UNIVERSITÀ DEGLI STUDI DI NAPOLI“Federico II”

DOTTORATO DI RICERCA IN
FISICA
Ciclo XXXV
Coordinatore: Prof. Vincenzo Canale
Search for proton decay in Super-Kamiokande andperspectives in the Hyper-Kamiokande experiments
Settore Scientifico Disciplinare FIS-01/FIS-04

Dottorando:
Nicola Fulvio Calabria

Tutore:Prof. Gianfranca De Rosa
ANNI 2019/2022

Contents
1 Physics motivation
1.1 The Standard Model of particle physics . . . . . . . . . . . . .
1.2 Grand Unified Theories . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Minimal SU(5) GUT . . . . . . . . . . . . . . . . . . .
1.2.2 SUSY SU(5) GUT . . . . . . . . . . . . . . . . . . . .
1.2.3 SO(10) GUT . . . . . . . . . . . . . . . . . . . . . . .
1.3 Proton decay searches . . . . . . . . . . . . . . . . . . . . . .

1
1
3
3
4
5
6

2 The Super-Kamiokande detector
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Principles of detection . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Cherenkov effect . . . . . . . . . . . . . . . . . . . . .
2.2.2 Photomultiplier tubes . . . . . . . . . . . . . . . . . .
2.3 Detector overview . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 SK data taking phases . . . . . . . . . . . . . . . . . .
2.3.2 Inner Detector (ID) and Outer Detector (OD) . . . . .
2.3.3 Water and air purification . . . . . . . . . . . . . . . .
2.3.4 Electronics and data acquisition . . . . . . . . . . . . .
2.4 ID calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 SK Coordinate axis system . . . . . . . . . . . . . . . .
2.4.2 Calibration of ID PMTs . . . . . . . . . . . . . . . . .
2.4.3 Water properties measurement . . . . . . . . . . . . . .
2.4.4 PMT and black sheet reflectivity measurement . . . . .

8
8
8
9
10
11
12
13
18
19
22
22
23
28
30

3 SK Data
3.1 Official FC reduction process . . . . . . . . . . . . . . . . . . .
3.1.1 First reduction (FC1) . . . . . . . . . . . . . . . . . . .
3.1.2 Second reduction (FC2) . . . . . . . . . . . . . . . . .
3.1.3 Third reduction (FC3) . . . . . . . . . . . . . . . . . .
3.1.4 Fourth reduction (FC4) . . . . . . . . . . . . . . . . .
3.1.5 Fifth Reduction (FC5) . . . . . . . . . . . . . . . . . .

33
33
33
34
34
38
40

i

3.1.6
3.1.7
3.1.8

Human eye scan of FC events . . . . . . . . . . . . . .
The final FC cut . . . . . . . . . . . . . . . . . . . . .
Generation of the atmospheric neutrino Monte Carlo
FC sample . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.9 Atmospheric neutrino flux . . . . . . . . . . . . . . . .
3.1.10 Neutrino interactions . . . . . . . . . . . . . . . . . . .
Final State Interactions . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Pion FSI . . . . . . . . . . . . . . . . . . . . . . . . . .
Detector simulation . . . . . . . . . . . . . . . . . . . . . . . .
Generation of the Proton Decay (PDK) Monte Carlo sample .

42
42
43
45
46
47
48

4 Reconstruction algorithms
4.1 Introduction: APFit and fiTQun . . . . . . . . . . . . . . . .
4.2 APFit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Vertex fitting . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Ring counting . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Particle Identification (PID) . . . . . . . . . . . . . . .
4.2.4 Momentum determination . . . . . . . . . . . . . . . .
4.2.5 Michel electron search . . . . . . . . . . . . . . . . . .
4.3 fiTQun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 The likelihood function . . . . . . . . . . . . . . . . . .
4.3.2 Predicted charge . . . . . . . . . . . . . . . . . . . . .
4.3.3 Unhit probability . . . . . . . . . . . . . . . . . . . . .
4.3.4 Charge likelihood . . . . . . . . . . . . . . . . . . . . .
4.3.5 Time likelihood . . . . . . . . . . . . . . . . . . . . . .
4.3.6 Vertex pre-fitting . . . . . . . . . . . . . . . . . . . . .
4.3.7 Hit clustering . . . . . . . . . . . . . . . . . . . . . . .
4.3.8 Single-ring fitter . . . . . . . . . . . . . . . . . . . . . .
4.3.9 Multi-ring fitter . . . . . . . . . . . . . . . . . . . . . .
4.4 Performance comparison between APFit and fiTQun . . . . .
4.5 Neutron tagging . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Neutron tagging algorithm . . . . . . . . . . . . . . . .

51
51
52
52
54
56
61
61
61
62
63
68
68
69
69
70
71
74
78
80
80

5 Search for p Ñ νK in SK-IV using fiTQun
5.1 Simulated samples used . . . . . . . . . . . . . . . . . . . . . .
5.2 Proton decay mode . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Decay kinematics . . . . . . . . . . . . . . . . . . . . .
5.2.2 Definition of visible energy . . . . . . . . . . . . . . . .
5.3 Event selections . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Distributions along cut parameters . . . . . . . . . . . . . . .
5.4.1 Number of reconstructed rings distributions . . . . . .

83
83
83
84
85
86
86
87

3.2
3.3
3.4

ii

41
42

5.5

5.6

5.7
5.8

5.4.2 Number of reconstructed e-like rings distributions . . . 87
5.4.3 Tagged Michel electrons distributions . . . . . . . . . . 88
5.4.4 Reconstructed π 0 mass and momentum distributions . 88
5.4.5 Reconstructed π momentum distributions . . . . . . . 89
5.4.6 Reconstructed K mass and momentum distributions . 90
5.4.7 Number of tagged neutrons . . . . . . . . . . . . . . . 90
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.5.1 Remaining background events . . . . . . . . . . . . . . 93
5.5.2 Sideband check . . . . . . . . . . . . . . . . . . . . . . 97
Estimation of systematic error . . . . . . . . . . . . . . . . . . 97
5.6.1 Physics model uncertainties for signal efficiency . . . . 98
5.6.2 Physics model uncertainties for remaining background . 105
5.6.3 Detector uncertainties . . . . . . . . . . . . . . . . . . 107
5.6.4 Hybrid sample . . . . . . . . . . . . . . . . . . . . . . . 110
5.6.5 Summary of systematic errors . . . . . . . . . . . . . . 118
Lifetime limit calculation . . . . . . . . . . . . . . . . . . . . . 119
Conclusions and perspectives . . . . . . . . . . . . . . . . . . . 122

6 Perspectives: Hyper-Kamiokande123
6.1 Detector overview . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.1.1 Water tank . . . . . . . . . . . . . . . . . . . . . . . . 124
6.1.2 Water purification and circulation system . . . . . . . . 125
6.1.3 Inner Detector (ID) . . . . . . . . . . . . . . . . . . . . 127
6.1.4 Outer Detector (OD) . . . . . . . . . . . . . . . . . . . 130
6.1.5 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.1.6 DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.2 HK data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.2.1 Proton decay kinematics . . . . . . . . . . . . . . . . . 133
6.2.2 Proton decay event generation . . . . . . . . . . . . . . 134
6.2.3 Detector simulation . . . . . . . . . . . . . . . . . . . . 136
6.2.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . 137
6.3 First study: fiTQun performance . . . . . . . . . . . . . . . . 138
6.3.1 Event selections . . . . . . . . . . . . . . . . . . . . . . 139
6.3.2 Distributions along cut parameters . . . . . . . . . . . 139
6.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.4 Second study: tuning of fiTQun ring counting for proton decay 143
6.4.1 Manual check of ring correction . . . . . . . . . . . . . 145
6.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

iii

Introduction
The Standard Model of particle physics (SM) is an incredibly successful theory which describes how all known particles interact with each other via electromagnetic, strong and weak forces, leaving gravitational force out. However, several experimental hints pointing at physics beyond the SM havebeen discovered, leading to the development of Grand Unification Theories(GUTs) of which the SM is a subgroup. While protons in the SM are described as stable, this constraint is absent in GUTs: the search for proton
decay is an excellent test to rule out and lead the development of new theories based on experimental lifetime limits or, hopefully, direct observation of
the event. Protons are estimated to have an average lifetime of up to 1033-34
years: proton decays are expected to be extremely rare events requiring alarge amount of protons and a low noise environment to be detected, such as
the Super-Kamiokande and Hyper-Kamiokande water Cherenkov detectors.
In this thesis we search for p Ñ νK proton decay by looking at the kaon
decay products π π 0 in water in Super-Kamiokande. Chapter 1 describes thephysics theory behind the search, Chapter 2 describes the Super-Kamiokande
detector, Chapter 3 describes data reduction and simulation process, Chapter 4 describes reconstruction algorithms and Chapter 5 reports the actual
search in the full span of SK-IV (3244.4 days) real data. We took advantage ofthe π fitter included in the reconstruction algorithm fiTQun to reconstruct
the kaon kinematics and achieve a low-background search. Furthermore, webuilt a control sample to evaluate detector systematic error using the hybid
technique, generating events from real data merged with simulated data. Finally, in Chapter 6 we describe the perspectives in Hyper-Kamiokande andtwo preliminary studies to evaluate fiTQun performance and ring counting
tuning with p Ñ e π 0 search.

iv

Chapter 1
Physics motivation
1.1

The Standard Model of particle physics

The Standard Model (SM) of particle physics is a quantum field theory basedon the gauge symmetry group
SU p3qC  SU p2qL  U p1qY

(1.1)

with three generations of fermions, and a scalar Higgs boson: the SU p3q partdescribes strong interactions carried by eight gauge bosons (G18 known asgluons) while the SU p2qL  U p1qY describes electro-weak interactions mediated by four gauge bosons (W13 and B).
As stated by Noether’s theorem, each of these symmetries has an associated conserved quantity: SU p3qC conserves color charge, SU p2qL conserves
the third component of weak isospin (T3 ) and U p1qY conserves weak hypercharge (Y ).
The matter content is divided in quarks which interact strongly and leptons which don’t. We can further classify the SM fermions by weak isospin,
as doublets and singlets and their hypercharge Y (Table 1.1). The L and R
subscripts stand for left and right handed chirality states respectively.
All of the SM particles enter the theory as massless: the W  and Z 0
bosons and all fermions, with the exception of neutrinos, acquire their mass
via the Higgs mechanism after the spontaneous breaking of the electro-weaksymmetry SU p2qL  U p1qY into the electromagnetic gauge symmetry UEM p1q,
which is associated to the conservation of the electric charge Q. The following
relation is valid:Y  2Q  2T3(1.2)
The SM is a very successful theory: in summer 2012 its missing piece, theHiggs boson, was discovered by the ATLAS [8] and CMS [21] experiments.
1

2

Table 1.1: SM fermion generations by weak isospin T and hypercharge Y .
quarksleptons(T ,Y )
(1/2, 1/3) (0, 4/3) (0, -2/3) (1/2, -1)(0, -2)
I generation

u
d



uR
L



II generationcs

III generation

t
b

νe
e

dR

e
R
L



cR

sR

L

νµ
µ

µ
R
L



tR
L

bR

ντ
τ

τR
L

But there are many unresolved issues that suggest that there is physics
beyond the SM, such as: neutrinos cannot gain mass via the Higgs mechanism but we know fromneutrino oscillations [32] [29] [28] that they are massive; the SM does not include a description of gravity;
 there are no suitable dark matter candidates in the SM; the SM doesn’t provide an explanation to the baryon asymmetry of
the Universe. Understanding the origin of baryon (B) and lepton (L)number violation is crucial to explain the origin of neutrino masses, themechanism for the matter-antimatter asymmetry in the Universe andpossible baryon and lepton number violating processes;
 the SM doesn’t explain the values of the electric charges of quarks andleptons.

Finally, the values of the three running coupling constants in the SM get
closer to each other in a very high energy region ¡ 1014 GeV, suggesting that
there is a larger gauge group which is approximated by the SM group in a
low energy limit. Such models are called Grand Unified Theories (GUTs).

3

1.2

Grand Unified Theories

Grand Unified Theories are extensions of the SM: they predict a single coupling constant for all three interactions at energies  1016 GeV (GUT scale).
GUT models incorporate quarks and leptons into common multiplets: they
predict proton decay as a direct transition between quarks and leptons andconsequently, the unification of interactions and unification of quark and lepton, thus with the possibility of transition from quark to lepton, that violates
baryon and lepton numbers. Proton decay features the violation of baryon
number, thus it is a fundamental test and source of information for GUT theories. Several GUT models based on different gauge symmetries have been
proposed, here we list those relevant for this thesis.

1.2.1

Minimal SU(5) GUT

The minimal choice for unification is SU p5q [34]: it’s the smallest group thatcan contain SU p2q  U p1q as a subgroup. SU p5q has 24 generators, so 12
new gauge bosons (X and Y ) are required in addition to those of the SM.
Each generation of fermions in SU(5) and gauge bosons have 10+5̄ and 24
representations respectively:




0
dc1
 uc
 dc 
 3
 2 
c 
 uc
d
,
10
:
5̄ : 
 2
 3 
u1
 e
d1
νe

uc3
0
uc1
u2
d2

uc2

uc1
0
u3
d3

u1
u2
u3
0
ec

d1
d2 

d3 

ec
0

(1.3)

where 1, 2, 3 are the color charge indexes and c is charge conjugation, and

G11  ?2B30
G12
G13
 G2
G22  ?2B30
G23
1


3
G32
G33  ?2B30
24 :  G1

X2
X3
 X1
Y1
Y2
Y3

?

W3
2

X̄1
X̄2
X̄3

?3B
30
W

Ȳ1
Ȳ2
Ȳ3
W

 W?2

3







(1.4)

?3B

30

where G, W and B are the SM gauge bosons. The charge operator Q is
traceless, since it’s a linear combination of generators which are traceless,then this model can explain electric charge quantization as follows:
5
¸



a 1

Qa  3Qdc

QeQνe  0Ñ

Qd  Qdc  

1
3

(1.5)

4

Figure 1.1: Feynman diagrams of proton decay p Ñ e π 0 via X (on the left)
and Y (on the right) bosons.
The predicted dominant proton decay mode is p Ñ e π 0 (Figure 1.1)
with a partial lifetime τ {B pp Ñ e π 0 q  10311 years, already excluded
by several experiments [26] [27] [31] [30]. This model predicts a value forsin2 pθW q  3{8, where θW is the Weinberg angle but this value is excluded
by experiments as well [45].
Notably, this model also fails to explain neutrino masses since no righthanded neutrino helicity state is contained.

1.2.2

SUSY SU(5) GUTThis model introduces into the SU(5) model a symmetry between fermionsand bosons, known as SUper-SYmmetry (SUSY). This symmetry associates a
super-symmetric partner to each SM particle (Table 1.2). These new particles
are expected to exist in a range of masses between 1 and 10 TeV: none ofthem has been detected so far.
Table 1.2: SM particles and their SUSY partners.
SM particle SpinSUSY partner Spin
q
l
g
W
Z
γ
H

quark
leptongluon
W bosonZ bosonphoton
higgs

1
2
1
2

1
1
1
1
0

q̃
˜l
g̃
W̃
Z̃
γ̃
H̃

squarksleptongluinowino
zino
photinohiggsino

0
0
1
2
1
2
1
2
1
2
1
2

In this model the three running coupling constants can match at around5

Figure 1.2: Inverse of the running coupling constants in SM (left) and Minimal Susy Standard Model (MSSM) (right) as a function of the logarithm of
the energy scale. Taken from [60].
.
2  1016 GeV (Figure 1.2) [24] [44] [39].
In the minimal SUSY SU(5) mode the predicted dominant proton decay mode is p Ñ νK (Figure 1.3), mediated by SUSY particles, with apredicted partial lifetime
2.9  1030 years: this model is excluded bySuper-Kamiokande results [51].

1.2.3

SO(10) GUT

The SO(10) GUT model can explain neutrino masses via the seesaw mechanism, by including a right-handed neutrino [49] [64] [47]. All fermions fromone generation have a representation 16=10+5̄+1.
Several models can be implemented, with different symmetry breaking
patterns and with or without SUSY.
The predicted dominant decay mode in SO(10) GUT is p Ñ e π 0 with alifetime in the range 1032 - 1039 years [53] [4].
SUSY GUTs based on SO(10) [43] [46], together with non-minimal SUSY
SU(5) GUTs [42], are interesting because they predict partial lifetimes forp Ñ νK in the range of 1032 to 1035 years which are still under experimental
investigation.

6

Figure 1.3: Diagram of proton decay p Ñ νK . In the diagram H̃3 stands
for color-triplet higgsino.

1.3

Proton decay searches

Historically, many attempts to find proton decay have been conducted, somebefore that SU(5) were formulated in 1974. The first experimental search
was performed in 1954 by M. Goldhaber [33], by looking for fission productsof Th232 induced by proton decay and set a lower lifetime limit of 1020 years.
Another attempt was made by Reines et al. [33] by looking for particles
with kinetic energy above 100 MeV in 300 liters of liquid scintillator at 200
meters of water equivalent depth. The formulation of GUTs guided and motivated new experimental searches: Learned et al. [38] fixed the first partial
lower lifetime limit for p Ñ e π 0 at 6  1029 years using liquid scintillatorsplaced underground. Figure 1.4 shows proton lifetime predictions according
to several theoretical models. Any proton decay search must involve a large
sample of protons to improve the probability of occurrence of a proton decay
within the time span of the experiment, the experiment must run for a longtime, usually years, and its efficiency for proton decay is crucial since only
a few events are expected even under the most optimistic assumptions. For
these reasons, water Cherenkov detectors are a good choice for proton decay
searches: they are relatively easy and cost-effective to scale, since water ischeap and abundant and the progression Kamiokande, Super-Kamiokande
and Hyper-Kamiokande confirms this, indeed.

7

Figure 1.4: Proton lifetime predictions according to several theoretical models.

Chapter 2
The Super-Kamiokande
detector
2.1

Introduction

Super-Kamiokande (SK) is the largest underground water Cherenkov detector in the world.
Since its operation begun in 1996, the Super-Kamiokande detector has
been successfully improving scientific knowledge in many research fields: itrecorded the first unambiguous evidence of atmospheric neutrino oscillations,
it confirmed the solar neutrino deficit with real-time neutrino imaging of theSun, it measured the solar neutrino energy spectrum above 5 MeV for the
first time, it set the world’s highest lower limits on partial lifetimes for proton
decay modes [22].
The detector is managed and operated by the Super-Kamiokande Collaboration, involving 200 people and about 50 institutes from 11 countriesof the world, including Italy, supported by the Kamioka Observatory of theInstitute of Cosmic Ray Research (ICRR, Tokyo University).

2.2

Principles of detection

Super-Kamiokande is a Cherenkov detector: it’s made of about 11000 photomultiplier tubes which look for Cherenkov light produced in water by charged
particles that meet their momentum threshold.

8CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

9

Figure 2.1: Schematic view of the Cherenkov effect.

2.2.1

Cherenkov effect

An electrically charged particle emits light when it travels in a dielectric
medium with refractive index n with a velocity v  βc greater than thephase velocity of light in that medium vp  c{n. This is known as the
Cherenkov effect (Pavel A. Cherenkov, Nobel 1958) [3] and the light emitted
is known as Cherenkov light.
Cherenkov light is emitted in a cone-shaped flash (Figure 2.1) whose
vertex lies on the particle track and with an opening angle θC with respect
to the particle momentum vector. The Cherenkov angle θC is given bycos θC 

1
nβ

(2.1)

from which we can calculate the threshold βth11¤
1 ùñ βth 
nβ
n

(2.2)

The corresponding threshold on momentum pth for a particle with rest mass
m0 is given by:1
1 b 1pth  cm0 βth γth  cm0 βth a

cm
0
2
n
1  βth
1


1 2
n



(2.3)

In water n is about 1.34 and for a particle with β  1 the Cherenkov angleθC  42 . Table 2.1 shows momentum thresholds for some relevant charged
particles in water.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

10

Table 2.1: Momentum thresholds for various particles in water.
eµπ K 
p
Momentum (MeV/c) 0.57 118 156 560 1052
Finally, the number of Cherenkov photons emitted per unit track lenght
x and per wavelength λ is given by

B2N  2πα 1  1
BxBλ λ2n2 β 2(2.4)

where α is the fine structure constant. A charged particle traveling at β  1
in water is expected to produce 340 photons/cm with wavelenght between
300 nm and 600 nm.

2.2.2

Photomultiplier tubes

Photomultiplier tubes (PMTs) are vacuum tubes with an internal photocathode, exposed to light through a transparent glass window (Figure 2.2). If an
incident photon extracts an electron (photoelectron) from the photocathodedue to photoelectric effect (Albert Einstein, Nobel 1922) [6], it is accelerated
and multiplied by a set of dynodes and finally collected by the anode where
it produces an electric signal which is digitized and stored by the front-end
electronics.

Figure 2.2: Simplified schema of a generic photomultiplier tube.
The output signal amplitude depends linearly from the number of extracted photoelectrons, making the measurement of the produced charge
possible.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

11

Characteristic parameters of PMTs
Quantum efficiency is defined as:
Quantum Efficiency (Q.E.) number of extracted photoelectrons
number of incident photons(2.5)

This parameter takes into account the failure in the conversion of photons
into photoelectrons: incident photons can be blocked by the glass window,
photoelectrons can fail their escape from the photocathode and so on. Quantum efficiency is usually given as a function of photon wavelength.
PMTs produce signals even in a perfectly dark environment, named darknoise. Some electrons in the conduction band of the photocathode may reachits surface with enough energy to escape from it, mimicking the emission of aphotoelectron and contributing to noise: this contribution to noise is known
as thermoionic noise and it’s the major contribution to dark noise.
The signal timing distribution is determined by the differences between
the paths each photoelectron has to walk in order to be multiplied and collected: the delay between the incidence of radiation and the peak of thesignal is called transit time, the full width at half maximum (FWHM) of its
distribution is called transit time spread (TTS).

2.3

Detector overview

The detector is located about 1000 m (2700 m water equivalent) in thedepths of Mt. Ikeno, Kamioka, Japan, in the Mozumi mine, operated by
the Kamioka Mining and Smelting Company. It is accessible from the surface via a 1.8 km long tunnel (Atotsu tunnel) or via a mine railway.
The rock surrounding the detector shields it from cosmic ray muons withenergy less than 1.3 TeV. The muon flux is 6  108 cm2 s1 sr1 on site, fiveorders of magnitude less than outside the mountain at sea level.
The detector is an upright self-supporting cylinder, 39.3 m in diameterand 41.4 m in height, made of welded stainless steel and it contains morethan 50 kton of ultra-pure light water (H2 O). It is separated in two opticallyinsulated sections: the Inner Detector (ID) and the Outer Detector (OD)
(Figure 2.3).
The ID has a diameter of 33.8 m and a height of 36.2 m and it contains
32 kton of water. More than 11000 50-cm PMTs are mounted on its wall,
facing inwards and providing about 40% of photocatode coverage.
The OD contains 1885 20-cm PMTs mounted on the outside of the ID
wall, behind the ID PMTs and facing outwards.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

12

Figure 2.3: The Super-Kamiokande detector.

2.3.1

SK data taking phases

SK data are divided in six phases, each corresponding to a different detector
configuration, including upgrades eventually. The first four phases, from
SK-I to SK-IV, are summarized in Table 2.2.
Table 2.2: SK epochs.
SK-I
SK-II
Observation
Start Apr. 1996 Oct. 2002
End Jul. 2001 Oct. 2005
Live time (days)
1489.2
798.6
Number of PMTs
ID
11146
5182
OD
1885
1885
Photocathode Coverage
40%
19%
Fiber Reinforced Plastics(FRP) & Acrylic CaseNo
Yes
Front-end electronics
ID
ATM
ATM
OD OD QTC OD QTC
Trigger
Hardware Hardware

SK-III
Jun. 2006
Aug. 2008
518.1
11129
1885
40%

SK-IV
Sep. 2008
May 2018
3244.4
11129
1885
40%

Yes
ATM
OD QTC
Hardware

Yes
QBEE
QBEE
Software

In SK-V, some new PMTs that will be used in the Hyper-Kamiokande experiment were installed for testing and the preparation for gadolinium sulfate
in water was started. In SK-VI 13.2 tons of gadolinium sulfate octahydrate(Gd2 (SO4 )*8H2 O) were dissolved in water to improve neutron tagging efficiency [48] while in SK-VII, which is still ongoing (2022), 26 more tons wereCHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

13

dissolved, bringing the concentration of Gd from 0.01% to 0.03%. This analysis has been designed for SK-IV only: we implicitly assume through all thisthesis that the detector configuration is SK-IV.

2.3.2

Inner Detector (ID) and Outer Detector (OD)

The boundary between ID and OD is a stainless steel frame structure madeof supermodules measuring 2.1 m in height, 2.8 m in width and 0.55 m inthickness. Each supermodule hosts 12 ID PMTs in a 3  4 layout on its innerside and 2 OD PMTs on its outer side (Figure 2.4).

Figure 2.4: Schematic view of supermodules mounted inside the tank.
Opaque black polyethylene therephthalate (PET) sheets cover the gaps
between the ID PMTs: they provide optical insulation between the ID andthe OD space and improve event reconstruction by reducing indirect lightinside the tank. A wavelenght shifting plate is attached to each OD PMT
and the OD volume is covered by reflective Tyvek sheets to improve lightcollection and classification efficiency of background events from penetrating
particles like cosmic-ray muons and the products of radioactive decays fromthe detector surroundings.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR(a) Schematic view

14(b) Picture

Figure 2.5: Hamamatsu R3600 photomultiplier tube.

Figure 2.6: Quantum efficiency of an ID PMT as a function of wavelength.
ID PMTsThe ID wall hosts Hamamatsu R3600 50 cm PMTs: their dynode structure
is a Venetian-blind type with 11 stages [7] (Figure 2.5(a)).
They have a bialkali (Sb-K-Cs) photocathode with a peak quantum efficiency of about 21% at 360-400 nm (Figure 2.6).
The collection efficiency for photoelectrons (pe) at the first dynode is over
70%. The transit time spread for a 1 pe signal is 2.2 ns (Figures 2.7 and 2.8).
The average dark noise rate at 0.25 pe threshold used in SK is about 3 kHz.
All figures and results are from [22].
The ID PMTs are fed with high voltage ranging from 1700 to 2000 V,
correspoding to a gain of 107 . The neck of each PMT is coated with asilver reflector to block external light: anyway this doesn’t prevent lightfrom entering through the back of the hemispherical portion of the PMTCHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

15

Figure 2.7: Single photoelectron pulse height distribution. The peak close tozero ADC count is due to PMT dark current.

Figure 2.8: Relative transit time distribution for a typical PMT tested with
410 nm wavelength light at the single photoelectron intensity level.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

16(Figure 2.5(b)).
Fiber Reinforced Plastics (FRP) and Acrylic Cases
During the maintenance phase at the end of SK-I, about 60% of all ID PMTs
happened to be destroyed in an accident. One ID PMT of the bottom sector
imploded during the tank refilling process, producing a shockwave propagating inside the whole tank, causing a chain implosion of ID and OD PMTs,
as well. As a temporary fix, the remaining PMTs were redistributed on the
ID wall in order to ensure a suitable coverage for the incoming SK-II epoch.
Broken OD PMTs were replaced. Before the beginning of SK-III, new ID
PMTs were installed to restore the original coverage but in order to prevent
new implosions all the PMTs were sealed inside a container consisting of twoparts: the back one made of Fiber Reinforced Plastics (FRP), the front oneof transparent acrylic (Figure 2.9).

Figure 2.9: The FRB (left) and transparent acrylic parts (right) combined
together to provide the sealed reinforcement case for the ID PMTs specificallydesigned to prevent accidental implosions.
The front acrylic cover brings two undesired effects: it reduces the amountof light reaching the photocathode and increases the amount of reflections
inside the tank but they are small considering that the trasmission coefficient
for a photon incident at a normal angle on the acrylic surface with 350 nm
of wavelenght is about 96%.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

17

OD PMTsThe OD wall hosts Hamamatsu R1408 20 cm PMTs. Light collection efficiency in the OD is enhanced by wavelenght shifter (WS) plates attached toeach OD PMT [18]. WS plates are square acrylic panels, 60 cm on a side
an 1.3 cm thick, doped with 50 mg L-1 of bis-MSB (bis-Methylstyryl Benzole). The PMT is mounted into a machined hole at the center of the plate(Figure 2.10), optically coupled by direct contact or partially through water.
The WS plates absorb UV light and radiate it back in the blue-green part ofthe spectrum, matching the sensitivity region of PMTs and improving lightcollection by a factor of 1.5.

Figure 2.10: Schema of an OD PMT with its wavelength shifter plate. Taken
from [18].
The plates do not degrade the timing resolution of the OD significantly,
considering that the decay constant of fluor (4 ns) is small relative to thetiming resolution of OD PMTs (13 ns): at single photoelectron illumination
the timing resolution of OD PMT with plate is 15 ns (FWHW) [18]. This
resolution is poor compared with the 2 ns resolution of ID PMTs, however the
OD was designed to be used as a calorimeter and veto counter, rather thana particle tracker, so the extra photons are of importance while the increasein timing resolution is of little consequence. The OD volume is lined with

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

18

a reflective layer made from Type 1073B Tyvek© manufactured by DuPont.
This inexpensive and tough paper-like material improves light collection in
the wavelength range where OD PMTs are most sensitive since it has ameasured light reflectivity of about 90% at 400 nm falling to 80% at about
340 nm [57]. It also minimizes the effect of dead OD PMTs by allowing
multiple Cherenkov light reflections: Cherenkov light is spread over many
PMTs reducing pattern resolution but increasing overall detection efficiency.
Black and white liners that define the inner surface of the OD were speciallymade from a sandwich of Tyvek© facing the OD volume, a central layer ofwhite Low-Density Polyethylene (LDPE) 25 mm thick and a 25 mm layer ofblack LDPE. This liner material provides a reflective surface on the OD side
and a black absorptive surface facing the dead space between the OD and
ID PMTs.
The dead space in between the ID and the OD
The thickness of the supermodules defines a dead space filled with water
surrounded with light-proof lining and where the PMTs are connected todata and power supply cables. The OD PMTs are enclosed in water-proof
housings which effectively block light from the dead space. The ID PMTs,
instead, can detect some light propagating in this space since their backs are
not fully covered.
Failing PMTs
PMTs can fail and this is taken into account during the operation of SK, sincemaintenance and replacement of any PMT is a task that can be performed
only when the tank is empty. A very common reason for PMT failure is
the flooding of the water-tight housing of their electrical connections. A
PMT can also fail as a flasher : internal electrical discharges happen inside it
and produce optical radiation and electrical noise which propagate inside thetank, requiring the PMT to be shut down. The rest of failing PMTs show awide variety of electrical and other problems. Failed PMTs, once identified,
are just left in place waiting for the next maintenance period the be replaced
and their status is registered along with event data.

2.3.3

Water and air purification

Water in the tank must be very transparent to reduce attenuation of Cherenkov
light along its path to the PMTs. The tank is filled with spring water fromthe mine after proper processing. Tank water is continuously purified andCHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

19

circulated at a rate of about 30 tons/hour by a complex system consistingof several filters, a UV sterilizer and two degasifiers which remove particles
larger than 0.2 µm, bacteria, radon and oxygen dissolved in water respectively. Radon is an unwanted source of natural radioactivity, since it’s aserious background event source for neutrinos analysis in the MeV energy
range while oxygen is a bacterial growth promoter. The water temperature
is controlled at around 13.5  C by heat exchangers to reduce PMT dark noiseand suppress bacterial growth. Typical radon concentrations in water coming into the purification system from the Super-Kamiokande tank are2
mBq m-3 and in water output by the system, 0.4  0.2 mBq m-3 . [22] The
rocks in the mine leak radon that can end dissolved into tank water. In
order to reduce radon induced background, the rock of the experimental hallis coated with a polyurethane cover and fresh air with a low radon concentration is continuously pumped from outside the mine into the experimental
area through a processing facility at a rate of approximately 10 m3 min-1 :this flow keeps the experimental area slightly pressurized, minimizing theentry of ambient mine air. This constant radon-reduced air supply is neededby the degasifier section of the water purification plant to work properly as
well. The fresh air intake opens 25 m above the Atotsu tunnel entrance
where radon level concentration was found to remain at 10-30 Bq m3 all year
long. Air is pumped through a dehumidifier, a carbon filter tank, and finallythrough a 1.8 km air duct to the experimental area. All this equipment ishoused inside the Radon Hut, a small building below the fresh air intake.
Radon concentration inside the experimental area is kept at 30-50 Bq m-3 .

2.3.4

Electronics and data acquisition

Each PMT output in SK is connected to an electronic acquisition front-end
channel via a 70 m long RG58 coaxial cable, one channel per PMT. If thenegative signal pulse height fed into this input exceeds the trigger thresholdlevel, the related PMT is tagged as hit. The trigger threshold for a PMT
hit is -1 mV, corresponding to 0.25 photoelectrons. If the number of hit
PMTs exceeds an event threshold, an event trigger is issued. The registered
event consist of times and collected charges of hit PMTs within a given time
window around the trigger timing. There are several event triggers dependingon visible energy: Super Low Energy (SLE) trigger, Low Energy (LE), HighEnergy (HE), Outer Detector (OD) and so on. Since the data acquisition(DAQ) system which was used in SK-I to SK-III was upgraded for SK-IV,
they must be discussed separately.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

20

DAQ in SK-I to SK-III
The front end electronics of the ID PMTs for SK-I to SK-III is the analog
timing module (ATM) (Figure 2.11) [9].

Figure 2.11: Schema of the analog input block of a single ATM channel.
Dashed arrows show the PMT signal, its split signals and accumulated
TAC/QAC signals. Solid arrows show the logic signals which control theprocessing of the analog signals.
One ATM has 12 channels: each channel records the integrated signal
charge and the signal arrival time with a charge-to-analog converter(QAC)
and time-to-analog converter (TAC) respectively. A total number of 960
ATMs were used. For each hit PMT, a 200 ns rectangular pulse with a 15mV pulse height is generated by a discriminator stage. The ATM outputs
the analog sum of all the rectangular pulses (HITSUM) from the PMTs
connected to it. Then an event trigger is issued if the sum of HITSUMs fromall ATMs exceeds a trigger threshold (Table 2.3). Once the event trigger has
been issued, each ATM starts to digitize and record the time when the hit
PMTs signal surpasses the threshold and the charge integrated in a 400 ns
time window around the PMT trigger timing.
Two switching pair of both the QAC and TAC are included in each channel and managed by a channel control chip to avoid missing successive events
as Michel electron, considering that the process time for one channel is 5.5µs. The time window for events is 1.3 µs wide centered around the event
trigger in a [-400 ns, +900 ns] fashion, where 0 ns corresponds to the event

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

21

Table 2.3: Hardware triggers used in SK-I to SK-III.
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
trigger timing. The signal arrived from 400 ns to 900 ns after the hit isneglected in order to ignore a reflection pulse caused by an impedance mismatch between ATMs and PMTs. The ADC/TDC output data have 12 bitof resolution (4096 channels). The ATM has about 450 pC dynamic range
for charge, with a resolution of 0.2 pC and about 1300 ns dynamic range
in timing with a resolution of 0.4 ns. Conversion tables, instead of fitted
linear functions, are used to maintain accuracy of the timing and charge information to convert ADC and TDC counts to pC and ns respectively. The
temperature dependence of ADC and TDC pedestals (offsets) is linear andless than 3 count/ C (0.6 pC/ C) and 2 count/ C (0.8 ns/ C), respectively,in the typical ambient temperature range. Pedestal data are taken every
30 minutes during detector operation and the measured values are used toconvert ADC and TDC counts within each half-hour period to take into account the effect of temperature dependence. Ambient temperature is kept
at about (27 C0.5 C) in the electronics huts. The inaccuracies caused bytemperature dependence are estimated to be less than 0.3 pC and 0.4 ns forthe charge and timing information respectively. Signals from the OD PMTs
are processed similarly by charge-to-time converter modules. When an event
trigger is issued, the time and charge information are converted to digital bymulti-hit time-to-digital converter modules (LeCroy 1877).
DAQ in SK-IV
SK-IV uses a new QTC-Based Electronics with Ethernet (QBEE) [10] frontend electronics, developed to improve dead time and fix the signal reflection
issue, for both ID and OD PMTs. One QBEE module has 24 channels, eachchannel consists of a custom charge-to-time converter (QTC) and a multi-hit
time-to-digital converted (TDC). The timing and charge resolutions of the
QTC are 0.3 ns for 2 pC and about 0.2 pC for below 50 pC, respectively. The
charge dynamic range of the QTC is 0.2-2500 pC and the charge non-linearity
is better than 1% for the overall range. The QTC records all the hits andimmediately integrates the charge from the signals in a 400 ns time window
for each hit and TDC converts the QTC output into the digitized time andCHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

22

charge. The digitized time and charge are recorded only after a software
trigger has been issued. The software trigger is issued when the number of
hit PMTs in a 200 ns sliding time window (N200 ) exceeds a threshold (Table
2.4). In this system the SLE, LE and HE triggers are redefined. In addition
to these triggers, the new Special High Energy (SHE) and After Trigger(AFT) are introduced: the AFT trigger is issued only for an event triggeredby a SHE trigger without an OD trigger and saves an additional 500 µs of
data.
Table 2.4: Software triggers used in SK-IV. The thresholds for the SLE andSHE triggers were lowered in May 2015 and September 2011 respectively.
Trigger type
N200 threshold
Time window (µs)
SLE
34 Ñ 31-0.5  +1.0
LE47
-5  +35
HE50-5  +35
SHE
70 Ñ 31-5  +35LE
47-5  +35
AFT
SHE without OD+35  +535
OD
22 in OD only
-5  +35

2.4

ID calibration

Each PMT in the ID outputs two direct measurements: hit integrate charge
and timing. PMT responses must be calibrated in order to collect reliable
data: the charge and time response of each PMT must be the same for thesame intensitiy and timing of the incident light. A proper calibration isrequired for simulation as well: transport of photons inside the tank must
be characterized, assumptions about detector response like symmetry underrotations around its axis must be validated and so on. A detailed account of
the official SK calibration procedures can be found in [12].

2.4.1

SK Coordinate axis system

The origin of the SK coordinate system is the exact center of the SK tank.
The z axis is parallel to the cylindrical tank axis and points upwards towards
the mountain surface. The x axis is perpendicular to the z axis and points
towards the SK access tunnel that connects the dome experimental area toCHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

23

the Atotsu mine tunnel. The y axis direction is calculated by cross productof the two other axis.

2.4.2

Calibration of ID PMTs

The gain of a PMT is defined as a conversion factor from the number ofphotoelectrons to charge (in units of pC). QE is defined as the product of
the quantum efficienc and collection efficiency of photoelectrons onto the firstdynode of the PMT [12].
Determination of high voltage (HV) setting for each ID PMT
The first step of calibration consists in setting the high voltage (HV) for each
PMT in such a way that the output charge of each PMT is the same for thesame light intensity. The light emission from a scintillator ball installed at
the tank center is used: it is fed via an optical fiber with the light of a Xenon
lamp passing through a UV filter. The calibration source is isotropic by construction: since the SK ID is cylindrical, there is a dependency between the
PMT location and the intensity of calibration light arriving at it. A simple
geometrical correction is not sufficient since there are important effects fromphoton propagation in water and ID reflections, then 420 standard PMTs
were pre-calibrated in a laboratory inside the mine and then mounted in the
ID at specific locations during the maintenance period between SK-II and
SK-III (Figure 2.12).
The reproducibility of the observed charge for all standard PMTs withrespect to their reference values was checked and evaluated as 1.3% RMS.
The standard PMTs provide a reference for other PMTs which share thesame geometrical relationship with the calibration light source.
Relative differences of gain
The gain of each ID PMT must be determined in order to interpret the output
charge in number of photoeletrons. This is done in two steps. The first step isto determine the relative difference among PMTs, using an isotropic diffuserball permanently placed in the middle of the tank as calibration light source.
The ball is fed by a Nitrogen laser (USHO KEC-100, pulse width of 0.4 ns
FWHM at a wavelenght of 337 nm) shifted by a dye to 398 nm with 0.2
ns pulse width, whose output is monitored by a 2-inch PMT (Hamamatsu
H2431-50, rise time 0.7 ns). The output wavelenght is chosen to correspondto the maximum of the convoluted response with Cherenkov spectrum, light

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

24

Figure 2.12: The location of standard PMTs inside the SK inner detector(left). The red points indicate the locations of the standard PMTs. These
PMTs served as references for other PMTs belonging to the same group withsimilar geometrical relationship to the light source (right). Taken from [12].
absorption spectrum and quantum efficiency of the PMTs. The output lightintensity can be adjusted using a set of neutral filters (Figure 2.13).
The first measurement uses high-intensity (IH ) light flashes, such thatevery PMT is reached by a several photons, and records the average observed
charge Qobs piq for each PMT i:
Qobs piq9IH piq  apiq  ϵpiq  Gpiq

(2.6)

Nobs piq9IL piq  apiq  ϵpiq

(2.7)

where apiq is the PMT light acceptance, ϵpiq is the PMT quantum efficiency
and Gpiq is the PMT gain. The second measurement uses low-intensity (IL )flashes, such that only a few PMTs are hit per flash: it’s reasonable to assume
that these are single-photoelectron hits. The number of times Nobs piq that
PMT i records a hit can be expressed as:

Since the location of the light is unchanged the complicating factors in both
expressions cancel out. The gain of each PMT can be derived from:
Gpiq9

Qobs piq
Nobs piq(2.8)

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

25

Figure 2.13: The apparatus used for PMT relative gain and timing calibration. A set of neutral filters is used to adjust the output intensity. Taken
from [12].
Then the relative gain of each ID PMT can be calculated by normalization
with the average gain over all PMTs.
Absolute gain conversion factor
The second step is to determine the average gain over the whole detector.
Then the absolute gain of each ID PMT can be extracted. The calibration
source is a Nickel sphere which emits 9 MeV gamma rays isotropically upon
capturing the neutrons produced by a 252 Cf source placed in its centre. The
sphere is placed at the centre of the ID and produces 0.004 photoelectrons/event at each PMT on average, 99% of hits are from single photoelectrons.
After correcting for the relative gain variation for each PMT, the observed
charge distribution for the single photoelectron hits is obtained by accumulating the hits from all PMTs (Figure 2.14).
From the average of this distribution, the conversion factor between theobserved charge and the number of photoelectrons is determined to be 2.658
pC/photoelectron for SK-IV.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

26

Figure 2.14: Number of hits versus charge produced with the Nickel source.
Taken from [12].
PMT gain variation over time
The gain of ID PMTs changes over time. The PMT gain time variationis measured by using the cosmic-ray muons going through the detector, socalled through-going muons. Since muons deposit in water 2 MeV/cm regardless of their energy, the muon track can be considered as a standard
light source. For SK-IV, the PMT gain time variation is evaluated by taking
the early off timing hit distribution for each PMT in the through-going muon
sample, in order to estimate the PMT absolute gain by looking at the single
photoelectron peak: the PMT gain time variation depends from the PMT
production year (Figure 2.15). This effect is corrected at reduction time.
Relative QE calibration
QE differs from one PMT to another one. The same NiCf source used for theabsolute gain calibration is used for the relative QE calibration, producing
hits whose probability is proportional to QE due to the low intensity of its
light flashes. During this calibration, tank water is convected to ensure its
uniformity over the ID volume. The number of photons reaching each PMT
is estimated by Monte Carlo (MC) simulation. If the simulation models tank

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

27

Figure 2.15: PMT production year dependence of the PMT gain time variation in SK-IV.
water properties, such as photon absorption and scattering and reflections
inside the ID, the remaining difference between simulation and calibration
data is due to the QE of individual PMTs. The ratio between the number ofobserved hits in data to MC is the PMT QE: it’s stored in tables and used
for simulation.
Timing calibration
The time response of each read-out channel must be calibrated for the differences in transit time of PMTs, lenght of coaxial cables and dependency ofelectronic processing time from collected charge (time-walk effect). Timing
calibration is performed using the same source as the one used for relative
gain calibration (Section 2.4.2). Time-of-flight (TOF) is defined for each
ID PMT as the difference between ID PMT and monitor PMT hit times
recorded after the emission of one flash: it takes into account the differencesin light path between different ID PMTs by fixing the monitor PMT timing
as a reference. Response times are corrected for relative timing differencesby subtracting TOF from them. The same measurement is performed at different laser intensities to take into account timing dependency from collectedcharge. The result is plotted for each PMT as a 2D distribution known as
TQ plot (Figure 2.16).
Each TQ distribution is fitted by an asymmetric gaussian in each chargebin, and the peak position of the gaussians is then fitted by a polynomial

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

28

Figure 2.16: Example of the TQ plot for an ID PMT. The vertical and horizontal axes represent to the TOF subtracted hit timing and the hit charge,
respectively. Taken from [12].
as a function of charge, named TQ map, which is used to correct PMT hit
timings for charge dependency.

2.4.3

Water properties measurement

The light attenuation in tank water is modeled by the law:
I pλq  exp pl{Lpλqq(2.9)

where I pλq is the intensity of light at wavelenght λ and l is the distancetraveled in water. Lpλq is the attenuation length in water at wavelenght λand it’s defined as:
Lpλq 

αsym pλq1αasy pλq

αabs pλq(2.10)

is the symmetric scattering amplitude which takes into account the effects ofRayleigh and symmetric Mie scattering, whose angular distribution depends
from the photon scattering angle θ as 1 cos2 pθq. αasy is the asymmetricscattering amplitude which accounts for forward Mie scattering with angular distribution cos θ, forward only. Finally, αabs is the absorption coefficient.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

29

These coefficients are empirical functions of the wavelenght λ which are measured using the laser injector system (Figure 2.17).

Figure 2.17: A schematic view of the laser injector system for measuring thewater property and the reflectivity of the PMTs.
A collimated laser beam is injected into the tank vertically from its top:
the light scattered in water and reflected from the bottom is detected by
the PMTs on the side and top wall of the ID. The TOF-subtracted hit time
distribution, calculated as the PMT hit timing distribution after subtracting
the time required by photons to travel from the beam spot at the bottom toeach PMT, for the PMTs in each detector region, as indicated in Figure 2.17,
is shown in Figure 2.19. The sharp peaks on the right between 1830-1900
ns are due to the photons reflected at the beam spot from the bottom of
the detector, whereas the hits at earlier times are caused by photons which
scattered in water before reaching the bottom. Data before 1830 ns is used
to tune the scattering and absorption coefficients at different wavelengths.
Figure 2.18 shows the scattering and the absorption coefficients as functionsof wavelenght which are tuned using data taken in April 2009, and the redhistograms in Figure 2.19 are the timing distributions for the best-tuned laser
injection simulation.
The measurement leads to an overall attenuation length of  120 m at
400 nm wavelength. The apparatus is permanently deployed in the detector
and constantly takes data during SK operation so that water parameters arecontinuously monitored.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

30

Figure 2.18: Light absorption and scattering coefficients as a function of
wavelength. The data points are the data taken in April 2009 and the red,
blue and magenta lines represent the tuned αabs pλq, αsym pλq and αasy pλq
respectively. The black line represents the sum of the three contributions,which is the inverse of the attenuation length Lpλq.

2.4.4

PMT and black sheet reflectivity measurement

Detector simulation models take into account PMTs reflectivity by ignoringreflections happening in their internal structure and considering interactions
with four layers and their interfaces: tank water, PMT glass, photocathodeand vacuum inside the tube.
Each layer is characterized by a wavelength-dependent refractive index
and, since the photocathode layer absorbs light, a complex refractive index
is assigned to the photocathode.
Using the laser injector data in the time range 1830-1900 ns, which contains the peaks from the light reflected at the tank bottom as shown in Figure
2.19, the complex refractive index of the photocathode is tuned such that thelaser injector simulation best agrees with the measured data in this region.
The tuning is performed at the wavelengths 337, 365, 400 and 420 nm.
The reflectivity of the black sheet is measured in the SK detector using

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

31

Figure 2.19: The TOF-subtracted hit time distributions for the laser injector
data taken at 405 nm. The top plot is for the PMTs on the top wall andthe following five plots correspond to the the five regions on the barrel as
indicated in Figure 2.17. The black circles represent the measured data andthe red histograms are the result from the laser injector simulation after
tuning the water properties and PMT reflectivity to data. The data before
1830 ns and between the two vertical blue lines on the left is used for thewater measurement and the data in the range 1830-1900 ns is used for tuning
the PMT reflectivity.
the apparatus shown in Figure 2.20: a laser injector unit to which a specimenof the black sheet is attached is placed in the centre of the water tank andthe laser reflected from the black sheet is projected horizontally to the sideof the ID. The intensity and the profile of the reflected light is then measured
by the ID for each of the the incident angles 30 , 45 and 60 and for the
wavelengths 377, 400 and 420 nm. The intensity of the injected light directly
projected onto the wall without reflection is also measured for normalizing
the reflected light data and the reflectivity calculated from the measured
result is used in the detector simulation.

CHAPTER 2. THE SUPER-KAMIOKANDE DETECTOR

32

Figure 2.20: A schematic view of the apparatus for black sheet reflectivity
measurement.

Chapter 3
SK Data
In a single day of operation, the SK detector is triggered about 106 times:
only a small part of these events are interesting enough to be saved and stored
for analysis. The process of selecting these events is known as reduction.
Events are classified in three categories: Fully Contained (FC): all the event energy is deposited in the ID;
 Partially Contained (PC): the event originates in the ID but a significant part of its energy is deposited in the OD;
 Up-going Muons (UPMU): high-energy muons produced by neutrino
interactions happening inside the Earth, entering the detector frombelow the horizon.

This analysis is performed using real FC data spanning the full livetimeof SK-IV, i.e. 3244.4 days equivalent to 200 kton*year of exposure.
A detailed reference for all the reduction processes can be found in [52]while further details for the FC process can be found in [35].

3.1

Official FC reduction process

An event is classified as FC if it passes five reduction steps, named from FC1
to FC5. These reduction steps aim at selecting high-energy events.

3.1.1

First reduction (FC1)

The purpose of this stage is to reject low-energy events from radioactive
background and cosmic-ray muons. Events pass this stage if:

33

CHAPTER 3. SK DATA

34

 PE300 ¡ 200 where PE300 is the total number of photoelectrons counted
in all the hit PMTs in a sliding 300 ns wide time window;
 NHITA800 ¤ 55 where NHITA800 is the total number of OD tubes hit
within a (-500 ns, +300 ns) time window around the trigger time (0ns).

The first condition checks if there is significant activity in the ID, equivalent to the activity produced by an electron with a 22 MeV/c momentum
at least, removing most of the background events coming from low-energy
radioactivity, from low-energy Michel electrons 1 and from solar neutrinos.
The second condition removes most cosmic-ray muons and rules out PC and
UPMU events. About 3000 events per day remain after this step.

3.1.2

Second reduction (FC2)

Events must meet these two conditions to pass:
 NHITA800
25 for events with PEtotal
100000 where PEtotal is thetotal number of photoelectrons counted in the ID PMTs;
 PEmax /PE300
0.5 where PEmax is the maximum number of photoelectrons counted in a single ID PMT.

The first condition further reduces the number of low-energy cosmic raymuons by eliminating low-energy events with significant OD activity.
The second criterion reduces the number of electrical noise events causedby an electrical discharge in a PMT: it rejects an event if more than half ofthe total ID charge originates from a single PMT.
The average number of events passing this step is  200 per day.

3.1.3

Third reduction (FC3)This reduction step targets specific event categories: it aims, in particular,
at reducing the remaining cosmic-ray muons, especially those with low OD
activity and the remaining low-energy radioactivity background events.
Through-going muonsThrough-going muons pass through the tank: they may produce low activity
in the OD while leaving a significant energy deposit in the ID. Through-going
muon event candidates are pre-selected by these two conditions:
1

A Michel electron is the electron produced in a muon decay.

CHAPTER 3. SK DATA

35

 over 1000 hit PMTs in the ID; PEmax ¡ 230.

Passing candidates are processed by a dedicated fit algorithm. First, a clustering algorithm searches for the two largest clusters of contiguous hit OD
PMTs and assumes that they correspond to the entrance and exit regions of
the muon candidate. The position of the earliest hit OD PMT is taken as
the entry point while the exit point is calculated as the centroid of the exit
cluster. A Monte Carlo simulation is used to estimate a set of expected hit
timings Ti and a goodness-of-fit value is calculated as:
gfit  °

1
1
i σi2



¸ 1
i

σi2




p
ti  Ti q2
exp 

3σi2

(3.1)

where ti and σi are the hit timing and timing resolution of the ith PMT.
The event is tagged as through-going muon and rejected if the following
two criteria are met:
 gfit ¡ 0.75;
 NHITAin ¡ 10 and NHITAout ¡ 10 where NHITAin and NHITAout are
the number of hit OD PMTs within 8 meters of the fitted entry andexit point respectively.

Hard muons
Critical energy of muons is about 1 TeV in water: above this threshold thealmost constant ionization loss of 2 MeV/c becomes secondary with respect
to other processes like bremsstrahlung and pair production, which produce
a large number of hits in a short time. High-energy ( ¡ 1 TeV) cosmic-ray
muons, known as hard muons, are identified by the following condition:
 NHITA500 ¡ 40

where NHITA500 is the number of hits in the OD in a sliding 500 ns wide
time window and rejected.
Stopping muons
Stopping muons enter the tank from the outside and stop there. Stoppingmuons produce events similar to the ones produced by through-going muons,
except for the absence of an exit cluster in the OD. The muon direction isreconstructed by maximizing the charge seen by the ID PMTs within a cone

CHAPTER 3. SK DATA

36

with a 42 opening angle2 having its vertex at the entry point. A goodnessof-fit gfit value is calculated in a similar way to Equation 3.1. The following
condition is used to identify stopping muons: gfit ¥ 0 and NHITAin ¥ 10.

If this condition is fulfilled the event is rejected.
Cable hole muons
The cables connecting OD and ID PMTs inside the tank to front-end electronics in the outside huts pass through twelve holes in the top section of the
OD. These holes interrupt the OD coverage: down-going muons may passthrough them and reach the ID without being detected in the OD, producing
an event which would be erroneously categorized as FC. In order to mitigate
this effect, four of the twelve holes have plastic scintillator veto countersinstalled beneath their openings (Figure 3.1).
An event is identified as cable muon event and rejected if:
 a cable veto counter is hit; the entry point or exit point is within 4 metres of the hit veto counter; PEtotal ¡ 4000;
 the entry point is within 2.5 meters of the nearest cable holeand if the stopping muon fitter applied to the event returns results matchingwith these conditions:
 goodness-of-fit for stopping muon ¥ 0.4;
 the reconstructed zenith angle θ of the muon is more vertical thanhorizontal: cos θ 0.6.

Flasher PMTs
A flasher is an event due to a repetitive electric discharge in the dynode stageof a PMT that may be detected by nearby PMTs as well. Such an event canbe recognized from its abnormally broad hit timing distribution (Figure 3.2).
In order to reduce flasher events, those ones presenting too much ID activity
well after the trigger time are rejected. This procedure translates into thefollowing condition:
This choice corresponds to the Cherenkov angle for a β  1 particle in water (n =1.34) as shown in Section 2.2.1.
2

CHAPTER 3. SK DATA

37

Figure 3.1: A schematic view of one of the cable holes and its veto counter.
Taken from [35].
 NMIN100 ¥ 20.

Where NMIN100 is the number of ID PMTs hit in a 100 ns wide time window
sliding in a range between 1200 ns and 1700 ns after the trigger time.
If an event meets this condition is rejected.
Coincidence muons
If a cosmic-ray muon enters the detector immediately after a low-energy
event has issued a trigger, its activity is recorded together as well. Theenergy deposited by the muon may let the low-energy event pass the lowenergy cuts, conversely it may pass the high-energy cuts due to the delayedmuon OD activity with respect to the trigger time.
Events matching this condition are identified as coincidence muons andrejected: NHITA ¥ 20

CHAPTER 3. SK DATA

38

Figure 3.2: Typical distributions of NMIN100 for a flasher (top) and an atmospheric neutrino MC event (bottom). The arrows indicate the region thatis removed with the third reduction flasher cut. Taken from [35].
where NHITAoff is the number of OD hits between 300 ns and 800 ns after
the trigger time.
Low energy events
Finally, a cut to reduce remaining low-energy events is applied. An event isrejected if:
 NHIT50

50 (25 for SK-II)

where NHIT50 is the number of hit ID PMTs within a sliding 50 ns wide
time window. Hit times are corrected using a time-of-flight (TOF) fitterthat assumes that all the photons detected come from a single vertex. This
energy threshold corresponds to visible energy of 9 MeV. After this reduction
 45 per day remain.

3.1.4

Fourth reduction (FC4)This step targets the remaining flasher events by detecting their typicalhighly-correlated charge pattern that spans several event timing windows.
A typical flasher event is shown in Figure 3.3.

CHAPTER 3. SK DATA

39

Figure 3.3: Typical flasher event display. A PMT in the middle of the ID
barrel has flashed light in consequence of an electric discharge in its dynodestage. The PMT color indicates the hit timing (red: early hit, blue: latehit). Taken from [56].
.
The following algorithm is defined to check if two events (A and B) showcorrelated charge patterns in the ID: the ID tank wall is divided into 1450 roughly equal 4 m2 partitions;
 the correlation r between event A and event B is calculated as:

r

A
B
B
1 ¸ pQAi  xQ yq  pQi  xQ yq
N i
σA  σB(3.2)

where N is the number of partitions, i refers to the ith partition, Qi is
the charge observed in the ith partition and xQy is the average charge
per partition observed in an event with RMS σ;CHAPTER 3. SK DATA

40

 the distance dmax between the PMTs with the maximum charge in each
event is calculated. For dmax 0.75 m, the correlation r is incremented:

rr

0.15

(3.3)

 two events are defined as a match if their correlation exceeds a threshold
rth :

PEA
PEB
tot
tot
rth  0.168  log10
0.130
(3.4)
2

where PEtot is the total number of photoelectrons detected in an event.
This threshold has been calculated by comparing correlation distributions of atmospheric neutrino Monte Carlo simulated events and handpicked real flasher events.
The correlation value r is calculated for 10000 events near the target eventand matching events are rejected:  18 events per day remain after this step.

3.1.5

Fifth Reduction (FC5)

The fifth reduction targets three specific categories of remaining background:invisible muons, coincidence muons and long-tail flashers.
Invisible muons
Muons below Cherenkov threshold can decay inside the tank: they are invisible but their Michel electron can be detected. If some OD activity isdetected, these events can be rejected as cosmic-ray muons. Events thatmeet these two conditions are rejected:
 PEtotal

1000;

 if Distclust 500 cm then NHITACearlyelse NHITACearly ¥ 5

NHITAC500 ¥ 10

where PEtotal is the total number of photoelectrons detected in the ID, NHITAC is the number of hit PMTs in the OD largest cluster: NHITACearly isdefined in a sliding 200 ns wide time window from -9000 ns to -200 ns prior
to the primary trigger time, NHITAC500 counts the hits in the time interval corresponding to -200 ns to 300 ns with respect to the trigger time andDistclust is the distance between the centroids of these clusters. These cuts
correspond to the maximum photoelectron yield of a Michel electron with asignificant early OD activity.

CHAPTER 3. SK DATA

41

Coincidence muons
Remaining coincidence muons are targeted by the following cut: it searches
for off-trigger OD activity in a longer time span than in the FC3 reduction
step.
An event meeting the following criteria is rejected:
 PEtotal

300;

 NHITAlate ¥ 20

where NHITAlate is the number of hit PMTs in the OD in a sliding 200 ns
wide time window from 300 ns to 2100 ns with respect to the trigger time.
Long-tail flashers
This cut targets the remaining flasher events using a TOF-fitter similar tothe one described in Section 3.1.3, using its evaluated goodness-of-fit as a cut
parameter. An event is rejected if the following criteria are met:
 NMIN100 ¥ 6 with TOF goodness-of-fit

0.4;

or
 MIN100

6 with TOF goodness-of-fit

0.3

where NMIN100 has the same definition as in Section 3.1.3.
Calibration related events cut
Some LASER or Xenon lamp calibration events may leak into the data set
due to some errors in data management. They can be removed by checking
if at least one of the dedicated reference PMTs is reported as hit. After thisstep  16 events per day remain.

3.1.6

Human eye scan of FC events

In addition to the automated FC reduction, a real time check in the data
quality is conducted by human operators by eye for the events after the third
reduction. The scanners check the hit charge and timing distribution andthe hit pattern for both the ID and OD using an event display tool, in orderto judge if the reduction algorithm works properly or not and notify any
unusual thing.

CHAPTER 3. SK DATA

3.1.7

42

The final FC cut

The final FC sample is defined by these three last cuts, that can be applied
only after a reconstruction algorithm has processed the event: dwall ¥ 200 cm
dwall is the distance of the reconstructed vertex from the nearest ID
wall. This distance defines the Fiducial Volume (FV), containing 22.5
kton of water: keeping only the events inside this subregion of the ID
ensures that the background from outside the tank is further reduced
and that vertexes are well reconstructed;
 NHITAC 16
NHITAC is the number of hits in the OD. Such a low activity in the
OD ensures that the event is, indeed, fully contained inside the ID;
 Evis ¥ 30 MeV
Evis is the visible energy i.e. the total energy of all reconstructed rings
assuming that they are all produced by electrons.

These cuts are called the FCFV cuts: after these cuts  8 events per day
remain.

3.1.8

Generation of the atmospheric neutrino Monte
Carlo FC sample

This analysis uses 500 years of Monte Carlo simulated atmospheric neutrino
interactions in SK-IV to study the expected background. The sample used
underwent the same reduction process as real data.

3.1.9

Atmospheric neutrino flux

Atmospheric neutrinos are produced in the interactions between primarycosmic rays, mainly protons and helium nuclei coming from outside the Solar
System, or from solar flares, and atmospheric nuclei.
Cosmic rays with energies lower than 10 GeV in the laboratory frame aremodulated by the solar wind, the expanded magnetized plasma generated
by the Sun which decelerates and prevents part of the incoming charged
particles from entering the inner Solar System: their flux shows a significant
anticorrelation with solar activity, which follows an 11-year periodic cycle.

CHAPTER 3. SK DATA

43

Cosmic rays in the GeV energy range are modulated by the geomagnetic
field, which must be penetrated by them to reach the top layer of the atmosphere: this makes the composition of cosmic rays reaching the Earth surface
dependent on both location and time.
Cosmic rays Acr produce kaons and pions in their hadronic interactions
with atmospheric nuclei Aatm .
Acr

Aatm Ñ π  , K  , K 0 , . . .

(3.5)

At low energies (¤ 1 GeV in the laboratory frame) K {π ratio is less than
7% [14], so the following decays are the dominating sources of neutrinos:Ñµ ν µµ Ñ e νe ν̄µπ  Ñµ ν̄µµ Ñ e ν̄e νµ
π

(3.6)
(3.7)

By neglecting the contribution from kaon decays and assuming that all of
the muons decay in flight before reaching the Earth surface, that is true forenergies ¤ 5 GeV, and counting the number of neutrinos and antineutrinos
produced for both flavors, this naive estimate can be made:

pνµ
pνe

ν̄µ q
2
ν̄e q

(3.8)

The observation of a lower-than-expected ratio for fluxes coming frombelow the horizon in Super-Kamiokande led to the experimental discoveryof neutrino oscillations [61]: νµ may oscillate to ντ while passing throughthe Earth, causing a reduction in the νµ measured flux from those zenith
angles. A detailed theoretical explanation of the oscillation phenomenon canbe found in [2].
The neutrino flux at Super-Kamiokande location has been precisely modelled and calculated by M. Honda et al.: this model is known as the Honda
flux [15] [16]. The Monte Carlo generator uses the Honda flux without considering neutrino oscillations: it provides an oscillation probability weight foreach generated event allowing to apply it later during the analysis.

3.1.10

Neutrino interactions

Neutrino interactions inside the tank are simulated by the NEUT software[36]. The software simulates neutrino interactions with Oxygen and Hydrogen nuclei in water: the cross section with electrons is three orders of magnitude smaller than the cross section with nuclei, so neutrino interactions withelectrons are neglected.

CHAPTER 3. SK DATA

44

Neutrinos can interact weakly with nuclei via the exchange of a charged W
boson or a neutral Z boson: the former interactions are known as Charged
Currents (CC) since they involve an exchange of electric charge, conversely
the latter ones are known as Neutral Currents (NC).
The charged lepton produced in a neutrino CC interaction retains theneutrino flavor, making it identifiable by SK, while in NC interactions theflavor of the interacting neutrino is unknown. This is the reason why the CC
interactions contribute to the signal for the analysis of neutrino oscillations
while the NC interactions contribute to the background.
In proton decay search analysis both CC and NC interactions contributeto the background.
Finally, even if atmospheric neutrinos are generated only in the e and µ
flavor, there is some ντ flux reaching SK due to neutrino oscillations that caninteract producing τ leptons via CC interactions: the decay of τ leptons iscomplex and it’s simulated by the software TAUOLA [23].
NEUT simulates the following neutrino interactions:
 elastic and quasi elastic scattering; resonant production;
 deep inelastic scattering.

Elastic and Quasi Elastic Scattering
In NC elastic scattering, a neutrino just scatters off a nucleon without producing any new particles. On the other hand, a neutrino converts into its
corresponding charged lepton in CC Quasi-Elastic (CCQE) scattering:νx

N Ñ lxN1(3.9)

where l is a lepton, charged in CCs or a neutrino in NCs, of the same flavor
as the interacting neutrino, N is the initial state of the target nucleon andN 1 is its final state.
CCQEs may happen with nucleons other than the target affecting the final
state [56]; this is known as Meson Exchange Current (MEC) interaction:
νxN

N 1 Ñ lx

N2

N3

(3.10)

Resonant production
Production of a single meson in a neutrino interaction is modeled in NEUT
primarily as a resonance production, in which a baryon resonance excitation

CHAPTER 3. SK DATA

45

produces a single meson in the final state as in:νxN Ñ lx N N Ñ N1m(3.11)

where N and N 1 are the nucleon in the initial and the final state, N  is theintermediate baryon resonance and m is a meson, such as π, K and η, or aphoton. Such interaction is considered in NEUT for W 2 GeV/c2 , where
W is the invariant mass of the hadronic final state.
Pions can also be produced via coherent production: a neutrino interacts
with the whole Oxygen nucleus and produces a pion as follows:νx16

O Ñ lx16Oπ(3.12)

Deep Inelastic Scattering (DIS)In DIS interactions, the incident neutrino interacts with a constituent quarkin the target nucleon producing one or more hadrons:νxN Ñ lxN1

hadrons(3.13)In NEUT the process is considered for the cases with hadronic invariant massW ¡ 1.3 GeV/c2 and becomes the dominant process for W ¡ 10 GeV/c2 .
For W 2 GeV/c2 NEUT considers only pions as produced hadrons, for W¡ 2 GeV/c2 NEUT considers the production of heavier mesons (K and η),as well, and simulates them using PYTHIA/JETSET [55].

3.2

Final State Interactions

The products of a simulated neutrino interaction are propagated throughthe nuclear matter they encounter along their path. Hadrons produced inneutrino interactions are known to interact with the nuclear medium: thismeans that the particles observed in the final state may differ from the particles produced in the primary interaction. These interactions between the
produced hadrons and the nuclear medium are known as Final State Interactions (FSIs): since their products are revealed in the detector, indeed, it’svery important to simulate them accurately. NEUT simulates the emissions
due to de-excitation of nuclei left in an excited state after an interaction has
happened as well.
Mesons and nucleons FSIs are simulated by NEUT using cascade models
tuned with data from several scattering experiments [62].

CHAPTER 3. SK DATA

3.2.1

46

Pion FSI

Pions are the most observed hadrons in SK. Pion FSI are simulated by the
NEUT pion cascade model [5]: pions are propagated classically in finite steps
through a nuclear medium described by the Woods-Saxon nuclear density
profile [63], starting from the generation point in the simulated direction.
The nuclear medium density ρ, according to the Woods-Saxon model,
is [56]:
ρp0q

(3.14)
ρprq 
1 exp rb awhere r is the distance from the nuclear center, a = 2.69 fm is the radius3 of
16
O, b = 0.41 fm is the nuclear surface thickness4 and ρp0q  0.48 m3π wheremπ is the invariant mass of charged pions.
Because of the Pauli exclusion principle, the nucleon final state shouldhave a larger momentum than the Fermi surface momentum pF prq:
pF 



3 2
π ρprq2

1
3(3.15)

Both distributions are shown in Figure 3.4.
At each step the pion position is increased by a unit length: NEUT
determines if any interaction happens for each step, according to interaction
probabilities known from models and data from other experiments. The
following interactions are possible:
 quasi elastic scattering in which a single pion of the same charge remains after the interaction;
 charge exchange in which a charged pion is converted into a π 0 andvice-versa;
 pion absorption in which no pions remain after the interaction;
 pion production in which multiple pions are produced.

If no interaction happens, the particle is moved again. This process proceeds
until an interaction occurs or the pion is moved outside the nucleus.
3

The radius of a nucleus is defined as the distance from the nuclear center where nuclear
density is 50% of the maximum value.
4
The nuclear surface thickness is defined as the thickness of the region of a nucleus
where the nuclear density falls from 90% to 10% of its maximum value.

CHAPTER 3. SK DATA

47

Figure 3.4: Nuclear density according to the Woods-Saxon model (in black)and the Fermi surface momentum (in red) as a function of the radial distancefrom the center of 16 O. Taken from [56].
.

3.3

Detector simulation

The information about the particles exiting the nucleus after a neutrino interaction simulated by NEUT is formatted in a vector and fed to a GEANT3based [1] detector simulator, named SKDETSIM.
SKDETSIM simulates particle interactions with water, particle decays
and Cherenkov photon production. The hadronic interactions of particles
are simulated via GCALOR [65], except for pions below 500 MeV/c of momentum whose interactions are simulated via NEUT cascade model, as in
Section 3.2.1.
The Cherenkov photons produced by the particles are propagated in thedetector using a custom code which models the scattering, both Rayleighand Mie components, and absorption in water.
Rayleigh scattering dominates for light wavelenghts λ
450 nm, it’ssymmetrical in the forward and backward directions with a characteristicλ4 dependence and it’s caused by small particles of radius r ! λ. Mie
scattering dominates for λ ¡ 450 nm, it’s asymmetrical with a sharp peak in
the forward direction and it’s caused by particles of radius r " λ [56]. Water
properties tuning in SKDETSIM is based on the results of the calibration
procedures explained in Section 2.4.3.
The calibration results from the procedures explained in Section 2.4.4
and Section 2.4.2 are used to tune PMT and black sheet reflectivity andCHAPTER 3. SK DATA

48

individual PMTs responses in both charge and time, respectively.
The output of SKDETSIM has almost the same structure as observed
data: it can be processed and analyzed in the same way but it comes withsome additional structures containing the Monte Carlo truth, which is a listof the particles involved in the simulated event, their kinematic parameters,
the position of their production and interaction vertexes and the kind ofinteractions they are subject to.

3.4

Generation of the Proton Decay (PDK)
Monte Carlo sample

The sample used in this thesis contains a simulation of the following proton
decay mode:pÑν K(3.16)The simulated K+ decay modes are:

Ñµ
K Ñπ
K

ν

(3.17)

π0(3.18)

Both are contained in the sample: mode 3.18 is the subject of the analysis
performed in this thesis.
Only protons from the Hydrogen nuclei, or free protons, and Oxygen
nuclei, or bound protons, from the water molecules (H2 O) inside the tank areconsidered: this means that ten protons per water molecule are available fordecay. The probability of decay is assumed to be the same for any proton,bound or free.
In the decay of a free proton, the ν and the K+ are emitted back-to-backwith a monochromatic momentum of 339 MeV/c in the laboratory frame [40].
Fermi momentum, correlation with other nucleons, nuclear binding energy
and kaon-nucleon interactions are taken into account for bound protons.
The nucleon momentum in 16 O is simulated according to the results ofthe electron-12 C scattering described in [13]. The binding energy is simulated
as a Gaussian distribution and this effect is considered by subtracting thebinding energy from the proton mass in the rest frame [56]. The mean andσ of the binding energy distributions are respectively 39.0 MeV/c and 10.2
MeV/c for the s-state and, respectively, 15.5 MeV/c and 3.82 MeV/c forthe p-state. Both the momentum and the invariant mass distributions for
simulated protons are shown in Figure 3.5.
The contribution from correlated decay protons is taken into account:when the wave function of a decaying proton is overlapped with the wave

CHAPTER 3. SK DATA

49

Figure 3.5: Distributions for the pÑ ν K+ decay simulation. The upper
figure shows the simulated proton momentum and the lower figure shows
the simulated proton invariant mass distributions in 16 O. The cyan, black,green, red and purple histograms correspond to free, bound, s-state, p-stateand correlated decay protons, respectively. Taken from [56].
.
function of a spectator nucleon, the momentum of the decaying proton ischanged. The predicted probability of correlated decay for a proton in 16 O
is 10% [56].
The position of a decay nucleon inside Oxygen is simulated according to
the Woods-Saxon nuclear density model, as explained in Section 3.2.1.
All the simulations described until this point are performed via a custom

CHAPTER 3. SK DATA

50

software. After a proton decay event has been simulated, NEUT is used topropagate its products inside the nuclear medium and calculate FSIs as in
Section 3.2.1. Finally SKDETSIM is used as in Section 3.3 to perform thesimulation of the detector response.

Chapter 4
Reconstruction algorithms
Reconstruction algorithms extract information about visible particles in theevents for physical analysis. Typical reconstructed information is the vertex of interaction, the number of Cherenkov rings produced in the ID, thetype and momentum of visible particles. Two reconstruction algorithms areavailable in SK: APFit and fiTQun. In this analysis fiTQun is used to selectsignal events, aiming at understanding its performance with multi-ring events
containing a charged pion ring, while APFit is used as a term of comparisonand for validation since it’s well known and reliable. In addition to these
two algorithms, a neutron tagging algorithm (Neut-Fit) is used to count the
number of neutrons emitted in a primary FC event.

4.1

Introduction: APFit and fiTQun

APFit is a sequential fitter that uses the time and charge information of hit
PMTs. It was used for the discovery of neutrino oscillation and in K2K and
T2K experiments. The growth of available computing power has led to thedevelopment of a different and more complex approach to event reconstruction: fiTQun is a maximum likelihood fitter that uses time and charge information of both hit and unhit PMTs. It was developed for the MiniBooNE
experiment, a Cherenkov detector at Fermilab, whose main motivation is
the study of neutrino oscillations, employing a spherical shaped container
lined with 1280 PMTs and filled with a mix of mineral oils, where charged
particles above Cherenkov threshold in oil are expected to produce photonrings as in SK. FiTQun was later adapted to SK for the T2K experiment,
finally it’s being used for SK analysis, including the search for proton decay.
Generally speaking, fiTQun shows a better reconstruction performance than
APFit [56] at the cost of a longer processing time per event. fiTQun can han51

CHAPTER 4. RECONSTRUCTION ALGORITHMS

52

dle up to six Cherenkov rings per event, each with its reconstructed vertex,
and three Particle Identification (PID) hypotheses: electron/gamma, muonand charged pion. APfit can handle up to five rings with a single vertex per
event and two PID hypotheses: electron/gamma and muon.

4.2

APFit

APFit performs these steps sequentially to reconstruct an event: vertex fitting; ring counting; particle identification;
 momentum determination;
 Michel electron search.

A complete reference on APFit can be found in [54].

4.2.1

Vertex fitting

The vertex fitting process consists of three steps:
 point-fit; search for the edge of the most energetic Chernekov ring; Time-to-Digital Converter TDC-fit.

Point-fit
The point-fit assumes that Cherenkov light is emitted from a single vertex in water. For hypothesis x of possible vertex, the time-of-flight (TOF)
subtracted hit timing distribution is calculated: the vertexes that produce
a narrower distribution are those closer to the true vertex as well. Hence,the point-fit vertex can be obtained by maximizing the following goodness
function:
1 ¸
ptipxq  t0q2
goodness 
exp 
(4.1)
N i
2p1.5σ q2
where N is the number of hit PMTs, ti is the TOF subtracted timing of thei-th PMT, t0 is the interaction time maximizing the goodness, σ is the PMT
timing resolution of 2.5 ns. The factor 1.5 at the denominator is chosen to
optimize the fitting performance.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

53

Ring edge searchThis step aims at the determination of the edge and direction of the mostenergetic Cherenkov ring. Using the point-fit vertex and assuming a test
direction, starting from the overall direction which is estimated by taking
a charge-weighted sum of each ID PMT, the observed charge distribution
PE(θ) in dependence of the opening angle θ can be calculated, as shownin Figure 4.1. The angle θedge corresponding to the ring edge satisfies thefollowing conditions:1. θedge ¡ θpeak
2.

 2

pq

d PE θ
d2 θθ θedge0where θpeak is the value of the angle corresponding to the maximum of PE(θ).

Figure 4.1: Observed charge distribution in dependence of the opening angle
for a test direction as seen from the point-fit vertex (top) and its second
derivative (bottom). Taken from [56].
.
By maximizing the following estimator Qpθedge q, the edge and the direc-

CHAPTER 4. RECONSTRUCTION ALGORITHMS

54

tion of the most energetic Cherenkov ring are determined:
Qpθedge q ³ θedgePEpθqdθ0sin θedge

dPEpθqdθθθedge



2

exp

2
 pθedge2σ2θexpq
θ(4.2)
where θexp and σθ are the expected Cherenkov angle using the total charge
inside the cone and its resolution, respectively. The charge in PE(θ) is corrected for attenuation and PMT angular acceptance.
TDC-fitTDC-fit refines the vertex position estimate: the track length of the charged
particle and the scattered Cherenkov photons are taken into account. The
initial track length, assuming that 3 MeV/cm are deposited along it, is estimated from the total charge. The timing residual for PMTs inside the coneis calculated assuming the Cherenkov light is emitted along the track withthe same angle. For PMTs outside the cone, the timing residual is calculated
assuming that Cherenkov light is emitted at the vertex and considering thescattering parameters.
ti  t0i 

1⃗ i  O|⃗  n  |P⃗i  X⃗ i | PMTs inside the ring

|X
c
c
(4.3)
n
⃗
PMTs outside the ringti  t0i   |P⃗i  O|c
⃗ is the vertex position, X⃗ i is the position at which Cherenkov photons
where Oare emitted toward the ith PMT, n is the refractive index of water, P⃗i is the
position and t0i is the hit timing of the ith PMT. The final vertex of the mostenergetic ring is determined by maximizing an estimator.

4.2.2

Ring counting

This step aims at searching additional Cherenkov rings: candidate rings arefound by a shape extraction algorithm known as the Hough transform, shownin Figure 4.2.
For each hit PMT a fake ring is projected onto the ID wall with a 42
opening angle calculated from the already fitted vertex. The intersectionof these fake rings is the direction of a candidate Cherenkov ring: a loglikelihood method is used to accept or reject any candidate additional ring.
The likelihood function is defined as:
LN 

¸
i



log P



qiobs ,

N
¸



n 1

exp
αn  qi,n(4.4)

CHAPTER 4. RECONSTRUCTION ALGORITHMS

55

Figure 4.2: A schematic of the ring-finding procedure.
.
where i runs over all the indexes of the hit PMTs inside the N Cherenkov
exp
is the expectedrings, qiobs is the observed charge in the ith PMT, αn  qi,ncharge in the ith PMT from the nth ring. The αn factors are allowed to varyin order to maximize the likelihood with a minimum momentum constraint,
applied to account for the charge produced in the hit PMTs. P is a gaussian
probability density function:
P


exp

qiobs , qi

 ? 1 2 exp
2πσ



exp
obs
 qi 2σ2qi



(4.5)

The hypothesis of N+1 rings is tested against the hypothesis of N rings:
if no candidates satisfy LN 1 ¥ LN the number of rings is finalized at N andthe search stops. Otherwise, further processing is performed to choose thebest-fit candidate. More details can be found in [59].
Figure 4.3 shows the ring counting likelihood distribution L2  L1 , calculated for the FCFV sub-GeV (visible energy 1.33 GeV) sample of the data
and the atmospheric neutrino MC for the L2 hypothesis. APFit repeats thesearch for additional rings up to a maximum of five rings per event.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

56

Figure 4.3: Ring counting likelihood distribution L2  L1 for the FCFV subGeV sample of the data (black points) and the atmospheric neutrino MC(stacked histograms, normalized to data livetime) in SK-IV. Events with noMichel electrons tagged are selected. The events in the positive likelihoodside are tagged as multi-ring, conversely those in the negative likelihood side
are tagged as single-ring.
.

4.2.3

Particle Identification (PID)

The reconstructed Cherenkov rings are processed by a Particle Identification(PID) classifier under two available hypotheses: an e-like ring hypothesis,
suitable for rings produced by gammas or electrons and a µ-like hypothesis
suitable for rings produced by muons, charged pions or protons.
High-energy electrons produce electromagnetic showers due to the chainof bremsstrahlung (e Ñ e γ) and photon pair production (γ Ñ e e ).
Photons can start the same process via pair production as well. The resulting Cherenkov ring is the sum of several rings produced by the charged
component of these showers, all approximately in the same direction: for thisreason e-like rings have diffuse edges.
Muons have a mass  200 times the mass of electrons, for this reason their

CHAPTER 4. RECONSTRUCTION ALGORITHMS

57

bremsstrahlung cross-section is negligibly small1 : muon-like rings have sharp,
thick edges, since they are produced by a single particle emitting Cherenkov
light along its track.
Charged mesons can also interact hadronically, so their direction can suddenly change: this leads to the production of one or more distinct thinnerrings, with respect to muons, with sharp edges due to the absence of electromagnetic showers.
Some differences come from the angles of Cherenkov emission: highenergy electrons usually have a 42 Cherenkov opening angle, corresponding
to βe  1, since they are always highly relativistic. Muons aren’t always
highly relativistic (βµ  vc ¤ β) and lose energy due to ionization, so their
Cherenkov angle can be less than 42 and may shrink during the emission,
as shown in Figure 4.4.

Figure 4.4: A schematic view of Cherenkov radiation from a muon.
Cherenkov photons are emitted to the area of 2πr sin θpdx sin θ rdθ) whilea muon travels the distance of dx.
.
Figure 4.5 shows the different shapes of typical e-like and µ-like rings:
these differences are exploited by the PID algorithm to classify the processedrings.
A likelihood test based on the observed and expected charge for each ringis performed. The expected charge is evaluated from Monte Carlo simulations
using a test vertex placed at a distance of R = 16.9 m from the ID wall and1Bremsstrahlung cross-section for a particle of mass m is proportional to m12 .

CHAPTER 4. RECONSTRUCTION ALGORITHMS

58

it has the following form for e-like and µ-like rings respectively:
qexp,i peq  αe Qexp ppe , θi q



R
ri

3
2

e L f pΘi qriqscat,i(4.6)



αµ sin2 θxi
qexp,i pµq    dθ 
ri sin θxi ri dxxxi

qknock,i e L f pΘi qriqscat,i(4.7)

where αe and αµ are normalization factors, Qexp ppe , θi q is the expected charge
distribution depending on the electron momentum pe and the angle θi for the
ith PMT, ri is the distance between the ring vertex and the ith PMT, L is
the light attenuation length in water, f pΘi q is the angular acceptance asa function of the photon incidence angle Θi for the ith PMT, qscat,i is the
expected charge due to scattered light for the ith PMT, xi is the estimatedpoint on the muon track from which photons detected by the ith PMT werereceived, θxi is the Cherenkov angle of a muon track length at xi , qknock,i isthe expected charge due to knock-on electrons, i.e. electrons produced by themuon ionization in water, for the ith PMT.
A gaussian probability density is calculated as in Equation 4.5 and fed toa likelihood function. The final probability density P takes into account thevariation of the Cherenkov angle of emission, too [35].
The PID likelihood function is given as:
LPID 

aa

 log P pµq   log P peq(4.8)

The single-ring and multi-ring LPID distributions for SK-IV are shown in
Figure 4.6.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

59

Figure 4.5: Display of Monte Carlo simulated e-like (top) and mu-like (bottom) rings from an e and a µ respectively, with a momentum of 800 MeV/c
both. The intensity scale shows the amount of charge produced in each PMT.
The main display shows the ID while the small display on the top right shows
the OD, whose negligible activity is compliant with the FC event definition.
The timing distributions for both the events is also reported at the bottom
right corner of each ID displays.
.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

60

Figure 4.6: PID likelihood distributions for the FCFV sub-GeV single-ring(top) and multi-ring (bottom) sample of the data (black points) and theatmospheric neutrino MC (stacked histograms, normalized to data livetime)in SK-IV. The events in the positive side are identified as µ-like events.
Conversely, the events in the negative side are identified as e-like.
.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

4.2.4

61

Momentum determination

The momentum of each particle is evaluated by the observed charge inside
the Cherenkov cone with a half angle of 70 . The observed charge of the ith
PMT for the nth ring is separated based on the expected charge distributions
from each ring, described as follows:
qobs,i,n  qobs,i °

qexp,i,n1
n1 qexp,i,n(4.9)

The total charge for each ring (RTOT) is calculated as follows:

RT OT 

GMC 
α
GData



¸

°

ri

qobs,i,n e L

θi,n 70
50ns ti 250ns



cos Θif pΘi q



¸

°



Si 

(4.10)

θi 70

where GMC and GData are the relative PMT gain parameters for the data andthe Monte Carlo simulation, α is a normalization factor, ri is the distance
between the ring vertex and the ith PMT, L is the light attenuation length inwater, f pΘi q is the angular acceptance as a function of the photon incidence
angle Θi for the ith PMT, θi,n is the angle between the ith PMT and the nth
ring direction, ti is the TOF subtracted hit timing of the ith PMT, Si is the
expected charge of the ith PMT due to scattered light.
RTOT is converted to the corresponding momentum according to conversion tables obtained from Monte Carlo simulations for both the e-like andµ-like hypotheses: Figure 4.7 shows that momentum dependence on RTOT
is quite linear.

4.2.5

Michel electron search

Michel electrons are an indicator of the presence of a muon. The tagging ofMichel electrons is based on the number of hits in a cluster, the total charge
and the goodness of the vertex fit.

4.3

fiTQunfiTQun is based on the maximization of a likelihood function. The reconstruction procedure consists of the following steps:
 vertex pre-fitting; hit clustering;CHAPTER 4. RECONSTRUCTION ALGORITHMS

62

Figure 4.7: Distributions of RTOT as a function of momentum up to 2000
MeV/c for both e-like and µ-like rings.
.
 single-ring fitting; multi-ring fitter.

Detailed information about fiTQun can be found in [56] and [62].

4.3.1

The likelihood function

The likelihood function to be maximized by fiTQun is defined as:
Lpxq 

unhit¹
jPj punhit|xq

hit¹

r1  Pipunhit|xqs fq pqi|xqftpti|xq(4.11)iwhere x is an event hypothesis consisting of particle types, vertexes andmomenta.
The index j runs over all unhit PMTs, conversely the index i runs over all
hit PMTs: for each of the hit ones, information about the charge produced
and the time of arrival of the first incident photon is stored in the event data
structures. Pi punhit|xq is the conditioned probability the ith PMT does notregister a hit for the given hypotesis x, qi and ti represent the charge andtime information registered by the ith hit PMT, fq pqi |xq and ft pti |xq are theCHAPTER 4. RECONSTRUCTION ALGORITHMS

63

conditioned probability density functions of observing charge qi and time ti
respectively in the ith hit PMT for the given hypotesis x. fiTQun searches
for the hypothesis x which maximizes Lpxq and uses it as the best estimate
for the particle configuration in the event.

4.3.2

Predicted charge

Predicted charges µi are introduced to decouple the process of particle andoptical propagation inside the tank from the response of the PMTs. µi is
defined as the mean number of photoelectrons produced in the ith PMT fora given hypothesis from which it explicitly depends. Equation 4.11 becomes:
Lpxq 

unhit¹

Pj punhit|µj q

hit
¹

j

r1  Pipunhit|µiqs fq pqi|µiqftpti|xq(4.12)

i

Likelihood is evaluated in two steps:
1. for a given hypothesis x the predicted charge µi is calculated for eachPMT;
2. using the calculated µi and the observed information, the likelihood
function (Equation 4.12) is evaluated.
For a multi-particle hypothesis, the predicted charges for each particle arecalculated separately and then summed. If n is the number of particles, thetotal predicted charge is calculated as follows:
µi 

¸

µdir
i,n

µsct
i,n



µdark

(4.13)

nsct
where µdark is the contribution from the PMT dark current, µdir
i,n and µi,n areth
the contributions from direct light and scattered light incident on the i anddue to the nth particle. For a single particle hypothesis, µdir and µsct are
given as integrals along the particle track length s from it initial position.

µdir Φppq»»g pp, s, cos θqΩpRqT pRqϵpη qds(4.14)

1ρpp, sqΩpRqT pRqϵpη qApsqds(4.15)
4π
where the variables θ, R and η indicate the relative orientation of the particle
and the PMT in dependence on s, as shown in Figure 4.8. Φppq is a normalization factor which is proportional to the average total number of photons
for a particle with initial momentum p. The other factors are explained in
the following paragraphs.
µ

sct ΦppqCHAPTER 4. RECONSTRUCTION ALGORITHMS

64

Figure 4.8: Reference diagram of the variables for the predicted charge calculations in Equations 4.14 and 4.15. The vertex position of the particle isshown as the white dot.
.
Cherenkov emission profile
The Cherenkov emission profile g is defined as the number of photons perunit track length per unit solid angle, at angle θ with respect to the particle
direction, emitted by a particle with initial momentum p. g is normalized as:»

g pp, s, cos θqdsdΩ  1(4.16)

Electron and muon Cherenkov emission profiles simulated in SKDETSIM for
four different values of initial momentum each are shown in 4.9 and 4.10
respectively. fiTQun exploits their differences for PID.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

65

Figure 4.9: Cherenkov emission profiles for electrons at various initial momenta, simulated in SKDETSIM. The emission has a peak near cos θ  0.75,
corresponding to 42 , which is the Cherenkov emission angle for a particle
with β  1 in water. This happens for all the initial momentum values,
since they are far beyond the ultra-relativistic threshold for electrons. The
broadening of the angle distribution is due to electromagnetic showering.
.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

66

Figure 4.10: Cherenkov emission profiles for muons at various initial momenta, simulated in SKDETSIM. As the initial momentum grows, the initialemission angle approaches the theoretical value of 42° for a particle of β  1
in water. The angle distribution is sharper than in the electron case due tothe absence of electromagnetic showering. Finally, muons lose energy due toionization, causing their average Cherenkov emission angle to shrink along
their tracks.
.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

67

Solid angle ΩpRq
The PMT sensitive area subtends a solid angle from the particle position on
the track which can be roughly evaluated, for R ¡1 m, as:ΩpRq 

πa2
R2

a2(4.17)

where a is the radius of an ID PMT (0.254 m).
Light transmission factor T pRq

The factor T pRq takes the absorption and scattering of the emitted Cherenkov
light in water into account. It is evaluated as:
T pRq  exp LRatt(4.18)

where Latt is the light attenuation length in water used in SKDETSIM(74.9646 m for SK-IV).
PMT angular acceptance ϵpη q

The PMT angular acceptance ϵpη q is obtained from SKDETSIM and fitted
by a polynomial function which is used in the predicted charge calculation
as ϵpη q, normalized in order to satisfy the condition ϵp0q  1 (Figure 4.11).
Light scattering and reflection: Apsq

The Apsq factor takes into account the indirect light caused by light scatteringand reflection happening inside the detector. It is evaluated as:
Apsq 

dµsct
dµiso,dir(4.19)

where µiso,dir is the predicted charge due to an hypothetical isotropic lightsource traveling along the same track as the actual particle with a total lightintensity same as that producing µdir , which is obtained by removing Apsq
from Equation 4.15 and defining ρpp, sq as follows:ρpp, sq »g pp, s, cos θqdΩ

(4.20)

Finally, tables containing the numerical values of Apsq are generated by
SKDETSIM simulations.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

68

Figure 4.11: PMT angular acceptance as a function of cos η obtained fromSKDETSIM. The vertical axis is in arbitrary unit. The solid line shows afitted polynomial function and it is normalized to be 1 at η = 0.
.

4.3.3

Unhit probability

The number of photoelectrons produced in a PMT follows a Poisson distribution whose mean µ is the total predicted charge defined in Equation 4.13.
According to Poisson distribution, the probability that k photoelectrons areproduced if the mean number is µ is:
P pk q 

µk µ
e
k!

(4.21)

Hence, the probability of no photoelectron is eµ . Due to the threshold of
the PMT signal, a photoelectron might not surpass the threshold and makea hit. This threshold effect is corrected up to the third order of µ as follows:
P punhit|µq  1

a1 µ

a2 µ 2a3 µ3 eµ(4.22)

where the coefficients an are obtained from SKDETSIM.

4.3.4

Charge likelihood

The charge likelihood fq pq |µq is the conditional probability to observe acharge q in the considered PMT, given the hypothesis that its predictedcharge is µ. In order to obtain fq pq |µq, normalized observed charge distributions are prepared by generating photoelectrons according to a Poisson

CHAPTER 4. RECONSTRUCTION ALGORITHMS

69

distribution with discrete values of µ at each PMT in SKDETSIM. Then,
those distributions are fitted by a polynomial as a function of µ at each fixedvalue of q. The final polynomial is obtained after a linear interpolation of
the fit parameters in terms of the observed charge q.

4.3.5

Time likelihood

The time likelihood ft pti |xq depends on the event hypothesis x and the position of the PMT. However, it is impractical to completely consider suchcomplex dependencies. In order to approximate ft pti |xq, we assume that all
Cherenkov photons are emitted at the midpoint of the particle track, andthen the time likelihood can be expressed by the residual hit time given as:itresi  ti  t  smid {c  |RPMT  x  smid d|{pc{nq(4.23)

where ti , RiPMT are the raw hit time and position of the ith PMT, x, t are thevertex position and time, d is the particle direction and smid is the half ofthe particle track lenght. For a single particle hypothesis, by using tres
i , time
likelihoods for the direct and indirect light are obtained by SKDETSIM andthe final likelihood is obtained by merging those two likelihoods as described
below:
dir res
ft ptresp1  ωqftsctptres(4.24)i q  ωft pti q
i q
where

1  eµi(4.25)
ωdirsct
1  eµi eµii.e. assuming that a hit is produced by an indirect photon if there is no direct
photon. For a multi-particle hypothesis, the tres for each particle hypothesis
are calculated separately. The particles are ordered by tres
i and the total timelikelihood is calculated as:
1
ft ptres±all pµdir µsct q
i q 
1  j 1 e i,j i,j
dir



all
¸







j 1



all
¹





eµi,j

k 1

k 1

4.3.6

j i
¹

eµi,k

dir

dir



j 1
¹



1  eµi,jdireµi,ksct



dir respti qft,j(4.26)
sct respti q
1  eµi,j ft,j
sct

k 1

Vertex pre-fitting

The maximization of Lpsq must be initialized with a single starting vertex
position as close as possible to the best-fit value, in order to prevent fiTQun

CHAPTER 4. RECONSTRUCTION ALGORITHMS

70

to get stuck in a local maximum instead of the global one. The pre-fitting
process calculates this initial seed value: assuming that all photons are emitted from a point-like light source, the seed is estimated by maximizing thefollowing goodness function:
Gpx, tq 

hit
¸
i



exp

 12



i
Tres

2



σ

(4.27)iwhere the residual hit time for the ith Tres
is calculated as:iTres ti  t  |RiPMT  x|{pc{nq(4.28)

A grid scan in the space of x, t is iteratively done for the goodness whileshrinking the grid size and σ.

4.3.7

Hit clustering

The time window for an event is  10 µs around an event trigger: it’s wide
enough for multiple hit clusters to be detected within the same event. For
example, a Michel electron produced by a muon in the primary event iscounted as a sub-event since it’s typically detected after  2 µs from thetrigger time, which is long enough to produce two separable hit clusters
in time. The hit clustering algorithm is performed before the maximum
likelihood reconstruction step, in order to keep the sub-events well separated.
The goodness function Gpx, tq defined in Equation 4.27 is evaluated, inthe vertex position returned by the pre-fitting procedure, every 8 ns step,
starting at 300 ns before the trigger and using all the hits in the interval(-200 ns, 15000 ns) around the trigger, with an optimized σ = 6.3 ns. An
example of the goodness distribution as a function of t for an event with a
primary muon and a Michel electron is shown in Figure 4.12.
The goodness peak is identified by using a goodness threshold curve function. A time window is set around each peak found, containing only the hits
that belong to it. The hits outside the time window are considered as unhit in the likelihood calculation. The residual time is re-evaluated for theipeak time and then the time window is defined as 180 ns
Tres
800
ns. Overlapping time windows are merged together. Finally, the vertex prefitting procedure and the peak search are repeated to improve peak-finding
precision. The final time windows are fixed for each remaining peak and the
maximum likelihood reconstruction is done in each of them.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

71

Figure 4.12: Goodness distribution as a function of hit time for an event witha parent muon and a Michel electron. The dots show the scanned goodness
points. The blue and green curves are the goodness threshold functions which
are used to determine the event time indicated by the red lines. The green
dotted lines are for the true time for each particle: they are consistent withthe peaks.
.

4.3.8

Single-ring fitter

After the hit-clustering step, the sub-events contained in an event are defined,
ready to be processed by the reconstruction algorithms. The single-ring fitteris the most basic reconstruction algorithm available. For each sub-event it
is applied to, it maximizes the likelihood Lpxq in order to obtain the bestfit single-particle hypothesis x. fiTQun considers three types of single-ring
hypotheses: electron, muon and charged pion. Three fits are applied to every
sub-event, one per hypothesis type.
Single-ring electron and muon fit
Both single-ring electron and muon hypothesis contain seven parameters: thevertex position ⃗x, the time t, the zenith angle and azimuth of the direction(θ,ϕ) respectively, and the momentum p.
The single-ring electron fit starts by setting the vertex initially at theposition determined by the vertex pre-fitting procedure and the time to thepeak time. In order to determine the initial value for the direction, a likelihood scan of the direction is performed by sampling the likelihood at 400
points that are equally spaced on the unit sphere. During the direction scan,

CHAPTER 4. RECONSTRUCTION ALGORITHMS

72

momentum is fixed at the value which is roughly estimated using the total
observed charge. After the direction is determined by the grid scan, themomentum seed value is set by performing another likelihood scan by only
varying the momentum.
Once all the seven track parameters are seeded, the parameters are thensimultaneously fit by minimizing the lnLpxq in Equation 4.11 using the
SIMPLEX algorithm in the MINUIT package, which provides the final maximum likelihood estimation of the particle track parameters assuming a single
electron.
After that, the single-ring muon-fitter is applied to the same sub-event,assuming the vertex, time and direction from the electron fit as their seedvalues. The momentum is then estimated by a likelihood scan as in theelectron fit, after which the full simultaneous minimization of the lnLpxq is
performed.
e/µ Particle Identification
The Particle Identification (PID) process between the e and µ hypotheses
exploits the differences between e-like and µ-like rings already explained in
Section 4.2.3. Since the likelihood function in Equation 4.12 embeds thedifferent emission profiles for electrons and muons via the evaluation of thepredicted charge (Section 4.3.2), in fiTQun PID is done by comparing thebest-fit likelihood values between different particle hypotheses.
In this case, electrons and muons are distinguished by making a cut on
lnpLe {Lµ q, the log-likelihood ratio between the best-fit electron and muon
hypotheses, as shown in Figure 4.13.
The cut is evaluated by processing the FC true-FV CCQE event sample
in the atmospheric neutrino Monte Carlo and set at:
lnpLe {Lµ q ¡ 10(4.29)

If this condition is satisfied, the ring is of electron, or showering, type. Otherwise it is of muon, or non-showering, type.
π

hypothesisA π propagating in water can interact hadronically with the nuclei containedin the surrounding molecules: this results in a sudden change of direction,
due to hard scattering, or even absorption. The portion of the π trajectory
before such an interaction is known as the upstream track : the ring emitted
in this part of the track is usually quite distinct from that of electrons being
thinner and sharper but very similar to that of muons due to the absence ofCHAPTER 4. RECONSTRUCTION ALGORITHMS

73

Figure 4.13: Likelihood separation of single-ring electron (left) and muon(right) events in the FC true-FV CCQE event sample in the atmospheric
neutrino Monte Carlo. The vertical axes are lnpLe {Lµ q and the horizontal
axes are the reconstructed single-ring electron fit momentum. The magentalines indicate the cut criteria for electron-muon separation.
.
electromagnetic showers. If a chain of hadronic interactions happens, several
upstream rings may be produced in the event. Finally, the remaining partof the track is known as the downstream track : a Cherenkov ring may beemitted from this part as well, if the necessary conditions are met (Figure4.14).
The single-ring π fitter reconstructs the upstream ring using the singlering muon fit result as a seed. The predicted charge of the upstream track is
obtained by subtracting the predicted charge of the downstream track fromthe predicted charge of an imaginary full track without any hadron interaction happening.
π hypothesis contains the same parameters as the electron and muon
ones, plus an additional fit parameter Eloss which is defined as the kinetic
energy deposit in the upstream track.
Using Eloss , the vertex of the downstream track is calculated by assuming
constant kinetic energy loss per unit track length. For the time likelihood, theresidual time is estimated using the midpoint of the upstream track. All eightparameters of the upstream track are simultaneously fitted by minimizing
lnL.
µ/π

identification

Since muons and charged pions have similar masses, in absence of any hadronicinteraction, they produce similar ring patterns. The single-ring π fitter,

CHAPTER 4. RECONSTRUCTION ALGORITHMS

Figure 4.14: Schematic of the rings produced by a π
hadronic scattering on a nucleus in water.

74

before and after

howewer, can distinguish between the two types of rings by a likelihood-ratio
value test, which includes the π specific Eloss parameter.
As Figure 4.15 shows, the separation between muons from νµ CCQE andpions NCπ in the T2K experiment2 accelerator neutrino Monte Carlo simulation is not as sharp as in the e/µ case: although there are some indistinguishable events, a significant fraction of about 60% of π events can beseparated from muons. The π hypothesis performance in fitting muon rings
improves as Eloss grows, reaching the top when the particle momentum at
the assumed upstream track endpoint drops below Cherenkov threshold.

4.3.9

Multi-ring fitter

fiTQun multi-ring fitter can reconstruct multi-particle events containing up
to six Cherenkov rings, like those ones relevant for this analysis.
The multi-ring fitter is applied only to the first sub-event, as defined in
Section 4.3.7 since it’s very unlikely that any subsequent sub-event carries
more than one ring.
The fitting procedure considers only two hypotheses: electron, for showering particles like gammas and electrons, and π , for non showering particles.
2

Tokai-to-Kamioka (T2K) is an experiment which consists in sending a beam of νµwith a narrow energy distribution peaked at  600 MeV from the town of Tokai to SuperKamiokande for detection, along a path  200 km long through the Earth, in order tostudy neutrino flavor oscillations.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

75

Figure 4.15: Likelihood separation of νµ CCQE (left) and NCπ (right)
events, in the T2K experiment accelerator neutrino Monte Carlo simulation.
The vertical axes are lnpLπ {Lµ q and the horizontal axes are Eloss . Taken
from [62].
.
The muon hypothesis is not considered since the single-ring π hypothesis
can fit muon rings with an acceptable performance.
The algorithm starts with the assumption that only one ring is in theevent: the ring is tested for both the electron and π hypotheses.
Then, using the result of each test as seeds, one more ring is assumed
for both and the fit repeated: the newly assumed ring is tested for both theelectron and π hypotheses and the process proceeds by adding one morering per step and per combination of hypotheses, until the number of rings
reaches the maximum of six.
The fit sequence can be summarized as a tree shaped graph: Figure 4.16
shows the tree starting with the electron hypothesis, another tree is generated
starting with the π one.
Four parameters of ring counting constrain which added rings are acceptable or not: Ea0 , M ua0 , a0 , a1 . When an n 1-th ring is added to an n-ring
hypothesis, the condition on hypotheses likelihoods Ln 1 and Ln for it to be
accepted is: if n = 1:



– ln


– ln

Ln 1
Ln

¡ Ea0

a1  Evis , if the added ring is e-like.

Ln 1
Ln

¡ M ua0

Ln 1
Ln

¡ a0

a1  Evis , if the added ring is π-like.

 if n ¡ 1:



– ln

a1  Evis

CHAPTER 4. RECONSTRUCTION ALGORITHMS

76

Figure 4.16: A tree diagram showing how the tree of the multi-ring hypotheses evolve as the number of rings is increased. The diagram is for the caseassuming the first ring as electron and an equivalent procedure is done forthe case of assuming a π as the first ring. Taken from [62].
.
For Super-Kamiokande the following values are used: Ea0 = 87.5
 M ua0 = 140
 a0 = 70
 a1 = 0

When the second ring is added to the first, they share a common vertex,
its initial direction is obtained by evaluating the likelihood for 400 uniformly
distributed points on the unit sphere, arbitrarily assuming for it a momentumof 50 MeV/c: the direction which minimizes lnL is chosen. Then thesecond ring momentum is fitted while all other parameters are fixed. Afterthe momentum of the second ring has been estimated, a simultaneous fitof direction and momentum of the second ring is performed while all otherparameters are still fixed. In the same fashion, a simultaneous fit of thetwo rings momenta is performed, in order to redistribute the visible energy
between the two rings especially in case of overlap and, finally, the momenta,
directions and the common vertex are all simultaneously fit to get the final
best-fit two-ring result. If the second ring is being tested under the πhypothesis, the fit of the Eloss parameter is included in the final step.
Once the two-ring fits are done, for each of the two particle hypotheses forthe new ring, whether the fitted second ring is an actual true ring is checkedCHAPTER 4. RECONSTRUCTION ALGORITHMS

77

by comparing the likelihoods between the hypotheses before and after adding
the new ring.
The process of adding a new ring, fitting and checking if the new ringcan be considered true or fake is repeated until the new ring fails the checkor a number of six rings is reached. The simultaneous fit of all parameters
is done only for the two-ring case: for the subsequent cases only the simultaneous momentum fit of all rings is performed, assuming that the two-ring
fit gives a reasonable estimate of the true interaction vertex. To save morecomputational time, for the fifth and sixth ring, only electron hypotheses are
considered.
In the end, the hypothesis with the smallest lnL among all the calculated
hypotheses containing true rings in both trees is chosen as the seeding multiring hypothesis.
The rings in the seeding multi-ring hypothesis are ordered by the visibleenergy of the ring, i.e. the reconstructed kinetic energy above Cherenkov
threshold. A ring correction algorithm is applied to remove fake rings, as
shown in [56]: for the most energetic ring, the angle between the directionsof the ring and each lower-energy ring is calculated and if the angle for agiven lower-energy ring is smaller than 20 , the lower-energy ring is merged
to the most energetic ring by adding their visible energies. After that, themost energetic ring is re-fitted assuming three particle types: electron, muonand π while all the other remaining rings which were not merged in the
ring-merge procedure are fixed at their original configurations. All the ringparameters are fit simultaneously including the vertex.
The best-fit likelihoods for the electron and π hypotheses of the mostenergetic ring are compared using the following inequality:
lnpLe {Lπ q ¡ 10(4.30)

which is the same condition as in Section 4.3.8, except for the π instead ofthe muon hypothesis. If this condition is satisfied, the ring is of electron, or
showering, type. Otherwise it’s of π , or non-showering, type. If the mostenergetic ring is found to be of non-showering type, it is assumed to havebeen produced by a muon. Any less energetic ring of non-showering typeis assumed to have been produced by a charged pion. This consideration isbacked by Monte Carlo simulations of the atmospheric neutrino CC and NC
events involving muons and charged pions.
After the most energetic ring, all the other rings are re-fitted one by one,
including their vertex, allowing each ring to have it in different positions.
The result obtained in the end of this sequential fit procedure is taken as thebest reconstruction of the processed event.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

4.4

78

Performance comparison between APFit
and fiTQun

The reconstruction performances of APFit and fiTQun have been studied
and compared when applied against Monte Carlo simulations of single ring
Fully Contained Charged Current events, with a single electron or a single
muon in the final state.
The Fiducial Volume for APFit is defined as the region of the inner 2 m
inside from the ID wall, while the fiTQun performance has been tested in
two different Fiducial Volume definitions: 1.5 m and 2 m.
Figure 4.17 shows the distributions of the distance between the reconstructed and true vertexes. The vertex resolutions defined at 1σ deviation
position for single electron (muon) events are; 20.1 (19.3) cm for the best
single ring fit of fiTQun and 29.4 (22.7) cm for APFit. The momentum
dependencies of the vertex resolution are shown in Figure 4.18.

Figure 4.17: Distributions of the distance between the true and reconstructedvertex of FC true-fiducial CCQE single electron (left) and muon (right) eventsin the atmospheric neutrino MC. The green (red) histogram is for the best
single ring fit of fiTQun with the distance from the ID wall Dwall ¡ 1.5(2.0) m cut and black histogram is for APFit with the Dwall ¡ 2.0 m cut.
The dotted lines show the vertex resolution which is defined at one standard
deviation.
The angle between the reconstructed and true directions and their momentum dependencies are also shown in Figure 4.19 and 4.20. For single
electron and muon events, the direction resolutions defined at one standard
deviation angle are 2.81 (2.91 ) and 1.73 (1.75 ) for the best single ring fit
of fiTQun (APFit).
In order to evaluate the momentum resolution, the fractional difference
between the reconstructed and true momenta is fitted by a Gaussian at eachCHAPTER 4. RECONSTRUCTION ALGORITHMS

79

Figure 4.18: Vertex resolution as a function of true momentum of FC truefiducial CCQE single electron (left) and muon (right) events in the atmospheric neutrino MC. The green (red) points are for the best single ring fit
of fiTQun with the distance from the ID wall Dwall ¡ 1.5 (2.0) m cut andblack points are for APFit with the Dwall ¡ 2.0 m cut.
true momentum bin and taking the sigma of the fitted Gaussian as the resolution. Figure 4.21 shows the momentum resolution as a function of the true
momentum.
Finally, the misidentification rates as a function of the true momentum
are shown in Figure 4.22.
In the end, this study allows to confirm that fiTQun overall reconstruction
performances are better than those of APFit.

Figure 4.19: Distributions of the angle between the true and reconstructed
direction of FC true-fiducial CCQE single electron (left) and muon (right)
events in the atmospheric neutrino MC. The green (red) histogram is for thebest single ring fit of fiTQun with the distance from the ID wall Dwall ¡ 1.5(2.0) m cut and black histogram is for APFit with the Dwall ¡ 2.0 m cut. The
dotted lines show the direction resolution which is defined as 1σ deviation
point.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

80

Figure 4.20: Direction resolution as a function of true momentum of FC
true-fiducial CCQE single electron (left) and muon (right) events in the atmospheric neutrino MC. The green (red) points are for the best single ring
fit of fiTQun with the distance from the ID wall Dwall ¡ 1.5 (2.0) m cut andblack points are for APFit with the Dwall ¡ 2.0 m cut.

4.5

Neutron tagging

Counting neutrons produced in a FC event can help to separate signal frombackground events. For example an anti-neutrino interaction such as:
ν̄e

pÑn

e

(4.31)

produces a neutron that after thermalisation in water is captured by an
Hydrogen atom:n p Ñ d Ñ d γ(4.32)The delayed detection ( 200 µs) of the electron Compton-scattered by the
2.2 MeV γ in coincidence with the detection of the positron from the primary
event is a signature of the process.

4.5.1

Neutron tagging algorithm

Tagging and counting neutrons in FC events is challenging due to the low
energy of the de-excitation photon produced in their capture: this task is
performed using a specifically developed algorithm [37] which is made of two
steps:
1. initial neutron candidate selection;
2. final neutron candidate selection with neural network.
One neutron capture is expected to produce less than 10 PMT hits in the
ID: first such PMT hit clusters are searched for as initial candidates, theneach candidate is fed to a dedicated neural network.

CHAPTER 4. RECONSTRUCTION ALGORITHMS

81

Figure 4.21: Momentum resolution as a function of true momentum of FC
true-fiducial CCQE single electron (left) and muon (right) events in the atmospheric neutrino MC. The green (red) points are for the best single ring
fit of fiTQun with the distance from the ID wall Dwall ¡ 1.5 (2.0) m cut andblack points are for APFit with the Dwall ¡ 2.0 m cut.
Initial neutron candidate selectionRAW
The number of hit PMTs in a sliding 10 ns time window (N10
) is counted.
Each PMT hit timing is corrected for time-of-flight using the primary FCRAW¡ 4 is tagged as neutron canevent vertex position. A cluster with N10
RAW¡ 50 or the number of hit PMTs in a 200 ns time
didate but if N10
window around the cluster timing (N200 ) is more than 200 it is rejected as
background.
Besides random dark noise, another type of time-clustered dark noise has
to be taken into account: its source has been identified to be the scintillation
light in the SK PMT glass. Since this clustered noise can mimic a neutron
capture signal, a cut is introduced to reject it. If there are multiple hits inthe same PMT within X µs these hits are removed. The value of X dependsRAWon the value of N10: for values of less than 7, X is set to 12 µs otherwise it
is set to 6 µs. Clusters with a remaining number of PMT hits (N10 ) greaterthan 4 are selected as initial neutron candidates.

Final neutron candidate selection with neural network
The vertex position of the Compton-scattered electron of initial neutron candidates is reconstructed using the Neut-Fit algorithm. Neut-Fit searches forthe vertex position that minimizes the RMS of the time-of-flight subtracted
residual timing distribution of the initial candidate hit cluster, defined as:
d

t1

rms



°N10n
i

pt1i  t1meanq2N10n(4.33)

CHAPTER 4. RECONSTRUCTION ALGORITHMS

82

Figure 4.22: Rate of erroneous particle identification (Mis-PID) as a functionof true momentum of FC true-fiducial CCQE single electron (left) and muon(right) events in the atmospheric neutrino MC. The green (red) points arefor the best single ring fit of fiTQun with the distance from the ID wall Dwall¡ 1.5 (2.0) m cut and black points are for APFit with the Dwall ¡ 2.0 m cut.
t1mean 

N¸
10n
i

t1i
N10n

(4.34)

where t1 is the i-th PMT’s time-of-flight corrected residual time for an asi

sumed vertex position and N10n is the number of PMT hits in a 10 ns timing
window in residual timing for an assumed vertex position. Neut-Fit is executed twice: in the first run the reconstructed vertex position is constrained
within 200 cm from the primary vertex position, in the second run it is unconstrained. Finally the candidate is fed to a neural network that performs
the final classification as signal or background by evaluating 23 calculated
input variables, as described in detail in [60].

Chapter 5Ñ νK in SK-IV

Search for pusing fiTQun

We searched for proton decay in the p Ñ νK , K Ñ π π 0 channel in thefull SK-IV FCFV data, with a livetime of 3244.4 days corresponding to an
exposure of 200.0 kton*year. This chapter describes the simulated samples
used, the signal definition and the selection criteria, the study of remaining
background, the estimation of systematic uncertainties and the search forcandidates in real data. The reference study for this analysis is [40].

5.1Simulated samples used

We used three simulated samples in this analysis, all reconstructed with
fiTQun: PDK MC: proton decay p Ñ νK
sample containing  600000 events;

Monte Carlo simulated FCFV ATM-ν MC: 500 years of atmospheric neutrino Monte Carlo simulated background FCFV sample, each event is weighted for oscillation
probability and neutrino flux;
 Hybrid sample: we built an hybrid sample to estimate detector systematic error, as described in Section (5.6.4).

5.2

Proton decay mode

We consider the proton decay mode:p Ñ νK
83(5.1)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

84

The two most probable decay modes of charged kaons are:KK

Ñ µ νµ (64%)Ñ π π0 (21%)(5.2)

of which the second one is relevant for this analysis. If we consider thatπ 0 Ñ γγ(98.8%)(5.3)

the particles in the final state considered for this study are
π γγ

5.2.1

(5.4)

Decay kinematics

Proton decay is assumed to happen in water molecules (H2 O) with equal
probability for each of its ten protons: in the case of a decay in Hydrogenthe proton is at rest since it’s free while in the case of a decay in Oxygen it’sin motion due to Fermi momentum since it’s bound. In the free proton casethe neutrino and charged kaon are emitted back-to-back with a 339 MeV/cmomentum each. In the bound proton case several effects are taken into
account: proton binding energy with nucleus, correlated decay with othernucleons, proton Fermi momentum, interaction of the decay products with
nuclear matter. These effects are all simulated in the Monte-Carlo samples
used.
Products from proton decays in Oxygen have an invariant mass lower thanthe mass of a free proton, due to the effect of binding energy and correlation
between nucleons: for this reason, bound proton decays are simulated witha lower proton invariant mass and a 10% correlated decay probability [58].
The position of the decay proton is simulated according to the Woods-Saxon
nuclear density model. Figure 5.1 shows the results of simulation with NEUT
[36].
Since the fraction of charged kaons produced above Cherenkov threshold(560 MeV/c in water) is negligibly small, we can assume that the charged
kaon from proton decay produces no visible ring.
The fraction of charged kaons decaying at rest in water is 89%, as simulated by SKDETSIM: in this case the decay is back-to-back and each produced π and π 0 carry a momentum of 205 MeV/c.
The π is above Cherenkov threshold (156 MeV/c in water), the expected
Cherenkov angle is  25 , narrower than the maximum angle of 42 .
The π 0 is a neutral particle and doesn’t produce any ring but it decays
99.8% [17] of the times in two photons which convert to positron-electron
couples in water and produce two visible rings.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

85

Figure 5.1: The top figure shows the decaying proton invariant mass distribution in 16 O and the lower figure shows the K+ momentum distribution
from the simulation of p Ñ νK . In the top figure, the single-bin histogramshows the free proton case and the broad histogram shows the bound proton case. The rightmost peak in the bound proton case corresponds to thep-state, located slightly lower than the proton mass by 15.5 MeV of binding
energy; the second rightmost peak is the s-state (39 MeV in binding energy).
The correlated nucleon decay makes the longer tail in the lower mass region.
In the bottom figure, the single-bin histogram shows the free proton case(339 MeV/c) and the broad histogram shows the bound proton case whichis smeared by Fermi motion.

5.2.2

Definition of visible energy

The visible energy Evis of a particle is defined as the difference between its
energy E and its Cherenkov thresold on energy Eth .
Evis  E  Eth bp 2 c2

m20 c4bp2th c2

m20 c4(5.5)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

86

where p, pth and m0 are the momentum, the Cherenkov momentum threshold
and the rest mass of the particle respectively.
Intuitively, the visible energy measures the maximum amount of energythat the particle could convert entirely into Cherenkov radiation.
A direct calculation shows that the visible energy for the charged pion, if
the parent kaon decays at rest, is  39 MeV, which is one order of magnitude
lower than the typical visible energy of the photons coming from the neutralpion decay: this means that the charged pion ring is expected to be thefainter ring in the signal events and its reconstruction is a challenging task.
Finally, this definition is equivalent to the one used in 3.1.7 for the FC
reduction process and it can be calculated using fiTQun reconstructed variables only.

5.3

Event selections

Signal events p Ñ νK , K Ñ π π 0 with π 0 Ñ γγ are selected in FCFV(Section 3.1.7) samples by the following criteria:
1. nring: 3 reconstructed rings,
2. PID: 2 e-like and 1 µ or π-like rings,
3. michel: 0 or 1 Michel electrons,
4. Mπ0 : reconstructed π 0 mass between 85 and 185 MeV/c2 ,5. Pπ0 : reconstructed π 0 momentum between 175 and 250 MeV/c,
6. Pπ : reconstructed π momentum between 175 and 250 MeV/c,
7. MK : reconstructed K mass between 450 and 530 MeV/c2 ,8. PK : reconstructed K momentum less than 60 MeV/c,
9. Ntag: 0 tagged neutrons.
The background for this analysis are the FCFV events from atmospheric
neutrino interactions: we estimate the remaining background by applying
the same event selections as for signal to the ATM-ν MC sample.

5.4

Distributions along cut parameters

We compare distributions along cut parameters for PDK MC and ATM-νMC overlaid one by one. We also show the same distributions for data andATM-ν MC scaled by data livetime and overlaid.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

5.4.1

87

Number of reconstructed rings distributions

Signal events contain three reconstructed rings. Figure 5.2(a) shows the PDK
MC and ATM-ν MC distributions of the number of reconstructed rings. Only
about 20% of true π π 0 with π 0 Ñ γγ events in PDK MC has three reconstructed rings as expected because the π ring is a faint object and hard toreconstruct. Nevertheless three rings are required in order to reconstruct thekaon kinematics. Figure 5.2(b) shows the data and ATM-ν MC distributions.

(a)

(b)

Figure 5.2: Number of reconstructed rings distributions for FCFV samples.
The left plot shows the PDK MC (orange) and the ATM-ν MC (blue) distributions normalized to unity. The shaded area shows true signal events(K Ñ π π 0 , π 0 Ñ γγ) in PDK MC. The right plot shows Data (blackdots) and ATM-ν MC (blue), scaled to Data livetime, distributions. Eventswith 3 reconstructed rings pass the nring cut.

5.4.2

Number of reconstructed e-like rings distributions

Signal is made of two e-like rings from the π 0 decay plus a third ring that
we require to be non-showering since it’s supposed to be produced by theπ : anyway we don’t constrain it to be a π-like ring to improve selection
efficiency (Section 4.3.8). Figure 5.3(a) shows the PDK MC and ATM-ν MC
distributions of the number of reconstructed e-like rings, Figure 5.3(b) shows
the same distributions for Data and ATM-ν MC.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

88

(b)

Figure 5.3: Number of reconstructed e-like rings distributions for FCFV
samples, with nring cut applied. The left plot shows the PDK MC (orange)
the ATM MC (blue) distributions normalized to unity. The shaded areashows true signal events (K Ñ π π 0 , π 0 Ñ γγ). The right plot shows data
(black dots) and ATM-ν MC (blue), scaled to data livetime, distributions.
Events with 2 reconstructed e-like rings pass the PID cut.

5.4.3

Tagged Michel electrons distributions

Signal contains one π whose final decay products include one Michel positron:
events with more than one tagged Michel electron are rejected. Figure 5.4(a)shows the distributions of the number of tagged Michel electrons for PDK
MC and ATM-ν MC, Figure 5.4(b) shows the same distributions for data
and ATM-ν MC.

5.4.4

Reconstructed π 0 mass and momentum distributions

Reconstructed π 0 mass (Mπ0 ) and momentum (Pπ0 ) are calculated as:
Mπ0 

b

2|p⃗γ1 ||p⃗γ2 | p1  cos θq

Pπ0  |p⃗γ1p⃗γ2 |

(5.6)
(5.7)

where p⃗γ1 and p⃗γ2 are the e-like rings reconstructed momenta and θ is theangle between their reconstructed directions.
Figure 5.5(a) shows the distributions of Mπ0 for PDK MC and ATM-ν
MC, Figure 5.5(b) shows the same distributions for Data and ATM-ν MC.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

89

(b)

Figure 5.4: Number of tagged Michel electrons distributions for FCFV samples, with nring and PID cuts applied. The left plot shows the PDK MC(orange) the ATM MC (blue) distributions normalized to unity. The shaded
area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ). The right plot shows
data (black dots) and ATM-ν MC (blue), scaled to data livetime, distributions. Events with 0 or 1 tagged Michel electrons pass the Michel cut.
Figure 5.6(a) shows the distributions of Pπ0 for PDK MC and ATM-ν
MC, Figure 5.6(b) shows the same distributions for Data and ATM-ν MC.

5.4.5

Reconstructed π momentum distributions

The reconstructed π momentum Pπ is equal to the reconstructed momentum of the non-showering ring in the event in case it is tagged as π-like. Incase it is tagged as µ-like, it is assumed to be a misidentified charged pion
and Pπ is calculated as:
mπ
 Pµ
(5.8)
Pπ 
mµ
where mπ and mµ are the π and µ masses from the PDG [17] respectively
and Pµ is the reconstructed momentum of the µ-like ring.
Figure 5.7(a) shows the distributions of Pπ for PDK MC and ATM-ν
MC, Figure 5.7(b) shows the same distributions for Data and ATM-ν MC.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

90

(b)

Figure 5.5: Reconstructed π 0 mass distributions Mπ0 for FCFV samples,with nring, PID and michel cuts applied. The left plot shows the PDK
MC (orange) the ATM MC (blue) distributions normalized to unity. The
shaded area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ). The rightplot shows data (black dots) and ATM-ν MC (blue), scaled to data livetime,
distributions. The fitted peak values agree with the π 0 mass value from the
PDG [17]. Events with reconstructed π 0 mass between 85 and 185 MeV/c2
pass the Mπ0 cut.

5.4.6

Reconstructed K
butions

mass and momentum distri-Reconstructed K mass (MK ) and momentum (PK ) are calculated as:
PK
MK



b
2
EK



 |p⃗πPK2bp⃗π0 |

 pEπ

(5.9)
Eπ0 q2  PK2(5.10)

Figure 5.8(a) shows the distributions of MK for PDK MC and ATM-ν
MC, Figure 5.8(b) shows the same distributions for Data and ATM-ν MC.
Figure 5.9(a) shows the distributions of PK for PDK MC and ATM-ν
MC, Figure 5.9(b) shows the same distributions for Data and ATM-ν MC.

5.4.7

Number of tagged neutrons

Figure 5.10 shows the distributions of the number of tagged neutrons per
event. No neutrons are expected to be tagged according to our signal defi-

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

91

(b)

Figure 5.6: Reconstructed π 0 momentum distributions Pπ0 for FCFV samples, with nring, PID, michel and Mπ0 cuts applied. The left plot shows
the PDK MC (orange) the ATM MC (blue) distributions normalized to unity.
The shaded area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ). The peakat 205 MeV/c is consistent with the expected value. The right plot shows
data (black dots) and ATM-ν MC (blue), scaled to data livetime, distributions. Events with reconstructed π 0 momentum between 175 and 250 MeV/cpass the Pπ0 cut.
nition. No data events reach this selection stage so no distribution is shownfor the data sample.

5.5

Results

Selection efficiency for PDK MC η is defined as:η# events passing the cuts
# of events generated in true FV(5.11)

Figure 5.11(a) shows selection efficiency after each cut. The nring cut
reduces selection efficiency to about 10% and PID cut further reduces it toabout 4%: these cuts are necessary to reconstruct the kaon kinematics. The
Pπ and PK cuts produce the dominant background reductions, as shownin Figure 5.11(b). No data candidates remain after all cuts. Results are
summarized in Table 5.1.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

92

(b)

Figure 5.7: Reconstructed π momentum distributions Pπ for FCFV samples, with nring, PID, michel, Mπ0 and Pπ0 cuts applied. The left plotshows the PDK MC (orange) the ATM MC (blue) distributions normalized
to unity. The shaded area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ).
The peak at 205 MeV/c is consistent with the expected value. The rightplot shows data (black dots) and ATM-ν MC (blue), scaled to data livetime,
distributions. Events with reconstructed π momentum between 175 and250 MeV/c pass the Pπ cut.
Table 5.1: Signal efficiency, remaining background and remaining data
events after each cut.
Cuts

Signalefficiency (%)
FCFV96.02  0.03
+nring9.50  0.04
+PID
4.09  0.03
+michel 4.08  0.03
+Mπ03.87  0.03
+Pπ02.99  0.02
+Pπ2.60  0.02
+MK
2.53  0.02
+PK
2.34  0.02
+Ntag
2.34  0.02

# Background# Dataevents (3244.4 days)
events27796.70  10.80
27485  88
2851.15  6.32
2848  51
1297.79  4.22
1321  36
1111.78  3.931160  34
673.49  3.01
706  26137.08  1.36
141  122.05  0.17
32
1.17  0.13
21
0.04  0.02
00.03  0.02
0

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

93

(b)

Figure 5.8: Reconstructed K mass distributions MK for FCFV samples,with nring, PID, michel, Mπ0 , Pπ0 and Pπ cuts applied. The left plotshows the PDK MC (orange) the ATM MC (blue) distributions normalized
to unity. The shaded area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ).
The fitted peak value agrees with the K mass value from the PDG [17].
The right plot shows data (black dots) and ATM-ν MC (blue), scaled todata livetime, distributions. Events with reconstructed K mass between
450 and 530 MeV/c2 pass the MK cut.

5.5.1

Remaining background events

Table 5.2 summarizes the remaining background interaction modes.
Table 5.2: Remaining background breakdown by interaction mode.
Interaction# Remaining backgroundmode
events (500 years)0νµ CC1π from ∆ resonance
2 (100%)
The two events in the remaining background are both νµ CC1π 0 from ∆resonance:ν µ n Ñ∆µ
∆ Ñ p π0(5.12)0π Ñ γγFigure 5.12 shows the event displays of the remaining background events:
in both cases the γ rings from π 0 decay are well reconstructed and correctly

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

94

(b)

Figure 5.9: Reconstructed K momentum distributions PK for FCFV samples, with nring, PID, michel, Mπ0 , Pπ0 , Pπ and MK cuts applied. The
left plot shows the PDK MC (orange) the ATM MC (blue) distributions normalized to unity. The shaded area shows true signal events (K Ñ π π 0 ,π 0 Ñ γγ). The peak is compatible with the expected momentum of 0 MeV/c,
considering reconstruction resolution. The right plot shows data (black dots)
and ATM-ν MC (blue), scaled to data livetime, distributions. Events withreconstructed K momentum below 60 MeV/c pass the PK cut.
identified as e-like rings, the µ rings are well reconstructed but misidentified
as π-like rings by fiTQun. These two events pass all the cuts by chance.
No events with true single K decays remain in the background, as we
could naively expect, because the selection cuts are designed to select K Ñπ π 0 decaying alone, with no other visible particles, while if we consider K
producing atmospheric neutrino interactions:νp Ñ νΛKν̄p Ñ ν̄ΛK

(5.13)or K 0 producing atmospheric neutrino interactions which can produce a K
after K 0 charge exchange:νn Ñ νΛK 0(5.14)
ν̄n Ñ ν̄ΛK 0
there is always a Λ produced in association with the kaon. The Λ particle isneutral, so it can’t produce any Cherenkov light but its decay modes are [17]:Λ Ñ nπ 0Λ Ñ pπ 

p35.8%q
p63.9%q(5.15)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

95

Figure 5.10: Number of tagged neutrons distributions for the PDK MC (orange) and for the ATM MC (blue) FCFV samples with nring, PID, michel,Mπ0 , Pπ0 , Pπ , MK and PK cuts applied, normalized to unity. The shaded
area shows true signal events (K Ñ π π 0 , π 0 Ñ γγ). Events with 0 tagged
neutrons pass the ntag cut.

(a)

(b)

Figure 5.11: The left plot shows selection efficiency after each cut. The rightplot shows remaining data events (black) and remaining background from
ATM-ν MC (blue) scaled to data livetime after each cut.
and they add visible particles in the final state. Table 5.5.1 summarizes
the number of remaining background events, scaled to data livetime, with atrue single K decay after each cut: the number of such events entering theanalysis is low (6.0) and the dominant reduction happens after nring and
PID cuts, as expected.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

96

(a)

(b)

Figure 5.12: Event display of the two remaining background events after all
cuts.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

97

Table 5.3: Remaining backround events, scaled to data livetime, with a true
single K decay
Cuts# Background events (3244.4 days)
with true single K decay
FCFV
6.00  0.20
+nring1.30  0.10
+PID
0.43  0.09
+michel0.34  0.08
+Mπ00.25  0.07
+Pπ00.13  0.05
+Pπ
0
+MK
0
+PK
0
+Ntag
0

5.5.2

Sideband check

We checked agreement between data and ATM-ν MC outside the signal box
i.e. in the sidebands. We defined the following cuts to exclude the presenceof any possible signal candidate from the selection, aiming at having enoughremaining events to evaluate the agreement:
1. nring: 3 reconstructed rings,
2. PID: 2 e-like and 1 µ or π-like rings,
3. michel: 0 or 1 Michel electrons,
4. Mπ0 : reconstructed π 0 mass between 85 and 185 MeV/c2 ,5. Pπ0 : reconstructed π 0 momentum greater than 330 MeV/c.
Figure 5.13 shows the reconstructed Kaon mass and momentum distributions for events in the sidebands: data and ATM-ν MC scaled to data
livetime distributions agree well.

5.6

Estimation of systematic error

We evaluated systematic error coming from physics model and detector uncertainties for both signal efficiency and remaining background.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

(a)

98

(b)

Figure 5.13: Distributions of reconstructed Kaon mass (left) and momentum(right) with sideband cuts defined in Section 5.5.2 for data (blue dots) andATM-ν MC (red histogram) scaled to data livetime.

5.6.1

Physics model uncertainties for signal efficiency

We identified these physics model uncertainties for signal efficiency:
 correlated nucleon decay,
 fermi momentum of nucleon,
 K

Final State Interactions (FSI), K

Secondary Interactions (SI), Pion SI.

Correlated nucleon decay
Proton decays in Oxygen are expected to happen under the effect of othernucleons in 10% of the cases, as explained in Section 5.2.1. A conservative
100% uncertainty is assigned to the correlated nucleon decay probability. The
related systematic error on signal efficiency is obtained by weighting PDK
MC events: correlated and normal proton decays from Oxygen are weighted
by wOcorr and wOnorm respectively:
wOcorr  1 αNOnorm  αNOcorr
wOnorm 
NOnorm

(5.16)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN

99

where α is the uncertainty magnitude and NOcorr and NOnorm are the numberof correlated and normal decay in Oxygen events in the true FV respectively. Proton decays from Hydrogen remain unweighted or, equivalently,
their weight is 1. Two weighted samples, one with α  1 and one withα  1, are processed with the analysis selection cuts to obtain selection
efficiencies ηα 1 and ηα1 respectively. The systematic error is taken as
the greatest of the two following fractional differences:σα 1 ηα1  ηdefηα 1  ηdef
0.5% , σα1 

ηdef
ηdef

0.5% (5.17)

where ηdef is the default selection efficiency for the unweighted sample.
Fermi momentum of nucleon
In the PDK MC sample the momentum of protons decaying in Oxygen issimulated using the experimental spectrum functions (Section 3.4). In the
ATM-ν MC the nucleon momentum in Oxygen is modeled by the Fermi
Gas Model, which assumes a uniform spherical momentum distribution in
3D phase space whose radius (Fermi surface momentum) is 225 MeV/c: we
consider this difference as a systematic uncertainty and we evaluate it byweighting PDK MC proton decay events from Oxygen. Weights are calculated by generating a Fermi Gas Model distribution with a number of entries
equal to the number of PDK MC events in true FV and binning it with
25 MeV/c of bin width. The distribution of proton momentum in PDK
MC proton decay events from Oxygen is obtained in the same way (Figure
5.14(a)).
The weight wi for proton decay events from oxygen with proton momentum in the i-th bin is calculated as:wi 

NOF ermi,iNO,i(5.18)

where NOF ermi,i and NO,i are the number of entries in the i-th bin for Fermi
Gas Model and PDK MC proton momentum distributions respectively (Figure 5.14(b)). The systematic error σ on signal efficiency is calculated as:σηwei  ηdef
 0.6%ηdef(5.19)

where ηwei is signal efficiency obtained by processing the weighted PDK MC
events with analysis selection cuts and ηdef is the default signal efficiency forthe unweighted sample.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 100

(a)

(b)

Figure 5.14: The left plot shows the distributions of true proton momentumin Oxygen for PDK MC (black) and Fermi Gas Model (red). The right plotshows the weight values for each momentum bin.
K

Final State Interactions (FSI)

We estimated systematic uncertainty from K FSI by comparing the model
we used to generate the PDK MC sample with the model in a version of
NEUT modified to improve total K p cross section (Figure 5.15) consistency
with experimental data [19] and to include some bug fixes. The effect of all
modifications on Kaon model for FSI are shown in Figure 5.16.
Two contributions to Kaon FSI systematic error on selection efficiency
are considered: K

momentum after FSI,

 K

charge exchange.

The first one is evaluated by generating a new PDK MC sample withmodified NEUT containing, normalized to the same number of events as theoriginal one, and comparing the distribution of K momentum after FSI inboth samples, using the same binning (Figure 5.17). Weights are calculated
and applied to PDK MC as in Section 5.6.1.
The same new PDK MC sample is used to evaluate the contribution
from charge exchange. Weights are calculated to make the fraction of charge
exchange events in the original PDK MC sample equal to that in the new
sample. Charge exchange (CX) K Ñ K 0 events fraction fCX grows from
0.09% in the original PDK MC sample to 1.65% in the new one. The weightCHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 101

(a)

(b)

Figure 5.15: The left plot shows K p total, elastic, single-pion-production,
double-pion-production cross sections as functions of kaon momentum, from[19]. The right plot shows the total K p cross section as a function of kaon
kinetic energy in NEUT before modification (blue) and after modification(orange) to match the left plot.

(a)

(b)

Figure 5.16: Elastic (black) and Charge Exchange (red) K 16 O cross sections
as functions of K momentum before (left) and after (right) modificationsin NEUT.
for true charge exchange events wCX is calculated as:
wCX 

fCX in new sample
 1.84fCX in original sample(5.20)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 102

(a)

(b)

Figure 5.17: The left plot shows true K momentum distributions after FSI
for original PDK MC sample (black) and the one generated with modified
NEUT (green). The broad distribution represents the contribution of kaons
from bound protons while the outlier bin at 339 MeV/c contains the contribution of kaons from free protons as well. The right plot shows the weights
calculated from the left plot.
The weight for true non-charge-exchange events wnoCX is calculated as:
wnoCX p1  fCX q in new sample  0.99
p1  fCX q in original sample(5.21)

Systematic error on selection efficiency is calculated for each contribution
as the fractional difference between selection efficiencies for weighted (ηwei )and unweighted (ηdef ) samples:σηwei  ηdef
ηdef

(5.22)

We found +0.3% for the momentum contribution and -1.6% for the charge
exchange contribution.
K

Secondary Interactions (SI)We estimate the systematic uncertainty due to K secondary interactions
in water using the same new PDK MC sample and the same method as
discussed in Section 5.6.1 for FSI, by comparing true K momentum at
decay time distributions (Figure 5.18) and fractions of events with charge

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 103

(a)

(b)

Figure 5.18: The left plot shows true K momentum distributions at decay
time after SI simulation for original PDK MC sample (black) and the one
generated with modified NEUT (green). The right plot shows the weights
calculated from the left plot.
Table 5.4: Fraction of true CX and non-CX events in PDK MC original andnew samples and weight values calculated to evaluate systematic error on
selection efficiency from K SI.
in original sample (%) in new sample (%) weight value
True CX
0.7
0.2
0.257346
True non-CX
99.3
99.8
1.0055exchange K Ñ K 0 in water in both new and original PDK MC samples(Table 5.4).
We found -0.1% for the momentum contribution and +0.5% for the charge
exchange contribution.
Pion Secondary Interactions SI
Charged and neutral pion from the decay of K can interact in water: thedetector simulator SKDETSIM stores the history and type of these interactions in each event. Possible interactions are: Quasi Elastic (QE), Inelastic
Scattering (INEL), Absorption (ABS) and Charge Exchange (CX). 24 setsof coefficients are calculated from experimental results [5] (Table 5.5) andused to change probabilities of interactions and each event probability accordingly: from these coefficients 24 weights are calculated for each event,CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 104
one per coefficient set.
Table 5.5: Sets of coefficients to evaluate pion FSI/SI systematic uncertainty.
The High label means that true pion momentum is over 500 MeV/c at interaction time.
#
QE QE(High) INEL ABS CX CX(High)0(default) 1
1.8
1
1.1
1
1.8
1
0.6
1.8
1
0.7 0.5
1.8
2
0.6
1.8
1
0.7 1.6
1.8
3
0.7
1.8
1
1.6 0.4
1.8
4
0.7
1.8
1
1.6 1.6
1.8
1.4
1.8
1
0.6 0.6
1.8
5
6
1.3
1.8
1
0.7 1.6
1.8
1.5
1.8
1
1.5 0.4
1.8
7
8
1.6
1.8
1
1.6 1.6
1.8
9
0.6
1.1
1.5
0.7 0.5
2.3
10
0.6
1.1
1.5
0.7 1.6
2.3
0.7
1.1
1.5
1.6 0.4
2.3
11
12
0.7
1.1
1.5
1.6 1.6
2.3
13
1.4
1.1
1.5
0.6 0.6
2.3
1.3
1.1
1.5
0.7 1.6
2.3
14
1.5
1.1
1.5
1.5 0.4
2.3
15
16
1.6
1.1
1.5
1.6 1.6
2.3
17
0.6
2.3
0.5
0.7 0.5
1.3
18
0.6
2.3
0.5
0.7 1.6
1.3
0.7
2.3
0.5
1.6 0.4
1.3
19
20
0.7
2.3
0.5
1.6 1.6
1.3
21
1.4
2.3
0.5
0.6 0.6
1.3
22
1.3
2.3
0.5
0.7 1.6
1.3
1.5
2.3
0.5
1.5 0.4
1.3
23
24
1.6
2.3
0.5
1.6 1.6
1.3
The PDK MC is weighted with each of the 24 weighting sets and selection
efficiency is evaluated (Figure 5.19). The mean and RMS of the 24 selection
efficiencies are calculated and systematic error on selection efficiency is estimated as:RMSσ 2.3%(5.23)Mean

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 105

Figure 5.19: Selection efficiency for each pion SI weighting set applied to
PDK MC.

5.6.2

Physics model uncertainties for remaining backgroundWe identified these physics model uncertainties for remaining background: atmospheric ν flux, atmospheric ν cross sections, K

FSI/SI, pion FSI/SI.

Atmospheric ν flux and cross sections
The systematic error on remaining background from atmospheric ν flux andcross sections is evaluated by weighting each event in the ATM-ν MC sample
with weighting sets, one per contribution, developed for the atmospheric
neutrino analyses in SK as reported in [25] and [50]. The systematic error
is taken as the fractional difference between the remaining backgrounds inweighted and unweighted ATM-ν MC samples (Table 5.6 and 5.7).

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 106
Table 5.6: Contributions to systematic uncertainty on remaining backgroundfrom ν flux.

0:
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:

Contribution
absolute normalization (Eν 1 GeV)
absolute normalization (Eν ¡ 1 GeV)νµ {νe ratio (Eν 1 GeV)νµ {νe ratio (1 GeV Eν 10 GeV)νµ {νe ratio (Eν ¡ 10 GeV)
anti-νe {νe ratio (Eν 1 GeV)
anti-νe {νe ratio (1 GeV Eν 10 GeV)
anti-νe {νe ratio (Eν ¡ 10 GeV)
anti-νµ {νµ ratio (Eν 1 GeV)
anti-νµ {νµ ratio (1 GeV Eν 10 GeV)
anti-νµ {νµ ratio (Eν ¡ 10 GeV)
up/down ratio
horizontal/vertical ratio
K/π ratioν flight length
Total

Systematic error
10.3%
0.1%
1.0%
0.1%
0.1%
0.1%
0.1%
0.1%
1.0%
0.1%
0.1%
0.2%
1.2%
4.2%
0.7%
11.3%

Table 5.7: Contributions to systematic uncertainty on remaining backgroundfrom ν cross sections.

15:
16:
17:
18:
19:
20:
21:
22:
23:
24:

K

Contribution
MA in QE and single-π production
NCEL and CCQE ratio
CCQE anti-ν/ν ratio
CCQE µ/e ratio
single meson production
single-π production anti-ν/ν ratio
DIS (model comparison)
DIS
coherent π production
NC/CC ratio
Total

Systematic error
5.7%
0.1%
0.1%
0.1%
20.0%
35.0%
0.1%
0.1%
0.1%
0.1%
40.7

FSI/SI

Considering that no background events containing K remain (Section 5.5.1)
we assign a systematic error on remaining background of  0% from system-

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 107
atic uncertainty on K FSI/SI model.
Pion FSI/SI
The systematic error on remaining background from Pion FSI/SI model uncertainty is calculated in the same way as described in Section 5.6.1. In
particular, information about FSI interactions is stored by NEUT in each
event as well as SI interaction information is stored by the detector simulator SKDETSIM. Figure 5.20 shows the remaining background for each Pion
FSI weight applied to ATM-ν MC sample. Events in the remaining background (Section 5.5.1) contain only neutral pions that decay after  1016
s: for this reason they are not expected to survive long enough to be subject
to Secondary Interactions in water. Therefore systematic error on remaining
background from Pion SI model systematic uncertainty is negligible.

Figure 5.20: Remaining background for each Pion FSI weighting set applied
to ATM-ν MC.
We found a value of 10.3% for the systematic error on remaining background from Pion FSI model systematic uncertainty.

5.6.3

Detector uncertainties

There are several sources of uncertainty in our detector that can affect theanalysis: propagation of light in water,

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 108
 reflections of light on inner surfaces,
 PMT responses,
 energy scale.

Even if these items are subject to accurate calibrations (Section 2.4) a perfectknowledge of the detector is unrealistic: this fact impacts on the simulations
used to estimate selection efficiency and remaining background. A real proton
decay control sample to estimate detector uncertainty impact on this analysis
is not available, so we built a control sample made of events obtained bymerging real data with simulated data, known as hybrid sample (Section
5.6.4).
Other uncertainty sources couldn’t be estimated by using the hybrid sample since it’s missing all the necessary information:
 Michel electrons count, tagged neutrons count.

They are estimated separately.
Michel electrons count
The systematic error from Michel electrons count is estimated by applying
the analysis event selections, as explained in Section 5.3, up to PID cut toboth FCFV real data and ATM-ν MC and comparing the two distributionsof counted Michel electrons obtained by normalizing the MC one by total
number of events (Figure 5.21).
The systematic error σ is evaluated by calculating the fractional difference
ϵ between the number of MC (#MC) and real data (#DATA) events passing
the michel cut (as defined in Section 5.3), summed in quadrature with its
statistical error σϵ :#MC  #DATA(5.24)
ϵ
#DATA
σ

a

ϵ2

σϵ2 

a

2.3%2

1.9%2  3.0%(5.25)

Tagged neutrons count
The systematic error from tagged neutrons count is estimated by applying
the analysis event selections, as explained in Section 5.3, up to michel cut(as defined in Section 5.3) to both FCFV real data and ATM-ν MC andCHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 109

Figure 5.21: Distributions of counted michel electrons in real FCFV data
(black) and ATM-ν MC (blue) samples after nring and PID cuts. ATM-ν
distribution is normalized to the total number of real data events in the plot.

Figure 5.22: Distributions of counted Michel electrons in real FCFV data
(black) and ATM-ν MC (blue) samples after nring, PID and michel cuts.
ATM-ν distribution is normalized to the total number of real data events inthe plot.
comparing the two distributions of counted Michel electrons obtained bynormalizing the MC one by total number of events (Figure 5.21).

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 110
The calculation is the same as in the Michel electrons count case:
σ

5.6.4

a

ϵ2

σϵ2 

a

3.7%2

4.1%2  5.5%(5.26)

Hybrid sample

Hybrid samples contain events built to mimic the signal final state π γγ
kinematics (Section 5.2.1). Four hybrid samples are used, their events arecomposed as follows (Figure 5.23):
 primary DATA sample: a single e-like ring event from real ATMν CCQE data is selected, reconstructed and matched by energy anddirection to the most energetic photon from a simulated signal event,then the remaining e-like and π-like rings are simulated accordingly
and merged to it; primary MC sample: same as the primary DATA sample, but thesingle e-like ring event is selected from the ATM-ν MC sample andreconstructed, its Monte Carlo truth is ignored; secondary DATA sample: same as the primary DATA sample, but
the single e-like ring is selected from the ATM-ν CCQE or stopping-µ
real data repositories and matched to the least energetic photon froma simulated signal event; secondary MC sample: same as the primary MC sample, but thesingle e-like ring from ATM-ν or stopping-µ MC is matched to the least
energetic photon from a simulated signal event.

The building process is performed using APFit reconstructed information,
since its performance is well known compared to fiTQun. Unfortunately, thisprevents us from building a tertiary sample with single π-like ring eventsfrom real data since APFit has no π-like ring hypothesis. Also, such rings
would be too few to have sufficient statistics for this study.
Construction of primary DATA and MC hybrid samples
As a first step, the single e-like ring events from the ATM-ν real data (for
DATA sample) or ATM-ν MC (for MC sample) repositories are selected by
the following criteria:
1. the event is FCFV,
2. the total visible energy (Evis ) is ¡ 30 MeV,CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 111

Figure 5.23: Composition of the events in the four evaluated hybrid samples.
3. the number of reconstructed rings is 1,
4. the reconstructed ring is e-like,5. the goodness of the fit provided by APFit is ¡ 0.6,
6. the e-like ring is unlikely to come from a π 0 decay (invariant mass forπ 0 hypothesis by APFit 100 MeV/c2 ).
Each selected event is given an identification number (iseq) to track theirre-use at analysis time: if multiple events share rings with the same iseq
they are not independent and this is taken into account when computing
statistical errors.
In the second step, for each true π π 0 PDK MC event its kinematics
are extracted: for each particle in the final state momentum, direction andproduction vertex are recorded. Production vertexes of photons are corrected
for conversion length in water ( 40 cm), since it’s only after conversion that
Cherenkov light is produced.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 112
In the third step each event kinematics extracted in the second step areassociated to one single e-like ring event from the first step. For each single
e-like ring, the event particle directions are rotated together to let the mostenergetic gamma true direction match the e-like ring reconstructed direction.
Two rotation axes are defined:
1. the direction of the escaping neutrino from the p Ñ νK decay,
2. the z-axis of the detector, which corresponds to the vertical axis ofsymmetry of the ID cylinder.
If no matches are found the event is discarded. Among all the found matches,
the ring whose reconstructed energy is the closest to the photon true energy
is chosen.
In the fourth step, for each vector with a match, the rings from the least
energetic photon and charged pion are simulated by SKDETSIM using therotated kinematics information and merged with the chosen single e-like ringin a single hybrid event (Figure 5.24).
In the fifth step the hybrid events are reconstructed with fiTQun.
Construction of secondary DATA and MC hybrid samples
The steps are the same as in the construction of the primary samples but
in this case two different kinds of single e-like rings are used to be matchedwith the least energetic photon of the PDK MC kinematics: single e-likering events from ATM-ν CCQE interactions, used to match least energetic
photons with true energies ¡ 60 MeV, and single e-like rings from the decay
electron of cosmic muons stopping in the ID tank produced at least 2.0 µs
after the primary muon event, used to match least energetic photons withtrue energies 60 MeV.
Error calculation taking into account the re-use of rings
Events in the final hybrid samples are not independent from each other: several of them may share the same single e-like rings used during construction,
each one identified by its own iseq number.
Each iseq identifies a class of events: we assume that the number of eventsfrom each class passing the cuts, or being counted in a bin, kiseq follows the
Poisson distribution, each one with a different expected value.
Breaking up the total number of events in a bin, or passing the cuts, k as
k

¸
iseq

kiseq

(5.27)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 113(a) ATM-ν CCQE e-like ring(b) Simulated rings from PDK MC vector(c) Rings merged in a hybrid event

Figure 5.24: The ring merging process of an event built for this analysis.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 114
from the well known properties of Poisson distributions, it follows
σk2 

¸

σk2iseq 

iseq

¸

2
kiseq

(5.28)

iseq

Finally, the error on signal efficiency can be calculated as:
1
σk

ση 
N
N

d¸

2
kiseq

(5.29)

iseq

where N is the total number of events generated in the Fiducial Volume.
Distributions along cut parameters
Hybrid samples events are selected using the same cuts as the analysis explained in Section 5.3, except neutron tagging since neutron capture is not
simulated in the hybrid samples. Distributions along cut parameters areshown in Figures from 5.25 to 5.32. The distributions have the expectedshapes, DATA and MC distributions show no significant disagreements forboth the primary and secondary samples. Finally, the fitted value for reconstructed π 0 mass and K mass both agree with the expected values from the
PDG [17].

(a)

(b)

Figure 5.25: Number of reconstructed rings distributions of FCFV hybrid
primary (left) and secondary (right) samples. The black dots show the DATA
sample, the blue boxes the MC sample in both plots.

Results
The signal efficiencies η after each cut for the primary and secondary samples are shown in Table 5.8 and 5.9 respectively, along with the fractional

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 115

(a)

(b)

Figure 5.26: Distribution of PID after nring cut in FCFV hybrid primary(left) and secondary (right) samples. The black dots show the DATA sample,
the blue boxes the MC sample in both plots.

(a)

(b)

Figure 5.27: Distribution of number of tagged Michel electrons after nring
and PID cuts in FCFV hybrid primary (left) and secondary (right) samples.
The black dots show the DATA sample, the blue boxes the MC sample inboth plots.
differences between MC and DATA efficiencies, defined as:ϵηMC  ηDATA
ηDATA(5.30)The systematic error for each sample is calculated as:
σ

a

ϵ2

σϵ2

(5.31)

where ϵ is the fractional difference after all cuts and σϵ is its statistical error.
By substituting numbers we obtain:
σprimary a1.81%2

10.83%2  10.98%(5.32)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 116

(a)

(b)

Figure 5.28: Distribution of reconstructed π 0 mass (Mπ0 ) after nring, PID
and michel cuts in FCFV hybrid primary (left) and secondary (right) samples. The black dots show the DATA sample, the blue boxes the MC sample
in both plots. Solid lines show gaussian fits for DATA and MC samples.
Fitted values are: primary DATA 133.4  4.7 MeV/c2 , primary MC 133.6 
5.2 MeV/c2 , secondary DATA 131.8  4.8 MeV/c2 , secondary MC 133.7 
4.6 MeV/c2 .

(a)

(b)

Figure 5.29: Distribution of reconstructed π 0 momentum (Pπ0 ) after nring,
PID, michel and Mπ0 cuts in FCFV hybrid primary (left) and secondary(right) samples. The black dots show the DATA sample, the blue boxes theMC sample in both plots. Solid lines show gaussian fits for DATA and MC
samples. Fitted values are: primary DATA 203.1  5.6 MeV/c, primary MC
201.5  6.0 MeV/c, secondary DATA 204.3  5.1 MeV/c, secondary MC
207.6  5.1 MeV/c.
σsecondary a20.96%2

10.38%2  23.39%(5.33)

The final systematic error is calculated by summing the systematic error

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 117

(a)

(b)

Figure 5.30: Distribution of reconstructed π momentum (Pπ ) after nring,
PID, michel, Mπ0 and Pπ0 cuts in FCFV hybrid primary (left) and secondary (right) samples. The black dots show the DATA sample, the blueboxes the MC sample in both plots.

(a)

(b)

Figure 5.31: Distribution of reconstructed K mass (MK ) after nring,
PID, michel, Mπ0 , Pπ0 and Pπ cuts in FCFV hybrid primary (left) andsecondary (right) samples. The black dots show the DATA sample, the blueboxes the MC sample in both plots. Solid lines show gaussian fits for DATA
and MC samples. Fitted values are: primary DATA 490.8  7.0 MeV/c2 ,primary MC 490.8  7.0 MeV/c2 , secondary DATA 492.9  6.9 MeV/c2 ,secondary MC 495.3  6.4 MeV/c2 .
from primary and secondary sample in quadrature:σfinal b2
σprimary2
σsecondary 25.84%(5.34)

This value for the systematic error is dominated by statistical error andprobably overestimated: hybrid sample statistics is limited by the amount ofCHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 118

(a)

(b)

Figure 5.32: Distribution of reconstructed K momentum (PK ) after nring,
PID, michel, Mπ0 , Pπ0 , Pπ and MK cuts in FCFV hybrid primary (left)
and secondary (right) samples. The black dots show the DATA sample, theblue boxes the MC sample in both plots.
Table 5.8: Signal efficiency η after each cut for the primary hybrid MC andDATA samples and their fractional difference ϵ.
CutηMC (%)
nring
13.77  0.68
+PID
9.88  0.53
+michel 9.85  0.53+Mπ09.42  0.52
+Pπ07.28  0.43+Pπ6.34  0.39
+MK
6.05  0.37
+PK
2.60  0.19

ηDATA (%)
15.28  0.78
10.79  0.57
10.77  0.57
10.30  0.54
7.40  0.43
6.53  0.39
6.19  0.38
2.56  0.19

ϵ (%)-9.85  6.38
-8.51  6.88
-8.52  6.90
-8.51  6.95
-1.56  8.20
-2.88  8.31
-2.26  8.45
1.81  10.83

real data used, in this case the whole span of SK-IV data, thus it can’t be
improved further for SK-IV.

5.6.5

Summary of systematic errors

The results of systematic error estimations are summarized in Table 5.10 for
selection efficiency and Table 5.11 for remaining background.

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 119
Table 5.9: Signal efficiency η after each cut for the secondary hybrid MC
and DATA samples and their fractional difference ϵ.
CutηMC (%)
nring
13.13  0.67
+PID
8.55  0.49
+michel 8.51  0.49+Mπ07.93  0.47
+Pπ05.65  0.39
+Pπ
4.96  0.35
+MK
4.71  0.34
+PK
1.69  0.16

ηDATA (%)
14.44  0.75
9.50  0.55
9.43  0.55
8.91  0.53
6.39  0.43
5.47  0.39
5.19  0.38
2.14  0.19

ϵ (%)-9.08  6.62
-10.01  7.34
-9.80  7.40
-11.01  7.48
-11.51  8.59
-9.25  9.13
-9.29  9.34
-20.96  10.38

Table 5.10: Systematic errors for signal efficiency.
Source of uncertainty
Systematic error
Physics model
Correlated nucleon decay
Fermi momentum of nucleon
K FSI: momentum
K FSI: CX
K SI: momentum
K SI: CX
Pion SI
Detector
Propagation of light in water
Reflections of light on inner surfaces
PMT responses
Energy scale
Michel electron count
Total

5.7

 0.5%- 0.6%+ 0.2%- 1.6%- 0.1%+ 0.5%
 2.3%

 25.8%
 3.0%
 26.1%

Lifetime limit calculation

Since we found no candidate events, we calculated lower limits on the proton
partial lifetime using a Bayesian method [40].
The probability to detect n candidate events is calculated by Poisson
statistics:epΓλ bq pΓλϵ bqn
P pn|Γλϵbq (5.35)n!

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 120
Table 5.11: Systematic errors for remaining background.
Source of uncertainty
Systematic error
Physics model
Atmospheric ν flux
Atmospheric ν cross sections
K FSI/SI
Pion FSI/SI
Detector
Propagation of light in water
Reflections of light on inner surfaces
PMT responses
Energy scale
Michel electron countTagged neutrons countTotal

 11.3%
 40.7%
 0%
 10.3%

 25.8%
 3.0%
 5.5%
 50.9%where Γ is the true decay rate, λ is the true detector exposure, ϵ is the truesignal selection efficiency and b is the true number of remaining background
events. Using Bayes’ theorem we obtain:P pΓλϵb|nq P pnq  P pn|Γλϵbq P pΓλϵbq
 P pn|Γλϵbq P pΓq P pλq P pϵq P pbq(5.36)

where P pX q stands for the prior probability of X and the second equality
holds because Γ, λ, ϵ and b are independent.
The probability density function of the decay rate is defined as follows:
P pΓ|nq 

» » »

 A1

P pΓλϵb| nqdλdϵdb» » »epΓλϵ bq pΓλϵ
n!

bq n

P pΓq P pλq P pϵq P pbq dλdϵdb(5.37)

where A is the normalization factor:
A

»8
0

P pΓ|nq dΓ

(5.38)

We assume that P pΓq is uniform and that P pλq and P pϵq are Gaussian:
P pλq

 pλ2σλ20 q

9 e

2

λ

(5.39)

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 121
P pϵq

9 e

 pϵ2σϵ0ϵ2q2(5.40)

where λ0 and ϵ0 are the estimates of exposure and signal selection efficiency
respectively, and σλ and σϵ their systematic errors. The probability of thenumber of remaining background events is calculated as a convolution ofPoisson and Gaussian distributions:
P pbq

9

»8
0

eB B nb  pCb2σ2Bq
b
dB
e
nb !
2

(5.41)

where nb is the number of remaining background events in the 500 year ATMν MC sample, C is a factor to normalize MC live time to data live time andσb is the systematic error on the number of remaining background events.
The lower limit of the decay rate, Γlimit , at 90% Confidence Level (CL) is
calculated as:»
0.9 

ΓlimitΓ 0

P pΓ|nq dΓ

The lower limit of the partial lifetime of p Ñ νK , K
τ {BpÑνK ,K Ñπ π0 (5.42)

Ñ π π0 is:

1Γlimit(5.43)In this analysis we have measured a lower partial lifetime limit:
τ {BpÑνK ,K Ñπ π0  6.7  1032

(5.44)

which is less stringent than the one in the latest reference analysis using
APFit (2017) (Table 5.12).
Table 5.12: Summary of results for p Ñ νK , K Ñ π π 0 analysis using SKIV only data (3244.4 days). Reference results are from Super-Kamiokande
Collaboration Meeting, November 2017.
This analysis 2017 analysis
Exposure (kton*year)
200
177# Remaining background0.03  0.02
0.14
Sys. err. on remaining background (%)
50.9
31.6
Signal selection efficiency (%)
2.9  0.02
9.4  0.1
Sys. err. on signal selection efficiency (%)
26.1
8.7# data candidates
0032
Limit (years)
6.7  10
2.4  1033

CHAPTER 5. SEARCH FOR P Ñ νK IN SK-IV USING FITQUN 122

5.8

Conclusions and perspectives

We searched for proton decay p Ñ νK , K Ñ π π 0 in the full livetime of
SK-IV equivalent to an exposure of 200 kton*years using the reconstruction
algorithm fiTQun. The final results are shown in Table 5.12. We foundno data candidates, same as 2017 reference analysis which used APFit. Our
method has a signal selection efficiency about 3 times lower than the reference
analysis but almost 4 times less remaining background is expected. Even if we
didn’t provide a more stringent lower partial lifetime limit for the proton, wewere successful in reconstructing the charged kaon kinematics with fiTQun,
which contributed to reduce significantly the remaining background, aiming asingle event discovery. We also used the hybrid sample technique to produce
for the first time a control sample to estimate detector error in this proton
decay mode.
Some ideas for future improvements are:
 extend the analysis to other SK epochs,
 include 2-ring events,
 expand Fiducial Volume [60].

Chapter 6
Perspectives:
Hyper-Kamiokande
Hyper-Kamiokande (HK) will be the largest water Cherenkov detector in
the world [11], currently (2022) under construction, it is expected to start its
operations in 2027.
Hyper-Kamiokande is designed to take advantage of the Kamiokande andSuper-Kamiokande experience but with some improvements to overcome the
new challenges it brings: a larger detector to improve statistics and improved
photo-sensors for better efficiency among all.
With  8 times the SK Fiducial Volume, Hyper-Kamiokande will be anatural candidate experiment to detect proton decay.
In this Chapter we present an overview of the Hyper-Kamiokande detector
and two studies towards proton decay detection in p Ñ e π 0 mode. Studiesof: fiTQun performance in Hyper-Kamiokande, tuning of the ring counting parameters of fiTQun.

6.1

Detector overview

Hyper-Kamiokande relies on the same detection principles as Super-Kamiokande,
explained in Section 2.2.1. The detector will be built in the Tochibora mineof the Kamioka Mining and Smelting Company, near the town of Kamioka,
Gifu Prefecture, Japan, about 8 km south of Super-Kamiokande and 650 m
below the peak of Mount Nijugo, equivalent to 1750 m of water.
The cylindrical cavern to house the detector will have height of 71 m anda diameter of 68 m (Figure 6.1), plus a 16 m high dome on top. The excava123

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

124

Figure 6.1: Drawing of the HK detector in its caverntion works will include smaller caverns for the collateral systems, like water
circulation and purification and access tunnels. Two types of photosensors
will be employed for physics studies: 20000 Box and Line (B&L) PMTs anda certain number of multi-PMTs (mPMTs), in the order of thousands, yet
to be confirmed.

6.1.1

Water tank

The cavern will be covered with a layer of shotcrete and a layer of waterproof
lining to prevent ultra pure tank water to leak out and cave water to leak in.
A 50 cm thick reinforced concrete layer lined with a 5 mm thick waterproof
high-density polyethylene (HDPE) will be added to improve stability andinsulation of the tank.
A combination of vertical rectangular coils (y-z plane) and circular coils(x-y plane) will be embedded in the concrete layer to compensate for geomagnetic field in the cave since it negatively affects PMTs collection efficiency.
A stainless-steel structure will separate the inner and outer detector regions and support the PMTs and their covers, as well as front-end electronics(Figure 6.2). While the bottom section will be free-standing on the bottomof the tank, same as in Super-Kamiokande, the barrel and top sections willsuspended from the ceiling of the cavern, reducing frame thickness, weightand cost.
The inner and outer detector regions will be optically insulated to allow

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

125

Figure 6.2: Design of the internal structure of the HK detector
the OD to operate as an active veto.

6.1.2

Water purification and circulation system

Water in the tank must be ultra-pure: radon emanating from materials in
the tank, like the glass of photosensors and the support structure, and fromthe surrounding rocks, is a major source of low-energy background that must
be removed. Impurities in water can absorb and scatter photons and must
be removed as well. In Super-Kamiokande water is constantly re-circulated
and purified: a water transparency of over 100 m and a Radon concentrationin the ID of less than 1 mBq/m3 is achieved: in Hyper-Kamiokande thediagonal size is about 100 m, for this reason a similar or better water quality
will be required.
The water purification systems will be made of two separate stages: onefor tank filling and one for constant re-circulation (Figure 6.3). The water
will come from the storage well of the snow-melting system of the townof Kamioka: during filling 105 tons/hour of water will be required to fill
the detector with purified water at a rate of 78 tons/hour, such that filling
operations will take about six months to be accomplished starting from anCHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

126

Figure 6.3: Schematic of the HK water systemempty tank. Water will be re-circulated at a rate of 310 tons/hour, suchthat the total water mass will be re-circulated once per month, same as inSuper-Kamiokande.
In the first stage the raw water is passed through a 10 µm filter to remove dust and larger particles and then it’s processed with reverse osmosis(RO) and additional filters (MB) to remove smaller particulates. A vacuum
degasifier (VD) removes dissolved Oxygen, to quench bacterial growth, andRadon.
In the second stage water coming from the tank is sterilized with UV lightand filtered before going through RO, further UV irradiation (UV TOC), a
cartridge polisher (CP) that removes heavy ions and more advanced filtration(MV, UF). An heat exchanged (HE) cools water down to remove heath produced by photosensors, electronics and the purification system itself. Finally,cooled water is degasified in a VD and pumped back into the tank.
Radon-free air with a concentration of less than 1 mBq/m3 will be used
as a cover gas for the tank as well for buffer tanks which are part of thewater system. To prevent Radon from entering the inner detector from thesurrounding rocks there will be no water exchange between the inner andouter detector.
Water flow will be controlled to improve efficiency of water replacement:
simulations show that the best configuration is to supply cold water at thebottom and to drain water at the top, effectively inducing laminar flow anda vertical quality gradient throughout the tank.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

6.1.3

127

Inner Detector (ID)The inner detector wall is divided into 40000 square cell with a size of 70
cm, which can house a single 50 cm PMT or a single mPMT module each
(Figure 6.4).

Figure 6.4: Inner detector cells
In this thesis we will consider two ID configurations: 20kBL: 19620 50 cm B&L PMTs,
 20kBL+10kmPMT: 19208 50 cm B&L PMTs plus 9616 mPMT modules.

In our simulations the ID has a radius of 32.4 m and it’s 65.751 cm high.
B&L PMTsThe Hamamatsu R12860-HQE is a new 50 cm PMT model (Figure 6.5) witha higher quantum efficiency and a box-and-line (B&L) dynode developedfor Hyper-Kamiokande. It features twice the total detection efficiency for asingle photon with respect to Super-Kamiokande R3600 PMTs by combining
an improved quantum efficiency (30% at 390 nm) (Figure 6.6(a)) and capture

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

128

efficiency (from 73% to 95% in the central 46 cm diameter) by changing glass
curvature, focusing electrode and by using the box-and-line dynode which has
a larger first stage with higher acceptance with respect to Venetian blind.
The time resolution is improved to 4.1 ns at FWHM, about half the one ofSuper-Kamiokande PMTs, (Figure 6.6(b)) and the charge resolution is 35%(50% in Super-Kamiokande PMTs).

(a)

(b)

Figure 6.5: Picture (left) and schematic (right) of a B&L PMT.
The nominal gain of B&L PMTs is 107 at 2000 V but bias voltage canrange from 1500 V to 2200 V.
Linearity of charge response is 5% up to 470 photoelectrons and saturationthreshold is higher than 2000 pe, covering the MeV to multi-GeV event range.

(a) Quantum Efficiency as a function of (b) Single photoelectron transit time distriwavelength.
bution.

Figure 6.6: Comparison of relevant parameters between B&L (R12860) andSK Venetian blind PMTs (R3600).
In 2018 136 B&L PMTs were mounted in Super-Kamiokande ID to test

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

129

them under real conditions and check gain and dark rate stability over time.
Current design considers a dark rate of 4.2 kHz.
B&L PMTs also feature mechanical improvements in their bulb shapeand thickness, optimized to survive below 60 m of water (0.6 MPa pressure).
Multi-PMT
Multi-PMTs (mPMTs) are composite hemispherical photosensors made of
19 smaller 7.7 cm PMTs (Figure 6.7), developed from an original design by
the KM3NeT collaboration to operate in the depths of the Mediterranean
Sea.

(a)

(b)

Figure 6.7: Picture (left) and drawing (right) of a mPMT photodetector
The mPMT module to be installed in Hyper-Kamiokande is made ofa cylindrical structure, which contains electronics and a support structure
holding the PMTs in place. The photosensitive surface of each PMT issurrounded by a conical reflector that increases light collection by 20%. An
acrylic window is placed in front of the PMTs and coupled to them with
optical gel. The main advantage of mPMTs with respect to B&L PMTs istheir higher granularity, which may improve reconstruction performance of
events close to the ID wall or for separating overlapping Cherenkov rings
in multi-ring events, like proton decay candidates. Different PMTs in themPMT modules have different fields of view: this can be exploited to identify
dark noise in the elements facing away from the reconstructed event vertex,
which would improve reconstruction performance especially for low energy
events. Finally, the smaller PMTs may be less sensitive to external magnetic
fields and show a better timing resolution. All these improvements come at

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

130

the cost of a significantly smaller sensitive area with respect to a 50 cm B&L
PMT.

6.1.4

Outer Detector (OD)In Super-Kamiokande the outer detector is approximately 2 m wide andequipped with 1885 20 cm PMTs that provide a photocoverage of 1% and are
attached to wavelenght shifting plates that increase light collection by about
50%. A 0.6 m wide dead space separates the ID from the OD. In HyperKamiokande 7.7 cm PMTs (0.21% and 0.42% photo-coverage respectively)
have been considered by providing a more uniform coverage.
Light collection
Eljen EJ-286 wavelenght shifting plates will be optically coupled by contact
around each PMT to increase light collection: the plates absorb photons
ranging between 280 nm and 400 nm and re-emit them with wavelengths
between 410 nm and 460 nm, close to the peak wavelength of PMTs quantum efficiency. Computer simulations and laboratory tests show that adding
square plates with a size of 60 cm around each PMT would increase lightcollection by a factor 3, achieving an effective photocoverage of about 1%,
same as Super-Kamiokande.
The outer wall of the OD will be lined with a sheet of highly reflective
Tyvek to help recognizing outgoing muon events.

6.1.5

Electronics

Front-end electronics provide PMTs with the necessary high voltage andcollect and digitize time and charge data whenever a hit is detected, buffering
them if necessary waiting to deliver them to the data acquisition system.
In Hyper-Kamiokande front-end electronics modules are mounted on the
PMT support structure and serve 24 nearby PMTs. Only one cable permodule descends into the tank from the electronics hut on top, reducing
cable cost and weight. Since the connection is digital, no signal degradation
is expected to happen due to cable length, which can reach 100 m for some
PMTs.
Front-end modules need to be water-tight and pressure-resistant, as wellas their connectors. Their case will be constructed from stainless steel toachieve good heath exchange but at the same time power consumption mustbe limited to avoid convection in nearby water due to heat dissipation.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

131

ID electronics
The electronics module for the ID is made of the following components:
 power supply: a single cable delivers DC power from the dome to eachelectronics module, 48 V by baseline design. A low voltage power supply system (LV PS) feeds the other components, while a separate stable and low-noise high voltage (HV) system feeds photosensors. Powerconsumption is expected to be below 1 W per channel;
 signal digitizer: a single signal digitizer module collects charge information from 24 PMTs and digitizes it at a maximum rate of 1 MHz
per PMT; clock and counter system: the clock system is designed to provide
uniform timing across the detector within 100 ps. A master clock generator is located above the water tank: it uses GPS and an atomic clock
to generate reference clock and counter signals, and sends them overoptical fiber connections to a distribution network serving the modules
in the tank. Each module contains a clock and counter component with
two optical interfaces for fault tolerance. It also works as a communication module for the digitizer, sending status and number of digitizedhits to the dome via the distribution network; data handling and digitizer control: the data handling and digitizer control component stores data from the digitizer in a dedicated
8 GB buffer, enough for several minutes of operation, before sending
it to the read-out system. This block implements data error checking
and can include data compression; slow control: the slow control component monitors environmental
conditions inside the electronics module using temperature and humidity sensors. It also monitors low and high voltages and can control HVand current for each channel following commands from the digitizer
control component; system control and network interface: the system control and network interface component routes communications between components
inside the module and between the module and the main electronics
in the dome via multiple redundant optical interfaces. Data transfers
use TCP/IP for error detection and correction while control commands
and monitoring use UDP/IP.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE132

OD electronics
The electronics modules for the OD are likely to be very similary to thosefor the ID: 7.7 cm PMTs require lower HV (600 V to 1100 V) and theiruse as a veto requires less precise charge and timing information. The cost
reduction from the replacement of some components with cheaper versions
competes with the cost reduction due to mass manufacturing of a single typeof electronics module.
Multi-PMT electronics
The mPMT modules contain individual front-end boards for every PMT
and one main board per module, which has the same functions as the ID
electronics modules.
The Hyper-Kamiokande mPMT electronics has been designed to fulfill
the following requirements:
 timing resolution: it should be about 500 ps for 1 p.e. and about
200 ps for large p.e. pulses;
 charge resolution: 0.1% FWHM in the range  0.05 p.e. up to 25
p.e.; power consumption: it should be less than 4 W per mPMT module to prevent interference with water circulation and its temperaturestability.

6.1.6

DAQ

The data acquisition system (DAQ) collects all PMTs digitized data fromthe front-end modules in the water tank, combines them to identify eventsand store them into mass storage for further analysis. The system if madeof four components:
 Readout Buffer Units (RBUs): the DAQ system will contain 70
RBUs connected to the front-end electronics modules via a a Gigabit
network switch for load balance and re-routing in case of failure. EachRBU reads digitized signals from about 30 front-end modules: it buffers
all data in memory for 100 seconds and temporarily saves older datato hard drives for one hour. RBUs also reduce data by removing all
PMT signals below hit threshold (0.25 photoelectrons, same as SuperKamiokande) and makes them available to trigger processing and event
building modules upon request;

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

133

 Trigger Processor Units (TPUs): The TPUs analyze time windows in reduced data, searching for possible events by applying several
trigger algorithms. The simplest trigger, which is the one used in thisstudy, is the NDigits or Simple Majority: if the number of hits in a
sliding time window meets a threshold an event is tagged. This is a
trigger suitable for high-events but low-energy events require a more
complex approach to cope with the unavoidable dark-noise hits. The
Vertex Reconstruction trigger exploits the fact that a low-energy lepton travels only a few centimeters in water before its energy falls below
Cherenkov threshold, so its track can be approximated as a pointlike source that emits all Cherenkov photons at the same time andfrom the same position. This algorithm uses a uniformly spaced threedimensional grid of test vertices inside the tank. For each vertex itcorrects the recorded hit times by the time-of-flight and applies an
NDigits trigger with a reduced time window of 20 ns. If the test vertex
is close to the true vertex of an event a narrow peak is produced whiledark noise remains randomly distributed.

All triggers are software-based, so they can be updated; Event Builder Units (EBUs): once a TPU has identified an event
it requests an EBU to associate data from the RBUs with event timestamps. The EBU retrieves relevant data and stores them to disk forlong-time preservation;
 brokers: two identical machines act as brokers, balancing load to
TPUs and EBUs, managing failing modules for seamless detector operation.

6.2

HK data

For this study in Hyper-Kamiokande we used a simulated proton decay p Ñ
e π 0 sample: here we describe the steps followed to generate it and the tools
used for this purpose.

6.2.1

Proton decay kinematics

Free protons decay back-to-back into a positron and a neutral pion, each carrying a momentum of 459 MeV/c (Figure 6.8). Then neutral pions promtply( 10-16 s) decay into two photons in 98.8% of the times.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

134

Figure 6.8: p Ñ e π 0 free proton decay scheme.
In the final state we expect three well visible e-like rings and well defined kinematics: this is the reason why we chose this decay mode for our
preliminary study.
For the decay of protons bound in Oxygen nuclear effects and pion FSI
must be considered as explained in Section 3.4: since this complicates the
final states, we restrict this preliminary study to free proton decays only.

6.2.2

Proton decay event generation

We generated proton decay events using NEUT [36] with primary vertexes
uniformly distributed inside the ID volume with a true distance from its wall
(dwallv ) ¡ 100 cm (Figure 6.9), to improve our statistics and to avoid non
physical simulation: events too close to the wall with light produced towards
it would have required the simulation of PMT saturation, which was not
implemented yet.
We generated 10000 events, of which 1942 (19.42%) are free proton decays. Table 6.1 shows the breakdown of final states in the events. While
the positron always escapes the Oxygen nucleus, the neutral pion undergoes
nuclear effects (FSI), as explained in Section 3.2.1, that produce different
meson configurations in the final state for bound proton decays.
Figure 6.10 shows true momentum distributions for positron and neutralpion in events with true final state e π 0 for both free and bound proton
decays. The distributions agree with the expected shapes and values: while
momentum distributions of free proton decay products are monochromatic,in the case of bound protons the decay products carry part of the nuclear
momentum of their parent which broadens their momentum distributions.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE(a) True x(b) True y(c) True z(d) dwallv

135

Figure 6.9: True proton decay vector primary vertex coordinates distributions and true distance from ID wall distributions (dwallv ). The black solidlines show the expected coordinates distributions assuming uniform primaryvertex generation in the ID volume with dwallv ¡ 100 cm.
In the case of neutral pions from bound proton decays a minor peak inmomentum distribution is due to scattering with nucleons.
Figure 6.11 shows the true cosine of the opening angle between positronand neutral pion in proton decay vectors after nuclear effects for both freeand bound proton case. The distributions agree with the expected shapes
and values: in the free proton case the opening angle is exactly 180 , as
expected for a two body decay at rest, while in the bound proton case theopening angle is less than 180 due to the conservation of the parent proton
momentum.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

136

Table 6.1: Breakdown of p Ñ e π 0 events final states after nuclear effects.
Total # events 10000
Free protons
1942
Breakdown: e π 0
1942
Bound protons 8058
Breakdown: e π 0
4713
e
1814

e π
759
e π
740
0
e π π
8
e π0π
5

e π π
5
0

e π π π4e π0π040 0 e π π π2e π ππ
2
e π π
1


e π π
1

6.2.3

Detector simulation

The Water Cherenkov Simulation (WCSim) package is a flexible, Geant4based code that is designed to simulate the geometry and physics responseof user-defined water Cherenkov detector configurations [11]. Geant4 [20] isused to track the particles as they pass through the detector and computethe final deposited energy. Geant4 also simulates Secondary Interactions (SI)of particles in water, their decays and Cherenkov light emission, in particular. Particles that reach photodetector glass and pass the quantum efficiency
and collection efficiency thresholds are registered as a hit. WCSim implements both B&L PMTs and mPMTs and simulates electronics response tophotodetector hits: each event contains information about hits before (raw )and after (digitized ) front-end electronics simulation for both photodetector
types.
We used WCSim to generate one proton decay sample for each of thefollowing configurations from the events we generated: 20kBL 20kBL+10kmPMT

as defined in Section 6.1.3.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

(b)

(c)

(d)

137

Figure 6.10: True positron (left) and neutral pion (right) momentum distributions for free proton (top) and bound proton (bottom) proton decay
vectors with true e π 0 final state after nuclear effects. The vertical red line
shows the expected momentum value in the free proton case of 459 MeV/c.

6.2.4

Reconstruction

The reconstruction algorithm for HK is fiTQun: the version we used was stillin development and for this reason it had four main important limitations
with respect to fiTQun for SK:
 the maximum number of rings per multi-ring events is 4, instead of 6,
to save computational time during development; the prediction of charge from indirect light (Section 4.3.2) was not
implemented;
 no ring correction algorithm to reject fake rings is applied; no refitting of the selected hypothesis is performed, thus all the ringsin one event share the same reconstructed vertex.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

138

(b)

Figure 6.11: True cosine of the opening angle between positron and neutralpion for free proton (left) and bound proton (right) proton decay vectors
with true e π 0 final state after nuclear effects. The vertical red line showsthe expected cosine value for the free proton case of -1, corresponding to a
back-to-back two body decay.
We applied the same version of fiTQun to reconstruct both samples.

6.3

First study: fiTQun performance

We studied the signal selection efficiency for proton decay p Ñ e π 0 searchfor both 20kBL and 20kBL+10kmPMT configurations. The reference studies
in Super-Kamiokande for this decay mode are [56] and [41].
For this preliminar study we used the Ea0 , M ua0 and a1 multi-ring fitterring counting parameters (see Section 4.3.9) obtained from the tuning forLong Baseline neutrino analysis. A tuned a0 parameter was not available,
so we set it to the same value as Ea0 in both configurations. All values areshown in Table 6.2.
Table 6.2: Multi-ring fitter ring counting parameters used for both 20kBL
and 20kBL+10kmPMT configurations.
Configuration

Ea0

M ua0

a0

a1

20kBL
167.5
20kBL+10kmPMT 227.5

167.5
227.5

167.5 1.65
227.5 1.55

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

6.3.1

139

Event selections

We apply the same event selections as those in [56], except for FC reduction,
since the OD is not simulated in our samples, and neutron tagging, for thesame reason:
1. FV: Distance of reconstructed vertex from wall dwall ¡ 150 cm,
2. nring: 2 or 3 reconstructed rings,
3. PID: all reconstructed rings are e-like,4. michel: no Michel electrons tagged,
5. Mπ0 : reconstructed π 0 mass is between 85 MeV/c2 and 185 MeV/c2
for 3-ring events,
6. Mtot : total reconstructed invariant mass is between 830 MeV/c2 and1050 MeV/c2 ,7. Ptot : total reconstructed momentum is below 250 MeV/c.

6.3.2

Distributions along cut parameters

(a)

(b)

Figure 6.12: Reconstructed distance of primary vertex from ID wall distributions for free proton decay samples p Ñ e π 0 events in 20kBL (left) and
20kBL+10kmPMT (right) configurations.
Figures from 6.12 to 6.18 show distributions along cut parameters forboth 20kBL and 20kBL+10kmPMT configurations.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

140

(b)

Figure 6.13: Number of reconstructed rings distributions for free proton decay p Ñ e π 0 samples in 20kBL (left) and 20kBL+10kmPMT (right) configurations, after FV cut.

(a)

(b)

Figure 6.14: PID distributions for free proton decay p Ñ e π 0 samples in
20kBL (left) and 20kBL+10kmPMT (right) configurations, after FV andnring cuts.
By comparing the distributions of the number of reconstructed rings forfree proton decays from the reference study [56] (Figure 6.19) and this study(Figure 6.13), we can spot an important discrepancy: in the reference study
the fraction of 3-ring events before ring correction dominates (68.9%), as
expected since three rings should be visible in each free proton event whilein this study the 2-ring events fraction dominates instead in both 20kBL(24.4%) and 20kBL+10kmPMT (26.6%) configurations. This effect is the
subject of the second preliminary study we performed (Section 6.4).
Reconstructed π 0 mass fitted values for 20kBL and 20kBL+10kmPMT
configurations are 1.9% and 3.1% higher than the expected value of 135.0

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

141

(b)

Figure 6.15: Counted michel electrons distributions for free proton decay p Ñ
e π 0 samples in 20kBL (left) and 20kBL+10kmPMT (right) configurations,after FV, nring and PID cuts.

(a)

(b)

Figure 6.16: Reconstructed π mass (Mπ ) ) distributions for free proton
decay p Ñ e π 0 samples in 20kBL (left) and 20kBL+10kmPMT (right)
configurations, after FV, nring, PID and michel cuts.
MeV/c2 but still compatible with it within statistical error. Reconstructed
total mass fitted values for 20kBL and 20kBL+10mPMT are significantly
higher than the expected value of 938.3 MeV/c2 by 4.2% and 4.4% respectively.

6.3.3

Results

Table 6.3 summarizes signal selection efficiencies η along cuts for both 20kBL
and 20kBL+10mPMT configurations.
Signal selection efficiency for the configuration with mPMTs is signifi-

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

142

(b)

Figure 6.17: Total reconstructed mass (Mtot ) distributions for free proton
decay p Ñ e π 0 samples in 20kBL (left) and 20kBL+10kmPMT (right)
configurations, after FV, nring, PID, michel and Mπ cuts.

(a)

(b)

Figure 6.18: Total reconstructed momentum (Ptot ) distributions for free proton decay p Ñ e π 0 samples in 20kBL (left) and 20kBL+10kmPMT (right)
configurations, after FV, nring, PID, michel, Mπ and Mtot cuts.
cantly higher than that of the one without, even if well below the signal
selection efficiency for the free proton case 85% from the reference study [56].
Figure 6.20 shows signal selection efficiencies for both configurations as afunction of true distance of primary vertex from the ID wall: signal selection
efficiency for the configuration with mPMTs is significantly higher than thatof the configuration with BL PMTs only in the region closest to ID wall.
This hints that, as expected, the addition of mPMTs improves performanceof events close to the wall.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

143

Figure 6.19: Number of reconstructed rings distributions for proton decayp Ñ e π 0 MC sample from reference study [56] in Super-Kamiokande, reconstructed with APFit (black) and with fiTQun before (blue) and after (red)ring correction.
Table 6.3: Signal efficiency, remaining background and remaining data
events after each cut
Cutsη20kBL (%) η20kBL+10kmPMT (%)
FV
97.8  0.5
98.9  0.3+nring84.4  1.2
87.9  1.1+PID
67.7  1.5
78.2  1.3+michel 67.5  1.5
77.9  1.3+Mπ066.6  1.5
76.7  1.4+Mtot
63.2  1.6
72.4  1.5+Ptot
63.1  1.6
72.4  1.5

6.4

Second study: tuning of fiTQun ring counting for proton decay

In the first preliminary study we performed (Section 6.3), we found that thefraction of p Ñ e π 0 MC events with 2 reconstructed rings is dominant whileaccording to expectations and the reference study [56] the dominant fraction
should be that of events with 3 reconstructed rings.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

144

Figure 6.20: Signal selection efficiencies for p Ñ e π 0 samples in both 20kBL(blue) and 20kBL+10kmPMT (red) as a function of true distance of primaryvertex from the ID wall (dwallv ) ranges.
We tuned the a0 fiTQun ring counting parameter in order to maximize the3-ring event fraction in both 20kBL and 20kBL+10kmPMT configurations:its value rules ring counting for a number of reconstructed rings greater thanone, as explained in Section 4.3.9. We kept the other fiTQun ring counting
parameters from the previous study.
The tuning plots are shown in Figure 6.21: the optimal values for a0 are
43 for 20kBL and 44 for 20kBL+10kmPMT, the distributions of the numberof reconstructed rings with these preliminary optimized a0 values are shownin Figure 6.22).
The expected 3-ring events fraction is 68.9% (Figure 6.19). The fractions
obtained from our optimization procedure are 57.6% for 20kBL and 60.5%
for 20kBL+10kmPMT, both dominant but still lower than expected.
Moreover, the 4-ring events fractions are 23.9% for 20kBL and 23.4% for
20kBL+10kmPMT, both higher than 13.7% as in the reference. In this studyfiTQun doesn’t consider indirect light contribution: there is no easy way toestimate its impact and to understand if it can explain these differences.
For this reason we tried to estimate how much the 4-ring fractions could
be reduced by applying the ring correction from the reference study by hand.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

(a)

145

(b)

Figure 6.21: Fraction of free proton p Ñ e π 0 MC events with 3 reconstructed rings, after FV cut, as a function of fiTQun ring counting parameter a0 in both 20kBL (left) and 20kBL+20kmPMT (right) configurations.
The red solid lines show gaussian fits of the peaks.

(a)

(b)

Figure 6.22: Distributions of the number of reconstructed rings in p Ñ e π 0
MC events, after FV cut, in both 20kBL with (left) and 20kBL+10kmPMT(right) configurations, using a0 values that maximize the 3-ring events fractions.

6.4.1

Manual check of ring correction

The ring correction algorithm from the reference study works by merging themost energetic reconstructed ring with the closest ring within 20 from its
reconstructed direction.

CHAPTER 6. PERSPECTIVES: HYPER-KAMIOKANDE

146

We manually scanned 5 events with 4 reconstructed rings and checked
if they can trigger this algorithm: 1/5 events would trigger it bringing a
reduction of 20%  18%, which is not sufficient to explain the excess of 4
ring events.

6.4.2

Results

We found the preliminar optimal value for the fiTQun ring counting parameter a0 for p Ñ e π 0 , in both 20kBL and 20kBL+10kmPMT configurations.
We still see a significant excess of events with 4 reconstructed rings that can’t
be fixed by tuning and that is only partially explained by the absence of aring correction algorithm.

Conclusions
We searched for proton decay p Ñ νK in 3244.4 days of data acquired by theSuper-Kamiokande experiment equivalent to an exposure of 200 kton*year:
we found no data candidates. The fiTQun reconstruction algorithm enabled us to successfully reconstruct kaon kinematics and to develop a lowbackground analysis. Finally, we checked fiTQun performance in reconstructing proton decay p Ñ e π 0 events in Hyper-Kamiokande. We found that the
introduction of multi-PMT photosensors significantly improves selection efficiency. Finally, we tuned fiTQun ring counting parameters: we found asignificant excess of events with 4 reconstructed rings which deserves further
investigation in the future.

147

Acknowledgements
First of all, I would like to express my gratitude to the Super-Kamiokande
and Hyper-Kamiokande Collaborations, especially to Prof. S. Mine and Prof.
M. Miura, for all their precious time and tutoring effort.
I would also like to thank the INFN group in Bari for its constant support: Prof. V. Berardi, Dr. M. G. Catanesi, Dr. L. Magaletti and Dr. E.
Radicioni for sharing with me their priceless advice and ideas, which will be
an important resource for my future.
Finally, a special word of thanks goes to the referee of this thesis, Prof.
G. De Rosa, who welcomed me to the INFN group in Naples and spent many
hours of tutoring with me. Her support made this work possible.

148

Bibliography[1] Geant3, CERN-DD-EE-84-1.
[2] S.M. Bilenky and B. Pontecorvo. Lepton mixing and neutrino oscillations. Physics Reports, 1978.
[3] P. A. Cherenkov. Visible emission of clean liquids by action of γ radiation. Doklady Akademii Nauk SSSR, 1934.
[4] M. K. Parida D. Lee, R. N. Mohapatra and M. Rani. Predictions for proton lifetime in minimal nonsupersymmetric so(10) models: An update.
Phys. Rev. D, 1995.
[5] P. de Perio. Neut pion final state interactions. In AIP Conf. Proc.
[6] A. Einstein. Ueber einen die erzeugung und verwandlung des lichtes
betreffenden heuristischen gesichtspunkt. Annalen der Physik, 1905.
[7] A. Suzuki et al. Improvement of 20-inch diameter photomultiplier tubes.
Nucl. Instrum. Meth. A, 1999.
[8] G. AAd et al. Observation of a new particle in the search for the standard
model higgs boson with the atlas detector at the lhc. Phys. Rev. Lett.,
2016.
[9] H. Ikeda et al. Front end hybrid circuit for super-kamiokande. Nucl.
Instrum. Meth. A, 1992.
[10] H. Nishino et al. High-speed charge-to-time converter asic for the superkamiokande detector. Nucl. Instrum. Meth. A, 2009.
[11] Hyper-Kamiokande Proto-Collaboration: K. Abe et al.
kamiokande design report. Technical report, 2018.

Hyper-[12] K. Abe et al. Calibration of the super-kamiokande detector. Nucl.
Instrum. Meth. A, 2014.
149

BIBLIOGRAPHY

150[13] K. Nakamura et al. The reaction c-12 (e, e’ p) at 700-mev and dwia
analysis. Nucl. Phys. A, 1976.
[14] M. Honda et al. Calculation of the flux of atmospheric neutrinos. Phys.
Rev. D, 1995.
[15] M. Honda et al. Calculation of atmospheric neutrino flux using theinteraction model calibrated with atmospheric muon data. Phys. Rev.
D, 2007.
[16] M. Honda et al. Improvement of low energy atmospheric neutrino flux
calculation using the jam nuclear interaction model. Phys. Rev. D, 2011.
[17] M. Tanabashi et al. Particle data group. Phys. Rev. D, 2018.
[18] R. Becker-Szendy et al. Imb-3: A large water cherenkov detector for
nucleon decay and neutrino interactions. Nucl. Instrum. Meth. A, 1993.
[19] R.W. Bland et al. The k p interaction from 864 to 1585 mev/c: Cross
sections and mass distributions. Nuclear Physics, 1969.
[20] S. Agostinelli et al. The super-kamiokande detector. Nuclear Instruments and Methods in Physics Research A, 2003.
[21] S. Chatrchyan et al. Observation of a new boson at a mass of 125 gev
with the cms experiment at the lhc. Phys. Lett. B, 2012.
[22] S. Fukuda et al. The super-kamiokande detector. Nuclear Instruments
and Methods in Physics Research A, 2003.
[23] S. Jadach et al. The tau decay library tauola: Version 2.4. Comput.
Phys. Commun., 1993.
[24] U. Amaldi et al. Comparison of grand unified theories with electroweak
and strong coupling constants measured at lep. Phys. Lett., 1991.
[25] Y. Ashie et al. A measurement of atmospheric neutrino oscillation parameters by super-kamiokande i. Physical Review D, 2005.
[26] C. McGrew et al. (IMB Collaboration). Search for nucleon decay using
the imb-3 detector. Phys. Rev. D, 1999.
[27] K. S. Hirata et al. (Kamiokande Collaboration). Experimental limits on
nucleon lifetime for lepton + meson decay modes. Phys. Lett. B, 1989.

BIBLIOGRAPHY

151[28] K. Eguchi et al. (KamLAND Collaboration). First results from kamland:
evidence for reactor antineutrino disappearance. Phys. Rev. Lett., 2003.
[29] Q. R. Ahmad et al. (SNO Collaboration). Direct evidence for neutrino
flavor transformation from neutral-current interactions in the sudbury
neutrino observatory. Phys. Rev. Lett., 2002.
[30] H. Nishino et al. (Super-Kamiokande Collaboration). Search for proton
decay via p Ñ e π 0 and p Ñ µ π 0 in a large water cherenkov detector.
Phys. Rev. Lett., 2009.
[31] M. Shiozawa et al. (Super-Kamiokande Collaboration). Search for proton decay via p Ñ e π 0 in a large water cherenkov detector. Phys. Rev.
Lett., 1998.
[32] Y. Fukuda et al. (Super-Kamiokande Collaboration). Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett., 1998.
[33] C. L. Cowan F. Reines and M. Goldhaber. Conservation of the numberof nucleons. Phys. Rev., 1954.
[34] H. Georgi and S. L. Glashow. Unity of all elementary particle forces.
Phys. Rev. Lett., 1974.
[35] Jeffrey D. Gustafson. A search for baryon number violation by two units
at the Super-Kamiokande detector. PhD thesis, Boston University, Graduate School of Arts and Sciences, 2016.
[36] Y. Hayato. A neutrino interaction simulation program library neut. In
Acta Phys. Polon.
[37] T. J. Irvine. Development of Neutron-Tagging Techniques and Application to Atmospheric Neutrino Oscillation Analysis in SuperKamiokande. PhD thesis, University of Tokyo, 2014.
[38] F. Reines J. Learned and A. Soni. Limits on nonconservation of baryon
number. Phys. Rev. Lett., 1979.
[39] S. Kelley J. R. Ellis and D. V. Nanopoulos. Implications of precisionelectroweak experiments for mt , ρ0 , sin2 pθw q and grand unification. Phys.
Rev. D, 1991.
[40] The Super-Kamiokande collaboration K. Abe et al. Search for proton
decay via p Ñ ν k+ using 260 kilotonyear data of super-kamiokande.
Phys. Rev. D, 2014.

BIBLIOGRAPHY

152[41] The Super-Kamiokande collaboration K. Abe et al. Search for proton
decay via p Ñ e π 0 and p Ñ µ π 0 in 0.31 megaton*years exposure of
the super-kamiokande water cherenkov detector. Phys. Rev. D, 2017.
[42] B. Bajc K. S. Babu and Z. Tavartkiladze. Phys. Rev. D, 2012.
[43] J. C. Pati K. S. Babu and Z. Tavartkiladze. JHEP, 2010.
[44] P. Langacker and M. Luo. Probing the desert using gauge coupling
unification. Phys. Lett., 1991.
[45] P. Langacker and N. Polonsky. Uncertainties in coupling constant unification. Phys. Rev. D, 1993.
[46] V. Lucas and S. Raby. Phys. Rev. D, 1997.
[47] P. Ramond M. Gell-Mann and R. Slansky. Complex spinors and unified
theories. Conf. Proc., 1979.
[48] Lucas Machado. Pre-supernova alert system for Super-Kamiokande withgadolinium. PhD thesis, University of Naples Federico II, 2021.
[49] P. Minkowski. µ Ñ eγ at a rate of one out of 109 muon decays? Phys.
Lett. B, 1977.
[50] G. Mitsuka. “Study of Non-Standard Neutrino Interactions with Atmospheric Neutrino Data in Super-Kamiokande. PhD thesis, University ofTokyo, 2009.
[51] H. Murayama and A. Pierce. Not even decoupling can save minimal
supersymmetric su(5). Phys. Rev. D, 2002.
[52] Euan Richard. Studies of the energy, azimuthal, and time spectra of theatmospheric neutrino flux at Super-Kamiokande. PhD thesis, Universityof Tokyo, 2015.
[53] N. T. Shaban and W. James Stirling. Minimal left-right symmetry
and so(10) grand unification using lep coupling constant measurements.
Phys. Lett. B, 1992.
[54] M. Shiozawa. Reconstruction algorithms in the super-kamiokande large
water cherenkov detector. Nucl. Instrum. Meth. A, 199.
[55] T. Sjostrand. Pythia 5.7 and jetset 7.4 physics and manual. 1994.

BIBLIOGRAPHY

153[56] Yusuke Suda. Search for Proton Decay Using an Improved Event Reconstruction Algorithm in Super-Kamiokande. PhD thesis, Universityof Tokyo, 2017.
[57] San Diego Surface Optics Corp. Report no. soc-r950- 001-0195. Technical report, 1995.
[58] Y. Akaishi T. Yamazaki. Nuclear medium effects on invariant mass
spectra of hadrons decaying in nuclei. Physics Letters B, 1999.
[59] Yumiko Takenaga. Atmospheric neutrino oscillation analysis with solar
terms in Super-Kamiokande. PhD thesis, University of Tokyo, 2008.
[60] Akira Takenaka. Search for Proton Decay via p Ñ e π 0 and p Ñ µ π 0with an Enlarged Fiducial Mass of the Super-Kamiokande Detector. PhD
thesis, University of Tokyo, 2020.
[61] Y. Fukuda et al. The Super-Kamiokande collaboration. Evidence foroscillation of atmospheric neutrinos. Phys.Rev.Lett., 1998.
[62] Shinpei Tobayama. An Analysis of the Oscillation of Atmospheric Neutrinos. PhD thesis, University of British Columbia (Vancouver), 2016.
[63] R.D. Woods and D.S. Saxon. Diffuse surface optical model for nucleonnuclei scattering. Phys. Rev., 1954.
[64] T. Yanagida. Horizontal symmetry and masses of neutrinos. Prog.
Theor. Phys., 1980.
[65] C. Zeitnitz and T.A. Gabriel. The geant-calor interface and benchmark
calculations of zeus test calorimeters. Nucl. Instrum. Meth. A, 1994.