KYOTO UNIVERSITY

Study of Neutrinos from Monopole-Catalyzed Proton Decay in Super-Kamiokande
DISSERTATION

submitted in partial satisfaction of the requirements
for the degree of

MASTERin Physics

byFeng Jiahui
2021© 2021 Feng Jiahui

DEDICATIONTo Feng Familyii

TABLE OF CONTENTS
Page
LIST OF FIGURESv

LIST OF TABLES

viii

ACKNOWLEDGMENTS

ix

ABSTRACT OF THE DISSERTATIONx

1 Introduction
1.1 The magnetic monopole . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 The Dirac monopole . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Grand Unified Theory monopole . . . . . . . . . . . . . . . . . . . . .
1.1.3 The Rybakov effect . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Review of Magnetic monopole searches . . . . . . . . . . . . . . . . . . . . .
1.2.1 Monopole flux limit from the electromagnetic induction experiment .
1.2.2 Monopole flux limit from the electromagnetic energy losses experiment1.2.3 Monopole flux limits from theory . . . . . . . . . . . . . . . . . . . .
1.2.4 Limit from the previous search in Super-Kamiokande . . . . . . . . .

1
1
2
2
4
5
6
6
7
8

2 Super-Kamiokande Experiment
2.1 Detector Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 The structure of the Super-Kamiokande Experiment . . . . . . . . . .
2.1.2 History of the Super-Kamiokande Experiment . . . . . . . . . . . . .
2.1.3 Cherenkov light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Electronics and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Water and Air Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
16
18
20
25
26

3 Event Reconstruction
3.1 Vertex Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Momentum Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Michel Electrons Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28
29
31
32
34
35
36

iii

4 Event Simulation
4.1 Monogenic Neutrino Simulation . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Atmospheric Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 CC/NC elastic and quasi-elastic scattering . . . . . . . . . . . . . . .
4.3.2 CC/NC single meson and gamma production . . . . . . . . . . . . . .
4.3.3 CC/NC coherent pion production . . . . . . . . . . . . . . . . . . . .
4.3.4 CC/NC deep inelastic scattering . . . . . . . . . . . . . . . . . . . . .
4.4 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37
38
41
43
45
46
47
47
48

5 FC Reduction
5.1 The First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 The Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 The Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 The Final Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49
50
50
51
53
53
55

6 Sensitivity study
6.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Sample Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Spectral Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Fitting Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Sensitivity study . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56
56
56
60
64
64
65
66

7 Summary and Future Prospects

84

Bibliography

86

Appendix A MCP PMT Flasher Measurement

92

iv

LIST OF FIGURES
Page
1.1
1.2
1.3

One possible structure of a Grand Unified Theory monopole. [10] . . . . . .
Heuristic diagram of monopole-induced proton decay. [1] . . . . . . . . . . .
The upper limits on the monopole flux as a function of monopole velocity, redline is the previous monopole analysis in Super-Kamiokande by using indirect
proton decay at 90%C.L , βM . Catalysis cross section (σ0 =1mb) and monopole
mass (MM = 1016 GeV) are assumed for indirect searches.[68] . . . . . . . .

2.1
2.2

Overview of the Super-Kamiokande detector.[38] . . . . . . . . . . . . . . . .
Photo from the bottom of the tank renovation in 2018. The upper part in thecenter of the photo is the inner water tank, and the lower part is the outerwater tank.[67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 A photo looking up from the bottom of the OD. An 8-inch PMT is attachedto the wall on the inner tank side, and the outer tank is covered with a white
Tyvek sheet.[67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Frame structure that supports PMT. [67] . . . . . . . . . . . . . . . . . . . .
2.5 Outline drawing of Cherenkov light. [3] . . . . . . . . . . . . . . . . . . . . .
2.6 Schematic diagram of the operating principle of PMT [72] . . . . . . . . . .
2.7 Quantum efficiency distribution of 20-inch PMT and relative Cherenkov light
distribution when passing through 15 m of pure water. [66] . . . . . . . . . .
2.8 20-inch PMT. [66] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Timing chart of QTC operation QBEE for SK-IV. From [51] . . . . . . . . .
2.10 Block diagram of data collection system until PMT signal is recorded on disk
From. [74] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6

3
5

11
16

17

17
19
20
22
24
24
26
26

An observed charge distribution as a function of Cherenkov opening angle(top) and its second derivative (bottom). [51]. . . . . . . . . . . . . . . . . . 30
An outline drawing of detecting additional rings. The shaded and dashedcircles stand for the Cherenkov ring and rings with 42o half angles [51]. . . . 31
Typical e-like ring pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Typical µ-like ring pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
PID likelihood distribution for data and atmospheric MC with a visible energy
below 1.33 GeV. Good separation between e-like and µ-like events is seen. [62]. 33
RTOT vs. momentum table for the electrons (blue crosses), muons (redcrosses) and the kaons (black crosses). [40] . . . . . . . . . . . . . . . . . . . 35

v

4.1
4.2
4.3
4.4
4.5

4.6

4.7
4.8

5.1
5.2
5.3
6.1
6.2
6.3

6.4

6.5
6.6
6.7
6.8

Abundances of the isotopes in the Sun as a function of mass number. Even
numbered nuclides are shown in blue, odd-numbered nuclides in red. [44] . .
Monogenic Neutrino Momentum Distribution, assuming 20,000 monopole neutrino is generated by MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Monogenic Neutrino Flavor Distribution, assuming 20,000 monopole neutrino
is generated by MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of cosmic ray interactions in the atmosphere. [45] . . . . . .
Calculation of the neutrino flux ratio (νµ + ν¯µ ) / (νe + ν¯µ )to the energy of
atmospheric neutrinos by the group [7]. The solid line is from Honda, thewavy line is from Bartol, and the dotted line is from Fluka. . . . . . . . . . .
The simulated cross sections for ν(ν̄) interactions in NEUT with data. The
red, blue, green, and black solid lines correspond to (quasi-)elastic scattering,
single π K, η, γ production, deep inelastic scattering, and the total of threeinteractions. [36] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CCQE reaction by νe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculated cross-sections of CCQE scattering with experimental data as thefunction of neutrino energy. The solid and dashed lines show the calculated
cross-sections for free and bound targets. [29] . . . . . . . . . . . . . . . . .
Schematic representation of the fully contained, partially contained, upwardgoing stopping and through-going muon event classes at Super-K.From [73].
Schematic figure of Cable hole Muon and VETO counter [37]. . . . . . . . .
Schematic diagram of the OD tank, ID tank and FV of the Super-Kamiokande
detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39
40
41
41

42

44
45

46
49
52
55

Distribution of neutrons in the final state from sub-GeV nuebar and numubar
CCQE interactions. Both lines are normalized by area. . . . . . . . . . . . . 57
schematic diagram about the steps for how to select the FC data to different
Sub-GeV samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59cos(θsun ) distributions of signal MC and BG atmospheric neutrino.Normalization
for the signal is the number of MC events, which is about 20,000 event, related
to the Parker Limit. νe and νµ and background is normalized by the SK-IV
livetime, which is 3244 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Momentum distributions of signal MC and BG atmospheric neutrino. Normalization for the signal is the number of MC events, which is about 20,000
events, related to the Parker Limit. same as figure 6.3 is normalized by the
SK-IV lifetime, which is 3244 days . . . . . . . . . . . . . . . . . . . . . . . . 63
fij distribution for CCQE cross section, particle ID separation, and flux error(up down ratio for atmospheric neutrino) . . . . . . . . . . . . . . . . . . 67
The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by assuming the true point is at null hypothesis. . . . . . . . . . . . . . . . . . . . . . 72
The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by assuming the ”true point” of the fitting is normalization at 90% C.L. from Fig 6.6
73
The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by using
different systematics error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
vi

6.9

Predicted cross section of the Hernandez model normalized by that of theRein and Sehgal model for νµ p → µ− pπ + (solid line), νµ n → µ− pπ 0 (dashedline) and νµ n → µ− nπ + (dotted line).[53] . . . . . . . . . . . . . . . . . . . .
6.10 Ratio of CCQE cross section, Nieves model normalized by the Smith andMonitz model. [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 π + scattering on carbon target in: quasi-elastic channel (top left), absorption
channel (top right), total reaction channel (bottom left) and single charge
exchange channel (bottom right).[53] . . . . . . . . . . . . . . . . . . . . . .
6.12 The toy MC sensitivity analysis fit for 459MeV Monopole neutrino by assuming the true point is at null hypothesis. . . . . . . . . . . . . . . . . . . . . .
6.13 cos(θsun ) distributions The background is normalized by the SK-IV lifetime,
which is 3244 days . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.14 Momentum distributions from the Asimov sensitivity study. The backgroundis normalized by the SK-IV lifetime, which is 3244 days . . . . . . . . . . . .

vii

75
76

77
78
82
83

LIST OF TABLES
Page
1.1

Summary of the monopole flux limit come from the electromagnetic energy
losses experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.1
2.2
2.3

The summary of SK data taking periods. . . . . . . . . . . . . . . . . . . . .
The summary of Cherenkov momentum thresholds in water. . . . . . . . . .
Specifications of the 20-inch ID PMTs. [66] . . . . . . . . . . . . . . . . . . .

19
21
23

6.1

The reaction mode fraction for 459MeV ν¯e neutrinos and ν¯µ neutrinos MC,
and atmospheric neutrinos MC after event selection. . . . . . . . . . . . . . .
The purities of FC sub-GeV single-ring sample for 459MeV ν¯e neutrinos andν¯µ neutrinos MC, and fraction of total MC . . . . . . . . . . . . . . . . . . .
The purities of FC sub-GeV single-ring sample for atmospheric neutrinos MC
The zenith angle and energy bin in each analysis sample . . . . . . . . . . .
Neutrino interaction, particle production, and PMNS oscillation parametersystematic errors for the spectral fits, with 1σ uncertainties and resulting fit
pull terms. Errors specific to signal and background are denoted by S and B.
SK-IVsystematic errors for the spectral fits, with 1σ uncertainties and resulting fit pull terms. Errors specific to signal and background are denoted by S
and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flux Systematic errors that are independent in for the spectral fits, with
1σ uncertainties and resulting fit pull terms. Errors specific to signal andbackground are denoted by S and B. . . . . . . . . . . . . . . . . . . . . . .
Values of ∆χ2 corresponding to confidence levels used in this thesis.. . . . . .
The value of β at the 90% C.L. changes for each of mainly contribute errors.

6.2
6.3
6.4
6.5

6.6

6.7

6.8
6.9

viii

60
60
60
61

68

69

70
71
75

ACKNOWLEDGMENTSFirst of all, I need to thank my advisor teacher Roger Wendell. Thanks to him, thispaper was completed. During my research, he gave me a lot of useful suggestions, and he wasable to find errors that I could not find very sensitively at the same time. At the same time,
thanks to his advice, I gradually improved my programming level and laid a solid foundation
for my future Ph.D. study. At the same time, thanks to his daily chats, I have a deeper
understanding of American culture. It can be regarded as the greatest consolation in 2020
when the COVID-19 virus epidemic.
Secondly, I also need to thank Professor, Nakaya Tsuyoshi, who allowed me to come to
Japan and allowed me to participate in the world-class Super Kamiokande experiment. At
the same time, he also gave me a lot of help in life when I first came to Japan.
After that, I would like to thank Ashida Yosuke, my Japanese teacher in some sense.
He gave me a lot of help when I first came to Japan and needed to adapt to the new schooland new environment. His hearty character and very personal Japanese characteristics leftme with very fond memories.
And Tani Mao. Everything in my life in Japan could not go on normally without him.
He helped me a lot, especially at the hardest moment in my life. I hope he can live well forthe rest of his life.
Then I would like to thank Mori Masamitsu, who played a very important role in myfinal research phase. At the same time, thanks to him, I was able to make great progress inhardware work.
At the same time, I would also like to thank the members of the Super Kamioka Experimental Cooperation Group, especially these people, Makoto Miura, Shunichi Mine, Takuya
Tashiro, Yasuhiro Nishimura, Christophe Bronner, whose suggestions have played a very
important role in my research.
I also need to thank the administrative staff of Kamioka, who carefully guided my life
and accommodation in Kamioka.
Finally, I would like to thank my classmates at Kyoto University, Kobayashi Ren, Sueno
Yoshinori, Tsujikawa Yoshiaki, Sugashima Bungo. Although our research directions are not
together, it is really because of them that I have had a wonderful two and a half years.

ix

ABSTRACT OF THE DISSERTATION
Study of Neutrinos from Monopole-Catalyzed Proton Decay in Super-Kamiokande
By
Feng Jiahui
Master in Physics
Kyoto University , 2021

The symmetry of the electromagnetic field is the diamond of the physics crown. Maxwell
describes the electromagnetic field by ultimately beautiful mathematics. However, there isa cloud just hanging on the top of this diamond. We have already found the single charged
particles such as electron and position, electric charge, but we still haven’t found the existenceof a magnetic monopole.
The Grand Unified Theory (GUT), which was born when people were looking for theultimate symmetry, predicts the existence of magnetic monopoles. The Rybakov effect also
predicts that magnetic monopoles will catalyze the proton decay, the most important prediction of the GUT. Therefore, this effect will become a powerful tool to search for magnetic
monopoles and verify the grand unified theory. Magnetic monopoles created in the early
universe could be captured in the sun, where they catalyzes the decay of its hydrogen. The
decay is mainly divided into direct decay and indirect decay. Both of these decay modes
could produce neutrinos with different energies.
The Super-Kamiokande experiment is a water Cherenkov experiment and is mainly used
to explore various neutrino physics. The SK collaboration has completed the analysis forsearching the indirect proton decay mode. The result is the flux of monopoles in the universe f + 

βM 2
σ0
−24
π
<
6.3
×
10
cm−2 s−1 sr−1 (90% C.L. ). However, there also have
FM 1mb−3
0.5
10
great potential for exploring magnetic monopoles through direct proton decay. In this thexsis we perform a sensitivity analysis of the neutrinos, produced when magnetic monopoles
catalyze direct proton decay, based on Super-Kamiokande experiment. The result of the  BRp→ν̄ 
σ0< 4.01 × 10−26 cm−2 s−1 sr−1 (90% C.L. ).
Asimov sensitivity analysis is FM 1mb
10−4This result is two orders of magnitude smaller than the indirect proton decay mode, so it
indicates that the search for such neutrinos from the catalyzed direct decay can provide
strong constraints on magnetic monopoles.

xiChapter 1
Introduction

1.1

The magnetic monopole

The symmetry of the electromagnetic field is the diamond of the physics crown. Maxwell
describes the electromagnetic field by ultimately beautiful mathematics. However, there isa cloud just hanging on the top of this diamond. We have already found the single charged
particles such as electron and position, electric charge. That leads to the next question, does
the universe have single magnetic charges, so-called magnetic monopoles?
In 1885, Heaviside changed the Maxwell equation, assuming monopoles exist, inducing
a symmetry withe the electron equations:∇ · D = ρe ,∇ × E + Ḃ = −Jm ,∇ · B = ρm ,∇ × H − Ḋ = Je .

(1.1)

We can see that this equation has a beautiful symmetry, the monopole electron symmetry.
In the equation Je is the current density, ρm is the magnet density, and Jm is the magnetic
field density. The magnetic charge is conserved as is the electric charge.

11.1.1

The Dirac monopole

In 1931, Dirac found out that if we want to explain how the electric charge is quantized[19], there should be in the universe, if there is only one. More precisely, we can use thefollowing equation to describe the relationship of the monopole and how the electric charge
is quantized:eg= 2πn.
h̄(1.2)

In this equation e is the elementary charge, g is the monopole’s magnetic charge, and n
is an integer which should be 0, ±1, ±2.
We can’t estimate the mass of the monopole with this equation. However, if we assume
the radius of the monopole is same as that of the electron, we can estimate the mass of Dirac
2

2

2

e
' n4700me ' n2.4GeV/c2 .
monopole is rM = mgM c2 = re = mee c2 , and mM = g em
2

After Dirac predicted the monopole has exists, scientists have been trying to search themonopole with accelerators. The most recent effort was published in 2006, Fermi Lab. Scien√tists try to search monopole by using electron-positron collisions at s = 1.96TeV, 35.7pb−1 .
The is result shows no any signature of a light monopole (mass of monopole is lighter than360GeV/c2 ) [5].

1.1.2Grand Unified Theory monopole

In 1974, Hooft and Polyakov found that maybe some perturbation solution of the quantum
field theory could describe the magnetic monopole [34, 20]. This prediction shows that themonopole is a necessary part of the universe, the same as Dirac prediction.

2

Figure 1.1: One possible structure of a Grand Unified Theory monopole. [10]GUTs Magnetic monopoles have an onion-like structure that contains all the interactionsof the Grand Unified Theory. Figure 1.1 shows a possible structures of the Grand Unified
Theory magnetic monopole.
In the core (radius 10−29 cm), the symmetry of the Grand Unified Theory is restored,
and X and Y bosons can be exchanged. There is an electroweak area ( 10−16 cm) on theoutside, where W, Z0 bosons interact. Furthermore, the outside ( 10−13 cm) is a confinementarea, which is composed of photons and gluons. Outside this electroweak area, is the fermionanti-fermion condensation region. If we observe the GUTs monopole from afar, it will behave
as a point particle like a Dirac magnetic monopole that produces a magnetic field [10].
GUTs predict that monopoles will be produced in the phase transition in the early
universe. If we assume the GUT has the gauge group SU(5), the phase transition and the3transition temperature will like below:

SU(5)1015 GeV
102 GeV
SU(3)×[SU(2)
×
U(1)]
SU(3)C × U(1)EM .
C
L
Y
10−35 s10−9 s(1.3)

Here, the numerator represents the transition temperature of each phase transition, and thedenominator represents the time with each phase transition occurs when the beginning of
the universe is taken as the time origin.
At the SU(5) phase transitions monopoles will be produced on the horizon. We canestimate the monopole density is ρM ∼ 5 × 10−18 g/cm3 under the hypothesis of steady statecosmology. However, this number far exceeds the observation ρc < 10−29 g/cm3 [55]. This
problem is called the monopole excess problem.
In 1981, the inflation universe theory [28, 61] make significant progress in solving thesteady-state cosmology problems, like the monopole excess problem. Universe inflation, or
inflation for short, is a process in which space expands rapidly during the early universe.
The period of inflation started 10−36 seconds after the Big Bang and lasted between 10−33
and 10−32 seconds. After inflation, the universe continues to expand but at a much slower
speed. At this time, the inflation field decays into different particles.

1.1.3

The Rybakov effect

GUTs predict the proton will interact with the GUT bosons X, Y in some situations, andthen this proton will decay into a lepton and some meson with some monopole as the catalyst.
However, this reaction has a small cross-section is about σ ∼ 10−56 cm2 . That means thisreaction will not happen in normal energy scales.
Nevertheless, in 1983, Rybakov and Callan found that catalyzation the mass of monopole
will not suppress cross-section. The Rybakov effect is a phenomenon in which the s wave
4

component of fermions is rapidly increases near the core of the magnetic monopole. In otherwords, while the wave function with finite angular momentum is strongly suppressed near
the core, only the s wave component can effectively interact with the core. This means the
cross-section has a constant value, about σ0 ∼ 1 Mb.[60, 69]. That shows that the monopole
catalyzed proton decay will have the same strengths as the normal strong interaction. This
result is called the Rybakov effect.

M + p → M + e+ + π 0 .

(1.4)

Figure 1.2: Heuristic diagram of monopole-induced proton decay. [1]

1.2

Review of Magnetic monopole searches

The GUTs monopole is very heavy compared with another particle which have already beenfound. However, we can search for the monopoles that were generated in the early universe.
So far there is no experimental evidence for monopoles. [24].In the following we show someof the limits from experiments and theoretical predictions..

5

1.2.1

Monopole flux limit from the electromagnetic induction experiment

If we assume the monopole is flying all over the universe, then when the magnetic monopole
passes through a coil, it will induce in the ring an electromotive force and a permanentcurrent (∆i). For a coil with N turns and inductance L, ∆i = 4πN ngD /L = 2∆io , where∆io is the current change corresponding to a change of one unit of the flux quantum of
superconductivity and ngD is the total magnetic charge of the GUTs monopole, which go
through coils [15, 23].
This search method has a great advantage for detecting monopole. Because this method
does not rely on the speed of the monopole, so we can measure the monopole flux in a huge
speed range. However, this measurement requires an exact sensitivity to the monopole signal,
so we have to use the superconductive coil. Because of the financial problem, it will not beeasy to build a superconductive coil that could cover a huge area. Moreover, it is also difficult
to reduce the background noise of the superconductive coil since the monopole signal is quite
small. The limit which comes from the superconductive coil result is [25]F < 2 × 10−14 cm−2 s−1 sr−1 .

1.2.2

(1.5)

Monopole flux limit from the electromagnetic energy losses
experiment

There are several ways to measure the monopole flux by using the electromagnetic energy
losses. Such as, we could use the plastic track detector, the scintillation counter, or proportional counter.
When a magnetic monopole passes through plastic, polymerization and radiation dam6

age occurs along the track. Therefore, a limit can be set by searching for the track of themagnetic monopole by chemical treatment. While plastic is inexpensive, making a large area
detector is easy, and the limit can be tightened.
The scintillation counter is a method, which searches for scintillation light emitted
by atoms and molecules that are excited and return to the ground state when magnetic
monopoles pass through a liquid or gas. Another method is proportional counter, which isused the signal generated by the ionized gas electrons when the magnetic monopole goes
through the proportional counter. All of the experimental method have have been used tosearch for the monopole. Experimental results are listed in table 1.1.
Table 1.1: Summary of the monopole flux limit come from the electromagnetic energy losses
experiment.
Experimental typeplastic track detector
scintillation counter
proportional counter

1.2.3

β rangeLimit

10−2 < β < 1 F < 3.2 × 10−16 cm−2 s−1 sr−1 [52]F < 6.6 × 10−14 cm−2 s−1 sr−1 [27]F < 8.7 × 10−15 cm−2 s−1 sr−1 [24]Monopole flux limits from theory

Limit from the universe density .
This limit assumes that the mass density of the universe is less than the critical density,
which is calculated assuming the universe is flat (cosmological constant Λ = 0) . If we takethe mass of the monopole as mM , and the speed of the monopole is β, the limit value is
nM βc
F =
< 3 × 10−14 h2
4π



β
10−3



1016 GeVmM



cm−2 s−1 .sr−1(1.6)

Here h is the Hubble parameter, h ≡ H0 /100kms−1 Mpc−1 , and H0 ∼ 70kms−1 Mpc−1 , andit assume the monopole is uniformly distributed in the universe.
7Limit from the magnetic field .
Because the galaxy is not uniformly distributed, a magnetic field is generated from theflow of cosmic rays since it contains the amount of the charged particles. The magnetic fieldstrength is about 3µG. Monopoles will be accelerated by the magnetic field. If the monopolego through the galaxy, then the monopole will get the energy from galaxy like2
E− = πrGr

rG(gB`)4πF τG .
`

(1.7)

Here, rG is the radius of the galaxy, ` is the galactic magnetic field range, and the g is themagnet charge of the monopole. B is the galaxy magnetic field strength. If the magnetic
field accelerates the monopole there will by a dynamo with energy generated likeE+ =3
B 2 4πrG
.
2 3

(1.8)

If the monopole generates, the energy is more significant than the energy of monopole lostin the galaxy, then the galactic magnetic field will be annihilated. However, we find thegalaxy magnetic field has not been annihilated in this way. [13]. We can therefore restrict
the monopole flux by this assumption. This monopole flux limit is called Parker limit [27].

−15

F < 10

1.2.4



B
3µG



rG
30kpc

1/2 

300pc`

1/2 

30Myr
τG



cm−2 s−1 sr−1 .

(1.9)

Limit from the previous search in Super-KamiokandeThis thesis searches for monopoles trapped within the Sun. Firstly, we assume that amonopoles present in the universe. Second, if those monopels are gravitationally capturedby the sun, they have a high probability to catalyze proton decay herein. So we search forneutrinos from proton decays in the Sun as our signal.

8

The Rybakov effect predicts that the monopole is cannot easily catalyze odd nuclei
since the odd nuclei, with odd atomic number are bosons. However, the Rybakov effect only
happened in fermion. Therefore, the odd nuclei have a great repulsion with the monopole.
Consequently, we cannot look forward to giving a solid limit by searching for monopolecatalysis-proton-decay neutrino in odd nuclei-dominated planets, such as Earth or Mars.
However, focusing on Sun or Jupiter, they are full of the free proton. Therefore, we mightsearch monopole flux by measuring the monopole-catalysis-proton-decay neutrino from theseobjects.
There are two types of decay mode in monopole catalyzed proton decay, the indirect
decay mode, and the direct decay mode.
The first one is the proton decay into meson and charged lepton.


p → ρ0 , ω, η, K + , · · · + e+ or µ+ .

(1.10)The heavy meson will decay into π + and π − . Because the negative charged particle will beabsorbed in the sun, we don’t consider them
ρ0 , ω, η, K + , · · · → π +(1.11)

π + → µ + νµ(1.12)µ+ → e+ + νe + ν̄µ .

(1.13)

If we only consider the π + particles which are generated by the proton decay meson
decay, it will finally decay into charged lepton and neutrino. Also, one of the charged lepton,muon, could decay into neutrino too. Consequently, this type of decay mode will generate
several neutrinos, which will arrive on Earth and be detected by the Super-Kamiokande ex9

periment. Because they are generated from the decay of meson or charged lepton, therefore,
the energy of these neutrinos is restricted by the mass of the mesons and the charged lepton.
The result shows that the momentum of the monopole-catalyzed-proton-decay neutrino inthis proton decay mode is only between 20 to 50 MeV.
This two-step-proton-decay mode neutrino has already been studied in Super-Kamiokande
in 2012 [68]. The monopole flux limit given by this search is shown in Figure 1.3.

10

Figure 1.3: The upper limits on the monopole flux as a function of monopole velocity, redline is the previous monopole analysis in Super-Kamiokande by using indirect proton decay
at 90%C.L , βM . Catalysis cross section (σ0 =1mb) and monopole mass (MM = 1016 GeV)
are assumed for indirect searches.[68]11However, from the recent theoretic result, we find the previously forbidden monopole
catalyze proton decay channel, the ’direct’ decay mode, [35]p → ν¯e + π +(1.14)

It becomes another possible channel to discover the monopoles. Previously, this decay
mode was considered was forbidden because monopole only carries SU(3)C × U(1). However,the SU(3)C × U(1) will be resolved to the Standard Model group, SU(3)C × SU(2)L × U(1). If
we consider this limit, the restriction will not be valid anymore. Furthermore, the two-step
proton decay mode will be suppressed by the electroweak suppression factor. Indeed, thedirect proton decay mode will have better discovery potential than the two-stage proton
decay mode.
The direct proton decay, flux is estimated as follows: σ   β   BR
NM
p→ν̄
0
cm−2 s−1 sr−1 .
Fν̄ ∼ 1.4 × 10
0.1mb
10−3
10−4
1025
4

(1.15)

where the σ0 is Rybakov effect cross-section , β is the velocity of the monopole, and BRp→ν̄is corresponding branching ratio. The characteristic neutrino energy isEν̄ = m2p − m2π+ /2mp = 458.755MeV.

(1.16)

Although the emitted neutrinos are a single flavor in the Sun, this neutrino will oscillate
into different neutrino flavors when they arrive on Earth. Furthermore, the different neutrino
flavors will interact with SK in different ways. Therefore, we must consider the neutrino

12

oscillation weight as follows.


∆21
∆31
P (να → να ) =1 − 4 |Uα2 |2 1 − |Uα2 |2 sin2
− 4 |Uα3 |2 1 − |Uα3 |2 sin222

(1.17)
2
2
2 ∆31
2 ∆21
sin
+ sin ∆21 sin ∆31+ 2 |Uα2 | |Uα3 | 4 sin
2
2

∆21
∆31
+ 4 |Uα3 |2 |Uβ3 |2 sin2
2
2


∗
2 ∆21
2 ∆31
∗
sin
+ sin ∆21 sin ∆31+2< Uα3 Uβ3 Uα2 Uβ2 4 sin
2
2


2 ∆21
2 ∆31
+ 4J(α,β) σsin ∆31 − sinsin ∆21 .
22

P (να → νβ ) =4 |Uα2 |2 |Uβ2 |2 sin2

(1.18)

 δm2  L 
GeVWe use the same notation as shown in [6], where ∆ij ≡ δm2ij L/2E = 2.534 eVij2
,
E
km

∗
∗
the Jarlskog invariant is taken as, J(α,β) = = Uα1Uβ1 Uα2 Uβ2. If we assume the Sun-Earthdistance is 1.496 × 108 km, then the oscillation probability for ν¯e and ν¯µ are.

P (ν̄e → ν̄e ) ≈ 0.38

(1.19)

P (ν̄µ → ν̄e ) ≈ 0.47

(1.20)and the monopole catalyze proton decay neutrino fluxes are.
 σ   β   BR
NM
p→ν̄
0
cm−2 s−1 sr−1Fν̄e ≈ 5.3 × 10
0.1mb
10−3
10−4
1025


 σ   β   BR
NM
0
p→ν̄
3
Fν̄µ ≈ 6.6 × 10
cm−2 s−1 sr−1 .
0.1mb
10−3
10−4
1025
3

(1.21)(1.22)

This thesis search antineutrino generated by the direct proton decay mode in the SuperKamiokande experiment. This neutrino flux is a mono-energetic 459 MeV antineutrino fluxthat comes from the Sun.

13

In chapter 2, We will introduce the Super-Kamiokande experiment. In chapter 3, We
will introduce the event reconstruction. In chapter 4, We will introduce the event simulation.
In chapter 5, We will talk about the event selection, and in the final chapter, the sensitivity
estimation using the SK4 Monte Carlo (MC) will be introduced.

14

Chapter 2
Super-Kamiokande Experiment

2.1

Detector Description

Super-Kamiokande (SK) is a detector that consists of 13000 photomultipliers (PMT) and acylindrical stainless steel water tank full of 50,000 tons ultra pure water. The water tankis 39.3 m in diameter and 41.4 m high. This tank is buried under 1000 m of the Mountain
Ikenoyama, in Kamioka town, Hida City, Gifu Prefecture, Japan. This buried is mainly
to reduces the cosmic ray background, the main background of SK. Because SK is a water
Cherenkov light detector, it detects the Cherenkov light generated by the charged particles
when that particle goes through the water. The buried depth the cosmic muon flux is
6 × 10−8 cm−2 s−1 sr−1 which is about 1 × 10−5 magnitude compared with earth surface flux.

15Figure 2.1: Overview of the Super-Kamiokande detector.[38]2.1.1

The structure of the Super-Kamiokande Experiment

SK is a detector separated into two parts. The inner detector is called ID, and outer part iscalled OD. Furthermore, there has a 55 cm wide steel-support structure to support PMTs.
The ID is positioned 2.6m from the wall of the SK and contains about 32 kilotons ofwater and uses about 11,000 20-inch PMTs which are facing inward. The space between the
ID PMTs is covered with a black sheet to reduce the unexpected photon reflection. The ID
PMT is installed in modules. Each of the modules holds 3×4 PMTs.
The OD is placed 2.2m from the wall of the SK tank and 2.1m from the top and bottomof the tank. It contains 18 kilotons of water. The main target for the OD is to reject thecosmic ray particles and the particles emitted by the rock of the mountain. It is uses 1885
8-inch PMTs. These PMTs face outward from the support structure. The Tyvek sheet
covers the space between the OD PMTs to maximize the light detection efficiency.
Apart from this equipment, there are also 26 Helmholtz coils to avoid the earth’s mag-16

netic field from disturbing the PMTs. The surface of SK has five electronic huts and a linear
accelerator for detector calibration.

Figure 2.2: Photo from the bottom of the tank renovation in 2018. The upper part in thecenter of the photo is the inner water tank, and the lower part is the outer water tank.[67]Figure 2.3: A photo looking up from the bottom of the OD. An 8-inch PMT is attached to
the wall on the inner tank side, and the outer tank is covered with a white Tyvek sheet.[67]172.1.2

History of the Super-Kamiokande Experiment

The SK start construction in 1991 as a successor to the Kamioka-NDe experiment. The
mining company excavated the cavity of the mine in 1994. Afterward, the PMT install work
finished in 1995. After a one-month test operation, SK officially started on 1996 1 April.
The SK data-taking period is divided into six parts as of 2020.
The first period is called SK1. It starts on 1 April 1996, ends in July 2001. In the SK1period, there are 11146 PMTs is installed in the ID, and the photo coverage is about 40%.
On 12 November 2001, one of the bottom PMTs imploded during a post-maintenancetank refill. This accident caused 7796 PMTs to be damaged (66779 ID PMTs and 1017
OD PMTs). The other PMTs which could still work rearranged to were resume observation.
Furthermore, every PMTs has since been covered with acrylic and fiberglass reinforced plastic(FRP) to protect the PMT so as not cause a subsequent chain reaction. This observation
period starts from October 2002 to October 2005, is called SK2. There are 5182 ID PMTs
and 1885 OD PMTs, and the photo coverage of ID is 19%.
In October 2005, newly produced PMTs were installed to the tank. This work is finishedin 2006 July, and the entire operation 11129 ID PMTs was resumed. The photo coverage isstill 40%. This data period from July 2006 to August 2008 is called SK3.
The SK4 is the most prolonged data-taking period, lasting from September 2008 to June
2018. The most different point compared with SK3 is that SK upgraded all of the front-end
electronics.
In June 2018, other upgrades and repairs were started. The goals were repairing the leakof the SK tank, installing a new plumbing system, and replacing dead ID and OD PMTs.
After those repairs the data-taking period is called SK5. That is also the preparation period
for SK Gd. It in started June 2018 and ran 2019 July.
18

Table 2.1: The summary of SK data taking periods.

SK-I
Operation Start
Operation End
Livetime(days)
ID PMTsID PMTs
Photo coverage

Apr. 1996
Jul. 2001
1489.2
11,146
1,885
40%

SK-II

SK-III

Oct. 2002 Jun. 2006
Oct. 2005 Sep. 2008
798.6
518.1
5,182
11,129
1,885
1,885
19%
40%

Figure 2.4: Frame structure that supports PMT. [67]
19

SK-IV
Sep. 2008
May. 20183244.4
11,1291,885
40%

The SK-Gd phase is a big project to improve the SK performance. The Gd is means
gadolinium is dissolved this ultra-pure water at SK. The gadolinium has a large cross-section
to capture the neutron and emit 8MeV gamma rays. Therefore, it will make us identify theneutrino interaction which emit neutrons. This makes it easier to separate neutrino fromantineutrino interactions. We will talk about the detail of how to separate the anti-neutrino
and neutrino in the next chapter.

2.1.3

Cherenkov light

Figure 2.5: Outline drawing of Cherenkov light. [3]The SK is designed for detecting the charged particles by using Cherenkov light. The
Cherenkov light will happen when charged particles go through the dielectric medium fasterthan light in the medium. SK uses that nature to detect the charged particle when thisparticle has a higher speed than the light speed in the water. The Cherenkov light momentum threshold for differently charged particles is listed Table2.2. A visualization of the The
Cherenkov light is shown in the Figure 2.4. We can find the Cherenkov light is just like acone surrounding the charged particle. The cone direction is same as the charge particle
20

Table 2.2: The summary of Cherenkov momentum thresholds in water.
partilce typemass(MeV)

threshold(MeV)electronmuon
pion
proton

0.511
105.6
140
938

0.57
118
156
1051

direction. The opening angle of the cone is related to the speed of the charged particles.
The relationship of this two parameter is likecos θc =

1
.
nβ

(2.1)

The θc is the opening angle, n is the refractive index of the medium, beta is the speed ofcharged particles divided by the speed of light in vacuum. The calculation of the momentum
threshold is
mcβthresh,
pthresh = p2
1 − βthresh

withβthresh

1
= n.
.

(2.2)

If beta is nearly to equal to 1, the opening angle is about 42 degree.
The spectrum of the Cherenkov light photon number by using the wavelength parameter
lambda by following this formula
d2 N
2πα
= 2
dλdx
λ


1−

1
n2 β 2.

(2.3)

The α is the fine structure constant. In SK PMTs have sensitivity to wavelengths from, 340
nm to 600 nm, and in this range are about 340 photons generated when one charged particle
goes through 1cm. Using this nature, we can reconstruct the charged particle energy by accounting for the number of photons. But if the charged lepton has less energy than 400MeV,
we could also use the opening angle to reconstruct the charged particle’s momentum.

21

The PMT (photomultiplier) is the photon sensor that uses the photoelectric effect totransfer the photon to electron and multiply the electron. The standard step of how totransmit the photon signal to electron signal is like this way:
1. The photon enters into the PMT and then interectats with the dynode and generates
the photoelectron.
2. The photoelectron is focused on the first dynode and interacts with it.
3. After the second photon electron has been generated. It will interact with the second
dynode and generate more electrons.
4. Repeat the steps 2 and 3 several times. Then we get the charge current from thepositive dynode.

Figure 2.6: Schematic diagram of the operating principle of PMT [72]Because the current is proportional to the number of entering photons, if we integrate
the charge, we could get a total charge and estimate the number of incoming photons.
Furthermore, if we do some calibration about the PMT, we could find the relationship of
the photon number and the total charge, then we could estimate the energy of the charged
particles.
There are two types of PMT installed in the SK. The first one is the 8-inch PMT that22

was established in the OD [14]. The second one is the 20-inch PMT which is installed in ID.
The 20-inch PMT is manufactured by Hamamatsu Photonics K. K. [42, 66]. Figure 2.6 shows
the structure of 20 -inch ID PMT. The photocathodes, is made of Bialkali, a type of alloy
containing Sb-K-Cs, and the quantum efficiency peaks at 22% percent at the wavelength of
390nm shown in Figure 2.4. And another performance parameter is summarized in Table2.3[66].
As I have mentioned before, the earth magnet will have an impact on the time resolutionof PMTs. Consequently, 26 sets of Helmholtz coils are installed around the water tank. The
currents of the Helmholtz are monitored in real-time. The original magnetic field, which
the SK group measured before SK1, is 450mG. After installing the Helmholtz coils, themagnet field is reduced to 32 mG. This value is less than 100mG. Beyond this value, thetime resolution will increase significantly. [4]Table 2.3: Specifications of the 20-inch ID PMTs. [66]Photocathode material
Quantum efficiency
Dynode structure
Operation high voltage
Gain
Dark current
Dark rate
Transit time
Transit time spread

Bialkali (Sb-K-Bs)
22% at λ=360 nm
11-stage Venetian blind type
1700-2000 V
107 at 2000 V
200 nA at 107 gain
3 kHz at 107 gain with 0.25 p.e. threshold
90 ns at 107 gain
2.2 ns(1 σ)Since learning the lessons of the PMT chain explosion in 2001, every PMT has been
covered with a 12 mm ultraviolet transparent acrylic dome. On the side of the PMT is beprotected by acrylic and fiberglass reinforced plastic (FRP). To make sure the pressure of thewater is constant, the FRP is designed with holes to make sure the water could flow aroundthe PMT. For the vertical photon with 3500nm wavelength, the acrylic dome trasparency isabout 96%. [4].

23Figure 2.7: Quantum efficiency distribution of 20-inch PMT and relative Cherenkov light
distribution when passing through 15 m of pure water. [66]Figure 2.8: 20-inch PMT. [66]

24

2.2

Electronics and Data Acquisition

As mentioned before, the front-end electronics were upgraded for the SK4 period. The
previous electronic circuit is called ATM for ID and ODQTC for the OD. For the SK4, it
uses the QTC-Based Electronics with Ethernet, called QBEE [51].
The QBEE consists of two main parts, Charge-to-Time Converter (QTC) and the Timeto-Digital Converter (TDC). One QBEE connects to eight QTC, and one QTC connects to
3 PMTs. The workflow of the QBEE is like this. Initially, The charge of the PMT signal isintegrated by QTC, and then the QTC output is converted to a digital signal by using the
TDC. And then, this time and charge information is recorded by FPGA at 60kHz. Figure
2.9 shows the workflow detail.
The dynamic charge range for one QEBB is from 0.2 to 2500 pC [53], and each channel
has three different gains, the relative ratios for divided channels is 1, 1/7,1/49, each of themcorresponding to the large medium, and small gains. Show the detailed structure and thesignal readout system and its surrounding equipment.
There are significant advantages for the QBEE compared with the previous front-end
electronic system. In QBEE the current is discharged as constant current, just as the figure
shows. Consequently, the output of QBEE gives time and charge information at the sametime. That will decrease the dead time compared with the old electronic ATM.
And another upgrade is the trigger. Previously, there was only a hardware trigger in
the SK. After that, SK4 used the software trigger and the SLE, LE, and HE triggers. We
should note that there should be two particular triggers: the Super High Energy (SHE) andthe after trigger (AFT). This trigger is associate with the neutron targeting system. And
the neutron information will help us to distinguish the anti-neutrino and neutrino. We will
describe this a little later.

25

Figure 2.9: Timing chart of QTC operation QBEE for SK-IV. From [51]Figure 2.10: Block diagram of data collection system until PMT signal is recorded on disk
From. [74]2.3

Water and Air Purification

The SK water uses underground water from the Kamioka mine. However, it is important tokeep water high transparency to ensure the light will not be absorbed or scattered. Furthermore, radioactive material, like the radon, comes from bedrock and dissolves into the water.
26

It will become the main background of the solar neutrino measurement. For this reason, weapply the water purifier system in the SK. The water flow of SK is about 60 tons/hour, andthe water used in SK is recycled water. There is also a heat exchanger system installed in
the water system to keep the water temperature in 13.6 degrees. This helps to prevent thebacteria from reproducing in the tank, and reduces the dark rate of the PMT.
Apart from the purified water system, an air purifier system is also installed in the SK.
Because the radioactive material in the air may be dissolved into the water and become
another background for solar neutrino measurement, we install the air purifier system topump the radon-free air into the SK tank.

27

Chapter 3
Event Reconstruction

The event reconstruction algorithm used in SK is called APFit. The APFit could use the time
information, the charge information, and the PMT positions to derive the physics informationfor every Cherenkov ring signal, such as the direction, momentum, particle identification.
The APFit is applied to the Monte Carlo simulation generated in this analysis and SK data.
I will introduce some of the basic ideas of the APFit. If you interest in the detail of the
APFit, please check this paper [62].
The reconstruction algorithm flow is like these steps.
1. Vertex fitting
2. Ring Counting
3. Particle Identification
4. Momentum Reconstruction
5. Michel Electron Finding28

6. Neutron Tagging
We should note that the neutron tagging step is only used for SK-IV MC data since
there is no AFT applied in the other SK periods.

3.1

Vertex Fitting

The vertex fitting has three steps. The first one is the point fit, then will be ring edge
search and TDC fit. Initially, APFit assumes that the charged particle generated all of theCherenkov light from one point, then it will calculate the time residual ((the photon arrivetime)-(the photon propagate time in the water)) as the fit parameter to find the peak. The
goodness of the fit is defined as follows.
(ti − t0 )2
1 X
exp −
G=
N i
2(1.5σ)2

!
.

(3.1)

Here N is the number of hit PMTs, ti is the time of flight meanwhile subtract the PMT
timing, t0 is the fit time to maximize the good, and the σ is the PMT timing resolution,
about 2.5 ns. After the Point Fit stage, the APFit will estimate the direction and the opening
angle of the Cherenkov ring. The opening angle θedge is defined satisfied
d2 PE(θ)
=0
d2 θ

(3.2)

Where P E(θ) is the angular distribution of the observed charge by using the opening angle
as function parameter. Figure 3.1 shows the distribution for PE and theta.

29

Figure 3.1: An observed charge distribution as a function of Cherenkov opening angle (top)and its second derivative (bottom). [51].

And the direction of the Cherenkov light is estimated using:R θedgePE(θ)dθQ (θedge ) = 0
×sin θedgedPE(θ)dθ
θ=θedge!2(θedge − θexp )2
× exp −
2σθ2

!
.

(3.3)

The θexp is the expected Cherenkov light opening angle calculated from the total charge
inside of the θedge , the σθ is the angular resolution. Initially, The Q will use the point fit
direction, and then it will calculate the different directions to choose the maximized Q.
Finally, APFit will recalculate the vertex position by using the directional and opening
angle information above. This recalculation will not assume the Cherenkov light generated
from one point. Instead it will consider all photons originated along the charged particle track
length, about 3MeV per cm, to get the residual PMT time mentioned before. Then APFit
will maximize the likelihood function. The scattering of Cherenkov light is also considered
here.

30

3.2

Ring Counting

From now we have identified the main ring. Other rings are searched by using a patternrecognition algorithm called Hough transform [17]. Here is the basic idea of Hough transform.
Initially, The APFit will assume a virtual ring pattern for very hit PMT. The virtual ring
will be weighted by the charge information from the hit PMTs. APFit will identify theactual ring from the peak of the overlapping virtual distributions. Just like the Figure 3.2
shows. In practice, APFit will implement all of the charge distribution functions from every
hit PMT, then identified the real ring by finding the peak in the overlapping distributions.
There is a log-likelihood method used to determine the actual ring.

Figure 3.2: An outline drawing of detecting additional rings. The shaded and dashed circles
stand for the Cherenkov ring and rings with 42o half angles [51].

31

3.3

Particle Identification

The charged particle identification in SK classifies events into two categories. The firstone is the e-like event which will contain the electron, positron, and gamma rays. Thispattern event will produce a fuzzy ring due to the scattering and electromagnetic shower(bremsstrahlung with the pair production). Another is the muon-like event. This type of
event will have a clear edge ring. The heavier particles will not be scattered so much. The
comparison of this two type of the event is illustrated Figures 3.3 and 3.4.
The reconstruction particle identification algorithm identifies the event type by considering the charge distribution function from MC simulations. The likelihood test will be used
for the identification to determined which type of event is seen, just like the figure shows.
The quality of the PID algorithm is checked by using a one kiloton water Cherenkov Detector
with electron and muon beams generated from the 12GeV synchrotron at KEK.

Figure 3.3: Typical e-like ring pattern.

32

Figure 3.4: Typical µ-like ring patternFigure 3.5: PID likelihood distribution for data and atmospheric MC with a visible energy
below 1.33 GeV. Good separation between e-like and µ-like events is seen. [62].

33

3.4

Momentum Reconstruction

The momentum of each ring is calculated from the integrated charge within a 70 degree conearound the reconstructed ring direction. The integrated charge for number of n ring, R isgiven by:
RTn OT =

GMC 
α
GData
θ

X
i,n

<70◦



h r i cos ω 
X
i
i
Obs
Exp
qi,n
−
Si  .
L f (ωi )
◦
θ <70

(3.4)

i,n

Here, variables are α: the normalization factor
G: the relative PMT gain parameter for Data and MC
θ: the opening angle between the n ring and the PMT direction
Obsqi,n: the integrated charge for the i PMT from n ringti : residual time for I PMT
L: attenuation length in waterri : the distance from the vertex to the PMT
f (ωi ): PMT acceptance correction as a function of incidence angle ωi
Si : the expected amount of p.e.s from scattered photon s for the i PMTWhen we finish, calculate the RTn OT , the corresponding ring momentum is determinedby using a correspondence table built from MC. The Figure 3.6 shows the correspondenceof three particle types.
The reconstructed momentum resolution for single ring event is estimated to for electronand 3% for muons.

34

Figure 3.6: RTOT vs. momentum table for the electrons (blue crosses), muons (red crosses)
and the kaons (black crosses). [40]3.5Michel Electrons Reconstruction

The Michel electrons from muon decays are a piece of essential information to determine if
a charged particle is muon or not. There are two different Michel electron types in SK. The
criteria for selecting a Michal electron is:
1.The time interval to the primary event is 1.2µs<∆t<20µs or 0.1µs<∆t<0.8µs
2. Number of the PMT is > 50
3. Vertex is well reconstruct
4.Total p.e.s < 2000
5. Number of hit PMTs in 50 ns window is > 60
6. Number of PMTs in the 30 ns window is > 40

35

The last two criteria are aimed to reduce the gamma-ray emitted when the oxygen
nucleus captures a muon. More Michel electrons are observed from positive muons sincenegative muons often capture on oxygen nuclei.

3.6

Neutron Tagging

When a neutrino interacts with the nucleus in the tank, some neutrons may be produced.
The number of the neutron will be different by different lepton interact with the nucleus.
Therefore, the neutron will be an essential part of distinguishing additional lepton.
The neutrons will finally capture on the hydrogen nucleus and emit de-excitation gammaray when traveling in the water. The gamma rays’ energy is fixed, about 2.2 MeV, and themean capture time is about 204.87µs. These two pieces of information could help us to tag
neutrons.
Here I will introduce some basic ideas of the neutron tagging algorithm used in SKIV.
If you interest in the detail of this technology, please check [36],[47].
Firstly, we reject the event which has two PMT hits within 10 µs, due to this type of
event might be the dark noise papers in PMTs in very high possibility. Then, we searchfor candidate hit cluster with 2.2 MeV gamma-ray. Finally, we put this candidate into 16
variables, which represent the characteristics of the cluster. The neural network is used
determines if this cluster is the 2.2 MeV gamma-ray cluster or not. Currently, the neutron
efficiency is 25.2% with a mistagging rate is 1.8%.

36Chapter 4
Event Simulation

The neutrino event in the Super-Kamiokande is simulated by the Monte Carlo method. This
simulation consists of three parts: the estimated neutrino flux, the neutrino interaction, andthe particle propagation simulation in the Cherenkov Detector.
For the first part of this simulation, the neutrino flux estimate is already calculated by
the theorists. [35] They estimated monogenic neutrino would have an energy of about 459
MeV. We will introduce the detail of this analysis in section 4.1.
And the background of this analysis mainly comes from the atmospheric neutrino since
the solar neutrino is too small (smaller than 10 MeV) to be accountable. The atmospheric
neutrino flux is modeled with the Honda Flux, calculated by M. Honda et al.[33, 30, 31, 32]
We will describe the detail of the atmospheric in section 4.2.
The neutrino interaction software used in SK is NEUT [46, 29]. NEUT could generate
the secondary particles after the neutrino interaction and the related physics information,such as momentum, direction. After the NEUT simulate the interaction of neutrinos, the secondary particles propagate in the water, and the scattering will be simulated by SKDETSim,

37

a GEANT3 based Monte Carlo simulation software. And the track will finally be recordedin electronics simulation by using SKDETSim too.

4.1

Monogenic Neutrino Simulation

To estimate how many high energy neutrino would arrive at the SK, we should accountfor the astrophysical monopole abundance at first. Using the primary constraint from theParker bound, the Galactic magnetic field constraint, the monopole flux limit is [27]−15

F < 10



B
3µG



rG
30kpc

1/2 

300pc`

1/2 

30Myr
τG



cm−2 s−1 sr−1 .

(4.1)

Here the Fm is the bound of the monopole flux, there is a more strict bound by estimate
the monopole catalysis of the neutron decay from the neutron star. However, this result hasa sizeable systemic error from neutron star structure since the physics in the neutron staris still unknown. Apart from this, some theorists suggest that the co-annihilation processes
might reduce these monopole flux from the Parker bound [43].
We could estimate the total number of captured monopoles by using the age and size
information of the Sun. In general, we should account for the monopole velocity and thecorresponding energy loss inside the Sun. After that, we could estimate the monopole capture
fraction in the Sun. It is already estimated that capture fraction of 1016 GeV GUT monopolesis almost one, and the number of monopoles captured in the Sun is approximately NM ∼1041 FM [22], which is the astrophysical monopole abundance.
As mentioned before, the total monopole number captured by the Sun may be suppressed by the co-annihilation processes. If we consider this effect, the number of captured
38monopoles should be estimated to NM ∼ 1033 (FM )1/3 [32]. However, a significant sourceof uncertainty comes from the nature of the magnetic field in the stellar interior, since themagnetic field could separate monopoles and anti-monopoles. Then, it would prevent annihilation. Furthermore, even if these processes occurred, we still couldn’t estimate thetimescale associated with the annihilation process. In principle the monopole anti-monopoleannihilation cross-section should be set by the GUT scale. Therefore, their co-annihilation
rates could be negligible for our analysis. If you interest in the monopolonium state, you
can get more information in [22].

Figure 4.1: Abundances of the isotopes in the Sun as a function of mass number. Even
numbered nuclides are shown in blue, odd-numbered nuclides in red. [44]Therefore, our analysis is based on the 459 MeV monoenergetic antineutrino search,which offers better discovery potential than the indirect decays. Since co-annihilation willaffect both direct and indirect processes equally, we don’t consider this effect in our analysis
unlike previous monogenic neutrino search in SK [68]. Therefore, we don’t struggle with theswamp of the detailed classification of monopole physics. We take it in a phenomenologicaland straightforward way called,’ bottom-up’ approach for the rest of the analysis [8].
39After considering the abundance of magnetic monopoles, we should estimate the momentum spectrum of proton decay neutrinos. If we ignore the binding energy brought by
the nuclear structure, the energy of the decaying neutrino should be limited to 459 MeV.
However, this is an advantage of this research, that is our research object is the Sun, and we
could conclude from the figure that the Sun’s interior is mainly composed of hydrogen andhelium and their isotopes. For hydrogen, we can regard them as a free proton. Furthermore,
the nuclear binding energy per nucleus is 7.1 MeV for helium. The binding energy is too
small to be comparable with the momentum of the decaying neutrino, not to mention tocompared to other systematic errors. Therefore, as shown in Figure 3.1 below, we assume
that the momentum spectrum of the decaying neutrino is an average distribution with thecenter value of 459MeV.

Figure 4.2: Monogenic Neutrino Momentum Distribution, assuming 20,000 monopole neutrino is generated by MC.

40

Figure 4.3: Monogenic Neutrino Flavor Distribution, assuming 20,000 monopole neutrino is
generated by MC.

4.2

Atmospheric Neutrino Flux

The main background for monogenic proton decay searches comes from the atmospheric
neutrinos produced by cosmic rays since the atmospheric neutrino has a wider momentum
spectrum and a higher event rate than the monogenic neutrino.

Figure 4.4: Schematic view of cosmic ray interactions in the atmosphere. [45]41

The cosmic rays, which could strike the atmosphere, are the mainly protons and αparticles. The cosmic rays interact with the atmosphere nuclei isotropically. This interaction
will produce several pions and kaons. The charged pions will decay into a muon neutrinos(νµ or ν¯µ ) and one muon. Then, the muon will decay into one electron and an electron
neutrino. It could make us estimated the neutrino flux composition at the surface of the
Earth. If we only consider the pion decay, the ratio of the νµ and νe should be 2. However,there is another decay mode after the comic ray interacted with the atmosphere nuclei, as
the Table is shown. Therefore, the ratio of the νµ and νe will be different with 2, just as thefigure 4.5 showed. The detail of the reaction chain is shown in Figure 4.4. However, most of
the neutrinos pass through Earth without any interaction. Only a little part of neutrino willinteract at Super-Kamiokande. The observed neutrino event rate in SK is eight events/day.

Figure 4.5: Calculation of the neutrino flux ratio (νµ + ν¯µ ) / (νe + ν¯µ )to the energy of
atmospheric neutrinos by the group [7]. The solid line is from Honda, the wavy line is from
Bartol, and the dotted line is from Fluka.

The detail of the Honda flux is shown in Figure 4.5. This flux model will calculate the42cosmic rays through the atmosphere in three dimensions. Furthermore, it will also accountfor the effects of the geomagnetic field and solar wind, which could affect the cosmic ray flux
by a factor of 2% at 1 GeV and a factor of 10% at 10 GeV. The interactions with the air
nuclei are using NUCRIN and DPMJET-III [59] models, with secondary particle informationof mesons and kaons calculate by neutrino flux computation. Neutrino flux calculations by
G.Battistoni et al. ( Fluka flux) [12], and G.D. Barr et al. (Bartol flux) [11] are used forcomparison with Honda flux, as shown in Figure 4.5. Flux calculations cover the neutrinoenergy ranging from 30 MeV to 3 TeV.

4.3

Neutrino Interaction

The atmospheric neutrinos nucleons interaction, which happened in the SK tank, are simulated by NEUT [46, 29]. The interactions mode of the atmospheric neutrino MC events are
divided into two catalogs, the Charged Current (CC) and Neutral Current (NC):
CC/NC elastic and quasi-elastic scattering ν + N → l + N 0
CC/NC single meson and gamma production ν + N → l + N ∗ N ∗ → N 0 + (π, K, η, γ)
CC/NC deep inelastic scattering ν + N → l + N 0 + hadrons
CC/NC coherent pion production ν + 16 O → l + 16 O + π
where the ν is a neutrino, N and N∗ are the initial state and final state for nucleons,and l is a lepton (neutrino for NC and charged lepton for CC interaction). The distributions
for the simulated cross sections of neutrino interactions in NEUT are shown in Fig. 4.6.

43

Figure 4.6: The simulated cross sections for ν(ν̄) interactions in NEUT with data. The red,
blue, green, and black solid lines correspond to (quasi-)elastic scattering, single π K, η, γ
production, deep inelastic scattering, and the total of three interactions. [36]44

4.3.1

CC/NC elastic and quasi-elastic scattering

The NC elastic scattering interaction is a neutrino is scattered by a nucleon without generating any particle.

ν + N → l + N 0.

(4.2)

For the interactions in bound nucleons in 16O, the Smith and Moniz model is applied, which
treats the nucleus by using the Fermi gas model with a flat momentum distribution up to
225 MeV/c (Fermi surface momentum). However, the CC quasi-elastic scattering interaction(CCQE) is a neutrino that converts into a corresponding charged lepton. The CCQE crosssections for free protons are calculated given by Llewellyn-Smith model [39] in the simulation.
Additionally, the model note [50, 49] is also accounted to provide the systematic error of
the bound nucleon scattering. The Pauli exclusion principle is evaluated by [65] when the
scattered nucleon momentum is higher than the Fermi surface momentum.

Figure 4.7: CCQE reaction by νe

The relationship of the cross-section of NC elastic scattering and the cross-section of
CC elastic scattering are estimated by [7, 2]: And the comparison of the NEUT calculated45

cross-sections of CCQE scattering with experimental data is shown in Figure 4.8..

Figure 4.8: Calculated cross-sections of CCQE scattering with experimental data as thefunction of neutrino energy. The solid and dashed lines show the calculated cross-sections
for free and bound targets. [29]4.3.2

CC/NC single meson and gamma production

Single meson, such as π K, and η and a γ-ray can be produced by the nucleon resonancestate N ∗ :ν + N → l + N∗

(4.3)

N ∗ → N 0 + (π, K, η, γ)(4.4)

Single-meson production of π K and η are simulated by using the Rein and Sehgal model.
[57, 56] There is a total of 28 resonances are considered in SK simulations. The final state pion
angular distribution could be derived from the ∆(1232) resonance. The angular distributionof pions coming from other resonances is assumed to be isotropic. This angular distribution
is derived by the experimental data from νp → µ− π + p scattering [41]. Pion-less ∆ decay [63]is also simulated. As before, the Pauli exclusion principle is accounted, when the scatterednucleon momentum is greater than the Fermi surface momentum.

46

4.3.3

CC/NC coherent pion production

Neutrinos could interact with oxygen nuclei with a charged pion production. The pion istransferred from the oxygen nucleus. The pion is emitted in the same direction with theneutrino and carries little momentum, given by the oxygen nucleus. This interaction modeis called the coherent pion production, and the Rein Sehgal model has also stimulated it[57, 56].

4.3.4

CC/NC deep inelastic scattering

If the neutrino energy is higher than 10 GeV, the deep inelastic scattering will become thedominant neutrino interaction mode. Neutrinos could interact with a quark in a nucleon andproduce multiple hadrons in such high energies regions. The cross-section of deep inelastic
scattering has been calculated by using the GRV98 (Gluck-Reya-Vogt) Parton distributionfunction [26]. In the energy region of W<2.0 GeV/c2 , we only consider the pions as produced
hadrons, and its multiplicity is estimated from the results of BEBC experiment [48]( andbubble chamber experiments [18]). When the energy of neutrino at the region of W>2.0
GeV/c2 , the PHYTIA/JETSET simulation package [64]is used to determine the hadronicsystem kinematics, and the productions of K and η mesons are also treated in the region.
Full MC simulation and data comparison of neutrino cross-section is shown in Figure
4.6. We could find that the simulations describe the data well.

4.4

Detector Simulation

As I have mentioned before, the particle propagation in water, Cherenkov photon emission,and the response of PMTs and electronics are simulated by SKDETSim, a GEANT3 based47

simulation package.
The Cherenkov photon propagation has been simulated by considering the Rayleighscattering, Mie scattering, and absorption by H2 O molecule. The Rayleigh scattering, only
caused by small particles, which r  λ, the r is the radius of a particle. And the Rayleighscattering will be the dominant scattering when photons have relatively short wavelengthsof ( λ ≤ 450 nm). The scattering coefficient dependence of λ−4 , so that the photons will bescattered symmetrically in the forward and backward directions.
And for longer wavelength ( λ ≥ 450 nm), the dominant scattering process is theabsorption by H2 O molecule. Besides, the Mie scattering is caused by large particles (r λ) to scatter photons. And the Mie scattering is more intensely in the forward direction.
Calibration data tune these scattering effects.

48Chapter 5
FC Reduction
Approximately 106 events/day are collected by Super-K. We must separate the data relevant
for physics studies from the background event, which is composed of low energy radioactivity
events (e.g., radon) and cosmic ray muon events. Additionally, We must also remove the“flasher” events caused by the PMT dynode discharge. Below, we provide an overview of
the automated “data reduction” algorithm for the fully contained (FC) data sample. This
type of sample means it deposited all of its energy to the ID volume. This sample is therelevant sample for our monogenic neutrino search. If you interest in the details of the FCdata reduction, as well as the decrease for the upward-going muon (UPMU) and the parts,
contained (PC) data samples, you could check the [9, 58]. Figure 5.1 schematically showsdifferent types of events in SK.

Figure 5.1: Schematic representation of the fully contained, partially contained, upwardgoing stopping and through-going muon event classes at Super-K.From [73].
49

5.1

The First Reduction

There are approximately 106 events triggered in SK per day. Most of them are downwardcosmic ray muons signals and low-energy radioactive signals. To remove this background,the following reduction is given as the first step in FC event selection.
1. PE300 ≥ 200 p.e.s
The total number of observed photoelectrons PE300 within the time width of 300 ns in
the inner water tank should be more than 200 photoelectrons (p.e.s).
2. NHITA800 ≤ 55
The number of hits in the outer tank within ± 400 ns, NHITA800 , should be less than55.
The first condition corresponds to a threshold of approximately 22 MeV/c for electron
momentum, which cuts most of his low-energy events such as radiation background. The
second condition is set for cutting cosmic-ray muons that pass through the outer water tank.
After this reduction, the event rate reduced from 106 events/day to about 3000 events/day.

5.2

The Second Reduction

The following reduction is given in the second stage FC event selection.
1.PEmax /PE300 ≤ 0.5
The ratio of the most significant number of photons PEmax divided by the total observed
ID PMT hits PE300 should be less than 0.5.

50

2. NHITA800 ≤ 25 (30 for SK-IV) or PEtot ≥ 100,000 pes (≥ 50,000 pes for SK-II)
The number of 1 hits in the OD tank NHITA800 is less than 25, or the total number ofphotoelectrons in the inner tank PEtot is more than 100,000.
The first condition can cut the event of the electrical noise of the PMT, which is observing a substantial signal compared to the surrounding PMT. The second condition is used tothe cosmic ray muons, which are remaining after the first reduction. After this reduction,
the event rate will be about 600 events/day.

5.3

Third Reduction

This reduction is used to remove much remaining background. The list of targets is shown
here.
• Hard muon cut
A cut for cosmic ray muons with very high energies above 1 TeV.
• Cut of passing muons
A cot of muon events which whose entry and the exit point is very near in the OD tanks.
• Stop muon cut
It cuts cosmic-ray muons that enter from the OD detector and stop in the ID tanks. In
this case, we could see there is an OD signal only.
• Cable hole muon cut
When the cosmic ray muon passes through a cable bundle connected to the PMT, the51

bundle will block the Cherenkov light. Therefore, it seems that this muon enters their tankwithout leaving a hit. To remove this muon, 2 m × 2.5 m plastic scintillators are attachedto the top of the cable hole. If this event is satisfied this condition, it will be cut. The firstand second event reduction cannot remove this muon.
– There is a hit in the plastic scintillator– Reconstruct event point is within 4 m region of the plastic scintillator.

Figure 5.2: Schematic figure of Cable hole Muon and VETO counter [37].

• Coincidence muon cut
If a cosmic ray muon event accidentally overlaps with a low-energy event in the OD,
the hit timing of the outer water tank will shift. We must remove such an event.
• Flasher event cut
Light emission may occur to the discharge of a PMT. This event is called a flasher event.
The hit pattern of the ID identifies this background.
52• Cut low energy events
After this reduction, the event rate will be about 50 events/day.

5.4

The Fourth Reduction

The fourth reduction is set up to remove the flasher event that the third could not remove
since the flasher events will repeatedly have similar patterns. Therefore, we divide the ID
tank into 1450 regions of 2 m × 2 m square, then the correlation r between the events could
be calculated by the following formula.

N

1 X (QA,i − hQA i) (QB,i − hQB i)
r=
.
N i=0
σA σB

(5.1)

Here, QA,i , QB,i are the photoelectrons number of the events A and B in the regioni, hQA i, hQB i are their mean values, and σA , σB are their standard deviations. When thecorrelation between the two events exceeds the threshold and the hit patterns are similar to
the flasher mode, The event will be cut.

5.5

The Fifth Reduction

The 5th reduction consists of:
The remaining background events are targeted and removed in the fifth reduction. After
this reduction, the event rate becomes about 30 events/day.
1. OD PMT hits in 200ns ≤ 10.
53

This condition aims to reject “invisible” cosmic-ray muons below the Cherenkov threshold but have an observed decay-electron.
2. cut the cosmic ray muon by using a more precise fitter
The list of the cut muon is as follows:• Stop muon cut• Cable hole muon cut• Coincidence muon cut• Longtail flasher event cut• Electronics events
Cut fake hits coming from the noise of high voltage systems and electric boards.
• Dead electronics hut
Cables and electric boards from the PMT are concentrated in the electronics hut locatedat the top of the tank. If the electronics hut are not working correctly, there could be somefake hit.
• Calibration event cuts. If the data contains laser events used to calibrate the detector,
it will be cut.

5.6

The Final Reduction

The final reduction is shown as follows:54

1. dwall>2.0m
2. NHITAC <16 (<10 for SK-I)
3. Evis > 30MeV
The dwall is the distance from the ID wall to the primary collision point. The area inside
2 m from the ID tank wall is called the fiducial volume (FV), just like figure 5.3 shows. We
apply this reduction becauses the event reconstruction near the wall isn’t working well. The
event which is happened within the fiducial volume is used for analysis. NHITAC is thecluster of PMTs hit with the highest charge in the OD. Evis is the total energy of the event
which assuming that the event generates all Cherenkov rings. The Events that don’t satisfy
the second condition will be classified as PC events. After these event selections, the event
rate will become approximately 8 event / day.

Figure 5.3: Schematic diagram of the OD tank, ID tank and FV of the Super-Kamiokande
detector.

55

Chapter 6
Sensitivity study

6.1

Event Selection

After the FC reduction, an event selection is applied to obtain the final analysis sample.

6.1.1

Event Selection

The target particle we are looking for is neutrino from GUT-monopole-catalyzed proton
decay in the sun. Due to oscillations, target particles are ν¯e neutrinos and ν¯µ neutrinos, andthe energy region is around the energy range of 459 MeV. However, we could see that thedominant neutrino reaction mode of ν¯e neutrinos and ν¯µ neutrinos in this energy range is
the CCQE. Please see the event reconstruction algorithm chapter and the neutrino reactions
chapter.

ν¯e + p → e+ + n(6.1)

ν¯µ + p → µ+ + n.

(6.2)

56

Since the leptons produced in the CCQE reaction will be reconstructed in different ways
in SK, therefore, the positron and the µ+ will have extra event reconstruction efficiency andsystem uncertainty estimates in the final event sample. On the other hand, the neutrino
oscillation probability of atmospheric neutrinos, which is the most significant backgroundfor this analysis, will also be changed with the energy and zenith angle of the neutrino.
From the first chapter we can see that our target particles are ν¯e neutrinos and ν¯µneutrinos, and from the neutrino reaction chapter, we can see that the CCQE process ofanti-neutrinos produces neutrons, and neutrinos produces protons. Note that the protons
produced by neutrinos (ν) will interact with other nuclei and release neutrons (via so-called
secondary interactions), the CCQE reaction of antineutrinos will also produce many neutrinos through nuclear interactions. However, from the MC simulation result, shown in Figure
6.1 below, we can conclude that the antineutrino CCQE reaction releases more neutrons on
average than the neutrino CCQE reaction. Therefore, the neutron is a good parameter that
could help us to separate neutrino from antineutrino interactions.

Figure 6.1: Distribution of neutrons in the final state from sub-GeV nuebar and numubar
CCQE interactions. Both lines are normalized by area.

57

Consequently, after we apply all of the reduction of FC, we also need to divide the FCdata to different samples by using the number of the Cherenkov rings (one-ring or multi-ring)and the energy of the events, dividing them into more than 1330 MeV(multi-GeV) or not(Sub-GeV). After that, we also separate the Sub-GeV, one ring, samples, which is basedon the number of Michel electrons for this sample, neutron number for this sample, andthe particle ID (PID). We could conclude from the above table that the dominated reaction
mode of the magnetic monopole catalyzed proton decay neutrino is CCQE. And, there is
only one lepton that could generate the Cherenkov ring, which equally means there is only asingle Cherenkov ring in SK. Therefore, I will focus on the case of SubGeV samples. Detailsof the event selection for other atmospheric neutrino analyses are present in [70].
The Sub-GeV data will be categorized into 5 sample such as follows :1. FC sub-GeV single-ring νe -like
2. FC sub-GeV single-ring e-like
3. FC sub-GeV single-ring ν¯e -like
4. FC sub-GeV single-ring νµ -like
5. FC sub-GeV single-ring ν¯µ -like
The momentum cut for single-ring e-like and mu-like events is different. The single ringe-like events has to satisfy the momentum cut, 100 MeV > pe < 1330 MeV, and for µ-likeevents it is, 200 MeV< pµ < 1330 MeV.
FC sub-GeV single-ring e-like sample contains νe CCQE interactions and also could be
NC π0 background events. The e-like sample which the highest fraction of CCQE events isthe 0 decay-e sample. For NC π0 event, one of the two gamma rays produced by π0 could
be missed by reconstruction, therefore the event could be misidentified as a single-ring e-like58

event. A specialized π0 fitter is used to reconstruct the second gamma-ray ring based on thefitted first ring.

Figure 6.2: schematic diagram about the steps for how to select the FC data to different
Sub-GeV samples.

After applying π0 likelihood method, remaining e-like events are divided into three
categories, depending on the detected number of Michel electrons and the neutron number:
0 decay-e sample with no decay electrons with zero tagged neutrons (e-like), 0 decay-e sample
with no decay electrons and one or more neutrons (ν¯e -like), and one decay-e sample which
has one or more decay electrons (νe -like).
On the other hand, νµ CCQE events are expected to produce one decay electron fromtheir muon. FC sub-GeV single-ring µ-like events are divided into two categories according
to the number of decay electrons and the number of the neutron: ν¯µ -like, νµ -like. If the
decay electron number is equal to one and the tagged neutron number is more significant
than 0, We will select this event to the ν¯µ -like the sample. We will choose the remaining
events to the νµ -like samples.
The other sub-GeV events are π0 -like multi-ring events, which have two or more e-likerings recognized. Figure 5.4 shows the schematic diagram about the steps for selecting the59

FC data for different Sub-GeV samples. Table 6.2 and Table 6.3 shows the summary of
purities of FC sub-GeV single-ring samples.
Table 6.1: The reaction mode fraction for 459MeV ν¯e neutrinos and ν¯µ neutrinos MC, andatmospheric neutrinos MC after event selection.
ν¯e

ν¯µ

ATM MC

CCQE
80.73% 99.89%
CC single π
16.08%0%
CC coherent π
0.322% 0.072%
CC multi π production 1.411%
0%
NC reaction
1.24% 0.036%

71.24%
17.80%
0.28%
2.076%
7.854%

Table 6.2: The purities of FC sub-GeV single-ring sample for 459MeV ν¯e neutrinos and ν¯µneutrinos MC, and fraction of total MCνe -likee-likeν¯e -likeνµ -likeν¯µ -likeCC νeCC ν¯eCC νµCC ν¯µNC event

Fraction

0%
0%
0%
0%
0%

80.95%
99.07%
99.77%
1.56%
0%

0%
0%
0%
0%
0%

19.04%
0.08%
0.05%
98.03%
99.75%

0%
0.84%
0.16%
0.39%
0.24%

0.23%
27.66%
19.97%
28.26%
17.95%

Table 6.3: The purities of FC sub-GeV single-ring sample for atmospheric neutrinos MCCC νe

CC ν¯eCC νµCC ν¯µνe -like 79.72% 1.61% 14.21% 2.71%
e-like 80.16% 17.18% 1.69% 0.03%
ν¯e -like 59.22% 36.92% 2.69% 0.11%νµ -like 1.39% 0.11% 79.84% 17.69%
ν¯µ -like 0.78%
0%55.43% 42.96%

6.1.2

NC event
1.72%
0.90%
1.03%
0.95%
0.81%

Sample Binning

The 5 event samples are distributed to more proper bins. The visible energy and reconstructed angle are used to define bins. For angular binning, the cosine value between the
direction of the Sun and the reconstructed lepton direction, cos(θSun ), is used. This value is60

calculated using the sun’s position compared to the SK tank at the time of each event. We
can check the cos(θsun ) distribution in Fig. 6.3 that atmospheric neutrino events are almost
evenly spread since we could assume that the particle is inserted into the SK isotropically.
We cannot use the neutrino direction since it cannot be reconstructed. However, the angularresolution of the lepton angle compared with the neutrino angle is 32 degrees.Therefore, thesignal events are not perfectly reconstructed as coming from the direction of the sun and we
can could see that the angular distribution for the signal will be more spread. Figures 6.3
shows the angular distributions of the five FC samples for the Signal event and BG event For
these samples, 10 equally sized angular bins which span from cos(θsun ) = -1 to 1 are used.
All samples are further divided into five momentum bins. As a result, events will be
distributed in 250 two-dimensional (angle and energy) bins for each Signal and BG respectively. During the fit, the Signal and BG MC bins are merged, so the total number of binsused to fit the flux of monopoles is 250 in total..
Table 6.4: The zenith angle and energy bin in each analysis sample

sampleenergy binscos θ bins

νe-like 5 e±momentum 10 in [−1, 1]
e-like 5 e±momentum 10 in [−1, 1]ν¯e-like 5 e±momentum 10 in [−1, 1]
νµ-like 5 µ±momentum 10 in [−1, 1]ν¯µ-like 5 µ±momentum 10 in [−1, 1]

61

(a)

(b)

(c)

(d)

(e)

Figure 6.3: cos(θsun ) distributions of signal MC and BG atmospheric neutrino.Normalization
for the signal is the number of MC events, which is about 20,000 event, related to the Parker
Limit. νe and νµ and background is normalized by the SK-IV livetime, which is 3244 days.

62

(a)

(b)

(c)

(d)

(e)

Figure 6.4: Momentum distributions of signal MC and BG atmospheric neutrino. Normalization for the signal is the number of MC events, which is about 20,000 events, related to
the Parker Limit. same as figure 6.3 is normalized by the SK-IV lifetime, which is 3244 days

63

6.2

Spectral Fit

6.2.1

Fitting TechniqueNow, we apply a spectral χ2 fit to the final momentum and cos(θsun ) distributions, as shownin the last chapter. By applying the χ2 spectral fit, we account for the shape difference
between the signal and the background distributions.
The χ2 minimization fit is based on the Poisson distribution. When the data is fitted,
it will be fitted with the systematic uncertainties by pull technique [21]. The χ2 function
definition in the analysis is

2

χ =2

nbins
X
i=1

 NX
2

syserr 
jNiobs,
ln exp − 1 +
Ni
σ
j
j=1
!
Nsyserrhi
X j jexp
sigfi
Ni = Niback + β · Ni
1+
σj
j=1

Niexp + Niobs

(6.3)

(6.4)

where the i is the index of the analysis bin. Here Niexp is the expectation for bin i, which is
generated by the MC (sum of the background and signal). Nisig , Niback are the signal MC,
background MC event in each bin separately. The Niobs is the observation data. In data
fit, Niobs should be take as the SK -IV data. The index j is the systematic errors index,
while j is the fit error parameter, fij is the fractional change of the i-th bin under a 1-sigma
variation of the system in the j-th systematic. The 1-sigma error uncertainty is defined as σj .
The fit is performed using one parameter, β, which denotes signal normalizations. This fij
will act separately on the signal and background. After the event selection, the background
MC distribution is normalized by the SK-IV lifetime. Since the monopole flux isn’t known
known, we need to identify the fit point with different β, to determine the sensitivity for
detecting the monopole neutrino in SK. The β is zero, means consistent with the no-signal
hypothesis. Similarly, β is one related to the monopole neutrino total number is 20,000 at
64

SK-IV, which is almost related to the Parker Limit, which could calculate by [27]. The χ2minimization is carried out for each β in grid according to ∂χ2 /∂j = 0. We can find further
details about the fit technique and the treatment of systematic errors in [70, 16], and issimilar to the standard SK oscillation analysis and the indirect dark matter search.
Our analysis is a sensitivity study. Therefore, we use two methods to do the sensitivity study here. The first method is Asimov sensitivity analysis, which uses the nominal
background MC assuming 0 signal (β = 0) as the observation and fits it with and without
the systematic error. By comparing the shape of these two curves from the fitting result,
we could be quantized how much the systematic errors related to the SK will impact thissearch. After that, we need to consider that there must be an random statistical differences
between the actual data and the MC. Therefore, we will add a random fluctuation to thenull hypothesis (β = 0) MC data and take it as fake data. Then, this simulated data is fitted
to test the sensitivity of the SK for magnetic monopole neutrinos. This method is called thetoy MC method.

6.2.2

Systematic Errors

The systematic errors in the analysis are calculated through the fij coefficients, as describedabove. For simplicity, we assumed that the bin content is affected linearly by the error.
Therefore, the fij can be defined as a slope of systematic error uncertainty, which is determined by the bin content, which changed by 1 σ. The definition of fij is shown as follows:

fij ≡

+σj

Ni

−σj

− Ni

2Ni0


.

(6.5)

The error estimation in our analysis is different with [70]. We take the way that the signal
and error bins are split to estimate various errors. That will ensure that signal systematic65

is applied to the signal bins and background systematic to the background bins. If the bins
should use both errors, it will be applied to both bins. Then the signal bins and backgroundbins will be merged during χ2 minimization.
The systematics can be divided into signal-specific (S) and background-specific (B).
Some systematics errors, such as detector and reconstruction errors, are familiar to signal
and background (SB). Since the dominant reaction mode of the signal, the neutrino, is the
CCQE, and the atmospheric neutrino could also interact via in CCQE, the CCQE crosssection uncertainty should apply to both signals and background(SB).
The systematic background errors are the neutrino flux, neutrino-interaction crosssection uncertainty. The systematic error of the background, is the same systematic error
which was employed in the SK oscillation analysis [70, 16]. Then we select the reconstruction
error, and the CCQE cross-section uncertainty and apply them to the signal. In Table 6.1,
Table 6.2, Table 6.3, we display the complete list of systematics, the uncertainties, and thefitted pull terms, which is calculated by j /σj the best-fit point under the toy MC hypothesis,
for the signal and background.
Although we use the same systematic error type as the previous SK analysis, because
the bin we use here is a two-dimensional bin of momentum and cos(θsun ), instead of thetwo-dimensional bin of momentum and zenith angle that previous SK analysis, our fij are
different. Our fij distribution here is shown in Figure 6.5

6.2.3

Sensitivity study

To calculate the MC sensitivity, we use atmospheric MC as ”fake data.” That corresponds
to the scenario in which is no evidence shows there is high energy monopole catalyze proton
decay is observed in the SK-IV. This hypothesis follows the background distribution, which

66

(a)

(b)

67

Table 6.5: Neutrino interaction, particle production, and PMNS oscillation parameter systematic errors for the spectral fits, with 1σ uncertainties and resulting fit pull terms. Errors
specific to signal and background are denoted by S and B.
Systematic error

1-σ uncertainty

CCQE cross section
DIS model difference
DIS cross section
Coherent cross section
NC CC ratio
CCQE νe ν¯e ratio
CCQE νµ νe ratio
CCQE cross section normalization sub GeV
CCQE cross section normalization multiply GeV
Hadron simulation
π0 π ratioν ν̄ ratio
θ13 error
δm221 error
θ12 error
MA in CCQE and single meson production
Single meson production cross section
DIS had mult2
Q spectrum in DIS (W < 1.3GeV /c2 )Q2 spectrum in DIS (W > 1.3GeV /c2 )DIS normalization in W > 1.3GeV /c2
Neutron mult
Neutron multiplicity generator comp

0.100
0.100
0.100
1.0
0.200
0.100
0.100
0.100
0.100
0.100
0.400
0.100
0.000
1.799
0.013
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100

68

SB
SB
SB
SB
SB
SB
SB
SB
SB
B
B
B
B
B
B
B
B
B
B
B
B
SB
SB

Table 6.6: SK-IVsystematic errors for the spectral fits, with 1σ uncertainties and resulting
fit pull terms. Errors specific to signal and background are denoted by S and B.
Systematic error

1-σ uncertainty

FC reduction for SK-IV
FC PC separation for SK-IV
Ring separation SK-IV
PID 1ring SK-IV
PID multi-ring SK-IV
Decay-e tagging SK-IV
Fiducial volume SK-IV
π decay tagging error
Up stop through separation SK-IV
Up stop energy cut SK-IV
Up/down asymmetry energy calibration SK-IV
Non Showering BG sub SK-IV
Non νe BG Multi-ring elike SK-IV
Non νe BG 1ring elike SK-IV
Non νe BG elike SK-IV
Non ν bg µ like
Sub-GeV 2-ring π0 SK-IV
Energy calibration

0.013
0.000
0.100
0.009
0.100
0.100
0.019
0.100
0.006
0.017
0.004
0.079
0.115
0.175
0.009
0.009
0.056
2.3

69

SB
SB
SB
SB
B
SB
SB
B
B
B
B
B
B
SB
SB
SB
B
SB

Table 6.7: Flux Systematic errors that are independent in for the spectral fits, with 1σuncertainties and resulting fit pull terms. Errors specific to signal and background are
denoted by S and B.
Systematic error

1-σ uncertainty

Solar Activity SK-IV
Absolute Normalization E less1GeVν ν̄ ratio E less 1GeVν ν̄ ratio E bigger 10GeVνe ν¯e E less 1GeVνe ν¯e E bigger 10GeVνµ ν¯µ E less 1GeVνµ ν¯µ E bigger 10GeVUp Down ratio
Horizontal Vertical ratio
K π ratio
Neutrino path length
Absolute Normalization E bigger 1GeV
Relative Normalization FC multi-GeVν ν̄ ratio 1 E bigger 10GeVνµ ν¯µ 1 E bigger 10GeVνµ ν¯µ 1 E bigger 10GeV
Matter Effect Error

0.070
0.25
0.019
0.050
0.050
0.079
0.019
0.150
0.009
0.009
0.100
0.100
0.150
0.050
0.029
0.050
0.059
0.068

70

B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B

means the signal’s normalization is β = 0, and the background normalized to the SK-period’s
lifetime. We determine the confidence of the monopole neutrino signal by calculating thedifference of chi-square to the best fit chi-square when the signal normalizations parameteris changing:χ2 ≤ χ2min + ∆χ2 .

(6.6)

This analysis has only one parameter and we set the confidence level to 90% for the convenience of comparison with other studies. Table 6.8 shows the ∆χ2 values we use for drawing
confidence regions. As an example of the χ2 contour output, we display the Asimov sensiTable 6.8: Values of ∆χ2 corresponding to confidence levels used in this thesis..
1-α (%)

m=1

68.27
90.
95.

1.00
2.71
3.84

tivity fit results in Figure 6.6. In all such χ2 contour plots, the black lines correspond to90% confidence level (CL) intervals, the blue lines correspond to the fit result, which does
not use the systematic error for fitting, and the red lines correspond to the fit result whichuses the systematic error for fitting.

71

Figure 6.6: The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by assuming
the true point is at null hypothesis.

According to Figure 6.6, we can get that the normalization at 90% C.L. is 0.00203 whichis correspond to 40.6 monopole events. The number of ν¯e event is 18.08 and the number ofν¯µ event is 22.51. To estimate how much the systematic error will impact our experiment,
we assume that the ”true point” of the next Asimov fit is set as the normalization at 90%
CL obtained from Figure 6.6 . The result is shown shown in Figure 6.7.
We can see that if we set the reference point at beta equal to 0.00204, then the χ2 witha systematic error when no magnetic monopole neutrino (β = 0) is 3.58, and the χ2 without
systematic error is 7.35, respectively. Although the systematic error impacts the sensitivityof our analysis, the χ2 at β = 0 is still higher than the 90% confidence level χ2 , which is 2.71.
That shows that could cause magnetic monopole neutrinos in SK with at slightly better than72

90% CL.

Figure 6.7: The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by assumingthe ”true point” of the fitting is normalization at 90% C.L. from Fig 6.6

We have seen that although the impact of systematic errors is not very large, it stillaffects our final results. Therefore, I investigated the source of systematic errors. The
investigation method is as follows:
Initially, removed the 77 systematic error terms one by one, assuming that these recurring error terms should be zero, and then perform the Asimov sensitivity test. If thissystematic error is vast for our fitting, then the number of magnetic monopole neutrinos with
a 90% confidence level will reduce if this error is deleted. If the influence of this systematic
error is not particularly large, then even if this periodic error is deleted, we will find thatthe number of neutrinos in the magnetic monopole has not decreased too much. Our fitting
curve will coincide with the error-free Asimov sensitivity analysis when we delete all the73systematic errors.
Although we have 77 systematic errors here, we can classify various systematic errors.
For example, we can set the flux error to the same type of systematic error because thissystematic error will only affect the background in our analysis, atmospheric neutrinos.
The final fitting result is shown in Figure 6.8 below. We can see that the primary error
term comes from six sources. That is single meson production cross-section, MA in CCQE
and Single Meson Production, neutron tagging, atmospheric neutrinos flux, Nuclear Effectin 16 O Nucleus, CCQE cross section. The impact of these errors on the analysis is listed in
the table below.

Figure 6.8: The Asimov sensitivity analysis fit for 459MeV Monopole neutrino by using
different systematics error

74

Table 6.9: The value of β at the 90% C.L. changes for each of mainly contribute errors.
β

the error which is omitted

0.00204
no error is rejected
0.00185
CCQE cross section
0.00177
Atmospheric Neutrinos Flux
0.00172
Nuclear Effect in 16 O Nucleus
0.00161
Neutron Tagging
0.00152 MA in CCQE and Single Meson Production
0.00138
Single Meson Production Cross Section
Single Meson Production Cross Section Uncertainty in the cross-section of single
meson production is estimated to be 20% by investigating the difference between the expectation and experimental data of νµ p → µ− pπ + observation. νµ n → µ− pπ 0 interaction is lessunderstood as there are only few experiment results. Hence the additional uncertainty is estimated by comparison with the Hernandez model. The cross-section ratio of νµ n → µ− pπ 0
is shown in the dashed line in figure 6.9. It is considered that π 0 production interaction has
40% uncertainty relative to the π ± emitting interactions.

Figure 6.9: Predicted cross section of the Hernandez model normalized by that of the Rein
and Sehgal model for νµ p → µ− pπ + (solid line), νµ n → µ− pπ 0 (dashed line) and νµ n →µ− nπ + (dotted line).[53]75CCQE Cross Section The cross-section CCQE for bound nucleon is calculated basedon the Smith and Monitz Fermi-gas model. The difference from the Nieves model is set toas the 1σuncertainty for CCQE cross-section [50]. Figure 6.10 shows the calculated CCQE
cross-section ratio of the Nieves model to Smith and Monitz model as a function of neutrinoenergy for the total cross-section.

Figure 6.10: Ratio of CCQE cross section, Nieves model normalized by the Smith and Monitz
model. [53]

Nuclear Effect in 16 O Nucleus The cross-section of pion final state interactions inside
nuclei is compared between NEUT simulation and external experimental data. The crosssections of these last state interactions in the simulation are varied with the weighing method
so that the difference with the experimental data is 1σ as shown in figure 6.11. Then the
difference between the minimum and maximum weights on each simulated event is then used
to compute the uncertainty on the nuclear effect in the oxygen nucleus.

76

Figure 6.11: π + scattering on carbon target in: quasi-elastic channel (top left), absorption
channel (top right), total reaction channel (bottom left) and single charge exchange channel(bottom right).[53]MA in CCQE and Single Meson Production For MA in CCQE and single meson
production, the difference of Q2 spectrum between MA = 1.2 and MA = 1.1 is set to be thesystematic uncertainty to take into account the 10% uncertainty of MA parameter.

Neutron Tagging The uncertainty in Neutron Tagging is estimated by comparing thedata and MC difference which is studied by R. Akutsu’s Ph.D. thesis by using neutrons
produced in CC νµ interactions in the T2K beam, and the MC generators NEUT 5.4.0 and
GENIE.
These six error sources can be expected to be reduced in the future. For meson exchange
current, the sources of these errors are mainly from the meson and nucleon reactions usedin Monte Carlo simulation. These systematic errors may be reduced in the future when weuse multiple models for Monte Carlo simulation.
The error for neutron tagging is mainly due to the low efficiency of neutron tagging in77

SK. However, we can expect that this error will be significantly decreased when gadolinium
is put into SK in the future. Gadolinium has a very high neutron capture cross-section, so
it will improve the efficiency of the neutron tagging in SK.

Figure 6.12: The toy MC sensitivity analysis fit for 459MeV Monopole neutrino by assuming
the true point is at null hypothesis.

It may be more challenging to reduce the error caused by the reaction cross-section,
nucleon axial mass, and the atmospheric neutrino flux because if we want to reduce thesystematic error of these items, new models and new experimental data are required at thesame time. The experimental data has not been updated recently. So these systematic errors
are more difficult to improve.
After we use the Asimov sensitivity test to estimate the systematic error effect of oursensitivity study, we use the toy MC method to evaluate the flux of the magnetic monopole

78

neutrino in SK. We display the toy MC sensitivity fit results in Figure 6.9. We find thatthe minimum χ2 has risen a lot compared to the Asimov sensitivity test. That is because
we added random fluctuations to the null hypothesis MC when doing the toy Monte Carlosensitivity test. As we state before, we are more concerned about is the difference of χ2 withthe change of the normalization, as shown in Figure 6.12.
According to Figure 6.12, we can get that the normalization at 90% C.L. is 0.00265
which is correspond to 51 monopole events. The number of ν¯e event is 22.71 and number ofν¯µ event is 28.28.
Assuming that the total flux of the magnetic monopole neutrinos is I0 , the total numberof events Ntotal is as follows:

Ntotal = Ntarget T det (T )I0 σ.

(6.7)

Here, det (T ) represents the detection efficiency which depends over the run time T, andNtarget represents the total number of water molecule contained in the SK fiducial volume,
which is 22.5 kilotons water. Here T integrates over the entire lifetime, the entire SK-IV
period is 3224 days. By setting Ntotal equal to Asimov sensitivity study result, the normalization at 90% C.L. is 0.00203 which is correspond to 40.6 monopole events, with number ofν¯e event is 18.08 and the number of ν¯µ event is 22.5. The reaction cross-section(σ) of a neutrino will change with different neutrino types and neutrino energy, but all signal neutrinosin this analysis have single energy of 459MeV, so we don’t need to consider the influenceof neutrino energy on the neutrino interacted cross-section. For the 459MeV anti-electron
neutrino and anti-muon neutrino, their reaction cross sections per nucleon are calculated by
NEUT, which is :σν¯e = 2.145 × 10−38 cm−2 , σν¯µ = 1.956 × 10−38 cm−2 .

79

(6.8)

And the detection efficiency here assumes as 1. The total flux of the magnetic monopole
neutrinos on Earth is found as follows:

I0 < 9.49 cm−2 s−1 (90% C.L. ).

(6.9)

The magnetic monopole neutrinos emission rate and flux on Earth have a relationship likethis [35]:I0 '1 BRp→ν̄ d
.
4πR2 mp c2 dt(6.10)

where BRp→ν̄ is the direct proton decay branching ratio. Here R is the average Earth-Sun
distance. We use the distance between earth and sun as 1.496 × 108 km. The d
is thedt
magnetic monopole neutrinos emission rate. mp is the mass of proton. Then the magnetic
monopole neutrinos emission rate is calculate as follows:
d
dt



BRp→ν̄
10−4



< 2.24 × 1027 s−1 (90% C.L. ).

(6.11)

This could also calculate the magnetic monopole neutrinos emission rate:Z
fp =nM σR vrel ρH NA d3 x = NM σR vrel ρH NA decay /s.

(6.12)

Here, nM is the number density of magnetic monopoles in the sun, and NM is the abundanceof magnetic monopoles in the entire solar core. σR is the cross-section of the Rubakov
effect and in order to facilitate the comparison with the previous SK results, we use 1mb.
And vrel is the relative velocity of the magnetic monopole and the proton, which is taken
as vrel = βrel c (= 2 × 10−3 c)[68]. ρH (= 50.4 g/cm3 ) is the mass density of hydrogen at thecenter of the sun. NA is Avogadro’s number. When we doing the caculation, we used theapproximation function, which is the function on the right.

80

Therefore, the abundance of magnetic monopoles in the entire solar core could be calculated as:

NM

 σ

  BR

R

1mb

p→ν̄
10−4



< 4.01 × 1015 (90% C.L. ).

(6.13)The relationship between this number and the magnetic monopole flux in the universe is asfollows NM = 1041 FM , where FM is the astrophysical monopole abundance, as introduced in
Chapter 4. Consequently, after we estimate the flux of the magnetic monopole neutrino in
SK, according to Figure 6.6. We could calculate that the astrophysical monopole abundancein the universe is

FM

 σ

R

1mb

  BR

p→ν̄
10−4



< 4.01 × 10−26 cm−2 s−1 sr−1 (90% C.L. ).

(6.14)

To visualize the analysis results, we have shown the 90% (CL) allowed signal multiplied by
50, obtained from the Asimov sensitivity study, with all event sample spectra overlaid foratmospheric neutrino MC.

81

(a)

(b)

(c)

(d)

(e)

Figure 6.13: cos(θsun ) distributions The background is normalized by the SK-IV lifetime,
which is 3244 days

82

(a)

(b)

(c)

(d)

(e)

Figure 6.14: Momentum distributions from the Asimov sensitivity study. The backgroundis normalized by the SK-IV lifetime, which is 3244 days

83

Chapter 7
Summary and Future Prospects

Here is the sensitivity study result of SK to detect magnetic monopole neutrinos.

FM σ   BR
0

1mb

p→ν̄
−4
10



< 4.01 × 10−26 cm−2 s−1 sr−1 (90% C.L. )(7.1)

Compared with the previous results of SK [68],FM σ  f + 
0

π

1mb

0.5

−24

< 6.3 × 10



βM
10−3

2

cm−2 s−1 sr−1 (90% C.L. )(7.2)

we can see that if we search the monopole catalyze proton decay by using the direct mode,
the SK will be roughly two orders of magnitude more sensitive than when searching for theindirect proton decay.
However, these results still need further discussion. For example, as we mentioned
before, we may need to consider the co-annihilation of magnetic monopoles in the Sun.
Nevertheless, we also need to consider the dependence of the Rybakov effect cross-section
with the speed of the magnetic monopole. In this analysis, we only take the cross-section of
the Rybakov effect as a fixed value, which is about one milibarn.
84More importantly, we can see that our result has the same shape as a result obtained byindirect proton decay. It is the product of the flux of the magnetic monopole in the universe
and the branching ratio of the corresponding proton decay. So far, we have not been able
to confirm the existence of proton decay after various experiments, so the branching ratio of
proton decay is still uncertain in our analysis.
However, the result of our sensitivity analysis still brought us an exciting result. And
we will use the result to fit the SK-IV data to test whether the magnetic monopole neutrino
exists.
SK is now running as a new phase, SK-Gd, which dissolves Gadolinium (Gd) in the tank.
Gd has a large capture cross-section of neutrons. Therefore, the neutron tagging technology
has improved. This phase started in August 2020, and the atmospheric neutrino events,
which is the background of our analysis, are expected to decrease. That could contribute to
the better sensitivity of proton decay searches. In addition, the Hyper-Kamiokande project(HK) [54], the successor to SK, has started its construction and plans to operate in 2027.
The magnitude is planned to be ten times larger than SK. It will be a cylindrical water tankof 74 m diameter and 60 m height, and will use 40,000 PMTs and 260 kilotons of pure water.
HK is expected to contribute to our analysis with more high statistics.

85

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Appendix A
MCP PMT Flasher Measurement

A.1

Hyper-Kamiokande Experiment

The Hyper-Kamiokande detector is a large water Cherenkov detector scheduled to be built
at 8 km south of Mt. Ikeno, where the Super-Kamiokande detector is located, 650 m underground of Mt. Ninjugo. It contains 190,000 tons of water, which is 8.4 times as much as theSK water tank. The tank is divided into two layers, an inner tank and an outer tank witha coaxial center. The inner tank is mainly equipped with about 40,000 20-inch diameters
PMTs inward for neutrino observation, and the outer tank is mainly installed 8 inch PMT
to eliminate cosmic ray-derived events. The photoelectric surface coverage of PMT is about
40% in the inner water tank.

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Figure A.1: Hyper-Kamiokande detector

The tank is cylindrical with a diameter of 68.0 m and a height of 71.0 m. The inner
water tank has a diameter of 64.8 m and a height of 64.8 m, and the area of 2m above andbelow the outside and 1 m outside the side surface is the outer water tank. In the SuperKamiokande detector, the tank was made of stainless steel to prevent the contaminationof radioactive substances such as radon from the bedrock, in the same way as the SuperKamiokande detector. However, the material of the tank itself and the material between thetank and the bedrock is currently being studied.
The inner and outer tanks are separated by a stainless steel structure for arranging the
PMT. The excavation cavity has the shape of a cylinder in which the tank is placed anda dome above it. The top and side surfaces of the structure in which this PMT is placed
are suspended from the ceiling of this dome-shaped space. This has been changed from the93

method adopted in the Super-Kamiokande detector in consideration of making the structure
thinner and lighter.
In addition, since the geomagnetism in the vertical direction will affect the photon
collection efficiency of the PMT, rectangular and circular coils are arranged in the verticaland horizontal directions of the tank to cancel the geomagnetism. If necessary, further
consideration will be given to the installation of coils.

A.2

The MCP PMT

One of the important elements in the water Cherenkov detector is the photodetector. HyperK plans to use about 40,000 photodetectors in the inner water tank and about 8,000 photodetectors in the outer water tank. The particle type, energy, reaction position, etc. arereconstructed by using the charge and time information obtained by these photodetectors.
Photodetectors are subject to various requirements because these reconstructions require
information in units of one photon and several ns, respectively. Table 3.1 summarizes theperformance requirements for photodetectors in Hyper-K.

Figure A.2: performance requirements for photodetectors in Hyper-K

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NNVT has been producing 20-inch PMTs based on micro-channel plates (MCP), whichis already applied to the JUNO experiment. Those PMTs had a good detection efficiency(30%), good pressure tolerance, and low radio-isotope glass. However, their weak point was
their timing resolution of approximatively 20 ns, which was insufficient for use in HyperKamiokande. NNVT developed a new version with focusing electrodes to improve the timing
resolution. Coupled with an optimization of the voltage divider circuit, they allowed thisnew model to reach a timing resolution of 4.3 ns (FWHM), better than the resolution of the
HPK R3600 used in Super-K (6.73 ns). This improved MCP PMT, the GDB-6203, is now
tested as an alternative option for the Hyper-Kamiokande inner detector.

Figure A.3: The MCP PMT

A.3

The MCP PMT Flasher Measurement

From the above table, we can see whether a flasher has existed as an important feature for us
to detect the photomultiplier tube (PMT). If there are flashers, especially flasher amplitudeis greater than 100 pe, the systematic error will be increased. As we described in Chapter 5
and Chapter 6.
The main reason for the flasher is caused by the PMT dynode discharge. So when wemeasure the flasher. We need to put PMT in an experiment box that is completely shaded95and has no background as much as possible and use two PMT that have been confirmed tohave no flasher, as monitoring PMT. The schematic diagram and photos of the experimental
equipment are shown in the figure below. If there is a signal greater than 100 pe, we willobserve the three PMT simultaneously appear flasher coincident signals.
We use two methods when measuring the flash characteristics of MCP PMT. The first
method is an indirect measurement, that is we do not directly observe the monitor PMT
signal to determine whether this signal is a flash signal or not. We measure the monitor
PMT event rate which is more than 100 p.e. If MCP PMT does not produce a flash signal,then the 100 p.e signal rate of the monitored PMT under long-term observation should be at
the same level as the background 100 p.e signal rate, which is the 100 p.e signal rate when
the MCP PMT is turned off.
However, if MCP PMT will continuously emits flash signals, the 100 p.e signal rate ofmonitoring PMT should be quite different from the background 100 p.e signal event rate.
A very important advantage of this method is that we can measure MCP PMT for a longtime. But there is still a disadvantage that is that we cannot determine whether the 100 p.e
signal comes from MCP PMT or not, since we couldn’t make a pure environment which is
no 100 p.e emit source.
We already know that the flashing characteristics of MCP PMT are positively correlatedwith the working voltage of PMT, so when we perform an indirect measurement, we will
start measuring from 0 and rise the voltage step by step. Each step is measured for 20
minutes to calculate an average signal rate. At the same time, we also set up a coincidence
signal here. If there is a flash event, then the two PMT will have a coincidence signal.
But when we performed the first measurement, we found that whether it was a 1-inch
monitoring PMT or a 20-inch monitoring PMT, their 100 p.e signal rate did not increasesignificantly compared to when the MCP PMT was turned off. Therefore, we gave up the

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(a)

(b)

(c)

Figure A.4: The result of indirect measurement of the flash characteristics of MCP PMT.
The three pictures are one-inch PMT 100 p.e signal event rate (c), 20-inch SK PMT 100
p.e signal event rate (monitoring PMT) (b), and the coincidence signal 100 p.e signal event
rate (the coincidence signal is 20-inch PMT and the coincidence with the signal of 1 inch
PMT) (a). The dot and the triangle point represent the 100 p.e signal measurement result
when the MCP PMT is working. The inverted triangle point and the cross represent themeasurement result when closed MCP PMT (background).

97

indirect method, and check the MCP PMT will emit a flash signal or not by using the direct
method, that is an oscilloscope is directly used to observe the MCP signal to determine
whether a flash signal appears.

Figure A.5: Schematic diagram of flasher measurement of MCP PMT

Figure A.6: Photos of flasher measurement of MCP PMT

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After about 30 days of long-term observation, we have confirmed that MCP PMT willshow about three flashes per hour. This does not meet the requirements of HK for photomultiplier tubes. Therefore, we need to invite NNVT to further conduct MCP PMT. The
improvement, because MCP PMT has very good cost performance and detection efficiency.

Figure A.7: A example of MCP PMT flasher event99