Study of Low Energy Electron
Anti-neutrinos at Super-Kamiokande IV

Dissertation Submitted toTsinghua University
in partial fulfillment of the requirement
for the degree ofDoctor of Philosophy
inPhysicsby
ZHANG Haibing
Dissertation Supervisor: Professor CHEN Shaomin

May 2012

Abstract
Detecting thermal neutrons produced in the inverse beta decay
reaction is of importance in the study of low energy neutrino physics.
A forced trigger scheme has been implemented in Super-Kamiokande
IV to search for the 2.2 MeV γ resulting from neutron captures onfree protons. A comprehensive study of neutron tagging in pure water
is presented for the first time. The neutron tagging efficiency is foundto be (19.3 ± 1.0)%, which is well verified with an Am/Be source.
The accidental background probability evaluated from real data is(1.0 ± 0.1)% per 500 µs of data.
Neutron tagging method is applied to identify the low energy ν̄evia a coincident detection of the prompt e+ and the delayed 2.2 MeV
γ. We employ this new technique to search for two ν̄e signals of
extraterrestrial origin: the supernova relic neutrino and possible ν̄efrom the Sun.
No events are found for both signals in 960 days of Super-Kamiokande
IV data. The 90% CL upper limits on the total flux are set. For thesupernova relic neutrinos, the flux upper limit is ∼ 6 times the model
prediction. And for the solar ν̄e , the flux upper limit is 4.5 × 10−4 ofthe total 8 B νe flux.
Model independent upper limits are also presented for ν̄e flux with
1 MeV energy bins. In the energy range 13.3 MeV < Eν¯e <21.3 MeV,
the obtained limits are currently world’s best.
In addition, we have successfully observed clear neutron capture
signals in the atmospheric neutrino data. Implication of improving proton decay search sensitivity by rejecting atmoshperic neutrino
backgrounds via neutron tagging is also discussed.

IContents
Abstract

I

List of Figures

V

List of Tables

VIII

List of Abbreviations

IX

Acknowledgements

X

1 Introduction
1.1 Neutrino Properties . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Neutrino Masses and Mixings . . . . . . . . . . . . . .
1.1.2 Neutrino Magnetic Moments . . . . . . . . . . . . . . .
1.2 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . .
1.2.1 Supernova Neutrinos . . . . . . . . . . . . . . . . . . .
1.2.2 Supernova Relic Neutrinos . . . . . . . . . . . . . . . .
1.3 Anti-neutrinos from the Sun . . . . . . . . . . . . . . . . . . .
1.3.1 The Solar Neutrino Problem and the MSW-LMA Solution . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Neutrino Spin-flavor Precession and ν̄e Generation . . .
1.4 Super-Kamiokande as an Anti-neutrino Detector . . . . . . . .
1.5 Previous Experimental Searches . . . . . . . . . . . . . . . . .

1
2
3
10
12
13
19
24

2 Super-Kamiokande Detector
2.1 Detection Methodology . . . . . . . . . . . . . . . . . . . . . .
2.2 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Photomultiplier Tubes (PMTs) . . . . . . . . . . . . . . . . .
2.4 Electronics and Data Acquisition System . . . . . . . . . . . .
2.4.1 Electronics . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Data Acquisition System . . . . . . . . . . . . . . . . .
2.4.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
35
36
37
39
39
40
41

II

25
27
29
32

2.5

2.4.4 Monitoring System . . . . . . . . . . . . . . . . . . . . 41
Water and Air Purification Systems . . . . . . . . . . . . . . . 42

3 Detector Calibration
3.1 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Relative Gain . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Water Transparency Measurement . . . . . . . . . . . . . . . .
3.2.1 Laser Measurements . . . . . . . . . . . . . . . . . . .
3.2.2 Decay Electrons . . . . . . . . . . . . . . . . . . . . . .
3.3 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 DT Generator . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Decay Electrons . . . . . . . . . . . . . . . . . . . . . .

45
45
45
45
46
47
48
48
49
50
51
51

4 Event Reconstruction
4.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . .
4.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . .
4.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . .
4.4 Muon Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Cherenkov Angle Reconstruction . . . . . . . . . . . . . . . .

53
53
54
54
56
57

5 Event Simulation
5.1 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Neutrino Interaction Simulation . . . . . . . . . . . . . . . . .
5.2.1 Supernova Relic Neutrinos . . . . . . . . . . . . . . . .
5.2.2 Solar Anti-neutrinos . . . . . . . . . . . . . . . . . . .

62
62
62
64
66

6 Selection of Neutron Capture Events
6.1 Characteristics of 2.2 MeV γ Events . . . . . . . . . . . . . . .
6.1.1 Vertex Resolution of the Primary Event . . . . . . . .
6.2 Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Further Reduction . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Summary of 2.2 MeV γ Cut Efficiency . . . . . . . . . . . . .

68
68
68
71
77
79

7 Validating Neutron Tagging Efficiency Using an Am/Be Source 83
7.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.2.1 Selection of Prompt Scintillation Events . . . . . . . . 84
7.2.2 Selection of Neutron Capture Events . . . . . . . . . . 85

III

7.3
7.4

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8 Tagging Neutrons in Atmospheric Neutrino Data
93
8.1 Observation of Neutrons in FC Data . . . . . . . . . . . . . . 94
8.1.1 Selection of Primary FC Neutrino Events . . . . . . . . 94
8.1.2 Searching Neutrons Associated with FC Events . . . . 94
8.1.3 Results and Discussions . . . . . . . . . . . . . . . . . 94
8.2 Background Rejection for Proton Decay Searches . . . . . . . 97
8.3 Reconstructing 2.2 MeV γ’s . . . . . . . . . . . . . . . . . . . 100
9 Data Reduction
102
9.1 Data Sets and Run Selection . . . . . . . . . . . . . . . . . . . 102
9.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.3 Spallation Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.3.1 The Spallation Likelihood . . . . . . . . . . . . . . . . 106
9.3.2 Applying the Spallation Cut . . . . . . . . . . . . . . . 108
9.4 External Event Cut . . . . . . . . . . . . . . . . . . . . . . . . 110
9.5 Solar Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.6 Cherenkov Angle Cut . . . . . . . . . . . . . . . . . . . . . . . 112
9.7 Pre-/post Activity Cut . . . . . . . . . . . . . . . . . . . . . . 114
9.8 Pion Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.9 Multi-ring Cut . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.10 µ/π Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.11 Reduction Summary . . . . . . . . . . . . . . . . . . . . . . . 118
10 Data Analysis and Results
121
10.1 Efficiencies and Systematic Uncertainties . . . . . . . . . . . . 121
10.2 Neutron Production in Low Energy Data . . . . . . . . . . . . 122
10.3 Search for Low Energy ν̄e ’s . . . . . . . . . . . . . . . . . . . . 126
10.3.1 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . 127
10.3.2 Solar ν̄e . . . . . . . . . . . . . . . . . . . . . . . . . . 128
10.3.3 Model Independent ν̄e Flux Limit . . . . . . . . . . . . 129
11 Summary and Outlook
130
11.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
11.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
11.2.1 SK-IV . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
11.2.2 GADZOOKS! . . . . . . . . . . . . . . . . . . . . . . . 133
Bibliography

135

IV

List of Figures
1.1 Feynman diagrams for the Dirac neutrino magnetic moment .
1.2 The classification scheme of supernovae . . . . . . . . . . . . .
1.3 Time evolution of neutrino luminosity and average energy . . .
1.4 Energy spectrum of νe of the numerical model . . . . . . . . .
1.5 Redshift evolution of SFR density . . . . . . . . . . . . . . . .
1.6 Model predictions of the SRN flux. . . . . . . . . . . . . . . .
1.7 Solar neutrino spectrum . . . . . . . . . . . . . . . . . . . . .
1.8 Sloar νe survival probability as a function of energy . . . . . .
1.9 Illustration of the detection scheme of ν̄e in SK-IV . . . . . . .
1.10 Time structure of the primary event and the delayed event . .
1.11 Effective cross sections for neutrinos in water . . . . . . . . . .
1.12 Low energy neutrino backgrounds . . . . . . . . . . . . . . . .

10
13
16
18
21
25
25
27
30
31
32
33

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

Schematic view of the Super-Kamiokande detector . . . . . . .
Schematic view of the 50 cm PMT . . . . . . . . . . . . . . .
The PMT quantum efficiency . . . . . . . . . . . . . . . . . .
Single photoelectron distribution . . . . . . . . . . . . . . . .
Block diagram of SK-IV DAQ system . . . . . . . . . . . . . .
New online event display . . . . . . . . . . . . . . . . . . . . .
Water purification system . . . . . . . . . . . . . . . . . . . .
Air purification system . . . . . . . . . . . . . . . . . . . . . .

36
37
38
38
40
42
44
44

3.1
3.2
3.3
3.4
3.5

Relative PMT gain . . . . . . . . . . . . . . . . . . . . . . . .
TQ-map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-IV water transparency . . . . . . . . . . . . . . . . . . . .
Reconstructed energy of LINAC data . . . . . . . . . . . . . .
Mean Neff of decay electrons . . . . . . . . . . . . . . . . . . .

46
47
49
50
52

4.1
4.2
4.3
4.4

Cherenkov opening angle distribution . . . . . . . . . . . . . .
Event display for an electron . . . . . . . . . . . . . . . . . . .
Event display for a muon . . . . . . . . . . . . . . . . . . . . .
Event display for a gamma . . . . . . . . . . . . . . . . . . . .

58
59
60
60

V

4.5

Event display for a pion . . . . . . . . . . . . . . . . . . . . . 61

5.1
5.2
5.3
5.4
5.5

Positron angular distribution . . . . . . . . . . . . . . . . . . .
SRN ν̄e event rate . . . . . . . . . . . . . . . . . . . . . . . . .
SRN positron energy spectrum . . . . . . . . . . . . . . . . . .
Solar ν̄e event rate . . . . . . . . . . . . . . . . . . . . . . . .
Solar positron energy spectrum . . . . . . . . . . . . . . . . .

63
65
65
66
67

6.1 PMT hits generated by 2.2 MeV γ . . . . . . . . . . . . . . .
6.2 TOF-subtracted PMT timings of 2.2 MeV γ events . . . . . .
6.3 Charge distribution of 2.2 MeV γ events. . . . . . . . . . . . .
6.4 Vertex resolution for 18 MeV electrons . . . . . . . . . . . . .
6.5 N10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Ncluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Nback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Nlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.13 N300, Trms , φrms and θmean . . . . . . . . . . . . . . . . . . . .
6.14 Distribution of the likelihood ratio . . . . . . . . . . . . . . .
6.15 Cut efficiency variation in the detector . . . . . . . . . . . . .
6.16 Time variation of the background probability . . . . . . . . . .

69
69
70
70
71
73
74
76
78
80
81
82

7.1
7.2
7.3
7.4
7.5
7.6
7.7

Configuration of Am/Be source . . . . . . . . . . . . . . . . .
Total p.e. of scintillation events . . . . . . . . . . . . . . . . .
N10 of the Am/Be data after the pre-selection . . . . . . . . .
Am/Be data v.s. MC: N300 − N10, Trms , φrms , θmean . . . . .
Am/Be data v.s. MC: N10 . . . . . . . . . . . . . . . . . . . .
Thermal neutron lifetime in water:source at center . . . . . . .
Thermal neutron lifetime in water:source at off-center . . . . .

84
85
87
88
89
90
91

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9

N300 − N10, Trms , φrms and θmean . . . . . . . . . . . . . . . . 95
Final N10 of the neutron candidates in the atm. FC data . . . 96
∆T of the neutron candidates in atm. FC data . . . . . . . . 96
Neutron yield of atm. FC events . . . . . . . . . . . . . . . . . 97
Neutron multiplicity of atm. FC events . . . . . . . . . . . . . 98
Total momentum vs. total invariant mass . . . . . . . . . . . . 99
Reconstructed energy of the 2.2 MeV γ’s . . . . . . . . . . . . 100
Distance between the 2.2 MeV γ vertex to the primary vertex 101
Distance between the 2.2 MeV γ vertex to the primary vertex 101

9.1
9.2
9.3

Definition of Ltran and Llong . . . . . . . . . . . . . . . . . . . 106
Distributions of the spallation likelihood variables . . . . . . . 107
Distributions of the spallation likelihood . . . . . . . . . . . . 108
VI9.4 Distributions of the spallation likelihood variables . . . . . . . 109
9.5 Definition of deff . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.6 Distribution of deff . . . . . . . . . . . . . . . . . . . . . . . . 111
9.7 Distribution of cos θsun for events below 20 MeV. . . . . . . . . 111
9.8 Muon momentum vs. reconstructed energy . . . . . . . . . . . 112
9.9 Cherenkov angle vs. energy for muons . . . . . . . . . . . . . 113
9.10 Distribution of the Cherenkov angle . . . . . . . . . . . . . . . 114
9.11 A double timing peaks event . . . . . . . . . . . . . . . . . . . 115
9.12 An event with pre-activity . . . . . . . . . . . . . . . . . . . . 116
9.13 N15 distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.14 Distribution of πlike . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.15 Q50/N50 of µ, π and e . . . . . . . . . . . . . . . . . . . . . . 118
9.16 Event display of a µ/π event . . . . . . . . . . . . . . . . . . . 119
9.17 Energy spectrum of e+ candidates . . . . . . . . . . . . . . . . 120
10.1 Neutrons observed in the µ-like events . . . . . . . . . . . . . 123
10.2 Neutrons observed in the isotropic events . . . . . . . . . . . . 124
10.3 Distribution of neutron capture time in low energy data . . . . 124
10.4 Inverse beta decay candidates . . . . . . . . . . . . . . . . . . 127
10.5 Model independent ν̄e flux upper limit . . . . . . . . . . . . . 129

VIIList of Tables
2.1

Specification of QBEE . . . . . . . . . . . . . . . . . . . . . . 39

5.1
5.2

Expected number of SRN events in 22.5 kton·year . . . . . . . 65
Expected number of solar ν̄e events in 22.5 kton·year . . . . . 66

6.1

2.2 MeV γ efficiency after each cut step . . . . . . . . . . . . . 80

7.1
7.2

Tagging efficiency of Am/Be generated neutrons . . . . . . . . 90
Fitted thermal neutron lifetime in water . . . . . . . . . . . . 91

8.1

Neutron production in proton decay backgrounds . . . . . . . 99

9.1
9.2

Radioactive isotopes induced by cosmic ray muons at SK . . . 105
Data reduction summary . . . . . . . . . . . . . . . . . . . . . 120

10.1 Total efficiency of observing an inverse beta decay signal . . . 122
10.2 Number of neutrons observed in the side bands . . . . . . . . 123
10.3 Number of observed candidates and expected background . . . 127

VIII

List of Abbreviations
AFT

After Trigger

DAQ

Data Acquisition

DSNB

Diffuse Supernova Neutrino BackgroundFC

Fully Contained

FV

Fiducial Volume

HE

High Energy

IBD

Inverse Beta Decay

ID

Inner DetectorLE

Low Energy

MCMonte Carlo

OD

Outer Detector

PMT

Photomultiplier Tube

SFP

Spin-Flavor Precession

SHE

Special High Energy

SK or Super-K

Super-Kamiokande

SLE

Super-Low Energy

SRN

Supernova Relic Neutrino

SSM

Standard Solar Model

TOF

Time of Flight

IX

Acknowledgements
This dissertation would never have been possible without many people’s support and assistance, both personally and professionally. First, I would like tothank my advisor, Shaomin Chen. He introduced me into the exciting fieldof neutrino physics and offered me the opportunity to work at the SuperKamiokande experiment. He has always been supportive and understanding
during the entire course of my graduate study. In many ways he is also avery good friend, too. I believe he is simply the nicest supervisor one can
ask for.
I’m grateful to many of the Super-Kamiokande collaborators. I havelearned a lot on both physics and the Super-Kamiokande experiment from
Masayuki Nakahata. As the convener of the low-energy group, Nakahatasensei’s capable and insightful leadership has ensured the team to operate
efficiently and consistently. I benefited greatly from discussions with Michael
Smy, Mark Vagins, Masato Shiozawa, John Learned, Yusuke Koshio and Yasuo Takeuchi. Special appreciation goes to Henry Sobel, the impact of whose
invaluable support and encouragement to me can never be overestimated.
Part of the data analysis is done with interactions with Kirk Bays, who
explained to me many of the cuts in great detail via numerous emails.
Living in another country is difficult for me. Luckily, there have been
many nice people in Kamioka and they made my life much easier in Japan.
I appreciate the assistance of the Kamioka Observatory stuff. I enjoyed thecompany of the students Motoyasu Ikeda, Takashi Iida, Takaaki Yokozawa,
Koh Ueno, Patrick de Periom, and Koun Choi. In particular, I would like tothank Roger Wendell. He is the one I had the most conversations with when
I stayed in Kamioka.
Back at Tsinghua, I would like to thank Yuanning Gao for teachingme particle physics. I always fell lucky to have met Yang Heng, who was
Shaomin’s Master student during my second to fourth year of graduate. We
traveled together, worked together and had many stimulating late night talks.
He is the best friend and colleague one can ever expect and I wish we could
work together again someday.
XFinally, I would like to offer my gratitude to my family. I could never
have reached this far without their support, caring and love.

XIChapter 1
Introduction
Water Cherenkov detectors, such as Kamiokande, IMB and most noticeably
Super-Kamiokande (SK), have led to numerous scientific contributions, e.g.
discovery of neutrinos from the core-collapse supernova [1, 2], discovery ofneutrino mass by oscillation of atmospheric neutrinos [3], determination ofsolar neutrino mixing parameters [4] and best limits on proton decay [5].
Through these achievements, water Cherenkov detectors have proven to be
one of the very effective neutrino and nucleon decay detectors. It has beenrealized that the scientific capability of SK can be enhanced if neutrons canbe observed as well. For instance, a delayed-coincidence detection of positronand neutron capture may allow an identification of low energy anti-neutrinos
via the inverse beta decay (IBD) reaction chainν̄e + p → e+ + n,n + p → d + γ (2.2 MeV),(1.1)

where the positron will be detected immediately and is referred to as theprimary event, while the neutron will be thermalized and eventually be captured on protons, releasing a 2.2 MeV γ after ∼200 µs average time, andis therefore referred to as the delayed event. In addition, the sensitivity of
proton decay searches can be improved by reducing potential atmospheric
neutrino backgrounds accompanied by neutrons.
In this thesis, we comprehensively study for the first time neutron tagging
in a large water Cherenkov detector by searching for a 2.2 MeV γ and explore
new physics opportunities facilitated by this new technique. The primary focus of this thesis is to search for ν̄e ’s from extraterrestrial sources. Candidates
include the long-sought-after supernova relic neutrinos (SRN), which is also
known as the diffuse supernova neutrino background (DSNB), and possible
solar ν̄e ’s resulting from some exotic generation mechanisms. An implication
on background rejection for proton decay searches is also discussed. In this1

Chapter 1

Introduction

chapter, a brief review is given for general neutrino properties, the physics
of SRN and solar ν̄e , as well as the previous experimental results.

1.1

Neutrino Properties

Neutrinos are electrically neutral particles of spin 1/2. There are at least
three generations of light neutrinos, νe , νµ and ντ , corresponding to the
leptons, e, µ, and τ . The interactions of neutrinos are well described by
the standard electroweak theory based on the SU (2)L × U (1)Y gauge model.
One of the peculiarities for neutrinos is that weak interactions couple only
to left-handed 1 neutrinos, or to right-handed anti-neutrinos. The charged
weak current that couples a νe to an electron has the V − A formµjweak
∝ νe γ µ (1 − γ 5 )e = 2νeL γ µ eL ,(1.2)

where the presence of 1 − γ 5 projects out the left chirality component of
νe . The right chirality component νR either does not exist (as in the Standard Model) or interacts extremely weakly, i.e. sterile. The lepton flavor isconserved in the weak interactions. A neutrino of flavor α(α = e, µ, τ ), να ,always couple to a charged lepton l with the same flavor, lα .
An open question regarding the nature of neutrinos is whether they are
Dirac or Majorana particles. To put it in another way, are neutrinos theirown antiparticles? The massive Dirac field consists of two independent Weyl
fields: a left-handed component ψL and a right-handed one ψR . In case of
the Majorana field, the right-handed component is just a particle-antiparticle
conjugation 2 of the left-handed one,T

ψR = (ψL )c ≡ CψL ,(1.3)

where C is the particle-antiparticle conjugation matrix, C = iγ2 γ0 . Evidently, a Majorana field satisfiesψ = ψL + ψR = ψL + (ψL )c = ψ c ,
1

(1.4)

Here it does not mean helicity -1 but rather left chirality. Only at the massless limit,chirality and helicity coincides. It’s customary to call the left chirality component of a fieldleft-handed. For massive neutrinos, the chirality is not a conserved quantum quantity. A
neutrino created with left chirality can develop a small fraction of right chirality componentof the order mν /Eν [6].
2A more common term encountered in the literature is the charge conjugation. But it’spointed out in Ref. [6] that charge conjugation, by definition, would turn a left-handed
neutrino into a left-handed anti-neutrino, which does not exist.

2

Chapter 1

Introduction

which means that Majorana particles are their own antiparticles. Distinction
between neutrinos and anti-neutrinos was first established in Davis’s radiochemical experiment. The experiment found that the reaction ν̄e + 37 Cl →37
Ar + e− did not occur while νe + 37 Cl → 37 Ar + e− did. However, thisdoes not disprove the Majorana nature of neutrinos. Because in this experiment the anti-neutrinos coming from reactors are dominantly right-handed,
while standard weak interactions require left-handed neutrinos for the process νe + 37 Cl → 37 Ar + e− to occur. It should be noted that the Dirac andMajorana description of neutrinos can have different phenomenological consequences only if neutrinos are massive. Because in the massless limit, ψLand ψR are decoupled and ψL in both descriptions obeys the Weyl equation
while ψR has no weak interactions. The most promising way to find out if
neutrinos are Majorana particles is to search for neutrinoless double beta(0νββ) decay, the rate of which is proportional to neutrino masses. If the0νββ decay is observed, no matter what diagrams are responsible, it will
imply neutrinos are Majorana particles.

1.1.1

Neutrino Masses and Mixings

Neutrinos are massless in the Standard Model (SM). Experimentally, up
to now all direct measurements of the neutrino mass give negative results.
The absolute mass of the electron neutrino can be measured by observing β
decays. The best limit on electron neutrino mass, obtained by measuring theend-point of the electron spectrum in Tritium decay, is [7]mνe < 2.3 eV (95% CL).

(1.5)

The mass of the muon neutrino can be determined from momentum analysis
of pion decay π + → µ+ νµ . The mass of tau neutrino is derived by fitting
the visible energy vs invariant mass in tau decays τ − → 2π − + π + + ντ andτ − → 3π − + 2π + + ντ (+π0 ). The upper limit on the masses of νµ [8] and ντ
[9] aremνµ < 0.17 MeV (90% CL),mντ < 18.2 MeV (95% CL).

(1.6)
(1.7)

Massive neutrinos play an important role in the evolution of the universeand consequently constrains on absolute neutrino masses can be derived fromcosmology. A latest analysis [10] of WMAP and SDSS data yields the limiton the sum of neutrino masses:
Xmν < 0.44 eV (95% CL).
(1.8)
3

Chapter 1

Introduction

However, there are compelling evidences from neutrino oscillation experiments that neutrinos have tiny but nonzero masses. How could the nonzero
neutrino mass be accommodated in particle theories? We shall briefly examine this issue in the context of the Standard Model and some simplest
extensions. For more thorough discussions, we defer to the literatures, seee.g. Refs. [11, 12, 13]. In the Standard Model, neutrinos can not have Diracmasses as other fermions do because of the absence of right-handed neutrinos νR . Neutrinos can not have Majorana masses involving only left-handed
neutrinos νL , either. Because the Majorana mass term is of the form
1
− LM = mνLT CνL + h.c.,
2

(1.9)

which has I3 = 1 and Y = −2. But the SM does not have any weak isospin
triplet Higgs field with Y = 2, so there is no way to construct a renormalizable
Lagrangian which can generate a Majorana mass. It is possible, however, toconstruct a composite Higgs operator out of two Higgs doublets that has thecorrect quantum number. The Majorana neutrino mass can be generated
from the lepton number violating term
− L5 =g(LT τ2 φ)C(φT τ2 LL ) + h.c.,
M L(1.10)

where g is a dimensionless coupling, M is a constant with dimension of mass,
LL = (νL , lL )T is the lepton SU (2)L doublet, φ is the Higgs doublet and τ2is the second Pauli matrix. After symmetry breaking, L5 generates the massterm
1 gv 2 T
ν CνL + h.c.,(1.11)− LM =
2M L
where v is the vacuum expectation value of the Higgs field. From this expression one can readily identify the Majorana mass
m=

gv 2
.
M

(1.12)

Although L5 respects SM symmetries, it’s not acceptable in the SM because
it contains dimension five operators, which is not renormalizable. However,such nonrenormalizable operators could be some manifestation of new physics
at a high energy scale characterized by M, which is analogous to the effective
nonrenormalizable Fermi theory of weak interactions. From Eqn. (1.12), it
is clear that m could be made small if M is large.
Alternatively, one can extend the Standard Model by adding right-handed
neutrinos νR . In principle, there is nothing prevents the existence of νR , which
is a SU (2)L singlet and has hypercharge Y = 0. In this case, neutrinos can
4Chapter 1

Introduction

have Dirac masses through the same Higgs mechanism that generates masses
for chargecd fermions. In this scenario, however, there is no explanation of
the smallness of mass for neutrinos compared to that for charged leptons andquarks. Note that Majorana mass term involves only νR is also allowed by
the symmetries of the SM. So the general mass term for one generation, in
the framework of the SM with the addition of νR , can be written as
1−LD+M = mD νR νL + mR νRT CνR + h.c.
2
1 T=
N CM NL + h.c.,
2 L(1.13)

where NL = (νL , (νR )c )T is a column of left-handed chiral fields and M is themass matrix


0 mD
M=
(1.14)mD mR
Diagonalization of (1.13), in the limit mD  mR , gives the mass eigenvalues
m1 '

m2D
,
mR

m2 ' mR ,(1.15)

for mass eigenstates ν1 and ν2 , which are Majorana neutrinos. Interestingly,
ν1 is very light, provided that mD  mR . It is νR being heavy that makes ν1light. This is the famous see-saw mechanism that provides a very plausible
explanation for the smallness of the neutrino mass [14]. Note that m1 has
the same structure as the Majorana mass (1.12) obtained with the effective
Lagrangian L5 , if mR is identified as the high-energ mass scale M. This is
not a surprise, since it is generally believed that the small neutrino mass isconnected to new physics at a high energy scale. Therefore, neutrino massis particularly important in particle physics.

Neutrino Oscillation in Vacuum
Neutrinos being massive means that there exists a spectrum of neutrino mass
eigenstates νi , each with mass mi (i = 1, 2, 3). The flavor state να (α = e, ν, τ )can be expressed as a superposition of mass eigenstates,X∗|να i =
Uαi
|νi i,(1.16)iwhere U is the neutrino mixing matrix. If U is not diagonal, να is a mixtureof νi . As a neutrino of flavor α at creation propagates, different mass components evolve differently, leading to an observable effect known as neutrino
5

Chapter 1

Introduction

oscillation, i.e. the probability of finding να in the original state (or any otherflavor state) oscillates with time.
The massive neutrino states νi are eigenstates of the free Hamiltonian
and the time evolution is simply|νi (t)i = e−iEi t |νi i.

(1.17)

From Eqn. (1.16), the time evolution of the flavor state να is thenX
∗ −iEi t|να (t)i =
Uαi
e
|νi i

(1.18)i

The amplitude of finding the neutrino at the time t in a flavor state νβ isX∗ −iEi tAνα →νβ (t) = hνβ |να (t)i =Uαiehνβ |νi i
i

=

XX

=

X

i

∗
Uαi
Uβj e−iEi t hνj |νi i

j∗Uαi
Uβi e−iEi t .

(1.19)

i

The transition probability is given byXX2∗∗ −i(Ei −Ej )tPνα →νβ (t) = Aνα →νβ (t) =Uαi
Uβi Uαj Uβje.
i(1.20)jp
For relativistic neutrinos, Ei = p2 + m2i ' p + m2i /2p ' p + m2i /2E. Thus,
the transition probability can be approximated byPνα →νβ (t) =

XX
i

∆m2
ij

∗
∗ −i 2E t
Uαi
Uβi Uαj Uβje,(1.21)jwhere ∆m2ij = m2i − m2j . In neutrino oscillation experiments, the measured
quantity is usually the distance L travelled by neutrinos instead of the time6

Chapter 1

Introduction

t. For relativistic neutrinos, t ' L, and one finds 3XX∆m2ij L∗∗Pνα →νβ (L) =Uαi Uβi Uαj Uβj exp −i
2E
i
j


X
∆m2ij L2∗∗
= δαβ − 4Re(Uαi Uβi Uαj Uβj ) sin
4E
i>j


X
∆m2ij L∗∗+2
Im(Uαi Uβi Uαj Uβj ) sin. (1.22)2Ei>jTo simplify the discussion, we shall consider a special case of two flavor
oscillation νe → νµ . The two-neutrino description is an adequate approximation in treating data from a number of neutrino oscillation experiments. In
this case, there is only one squared-mass difference ∆m2 = m22 − m21 and themixing matrix U takes the form
cos θ sin θU=.
(1.23)− sin θ cos θ
From Eqn. (1.22), it follows that the transition probability of νe → νµ is
simply


∆m2 L
2
2
Pνe →νµ = sin 2θ sin4E∆m2 (eV2 )L(m)22= sin 2θ sin 1.27.
(1.24)
E(MeV)
It is clear from (1.24) that the neutrino oscillation can take place only if boththe mass spliting ∆m2 and the mixing angle θ are nonzero. Indeed, it is theobservation of neutrino oscillation that leads to the conclusion that neutrinos
are massive and they mix.

Neutrino Oscillation in Matter
When propagating through matter, neutrinos acquire extra interaction potential energy due to the coherent forward scattering [15], which can significantly modify their propagation [16]. This is the famous MSW effect. For
3This derivation is done in the plane-wave approximation, which may raise some theoretical concerns. For example, applying energy-momentum conservation will lead to theconclusion that neutrino oscillation can not happen at all. However, it can be shown ,in the framework of quantum field theory, such inconsistency can be reconciled and thetransition probability (1.22) is correct [13].

7Chapter 1

Introduction

neutral unpolarized medium, the effective potentials are given by
Ve = VCC + VNC ,Vµ = Vτ = VNC ,with the charged-current and neutral-current potentials,√√
2
VNC = −GF Nn ,VCC = 2GF Ne ,2

(1.25)(1.26)

where Ne and Nn are the number densities of electron and neutron, respectively. For anti-neutrinos, the matter potentials change sign.
In vacuum, the time-evolution equation in the mass eigenstate basis is

 


d
ν1
E1 0
ν1
=
.
(1.27)
i
0 E2
ν2
dt ν2
This gives the evolution equation in flavor basis



 

d
νe
E1
νe
†
i
= U
U
E2
νµ
dt νµ
 ∆m2


2
sin
2θ
− 4E cos 2θ ∆m
ν
e
4E
=
,
∆m2
∆m2
νµ
sin
2θ
cos 2θ
4E
4E(1.28)(1.29)

where a common diagonal element is omitted since it modifies the common
phase of the neutrino states and hence has no effect on neutrino oscillations.
To derive the neutrino evolution equation in matter, one has to add thematter-induced potentials to the diagonal elements of the Hamiltonian in
Eqn. (1.29). Neglecting again a common term due to NC interactions, theneutrino evolution equation in matter is given by√  ∆m22dνe− 4E cos 2θ + 2GF Ne ∆m
sin
2θ
ν
e
4E
=
. (1.30)
i
∆m2
∆m2
νµ
dt νµ
sin
2θ
cos 2θ
4E
4E
In general, Ne varies along the neutrino trajectory and the evolution equation (1.30) must be solved numerically. We shall consider a simple casewhere matter density is constant. The Hamiltonian in Eqn. (1.30) can be
diagonalized by the mixing matrix
cos θM sin θM
UM =,(1.31)− sin θM cos θMwith θM given bytan 2θM = ∆m2∆m2
sin 2θ
2E

cos 2θ −2E
8√

2GF Ne.

(1.32)

Chapter 1

Introduction

The effective squared-mass difference in matter isq√2∆mM = (∆m2 cos 2θ − 2 2EGF Ne )2 + (∆m2 sin 2θ)2 .

(1.33)In analogy to the vacuum case, the oscillation probability of νe → νµ is givenby
∆m2M L22
Pνe →νµ = sin 2θM sin(1.34)
4E
From Eqn. (1.32), one can see the most striking characteristic of matter
effect is that there is a resonance when√∆m2
cos 2θ.
2GF Ne =2E(1.35)

When the MSW condition (1.35) is satisfied, mixing in matter is maximal(θM = 45◦ ) even if the vacuum mixing angle θ is small. The matter enhanced
neutrino oscillation plays a crucial role in solving the solar neutrino problem
that will be discussed in section 1.3. Note that once the mixing angle is fixed,
the MSW effect is sensitive to the sign of ∆m2 . In the context of full threeflavor oscillations, this feature can be employed to solve the long-standing
neutrino mass hierarchy problem, i.e. whether m3 is heavier than m1 or not,provided that the mixing angle θ13 is nonzero.

What We Have Learned from Neutrino Oscillations?
Assuming three generations of Dirac neutrinos, the mixing matrix U canbe parameterized by three mixing angles θ12 , θ23 and θ13 and one possible
CP-violating phase δ. In case of Majorana neutrinos, there are two additional Majorana phases, which have no significance in neutrino oscillation
experiments. As seen from the previous discussions, neutrino oscillations are
only sensitive to the difference of mass squared. It is conventional to define
two independent mass splittings ∆m221 = m22 − m21 and ∆m231 = m23 − m21
in neutrino oscillation analysises. Many experiments have been devoted tomeasure the neutrino mixing parameters and mass differences. Recent global
analysises [17, 18] of existing neutrino oscillation data imply∆m221
sin2 θ12|∆m231 |sin2 θ23''''

7.6 × 10−5 eV2 ,0.31,
2.4 × 10−3 eV2 ,0.5.

9(1.36)(1.37)(1.38)(1.39)

Chapter 1

Introduction

These parameters have been determined with fairly good accuracy (for ∆m231 ,only the absolute value is known). The small mixing angle θ13 is now afocus of neutrino physics research. In 2011, the T2K, MINOS and Double
Chooz collaborations announced indications of nonzero θ13 [19, 20, 21]. Veryrecently, a conclusive result has been released by the Daya Bay collaboration[22], which finds
sin2 2θ13 = 0.092 ± 0.016 ± 0.005.
(1.40)
From an experimental point of view, a nonzero θ13 is very important because
it opens up the possibility to search CP violations in the lepton sector andto determine the neutrino mass hierarchy (the one with ∆m231 > 0 is called
normal hierarchy, otherwise inverted hierarchy) exploiting matter effects.

1.1.2

Neutrino Magnetic Moments

Neutrinos do not have electric charge, but they may have dipole magnetic
moments arising from quantum loops (see Fig. 1.1). In the Standard Model,
similar quantum effects contribute to the anomalous magnetic moment of acharged fermion. Dirac and Majorana neutrinos exhibit distinctive electromagnetic properties. A massive Dirac neutrino will in general have a magnetic moment. On the other hand, based on general grounds such as CPT
invariance, the magnetic moment of a Majorana neutrino vanishes [11, 23].
However, Majorana neutrinos can have nonzero transition magnetic moments
between different flavors which can induce an anti-neutrino flux from the Sun(see section 1.3.2).

Figure 1.1: One-loop radiative contribution to the magnetic moment of a
Dirac neutrino.
Consider first Dirac neutrinos in a minimal extension of the Standard
Model with the introduction of right-handed neutrinos, one-loop Feynman
diagrams contributing to the neutrino magnetic moments yield [24, 11, 25]
X
eGF
√
=
µD
(m
+
m
)
f (al )Ulj Uli∗ ,(1.41)ij
ij
8 2π 2l10Chapter 1

Introduction

where mi (i = 1, 2, 3) is the neutrino mass, U is the neutrino mixing matrix
and


1
3
1 − al ,(1.42)f (al ) ≈2
2
with al = m2l /m2W (l = e, µ, τ ). From Eqn. (1.41), the diagonal magnetic
moment of Dirac neutrinos, at the leading order in al , are given by
µD
ii =

m 
3eGF mii√µB ,≈ 3.2 × 10−19
2
1eV
8 2π

(1.43)

where the unitarity of the mixing matrix U is used. For i 6= j, the leading
term of f (al ) sums up to zero. Therefore, the transition moments come only
from the next leading order of f (al ) and thus are suppressed by a factor ofal = m2l /m2W with respect to diagonal moments.
For Majorana neutrinos, additional Feynman diagrams should be considered [26, 11]. As mentioned above, the diagonal magnetic moments ofMajorana neutrinos vanish identically, µM
ii = 0. The transition magnetic
moments, at the one-loop level, is given by [12](see also [26, 11]),
µM
ij =

X
3eGF
√
(mi + mj )iIm (al Ulj Uli∗ ),16 2π 2l

(1.44)The interpretation of Eqn. (1.44) simplifies if CP invariance is assumed. If
the relative CP νi and νj is even, Ulj Uli∗ is real and thus µM
ij vanishes. On
the other hand, if the relative CP is odd, Ulj Uli∗ is pure imaginary and µM
ij is
M
M
antisymmetric, i.e. µji = −µij .
The neutrino magnetic moment derived within the Standard Model is
proportional to the neutrino mass, which is known to be very small andthus imposes natural suppression on the magnitude of the neutrino magnetic
moment. Beyond the Standard Model, it is possible to construct larger neutrino magnetic moment. For example, in the left-right symmetric model withright-handed neutrino interactions, the neutrino magnetic moment is proportional to the lepton mass instead of the neutrino mass, resulting in a muchlarger magnetic moment [27, 28, 29]. In another model which introduces aSU (2)L –singlet charged scalar particle, the magnetic moment for Dirac neutrinos can be as large as µν ' 10−10 µB [30]. More discussions on models
beyond the Standard Model that generate large neutrino magnetic moments
can be found in Refs. [11, 12]. On the other hand, model-independent considerations place strong limit on the magnetic moments of Dirac neutrinos−15(µDµB ) while the bounds on magnetic moments of Majorana neuν . 10
trinos are weaker than present experimental limit [31]. In view of the large
11Chapter 1

Introduction

variety of predictions, we shall keep an open mind regarding the magnitudeof the magnetic moments of neutrinos.
The electromagnetic properties of neutrinos can be studied by direct laboratory measurements. For example, neutrino magnetic moments can manifest
themselves through the additional contribution to the ν–e scattering crosssection:  2
 
πα2 1
1
µν
dσ
= 2
−
,
(1.45)
dT EM
me T
Eν
µB
where Eν is the incident neutrino energy and T is the electron recoil energy;
in case of long baseline experiments (e.g. solar), the observable µν is theeffective value including mixing effects [32]. Many searches have been conducted to look for distortion of the recoil electron spectrum in solar, reactor
and accelerator neutrino data. The current best limit obtained is by the
GEMMA experiment and is [33],µν < 3.2 × 10−11 µB(90% CL).

(1.46)

Constrains on the neutrino magnetic moments can also be derived from astrophysical objects. Nonzero neutrino magnetic moments would allow for anenhanced rate of plasmon decay γ → ν ν̄, which would increase the core massof red giants at the helium flash by δMC = 0.015M µν /10−12 µB . By comparing the predicted δMC with observations, a stronger limit on the neutrino
magnetic moment is obtained [34]:µν < 3 × 10−12 µB(3σ CL).

(1.47)

Note that there is a vast gap between present experimental bounds on neutrino magnetic moments and prediction (1.43) of the minimal extension of
the Standard Model. Detection of a large neutrino magnetic moment near
the current experimental limit will signify new physics beyond the Standard
Model.

1.2

Supernova Relic Neutrinos

A detection of neutrinos from supernovae provides a unique tool to probe stellar interiors and study neutrino properties. Much has already been learned
from the handful of events from SN 1987A. It is expected that knowledge
on supernova and neutrinos will be greatly advanced with next detection of
Galactic supernova explosion. Unfortunately, core-collapse supernova explosion is very rare in our galaxy, . 3 per century (see e.g. [35, 36]). However,neutrinos emitted from all past core-collapse supernovae should cumulate to12

Chapter 1

Introduction

form the supernova relic neutrino flux, which might be detectable in SK andfuture neutrino detectors. Detection of SRN will provide invaluable information on supernova neutrino emission, global core-collapse supernova rate
and neutrino properties. Although all flavors of neutrinos are emitted fromcore-collapse supernovae, we focus on ν̄e , which is most likely to be detected
at water Cherenkov detectors (see section 1.4).

1.2.1

Supernova Neutrinos

Supernova explosions occur at the final stages of evolution of isolated massive stars. For historical reasons, supernovae are classified into different types
based on their spectroscopic characteristics and properties of the light curve,
as shown in Fig. 1.2. Supernovae can also be divided into two categories
according to the mechanism that triggers the explosion. Type Ia supernovae
are believed due to the thermonuclear disruption of white drafts, while TypeIb, Ic and II supernovae are generated by the collapse of the core of massive
stars (M & 8M ). From the point of view of neutrino physics, core-collapse
supernovae are more interesting, because they can produce all types of copious neutrinos.

Figure 1.2: The classification scheme of supernovae [13].
During a core-collapse explosion, about 99% of the gravitational binding
energy liberated by the collapse is carried away by neutrinos, leaving behinda neutron star or a black hole. The current understanding of core-collapse
explosion and neutrino emission is briefly outlined below [13, 37, 38].
1. Photodisintegration and neutronization In the iron core of a massive
star at its last stage of evolution, the gravitational force is sustained by
13

Chapter 1

Introduction

the pressure of degenerate relativistic electrons. At the very high temperature and densities that exists in the core, the photodisintegrationof iron nuclei
γ +56 Fe → 13α + 4n − 124.4 MeV,
(1.48)and the electron capture of nuclei
e− + N (Z, A) → N (Z − 1, A) + νe ,(1.49)

occur, leading to a reduction of pressure support and triggering a rapid
collapse of the core. In this so-called capture phase, only νe ’s are emitted and can escape freely from the core, since the mean free path ismuch longer than the radius of the core. However, the amount of emitted neutrinos are negligible compared to the later phases.
2. Neutrino trapping In the inner part of the core, the collapse is homologous (i.e. the velocity roughly proportional to the radius). On theother hand, the material outside of some point collapse supersonicallyin quasi-free fall with velocity proportional to the inverse square of
the radius. When the density of the inner part of the core exceeds
1011 − 1012 g cm−3 , electron neutrinos begin to be trapped in the core,
driven by the coherent scattering off nuclei. There exists a characteristic surface with radius


Eν
7
,
(1.50)
Rν ≈ 1.0 × 10 cm
10 MeV
which defines the neutrinosphere. Neutrinos produced at R > Rν canfreely escape from the core, while neutrinos produced inside can only
diffuse out like the photons from the photosphere of normal stars.
3. Core bounce and neutrino emission The homologous collapse continues
until the inner core reaches the nuclear density (∼ 1014 g cm−3 ). The
repulsive nuclear forces halt the collapse and drive a shock wave outwards into the in-falling outer core. As the shock propagates into theouter core dissociating nuclei into free protons and neutrons, a huge
number of electron neutrinos are produced through electron capturee− + p → n + νe . Furthermore, since the cross section of coherent
scattering is proportional to the square of mass number (σcoh ∝ A2 ),the previously trapped νe ’s now decouple from the matter. Such asudden liberation of electron neutrinos is called a prompt electron neutrino burst or neutronization burst. The peak luminosity exceeds 1053
erg s−1 , but the total energy emitted is of the order of 1051 erg due tothe short duration timescale ( ∼ a few ms).
14

Chapter 1

Introduction

At about the same time, neutrinos of all flavors emerge thermally inthe hot post-bounce region via processes such as the electron-positronannihilatione− + e+ → ν + ν̄,(1.51)and the nucleon-nucleon bremsstrahlung
N + N → N + N + ν + ν̄.

(1.52)In addition, νe and ν̄e are produced by the charged-current interactions,e− + p → n + νe and e+ + n → p + ν̄e .
4. Delayed explosion When propagating outwards, the shock loses energy
by photodisssociation of nuclei (∼ 1.7 × 1051 erg to disintegrate 0.1
M iron) and neutrino emission behind the shock front. So only forspecial combinations of physical parameters, e.g. the progenitor star isrelatively small (∼ 10 M ) and the equation of state is soft enough, theshock is able to expel the envelope of the star, generating the prompt
explosion on the time scale of ∼10 ms. In more realistic cases, the shockstalls after losing a fair amount of energy. A supernova explosion canstill be achieved through the neutrino-heating mechanism, in which theshock is revived by the energy deposition of neutrinos. This neutrinodriven mechanism can delay the timescale of the explosion up to ∼1
second, and is referred to as the delayed explosion mechanism, which
is believed more likely.
5. Remnant of the star The duration of thermal neutrino emission is of
the order of 10 seconds. Eventually, the protoneutron star cools andturns into a neutron star or a black hole, depending on its mass andinitial metallicity.
The total amount of gravitational binding energy released in a supernova
explosion is estimated to be

2 
−1
2
MNS
RNS
3 GMNS53∼ 3 × 10erg,
(1.53)
Ebind ∼
5 RNS
1.4 M
10 km
where MNS and RNS are the typical mass and the radius of a neutron star.
Only a small fraction (∼1%) of the total energy is radiated kinetically; therest are carried away by neutrinos. It’s generally believed that each flavorof the six neutrinos and anti-neutrinos carries away approximately the sameamount of energy, since most neutrinos are emitted in pairs (see Eqn. (1.51)
and (1.52)). The total energy derived from SN 1987A data is consistent with
15

Chapter 1

Introduction

the estimation in (1.53) [39]. A recent improved analysis of SN 1987A datafinds the best fit of total energy to be 2.2×1053 erg [40], which is also close to
expectations. In numerical simulations, however, the equipartition of luminosity is still controversial. Although some simulations find the luminosities
are indeed nearly equal for all flavors (see e.g. Ref. [41]), significant deviations are also seen in other simulations, e.g. a factor of 2 difference between
νx and ν̄e luminosities [42]. We remark that in the existing literature, there
is still no consistent picture of neutrino luminosities and spectra. The simulation done in Ref. [41] succeeded in obtaining an delayed explosion, but
it lacked some relevant neutrino processes. On the other hand, although thesimulation in Ref. [42] did include the relevant neutrino processes, it only
reached 150 ms, when the bulk of neutrinos have not been emitted. This ambiguity seriously complicates the calculation of SRN flux, as will be discussed
in section 1.2.2.

Figure 1.3: Time evolution of neutrino luminosity and average energy obtained with a numerical simulation of supernova explosion [41]. The dashedline represents νe , solid line indicates ν̄e and dot-dashed line is for νµ , ν̄µ , ντ ,ν̄τ , which are collectively denoted as νx .
Fig. 1.3 shows the time evolution of neutrino luminosity and averageenergy in the first 1.5 seconds obtained with a numerical simulation of supernova explosion [41]. The involved model is for a progenitor star of about∼ 20 M which explodes by the delayed explosion mechanism. The strong
peak on νe spectrum in Fig. 1.3 corresponds to the neutronization burst.
16

Chapter 1

Introduction

Note also that there is a “hump” in the neutrino luminosity curve due tothe accretion of matter on the protoneutron star. The neutrino energy during the hump is low because the dense matter above the neutrinosphere isopaque to high energy neutrinos. In case of a prompt explosion, the envelope
would be expelled in O(10) ms after the core bounce and there would be nohump in the luminosity curve and the neutrino spectrum would be harder.
The detection of neutrinos from SN 1987A in the Large Magellanic Cloud(at a distance of ∼50 kpc) by Kamiokande II [1] and IMB [2] experiments
confirms the basic understanding of supernova explosion. The detected number of events (11 for Kamokande II and 8 for IMB), however, is too small
to derive a solid conclusion about the explosion mechanism. A future detection of a nearby neutrino burst , e.g. a supernova at the Galactic center, by
the Super-Kamiokande detector will reveal clearly the signatures in the time
evolution of the delayed explosion mechanism.
Fig. 1.3 (lower panel) also suggests the following hierarchy of average
neutrino energyhEνe i < hEν̄e i < hEνx i .
(1.54)
The average energy of neutrinos reflects the temperature of matter aroundthe neutrinosphere, inside which thermal equilibrium is established. Neutrinos emitted from a deeper and hotter layer (corresponds to a smaller
neutrinosphere) have higher energies. The νx ’s only experience the neutral
current interactions , hence the corresponding neutrinosphere for νx is smallest among all neutrino species. On the other hand, although both νe andν̄e undergo the charged current as well as neutral current interactions, theneutrinosphere for ν̄e is smaller than that for νe because the protoneutronstar is neutron rich. The energy hierarchy (1.54) is a fairly robust predictionof the current supernova theory, but it is not easy to derive quantitatively
the time-integrated average energies without detailed numerical simulations.
The average neutrino energies for all flavors obtained in [41, 43] are roughlyhEνe i ' 13 MeV
hEν̄e i ' 16 MeV
hEνx i ' 23 MeV(1.55)In the literature, the energy spectrum of supernova neutrinos of eachflavor is usually approximated by the Fermi–Dirac (FD) distribution with azero potential (see e.g. [44])120 E 2
1
dN
= L 4 4 E/T,
dE
7π T e+117(1.56)

Chapter 1

Introduction

where T ' hEi /3.1514 is the effective neutrino temperature and L is thetotal luminosity. However, the neutrino emission in a supernova burst is not
perfectly thermal because the interaction cross sections ∝ E 2 so that the neutrinosphere radius vary even for the same species of neutrinos. Fig. 1.4 showsthe energy spectrum of ν̄e obtained from a numerical supernova simulation[41], where both the low- and high-energy range are suppressed compared
to a pure FD distribution. This feature can be accommodated by using a”pinched” FD distribution [45, 42]
1 E2
1
dN
=L
,
4
E/T
−η
dE
F (η) T e
+1

(1.57)

where η is a pinching parameter and F (η) = dx x3 /(ex−η + 1) is a normalization factor. In this case, the average energy depends on both T and η, andup to second order, hE/T i ≈ 3.1514 + 0.1250η + 0.0429η 2 . Another popular
way to parametrize the neutrino spectrum is [42, 46] β(1 + β)1+β E
dN=L(1.58)
e−(β+1)E/E ,2dEEΓ(1 + β)Ewith E being the average energy and β a parameter related to the width of
the spectrum.

Figure 1.4: Energy spectrum of νe of the numerical model in Ref. [41]. The
dashed lines are for FD fits with zero chemical potential.

18

Chapter 1

1.2.2

Introduction

Supernova Relic Neutrinos

Supernova relic neutrino has been the focus of many theoretical studies,dating back more than forty years. The predicted SRN flux in early papers,
however, have very large uncertainties (see [47] and references therein). Since
mid-1990s, more detailed and realistic calculations of SRN flux emerge [48,49, 50, 51, 44, 52, 53, 54, 55, 56]. The SRN flux is a convolution of corecollapse supernova rate with the neutrino emission per supernova, taking into
account the redshift effects. The present differential number flux of SRN at
Earth is given by [47, 57]
Z ∞dN [Eν (1 + z)] dt
dφ(Eν ) = c
RSN (z)(1 + z)dz,
(1.59)dEν
dEν
dz
0where RSN is the core-collapse supernova rate at redshift z; dN/dEν is thenumber spectrum emitted by one supernova explosion, where a neutrino received at energy Eν was emitted at a higher energy Eν (1 + z); the relation
between the cosmic time t and the redshift z is given by the Friedmannequation aspdz= −H0 (1 + z) (Ωm (1 + z)3 + ΩΛ ),(1.60)
dt
with H0 being the Hubble constant; Ωm and ΩΛ are the cosmic matter density and cosmological constant, respectively. Essentially all theoretical predictions of SRN flux follow from (1.59), with variations in the modeling of
core-collapse supernova rate, neutrino emission and possibly the choice ofcosmological parameters. As noted in [48, 44], the SRN flux is insensitive
to the cosmology model. With an appropriate choice, the SRN flux can bemade independent of the cosmological parameters [53, 55]. In any case, theuncertainty due to the cosmology models can be neglected. The distinctive
features of each SRN model reside in the derivation of core-collapse supernova rate and the choice of neutrino emission models, which we will examine
in more details below.

Rate of Core-collapse Supernovae
Over the last two decades, understanding of the supernova rate and its timedependence has been steadily improved. In the first detailed calculation of
SRN flux by Totani and Sato [48], the supernova rate is estimated from theabundance of oxygen, which is produced chiefly in Type II supernovae, andit’s assumed to be constant over time. In their second paper [49], a standard
model of galaxy evolution based on the population synthesis method wasused to derive the supernova rate. Later Malaney [50] proposed a model for
19Chapter 1

Introduction

the evolution of cosmic gas, from which the supernova rate is determined.
At about the same time, Hartmann and Woosley [51] published their SRN
model where the time dependence of the supernova rate was evaluated basedon the cosmic chemical evolution. In another model by Kaplinghat et al. [44]the supernova rate was calculated using the metal enrichment history under
the assumption that the supernova rate tracks the metal enrichment rate. In
recent SRN models [53, 54, 55, 56], the supernova rate was derived directlyfrom the cosmic star formation history. The supernova rate is expected to be
proportional to the star formation rate (SFR) since the lifetime of massive
stars is much shorter than the cosmological time scale. The precision on SFR
has been greatly improved by direct measurements based on emission of massive stars (see e.g. Ref. [58]), which enables a fairly accurate determinationof the core-collapse supernova rate.
The SFR is usually derived from measurements of living massive stars (seeRef. [47] for details). When converting observables to SFR, one has to assume
that the distribution of stellar masses at formation follows an initial massfunction (IMF). The widely adopted Salpeter IMF scales as φ(m) ∝ m−2.35
for stellar mass between 0.1 M and 100 M [59]. Fig. 1.5 shows the SFR
density ρ̇∗ (z) (in units M Mpc−3 year−1 ) derived from various indicators,
which are scaled to a Salpeter IMF. A general consistency is clearly seen,
especially for redshift z . 1 – 2, which is most relevant for the SRN prediction[57]. Note that the SFR is about ten times larger at z = 1 than at present,z = 0. In the literature, several parameterizations of ρ̇∗ (z) exist, see e.g.
[53, 54, 58]. For z . 1, ρ̇∗ (z) can be approximated byρ̇∗ (z) = ρ̇0 (1 + z)β ,(1.61)

where ρ̇0 is a normalization factor and β ≈ 3 [58].
For a given SFR, the core-collapse supernova rate is calculated as
R 50
φ(m)dm8.
(1.62)
RSN(z) = ρ̇∗ (z) R 100
mφ(m)dm
0.1
The mass limits (in units M ) in the integrals of (1.62) are the values adopted
in Ref. [54]; different values are used by other authors, see e.g. [52, 53, 55].
It has been pointed out by those authors, however, the upper mass bounds
are not important as long as they are large. The lower mass threshold in
the upper integral, on the other hand, is more profound. It was generally
believed that the minimum stellar mass that leads to a core-collapse is about
8 M . Recent studies find the minimum mass has converged to 8 ± 1M [60],which leads to about 10% uncertainties in RSN [54]. It should be noted that20

Chapter 1

Introduction

Figure 1.5: Redshift evolution of SFR density [54]. Data points represent
measurements using various techniques, scaled to a Salpeter IMF. Curves
show the parameterization (thick) and adopted uncertainty range (thin) in
Ref. [54].
RSN predicted in this way depends weekly on the IMF because the effects of
the IMF between ρ̇∗ (z) and the integrals are largely canceled out [54].
Ref. [54] compared the predicted RSN with the direct observations andfound good agreements. Together with other cross-checks, the authors concluded that the uncertainties associated with RSN is fairly small, which translates into a variation of ±40% in the SRN event spectrum. It’s worth notingthat RSN derived in these models include all core collapses. The collapse ofstars with stellar mass 8M . M . 25M leads to an explosion and produces
a neutron star; stars with 25M . M . 40M also result in (weaker) explosions but produce black holes via fallback; for M & 40M , the collapse leads
to direct black hole formation without an explosion, i.e. a failed supernova[61]. Recent studies show that neutrino emission from a black hole-forming
collapse is more energetic than that from a neutron star-forming one (see [56]and references therein). This will lead to a harder SRN spectrum, which iseasier to detect.

Supernova Neutrino Emission
While the supernova rate has been known with rather good accuracy andthe precision will continuously improve in future, uncertainties on supernova
21

Chapter 1

Introduction

neutrino emission remain quite large. Neither the total luminosity of eachflavor of neutrino nor the exact functional form of the energy spectrum iswell known, see section 1.2.1. Neutrino mixings make the situation more
complicated.
The neutrino emission for each flavor is characterized by the total luminosity Lν and neutrino temperature Tν if the neutrino spectrum is perfectly
thermal (see Eqn. (1.56)). An additional parameter, usually dictated by thenumerical simulation, is needed if one uses Eqn. (1.57) or (1.58). The total luminosity is often taken as Lν = Ebind /6 ' 5×1052 erg assuming equipartition[52, 55, 54], or adopted from numerical simulations [48, 49, 50, 51, 44, 53, 56].
The choice of neutrino temperature also heavily relies on numerical simulation results. In typical scenarios, Tν̄e ' 5 MeV and Tνx ' 8 MeV. Based ontheoretical arguments, experimental results of SN 1987A data and SK 2003
SRN limit, Tν̄e < 4 MeV or Tν̄e > 8 MeV is disfavoured [54], where Tν̄e is theeffective neutrino temperature including neutrino mixing effects. In principle, the neutrino emission spectrum dN/dEν in Eqn. (1.59) should integrate
over progenitor masses that lead to core-collapse supernovae. However, it has
been shown that neither the neutrino temperature nor the binding energy ofthe neutron star depends sensitively on the mass of the progenitor [51, 62].
Hence, using a single neutrino spectrum is a valid approximation, as often
done in the literature.
Neutrino oscillations also play an important role in predicting SRN flux.
The observed ν̄e spectrum φē is a linear combination of ν̄e and ν̄x at production, i.e.
φē = p̄φ0ē + (1 − p̄)φ0x̄ ,(1.63)
where φ0ē and φ0x̄ are original fluxes for ν̄e and ν̄x , respectively; p̄ is the total ν̄esurvival probability including both oscillation effects in the star and Earthmatter [63]. Presence of a ν̄x component will make the spectrum harder,
since the temperature of ν̄x is higher than ν̄e . The Earth matter effect on
SRN flux is estimated to be small [64]. Inside the star, MSW-enhanced neutrino mixings is rather complex, crucially depends on the progenitor density
profile, the neutrino mass hierarchy and the magnitude of θ13 (see Ref. [63]for details). Recently it has been realized that collective flavor conversions
induced by neutrino-neutrino interactions can cause spectral swaps [65, 66].
Furthermore, as described earlier, the initial neutrino spectra are not well understood. Therefore, we stress that a full quantitative treatment of neutrino
mixing effects for SRN is impractical. SRN models [53, 56] that take into
count explicitly neutrino oscillation effects depend on numerical simulations
and mixing parameters, which is not universally applicable. Alternatively,
one can use an effective spectrum to account for the mixing effects, which is
22

Chapter 1

Introduction

the approach of model [54] (see discussions of HBD09 below).

SRN models
We now introduce in some detail several specific SRN models and predictions.
Early models will not be assessed in this thesis due to the lack of accuracy
in the supernova rate and the omission of neutrino mixing. The models of
the following are representative and reflect some new developments on thissubject.
• Ando, Sato and Totani [53] (Ando LMA)
This is the first model that takes into account neutrino oscillation in
the calculation of SRN flux. The supernova rate is inferred from SFR
assuming a Salpeter IMF. The initial neutrino spectra are based on numerical simulations in Ref. [41]. Neutrino mixings are included under
the assumption of normal hierarchy. The oscillation probability for ν̄eis treated as the vacuum oscillation, which is actually inappropriate. In
a latter paper by Ando and Sato [64], neutrino oscillations are treatedmore rigorously for both normal and inverted hierarchy. In case of inverted hierarchy, the observed spectrum is almost completely due to ν̄x
if the conversion is adiabatic, leading to a even harder spectrum thanin normal hierarchy.
• Lunardini [56] (Failed SN)
The main point of this model is that it treats separately the neutrino
spectra from neutron star-forming core-collapses (NSFCs) and black
hole-forming ones (BHFCs). The observed ν̄e spectrum is written asφē = fNS φNSFC+ (1 − fNS )φBHFC,ēē

(1.64)

where fNS is the fraction of NCFCs. Evidently, the calculation of the
SRN spectrum from (1.64) introduces additional uncertainties associated with fNS and the neutrino spectra from BHFCs. For the evaluationin this thesis, we choose parameters that maximize the observable SRN
flux. Since neutrinos emitted from NSFCs are more energetic, the observable ν̄e spectrum might be further hardened. In turn, observationof SRN can provide information on the rate of BHFCs, which is difficult
to study otherwise.
• Horiuchi, Beacom and Dwek [54] (HBD 6 MeV)
In this model, the core-collapse supernova rate is derived from most
up-to-date SFR data. The authors find that the uncertainties on the23Chapter 1

Introduction

supernova rate is already fairly small, allowing to study the supernova
neutrino emission in more details. The ν̄e spectrum per supernova
is approximated by the Fermi-Dirac distribution (1.56), where Tν̄e isinterpreted as the effective temperature including neutrino mixing effects. The SRN flux predicted in this way is characterized entirely by
the total luminosity Lν̄e and the effective temperature Tν̄e . One might
consider that using the Fermi-Dirac distribution to represent ν̄e spectrum after neutrino mixing is an oversimplification. Even if the initial
spectra can be approximated by Fermi-Dirac distributions, in general itdoes not hold that the superimposition of two spectra with different Tν̄estill follows the Fermi-Dirac distribution. However, such “fine points”
are probably washed out by the redshift integral, detector resolution,etc. Besides, the expected rate at SK is only 1.2-5.6 events yr−1 inthe range of 10-26 MeV. Details of the neutrino spectrum can not be
resolved with such small statistics. Therefore, despite of the uncertainties in neutrino spectrum, we consider this model as a main guidance
since it provides a general and simple framework to extract physicalinformation from SRN observations. For evaluation in this thesis, theadopted effective neutrino temperature is 6 MeV.
Fig. 1.6 shows the ν̄e flux spectra predicted by some SRN models, which
peak at below 10 MeV due to redshift. Although the total flux predictedby various models span a fairly wide range, the shape of the spectra is quite
similar, especially above 10 MeV.

1.3

Anti-neutrinos from the Sun

The Sun is an intense source of neutrinos produced in thermonuclear reactions that are thought to power the Sun. There are two groups of nuclear
reactions occurring in the Sun: the main proton-proton chain (pp chain) andthe sub-dominant Corbon-Nitrogen-Oxygen cycle (CNO cycle). The main
result of both the pp chain and the CNO cycle is a fusion of hydrogen into
helium:
4p + 2e− → 4 He + 2νe + 26.73 MeV.
(1.65)
Fig. 1.7 shows the solar neutrino spectra predicted by the Standard Solar
Model (SSM). Uncertainties on theoretical predictions of neutrino flux comemainly from the surface composition of the Sun and nuclear reaction crosssections [67]. The 1σ theoretical uncertainties on solar neutrino flux is also
shown in Fig. 1.7.

24

Chapter 1

Introduction

Figure 1.6: Model predictions of the SRN flux.

Figure 1.7: Spectra of solar neutrinos from the pp and CNO chains, predictedby the SSM BS05(OP). Figure taken from Ref. [68].

1.3.1

The Solar Neutrino Problem and the MSW-LMA
Solution

Solar neutrinos were originally conceived as a unique tool to investigate theSun’s interior. For over 40 years, a large amount of solar neutrino data25

Chapter 1

Introduction

have been accumulated by various types of detectors. However, a deficit ofsolar neutrinos relative to the SSM prediction was observed in all early solar
neutrino experiments Homestake, Kamiokande, Gallex/GNO and SAGE. Fora long time, the discrepancy between the observed solar neutrino flux and
the SSM prediction was referred to as the solar neutrino problem.
The standard solar model is very successful at describing many otheraspects of the Sun (e.g. the results from helioseismology). In addition, sincedifferent neutrino experiments are sensitive to neutrinos produced by different
reactions in the pp chain, there’s no apparent way to solve the solar neutrino
problem by modifying the astrophysical prediction. The problem may lie in
our understanding of neutrinos. A number of particle physics solutions were
proposed to reconcile the SSM prediction with data. It turns out the solar
neutrino problem can be naturally explained in terms of neutrino oscillation.
The neutrino oscillation solution became more plausible after the discoveryof neutrino oscillation in atmospheric neutrino data by Super-Kaimiokande
in 1998.
The oscillations of solar neutrinos can be enhanced in the Sun by the
MSW effect (see section 1.1.1). The solar neutrino data before Super-Kamiokande
can be fit with the small mixing angle (SMA), large mixing angle (LMA)
and low ∆m2 (LOW) MSW enhanced oscillations and the vacuum oscillation (VO). This situation was cleared up with the results from SK and SNO,
which were complemented by KamLAND.
Super-Kamiokande measured the solar 8 B neutrino flux with unprecedented precision. There is no indication of seasonal variation in oscillation
probability and hence VO is disfavored. The recoil electron energy spectrum
is flat, which disfavors SMA. SNO measured the total active neutrinos fromthe Sun via the NC reaction and found a good agreement with the SSM prediction. Therefore, SNO results provided a decisive proof that solar νe ’s dochange to the other flavors of neutrinos (νµ , ντ ). Combined SK and SNO data
indicate that LMA is a better solution to the solar neutrino problem. The
LMA oscillation scenario was then confirmed by KamLAND using reactor
neutrinos.
The neutrino oscillation probability from MSW-LMA prediction varies
with neutrino energy. The vacuum oscillation dominates for Eν .1 MeV.
For Eν &5 MeV, the oscillation is independent of neutrino energy due to
MSW resonance enhancement. Data in both low energy region (pp neutrino)
and high energy region (8 B neutrino) are consitent with the MSW-LMA oscillation. Data in the intermediate region are eagerly awaited to further test
the characteristic transition of the MSW-LMA prediction. The new measurements of 7 Be and pep neutrinos from Borexino are also in good agreementwith the MSW-LMA prediction (see Fig. 1.8). In sum, the MSW-LMA os26

Chapter 1

IntroductionPee:ν e survival probability

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10-1

pp - All solar
7
Be - Borexino
pep - Borexino
8
B - SNO LETA + Borexino
8
B - SNO + SK
MSW-LMA Prediction
1

10Eν [MeV]Figure 1.8: Sloar νe survival probability as a function of energy [69].
cillation fits all available solar neutrino data and is the present best solution
to the solar neutrino problem.

1.3.2

Neutrino Spin-flavor Precession and ν̄e Generation

A nonzero neutrino magnetic moment (see section 1.1.2) gives rise to spin
precession in a magnetic field, leading to νeL → νeR . Since light right-handed
neutrinos are sterile, they will escape detection. Historically, such mechanism was investigated in attempting to explain the solar neutrino depletion[70]. Although it has now been established that the solar neutrino deficit
is due to MSW-LMA neutrino oscillations, neutrino magnetic moment canstill play a role at a subdominant level. Most interestingly, if neutrinos havetransition magnetic moments and neutrinos are Majorana particles, the combined effects of neutrino oscillation and spin-flavor precession may result inan observable ν̄e flux from the sun.
It is instructive to consider first the ordinary spin-precession for a Diracneutrino, which can have a diagonal magnetic moment. The evolution equation in a transverse magnetic filed B and in the presence of a matter potential
Ve , is given by

 


d
νeL
Ve µB
νeL
=
,
(1.66)iµB 0
νe Rdt νeR
where µ is the magnetic moment. For simplicity, assuming constant matter
27

Chapter 1

Introduction

density and constant B, solving Eqn. (1.66) gives the transition probability(2µB)21 2
2 1/2
2PνeL →νeR = 2
V + (2µB)
t .
(1.67)
sin
Ve + (2µB)22 e
In case of Ve = 0, i.e. in vacuum, the amplitude is unity and complete
νeL → νeR can take place. The conversion probability is suppressed by thematter potential Ve .
If transition magnetic moments exist, spin-flavor precession (SFP) νeL →νµR can occur. Considering two flavors of Dirac neutrinos, the evolution
equation is governed by a four-dimensional Hamiltonian [71, 72, 73, 25],

 


νe L
−c2 δ + Ve
s2 δ
µee B µeµ B
νeL



d  νµ L 
s2 δ
c2 δ + Vµ µµe B µµµ B =  νµL  , (1.68)
i 
µµe B
−c2 δ s2 δ   νeR 
dt  νeR   µee B
νµR
µeµ B
µµµ B
s2 δ
c2 δ
νµ R
where c2 = cos 2θ, s2 = sin 2θ, and δ = ∆m2 /4E. As noted above, thematter potentials suppress νeL → νeR conversion. However, in addition to
MSW resonances, the matter potentials can generate resonant spin-flavor
precession, which can be identified by equating terms along the diagonal in
Eqn. (1.68). There is a resonance in the νeL  νµR channel for∆m2
cos 2θ.
(1.69)
2E
Note that this resonance condition is different from that of the MSW resonance (1.35), because of the neutral-current contribution to Ve . There is alsoa resonance in the νµL  νeR channel for
Ve =

∆m2
cos 2θ.
(1.70)
2E
This resonance, however, requires too large a Nn which does not exist in theSun. In practice, these resonances can lead to the disappearance of active
left-handed neutrinos into sterile right-handed ones.
If neutrinos are Majorana particles, they have no diagonal magnetic moments and only one transition magnetic moment µeµ = −µµe ≡ µ. The
Majorana nature means that the right-handed states are not sterile, butinteract as active anti-neutrinos. The evolution equation for Majorana neutrinos becomes

 


−c2 δ + Ve
s2 δ
0
µB
νeL
νeL
  νµL d  νµL s2 δc2 δ + Vµ
−µB
0


=
i 


  ν̄eR  ,
0−µB−c2 δ − Ve
s2 δ
ν̄eR
dt
µB
0
s2 δ
c 2 δ − Vµ
ν̄µR
ν̄µR
(1.71)
Vµ = −

28

Chapter 1

Introduction

There are also two spin-flavor resonances, one in the νeL  ν̄µR channel for
Ve + Vµ =∆m2
cos 2θ,2E(1.72)and the other in the νµL  ν̄eR channel for
Ve + Vµ = −∆m2
cos 2θ.
2E(1.73)For cos 2θ > 0, only the first resonance can be realized in the Sun where
Nn ' Ne /6. Experimentally, the resultant ν̄µR ’s are difficult to observe
since they only participate in neutral-current interactions, given that solar
neutrinos are below 20 MeV.
Now, if we combine the actions of oscillations and SFP, for Majorana neutrinos, an interesting phenomenon occur: emergence of solar ν̄e . To achievethis, there are essentially two ways that can be schematically shown as
osc.

SFP

SFP

osc.

νeL −→ νµL −→ ν̄eR ,νeL −→ ν̄µR −→ ν̄eR .

(1.74)(1.75)

In practice, only the processes (1.75) is important [74]. The combined probability for νeL → ν̄eR conversion, in the context of MSW-LMA oscillations,is worked out in Ref. [74] asB⊥ (0.05R )
µ
−10
2
,
(1.76)P (νeL → ν̄eR ) ' 1.8 × 10 sin 2θ
10−12 µB
10 kG
where B⊥ is the traverse magnetic field in the region where the productionof solar 8 B neutrinos are maximum. Sufficient large µ and B⊥ may lead toa solar ν̄e flux observable at SK. In turn, studies of solar ν̄e will provide aprobe of the magnetic moment µ and the stregth of the magnetic field in the
Sun.

1.4

Super-Kamiokande as an Anti-neutrino
Detector

The inverse beta decay reaction (1.1) has a unique signature given by the close
temporal and spatial correlation between the positron and neutron events,
which is employed by liquid scintillator detectors, such as KamLAND and
Borexino, to identify low energy ν̄e . Unfortunately, this didn’t work through29

Chapter 1

Introduction

SK-I to III because the 2.2 MeV γ resulting from neutron captures on free
protons is not energetic enough to make a trigger.
In 2004, Beacom and Vagins proposed to modify SK by adding gadolinium compound [75], neutron capture on which yields a gamma cascade witha total energy ∼8 MeV. These relatively high energy γ-rays should be readily seen in SK whose trigger threshold is ∼5 MeV. However, a number oftechnical issues (e.g. effects of Gd on materials and environment, upgrading
water system to recirculate Gd solution) have to be settled before this idea
can finally be realized in SK. In the second approach [76], a new trigger logic
is introduced to force the DAQ system to take 500 µs data without a trigger threshold following each primary event above the so-called special highenergy (SHE, see section 2.4.3) trigger (∼10 MeV). A search of 2.2 MeV γ
emitted from neutron capture on free proton is then performed offline exploiting the spatial and temporal correlation between the primary event andthe 2.2 MeV γ. Fig. 1.9 illustrates the detection scheme of anti-neutrinos forboth approaches. In the 2.2 MeV γ case, the temporal and spatial differences
between the primary e+ and delayed γ are ∼200 µs and ∼20 cm, respectively.

Figure 1.9: Illustration of the detection scheme of anti-neutrinos in SK-IV.
Following a successful demonstration of detecting neutron capture on free
protons in SK-III [77], the forced trigger scheme has been incorporated into
the SK DAQ system to record neutron capture events since the start of SKIV in 2008. The time structure of the primary event (SHE trigger) andthe delayed event (AFT trigger, see section 2.4.3) is illustrated in Fig. 1.10.
Neutron tagging opens up a window to anti-neutrino physics in a large water
Cherenkov detector. Note that at high energies, both neutrinos and antineutrinos can induce neutrons through various interactions (see chapter 8).
30

Chapter 1

Introduction

So we will content ourselves with ν̄e search via the IBD reaction for Eν̄e well
below 100 MeV.

Figure 1.10: Illustration of the time structure of the primary event and thedelayed event.
Fig. 1.11 shows the relevant cross sections for neutrino interactions in water. The IBD reaction has much larger cross section than the other channels,
especially in the energy range . 30 MeV. Actually, for the SRN search, event
rate due to the IBD reaction dominates the other channels by two orders ofmagnitude [48]. So in the first approximation, SK observes the ν̄e componentof SRN flux only through the IBD reaction. Note also in the energy range
10–20 MeV, the cross section for the inverse beta decay reaction is two ordersof magnitude greater than the elastic scattering process νe + e− → νe + e− .
Therefore, the inverse beta decay reaction can also be a probe to the verysmall solar νe → ν̄e conversion probability.
Fig. 1.12 (a) shows fluxs of SRN and electron (anti)neutrinos from othersources at SK site. The flux of reactor ν̄e is overwhelmingly large below ∼8
MeV. Atmospheric ν̄e ’s become dominant above ∼30 MeV. Solar neutrinos
are not a big concern, since they are not ν̄e ’s but νe ’s. Therefore, taking into
account the detector resolution, there is a detection window 10–30 MeV forthe search of extraterrestrial ν̄e ’s.
In practice, several backgrounds exist in the relevant energy range that
may hinder the detection, e.g. decay electrons or positrons from invisible
muons (atmospheric νµ /ν̄µ below Cherenkov threshold). These backgrounds
will be discussed in details in chapter 9. It suffices to mention here thatmost background events are not accompanied by neutrons. So the majorityof irreducible backgrounds in the SK previous study can be eliminated withneutron tagging.
Although the neutron tagging efficiency is relatively low in SK-IV (seechapter 6), this disadvantage is compensated by its large target mass. In
addition, liquid scintillator detectors suffer greatly from atmospheric neutral
current background [79], which is much more modest in SK because theneutral current γ-rays can be distinguished from electrons (see section 9.6).
In conclusion, SK-IV can serve as a competitive low energy anti-neutrino
detector.
31

Chapter 1

Introduction

Figure 1.11: Effective cross sections for neutrino interactions in water, including the SK energy resolution and threshold effects. Figure from Ref.
[78].

1.5

Previous Experimental Searches

A number of searches for SRN and solar ν̄e have been conducted using various
detection techniques. Until now, all the searches are negative and upper
limits are set. We summarize previous experimental results in the following.
Here, energy refers to neutrino energy and all limits are set at the 90%
confidence level.

SNO
SNO is a Cherenkov detector using heavy water to detect ν̄e ’s via
ν̄e + d → e+ + n + n.

(1.77)

The coincidence of a positron with two neutrons allows SNO to search forν̄e with very low background. Using the SNO phase I data, the integral
limit on the flux of solar ν̄e in the energy range 4–14.8 MeV is found to beφν̄e ≤ 3.4 × 104 cm−2 s−1 , which corresponds to 0.81% of the SSM 8 B νe flux[80]. While no result on the ν̄e component of SRN is reported, SNO also
performs a direct search of the νe component of SRN primarily throughνe + d → p + p + e− .
32

(1.78)

Chapter 1

Introduction

Figure 1.12: Fluxs of SRN (Ando03) and electron (anti)neutrinos from othersources at SK site [57].
An upper limit of 70 cm−2 s−1 is set for the νe component of SRN flux in theenergy range 22.9–36.9 MeV [81].

KamLAND and Borexino
Both KamLAND and Borexino are liquid scintillator detectors, which searchν̄e ’s via the inverse beta decay reaction. KamLAND searches both SRN andsolar ν̄e in the energy range 8.3–30.8 MeV using 4.54 kton·year data. The
upper limit on solar ν̄e flux is 90 cm−2 s−1 above 8.3 MeV, corresponding to
5.3 × 10−5 conversion probability which is the current best limit on solar ν̄eflux. Assuming Ando LMA model, the upper limit for SRN is found to be
139 cm−2 s−1 [79].
Borexino has obtained an upper limit for solar ν̄e flux of 760 cm−2 s−1 ,which corresponds to a limit on νe → ν̄e conversion probability of 1.3 × 10−4
[82].

33

Chapter 1

Introduction

Super-Kamiokande-I/II/III
In 2003, the Super-Kamiokande collaboration reported a very stringent limit
on SRN flux based on SK-I data, which reads [83]:φν̄e (Eν̄e > 19.3 MeV) < 1.2 cm−2 s−1 .

(1.79)

The analysis threshold is then lowed to 17.3 MeV, mainly due to improvementon the spallation cut. Combining with SK-II/III data, the new limit becomessomewhat less constraining [84]:φν̄e (Eν̄e > 17.3 MeV) < 2.8 − 3.0 cm−2 s−1 .

(1.80)

Note that the SK limit is already encouragingly close to theoretical predictions. Indeed, adding neutron tagging capability is mainly motivated by thesearch of SRN.
A search of solar ν̄e was also conducted in the energy range 8–20 MeV(visible energy) using SK-I data. This search is obscured by the huge spallation background and a rather poor limit of 0.8% was set on the νe → ν̄econversion probability [85].

34Chapter 2
Super-Kamiokande Detector
2.1

Detection Methodology

A charged particle that passes through a medium emits Cherenkov light when
it moves faster than the speed of light in that medium, i.e.
vparticle > c/n(λ)(2.1)

where c is the speed of light in vacuum, n is the index of refraction and λis the wavelength of the photon. The refraction index n in general decreases
slightly with increasing λ and is ∼1.33 for pure water. Formula (2.1) defines
the minimum energy to generate Cherenkov radiation for a particle with mass
m as
m
.
(2.2)
Ethr = p
1 − (1/n)2
Cherenkov photons are emitted in a cone with opening angle defined bycos θC =

1
βn(λ)

(2.3)

For ultra-relativistic particles (β ≈ 1), θC ≈ 42◦ . The number of photons
emitted per unit wavelength per unit length of radiator is given by
2πz 2 α1d2 N
1− 2 2
=
(2.4)
dλdx
λ2
β n (λ)where z is particle charge in unit of e, α is the fine structure constant. In
the SK detector, Cherenkov photons are detected by photomultiplier tubes
whose typical sensitivity ranges from 300 nm to 600 nm. Integrating (2.4)
over λ gives
Z λ2
dN
dλ
2
2
= 2πz sin θC= 760 z 2 sin2 θC photons/cm
(2.5)
2
dx
λ1 λ
35

Chapter 2

The Super-Kamiokande Detector

For an ultra-relativistic particle with unit charge, about 340 Cherenkov photons are emitted per cm. Note the energy loss due to Cherenkov radiation israther small compared to the collision loss. Take λ = 400 nm, for example,
× hc/λ ≈ 1 × 10−3 MeV/cm, while thethe radiated energy is Erad = dN
dx
minimum ionization of a charged particle in water is about 2 MeV/cm.

2.2

Detector Overview

Super-Kamiokande is a water Cherenkov detector located under Mt.Ikenoyama
in Gifu Prefecture, Japan. The mean overburden is 1000 m of rock, or 2700
meter-water-equivalent, reducing the comic ray muon rate to ∼2 Hz. The
SK detector consists of a cylindrical stainless-steel tank with a diameter of
39.3 m and a height of 41.4 m. A PMT support structure of thickness 55 cm
divides the tank into two optically isolated volumes: an inner detector (ID)and an outer detector (OD). The ID has dimensions 33.8 m (diameter) by
36.2 m (height) and is viewed by 11,146 inward-facing 50 cm PMTs giving∼40% photo coverage. The OD is instrumented with 1185 outward-facing 20
cm PMTs. A schematic view of the SK detector is shown in Fig. 2.1.

Figure 2.1: Schematic view of the Super-Kamiokande detector.
The OD volume has a thickness of ∼2 m, serving as an active veto forincoming charged particles and a passive shield for neutron and γ rays fromsurrounding rock. To further reduce ambient background, it is required that36

Chapter 2

The Super-Kamiokande Detector

the event vertex should be at least 2 m away from the ID wall, defining thefiducial volume (FV) used for data analysis as 22.5 kton.

2.3

Photomultiplier Tubes (PMTs)

The 50 cm PMT was originally developed by the Hamamatsu Photonics
Company and Kamiokande collaborators for use in the Kamiokande experiment. The model (Hamamatsu R3600) used in SK was improved in orderto get better timing resolution and have better separation from dark current
for single photoelectron [86]. Fig. 2.2 shows the structure of the 50 cm PMT.
The photocathode material is bialkali (Sb-K-Cs) which has a sensitive regionof 300-600 nm and the quantum efficiency peaks at 360-400 nm, as shown in
Fig. 2.3. A good time resolution is critical to have better vertex resolution
for low energy events. For single photoelectron the transit time spread is
about 2.2 ns. The desired 1 p.e. peak can be clearly seen in Fig. 2.4, where
the peak close to zero ADC count is due to the dark current.

Figure 2.2: Schematic view of the 50 cm PMT.
The 50 cm PMTs are operated with a gain of 107 at a supply of highvoltage ranging from 1700 to 2000 V. To minimize the geomagnetic field
effect on PMTs, 26 sets Helmholtz coils are arranged in SK tank to reduce
the geomagnetic filed down to 50 mG. The average dark noise rate at 0.25
pe threshold is about 3.5 kHz for SK-I. After the accident in 2001 whenhalf of the PMTs were destroyed from the shock wave induced by a single
PMT implosion, all ID PMTs are protected by acrylic covers and FRP cases.
Although the acrylic covers have good transparency, the dark noise in SK-IV

37

Chapter 2

The Super-Kamiokande Detector

Figure 2.3: The quantum efficiency of the 50 cm PMT as a function of
wavelenth.

Figure 2.4: Single photoelectron pulse height distribution.

38

Chapter 2

The Super-Kamiokande Detector

is increased compared to SK-I due to additional radioactivities from the FRP
cases.

2.4

Electronics and Data Acquisition System

In August 2008, the SK electronics and data acquisition (DAQ) system were
upgraded. The new system has a larger charge dynamic range and can handle
a larger event rate. In addition, every hit is recorded and all hit data arefiltered with software trigger, where complex triggers can be implemented.
The new electronics and DAQ can enhance the physics of the SK experiment.

2.4.1

Electronics

PMT signals are processed by the newly developed front-end electronics
QBEE (QTC Based Electronics with Ethernet). The primary functions of
QBEE are to record the integrated charge and arrival timing of each PMT
signal and send data to online PCs. Signals from 24 PMTs are fed to one
QBEE board. Table 2.1 lists the basic specification of QBEE. Compared tothe previous one, the new electronics has a larger charge dynamic range andbetter data transfer capability.
Table 2.1: Specification of QBEE [87].
Number of Inputs
24
Processing speed of QTC about 900 ns/cycle
Number of ranges
3 (small, medium, large)
Discriminator-0.3 to -14 mV (small range)
Charge dynamic range
0.2 to 2500 pC
Charge resolution
about 0.2 pC (small range)
Charge linearity< 1%
Timing resolution
0.3 ns (2 pC input)<0.2 ns (> 10 pC input)
Power consumption< 1 W/ch
A new custom application-specific integrated circuit (ASIC), the highspeed charge-to-time converter (QTC), is developed for the PMT charge
measurement [88]. The ASIC detects PMT signals and issues output timing
signals whose width represents the integrated charge of the PMT signal. This
ASIC has a wide dynamic range for charge measurements by offering threegain ranges (small, medium, large). Each QTC chip has three inputs and39

Chapter 2

The Super-Kamiokande Detector

eight QTC chips are assembled in one QBEE board. The output of QTC is
processed by the multi-hit Time-to-Digital converter (TDC) called ATM-3[89]. The TDC measures the width of QTC output pulse by detecting theleading and trailing edges.
Digitized data of the width and arrival timing are sent from TDC to a
FPGA called Data Sort Mapping (DSM). DSM makes for each hit a 6-byte
cell containing charge, timing and input channel information. Outputs from
DSM are sent to another FPGA, where the data are sorted and stored in a
FIFO memory. The stored data are then sent to a network interface card
when a request is received from the card. The capability of data transferfrom QBEE to online PCs is improved by using Ethernet. The throughput
is measured to be 11.8 MB/s per QBEE board.

2.4.2

Data Acquisition System

Fig. 2.5 shows the block diagram of the new DAQ system. Data from about
500 QBEE boards are sent to 20 front-end PCs as TCP packets. The frondend PCs sort received data in time order and send them to 10 Merger PCs via
10-Gigabit Ethernet. In the Merger PCs, data blocks from 20 frond-end PCs
in the same time region are sent to one process for event building. There are
40 event building processes running in parallel on 10 Merger PCs. Data fromthe front-end PCs are merged and sorted in time order again and scannedby the software trigger. Via Gigabit Ethernet, triggered events are sent toan Organizer PC where all data blocks are sorted in time order and written
to the disk for further analysis.

Figure 2.5: Block diagram of the data acquisition system for SK-IV [87].

40Chapter 2

The Super-Kamiokande Detector

The new DAQ system has been running stably 24 hours/day since its
installation in September 2008. The increased throughput of the DAQ systemenables SK to handle higher trigger rate, which is critical for detecting lower
energy events. The new DAQ system can process data without loss up to 12
kHz trigger rate, which is much higher than the 4 kHz limit of the previous
system. The new DAQ system also performs well for high rate bursts suchas a nearby supernova neutrino explosion. The expected number of eventsfrom a supernova burst at the galactic center (∼8.5 kpc away) at SK is about
10000. Tests show that the new DAQ system can process data without loss
up to 6 millions events in the 10-second time window. The bottleneck of the
new DAQ system is the disk writing speed of the Organizer PC, which has
a limit of about 50 MB/s.

2.4.3

TriggerIn the previous DAQ system, a hardware trigger (HITSUM) was implemented
based on the number of PMT hits within a 200 ns time window. There werefour types of major triggers: high energy (HE), low energy (LE), super-low
energy (SLE) and outer detector trigger (OD) [90]. In addition, several
external triggers were prepared for the calibration purpose. In the new DAQ
system, the software trigger simulates the HITSUM trigger by counting thenumber of hits in a 200 ns sliding window. The trigger thresholds for SLE,
LE, HE, OD are 34, 47, 50 and 22 hits, respectively.
The event width is 1.3 µs in SK-I/II/III. Events with LE/HE trigger in
SK-IV have a width of 40 µs, ranging from -5 µs to 35µs. The wider event
width is ideal for catching possible pre-activity (e.g. prompt γ-ray) and postactivity ( e.g. decay electron). The width of SLE-only events in SK-IV is 1
µs. Two new triggers are added in SK-IV primarily for the SRN study. A
special high energy (SHE) trigger is issued if the number of ID hits exceeds
70, which corresponds to ∼10 MeV. If a SHE triggered event has no OD
trigger, an After Trigger (AFT) is then issued to take 500 µs data without
trigger threshold following that event. The combination of SHE and AFT
trigger is used to detect the prompt positron and delayed 2.2 MeV γ resulted
from the inverse beta decay reaction. The SHE threshold was lowered from70 hits to 58 hits in September 2011 to study lower energy events that areaccompanied by neutrons.

2.4.4

Monitoring System

A variety of tools are used to monitor the detector performance. A process
called the “slow control” monitor watches the status of the HV systems and41

Chapter 2

The Super-Kamiokande Detector

the temperatures of electronics crates. A histogram making process checks
the data stream and make various distributions to check the PMT status
and event trigger rates. The data transfer and offline data process are also
monitored by a set of sophisticated software.
As part of the online monitor system, a new online display program isdeveloped by the author of this thesis to visualize SK events in real time.
The primary goals of this program are to provide visual investigations of
the detector status and understandings of the physics of various events. A
screenshot of the new event display is shown in Fig. 2.6. Graphical events flyon the big head-on screen at the rate about 1 Hz in the control room serveas the most direct and efficient way for shifters to monitor the DAQ systemand the working status of PMTs in the detector.

Figure 2.6: A screenshot of the new online event display.

2.5

Water and Air Purification Systems

To maximize the water transparency and minimize backgrounds arising fromthe natural radioactivity, the 50 ktons of purified water in the SK tank is

42

Chapter 2

The Super-Kamiokande Detector

continuously recirculated at the rate about 60 ton per hour through a multistep purification system. A schematic view of the water purification system
is shown in Fig. 2.7. The various process stages are described as follows:• 1 µm filter:
Removes dust and particles.
• Heat exchanger:
Cool the water to reduce PMT dark noise and growth of bacteria.
• Cartridge polisher:
Removes heavy ions.
• UV sterilizer:
Kills bacteria.
• Rn-less air dissolve tank:
Dissolve Rn-reduced air into the water to increase radon removal efficiency of the vacuum degasifier.
• Reverse osmosis:
Further removes contaminants heavier than 100 molecular weight.
• Vacuum degasifier:Remove dissolved gases such as radon and oxygen from the water.
• Ultra filter:
Remove small particles down to the size of 10 nm in diameter.
• Membrane degasifier:Further remove dissolved radon and oxygen gas.
Radon levels in the mine are relatively high, which typically reach 2000
Bq m−3 during the warm season and is about 200 Bq m−3 in the cold season.
To reduce radon background, purified air is supplied to the experimental
area from outside. Fresh air is continuously pumped in at approximately 10
m3 min−1 , keeping the radon levels in the experimental area around 40 Bq
m−3 throughout the year. Another super-radon-free-air system, as shown in
Fig. 2.8, is used to keep the radon level less than a few mBq m−3 in the air
between the top of water and the cover of the tank.

43

Chapter 2

The Super-Kamiokande Detector

Figure 2.7: The water purification system at SK.

Figure 2.8: The air purification system at SK.

44

Chapter 3
Detector Calibration
Various calibrations are needed to gauge the performance of the SuperKamiokande detector. This chapter summarizes the calibrations relevant
for the data analysis in this thesis. More details on detector calibration canbe found in Ref. [90].

3.1

PMT Calibration

The PMTs need to be calibrated in order to properly interpret the charge andtiming recorded by each PMT. First of all, the high voltage supply for each
PMT is adjusted to obtain a near-uniform response throughout the detector.
Then the PMT gain is precisely measured for each PMT to correctly convert
the ADC count to photo-electrons. The relative timing of PMTs is also
corrected.

3.1.1

Absolute Gain

The global absolute gain (pC to p.e. conversion factor) is measured by usinga Ni-Cf light source. Since the energy of γ-rays from the Ni-Cf source is only
a few MeV, the resulting PMT hits are almost all due to single photons. The
absolute gain is determined from the averaged charge distribution for single
photo-electrons. The pC to p.e. factor is 2.645 pC/p.e. for SK-IV.

3.1.2

Relative Gain

The relative gain is measured using a laser system with a high and a low
intensity light. The charge detected by the i-th PMT (Qobs (i)) in the high45

Chapter 3

Detector Calibration

intensity data obey the following relation:
Qobs (i) ∝ Ihigh (i) × QE(i) × G(i),(3.1)

where Ihigh (i) is the light intensity seen by the i-th PMT, QE(i) is the PMT
quantum efficiency and G(i) is the relative gain. On the other hand, the hit
times of each PMT in the low intensity data scale as:
Mhit (i) ∝ Ilow (i) × QE(i).

(3.2)

Taking the ratio of Eqn. (3.1) and Eqn. (3.2), one finds
G(i) =

Qobs (i)Ilow (i)×,
Mhit (i) Ihigh (i)(3.3)

where light attenuation and geometric effects are all canceled out. The measured relative PMT gain is shown in Fig. 3.1. Both the absolute and relative
gain are used to convert the ADC count to p.e. in processing real data.

Figure 3.1: Measured relative PMT gain. The 1-σ spread is about 6%.

3.1.3

Timing

The relative timing of PMT hits is important for vertex reconstruction. The
difference arises from variations in transit time and cable length of each PMT.
It also depends on the observed charge due to the discriminator slewing effect.
46

Chapter 3

Detector Calibration

The PMT relative timing is measured using a laser system. The N2 laser
beam is injected via an optical fiber into a diffuser ball, which is deployedat the center of the tank to produce diffuse light. The light intensity ischanged using an optical filter to measure the PMT timing at various pulse
heights. Fig. 3.2 shows a typical 2-D plot of PMT timing versus pulse height,
which is referred to as a “TQ-map”. A TQ-map is made for each PMT. Withcorrections according to the TQ-maps, the residual timing differences of PMT
hits are used to determine the global timing resolution. This global timing
resolution is an input for vertex reconstruction and Monte Carlo simulation.
At single p.e. level, the timing resolution is about 3 ns.

Figure 3.2: A typical 2-D plot of timing vs. charge, known as “TQ-map”.
The upper horizontal axis shows the PMT charge. The QBin in the lower
horizontal axis is defined as: QBin = 5·Q (0 < Q < 10) or QBin = 50·log10 Q(10 < Q < 3981). Hits in the lower left are due to scattered photons. Hitsin the upper right are pre-pulses.

3.2

Water Transparency Measurement

Light absorption and scattering in water affect the number of Cherenkov
photons that are detected by PMTs. Therefore, it’s important to precisely
determine the water transparency for accurate energy measurements. There
are two ways to measure water transparency at SK. Firstly, the absorption
and scattering parameters are separately measured using the N2 laser. And
secondly, the effective attenuation length is measured using the decay electrons from cosmic ray muons.
47

Chapter 3

3.2.1

Detector Calibration

Laser Measurements

In terms of the absorption (αabs ) and scattering (αscat ) parameters, the lightattenuation length isLatten =1
αabs + αscat, sym + αscat, asym

,

(3.4)

where αscat, sym includes Rayleigh scattering and the symmetric part of Mie
scattering while αscat, asym represents the asymmetric part of Mie scattering.
A set of N2 lasers of wavelengths 337, 375, 405, 445 and 473 nm are used
to directly measure these parameters. The laser beam is vertically injected
into the SK detector from the top via optical fibers. Each laser fires every 6s during normal data taking period.
In such laser events, PMT hits at the bottom of the tank are due to
direct light, while PMT hits on the barrel and the top are due to photons
scattered in water or reflected by bottom PMTs and black liner sheets. The
absorption and scattering parameters are studied using the total number ofscattered photons and the distribution of the arrival-time of PMT hits. These
parameters are tuned in the Monte Carlo so that the simulation matches thelaser data. The absorption and scattering parameters determined in this way
are then used to model the water property when generating physics Monte
Carlo simulation. The water attenuation length calculated using Eqn. (3.4)
is in agreement with the decay electron measurement described below.

3.2.2

Decay Electrons

Each day thousands of cosmic ray muons stop in the inner detector to produce
decay electrons. These decay electrons can serve as a calibration sample tocontinuously monitor the water transparency. In order to have a pure sample
of decay electrons, the following selection criteria are applied:• The time difference ∆T between the stopping muon and the decay
electron should satisfy: 3.0µs < ∆T < 8.0µs.
• The vertex of the electron must be reconstructed within the fiducial
volume.
• The distance between the reconstructed electron vertex and the muon
stopping point must be less than 250 cm.
• The number of PMT hits with residual time within 50 ns must be
greater than 50.
48

Chapter 3

Detector Calibration

These criteria selects ∼700 µ − e decay events each day.
Using selected decay-e events, PMT hits are divided by the distance fromthe reconstructed decay-e vertex to each hit PMT. The water transparency isdetermined by fitting the number of PMT hits versus distance distribution.
To remove the effects of noise hits and indirect light, only PMT hits withina corn of opening angle between 32◦ ∼ 52◦ and with residual time within 50
ns are used. The amount of contribution from each PMT is corrected in thesame way as that for the energy reconstruction (see section 4.3). To reduce
statistical fluctuation, the water transparency given for each day is calculatedusing +/− one week data. The water transparency obtained by this method
is shown in Fig. 3.3 for the SK-IV period. As discussed in section 4.3, thisdaily water transparency is an input parameter for the energy reconstruction.

Figure 3.3: Water transparency of SK-IV measured from decay electrons.

3.3

Energy Calibration

Precise energy measurement is critical for low energy data analysis. Various techniques are used at SK to calibrate the absolute energy scale, its
directional and position dependence and time variation.

49

Chapter 3

3.3.1

Detector Calibration

LINAC

The absolute energy scale for low energy data analysis at SK is primarily
determined by using an electron linear accelerator (LINAC). The LINAC
is used to inject into the SK tank downward-going single mono-energetic
electrons with energy up to ∼19 MeV. The beam energy is precisely measured
to ±20 keV accuracy using a Germanium detector. The LINAC system andits performance is detailed in Ref. [91].
The LINAC data were taken in August 2009 and August 2010 during
the SK-IV period. Each time data were taken at several positions and withseveral different energies at each position. The LINAC data are used to tune
various parameters in the Monte Carlo. Fig. 3.4 shows the reconstructedenergy of LINAC data with comparison to the Monte Carlo at one of thebeam positions. Very good agreement is obtained for all tested beam energies.

Figure 3.4: Distributions of reconstructed energy for LINAC data (cross) andMC (line) at the beam position (x,y,z)=(-388.9 cm, -70.7 cm, -6 cm). The
LINAC data were taken in August 2010.
The LINAC calibration is responsible for converting the effective numberof PMT hits (Neff , see section 4.3) to the total energy. However, the LINAC
data is only available in the downward-going direction and several fixed positions. Hence the correlation between Neff and the energy can not be obtained
directly from the LINAC data. Instead, the LINAC-tuned Monte Carlo isused to generate uniformly distributed events at several fixed energies. The
mean value of Neff is obtained for each energy by fitting the Neff distribution
with a Gaussian function. The correlation between Neff and energy is thenfit with a 4-th order polynomial function. The energy conversion function
obtained in this way sets the absolute energy scale of the detector. The accuracy of the absolute energy scale is better than 1% as determined from
LINAC data.

50

Chapter 3

Detector Calibration

In addition to set the absolute energy scale, the LINAC data are also
used to study the energy resolution, vertex resolution and angular resolution
because LINAC events have known energy, position and direction. Detailsof these resolutions and their systematic uncertainties can be found in Ref.
[91].

3.3.2

DT Generator

A deuterium-tritium (DT) neutron generator is used to cross check the absolute energy scale [92]. The generated neutrons are employed to create 16 N
via the (n,p) reaction on 16 O in water. The decay of 16 N has a Q value of
10.4 MeV and is dominated by an electron, with a maximum energy of 4.3
MeV, coincident with a 6.1 MeV γ-ray. DT data is taken every a few months,
and the reconstructed energy of DT events agrees with LINAC-tuned Monte
Carlo better than 1%.
Since DT events are isotropic, the directional dependence of the energy
scale can be checked using DT data. This directional dependence is foundto be less than ±0.5%. Due to the better portability of the DT generator,
DT data are taken at more positions than LINAC to study the position
dependence of the energy scale. The radial and z-dependence of the energy
scale is found to be less than ±0.5% and ±1%, respectively.

3.3.3

Decay Electrons

The energy of decay electrons from stopping cosmic ray muons follows thewell known Michel spectrum. Therefore, decay electrons can be used to checkthe energy scale up to about 60 MeV. Taking into account effects due to µ−
capture by oxygen nuclei, the data can be reproduced by Monte Carlo with
better than 2% accuracy.
In addition to determine the absolute energy scale, decay electrons areused to check the time variation of the energy scale. Using the same decaye sample as that for water transparency measurement, the mean effective
number of PMT hits Neff is calculated for each 30 days period using thecorrected water transparency. Fig. 3.5 shows the mean Neff distribution for
SK-IV. The energy scale is stable within ±0.5% during the operation of SKIV.

51

Chapter 3

Detector Calibration

Figure 3.5: Mean Neff of decay electrons. The dashed lines indicate ±0.5%
deviation from the average.

52

Chapter 4
Event Reconstruction
All events that meet the software trigger conditions and have less than 1000
PMT hits are applied with low energy reconstruction tools. The primaryreconstructed quantities are the vertex, direction and energy of the event.
Events with more than 1000 photo-electrons are considered to be cosmic raymuons 1 and are reconstructed with muon track fitters. Reconstructed muons
are used to identify spallation events. In order to distinguish electrons fromother particles, Cherenkov angle is calculated after events passing certain
selection criteria.

4.1

Vertex Reconstruction

Low energy electrons and positrons can only travel a short distance (e.g.
∼20 cm at 50 MeV), and thus the Cherenkov light is considered as emitted
from a point source. Since for low energy events at Super-Kamiokande,most PMT signals are due to single photon hits, little information about the
distance from PMT hits to the source can be extracted from PMT charge.
Therefore, the reconstruction of vertex for low energy events relies entirely on
the timing of PMT hits. Among the several existing vertex fitters, BONSAI[93] has the best vertex resolution and lowest misfit rate and is used for vertex
reconstruction in this thesis.
The BONSAI is a maximum likelihood fit to the timing residuals of thehit PMTs. The timing residual is defined as:∆t = t − tof(~v ) − t0 ,(4.1)

where t is the PMT hit timing, ~v and t0 are the vertex and Cherenkov lightemission time under testing and tof is the time-of-flight (TOF) from the1

The atmospheric neutrino event rate is about 10 events per day.

53

Chapter 4

Event Reconstruction

testing vertex to the hit PMT. The signal probability density function of ∆tused in the fit is taken from LINAC calibration data and the PMT dark noise
is assumed to be flat. The likelihood constructed from the ∆t distribution
is then maximized to give the reconstructed vertex. The BONSAI vertex
resolution is ∼70 cm for 10 MeV electrons. BONSAI also returns a goodness
value which can be used to evaluate the quality of the fit.

4.2

Direction Reconstruction

The direction of an electron can be reconstructed utilizing the Cherenkov
ring pattern. This is accomplished by maximizing the following likelihood
function:
N20
X
cos θi~,(4.2)
L(d) =
log(f (cos θdir,E )i ) ×
a(θ
)
i
i
where N20 is the number of PMT hits within a 20 ns window around ∆t = 0
while f (cos θdir,E ) is the expected distribution of the opening angle between
the particle direction d~ and the vector from the reconstructed vertex to thehit PMT. The distribution of f (cos θdir,E ) is obtained from MC for various
energies. It peaks around 42 degree but expands a wide range because of themultiple scattering. The factor cos θi /a(θi ) corrects for the PMT acceptance,
where θi is the opening angle between the vector from the reconstructedvertex to the i-th hit PMT and the vector normal to the PMT surface. Enq.
(4.2) is maximized by scanning various directions. The best solution thatgives the maximum likelihood is chosen as the reconstructed direction. For
a 10 MeV electron, the angular resolution is about 25 degree.

4.3

Energy Reconstruction

The basic idea behind the energy reconstruction is that the energy depositedby a charged particle is approximately proportional to the number of generated Cherenkov photons. For low energy events, it is also proportional to thenumber of PMT hits since in such case most PMTs are hit by single photons.
Before converting the number of PMT hits to the energy, several corrections
should be applied to get an effective number of hits, which is defined as:
Neff =

N50 
X
i=1


Rcoverri
Nall
×× exp() × Gi (t)(Xi − tail − dark ) ×
Nnorm S(θi , φi )λ(run)(4.3)

54

Chapter 4

Event Reconstruction

where N50 is the number of PMT hits with residual time within a 50 ns
window. Most dark noise is filtered out by using this narrow time window.
The quntities in Eqn. (4.3) are explained as follows:• Occupancy
The assumption of single photon per PMT breaks down at higher energies. If a PMT detects multiple photons, it is likely that many PMTs
surrounding this PMT are also hited. Xi is an occupancy used to estimate the effect of multiple photo-electrons for the i-th PMT and isdefined as:(1
log 1−xi, xi < 1
xi
Xi =
(4.4)
3.0,
xi = 1
where xi is the ratio of the number of hit PMTs to the total numberof PMTs in a 3 × 3 patch around the i-th hit PMT.
• Late hits
Some Cherenkov photons can be scattered or reflected, and thus falloutside the 50 ns window. This effect is corrected by the term tail .
• Dark noise
The contribution of dark noise dark is estimated from the total numberof operating PMTs and dark rate of each PMT, and is subtracted fromoccupancy.
• Bad PMTs
The second factor in Eqn. (4.3) corrects for bad PMTs, where Nallis the number of total PMTs and is 11129 in SK-IV, an Nnorm is thenumber of properly operating PMTs.
• Photo-cathode coverage
The third factor accounts for the effective photo coverage, which isdependent on the incident angle of the photon to the PMT.
• Water transparency
The fourth factor corrects for water transparency variation, where ri isthe distance from the reconstructed vertex to the i-th hit PMT, and λis the measured water transparency.
• PMT gain
The last factor corrects time dependent PMT gain at the single photon
level.

55

Chapter 4

Event Reconstruction

Finally, the total energy of an event is calculated as a function of Neff . As
discussed in section 3.3.1, the energy conversion is precisely calibrated using
the LINAC data and the accuracy of the absolute energy scale is better
than 1%. The energy resolution is about 14% for 10 MeV electrons. It
should be noted that the energy reconstruction described here always assumes
the particle is either an electron or a positron. This energy reconstruction
algorithm does not apply to other particles. For example, a muon with
momentum p = 200 MeV/c can be reconstructed as if it was a 25 MeV
electron. So unless otherwise stated, all energy values quoted in this thesis
refer to total electron equivalent energy.

4.4

Muon Fitting

Most low energy events above 8 MeV observed in SK are spallation products
induced by cosmic ray muons. Such events can be rejected by searching for
spatial and temporal correlations with proceeding muons. Therefore, it’s
critical to precisely reconstruct the muon tracks.

Muboy
All events with more than 1000 photo-electrons are fitted using a software
called Muboy. Muboy can fit not only a single muon track but also multiple
muon tracks (assumed to have parallel track directions). Muons successfully
fit by Muboy are classified into the following categories: single through-going
muons, stopping muons, multiple muons and corner clippers. For multiple
muons, up to 10 tracks can be fit; there may have only one track if too few
hits are left after removing the hits closely associated with the first track (butclassification is still multiple muons). Muboy also returns a goodness value toevaluate the quality of fit. The muon type classification and fit goodness arevery useful in determining spallation (see section 9.3). Detailed descriptionsof the algorithm and performance of Muboy can be found in Refs. [94, 95].
SK-IV events have a wide width. When an incident muon happens to bewithin the time window of another triggered event (except SLE only event),
it will not register a trigger. There are a few hundreds of such untagged
muons per day in SK-IV data. It is important to identify these untagged
muons so that decay electrons and spallations resulting from these muons
can be correctly identified. To locate untagged muons offline, the software
trigger is applied again to each event to search for a muon candidate (withHE and OD trigger). The untagged muons are then extracted for processing
with Muboy.
56

Chapter 4

Event Reconstruction

BFF
In rare cases, the Muboy fit result is not reliable as indicated by the poor
goodness value. An alternative muon fitter is developed to refit the single
through-going muons for which Muboy reports a bad goodness (< 0.4). This
new fitter is called Brute Force Fitter (BFF). It simply performs a grid search
for the entry and exit points in the inner surface of the detector, and hence
is rather slow. BFF can improve the power of the spallation cut by correctly
refitting ∼75% of the muons that poorly fit by Muboy. More details about
BFF can be found in Ref. [96].

dE/dx
After muon tracks are fit, Cherenkov light emission per unit track length,
dE/dx, is also calculated. This is done by matching the light seen by each
PMT to a location along the muon track using timing information. The
dE/dx of the muon track is histogrammed in 50 cm bins. It is found thatmuons tend to have a peak in the dE/dx distribution at where the spallation
occurred.

4.5

Cherenkov Angle Reconstruction

For the low energy analysis at SK, particle identification (PID) is mainly doneby studying the opening angle of the Cherenkov ring caused by a charged
particle. Electrons (or positrons) above the analysis threshold are ultrarelativistic particles and have a Cherenkov opening angle around 42◦ . Heavier
particles such as muons and pions are not ultra-relativistic and would havea smaller opening angle as determined by Eqn. (2.3). In addition, PMT hits
induced by mutiple γ-rays tend to appear isotropically in the detector, where
no clear Cherenkov ring can be identified. The reconstructed Cherenkov angle
can be used to reject muons, pions and γ-rays.
The Cherenkov opening angle is reconstructed using 3-hit combinations.
Each set of 3 PMT hits uniquely defines a cone with a particular opening
angle. The resulting distribution of opening angles evaluated from all combinations should peak at the opening angle of the Cherenkov cone. In order tominimize the effects of noise hits, only PMT hits with residual time within a
15 ns window are considered. A typical opening angle distribution for an electron is shown in Fig. 4.1 in black line. The peak of this distribution is taken
as the Cherenkov angle of the event. The opening angle distributions do nothave a well defined shape and it’s impractical to apply a fit for all events.
Instead, the peak is located using a sliding 7-bin. The Cherenkov opening
57

Chapter 4

Event Reconstruction

angle is determined to be 45.9◦ for this event. Fig. 4.2 shows the event display for this electron, where the big circle shows the expected Cherenkov ringassuming an opening angle of 42◦ (unless otherwise stated, rings appear indisplays are shown under this assumption). It can be seen that the actual
PMT hit pattern matches the expected Cherenkov ring quite well.

Figure 4.1: Example of distributions of opening angle from 3-hit combinations for various particles. Bin entries of the red and blue histograms areshrinked by a factor of 2 and 10, respectively, for better visualization. Event
displays are shown for these events in Fig. 4.2–4.5.
A typical opening angle distribution for a muon is shown in Fig. 4.1 in
red line. The Cherenkov opening angle determined for this event is 27.9◦ .
Event display for this muon is shown in Fig. 4.3, which exhibits a significant
deviation from an electron ring. A typical opening angle distribution for a
γ-ray event is shown in Fig. 4.1 in green line. The Cherenkov opening angle
determined for this event is 87.3◦ . Such events tend to have isotropic PMT
hits, as shown in Fig. 4.4.
The reconstructed Cherenkov opening angle value is used to reject muonsand pions with relatively low momentum and γ-rays, see section 9.6. In
58

Chapter 4

Event Reconstruction

addition, the width of the opening angle distribution can be used to rejectanother type of event: pions with higher momentum. In some cases, atmospheric neutrino induced pions are absorbed by oxygen nuclei after emittingsome Cherenkov light and can be reconstructed as a low energy event. If the
momentum of the pion is high enough, the reconstructed Cherenkov angle isclose to 42◦ and hence can not be distinguished from an electron. However,unlike the fuzzy rings caused by electrons, pion rings are in general very
sharp (see Fig. 4.5). A sharper ring corresponds to a narrower peak in the
opening angle distribution. A typical opening angle distribution for such apion is shown in Fig. 4.1 in blue line. Although its peak value is similar to anelectron, the width of the peak is much smaller than that of an electron. To
quantify this characteristic, a pion likelihood is calculated as the following:
πlike =

#entries ± 3◦ from peak.
#entries ± 10◦ − #entries ± 3◦

(4.5)

Events with large πlike value are considered to be pion events, see section 9.8.

Figure 4.2: A typical electron MC event. The reconstructed energy is 17.2
MeV. The circle shows the expected Cherenkov ring for a ultra-relativistic
particle.

59

Chapter 4

Event Reconstruction

Figure 4.3: A typical muon MC event. The muon momentum is 185.8 MeV/c
and the reconstructed energy is 19.5 MeV.

Figure 4.4: A typical isotropic MC event. The reconstructed energy is 19.1
MeV.

60

Chapter 4

Event Reconstruction

Figure 4.5: A typical pion MC event. The pion momentum is 402.9 MeV/c
and the reconstructed energy is 21.5 MeV. This pion is absorbed by an oxygen
nucleus before depositing all of the energy.

61

Chapter 5
Event Simulation
Monte Carlo simulated samples are used to evaluate the data reduction efficiency and to understand the energy spectra of signal events. In addition,
the simulated samples can be used to precisely predict the expected numberof events at SK, including the detector response.

5.1

Detector Simulation

The Super-Kamiokande detector simulation package, SKDETSIM, is basedon GEANT 3.21. SKDETSIM models the emission of Cherenkov photons,
the propagation of these photons in water and the detector response. In
SKDETSIM, some parameters such as the water attenuation length and PMT
timing resolutions are specifically tuned to reproduce the calibration data
[97, 98].

5.2

Neutrino Interaction Simulation

The inverse beta decay reaction chain has been theoretically studied in details
for its special importance in low energy neutrino experiments. In this thesis,
we adopt Strumia and Vissani’s calculation for ν̄e p → e+ n cross-section [99].
In the simulation, we also take into account the angular distribution of theoutgoing positron, which is in particular relevant for the solar ν̄e search.
Vogel and Beacom’s first order approximation [100], which is accurate in theenergy range of interest, is used for the angular distribution. Fig. 5.1 shows
the angular distributions for various incident neutrino energies.
The outgoing positron energy is strongly correlated with the ν̄e energy.
At zeroth order in 1/M (M is the average nucleon mass), the positron energy

62

Chapter 5

Event Simulation

Figure 5.1: Distribution of the positron scattering angle in the inverse beta
decay reaction.
isEe(0) = Eν − ∆,(5.1)

where ∆ = Mn − Mp ≈ 1.293 MeV. This simple relation is used in previous
SK SRN searches. In this thesis, we use Vogel and Beacom’s first orderapproximation because it’s more accurate at relatively high energies (Eν & 20
MeV). At the first order in 1/M , the positron energy has a weak dependence
on the scattering angle and is


y2
Eν
(0)
(1)
(0)
(1 − ve cos θ) − ,(5.2)
Ee = Ee 1 −
M
M
(0)

(0)

(0)

where ve = pe /Ee is the velocity of the positron, and y 2 = (∆2 − m2e )/2[100]. Eqn. (5.2) is accurate to ∼1% at Eν = 60 MeV.
To simuilate inverse beta decay, we first use the flux and IBD cross-section
to give the interaction rate spectrumdNIBD = Np, full × τ1y × f (Eν ) × σ(Eν )dEν ,(5.3)

where NIBD is the number of inverse beta decay events, Np, full is the numberof free protons in the SK full inner volume, τ1y is the time of one year, f (Eν )is the differential flux and σ(Eν ) is the IBD cross-section. The total numberof events in the SK full inner volume in one year is given by
Z ∞
N0 =
dNIBD
(5.4)
0

Then the generation of IBD MC events proceeds as follows:
63

Chapter 5

Event Simulation

1. Generate Eν according to Eqn. (5.3).
2. Generate the scattering angle of the outgoing positron. For a givenEν , make angular distribution dσ/d cos(θ) according to the first orderapproximation formula of Vogel and Beacom [100]. Then randomly
generate a cos(θ) according to the distribution of dσ/d cos(θ).
3. Calculate the positron energy using Eqn. (5.2).
4. Generate a vertex randomly distributed in the SK full inner volume.
5. Generate the event direction according to the Sun position and cos(θ).
This direction is only relevant for the solar ν̄e search.
6. Attach time information to this event to take into account the time
variation of water transparency.
7. Feed the event information into SKDETSIM to simulate the detector
response.
The simulated data are reconstructed with the same tools that are applied
to the real data. Let N1 be the total number of generated MC events, andN2 be the number of events that are reconstructed in the fiducial volume andwith an energy between Elow and E. Then the expected number of signal
R up∞
events from the total flux F ( F = 0 f (Eν )dEν ) is
Nexp =

N0
× N2 / 22.5 kton / year (Elow < Ee+ < Eup ).
N1

(5.5)

Eqn. (5.5) can be used to predict the expected number of events at SK, orto convert the number of events back to flux.

5.2.1

Supernova Relic Neutrinos

For the purpose of evaluation, we consider the Ando LMA model and HBD
6 MeV model. The predicted event rate from these models are shown in
Fig. 5.2.
Fig. 5.3 shows the generated and reconstructed positron energy spectrum
for the Ando LMA model. The expected annual number of events in theenergy range 12 MeV < Ee+ < 30 MeV (see chapter 9) is calculated from
Eqn. (5.5) and is shown is Table 5.1.

64

Chapter 5

Event Simulation

Figure 5.2: SRN ν̄e induced event rate for the theoretical models.

Figure 5.3: Positron energy spectrum predicted by the LMA model.
Table 5.1: Expected number of SRN events in 22.5 kton·year.
SRN model Total flux (/cm2 /sec)
LMA
28.8
HBD 6 MeV
21.8
65

12 MeV < Ee+ < 30 MeV
4.15
4.36

Chapter 5

5.2.2

Event Simulation

Solar Anti-neutrinos

For solar ν̄e ’s, we assume an undistorted 8 B neutrino energy spectrum. The
total 8 B neutrino flux is taken from BP04 predictions [67]. The 8 B neutrinoenergy spectrum is adopted from the Winter06 measurement [101]. Assuming
1% νe → ν̄e conversion probability, the expected annual event rate in SK fullinner volume is shown in Fig. 5.4.

Figure 5.4: Annual event rate for possible solar ν̄e in SK full inner volume,
assuming 1% νe → ν̄e conversion probability.
Fig. 5.5 shows the generated and reconstructed positron energy spectrum.
Note the significant modification of the energy tail by the detector response.
The expected annual number of events in the energy range 12 MeV < Ee+ <20 MeV is calculated from Eqn. (5.5) and is shown is table 5.2.
Table 5.2: Expected number of solar ν̄e events in 22.5 kton·year, assumingνe → ν̄e conversion probability is 1%.
SSM Total flux (/cm2 /sec)
BP04
5.79 × 106

66

12 MeV < Ee+ < 20 MeV
503

Chapter 5

Event Simulation

Figure 5.5: Positron energy spectrum induced by the hypothetical solar ν̄e ’s.

67Chapter 6
Selection of Neutron Capture
EventsThis chapter introduces cuts used to select neutron capture events. Since
neutron capture on free proton emits a monoenergetic 2.2 MeV γ, this iseffectively a search of 2.2 MeV γ’s. To study the signal efficiency, 1.6 millionof 2.2 MeV γ MC events are generated uniformly in the fiducial volume.
The background probability is evaluated using SK-IV random trigger data.
Validation of the signal efficiency with an artificial neutron source will be
discussed in the next chapter.

6.1

Characteristics of 2.2 MeV γ Events

The 2.2 MeV γ fires on average ∼7 PMT hits in the SK detector. Fig. 6.1
shows the total number of PMT hits generated by a 2.2 MeV γ with the vertex
randomly distributed in the fiducial volume. The TOF-subtracted timing
distribution is shown in Fig. 6.2, where the solid line histogram uses the true
vertex, while the dashed histogram includes the effect of vertex resolutionof the primary events. Fig. 6.3 shows the distribution of the number ofphotoelectrons for each PMT hit. This is very similar to the PMT noise,indicating that the charge information is not useful in searching the 2.2 MeV
γ.

6.1.1

Vertex Resolution of the Primary Event

The search of 2.2 MeV γ relies on the primary event vertex for the TOF
correction. So the accuracy of primary event vertex reconstruction is of
crucial importance. In general the vertex resolution decreases as the event
68

Chapter 6

Selection of Neutron Capture Events

Figure 6.1: Distribution of the total number of PMT hits generated by a 2.2
MeV γ at SK.

Figure 6.2: Distribution of TOF-subtracted timing for 2.2 MeV γ events.
Solid line is for the true vertex. Dashed line includes the vertex resolution
effect of the primary event.

69

Chapter 6

Selection of Neutron Capture Events

Figure 6.3: Charge distribution of 2.2 MeV γ events.
energy increases. For a 15 MeV electron, the resolution is ∼50 cm [102].
The effect of vertex resolution is included by smearing the true MC vertex of
the 2.2 MeV γ. The smearing parameter is obtained by studying the vertex
resolution of monoenergetic 18 MeV electrons generated by LINAC. Fig. 6.4
shows the distribution of distance from the reconstructed vertex to the true
vertex for 18 MeV electrons. This is used as a reference histogram to smear
MC vertex. As a result, 2.2 MeV γ’s timing peak spreads slightly wider, as
shown by the dashed histogram in Fig. 6.2.

Figure 6.4: Distance from the reconstructed vertex to the true vertex for 18
MeV electrons.
70

Chapter 6

6.2

Selection of Neutron Capture Events

Pre-selection

To select the 2.2 MeV γ event following a primary event, the first step is todo the TOF subtraction using the primary event vertex. And then sort the
PMT timings in increasing order and search the timing peaks with a sliding
time window. Backgrounds to the 2.2 MeV γ events include PMT noise,radioactivities from the surrounding rock, radon contamination in water and
PMT FRP case, etc.
The background level depends on the size of data that is being searched
after each primary event. Unless otherwise stated, in the following background is referring to the number of fake 2.2 MeV γ peaks in a 500µs data
pack. Since these fake peaks have no time correlation with the primary event,background can be easily scaled if a different size of data is searched.

N10
The sliding time window used to search a 2.2 MeV γ peak is 10 ns. The
background level increases dramatically if the timing window is widened. On
the other hand, more signal PMT hits are uncovered if the timing window
is smaller, as can be seen from Fig. 6.2. Fig. 6.5 shows the distribution of
the maximum number of PMT hits in a 10 ns window (N10). From thisfigure, one can see on average there are 11 peaks with N10=6 in a 500µs
data pack, much higher than signal. We require N10>7 to reject majority ofbackgrounds.

Figure 6.5: Distributions of N10 for signal (black) and background (red).
Note that the signal distribution is scaled up by a factor of 10.

71

Chapter 6

Selection of Neutron Capture Events

NclusterIt’s found that most remaining backgrounds have cluster structures in PMT
hits. These backgrounds most likely originate near the detector wall (e.g.
radioactivities from PMT glasses and FRP cases) and hence the PMT hits
have both tight spatial and temporal correlation. After the TOF subtraction,
the hit timing peak remains and can thus pass the N10 cut. Fig. 6.6 (a)shows the distribution of cosα, where α is the angle between any two hit
vector combinations. Background’s cosα strongly peaks at 1, suggesting
many PMT hits are very close to each other. This feature, however, does notshow up in the 2.2 MeV γ events.
A search of hit clusters is performed for the PMT hits within the 10 ns
window. Starting with a certain hit, the search looks for the next hit whose
hit vector is closest. If the angle between these two PMT hits is less than
14.1◦ (driven by the cosα distribution), these two hits are considered to forma cluster candidate, and therefore are put into a group. Then the third PMT
hit that is closest to any PMT hit in the group is determined. If the angle
between the third hit and any hit in the group is less than 14.1◦ , this hit
is added into the group. This algorithm continues until all PMT hits in
the 10 ns window have been examined. Multiple clusters in the 10 ns time
window is possible. The total number of PMT hits that are in clusters iscalled Ncluster.
As shown in Fig. 6.7 (a), 86% background peaks have cluster structures,
while only 26% signals are found to have clusters. The actual quantity used
as a cut is N10 − Ncluster, which is shown in Fig. 6.7 (b). This is better
because N10 spectrum of signal is harder than background’s (see Fig. 6.5)
and using N10 − Ncluster instead of Ncluster can keep most of signals thatare found to have clusters. Events with N10 − Ncluster < 6 are rejected. Fig
6.6 (b) shows the distribution of cosα after the cluster cut. The strong peakon background disappears.

Nback
This cut is designed to remove the background due to the PMT noise. The
Cherenkov light generated by charged particles in water has a cone structure.
For the 2.2 MeV γ events, this cone structure is smeared because the electron
scattered by the 2.2 MeV γ is subjected to multiple scattering. Nevertheless,
PMT hits generated by a 2.2 MeV γ concentrate in the forward hemisphere.
Noise hits, on the other hand, are more uniformly distributed in the detector.
To employ this difference in the hit pattern between signal and background,
we calculate the angle θ between each hit vector and the estimated direction72

Chapter 6

Selection of Neutron Capture Events

Figure 6.6: Distribution of cosα before (a) and after (b) the cluster cut. Hereα is the angle between any two hit vector combinations.

Figure 6.7: Distribution of Ncluster (a) and N10 − Ncluster (b). Definitionof Ncluster is given in the text.

73

Chapter 6

Selection of Neutron Capture Events(i.e. sum of all the hit vectors). The number of hits with θ > 90◦ is called
Nback.
For the same reason as using N10 − Ncluster instead of Ncluster, we
use N10 − Nback to form a cut, which is shown in Fig. 6.8. Events with
N10 − Ncluster < 7 are rejected. Furthermore, those backward going hits
are excluded for remain events in calculating other discriminating variables
such as Trms , φrms and θmean , which will be introduced in the next section.
Because some noise hits may happen in coincidence with the signal peakand some Cherenkov photons may be scattered away when propagating inwater, excluding the backward going hits help to make cleaner distributions
for signals.

Figure 6.8: Distribution of N10 − Nback.

Nlow
This cut is devised based on the consideration that some PMTs are more
likely to be hit than others for a given vertex position. As illustrated inFig. 6.9, the hit probability for the i-th PMT is
hit prob. ∝(cos θi )ef f −R /L
e i
Ri2

(6.1)

where Ri is the distance from the vertex to i-th PMT, θi is the incident
angle, (cos θi )ef f includes the angular dependence of PMT response, while74

Chapter 6

Selection of Neutron Capture Events

L is the attenuation length of Cherenkov light in water, which is taken as
90 m. Formula (6.1) defines the effective acceptance area for the i-th PMT
up to an irrelevant normalization constant for Cherenkov photons emitted at
the given vertex. When the vertex of the primary event is given, we knowthat some PMTs (e.g. large θ and/or small R) have larger hit probability
than the others (e.g. small θ and/or large R). Noise hits or low energy
backgrounds originated in other positions, however, do not follow this law.
In particular, noise hits can happen anywhere in the detector with similar
probability (assuming PMTs have a similar dark noise rate).

Figure 6.9: Illustration of the idea using Nlow. For a given vertex, hit
probability is not equivalent for different PMTs.
Nlow is calculated in the following way. First calculate the effective acceptance area for each PMT for a given vertex according to formula (6.1)
and then sort them in decreasing order. Select PMTs that have the largest
acceptance area which make up, say, 70% of the total acceptance. The rest
PMTs are said to have low hit probability. The number of hits with a low hit
probability is called Nlow. Note that for the same fraction of acceptance (e.g.
70%), the number of low hit probability PMTs is not the same for different
positions. For example, this number is 4972 for (0, 0, 0) m and 10132 for(14, 0, 15) m. So this cut is tighter near the detector wall, which is desirable
because it is observed that background level is much higher near wall thanat the center.
Left figure in Fig. 6.10 shows N10−Nlow distribution with acceptance=70%
for zone I (0 m2 < R2 < 40 m2 , 0 m < |Z| < 3 m), middle figure for zone II(140 m2 < R2 < 180 m2 , 12 m < |Z| < 15 m) and right figure includes all
events. We reject events with N10 − Nlow < 5. It is clear from Fig. 6.10
75

Chapter 6

Selection of Neutron Capture Events

that a larger fraction of background is rejected for events near the wall thanat center. However, the background level is still higher near the wall if using
the same acceptance for the whole detector. To make the background level
flat through the entire detector, we use position dependent acceptance, thechoice of which is shown in Fig. 6.11.

Figure 6.10: The distribution of N10 − Nlow for events in zone I (left), zone
II (middle) and all events (right). The definition of zone I and zone II isgiven in the text.

Figure 6.11: The choice of position dependent acceptance used in calculating
Nlow.

76

Chapter 6

6.3

Selection of Neutron Capture Events

Further Reduction

The hard cuts used in the pre-selection eliminates the bulk of backgrounds.
There are four more variables that can be used to further separate signal
from background.

N300
The 2.2 MeV γ event should be an isolated small timing peak sitting on the
PMT dark noises, as illustrated in Fig. 6.12 (a). Fig. 6.12 (b) shows anothertype of background. The 10 ns window picks up a peak which is part ofhit timings of some low energy event. In this case, there must be more hits
than expected dark noise around the N10 peak. We use N300 − N10 to lookfor excess of PMT hits around the N10 peak. The distribution is shown in
Fig. 6.13 (a).

Figure 6.12: Illustration of the definition of N300.

Trms
Trms is the root mean square (RMS) of PMT hit timings. For 2.2 MeV γ
events, the spread of hit timings is mainly driven by the PMT time resolution.
The distribution of Trms is shown in Fig. 6.13 (b).

77

Chapter 6

Selection of Neutron Capture Events

Figure 6.13: The distributions of N300−N10 (a), Trms (b), φrms (c), θmean (d).
The points represent signal (black) and background (red) histograms and thelines indicate the corresponding PDF’s.

78

Chapter 6

Selection of Neutron Capture Events

φrms
φrms is the RMS of azimuth angle of hit vectors, measuring the azimuth
uniformity of hits. It’s distribution is shown in Fig. 6.13 (c).

θmeanθmean is the mean angle between the hit vector and the estimated direction.
Fig. 6.13 (d) shows the distribution of θmean .
These four discriminating variables have weak correlation and little position dependence. Hence a global likelihood function can be formulated.
The PDF for each variable is obtained by a nonparametric histogram fitting
using the TMVA [103] package. All PDF’s are also shown in Fig. 6.13. The
likelihood ratio rL (i) for event i is defined byrL (i) =where
LS(B) (i) =LS (i)LS (i) + LB (i)4YpS(B),k (xk (i))

(6.2)

(6.3)

k=1

and pS(B),k is the signal (background) PDF for the kth input variable xk .
Fig. 6.14 shows the distribution of the likelihood ratio. Events with rL < 0.35
are rejected.

6.4

Summary of 2.2 MeV γ Cut Efficiency

Table 6.1 summarizes the cut efficiency after each cut, where all quoted
numbers for signal assumes true vertex. If the vertex is smeared according
to the scheme described in Sec. 6.1.1, the efficiency for signal after all cutsis 19.3%.
The efficiency variation in the detector is studied by dividing the detector
volume into 10×11 cells. As shown in Fig. 6.15, after the tuning of Nlow cut,
both the signal efficiency and background probability are quite uniform in
the entire detector volume. The 1-σ uncertainty is 1.0% and 0.1% for signal
efficiency and background probability, respectively.
The accuracy of the background probability is very important when applying the neutron tagging to data analysis. Time variation of the background probability is checked using availible random trigger data. Fig. 6.16
79

Chapter 6

Selection of Neutron Capture Events

Figure 6.14: Distribution of the likelihood ratio.

Table 6.1: Summary of efficiency after each cut step.
Cut
N10 > 7
N10 − Ncluster > 5
N10 − Nback > 6
N10 − Nlow > 4
likelihood ratio > 3.5

Signal (MC)
33.3%
31.3%
29.6%
21.2%
19.8%

80

Background (500 µs)
150.1%
23.8%
19.7%
3.9%
1.0%

Chapter 6

Selection of Neutron Capture Events

Figure 6.15: Efficiency variations in the detector for signal (left) and background (right). The statistical uncertainty in each cell is 0.4% and 0.1% forsignal and background, respectively.
shows the background probability thoughout the SK-IV period, where thebackground probability is (1.00±0.02)%.
Both the signal efficiency and background probability are evaluated usinga large sample and hence have a small statistical uncertainty, which is 0.04%
and 0.01%, respectively. In sum, the selection efficiency for the 2.2 MeV γ is(19.3 ± 0.04(stat.) ± 1.0(sys.))%. And the background probability for 500µs data is (1.0 ± 0.01(stat.) ± 0.1(sys.))%.

81

Chapter 6

Selection of Neutron Capture Events

Figure 6.16: Time variation of the background probability from random trigger data. The horizontal line indicates the average value.

82

Chapter 7
Validating Neutron Tagging
Efficiency Using an Am/Be
SourceThe neutron tagging efficiency evaluated with the MC sample in the previous
chapter will be verified in this chapter. An Am/Be radioactive source is used
to mimic the inverse beta decay reaction chain and to confirm the neutron
tagging efficiency. Such a test was firstly conducted in SK-III [77]. In that
test, however, due to the limitation of old electronics, only ∼120 µs data
could be taken after the prompt event, resulting in that the neutron tagging
efficiency can not be determined precisely. The same experiment is repeatedin SK-IV, dring which the AFT trigger (see section 2.4.3) gate width istemporarily enlarged to 800 µs, in order to obtain a more complete neutron
capture time spectrum.

7.1

Experimental Setup

The Am/Be source is embedded in a bismuth germanate oxide (BGO) scintillator cube. The detailed configuration of this apparatus is shown in Fig. 7.1.
The prompt and delayed event-pair is generated via
α + 9 Be → 12 C∗ + n
12 ∗C → 12 C + γ
n+p → d+γ

(prompt)(delayed).

(7.1)

Note that the reaction to the ground state of 12 C also exists, where no 4.43
MeV deexcitation γ is emitted. The intensity of the source is 97 µCi, leading83Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

to 87 Hz of 4.43 MeV γ emittion and 76 Hz of ground state transition [77].
The neutrons emitted in the ground transition have no associated prompt
signal, and thus appearing as a flat background to the prompt and delayed
event pair search. The BGO crystal is used to compensate the disadvantage
of low Cherenkov light generation for the 4.43 MeV γ in water. The observed
scintillation light is typically ∼1000 p.e.’s (see Sec. 7.2.1), which is capableof issuing a SHE trigger.
The experimental apparatus was firstly deployed at the center (35.3, 70.7, 0.) cm (A) of the tank. To estimate the source related background(e.g. ground transition neutron), a 10 Hz of 800 µs random data was also
taken without a trigger threshold. Additional data was taken with the source
located at (35.3, -1201.9, 0.) cm (B) and (35.3, -70.7, 1500) cm (C), but for ashorter time and without random trigger. Dummy data without the source
was also taken to evaluate accidental background.

Figure 7.1: Configuration of the experimental apparatus. The Am/Be sourceis embedded in the center of 8-piece BGO crystal, which is held together withan acrylic case.

7.2

Data Analysis

7.2.1

Selection of Prompt Scintillation Events

The prompt event of interest is that generated by the 4.43 MeV γ. Fig. 7.2
shows the totle p.e. distribution of prompt scintillation events that have SHE
trigger for the source at A (a), B (b) and C (c). The peak around ∼1000 p.e.
corresponds to the 4.43 MeV γ. Only events around this peak are selected
for the analysis. To avoid the neutrons coming from the previous scintillation
events, a good prompt event should have sufficient large time difference to theprevious event. Finally, there should be no overlapping scintillation events.
A sliding 200 ns window is used to search possible major timing peaks after
the prompt event. In sum, the selection criteria for prompt events are:84

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

1. 750 < totle p.e. < 1050 for source at A, 850 < totle p.e. < 1150 for B
and 900 < totle p.e. < 1150 for C.
2. Time difference to the previous event > 1.5 ms.
3. N200 (after the prompt event) < 50.

Figure 7.2: Total p.e. of the primary scintillation events for the source at A(a), B (b) and C (c).

7.2.2

Selection of Neutron Capture Events

The cuts introduced in the previous chapter are applied to select the delayed
neutron capture signal. Here we explain the details using data taken at A as
85

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

an example. The application to data taken at the other two locations is in asimilar fashion.
Pre-selection
Fig. 7.3 shows the N10 distribution after the pre-selection (see section 6.2).
Note that the delayed events associated with the prompt scintillation events
have a tail on the right. This significantly deviates from the expectation fora 2.2 MeV γ signal. Similar structure is also seen in the random trigger data
but not in dummy data. So there’s another apparatus related backgroundbesides that arised from the ground state transition . In total, there are three
types of backgrounds:• neutrons emitted in ground state transition.
• unknown source related background having larger N10.
• accidental background.
The time difference between the delayed event and the prompt event (∆T)
for all the backgrounds is flat (see Fig. 7.6 (a)), as opposed to the signal
which is exponential (Fig. 7.6 (b)). Hence the signal events can be extracted
by fitting the ∆T spectrum. Actually, the identical backgrounds also present
in the random trigger data and can be easily estimated for the case of sourceat the center. The difference between the scintillation correlated and therandom triggered delayed events gives the pure signal and can be comparedwith MC directly.
Further Reduction
Fig. 7.4 shows a comparison between data and MC for discriminating variables used in the further reduction, where all backgrounds are subtractedusing the random trigger data. A likelihood cut described in section 6.3 isthen applied and the distribution of final N10 is shown in Fig. 7.5. Simulation of the 2.2 MeV γ is justified by the good agreement between data and
MC.

7.3

Results

As mentioned above, the ∆T distribution of backgrounds is flat (Fig. 7.6(a)) and signal fraction can be extracted by fitting the ∆T spectrum. An

86

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

Figure 7.3: N10 of the Am/Be data after the pre-selection. Histrogram inblack represents MC, the blue line indicates the delayed signal that have theprompt scintillation event, the green line shows the events in the random
trigger data and the red line represent the accidental background from thedummy data.

87

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

Figure 7.4: Comparison of Am/Be data and MC for N300−N10 (a), Trms (b),φrms (c), θmean (d). Solid histograms represent MC and dots indicate theAm/Be data.

88

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

Figure 7.5: Comparison of N10 between the Am/Be data and MC after all
cuts applied.
unbinned maximum likelihood fit is performed using the following function:t

f = cs fs e− τ + cb (1 − fs )(7.2)

where fs is the signal fraction, τ is the mean neutron capture time in water
and, cs , cb are the normalization constant for signal and background, respectively. Since neutron is first thermalized before being captured, ∆T is thesum of thermalization time and capture time. And hence the ∆T distribution of signal is not simply exponential. But it can be shown that neutron
capture ∆T is well approximated by an exponential function when ignoring
the first few ten’s of µs data. In our fit, the starting point is 75 µs.
The fitting result for source at A is shown in Fig. 7.6 (b). As previously
stated, in this case, the signal fraction can be estimated using the random
trigger data, resulting in one less parameter to fit. A fit fixing the signal
fraction is shown in Fig. 7.6 (c), where the uncertainty on the neutron capture
time is reduced. Fig. 7.7 shows the fitting result for source at B (left) and C(right), respectively.
The neutron tagging efficiencies in the Am/Be data are summarized inTable 7.1. Data is in good agreement with MC. Table 7.2 lists the thermal
neutron lifetime in water for the three locations, which give the combined
result:τ = (203.7 ± 2.8)µs.
(7.3)
This agrees with the previous works (see e.g. [104]).

89

Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

Figure 7.6: (a) ∆T of backgrounds in the random trigger data. (b) Unbinned
maximum likelihood fit with the signal fraction as a free parameter. (c)Unbinned maximum likelihood fit with the signal fraction fixed. Shaded areain (b) and (c) represent the fitted and estimated background, respectively.

Table 7.1: Tagging efficiency of neutrons generated by the Am/Be source.
Source MC (%) ML fit (%) Estimated using random data (%)
A
19.2±0.1 19.0±0.3
19.0±0.2B
20.3±0.1 19.3±0.6
C
22.4±0.1 22.2±0.7-

90Chapter 7

Validating Neutron Tagging Efficiency using AmBe Source

Figure 7.7: Unbinned maximum likelihood fit for the source at B (left) andC (right).

Table 7.2: Fitted thermal neutron lifetime in water.
Source ML fit (µs)
A
201.8±4.7
A202.5±3.2
B203.0±8.6
C
213.1±8.891Comment
bkg. freebkg. fixed-Chapter 7

7.4

Validating Neutron Tagging Efficiency using AmBe Source

Conclusion

Given the good agreement between data and MC in various comparisons, weconclude that the neutron tagging efficiency obtained by the 2.2 MeV γ MC
is well reproduced by the Am/Be source data.

92

Chapter 8
Tagging Neutrons in
Atmospheric Neutrino Data
A detailed description of SK atmospheric neutrino data can be found elsewhere [105]. Here we only mention some jargons that will be used in our
discussion. Atmospheric neutrino events in SK are classified as fully contained (FC) if all of the energy is deposited in ID, partially contained (PC)
if a high energy muon exits ID and upward going muon (UPMU) which originated in the surrounding rock. In this chapter, we will focus on searching
the neutrons associated with the FC neutrino events.
For atmospheric neutrino events in SK, neutrons can be produced in thefollowing ways:
1. Direct production in neutrino interaction with water, e.g. inverse beta
decay.
2. Nucleon and pion interactions in oxygen before exiting.
3. Nucleon ejection in π/∆ absorption in oxygen.
4. Secondary interactions with water.
The simulated SK atmospheric neutrino events are generated using NEUT
(see [105] and references therein). Because neutrons were previously undetectable at SK, the production of the neutron was not fully simulated. Item
1 and 2 are already implemented in the current simulation in SK, item 4 ispartially implemented and item 3 has not been included yet.

93

Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

8.1

Observation of Neutrons in FC Data

8.1.1

Selection of Primary FC Neutrino Events

In this analysis, we use only data since when the AFT gate was changed to
500 µs to present. Events that have no associated AFT trigger are also notincluded. Finally, events with visible energy below 100 MeV are excluded.
The vertex resolution is estimated to be 30 cm for the single-ring events [105].

8.1.2

Searching Neutrons Associated with FC Events

Due to the complicated production mechanism, the yield of neutron capture
signal is unknown as a priori. The background probability, on the other
hand, is known to be ∼1% (see section 6.4). Fig. 8.1 shows the distributionsof discriminating variables after the pre-selection. The solid histograms show
the expected spectra obtained via:
hi = (1 − fb )hs,i + fb hb,i(8.1)

where hs(b),i is the normalized reference histogram for the ith variable forsignal (background), while fb is the fraction of background, determined byfb =Nprimary × Pb
,
Nn

(8.2)

where Nprimary is the number of primary events, Pb is the background probability and Nn is the total number of the neutron candidates after preselection. The reference histogram hs,i is from the 2.2 MeV γ MC and hb,ifrom the random trigger data, same as that presented in chapter 6. The
composite histogram hi is normalized to the data indicated by the dots in
Fig. 8.1.
The final N10 after the likelihood cut is shown in Fig. 8.2. The expected
spectra are reproduced by data fairly well. Fig. 8.3 shows the ∆T distribution together with the fitted neutron lifetime, which is consistent withthe measurements using the Am/Be source. These distributions collectively
demonstrate, for the first time, a clear observation of neutrons produced inneutrino interactions in a water Cherenkov detector.

8.1.3

Results and Discussions

Fig. 8.4 shows the neutron yield (number of neutrons in one event) as afunction of the visible energy of atmospheric neutrino events, where the data
has already been corrected by the neutron tagging efficiency. Similar energy
94Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

Figure 8.1: Distribution of N300 − N10 (a), Trms (b), φrms (c) and θmean (d)after the pre-selection. The dots represent the neutron candidates in FC
neutrino data and the solid histograms indicate the expected spectra which
is normalized to the data.

95

Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

Figure 8.2: Final N10 of the neutron candidates in the atmospheric FC data.
The solid histogram represents the expected distribution which is normalized
to the data as indicated by the dots.

Figure 8.3: Distribution of ∆T of the neutron candidates in the atmospheric
neutrino data . The dots are for the data, the curve shows the fitted lifetimeand the shaded histogram shows the expected accidental background.

96Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

dependence is seen in both MC and data. The deficit in MC is understood
to be due to that the neutron production in SK is not fully simulated in MC.
More information is carried by the multiplicity of neutrons, which is shownin Fig. 8.5.

Figure 8.4: The efficiency-corrected neutron yield as a function of visibleenergy. Solid histogram and dots are for the MC and data, respectively.

8.2

Background Rejection for Proton Decay
Searches

Backgrounds in the proton decay searches at SK arise mainly from the atmospheric neutrino interactions. The estimated background is 0.3 ± 0.04 ± 0.11
events for SK-I [5], which is not a big problem for SK-scale detector. However, the background becomes serious when going to the next generation
megaton-scale detectors. According to Ref. [5], the background rate is estimated to be 2.1 ± 0.3 ± 0.8 events/megaton·year. The sensitivity of proton
decay searches could be significantly improved if backgrounds can be further
reduced.
It turns out that the neutron tagging could reject a large fraction of remain background for the proton decay searches. No neutron is expected in
the final state of proton decay, while many background processes are accom-

97

Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

Figure 8.5: Neutron multiplicity in one event. Solid histogram and points
represent MC and data, respectively.
panied with neutrons. Here we take p → eπ 0 as an example, some backgroundprocesses are:(a) νe + p → e− + p + π + , π + induce π 0 through charge exchange(b) νe + n → e− + p + π 0(c) νe + n → e− + n + π + , π + induce π 0 through charge exchange(d) νe + n → e− + p + π 0 , p interacts in 16 O to give one neutron
Neutrons can be produced directly (c) or indirectly (d). Process (a) and (b)do not have neutrons in the final state and remains irreducible. Process (c)and (d) can be rejected if neutrons in the final stated can be identified.
We use the atmospheric neutrino MC to estimate the neutron production
in background processes for the proton decay searches. Fig. 8.6 shows the
distribution of the invariant proton mass versus the total momentum for the
events passed all the proton decay search criteria, except for the momentum
cut and the invariant mass cut. The proton decay signal region is defined as:
total momentum < 250 MeV/c, 800 MeV/c2 < total invariant mass < 1050
MeV/c2 . Since there are not sufficient statistics inside the signal box, we
use an enlarged area (indicated by the outer box in Fig. 8.6) to estimate theneutron production assuming those events having a similar profile as that in98Chapter 8

Tagging Neutrons in Atmospheric Neutrino Datathe signal region (inner box in Fig. 8.6). The neutron yield in these eventsis listed in Table 8.1, from which one can estimate how much backgroundcan be reduced by tagging neutrons in the final state. For example, ∼23%
backgrounds can be rejected by tagging neutrons in pure water. In case ofa Gd-loaded detector, ∼56% backgrounds can be rejected assuming neutron
tagging efficiency is 67.7% [77].

Figure 8.6: The total momentum versus the total invariant mass for 500
year-equivalent atmospheric MC. The inner box indicates the proton decay
signal region. The outer box represent the area that is used for an estimationof neutron production.

Table 8.1: Neutron production in proton decay backgrounds.
# of neutrons in one event
0
1
2
3
4
>=5

99

Fraction (%)
31.5
30.1
18.2
9.2
5.2
5.8

Chapter 8

8.3

Tagging Neutrons in Atmospheric Neutrino Data

Reconstructing 2.2 MeV γ’s

The low energy reconstruction tool BONSAI can not be directly applied to
the 500 µs data pack. However, once the 2.2 MeV γ peak is located using
the method described in chapter 6, it is possible to apply BONSAI to the
1 µs data around the 2.2 MeV γ peak. We use the 2.2 MeV γ sample
selected in the atmospheric neutrino data to check the performance of thereconstruction. Fig. 8.7 shows the reconstructed energy for the 2.2 MeV γ
candidates selected from atmospheric neutrino data and the 2.2 MeV γ MC.
Note that the reconstructed energy is larger than 2.2 MeV due to the N10> 7 selection. Distance between the reconstructed the 2.2 MeV γ vertex tothe primary event vertex is shown in Fig. 8.8. About half of the 2.2 MeV γ
candidates are reconstructed within 300 cm to the primary event vertex. The
correlation of the primary event vertex and the 2.2 MeV γ vertex is clearly
seen. On the other hand, the accidental background events do not have sucha tight correlation, as shown in Fig. 8.9. In principle, using the distance asa cut can improve the signal-to-noise ratio for the 2.2 MeV γ selection. But
no significant improvement is found for the ν̄e analysis (see chapter 10) by
requiring the distance less than 300 cm, because the distance cut reduce thesignal efficiency by a factor of two. The reconstruction of the 2.2 MeV γ’s ismainly for cross-checking the analysis method presented in chapter 6.

Figure 8.7: Reconstructed energy for the 2.2 MeV γ’s selected from atmospheric neutrino data (dots) and the 2.2 MeV γ MC (line).

100Chapter 8

Tagging Neutrons in Atmospheric Neutrino Data

Figure 8.8: Distance between the reconstructed 2.2 MeV γ vertex to theprimary event vertex for atmospheric neutrino data (dots) and the 2.2 MeV
γ MC (line).

Figure 8.9: Distance between the reconstructed 2.2 MeV γ vertex to theprimary event vertex for MC (solid) and accidental background (dashed).

101Chapter 9
Data Reduction
The primary goal of this analysis is to search for ν̄e signal, i.e. a prompt e+
and a delayed 2.2 MeV γ. This chapter introduces reduction steps that aim
at making a final sample of e+ candidates. The search of 2.2 MeV γ is only
conducted to the AFT events that follows a SHE event in this e+ sample andwill be discussed in the next chapter.
The ν̄e ’s are searched in the energy range of 12–30 MeV. Below 12 MeV,
there are too many spallation events even after the spallation cut, resulting in
too large an accidental background. Above 30 MeV, the atmospheric neutrino
background becomes dominant. Unless explicitly stated, distributions shownin this chapter are for events with energy below 30 MeV.

9.1

Data Sets and Run Selection

Super-Kamiokande data are collected in a unit of “run”. Each run has amaximum duration of 24 hours and is divided into subruns that each lasts
approximately for one minute. The whole data sets are classified into thenormal run, test run and various calibration run category. Only the normal
runs are used for physics analysis. At the beginning of SK-IV data taking, thegate width of AFT events was tentatively set to 350 µs and then changed to
500 µs after 28 November 2008 to improve the detection efficiency for neutron
capture events. The data used in this analysis span from 28 November 2008
to 27 December 2011, corresponding to a live time of 960 days after removing
bad runs or subruns that are described below.
All the normal runs are carefully checked offline and a list of bad runs/subruns
is complied. Such bad runs/subruns are removed in data analysis. Firstly,
runs with less than 5 minutes long data and subruns with less than 30 seconds long data are rejected. Secondly, runs with hardware or software trouble
102Chapter 9

Data Reduction

are removed. Thirdly, runs or subruns with event clusters or strange trigger
rates are regarded as bad and thus removed. The remaining data are thenprocessed by the reduction steps discussed in the rest of this chapter.

9.2

First Reduction

The first reduction consists of a number of loose cuts to eliminate the apparent non-e+ events. The main criteria for the first reduction are the following:
Calibration event cut: Calibration (e.g. LED, laser) and pedestal data
are taken regularly even during the normal data taking. These events
are indicated by special trigger flags and are removed.
OD cut: Events resulting from the ν̄e interactions in FV should have no OD
trigger. An OD trigger indicates a charged particle enters the detector
from outside. Hence, events with an OD trigger are removed. In addition, events with more than 19 OD hits are also rejected, regardlessof whether the OD trigger is present. Such events can occur if the OD
DAQ has a trouble.
Time difference cut: It is required that an event should occur at least
50 µs after the previous LE triggered event. This time difference cut
is mainly to remove the decay electrons from cosmic ray muons and“ringing” noise events that typically follow the very energetic muons.
For the SK-IV data analysis, the untagged muons (see section 4.4) arealso taken into account when calculating the time difference to theprevious event.
Noise event cut: PMT hits induced by electric noise tend to have a small
charge. To characterize the noise events, a noise ratio is defined as thefraction of PMT hits with |Q| < 0.5 p.e.. Events with a noise ratio
greater than 0.55 are rejected.
Fiducial volume cut: Many low energy events are reconstructed close to
the ID wall. Most of these events originate from the detector material
and the surrounding rock. To remove this background, a fiducial volume cut is applied to reject events that are reconstructed less than 200
cm from the ID wall. The fiducial volume defined by this cut is 22.5
kton.
Goodness cut: The goodness value GV returned by BONSAI indicates thequality of the vertex reconstruction. The calculation of GV is based103

Chapter 9

Data Reduction

on the PMT hit timings. Another goodness quantity, DirKS, evaluates
the PMT hit pattern in space. The DirKS measures the azimuthal
uniformity in the Cherenkov ring pattern. These two goodness values
are combined to form a cut called ovaQ (One dimensional variable of
Vertex and Angular reconstruction Quality) [98], which is defined as:
ovaQ = G2V − DirKS2 .

(9.1)

Events with a ovaQ less than 0.25 are removed.

9.3

Spallation Cut

The remaining events after the first reduction are dominated by the comic ray
muon induced spallation products. When energetic muons pass through thedetector, they can spall oxygen nuclei, producing unstable isotopes. Table 9.1
lists possible radioactive isotopes induced by cosmic ray muons at SK. The
β decay products from these isotopes can be reconstructed as e+ candidates.
In particular, some isotopes have a β-n decay mode, which can mimic ananti-neutrino signal. The maximum kinetic energy of spallation events is20.6 MeV. Considering the energy resolution effects, all events reconstructed
below 24 MeV are applied with the spallation cut.
Removing the spallation background is perhaps the most difficult task
in the data reduction. The basic idea to determine spallation is to lookfor correlations between the e+ candidate and the proceeding muon tracks.
There are four variables used in searching for the spallation activity:
dt:

The first variable, dt, is the time difference between the e+ candidate
and the proceeding muon, which is very powerful in identifying shortlived spallation products. The smaller the dt, the greater the likelihoodthat an event being spallation.

Ltran : The second variable, Ltran , is the transverse distance from the e+
candidate to the muon track. The isotopes are created along the muontrack and in general cannot travel far before decaying. A short Ltran
indicates spallation.
Llong : The third variable, Llong , is the distance from the dE/dx peak to where
the e+ candidate lies on the muon track (see Fig. 9.1). As mentioned
in section 4.4, spallation causing muons tend to peak at the spallation
occurring location in their dE/dx plot. Spallation events tend to havea smaller Llong .
104

Chapter 9

Data Reduction

Table 9.1: Possible radioactive isotopes induced by cosmic ray muons at SK.
Isotope
11
3 Li
13
8 O
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
Decay mode
0.0085β−β− + n0.0090β+ + p0.0110β+0.0138β−0.0174β−0.0202β−0.0236
β−
0.119
β−
−
β +n
0.127
β+ + p0.178
β−β− + n0.747
β− + n
0.77
β+
0.84
β−
2.449
β−
β−
7.134
β−
β−
13.8
β−
β−

105

Kinetic energy (MeV)
20.62
∼16
8∼14
16.38
14.55+6.09(γ)
13.44
13.37
11.71
9.67+0.98(γ)
3∼15
13.6
∼10
∼4
∼13.9
∼13.0
9.77
4.51+5.30(γ)
10.44
4.27+6.13(γ)
11.51
9.41+2.1(γ)

Chapter 9

Data Reduction

Figure 9.1: Illustration of the definition of Ltran and Llong for a spallation
activity induced by a cosmic ray muon.
Qpeak : The last variable, Qpeak , is the amount of light deposited around thedE/dx peak. Strong peaks in the dE/dx plot usually indicate spallation.

9.3.1

The Spallation Likelihood

The primary method to identify a spallation activity is to use a likelihood
constructed from the four variables described above. Muons are divided into
categories according to the Muboy fit results: single-through going, stopping,
multiple muons with a single track and multiple muons with more than one
tracks. Likelihood functions are provided for each muon type.
All proceeding muons within 30 seconds of the event time of the e+ candidate are checked for correlations. The muons occuring before the candidate
event is used as the spallation sample. And the muons occuring within 30
seconds after the candidate event which are used to evaluate the random correlation is used as the random sample. Distributions of the four variables, dt,
Ltran , Llong , and Qpeak , are first made separately for the spallation sample andrandom sample. Distributions obtained from the random sample represent
the random correlations. Spallation correlations are obtained by subtracting
the random sample distributions from the spallation sample distributions.

106

Chapter 9

Data Reduction

Fig. 9.2 shows both the spallation correlations and the random correlations
for the single through-going muons.

Figure 9.2: Distributions of the spallation likelihood variables dt (A), Ltran(B), Llong (C), and Qpeak (D) for the single through-going muons.
Both the spallation and random correlations are then parameterized byanalytic functions, which are used as PDFs to make the spallation likelihood.
The PDFs for the single through-going muons are also shown in Fig. 9.2. For
each muon that to be checked, an initial full likelihood is calculated as:
L=

X
i

log

PDFispall
PDFirandom

,

(9.2)

where i runs over dt, Ltran , Llong , and Qpeak . Fig. 9.3 shows the distributionsof the spallation likelihood for the single through-going muons.
In addition to the standard likelihood utilizing all the four variables, otherlikelihood functions are also used for special cases. For example, if the dE/dx
profile is found to have a bad quality, then the dE/dx information is not used.
In this case, a likelihood function constructed from only dt and Ltran will be
used. For the multiple muons with more than one tracks, each track will be
examined.

107

Chapter 9

Data Reduction

Figure 9.3: Distributions of the spallation likelihood for the single throughgoing muons.

9.3.2

Applying the Spallation Cut

Spallation events are rejected primarily using the spallation likelihood value.
A likelihood threshold is determined for each muon type. In addition, some
cuts on specific quantities are also present. For example, if the goodness ofboth Muboy and BFF fit for a single through-going muon is poor, the detector
is vetoed for 2 seconds. The spallation cuts are tighter for e+ candidate below
18 MeV than that above 18 MeV, as there are more longer lived spallation
products at lower energies. A detailed description of the spallation likelihoods
and the cut criteria can be found in Ref. [96].
The spallation cut was originally tuned for the SRN analysis using SKI/III data. It is confirmed that SK-IV distributions are very similar to SKI/III data, so the same likelihood and cut criteria are adopted for this analysis. Fig. 9.4 shows the correlations after applying the spallation cut, where no
statistically significant spallation events can be seen in the remaining data1 .
To evaluate the inefficiency of the spallation cut, a position dependent
inefficiency map is made using data. The overall inefficiency is obtainedusing the inefficiency map and the MC vertex distribution. The efficiencies
1

The spallation cut was initially optimized in attempting to completely eliminate spallation events above 16 MeV. It’s impractical to remove all spallation events at lower
energies because of the long lived isotopes. But it is expected that the performance of thespallation cut can be somewhat improved for analysis below 16 MeV and worth further
investigation.

108

Chapter 9

Data Reduction

Figure 9.4: Distributions of the spallation likelihood variables dt (A), Ltran(B), Llong (C), and Qpeak (D) for the single through-going muons after applying the spallation cuts. No discernible spallation events remain.

109

Chapter 9

Data Reduction

for events below and above 18 MeV is 82.6% and 91.3%, respectively.

9.4

External Event Cut

External gamma rays and radioactivity from the detector material can bereconstructed inside the FV. This background can be recognized by the inward going direction. To reject this background, an effective distance fromthe wall, deff , is calculated using the reconstructed vertex and direction (seeFig. 9.5). Small deff indicates that an event comes from outside of the FV.
The distribution of deff is shown in Fig. 9.6. All events with deff < 300 cm
are rejected. For events below 22 MeV, a tighter cut deff > 450 is applied.

Figure 9.5: Illustration of the definition of deff .

9.5

Solar Cut

Electrons elastically scattered by solar νe ’s are a background to this analysis.
The distinctive feature of solar νe events is that they carry the direction
information of the incident νe ’s. To reject solar νe events, we can utilize theangle, θsun , between the reconstructed event direction and the expected νedirection calculated from the position of the Sun at the event time. Althoughsolar 8 B νe ’s have an energy less than 16 MeV (the endpoint of hep neutrino
spectrum is 18.77 MeV), the scattered electrons can be reconstructed up
to 20 MeV due to the energy resolution effects. Therefore, all the eventsreconstructed below 20 MeV are applied with this solar cut. Fig. 9.7 shows
110Chapter 9

Data Reduction

Figure 9.6: The distribution of deff . Solid histogram indicates data, while
shaded histogram represents the MC of SRN (LMA model).
the distribution of cos θsun for the events below 20 MeV. The strong peaknear cos θsun = 1 indicates elastic scattering solar νe events. Events thathave cos θsun > 0.9 are rejected. There are still some solar events remain in
the data sample, as can be seen from the cos θsun distribution. But this is
not a problem in searching for ν̄e , since solar νe events do not have a delayed
2.2 MeV γ.

Figure 9.7: Distribution of cos θsun for events below 20 MeV.

111

Chapter 9

9.6

Data Reduction

Cherenkov Angle Cut

Low momentum heavy particles (mainly muons) created by atmospheric neutrinos can be reconstructed in the relevant energy region. Fig. 9.8 shows
the muon momentum versus the electron equivalent energy reconstructed by
BONSAI. Such muons are not ultra-relativistic particles, and hence shouldhave a smaller Cherenkov angle (see section 4.5) than that of the electrons(∼ 42◦ ). Fig. 9.9 shows the Cherenkov angle versus the reconstructed energy
for muons using the atmospheric neutrino Monte Carlo sample.

Figure 9.8: A 2-D plot of the muon momentum versus the reconstructed
electron energy. The sample is from the atmospheric neutrino Monte Carlo.
The Cherenkov angle cut also rejects multiple γ-ray events induced byneutral current atmospheric neutrino interactions. Events caused by themultiple γ-rays tend to have a larger Cherenkov angle (see section 4.5). In
addition, events consist of an electron and a γ exhibit a similar hit pattern. Therefore, the Cherenkov angle cut is also useful in further removing
spallation events that are due to a beta decay plus a γ emission (see Table
9.1).
Fig. 9.10 shows the Cherenkov angle distribution for data and SRN MC.
Muons, electrons, and gammas are clearly separated. Events with the Cherenkov
angle less than 38 degree or larger than 50 degree are eliminated.

112

Chapter 9

Data Reduction

Figure 9.9: A 2-D plot of the Cherenkov angle versus the reconstructed
electron energy for muons using the atmospheric neutrino Monte Carlo. Dueto the kinematics constrains, the Cherenkov angle of the muons should beless than 38 degree. Some muons are reconstructed with a larger Cherenkov
angle in the following cases:1) The number of PMT hits is too small toreconstruct the Cherenkov angle correctly; 2) A de-excitation γ is emitted in
the interaction of a muon with an oxygen nucleus; 3) The muon is too close
to the detector wall.

113

Chapter 9

Data Reduction

Figure 9.10: Distributions of the Cherenkov angle for data (solid) and SRN
MC (dashed). From left to right, the three peaks correspond to muons,electrons and gammas.

9.7Pre-/post Activity Cut

The candidate event should have a single timing peak, if we ignore the 2.2
MeV γ for the moment. Events with interactions closely before or after themain timing peak identified by BONSAI should be removed. We use a 15
ns sliding window to search for a possible second timing peak in the residual
time distribution. If the number of hits in the 15 ns window (N15 ) exceeds
the threshold, the event is rejected. This cut mainly removes events induced
by atmospheric muon neutrinos.
Most muons are removed by the Cherenkov angle cut. But if the muonand the decay electron are close in time and the muon generates less hits thanthe electron does, BONSAI may fit the electron timing peak. In this case,
the Cherenkov angle is reconstructed for the decay electron and will survive
from the Cherenkov angle cut. Such events can be recognized by looking fora muon timing peak before the electron timing peak. Fig. 9.11 shows theevent display for such an event. In addition, in rare cases the Cherenkov
angle of the muon can be misreconstructed above 38 degree. Such events
can be rejected by looking for an electron timing peak after the muon timing
peak.
A muon with an energy below the Cherenkov threshold emits no light114

Chapter 9

Data Reduction

Figure 9.11: Event display for a typical µ-e decay event. The two timing
peaks correspond to the parent muon and the decay electron, respectively.
The decay electron is reconstructed by BONSAI.
and hence is invisible to the detector. The decay electrons from invisible
muons are the major background in the previous SRN searches [83]. Suchdecay electrons can still be traced if a prompt γ is emitted after the muon
neutrino interacts with the oxygen nucleus. Since the lifetime of the muonis 2.2 µs, a prompt γ may exist previous to the decay electron within a fewµs. Fig. 9.12 shows the event display for a typical event of this type.
The wider event gate in SK-IV makes it ideal to catch possible pre-/post
activities. The 5 µs data before the main timing peak cover ∼90% of theprompt γ’s. The 35 µs data after the main timing peak contain all the decay
electrons. The entire 40 µs data pack is searched for a second timing peak.
Fig. 9.13 shows the N15 distribution before (left) and after (right) the main
timing peak. Events with N15 greater than 11 (19) before (after) the main
timing peak are rejected. The post-activity cut is looser for three reasons:first, the size of the data after the main timing peak is larger and hence themaximum N15 has a larger chance to fluctuate to a higher value; second,the decay electron is expected to generate a larger amount of hits than theprompt γ does; third, a 2.2 MeV γ may exist after the main timing peak.
The inefficiency of the pre-post activity cut is evaluated using the dummy
data and is 0.2%.

115Chapter 9

Data Reduction

Figure 9.12: Event display for a decay electron, the parent muon of whichis invisible. The small timing peak before the electron corresponds to thede-excitation γ-ray.

Figure 9.13: Distributions of the maximum N15 before (left) and after (right)
the main timing peak.

116

Chapter 9

9.8

Data Reduction

Pion Cut

Some events in the data sample are atmospheric neutrino induced pions withhigher momentum than those rejected by the Cherenkov angle cut (see section
4.5). The pion likelihood πlike described in section 4.5 is used to reject suchpion events. Fig. 9.14 shows the distribution of πlike for data and SRN MC.
Events with πlike > 0.58 are rejected.

Figure 9.14: Distribution of πlike .

9.9

Multi-ring Cut

Atmospheric neutrino interactions with water may create multiple charged
particles at the same time. Such events will survive from the pre-/post activity cuts since all the particles share a common timing peak. This backgroundcan be eliminated by looking for multiple Cherenkov rings. To that end, we
adopt the same ring counting tools as that are used in the ATMPD analysis [106], which return the number of rings and the direction of each ring.
Sometimes a fuzzy electron ring can be mis-treated as two distinctive rings,
especially for the low energy events. In such case, the directions of the tworings are typically very close to each other. To reduce inefficiency due to aring miscounting, we calculate the opening angle, θring , between the directionsof the two rings. Only events with θring > 60◦ are removed.

117

Chapter 9

9.10

Data Reductionµ/π Cut

It has been known that there are still a small amount of muons and pions (∼2 events per year between 10–90 MeV) remaining in the data sample evenwith all the above cuts applied. Prior to this work, these leftover µ/π’s wereregarded as an irreducible background [96]. It is observed in this analysis
that these µ/π events can be differentiated from electrons using the charge
information. We calculate the total charge of an event using the PMT hitswith residual time within a 50 ns window (Q50) and define the average hit p.e.
as the ratio of Q50 and N50. Fig. 9.15 shows a 2-D plot of Q50/N50 versus thereconstructed electron energy for µ, π and e using the atmospheric neutrinoMonte Carlo. It is clear that the Q50/N50 of µ/π events are significantly
larger than that of the electron. Events with Q50/N50 greater than 2.2 areremoved. Fig. 9.16 shows the event display of a typical µ/π event rejectedby this cut.

Figure 9.15: Distribution of Q50/N50 versus reconstructed electron energy
for µ (cross), π (triangle) and e (dot) from the atmospheric neutrino Monte
Carlo.

9.11

Reduction Summary

The final energy spectrum of e+ candidates is shown in Fig. 9.17. After all
reductions, the data sample still consists of a lot of spallation events and118

Chapter 9

Data Reduction

Figure 9.16: Event display of a typical µ/π event. The Q50/N50 value of
this event is 3.5.
solar neutrino events. Since no neutrons are produced in these events2 , they
do not pose a serious problem for the ν̄e search.
On the other hand, atmospheric neutrino events should be removed asmuch as possible, especially muons and pions, because such events are likely
to be accompanied by neutrons (see section 10.2). Unfortunately, there areat least three types of atmospheric neutrino backgrounds remaining in thedata sample: NC γ-rays, decay-e from invisible muons and νe /ν̄e CC events.
A detailed description of the atmospheric neutrino background can be foundin Ref. [96].
Most cut efficiencies are evaluated using the Monte Carlo. The efficiencyof the spallation cut is calculated using the inefficiency map, which is madefrom the data, and the vertex distribution of the Monte Carlo. The efficiencyof the pre-/post activity cut is calculated using the dummy data. Table 9.2
show the number of events after each cut and the efficiency of that cut. For
the SRN analysis, the energy range is 12–30 MeV, while for the solar ν̄eanalysis, the energy range is 12–20 MeV.
2

There are a few isotopes that have βn decay modes (see Table 9.1), which can mimic
the inverse beta decay reaction chain. However, most such spallation events either are
removed by the spallation cut due to the short lifetime of the parent isotope or have a too
low energy to contaminate the final data sample.

119Chapter 9

Data Reduction

Figure 9.17: Energy spectrum of e+ candidates after all reductions.

Table 9.2: Summary of reductions steps. The number of events after eachcut and the efficiency of that cut are listed.
Reduction stepFirst reduction
Spallation cut
External event cut
Solar cut
Chenrekov angle cut
Pre-/post activity cut
πlike cutMulti-ring cutµ/π cut
Total efficiency

SRN (12–30 MeV)
Solar (12–20 MeV)
# of events Efficiency # of events Efficiency
49288
>99%
49082
>99%
2417
86.7%
2249
82.6%
2148
94.6%
1987
92.6%
1625
95.0%
1476
94.5%
983
91.6%
939
87.0%
951
99.8%
933
99.8%
940
99.2%
925
99.6%
935
99.3%
920
99.7%
934
99.8%
920
100.0%
70%
62%

120

Chapter 10
Data Analysis and Results
This chapter presents an analysis of the neutron production in the low energy
data and the searches of supernova relic neutrinos and solar ν̄e ’s.

10.1

Efficiencies and Systematic Uncertainties

To identify ν̄e ’s via the inverse beta decay reaction, a search of the 2.2 MeV
γ is conducted after each e+ candidate in the final sample obtained in theprevious chapter. The first 2 µs data following the prompt e+ are excluded
to avoid overlapping with the e+ event. Therefore, the data size used for the
2.2 MeV γ search is 535 µs, covering ∼92% of all the neutron captures. The
neutron tagging efficiency presented in section 6.4 should be corrected by afactor of ∼92%, resulting in an efficiency of n = 17.8% to observe the 2.2
MeV γ in the time window 2 – 535 µs.
The dominant contribution to the systematic uncertainty on n comesfrom the position dependence. Since the inverse beta decay events are rare,
any possible non-uniformity of the neutron tagging efficiency must be taken
into account. The position dependence of n is evaluated by dividing the FV
into 10×11 cells (see section 6.4). The 1-σ uncertainty is found to be 1%.
The 1% accidental background probability shown in section 6.4 is for 500µs data, which can be scaled to calculate a different size of data since thebackground probability is flat in time. So the accidental background probability for 535 µs data is Pb = 1.07%. The position dependence and thetime variation can induce a (relative) 10% uncertainty on the backgroundprobability. The primary events are uniformly distributed in the FV andin the operation period. Therefore, the systematic uncertainty on the background probability is negligible. To be conservative, we assign a (relative)
121

Chapter 10

Data Analysis and Results

10% uncertainty to the background probability.
The efficiency of the primary event (e+ ) is given in Table 9.2. Systematic
uncertainties on e+ originate from the fiducial volume (1%), the live time
calculation (0.1%), the inverse beta decay cross section (1%) and the data
reduction (3.1%). The uncertainty on data reduction is quoted from theprevious SRN study [96] since the cuts used are very similar. Individual
contributions are added in quadrature and the total uncertainty on e+ isrounded to 4%. The total efficiency of observing an inverse beta decay signal( tot = e+ · n ) and its systematic uncertainty are listed in Table 10.1.
Table 10.1: Total efficiency of observing an inverse beta decay signal.
Signal tot Sys. uncertainty
SRN 0.125
0.011
Solar 0.110
0.010

10.2

Neutron Production in Low Energy Data

This section provides a general description of neutron production in the low
energy data at SK. The event signature of the IBD reaction is very clear,so we will focus on the non-IBD events, i.e. events in the side bands. Since
the neutron production in the side bands are much more complicated anddifficult to quantify, our discussion is rather qualitative.
We first examine two types of events rejected by the Cherenkov angle
cut: the µ-like events (Cherenkov angle < 38◦ ) and the isotropic events(Cherenkov angle > 50◦ ). Table 10.2 lists the number of primary events,
the expected accidental background and the number of observed neutrons
for both types of events. Fig. 10.1 (10.2) shows the number of observed
neutrons as a function of the reconstructed electron energy of the primaryµ-like (isotropic) event. A clear excess of neutron candidates is observed inboth types of events. Fig. 10.3 shows the time difference between the delayed
event and the primary event (∆T ), which is fit by an exponential distribution
with τ = (195.4 ± 47.8)µs. The exponential structure of ∆T confirms thatthe delayed signal is indeed the 2.2 MeV γ released in neutron captures.
Obviously, muon anti-neutrinos can produce neutrons throughν̄µ + p → µ+ + n.

(10.1)

Among all µ-like events, µ+ (created by ν̄µ ) accounts for about 30%. Therefore, ∼40 neutrons are produced via reaction (10.1). But reaction (10.1) is
122

Chapter 10

Data Analysis and Results

Table 10.2: Number of neutrons observed in the side bands.
Event type Primary events Accidental bkg. Observed neutronsµ-like140
1.48
21
Isotropic
487
5.14
46

Figure 10.1: Neutrons observed in the µ-like events as a function of thereconstructed electron energy.

123Chapter 10

Data Analysis and Results

Figure 10.2: Neutrons observed in the isotropic events as a function of thereconstructed electron energy.

Figure 10.3: Distribution of neutron capture time observed in the µ-likeevents and the isotropic events. Shaded histogram indicates the expected
accidental background. Curve shows the unbinned maximum likelihood fit
to data.

124

Chapter 10

Data Analysis and Results

not the only source of neutrons in the µ-like events. Taking into account theneutron tagging efficiency, there should be about 110±25 neutrons producedin the 140 µ-like events. Therefore some other processes must contributeto the neutron production. The incident muon neutrino may undergo thefollowing interactions:ν̄µ + 16 O → µ+ + 16 O + π − ,νµ + 16 O → µ− + 16 O + π + .

(10.2)(10.3)

If the pions produced in these reactions are absorbed in the oxygen, protons
and neutrons might be ejected out of the oxygen. Furthermore, pions arelikely to produce neutrons when propagating in water. When a µ− gets
captured, neutrons can be produced via the following reaction chain:µ− + 16 O → νµ + 16 N ∗ ,16 ∗N → 15 N (14 N ) + n(2n).

(10.4)(10.5)

Also π − capture on 16 O can result in neutron production.
The isotropic events with energy below 14 MeV are dominated by spallation products (see section 9.6). If we consider events above 14 MeV only, thedata suggests that 184±33 neutrons are produced in the 122 isotropic events.
The isotropic events mainly originate from the NC neutrino interactions. The
most important process is the NC elastic scattering:ν + n → ν + n,

(10.6)

Gamma-rays and secondary neutrons can be produced when the energetic
outgoing neutron interacts with water. Here the γ-rays serve as the primary
event.
Besides the µ-like events and the isotropic events, neutrons are also foundin the events rejected by the pre-/post activity cut, the πlike cut, the multiring cut and the µ/π cut. Since none of these cuts are 100% effective, a small
leakage of the atmospheric neutrino events in the signal region may cause aproblem when applying neutron tagging to search for ν̄e ’s. The known major
background components in the final sample are: decay-e from the invisible
muon(created in νµ /ν̄µ CC), νe /ν̄e CCQE and NC elastic process. A quantitative treatment of neutron yield in these backgrounds requires an accurate
simulation of neutron production and propagation in water. Unfortunately,some relevant processes are omitted in the current SK Monte Carlo, because
the 2.2 MeV γ was previously not observable at SK. A complete simulation regarding the neutron production and propagation in water is eagerly
awaited.
125

Chapter 10

Data Analysis and Results

Even with the qualitative discussions presented above, two important
conclusions can be drawn. First, the neutron correlated CC backgrounds are
not limited to the ν̄e and ν̄µ CCQE processes. Neutrons can be produced inother CC reactions and both the neutrino and the anti-neutrino may contribute. Second, the NC elastic events are a very important background witha high neutron yield. The NC elastic background is particularly dangerous
because they lie in the energy region where the SRN interactions most likely
to occur.
As a closing remark to this section, we emphasize that there are some important differences between the atmospheric neutrino backgrounds and thetrue inverse beta decay signal. The signal of interest is ν̄e ’s with energy .30
MeV, which interact primarily with free protons. The outgoing neutron has avery low momentum and will be captured within ∼20 cm. The neutrons produced in the atmospheric neutrino backgrounds, on the other hand, typicallyhave a momentum of a few hundreds of MeV/c, which can travel a significant
larger distance before being captured. Therefore, if the vertex of the neutron
capture event can be precisely reconstructed, the displacement of the neutron
capture vertex can be used to differentiate atmospheric neutrino backgrounds
from the true inverse beta decay signal. Furthermore, atmospheric neutrino
backgrounds, especially the NC background, are often accompanied by multiple neutrons. Hence, atmospheric neutrino backgrounds can be further
rejected if all the produced neutrons are detected.

10.3

Search for Low Energy ν̄e’s

In the e+ candidate sample obtained in the previous chapter, 14 neutrons
are observed out of 12 events. Fig. 10.4 shows the energy distribution for
the 12 primary events with neutron(s) tagged, which is consistent with the
expected accidental background. In absence of a ν̄e signal, the upper limits
will be set at the 90% confidence level.
As discussed in the previous section, there are also atmospheric neutrino
induced backgrounds. Such backgrounds are difficult to quantify and will be
neglected in this analysis. Only the accidental background is considered forsetting the upper limits, rendering the results conservative.
Due to the limited statistics, there is no way to model a reliable PDF
for the accidental background. So a spectral fitting is impractical in thiscase. Instead, we adopt a simple counting method and set the upper limits
based on Poisson statistics. The number of primary e+ candidates (Ne+ , see
Table 9.2), the number of expected accidental background (nbkg = Ne+ × Pb )and the number of observed delayed signal (nobs ) are shown in Table 10.3.
126Chapter 10

Data Analysis and Results

Figure 10.4: Energy distribution of the candidates. Dots show the observed
events with at least one neutron tagged. The histogram represents the expected accidental background.
The upper limits are computed using the Rolke method [107], which uses
the profile likelihood to handle uncertainties on the background expectationand the efficiency. Specifically, the limit is calculated using TRolke1 , whichtakes as inputs nobs , nbkg , uncertainty on nbkg (our generous 10% uncertainty
increases the limit by only ∼2%), tot and uncertainty on tot .
Table 10.3: Number of observed candidates and expected background.
SRN (12–30 MeV)
Solar (12–20 MeV)

10.3.1

Ne+
934
920

nbkg
10.0
9.8

nobs
12
10

Supernova Relic Neutrinos

The efficiency-corrected 90% C.L. upper limit is calculated to be N90 = 71.5
events for the SRN ν̄e signal. This can be translated into a limit on theannual event rate:
365 days0
N90 = N90 ×= 27.2 events / 22.5 kton · year,(10.7)
live time1

A tool available in ROOT [108].

127

Chapter 10

Data Analysis and Results

where the live time is 960 days.
0
The upper limit on the SRN flux F90 can be derived from N90 using thefollowing simple relation:
0

F90
N90
=
,
FmodelNprediction(10.8)

where Fmodel is the total flux of a certain model and Nprediction is the predicted
annual event rate in the energy range of 12 MeV < Ee+ < 30 MeV. From
Table 5.1, the annual event rate predicted by the LMA model and the HBD 6
MeV model is 4.15 and 4.36 events/22.5 kton · year, respectively. Therefore,
F90 =

27.2
× FLMA = 6.5 × FLMA ,4.15(10.9)

or
27.2
× FHBD 6 MeV = 6.2 × FHBD 6 MeV .
(10.10)4.36This limit is 2.2 times smaller than that obtained by KamLAND [79]2 , thelargest operating low energy anti-neutrino detector.
The current most stringent limit on the SRN flux is obtained from theSK-I/II/III data by searching for e+ singles above 16 MeV. The combined
limit is only ∼2 times of the model prediction [96]. Although our limit is lessstringent, this is the first time at SK that the analysis goes below 16 MeV
using a coincident detection technique.
F90 =10.3.2

Solar ν̄e

For solar ν̄e , the upper limit on the annual event rate is0

N90 = 22.7 events / 22.5 kton · year.

(10.11)

From Table 5.2, the expected annual event rate is 503 events/22.5 kton · year
assuming 1% νe → ν̄e conversion probability. The ν̄e flux upper limit is22.7
× 10−2 × FBP04 = 4.5 × 10−4 × FBP04 ,(10.12)503
where FBP04 is the solar νe flux predicted by BP04 SSM. Due to the powerfulbackground reduction by neutron tagging, this limit is about 20 times more
stringent than the SK-I result [85]. However, our limit is less strict than
KamLAND’s. This is mainly because of our high analysis threshold.
F90 =

2

The KamLAND limit is 36 times the LMA model. However, the old flux for the
LMA model is used in that calculation. The author of the LMA model increased the flux
prediction by a factor of 2.56 due to the change in the star formation rate [109]. Therefore,
the KamLAND limit corresponds to 14 times of the revised LMA prediction.

128

Chapter 10

10.3.3

Data Analysis and Results

Model Independent ν̄e Flux Limit

Both searches of the supernova relic neutrino and the solar ν̄e describedabove are model dependent. We also calculate model independent upper
limits for ν̄e flux with 1 MeV energy bins. Here we approximate the ν̄eenergy by Eν̄e ' Ee+ + 1.3 MeV. The 90% C.L. upper limits on the numberof events are calculated for each bin and the corresponding flux upper limits
are computed byN90
cm−2 s−1 ,(10.13)
φ90 =T · Np · σ̄ · 
where T is the live time in seconds, Np is the number of free protons, σ̄ isthe inverse beta decay cross section at the center of the energy bin and  isthe efficiency to detect both the primary signal and the delayed 2.2 MeV γ.
Fig. 10.5 shows the upper limits for ν̄e energy in the 13.3 – 21.3 MeV range(e+ energy 12 – 20 MeV). Results from SK-I and KamLAND are also shownfor comparasions. SK-IV limits are almost two orders of magnitude better
than SK-I owning to the powerful background reduction by neutron tagging.
SK-IV limits are already comparable to (or better than) KamLAND’s with
only ∼40% of KamLAND’s live time. We conclude that in the positronenergy range of 12 – 20 MeV, SK is operating as a competitive ν̄e detector.

Figure 10.5: Model independent 90% C.L. upper limits on ν̄e flux from SKIV (black line). Limits from SK-I (green line) and KamLAND (red line) arealso shown for comparasions.

129

Chapter 11
Summary and Outlook
11.1

SummaryThis thesis presents the first study of neutron tagging in a water Cherenkov
detector and a search of low energy electron anti-neutrinos of extraterrestrial
origin using this newly established technique.

Neutron Tagging in Pure Water
The 2.2 MeV γ released in neutron capture on free protons is previously
unobservable at SK. A forced trigger scheme has been implemented at SK-IV
to take 500 µs data after each primary trigger, covering ∼92% of all neutron
captures. The most challenging work is to extract the faint 2.2 MeV γ signal
from the 500 µs data pack. A set of selection criteria are devised, yielding
a 19.3% efficiency at 1%/500 µs accidental background level. The signal
efficiency is derived from Monte Carlo, while the background probability isevaluated using real data.
An Am/Be neutron source is used to verify the delayed coincidence detection concept and the neutron tagging efficiency in SK. Distributions of
the discriminating variables are compared between the Am/Be data andthe Monte Carlo and good agreements are found in all cases. We have observed the exponential neutron capture time distribution with fitted lifetimeτ = (203.7 ± 2.8)µs. The neutron tagging efficiency from Am/Be data isfound to be in good agreement with Monte Carlo. Therefore, we conclude,
for the first time, that neutrons can be observed in a large water Cherenkov
detector.
Shortly after the start of SK-IV, neutrons produced in atmospheric neutrino interactions were observed for the first time in a water Cherenkov
detector. As of this writing, a high statistics of neutron signal has been130

Chapter 11

Summary and Outlook

accumulated. This data sample is used to further validate the 2.2 MeV γ
Monte Carlo and the neutron tagging data analysis. In addition, this observation provides the first data to study background reduction for proton
decay searches using neutron tagging.

Study of Low Energy Electron Anti-neutrinos
A number of new physics topics can be studied at SK once the neutron tagging is in place. This thesis focuses on searching for supernova relic neutrinosand ν̄e from the Sun. Some other interesting topics worth investigation are
outlined in section 11.2.1.
The supernova relic neutrinos are believed to lie just below SK’s reach.
Previously, SK’s sensitivity is limited by the spallation products and theatmospheric neutrino backgrounds. The most promising way to improveSK’s sensitivity is to use neutron tagging to identify ν̄e . As the first attemptin this direction, we applied neutron tagging to search for ν̄e ’s in the energy
range of 12–30 MeV. No appreciable signal events are observed. So we set
upper limits on the flux for supernova relic neutrinos and solar ν̄e . The 90%
C.L. flux upper limit for SRN is about 6 times the model predictions. The
90% C.L. flux upper limit for solar ν̄e is 4.4 × 10−4 times the solar νe flux.
We also presented model independent upper limits on ν̄e flux for 13.3 MeV< Eν̄e < 21.3 MeV, which provide the most sensitive result in the world.
In addition, neutron correlated low energy background for the SRN searchhas been intensively studied by means of a side band method, which enhancesvarious background sources on purpose. By counting neutrons produced inµ-like events and isotropic events, we found the background level to the
SRN search is higher than previously expected. The background can bebetter quantified with more upcoming SK-IV data. This will provide useful
information for designing future experiments.

11.2

Outlook

Neutron tagging in water Cherenkov detectors is a relatively new idea. Work
presented in this thesis is the first comprehensive study on this subject.
Prospects of neutron tagging and its application to physics in water Cherenkov
detectors are briefly outlined below.

131Chapter 1111.2.1

Summary and Outlook

SK-IV

Note that the predicted SRN event rate in the energy range of 12–30 MeV isonly 4.15 events/22.5 kton · year. So the expected number of SRN events is∼ 5 after all reductions (including neutron tagging) for 10 years of operationof SK. On the other hand, the accidental background is about 38 for 10
years. If we consider the energy range of 14–30 MeV, the expected signal andaccidental background are 4 and 6 events, respectively, for 10 years. There
are also at least a few atmospheric neutrino background events. Therefore,
in any case, it is unlikely to detect the supernova relic neutrino at SK withneutron tagging in pure water in near future.
Nevertheless, SK-IV provides the only available data for neutron tagging
study in water Cherenkov detectors. The SK-IV data can be used but not
restricted to study the following topics.
Background study for future SRN search
The background analysis presented in section 10.2 should be expanded whenmore data is available. A complete simulation of neutron production at SK ishighly desirable. A good understanding of atmospheric neutrino backgroundto the ν̄e signal is very important to the GADZOOKS! project (see section
11.2.2).
The cosmic ray muons can produce 9 Li. The β-n decay of 9 Li is an
important background to the inverse beta decay reaction. The contaminationof 9 Li below 12 MeV is no longer negligible. Little is known about the 9 Li
yield at SK, because currently there is no existing data about 9 Li production
in water. SK-IV data could provide useful information regarding 9 Li. If
the 9 Li yield is large, it can be measured at SK. Otherwise, the 9 Li may beneglected for ν̄e analysis. A preliminary study has been carried out, where
no evidence of 9 Li is found. It should be noted that the 9 Li yield in water ismuch smaller than in liquid scintillator [110].
Muon induced neutrons
Cosmic-ray muon induced neutrons have significant impact on undergroundlow energy experiments. Accurate prediction of this background using Monte
Carlo has not been achieved yet, see e.g. Ref. [111]. Currently all available
data come from liquid scintillation detectors (see e.g. Ref. [110]) and significant discrepancies exists between data and Monte Carlo. It is possible to
make a first measurement of muon induced neutrons in water at SK-IV.
Actually the muon induced neutrons have already been observed at SKIV. There’s no 500 µs data taken right after the muon event. However,132

Chapter 11

Summary and Outlook

the 500 µs data are taken after spallation events as long as the β decay
electron has sufficient energy to issue the SHE trigger. If a spallation event
happens close enough to the muon (< 1 ms), muon induced neutrons canbe catched in the 500 µs data that follows the spallation events. Althoughmuon induced neutrons can be observed in this way, its difficult to precisely
calculate the neutron yield. It is necessary to change the trigger condition totake data right after the muon to cover all neutrons induced by muons. It isalso needed to change the 2.2 MeV γ search method in order to identify all
neutrons produced along the muon track.
Reactor ν̄e
There are ∼ 30 reactor ν̄e ’s interact at SK each day. In order to observe
reactor ν̄e , we need to push down the analysis threshold down to, say, 8
MeV. The accidental background will be much higher, but it is possible tosee evidence of reactor neutrinos as long as there are a few hundreds reactorν̄e events above 8 MeV each year. First observation of reactor ν̄e in a water
Cherenkov detector will be certainly very interesting.
Atmospheric neutrinos
Although both high energy ν and ν̄ can create neutrons, there is some asymmetry between the neutron yield. Neutron tagging may help to divide thedata into a ν-enhanced sample and an ν̄-enhanced sample to study the difference in the oscillations of neutrinos and anti-neutrinos.
Neutrons observed in the atmospheric neutrino data can be used to tune
the neutron related part in the Monte Carlo. Once the neutron production in
the Monte Carlo agrees with data, it can be used to predict how many backgrounds can be rejected by neutron tagging for the proton decay searches.

11.2.2GADZOOKS!

Tagging neutrons by adding into SK 0.2% gadolinium compound (GADZOOKS! [75]) was proposed nearly a decade ago. The GADZOOKS! projectis very attractive not only because the neutron tagging efficiency is ∼ 4 times
higher, but also because the accidental background probability is as low as
10−4 [77], allowing to lower the analysis threshold.
But before putting Gd into SK, several technical issues have to be settled.
A dedicated prototype tank has been constructed at Kamioka Observatory
for Evaluating Gadolinium’s Action on Detector Systems (EGADS). Key
issues being addressed include: effects of Gd on water transparency and133

Chapter 11

Summary and Outlook

detector components, how to dissolve and remove Gd, and how to modify
the water circulation system to remove other impurities while keeping Gd in
the detector. Based on the performance of EGADS, a decision on the futureof GADZOOKS! will be made in the year of 2013.
If GADZOOKS! can be realized, SK will turn into a very effective giant ν̄edetector. All physics mentioned above can be better done in the Gd-loaded
SK. In particular, first observation of the supernova relic neutrinos is highly
expected.

134

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