Search for proton decay into three charged leptons
in Super-Kamiokande
Masahiro Tanaka
Department of Physics, Tokyo Institute of Technology
August 2019

ii

Acknowledgements
I am deeply grateful to my supervisor Prof. Masahiro Kuze. He taught me many importantand useful things about not only physics but also the skills of discussion, presentation, communication and so on. I will go forward my career being proud of the experience of 6 years as
the member of Kuze group.
I want to thank all members in SK group, in particular Dr. Makoto Miura and Dr. Shunichi
Mine. My analysis would have never finished without their great helps about many technicalthings for the proton decay analysis. I also want to thank Prof. Edward Kearns, Prof. Roger
Wendell, Prof. Yoshinari Hayato, Prof. Masato Shiozawa, Dr. Christophe Bronner, Mr. Akira
Takenaka, Mr. Yutaro Sonoda, for giving me many useful suggestions.
I want to show my appreciation to Prof. Masaki Ishitsuka who belonged to Kuze group.
He taught me many basic and essential things as the scientist. I also want to thank Dr. Yohei
Yamaguchi, who is the assistant professor of Kuze group, for giving me many comments on
my PhD thesis.
I express my gratitude to Prof. Osamu Jinnouchi, Dr. Koji Terachi, Dr. Masato Aoki, Dr.
Shintaro Kawade, Dr. Takuya Nobe, who are working on ATLAS experiment. They taught me
many essential things about physics analysis at the beginning of my PhD course.
My deepest appreciation to all the current and old colleagues in Kuze group. The conversations with them were one of the most enjoyable time in my daily life. Ms. Tomoyo Yoshida
and Mr. Lukas Berns often taught me many technical things about my analysis or SK detector.
Thank you very much.
Finally, I want to express my appreciation to my family. They continued to support 9 yearsof my long long life as a student. Thank you very much.

iii

Abstract
In nature, there are four interactions: strong, electromagnetic, weak and gravity and they
are considered to be one unified interaction at the very beginning of the universe. One of the
final goals in particle physics is explaining these four interactions by one unified theory. Now
we are on the way of unifying the three interactions of strong, electromagnetic and weak.
One of the candidates for this goal is grand unified theory (GUT). Basically the energy scaleof GUT is considered to be ∼ 1015 GeV. In such significantly high energy scale, the direct
search for GUT is impossible by any current high energy experiments. On the other hand,in GUT, the proton which is a stable particle in Standard Model (SM) is predicted to decay.
A search for such proton decay events is a strong way to prove the GUT. Since the life timeof proton is predicted to be much longer than the age of the universe, we need to preparea tremendous number of proton source for the discovery. Water is often used as the protonsource in pure water Cherenkov detectors like IMB, KAMIOKANDE and Super-Kamiokande(SK). Many decay modes of proton decay have been searched by these experiments but it has
never been observed yet.
In this thesis, a search for proton decay into three charged leptons has been performed byusing 0.37 Mton·years of data collected in Super-Kamiokande(SK). All combinations of electrons, muons and their anti-particles were considered as decay modes. The modes are complementary to decays to a lepton and a meson, which are already extensively searched for.
The lifetime of proton is predicted to be ∼ 1033 years for these modes at the energy scale of
100 TeV according to the theory suggested by T. Hambye and J. Heeck[1]. This is a reachable
lifetime scale in SK. Indeed, the last search performed for these modes was by IMB-3 detector
20 years ago, thus a huge improvement in sensitivity is expected with the exposure of SK,
possibly leading to a discovery.
After dedicated selection criteria for each of six decay modes, the data are compared withbackground expectations derived from atmospheric neutrino Monte Carlo. Since no significant excess of events has been found over the background, lower limits on the proton lilfetime
divided by the branching ratio have been obtained for each mode. The limits range between
9.2 × 1033 to 3.4 × 1034 years at 90% confidence level, largely improving upon previous experiments. The improvement factors range between 15 to 1,800, and in one of the modes firstlimit has been set.

Contents
1 Introduction
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Particles in the Standard Model . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Gauge symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Spontaneous symmetry breaking . . . . . . . . . . . . . . . . . . . . .
1.1.4 Electroweak unification . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Grand Unified Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 SU(5) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 SUSY SU(5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 SO(10) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Proton decay into three charged leptons . . . . . . . . . . . . . . . . .
1.3 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
1
2
4
5
7
7
9
9
10
11

2 Super-Kamiokande Experiment
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Principle of the Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Water Purification Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Air Purification Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 PMTs and associated structures . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Electronics and data acquisition systems . . . . . . . . . . . . . . . . . . . . .
2.6.1 Electronics and data acquisition systems in SK-I to SK-III . . . . . . . .
2.6.2 Electronics and data acquisition systems in SK-IV . . . . . . . . . . . .
2.7 Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 High-voltage setting of the PMTs . . . . . . . . . . . . . . . . . . . . .
2.7.2 Relative gain difference . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.3 Absolute gain conversion factor . . . . . . . . . . . . . . . . . . . . .
2.7.4 Relative difference of QE . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.5 Light absorption and scattering in water . . . . . . . . . . . . . . . . .
2.7.6 Light reflection at PMTs and black sheets . . . . . . . . . . . . . . . .
2.7.7 PMT timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.8 OD PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.9 Energy Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13
13
14
17
18
18
20
20
24
26
26
28
28
30
30
34
34
36
36

3 Monte Carlo Simulations
3.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39
39
40

v

vi

CONTENTS
3.2.1 Neutrino flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Neutrino interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Nuclear effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Neutron generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41
43
48
50
50

4 Event Preselection
4.1 Low Energy Event Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Electric Noise Event Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Specific Background Rejection I . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Hard muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Through going muon . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Stopping muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Cable hole muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.5 Coincidence muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.6 Flasher event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.7 Low energy event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Flasher Event Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Specific Background Rejection II . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Stopping muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Cable hole muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Coincidence muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.4 Invisible muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.5 Long tail flasher event . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Rejection for ID/OD cross talk . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
52
52
52
53
53
53
53
54
54
55
55
55
56
56
56
56
57
57

5 Event Reconstruction
5.1 Vertex Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Point fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Ring edge search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 TDC fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Ring candidate selection . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Ring candidate test . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Expected p.e.s distribution . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Ring separation I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Determination of particle type . . . . . . . . . . . . . . . . . . . . . . .
5.3.4 Ring separation II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Momentum Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Michel Electron Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59
59
61
62
63
65
66
66
68
69
70
71
72
74
74
75

6 Proton Decay Search
6.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Number of reconstructed rings . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Number of e-like or µ-like rings . . . . . . . . . . . . . . . . . . . . . .

79
79
80
80

3.3

CONTENTS

6.2

6.3
6.4

6.5

6.1.3 Number of decay electrons . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 π 0 veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.5 Neutron veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.6 Total mass and momentum . . . . . . . . . . . . . . . . . . . . . . . .
6.1.7 Selection summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Correlated decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Fermi motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Neutrino flux & cross section . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Pion FSI/SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.5 Fiducial volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.6 Detector non-uniformity . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.7 Energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.8 Ring counting & PID . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.9 Decay electron tagging . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.10 Neutron tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.11 Total systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . .
Data and MC agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Data open results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Observed candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lifetime limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii
81
84
84
85
85
97
97
97
99
99
99
101
102
102
104
104
107
107
116
116
119
127

7 Discussion

131

8 Conclusion

133

A Period by Period Comparisons135

B Previous Experiments
159
B.1 IMB-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.2 HPW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Chapter 1
Introduction
There are four interactions in our universe: Strong, Electromagnetic, Weak and Gravity andthese interactions are believed to be one unified interaction at the very beginning of the universe. One of the main goals in particle physics is understanding these four interactions by one
unified explanation. Strong, Electromagnetic and Weak interactions are explained by the Standard Model (SM) and Electromagnetic and Weak interactions are already unified by WeinbergSalam theory in 1961. Next step is unifying Strong, Electromagnetic and Weak interactions
and many theories are suggested. One of the strong candidates is the Grand Unified Theory(GUT). In this section, SM and GUT are explained.

1.1 The Standard Model
1.1.1

Particles in the Standard Model

SM can explain almost all phenomena in particle physics. There are 6 quarks and 6 leptons
called as fermion (Spin S = 1/2), 4 gauge boson (S = 1) and Higgs boson (S = 0) in SM.
Each quark and lepton has so called flavor: 6 quarks correspond to u, d, c, s, t, b and 6 leptons
correspond to e− , νe , µ− , νµ , τ − , ντ . The couplings of Weak interaction for (u ↔ d), (c ↔
s), (b ↔ t) are stronger than other combinations. The mass scales are also different throughout
these pairs. This categorization is called as the generation and lepton is also categorized by 3
generations. Quark has strong ”charge” so called color and interacts with gluon by Strong
interaction. There are 3 colors called as R(red), G(green) and B(blue). Fermion has 2 states
depending on the direction of its spin. If the direction of the momentum and the spin of theparticle is same, the particle is defined as helicity plus and minus for inverse situation. The
chirality is a similar value with helicity, which is important in Weak interaction. The helicity
and chirality are same under the relativistic situation. The chirality corresponding to helicity
plus is called as right-handed, and helicity minus is called as left-handed. Charge and massfor each quark and leptons are summarized in Table1.1. Each particle has its pair of so called
anti-particle which has the same mass and spin but inverse charge with original particle.
There are 4 bosons of S = 1 (γ, W ± , Z 0 ,gluon) which intermediate each interaction and
Higgs boson (H 0 ) of S = 0 which gives the mass to other elemental particles. γ, W ± , Z 0 ,gluon
are called gauge boson as these particles are introduced from gauge symmetry. The gauge boson carries energy and momentum by being created from one particle and absorbed by anotherparticle. γ is the massless vector particle which intermediates Electromagnetic interaction and
1

2

CHAPTER 1. INTRODUCTION

Table 1.1: Charge and mass for each quark and lepton. The mass for quark is so called current
mass.[2]Generation Quark Charge [e] Mass [MeV/c2 ] Lepton Charge [e] Mass [MeV/c2 ]
u
2/3
∼ 2.3
e−
-1
0.511
1
d
-1/3
∼ 4.8
νe
0
< 2.2 × 10−6−c2/3
∼ 1, 280
µ
-1
105.7
2
s
-1/3
∼ 95
νµ
0
< 0.195−
t
2/3∼ 1.73 × 10
µ
-1
1,777
3
b
-1/3
∼ 4, 200
νµ0< 18
couples with charged particles. W ± and Z 0 bosons are also vector particle with finite mass
which intermediate Weak interaction and couples with all quarks and leptons. W ± boson caninteract with only left-handed fermion or right-handed anti-fermion. Z 0 boson can interact
with both left- and right-handed particles but the strength of the coupling is different between
left- and right-handed. Gluon is the massless vector particle which intermediates Strong interaction by being created and absorbed from quarks or other gluons. Gluons have color andanti-color and couples with color charge of quark or couple themselves. So called Higgs fieldinteracts with other fermions or gauge bosons and they get the mass according to the Higgs
mechanism. The strength of the coupling between Higgs boson and other particles is proportional to the mass of the particles. The interaction, charge and mass of each boson aresummarized in Table1.2.
Table 1.2: Interaction,charge and mass of each boson[2].
BosonInteraction
Charge [e] Mass [GeV/c2 ]γElectromagnetic
0
0
W±
Weak
±1
80.4
Z0
Weak
0
91.2
gluon
Strong
0
0
0
H
0
125

1.1.2

Gauge symmetry

In the quantum mechanics, the probabilities of the physics events P are described by using
the wave function ψ(x) as below.
P = |ψ(x)|2(1.1)
On the other hand, same wave function but with arbitrary complex phase ψ ′ (x) is considered
as below.
ψ ′ (x) = eif (x) ψ(x)(1.2)
This is called as the gauge conversion. Since the probability P of both states are same, ψ(x)and ψ ′ (x) should describe the same physics phenomenon.
When ψ(x) is an electron, ψ(x) follows the Dirac equation as below.
(iγµ ∂ µ − m)ψ(x) = 0(1.3)

1.1. THE STANDARD MODEL3

But ψ ′ (x) does not follow the Dirac equation. This result is contradicted that ψ(x) and ψ ′ (x)describe the same physics phenomenon (electrons). Actually in case ψ(x) is an electron, equation of motion for electromagnetic field Aµ also needs to be considered as below.
{(iγµ ∂ µ − m)ψ = eγν Aν ψ
(1.4)∂µ ∂ µ Aν = e[ψ̄γ ν ψ]
The first equation describes the states of electron under the electromagnetic field Aν and thesecond equation describes the electromagnetic field Aµ generated by 4-dimensional current.
The electromagnetic field is also changed by gauge conversion as below.
Aµ → A′µ = Aµ − (∂ µ f )/e
Then equation (1.6) becomes as below after gauge conversion.
{(iγµ ∂ µ − m)ψ ′ = eγν A′ν ψ ′∂µ ∂ µ A′ν = e[ψ̄γ ν ψ ′ ]

(1.5)

(1.6)

Therefore, this system is invariant under the gauge conversion and this is called as gauge
symmetry. In the Standard Model, gauge bosons are introduced by the gauge symmetry. Generally in particle physics, certain phenomenon is described by the Lagrangian L which is notchanged under certain symmetry. The Lagrangian for the first function in equation (1.6) is
described as below.
L = ψ̄(iγµ Dµ − m)ψ
Dµ = ∂ µ + ieAµ(1.7)

This Lagrangian is invariant under the gauge conversion. The Lagrangian for the QED LQED
is described as below by adding the factors for the photon motion.
1
LQED = ψ̄(iγµ Dµ − m)ψ − f µν fµν
4f µν ≡ ∂ µ Aν − ∂ ν Aµ

(1.8)

Strong interaction is described by the Quantum Chromodynamics (QCD) which is directly
introduced by gauge symmetry. The gauge boson, gluon is introduced from color symmetry.
Then the strong interaction occurs by the coupling between colors and gluons. The wave
function of quark Ψ is described by 3 color components as below.
 qRΨ = qG (1.9)
qB
The strong interaction is invariant to color conversion as below.
Ψ → Ψ′ = US Ψ

(1.10)

Here, US is so called SU(3) conversion which is a kind of gauge conversion described as below.
US = exp{−i[θa (x)Ta ]};a = 1, 2, ..., 8(1.11)

4

CHAPTER 1. INTRODUCTION

Here, Ta is 8 Hermitian matrixes whose trace is 0. The Lagrangian for the strong interaction
should be invariant for SU(3) gauge conversion and described as below.
1a
LQCD = Ψ̄(iγµ Dµ − m)Ψ − Faµν Fµν
4Dµ = ∂ µ + igS (Gµa T a )aFµν= ∂µ Gaν − ∂ν Gaµ − gS fabc Gbµ Gcν

(1.12)(1.13)(1.14)

Here, Gµa describes the gluon, fabc is the SU(3) structure constant which is completely antisymmetric for the swapping of (a, b, c). Now gS fabc Gbµ Gcν appears because this gauge conversion
is asymmetric for exchange (U1 U2 ̸= U2 U1 ). This factor leads to the 3 gluon coupling or quark
confinement effects which do not appear in electromagnetic interaction.

1.1.3

Spontaneous symmetry breaking

The Lagrangian for Z 0 boson and fermion should be almost the same as LQED but with thefactor for Z 0 mass.
1
1
LZf f = ψ̄(iγµ (∂ µ − gZ µ ) − m)ψ − F µν Fµν + M 2 Z µ Zµ42
F µν = ∂ µ Z ν − ∂ µ Z µ(1.15)(1.16)

Here, Z µ is the wave function for Z 0 boson. But the factor of Z 0 mass M 2 Z µ Zµ /2 is notinvariant for the gauge conversion Z µ → Z ′µ = Z µ + ∂ µ b. This means the mass of Z 0 boson
cannot be introduced by gauge symmetry. In order to solve this problem, the ”spontaneous
symmetry breaking” is introduced.
First, mass of Z 0 is assumed to be created by interaction with spin 0 boson ϕ. Generally
the Lagrangian for massless boson is described as below.
1
L = ∂ µ ϕ∗ ∂µ ϕ2(1.17)

If the wave function of this boson ϕ is invariant for gauge conversion ϕ(x) → ϕ′ (x) =eiβ(x) ϕ(x), the Lagrangian for ϕ is described as below by adding the corresponding gauge
field B µ and potential V (|ϕ|2 ).
1 µ
1|(∂ + igB µ )ϕ|2 − V (|ϕ|2 ) − fµν f µν24
= ∂µ Bν − ∂ν BµLϕB =(1.18)

fµν(1.19)

This Lagrangian is invariant for gauge conversion. Then V (ϕ2 ) is described with first two
factors of ϕ2 as below.
V (ϕ2 ) = aϕ2 + bϕ4 (a < 0, b > 0)
(1.20)The shape of this potential is shown in Fig.1.1. This potential has a local minimum value at√a(1.21)
ϕ = ± − ≡ ±v02bHere, v0 is called as vacuum expectation value and measured as v0 = 246 GeV. In this potential,
ϕ = 0 is not stable as the energy is higher but either of ϕ = ±v0 is stable. In such kind of1.1. THE STANDARD MODEL

5
V

v0 =
<latexit sha1_base64="ypDvWcGxvp06hZc4I0HwY/lZEAc=">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</latexit>

r

a
2b
φ

Figure 1.1: The shape of V (ϕ2 ) = aϕ2 + bϕ4 [2].
symmetric potential with asymmetric stable states, either of stable states are selected andsymmetry is broken. This idea is called as spontaneous symmetry breaking. The Lagrangian(1.19) can be redefined as below by using the gaps from stable states φ = ϕ ± v0 .
1
1
1
Lφ = (∂ µ φ)2 + 2aφ2 + g 2 v02 B 2 − fµν f µν + · · ·224(1.22)√
Now (∂ µ φ)2 /2 + 2aφ2 is the Lagrangian for boson φ of mass mφ = 2 −a, g 2 v02 B 2 /2 −fµν f µν /4 is the Lagrangian for boson B of mass mB = gv0 and other factors are for various
couplings. While the factors for mass themselves break the gauge symmetry, total Lagrangianis kept to be gauge invariant by spontaneous symmetry breaking. The mass of gauge boson isconsidered to be created like this.

1.1.4

Electroweak unification

The unification of the electromagnetic and weak interactions is described by the GlashowWeinberg-Salam (GWS) theory. Since the weak interaction exchanges the u and d quarks, thewave function for weak interaction is the mixing states of |u⟩ and |d⟩ as below.
()u(x)Ψ(x) = u(x)|u⟩ + d(x)|d⟩ =(1.23)d(x)The physics is not changed by exchanging the u and d quarks components, which is called as
SU(2) flavor symmetry as below.
Ψ → Ψ′ = UW Ψ
(1.24)
The conversion matrix UW is described with Pauli matrix ⃗σ as below.
UW = exp[i⃗α(x) · ⃗σ ](1.25)

Then the wave function after SU(2) conversion is described as below.
⃗

Ψ → Ψ′ = eiα(x)·⃗σ Ψ(1.26)

6

CHAPTER 1. INTRODUCTION

Assuming from the Lagrangian for QCD, the Lagrangian which is invariant for SU(2) conversion (1.26) is described as below.
⃗ µ · ⃗σ )]Ψ
Lf f G = Ψ̄γµ [i∂ µ − g0 (W⃗ µ = (W1µ , W2µ , W3µ )W(1.27)

Considering the gauge symmetry, the simplest Lagrangian with both U(1) and SU(2) symmetry
is described as below.
⃗ µ · ⃗σ )]Ψ
Lf f G = Ψ̄γµ [i∂ µ − g1 B µ I − g0 (W(1.28)

Here, g0 and g1 are different for the types of fermions which are determined by experimental
results. In order to generate non-zero mass for W ± or Z 0 bosons by Higgs mechanism, moredegrees of freedom of the Higgs field are needed. Therefore Higgs field is assumed to have 2
components and 4 degrees of freedom as below.
( +))(1 ϕ1 + iϕ2
ϕΦ==√(1.29)
ϕ0
2 ϕ3 + iϕ4Then the Lagrangian for Higgs field with U(1) and SU(2) symmetry is described as below.
[

] 2
g ⃗µ
g′ µ
i∂ − B I − (W · ⃗σ ) Φ − a|Φ|2 − b|Φ|4 ;2
2µ

b > 0, a < 0(1.30)

The factor 1/2 is just for making later calculation simple. This potential has a local minimum
value in the case below.
a1|Φ|2 = (ϕ21 + ϕ22 + ϕ23 + ϕ24 ) = −22b(1.31)

Now the case of ϕ1 −ϕ2 = ϕ4 = 0 is considered and the spontaneous symmetry breaking (SSB)
is introduced by describing Φ with Taylor series around ϕ23 = −a/b ≡ v02 . This procedurecorresponds to following conversion.
( +)
(
)
1
ϕ
0
SSB
Φ=
−−→ √
(1.32)
ϕ0
2 v0 + h(x)Then the Lagrangian for interaction between Higgs and gauge fields is converged as below.
1⃗ µ · ⃗σ )]Φ|2 −SSBLΦGG = |[g ′ B µ + g(W−→4(v0 + h)2 2{g (|W + |2 + |W − |2 ) + [g 2 W32 + g ′2 B 2 − gg ′ (W3 B + BW3 )]} (1.33)
8√
Here W ± = (W1 ∓ iW2 )/ 2 describe the charged bosons. Considering the factor of boson
mass in the Lagrangian is described as (M 2 /2)W 2 , the mass of W ± is described as below.
1
MW = v0 g
2(1.34)

1.2. THE GRAND UNIFIED THEORY

7

Remaining factors in (1.33) of B and W3 mean the exchange of B and W3 in Higgs field andtheir behavior is described by following equation.
( ′2
( )
)( )
v02
B
g
−gg ′
B
µ
∂µ ∂
=
(1.35)
′
2
g
W3
W3
8 −gg
By solving this equation, the mass eigenstates and the mass are obtained as below.
{√
Z 0 = − sin θW B + cos θW W3 : MZ = 12 v0 g 2 + g ′2
A = cos θW B + sin θW W3 : MA = 0(1.36)

Here θW is the so called Weinberg angle and defined as tan θW ≡ g ′ /g. The massless boson A
corresponds to γ and the Z 0 corresponds to the weak neutral boson. The relationship between
MZ , MW and θW is also introduced as below.
MW = MZ cos θW(1.37)

Therefore, electromagnetic and weak interactions are described by one unified explanation,
GWS theory. Most of experiments prove that the observed results are consistent with the
expectation of GWS theory.

1.2 The Grand Unified Theory
After the success of electroweak theory, next step is unifying electroweak and strong interactions. The difference of the interactions for various particles at lower energy scale is mainly
due to the mass of the gauge bosons which intermediate each interaction. When we focus
on the interactions at higher energy scale, the differences among each interaction are mainly
their coupling constants. Furthermore, coupling constants depend on the energy. Their valuesof electroweak and strong interactions become almost the same at the energy scale of 1015
GeV as shown in Fig.1.2. This is the main motivation for unification of electroweak and strong
interactions. The Grand Unification Theory (GUT) tries to explain 3 interactions of strong,weak and electromagnetic with one gauge interaction by focusing that the coupling constantsof each interaction become close to each other at higher energy scale.

1.2.1

SU(5) model

SU(5) model is the minimum group which satisfy SU(3)×SU(2)×U(1) group. It has 24 parameters and can be separated to the expression of SU(3)×SU(2)×U(1) as below.
24 = (8, 1) + (3∗ , 2) + (3, 2∗ ) + (1, 3) + (1, 1)(1.38)

Here (8, 1), (1, 3) and (1, 1) correspond to SU(3),SU(2) and U(1) gauge field. Since the groupof SU(3)×SU(2)×U(1) has only 12 parameters, new parameters described by (3∗ , 2) and (3.2∗ )are introduced. Then the new gauge field for SU(5) is described as below.
Grr̄ − √230 B
Grḡ
Grb̄
X1
Y1


Ggb̄
X2
Y2
Ggr̄
Ggḡ − √230 B




2
√
G
G
G
−
B
X
Y
VSU(5) = 
br̄
bḡ
3
3

bb̄
30


1
3
3
+
√
√
X1
X2
X3
W + 30 B
W


2
√
√
3
−
3
√
Y1
Y2
Y3
W
− 1 2W + 30 B
(1.39)

8

CHAPTER 1. INTRODUCTION

Figure 1.2: Running coupling constants of SM as the function of energy scale with respect toeach interaction[3].

Here G is the gluon, B, W ± , W 3 are gauge bosons in electroweak theory, Xi , Yi are the new
12 gauge bosons of SU(3)C -triplet and SU(2)L -doublet, respectively, introduced in SU(5) model.
Since these bosons can intermediate quarks and leptons, baryon and lepton numbers are notconserved under the SU(5) model. This feature predicts the nucleon decay which can neveroccur in the SM. The fermions in the SM are summarized by the following 5̄ and 10 expressions
in SU(5) model.
d¯r
 d¯g ¯b d5̄ = 
 −
e 
−νe




0
ūb −ūg
−ūb 0ūr
0
10 =  ūg −ūr
 ur
ug
ub
dr
dg
db


−ur −dr−ug −dg −ub −db 

0
e+ 
−e+ 0

(1.40)

Here U(1)Y hypercharge can be automatically calculated by this SU(5) model, which means
the charge of each particle in the SM can be naturally explained by this model. In order tobreak the electroweak symmetry at the energy of weak scale and obtain the mass of quarks
and leptons, Higgs doublets are needed. In the SU(5) model, they are contained in either 5H
or 5̄H . Three additional states are color-triplet Higgs scalars and their couplings also violate
the baryon and lepton numbers, which leads to nucleon decay. The dominant decay mode ofnucleon decay in SU(5) model is p → e+ π 0 mode and the lifetime of this mode is predicted
as 1031±1 years[4]. However this was already excluded by KAMIOKANDE experiment[5].
Furthermore, Weinberg angle is predicted as sin2 θW = 3/8 in this model, but experimental
results say sin2 θW = 0.23. Therefore this SU(5) model is already ruled out.

1.2. THE GRAND UNIFIED THEORY

1.2.2

9

SUSY SU(5)Another idea is introducing so called super-symmetry (SUSY)[6][7][8] in SU(5) model. SUSY
is the symmetry for the exchange of fermions and bosons. In order to cancel anomalies andget the mass for both up and down quarks, both Higgs multiplets 5H or 5̄H are required.
One of interesting features of this SUSY SU(5) model is that running coupling constants cancompletely match at the energy around 2 × 1016 GeV as shown in Fig.1.3. The most dominantFigure 1.3: Running coupling constants of MSSM as the function of energy scale with respect
to each interaction[3].
decay mode of proton decay in SUSY SU(5) is p → ν̄K + . The predicted upper limits of proton
lifetime are, < 2.9 × 1030 years for p → ν̄K + and < 4.1 × 1033 years for p → e+ π 0 [9]. The
most stringent limit by proton decay search of SK is 5.9×1033 years for p → ν̄K + [11] and1.6×1034 years for p → e+ π 0 [10]. Comparing with these limits, this SUSY SU(5) model is also
excluded as well.

1.2.3

SO(10) model

Since SU(5) model uses two independent representation 5̄ and 10, unification is not complete.
In order to describe quarks and leptons by 1 unified representation, a right-handed neutrino
is added to SU(5). While the right-handed neutrino is not contained in SM, it is introducedin the seesaw mechanism[12][13][14]. Then SM fermions can be described by one unified
representation of SO(10) model, 16 = 10 + 5̄ + 1. The simplest decaying pattern of SO(10) isSO(10)→SU(5)×U(1). The right-handed neutrino can give the explanation for too small lefthanded neutrino mass or the asymmetry of matter and anti-matter. The dominant decay modeof proton decay in SO(10) model is also p → e+ π 0 and the lifetime is predicted to be 1032 −1039
years[15][16]. Comparing with most stringent limit of 1.6×1034 years for p → e+ π 0 by SK,
this SO(10) model is still alive.

10

CHAPTER 1. INTRODUCTION

1.2.4

Proton decay into three charged leptons

Adopting not only baryon number (B) and lepton number (L) symmetries, but also adopting
lepton flavor symmetries, many different decay modes are introduced. This model was introduced by T. Hambye and J. Heeck in 2018[1]. They theoretically estimated the decay rate of the
proton decay into three charged leptons and explained the physics advantages of these decay
modes for the first time. In this theory, proton decay at the level of dimension d = 10 operators is considered. There are two cases for d = 10 operators with three leptons, 1) ∆B = ∆L
which introduce six proton decay channels p → lα+ lβ+ lγ− , 2) ∆B = −∆L/3 which introduce
nucleon decay of four body decay such as n → ννlπ + . Since the former case has only charged
leptons in final states, it is more interesting mode to be searched by Super-Kamiokande. Especially p → µ− e+ e+ and p → e− µ+ µ+ modes can be dominant in all commonly discussed
modes by a symmetry B − L, Le + 2Lµ + xLτ and 2Le + Lµ + xLτ respectively (x is arbitrary value). Each symmetry value in each proton decay mode are summarized in Table1.3.
Thus it is possible to generate only d = 10 proton decay modes assuming certain pattern ofparticles or symmetries in this world. Other four decay modes, p → e+ e+ e− , p → µ+ e+ e− ,p → e+ µ+ µ− and p → µ+ µ+ µ− , cannot be singled out from two-body decays as the e+ e−
and µ+ µ− is replaced by a π 0 . The proton decay rate considering d = 10 operators without acovariant derivative for the three charged leptons channel involving SM scalar double field H
is calculated as follows.
Γ(p → lα+ lβ+ lγ− ) ∼⟨H⟩2 βh2 m5p(100TeV/Λ)12≃6144π 3 Λ121033 yrs(1.41)

Here βh ≃ 0.014 GeV3 is the hadronic matrix element, mp is the mass of proton and Λ is the
probing energy scale. Considering the probing energy scale of Λ ∼ 100 TeV, life time of suchorder is reachable in SK.
Proton decay into three charged leptons occurs by exchanging heavy particles along two
different types of topologies. Topology A involves new heavy scalars and topology B involves
a new heavy scalar and 2 new heavy fermions. The scalars in both topologies always couples
to two SM fermions. The candidates of the scalars are SU(2)L single di-quarks, di-leptons andleptoquarks (LQs)[17][18][19]. For the d = 10 operators, there are various places where theSM double H can be inserted. In the minimal model for p → e− µ+ µ+ , two heavy LQs mediate
the proton decay as shown in Fig.1.4.
Some of these proton decay modes were searched by some pure water Cherenkov detector
experiments. The most stringent limit for following proton decay modes were set by IMB-3
experiment[20] with the exposure of 7.6 kton·years.
• p → e+ e+ e−• p → µ+ e+ e−• p → e + µ+ µ−• p → µ+ µ+ µ−
And the most stringent limit for p → e− µ+ µ+ mode was set by HPW experiment[21] withthe exposure of 0.14 kton·years. The observed data was consistent with expected backgroundin these experiments and lower lifetime limit for each proton decay mode was set. The details

1.3. STRUCTURE OF THIS THESIS

11

Figure 1.4: Diagram for p → e− µ+ µ+ mediated by two heavy LQs ϕ1 , ϕ2 .[1]about these experiments are described in Appendix B. The latest results of these proton decay
modes are summarized in Table1.4. Compared with the predicted lower limit of ∼1033 years,
these decay modes are not excluded yet. Furthermore, considering the most stringent limit
1.6×1034 years for p → e+ π 0 and 7.7×1033 years for p → µ+ π 0 in SK, similar decay modes ofproton decay into three charged leptons have potential for discovery in SK. The discovery ofthese proton decay modes can be one of the strong evidence of GUT theory.
Table 1.3: B − L, 2Le + Lµ + xLτ and Le + 2Lµ + xLτ values in each proton decay mode.
p → µ− e+ e+ mode can conserve both B − L and Le + 2Lµ + xLτ . p → e− µ+ µ+ mode canconserve both B − L and 2Le + Lµ + xLτ .
Proton decay mode B − L 2Le + Lµ + xLτ Le + 2Lµ + xLτ
p → e+ π 0
1→1
0 → −20 → −1p → µ+ π 0
1→1
0 → −10 → −2+ + −p→e e e1→1
0 → −20 → −1p → µ+ e+ e−
1→1
0 → −10 → −2− + +p→µ e e1→1
0 → −30→0+ + −p→e µ µ1→1
0 → −20 → −1p → e − µ+ µ+
1→10→0
0 → −3+ + −p→µ µ µ1→1
0 → −10 → −2

1.3 Structure of this thesis
This thesis describes the search for proton decay into three charged leptons by using 0.37 Mton·years
exposure of data measured in SK. In Chapter 2, SK detector and its calibration are described.
In Chapter 3, Monte Carlo simulations for signal and background events are described. In
Chapter 4, preselection criteria is described. In Chapter 5, event reconstruction algorithm is

12

CHAPTER 1. INTRODUCTION
Table 1.4: The latest results of the search for proton decay into three charged leptons.
Proton decay mode Experiment Lower lifetime limit [years] (90% CL)
p → e+ e+ e−
IMB
7.9×1032+ + −p→µ e eIMB
5.3×1032p → µ− e + e +p → e+ µ+ µ−
IMB
3.6×1032
p → e− µ+ µ+
HPW
6×1030p → µ+ µ+ µ−
IMB
6.8×1032

described. In Chapter 6, selection criteria and the result are described. In Chapter 8, conclusionof this analysis is described.

Chapter 2
Super-Kamiokande Experiment
2.1 Overview
Super-Kamiokande (SK) is the largest pure water Cherenkov detector in the world, located in
Kamioka township, Gifu prefecture, Japan. The scientific motivation of the SK is searchingfor proton decays and studies of neutrinos from various sources: the Sun, atmosphere, supernovae, gamma ray burst and other astrophysical sources or artificial neutrino beams. The SK
detector mainly consists of a stainless tank (39.3 m diameter, 41.4 m height), 50 kton of ultra
pure water (H2 O) and the photomultiplier tubes (PMTs). The schematic view of the SK detector is shown in Figure 2.1. In order to reduce cosmic muon background, the detector is locatedFigure 2.1: Schematic view of the SK detector.[22]1,000 m under the peak of Mt. Ikenoyama (2,700 m water equivalent). Cosmic ray muons ofenergy less than 1.3 TeV cannot penetrate to the depth of 2,700 m.w.e. Observed muon flux
is 6 × 10−8 cm−2 s−1 sr−1 (2 kHz in SK detector) and this is 5 orders of magnitude smaller flux
compared to that on the surface of the Earth. The rate of cosmic ray muons observed in the13

14

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENTSK detector is about 2 kHz.
A stainless-steal framework of 55 cm width, placed 2-2.5 m from the all top, bottom andbarrel walls inside the SK tank, supports inward and outward facing PMTs. Inward facing
PMTs and the water inside the volume is called as Inner Detector (ID). ID is a main detectorof 36.2 m height and 33.8 m diameter which contains 32 kton of water. Outward facing PMTs
and the water in the thickness of 2 m between the framework and wall is called as Outer
Detector (OD) which is mainly used for the cosmic muon veto or preventing gamma raysfrom surrounding rock. ID and OD are optically separated by PET black sheets. On the ID
surface 20-inch PMTs are uniformly mounted facing inward viewing direction and on the OD
surface 8-inch PMTs are mounted facing outward viewing direction. There are twelve cableholes on top of the SK tank for signal and high voltage cables. Veto counters which consist of
2 m×2.5 m plastic scintillation counters are installed into four of these cable holes. The averagegeomagnetic field inside the SK tank is about 450 mG inclined by about 45◦ to the horizon at
the detector site. Such a scale and uniform direction of geomagnetic field can make systematic
bias against photoelectron trajectory and timing in the PMTs. In order to solve this problems,
26 sets of horizontal and vertical Helmholtz coils are arranged around the inner surface of thetank. As the result average magnetic field in the tank is reduced to about 50 mG.
The excavation started in December 1991 and the detector construction was completed in
December 1995. Then more than 2 months were spent for filling up the water in the tank.
Finally Super-Kamiokande successfully started operation on April 1st 1996 with 11,146 ID
PMTs and 1,885 OD PMTs. This operation stopped in July 2001 to replace bad PMTs. This
period is called as SK-I. Unfortunately, an accident happened during water filling after the
replacement of PMTs in July 2001. One of the ID PMTs at the bottom collapsed and big shock
wave was generated because the inside of the PMT is vacuum. The shock wave propagated via
water and destroyed other PMTs continuously. Due to this accident 6,777 ID PMTs and 1,100
OD PMTs were destroyed. In order to avoid such accident, remained PMTs were protectedby fiber reinforced plastics (FRPs) and acrylic cases and rearranged on the wall. Operationof so called SK-II period started with 5,182 ID PMTs and 1885 OD PMTs in October 2002 andstopped in October 2005. After the SK-II period, SK tank was opened again and PMTs wereadded. As the result, the number of PMTs was almost the same as SK-I period. In June 2006,
operation of the SK-III period started and stopped in September 2008. In September 2008, readout electronics and data acquisition system were upgraded. The SK-IV period started in thattime and stopped in May 2018. This is the longest period in all SK periods. Photo coverageof ID is 40 % in all SK periods excepting for SK-II (19 %) Information of all SK periods are
summarized in Table,2.1

2.2 Principle of the Detector
When a charged particle passes through certain medium with greater speed than the speed ofthe light in the medium, electromagnetic shock wave is emitted radially. This phenomenon is
known as Cherenkov-radiation and emitted light is called as Cherenkov-light or Cherenkovring. Schematic view of Cherenkov-light emission is shown in Fig.2.2 and opening angle θc isdescribed as below.
1
cos θc =(2.1)
nβ2.2. PRINCIPLE OF THE DETECTOR

15

Table 2.1: Summary of all SK periods.
SK-I
SK-II
SK-III
SK-IV
Operation
Start Apr. 1996 Oct. 2002 Jun. 2006 Sep. 2008
End Jul. 2001 Oct. 2005 Sep. 2008 May. 2018
Livetime (days)
1489.2798.6
518.1
3244.4
Number of PMTs
ID
11,146
5,182
11,12911,129
OD
1,885
1,885
1,885
1,885
Photo coverage
40%
19%
40%
40%
FRP & Acrylic cases
No
Yes
Yes
Yes
Electronics
ID
ATM
ATM
ATM
QBEE
OD
OD QTC OD QTC OD QTC
QBEETrigger
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✓c
<latexit sha1_base64="Z07qt4whWquGillxVlL1NdmudJk=">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</latexit><latexit sha1_base64="7wJCkakADGCXuO1VoS7+m16bvZo=">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</latexit>

ct

Figure 2.2: Schematic view of Cherenkov Radiation. Red and blue arrows show the directionof the charged particle and emitted Cherenkov light respectively.

16

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Here n is the refractive index of the medium, β = v/c, v and c is the speed of the charged
particle and the light respectively. Since the speed of the charged particle βc has to be greaterthan the speed of the light in the medium c/n, the minimum momentum of the charged particle
to emit Cherenkov-light is described as below.
βc >

c
n

(2.2)

Here p, E and m is the momentum, energy and mass of the charged particle respectively. Using
β = p/E by natural unit, above condition can be described with the mass m, momentum p
and energy E of charged particle as below.
p> √mn2 − 1(2.3)

Minimum momentum of each charged particle to make Cherenkov-light in water (n = 1.34) issummarized in table 2.2. The opening angle of emitted Cherenkov ring in water as the function
Table 2.2: Minimum momentum to emit Cherenkov-light in water.
e − µ− π −pMinimum momentum [MeV/c] 0.57 118 156 1052

Opening angle [degree]of the momentum of electron and muon is shown in Fig.2.3. Charged particles gradually lose
their energy by the interaction with the nucleus in water. When the speed of the particle
becomes β < 1/n, Cherenkov-light is not emitted anymore and the emitted light is observed
as a ring shape on the detector wall.

50
45

Electron

40
35

Muon

30
25
20
15
10
5
0
10-1

1

10

102

3

10
104
Momentum [MeV]

Figure 2.3: The opening angle of emitted Cherenkov ring in water as the function of the momentum of electron and muon.

2.3. WATER PURIFICATION SYSTEMS

17

The number of emitted photons N per wavelength λ per unit travel distance x of a charged
particle is described as follow.
(
)
d2 N
2πα
1
= 2 1− 2 2
(2.4)
dxdλ
λ
nβ
Here α is the fine structure constant. ∼ 340 photons of wavelength between 300 nm and
600 nm are emitted per 1 cm by a charged particle with β ∼ 1 in water.

2.3 Water Purification Systems
Since Cherenkov-light travels in water until it reaches the PMTs on the wall, high transparencyof the water is important to achieve higher detection efficiency. In order to keep high transparency of the water, 50 ktons of water in the tank is continuously reprocessed in the water
purification systems at a rate of about 30 tons/hour. Fig.2.4 shows the schematic view of thewater purification systems of early 2002.

Figure 2.4: Schematic view of water purification systems.[22]First, water passes through the 1 µm mesh filters to remove dusts and particles which reduce the transparency of the water or can be a possible radon source. The heat exchanger
cools the water to reduce the dark noise level of PMTs and suppresses the growth of bacteria
which can degrade the transparency of the water. Typical water temperature before 1st heatexchanger and after 2nd heat exchanger is 14.2 C◦ and 12.9 C◦ , respectively. Surviving bacteria
are killed in UV sterilizer system. The Cartridge Polisher (CP) is used to remove heavy ionswhich can reduce the water transparency and include radioactive sources. 1,500 L of resin isused in this system. The Reverse Osmosis (RO) system and the tank to dissolve Rn-reduced
air into the water were installed in 1999. The RO system removes additional particulates. Rnreduced air into the water increases the removal efficiency of Rn in Vacuum Degasifier (VD)18

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Figure 2.5: Schematic view of the air purification systems.[22]system. The VD consists of a cylindrical stainless steal vessel and a vacuum pump. This systemremoves dissolved gas in the water like radon which is a serious background event source forsolar neutrinos in the MeV energy scale, or oxygen which encourage the growth of bacteria
in the water. The removal efficiency of radon gas is estimated to be about 96 %. The Ultra Filter(UF), which consists of hollow fiber membrane filters, can remove molecules of size morethan 10 nm diameter. Typical number of particles with a size more than 0.2 µm before the water
purification system is 1,000 particles/cc and this is reduced to 6 particles/cc after reprocessing
by all systems. The Membrane Degasifier (MD) consists of 30 hollow membrane modules anda vacuum pump can also remove radon dissolved in the water. Removal efficiency of radon ismeasured to be about 83 %.

2.4 Air Purification Systems
Rn-reduced air is produced by the air purification systems and supplied to the gap between
the water surface and the top of the SK tank. Rn-reduced air is kept at a slight over pressure
to prevent radon-laden air from entering the SK tank. Schematic view of the air purification
systems is shown in Fig.2.5. It consists of a buffer tank, dryers, filters and activated charcoal
filters. 8,000 L of activated charcoal is used in total and the last 50 L of it is cooled to -40 C◦
to increase removal efficiency of radon. These systems are equipped near the entrance of
Atotsu tunnel outside the mine. Fresh air produced by this system is continuously pumped
at approximately 10 m3 min−1 to the experimental area through an air duct along 1.8 km of
Atotsu tunnel. Radon level of air in the mine tunnel changes dependent on the seasons. Fig.2.6
shows the radon level of air inside(lower) and outside(upper) the experimental area. During
the cool season, since the air flows into Atotsu tunnel entrance and path through the exposed
rocks for relatively short distance, radon level is approximately 100-300 Bq m−3 . On the other
hand, during the warm season, since air flows from deep in the mine to outside and passes
through exposed rock for a long distance, radon level near the experimental area is increased
to approximately 2000-3000 Bq m−3 . Thanks to this air purification system, radon level of air
in the experimental area is kept to be 30-50 Bq m−3 throughout the year.

2.5 PMTs and associated structures
20-inch PMTs of 11-stage Venetian blind type (R3600) produced by Hamamatsu Photonics K.K.
are used in the ID detector (Fig.2.7). The bialkali (Sb-K-Cs) is used for the photocathode which2.5. PMTS AND ASSOCIATED STRUCTURES

19

Figure 2.6: Seasonal radon level inside(lower) and outside(upper) the experimental area.[22]has a peak quantum efficiency of about 21 % at 360-400 nm wavelength as described in Fig.2.8.

Figure 2.7: Schematic view of 20-inch PMT.[22]ID PMTs operate with high voltages from 1,700 V to 2,000 V. The collection efficiency of
the first dynode, transit time spread and gain for single photoelectron are 70 %, 2.2 ns and 107 ,respectively. Average dark noise rate at 0.25 pe threshold is about 3 kHz. Although the acrylic
cover is attached to the PMTs in SK-II to SK-IV, transparent efficiency of photon with 350 nm
wavelength is about 96 %. The basic unit for ID PMTs is a stainless frame which supports a 3×4
array of PMTs (super-module). Height, width and depth of the super-module is 2.1 m, 2.8 m,
0.55 m respectively. Super-modules are connected each other and stacked from bottom to the20

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Figure 2.8: Quantum efficiency of the R3600 photocathode as the function of wavelength.[22]top structure. Opaque PET black sheets cover the gaps between PMTs on the ID surface. These
sheets can improve the optical separation between ID and OD and suppress low energy radio
activity occurring behind ID PMTs. Schematic view of the support structure in ID detector isshown in Fig.2.9.
8-inch Hamamatsu PMTs (R1408) are used in OD detector. These PMTs were used in IMB
experiment and SK is reusing them. Each super-module has two OD PMTs. In order to improve
the photon collection, reflective layers made from Type 1073B Tyvek sheets manufactured by
DuPont cover the all surfaces of OD. Measured reflective efficiency of these sheets is order of
90 % in excess of 400 nm wavelength and falling to 80 % at about 340 nm. For further improvement of the photon collection efficiency, each PMT is coupled with wavelength-shifting plateof 1.3 cm thickness and 60×60 cm size as Fig.2.10. Thanks to this structure, not only the light
directly striking the photocathode of the PMT but also the light missing the PMT but striking
the plate can be detected.

2.6 Electronics and data acquisition systems
New electronics and data acquisition systems were installed from SK-IV. The systems in SK-I
to SK-III are described first, and then the systems in SK-IV are described in this section. Thesesystems are contained in ”quadrant-huts” and ”Central hut” located on top of the SK tank.
The quadrant-huts contain electronics racks and frontend DAQ computer serving ID and OD
PMTs. The Central hut contains electronics and computers for triggering, housekeeping and
Global Positioning System (GPS) time synchronization system.

2.6.1

Electronics and data acquisition systems in SK-I to SK-III

ID PMT signals are processed by custom built TRISTAN KEK Online (TKO) modules called
ATM (Analog Timing Module). The ATM consists of Analog-to-Digital Converter (ADC) and2.6. ELECTRONICS AND DATA ACQUISITION SYSTEMS

Figure 2.9: Schematic view of the support structure in ID detector.[22]Figure 2.10: Schematic view of the OD structure[23].

21

22

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Figure 2.11: Schematic view of the analog input block of the ATM.[22] Only one channel isshown in this figure.
Time-to-Digital Converter (TDC), which records the integrated charge and arrival time of each
PMT signal. There are 960 ATM boards, and each ATM reads the signals from twelve PMTs.
Fig.2.11 shows a schematic view of the analog input block of the ATM. Input PMT signals
are divided into four lanes by Current splitter. One of them is fed to a discriminator with athreshold of −1 mV for each channel which corresponds to 1/4 p.e. When the PMT signal is
above the threshold, a HITSUM signal of 200 ns width and 15 mV pulse height is asserted. The
HITSUM signals are summed up for all 12×960 PMTs signals and this ”sum of HITSUM” isused to generate global trigger signal. At the same time, two of divided signals A, B are fed toCharge-to-Analog Converter (QAC) and Time-to-Analog Converter (TAC) starts integrating
constant current. Once the global trigger is issued, integration of TAC is stopped. Then theinformation in the QAC/TAC is digitized by Analog-to-Digital Converter (ADC) and stored ininternal memory buffers. If the global trigger is not issued within 1.3 µs, all information in
QAC/TAC is cleared. A channel control chip generates start/stop signals for the TAC, the gate
signal for QAC and clear signal for TAC/QAC. There are two TACs and QACs with respect toeach channel to record events in rapid succession, such as muon with its decay electron, without dead time. Even though there are two TACs and QACs, actually the signal from +400 ns to+900 ns after the hit timing is neglected due to a cable reflection pulse caused by a impedancemismatch between ATM and PMT.
An ID trigger is issued when the sum of ID HITSUM signal exceeds the threshold. Overview
of ID trigger in SK-I to SK-III is summarized in Figure.2.12. There are three types of ID event
trigger, super low energy (SLE), low energy (LE) and high energy (HE) respectively. Thresholdfor sum of HITSUM with respect to each trigger in each period is summarized in Table2.3.
In OD, signals from PMTs are processed and digitized in a similar way with ID systems.
An OD trigger is issued when the OD HITSUM signal exceeds a threshold. The threshold of
the OD trigger corresponds to 19 hits within 200 ns time window.

2.6. ELECTRONICS AND DATA ACQUISITION SYSTEMS

Figure 2.12: Overview of the ID trigger in SK-I to SK-III.[25]Table 2.3: Trigger threshold for sum of HITSUM with respect to each ID event trigger.
SK-I
SK-II
SK-IIISLE 186 mV 110 mV 186 mV
LE 320 mV 152 mV 302 mV
HE 340 mV 180 mV 320 mV

23

24

2.6.2

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENTElectronics and data acquisition systems in SK-IV

In order to solve the dead time and cable reflection problems, new electronics QBEE (QTC
Based Electronics with Ethernet) was introduced instead of the ATM from SK-IV. An applicationspecific integrated circuit (ASIC), called the high-speed QTC IWATSU CLC101, was designed
in CMOS 0.35 µm technology and is build-in discriminators of QBEE. This new ASIC offers
three charge dynamic ranges: Small, Medium and Large, each with a short cycle time (≤ 1 µs).
Output signal from each range is digitized and one most appropriate range is chosen by fieldprogrammable gate array (FPGA), then sent to data acquisition computers. The gain of eachrange can be adjusted to cover a wide dynamic range with reasonable resolution. For example,
the overall charge dynamic range of the QTC is 0.2 - 2500 pC if the gain ratio of three ranges
is set to 1 : 1/7 : 1/49. Block diagram of the QTC is shown in Fig.2.13.

Figure 2.13: Block diagram of the QTC.[24]A block diagram of the one QTC channel is shown in Fig.2.14. Input signals from PMTs
are amplified by a low-noise-amplifier (LNA), delayed by a low-pass filter (LPF), processed byvoltage-to-current (V/I) convertor, and integrated by capacitor. Timer block consists of three
timers: a charging timer, a discharging timer and VETO timer. Once the amplified input signal
exceeds the discriminator threshold, charging timer operates a ∼400 ns charge gate and at thesame time a trigger flag HIT is generated. The leading edge of the output signal corresponds
to this timing. During the charge gate, input charge is integrated in the capacitor. Soon after
the end of the charge gate, discharging timer operates a ∼350 ns discharge gate. During thedischarge gate, the integrated charge is discharged by a constant current. This discharging
time which can be known by the width of output QTC signal is proportional to the integrated
charge. Thus QTC output signals contain both charge and timing information. After the endof the discharge gate, reset and VETO signals are issued. Input signals during the VETO gate
are ignored. Processing time for one input signal is ∼900 ns. Timing chart of QTC operationin SK-IV is shown in Fig.2.15. This new system records all the hits and immediately integrates
the charge and digitizes the timing and charge information. When the number of PMT hits
within 200 ns sliding time window (N200 ) exceeds the threshold, a software trigger is issued.
The digitized charge and timing are recorded when the trigger is issued. In this new system,
there is no dead time and timing window of each event trigger is larger compared to previous
systems in SK-I to SK-III because all hits can be recorded. SLE, LE and HE triggers are stillused in this new systems with a larger timing window. In addition to these triggers, special
high energy trigger (SHE) and after trigger (AFT) are introduced for using neutron tagging

2.6. ELECTRONICS AND DATA ACQUISITION SYSTEMS

Figure 2.14: Block diagram of the one QTC channel.[24]Figure 2.15: Timing chart of QTC operation in SK-IV.[24]

25

26

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT
Table 2.4: Software triggers used in SK-IV.
Trigger N200 threshold (PMT hits) Time window (µs)
SLE
31[−0.5, +1.0]LE47[−5, +35]HE
50[−5, +35]SHE
58[−5, +35]
AFT
SHE without OD[+35, +535]
OD
22[−5, +35]

technique. The AFT trigger is only issued in case the SHE trigger is issued but the OD trigger
is not issued and records additional 500 µs data. The information of each software trigger issummarized in Table2.4.

2.7 Detector Calibration
In order to keep good sensitivity of the physics analysis, it is important to understand the PMT
response of charge and time in the SK detector precisely. We also need to understand how theCherenkov photon propagates in the water to the PMTs. In this section, calibration methodsof PMT gain or timing and water transparency are described.

2.7.1

High-voltage setting of the PMTs

All PMTs are required to give the same output charge for the same input light intensity bytuning the high-voltage(HV) of each PMT. This calibration is performed by an isotropic lightsource placed in the center of the SK tank. Since the SK tank is very large, amount of lightreaching to each PMT from the source depends on the distance between the source and each
PMT. Correcting only this geometrical difference is not sufficient because photon propagationin the water, which depends on the water quality, and reflection from the ID surface also needs
to be considered. First 420 ”standard PMTs” are determined to tune HV individually before theinstallation on the ID wall. Pre-calibration was performed to these standard PMTs and later
mounted in ID as the reference for other PMTs. Fig.2.16 shows the schematic view of the
pre-calibration system. The light from a Xe flash lamp goes through a UV filter and injected
into three optical fibers. One fiber is connected to ”scintillator ball” in dark box made fromµ-metal to shield against geomagnetic field. The scintillator ball is used to diffuse the lightemission uniformly. Other two fibers are connected to avalanche photodiode(APD) modules
to monitor the light intensity of the Xe lamp. Two 2-inch PMTs are mounted in the box tomonitor the light intensity of the ball. HV values of 420 standard PMTs are adjusted to givethe same output charge by using this system.
The 420 standard PMTs after pre-calibration are placed in ID as the red points shown in theleft figure of Fig.2.17. These standard PMTs are used as references for other PMTs which canhave similar geometrical relationships to the light source as shown in right figure of Fig2.17.
The same Xe lamp and scintillator ball are used, and the HV of PMTs in the same group are
tuned to give the same output charge as the reference PMT.

2.7. DETECTOR CALIBRATION

Figure 2.16: Schematic view of the pre-calibration system.[26]Figure 2.17: The location of the standard PMTs.[26]

27

28

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

2.7.2

Relative gain difference

In order to know the number of p.e.s from the output charge of PMTs, we need to determine thegain of each PMT. In the first step, relative gain difference of each PMT is measured. In thismeasurement, a stable light source emitting constant-intensity flashes is placed at a certain
position in the tank. The light source is nitrogen-laser-driven dye laser fed into the diffuserball. There are two measurements.
• High intensity flash is emitted so that every PMT gets a suitable number of photons.
The average charge Qobs (i) for each ID-PMT i is measured. Qobs (i) is described by thefollowing equation.
Qobs (i) ∝ Is × a(i) × ϵqe (i) × G(i)(2.5)
Here Is is the average intensity of high intensity flash, a(i), ϵqe (i), G(i) are the acceptance, quantum efficiency (QE) and the gain of i-th PMT respectively.
• Low intensity flash is emitted so that only a few PMTs are hit in each event to ensureeach of hit is single p.e. The number of times Nobs (i) that i-th PMT records the charge
which exceeds the threshold value. Now Nobs (i) is described as follow.
Nobs (i) ∝ Iw × a(i) × ϵqe (i)(2.6)

Here Iw is the average intensity of low intensity flash.
Since the locations of light source are the same between two measurements, factors in Qobs (i)and Nobs (i) are almost identical. Then G(i) is obtained by the ratio of (2.5) and (2.6).
G(i) ∝

Qobs (i)Nobs (i)(2.7)

Then relative gain of each PMT is obtained from G(i) normalized by the average gain of all
PMTs. In order to get the mean value of the relative gain of each PMT, this measurement
is repeated while changing the intensity of the flash. Fig.2.18 shows the normalized relative
gain (2.7) of each PMT. Since the HV is tuned to make output charge of each PMT same forthe same input light intensity, cause of deviation in Fig.2.18 is considered to be the differenceof QE among PMTs. This factor is used for fine correction of charge to the number of p.e.s
conversion.

2.7.3

Absolute gain conversion factor

In the second step, average gain over the whole detector is determined. In this measurement,a uniform and stable ”nickel source” of single p.e level light is used. The source isotropicallyemits gamma rays of about 9 MeV from thermal neutron capture on nickel. It is placed at thecenter of the ID and delivers 0.004 p.e/PMT on average when the emitted γ hits one of PMTs.
More than 99% of observed signal in each PMT are due to single p.e. The charge distribution
obtained by this measurement after the relative gain correction and accumulating data fromall PMTs is shown in Fig.2.19. In order to minimize the effect of dark hits, off-time (the timing
window where the signal is not expected) data is subtracted from on-time (the timing window
where the signal is expected) data. The value averaged over the whole pC region is defined as
the conversion factor of single p.e. The conversion factors are measured to be 2.055, 2.293,2.247
and 2.658 pC with respect to SK-I, II, III and IV respectively. This single p.e distribution is also
implemented in MC simulations.

2.7. DETECTOR CALIBRATION

29

Figure 2.18: The normalized relative gain of each PMT.[26]Figure 2.19: Charge distribution of nickel source calibration after the relative gain correction
and accumulating data from all PMTs.[26]

30

2.7.4

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Relative difference of QE

As described in equation (2.6), observed hit probability for each PMT is proportional to thevalue of QE if the intensity of the light source is low enough. While the number of hits in each
PMT can be measured, it is difficult to know how many photons exactly reach the PMT. MC
simulation is used to know the number of photons arriving at the PMT. In this measurement, anickel source measurement described in section.2.7.3 is used. The hit probability in each PMT
is corrected by the following function.
Nobs (i) × R(i)2 /a(θ(i))(2.8)

Here i is the index of ID PMTs, R(i) is the distance between the nickel source and i-th PMT
position, a(θ(i)) is acceptance as a function of photon incident angle θ(i). The hit probability
after this correction as a function of PMT position is shown in Fig.2.20. Even after the cor-Figure 2.20: The hit probability as a function of PMT position. Vertical axis is the numberof PMT hits normalized by average of all PMT hits. Horizontal axis is the height (cm) of the
PMTs. Red shows the data and blue shows the MC. [26]rection (2.8), position dependence still remains due to the reflection from neighboring surface
or scattering and absorption by the water. Considering these position dependence, remaining
differences are due to QE differences of individual PMTs. The quantities of QE differences aretabulated and used in MC simulation.

2.7.5

Light absorption and scattering in water

In order to extract light absorption and scattering coefficients as a function of wavelength,
collimated laser beam is injected into the tank and the observed timing and spatial distributions
are compared with MC. Schematic view of the calibration setup is shown in Fig.2.21. Fig.2.22
shows the data and MC results for typical PMT hit timing distribution after time-of-flight is
subtracted. TOF is now based on the distance between the PMT position and target of the laser
at the bottom. The left region consists of scattered photons and used to tune the symmetricand asymmetric scattering parameters and absorption parameter. The right peak represents

2.7. DETECTOR CALIBRATION

31

Figure 2.21: Schematic view of the calibration setup for light absorption and scattering. [26]the photons reflected by the bottom PMT and black sheets, which is used to tune the reflection
parameter (Section.2.7.6). Total number of scattered photons and the shape of time distribution
in the left region are compared between data and MC. Various MC samples with different
parameters are generated and the one which minimizes the χ2 value for difference between
data and MC is selected finally. The number of photons in the water is described as follow.
()lI(λ) = I0 (λ) exp −
(2.9)
L(λ)
Here λ, l are the wavelength and travel length of the light, I0 (λ) is the initial intensity, I(λ)
is the intensity at l and L(λ) is total attenuation length caused by absorption and scattering.
Now L(λ) is called as ”water transparency” and defined as follow.
L(λ) =

1αabs (λ) + αsym (λ) + αasym (λ)(2.10)

Here αabs (λ),αsym (λ) and αasym (λ) is the absorption, symmetric and asymmetric scatteringparameters respectively. The absorption parameter αabs (m−1 ) as the function of wavelength
λ (nm) is determined empirically using the laser beam data as follow.
P1
+C
λ4

(2.11)C = P0 × P2 × (λ/500)P3(2.12)

αabs (λ) = P0 ×

Here C is the amplitude based on the experimental data and P0 −P3 are the fitting parameters.

32

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENT

Figure 2.22: Typical TOF subtracted timing distribution in the measurement for the calibrationof light absorption, scattering and reflection. Black circle is the data and red line is the MC ofbest tuned. Both distributions are normalized by total observed p.e.s. The top plot is for the
SK top wall and the second to bottom plots corresponds to the SK barrel wall regions shownin Fig.2.21 [26].

2.7. DETECTOR CALIBRATION

33

The angular distribution of the scattered photons is divided into two components, ”symmetric” and ”asymmetric”. The symmetric component consists of Rayleigh and symmetric Mie
scattering described by 1 + cos θ2 where θ is the scattered angle of photon. The asymmetriccomponent consists of forward Mie scattering and the scattering probability increases linearly
from cos θ =0 to 1, and no scattering occurs for cos θ < 0. The Mie scattering has a forward
peaked distribution for the particle size greater than wavelength of the light. The asymmetriccomponent is simply approximated because the particle sizes are unknown. The symmetricand asymmetric factors αsym and αasym are empirically determined as follow.
(
)
P4
P5
αsym (λ) = 4 × 1.0 + 2
λ
λ
(
)
P7
2
αasym (λ) = P6 × 1.0 + 4 × (λ − P8 )λ(2.13)(2.14)

Here P4 − P8 are the fitting parameters. Typical fitting results for αabs (λ),αsym (λ), αasym (λ)
and the total attenuation length L(λ) is shown in Fig.2.23.

Figure 2.23: Typical fitting results for attenuation length in water. The points show the data
and the line is the fit function of the points[26]. Each data point is obtained by fitting MC todata in left region of Fig.2.22.

34

2.7.6

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENTLight reflection at PMTs and black sheets

Light reflection at PMT surface is tuned by using data and MC in right peak of Fig.2.22. Fourlayers of material (refractive index) are taken into account from the surface to the inside of
the PMT: water (1.33), glass(1.472 + 3670/λ2 ), bialkali (nreal + i · nimg )[32] and vacuum (1.0).
nreal and nimg are the real and imaginary parts of complex refractive index. Best fit value of
nreal and nimg are obtained finally.
Cherenkov photons are also reflected and absorbed on the black sheets. The reflectivityof the black sheets are measured by using laser light injected to black sheets in the tank.
Schematic view of this measurement is shown in Fig.2.24 The reflected charge (Qscat ) is mea-

Figure 2.24: Schematic view of the measurement for the reflectivity of the black sheets. [26]sured at three incident angles (30◦ , 45◦ and 60◦ ) with three wavelengths (337 nm, 400 nm and
420 nm). As the reference of the Qscat , the direct charge (Qdirect ) without black sheets is alsomeasured and the ratio R = Qscat /Qdirect is used for the tuning of the reflectivity.

2.7.7

PMT timing

Understanding the timing response of each readout channel including PMTs and readout electronics is important for a precise reconstruction of the vertex and track direction. The responsetime of readout channel depends on the transit time of the PMTs, length of PMT signal cables
and processing time of readout electronics. In addition to these issues, the response time ofreadout channel (the timing of descriminater output) also depends on the pulse height of PMTs,
because the rise time of larger pulse is faster than smaller one. This is known as ”time-walk”
effect. The total process time and time-walk effect are calibrated by injecting fast light pulse
into PMTs and changing the intensity of the light. Schematic view of the timing calibration
system is shown in Fig.2.25. Nitrogen laser is used as the light source of the calibration whichemits fast pulsing light of 0.4 ns FWHM and 337 nm wavelength. The laser output is monitored2.7. DETECTOR CALIBRATION

Figure 2.25: Schematic view of the timing calibration system. [26]

35

36

CHAPTER 2. SUPER-KAMIOKANDE EXPERIMENTby a 2-inch PMT to know the time of laser light injection. The wavelength of the laser light isshifted to 398 nm by a dye, where the response with Cherenkov spectrum of PMTs is almost
maximum. The pulse width of the dye is 0.2 ns FWHM. The filtered light is injected into a
diffuser ball located in the center of the tank by optical fiber to emit isotropic light. Timing
calibration is conducted based on a two dimensional map of timing and pulse height (charge)
so called ”TQ distributions”. Fig.2.26 shows a typical TQ distribution for one readout channel.
The calibration constants so called ”TQ map” is obtained by fitting the TQ distribution with

Figure 2.26: Typical TQ distribution for one readout channel. Vertical axis is the time-of-flight
subtracted timing of the hits. Larger (smaller) T corresponds to earlier (later) hits. Horizontal
axis is the charge of each hit. [26]a polynomial function with respect to each channel. The TQ map is used to correct the hit
timing.

2.7.8

OD PMTs

Precision of the OD calibration is not as important as ID calibration. Accuracy of 10-20% forcharge reconstruction and 5-10 ns for timing is sufficient for physics analysis. In order todetermine the charge in pC corresponding to single p.e, OD hits outside the trigger window
are used. Since the hits preceding the trigger time have a high probability to be single p.e hits,
such events are accumulated and the mean value is taken as pC per single p.e. The charge
response per single p.e is validated by nitrogen dye laser flushed at very low light levels. OD
timing information is only used for selection of OD hits within the time window around thetrigger time. The goal of OD time calibration is to confirm that timing offset between ID and
OD and the relative timing offset of each OD PMT are sufficiently small. These are measured
with a laser system and cosmic ray muons.

2.7.9

Energy Scale

Understanding the detector energy scale precisely is important for proton decay analysis. The
Michel electrons, stopping muons and neutral pion samples are used for this.

2.7. DETECTOR CALIBRATION

37

Since the energy spectrum of Michel electrons is already well known, it is useful for energy
scale check. Michel electrons produced by stopping muon are used to determine the absoluteenergy scale in the range of a few tens of MeV.
The Cherenkov angle is described by a function of the momentum as equation (2.1). The
stopping muon sample is useful for checking this correlation between the Cherenkov angle
and momentum of muons. However, since the Cherenkov angle soon reaches the limit (∼42◦ )as the momentum increases, this check is useful for lower energy muons. Therefore, stoppingmuons with a momentum below 400 MeV are collected for this check. Then measured momentum and calculated momentum expected from measured Cherenkov angle are compared.
For high energy muons, the correlation between the stopping range of muon track in thedetector and the momentum is used for energy scale check. The range of muon track is obtained by the distance between the muon entering point and the vertex of Michel electron.
Neutral current interaction of atmospheric neutrinos with the nucleus often generates neutral pions π 0 . Such events can be identified easily and used for absolute energy scale calibration. The mass of π 0 is reconstructed by 2 e-like rings assuming both of rings are created fromγ.
In order to estimate the systematic uncertainty for the energy scale, the ratio of values
between data and MC in each calibration method is used as shown in Fig.2.27. The largest
difference in all calibration methods is used for the error value for energy scale with respect
to each SK period. The error values are estimated to be 3.3%, 2.8%, 2.4% and 2.1% for SK-I,II,III
and IV, respectively.

Figure 2.27: Absolute energy scale measurements for each SK period[26]. Vertical error bars
correspond to statistical uncertainty and horizontal error bars correspond to the momentum
range of each calibration method.
The detector uniformity of the energy scale is also estimated by using decay electron samples, because the vertex and momentum distribution of the decay electron are almost uniform.
In order to consider the muon polarization, the electron with the direction perpendicular tothe parent muon direction (| cos Θeµ | < 0.25) is only used for this measurement. The difference of the electron momentum between data and MC as a function of the electron direction
is checked. Then the largest deviation is used as the detector uniformity error with respect toeach SK period. The error values correspond to 0.6%, 0.6%, 1.3% and 0.5% for SK-I, II, III andIV, respectively.

Chapter 3
Monte Carlo Simulations
Signal and background samples are created by using Monte Carlo method. For the signal samples, each mode of proton decay into three charged leptons is created. For the backgroundsample, only atmospheric neutrino events are considered as other backgrounds become negligible by applying the event reduction described in Chapter4. Finally, Geant3[105] based
detecter simulation is performed to both signal and background samples.

3.1 Signal
The source of proton decay is protons contained in H2 O molecules. One H2 O molecule has
10 protons: 2 protons from hydrogen and 8 protons from oxygen. The protons in hydrogenso called ”free proton” do not interact with other nuclei. In case of free proton, mass of free
proton is exactly 938.27 MeV and momentum is 0. On the other hand, the protons in oxygen socalled ”bound proton” interact with other nucleus. In case of bound proton, the mass of proton
is smaller than its exact mass. Also momentum is not 0 due to some effects described later. In
the simulation, phase space is only considered. Any correlations between charged leptons are
not considered. Mass and momentum of the initial protons are distributed to decayed three
leptons. The true momentum of 3 electrons for free protons in p → e+ e+ e− is shown in Fig.3.1.
Since the signal is three body decay, momentum of each charged lepton distributes widely. In
case of free proton, maximum limit of the charged lepton momentum corresponds to the halfof proton mass (469 MeV).
In case of bound proton, mainly three effects are considered: nuclear binding energy in 16 O,
Fermi motion and the correlated decay. For the nuclear binding energy, two bound states pstate and s-state are considered. These two types of binding energy are simulated as Gaussian
distribution. Each mean and σ of the binding energy is (39.0 MeV, 10.2 MeV) for s-state and(15.5 MeV, 3.82 MeV) for p-state. The ratio of s-state is 22.5%, p-state is 67.5% (45% for P(3/2)
and 22.5% for P(1/2)) and the correlated decay is 10%. The binding energy is subtracted fromproton mass in the simulation. The proton momentum from Fermi motion is simulated basedon electron-12 C scattering data[36]. The invariant mass and momentum distribution of eachbound state are shown in Fig.3.2.
The bound proton sometimes correlates with surrounding nucleus during its decay andthis effect is called as correlated decay[37]. Due to this effect, the kinematics of the proton ischanged because of the momentum transfer to the surrounding nucleons. The correlated decay
is considered to happen with 10% probability and produce broad pseudo peak at lower mass in39

CHAPTER 3. MONTE CARLO SIMULATIONSEvents40

250 SK4
p→e+e+eFree proton
200

Minimum
150

MiddleMaximum

100

50

0
0

100

200

300

400
500
True momentum[MeV]

Figure 3.1: True momentum of charged leptons for free proton in p → e+ e+ e− . Each histogram
corresponds to the lepton with minimum(red), middle(green) and maximum(blue) momentum.
The error bars correspond to the statistics error. There is kinematic edge of half of proton massin maximum momentum lepton.
proton mass distribution. The invariant mass and momentum distribution of the proton withcorrelated decay are also shown in Fig.3.2.
In this analysis, all patterns of electron, muon and their anti-particles are considered as signal. Any correlations between charged leptons are not considered in the simulation. Therefore
following six types of signal samples are created.
• p → e+ e+ e−• p → µ+ e+ e−• p → µ− e+ e+• p → µ+ µ+ e −• p → µ+ µ− e +• p → µ+ µ+ µ−

3.2 Background
Only atmospheric neutrino events are only considered for the background in this analysis
since other non-neutrino backgrounds are negligibly small. This sample is created by Monte
Carlo simulation composed of three parts: neutrino flux, neutrino interaction with water andparticle tracking in the detector.

3

10

41

EventsEvents

3.2. BACKGROUND

SK4
p→e+e+e-

3

10

SK4
p→e+e+e-Free proton

Free protons-state102

s-statep-statep-state102

correlated decay

correlated decay

10

1
0

10

200

400

600

800
1000
True proton mass[MeV]

1
0

100

200

300

400

500
600
700
800
True proton momentum[MeV]

Figure 3.2: True mass(left) and momentum(right) distribution of proton with respect to eachstate.

3.2.1

Neutrino flux

The flux of atmospheric neutrino at the Super-Kamiokande detector is calculated by the modelof M.Honda et.al.[38][39].
In order to reproduce real hadronic interactions accurately, DPMJET-III[40] is used for thesimulation. The original DPMJET-III is modified by changing so called Z-factor to reproduce
atmospheric muon and neutrino flux at high energy better[41]. This modified DMPJET-III
can reproduce observed atmospheric neutrino flux above 1 GeV accurately at sea level andmountain altitude[42]. However, since neutrino flux below 1 GeV cannot be reproduced wellby DPMJET-III, another interaction model called JAM which is used in PHITS (Particle andHeavy-Ion Transport code System)[43] is used. Calculated results of DPMJET-III and JAM arecompared with experimental results of HARP collaboration which released detailed studies ofproton hadronic interactions on thin N2 and O2 targets at 12 GeV/c[44] as shown in Fig.3.3.
As the JAM has an upper limit on projective energy, for the energy below 32 GeV JAM is used
and for the energy above 32 GeV DPMJET-III is used in the simulation.
The primary flux model is based on the data of cosmic ray flux measurements by the
BESS[99][100] and AMS[97][98] experiments. For the model of the atmosphere and the geomagnetic field, US-standard ’76[101] and IGRF2005[102] are used respectively. The combination of 3-dimensional and 1-dimensional calculation is used to get the atmospheric neutrino
flux averaged over all azimuthal angles. For the 3-dimensional calculation, the Earth is assumed to be sphere with the radius Re = 6378.180 km. In addition to this sphere, 3 more
spheres: injection, simulation and escape spheres are considered. The injection sphere is defined as Rinj = Re + 100 km, the simulation sphere and the escape sphere are defined as
Rsim = Resc = 10 × Re . First, cosmic rays are generated on the surface of injection sphere
uniformly toward the inward direction followed by given primary cosmic ray spectra. Before
the simulation in the atmosphere, generated cosmic rays are tested whether they could pass
the geomagnetic barrier by checking the motion in the inverse time direction. If the cosmic
ray reaches the escape sphere without touching injection sphere again in the inverse time
direction, it’s determined to pass the geomagnetic barrier in the normal time direction. The
propagation of the cosmic ray in the atmosphere is simulated in the space between the surfaceof the Earth and the simulation sphere. When the cosmic rays enter the Earth, the events are
discarded. Since the detector is very small compared to the size of Earth, finite size ”virtual

42

CHAPTER 3. MONTE CARLO SIMULATIONS

Figure 3.3: Comparison of interaction models and experimental results of HARP (data points).
The solid line is JAM and the dashed line is DPMJET-III. [39]

3.2. BACKGROUND

43

detector” is used in 3-dimensional calculation with some corrections. 3-dimensional calculation is used for the neutrino energy below 32 GeV, and 1-dimensional calculation is used above
32 GeV. Calculated atmospheric neutrino flux averaged over all directions as a function of neutrino energy at Kamioka compared with other flux models is shown in Fig.3.4. The zenith angle
dependences averaged over all azimuthal angles for Kamioka at 3 ranges of neutrino energy
are also shown in Fig.3.5.

Figure 3.4: The atmospheric neutrino flux for Kamioka averaged over all directions (left) andthe flux ratio (right) compared with other flux model, HKKM06 (previous calculation of thismodel), model by Bartol group[45][46] and model by FLUCA group[47].

3.2.2

Neutrino interaction

The interaction of atmospheric neutrino with hydrogen or oxygen nucleus in water is simulated by NEUT program[48]. This program covers a wide energy range of neutrino from several
tens of MeV to hundreds of TeV. In NEUT, following neutrino interactions are considered.
• CC/NC (quasi-) elastic scattering (νN → lN ′ )• CC/NC single π production (νN → lN ′ π)
• CC/NS single γ production (νN → lN ′ γ)
• CC/NC single K production (νN → lΛK)
• CC/NC single η production (νN → lN ′ η)
• CC/NC deep inelastic scattering (νN → lN ′ hadrons)• CC/NC coherent π production (ν 16 O → lπX)
Here N, N ′ are proton or neutron, l is the lepton and X is the remaining nucleon.

44

CHAPTER 3. MONTE CARLO SIMULATIONS

Figure 3.5: The atmospheric neutrino flux by Honda model as a function of zenith angle
for Kamioka averaged over all azimuthal angles. For the neutrino energy of 0.32 GeV (left),
1.0 GeV(center) and 3.2 GeV(right). θ is the arrival direction of neutrinos. cos θ = 1 corresponds to vertically downward going neutrinos, and cos θ = −1 corresponds to verticallyupward going neutrinos. Neutrino oscillation effect is not considered.
Elastic and quasi-elastic scattering
The cross section for the neutrino nucleon CC quasi-elastic (CCQE) scattering is evaluatedbased on the Llewellyn-Smith model[50]. In order to calculate the cross section for nucleons in
the nucleus, the relativistic Fermi gas model by Smith and Monitz [51] is used in NEUT. Bothmodels use the vector and axial-vector form factors of nucleon. The axial-vector coupling
constant is set to 1.2 GeV/c2 to have good agreement with the recent neutrino experiments[52][53]. Comparison of calculated CCQE cross section and observed cross section in someexperiments is shown in Fig.3.6.

Figure 3.6: Cross section of neutrino CCQE scattering as the function of neutrino energy [48].
Solid line is calculated cross section for free proton and dashed line is for proton in Oxygen. Data points corresponds to ANL[54], Gargamelle [55][56], BNL[57], Serpukhov[58] andSKAT[59].

3.2. BACKGROUND

45

The cross section for NC elastic scattering is estimated by using following relations [60].
σ(νp → νp)
σ(ν̄p → ν̄p)
σ(νn → νn)σ(ν̄n → ν̄n)

=
=
=
=

0.153 × σ(νn → e− p)0.218 × σ(ν̄p → e+ n)
1.5 × σ(νp → νp)
1.0 × σ(ν̄p → ν̄p)

(3.1)
(3.2)
(3.3)
(3.4)

In this process, π 0 or π ± are sometimes additionally generated. π 0 decays to 2 γ and emitted
Cherenkov ring from γ is basically identified as electron ring. Then CCQE events with electron(muon) created from neutrino by charged interaction and 2 γ from π 0 can have similar final
states as p → e+ e+ e− (p → µ+ e+ e− ) signals. On the other hand, Cherenkov ring from π ± isoften mis-identified as a muon ring. Then CCQE events with electron or muon from neutrino
and some π ± can have similar final states as p → e+ µ+ µ− or p → µ+ µ+ µ− signals.
Single π, γ, K and η production
The process of single π production is separated to following 2 steps in the simulation by using
Rein and Sehgal’s method [61].
ν + N → l + N∗
N∗ → π + N′

(3.5)

Here N, N ′ are nucleons and N ∗ is a baryon resonance. In order to calculate cross section,
amplitude of each resonance production and the decay probability of each resonance into one
π and one nucleon are taken into account. 18 resonances below 2 GeV/c2 and axial-vector massof 1.2 GeV/c2 are considered. Comparison of calculated cross section and experimental results
are shown in Fig.3.7 The cross section of single γ, K and η productions can be calculated bychanging the decay probability of the resonances.
Single π production can have similar final states as each signal process due to the same
reasons as CCQE events associated with pion. Single η production can also have similar final
states as p → e+ e+ e− or p → µ+ e+ e− signals because η often decays to 2 γ.
Deep inelastic scattering
In order to calculate the cross section, following function is integrated in the range of W >1.3 GeV/c2 , here W is the invariant mass of the hadronic system.
d2 σ
G2F MN Eν
11=[(1 − y + y 2 + C1 )F2 (x, q 2 ) ± y(1 − y + C2 )xF3 (x, q 2 )] (3.6)
dxdy
π
2
2
2
2
2
yMl
xyMN
M
Ml
C1 =
(3.7)
−
− l2 −
4MN Eν x
2Eν
4Eν
2MN Eν x
Ml2
C2 = −(3.8)
4MN Eν x
Now x = −q 2 /(2M (Eν − El )), y = (Eν − El )/Eν , MN is the mass of nucleon, Ml is the massof lepton, Eν and El are the energy of incoming neutrino and outgoing lepton in the laboratory
frame, respectively. Here F2 and xF3 are nucleon structure functions taken from parton distribution function GRV98[62] with corrections proposed by Bodek and Yang [63]. Comparison of

46

CHAPTER 3. MONTE CARLO SIMULATIONS

Figure 3.7: Comparison of calculated cross section (solid line) and experimental results (black
points)[48].

Figure 3.8: Calculated cross sections and experimental results for total CC cross sections[48].
Upper 4 lines corresponds to neutrino and lower 4 lines corresponds to anti-neutrino. Solidline is calculated cross section with each PDF and data points shows some experimental results
as below. CCFR90[64], CDHSW87[65], GGMPS79[66], GHARM88[67], BNL80[68], CRS80[69],
BEBCWBB79[70], IHEPJINR96[71], IHEPITEP79[72], CCFRR84[73], SKAT[74]3.2. BACKGROUND

47

calculated cross sections and experimental results for total CC cross sections including CCQE
scattering, single meson productions and deep inelastic interactions are shown in Fig.3.8.
In this process, multiple pions are often generated and the events can have similar background states as each signal. Furthermore, proton is also generated or scatted by DIS. Such
events can have similar final states as signal with muon because the Cherenkov ring fromproton is often identified as a muon ring.
In order to calculate the cross section for NC multi π production, following relations areused which are estimated by the experimental results[75][76].
σ(νN → νX)
σ(νN → µ− X)
σ(νN → νX)
σ(νN → µ− X)
σ(νN → νX)
σ(νN → µ− X)
σ(ν̄N → ν̄X)
σ(ν̄N → µ+ X)
σ(ν̄N → ν̄X)
σ(ν̄N → µ+ X)
σ(ν̄N → ν̄X)
σ(ν̄N → µ+ X)= 0.26 (forEν < 3 GeV)

(3.9)

Eν − 33(3.10)= 0.26 + 0.04 ×(for 3 < Eν < 6 GeV)

= 0.30 (forEν > 6 GeV)

(3.11)= 0.39 (forEν < 3 GeV)

(3.12)

Eν − 33(3.13)= 0.39 − 0.02 ×= 0.37 (for(for 3 < Eν < 6 GeV)

Eν > 6 GeV)

(3.14)

Coherent π production
The differential cross section for NC coherent π production is described as below. [77]()
d3 σ
G2 MN 2 2
1
m2A
πN 2
2
=
f A Eν (1 − y)[σ ] × (1 + r )e−b|t| Fabs(3.15)
dQ2 dydt
2π 2 π16π totm2A + Q2
r = RefπN (0)/ImfπN (0)(3.16)−⟨x⟩/λFabs = e(3.17)−1πN
λ= σinel ρ(3.18)
Here Q2 is the square of 4-momentum transfer of lepton, t is the square of 4-momentum
transfer to the nucleus, mA is the axial vector mass, fπ = 0.93mπ , b = 80 GeV−2 , G is the
weak coupling constant, MN is the mass of nucleon, y = (Eν − El )/Eν is the fraction of
lepton energy loss, Eν , El are energy of neutrino and outgoing lepton and A is the atomic
number of target nucleus. And Fabs is the factor for pion absorption in nucleus, ⟨x⟩ is theR3 )−1 is the nuclear density, R is the radius ofmean path length of pion in Oxygen, ρ = ( 4π3πNπN
the nuclear, σtot , σinel are averaged total and inelastic pion-nucleon cross sections obtained
from the experimental results and fitted results of Rein and Sehgal [61].
In order to calculate the cross section for CC coherent π production, the correlation factorof the lepton mass (COR) as below is additionally taken into account [78].
)2(
1 Q2min (Q2 − Q2min )1 Q2min+y
COR = 2 1 −(3.19)
2 Q2 + m2π
4(Q2 + m2π )2yQ2min = m2l(3.20)1−y

48

CHAPTER 3. MONTE CARLO SIMULATIONS

Figure 3.9: The cross section of CC (left) and NC(right) coherent π production as the functionof neutrino energy[48]. Solid, dotted and dash-dotted lines correspond to the calculated crosssection with the model by Rein and Sehgal[78], Kartavsev et al. [79] and Alvarez-Russo et al.
[80]. The filled box and circle shows the upper limit from the measurements by the K2K [81]and SciBooNE [82] experiments respectively. The open box, circle and cross correspond to theobserved results by MiniBooNE [83], Aachen-Padova [84] and Gargamelle [85] experiments
respectively.
Comparison of calculated cross section and experimental results is shown in Fig.3.9.

3.2.3

Nuclear effects

Since the hadrons generated by neutrino interactions in nucleus can interact within the nucleus, observed particles are not always same as the ones initially generated. In order to take
into account this effect, the interactions of π, K, η and nucleon in the target nucleus are simulated in NEUT by using the cascade model [48][49]. In the cascade model, first particle is
moved by a unit length starting from generated point of hadrons. Then the interaction types(including no interaction) are determined by following the probabilities of each interaction.
This procedure continues until one of the interactions happens or the particle exits the nucleus.
The pion production is one of the dominant modes in neutrino interactions and the crosssection of pion interaction in the nucleus is also quite large. In NEUT, inelastic scattering,
charge exchange and absorption are considered for pion interactions. Particle production is
also considered for high energy pions. The mean free path (MFP) of various internuclear mechanisms are calculated by Delta-hole model[91] for low energy pion (pπ < 500 MeV/c). In thismodel, Fermi motion of the nucleon in the nucleus and Pauli blocking effect are taken into
account. Additionally MFPs for absorption and scattering are tuned so that calculated crosssections agree with π 12 C scattering data as shown in Fig.3.10.
For high energy pions (pπ > 500 MeV/c), experimental data of free π ± cross section is used.
f ree
f ree
and for single
The cross section for quasi-elastic scattering σQE, for hadron production σhad
f reecharge exchange σSCX are calculated by SAID partial wave analysis fit[92] shown in Fig.3.11.
f ree
f ree
Then the cross sections for π-nucleus scattering are calculated as σQE = σQE, σhad = σhad
f ree
and σSCX = σSCX
. Finally both σQE and σSCX are scaled by factor 1.8 which was obtainedby π 12 C QE scattering[86] and SCX[87] data. Simulated results show a good agreement withdata.
The interaction of K in nucleus is also simulated by using similar method as pion interac-3.2. BACKGROUND

49

Figure 3.10: The cross section of π +12 C (left) and π −12 C scattering as a function of pionenergy[49]. Solid lines are simulated cross section and data points are experimental
results.[86][87][88][89][90]Figure 3.11: The cross section of free π ± p scattering[49]. Data from PDG and fit by SAID.

50

CHAPTER 3. MONTE CARLO SIMULATIONS

tion but refers to experimental results of KN and K̄N scattering[93]. For the interaction ofη, absorption of η (ηN → N ∗ → π(π)N ′ ) is considered. The main resonances related to thisprocess are N (1540), N (1650) and the cross section for ηN → N ∗ → π(π)N ′ is calculated asfollows[94].
()ΓηN Γπ(π)N
π1(3.21)
σ= 2 J+k
2 (W − M ∗ )2 + Γtot /4
Here k is the momentum of η in center of mass system, J, Γ and M ∗ are spin, decay width andmass of the resonance, W is the invariant mass of the ηN system. The nucleon re-scatteringin the nucleus is simulated by almost the same way as pion interactions, considering elastic
scattering and a single or two delta(s) production for the pion production. The interaction
probabilities are extracted from nucleon-nucleon scattering experiments[95]. The delta production is simulated based on the isobar production model[96].

3.2.4

Neutron generation

Neutrons are generated in primary interactions (10%), hadron and meson interactions in the
nucleus (17%), and interactions of hadrons in water (73%). For hadron-water interactions at energies below 3.5 GeV, Nucleon-Meson-Transport-Code (NMTC) is used, which is based on the
Bertini internuclear hadronic cascade model[103]. For low energy (<20 MeV) neutron propagation, the Monte Carlo Ionization Chamber Analysis Package (MICAP) code[104] is used.
Thermalized neutrons are simulated until they captured by hydrogen and 2.2 MeV gamma ray
is emitted.

3.3 Detector
The particle propagation, Cherenkov radiation, propagation of Cherenkov photons in waterand PMTs or electronics response are simulated by Geant3[105] based package SKDETSIM.
Cherenkov photons are generated by following the equations (2.1) and (2.4). The groupvelocity vg of photons propagated in water is calculated as follows.
cvg =(3.22)n(λ) − λ ∂n(λ)∂λ
Here c is the speed of light in vacuum, λ is light wave length and n(λ) is the refractive index asa function of wave length. The process of absorption and scattering is taken into account forphoton propagation in water. For the photon with shorter wavelength (λ ≲ 450 nm), Rayleighscattering is the dominant interaction which is caused by small particles (r ≪ λ, where r is
the radius of the particles). For longer wavelength (λ ≳ 450 nm) absorption by H2 O moleculeis the dominant process. The probability of absorption as a function of wavelength is obtainedby experimental data (2.7.5). In addition to these processes, Mie scattering which is caused byrelatively large particle (r ≫ λ) is considered in the simulation. The attenuation coefficientsof Rayleigh and Mie scattering are tuned to be consistent with laser measurements, and theparameters are confirmed by cosmic ray muon events. The reflection or absorption at the black
sheets or the reflection on the PMTs surface are also simulated by using measured results. The
PMT timing is smeared by the measured timing resolution.
For the hadronic interaction, GCALOR[106] and NEUT pion cascade model are used forpion momentum above and below 500 MeV/c respectively.

Chapter 4
Event Preselection
In this analysis, reconstructed vertex and all visible particles are required to be inside the Inner
Fiducial Volume (FV). FV is defined as the area 2 m inside the top, bottom and barrel wall of
the ID, which corresponds to the mass of 22.5 kton. These events are called as fully contained(FC) events. Most of FC events consist of atmospheric neutrino events. In SK, there are three
types of atmospheric neutrino events: FC, partially contained (PC) and upward going muon
(UPMU) events. PC events require that reconstructed vertex is inside the Inner FV but any ofcharged particles go outside. UPMU events consist of high energy muons generated by upward
going neutrinos interacted with the rock around the detector. Schematic view for each typeof atmospheric neutrino in SK is shown in Fig.4.1. In order to make data set of FC events,

Figure 4.1: Schematic view of atmospheric neutrino types in SK.
we need to remove background events caused by cosmic ray muons, radioactivities, electronicnoise and so on. This event preselection consists of following 5 steps.
• Low energy event rejection• Electric noise event rejection• Specific background rejection I• Flasher event rejection51

52

CHAPTER 4. EVENT PRESELECTION• Specific background rejection II

In addition to these reduction steps, real time data check by human eyes is performed after
the specific background rejection I.

4.1 Low Energy Event Rejection
Trigger rate in SK is 106 events a day mainly fired by low energy events from radioactive
background or cosmic ray muon events. In order to reject such low energy events we require
following 2 cuts.
PE300 ≥ 200 p.e.s (100 p.e.s for SK-II)(4.1)
Here PE300 is the maximum number of photoelectrons (p.e.s) observed by ID PMT in sliding
300 ns time window. The threshold roughly equals to an electron momentum of 22 MeV/c.
Most of radioactive background, low energy Michel electron from cosmic ray muons and solar
neutrino events are rejected after this cut. Since the number of PMT in SK-II is half comparedto other periods, the threshold is also half in SK-II.
NHITA800 ≤ 50 (55 for SK-IV) or OD trigger is off(4.2)

Here NHITA800 is the number of OD PMT hits in the time window of [-400 ns, +400 ns]. Thiscut rejects cosmic ray muon, PC and UPMU events. The threshold is different in SK-IV because OD electronics and PMT gains are changed in the period. After these cuts, event rate isdecreased to 103 events a day.

4.2 Electric Noise Event Rejection
Events satisfying the following two cuts are kept in this step.
PEmax /PE300 ≤ 0.5(4.3)

Here PEmax is the highest observed p.e.s of single PMT in all ID PMTs. This cut can reject
electrical noise events which tend to have one larger PMT hit.
NHITA800 ≤ 25 (30 for SK-IV) or PEtot ≥ 100, 000(50, 000 for SK-II)(4.4)

Here PEtot is the total observed p.e.s in the ID. This is a more stringent cut for OD PMT hit
than First Reduction. The cut for total p.e.s can keep very high energy FC events which havelight leakage in OD area. After these cuts, event rate is decreased to the order of 100 events aday.

4.3 Specific Background Rejection I
This step rejects some specific background like hard muons, through going muons, stoppingmuons, cable hole muons, coincidence muons, flasher and low energy events. After this step,
event rate is decreased to about 40 events a day.

4.3. SPECIFIC BACKGROUND REJECTION I

4.3.1

53

Hard muon

Cosmic ray muons of energy ≥ 1 TeV is defined as hard muons. Such hard muons are rejectedby the following cut.
NHITA500 ≤ 40
(4.5)
Here NHITA500 is the number of observed OD p.e.s in sliding 500 ns time window.

4.3.2

Through going muon

The cosmic ray muons which penetrate the SK tank are called as the through going muons.
Through going muons deposit a lot of energy in ID so we require more than 1,000 PMTs have
230 p.e.s for each. Then through going muon fitter is applied for such events to find muons
entering and exiting point. The goodness of the through going muon fit is defined as follow.
{
}
∑ 1
1
(ti − Ti )2
Goodness = ∑
×
(4.6)
exp −
2
2
1
σ
2(1.5
×
σ
)
i
i
i
σi2
i
Here ti , Ti , σi are the observed hit time, estimated hit time from the muon entering time and its
track, time resolution of i-th PMT. Events satisfying following two requirements are classified
as the through going muon and rejected.
Goodness ≥ 0.75
NHITAin ≥ 10 or NHITAout ≥ 10

(4.7)
(4.8)

Here NHITAin (NHITAout ) is the number of OD PMT hits located in 8 m from the entrance(exit) point within fixed 800 ns time window. Events which pass this cut are rejected.

4.3.3

Stopping muon

The cosmic ray muons which enter the SK tank but stopped inside the ID region are called as astopping muon. Stopping muon fitter is applied to find muon entering point by using similar
way with through going muon fitter. The goodness of the fitter is defined by equation (4.6).
Events which satisfy following requirement are rejected as stopping muon.
NHITAin ≥ 10

(4.9)

Additional rejection criterion is defined only for SK-I as follow.
NHITAin ≥ 5

4.3.4

and

goodness > 0.5(4.10)

Cable hole muon

There are twelve cable holes on top of the SK tank for signal and high voltage cables. Since no
OD PMTs are installed in the holes, cosmic ray muons can enter through these holes into ID
region without OD PMT hits. Such events can be misidentified as FC or PC neutrino events.
In order to avoid such misidentified events, veto counters consisting of 2 m × 2.5 m plastic

54

CHAPTER 4. EVENT PRESELECTION

scintillation counters were installed into four out of the twelve cable holes in April 1997. We
require one veto counter hit and following rejection criteria:
Lveto ≤ 4 m(4.11)

Here Lveto is the distance between the cable hole and reconstructed vertex. Additional cut for
the holes without veto counter are introduced in SK-IV as follows.
Goodness of stopping muon fit ≥ 0.4(4.12)

PEtotal ≥ 4, 000(4.13)

Traveled in downward direction (cos θ ≤ −0.6)(4.14)

Lveto ≤ 2.5 m(4.15)

Events which satisfy these rejection criteria are rejected. The probability of rejecting true
neutrino events is estimated to be less than 0.01 %.

4.3.5

Coincidence muon

Cosmic ray muons sometimes enter the tank just after the low energy trigger by coincidence.
Such events are called as coincidence muon events and can pass former selection criteria.
Following cuts are applied to reject coincidence muon events.
NHITAoﬀ ≤ 20

(4.16)

Here NHITAoﬀ is the number of OD PMT hits in fixed 500 ns timing window from +400 ns to+900 ns after the trigger timing.
PEoﬀ ≤ 5, 000 p.e.s (2,500 p.e.s for SK-II)(4.17)

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

4.3.6

Flasher event

Light is sometimes emitted from PMT itself due to electrical discharge. Such events are called
as flasher events and sometimes misidentified as FC neutrino events. Usually hit timing distribution of the flasher events is wider than that of particle induced events. In order to rejectsuch events, following cut is applied.
NMIN100 ≤ 20 (15 for SK-I)(4.18)

Here NMIN100 is the minimum number of ID PMT hit in sliding 100 ns time window from+200 ns to +700 ns after trigger timing.

4.4. FLASHER EVENT REJECTION

4.3.7

55

Low energy event

Remaining low energy events like radioactive background or electrical noise are rejected by
the following cut.
NHIT50 ≥ 50 (25 for SK-II)(4.19)
Here NHIT50 is the maximum number of ID PMT hits in sliding 50 ns time window. Hits arecounted after subtracting the time of flight of observed photons assuming all photons comefrom one vertex point. The vertex is defined as the position where the time of flight subtracted
PMT timing distribution makes sharpest peak. Now NHIT50 = 50 equals to visible energy of
9 MeV and this cut is low enough to keep efficiency.

4.4 Flasher Event Rejection
In this step, additional selection criteria is applied to reduce remaining flasher events. Flasher
events are caused by electrical discharge in PMTs, so the events usually have patterns repeatedin a cycle of a few hours or days. Pattern matching algorithm is used to find such events asfollows.
• ID wall is divided into 1,450 patches of 2 m × 2 m.
• Correlation factor r is calculated as follow.
B
AB
1 ∑ (QAi − ⟨Q ⟩) × (Qi − ⟨Q ⟩)r=
N i
σA × σB(4.20)

A(B)

Here N is the number of the patches, Qi
is total observed p.e.s in i-th patch for event
A(B), ⟨QA(B) ⟩ and σA(B) are the averaged observed p.e.s of all patches and its standard
deviation for event A(B), respectively.
• Then DISTmax is calculated as the distance between PMTs with maximum pulse heightin event A and B.
• If DISTmax ≤ 75 cm, offset value is added as r = r + 0.15
• If r exceeds the threshold rth , event A and B are determined to be matched events. rth
is defined as follows.
B
rth = 0.168 × log10 {(PEA
tot + PEtot )/2} + 0.130(4.21)• Above calculations are repeated over 10,000 events around the target event and thenumber of matched events are counted. Target events with large r or large numberof matched events are rejected finally.
After this step, event rate is decreased to about 18 events a day.

4.5 Specific Background Rejection II
In this step, remaining cosmic ray muons, flasher events, electronic noise and calibration related events are rejected by applying some additional selection criteria.

56

4.5.1

CHAPTER 4. EVENT PRESELECTION

Stopping muon

Following cuts are applied to reduce remaining stopping muon events.
NHITAin ≤ 10

(4.22)NHITAin ≤ 5 if goodness of stopping muon fit ≥ 0.5(4.23)orDefinition of the goodness is same as (4.6).

4.5.2

Cable hole muon

In order to reject remaining events of cosmic ray muon which enter the cable holes withoutveto counter, tighter cut by more precise event reconstruction is necessary. Following rejection
criteria is applied only for SK-IV in addition to the selection (4.12), (4.13), (4.14),(4.15).
NHITAAPfit ≥ 4(4.24)

Here NHITAAPfit is the maximum number of OD PMT hits within 8 m from the muon entering
point fitted by an event reconstruction algorithm APfit (chapter 5), in a sliding 200 ns time
window from −400 ns to +400 ns. Events which satisfy these rejection criteria are rejected.

4.5.3

Coincidence muon

In addition to the coincidence muon cut in the third reduction, tighter rejection criteria is
applied as follows.
PE500 ≤ 300 p.e.s (150 p.e.s for SK-II)(4.25)
PE500 is the total number of observed ID p.e.s in a fixed time window from −100 ns to +400 ns.
PElate ≥ 20 p.e.s(4.26)

Here PElate is the maximum number of the OD PMT hits in a sliding 200 ns time window from+400 ns to +1600 ns. Events which satisfy these rejection criteria are rejected.

4.5.4

Invisible muon

Cosmic ray muons below the Cherenkov threshold can enter ID region without OD PMT hits
and decay into Michel electron. Cherenkov light emitted from the Michel electron can bedetected by ID PMT and then such events can be misidentified as FC events. Such invisible
muon events which satisfy the following rejection criteria are rejected.
PEtot ≤ 1, 000 p.e.s (500 p.e.s for SK-II)(4.27)NHITACearly ≥ 5(4.28)

Here NHITACearly is the maximum number of OD PMT hits in a sliding 200 ns time window
from -800 to -100 ns.
NHITACearly + NHITAC500 ≥ 10 (if DISTclust ≤ 500 cm)(4.29)

Here NHITAC500 is the number of OD PMT hits in a fixed time window from -100 ns to +400 ns
and DISTclust is a distance between two OD hit clusters used for NHITACearly and NHITAC500 .

4.6. REJECTION FOR ID/OD CROSS TALK

4.5.5

57

Long tail flasher event

In addition to the flasher event cut in the third reduction, tighter rejection criteria is applied
as follows.
NMIN100 ≥ 6 if goodness of TOF fitter ≤ 0.4(4.30)
From SK-II to SK-IV, the rejection criteria is changed as follows.
NMIN100 ≥ 5 if goodness of TOF fitter ≤ 0.3(4.31)

Events which pass above criteria are rejected.

4.6 Rejection for ID/OD cross talk
The new rejection step for ID/OD cross talk was implemented recently by H.Tanaka et al. only
in SK-IV [109]. OD PMT hits are induced just after the ID PMT hits by ID/OD cross talk.
Basically such OD cross talk hits have very low charge (<0.2 p.e) and appear after ∼50 ns
after ID hits. Therefore OD PMT hits satisfying the following requirements are excluded in all
rejection steps.
QOD < 0.2 p.e∆TID−OD > 50 ns(4.32)(4.33)

Here QOD is the charge of the OD PMT hits and ∆TID−OD is the difference of OD PMT hit
time and the time of most recent ID PMT hits from 4 closest ID PMTs.

Chapter 5
Event Reconstruction
In the physics analysis, charge and time information of PMTs need to be converted to theinformation of physics quantities: the number of Cherenkov rings, momentum of the ring,particle type and so on. A reconstruction scheme APfit is used in this analysis. APfit is applied
to the events which pass the preselection (chapter 4). APfit reconstructs events step by step
as follow.
• Vertex fitting• Ring counting• Particle identification• Momentum reconstruction• Michel electron search• Neutron tagging (SK-IV only)
Typical hit maps and timing distributions for single electron and single muon MC events areshown in Fig.5.1.

5.1 Vertex Fitting
Once the speed of charged particle exceeds the threshold, it starts to emit Cherenkov light.
This start point is defined as the vertex, and the precise vertex reconstruction is importantto estimate Cherenkov angle precisely. Event reconstruction starts from vertex fitting which
consists of three steps as follows.
• Point fit• Ring edge search• TDC fit
First, the vertex position is roughly estimated assuming the Cherenkov light is emitted fromone point (Point fit). Then, the most energetic Cherenkov ring and its ring edge are searched(Ring edge search). Actually, the electrons (muon) with a few hundreds MeV, which is the59

60

CHAPTER 5. EVENT RECONSTRUCTION

Figure 5.1: Typical hit maps (top) and timing distributions [ns] (bottom) for single electron(left) and single muon (right) of MC events. The hits aroung 1,250 ns in the single muon event
correspond to the decay electron.

5.1. VERTEX FITTING

61

typical energy scale for the decayed charged leptons in the proton decay, run for a few tensof cm (a few m) in water until they stop by losing their energy. Therefore, Cherenkov lightis continuously emitted along the track of charged particles. Finally the vertex position isprecisely reconstructed by considering this feature (TDC fit).

5.1.1

Point fit

The point fit assumes all Cherenkov light comes from one point at the same time and does notconsider the track length of charged particles. The principle of this algorithm is that timing
residual of (photon arrival time at each PMT) − (time of flight) should be peaked at correctvertex position. Fig.5.2 shows the residual distribution with true vertex position and 4 m offfrom the true vertex position. The residual with true vertex position clearly shows a sharper
peak. In order to find the vertex position, Goodness of the point fit is defined as follow.

Figure 5.2: The timing residual of (photon arrival time at each PMT) − (time of flight) withcorrect vertex position (top) and 4 m off from true vertex position(bottom) by using p → e+ π 0MC[28].
[]1 ∑{ti (x) − t0 }2
Goodness(Pointfit) =
exp −
N i
2 × (1.5σ)2(5.1)

Here N is the number of PMT hits, ti is time of flight (TOF) subtracted timing of the i-th
PMT, t0 is a free parameter chosen to maximize the Goodness(Point fit), σ is the PMT timing
resolution of 2.5 ns and factor 1.5 is chosen to optimize the performance of the fit. Finally, the62

CHAPTER 5. EVENT RECONSTRUCTION

position which maximizes the Goodness(Point fit) is chosen as the reconstructed vertex by
Point fit.

5.1.2

Ring edge search

Next step is finding the ring edge and the direction of most energetic Cherenkov ring. First,
the number of p.e.s is calculated as a function of opening angle θ of the ring with respect tothe vertex position determined by the point fit and assumed test direction (PE(θ)). Example
for the distribution of PE(θ) with certain vertex and direction in a single ring event is shownin Fig.5.3. Then the opening angle of the ring edge θedge is defined which satisfies following

Figure 5.3: Example for the distribution of PE(θ) in single ring event (top). Bottom plot shows
second derivation of top figure[29]. θedge and θpeak values of this ring are pointed out byarrows.
equation. And θedge is also required to be more than θpeak , where the θpeak is the opening angle
at the maximum point of PE(θ).
d2 PE(θ)=0d2 θ
θ=θedge(5.2)

Finally, in order to determine the ring direction, the estimator Q(θedge ) is defined as follow.
∫ θedgePE(θ)dθQ(θedge ) = 0
×sin θedge(dPE(θ)dθ
θ=θedge)2[(θedge − θexp )2
× exp −
2σθ2

]
(5.3)

5.1. VERTEX FITTING

63

Here θexp is expected opening angle calculated from total charge inside θedge assuming theCherenkov ring is emitted from electron and σθ is its resolution. The θedge and Q(θedge ) is
calculated changing the direction of the charged particle. Then the direction which maximizes
Q(θedge ) is chosen and the θedge in that case is determined as the opening angle of the ring edge.
The motivation of Q(θedge ) is selecting the direction with larger amount of p.e.s inside θedge ,larger slope of PE(θedge ) and smaller difference between θedge and θexp . In case of θedge > 43
degree, definition of Q(θedge ) is changed as follows.
∫ θedgeQ(θedge ) =0[]PE(θ)dθ(θedge − θexp )2
× exp −sin θedge
2σθ2

(5.4)

PMTs on the ring edge determined by θedge are tagged and used in the next step, precise vertex
fitting.

5.1.3

TDC fitFinally, vertex is reconstructed more precisely by TDC fit. TDC fit assumes that photons are
emitted along the track of the charged particle. First, the track length between the vertex andphoton emitting point, which is detected in i-th PMT, is calculated as below.
∫ li
Q(l)dl′li = ∫ 0∞× Lt
Q(l)dl0(5.5)

Here li is the position on the track of charged particle extrapolated from i-th PMT by using the
opening angle θc , where θc is averaged opening angle of the PMTs tagged by previous step.
And Q(l) is the charge distribution of PMTs projected on the track of the charged particle.
Now li′ is replaced by li in case li′ > li to avoid to calculate too long track length for theelectron ring. Schematic view for the definition of the parameters is shown in Fig.5.4.
Then the residual of observed and expected photon arrival timing of i-th PMT ti is considered as follows.
′t0 − l − n × |P⃗ − X⃗ ′ i | for PMTs inside ring edge
i
i
cn c
ti =
(5.6)
t0 − × |P⃗ − O|
⃗
for
PMTs
outside
ring
edge
i
i
c
Here t0i is the hit timing of i-th PMT, n is the refractive index of water and c is the speed of light⃗ ′ i is the photon emitting position, which is detected by i-th PMT estimatedin vacuum. And X⃗ is the vertex position. PMT hits insideby equation (5.5), P⃗i is the position of i-th PMT and O
the ring edge are mainly from direct photons and outside the ring are mainly from scatteredor reflected light on the detector wall. Different fitting estimators are used for PMT hits insideand outside the ring edge. The estimator GI for the PMT hits inside the ring edge is defined
as follow.
∑ 1
Gdirect (ti , t0 )
(5.7)
GI =
σi2
i
[

{ti − t0 }2Gdirect (ti , t0 ) = exp −2(1.5 × ⟨σ⟩)2

]

(5.8)

64

CHAPTER 5. EVENT RECONSTRUCTION

Figure 5.4: Schematic view of the parameters used in TDC fit[29].

5.2. RING COUNTING

65

Here σi is the timing resolution of i-th PMT as a function of detected p.e.s, ⟨σ⟩ is averaged
timing resolution for detected p.e.s over hit PMTs, ti is the same value as (5.6) and t0 is afree parameter chosen to maximize the GI . There are two estimators GO1 , GO2 for the PMT
hits outside the ring edge. In case ti is greater than t0 contribution from scattered photon isconsidered. Then GO1 and GO2 are defined as follows.
∑ 1
GO1 =
(Gdirect (ti , t0 ) × 2 − 1) for ti ≤ t0
(5.9)
σi2
i
GO2 =

∑ 1
i

σi2

(max[Gdirect (ti , t0 ), Gscatt (ti , t0 )] × 2 − 1) for ti > t0

(5.10)

(
)
(
)
Rq
Rq
ti − t0
Gscatt (ti , t0 ) =× Gdirect (ti , t0 ) + 1 −× exp −
(5.11)
1.52
1.52
60 ns
Here Rq is the fraction of the number of p.e.s inside the ring edge over inside the opening
angle 70 degree. Total estimator of TDC fit is defined as follow.
GT =GI + GO1 + GO2∑
2i 1/σi(5.12)

EventsThe vertex position which maximizes GT is chosen finally. The distance between true andreconstructed vertex for p → e+ e+ e− signal is shown in Fig.5.5. The accuracy of the vertex
reconstruction is a few tens of cm.
MC

600

p → e+ e+ eSK4

500
400
300
200
100
0
0

10

20

30

40

50

60

Distance between true and reconstructed vertex [cm]Figure 5.5: The distance between true and reconstructed vertex for p → e+ e+ e− signal.

5.2 Ring Counting
After vertex and angle of most energetic Cherenkov ring are determined, additional Cherenkov
rings are searched. Ring counting consists of two steps as follows.
• Ring candidate selection• Ring candidate test

66

5.2.1

CHAPTER 5. EVENT RECONSTRUCTION

Ring candidate selection

The pattern recognition algorithm known as Hough transformation technique [31] is used
for ring candidate selection. Fig.5.6 shows the concept of Hough transformation technique.
For example, four hit PMTs on unknown ring with radius r are considered. By using Hough

Figure 5.6: The concept of Hough transformation technique[28]. Actually the PMT hits andcircles are projected on (Θ,Φ) Hough space.
transformation, circles with radius r whose center are each hit PMT are drawn. All circles
are crossed at the center of unknown ring. Thus the center of unknown ring is determinedby finding peak accumulated by each circle. Before drawing the circles, PMTs which belong
to the Cherenkov ring already found are removed. Hough space is defined by 36 bins of Polar
angle Θ and 72 bins of azimuthal angle Φ. Now Θ and Φ are measured from the position ofreconstructed vertex. Detected p.e.s in each PMT which are corrected for attenuation lengthand acceptance are mapped on (Θ, Φ) Hough space. Actually, the opening angle of 42◦ towards
each hit PMT is assumed and the circle is projected on Hough space around each PMT hit.
Then the peak accumulated by each circle is searched and it is determined as the center of thering candidate. An example of p.e. distribution on (Θ,Φ) Hough space is shown in Fig.5.7. Inorder to avoid to find fake rings, any ring candidates which are very close to the ring (angle< 15◦ ) already found are discarded. In order to take into account the different Cherenkov
angle for non-electron particles, Hough transformation on Qe (θ) space is performed. HereQe (θ) is expected p.e. distributions with respect to the vertex and determined ring center as
the function of opening angle θ.

5.2.2

Ring candidate test

Ring candidates are checked by likelihood method to know if the ring is true or fake. In casethe number of rings is N , (N + 1)-th ring candidate is newly assumed. Then p.e.s inside the(N + 1)-th ring is expected by considering the contribution from other rings and (N + 1)-thring itself. Actually p.e.s from crossed Cherenkov rings are overlapped in some PMTs, so wehave to know the fraction of p.e.s in one PMT contributed from other rings. The ring separation
method is used for this (section.5.3.2). Expected charge inside the (N + 1)-th ring is comparedwith observed charge and the likelihood is defined as follows.
{
(
)}
N
+1
∑
∑
exp
LN +1 =
log prob qiobs ,αn · qi,n(5.13)in=1

5.2. RING COUNTING

67

Figure 5.7: An example of p.e. distribution on (Θ,Φ) Hough space[29]. Two clear peaks areseen, which are identified as centers of Cherenkov rings.
The sum of i extends over PMT hits inside the (N + 1)-th Cherenkov ring. qiobs is observedexp
is expected p.e.s in the i-th PMT from n-th ring and αn is a changing
p.e.s in i-th PMT, qi,nscale which maximize the LN =1 . The probability prob(qiobs , qiexp ) is defined as follows.
(
exp 2 )obs
 √ 1 exp − (qi − qi )( for qiexp > 20 p.e.)2σ 2prob(qiobs , qiexp ) =2πσConvolution of single p.e and Poisson distribution ( for qiexp < 20 p.e.)(5.14)
Here σ is the resolution for qexp . If there are no ring candidates which satisfy LN +1 ≥ LN , thenumber of ring is determined to be N . If any of ring candidates satisfy LN +1 ≥ LN , following
functions are calculated.
F1 : LN +1 − LN corrected for the total p.e.s.
F2 : Average of expected p.e.s on the ring edge of the (N + 1)-th ring candidate (Qedge ).
F3 : Average of expected p.e.s outside the (N + 1)-th ring candidate (Qout ) is calculated. Thenthe difference Qedge − Qout is corrected for total p.e.s.
F4 : The residual of p.e.s detected and expected in i-th PMT.
As the value of each function is larger, the (N + 1)-th ring candidate becomes more reliable.
Then the four functions are used for the final evaluator as follows.
F =

4
∑
i

αi Fi

(5.15)

68

CHAPTER 5. EVENT RECONSTRUCTION

EﬃciencyEﬃciency

Here αi are optimized weights for each function. In case F is positive, (N + 1)-th ring isdetermined to be true ring and process of ring candidate selection is repeated again.
The ring reconstruction efficiency as a function of the particle momentum for single electron and single muon MC is shown in Fig.5.8. The turn on in both efficiency plots are basically
due to the Cherenkov threshold of the particle or lack of p.e.s. At the plateau region of theefficiency, almost all Cherenkov rings can be reconstructed both for single electron and muoncases. For the multi ring case, reconstruction efficiency basically becomes lower due to theoverlap of the rings.

1

0.8

1

0.8

MC

MC

Single electron

0.6

SK4

0.4

0.4

0.2

0.2

0
0

50

100

150

200

250

300

350

400

450

500

True momentum [MeV]Single muon

0.6

0
0

SK4

50

100

150

200

250

300

350

400

450

500

True momentum [MeV]

Figure 5.8: The ring reconstruction efficiency as a function of the particle momentum for single electron (left) and single muon (right) events. The vertical error bars correspond to thestatistical uncertainty of each bin. If the angle between the true particle and reconstructedring is below 20◦ , the Cherenkov ring is defined to be reconstructed.

5.3 Particle Identification
Particle identification (PID) algorithm can classify each Cherenkov ring into showering (e-like)and non-showering (µ-like) types. Showering particles such as electrons or gamma-rays are
multiple scattered and make electromagnetic showers in water. As a result Cherenkov rings
with diffuse edge are detected on ID wall. On the other hand, non-showering particles suchas muons or pions make Cherenkov rings with clear edge. Such differences of detected ringpattern are used in PID algorithm. Another important information for PID is opening angle ofeach Cherenkov ring. Since electron is highly relativistic (β ∼ 1) as their mass is very small,
opening angle of Cherenkov rings from electron or gamma-rays are 42◦ . On the other hand,muons or pions can make Cherenkov angle with smaller opening angle when they are nothighly relativistic.
PID algorithm starts from ring separation in order to know exact observed p.e.s contributed
from each ring. Then observed p.e.s distribution of each ring is compared with expected p.e.s
distributions of electron or muon. One of expected p.e.s distributions which can reproduce theobserved one better is determined as the particle type of the ring.

5.3. PARTICLE IDENTIFICATION

5.3.1

69

Expected p.e.s distribution

Expected p.e.s distribution of electron is made by using Monte Carlo simulation. First expected p.e.s distribution on hypothetical spherical surface with Rsph = 16.9 m as a function of
opening angle θ is made. Actually distributions of expected p.e.s Qexp (θ, p) are tabulated forelectron momentum p = 100 MeV, 300 MeV and 1,000 MeV. Then expected p.e.s of i-th PMT
for electron is calculated as follows.
( sph )1.5
R
1
exp
exp
qi (e) = αn (e) × Q (θi,n , pn ) ××× f (Θi ) + qiscatt(5.16)ri
exp(ri /L)
qiexp (e): expected p.e.s for i-th PMT from n-th ring assuming particle is electron.
αn (e): normalization factor for electron.
θi,n : opening angle between i-th PMT and direction of n-th ring.
pn : momentum of n-th ring.
ri : distance between vertex and i-th PMT.
L: attenuation length of light in water.
f (Θi ): correction factor for the acceptance to i-th PMT as a function of the photon incident
angle Θi shown in Fig.5.9.
qiscatt : expected p.e.s for i-th PMT from scattered photon.

Figure 5.9: Correction factor f (Θ) for the acceptance to PMT as the function of the photon
incident angle Θ [29].
Expected p.e.s for muon is analytically calculated as follows.


[ (
)
]−1
dθ
1
qiexp (µ) = αn (µ) × ri sin θxi,n + ri ·×f (Θi )+qiscatt× sin2 θxi,n+ qiknock ×
dx x=xi,nexp(ri /L)(5.17)

70

CHAPTER 5. EVENT RECONSTRUCTION

qiexp (eµ): expected p.e.s for i-th PMT from n-th ring assuming particle is muon.
αn (µ): normalization factor for muon.
x: distance between vertex and muon.
xi,n : distance between vertex and Cherenkov light emission point of n-th ring estimated fromi-th PMT.
θ: opening angle of muon traversing at x. Energy loss of the muon is taken into account.
θxi,n : opening angle of muon traversing at x = xi,n .
qiknock : expected p.e.s of knock-on electrons estimated by Monte Carlo simulation.
Here sin2 θ comes from photon intensity of Cherenkov light described in (2.4). And r(sin θ +r · (dθ/dx)) comes from the cross section of Cherenkov photon 2πr sin θ(dx sin θ + rdθ). It
considers that a muon traverses for dx changing the opening angle θ as a function of the muonenergy loss. Schematic view of the cross section is shown in Fig.5.10

Figure 5.10: The cross section of Cherenkov photon 2πr sin θ(dx sin θ +rdθ).A muon traverses
for dx changing the opening angle θ as a function of the muon energy loss. [29]5.3.2

Ring separation I

In this step, contribution of each ring to the detected p.e.s in each PMT is determined assuming
the charged particle is electron. First observed p.e.s in i-th PMT qiobs and sum of expected p.e.s
exp
exp
from n-th ring in i-th PMT qi,nare compared with in 70◦ opening angle of n-th ring. qi,nis
2
calculated by (5.16). Initial p.e distributions are determined by minimizing following χ .
χ2n =∑θi′ ,n <70◦

(

)2
∑
qiobs
− n′ qiexp
′
′ ,n′
√
qi′

(5.18)

5.3. PARTICLE IDENTIFICATION

71

Summation is performed for all i′ -th PMTs within 70◦ opening angle of n-th ring. Calculationof χ2n continues changing the momentum of n-th ring until minimum χ2n value is found. This
procedure is performed continuously ring by ring until all χ2n values are converged. As aexp
result, we get initial separated p.e.s qi,n from n-th ring in i-th PMT by using determined qi,nand following function.
exp
qi,n
obs
qi,n = qi × ∑ exp(5.19)
n′ qi,n′Using this initial separated p.e.s qi,n , expected p.e distribution Qexp
n (θ) as the function ofexp
opening angle θ towards n-th ring direction is calculated. Qn (θ) is expected p.e distribution
projected on hypothetical spherical surface whose center is the reconstructed vertex. In orderto make Qexp
n (θ), qi,n needs to be corrected by considering the distance from the vertex, theattenuation length and PMT acceptance as follows.
(
)
Rsph
1
1
′
qi,n = qi,n × exp − abs ××(5.20)
L
exp(−ri /L) f (Θ)′
is corrected p.e distribution and Labs is a parameter for absorption length in Monte
Here qi,n′Carlo simulation set to be 55 m. And Qexp
n (θ) is made by summing up qi,n within opening angle
θ of n-th ring. Then Qexp
n (θ) is optimized by considering non-overlap region of the ring, byapplying proper normalization and smoothing and by using the likelihood.
exp
In the next step, qi,nis recalculated again by using optimized Qexp
n (θ) as follows.

(
exp
qi,n
= Qexpn (θi,n ) × exp

Rsph
Labs

)
×

1
× f (Θ)exp(ri /L)(5.21)

Optimization of charge separation is performed by using following likelihood function.
(
)
√
√
∑
∑
exp
exp
obs
Ln =
(5.22)
prob(qi′ ,αn′ · qi′ ,n′ ) × Qn (θi′ ,n ) × min[1, θnc /θi′ ,n ]θi′ ,n <70◦n′

prob is the same function as (5.14) to calculate the probability of how the observed and expected p.e.s in each PMT are same. θnc is the reconstructed opening angle of n-th
ring. αn is√ exp
the normalization
parameter of n-th ring for the optimization. The factors of Qn (θi′ ,n ) ×√c
min[1, θn /θi′ ,n ] enhance the contribution from the PMTs around and inside the Cherenkov
edge. αn which maximizes the Ln is taken and this optimization is iterated until all αn converge. Finally, observed p.e.s are separated again by using optimized αn as follows.
exp
αn · qi,nobs
qi,n = qi × ∑expn′ αn′ · qi,n′5.3.3(5.23)

Determination of particle type

In order to determine the particle type of the ring, following likelihood function is used.
(
)
∏
∑
exp
exp
Ln (e or µ) =prob qiobs , qi,n(e or µ) +qi,n(5.24)′
θi <1.5×θcn′ ̸=n

72

CHAPTER 5. EVENT RECONSTRUCTION

exp
Here prob is the same function as (5.14), qi,nis expected p.e from n-th ring assuming the parexp
ticle is electron (5.16) or muon (5.17). And qi,n
′ is the contribution from other rings determinedby ring separation method described in section5.3.2. Now Ln is optimized to get the maximum
value by changing the direction and opening angle of n-th ring. Then Ln is converted to theprobability to determine the particle type from the pattern of p.e.s. as follows.
(
)
2
2
2
2
{χ
(e
or
µ)
−
min[χ
(e),
χ
(µ)]}
n
n
Pnpattern (e or µ) = exp − n(5.25)2σχ2 2n√χ2n (e or µ) = −2 log Ln (e or µ) + constant(5.26)

Now σχ2 2n = 2N and N is the number of PMTs used in the calculation. The probability fromthe opening angle of Cherenkov ring is defined as follow.
(){θnobs − θnexp (e or µ)}2
angle
(5.27)Pn (e or µ) = exp −2(δθn )2
Here θnobs and δθn are reconstructed opening angle and its fitting error respectively. And θnexp
is expected opening angle of n-th ring from the reconstructed momentum assuming electron
or muon. Then the combined probability is calculated as follows.
Pn (e or µ) = Pnpattern (e or µ) × Pnangle (e or µ)
Finally following probability is calculated and used to determine the particle type.
√√
PPID = − log P (µ) − − log P (e)(5.28)(5.29)

In case PPID < 0 the ring is determined to be e-like and in case PPID > 0 the ring is determined
to be µ-like.
Now PPID values for true electrons and muons in are shown in Fig.5.11. The PID efficiency plots for electrons and muons as a function of the particle momentum are also shownin Fig.5.12. The inefficiency for lower momentum electron and muon is mainly due to the lackof PMT hits. For higher momentum electrons and muons, almost all rings from electron ormuon can be identified correctly in case the ring is well independent. For the multi ring case,
the PID efficiency basically becomes lower due to the overlap of the rings.

5.3.4

Ring separation II

In this step, contribution of p.e.s from each ring in each PMT is calculated again by assuming
the particle type determined in PID process. In order to get expected p.e in each PMT, tabulated
p.e distribution made by MC simulation is used. Scattered and reflected light on the detector
wall is also taken into account. Ring separation is optimized by using the following likelihood
function.
()∑∑
prob(qiobs
αn′ · qiexp(5.30)Ln =′ ,′ ,n′ )
θi′ ,n <70◦n′

prob is the same function as (5.14). αn is changed repeatedly until finding the maximum Ln .
Finally separated p.e.s is calculated by using the function (5.19).
For the multi ring case, additional correction is applied as below.

Events

5.3. PARTICLE IDENTIFICATION

73

MC

1000

Single electron
Single muon
SK4

800

Electron
600

Muon

400

200

0
-10

-8

-6

-4

-2

0

2

4

6

8

10

PID (pattern & angle) likelihood

PID Eﬃciency

PID Eﬃciency

Figure 5.11: PPID values for true electrons (black) and true muons (red) in single electron andmuon MC, respectively.

1

0.8

MC
Single electron

0.6

SK4

1

0.8

Single muon

0.4

0.4

0.2

0.2

0
0

50

100

150

200

250

300

350

400

450

500

True momentum [MeV]

SK4

0.6

0
0

50

100

150

200

250

300

350

400

450

500

True momentum [MeV]

Figure 5.12: The PID efficiency as a function of the particle momentum for single electron (left)
and single muon (right) events. The vertical error bars correspond to the statistical uncertainty
of each bin. The definition of the PID efficiency is that the number of e-like (µ-like) rings withrespect to the number of rings matched (angle below 20◦ ) to the true electron (muon).

74

CHAPTER 5. EVENT RECONSTRUCTION• 2 close rings a and b with the energy Ea and Eb , respectively are considered (Eb > Ea ).
If the angle between 2 rings θ is less than 30◦ and Ea sin θ < 60 MeV, ring a is rejected.
• If Ea /Eall < 0.05 and Ea < 40 MeV, ring a is rejected. Eall is the total energy of allrings.

5.4 Momentum Reconstruction
The momentum of each ring is reconstructed from the total number of p.e.s within a 70◦ half
opening angle towards the ring direction. Contribution of exact p.e in each PMT from otherrings are calculated by ring separation process. In order to obtain the total charge, p.e.s ineach PMT from n-th ring is summed up and corrected for light attenuation in water as thefollowing equation.
(r )
∑
Gdata
1
i,n
RTOTn = constant × MC ×
qi,n × exp
×× cos ΘiGL
f (Θi )
θ <70◦(5.31)

i,nHere G is PMT gain parameter deduced from cosmic ray muon sample. The ratio of G corrects for the difference of PMT gain between data and MC. RTOT is converted to the proper
momentum depending on the particle type by using conversion table made from MC.

5.5 Michel Electron Search
Tagging the decayed electron from muon so called Michel electron is a good indicator forthe existence of muons. In this tagging method, delayed hit clusters from primary timing aresearched. Observed Michel electron is classified to three types as follow.
sub-event type (∆t > 0.9 µs)
Michel electron observed in separated event (sub-event).
primary-event type (∆t < 0.9 µs)
Michel electron observed in primary event.
split type (∆t ∼ 0.9 µs)
Michel electron observed around the border timing of event window. Observed PMTs
from Michel electrons are separated into both primary-event and sub-event.
Here ∆t is the timing difference between primary event and following Michel electron event.
Following selection criteria are required for sub-event type.
• ∆t < 30 µs• NHIT > 50. NHIT is the number of ID PMT hits.
• Reconstructed vertex is well fitted.
• NHIT(50 ns)> 30. NHIT(50 ns) is the maximum number of ID PMT hits in a 50 ns sliding
timing window after subtracting TOF.

5.6. NEUTRON TAGGING

75• Total number of p.e.s is less than 2,000.
For primary-event type, second peak from Michel electron is searched. Following selection
criteria are required for primary-event type.
• NHIT(30 ns)> 20. NHIT(30 ns) is the maximum number of ID PMT hits in a 30 ns sliding
timing window after primary peak.
In addition to the above selection criteria, additional selections are applied as follows for
proton decay analysis only in SK-I to SK-III.
1. NHIT > 60 (30 for SK-II) for sub-event type.
2. NHIT > 40 (20 for SK-II) for primary-event type.
3. 0.1 µs < ∆t < 0.8 µs or 1.2 µs < ∆t < 30 µs
The selections 1 and 2 reject the gamma emission from µ− captured in 16 O nuclei. The selection
3 rejects the dead time due to the impedance mismatch of ATM boards between 800 ns and1,200 ns from the primary event timing. This dead time region is solved in SK-IV by using newelectronics QBEE.
Since about 20% of µ− are captured by nucleus and does not emit a decay electron, thetagging efficiency of decay electron for µ− is lower than that of µ+ . The tagging efficiency is∼95% for µ+ and ∼80% for µ− in SK-IV. Furthermore, due to the electronics dead time, thetagging efficiency in SK-I-III are lower than that in SK-IV. The tagging efficiency in SK-I-III is∼80% for µ+ and ∼65% for µ− .

5.6 Neutron Tagging
Neutrons are often produced by atmospheric neutrino interaction. On the other hand, theprobability of the neutron emission by the de-excitation of nucleus after proton decay is small
and no neutrons are emitted from hydrogen. So the neutron tagging technique is important
for the sensitivity of proton decay analysis[33]. Recent improvement of neutron tagging by T.
Mochizuki is also included in this analysis.[110]Free neutrons traveling in water is quickly thermalized and captured by oxygen or hydrogen nucleus. Neutrons are mainly captured by the following interaction and its probability is∼100%.
n + p → d + γ (2.2 MeV)
(5.32)
This 2.2 MeV γ is the key of the neutron tagging technique. The mean traveling time of neutron
until capturing is measured to be 204.87 µs[34]. In order to access such a long time range,
additional trigger ”AFT” is introduced from the beginning of SK-IV. AFT is issued when SHE
trigger is issued without OD trigger and saves additional 500 µs data following 35 µs data
saved by SHE trigger. ∼92% of neutron capture data can be saved in the data. There are manybackground sources like radioactive decays from the surrounding rocks and detector material,radon in water, PMT dark noise and so on. In order to distinguish 2.2 MeV γ signal fromneutron capture, two steps of neutron tagging techniques are applied.
First, dark noise cut is applied which is recently implemented by T.Mochizuki. The darknoise sometimes appears in PMTs by burst dark noise or just randomly. It is important for the

76

CHAPTER 5. EVENT RECONSTRUCTION

algorithm with small number of PMT hits like neutron tagging to reject such dark noise hits.
Main cause of burst dark noise is considered to be the scintillation light of glass induced by
RI in the glass. The timing constant of burst dark noise is found to be about 10 µs. In orderto reject burst dark noise events, PMT hits which have other hits in 10 µs in same PMT arerejected.
Then, in order to select 2.2 MeV γ candidate, following selection is applied.
N10 ≥ 5(5.33)

Here N10 is the number of PMT hits in a 10 ns sliding time window within 18 µs to 535 µs.
Once first window of N10 ≥ 7 is found, the time is defined as t0 . In order to avoid multiple
counting of one neutron capture event, a peak value within 20 ns after t0 is defined as the same
2.2 MeV γ candidate. Peaks after t0 + 20 ns are defined as different candidates. Then additional
two selections are applied as follows.
N10 ≤ 50

(5.34)

N200 ≤ 200(5.35)

Here N200 is the number of PMT hits in 200 ns time window around t0 . These selections areapplied for removing high energy events like cosmic ray muons.
Finally, neural network based selections are applied. Following 16 variables are used as
inputs of the neural network in the default neutron tagging algorithm.
N10 : Background increase exponentially for smaller N10 values.
Nc : Each of N10 hit vector is calculated and if the angle between two vectors is less than 14.1◦ ,the pair is defined as a cluster. Calculations are repeated over all PMT hits in N10 . Total
number of hits in the cluster is defined as Nc . Background events tend to occur near the
PMTs so Nc is relatively larger. On the other hand, it is rare that neutron capture eventsoccur near the PMTs so Nc tends to be smaller.
Nlow : Most neutron captures occur within 200 cm from vertex point of neutrino interaction.
Therefore PMTs close to the neutrino interaction point have higher probability of detecting γ from neutron capture. First, probability of detecting hits in i-th PMT is calculated
and area of high probability PMTs is defined. Then the number of PMT hits outside thearea is counted as Nlow . Since 2.2 MeV γ signals are concentrated on higher probability
area, Nlow in neutron capture events tends to be smaller. On the other hand, since background events are originated from anywhere in the tank, Nlow in background events
does not show any biases.
N300 : N300 is the number of hits in 300 ns time window around 10 ns time window. Somebackgrounds have widely distributed hits. This parameter is sensitive to such kind of
backgrounds.
ϕrms : ϕrms is the root mean square of the hit vectors in N10 . 2.2 MeV γ from neutron capture
deposits most of energy in a single direction. On the other hand, background events
such as PMT dark noise make relatively random hit pattern.

5.6. NEUTRON TAGGING

77

θmean : θrms is the average of the angles between the direction of charged particles and each
PMT hits. 2.2 MeV γ from neutron capture tends to make clustered hit patterns.
trms : 2.2 MeV γ signal has narrow hit timing distribution. trms is the root mean square of all
N10 hits.
trms,Min : Many candidates with a few hits from 2.2 MeV γ and rest of hits from dark noiseor other background can be selected only by using trms . In order to reject such events,
minimum value of trms calculated from all the combinations of hits in N10 is used.
BSwall , BSenergy : The vertex and energy for low energy events in SK are reconstructed by special fitting tool Bonsai[35]. BSwall is the distance between reconstructed vertex and thenearest ID wall. Many background sources tend to be generated near the wall. BSenergy
is the reconstructed energy of candidate events. 2.2 MeV γ is mono-energetic.
N Fwall , ∆N10 , ∆trms : N Fwall is the distance between reconstructed vertex by Neut-fit andnearest wall. Neut-fit is another vertex fitter for small number of PMT hits. Neut-fit
only uses the hits in N10 so the reconstructed values are biased in the region. ∆trmsand ∆N10 are the differences between trms , N10 , respectively, calculated with APfit andNeut-fit. Since Neut-fit focuses on 2.2 MeV γ related region, difference of reconstructedvalues with APfit and Neut-fit can be good values for separating signal and background.
(N F − BS)dis , (N F − AP )dis : (N F − BS)dis and (N F − AP )dis are the distances between
reconstructed vertexes with Neut-fit and Bonsai, Neut-fit and APfit, respectively.
In addition to these variables, new variables: Cherenkov angle, Dwall along hit direction, acceptance and spread of hits are added recently by T.Mochizuki. Efficiency of neutron tagging
including recent improvement is 25.2% and the fake rate is 0.018. Systematic uncertainty forneutron tagging is estimated to be 6%.

Chapter 6
Proton Decay Search
A search for proton decay into three charged leptons is performed in this chapter using the
SKI-IV data corresponding to 6050.3 days of live time. First, selection criteria are defined foreach signal mode by comparing signal and background MC. Then systematic uncertainty is
estimated for both signal and background. Events in background MC are reweighed by considering solar activity and 3 flavor neutrino oscillation based on the recent neutrino oscillation
analysis in SK[108]. Before opening the data in signal box, data and MC agreement in control
region is checked. Finally data is opened in the signal box and checked if there are any proton decay candidates. The candidates are carefully checked and judged if they are true proton
decay events or not. Even if no proton decay events are discovered, lower lifetime limit for
proton is calculated finally with respect to each decay mode.

6.1 Event selection
FC data set is used in this analysis. First, following selection criteria is applied to the events
which pass the preselection (chapter 4).
Dwall ≥ 2.0 m(6.1)

Here Dwall is the distance between the ID wall and reconstructed vertex by APfit.
NHITAC ≤ 15 (9 for SK-II)(6.2)

Here NHITAC is the number of OD PMT hits in the largest charge cluster.
Evis ≥ 30 MeV(6.3)

Here Evis is the total energy of all reconstructed rings assuming all rings are from electrons.
Final event rate is about 8 events a day.
Most of remained background is atmospheric neutrino events and other backgrounds are
negligible. In order to further reduce background events, additional kinematic selections areapplied. Selection criteria are defined for each signal mode using reconstructed variables asfollows.
79

80

CHAPTER 6. PROTON DECAY SEARCH

6.1.1

Number of reconstructed rings

EventsSince signal has three charged leptons in final states, basically three Cherenkov rings are emitted. We require that exactly three rings are reconstructed. Number of reconstructed rings for
p → e+ e+ e− and background is shown in Fig.6.1. ∼80% of events can reconstruct 3 rings in
p → e+ e+ e− mode. The main cause of 2 ring events in p → e+ e+ e− mode is two leptons decayed close to each other and detected rings are overlapped on the wall. There is another causeof 2 ring events in other muon including signal modes. Since Cherenkov threshold for muon ismuch larger than that of electron, some of low momentum muons cannot emit Cherenkov lightin muon including modes. As more muons contained in the signal, larger phase space is takenby created muon mass. This feature decreases the momentum scale of muons and makes moremuons below the Cherenkov threshold. Number of reconstructed rings with respect to eachsignal mode is also shown in Fig.6.1. After this requirement, about 90% of background is decreased and signal is kept to be ∼80%, ∼70%, ∼50% and ∼40% for p → e+ e+ e− , p → µ+ e+ e− ,p → e+ µ+ µ− and p → µ+ µ+ µ− respectively. Performance of ring counting is almost the same
between p → µ+ e+ e− and p → µ− e+ e+ or p → e+ µ+ µ− and p → e− µ+ µ+ . Using 2 ring
events can increase the signal efficiency but background events are increased as well. Hence
only 3 ring events are used in this analysis.
20000

SK4

0.8
SK4
Area normalized

18000
0.7

16000

0.6

14000

Background

12000

+ + -

0.5

+ + -

0.4

p→ e e e

10000
p→e e e (free proton)

8000

p→e+µ+µp→µ+µ+µ-

0.3

6000
4000

0.2

2000

0.1

0
0

p→µ+e+e-

1

2

3

4
5
6
7
Number of reconstructed rings

0
0

1

2

3

4
5
6
7
Number of reconstructed rings

Figure 6.1: Number of ring distributions for background and signal in p → e+ e+ e− mode after
FC & FV cut (left). Arrows and dotted lines show selected events by this selection. Signal of
free protons is also shown by dotted line. Scale of signal is arbitrary. Right figure show thecomparison of p → µ+ e+ e− , p → e+ µ+ µ− and p → µ+ µ+ µ− modes.

6.1.2

Number of e-like or µ-like rings

Each detected ring is classified as electron like or muon like by PID technique described in 5.3.
Not only the information of charge distribution on the wall but also opening angle information
is used for the PID, because the Cherenkov light from charged leptons should be emitted fromexact vertex position. Requirements for the number of e-like or µ-like rings are set dependingon the exact number of electrons and muons in each signal mode. For example, 3 e-like rings
are required for p → e+ e+ e− mode or 2 e-like and 1 µ-like rings are required for p → µ+ e+ e−mode. Number of e-like rings for p → e+ e+ e− and background or number of µ-like rings forp → µ+ e+ e− and background after 3 rings cut are shown in Fig.6.2. Same distributions for6.1. EVENT SELECTION

81

1200

BackgroundSK4
3 rings

p→e+e+e-

1000

EventsEventsp → e+ µ+ µ− and p → µ+ µ+ µ− after 3 rings are also shown in Fig.6.3. More than 90% of
signal events can be kept after this cut for all modes. There are almost no period dependence.
Performance of PID is almost the same between p → µ+ e+ e− and p → µ− e+ e+ or p →e+ µ+ µ− and p → e− µ+ µ+ .

p→e+e+e-(free proton)

1200
SK4
3 rings

1000

800

800

600

600

400

400

200

200

Backgroundp→µ+e+e-00p→µ+e+e-(free proton)

0.5

1

1.5

2

2.5

3

0
0

3.5
4
4.5
5
Number of e-like rings

0.5

1

1.5

2

2.5

3

3.5
4
4.5
5
Number of µ-like rings

1200
SK4
3 rings

1000

EventsEventsFigure 6.2: Number of e-like rings for background and signal in p → e+ e+ e− mode after FC& FV cut and number of ring cut (left). Arrows and dotted lines show selected events by thisselection. Signal of free protons is also shown by dotted line. Scale of signal is arbitrary. Right
figure shows the Number of µ-like rings for background and signal in p → µ+ e+ e− mode.

1200
SK4
3 rings

1000

Background800

Background800

p→e+µ+µ-p→µ+µ+µ-600

600p→e+µ+µ-(free proton)p→µ+µ+µ-(free proton)

400

400

200

200

0
0

0.5

1

1.5

2

2.5

3

3.5
4
4.5
5
Number of µ-like rings

0
0

0.5

1

1.5

2

2.5

3

3.5
4
4.5
5
Number of µ-like rings

Figure 6.3: Number of µ-like rings for background and signal in p → e+ µ+ µ− (left) and p →µ+ µ+ µ− (right) modes after FC & FV cut and number of ring cut (left). Arrows and dottedlines show selected events by this selection. Signal of free protons is also shown by dottedline. Scale of signal is arbitrary.

6.1.3

Number of decay electrons

Decayed electrons from muons can be tagged by searching for the delayed signal after primary
signal which is described in 5.5. Number of tagged decay electrons can be used for the signal
background separation. Since there is no muon and decay electron in p → e+ e+ e− mode,
the number of decay electrons is required to be 0. On the other hand, p → µ+ e+ e− and82

CHAPTER 6. PROTON DECAY SEARCH

600
SK4
3 rings
3 e-like

500

EventsEventsp → e+ µ+ µ− modes require 1 and 2 decay electrons, respectively. p → µ+ µ+ µ− mode require
2 or 3 decay electrons to keep higher signal efficiency. Number of decay electrons for eachsignal mode and background after all previous all cuts is shown in Fig.6.4 and Fig.6.5.
Since µ− is sometimes captured by nucleus before the decay with the probability of ∼20%and does not emit decay electron, there are some difference in the number of decay electrons
between p → µ+ e+ e− and p → µ− e+ e+ or p → e+ µ+ µ− and p → e− µ+ µ+ . Comparison ofthese modes are shown in Fig.6.6. Furthermore, there are period dependences on the number ofdecay electrons. Since SK-I-III has dead time between 800 ns and 1,200 ns due to the impedancemismatch of ATM boards, efficiency of decay electron tagging is worse than that of SK-IV.
Number of decay electrons for p → µ+ e+ e− with respect to SK-I-IV is shown in Fig.6.7.
500

SK4
3 rings
1 µ-like & 2 e-like

450
400
350

400

300

Background300

Background

250
+ + -

p→e e e200p→µ+e+e-

200

p→e+e+e-(free proton)

p→µ+e+e-(free proton)

150
100

100

50

0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
4
4.5
5
Number of decay electrons

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electrons

SK4
3 rings
2 µ-like & 1 e-like

140
120

EventsEventsFigure 6.4: Number of decay electrons for background and signal in p → e+ e+ e− (left) andp → µ+ e+ e− (right) modes after all previous cuts. Arrows and dotted lines show selected
events by this selection. Signal of free protons is also shown by dotted line. Scale of signal is
arbitrary.

30
SK4
3 rings
3 µ-like

25
Background

20

100

p→µ+µ+µ-

Background80

15p→µ+µ+µ-(free proton)

p→e+µ+µ-60

p→e+µ+µ-(free proton)

10

40

5

20
0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electrons

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electrons

Figure 6.5: Number of decay electrons for background and signal in p → e+ µ+ µ− (left) andp → µ+ µ+ µ− (right) modes after all previous cuts. Arrows and dotted lines show selected
events by this selection. Signal of free protons is also shown by dotted line. Scale of signal is
arbitrary.

6.1. EVENT SELECTION

83

SK4

Area normalized

3 rings
2 μ-like & 1 e-like
Area normalized

0.8

0.8

0.6

p→μ+e+e-

0.6

SK4

1

3 rings
1 μ-like & 2 e-like

1p→e+μ+μ-p→μ-e+e+p→e-μ+μ+

0.4

0.4

0.2

0.2

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0
0

5

0.5

1

1.5

2

2.5

Number of decay electrons

3
3.5
4
4.5
5
Number of decay electrons

Figure 6.6: Comparison of number of decay electrons between p → µ+ e+ e− and p → µ− e+ e+(left) or p → e+ e+ µ− and p → e− µ+ µ+ (right) modes after all previous cuts.

p→μ+e+e3 rings
1 μ-like & 2 e-like

1

Area normalized

0.8

SK1
0.6

SK2
SK3

0.4

SK4

0.2

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electrons

Figure 6.7: Comparison of number of decay electrons in p → µ+ e+ e− for each period after all
previous cuts.

84

CHAPTER 6. PROTON DECAY SEARCH

6.1.4

π 0 veto30
SK4
3 rings
3 e-like
No decay electron

25

Background20

EventsEventsMain background for p → e+ e+ e− and p → µ+ e+ e− modes are charged current π 0 production
events which decays to 2 γ. Mass of 2 e-like rings can be a good parameter for the separationof signal and such backgrounds. But in case of p → e+ e+ e− mode, background rejection is
not so good compared to the loss of the signal. Therefore this requirement is only applied forp → µ+ e+ e− mode. In order to reduce π 0 production events, events with mass of 2 e-like rings
below 185 MeV are rejected. Mass of 2 e-like rings for p → µ+ e+ e− and background is shownin Fig.6.8. p → µ− e+ e+ shows almost the same distribution.

50

SK4
3 rings
1 µ-like & 2 e-like
1 decay electron

45
40
35

Background30
p→e+e+e-

15
p→e+e+e-(free proton)

10p→µ+e+e-

25
p→µ+e+e-(free proton)

20
15
10

5

0
0

5

100

200

300

400
500
600
700
800
Mass of 2 e-like rings [MeV/c2]

0
0

100

200

300

400
500
600
700
800
Mass of 2 e-like rings [MeV/c2]

Figure 6.8: Mass of 2 e-like rings after all previous cut for background and signal in p →e+ e+ e− (left) and p → µ+ e+ e− (right) modes. Arrows and dotted lines show selected eventsby this selection. Signal of free proton is also shown by dotted line. Scale of signal is justarbitral. In p → e+ e+ e− mode, a pair with closest mass to true π 0 mass (135 MeV) is chosen.
π 0 mass is not used in the selection of p → e+ e+ e− mode.

6.1.5

Neutron veto

The probability of neutron generated by deexcitation of a nucleus after proton decay is rather
small, and neutrons are not generated from free proton decay. Furthermore, proton decay
events do not produce neutrons by secondary interactions because there are only charged
leptons in final states. On the other hand, neutron is often emitted by the interaction of the atmospheric neutrino and the nucleus in water. Emitted neutron is captured by nucleus in waterand delayed γ signal is emitted. Searching for this γ signal, neutron can be tagged. Detail of
this neutron tagging technique is described in section 5.6. Information of this tagged neutron
can be a good parameter for the separation of signal and background. The number of tagged
neutron is required to be 0 for all modes only in SK-IV because the neutron tagging technique
is only available in SK-IV. Number of tagged neutron for p → e+ e+ e− and background after
all previous cuts is shown in Fig.6.9. About 5% of signal events have tagged neutron because
neutron is sometimes emitted in signal by correlated decay. Basically more than 90% of signal
can be kept and about 50% of background events in SK-IV are rejected after this requirement
for all modes.

Events

6.1. EVENT SELECTION

85

350

SK4
3 rings
3 e-like
No decay electron

300
250
200

Background150

p→e+e+ep→e+e+e-(free proton)

100
50
0
0

1

2

3

4

5

6
7
8
9
10
Number of tagged neutron

Figure 6.9: The number of tagged neutrons after all previous cuts for background and signal
in p → e+ e+ e− mode. Arrows and dotted lines show selected events by this selection. Signalof free proton is also shown by dotted line. Scale of signal is arbitrary.

6.1.6

Total mass and momentum

Invariant mass (total mass) and momentum (total momentum) reconstructed from 3 rings are
the most important parameters in selection criteria. Basically these values correspond to theinitial proton mass and momentum in signal mode. Total mass and momentum for signal andbackground after all previous cuts without the requirement of the number of tagged neutron
with respect to each mode are shown in Fig.6.10-6.13. Total mass makes a peak around the true
proton mass at 938 MeV in signal events. Hence total mass is required to be between 800 MeV
and 1,050 MeV. Total momentum for free proton distributes at lower momentum region as thetrue momentum of free proton is almost 0. Total momentum for bound proton distributes atrelatively higher momentum region as the true bound proton has finite initial momentum due
to Fermi motion. Total momentum is required to be below 250 MeV. In order to make almost
background free selection criteria, requirement for total momentum is further separated to
2 categories: Low signal box (total momentum below 100 MeV) and High signal box (total
momentum between 100 MeV and 250 MeV). The effect of the correlated decay makes the lowerand higher tail of total mass and total momentum, respectively.

6.1.7

Selection summary

Selection criteria for each mode is summarized in Table6.1. The signal efficiency and expectedbackground events after all selections are summarized in Table6.2. The signal efficiency is defined as the number of signal events after all selection criteria divided by the initial numberof signal events with true Dwall above 2 m. Cut flow for the signal and background are summarized in Table6.3-6.8 and Table6.9-6.12, respectively. The interaction modes of background
events remained in signal box for 2,000 years MC are also summarized in Table6.13. Event
displays for signal and typical background events in each mode are shown in Fig.6.14 - 6.17
and Fig.6.18 - 6.21, respectively.

CHAPTER 6. PROTON DECAY SEARCH

100
90
80

EventsEvents86

SK4
3 rings
3 e-like
No decay electron

70
Background60

50

p→e+e+e-

50

40

p→e+e+e-(free proton)

40

30

30

20

20

10

10

0
0

SK4
3 rings
3 e-like
No decay electron

90
80

70
60

100

200

400

600

800

0
0

1000
1200
Total mass [MeV/c2]

Backgroundp→e+e+ep→e+e+e-(free proton)

100

200

300

400

500

600 700 800 900 1000
Total momentum [MeV/c]

14
12
10
8
6

EventsEventsFigure 6.10: Total mass (left) and total momentum (right) for background and signal in p →e+ e+ e− (left) mode after all previous cuts without neutron tagging. Arrows and dotted lines
show selected events by this selection. Signal of free protons is also shown by dotted line.
Scale of signal is arbitrary.

SK4
3 rings
1 µ-like & 2 e-like
1 decay electron
π0 veto12
10

Background

4

2

2

400

600

p→µ+e+e-

6p→µ+e+e-(free proton)

200

Background8p→µ+e+e-

4

0
0

SK4
3 rings
1 µ-like & 2 e-like
1 decay electron
π0 veto

14

800

1000
1200
Total mass [MeV/c2]

00p→µ+e+e-(free proton)

100

200

300

400

500

600 700 800 900 1000
Total momentum [MeV/c]

Figure 6.11: Total mass (left) and total momentum (right) for background and signal in p →µ+ e+ e− (left) mode after all previous cuts without neutron tagging. Arrows and dotted lines
show selected events by this selection. Signal of free protons is also shown by dotted line.
Scale of signal is arbitrary.

87

10
9
8

EventsEvents

6.1. EVENT SELECTION

SK4
3 rings
1 e-like & 2 µ-like
2 decay electron

SK4
3 rings
1 e-like & 2 µ-like
2 decay electron

9
8

7
6

10

7
Background

Background65p→e+µ +µ -5p→e+µ +µ -4p→e+µ +µ -(free proton)

4p→e+µ +µ -(free proton)

3

3

2

2

1

1

0
0

0
0

200

400

600

800

1000
1200
Total mass [MeV/c2]

100

200

300

400

500

600 700 800 900 1000
Total momentum [MeV/c]

5
4.5
4

EventsEventsFigure 6.12: Total mass (left) and total momentum (right) for background and signal in p →e+ µ+ µ− (left) mode after all previous cuts without neutron tagging. Arrows and dotted lines
show selected events by this selection. Signal of free protons is also shown by dotted line.
Scale of signal is arbitrary.

SK4
3 rings
3 µ-like
2 or 3 decay electron

2.5
2

3.5
Background

Background3

p→µ +µ +µ -p→µ +µ +µ -

2.5p→µ +µ +µ -(free proton)2p→µ +µ +µ -(free proton)

1.5

1.5

1

1

0.5

0.5

0
0

SK4
3 rings
3 µ-like
2 pr 3 decay electron

4.5
4

3.5
3

5

200

400

600

800

1000
1200
Total mass [MeV/c2]

0
0

100

200

300

400

500

600 700 800 900 1000
Total momentum [MeV/c]

Figure 6.13: Total mass (left) and total momentum (right) for background and signal in p →µ+ µ+ µ− (left) mode after all previous cuts without neutron tagging. Arrows and dotted lines
show selected events by this selection. Signal of free protons is also shown by dotted line.
Scale of signal is arbitrary.

88

CHAPTER 6. PROTON DECAY SEARCH

Table 6.1: Summary of selection criteria for each mode.
◦3
3 e-like0p → µ+ e + e −(p → µ− e+ e+ )◦3
2 e-like & 1 µ-like1

p → e+ µ+ µ−(p → e− µ+ µ+ )◦3
1 e-like & 2 µ-like
2

-

◦

-

-

0

0

0

0

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

p → e+ e+ e−
FC & FV
Number of rings
PID
Number of decay electrons
π 0 veto(M > 185 MeV)
Number of neutron (SK-IV)
Total mass(800 < M < 1, 050 MeV)
Total momentum Low(P < 100 MeV)
Total momentum High(100 < P < 250 MeV)

p → µ+ µ+ µ−◦
33 µ-like
2 or 3

Table 6.2: Summary of signal efficiency, expected background events with respect to eachmode. The error values correspond to the statistic uncertainty of MC sample.
Efficiency (%)
Background (events)
Modes
I
II
III
IV
I
II
III
IV
+ + −
p→e e e(Low)
22.7 19.8 23.1 22.4
<0.01
<0.01
<0.01
<0.01
(High)
43.9 40.4 44.3 41.1 0.19±0.04 0.10±0.02 0.05±0.01 0.24±0.07
p → µ+ e+ e−(Low)
15.0 13.5 16.3 17.6 0.02±0.01 0.02±0.01 0.01±0.00<0.01(High)
27.1 26.0 27.3 30.3 0.13±0.03 0.10±0.02 0.05±0.01 0.17±0.05
p → µ− e+ e+(Low)
11.9 11.1 12.6 14.9 0.02±0.01 0.02±0.01 0.01±0.00<0.01(High)
20.8 19.8 22.3 25.9 0.13±0.03 0.10±0.02 0.05±0.01 0.17±0.05+ + −p→e µ µ(Low)
9.2 8.1 9.1 11.7
<0.01
<0.01
<0.01
<0.01
(High)
15.8 14.1 16.2 20.9 0.09±0.02 0.07±0.02 0.03±0.01 0.08±0.03
p → e − µ+ µ+(Low)11.1 10.9 11.9 14.4
<0.01
<0.01
<0.01
<0.01
(High)
19.9 18.2 20.0 24.2 0.09±0.02 0.07±0.02 0.03±0.01 0.08±0.03
p → µ− µ+ µ+(Low)10.8 10.4 12.0 12.2
<0.01
<0.01
<0.01
<0.01
(High)
19.9 17.2 20.4 20.4 0.10±0.03 0.05 ±0.01 0.03±0.01 0.22±0.06

6.1. EVENT SELECTION

89

Table 6.3: Signal efficiency [%] at each step of selection criteria for p → e+ e+ e− mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
FC & FV
98.7±1.5
98.7±1.598.8±1.598.9±1.5
Number of rings
80.4±1.376.7±1.3
81.0±1.3
81.1±1.3
PID
75.1±1.3
68.6±1.275.8±1.375.5±1.3
68.4±1.275.8±1.375.5±1.3
Number of decay electrons 75.1±1.3
Total mass & momentum
66.6±1.1
60.2±1.0
67.4±1.1
66.5±1.0
Neutron veto
63.5±1.0
Low signal box
22.7±0.6
19.8±0.523.1±0.6
22.4±0.6(Free proton)(14.3±0.4) (12.1±0.4) (14.4±0.4) (14.0±0.4)High signal box
43.9±0.940.4±0.844.3±0.941.1±0.8(Free proton)(1.0±0.1) (1.4±0.1) (0.9±0.1) (0.9±0.1)

Table 6.4: Signal efficiency [%] at each step of selection criteria for p → µ+ e+ e− mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
FC & FV
98.9±1.5 99.0±1.5 99.1±1.5 98.9±1.5
Number of rings
67.0±1.2 65.0±1.3 67.5±1.2 68.2±1.2
PID
62.3±1.1 58.9±1.1 63.5±1.1 63.2±1.1
Number of decay electrons 50.8±1.0 47.3±0.9 52.3±1.0 60.5±1.1
π 0 veto46.8±0.9 43.9±0.9 48.3±0.9 55.6±1.0
Total mass & momentum
42.0±0.8 39.5±0.8 43.5±0.8 50.3±0.9
47.8±0.9
Neutron veto
Low signal box
15.0±0.5 13.5±0.4 16.3±0.5 17.6±0.5(9.2±0.3) (8.3±0.3) (9.9±0.3) (10.9±0.4)(Free proton)
High signal box
27.0±0.6 26.0±0.6 27.2±0.6 30.2±0.7(Free proton)(0.3±0.1) (0.7±0.1) (0.3±0.1) (0.3±0.1)

90

CHAPTER 6. PROTON DECAY SEARCH

Table 6.5: Signal efficiency [%] at each step of selection criteria for p → µ− e+ e+ mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
FC & FV
98.9±1.5 98.9±1.5 99.1±1.5 98.9±1.5
Number of rings
66.1±1.2 64.8±1.1 68.1±1.2 68.1±1.2
PID61.7±1.1 58.7±1.1 64.0±1.1 63.2±1.1
Number of decay electrons 39.9±0.8 37.5±0.8 42.0±0.8 51.3±1.0
π 0 veto36.6±0.8 34.5±0.8 38.8±0.8 46.7±0.9
Total mass & momentum
32.7±0.7 30.9±0.7 34.9±0.7 42.4±0.8
Neutron veto40.7±0.8
Low signal box
11.9±0.4 11.1±0.4 12.6±0.4 14.8±0.5(Free proton)(7.7±0.3) (6.3±0.3) (7.7±0.3) (9.3±0.4)High signal box
20.8±0.6 19.8±0.5 22.3±0.6 25.8±0.6(Free proton)(0.2±0.0) (0.5±0.1) (0.2±0.1) (0.3±0.1)

Table 6.6: Signal efficiency [%] at each step of selection criteria for p → e+ µ+ µ− mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
FC & FV
99.0±1.5 99.1±1.5 99.1±1.5 99.0±1.5
Number of rings
52.7±1.0 51.1±1.0 53.9±1.0 52.5±1.0
49.6±0.9 46.2±0.9 50.5±1.0 49.4±0.9
PID
Number of decay electrons 27.5±0.7 24.6±0.6 28.0±0.7 37.3±0.8
Total mass & momentum
25.1±0.6 22.2±0.5 25.3±0.6 34.0±0.7
32.5±0.7
Neutron veto
Low signal box
9.2±0.3
8.1±0.3
9.1±0.3 11.7±0.4(6.0±0.3) (5.0±0.3) (5.9±0.3) (7.3±0.3)(Free proton)
High signal box
15.8±0.5 14.1±0.3 16.2±0.5 20.9±0.6(Free proton)(0.1±0.0) (0.3±0.1) (0.1±0.0) (0.2±0.1)

6.1. EVENT SELECTION

91

Table 6.7: Signal efficiency [%] at each step of selection criteria for p → e− µ+ µ+ mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
98.9±1.5 98.9±1.5 99.2±1.5 98.9±1.5
FC & FV
Number of rings
52.4±1.0 51.8±1.0 52.7±1.0 53.1±1.0
PID49.6±1.0 47.0±0.9 49.9±0.9 49.8±1.0
Number of decay electrons 34.1±0.7 32.2±0.7 34.8±0.8 44.5±0.9
Total mass & momentum
31.0±0.7 29.2±0.6 31.8±0.7 40.5±0.8
38.6±0.8
Neutron veto
Low signal box
11.1±0.4 10.9±0.4 11.9±0.4 14.4±0.4(Free proton)(7.1±0.3) (6.9±0.3) (7.4±0.3) (9.3±0.4)High signal box
19.9±0.5 18.2±0.5 20.0±0.5 24.2±0.6(Free proton)(0.1±0.0) (0.2±0.1) (0.1±0.0) (0.2±0.0)

Table 6.8: Signal efficiency [%] at each step of selection criteria for p → µ+ µ+ µ− mode. The
error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial
100
100
100
100
98.8±1.5 98.4±1.5 98.7±1.5 98.6±1.5
FC & FV
Number of rings
38.2±0.8 35.4±0.8 40.3±0.8 38.7±0.8
37.4±0.8 33.8±0.7 39.2±0.8 37.6±0.8
PID
Number of decay electrons 32.9±0.7 29.7±0.7 34.9±0.8 36.4±0.8
Total mass & momentum
30.7±0.7 27.6±0.6 32.3±0.7 34.0±0.7
32.6±0.7
Neutron veto
Low signal box
10.8±0.4 10.4±0.4 12.0±0.4 12.2±0.4(6.6±0.3) (6.5±0.3) (7.5±0.3) (7.6±0.3)(Free proton)
High signal box
19.9±0.5 17.2±0.5 20.4±0.5 20.4±0.5(Free proton)(<0.1)(0.1±0.0) (0.1±0.0) (0.1±0.0)

Table 6.9: Expected background events at each step of selection criteria for p → e+ e+ e− mode.
The error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial17,380±12 9,225±6
6,138±4 38,627±26
12,097±10 6,546±5
4,285±3 26,563±21
FC & FV
Number of rings
966±3
555±2
340±1
2,247±6
PID
460±2
243±1
157±1
1,038±4
270±1
152±1
97±1
568±3
Number of decay electrons
Total mass & momentum
0.18±0.04 0.11±0.02 0.05±0.01 0.58±0.10
0.23±0.06
Neutron veto
Low signal box<0.01
0.01±0.01
<0.01
<0.01
0.18±0.04 0.10±0.02 0.05±0.01 0.23±0.06
High signal box

92

CHAPTER 6. PROTON DECAY SEARCH

Table 6.10: Expected background events at each step of selection criteria for p → µ+ e+ e− andp → µ− e+ e+ mode. The error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial17,380±12 9,225±6
6,138±4 38,627±26
FC & FV
12,097±10 6,546±5
4,285±3 26,563±21
Number of rings
966±3
555±2
340±1
2,247±6
PID
372±2
218±1
135±1
879±4
Number of decay electrons
166±1
90±1
61±0
440±3
0
81±1
47±0
30±0
202±2
π massTotal mass & momentum
0.15±0.03 0.12±0.02 0.06±0.01 0.56±0.10
Neutron veto
0.18±0.06
Low signal box
0.02±0.01 0.01±0.01 0.01±0.00<0.01High signal box
0.13±0.03 0.11±0.02 0.05±0.01 0.18±0.06

Table 6.11: Expected background events at each step of selection criteria for p → e+ µ+ µ− andp → e− µ+ µ+ mode. The error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial17,380±12 9,225±6
6,138±4 38,627±26
FC & FV
12,097±10 6,546±5
4,285±3 26,563±21
Number of rings
966±3
555±2
340±1
2,247±6
108±1
78±1
38±0
265±2
PID
Number of decay electrons
17±0
11±0
6±0
58±1
Total mass & momentum
0.09±0.02 0.07±0.01 0.03±0.01 0.30±0.07
Neutron veto
0.07±0.03
Low signal box
<0.01
<0.01
<0.01
<0.01
High signal box
0.09±0.02 0.07±0.01 0.03±0.01 0.07±0.03

Table 6.12: Expected background events at each step of selection criteria for p → µ+ µ+ µ−
mode. The error values correspond to the statistic uncertainty of MC sample.
SK-I
SK-II
SK-III
SK-IV
Initial17,380±12 9,225±6
6,138±4 38,627±26
12,097±10 6,546±5
4,285±3 26,563±21
FC & FV
Number of rings
966±3
555±2
340±1
2,247±6
PID
26±0
17±0
9±0
64±1
Number of decay electrons
8±0
5±0
3±0
28±1
0.10±0.03 0.05±0.01 0.03±0.01 0.47±0.08
Total mass & momentum
Neutron veto
0.21±0.06
Low signal box
0.01±0.01
<0.01
<0.01
<0.01
High signal box
0.09±0.03 0.05±0.01 0.03±0.01 0.21±0.06

6.1. EVENT SELECTION

93

Table 6.13: The expected fraction of the interaction modes [%] for background events remainedin signal box.
p → µ+ e+ e−
p → e+ µ+ µ−
p → e+ e+ e−
p → µ+ µ+ µ−− + +(p → µ e e ) (p → e− µ+ µ+ )
CCQE
12.9
7.1
9.7
21.4
CC single π
41.0
32.2
34.0
58.2
CC multi π
11.8
27.2
42.5
12.5
CC η
9.0
6.1
0
0
CC K
0
0
0
0.3
CC DIS
3.9
6.2
4.7
3.4
NC single π
1.2
1.3
0
0
NC multi π
3.8
6.7
2.4
2.0
NC η
0
1.3
0
0
NC DIS
16.3
11.9
6.6
2.2

Figure 6.14: Simulated event displays of signal events in p → e+ e+ e− mode. The left figure
shows true information and the right figure shows reconstructed information. Type of true
particles are described in left figure. In right figure, blue circle shows TDC fit result, red andlight blue bold circles show ring fit result for e-like and µ-like, respectively.

94

CHAPTER 6. PROTON DECAY SEARCH

Figure 6.15: Simulated event displays of signal events in p → µ+ e+ e− mode. The left figure
shows true information and the right figure shows reconstructed information. Type of true
particles are described in left figure. In right figure, blue circle shows TDC fit result, red andlight blue bold circles show ring fit result for e-like and µ-like, respectively.

Figure 6.16: Simulated event displays of signal events in p → e+ µ+ µ− mode. The left figure
shows true information and the right figure shows reconstructed information. Type of true
particles are described in left figure. In right figure, blue circle shows TDC fit result, red andlight blue bold circles show ring fit result for e-like and µ-like, respectively.

6.1. EVENT SELECTION

95

Figure 6.17: Simulated event displays of signal events in p → µ+ µ+ µ− mode. The left figure
shows true information and the right figure shows reconstructed information. Type of true
particles are described in left figure. In right figure, blue circle shows TDC fit result, red andlight blue bold circles show ring fit result for e-like and µ-like, respectively.

Figure 6.18: Simulated event displays of typical background events in p → e+ e+ e− mode.
The left figure shows true information and the right figure shows reconstructed information.
Type of true particles are described in left figure. In right figure, blue circle shows TDC fit
result, red and light blue bold circles show ring fit result for e-like and µ-like, respectively.
The interaction mode of this event is CC single π production (νe n → e− nπ 0 )96

CHAPTER 6. PROTON DECAY SEARCH

Figure 6.19: Simulated event displays of typical background events in p → µ+ e+ e− mode.
The left figure shows true information and the right figure shows reconstructed information.
Type of true particles are described in left figure. In right figure, blue circle shows TDC fit
result, red and light blue bold circles show ring fit result for e-like and µ-like, respectively.
The interaction mode of this event is CC single π production (νµ n → µ− pπ 0 )Figure 6.20: Simulated event displays of typical background events in p → e+ µ+ µ− mode.
The left figure shows true information and the right figure shows reconstructed information.
Type of true particles are described in left figure. In right figure, blue circle shows TDC fit
result, red and light blue bold circles show ring fit result for e-like and µ-like, respectively.
The interaction mode of this event is CC multi π production (νµ p → µ− pπ + π 0 )6.2. SYSTEMATIC UNCERTAINTY

97

Figure 6.21: Simulated event displays of typical background events in p → µ+ µ+ µ− mode.
The left figure shows true information and the right figure shows reconstructed information.
Type of true particles are described in left figure. In right figure, blue circle shows TDC fit
result, red and light blue bold circles show ring fit result for e-like and µ-like, respectively.
The interaction mode of this event is CC single π production (νµ n → µ− pπ + )6.2 Systematic uncertainty
Estimation for systematic uncertainties for signal and background samples with respect toeach SK period is described in this section. Since observation time is well defined and SK tankis always full of water, systematic uncertainty for the detector exposure is negligible. But 1%
error for the detector exposure is assigned to be conservative.

6.2.1

Correlated decay

In the theory, correlated decay is considered to be happened with about 10% probability[37].
Since this effect is not understood well, 100% source error is considered to be conservative.
Therefore, signal samples with 20% probability of correlated decay and 0% probability are created with respect to each mode and compared with nominal sample of 10% probability. Total
mass and momentum distributions are mainly changed depending on the probability of correlated decay. Comparison of total mass and momentum with respect to each probability ofcorrelated decay for p → e− e+ e+ are shown in Fig.6.22. Ratios of signal efficiency in low
or high signal box between nominal 10% probability and 0% or 20% probability is calculated.
Then larger value with respect to each box is assigned as the systematic uncertainty of thecorrelated decay only for the signal.

6.2.2

Fermi motion

In the signal MC sample, Fermi motion is simulated based on the electron-12 C scatteringexperiment[107]. On the other hand, in the background MC sample it’s based on Fermi gas

98

CHAPTER 6. PROTON DECAY SEARCH

SK4

SK4

0.6

3 rings
3 e-like

0.5

Area normalized

3 rings
3 e-like

0.25

Area normalized

0.2
0.4
0.3

10% correlated decay (default)

10% correlated decay (default)

0.15

20%

20%

0%

0%

0.1
0.2
0.05

0.1
0
0

200

400

600

800

1000
1200
Total mass [MeV/c2]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure 6.22: Total mass (left) and total momentum (right) for p → e+ µ+ µ− (left) signal after thenumber of ring and PID cuts. Each histogram corresponds to the samples with each probabilityof correlated decay. The vertical error bars correspond to the statistical uncertainty of the MC
sample.

A.U.

model. Hence this model difference can be a source of systematic uncertainty. In order toestimate the error value, a signal sample simulated with Fermi gas model is created. Thenthe signal efficiencies in low or high signal box is compared with the nominal signal sample.
Initial proton momentum distributions of the two models are shown in Fig.6.23. The difference is mainly shown in total momentum distribution as shown in Fig.6.24. The ratio between
two different model is assigned as the systematic uncertainty of the Fermi motion only for thesignal.

0.2
0.18
0.16

Experimental spectrum
Fermi gas

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

50

100

150
200
250
300
Initial proton momentum [MeV/c]

Figure 6.23: Comparison of initial proton momentum between Fermi gas model and experimental spectrum[107]. The vertical error bars correspond to the statistical uncertainty of theMC sample.

6.2. SYSTEMATIC UNCERTAINTY

99

SK4

0.25

3 rings
3 e-like
Area normalized

0.2

Experimental spectrum (default)

0.15

Fermi gas
0.1

0.05

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure 6.24: Comparison of total momentum after number of ring and PID cuts between Fermi
gas model and experimental spectrum for p → e+ e+ e− . The vertical error bars correspond to
the statistical uncertainty of the MC sample.

6.2.3

Neutrino flux & cross section

The systematic errors for atmospheric neutrino flux and cross section are estimated by eventby-event weighting method. The source errors for this method are already estimated in thelatest neutrino oscillation analysis in SK[108]. The ratio of background events remaining inthe signal boxes between default and weighted samples is assigned as the systematic error. In
order to cover the low statistics in the signal box, 2,000 years MC is used for estimation. Eachsystematic error for neutrino flux and cross section is summarized in Table6.14,6.15.

6.2.4

Pion FSI/SI

A neutral pion generated by neutrino interaction in oxygen can interact with nucleus in thatoxygen. By this effect so called pion final state interaction (FSI), pion can be scattered, beabsorbed or exchange its charge. Generated pion can also interact with other nucleus in water
after escaping from the original nucleus. This effect is called as pion secondary interaction (SI).
These interactions are simulated by the NEUT pion cascade model described in section 3.2.3.
17 parameter sets are prepared and the number of events are calculated with respect to eachset. For the systematic uncertainty for Pion FSI/SI, RMS/Mean value of remaining background
events for 17 parameter sets is used.

6.2.5

Fiducial volume

A systematic uncertainty for the fiducial volume is considered as the difference of entry orexit events at the boundary of FV (Dwall = 200 cm) between data and MC. FC samples of
3 rings events are used for this estimation. Dwall distributions are compared between data
and background MC which is area normalized to data. In order to determine the area for MC
normalization, true Dwall value is smeared by gaussian with σ = 40 cm, 100 cm , then compared with reconstructed Dwall in background MC. Fig.6.25 shows a comparison of smeared

100

CHAPTER 6. PROTON DECAY SEARCH

Table 6.14: Systematic sources and their estimated error values [%] for neutrino flux in eachmode. The detail of each systematics are summarized in [108].
Absolute normalization(Eν < 1 GeV)
(Eν > 1 GeV)(νµ + ν¯µ )/(νe + ν¯e ) ratio(1 < Eν < 10 GeV)
(Eν > 10 GeV)ν¯e /νe ratio(Eν < 1 GeV)
(1 < Eν < 10 GeV)ν¯µ /νµ ratio(Eν < 1 GeV)
(1 < Eν < 10 GeV)
(Eν > 10 GeV)
Relative normalization FC multi-GeV
Up/down asymmetry
Horizontal/vertical ratio
K/π production ratio
Neutrino flight length
Total

p → e+ e+ e−

p → µ+ e+ e−

p → e+ µ+ µ−

p → µ+ µ+ µ−

0.6
6.7

<0.1
7.1

<0.1
7.0

0.7
6.4

<0.1
0.2

0.2
0.1

1.2
<0.1

1.3
<0.1

0.1
1.7

<0.1
1.1

<0.1
0.1

<0.1
<0.1

<0.1
0.2
0.3
0.1
<0.1
<0.1
0.3
<0.1
7.0

<0.1
1.1
<0.1
0.9
0.1
0.1
0.4
<0.1
7.3

<0.1
2.5
<0.1
3.3
<0.1
<0.1
0.6
0.3
8.2

<0.1
2.5
<0.1
4.3
<0.1
<0.1
0.5
0.4
8.3

Table 6.15: Systematic sources and their estimated error values [%] for neutrino cross sectionin each mode. The detail of each systematics are summarized in [108].
MA in QE
Single π production, Axial coupling
Single π production, CA5
Single π production, Background
CCQE ν̄/ν ratio
CCQE µ/e ratio
DIS model difference
DIS cross section
DIS Q2 distribution (high W )DIS Q2 distribution (low W )Coherent pi cross section
NC/CC ratio
Total

p → e+ e+ e−
5.4
6.7
2.7
1.6
0.1
0.1
9.5
1.8
<0.1
<0.1
<0.1
4.3
14.0

p → µ+ e + e −
3.4
6.9
2.8
1.7
0.2
<0.1
13.8
2.6
0.2
0.2
<0.1
4.3
16.9

p → e+ µ+ µ−
4.8
10.8
3.1
1.1
0.2
<0.1
19.8
2.8
<0.1
1.7
<0.1
1.8
23.6

p → µ+ µ+ µ−
8.8
11.0
4.9
0.7
0.5
<0.1
6.7
1.0
<0.1
< 0.1
2.1
0.9
16.6

6.2. SYSTEMATIC UNCERTAINTY

101

Eventstrue Dwall and reconstructed Dwall . In Dwall between 600 cm and 1,000 cm, reconstructed andeach smeared distributions agree well. This means that, the difference of the accuracy for thevertex reconstruction between data and MC does not affect on the normalization in this area.
Therefore, 600 < Dwall < 1, 000 cm is defined as the area for the MC normalization.
Fig.6.26,6.27 shows reconstructed Dwall for data and MC after area normalization with respect to each period. Ratio of the number of events in fiducial volume (Dwall > 200 cm)
between data and MC is assigned as the systematic uncertainty of fiducial volume.

Background MC
SK4

50000

Sub GeV multi-ring
40000

MC reco

30000

True
True (σ=40cm)

20000

True (σ=100cm)

Ratio

10000

1.5
0
1.4
1.3
-200
1.2
1.1
0.91
0.8
0.7
0.6
0.5

-200

0

200

400

600

800

1000

1200

1400

1600

1800

0

200

400

600

800

1000 1200 1400 1600 1800
Distance to wall [cm]

250

SK1
Sub GeV multi-ring

EventsEventsFigure 6.25: Comparison of reconstructed, true and smeared true distance to wall of background MC.

SK2

200

Sub GeV multi-ring
180

200
160

Data

Data

140

150

120

MC

MC

100
100

80
60

50

40

0

200

400

600

800

1000

1200

1400

1600

1800

200

400

600

800

1000

1200 1400 1600 1800
Distance to wall [cm]

Ratio

Ratio

20
1.5
0
1.4
1.30
1.2
1.1
0.91
0.8
0.7
0.6
0.5

1.5
0
1.4
1.30
1.2
1.1
0.91
0.8
0.7
0.6
0.5

0

200

400

600

800

1000

1200

1400

1600

1800

200

400

600

800

1000

1200 1400 1600 1800
Distance to wall [cm]Figure 6.26: Distance to wall for data and MC after area normalization in SK-I (left) and SK-II(right). MC is normalized to data in the region 600 < Dwall < 1, 000 cm.

6.2.6

Detector non-uniformity

Energy scale of the Cherenkov rings depends on the position they are detected. This effect iscalled the detector non-uniformity and its difference between data and MC can be a source of

SK3

120

Sub GeV multi-ring
100

80

Ratio

60

EventsCHAPTER 6. PROTON DECAY SEARCH
600

Sub GeV multi-ring

Data

400

Data

MC

300

MC

40

200

20

100

1.5
0
1.4
1.30
1.2
1.1
0.91
0.8
0.7
0.6
0.5

0

SK4

500

200

400

600

800

1000

1200

1400

1600

1800

200

400

600

800

1000

1200 1400 1600 1800
Distance to wall [cm]Ratio

Events

102

1.5
0
1.4
1.30
1.2
1.1
0.91
0.8
0.7
0.6
0.5

0

200

400

600

800

1000

1200

1400

1600

1800

200

400

600

800

1000

1200 1400 1600 1800
Distance to wall [cm]Figure 6.27: Distance to wall for data and MC after area normalization in SK-III (left) and SK-IV(right). MC is normalized to data in the region 600 < Dwall < 1, 000 cm.
systematic uncertainty. This is already estimated in the latest neutrino oscillation analysis[108]by using Michel electron sample. The error values are estimated to be 0.6%, 0.6%, 1.3% and 0.5%
for SKI, II, III and IV respectively (section2.7.9). In case two charged particles decay back toback, detector non-uniformity error for total momentum of these two particles should be twiceof the source error. On the other hand, now there are isotropically decayed three charged
leptons in this analysis. this non-uniformity error should be less than twice of the source
error. But to be conservative, twice of the detector non-uniformity error is also considered as
the source error in this analysis. Therefore, the range of total momentum cut is shifted up anddown by the twice of source error, and the ratio of remained events in signal box is assigned
as the systematic uncertainty. In order to cover the low statistics in the signal box, sum of SK-I
to SK-IV samples (2000 years MC) is used for estimation.

6.2.7

Energy scale

Energy scale error estimated in the latest neutrino oscillation analysis[108] is used as thesource error of this systematic uncertainty. They are estimated to be 3.3%, 2.8%, 2.4% and2.1% respectively (section2.7.9). The range of π 0 mass, total mass and momentum cuts are
shifted up and down by these source error and the ratio of remained events in signal box isassigned as the systematic uncertainty. In order to cover the low statistics in the signal box,
2,000 years MC is used for estimation.

6.2.8

Ring counting & PID

Difference of data and MC in ring counting and PID distribution can be a source of systematic
uncertainty. In order to get the source error for them, the PID values in MC are scaled andshifted and compared with data by using sub-GeV multi-ring samples. Then the scale and shiftparameters with the smallest χ2 are obtained. Comparison of PID is performed for 1st,2nd and3rd reconstructed rings. Comparison plots for default, scaled and shifted MC events and datawith respect to each ring in SK-IV are shown in Fig.6.28, 6.29. Scaled and shifted parameters
for PID are summarized in Table6.16.
For the ring counting, ring counting likelihood for 3 or 4 rings is used. Comparison plots

6.2. SYSTEMATIC UNCERTAINTY80

SK4Sub GeV multi-ring70

1st ring

EventsEventsTable 6.16: Scale and shift parameters for PID value.
SK-I
SK-II
SK-III
SK-IV
Ring
Ring
Ring
Ring
2
3
1
2
3
1
2
3
1
2
3
1.02 0.98 1.04 0.95 1.04 0.84 1.08 0.96 0.96 0.96 0.96
0.08 -0.02 0.04 0.01 0.35 -0.37 0.18
0-0.04 0.07 -0.03

1
0.98
0.01

Scale
Shift

103

SK4
Sub GeV multi-ring120

2nd ring

100

60

Data
50

Data

80

MC

40

MC
60

Tuned MC30

Tuned MC

40

20
20

10
0
-10

-8

-6

-4

-2

0

2

4

6

8
PID

0
-10

10

-8

-6

-4

-2

0

2

4

6

8
PID

10

EventsFigure 6.28: PID value with respect to default MC events, scaled and shifted MC events (labeled
as Tuned MC) and data for 1st (left) and 2nd (right) rings in SK-IV

140

SK4
Sub GeV multi-ring120

3rd ring

100

Data
80

MC
Tuned MC

60
40
20
0
-10

-8

-6

-4

-2

0

2

4

6

8
PID

10

Figure 6.29: PID value with respect to default MC events, scaled and shifted MC events (labeled
as Tuned MC) and data for 3rd ring in SK-IV

104

CHAPTER 6. PROTON DECAY SEARCH

Eventsof ring counting likelihood for 3 or 4 rings between scaled and shifted MC events and data in
SK-IV are shown in Fig.6.30. (Scale, Shift) parameters for ring counting are (1.0,-0.34),(1.02,0.02),(1.05,0) and (0.98,-0.02) for SKI,II,III,IV respectively.
Finally these scaled and shifted parameters are propagated to signal and background samples. Then the ratios of remaining events in the signal boxes between nominal and scaled andshifted events are assigned as the systematic uncertainties.
SK4

60 Sub GeV multi-ring
50
40
30
20

Data
MC

10

Tuned MC
0
-10

-8

-6

-4

-2

0

2

4

6

8

10

Ring counting likelihood (3 or 4 rings)

Figure 6.30: Ring counting likelihood for 3 or 4 rings with respect to default MC events, scaled
and shifted MC events (labeled as Tuned MC) and data in SK-IV

6.2.9

Decay electron tagging

The difference of the number of decay electrons between data and MC after the area normalization is considered as the systematic error for decay electron tagging. Almost the same
signal selection, but vetoing the signal boxes, is applied to each analysis mode. Data and MC
comparison plots for the number of decay electrons with respect to each mode in SK-IV areshown in Fig.6.31,6.32. The ratios of events between data and MC are used for the errors where
the number of decay electrons is 0,1,2 for p → e+ e+ e− , p → µ+ e+ e− and p → e+ µ+ µ− , respectively. For p → µ+ µ+ µ− mode, the ratio where the number of decay electrons is 2 or 3
is used for the error. In order to cover the low statistics, weighted average values are used for
SK-I,II,III.

6.2.10

Neutron tagging

In order to estimate the systematic uncertainty for neutron tagging, pseudo distributions are
created from the number of true neutrons remaining in the signal boxes by using the background MC. The number of true neutron for background events remained in signal box isshown in Fig.6.33. Uniformly distributed random numbers between 0 and 1 are applied toeach true neutron in certain event. If the random number is below the neutron tagging efficiency, the neutron is assumed as tagged neutron. In order to cover the small statistics thisprocedure is iterated 50 times. For the first test, exact multiplicity of tagged neutrons and

600

SK4

500

3 rings
3 e-like

105

EventsEvents

6.2. SYSTEMATIC UNCERTAINTY

500

3 rings
1 μ-like & 2 e-like

400

Veto signal box

400

SK4

Data

Veto signal box

Data

300

MC

300

MC

MC(Area normalized)

MC(Area normalized)
200

200
100

100
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0
0

5

0.5

1

1.5

2

2.5

Number of decay electrons

3

3.5

4

4.5

5

Number of decay electrons

EventsEventsFigure 6.31: Data and MC comparison for the multiplicity of decay electrons in p → e+ e+ e−(left) and p → µ+ e+ e− (right) modes in SK-IV.

SK4
3 rings
2 μ-like & 1 e-like

140
120
100

35
30

Veto signal box

Data

SK4
3 rings
3 μ-like
Veto signal box

25

MC
80

20

MC(Area normalized)

60

15

40

10

20

5

Data
MC

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Number of decay electrons00MC(Area normalized)

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Number of decay electrons

Figure 6.32: Data and MC comparison for the multiplicity of decay electrons in p → e+ µ+ µ−(left) and p → µ+ µ+ µ− (right) modes in SK-IV.

106

CHAPTER 6. PROTON DECAY SEARCH

Number of events

Number of events

the one created from the true neutron under the neutron tagging efficiency 20% or 30% areshown in Fig.6.33 When the exact neutron tagging efficiency of 25.2% is considered, a pseudo
distribution created from true information agrees well with the reconstructed one. Changing
Background MC
SK4

0.1

3 rings
3 e-like

0.08

No decay electron
Total mass & momentum

0.06

0.04

0.2

Background MC

0.18

SK4
3 rings

0.16
0.14

3 e-like
No decay electron

0.12

Total mass and momentum

0.1

Reconstructed

0.08

True (20%)

0.06

True (30%)

0.04

0.02

0.02

0
0

2

4

6

8

0
0

10
12
14
Number of true neutron

1

2

3

4

5

6

7

8

9

10

Number of tagged neutron

Figure 6.33: Number of true neutron for background events remained in the signal box (left).
Number of tagged neutron in background MC, estimated from true neutron under the tagging
efficiency of 20% and 30%.

Background rate

the assumption of tagging efficiency for true neutron, we get the correlation plots between
neutron tagging efficiency and background rate as shown in Fig.6.34. Now the backgroundrate for tagging efficiency of 0% is defined as 1. The plot is fitted by exponential function. We
get the background rate at estimated tagging efficiency of 25.2% from the fitted function. Thenthe estimated source error of neutron tagging technique of 6% is considered. We can also get
the background rates at the efficiency 23.7% and 26.7%. These efficiencies correspond to the
6% shifted up and down values of 25.2%. Finally the larger value of the difference between default background rate and those with shifted tagging efficiencies is assigned as the systematic
uncertainty of the neutron tagging.

1
Background rate
Default: 0.434

0.8

Up: 0.417 (-4.1%)
Down: 0.452 (+3.9%)

0.6
0.12777 + exp(-3.75875x + -0.236474)

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Eﬃciency of neutron tagging

Figure 6.34: Correlation plot between neutron tagging efficiency and background rate.

6.3. DATA AND MC AGREEMENT

6.2.11

107

Total systematic uncertainty

Systematic uncertainties for signal and background are summarized in Table6.17 and Table6.18.
The detail of each systematic uncertainty for signal and background of each mode are summarized in Table6.19-6.28.
Table 6.17: Summary of systematic uncertainty [%] for signal. Each error is averaged by live
time of each period. Detector & Reconstruction is the quadratic sum of the errors 6.2.5-6.2.10.
Modes
Correlated decay Fermi momentum Detector & Reconstruction Total+ + −p→e e e
(Low)
4.0
10.4
5.9
12.6
(High)
9.3
3.1
4.4
10.8
+ + −
p→µ e e
(Low)
3.9
10.3
8.1
13.7
(High)
9.4
3.4
7.5
12.6
− + +
p→µ e e
(Low)
3.9
10.3
8.1
13.7
(High)
9.6
3.0
7.6
12.5
+ + −
p→e µ µ
(Low)
3.7
10.1
8.3
13.6
(High)
9.5
3.5
7.2
12.7
p → e − µ+ µ+
(Low)
3.7
9.4
8.0
13.1
(High)
8.8
5.6
7.2
12.9
p → µ+ µ+ µ−
(Low)
3.8
10.5
18.9
22.1
(High)
9.7
6.5
18.6
22.1

Table 6.18: Summary of systematic uncertainty [%] for background. Each error is averaged
by live time of each period. Detector & Reconstruction is the quadratic sum of the errors
6.2.5-6.2.10.
Neutrino
Neutrino
Pion
Detector &
Modes
flux
cross section FSI/SI Reconstruction Total+ + −p→e e e
7.0
14.1
1.9
32.4
36.1
p → µ+ e+ e− (p → µ− e+ e+ )
7.3
16.9
1.9
19.3
26.7
+ + −
− + +
p → e µ µ (p → e µ µ )
8.2
23.6
3.3
19.6
32.0
p → µ+ µ+ µ−
8.3
16.6
1.8
32.4
37.4

6.3 Data and MC agreement
Data and MC agreements for basic cut parameters are checked first. Comparison for the number of rings or e-like rings is shown in Fig.6.35. Comparisons for number of decay electrons
with respect to each mode are shown in Fig.6.36,6.37. Comparison for mass of 2 e-like rings

108

CHAPTER 6. PROTON DECAY SEARCH

Table 6.19: Systematic uncertainty [%] for signal in p → e+ e+ e− mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

4.0
10.1

9.3
2.9
0.3

1.5
4.5
0.5
2.5

0.2
0.8
0.3
2.6
2.0
-

12.2

10.3

4.2
10.3

9.5
2.9

4.0
10.4

9.4
2.9

0.4

0.3

1.9
0.1
4.6
1.1
0.2
0.2
<0.1 0.3
2.0
12.4 10.2

3.3
0.4
2.9
0.6
0.5
0.2
<0.1 <0.1
2.0
12.2 10.1

4.0
10.5

9.3
3.2
3.0

1.2
2.5
0.4
0.1

0.3
0.3
0.2
0.2
2.4
4.1

12.9

11.3

Table 6.20: Systematic uncertainty [%] for background in p → e+ e+ e− mode.
SK-I SK-II SK-III SK-IV(Model)Neutrino flux
7.0
14.0
Neutrino cross section
Pion FSI/SI
1.9(Detector & Reconstruction)
Fiducial volume
0.3
0.4
0.3
3.0
Detector non-uniformity
12.9
29.3
Energy scale
PID
2.3
<0.1
Ring counting
Decay electron
2.0
2.0
2.0
2.4
Neutron tagging
4.1
Total
35.8 35.8
35.8
36.2

6.3. DATA AND MC AGREEMENT

109

Table 6.21: Systematic uncertainty [%] for signal in p → µ+ e+ e− mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

4.0
10.0

9.5
2.4

3.9
10.3

0.3
1.9
3.6
0.2
1.8

0.4
1.0
0.1
1.9
7.1
-

13.7

12.3

9.0
2.5

4.0
10.8

9.4
4.4

3.9
10.4

9.5
4.0

0.4

0.3

3.0

0.1
1.3
<0.1
0.3
7.1
13.6 11.8

3.0
0.4
2.4
0.6
0.9 <0.1<0.1 <0.1
7.1
14.1 12.6

1.4
0.1
1.9
0.6
0.2
0.1
<0.1 <0.1
4.5
5.5
13.7 12.9

1.6
3.1
0.1
0.1

Table 6.22: Systematic uncertainty [%] for signal in p → µ− e+ e+ mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

3.8
9.6

9.9
3.6

4.0
11.4

0.3
1.7
3.3
0.1
1.3

0.5
0.8
0.2
2.0
7.1
-

13.1

12.9

9.5
2.5

3.8
9.9

9.6
3.7

4.0
10.5

9.4
2.7

0.4

0.3

3.0

0.3
1.2
<0.1
0.1
7.1
14.5 12.2

2.7
0.5
2.1
0.2
0.4
0.1
<0.1 <0.1
7.1
13.2 12.5

1.4
0.4
2.4
0.6
0.2 <0.1<0.1 <0.1
4.5
5.5
13.9 12.5

1.5
3.5
0.1
0.3

110

CHAPTER 6. PROTON DECAY SEARCH

Table 6.23: Systematic uncertainty [%] for background in p → µ+ e+ e− and p → µ− e+ e+
mode.
SK-I SK-II SK-III SK-IV(Model)Neutrino flux
7.3
16.9
Neutrino cross section
Pion FSI/SI
1.9(Detector & Reconstruction)
Fiducial volume
0.3
0.4
0.3
3.0
Detector non-uniformity
8.9
Energy scale
12.0
PID
9.7
<0.1
Ring counting
Decay electron
7.1
7.1
7.1
4.5
5.5
Neutron tagging
Total
26.8 26.8
26.8
27.0

Table 6.24: Systematic uncertainty [%] for signal in p → e+ µ+ µ− mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

3.1
9.0

10.0
4.8
0.3

1.2
3.7
0.3
3.2

0.7
1.1
0.2
2.0
3.7
-

11.4

11.5

4.3
10.7

9.3
1.3

0.4
3.0
0.9
3.9
0.9
0.3 <0.1<0.1 0.1
3.7
13.1
9.7

3.5
9.8

9.3
6.1

0.3
3.2
0.4
2.7
0.5
1.1
0.5
<0.1 <0.1
3.7
11.9 11.8

3.9
10.5

9.4
3.0

3.0
0.8
0.5
2.4
1.0
0.1
0.1
<0.1 0.3
7.1
6.0
15.1 13.9

6.3. DATA AND MC AGREEMENT

111

Table 6.25: Systematic uncertainty [%] for signal in p → e− µ+ µ+ mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

3.8
9.2

9.0
5.3

3.8
10.6

9.5
2.5

3.8
10.1

9.1
6.5

3.7
9.0

8.4
6.4

0.3

0.4

0.3

3.0

1.3
0.2
3.4
0.4
<0.1 0.2
1.6
2.5
3.7
11.3 11.4

1.7
0.3
3.4
0.9
0.1
0.1
<0.1 0.2
3.7
12.5 10.5

3.5
1.1
3.1
0.9
0.1
0.2
<0.1 <0.1
3.7
12.3 11.9

1.4
0.3
2.7
0.5
<0.1 0.3
0.2 <0.1
7.1
6.0
14.1 14.4

Table 6.26: Systematic uncertainty [%] for background in p → e+ µ+ µ− and p → e− µ+ µ+
mode.
SK-I SK-II SK-III SK-IV(Model)Neutrino flux
8.2
23.6
Neutrino cross section
Pion FSI/SI
3.3(Detector & Reconstruction)
Fiducial volume
0.3
0.4
0.3
3.0
Detector non-uniformity
9.0
13.4
Energy scale
PID
8.3
Ring counting<0.1
Decay electron
3.7
3.7
3.7
7.1
Neutron tagging
6.0
Total
32.0 32.0
32.0
33.3

112

CHAPTER 6. PROTON DECAY SEARCH

Table 6.27: Systematic uncertainty [%] for signal in p → µ+ µ+ µ− mode.
SK-I
SK-II
SK-III
SK-IV
Low High Low High Low High Low High(Model)Correlated decay
Fermi motion(Detector & Reconstruction)
Fiducial volume
Detector non-uniformity
Energy scale
PID
Ring counting
Decay electron
Neutron tagging
Total

4.0
10.8

10.0
7.3

3.8
10.8

9.4
7.4

3.7
9.6

8.9
5.7

3.7
10.5

9.7
6.1

0.3

0.4

0.3

3.0

1.8
0.1
3.9
0.5
<0.1 0.1
0.6
0.6
23.5
26.5 26.6

1.6
0.5
3.4
0.9
<0.1 <0.1
0.1 <0.1
23.5
26.4 26.4

2.6
0.5
2.6
0.3
0.6
0.7
<0.1 <0.1
23.5
25.9 25.9

1.4
0.5
2.4
0.5
0.1
0.1
<0.1 0.1
13.7
3.3
18.4 18.4

Table 6.28: Systematic uncertainty [%] for background in p → µ+ µ+ µ− mode.
SK-I SK-II SK-III SK-IV(Model)Neutrino flux
8.3
16.6
Neutrino cross section
Pion FSI/SI
1.8(Detector & Reconstruction)
Fiducial volume
0.3
0.4
0.3
3.0
Detector non-uniformity
18.1
13.3
Energy scale
PID
13.5
<0.1
Ring counting
Decay electron
23.5 23.5
23.5
13.7
Neutron tagging
3.3
Total
40.2 40.2
40.2
37.8

6.3. DATA AND MC AGREEMENT

113

40000

SK1-4

EventsEventswith respect to p → µ+ e+ e− mode is shown in Fig.6.38. Comparisons for the number of tagged
neutrons in each mode are shown in Fig.6.39,6.40.

35000
30000

2200

SK1-4

2000

3 rings

1800
1600

25000
20000

Data

1400

MC

1200

Data

1000
15000

800

10000

600

MC

400
5000
0
0

200
1

2

3

4

5

6

7

8

9

0
0

10

1

2

3

Number of ring

4

5

6

Number of e-like ringSK1-4
3 rings

1200

3 e-like

1000

EventsEventsFigure 6.35: Data and MC comparison for number of ring (left) and number of e-like ring.

SK1-4
3 rings

900
800

1 μ-like & 2 e-like

700
600

800

Data

600

MC

500

Data

400

MC

300

400

200
200
100
0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

Figure 6.36: Data and MC comparison for number of decay electron with respect to p →e+ e+ e− (left) and p → µ+ e+ e− (right) modes.
In order to check data and MC agreement in total mass and total momentum distribution
before opening the signal box, a control region outside the signal box is defined to avoid thecontamination of the signal events. First the difference of total mass and momentum between
true and reconstructed value in signal MC sample are checked as shown in Fig.6.41. Considering the fluctuation for total mass and momentum, the validation region is defined 200 MeV
far from the signal box as M < 600 MeV or M > 1, 250 MeV or P 450 MeV. The definition of
the validation region is shown in Fig.6.42.
Comparisons for total mass and momentum distributions in the validation region in eachmode are shown in Fig.6.43-6.46. A small excess of data is seen in total mass around 750 <M < 900 MeV in p → e+ e+ e− mode. In this region, the number of expected background
events is 81.2 and the number√of observed events is 111. Then the significance of this excess iscalculated to be (111−81.2)/ 81.2 = 3.3. Generally, the significance of 3.3 is not a significant
excess. Comparison of total momentum focussing on total mass between 750 and 900 MeV in
the control region is also shown in Fig.6.47. A small excess is also seen in total momentum
between 600 and 800 MeV or 1,000 and 1,200 MeV. Such kinematic region of 750 < M <CHAPTER 6. PROTON DECAY SEARCH

300

SK1-4
3 rings250

2 μ-like & 1 e-like

200

EventsEvents114

SK1-4
3 rings70

3 μ-like

60
50

Data

150

MC

40

Data
MC

30

100
20
50

0
0

10
0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

EventsFigure 6.37: Data and MC comparison for number of decay electron with respect to p →e+ µ+ µ− (left) and p → µ+ µ+ µ− (right) modes. The black point shows the data and red line
shows the background MC.

SK1-4

300

3 rings
1 μ-like & 2 e-like250

1 decay electron

200

Data

150

MC
100
50
0
0

200

400

600
800
1000
1200
Mass of 2 e-like rings [MeV/c2]

Figure 6.38: Data and MC comparison for mass of 2 e-like rings with respect to p → µ+ e+ e−(left) mode. The black point shows the data and red line shows the background MC.

350

115

EventsEvents6.3. DATA AND MC AGREEMENT

SK4
3 rings300

3 e-like
No decay electron

250

SK4
100

3 rings
1 μ-like & 2 e-like
1 decay electron80

π0 veto
200

60

Data
150

Data

MC

MC
40

100
20

50
0
0

1

2

3

4

0
0

5
6
7
8
9
10
Number of tagged neutron

1

2

3

4

5
6
7
8
9
10
Number of tagged neutron

SK4
3 rings30

2 μ-like & 1 e-like

EventsEventsFigure 6.39: Data and MC comparison for number of tagged neutron with respect to p →e+ e+ e− (left) and p → µ+ e+ e− (right) modes in SK-IV. The black point shows the data and redline shows the background MC.

2 decay electron

25

14

SK4
3 rings

12

3 μ-like
2 or 3 decay electron

10

20

8

Data
15

Data
6

MC

10

4

5

2

0
0

1

2

3

4

0
0

5
6
7
8
9
10
Number of tagged neutron

MC

1

2

3

4

5
6
7
8
9
10
Number of tagged neutron

300

p → e+ e+ e-

250

SK4
3 rings

EventsEventsFigure 6.40: Data and MC comparison for number of tagged neutron with respect to p →e+ µ+ µ− (left) and p → µ+ µ+ µ− (right) modes in SK-IV. The black point shows the data andred line shows the background MC.

3 e-likep → e+ e+ e250

200

SK4
3 rings
3 e-like

200
150
150
100

100

50

50
0
-200

-150

-100

-50

0

50

100

150

200

(Reconstructed - True) of total mass [MeV/c2]

0
-200

-150

-100

-50

0

50

100

150

200

(Reconstructed - True) of total momentum [MeV/c]

Figure 6.41: The difference of reconstructed and true value for total mass and total momentum
with respect to p → e+ e+ e− signal MC.

CHAPTER 6. PROTON DECAY SEARCH
Total momentum [MeV]116

Validation Region

450

250

SR High100

SR Low
600

1,050

800

1,250

Total mass [MeV]

Figure 6.42: The definition of the validation region.

70

SK1-4

60

3 rings
3 e-like
No decay electron50

M<600MeV or M>1250MeV
or P>450MeV

EventsEvents900 MeV and 600 < P < 800 MeV or 1, 000 < P < 1, 200 MeV is far from typical p → e+ e+ e−
signal events as shown in Fig.6.49. The event displays of data in the region of excess are also
checked. There are basically typical background events and no abnormal events found. Someof event displays in this region are shown in Fig.6.48. As a conclusion, this excess is attributed
to a statistical fluctuation.
The period by period comparisons for these parameters are summarized in Appendix A.
SK1-4

60

3 rings
3 e-like
No decay electron50

M<600MeV or M>1250MeV
or P>450MeV

40
40
30

30

Data

20

MC
10

10
0
0

Data

20

MC

200

400

600

800

1000

1200

Total mass [MeV/c2]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure 6.43: Data and MC comparison for total mass (left) and total momentum (right) distributions in the validation region with respect to p → e+ e+ e− mode .

6.4 Result
6.4.1

Data open results

Since data and background MC agree well in the validation region as described in section6.3,
we opened the data in signal box. As a result, 1 signal candidate is observed in both p →

117

30

40

SK1-4

35

3 rings
1 μ-like & 2 e-like

30
25

EventsEvents

6.4. RESULT

1 decay electron
π0 vetoM<600MeV or M>1250MeV

25

20or P>450MeV

SK1-4
3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV
or P>450MeV

15

20
15

10

Data

10

Data
5

MC

5
0
0

200

400

600

800

1000

0
0

1200

MC
100

200

300

400

500

Total mass [MeV/c2]

600

700

800

900

1000

Total momentum [MeV/c]

Figure 6.44: Data and MC comparison for total mass (left) and total momentum (right) distributions in the validation region with respect to p → µ+ e+ e− mode.

16
14
12

SK1-4

EventsEvents18

3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

10

14

SK1-4

12

3 rings
2 μ-like & 1 e-like
2 decay electron

10

M<600MeV or M>1250MeV
or P>450MeV

8

8

6

6
4

Data

4

Data

MC
0
0

200

400

600

800

MC

2

2
1000

0
0

1200

100

200

300

400

500

Total mass [MeV/c2]

600

700

800

900

1000

Total momentum [MeV/c]

7

SK1-4

6

3 rings
3 μ-like

5

EventsEventsFigure 6.45: Data and MC comparison for total mass (left) and total momentum (right) distributions in the validation region with respect to p → e+ µ+ µ− mode.

2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

4
3

7

SK1-4

6

3 rings
3 μ-like
2 or 3 decay electron

5

M<600MeV or M>1250MeV
or P>450MeV

4

Data

Data

3

MC

MC

2

2

1

1

0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure 6.46: Data and MC comparison for total mass (left) and total momentum (right) distributions in the validation region with respect to p → µ+ µ+ µ− mode.

CHAPTER 6. PROTON DECAY SEARCH

Events

118

25

SK1-4
3 rings
3 e-like
No decay electron

20

P > 450 MeV
750 < M < 900 MeV

15

Data
10

MC

5

0
0

500

1000

1500

2000

2500

3000

Total momentum [MeV/c]

Figure 6.47: Data and background mc comparison for total momentum distributions focussing
on total mass between 750 and 900 MeV in the validation region.

Figure 6.48: Examples of the event displays of data in the region of excess in p → e+ e+ e− .The
blue circles show TDC fit result, red circles show ring fit result by the APfit. The total mass is874 MeV and total momentum is 728 MeV in the left event. The total mass is 769 MeV and total
momentum is 1,069 MeV in the right event.

6.4. RESULT

119

Total momentum [MeV/c]

e+ µ+ µ− (p → e− µ+ µ+ ) and p → µ+ µ+ µ− modes, respectively. 2 dimensional plots for total
mass and momentum for signal MC, background MC and data for each mode are shown in
Fig.6.49-6.52. Comparison of data and background MC around the signal boxes for total massand momentum distribution is also shown in Fig.6.53-6.56. Period by period comparisons forthese plots are also summarized in Appendix A. The observed data are consistent with theprediction of atmospheric background events. Cut flow for data with respect to each mode aresummarized in Table6.29-6.32. The observed number of events at each cut step is consistent
with the expected number of background events.
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

Total mass [MeV/c 2]

Total momentum [MeV/c]

Figure 6.49: 2 dimensional plots of total mass and momentum for signal (left), background(center) and measured data (right) in p → e+ e+ e− mode after all selections are applied. Light
blue shows free proton and dark blue shows bound proton in signal plot. Two black squares
show the low and high signal boxes. The exposure of background MC is 500 years, whichcorresponds to 30 times that of data.

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

Total mass [MeV/c 2]

Figure 6.50: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → µ+ e+ e− mode after all selections are applied.
Light blue shows free proton and dark blue shows bound proton in signal plot. Two blacksquares show the low and high signal boxes. The exposure of background MC is 500 years,
which corresponds to 30 times that of data.

6.4.2

Observed candidates

1 event is observed in the high signal box in p → e+ µ+ µ− (p → e− µ+ µ+ ) mode and 1 eventis also observed in the high signal box in p → µ+ µ+ µ− mode. Detail about both events are

CHAPTER 6. PROTON DECAY SEARCH

Total momentum [MeV/c]

120

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

Total mass [MeV/c 2]

Total momentum [MeV/c]

Figure 6.51: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → e+ µ+ µ− mode after all selections are applied.
Light blue shows free proton and dark blue shows bound proton in signal plot. Two blacksquares show the low and high signal boxes. The exposure of background MC is 500 years,
which corresponds to 30 times that of data.

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

Total mass [MeV/c 2]

Figure 6.52: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → µ+ µ+ µ− mode after all selections are applied.
Light blue shows free proton and dark blue shows bound proton in signal plot. Two blacksquares show the low and high signal boxes. The exposure of background MC is 500 years,
which corresponds to 30 times that of data.

Number of events

6.4. RESULT

121

102

P<250MeV/c 10

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
12000
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Number of events

Figure 6.53: Data and background comparison for total mass (left) and momentum (right) in
p → e+ e+ e− mode after all selections are applied. Black point shows data, red line shows
background, dark blue line shows total and filled light blue shows free proton of signal. Dottedblack line show the signal box.

102

P<250MeV/c 10

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
12000
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure 6.54: Data and background comparison for total mass (left) and momentum (right) in
p → µ+ e+ e− mode after all selections are applied. Black point shows data, red line shows
background, dark blue line shows total and filled light blue shows free proton of signal. Dottedblack line show the signal box.

CHAPTER 6. PROTON DECAY SEARCH

Number of events

122

102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Number of events

Figure 6.55: Data and background comparison for total mass (left) and momentum (right) in
p → e+ µ+ µ− mode after all selections are applied. Black point shows data, red line shows
background, dark blue line shows total and filled light blue shows free proton of signal. Dottedblack line show the signal box.

102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure 6.56: Data and background comparison for total mass (left) and momentum (right) in
p → µ+ µ+ µ− mode after all selections are applied. Black point shows data, red line shows
background, dark blue line shows total and filled light blue shows free proton of signal. Dottedblack line show the signal box.

6.4. RESULT

123

Table 6.29: Observed events at each step of selection criteria for p → e+ e+ e− mode. The
expected number of background events at each step is also shown in brackets. The error values
correspond to the statistic uncertainty.
SK-I
SK-II
SK-III
SK-IV
FC & FV
12,178±110
6,626±81
4,347±66
26,542±163(12,097±10) (6546±5)(4285±3) (26,563±21)
Number of rings
995±32551±23368±192,282±48(966±3)(555±2)(340±1)(2,247±6)PID
458±21231±15191±14
1,053±32(460±2)(243±1)(157±1)(1,038±4)
Number of decay electrons
256±16137±12
113±11570±24(270±1)(152±1)(97±1)(568±3)
Total mass & momentum
0000(0.18±0.04) (0.11±0.02) (0.05±0.01) (0.58±0.10)
Neutron veto
0
(-)
(-)
(-)
(0.23±0.06)
Low signal box
0000(<0.01)(0.01±0.01)(<0.01)(<0.01)High signal box
0000(0.18±0.04) (0.10±0.02) (0.05±0.01) 0.23±0.06

Table 6.30: Observed events at each step of selection criteria for p → µ+ e+ e− and p → µ− e+ e+mode. The expected number of background events at each step is also shown in brackets. The
error values correspond to the statistic uncertainty.
SK-I
SK-II
SK-III
SK-IV
FC & FV
12,178±110
6,626±814347±66
26,542±163(12,097±10) (6546±5)(4285±3) (26,563±21)
Number of rings
995±32551±23368±192,282±48(966±3)(555±2)(340±1)(2,247±6)PID
382±20204±14135±12902±30(372±2)(218±1)(135±1)(879±4)
Number of decay electrons
182±1394±1057±8
473±22(166±1)(90±1)(61±0)(440±3)π 0 veto
86±9
49±7
26±5
227±15(81±1)(47±0)(30±0)(202±2)00
00
Total mass & momentum(0.15±0.03) (0.12±0.02) (0.06±0.01) (0.56±0.10)
0Neutron veto
(-)
(-)
(-)
(0.18±0.06)
Low signal box
0000(0.02±0.01) (0.01±0.01) (0.01±0.00)(<0.01)High signal box
0000(0.13±0.03) (0.11±0.02) (0.05±0.01) (0.18±0.06)

124

CHAPTER 6. PROTON DECAY SEARCH

Table 6.31: Observed events at each step of selection criteria for p → e+ µ+ µ− and p →e− µ+ µ+ mode. The expected number of background events at each step is also shown inbrackets. The error values correspond to the statistic uncertainty.
SK-I
SK-II
SK-III
SK-IV
FC & FV
12,178±110
6,626±814347±66
26,542±163(12,097±10) (6546±5)(4285±3) (26,563±21)
Number of rings
995±32551±23368±192,282±48(966±3)(555±2)(340±1)(2,247±6)127±1194±1032±6257±16PID(108±1)(78±1)(38±0)(265±2)
Number of decay electrons
27±5
15±4
5±2
56±7
(17±0)(11±0)(6±0)(58±1)
Total mass & momentum
0
0
0
1±1
(0.09±0.02) (0.07±0.01) (0.03±0.01) (0.30±0.07)
Neutron veto
1±1
(-)
(-)
(-)
(0.07±0.03)
Low signal box
0000(<0.01)(<0.01)(<0.01)(<0.01)0001±1High signal box(0.09±0.02) (0.07±0.01) (0.03±0.01) (0.07±0.03)

Table 6.32: Observed events at each step of selection criteria for p → µ+ µ+ µ− mode. The
expected number of background events at each step is also shown in brackets. The error values
correspond to the statistic uncertainty.
SK-I
SK-II
SK-III
SK-IV
FC & FV
12,178±110
6,626±814347±66
26,542±163(12,097±10) (6546±5)(4285±3) (26,563±21)
Number of rings
995±32551±23368±192,282±48(966±3)(555±2)(340±1)(2,247±6)
PID
28±5
22±5
10±3
70±8
(26±0)(17±0)(9±0)(64±1)
8±3
6±2
1±1
28±5
Number of decay electrons
(8±0)
(5±0)
(3±0)
(28±1)
Total mass & momentum
1±1
0
0
0
(0.10±0.03) (0.05±0.01) (0.03±0.01) (0.47±0.08)
Neutron veto
0
(-)
(-)
(-)
(0.21±0.06)
Low signal box
0000(0.01±0.01)(<0.01)(<0.01)(<0.01)High signal box
1±1
0
0
0
(0.09±0.03) (0.05±0.01) (0.03±0.01) (0.21±0.06)

6.4. RESULT

125

discussed in this section.
Considering the number of expected background to be 0.27 in p → e+ µ+ µ− ( p → e− µ+ µ+) mode, the poisson probability of observing greater than or equal to 1 event is calculated to
be 18.4%. This probability means that 1 observed event is not significant excess compared to
the number of expected background events in this mode. For p → e− µ+ µ+ mode, the poisson
probability of observing greater than or equal to 1 event is 25.8% with respect to the numberof expected background events to be 0.40. This is not a significant excess in this mode either.
These values are summarized in Table6.33.
Table 6.33: Summary of background events, the number of candidate, Poisson probability toobserve events greater than or equal to the number of data candidates. The probability is
calculated for the total signal box.
Modes
Background [events]
Candidate [events] Probability [%]
High
Low
Total
p → e+ e+ e−
0.56±0.08 0.01±0.01 0.58±0.08
0p → µ+ e + e −0.47±0.06 0.04±0.01 0.50±0.06
0(p → µ− e+ e+ )p → e+ µ+ µ−
0.26±0.04<0.01
0.27±0.04
1 (High)
18.4(p → e− µ+ µ+ )p → µ+ µ+ µ−
0.38±0.07 0.01±0.01 0.40±0.07
1 (High)25.8
Sum1.67±0.13 0.06±0.02 1.75±0.13240.9

Event displays for both candidates are shown in Fig.6.57,Fig.6.58 Information of both candidates is summarized in Table6.34 Reconstructed values of each ring for both candidates are also
summarized in Table6.35,6.36. For the p → e+ µ+ µ− candidate, 2 rings near Ring1 are clearly
not reconstructed by APfit. Such events are also often seen in typical background events likeFig.6.20. For the p → µ+ µ+ µ− candidate, 1 ring near Ring1 is clearly not reconstructed by
APfit either. This event is also similar to the typical background events like Fig.6.21. As a conclusion, these observed candidates are typical atmospheric neutrino background events likesingle or multi π production events.
Table 6.34: Information of candidates in p → e+ µ+ µ− ( p → e− µ+ µ+ ) and p → µ+ µ+ µ−
modes.
p → e+ µ+ µ−
p → µ+ µ+ µ−
PeriodSK-IV
SK-I70589 / 37485314
8854 / 36673156
Run # / Event #Vertex X/Y/X [cm]-400.1/1004.7/-54.5 -357.3/1118.0/-1270.3
608.6
516.3
Distance to wall [cm]
3 (1,2)3 (0,3)
Number of rings (e-like,µ-like)
Number of decay electrons2
2
Number of tagged neutron
0
Total mass/momentum [MeV]
882.4/159.8
835.1/170.0

126

CHAPTER 6. PROTON DECAY SEARCH

Figure 6.57: Event displays of the observed candidate in p → e+ µ+ µ− (p → e− µ+ µ+ ) mode
before (left) and after (right) ring reconstruction. Blue circle shows TDC fit result, red andpurple bold circles show ring fit result for e-like and µ-like respectively in right figure. Indexof each ring is also described in right figure for Table6.35

Figure 6.58: Event displays of the observed candidate in p → µ+ µ+ µ− (p → µ− µ+ µ+ ) mode
before (left) and after (right) ring reconstruction. Blue circle shows TDC fit result, red andpurple bold circles show ring fit result for e-like and µ-like respectively in right figure. Indexof each ring is also described in right figure for Table6.36

6.5. LIFETIME LIMIT

127

Table 6.35: Reconstructed values of each ring for candidate observed in p → e+ µ+ µ− ( p →e− µ+ µ+ ) mode. Definition of ring index is described in Fig.6.57
Ring1
Ring2
Ring3
Direction from vertex X/Y/Z (vector)
0.15/0.28/-0.95 -0.30/0.49/0.82 -0.17/-0.79/0.59
PID likelihood value
0.82 (µ-like)1.87 (µ-like)-3.4 (e-like)
Reconstructed opening angle [degree]
40.3
33.8
43.1
Momentum [MeV]
412.3
296.7
156.2
Expected opening angle [degree]
39.2
37.2
41.4
Table 6.36: Reconstructed values of each ring for the candidate observed in p → µ+ µ+ µ−
mode. Definition of ring index is described in Fig.6.58
Ring1
Ring2
Ring3
Direction from vertex X/Y/Z (vector)-0.51/0.37/0.77 0.28/0.67/-0.69 0.72/-0.70/-0.03
PID likelihood value
2.21 (µ-like)2.55 (µ-like)
1.88 (µ-like)
Reconstructed opening angle [degree]
37.1
36.8
33.8
Momentum [MeV]
277.0
289.7
223.8
36.6
37.0
33.9
Expected opening angle [degree]

6.5 Lifetime limit
There are no significant excess of data compared to the number of expected background eventsin all modes. Two events are observed in the signal box, which are considered as typicalatmospheric neutrino background events. As a conclusion, any events of proton decay into
three charged leptons are not discovered in this analysis. Finally, we set lower limits for the
proton lifetime with respect to each decay mode by using Bayesian method. Now we have 8
signal regions (4 periods×2 boxes). The probability density function (PDF) is calculated foreach region. Then all PDFs are combined to estimate the lifetime limit for each decay mode.
The probability of detecting ni events under the assumption of expected signal and background events Γλi ϵi + bi by Poisson statistics is defined as follow. i is the index of each signal
box, Γ is the decay rate, λi is the exposure (unit is the number of protons1 multiplied by live
time [year] ), ϵi is the signal effieincy and bi is expected background events.
P (ni |Γλi ϵi bi ) =e−(Γλi ϵi +bi ) (Γλi ϵi + bi )ni
ni !

(6.4)

When we follow the Bayesian theory this probability is described as below.
P (ni ) = P (ni |Γλi ϵi bi )P (Γλi ϵi bi )= P (ni |Γλi ϵi bi )P (Γ)P (λi )P (ϵi )P (bi )(6.5)

Here we assume the probabilities of decay rate, exposure, signal efficiency and backgroundare independent. Then the PDF for ni observed events as the function of decay rate P (Γ|ni )1Note that there are 10 protons in a molecule of water, two free and eight bound protons in Oxygen.

128

CHAPTER 6. PROTON DECAY SEARCH

is calculated as follow.
∫∫∫
P (Γ|ni ) =P (ni )dϵi dλi dbi∫ ∫ ∫ −(Γλi ϵi +bi )1e(Γλi ϵi + bi )ni=
P (Γ)P (λi )P (ϵi )P (bi )dϵi dλi dbi
Aini !
Then Ai is the normalization constant defined as below.
∫ ∞Ai =P (Γ|ni )dΓ

(6.6)

(6.7)

0

We assume the probabilities for decay rate is uniform as below.
P (Γ) = 1

(6.8)

We also assume the probabilities for exposure and signal efficiency follow Gaussian as below.
P (λi ) = exp{−(λi − λ0,i )2 /2σλ2i }P (ϵi ) = exp{−(ϵi − ϵ0,i )2 /2σϵ2i }(6.9)(6.10)

Here λ0,i (σλi ) and ϵ0,i (σϵi ) are estimations (systematic errors) for exposure and signal efficiency, respectively. Here the normalization factors for P (Γ), P (λi ) and P (ϵi ) are not described in each expression. Since the number of background events is very small, the probability for background is described as the convolution of Gaussian and Poisson distributions as
below.
∫ ∞ −B nbe B i(6.11)
exp{−(Ci bi − B)2 /2σb2i }dB
P (bi ) ∝!
nb0iHere nbi is the number of expected background events in 500 years MC, Ci is the constant value
to normalize MC live time to data live time and σbi is the systematic error for the background.
The upper limit of the decay rate Γlimit at 90% confidence level is calculated from following
equation.
∫ Γlimit N∏=8
P (Γ|ni )dΓ = 0.9(6.12)
Γ=0

i=1

Finally the lower limit of partial lifetime is calculated as below.
τ /B =

1Γlimit(6.13)

Here B is the branching ratio of each decay mode.
The lower limit of partial lifetime for each decay mode at 90% confidence level is calculated
as below.
τ /Bp→e+ e+ e− > 3.4 × 1034 years
τ /Bp→µ+ e+ e− > 2.3 × 1034 years
τ /Bp→µ− e+ e+ > 1.9 × 1034 years
τ /Bp→e+ µ+ µ− > 9.2 × 1033 years

6.5. LIFETIME LIMIT

129
τ /Bp→e− µ+ µ+ > 1.1 × 1034 years
τ /Bp→µ+ µ+ µ− > 1.0 × 1034 years

Comparison of current most stringent limit by IMB-3[20] and HPW[21] experiments are summarized in Fig.6.59 and Table?? The partial lifetime limit for proton decay into three charged
leptons are largely improved and the first result for p → µ− e+ e+ mode is obtained by thisanalysis.

Lifetime Limit [years] (90%CL)
1030

1031

1032

1033

1034

p→e+e+eIMB-3

SKp→μ+e+e-

p→μ-e+e+HPWp→e+μ+μ-p→e-μ+μ+p→μ+μ+μ-Figure 6.59: Estimated partial lifetime limit for each mode of proton decay into three charged
leptons by this analysis (red histogram), IMB (star)[20] and HPW (circle)[21] experiments.

Chapter 7
Discussion
The observed data were consistent with the atmospheric neutrino background prediction for
all modes of proton decay into three charged leptons. Therefore, these decay modes predictedby the model (section 1.2.4) at the energy scale below 100 TeV could not be verified. In thismodel, p → µ− e+ e+ and p → e− µ+ µ+ can be dominant in all proton decay modes by assuming some symmetries. Such scenario below 100 TeV energy scale could not be verified either
by this analysis. The decay rates of these modes are proportional to the Λ12 (Λ is the energy
scale) according to the equation (1.41). Then proton decay of longer lifetime than calculated
limits is still considerable at higher energy scale. We need to improve the sensitivity of theanalysis to discover such longer lifetime proton decay events.
New operation period SK-V already started in Super-Kamiokande. This new period simply increases the statistics. Furthermore, SK-Gd project will start soon in this period. In thisproject, Gadolinium (Gd) is dissolved in water, which increase the capturing efficiency forthermal neutron. Then the performance of neutron tagging will be improved, which can decrease the atmospheric neutrino background. These improvements leads to better sensitivityof proton decay analysis.
Future plan, Hyper-Kamiokande (HK) project[111] can further increase the statistics. The
HK detector plans to be cylindrical tank of 74 m diameter and 60 m height. 40,000 PMTs will
be arranged on the tank wall. The tank will be filled with 26 Mton ultra pure water. FV willbe 19 Mton, which is about 10 times larger volume than SK FV. Schematic view of the HK
detector is shown in Fig.7.1. HK can collect 10 times larger exposure of data than SK during
same live time. In the proton decay analysis with such larger statistics, background rejection
is more important. One of the way to reject more background events is improvement of thering counting. In this analysis, background MC events remained in signal box mainly consistof the events that some rings are not reconstructed, mainly due to the rings close to each other.
2 observed events also have same features. The improvements of ring fitter for such kind ofclose ring events can reject more background events.

131

132

CHAPTER 7. DISCUSSION

Figure 7.1: Schematic view of the HK detector[111].

Chapter 8
Conclusion
Proton decays into three charged leptons is predicted in GUT theory of d = 10 operators.
Following decay modes without any correlation between charged leptons were searched byusing 0.37 Mton·years exposure of data collected by Supker-Kamiokande.
• p → e+ e+ e−• p → µ+ e+ e−• p → µ− e+ e+• p → e + µ+ µ−• p → e − µ+ µ+• p → µ+ µ+ µ−
The observed data were consistent with the atmospheric neutrino background prediction andno clear signal for proton decay was observed. Therefore, the model of these decay modes atthe energy scale below 100 TeV could not be verified in this analysis. The lower partial lifetime
limits at 90% CL were calculated as below.
τ /Bp→e+ e+ e− (SK) > 3.4 × 1034 years
τ /Bp→µ+ e+ e− (SK) > 2.3 × 1034 years
τ /Bp→µ− e+ e+ (SK) > 1.9 × 1034 years
τ /Bp→e+ µ+ µ− (SK) > 9.2 × 1033 years
τ /Bp→e− µ+ µ+ (SK) > 1.1 × 1034 years
τ /Bp→µ+ µ+ µ− (SK) > 1.0 × 1034 years
Comparing with the previous stringent limits by IMB and HPW experiments, each limit waslargely improved by this analysis. The lower limit for p → µ− e+ e+ mode was obtained for the
first time. These are the most stringent limits in the world.

133

Appendix A
Period by Period Comparisons

10000

SK1

EventsEventsData and background MC comparison plots with respect to SK-I to SK-IV are shown in thissection. They also agree well in each period.

8000

SK2

5000

4000

Data

6000

Data
3000

MC
4000

2000

2000

0
0

MC

1000

1

2

3

4

5

6

7

8

9

0
0

10

1

2

3

4

5

6

7

8

9

10

Number of ring

22000

3500

SK3

EventsEventsNumber of ring

3000

SK4

20000
18000
16000

2500

14000

Data
2000

Data

12000

MC

MC

10000

1500

8000
1000

6000
4000

500
0
0

2000
1

2

3

4

5

6

7

8

9

0
0

10

Number of ring

1

2

3

4

5

6

7

8

9

10

Number of ring

Figure A.1: Data and MC comparison for the number of ring with respect to each period. Sameplot for all periods is shown in Fig.6.35 left.

135

APPENDIX A. PERIOD BY PERIOD COMPARISONS

SK1

500

EventsEvents136

3 rings
400

SK2
250

3 rings

200

300

150

Data

Data

MC

200

100

0
0

MC

100

50

1

2

3

4

5

0
0

6

1

2

3

220

SK3

200

3 rings

180

4

5

6

Number of e-like ring

EventsEventsNumber of e-like ring

1200

SK4
3 rings

1000

160
800

140
120

Data

100

Data

600

MC

80

MC
400

60
40

200

20
0
0

1

2

3

4

5

6

Number of e-like ring

0
0

1

2

3

4

5

6

Number of e-like ring

Figure A.2: Data and MC comparison for the number of e-like ring with respect to each period.
Same plot for all periods is shown in Fig.6.35 right.

137

SK1
3 rings

250

EventsEvents300

3 e-like160

SK2
3 rings

140

3 e-like
120

200
100
150

80

Data
MC

Data
MC

60

100

40
50

0
0

20
0.5

1

1.5

2

2.5

3

3.5

4

4.5

0
0

5

0.5

1

1.5

2

2.5

SK3
3 rings120

3 e-like

EventsEventsNumber of decay electron

3 e-like
500

80

400

Data

SK4
3 rings

600

100

60

Data

300

MC

MC

40

200

20

100

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

Figure A.3: Data and MC comparison for the number of decay electron in p → e+ e+ e− modewith respect to each period. Same plot for all periods is shown in Fig.6.36 left.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

200
180

SK1
3 rings160

1 μ-like & 2 e-like

EventsEvents138

SK2
3 rings100

1 μ-like & 2 e-like
80

140
120

60

100

Data

80

MC

Data
MC

40

60
40

20

20
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0
0

5

0.5

1

1.5

2

2.5

70

SK3
3 rings60

1 μ-like & 2 e-like

EventsEventsNumber of decay electron

500

3
3.5
4
4.5
5
Number of decay electron

SK4
3 rings
1 μ-like & 2 e-like

400

50
300

40

Data
30

MC

Data
MC

200

20
100
10
0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

Figure A.4: Data and MC comparison for the number of decay electron in p → µ+ e+ e− (p →µ− e+ e+ ) mode with respect to each period. Same plot for all periods is shown in Fig.6.36 right.

139

2 μ-like & 1 e-like

50

EventsEvents45

SK1
3 rings

60

40

SK2
3 rings35

2 μ-like & 1 e-like

30
40
25

Data

30

Data

20

MC

MC

15

20

10
10

0.5

1

1.5

2

2.5

0
0

3
3.5
4
4.5
5
Number of decay electron

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

140

20

SK3
3 rings

18

2 μ-like & 1 e-like

16

EventsEvents00

5SK4
3 rings120

2 μ-like & 1 e-like
100

14
12

80

10

Data

8

MC

6

Data
60

MC

40

4

20

2
0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

Figure A.5: Data and MC comparison for the number of decay electron in p → e+ µ+ µ−(p → e− µ+ µ+ ) mode with respect to each period. Same plot for all periods is shown in Fig.6.37
left.

140

APPENDIX A. PERIOD BY PERIOD COMPARISONS

14

SK1
3 rings

12

EventsEvents14

3 μ-like
10

SK2
3 rings

12

3 μ-like
10

8

8

Data
6

Data
6

MC

4

4

2

2

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0
0

5

MC

0.5

1

1.5

2

2.5

Number of decay electron

3
3.5
4
4.5
5
Number of decay electron

SK3
3 rings

6

EventsEvents7

3 μ-like30

SK4
3 rings25

3 μ-like

5
20
4

Data
3

MC
10

2

5

1
0
0

Data

15

MC

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

0
0

0.5

1

1.5

2

2.5

3
3.5
4
4.5
5
Number of decay electron

Figure A.6: Data and MC comparison for the number of decay electron in p → µ+ µ+ µ− modewith respect to each period. Same plot for all periods is shown in Fig.6.37 right.

SK1
70

3 rings
1 μ-like & 2 e-like

60

EventsEvents

141

30

SK2
3 rings25

1 μ-like & 2 e-like

1 decay electron

1 decay electron
20

50
40

Data

Data

15

MC

30

MC
10

20
5

10
200

400

SK3

20

3 rings

18

1 μ-like & 2 e-like
16

0
0

600
800
1000
1200
Mass of 2 e-like rings [MeV/c2]

1 decay electron

EventsEvents

0
0

200

400

600
800
1000
1200
Mass of 2 e-like rings [MeV/c2]

SK4

160

3 rings140

1 μ-like & 2 e-like120

1 decay electron

14
100

12

Data

10

Data

80

MC

8

MC
60

6
40
4
20

2
0
0

200

400

600
800
1000
1200
Mass of 2 e-like rings [MeV/c2]

0
0

200

400

600
800
1000
1200
Mass of 2 e-like rings [MeV/c2]

Figure A.7: Data and MC comparison for mass of 2 e-like rings in p → µ+ e+ e− mode withrespect to each period. Same plot for all periods is shown in Fig.6.38.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

20

SK1

35

EventsEvents142

30

3 rings
3 e-like
No decay electron

25

M<600MeV or M>1250MeV
or P>450MeV

SK2

18

3 rings
3 e-like
No decay electron

16

M<600MeV or M>1250MeV
or P>450MeV

14
12

20

10
8

15

Data
10

MC

4

5
0
0

Data

6

MC

2
200

400

600

800

1000

0
0

1200

200

400

600

800

Total mass [MeV/c2]
SK3

EventsEvents16

3 rings
3 e-like
No decay electron

14
12

M<600MeV or M>1250MeV
or P>450MeV

10

1200

SK4

70

3 rings
3 e-like
No decay electron60

M<600MeV or M>1250MeV
or P>450MeV

50
40

8

30

6

Data
4

Data

20

MC

MC

10

2
0
0

1000

Total mass [MeV/c2]

200

400

600

800

1000

1200

Total mass [MeV/c2]

0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

Figure A.8: Data and MC comparison for total mass in validation region of p → e+ e+ e− modewith respect to each period. Same plot for all periods is shown in Fig.6.43 left.

18

SK1

25

EventsEvents143

3 rings
3 e-like
No decay electron

20

M<600MeV or M>1250MeV
or P>450MeV

15

SK2

14

3 rings
3 e-like
No decay electron

12

M<600MeV or M>1250MeV
or P>450MeV

16

10
8

10

5

Data

6

Data

MC

4

MC

2
0
0

100

200

300

400

500

600

700

800

900

0
0

1000

100

200

300

400

500

14

SK3
3 rings
3 e-like
No decay electron

12

M<600MeV or M>1250MeV
or P>450MeV

10
8

700

800

900

1000

SK4

70

3 rings
3 e-like
No decay electron60

M<600MeV or M>1250MeV
or P>450MeV

50
40

6

30

Data

4

Data

20

MC
2
0
0

600

Total momentum [MeV/c]

EventsEventsTotal momentum [MeV/c]

MC

10

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure A.9: Data and MC comparison for total momentum in validation region of p → e+ e+ e−mode with respect to each period. Same plot for all periods is shown in Fig.6.43 right.

144

APPENDIX A. PERIOD BY PERIOD COMPARISONS

9
8
7
6

10

SK1

EventsEvents10

3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV

3 rings
1 μ-like & 2 e-like8

1 decay electron
π0 vetoM<600MeV or M>1250MeV

7or P>450MeV

SK2

9

6

or P>450MeV

5

5

Data

4

4

MC

3

3

Data
2

2

MC

1

1

0
0

0
0

200

400

600

800

1000

1200

200

400

600

Total mass [MeV/c2]
SK3

5

3 rings
1 μ-like & 2 e-like4

1 decay electron
π0 vetoM<600MeV or M>1250MeV

24
22
20
18
16

or P>450MeV

14

3

1000

1200

Total mass [MeV/c2]

EventsEvents

6800

SK4
3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV
or P>450MeV

12
10
8

2

1

Data

6

Data

MC

4

MC

2
0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

Figure A.10: Data and MC comparison for total mass in validation region of p → µ+ e+ e−(p → µ− e+ e+ ) mode with respect to each period. Same plot for all periods is shown in Fig.6.44
left.

145

6
5
4

7

SK1

EventsEvents7

3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV

5or P>450MeV

4

Data

3

6

2

1

1

100

200

300

3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV
or P>450MeV

Data

3

MC

2

0
0

SK2

400

500

600

700

800

900

0
0

1000

MC

100

200

300

400

500

Total momentum [MeV/c]

5

4

18

SK3

EventsEvents6

3 rings
1 μ-like & 2 e-like
1 decay electron
π0 vetoM<600MeV or M>1250MeV

600

700

800

900

1000

Total momentum [MeV/c]
SK4

14

3 rings
1 μ-like & 2 e-like
1 decay electron

12

π0 vetoM<600MeV or M>1250MeV

16or P>450MeV

or P>450MeV

10
3

Data

Data

8

MC

MC
6

2

4
1
2
0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure A.11: Data and MC comparison for total momentum in validation region of p →µ+ e+ e− (p → µ− e+ e+ ) mode with respect to each period. Same plot for all periods is shownin Fig.6.44 right.

146

APPENDIX A. PERIOD BY PERIOD COMPARISONS

8
7
6

6

SK1

EventsEvents9

3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

SK2

5

3 rings
2 μ-like & 1 e-like4

2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

5
3
4
3

2

Data

2

Data
1

MC

MC

1
0
0

200

400

600

800

1000

0
0

1200

200

400

600

2
1.8
1.6
1.4

SK3
3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

14
12
10

1.2

800

1000

1200

Total mass [MeV/c2]

EventsEventsTotal mass [MeV/c2]
SK4
3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

8

1
6

0.8
0.6

4

Data

0.4

MC

200

400

600

800

MC

2

0.2
0
0

Data

1000

1200

Total mass [MeV/c2]

0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

Figure A.12: Data and MC comparison for total mass in validation region of p → e+ µ+ µ−(p → e− µ+ µ+ ) mode with respect to each period. Same plot for all periods is shown in Fig.6.45
left.

147

7
6
5

SK1

EventsEvents8

3 rings
2 μ-like & 1 e-like
2 decay electron

4
3.5
3

M<600MeV or M>1250MeV
or P>450MeV

2.5

4

2

3

1.5

2

1

Data
MC

1
0
0

100

200

300

400

500

600

700

800

900

SK2
3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

Data
MC

0.5
0
0

1000

100

200

300

400

500

2
1.8
1.6
1.4

16

SK3
3 rings
2 μ-like & 1 e-like
2 decay electron

10

1.2

700

800

900

1000

SK4
3 rings
2 μ-like & 1 e-like
2 decay electron
M<600MeV or M>1250MeV
or P>450MeV

8

1
0.8

6

0.6

Data

0.4

Data

4

MC

MC
2

0.2
0
0

14
12

M<600MeV or M>1250MeV
or P>450MeV

600

Total momentum [MeV/c]

EventsEventsTotal momentum [MeV/c]

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure A.13: Data and MC comparison for total momentum in validation region of p →e+ µ+ µ− (p → e− µ+ µ+ ) mode with respect to each period. Same plot for all periods is shownin Fig.6.45 right.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

4
3.5
3
2.5

SK1

EventsEvents148

3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

4
3.5
3
2.5

2

SK2
3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

2

Data
1.5

Data
1.5

MC

1

1

0.5

0.5

0
0

200

400

600

800

1000

MC

0
0

1200

200

400

600

2
1.8
1.6
1.4

SK3
3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

800

1000

1200

Total mass [MeV/c2]

EventsEventsTotal mass [MeV/c2]
12

SK4

10

3 rings
3 μ-like

8

2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

1.2
6

1
0.8

Data

Data

MC

0.6

MC

4

0.4

2

0.2
0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

0
0

200

400

600

800

1000

1200

Total mass [MeV/c2]

Figure A.14: Data and MC comparison for total mass in validation region of p → µ+ µ+ µ−mode with respect to each period. Same plot for all periods is shown in Fig.6.46 left.

149

5

4

SK1

EventsEvents6

3 rings
3 μ-like
2 or 3 decay electron

4
3.5
3

M<600MeV or M>1250MeV
or P>450MeV

2.5

3

SK2
3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

2

Data

Data
1.5

MC

2

MC

1
1

0
0

0.5
100

200

300

400

500

600

700

800

900

0
0

1000

100

200

300

400

500

2
1.8
1.6
1.4

SK3
3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

14
12
10

1.2

600

700

800

900

1000

Total momentum [MeV/c]

EventsEventsTotal momentum [MeV/c]
SK4
3 rings
3 μ-like
2 or 3 decay electron
M<600MeV or M>1250MeV
or P>450MeV

8

1

Data

0.8

Data

6

MC

0.6

MC
4

0.4
2

0.2
0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

0
0

100

200

300

400

500

600

700

800

900

1000

Total momentum [MeV/c]

Figure A.15: Data and MC comparison for total momentum in validation region of p →µ+ µ+ µ− mode with respect to each period. Same plot for all periods is shown in Fig.6.46
right.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

Total momentum [MeV/c]

150

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

Total mass [MeV/c 2]

Figure A.16: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → e+ e+ e− mode after all selections are applied.
Top to bottom plots correspond to SK-I to SK-IV periods. Light blue shows free proton anddark blue shows bound proton in signal plot. Two black squares show the low and high signal
boxes. Same plot for all periods is shown in Fig.6.49.

Total momentum [MeV/c]

151

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

0
0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

Total mass [MeV/c 2]

Figure A.17: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → µ+ e+ e− mode after all selections are applied.
Top to bottom plots correspond to SK-I to SK-IV periods. Light blue shows free proton anddark blue shows bound proton in signal plot. Two black squares show the low and high signal
boxes. Same plot for all periods is shown in Fig.6.50.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

Total momentum [MeV/c]

152

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

500

500

400

400

400

300

300

300

200

200

200

100

100

100

0
0

0
12000

200

400

600

800

1000

200

400

600

800

1000

0
12000

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

200

400

600

800

1000

1200

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

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600

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300

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200

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100

100

0
0

0
12000

200

400

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800

1000

200

400

600

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1000

0
12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

600

500

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100
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12000

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

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900

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600

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0
0

200

400

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0
12000

100
200

400

600

800

1000

0
12000

Total mass [MeV/c 2]

Figure A.18: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → e+ µ+ µ− mode after all selections are applied.
Top to bottom plots correspond to SK-I to SK-IV periods. Light blue shows free proton anddark blue shows bound proton in signal plot. Two black squares show the low and high signal
boxes. Same plot for all periods is shown in Fig.6.51.

Total momentum [MeV/c]

153

1000

1000

1000

900

900

900

800

800

800

700

700

700

600

600

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500

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800

1000

1200

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1200

Total momentum [MeV/c]

Total mass [MeV/c 2]
1000

1000

1000

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600

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600

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0

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Total mass [MeV/c 2]
1000

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700

700

700

600

600

600

500

500

500

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0

200

400

600

800

1000

0
12000

100
200

400

600

800

1000

0
12000

Total mass [MeV/c 2]

Figure A.19: 2 dimensional plots of total mass and momentum for signal MC (left), backgroundMC (center) and measured data (right) in p → µ+ µ+ µ− mode after all selections are applied.
Top to bottom plots correspond to SK-I to SK-IV periods. Light blue shows free proton anddark blue shows bound proton in signal plot. Two black squares show the low and high signal
boxes. Same plot for all periods is shown in Fig.6.52.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

Number of events

154
102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure A.20: Data and background comparison for total mass (left) and momentum (right) in
p → e+ e+ e− mode after all selections are applied. Top to bottom plots correspond to SK-I to
SK-IV periods. Black point shows data, red line shows background, dark blue line shows total
and filled light blue shows free proton of signal. Dotted black line show the signal box. Sameplot for all periods is shown in Fig.6.53.

Number of events

155
102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure A.21: Data and background comparison for total mass (left) and momentum (right) in
p → µ+ e+ e− mode after all selections are applied. Top to bottom plots correspond to SK-I to
SK-IV periods. Black point shows data, red line shows background, dark blue line shows total
and filled light blue shows free proton of signal. Dotted black line show the signal box. Sameplot for all periods is shown in Fig.6.54.

APPENDIX A. PERIOD BY PERIOD COMPARISONS

Number of events

156
102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure A.22: Data and background comparison for total mass (left) and momentum (right) in
p → e+ µ+ µ− mode after all selections are applied. Top to bottom plots correspond to SK-I to
SK-IV periods. Black point shows data, red line shows background, dark blue line shows total
and filled light blue shows free proton of signal. Dotted black line show the signal box. Sameplot for all periods is shown in Fig.6.55.

Number of events

157
102

10
P<250MeV/c

2

10

10

1

1

10-1

10-1

Data
Background10-2

800<M<1050MeV/c2

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

Number of events

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

102

10
P<250MeV/c

10

10

1

1

100

200

300

400

500

2

10-1

700
800
900 1000
Total momentum [MeV/c]

800<M<1050MeV/c2

10-1

Data
Background

10-2

600

10-2

SignalSignal(free proton)

10-3

10-4

0

200

400

600

10-3

800

10-4
1000
1200
0
Total mass [MeV/c2]

100

200

300

400

500

600

700
800
900 1000
Total momentum [MeV/c]

Figure A.23: Data and background comparison for total mass (left) and momentum (right) in
p → µ+ µ+ µ− mode after all selections are applied. Top to bottom plots correspond to SK-I to
SK-IV periods. Black point shows data, red line shows background, dark blue line shows total
and filled light blue shows free proton of signal. Dotted black line show the signal box. Sameplot for all periods is shown in Fig.6.56.

Appendix B
Previous Experiments
B.1 IMB-3
The IMB-3 detector is the water Cherenkov detector located ∼600 m underground in Fairport
Salt Mine. 3.3 kton of water filled in a cube ∼15 m on a side is defined as a FV. Since the neutral
particles generated with the proton decay events travel about 2.5 m in water, an additional 2 mveto region is needed outside the FV. Total detector size is 22.5×17×18 m3 rectangular filledwith 8 kton water. 2,048 20 cm PMTs with wavelength shifters are arranged on the detector
wall. 935 events were collected during 851 days from 1986 to 1991. Schematic view of the IMB3 detector is shown in Fig.B.1. Selection criteria for proton decay into three charged leptons

Figure B.1: Schematic view of the IMB-3 detector[23].

159

160

APPENDIX B. PREVIOUS EXPERIMENTS

basically consist with following requirements.
1. Visible energy cut.
2. Anisotropy cut which basically corresponds to the total momentum cut in this analysis.
3. The number of muon decay signals.
4. The number of tracks found by multiple track fitter.
5. Invariant mass cut which basically corresponds to the total mass cut in this analysis.
6. Human scan for track verification.
Cuts, signal efficiency, expected background events, observed events and calculated limits at
90% CL for each proton decay mode are summarized in Table. B.1.
Table B.1: Cuts, signal efficiency, expected background events, observed events and calculated
limits at 90% CL for each proton decay mode. The numbers in cuts correspond to the eachrequirement described in this section.
SignalExpected
Observed Limit [years]
Mode
Cuts Efficiency [%] Background
Events(90% CL)+ + −p→e e e
12346
71
0.5
0
7.9×1032+ + −p→µ e e
12345
47
1.0
0
5.3×1032
p → e + µ+ µ−
123
47
0.9
1
3.6×1032p → µ+ µ+ µ−
123
60
0.3
0
6.8×1032

B.2 HPW
The HPW detector is also water Cherenkov detector located at a depth of 1,500 m of waterequivalent. 680 Mton water is filled in a cylindrical tank of 5.6 m in radius and 7 m deep. 704
five-inch PMTs are arranged on the tank wall. The inside wall of the tank are covered withmirrors to increase the light collection efficiency. The detector is surrounded by wire chambers
to record the position of charged particles which pass into or go outside the detector. Schematic
view of the HPW detector is shown in Fig.B.2. The entire data set consists of 17.2×106 events
collected in 282 days from 1983 to 1984. The maximum numbers of muon decay signal are
required to be 2 for p → e+ µ+ µ− and p → e− µ+ µ+ , and 3 for p → µ+ µ+ µ− . Cherenkov
equivalent energy ranges are required to be [540,800] MeV for p → e+ µ+ µ− and p → e− µ+ µ+ ,and [320,540] MeV for p → µ+ µ+ µ− . Signal efficiencies are 5.6-7.9%, 6.6-9.4% and 11.8-16.2%
for p → e+ µ+ µ− , p → e− µ+ µ+ , and p → µ+ µ+ µ− modes, respectively. 2 candidates wereobserved, but they were determined to be caused by entering particles. The expected numberof background events from neutrino interaction is estimated to be 0.7±0.2 events.

B.2. HPW

161

Figure B.2: Schematic view of the HPW detector[21].

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