removed from the relic sample.

Noise cutWith a dark noise rate of several kHz in the PMTs, sometimes accidental coincidence
can conspire to cause enough tubes to fire inside a 200 ns window to trigger thedetector. For events such as these, most of the tubes channels will record very little
charge. If the fraction of PMTs that see less then 0.5 p.e.’s in an event is more then
40%, then the event is cut. Also, sometimes noise in an ATM board itself will cause
all the channels on the board to fire simultaneously; thus, if an event contains an
ATM board where more then 95% of the channels counted a hit, which should notnormally happen for low energy events like a relic, then the event is removed.

67

Super-Kamiokande I
Run 7765 Sub 169 Ev 9269513
99-08-10:12:40:31
Inner: 395 hits, 510 pE
Outer: 1 hits, 0 pE (in-time)
Trigger ID: 0x07
D wall: 1690.0 cm
Fully-Contained Mode

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
75
60
45
30
15
0
0

500

1000

1500

2000

Times (ns)Figure 6.2: Example event in SK-I that exhibits a double timing peak structure,visible in the timing plot in the lower right of the display.

6.2

2-peak cut

Although most decay electrons are eliminated by the 50 µs cut, occasionally it occursthat the muon decays quickly enough that both the muon and the decay electron
information are captured in the same 1.3 µs timing window that comprises a single
event. In these cases, the timing information for that event will have a double peakstructure [see Fig. 6.2]. Other, even rarer events can cause multiple peaks as well.
In order to find and reject such events, the timing information of the event was
searched for any indication of a peak outside the main timing peak. The algorithm
uses the BONSAI (see section 4.1) fit time to determine the probable timing locationof the main timing peak. Any hits with time of flight subtracted times earlier than 12
ns before the BONSAI event time is considered possible pre-activity; any time after
20 ns after the BONSAI event time is considered post activity.
Each hit is assigned a goodness, which is a sum of all other hits within 25 ns,
2each weighted by a Gaussian e(−t/2) , where t is the time difference between the hits,
divided by a characteristic time of 5 ns. This goodness is used to noise filter the hits;
68number of events

10

4

data
MC

10

3

10

2

10

1
0

10

20

30 40 50 60 70 80 90 100
number of hits outside of main peakFigure 6.3: Distribution of maximum number of grouped hits outside the main timing
peak, for the SK-I/III data sample (no cuts except first reduction), compared to SN
relic MC.
all hits are required to be above a certain goodness to be considered. In most cases
this goodness threshold is 4, but an exponentially decaying signal of late time hits
are assumed (from multiple Coulomb scattering), increasing the required goodness
threshold for hits at the beginning of the post-activity region.
Each of the 3 regions (pre-activity, main, and post-activity) then have the remaining hits (that pass the goodness threshold cut) searched in a sliding 15 ns window.
If the maximum number of hits found in a 15 ns time window in either the pre or
post-activity region is five or more, the event is rejected.
This cut is estimated to have a signal inefficiency of < 0.02%, as estimated by
MC.

69

6.3

Incoming Event Cut

Physics events that are incoming into the detector from the outside or the walls(such as radioactivity from the PMT glass itself) can be a background. Although the
FV cut eliminates most of these types of events, some travel farther than 2 meters.
Rather then tightening the FV cut, which causes significant inefficiency, we can use
the reconstructed direction of the event. An effective distance parameter def f is used,which is defined in the same way as the SK solar neutrino analysis [31] (where it iscalled the ‘Gamma ray cut’), by projecting the event back opposite its reconstructed
direction until we hit the wall of the ID. That distance (the distance ’traveled’ in thedetector) is the def f variable.
An artifact of the vertex fitting method also causes many misreconstructed events
to have low def f , which are eliminated by the same cut. This effect is not fully
understood, and may even be a larger contribution to low def f events than the physics
backgrounds, making this cut doubly important.
In all data periods, a 300 cm def f cut was applied at all energies. Due to higher
amounts of background at low energy, however, additional cuts were required. In
SK-I sufficient statistics (1497 days) existed to allow tuning of an energy dependent
cut for the low energy region, maximizing efficiency (98% efficient; see Fig. 6.4).
This energy dependent function is simply a linear cut off from 300 cm at 19 MeV to450 cm at 16 MeV. In SK-II and SK-III, the cut needed to be reconsidered, as the
addition of FRP shielding on the tubes added a new radioactive source, potentially
increasing background. Also, the smaller cathode coverage in SK-II worsened theenergy and vertex resolution compared to SK-I and SK-III. So, all three periods had
to be considered separately, and due to the decreased statistics, an energy dependent
cut was not possible for SK-II (794 days) or SK-III (562 days). Instead, a single def f
cut was implemented for events less then 22 MeV, with a value of 450 cm for SK-III(96% efficient), and 500 cm for SK-II (95% efficient). No evidence of contamination70

effective distance (cm)

2500

2000

1500

1000

500

0

15

20

25

30

35

40

45

50 55 60
Energy (MeV)

Figure 6.4: SK-I data distribution showing original published analysis def f cut valueof 450 cm, and new value of 300 cm at most energies, with an energy dependent cut
at low energy. The vertical axis is def f (cm) and the horizontal axis is reconstructed
event candidate energy (MeV). The red dots represent events that would have been
eliminated by the old cut. A line is drawn at 16 MeV to represent the current energy
threshold; it should be recalled the 2003 published analysis used a threshold of 18
MeV instead.
remains after the cuts (Fig. 6.5).

71

number of events number of events
number of events

20
15
10
5
0

10
7.5
5
2.5
0

10
7.5
5
2.5
0

500

1000

1500
2000
2500
3000
effective distance (cm), SK-I

data
MC
500

1000

1500
2000
2500
3000
effective distance (cm), SK-II

500

1000

1500
2000
2500
3000
effective distance (cm), SK-III

Figure 6.5: def f distribution of final data for all three data phases (black, all cuts
applied) compared to SN relic MC (LMA model, red, scaled to data). No evidence
of def f excess (expected in the first bin, if at all) is indicated.

6.4

Solar Cut

Solar neutrinos from the sun can elastically scatter in the detector, creating events
that look like SN relics. In order to eliminate such events, we can use the angle
between the reconstructed direction vector of the event and the direction vector from
where the sun was in the sky at the time of the event. The cosine of this angle isused; a cos(θsun ) of one means the event came from the solar direction.
Unfortunately, due to electron multiple Coulomb scattering leading to imperfectly reconstructed event directions, as well as up to 15 degree differences between
the angle of the neutrino and the electron, solar neutrino events rarely have a cos(θsun )of exactly one. This distribution makes cutting solar events using cos(θsun ) tricky,
especially since solar neutrino flux increases sharply right at the critical lower energy

72Integrated fraction

1

goodness < 0.4
0.4 ≤ goodness < 0.5
0.5 ≤ goodness < 0.6

0.8

0.6 ≤ goodness
0.6

0.4

0.2

0
0.2

0.3

0.4

0.5

0.6

0.7 0.8 0.9
1Integrated cos(θsun)

Figure 6.6: SK-I/III solar MC integrated cos(θsun ) distributions by multiple Coulomb
scattering goodness bin.
edge of our analysis, where any inefficiency hurts the most. In order to maximize
our sensitivity, we used an energy dependent cut coupled with the multiple Coulomb
scattering goodness (see section 4.5).
To quantitatively determine the best cut thresholds, the SN relic candidate sample was divided into four different multiple Coulomb scattering goodness bins (see Fig.
6.6), and a significance function was developed:√
Significance = ǫ/ κS + ǫα

(6.1)

where ǫ is the cut efficiency, S is the number of solar neutrino events, κ is the
reduction effectiveness of the cut (such that κ × S is the number of solar neutrino
events remaining after the cut is applied), and α represents the non-solar neutrino
background.
73

The solar neutrino spectrum is modeled using the Monte Carlo developed for the
SK solar analysis. The solar neutrino flux was normalized using real SK data below
energy threshold (14-16 MeV), with all cuts applied (except the one on cos(θsun )). To
normalize, it was assumed that all events with cos(θsun ) < 0 were not solar neutrino
events, and that all non-solar remaining events had no cos(θsun ) dependence (it is difficult to imagine a situation where this would not be true). Thus, simply subtracting
the number of events with cos(θsun ) < 0 from the number of events with cos(θsun ) > 0
allows us to estimate the number of solar neutrino events at a particular energy, andthen extrapolate the number of solar neutrino events at all energies.
The dominant non-solar neutrino background was assumed to be decay electrons
from atmospheric νµ CC events, which is our largest background (see section 5.2). The
spectrum was modeled using a sample of data that was identified as decay electrons
by timing and spatial correlation to a preceding muon that had no OD trigger (muonfrom a fully contained atmospheric muon neutrino reaction). The normalization of
the background was determined by fitting to the data (see Fig. 6.7).
As with many of the cuts, SK-I and SK-III used one cut, and a separate versionof the cut was tuned for SK-II. The SK-II cut criteria is simply the SK-I/III cut
with the energy bins shifted by +6% to reflect the poorer energy resolution. The
cut is multiple Coulomb scattering goodness bin dependent for E < 19 MeV (SKI/III, < 20.14 MeV SK-II), while for 19-20 MeV (20.14-21.2 MeV SK-II) there is a
simple, multiple scattering goodness bin-independent cut that eliminates events withcos(θsun ) > 0.93. More cut details can be found in Table 6.1. Note that the cut values
in the table mean that events with cos(θsun ) > cut value are rejected. Also note thatthe inefficiencies are already weighted by the fraction of events in that MCS goodness
bin, so that they can be simply added for the total.
After the cut, no statistically significant evidence for remaining solar neutrino
events exists, and the estimated number of remaining solar neutrino events in the

74

60
50
40
30
20
10
0

20

30

40

50
60
spectrum

70

80

90

Figure 6.7: SK-I fit to data to determine amount of background. Horizontal axis isenergy (MeV), vertical is number of events. Black is SK-I final data sample (without solar cut), red is estimated solar (from MC) + background (estimated to bemostly decay electrons, modeled by decay electrons from near-threshold fully contained muons). The 15-16 MeV bin is shown, which is not used in the final analysis
due to the left over spallation.
combined SK-I/II/III final data sample is two or less.

75

Table 6.1: SK-I/III solar cos(θsun ) cut value (inefficiency)
Goodness bin
g < 0.4
0.4 ≤ g < 0.5
0.5 ≤ g < 0.6
0.6 ≤ gTotal

6.5

16-17 MeV
0.05 (7.2%)
0.39 (9.7%)
0.59 (6.7%)
0.73 (2.4%)
26.2%

17-18 MeV
0.35 (5.0%)
0.61 (6.4%)
0.73 (4.5%)
0.79 (2.0%)
17.9%

18-19 MeV
0.45 (4.3%)
0.77 (3.8%)
0.81 (3.2%)
0.91 (1.0%)
12.2%

Spallation Cut

Perhaps the most difficult reducible background to eliminate is spallation. Cosmic
ray muons enter the detector at a rate of around 2 Hz, even with the rock overburden.
These high energy muons can spall an oxygen nuclei, as well as cause other reactions
resulting in radioactive isotopes which then decay in the detector, mimicking a relicsignal.
The highest energy spallation product believed to be produced in the detector
is 11 Li and 14 B, each with beta decay end point energies of up to 20.6 MeV. Becauseof energy resolution effects, these events can have a reconstructed energy up to 23 oreven 24 MeV. Luckily, these events only have a half-life of around 0.01 seconds, sothey are rather easy to associate with the muon which created them.
As we go lower in energy, however, the number of possible isotopes increases
rapidly, as do their half-lives. Therefore spallation events become increasingly abundant and difficult to deal with as the energy threshold of our analysis is lowered. The
original 2003 SK analysis had an energy threshold of 18 MeV total positron energy,
and the spallation cut was 37% inefficient. For this thesis, after much work, thiscut has been significantly improved. Now, for the same SK-I data as the publishedanalysis, the energy threshold has been lowered to 16 MeV, and in the E > 18 MeV
region, inefficiency has been lowered from 37% to around 9%.

76

Half-life (s)

11

10
16

15
16

1

Be

N

C
8

Li

C

8

B

9

C

9

Li

-1

10

8

He

12
12

-2

Be

10
6

8

10

12

B

13

12

B

14

14

N
13

16

B
Li

11

O

18
20
22
Energy (MeV)

Figure 6.8: Scatterplot of spallation products expected to occur in SK, showing theirhalf life and energy. Energy values are maximum possible; decays may often be lower
in energy, and multiple modes may be involved. Data is listed in Table A.1.

6.5.1

Spallation Likelihood Variables

To eliminate spallation products, we correlate relic candidates to preceding muons.
In the SK data, we have four main handles on spallation events.
The first, and most important, is simply the time difference of the relic candidate
compared to that of the preceding muon, dt. Most spallation products have half-livesof less then 0.1 seconds (see Fig. 6.8), while the muon rate is about 2 Hz; thus any
event with a muon preceding it by less the 0.1 seconds is quite likely to be spallation.
Some spallation products have longer half-lives however. Some events with around
0.7 or 0.8 s half-lives have sufficient energy that energy resolution effects can cause
a reconstructed energy above 16 MeV. If we try to lower the energy threshold below
16 MeV, we start to acquire events with even longer half-lives, from over a second,
up to 13.8 s for 11 Be. The longer lived events are especially difficult to remove from77

µ track

peak ofdE/dx plot

LLONG

LTRAN
relic candidate

Figure 6.9: Schematic showing spallation distance variables.
our sample, and because of these events our energy threshold can be no lower then
16 MeV if we want to be able to remove all the spallation background.
The second most important variable used in determining spallation is the transverse distance (LT RAN S ). This is defined as the perpendicular distance from the muontrack to the reconstructed event vertex of the relic candidate (see Fig. 6.9). The vertex resolution of events 16-30 MeV tends to be around 30 or 40 cm. The resolution of
the muon track is about a meter. The spallation product itself cannot travel far in thedetector before decaying, especially for short lived events. For muons unassociated78with the relic candidate, accidental coincidence of LT RAN S less then a few meters isquite rare. Thus LT RAN S is a powerful handle on spallation, and a 16-20 MeV reliccandidate with a preceding muon within a second of dt and a meter of LT RAN S is
almost certainly a spallation product.
The third and fourth variables used for spallation determination come from themuon dE/dx plots described in section 4.7. Spallation causing muons tend to have apeak in their dE/dx plots at approximately where the spallation occurred. Thus, thedistance from where the peak in the dE/dx plot occurs and where the relic candidatelies on the muon track is called the longitudinal distance, or LLON G , and is usedas our third variable. LLON G is not as powerful of a correlation as LT RAN S , but isstill useful. The longitudinal spallation tagging used was discovered and developed
for this analysis. The underlying physics behind the utility of the dE/dx plot in
predicting spallation longitudinally is not fully understood and may deserve further
investigation. For the sake of this thesis, the correlation has been proven and is usedwithout further questions.
The last variable used is the amount of light seen in the dE/dx plot in a widthof 4.5 m centered on the peak. Very strong peaks, which show that lots of light was
deposited in the detector originating from that region of the muon track, usually indicate spallation. This variable, QP EAK , is similar to a variable used in the spallation
cut of the 2003 analysis, called the residual charge. The residual charge means theamount of light deposited in the detector above that expected by a minimum ionizing
particle of the same track length. The QP EAK is like a local residual charge. Again,
the power of QP EAK is not as great as that of dt and LT RAN S , but we still gain
information by using it.

79

6.5.2

Method of Determining Spallation

All relic candidates are compared to preceding muons to check for the possibilityof being spallation. The primary means of determining whether or not an event isspallation is by use of a likelihood method utilizing the four variables described in
the previous section. The cut also includes a mix of cuts on specific quantities. The
complete cut algorithm is described in Appendix A.3.
First, the data set is broken into relic candidates (events that have passed thefirst reduction) and muons (events that deposit more than 1000 p.e.’s in the detector).
Then, the muons are fit and subdivided into the various Muboy categorizations (seesection 4.4): single through-going, stopping, multiple, and corner clipper. If the fit
is poor (Muboy goodness < 0.4) for single-through going type muons, a BFF fit (seesection 4.8) is used instead (if the BFF goodness is < 0.3, neither fit is trusted and all
events are vetoed for 2 s. Even if the BFF fit is good, both the BFF fit and the Muboy
fit are checked for indications of spallation; if either find a correlation that looks likespallation, the event is rejected). Then, the relic candidates are compared to every
muon within 30 seconds of the event time. From these correlations, distributions
are made of each spallation variable, for each muon type. Correlations to muonspreceding the relic candidates make the ‘data’ distributions; correlations to muonsfollowing the relic candidates in time comprise a random sample. The random sample
distributions are subtracted from the data distributions, which gives the spallation
correlations.
The spallation correlation and random sample distributions are then parameterized by analytic functions (as are shown in Figures 6.10 and 6.11, for example, or see[Appendix A] for a reference of all such plots), and these functions are used as PDFs
to make the spallation likelihood. Then, when a correlation between a relic candidate and a preceding muon is checked to determine whether or not it is spallation,a full log-likelihood is calculated from the PDF distributions. In most cases the full80

normalized likelihood

x 10

-2

0.18
0.16

spallation data

0.14

spallation likelihood

0.12

random sample data

0.1

random sample likelihood

0.08
0.06
0.04
0.02
0

-2000

-1000

0

1000

2000
LLONG (cm)normalized likelihood

Figure 6.10: SK-I/III longitudinal distance correlations from data with longitudinal
distance likelihood functions overlaid for single through-going muons.
10-2
spallation data
spallation likelihood
random sample data

10

10

-3
random sample likelihood

-4

100

200

300

1000

2000

3000
LTRANS (cm)Figure 6.11: SK-I/III transverse distance correlations from data with transverse distance likelihood functions overlaid for single through-going muons.
log-likelihood is simply:
h Ldt
LLON GQP EAK i
L
Lspall
Lspall
L T RAN S··
Ltotal = log Ldtspall · spall
LT RAN S
LLON GQP EAK
randomLrandom

Lrandom

Lrandom

A likelihood threshold is determined for each muon type and energy range, and,if the calculated likelihood for an event is larger then the threshold, the event iseliminated. While the likelihood is the primary way that spallation events are elim-81inated, some cuts on specific quantities also exist. For instance, after the most rareand energetic muons (total detected light > 400,000 p.e.’s), all data is rejected fora few seconds. Furthermore, multiple muon type events have further complications
explained later.
The likelihood thresholds are tuned to remove all statistically significant tracesof spallation and still be highly efficient. Due to the low statistics of the analysis, it
is virtually impossible to determine with certainty if all spallation events have been
removed from the sample. However, if one or two events remain in the sample, they
will occur at low energy, and any resulting limit on relic flux will be worsened; thus,
as long as no relic signal is claimed, any error introduced will make the results moreconservative.
The basic method of tuning the cut is to look at the distribution of the spallation
variables, especially dt and LT RAN S , as well as the likelihood distribution itself, forthe final sample after the spallation cut is applied, and compare it to the random
sample. If there is an excess in the final data sample at low dt or LT RAN S , or highlikelihood, compared to the random sample, then we cut more stringently (lower the
likelihood threshold for the appropriate muon type), until the distributions look as
close as can be statistically determined.

6.5.3

Multiple Muons

Multiple muons events are when more than one muon is physically traveling throughthe detector in the same event window. The muons in these muon bundles arise froma common parent atmospheric interaction, and thus not only is the similar timing no
coincidence, but the muon directions should be virtually identical. Even though thedirections are the same, the muons can be spread out, having entry and exit positions
that can be quite different. Also, the dE/dx plot information is compromised, since
the electronics only saves the timing information of the first time a PMT is hit inside82

an event. Muboy is very good at identifying multiple muon events, and attempts todetermine the number of muons involved and fit a track for each. However, the moremuons in the bundle, the more difficult it is, and the poorer a job Muboy does witheach track. The primary track will be the one Muboy is best able to determine (either
due to being the brightest, or the first), and each subsequent track fit will be less andless reliable. Muboy can try to fit a maximum of 10 tracks; furthermore, in somecases Muboy is certain there is many muons involved, but is unable to fit more than a
primary track, thus returning the seemingly contradictory result that the muon event
is a multiple muon with only one muon track. These multiple muons with one tracktend to behave strangely and were considered and tuned separately. Not only does all
this make the multiple muon case more complicated than the single muon case, but
because there are more muons in each event, multiple muon events are almost fourtimes more likely on average to cause spallation than a single through-going muon(although they occur more than 10 times less often), making this case both difficultand important.
It was found that, even with the light from many muons overlapping, the LLON G
and QP EAK information extracted from a dE/dx plot calculated using the primarymuon track information still correlated to real spallation events, although not asstrongly as for single muons. For our cut, each muon track was treated as a separate
muon event. A second dE/dx profile was calculated for the secondary track, and thesecondary track LLON G and QP EAK variables are used in attempting to determine
spallation from the secondary track. When three or more tracks are present, these
additional tracks, which were least likely to cause spallation, were grouped together
in a cut utilizing only dt and LT RAN S information, specially tuned to cut stringently,
even at the cost of additional inefficiency, so as to ensure no spallation slipped through.
Even the LT RAN S distributions for tracks beyond the first differed from the primary
track distribution, and required its own likelihood (Fig. A.9). Again, the full details

83

of the cut can be found in Appendix A. As these events occur only rarely, the increased
inefficiency cost of a stricter tuning was not great.

6.5.4

Spallation Summary

SK-I and SK-III likelihood distributions were so similar that they were merged into
one combined SK-I/III spallation cut. As with many other cuts, the differences in SKII required that it be treated separately, so new likelihood functions were constructed
for SK-II; it was tuned separately, and has a worse energy threshold due to poorer
resolutions. Position dependent efficiency maps were calculated for each spallation
cut, revealing that the cut is more efficient near the walls (probably because there areless muons to correlate to). Relic MC vertex distributions, coupled with the position
dependent inefficiency maps, were utilized to obtain overall inefficiency numbers (seeTable 6.2).
Each cut has two separate tunings - one, stricter cut at lower energies (16-18
MeV for SK-I/III, 17.5-20 MeV for SK-II), and a more efficient higher energy tuning(18-24 MeV for SK-I/III and 20-26 MeV for SK-II).

Table 6.2: Spallation Cut Signal Efficiencies
EFFICIENCY
Low energy
High energy

SK-I/III81.8 % (16-18 MeV)
90.8 % (18-24 MeV)

84

SK-II
76.2 %(17.5-20 MeV)
88.2 %(20-26 MeV)

6.6

Pion Cut

Some of the higher energy events in our sample (usually > 30 MeV) are actuallypions that are created by atmospheric neutrino interactions. One way to distinguishbetween pions and electrons is by looking at the ’fuzziness’ or ’sharpness’ of theCherenkov ring. This is because pions are quickly captured by an oxygen nucleus,
while electrons tend to travel a little farther and multiple scatter. This multiple
scattering causes the electron direction to change as it travels, causing the Cherenkov
ring to be more poorly defined.
Quantitatively, this difference can be used to construct a tool for discriminating
pions and electrons. When the Cherenkov angle for an event is calculated (see section
4.6), a distribution of the cone angles from three-hit combinations (or triplets) isformed. This distribution will be narrower for pions then for electrons, though the two
peak at the same angle. Using this logic, a pion likelihood variable was constructed,
where pion likelihood is defined as follows (using the triplet distribution):LP ION = #entries ± 3◦ from peak/#entries ± 10◦ from peak
By looking at SN relic MC compared to pion MC, the cut criterion was determined to be 0.58 for all SK run periods. This cut is approximately 1% inefficient.

6.7

Multi Ring Cut

Sometimes an atmospheric neutrino can create several charged particles at the sametime. As the particles all come from a common parent interaction, the timing information for the event only shows one timing peak, and thus the event won’t beremoved by the 2-peak cut. Although most are removed by the Cherenkov angle andpion cuts, a few can survive. To remove these specifically, we use the fact that these
multi-particle events have multiple Cherenkov rings (for example, Fig. 6.12).
85

Super-Kamiokande I
Run 7312 Sub 39 Ev 1821613
99-05-09:08:29:47
Inner: 344 hits, 514 pE
Outer: 2 hits, 1 pE (in-time)
Trigger ID: 0x07
D wall: 1690.0 cm
Fully-Contained Mode

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
69
55
41
28
14
0
0

500

1000

1500

2000

Times (ns)Figure 6.12: Event display of an example multi-ring event. A sharp ring can be seenon the right half of the detector display, and a diffuse ring on the far left.
A ring counting method has already been developed for SK atmospheric neutrino
analyses utilizing Hough transforms, and is described in [50]. We used the same
method to look for multi-ring events. The software determines an angle between therings we can use. In rare cases overly fuzzy electron rings can be mistaken for two
different rings by the software; for this reason events determined to be multi-particle,
but separated by less then 60 degrees, were kept, while events with multiple rings
separated by more then 60 degrees were rejected.

6.8

OD-Correlated Cut

Any event that has an OD trigger is rejected in the first reduction. However, since the
OD has such low photo-cathode coverage (the PMTs are more sparsely distributed
than in the ID, and are smaller), it sometimes happens that events originating fromoutside the detector, such as cosmic ray muons, can enter the detector without depositing enough light to trigger the OD. This is especially problematic if the muonthen decays into an electron, as decay electrons mimic the SN relic signal and cannot86be rejected by other cuts.
Even if the OD doesn’t trigger, however, traces of the muon’s passage usuallyremain in the OD. OD PMTs will still record light, even if it is not enough to reachtrigger threshold. By correlating the timing and position of PMT light between OD
hits and ID hits, we can look for correlations. If tubes in the OD are hit, and can becorrelated to the reconstructed event position in the ID, and the timing informationof the hit ID tubes is correlated to that of the hit OD tubes, it may indicate an
entering event.
The ID time of flight subtracted timing information for each relic candidate issearched with a 50 ns sliding time window. The time value for which the most hits
are seen is considered the peak. Then all OD tubes within 5 m of the reconstructed
candidate position are searched. The amount of tubes that saw any light within 150
ns of the ID peak time is determined. If this is two or more tubes, the event isrejected.
The OD timing information is then searched with a 100 ns sliding time window.
The maximum number of OD PMTs hit within 100 ns and within 5 m of the candidate
vertex is determined; if this is three or more tubes, the event is rejected.

6.9‘Sub-event Cut’

In the first reduction, a 50 µs cut is applied, which removes any event occurring
within 50 µs of an LE or HE triggered event. Events occurring after an SLE event
are ignored, however, as the rate of SLE events is so high, the inefficiency would be
too great. However, some events that are only triggered as SLE may be correlated
to backgrounds. For instance, atmospheric neutrino interactions that produce subCherenkov muons may also create a prompt gamma (which is therefore earlier intime than the decay electron, which comes from the muon with a half-life of 2.287µs). This gamma will usually be low energy ( 6 MeV) and trigger as SLE only.
Furthermore, if the relic candidate is itself a low energy muon that has somehow
survived the Cherenkov angle cut, then it may have decayed into a decay electron
itself. So although the 50 µs cut in the first reduction looks to see if there is a LE or
HE trigger before the relic candidate, we also need to check after the relic candidate.
This collection of additional timing and distance correlation cuts removes such eventsand is referred to as the ’sub-event cut’.

6.10

Cherenkov Angle Distribution

Charged particles traveling close to the speed of light in pure water emit Cherenkov
light in a cone shape with an opening angle of about 42 degrees. Heavier particles,
such as muons, pions, and nucleons, may travel slower if their energies are relatively
small, producing Cherenkov light with an opening angle that is smaller then 42 degrees. The resolution of our reconstruction algorithm is not perfect (see section 4.6),
and multiple scattering can confuse the ring, so the reconstructed Cherenkov angle
distribution is not as sharp as we could hope. Fig 6.13 shows the Cherenkov angle distribution of SN relic MC (LMA model). The main peak is determined to be
between 38 and 50 degrees, and this is the cut applied to the data to eliminate remaining heavy particles at lower angles, and more isotropic events at higher angles.
The region from 38-50 degrees is called the ‘signal region’. Due to the poorer energy
resolution of SK-II, the cut loses more of the signal for that phase, as the events arepushed to above 50 degrees.
This is not strictly a cut, as the information in these excluded regions is not
thrown away, but instead is utilized at a later stage in the analysis.

88Number of Events

4000
3500

SK-I/III relic MC

3000

SK-II relic MC

2500
2000
1500
1000
500
0

0

10

20

30

40 50 60 70 80 90
Cherenkov Angle (degrees)

Figure 6.13: Reconstructed Cherenkov angle distribution of SN relic MC (LMA
model).

6.11

Reduction Efficiency Summary

Most cut efficiencies were calculated using relic MC. Each relic model has slightly
different efficiencies; the ones listed in Table 6.3 are from the LMA model. The
systematic error of most cuts was calculated by comparing LINAC [41] MC to LINAC
data, or by using the values established in the solar analyses when the cuts are similar(noise reduction, incoming event cut). The OD correlated cut uses a random sample
of cosmic ray muon data for OD hit information for determining efficiency. The
efficiency of the spallation cut is a function of position (efficiency is greater near theedges of the detector, where the candidate can be correlated to fewer muons), and thevertex distribution of relic MC is used to estimate the average efficiency. The error
on this estimation is likely dominated by the statistics of our relic MC and spallation
random sample, and is rounded up to be conservative. The efficiency of the solar
angle cut is mostly geometric and therefore exact; the only source of systematic error
89Signal efficiency

1

0.9
0.8
0.7

Signal Efficiency

0.62003 Efficiency
unnormalized LMA flux

0.5
0.4
0.3
0.2
0.1
0

20

30

40

50

60

70
80
90
Energy (MeV)

Figure 6.14: Signal efficiency of new analysis compared to 2003 study. An unnormalized LMA spectrum is overplotted to show the importance of the improvements.
comes from the ratio of events falling in each multiple Coulomb scattering goodness
bin, as determined from solar MC. Values of the systematic errors, along with the cut
efficiencies, can be seen in Table 6.3.

90

Table 6.3: Cut Signal Efficiency (Systematic Error)
Cut
Noise Reduction
Spall + Solar
Incoming event
Pion
Cherenkov angle
Other cuts
Total

SK-I
99% (1%)88% (1%)98% (0.5%)
98% (0.2%)
95% (0.4%)
98% (2%)
78.5% (2.5%)

91

SK-II
99% (1%)87% (1.4%)
95% (0.3%)
97% (0.5%)
88% (3%)98% (2%)
69.2% (4.0%)

SK-III
99% (1%)89% (1%)96% (0.3%)
98% (0.5%)
94% (0.3%)
98% (2%)
76.7% (2.5%)

Chapter 7
Analysis: Limit Extraction
After the event selection, a final sample is obtained, which is searched for any indication of SRN events. This chapter describes the methods used to accomplish this.

7.1

Cherenkov Angle Regions

Inverse beta decay positrons in our final sample (> 16 MeV) are highly relativistic
and will have a Cherenkov angle of around 42 degrees. For heavier particles, suchas muons and pions, only the highest energy ones will have a comparable velocity,and most will travel more slowly and emit light with a small Cherenkov angle. On
the other hand, some events can actually reconstruct at higher Cherenkov angles;
especially events with a more isotropic nature, such as multiple gamma events.
SK-I SRN MC simulations show that most SRN events are expected to reconstruct at a Cherenkov angle of between 38 and 50 degrees, which is the region of
the Cherenkov angle cut (henceforth called the ‘signal region’). However, important
information exists at other Cherenkov angles that can be utilized. Although the tworemaining backgrounds (see section 5.2) that were considered in the 2003 study (νµand νe CC) also mostly fall in the same Cherenkov angle region, the two newly considered remaining backgrounds (NC elastic and µ/π) mostly fall outside the signal
92

region (see Fig. 7.1). By understanding the behavior of these two backgrounds everywhere, we can use the data at other Cherenkov angles to help normalize the two
new backgrounds in the signal region.
To this end, two new Cherenkov angle regions are defined: 20-38 MeV (the ‘lowangle’ or ‘µ/π’ region) and 78-90 degrees (the ‘high angle’ or ‘NC elastic’ region).
Using such broadly defined regions (only three bins in Cherenkov angle) allows us
to bypass concerns about Cherenkov angle resolution yet still take advantage of theimportant information present in the data.
PDFs following the spectrum shape were constructed for each of the four remaining backgrounds and each SRN model considered, for all three Cherenkov angle
regions, for all three SK data phases. Most spectra were obtained from MC (seechapter 5), with the exception of the νµ spectra, which were obtained from real decay
electron data, whose Michel spectrum should be identical to that from the decay of
sub-Cherenkov muons. This has the advantage of not requiring any MC systematic
errors for this channel, which is our dominant background. The high statistics of
decay electrons in SK allows this spectrum to be measured with negligible statisticalerror as well.
All of the PDFs can be found in Appendix B.

93

number of eventsµ/πregion250

signalregionNC
region200
SK-I final sample
νµ + νe CC

150

µ/π
NC elastic

100

50

0

20

30
40
50
60
70
80
90
SK-I final sample Cherenkov angle (degrees)

Figure 7.1: Cherenkov angle of SK-I combined final data (all cuts except Cherenkov
angle cut applied) overlaid with distributions of the four remaining backgrounds from
SK-I MC (same cuts applied). The division of Cherenkov angle regions is also pictured.

7.2

Extended Maximum Likelihood Fit

An unbinned maximum likelihood fit on the final sample spectrum determines how
much (if any) SRN signal existed in the final sample. For each SK data phase four
remaining backgrounds and a possible SRN component were assumed (5 parameters). The fit is done on the spectrum in each of the three Cherenkov angle regions94

simultaneously. For each combination of parameter coefficients c (the coefficients are
simply how many events of each channel is assumed in all three Cherenkov angle
regions combined), and for each parameter PDF pdf (E), a likelihood is constructed,
as follows:

L =Nevents
Y
i=1

e

−

P5

j=1 cj×

5
X

cj pdfj (Ei )

(7.1)

j=1

The likelihood is maximized for each SK phase separately.
In this formulation the relative normalizations of each Cherenkov angle regionis fixed; for instance, for SK-I, if we disregard the 50-78 degree region, which is not
used, and normalize the rest to 1, then 99.2% of SRN events (LMA model) are foundin the signal region, 0.5% in the high angle region, and the other 0.3% in the low
angle region. However, the relative normalization of how many events are in eachchannel (relic, NC elastic, etc.) is free floating.
The 5 parameter likelihood space is searched, starting at a contribution of 0
relic events. The number of relic events is incremented with a 0.1 event spacing, andfor each number of relic events, all reasonable combinations of the four remaining
backgrounds is searched, and the combination with the maximum likelihood value
is recorded. As the number of relic events is incremented, this gives us a curve of
likelihood vs. number of relic events. This roughly Gaussian curve has a peak (bestfit), with a width that indicates the significance of any positive indication. The curvealso allows us to extract a 90% confidence level limit on the relic flux rate, simply byintegrating the curve starting at 0 relic events, and finding the point at which 90%of the area under the entire curve is reached.
Put another way, the 90% CL point limit90 is determined by the following simple

95

relationship, where r represents the number of SN relic events:

Z limit90
0

L(r) dr/Z ∞0

L(r) dr = 0.9(7.2)

The likelihood curves for each different relic model are very similar, and a representative example is shown in Fig. 8.4.

7.3

Inclusion of Systematic Errors

The following systematic errors are considered:

7.3.1

Energy Scale and Resolution Uncertainty

The energy scale and energy resolution systematic uncertainties are considered to be
uncorrelated. They are separately calculated, then added in quadrature. The amountof the energy scale and energy resolution systematic errors are based on the SK solar
analyses [32], then slightly increased due to the larger energies involved. The energy
resolution systematic uncertainty used in our study is 3%, while the energy scale
uncertainties used are 1% for SK-I and SK-III, and 2% for SK-II. Inclusion of thissystematic error was not found to have an appreciable effect on the results.
To take the energy scale systematic uncertainty into account, the PDFs for four ofthe five channels (the νµ CC was taken from decay electron data, and is thus not MC,
and not susceptible to this error) were shifted by the amount of the uncertainty. To
take into account the energy resolution systematic uncertainty, the energy resolutionfunction from reference [32] was applied to the likelihood functions to distort them.
Finally, the full uncertainty was incorporated into the likelihood calculation algorithm as follows. Let ǫ be a variable representing the amount of spectral distortion,such that an ǫ of 1 represents a 1σ deviation in the energy scale and resolution; and96

let L(ǫ) be the likelihood evaluated with the likelihoods distorted by an amount ǫ.
Then the new final likelihood L′ is:

1
L =√
2π
′

Z ∞

−∞

2

e−ǫ /2 L(ǫ) dǫ(7.3)

such that the originally calculated likelihood L is now simply the ǫ = 0 case.

7.3.2

Atmospheric ν Background Systematic Errors

Three of the four remaining backgrounds are modeled by SK MC (the exception being
the νµ CC background, which is modeled by decay electron data). The SK MC iswell verified above 100 MeV; however, in the lower energy region of 16-100 MeV thatis relevant to our study, the MC accuracy is less well studied. Little data exists tocompare to the MC, especially for the NC elastic mode. To incorporate these concerns
into the analysis, two systematic errors on the νe CC and NC elastic backgrounds
were included. These systematics were designed to cover any remaining uncertainties
in the MC. As for the other two background channels, the νµ CC comes from real
data and therefore is not vulnerable to MC inaccuracies, and the µ/π channel is by
far the least relevant of the four channels, and therefore the safest to neglect.
For the NC elastic channel, the greatest potential for error lies in the relative
normalization across Cherenkov angle regions. The amount of NC elastic found in the
78-90 degree region determines the amount of the fit in the signal region. If the ratioof the amount of NC elastic in the high angle region compared to the signal region
as determined by MC is off by some factor, this will tend to have a larger influenceon the result than a distortion of the spectrum of the NC elastic in the signal region
by the same factor.
For SK-I, the NC elastic MC has 7.4% of events occur in the signal region, while9787% of events occur in the high angle region. Considered is a 100% change in thenormalization of the number of NC elastic events in the signal region, with all changes
to be correspondingly balanced by a change in the normalization of the high angle
region. Thus, a +1σ effect would be for 14.8% of events to occur in the signal region,and 79.6% of events to occur in the high angle region, while a -1σ effect would be forno NC elastic events to occur in the signal region, and 94.4% of the events to occur
in the high angle region. As we can’t have less than 0 events in the signal region,
there is a physical boundary at -1σ. Thus, we applied the error asymmetrically from
-1 to +3 σ.
For the νe CC channel, the relative normalization across Cherenkov angle regions
is not a concern, as more than 99% of the events fall into the signal region, so insteada distortion of the spectrum in the signal region was considered. The νe CC PDF in
the signal region was distorted as follows:

PDFnew = PDFold × N (1 +0.5ǫ(E − 16))
74 MeV

(7.4)

where E is the energy (MeV), σ is the magnitude of the spectral distortion, andN is a constant such that the new PDF is normalized the same as the old.
A -2σ effect would reduce the PDF to 0 at 90 MeV. This was considered to beunphysical, and thus a -1σ effect was considered the physical lower bound, forcing us
to apply this error in the same asymmetric manner as the NC elastic, from -1 to +3σ.
We applied the background channel systematics using an integral method with aweighting function (which acts as a Bayesian prior). However, as our error is applied
over an asymmetric region (-1 to +3 σ), we could not use a symmetric Gaussian (suchas we use in the next section) without introducing a bias in our result. Instead, weused a weighted Gaussian that as closely as possible maintained the properties of the

98

0.3

0.25

0.2

0.15

0.1

0.05

0

-3

-2

-1

0

1

2

3

Figure 7.2: Example of a symmetric Gaussian (black) and the asymmetric weighted
Gaussian used to normalize the atmospheric neutrino background systematics. Horizontal axis is the amount of the systematic distortion in units of sigma.
symmetric Gaussian.
Specifically, in the case of a symmetric error (i.e., -∞ to ∞), a normal Gaussian
would have the following properties: (1) expectation value (first moment) = 0, (2)variance (second moment) = σ 2 . Our weighted Gaussian (see Fig. 7.2) was constructed such that its properties (integrated over σ from -1 to 3) were the same as
the symmetric case. This weighted Gaussian was normalized to 1 and used in boththe νe CC and NC elastic cases, as their integration ranges were identical.
The integral method of applying the systematic error is as follows. Let G(σ)
be our weighted Gaussian function described above. Let L(r, σ) be the likelihood as
a function of SN relic events and whichever systematic error is under consideration.
Then, the likelihood after the application of the systematic error of either of the
background channels is:99′

L (r) =Z 3

−1

L(r, σ)G(σ)dσ(7.5)

Inclusion of the atmospheric ν background systematics changed the result (towards a less stringent limit) by less than 6%.

7.3.3

Energy Independent Efficiency Systematic Error

The energy independent portion of the efficiency systematic error is assumed uncorrelated. The systematic error of each cut, as shown in Table 6.3, is added in quadrature,
to get the total efficiency systematic error of the reduction. The total efficiency systematic error also includes the uncertainty in the fiducial volume cut, inverse beta
cross section, and livetime calculation, as shown in Table 7.1.
The fiducial volume and livetime calculation systematic errors are the same as,
and taken from, the SK solar analyses [31, 32].
To apply this systematic error, the likelihood curve (likelihood as a functionof number of SN relic events) is modified. The modification for each value of thelikelihood is as follows, where ǫ is the efficiency, σ is the efficiency systematic error,
P(ǫ) is a probability function in the shape of a Gaussian centered on ǫ0 with widthǫ0 σ, r is the number of relic events seen in the data, and R is the number of relic
Table 7.1: Total Efficiency Systematic Error
Error Source
Cut reduction
Fiducial Volume
Cross Section
Livetime
Total

SK-I
3.1%
1.3%
1.0%
0.1%
3.51%

100

SK-II
4.4%
1.1%
1.0%
0.1%
4.65%

SK-III
3.1%
1.0%
1.0%
0.1%
3.41%

events actually interacting in the detector, such that r = ǫR:′

L (R) =Z 1

ǫ=0

L(ǫR)P (ǫ)ǫ dǫ(7.6)

This error is applied last, after all other calculations are complete. Inclusion ofthis systematic error changed the result (making the limit less stringent) by a few
percent.

101

Chapter 8
Results
8.1

Basic Results

Figures 8.1, 8.2, and 8.3 show the final sample data spectrum in each Cherenkov angle
region, overlaid with the best fit results for the LMA model. For SK-I, the relic best
fit is negative and unphysical (for all models), so zero relic contribution is shown.
For SK-II and SK-III, a positive indication (not significant) of a relic component was
found. The 90% CL upper flux limits differ for each model, and are summarized inTable 8.1. Example likelihood curves for the LMA model fit are shown in Fig. 8.4.
More detailed numerical values for the results are given in Appendix D.

Table 8.1: 90 % CL flux limit (ν̄ cm−2 s−1 ), Eν > 17.3 MeV
Model
Gas Infall (97)
Chemical (97)
Heavy Metal (00)LMA (03)
Failed SN (09)
6 MeV (09)

SK-I
<2.1
<2.2
<2.2
<2.5
<2.4
<2.7

SK-II
<7.5
<7.2
<7.4
<7.7
<8.0
<7.4

102

SK-III
<7.8
<7.8
<7.8
<8.0
<8.4
<8.7

All
<2.8
<2.8
<2.8
<2.9
<3.0
<3.1

Predicted
0.3
0.6
< 1.8
1.7
0.7
1.5

Number of events

30

relic
all background
νµ CC

25

20

νe CC
NC elastic

SK-I

µ/π

15

10

5

0

25
50
75
20-38 degrees (MeV)

25
50
75
38-50 degrees (MeV)

25
50
75
78-90 degrees (MeV)

number of events

Figure 8.1: SK-I LMA best fit result. The relic best fit is negative, so a relic fit of 0
is shown.

20
relic

18

all background
νµ CC

16
14

νe CC

SK-II

NC elastic

12

µ/π

10
8
6
4
2
0

25
50
75
20-38 degrees (MeV)

25
50
75
38-50 degrees (MeV)

25
50
75
78-90 degrees (MeV)

Figure 8.2: SK-II LMA best fit result. The relic best fit is 3.05 events per year
interacting in the detector (before reduction efficiencies).

103

Number of events

14

relic
all background
νµ CC

12

νe CC

10

SK-IIINC elastic
µ/π

8
6
4
2
0

25
50
75
20-38 degrees (MeV)

25
50
75
38-50 degrees (MeV)

25
50
75
78-90 degrees (MeV)

Figure 8.3: SK-III LMA best fit result. The relic best fit is 6.9 events per year
interacting in the detector (before reduction efficiencies).

104

Likelihood

0

-0.25

-0.5

-0.75

SK-I

-1

SK-II
-1.25

SK-III
Combined

-1.5

-1.75

-2

0

2

4

6

8

10

12

14

16

SNR events/year

Figure 8.4: Example likelihood curves from the LMA model. Vertical lines represent
best fit and 90 % CL results for the combined fit.

105

8.2

Comparison to 2003 Result

The new analysis has a lower energy threshold than the 2003 study, so the results are
not immediately comparable. Furthermore, the previous study presented its result ina model independent fashion, since the result for all models were so similar. Although
we verified that with an 18 MeV energy threshold the SK-I results were similar enoughto justify a model-independent approach, the lower energy threshold and new datarequired model dependent results. For comparison purposes, we consider the LMA
model. The limit is 2.9 ν̄ cm−2 s−1 > 16 MeV (positron energy), which is equivalent
to 2.0 ν̄ cm−2 s−1 > 18 MeV positron energy. It is notable that this result is lessstringent than the 2003 result of 1.2 ν̄ cm−2 s−1 positron energy > 18 MeV. There
are multiple reasons for this.
First, a 0th order approximation of the inverse beta cross section was then used.
Now, the full cross section from [51] is used. This raises the limit by about 8%.
If events with pre and post-activity are also removed, the old-style analysis limit
becomes 1.35 cm−2 s−1 . Furthermore, the binned χ2 method used assumed Gaussianstatistics, while Poissonian statistics are more appropriate considering how few events
there are at low energy. This alone would change the limit from 1.2 to 1.7 cm−2 s−1 .
When all these corrections are combined, the original analysis result of 1.2 ν̄ cm−2
s−1 instead becomes 1.9 ν̄ cm−2 s−1 .
With my improved analysis, if we neglect atmospheric ν background systematics,(but keep the other systematics, none of which were included in the 2003 study), theSK-I only LMA result is 1.6 ν̄ cm−2 s−1 (> 18 MeV positron energy), which is more
stringent than the published analysis with these corrections. However, the SK-II and
SK-III data shows a hint of a signal, which causes the limit to become less stringent
when all the data are combined, for the final LMA result (with all systematics) of 2.0
ν̄ cm−2 s−1 > 18 MeV positron energy, or 2.9 ν̄ cm−2 s−1 > 16 MeV positron energy.
So, in summary, the difference is in part due to corrections that should be made106

to the 2003 result; in part due to inclusion of many new conservative systematics;
and also in part due to the positive indication of a relic signal in SK-II and SK-III
data.

107

Chapter 9
Limit on SN Emission Spectrum
As well as giving the usual model dependent limit result, another formulation ispossible, following the procedure outlined in [19, 52]. The basic idea is to parameterize
all relic models into two free parameters, and then to express the result as an exclusion
contour in this two dimensional space. The goal is to simplify matters for modelers
and the community.

9.1

Making a General Relic Model

To summarize [52], the SN relic spectrum at SK φ is as follows:dφ(Eν ) =
dEν

Z ∞h
0

ih

(1 + z)ϕ[Eν (1 + z)] RSN (z)ih c dt
dz

dz

i

(9.1)

where Eν is the neutrino energy; ϕ is the neutrino emission per supernova; RSN
is the evolving core-collapse supernova rate; and z is the standard redshift parameter.
RSN (z) can be expressed in terms of the star formation rate RSF (z) by:RSN ≃RSF (z)
143M⊙

(9.2)

where the Saltpeter IMF is assumed, and the star formation rate is well mea108

sured, with an error of approximately 20% at z = 0.
Furthermore, the neutrino emission spectrum can be modeled in terms of a
Fermi-Dirac function:
ϕ(Eν ) = Eν̄e ,tot

1
120 Eν2
4
4E/Tν
7π T e+1(9.3)

With T being the energy (in units of MeV), and Eν̄e ,tot being the total energy.
With this formulation, the SN relic rate can be directly related to the two freeparameters: T (the neutrino temperature in MeV), and the luminosity (or totalenergy) of an average supernova.

9.2

MethodThe kinematics of inverse beta decay are well understood, as is the cross section [51].
The volume of water in SK, and therefore the amount of proton targets in the volume(∼ 1.5 x 1033 in 22.5 ktons of water), can be calculated.
MC was made from 2 to 8 MeV neutrino temperature, in half MeV steps. A
spectrum of positrons in SK was simulated for each temperature (Fig. 9.1).
300,000 events were made for each temperature. These events had the full relicanalysis applied to them; all the cuts from the event reduction (see chapter 6) wereapplied, and the final samples had the full unbinned maximum likelihood fit applied.
Two types of limits were obtained. In one case, each neutrino temperature wasconsidered separately, as a separate relic model, and a limit on rate (and therefore
average luminosity) was obtained. These 1-D limits can be connected with a line. In
the second case, the likelihoods of all neutrino temperatures were considered simultaneously, and a true 2-D exclusion contour obtained.
The results are shown in two plots. In the first (Fig. 9.2, neutrino temperatureis plotted against event rate in the SK fiducial volume (before efficiency losses). On
109

Event Rate (/22.5kt yr MeV)

0.3

3MeV
0.25

4MeV
5MeV

0.2

6MeV
7MeV

0.15

8MeV
0.1

0.05

0

10

15

20

25

30

35

40

45
50
55
60
Positron Energy (MeV)

Figure 9.1: True spectra of positrons in SK originating from SN relic neutrinos of aparticular temperature (SN ν̄e luminosity of 51052 ergs assumed).
this plot each of the SN relic models we considered are plotted as well for comparison.
In the second plot (Fig. 9.3, both free parameters (neutrino temperature and averageluminosity) are plotted, as well as allowed regions from IMB and Kamiokande fromthe 1987A data. The various considered relic models are not overplotted on thesecond plot; this is because some of the models are older, and may have used different
values of the star formation rate, IMF, etc, than the modern values assumed in thisformulation. Thus, overplotting is not appropriate unless each model is checked indetail, and in some cases modified to reflect differences.
The results (1-D limit) are also summarized in Table 9.1.

110

SK 1497+794+562 Days

8

Excluded (E>16MeV)

7

νe→e+ (90%C.L.)

6
5
4

HMA

LMA

3

6 MeV

2
CE

1

4 MeV

FS

CGI

+

e candidates>16MeV/22.5kton year

90
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Tν in MeV

Figure 9.2: Exclusion contour plotted in a parameter space of SRN event rate vs.
neutrino temperature. The red shows the 90% CL result. The dashed line shows theindividual 90% CL results of each temperature considered separately, which is not atrue 2-D exclusion contour. CGI is Cosmic Gas Infall model, HMA is Heavy Metal
Abundance model, CE is Chemical Evolution model, LMA is Large Mixing Anglemodel, FS is Failed Supernova model, and the 6 and 4 MeV cases are assuming thatneutrino temperature, from [19].

111

53

SN νe Energy in 10 erg

3

SK 1497+794+562 Days
Excluded (E>16MeV)
νe→e+ (90%C.L.)

2

1

0
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Tν in MeV

Figure 9.3: Results plotted as an exclusion contour in SN neutrino luminosity vs.
neutrino temperature parameter space. The green and blue contours show IMB and
Kamiokande allowed areas for 1987A data, respectively (originally from [53]). The
red shows our new 90% CL result. The dashed line shows the individual 90% CL
results of each temperature considered separately, which is not a true 2-D exclusion
contour. Results are in the form of Fig. 6 from [52].

112Table 9.1: Summary of limit values.
ν̄e Temperature (MeV)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0

113

Eν̄e ,tot (×1053 ergs)
9.0
4.8
2.9
2.1
1.5
1.3
1.1
0.92
0.82
0.75
0.70

Chapter 10
Conclusion and Future
As of this writing, this analysis replaces the published 2003 limit [20] as the mostsensitive study and limit on the SN relic neutrino flux to date. The SK study has
been improved with an expanded data set, greatly improved event selection (average
efficiency improved for SK-I data from 52% to 75%), lowered energy threshold (from18 to 16 MeV positron energy for SK-I/III), an unbinned maximum likelihood fit (asopposed to a χ2 ), and many new systematics.
Although the SN relic signal was not seen, limits were placed on a variety ofmodels, and a positive indication was seen in the new (SK-II and SK-III) data which
could be a tantalizing hint of a signal, although the indication was not significant. A
limit is also on the neutrino emission spectrum.
Already (2011) SK-IV has over 50 kt-years of data, and the new electronics
may allow for improved identification of low energy pre-activity, which could reduce
backgrounds further for this new data. However, even if we are on the threshold ofseeing the SN relic signal, it is unlikely that a discovery can be made in the near
future, due to the low rate and the significance required for a certain discovery. The
best prospect for near future SN relic detection is through neutron tagging, for which
proposals have already been made [36]. A test facility to determine the feasibility of114

such an experiment is already in operation.

115

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119AppendicesA

Appendix A - Spallation

Likelihoods are fit based on data. For the random sample, real correlations to muons
30 seconds after relic candidates are used. For the spallation sample, real correlations
to muons 30 seconds before relic candidates are used, minus the random sample.
Samples of correlations for relic candidates > 14 MeV, 15 MeV, and 16 MeV were
examined. Initially, there were hopes of lowering the energy threshold below 16 MeV.
Using correlations from data lower in energy than the analysis threshold risks thepossibility of introducing new spallation products that could alter the distributions;however, using the above 16 MeV distributions alone meant insufficient statistics forgood fits for all muons types except the single through-going muon sample. Data
above 15 MeV was eventually decided on and used as the basis of the likelihoods.
The likelihoods used, compared to the data distributions, are shown in the following plots, for all four spallation likelihood variables (dt, LT RAN S , LLON G , andQP EAK ), for all four different muon categorizations (single through-going, stopping,
multiple muons with only one track fit by Muboy [type 1], and multiple muons withmore than one track fit [type 2]), for both spallation and random samples (the dt
random sample is simply a flat line and not shown).

120

Table A.1: Information on spallation products expected in SK. Energies are totalenergy released, which can, depending on the decay mode, in some cases be divided
into multiple decay particles. All decays are beta decays, some can include neutrons
or gammas. Whether or not a neutron emitting mode is common or not is also listed,which can be important for neutron tagging background reduction. Data is from
NuDat 2.5 project, NNDC, Brookhaven. Some decays may release more energy thanshown, but the beta particle isn’t allowed all the way to the ground state, limiting
the beta end-point energy to less than the total energy release - for instance, in 8 B[54].
Isotope
13
8 O
11
3 Li
12
7 N
14
5 B
13
5 B
12
5 B
12
4 Be
8
2 He
9
6C
9
3 Li
16
6 C
8
5B
8
3 Li
15
6 C
16
7 N
11
4 Be

τ1/2 (sec)0.00858
0.00875
0.011
0.01250.01730.02020.0215
0.119
0.127
0.178
0.747
0.77
0.838
2.45
7.13
13.8

released E (MeV)
17.8
20.6
17.3
20.6
13.44
13.37
11.7
10.65
16.8
13.6
8.01
15.0
16
9.77
10.4
11.5

121

Neutron?
no
yes
no
no
no
no
<1%
yes
no
yes
yes
no
no
no
no
no

A.1

Spallation: SK-I/III Combined Likelihoods

0.012
20

0.01
0.008

15
0.006
10

0.004
0.002

5

0
0

0

0.2

0.4

0.6
0.8
dtspall1

1

1.2

1.4

0

200 400 600 800 1000 1200 1400 1600 1800
ltspall1(a) SK-I/III dt spallation likelihood (red) vs (b) SK-I/III LT RAN S spallation likelihood
SK-I/III spallation data > 15 MeV (black) for (red) vs SK-I/III spallation data > 15 MeV
single through-going muons(black) for single through-going muons
x 10

x 10

-2

-4

0.35
0.18
0.16

0.3

0.14

0.25

0.12
0.2
0.1
0.08

0.15

0.06

0.1

0.04
0.05
0.02
0

0
-3000 -2000 -1000

01000
lnspall1

2000

3000

0

500

1000

1500
2000
totalspall1

2500

3000
2
x 10

(c) SK-I/III LLON G spallation likelihood (red) (d) SK-I/III QP EAK spallation likelihood
vs SK-I/III spallation data > 15 MeV (black) (blue) vs SK-I/III spallation data > 15 MeV
for single through-going muons(black) for single through-going muons

Figure A.1: Single muon SK-I/III spallation likelihoods

122

0.01
25

0.008

20

0.006
0.004

15

0.002
10
0
5

-0.002-0.004

0
0

0.2

0.4

0.6
0.8
dtspall2

1

1.2

1.4

0

200 400 600 800 1000 1200 1400 1600 1800
ltspall2(a) SK-I/III dt spallation likelihood (red) vs (b) SK-I/III LT RAN S spallation likelihood
SK-I/III spallation data > 15 MeV (black) for (red) vs SK-I/III spallation data > 15 MeV
stopping muons(black) for stopping muons
x 10
x 10

0.175

0.15

0.15

0.125

0.125

0.1

0.1

0.075

0.075

0.05

0.05

0.025

0.025

0

0

-0.025-0.025

-0.05

-3

-2

-0.05
-3000 -2000 -1000

01000
lnspall2

2000

3000

0

2000

4000
6000
totalspall2

8000

10000
x 10

(c) SK-I/III LLON G spallation likelihood (red) (d) SK-I/III QP EAK spallation likelihood (red)vs SK-I/III spallation data > 15 MeV (black) vs SK-I/III spallation data > 15 MeV (black)for stopping muons
for stopping muons

Figure A.2: Stopping muon SK-I/III spallation likelihoods

123

25

0.005

20

0.004

15

0.003

10

0.002

5

0.001

0

0

0.2

0.4

0.6
0.8
dtspall3

1

1.2

0

1.4

0

100 200 300 400 500 600 700 800 900
likelt(a) SK-I/III dt spallation likelihood (red) vs (b) SK-I/III LT RAN S spallation likelihood
SK-I/III spallation data > 15 MeV (black) for (red) vs SK-I/III spallation data > 15 MeV
multiple muons (type 1)(black) for multiple muons (type 1)
x 10

-2

0.12

x 10

-5

0.4
0.1
0.3

0.08

0.06

0.2

0.04

0.1

0.02
0
0

-3000 -2000 -1000

01000
likeln

2000

3000

0

1000

2000

3000
4000
totalspall3

5000

6000
2
x 10

(c) SK-I/III LLON G spallation likelihood (red) (d) SK-I/III QP EAK spallation likelihood (red)vs SK-I/III spallation data > 15 MeV (black) vs SK-I/III spallation data > 15 MeV (black)for multiple muons (type 1)
for multiple muons (type 1)

Figure A.3: Multiple muon (type 1) SK-I/III spallation likelihoods

124

x 10

-2

22.5
0.3
20
0.25

17.5
15

0.2

12.5
0.15

10
7.5

0.1

5
0.05
2.5
0

0

0.2

0.4

0.6
0.8
dtspall4

1

1.2

0

1.4

0

500

1000

1500
likelt

2000

2500

3000

(a) SK-I/III dt spallation likelihood (red) vs (b) SK-I/III LT RAN S spallation likelihood
SK-I/III spallation data > 15 MeV (black) for (red) vs SK-I/III spallation data > 15 MeV
multiple muons (type 2)(black) for multiple muons (type 2)
x 10

x 10

-2

-4

0.2
0.12
0.175
0.1

0.15

0.08

0.125
0.1

0.06

0.075
0.04
0.05
0.02

0

0.025

-3000 -2000 -1000

01000
likeln

2000

0

3000

0

500

1000

1500
2000
totalspall4

2500

3000
2
x 10

(c) SK-I/III LLON G spallation likelihood (red) (d) SK-I/III QP EAK spallation likelihood (red)vs SK-I/III spallation data > 15 MeV (black) vs SK-I/III spallation data > 15 MeV (black)for multiple muons (type 2)
for multiple muons (type 2)

Figure A.4: Multiple muon (type 2) SK-I/III spallation likelihoods

125

x 10

-3

x 10

-3

0.45

0.5

0.4
0.4

0.35
0.3

0.3

0.25
0.2

0.2
0.15
0.1

0.1

0.05
0

0

500

1000

1500 2000
ltrand1

2500

3000

0

3500

-3000 -2000 -1000

01000
lnrand1

2000

3000

(a) SK-I/III LT RAN S random likelihood (red) (b) SK-I/III LLON G random likelihood (red)vs SK-I/III random sample data > 15 MeV vs SK-I/III random sample data > 15 MeV(black) for single through-going muons(black) for single through-going muons

x 10

-4

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0 100002000030000400005000060000700008000090000
totalrand1(c) SK-I/III QP EAK random likelihood (blue)
vs SK-I/III random sample data > 15 MeV(black) for single through-going muons

Figure A.5: Single muon SK-I/III random likelihoods

126

x 10
x 10

-3

-3

0.7

0.6
0.6
0.5
0.5
0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

500

1000

1500 2000
ltrand2

2500

3000

0

3500

-3000 -2000 -1000

01000
lnrand2

2000

3000

(a) SK-I/III LT RAN S random likelihood (red) (b) SK-I/III LLON G random likelihood (red)vs SK-I/III random sample data > 15 MeV vs SK-I/III random sample data > 15 MeV(black) for stopping muons(black) for stopping muons
x 10

-3

0.1

0.08

0.06

0.04

0.02

0

0

2000

4000
6000
totalrand2

8000

10000
x 10

(c) SK-I/III QP EAK random likelihood (red)vs SK-I/III random sample data > 15 MeV(black) for stopping muons

Figure A.6: Stopping muon SK-I/III random likelihoods

127

x 10

x 10

-3

-3

0.35
0.5
0.3
0.4
0.25
0.2

0.3

0.15
0.2
0.1
0.1
0.05
0

0

500

1000

1500 2000
likerandlt

2500

3000

0

3500

-3000 -2000 -1000

01000
likerandln

2000

3000

(a) SK-I/III LT RAN S random likelihood (red) (b) SK-I/III LLON G random likelihood (red)vs SK-I/III random sample data > 15 MeV vs SK-I/III random sample data > 15 MeV(black) for multiple muons (type 1)(black) for multiple muons (type 1)
x 10

-4

0.225
0.2
0.175
0.15
0.125
0.1
0.075
0.05
0.025
0

0

1000

2000

3000
4000
totalrand3

5000

6000
2
x 10

(c) SK-I/III QP EAK random likelihood (red)vs SK-I/III random sample data > 15 MeV(black) for multiple muons (type 1)

Figure A.7: Multiple muon (type 1) SK-I/III random likelihoods

128

x 10

x 10

-3

-3

0.35

0.5
0.3
0.4

0.25
0.2

0.3

0.15
0.2
0.1
0.1
0.05
0

0

500

1000

1500 2000
likerandlt

2500

3000

0

3500

-3000 -2000 -1000

01000
likerandln

2000

3000

(a) SK-I/III LT RAN S random likelihood (red) (b) SK-I/III LLON G random likelihood (red)vs SK-I/III random sample data > 15 MeV vs SK-I/III random sample data > 15 MeV(black) for multiple muons (type 2)(black) for multiple muons (type 2)

x 10

-4

0.6
0.5
0.4
0.3
0.2
0.1
0

0 100002000030000400005000060000700008000090000
totalspall4(c) SK-I/III QP EAK random likelihood (red)vs SK-I/III random sample data > 15 MeV(black) for multiple muons (type 2)

Figure A.8: Multiple muon (type 2) SK-I/III random likelihoods

129

x 10

-3

x 10

0.7

-3

0.6
secondary track

secondary track

0.6

0.5
0.5
0.4
0.4
0.3
0.3
0.2

0.2

0.1

0.1
0

0

0

500 1000 1500 2000 2500 3000 3500 4000 4500
transverse distance (cm)-4000-3000-2000-1000

01000 2000 3000 4000
longitudinal distance (cm)(a) SK-I/III LT RAN S random likelihood (red) (b) SK-I/III LLON G random likelihood (red)vs SK-I/III spallation likelihood (black) for sec- vs SK-I/III spallation likelihood (black) for secondary tracks.
ondary muon tracks.)
x 10

-3

x 10

0.7

0.35
third or higher track

0.6

0.3

0.5

0.25

0.4

0.2

0.3

0.15

0.2

0.1

0.1

0.05

0

-5

0

0

500 1000 1500 2000 2500 3000 3500 4000 4500
transverse distance (cm)third and higher tracks

0

200 400 600 800 10001200 14001600 1800
3
total charge deposited (p.e.)x 10(c) SK-I/III LT RAN S random likelihood (red) (d) SK-I/III Qµ random likelihood (red) vsvs SK-I/III spallation likelihood (black) for SK-I/III likelihood (black) for third and higher
third and higher order tracks.
order tracks.

Figure A.9: Multiple track SK-I/III likelihoods. In all cases black shows the spallation
likelihood, and red the random sample.

130

A.2

SK-II likelihoods
0.012

20
0.01
17.5
0.008

15
12.5

0.006

10
0.004

7.5
5

0.002

2.5
0
0

0

0.2

0.4

0.6
0.8
dtspall1

1

1.2

1.4

0

200 400 600 800 1000 1200 1400 1600 1800
ltspall1(a) SK-II dt spallation likelihood (red) vs SK- (b) SK-II LT RAN S spallation likelihood (red)II spallation data > 15 MeV (black) for single vs SK-II spallation data > 15 MeV (black) for
through-going muons
single through-going muons
x 10

-2

x 10

0.16

-3

0.14

0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06

0.06
0.04

0.04

0.02

0.02

0

-3000 -2000 -1000

01000
lnspall1

2000

0

3000

0

500

1000

1500
2000
totalspall1

2500

3000
2
x 10

(c) SK-II LLON G spallation likelihood (red) vs (d) SK-II QP EAK spallation likelihood (blue)
SK-II spallation data > 15 MeV (black) for sin- vs SK-II spallation data > 15 MeV (black) for
gle through-going muons
single through-going muons

Figure A.10: Single muon SK-II spallation likelihoods

131

20

0.01

17.5

0.008

15

0.006

12.5

0.004

10

0.002

7.5

0

5

-0.0022.5-0.0040-0.006
0

0.2

0.4

0.6
0.8
dtspall2

1

1.2

1.4

0

200 400 600 800 1000 1200 1400 1600 1800
ltspall2(a) SK-II dt spallation likelihood (red) vs SK-II (b) SK-II LT RAN S spallation likelihood (red)spallation data > 15 MeV (black) for stopping vs SK-II spallation data > 15 MeV (black) formuons
stopping muons
x 10

-2

x 10

0.175

0.35

0.15

0.3

0.125

-3

0.25

0.1

0.2

0.075

0.15

0.05
0.1
0.025
0.05
0
0
-0.025-3000 -2000 -1000

01000
lnspall2

2000

3000

-0.05

0

500

1000

1500
2000
totalspall2

2500

3000
2
x 10

(c) SK-II LLON G spallation likelihood (red) vs (d) SK-II QP EAK spallation likelihood (red)SK-II spallation data > 15 MeV (black) for vs SK-II spallation data > 15 MeV (black) for
stopping muons
stopping muons

Figure A.11: Stopping muon SK-II spallation likelihoods

1320.005
20
17.5

0.004

15
0.003

12.5
10

0.002

7.5
5

0.001

2.5
0

0

0.2

0.4

0.6
0.8
dtspall3

1

1.2

0

1.4

0

100 200 300 400 500 600 700 800 900
likelt(a) SK-II dt spallation likelihood (red) vs SK-II (b) SK-II LT RAN S spallation likelihood (red)spallation data > 15 MeV (black) for multiple vs SK-II spallation data > 15 MeV (black) formuons (type 1)
multiple muons (type 1)
x 10

-2

x 10

0.12

-5

0.9
0.8

0.1
0.7
0.08

0.6
0.5

0.06
0.4
0.04

0.3
0.2

0.02
0.1
0

-3000 -2000 -1000

01000
likeln

2000

0

3000

0

1000

2000

3000
4000
totalspall3

5000

6000
2
x 10

(c) SK-II LLON G spallation likelihood (red) vs (d) SK-II QP EAK spallation likelihood (red)SK-II spallation data > 15 MeV (black) for vs SK-II spallation data > 15 MeV (black) for
multiple muons (type 1)
multiple muons (type 1)

Figure A.12: Multiple muon (type 1) SK-II spallation likelihoods

133

x 10

-2

0.3

20
17.5

0.25

15
0.2

12.5
10

0.15

7.5

0.1

5
0.05

2.5
0

0

0.2

0.4

0.6
0.8
dtspall4

1

1.2

0

1.4

0

500

1000

1500
likelt

2000

2500

3000

(a) SK-II dt spallation likelihood (red) vs SK-II (b) SK-II LT RAN S spallation likelihood (red)spallation data > 15 MeV (black) for multiple vs SK-II spallation data > 15 MeV (black) formuons (type 2)
multiple muons (type 2)
x 10

x 10

-2

-4

0.25

0.12

0.1

0.2

0.08

0.15

0.06
0.1
0.04
0.05

0.02

0

-3000 -2000 -1000

01000
likeln

2000

0

3000

0

500

1000

1500
2000
totalspall4

2500

3000
2
x 10

(c) SK-II LLON G spallation likelihood (red) vs (d) SK-II QP EAK spallation likelihood (red)SK-II spallation data > 15 MeV (black) for vs SK-II spallation data > 15 MeV (black) for
multiple muons (type 2)
multiple muons (type 2)

Figure A.13: Multiple muon (type 2) SK-II spallation likelihoods

134

x 10

-3

x 10

0.5

-3

0.45
0.4

0.4

0.35
0.3

0.3
0.25
0.2
0.2
0.15
0.1

0.1

0.05
0

0

500

1000

1500 2000
ltrand1

2500

3000

0

3500

-3000 -2000 -1000

01000
lnrand1

2000

3000

(a) SK-II LT RAN S random likelihood (red) vs (b) SK-II LLON G random likelihood (red) vs
SK-II random sample data > 15 MeV (black) SK-II random sample data > 15 MeV (black)for single through-going muons
for single through-going muons
x 10

-3

0.3

0.25

0.2

0.15

0.1

0.05

0

0 100002000030000400005000060000700008000090000
totalspall1(c) SK-II QP EAK random likelihood (blue) vs
SK-II random sample data > 15 MeV (black)for single through-going muons

Figure A.14: Single muon SK-II random likelihoods

135

x 10

x 10

-3

-3

0.45

0.7

0.4
0.6
0.35
0.5

0.3
0.25

0.4

0.2

0.3

0.15
0.2
0.1
0.1
0

0.05
0

500

1000

1500 2000
ltrand2

2500

3000

0

3500

-3000 -2000 -1000

01000
lnrand2

2000

3000

(a) SK-II LT RAN S random likelihood (red) vs (b) SK-II LLON G random likelihood (red) vs
SK-II random sample data > 15 MeV (black) SK-II random sample data > 15 MeV (black)for stopping muons
for stopping muons
x 10

-3

0.25

0.2

0.15

0.1

0.05

0

0 5000100001500020000250003000035000400004500050000
totalrand2(c) SK-II QP EAK random likelihood (red) vs
SK-II random sample data > 15 MeV (black)for stopping muons

Figure A.15: Stopping muon SK-II random likelihoods

136

x 10

x 10

-3

-3

0.35
0.5
0.3
0.4
0.25
0.2

0.3

0.15
0.2
0.1
0.1
0.05
0

0

500

1000

1500 2000
likerandlt

2500

3000

0

3500

-3000 -2000 -1000

01000
likerandln

2000

3000

(a) SK-II LT RAN S random likelihood (red) vs (b) SK-II LLON G random likelihood (red) vs
SK-II random sample data > 15 MeV (black) SK-II random sample data > 15 MeV (black)for multiple muons (type 1)
for multiple muons (type 1)

x 10

-4

0.5

0.4

0.3

0.2

0.1

0

0

1000

2000

3000
4000
totalrand3

5000

6000
2
x 10

(c) SK-II QP EAK random likelihood (red) vs
SK-II random sample data > 15 MeV (black)for multiple muons (type 1)

Figure A.16: Multiple muon (type 1) SK-II random likelihoods

137

x 10

x 10

-3

-3

0.35

0.5
0.3
0.4

0.25
0.2

0.3

0.15
0.2
0.1
0.1
0.05
0

0

500

1000

1500 2000
likerandlt

2500

3000

0

3500

-3000 -2000 -1000

01000
likerandln

2000

3000

(a) SK-II LT RAN S random likelihood (red) vs (b) SK-II LLON G random likelihood (red) vs
SK-II random sample data > 15 MeV (black) SK-II random sample data > 15 MeV (black)for multiple muons (type 2)
for multiple muons (type 2)
x 10

-4

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

200

400

600 800 1000 1200 1400
2
x 10
totalrand4(c) SK-II QP EAK random likelihood (red) vs
SK-II random sample data > 15 MeV (black)for multiple muons (type 2)

Figure A.17: Multiple muon (type 2) SK-II random likelihoods

138

x 10

x 10

-3

-3

0.6
0.7
0.5

secondary track

0.6

secondary track
0.5

0.4

0.4
0.3
0.3
0.2
0.2
0.1

0.1
0

0

0

500 1000 1500 2000 2500 3000 3500 4000 4500
transverse distance (cm)-4000-3000-2000-1000

01000 2000 3000 4000
longitudinal distance (cm)(a) SK-II LT RAN S random likelihood (red) (b) SK-II LLON G random likelihood (red) vsvs SK-II spallation likelihood (black) for sec- SK-II spallation likelihood (black) for secondary tracks.
ondary muon tracks.)
x 10

-3

x 10

0.7

-4

0.1
third or higher track

0.6

0.08
0.5
0.06

0.4
0.3

0.04

0.2
0.02
0.1
0

0

0

500 1000 1500 2000 2500 3000 3500 4000 4500
transverse distance (cm)0

200 400 600 800 10001200 14001600 1800
3
charge deposited (p.e.)x 10(c) SK-II LT RAN S random likelihood (red) vs (d) SK-II Qµ random likelihood (red) vs SKSK-II spallation likelihood (black) for third and II likelihood (black) for third and higher orderhigher order tracks.
tracks.

Figure A.18: Multiple track SK-II likelihoods. In all cases black shows the spallation
likelihood, and red the random sample.

139

A.3

Spallation: Algorithm

The full spallation cut is multi-branched and algorithmically complicated. This section is an attempt to describe it in a complete fashion. The description will be of the
SK-I/III combined cut, with SK-II information in parenthesis when appropriate.
The muons are divided into four categories by Muboy: Type 1 muons are simply
single muons that travel through the detector (‘singles’). Type 2 muons are single
muons that stop in the detector (‘stoppers’). Type 3 muons are those which Muboy
believes to be multiple muon bundles, but for which it can not fit more than a single
muon track. Type 4 muons are multiple muons for which Muboy can find and fit
more than one track. Type 5 muons are ‘corner clippers’, which are of very low track
length and deposit very little light in the detector. Finally, Type 0 muons are thosewhich Muboy fails to fit at all (‘misfits’).
The spallation cut utilizes a number of variables. The first four comprise thelikelihoods: dt (time difference from relic candidate to muon in seconds); LT RAN S(transverse distance from reconstructed muon track to relic candidate vertex in cm);
LLON G (reconstructed distance between where relic candidate falls ’along’ the muontrack and where spallation is predicted by a peak in the muon dE/dx profile in cm);and QP EAK (the sum of the nine dE/dx bins surrounding the dE/dx peak in p.e.; ninebins is 4.5 m). Also utilized is the total muon charge deposited in the detector in p.e.
(Qµ ), the number of empty dE/dx bins between the first and last bin (emptyfrac),
which is an indication of dE/dx profile quality, and the goodnesses of the muon fits:
GoodM uboy and GoodBF F for the Muboy and BFF fitters respectively. Finally, formuon bundles, the number of reconstructed tracks is considered (NT RACKS ).
Spallation likelihood values are mostly determined from the PDFs of the four
spallation variables for the appropriate muon type (P DFS1 for dt, P DFS2 for LT RAN S ,P DFS3 for LLON G , and P DFS4 for QP EAK ), as well as the four random sample PDFs
for the same variables (P DFR1 through P DFR4 . The PDFs (shown in Appendix A.1
140

(A.2)) can be combined in more than one way. The standard (Type A) likelihood is
Q
DFSi), the natural logarithm of the productsimply as follows: LSP ALL = Ln( 4i=1 PP DF
Ri

of the ratios of spallation PDF to random sample PDF for the four variables. Unlessotherwise stated, this spallation likelihood is used.
In some rarer cases, other likelihood formulations are used. When the dE/dx
information is found to be untrustworthy, the variables from the dE/dx profile are not
DFS1
DFS2
used, and the likelihood becomes simply: L2SP ALL = Ln( PP DF× PP DF). Multiple
R1
R2

muons also have special likelihoods. Finally, in the case of three or more muon tracks,
each track beyond the second is considered without utilizing dE/dx information.
However, for these cases Qµ is utilized as a third variable, and the likelihood becomes:
P DF

DFS2
DFS1
SQµ
L3SP ALL = Ln( PP DF× PP DF) × P DFRQµ.
R1
R2

Lastly, the cut is different for relic candidate energy 16-18 MeV (17.5-20 MeV
SK-II), which will be denoted as < 18 MeV, and for events 18-24 MeV (20-26 MeV
SK-II), which will be denoted > 18 MeV.
Before the spallation likelihood is even considered, there are a number of precuts.
First, the muon sample is checked for ‘ringing’. This is an electronics effect where
after a high charge muon, many phantom muons will appear shortly following in time
due to pulse reflections and electronics saturation. Any muons following a muon with
Qµ > 90,000 p.e. and within 20 µs are eliminated from the muon sample.
Next a detector veto is instituted after the muons that deposit the most lightin the detector, as muons in the upper tail end of the Qµ distribution are far more
likely to cause spallation than other muons and are comparatively rare. This veto isfor 4 seconds after muons with Qµ > 1,000,000 and 8 seconds after muons with Qµ> 2,000,000.
Additionally, a cut is instituted that is a combination of Qµ , dt, and NT RACKS ,which includes all muon types, which have NT RACKS = 1. This cut is motivated by a
combination of how not only do muons with high Qµ tend to make more spallation,141

but muons with many tracks or poor GoodM uboy have less trustworthy tracks. An
incorrectly fit muon track is more likely to cause improper correlations and allow
a spallation event to slip through, which we wish to avoid. This cut looks for any
events for which the following condition is met: (NT RACKS × 0.1 + 0.1) < GoodM uboy .
If this condition is met, then any relic candidates with the following correlations are
eliminated: 1) Qµ > 400,000 and dt < 0.2; 2) Qµ > 600,000 and dt < 1; or 3) Qµ >750,000 and dt < 5.
A further special consideration is given to muons with NT RACKS = 10, as 10 isthe highest number of tracks Muboy will attempt to fit, and so this is actually a pile
up of NT RACKS = 10 or higher. Furthermore these muons have the least trustworthy
muon tracks, and are the most likely to create spallation. They are also quite rare.
For such muons, a full detector veto of 1 second is implemented.
For all muons an initial likelihood is calculated for the first (and usually only)
track. This is the four variable standard likelihood described above unless emptyfrac> 0.3 or the peak of the dE/dx profile is found to occur at a point farther fromthe entry position than the muon track length. In these cases there is something
wrong with the dE/dx profile, and the information is not trusted, so the two variable
likelihood L2SP ALL is used instead.
For all muon types, for events E < 18 MeV, all events with dt < 0.01 and LT RAN S< 500 were rejected.
From here the cut branches depending on muon type and relic candidate energy.
For Muboy misfits (Type 6 muons), a simple detector veto was implemented,
for 1.5 seconds < 18 MeV and 1 second > 18 MeV.
Corner clippers (Type 5 muons) were not found to cause any spallation.
Stoppers (Type 2 muons) are cut as follows: for E < 18 MeV, if LSP ALL > 0.5
or dt < 0.02 the event is rejected. For E > 18 MeV, if LSP ALL > 3 or dt < 0.01 theevent is rejected.

142

The bulk of the muons are singles (Type 1). All correlations to singles with
GoodM uboy > 0.4 and the following properties are rejected: for E < 18 MeV, if LSP ALL> 3 and LT RAN S < 600, or if LT RAN S < 150 and dt < 7. For E > 18 MeV, if LSP ALL> 4.2, or if LT RAN S < 100 and dt < 7, or if LT RAN S < 300 and dt < 0.1.
For singles with GoodM uboy < 0.4 the track isn’t trusted. Just in case the Muboy
information is good, all events (any relic candidate energy) with LSP ALL > 3 arerejected. However, the BFF muon fit is also checked. The distance variables LT RAN S
and LLON G are recalculated using the BFF fit information, and a new likelihood
obtained. If this new LSP ALL > 3, the event is rejected. GoodBF F is also checked; if
it is < 0.3, the BFF fit isn’t trusted either, and all events that have survived to thispoint with dt < 2 are rejected.
For multiple muons with only one fit track, the following events are rejected:
for E < 18 MeV, if LSP ALL > -1.5 or dt < 0.01; for E > 18 MeV, if LSP ALL > -0.5 or
dt < 0.001.
Lastly, for multiple muons with many fit tracks, each track is considered
as a separate muon. The primary track uses the standard PDFs such as shown in
Fig. A.4 (A.13). The secondary track is separately tuned and uses the distance PDFs
shown in Fig. A.9 (A.18). For tracks three and above, the special likelihood L3SP ALL
is used, which is also separately tuned and uses Qµ instead of the dE/dx variables.
These PDFs are also shown in Fig. A.9 (A.18). All these likelihoods use the same dt
PDF.
The cut values are as follows: first, any event with dt < 0.1 is rejected. For the
primary track the event is rejected if: dt < 1 and LT RAN S < 400 (all energies); or if
LSP ALL > 2 for E > 18 MeV, or LSP ALL > 0.9 for E < 18 MeV. For the secondary
track, the event is cut if LSP ALL > 2 for E > 18 MeV, or if LSP ALL > 0.5 for E <18 MeV. For the third and higher tracks, the event is cut if L3SP ALL > 2 for E > 18
MeV, or if L3SP ALL > 1 for E < 18 MeV.

143

B

Appendix B - spectral PDFs

B.1

SRN PDFs

Shown here are the PDFs used to represent the SRN spectrum for various models inthe signal region. Included in the plots are spallation and solar inefficiencies, which
gives rise to the sawtooth shape below 24 MeV. The low and high Cherenkov angle
PDFs are not shown as they are entirely negligible (although I fit and used PDFs
from the MC for the sidebands as well). The neutrino temperature formulation isseparated from the other five models for convenience.

144

0.1

LMA
CGI
HMA
FS
CE

0.08
0.06
0.04
0.02
0

16

18

20

22

30

40

24

26

28

30 32 34
Energy (MeV)

-1

10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10

LMA
CGI
HMA
FS
CE
20

50

60

70
80
90
Energy (MeV)

Figure B.19: SK-I SRN PDFs for five models in the signal region. Solar and spallation
inefficiencies are applied. The PDF is normalized to 1 between 16 and 90 MeV, minus
a tiny amount that falls into the sidebands (∼0.5%).

145

0.1

LMA
CGI
HMA
FS
CE

0.08
0.06
0.04
0.02
0

16

18

20

22

30

40

24

26

28

30 32 34
Energy (MeV)

-1

10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10

LMA
CGI
HMA
FS
CE
20

50

60

70
80
90
Energy (MeV)

Figure B.20: SK-II SRN PDFs for five models in the signal region. Solar and spallation inefficiencies are applied. The PDF is normalized to 1 between 16 and 90 MeV,
minus a tiny amount that falls into the sidebands (∼1%).

146

0.1

LMA
CGI
HMA
FS
CE

0.08
0.06
0.04
0.02
0

16

18

20

22

30

40

24

26

28

30 32 34
Energy (MeV)

-1

10
10
10
10
10
10
10

-2
-3

LMA

-4

CGI

-5

HMA

-6

FS

-7

CE
20

50

60

70
80
90
Energy (MeV)

Figure B.21: SK-III SRN PDFs for five models in the signal region. Solar and spallation inefficiencies are applied. The PDF is normalized to 1 between 16 and 90 MeV,
minus a tiny amount that falls into the sidebands (∼0.5%).

147

0.25
2 MeV
3 MeV
0.2

4 MeV
5 MeV
6 MeV

0.15

7 MeV
8 MeV
0.1

0.05

0

20

25

30

35

40

45
50
Energy (MeV)

Figure B.22: SK-I SRN PDFs for various neutrino temperatures in the signal region.
Solar and spallation inefficiencies are applied. The PDF is normalized to 1 between
16 and 90 MeV, minus a tiny amount that falls into the sidebands (∼0.5%).

148

0.25
2 MeV
3 MeV
0.2

4 MeV
5 MeV
6 MeV

0.15

7 MeV
8 MeV
0.1

0.05

0

20

25

30

35

40

45
50
Energy (MeV)

Figure B.23: SK-II SRN PDFs for various neutrino temperatures in the signal region.
Solar and spallation inefficiencies are applied. The PDF is normalized to 1 between
16 and 90 MeV, minus a tiny amount that falls into the sidebands (∼1%).

149

0.25
2 MeV
3 MeV
0.2

4 MeV
5 MeV
6 MeV

0.15

7 MeV
8 MeV
0.1

0.05

0

20

25

30

35

40

45
50
Energy (MeV)

Figure B.24: SK-III SRN PDFs for various neutrino temperatures in the signal region.
Solar and spallation inefficiencies are applied. The PDF is normalized to 1 between
16 and 90 MeV, minus a tiny amount that falls into the sidebands (∼0.5%).

150

B.2

SK-I remaining background fits

x 10

-3

0.1
0.05
0

0.03
0.02
0.01
0
x 10

-3

20

30

40

50
60
numuCC low

70

80

90

20

30

40

50
60
numuCC signal

70

80

90

20

30

40

50
60
numuCC high

70

80

90

0.15
0.1
0.05
0

Figure B.25: PDF for νµ CC is shown compared to the decay electron data it is fit
from for SK-I. Spallation inefficiency is not shown here, and is manually added to
the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation cut
inefficiency is added.
151

x 10

-3

0.2
0.1
0

20

30

40

50
60
nueCC low

70

80

90

20

30

40

50
60
nueCC signal

70

80

90

20

30

40

50
60
nueCC high

70

80

90

0.03
0.02
0.01
0
x 10

-2

0.15
0.1
0.05
0

Figure B.26: PDF for νe CC is shown compared to the MC it is fit from for SK-I.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

152

0.002
0.001
0

0.02
0.015
0.01
0.005
0

20

30

40

50
60
ncel low

70

80

90

20

30

40

50
60
ncel signal

70

80

90

20

30

40

50
60
ncel high

70

80

90

0.15
0.1
0.05
0

Figure B.27: PDF for NC elastic is shown compared to the MC it is fit from for SK-I.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

153

0.015
0.01
0.005
0

20

30

40

50
60
mupi low

70

80

90

20

30

40

50
60
mupi signal

70

80

90

20

30

40

50
60
mupi high

70

80

90

0.004
0.002
0
0.01
0.00750.005
0.00250

Figure B.28: PDF for µ/π is shown compared to the MC it is fit from for SK-I.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

154

B.3

SK-II remaining background fits

x 10

-2

0.1
0.075
0.05
0.025
0
0.04
0.03
0.02
0.01
0
x 10

-3

20

30
40
50
60
70
80
SK-II decay electrons low region

90

20

30
40
50
60
70
80
SK-II decay electrons signal region

90

20

30
40
50
60
70
80
SK-II decay electrons high region

90

0.6
0.4
0.2
0

Figure B.29: PDF for νµ CC is shown compared to the decay electron data it is fit fromfor SK-II. Spallation and solar cut inefficiencies are not shown here, and are manually
added to the PDFs later. The data is scaled to the PDF, which is normalized to one
when integrated over energy for all three Cherenkov angles combined, after spallationand solar cut inefficiencies are added.
155

x 10

-3

0.4
0.2
0

20

30

40

50
60
nueCC low

70

80

20

30

40

50
60
nueCC signal

70

80

20

30

40

50
60
nueCC high

70

80

0.03
0.02
0.01
0

0.003
0.002
0.001
0

Figure B.30: PDF for νe CC is shown compared to the MC it is fit from for SK-II.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

156

0.002
0.001
0

20

30

40

50
60
ncel low

70

80

20

30

40

50
60
ncel signal

70

80

20

30

40

50
60
ncel high

70

80

0.01
0.005
0
0.1
0.075
0.05
0.025
0

Figure B.31: PDF for NC elastic is shown compared to the MC it is fit from for SK-II.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

157

0.015
0.01
0.005
0

20

30

40

50
60
mupi low

70

80

20

30

40

50
60
mupi signal

70

80

20

30

40

50
60
mupi high

70

80

0.006
0.004
0.002
0

0.006
0.004
0.002
0

Figure B.32: PDF for µ/π is shown compared to the MC it is fit from for SK-II.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

158

B.4

SK-III remaining background fits

x 10

-3

0.15
0.1
0.05
0
0.04
0.03
0.02
0.01
0
x 10
0.15
0.1
0.05
0

-3

20

30

40

50
60
numuCC low

70

80

90

20

30

40

50
60
numuCC signal

70

80

90

20

30

40

50
60
numuCC high

70

80

90

Figure B.33: PDF for νµ CC is shown compared to the decay electron data it is fit
from for SK-III. Spallation and solar cut inefficiencies are not shown here, and aremanually added to the PDFs later. The data is scaled to the PDF, which is normalized
to one when integrated over energy for all three Cherenkov angles combined, after
spallation and solar cut inefficiencies are added.
159

x 10

-3

0.4
0.2
0

20

30

40

50
60
nueCC low

70

80

90

0-2
20
x 10

30

40

50
60
nueCC signal

70

80

90

30

40

50
60
nueCC high

70

80

90

0.03
0.02
0.01

0.15
0.1
0.05
0

20

Figure B.34: PDF for νe CC is shown compared to the MC it is fit from for SK-III.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

160

0.002
0.001
0

20

30

40

50
60
ncel low

70

80

90

20

30

40

50
60
ncel signal

70

80

90

20

30

40

50
60
ncel high

70

80

90

0.015
0.01
0.005
0
0.15
0.1
0.05
0

Figure B.35: PDF for NC elastic is shown compared to the MC it is fit from for
SK-III. Spallation and solar cut inefficiencies are not shown here, and are manually
added to the PDFs later. The data is scaled to the PDF, which is normalized to one
when integrated over energy for all three Cherenkov angles combined, after spallationand solar cut inefficiencies are added.

161

0.015
0.01
0.005
0

20

30

40

50
60
mupi low

70

80

90

20

30

40

50
60
mupi signal

70

80

90

20

30

40

50
60
mupi high

70

80

90

0.004
0.002
0

0.008
0.006
0.004
0.002
0

Figure B.36: PDF for µ/π is shown compared to the MC it is fit from for SK-III.
Spallation and solar cut inefficiencies are not shown here, and are manually added
to the PDFs later. The data is scaled to the PDF, which is normalized to one when
integrated over energy for all three Cherenkov angles combined, after spallation andsolar cut inefficiencies are added.

162

C

Appendix C - NC

In order to study and understand the remaining atmospheric neutrino backgrounds
in the final sample, SK MC was used. 500 years of MC was generated for each SK
experiment phase (SK-I, SK-II, SK-III). As described in Chapter 5, the MC is basedon GEANT 3 and NEUT. Unfortunately, extensive verification of the MC < 100 MeV,
especially for the NC modes, had not been previously done, and a few things were
found to be outdated or in error.
The MC allows each event to be tracked according to NEUT mode, which records
the underlying physics. Also, each particle and momentum created by NEUT isrecorded and tracked.
Two main errors were found in the NC particle production. First involved the
production of 15.1 MeV gamma rays during nuclear de-excitation (of a residual 15 N
or 15 O remaining after an atmospheric ν interaction in the oxygen nucleus). The
branching ratio for this mode in NEUT was set to 1.3%; however it should be lessthat 0.007% ([55]). This caused immensely many more de-excitation gammas to occur
than should have. A 15.1 MeV gamma can cause an event that reconstructs above
16 MeV (due to energy resolution) and enters our final sample at the most important
low energy region. Thus, all 15.1 MeV gamma events were removed from the MC
sample.
The second error discovered involved events due to pion absorption in the oxygen,leading to an excited 14 N state, along with two protons (from a π + ) or two neutrons(π − ). The excited 14 N will release de-excitation gammas. In the NEUT code, theenergy of de-excitation photons was randomly generated from 5-20 MeV. However,in truth, the creation of photons of greater than 7.6 MeV is highly suppressed. The
result of a SK investigation was that the chance of any pion absorption events making
it into our final sample was very small, and that the events we found in our MC should
not be there. Thus, they were removed as well.
163

The spectrum of all NC events in 500 years of SK-I MC is shown in Fig. C.37,
along with the spectra of the 15.1 MeV gamma events and the pion absorption events.
From this point forwards, all discussion of the NC will have these erroneously created
events removed.
The NC events that remain after removing the incorrect events (1725 events innumber of events

500 years MC) can be further subdivided into the following categories:

10

3

10

2

10

10

20

30

40

50

60

70

80 90 100
Energy (MeV)

Figure C.37: Spectrum of NC events for 500 years SK-I MC. Shown is all NC (black);
15.1 MeV gamma events (red); and pion absorption events (blue).

1641) single pion events (969)2) NC elastic scattering (on nucleon) (647 events)
3) multiple pion production (85 events)
4) single η production (15 events)
5) deep inelastic scattering (9 events)
Modes 4) and 5) are so rare as to be negligible. Fig. C.38 shows the spectrumof all the events left after removing 15.1 MeV gamma events and pion absorption
events, as well as the spectra of the first three backgrounds.
The multiple pion production mode is not only of very little importance (a factorof 10 smaller than the NC elastic mode) but has a similar spectrum to the NC elastic,
meaning any of this signal will be absorbed into the NC elastic mode during the fit
to the final data, which allows each background a free-floating normalization.
The single pion channel can be further subdivided (Fig. C.39):
1) events resulting in a π − (such as ν + n → ν + p + π − ) or a π + (such asν + p → ν + n + π + ), but only if the π + is > 200 MeV.
2) π + < 200 MeV events. These are singled out as they basically follow a Michel
spectrum, which is different than other single pion events.
3) π 0 events4) ν + O(16) → ν + O(16) + π 0
From the spectra, it can be seen that the last mode is tiny and can be neglected.
Furthermore, the second mode mostly follows the Michel spectrum, and is highly
similar to the spectrum of decay electrons from sub-Cherenkov muons. This once
again means it will be accounted for by that channel in the free floating fit, andcan be ignored. It can also be shown that the third mode (π 0 events) can be welldescribed by a linear combination of the four backgrounds we use; this means it will
not uniquely contribute to the free floating fit and is safe to ignore.
Clearly the largest and most important background is due to the first channel.

165

After all considerations, this leaves the first of the single pion channels and the NC
elastic channels as the ones necessary to model and consider for the analysis. The
single pion channel considered is combined with remnant events from low energymuons from muon neutrino interactions that slip into the final sample, as describedin chapter 5.2.

10

2

10

10

20

30

40

50

60

70

80

90

100

Figure C.38: Spectrum of NC events for 500 years SK-I MC, with 15.1 MeV gammas
and pion absorption events removed. Shown is all NC (black); single pion events(red); NC elastic (blue); and multiple pion production (purple).
166

number of events

40
35
30
25
20
15
10
5
0

20

30

40

50

60

70
80
Energy (MeV)

Figure C.39: Spectrum of single pion NC events for 500 years SK-I MC, with 15.1
MeV gammas and pion absorption events removed. Shown is single π − events of allenergies and events with π + ’s > 200 MeV (black); single π + ’s < 200 MeV (red); π 0events (blue); and events from a more complicated interaction with oxygen (purple).

167

D

Appendix D - Expanded fit results

168

Table D.2: Complete raw fit results for SK-I. Best fits for all five channels given in
number of events seen in final sample, in all three Cherenkov regions combined. The
signal efficiency for each model is given (as evaluated in the signal region, as theamount of SRN signal in the sidebands is negligible). As the SK-I best fit is less than0 SRN events, the backgrounds are the same for all models. In the final sample, there
were 245 events in the signal region, 47 events in the low angle region, and 51 eventsin the high angle region. The SK-I livetime is 1497 days.
Model
LMA
Gas Infall
Heavy Metal
Failed SN
Chemical
6 MeV

SRN
0
0
0
0
0
0

90% CL (ev, cm−2 s−1 )<15, <2.5<12.6, <2.3
<13.4, <2.3
<16.2, <2.5
<13.8, <2.4
<15.5, <2.6

νµ CC
146.6
146.6
146.6
146.6
146.6
146.6

νe CC
86.8
86.8
86.8
86.8
86.8
86.8

NC
47.0
47.0
47.0
47.0
47.0
47.0

µ/π
62.6
62.6
62.6
62.6
62.6
62.6

ǫ
0.798
0.791
0.791
8.0
0.788
0.797

Table D.3: Complete raw best fit results for SK-II. Best fits for all five channels given
in number of events seen in final sample, in all three Cherenkov regions combined.
The signal efficiency for each model is given (as evaluated in the signal region, as theamount of SRN signal in the sidebands is negligible). In the SK-II final data sample,
there were 129 events in the signal region, 29 in the low angle region, and 26 eventsin the high angle region. The SK-II livetime is 794 days.
Model
LMA
Gas Infall
Heavy Metal
Failed SN
Chemical
6 MeV

SRN
4.7
4.4
4.5
5.3
4.4
4.3

90% CL (ev, cm−2 s−1 )<17.6, <7.7
<14.7, <7.5
<15.4, <7.3
<19.6, <8.0
<15.7, <7.2
<18.1, <7.0

169

νµ CC
72.4
72.7
72.6
71.8
72.6
72.7

νe CC
44.9
45.0
45.0
44.9
45.0
44.9

NC
19.9
19.7
19.7
19.9
19.8
20.0

µ/π
42.1
42.1
42.1
42.1
42.1
42.1

ǫ
0.567
0.533
0.545
0.585
0.552
0.635

Table D.4: Complete raw best fit results for SK-III. Best fits for all five channels given
in number of events seen in final sample, in all three Cherenkov regions combined.
The signal efficiency for each model is given (as evaluated in the signal region, as theamount of SRN signal in the sidebands is negligible). In the SK-III final data sample,
there were 105 events in the signal region, 17 in the low angle region, and 15 eventsin the high angle region. The SK-III livetime is 562 days.
Model
LMA
Gas Infall
Heavy Metal
Failed SN
Chemical
6 MeV

SRN
8.3 +6.6−5.5
7.4 +5.7−4.8+5.9
7.7 −5.0+7.3
9.1 −6.2
7.9 +6.1−5.2+6.5
8.2 −5.6

90% CL (ev, cm−2 s−1 )<18, <8.1<15.9, <7.9
<16.5, <7.8
<19.9, <8.5
<17, <7.9<17.9, <8.2

170

νµ CC
48.6
49.5
49.2
47.8
48.9
48.6

νe CC
44.9
45.0
44.9
44.9
45.0
45.0

NC
10.8
10.7
10.7
10.8
10.8
10.8

µ/π
24.4
24.4
24.5
24.4
24.4
24.4

ǫ
0.780
0.766
0.774
0.783
0.776
0.771