Non-Standard Neutrino Interaction
Analysis with Atmospheric Neutrino
Data in Super-Kamiokande I-IV and the
Design of the Hyper-Kamiokande Outer
Detector

Mahdi TaaniN I V E R

S

Y

T H

IT

E

U

G

H

O F
R

E

D I

U
N B

Doctor of Philosophy
The University of Edinburgh
June 2020

Dedicated to my motheriAbstract
Neutrino oscillation is a well-established phenomenon and oscillation parameters
are being measured with great accuracy. This unprecedented accuracy allows
sensitivity to sub dominant effects which could indicate new physics. Nonstandard interactions (NSI) is a general term for interactions not describedby the Standard Model. In this thesis NSIs are studied using 5326 days ofSuper-Kamiokande atmospheric neutrino data. This work focuses on NSIs whichallow neutral current induced flavour transitions and interactions which allow
different neutral current interaction amplitudes for different neutrino flavours.
The strength of the NSI between neautrino flavours α and β is characterised by theparameter εαβ . A limit is obtained for the NSI strength, −0.046 < εµτ < 0.019 at
90% C.L., which is a slight improvement over the previous Super-K measurement
and is consistent with recent IceCube measurements. Additional constraints onεeτ and ετ τ are obtained for different values of εee ; the constraints in the e − τsector are somewhat looser than previous Super-K measurements.
Further improvements are expected with the next generation neutrino oscillation
experiment Hyper-Kamiokande (Hyper-K). Hyper-K is a water Cherenkov detector which will make use of an outer detector to veto incoming charged particles
and reduce backgrounds. This work details the design of the outer detector for
Hyper-K, in particular research and development work carried out to enhance
the light collection. Wavelength shifting plates are modelled and their efficiencies
are studied. Reflective materials and their impact in the outer detector are also
discussed.

iiDeclaration
I declare that this thesis was composed by myself, that the work contained herein
is my own except where explicitly stated otherwise in the text, and that this work
has not been submitted for any other degree or professional qualification except
as specified.

(Mahdi Taani, June 2020 )iii

Lay Summary

Neutrinos are the most abundant massive particle in the universe and they very
rarely interact with anything, travelling the universe largely undisturbed. Dueto their low interaction rates, neutrinos created in stars or in different galaxies
can still reach us without being stopped. This makes them an excellent source tolook far out into the universe and understand star formation and supernovae aswell as back in time to understand the early universe.
As they rarely interact, large detectors are required in order to increase the chanceof detecting a neutrino. One such large detector is called Super-Kamiokandeor Super-K; it is a 50 kton tank filled with ultrapure water and 13,000 highly
sensitive light detectors which are used to observe neutrino interactions. SuperK has been taking data since 1996 and has detected many neutrinos from various
sources. Examining the energy, direction and flavour of the detected neutrinos
allows us to determine their fundamental properties.
All known fundamental particles and the interactions between them are describedby a theory known as the Standard Model of particle physics. The theory is very
successful and experiments have consistently verified its predictions. However, theStandard Model does not correctly describe the neutrino. For many years theseparticles were thought to be massless but experimental evidence shows that theparticles do have mass. These particles come in three flavours and experiments
have proven that a neutrino of one flavour can change into a neutrino of a different
flavour. This property of neutrinos is exciting as it indicates new physics beyond
the Standard Model.
Extensions to the Standard Model which account for the neutrino mass havebeen proposed; naturally, these extended models allow exotic interactions which
are not allowed by the Standard Model. These interactions are known as nonstandard interactions (NSIs) and have not yet been observed. Observation ofneutrino NSIs could indicate the existence of new particles or other exotic physics
scenarios. In this thesis, 15 years of Super-K data has been analysed in order tolook for possible non-standard interactions. No evidence of NSI was found andtight limits have been set on the possible strength of neutrino NSIs.
While the understanding of neutrino properties has advanced significantly in thelast two decades, some questions remain open. Possibly the most important quesiv

tion is whether or not neutrinos and antineutrinos, their antimatter counterpart,
behave in the same way. If they do not, then neutrinos could be the reason thatthe universe is dominated by matter while there is hardly any antimatter. To
answer this question a much larger number of neutrinos must be detected which
requires a larger detector.
In 2028 a new large detector Hyper-Kamiokande (Hyper-K), eight times larger
than Super-K, will begin taking data. This thesis details the work carried out todesign and eventually build Hyper-K. The detector will observe many neutrino
events and will make use of a veto system to reject non-neutrino events. The
work shown in this thesis is the design and optimisation of the Hyper-K vetodetector.

v

Acknowledgements

Firstly, I would like to sincerely thank my supervisor Matthew Needham for his
excellent guidance and advice. I am very grateful for the constant support andthe freedom you allowed me in exploring new ideas. Without your counsel overthe last four years, this work could not have been completed.
I am hugely indebted to my second supervisor Stephen Playfer who was extremely
generous in sharing his expertise and knowledge. Thank you for always being
available to discuss ideas and for being great fun.
I spent a lot of time in Nagoya and would like to express my deepest appreciation
towards my third supervisor Yoshitaka Itow. Thank you for sharing your intimate
knowledge of Super-K and for welcoming me to Nagoya. Thank you for all thehelp in physics and day-to-day life in Japan.
The NSI analysis in this thesis would most definitely not have been possible
without Roger Wendell. I am extremely grateful to you for sharing your wisdom
and for being patient with me.
It has been fantastic working on Super-K and I am grateful for the discussions
with all of the collaborators, especially the ATMPD group. Thank you Ed Kearns
for your advise throughout my analysis.
I have really enjoyed being a part of Hyper-K and I am thankful to the wholecollaboration, particularly the OD group. I have been fortunate enough to workwith Lilia Drakopoulou, Stephane Zsoldos and Federico Nova; it has been apleasure working with you, striving for perfect plates!
Outside of physics I would like to thank my brothers: Bruno, Daniele, Farhang,
Jerry, Junzy, Louis and Nadeem for helping me to stay sane, and giving me alittle perspective in life.

viContents

Abstractii

Declarationiii

Lay Summaryiv

Acknowledgements

vi

Contents

vii

List of Figures

xiii

List of Tables

xxvi

1

Thesis Overview

1

2

Introduction

4

2.1

Standard Model..................................................................

5

2.2

Neutrino Oscillations ...........................................................

6

2.2.1

Neutrino Oscillation Theory .........................................

7

2.2.2

Neutrino Oscillations in a Vacuum.................................

7

2.2.3

Neutrino Oscillations in Matter..................................... 10

2.2.4

Non-Standard Neutrino Interactions............................... 14

vii

2.3

3

4

Experimental Status ............................................................ 16
2.3.1

Standard Oscillations.................................................. 16

2.3.2

NSI Parameters......................................................... 18

The Super-Kamiokande Detector

23

3.1

Cherenkov Radiation ........................................................... 23

3.2

Detector Design .................................................................. 26

3.3

Photomultiplier Tubes.......................................................... 29

3.4

Electronics and Data Acquisition ............................................ 30

3.5

Water System .................................................................... 33

3.6

Air Purification .................................................................. 35

3.7

Run Periods....................................................................... 36

Detector Calibration
4.1

4.2

PMT Calibration ................................................................ 38
4.1.1

High Voltage Setting .................................................. 39

4.1.2

Relative Gain ........................................................... 40

4.1.3

Absolute Gain........................................................... 41

4.1.4

Timing Calibration .................................................... 42

Water Calibration ............................................................... 45
4.2.1

4.3

38

Absorption and Scattering ........................................... 46

Energy Calibration .............................................................. 48
4.3.1

Range of Stopping Muons............................................ 48

4.3.2

Cherenkov Angles of Stopping Muons............................. 49

4.3.3

Invariant Mass of Neutral Pions .................................... 49

viii

5

Decay Electrons ........................................................ 52

4.3.5

Energy Scale Summary ............................................... 53

Atmospheric Neutrino Monte Carlo Simulation

55

5.1

Atmospheric Neutrinos ......................................................... 55

5.2

Atmospheric Neutrino Flux ................................................... 57

5.3

Neutrino Interactions ........................................................... 60

5.4
6

4.3.4

5.3.1

Elastic Scattering ...................................................... 62

5.3.2

Meson Exchange Current............................................. 62

5.3.3

Single Meson Production ............................................. 63

5.3.4

Coherent Pion Production ........................................... 63

5.3.5

Deep Inelastic Scattering ............................................. 63

5.3.6

Nuclear Effects.......................................................... 64

Detector Simulation: SKDETSIM ........................................... 65

Event Selection
6.1

6.2

67

Fully-Contained Reduction .................................................... 69
6.1.1

FC1........................................................................ 69

6.1.2

FC2........................................................................ 70

6.1.3

FC3........................................................................ 70

6.1.4

FC4........................................................................ 73

6.1.5

FC5........................................................................ 74

6.1.6

FC Data Sample........................................................ 75

Partially Contained Reduction ............................................... 76
6.2.1

PC1........................................................................ 77

ix

6.3

6.4

6.2.2

PC2........................................................................ 78

6.2.3

PC3........................................................................ 78

6.2.4

PC4........................................................................ 79

6.2.5

PC5........................................................................ 80

6.2.6

PC Data Sample ....................................................... 82

Upward-going Muon Reduction .............................................. 83
6.3.1

Charge Cuts ............................................................. 83

6.3.2

Zenith Angle Cuts ..................................................... 83

6.3.3

Eye Scan ................................................................. 84

6.3.4

UPMU Data Sample .................................................. 84

6.3.5

Background Estimation for Upward-going Muons .............. 85

6.3.6

Through-going Showering Muons................................... 88

ID OD Crosstalk Cuts.......................................................... 90
6.4.1

6.5
7

Selecting a Cut ......................................................... 91

Event Reconstruction........................................................... 95

Neutrino Oscillation Analysis

98

7.1

Dataset and Event Classification ............................................ 98

7.2

Analysis Method................................................................. 101
7.2.1

7.3

Definition of χ2 ......................................................... 101

Systematic Uncertainties....................................................... 105
7.3.1

Atmospheric Neutrino Flux.......................................... 106

7.3.2

Neutrino Interaction................................................... 108

7.3.3

Event Selection and Reconstruction ............................... 109x

8

NSI in Atmospheric Neutrinos
8.1

8.2

9

111

NSI in the µ − τ Sector ....................................................... 113
8.1.1

Oscillation Effect ....................................................... 113

8.1.2

Analysis .................................................................. 115

8.1.3

Limit on εµτ from three-flavour fit ................................. 117

8.1.4

Limit on µ − τ NSI parameters from two-flavour fit ........... 117

8.1.5

Discussion................................................................ 121

NSI in the e − τ Sector........................................................ 123
8.2.1

Oscillation Effect ....................................................... 123

8.2.2

Limits On εeτ and ετ τ ................................................. 124

8.2.3

Discussion................................................................ 125

Hyper-Kamiokande
9.1

130

Physics Goals..................................................................... 130
9.1.1

Long Baseline and Atmospheric Neutrinos ....................... 131

9.1.2

Solar Neutrinos ......................................................... 135

9.1.3

Supernova Neutrinos .................................................. 136

9.1.4

Proton decay ............................................................ 138

9.2

Detector Design .................................................................. 139

9.3

Photosensors...................................................................... 140
9.3.1

9.4

Electronics ............................................................... 144

Detector Simulation............................................................. 145

10 Hyper-Kamiokande Outer Detector

146

10.1 Simulating Plate Response .................................................... 147

xi

10.2 Plate Shapes ...................................................................... 150
10.3 Absorption and Emission Spectra ........................................... 152
10.3.1 Measuring Emission ................................................... 155
10.3.2 Measuring Absorption................................................. 157
10.4 Plate Efficiency Measurement ................................................ 160
10.4.1 First Setup............................................................... 161
10.4.2 Second Setup ............................................................ 163
10.5 Fit To Data ....................................................................... 164
10.5.1 Results.................................................................... 166
10.6 WCSim Simulation.............................................................. 170
10.7 Tyvek............................................................................... 171
10.7.1 Simulations .............................................................. 171
10.7.2 Measurements ........................................................... 173
10.8 Discussion ......................................................................... 176
10.8.1 Combined WLS Results .............................................. 179
10.8.2 Tyvek ..................................................................... 180
10.8.3 Next Steps ............................................................... 181
11 Conclusions and Outlook

182

A Systematic Uncertainties

186

Bibliography

199

xii

List of Figures

2.1
2.2

2.3

2.4

A summary showing the fermions and bosons in the Standard
Model. Taken from [1]. . . . . . . . . . . . . . . . . . . . . . . . .

6

Two flavour survival probability of να as a function of propagation
length. The black curve represents Eν = 1 GeV, the red curve isEν = 10 GeV and the blue curve for Eν = 100 GeV. This is for
maximal mixing θ = π/4 and ∆m2 = 2.56 × 10−3 eV2 . . . . . . . .

11

Feynman diagrams of the elastic coherent forward scatteringinteractions that neutrinos undergo through propagation in a
medium. The flow of time is left to right. . . . . . . . . . . . . . .

11

A pseudo-Feynman diagram of a neutral-current non-standard
neutrino interaction. α is the initial neutrino flavour, β is the
final neutrino flavour and f is a first generation fermion (e, u ord). The flow of time is left to right. . . . . . . . . . . . . . . . . .

15

2.5

The 68% and 90% confidence regions for the sin2 θ23 -|∆m232 | plane,assuming normal mass hierarchy. Contours from NOvA [26],MINOS [24], SK [158] and IceCube [3] are included. Taken from [16]. 17

2.6

A plot of the allowed ν1 − ν2 neutrino oscillation parameter region.
Solar experiments are shown in green with contours showing 15σ, KamLAND (reactor) is shown in blue and the red shows the
combined analysis results. The filled regions indicate the 3σ region.
The overlaid red lines show the contours for day-night asymmetry.
Taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiii

18

2.7

3.1

The expected survival probability of solar neutrinos for various
physics scenarios, including data from solar neutrino experiments.
All scenarios use sin2 θ13 = 0.022. The standard oscillations use(sin2 θ12 , ∆m221 ) = (0.31, 7.5 × 10−5 eV 2 ). The single additional
sterile neutrino uses (sin2 θ12 , ∆m221 , sin2 2α, ∆m201 ) = (0.31, 7.5 ×
10−5 eV 2 , 0.005, 1.2 × 10−5 eV 2 ). NSI on up quarks scenario uses
(sin2 θ12 , ∆m221 , εuD , εuN ) = (0.30, 7.25 × 10−5 eV 2 , −0.22, −0.30) andthe NSI on down quarks scenario uses (sin2 θ12 , ∆m221 , εdD , εdN ) =(0.32, 7.35 × 10−5 eV 2 , −0.12, −0.16). Taken from [127]. . . . . . .

20

A sketch of the Super-Kamiokande detector site under Mt Ikeno.
Taken from [82]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.2

A diagram showing Cherenkov light production by a charged particle. 24

3.3

A typical event display for an electron-like event [left] and muonlike event [right]. The blue dots represent a low number of photons
and the red dots represent a larger number of photons. . . . . . .

25

A schematic view of the Super-Kamiokande support structure forthe inner detector. Taken from [82]. . . . . . . . . . . . . . . . . .

26

A picture of the Super-K inner detector taken in July 2018. The
detector was being drained and refurbished. Photo taken by
Nakahata-san. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

A picture of the Super-K outer detector taken in July 2018. The
detector was being drained and refurbished. . . . . . . . . . . . .

28

Schematic diagram showing the optical separation of the end caps
and barrel regions of the OD. . . . . . . . . . . . . . . . . . . . .

29

A schematic diagram of the 50 cm SK ID PMT, taken from [82].
All measurements are in mm. . . . . . . . . . . . . . . . . . . . .

30

Plot showing the relative Cherenkov spectrum through pure waterin addition to the quantum efficiency of the R3600 PMT. Taken
from [136]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.10 Relative transit time distribution for the SK ID PMT tested with
410 nm light source at single photon level. Taken from [82]. . . . .

31

3.11 Schematic view of the new data acquisition system [163]. . . . . .

32

3.4
3.5

3.6
3.7
3.8
3.9

3.12 A schematic diagram of the water purification system used in SK [82]. 34
3.13 A schematic diagram of the air purification system used in SK [82]. 36
4.1

A schematic view of the pre-calibration setup. Taken from [12]. .
xiv

39

4.2

The position of the reference ID PMTs in red [left] and examples
of how PMTs with a similar geometric relationship are grouped[right]. Taken from. Taken from [12]. . . . . . . . . . . . . . . . .

40

The single photoelectron charge distribution for the Cf-Ni sourcein SK-III, taken from [12]. The solid line shows the data withnormal PMT gain and a 0.25 photoelectron threshold, the dashedline shows the data with double the gain and half the threshold.
The dotted line shows a linear extrapolation. . . . . . . . . . . . .

42

A schematic diagram showing the time calibration system. Taken
from [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

A diagram showing the time-walk effect. A larger signal has afaster rise time, thus reaching the threshold sooner than a smaller
signal starting at the same time. . . . . . . . . . . . . . . . . . . .

44

4.6

Cross-section of the MgO diffuser ball. Taken from [12]. . . . . . .

45

4.7

Time vs charge for readout channel 00010. Qbin refers to theamount of charge (pC) of each hit, which are binned in a linear scale(0.2 pC/Qbin) from 0 to 10 pC and a log scale (50log(pC)/Qbin)from 10 to 3981 pC. The timing (T) has been corrected for TOF,
the larger T corresponds to earlier hits. The plot is referred to as
a TQ distribution and the fitted polynomial (black line) is known
as the TQ-map. Taken from [12]. . . . . . . . . . . . . . . . . . .

45

A diagram showing the real-time water quality calibration system.
The analysis splits up the PMTs into 5 barrel regions and thetop. The blue circle indicates the laser target used for the TOF
calculations. Taken from [12]. . . . . . . . . . . . . . . . . . . . .

46

SK-MC typical fitted functions for the absorption and scattering
coefficients. The circles are data points obtained in April 2009 andthe lines show the fitted functions. The solid black line shows thetotal sum of the dotted lines. Taken from [12]. . . . . . . . . . . .

47

4.10 The energy calibration using low-energy stopping muons withreconstructed Cherenkov opening angles. The upper plots show thereconstructed momentum (left) and reconstructed opening angle(right) for data (black circles) and MC (black lines). The lower
plots show the reconstructed momentum versus opening angle fordata (left) and MC (right). All plots are made using SK-II data
and MC. Taken from [143]. . . . . . . . . . . . . . . . . . . . . . .

50

4.11 The invariant mass distribution of reconstructed neutral pions for2520 days of SK-IV live time. The black circles represent data andthe red lines represent the MC. The MC has been normalised to
the live time of the data. . . . . . . . . . . . . . . . . . . . . . . .

51

4.3

4.4
4.5

4.8

4.9

xv

4.12 Momentum of decay electrons for data (black dots) and MC (bluehistogram). The MC has been normalised to the live time of thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4.13 The energy scale deviation at various momenta for SK-IV. Taken
from [110]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

4.14 The Super-K average reconstructed particle momentum since
1st April 2006. The plots on the left show the reconstructed
momentum for decay electrons and the plots on the right show
the reconstructed muon momentum per unit track length. From
top to bottom the plots are shown for SK-I, SK-II, SK-III and SKIV respectively. The dotted and dashed lines represent a 1% and
2% variation respectively. Taken from [143]. . . . . . . . . . . . .

54

5.1

5.2
5.3

5.4

5.5

5.6

5.7

Diagram of neutrino production in the Earth’s atmosphere. The
typical height of neutrino production is 15 km above the ground.
Taken from [115]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

Neutrino flux ratios from various atmospheric neutrino calculations. Taken from [104]. . . . . . . . . . . . . . . . . . . . . . . .

57

A compilation of primary cosmic ray observations from various
experiments. The green dashed line shows an initial calculated
flux, the green dotted line includes corrections to bring the model
into agreement with data above 10 TeV. The solid pink line is
the Honda flux model [102]. The various points represent datataken by different experiments at solar minimum. See Ref [104]for further details. . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

The (calculated) zenith angle dependence of the atmospheric
neutrino flux of neutrinos reaching Kamioka. θ is the incoming
neutrino direction, where cos θ = 1 for vertically downward-goingneutrinos and cos θ = -1 for vertically upward-going neutrinos.
Taken from Ref [106]. . . . . . . . . . . . . . . . . . . . . . . . . .

59

The (calculated) azimuthal angle dependence of the atmospheric
neutrino flux of 1 GeV neutrinos reaching Kamioka. Taken from
Ref [106]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

The atmospheric neutrino flux reaching Kamioka [left] and the flux
ratios [right] calculated using various models. ”This Work” refers
to the Honda 2011 calculation. Taken from Ref [106]. . . . . . . .

60

NEUT simulation cross sections for neutrinos [left] and antineutrinos [right] compared to experiment data [75]. Contributions fromdifferent interaction modes shown. Taken from Ref [111]. . . . . .

61

xvi

5.8

The charged current quasi-elastic cross sections for muon neutrinos [left] and muon antineutrinos [right]. Solid lines show thecalculated cross sections for free target nucleons and the dottedline shows the calculated cross sections for bound target nucleons(protons in oxygen). The points represent data from several
experiments. Taken from Ref [96]. . . . . . . . . . . . . . . . . . .

62

The total charged current neutrino (upper) and antineutrino(lower) cross sections. Lines show the models used and the points
represent data from several experiments. Taken from Ref [96]. . .

64

5.10 NEUT simulation of π-12 C scattering compared to experiment
data [38, 43, 80, 114, 122] for π + [left] and π − [right]. Taken from
Ref [65]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.9

6.1
6.2

6.3
6.4

6.5

6.6

6.7

An atmospheric neutrino event, detected in SK-V, shown on an
event display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

Different event classifications in Super-K. The dashed lines show
the neutrino path whereas the solid lines show the path ofsecondary particles. . . . . . . . . . . . . . . . . . . . . . . . . . .

68

Distributions of the zenith angle vs azimuth angle for stoppingmuons and through-going muons. Taken from [143]. . . . . . . . .

86

Azimuth angle distributions for stopping muons and through-going
muons in SK-IV. Region (1) indicates a muon path through athicker mountain region and region (2) indicates a muon paththrough a thinner mountain region. Taken from [143]. . . . . . . .

86Background estimation for stopping (left) and through-going(right) muons in SK-IV. The plots show the zenith angle distributions for the muons. The black and white points show the datafor regions (1) and (2) respectively. Region (1) indicates a muon
path through a thicker mountain region and region (2) indicates amuon path through a thinner mountain region. A function is fitted(black solid line) to the data and used to estimate the background.
Taken from [143]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

The average energy loss per meter water equivalent for muonsin rock (green) and sea water (black) as a function of muonenergy. The contributions of the different processes are shown
separately for water. This plot was generated using MUSIC,a muon
propagation simulator. Taken from [98]. . . . . . . . . . . . . . .

88

dE/dX distribution for an MC non-showering muon vs showeringmuon. Both muons have the same entry and exit point. Taken
from [66]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

xvii

6.8

A Super-K event display showing an FC e-like event with crosstalk
between the ID and OD. The coloured circles represent hit PMTs,
the large unfolded cylinder is the ID and the smaller unfolded
cylinder in the upper right corner is the OD. . . . . . . . . . . . .

90

Histograms showing the number of photoelectrons for each hit OD
PMT in the FC data sample. Blue lines show the MC scaled bylivetime to the data (red). . . . . . . . . . . . . . . . . . . . . . .

91

6.10 A Super-K event display showing a laser event with crosstalk
between the ID and OD. The coloured circles represent hit PMTs,
the large unfolded cylinder is the ID and the smaller unfolded
cylinder in the upper right corner is the OD. . . . . . . . . . . . .

92

6.11 The time distribution of PMT hits for a PC MC event on the left
and an FC crosstalk event on the right. The top and bottom plotsshow ID and OD hits respectively. . . . . . . . . . . . . . . . . . .

92

6.12 A plot showing the time difference between OD hits and nearby
ID hits for PC MC in blue, PC data in red and laser data in black.
The histograms were normalised by area. . . . . . . . . . . . . . .

93

6.13 Plots showing the number of photoelectrons for each OD hit vs thetime difference between the hit OD tube and its nearby ID tubes.
The left plot is for the laser data and the right plot is for PC MC.

94

6.9

6.14 OD hit distributions for FC MC (magenta), PC MC (blue), PC
data (red) and laser data (black). The histograms have been scaled
down to the laser data using the region 0.8→1.2 pe. The left plotshows the OD hit distributions before the crosstalk cut is applied,
the right plot shows the distributions after the cut has been applied. 94
6.15 An illustration of the basic principle of ring-finding. Taken
from [143]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

6.16 PID likelihood distribution for single-ring FC events with visibleenergy less than 1.33 GeV. The black points are data from 1097
days of SK-IV, the red histogram is the MC and the shaded green
region is the MC CCQE νµ events. . . . . . . . . . . . . . . . . .

97

7.1

The calculated uncertainty of the neutrino flux normalisation
including contributions from the hadronic interaction cross section(δσ ), pion production (δπ ), kaon production (δK ) and air density(δair ) (top). The uncertainty on the flux normalisation as afunction of energy taking only contributions from the hadronicinteraction model and pion production (bottom), taken from
Ref [143]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

xviii

7.2

The anti-neutrino/neutrino double ratio for ν̄e /νe (left) and ν̄µ /νµ(right). The solid black line shows the ratio between the Honda
and Fluka ratios while the dashed red line shows the ratio between
the Honda and Bartol ratios. Taken from Ref [143]. . . . . . . . 108

8.1

The density of the Earth versus the depth (left). The black line
shows the full measured values of the PREM model and the redline shows the values used in the analysis. The right plot shows
the different density layers of the Earth. . . . . . . . . . . . . . . 113

8.2

Oscillation contours showing the νµ survival probability for different values of µ − τ NSI parameters. Oscillation probabilities
calculated using full three-flavour equations with all other NSI set
to zero. The horizontal axis shows the energy and the verticalaxis shows the zenith angle. The top left plot shows standard
oscillation only, top right shows standard plus flavour-changing
neutral currents. The bottom left plot shows standard plus
lepton non-universality and the bottom right plot includes flavourchanging neutral currents and lepton non-universality. . . . . . . 114

8.3

The allowed standard oscillation parameter regions. Solid lines
show allowed regions when including NSI and the dotted lines show
the regions without NSI. Taken from [133]. . . . . . . . . . . . . . 116

8.4∆χ2 distribution as a function of εµτ . The three flavour standard
oscillation parameters are fixed and all other NSI parameters are
set to zero. The three horizontal lines correspond to the 68%, 90%
and 99% C.L. defined by ∆χ2 = 0.99, 2.71, 6.63 respectively. . . 118

8.5

The zenith angle distribution for the UPMU stopping sample(left) and the UPMU showering sample (right). The black points
show the data, the red line shows the best fit standard oscillation
parameters from [18] and the blue case shows the best fit NSI result
from the two flavour fit. . . . . . . . . . . . . . . . . . . . . . . . 119

8.6

Allowed NSI parameter region assuming two-flavour standard
oscillations with NSI in the µ − τ sector. The horizontal axis
shows εµτ and the vertical axis shows (ετ τ - εµµ ). ∆m232 and θ23 are
fixed while ∆m221 , θ12 and θ13 are set to zero. The three contours
correspond to the 68%, 90% and 99% C.L. defined by ∆χ2 = 2.30,
4.61 and 9.21 respectively. The star represents the best-fit point
for the NSI parameters. . . . . . . . . . . . . . . . . . . . . . . . 119

8.7∆χ2 distribution as a function of εµτ . ∆m232 and θ23 are fixed while∆m221 , θ12 and θ13 are set to zero. (ετ τ - εµµ ) is integrated out. The
three horizontal lines correspond to the 68%, 90% and 99% C.L.
defined by ∆χ2 = 2.30, 4.61 and 9.21 respectively. . . . . . . . . 120

xix

8.8

∆χ2 distribution as a function of (ετ τ - εµµ ). ∆m232 and θ23 are
fixed while ∆m221 , θ12 and θ13 are set to zero. εµτ is integrated out.
The three horizontal lines correspond to the 68%, 90% and 99%
C.L. defined by ∆χ2 = 2.30, 4.61 and 9.21 respectively. . . . . . 120

8.9

Allowed NSI parameter regions in εeτ − ετ τ plane for fixed valuesof εee . The contours represent the 68%, 90% and 99% C.L. definedby ∆χ2 = 2.30, 4.61, 9.21 respectively. . . . . . . . . . . . . . . . 124

8.10 Oscillation contours showing the νµ → νe oscillation probability
for different values parameters. Oscillation probabilities calculatedusing full three-flavour equations with all other NSI set to zero.
The horizontal axis shows the energy and the vertical axis shows
the zenith angle. The top left plot shows standard oscillation
only, top right shows standard plus flavour-changing neutral
currents. The bottom left plot shows standard plus lepton nonuniversality and the bottom right plot includes flavour-changing
neutral currents and lepton non-universality. Normal hierarchyhas been assumed. . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.1

An illustration of a Hyper-Kamiokande cylindrical tank. Taken
from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9.2

The ND280 near detector complex with the INGRID on-axis
detector (left) and the ND280 off-axis detectors (right). Taken
from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

9.3

A diagram of the upgraded ND280 detector where the TOF
detectors have not been drawn. Two High-Angle TPCs (yellow)
with a scintillator detector ”Super-FGD” (grey) will be installedin the most upstream portion of the detector (left). The three(orange) TPCs and two (green) FGDs make up the tracker systemin the downstream portion in the current ND280 detector and willremain after the upgrade. Taken from [19]. . . . . . . . . . . . . . 132

9.4

A conceptual design of the IWCD detector facility [164]. . . . . . 133

9.5

Reconstructed neutrino energy distribution for several values ofδCP (top) and the difference in reconstructed neutrino energy
distribution from the case of δCP . The plots are for the νeappearance mode for neutrinos (left) and antineutrinos (right).
Normal hierarchy is assumed and sin2 θ13 = 0.1. Taken from [17]. . 134

9.6

Expected significance, for a single Hyper-K tank running for 10
years, to exclude CP conservation (δCP = 0). Normal hierarchy isassumed with sin2 θ13 = 0.1 and sin2 θ23 = 0.5. Taken from [17]. . 135

xx

9.7

Upward-going oscillated νe flux relative to the non-oscillated flux
as a function of neutrino energy. Thick solid lines indicate the total
flux whereas the thin line, dashed line and dotted line indicate thecontribution from the solar term, interference term and the θ1 3
resonance term respectively. The top two plots show the effectof the θ23 octant. The top right plot and bottom left plot show
the effect of δCP . The bottom right plot is for inverted hierarchy
the resonance is not seen in this sample but is seen in ν̄e instead.
Taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

9.8

The expected number of supernova neutrino events, for eachneutrino interaction, as a function of the distance to the supernova.
The figure is for a single Hyper-K tank and the bands for eachline indicate the variation based on the assumption of neutrino
oscillation parameters. Taken from [17]. . . . . . . . . . . . . . . . 137

9.9

A comparison of the experimental limits on the rates of nucleon
decay and projected limits for Hyper-K (10 years, single tank)and DUNE. Ranges of theoretical predictions also shown. Taken
from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

9.10 The total momentum of events passing the p → e+ π 0 event
selection criteria except the momentum cut (left) with solid verticallines indicating the momentum cuts. The reconstructed invariant
mass of events passing the p → e+ π 0 event selection criteria except
the invariant mass cut (right), for free (top) and bound (bottom)
protons. The hatched regions in the plots indicate the atmospheric
neutrino background whereas the black dots represent the sumof proton decays and background. All plots are for a 10 year
exposure of a single Hyper-K tank with an assumed proton lifetimeof 1.7x1034 years. Taken from [17]. . . . . . . . . . . . . . . . . . 139
9.11 A picture of the 50 cm Hamamatsu R12860-HQE box-and-line
PMT. Taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . 140
9.12 The single photoelectron transit time distribution of the Hyper-K
PMT (blue) and Super-K PMT (black). Taken from [17]. . . . . . 141
9.13 The single photoelectron charge distribution of the Hyper-K PMT(blue) and Super-K PMT (black). Taken from [17]. . . . . . . . . 141
9.14 A sketch of the Venetian Blind dynode structure used in SuperK PMTs (left) and the Box-and-Line dynode structure used inHyper-K PMTs (right). Taken from [138]. . . . . . . . . . . . . . 142

xxi

9.15 Relative single photon detection efficiency as a function of theposition on the photocathode. The PMT centre is at a position
angle of 0° and the PMT edges are at ±90°. The black lines show
the average measured values for of four Super-K PMTs whereas
the blue lines show the measured value of a Hyper-K PMT. Scans
were taken along perpendicular lines and the results are shown inthe dashed and solid lines. Taken from [17]. . . . . . . . . . . . . 143
9.16 A conceptual drawing of a multi-PMT with 19 7.7 cm PMTs
outward-facing PMTs, on each side, for the ID and OD. The PMTs
are enclosed in a 50 cm acrylic vessel and readout electronics areembedded inside. Taken from [17]. . . . . . . . . . . . . . . . . . . 144
10.1 A diagram showing a side view of a PMT+WLS setup. the redlines show photons reaching the PMT directly while the purple
lines show light reaching after being internally reflected from the
top and bottom of the plate. . . . . . . . . . . . . . . . . . . . . . 148
10.2 A distribution showing the number of reflections it took before
a photon was detected in the simulation. The simulation is for a
23 cm square plate with 90% reflective edges and a refractive index
of 1.58. The plate was simulated in air. The different coloured lines
show various attenuation lengths. . . . . . . . . . . . . . . . . . . 149
10.3 Distribution showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate with reflective edges andno attenuation. The black circles show the overall efficiency while
the blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively. 100% edge
reflectivity and perfect coupling between the PMT and plate areassumed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4 Heatmaps showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate without reflective edges
and no attenuation. The top left plot shows the overall efficiency
and the top right plot shows the contribution from 0 reflections.
The bottom left and right plots show the contribution 1 and 2
reflections respectively. . . . . . . . . . . . . . . . . . . . . . . . . 151
10.5 Heatmaps showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate with reflective edges andno attenuation. The top left plot shows the overall efficiency
and the top right plot shows the contribution from 0 reflections.
The bottom left and right plots show the contribution 1 and 2
reflections respectively. . . . . . . . . . . . . . . . . . . . . . . . . 152

xxii

10.6 Distribution showing the efficiency of a simulated WLS plate.
The simulation is for a 23 cm circle plate with reflective edges
and no attenuation. The black circles show the overall efficiency
while blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively. . . . . . . . . 153
10.7 Distribution showing the efficiency of a simulated WLS plate. The
simulation is for a 23x46 cm rectangle plate with reflective edges
and no attenuation. The black circles show the overall efficiency
while blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively. . . . . . . . . 153
10.8 A diagram showing an example rectangle petal design, the image
on the right shows possible light reflections. . . . . . . . . . . . . 154
10.9 A diagram showing an example triangle petal design, the image on
the right shows possible light reflections. . . . . . . . . . . . . . . 154
10.10A diagram of the emission spectrum measurement setup. . . . . . 155
10.112D emission spectrum for the SK WLS sample. Left plot shows theemission intensity for different excitation wavelengths and the rightplot shows the intensity normalised for each excitation wavelength. 156
10.12The measured emission spectrum for four WLS samples. The
excitation wavelength for these measured values is 350 nm. The
dotted brown line shows the QE of the ETEL PMT which is takenfrom Reference [70]. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.13A diagram of the absorption spectrum measurement setup. . . . . 157
10.14The measured absorption spectrum for four WLS samples. The
vertical axis shows the probability of absorption at 1.3 cm. . . . . 159
10.15The measured absorption spectrum for four WLS samples. The
vertical axis shows the probability of absorption at 0.6 cm. . . . . 159
10.16A closeup picture of the curved WLS hole before the plate ismounted onto a PMT. . . . . . . . . . . . . . . . . . . . . . . . . 160
10.17A picture of the efficiency measurement setup. . . . . . . . . . . . 161
10.18A Block diagram of the electronic readout chain. . . . . . . . . . . 162
10.19The MCA spectra when the LED is turned on (left) and turnedoff (right). The measurement was taken with the LED positioned
at the centre of the PMT. . . . . . . . . . . . . . . . . . . . . . . 163
10.20A typical waveform for the amplified PMT signal in the second
setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

xxiii

10.21The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for WLS plate with reflective
edges and the pink dots represent measurements on the WLS plate
without reflective edges. The red and blue lines show the fitted
model for the reflective and non reflective edges respectively. This
plate is the Eljen 23×23×1.3 cm plate. . . . . . . . . . . . . . . . 167
10.22The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for WLS plate with reflective
edges and the pink dots represent measurements on the WLS plate
without reflective edges. The red and blue lines show the fitted
model for the reflective and non reflective edges respectively. This
plate is the Eljen 30×50×1.3 cm plate. . . . . . . . . . . . . . . . 167
10.23The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for WLS plate with reflective
edges and the pink dots represent measurements on the WLS plate
without reflective edges. The red and blue lines show the fitted
model for the reflective and non reflective edges respectively. This
plate is the Eljen 23×23×1.3 cm plate but the model uses the best
fit point of the larger 30×50×1.3 cm plate. . . . . . . . . . . . . . 168
10.24The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for the Eljen square and the blue
dots represent measurements on the Kuraray plate. The plates do
not have reflective material around the edges. . . . . . . . . . . . 168
10.25The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for the Eljen square and the blue
dots represent measurements on the Kuraray plate and the red
dots represent the SK plate. The plates have reflective material
around the edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.26The efficiency vs radial distance from the centre of the PMT. Black
dots represent the measurements for a square, the blue dots for acircle and the red dots for a rectangular petal. All shapes are
made from the SK WLS plate. The plates have reflective material
around the edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.27Visualisation of the Hyper-K OD. The figure on the left shows azoomed out image of the outer detector, blue squares show the
WLS plates and red circles show the OD PMTs. ID PMTs havebeen turned off to easily see the OD. The image on the right showsa zoomed in image of a single WLS plate. . . . . . . . . . . . . . . 170
10.28The average number of photoelectrons detected (right) and theaverage number of hit PMTs (left) per event, for a 1 GeV incoming
muon with various Tyvek reflectivity. . . . . . . . . . . . . . . . . 172

xxiv

10.29The average number of photoelectrons detected (right) and theaverage number of hit PMTs (left) per event, for a 1 GeV incoming
muon with various Tyvek specular lobe contributions. . . . . . . . 172
10.30The absolute reflectivity of the Spectralon reference sample. . . . 173
10.31A picture of two Tyvek samples, 1082D on the left and 1073B on
the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
10.32The absolute reflectivity of several Tyvek samples. . . . . . . . . . 174
10.33The absolute reflectivity of Super-K Tyvek (without black PE
layer) in black and 1082D in blue. The solid and dashed lines
represent measurements taken at slightly different positions. . . . 175
10.34The absolute reflectivity of Super-K Tyvek with multiple layers.
The first layer has black PE backing and the remaining layers arebonded around the edges via ultrasonic welding. . . . . . . . . . . 176
10.35The absolute reflectivity of Super-K Tyvek with multiple layers.
The first layer has black PE backing and the remaining layers arebonded together using glue. . . . . . . . . . . . . . . . . . . . . . 177
10.36A picture of a multi-layer Tyvek sample, joined using glue. The
spotted region in the middle is referred to as the ”dark spot”. . . 177
10.37The absolute reflectivity of 1082D Tyvek. The black line shows
the values for a single layer of 1082D and the blue lines shows thereflectivity for the same sample folded in half (two layers). . . . . 178

xxv

List of Tables

2.1

Three flavour oscillation parameters from a 2019 global analysis [71]. For normal ordering ∆m23l ≡ ∆m231 > 0 and for invertedordering ∆m23l ≡ ∆m232 < 0. The best fit point was with normal
hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

The Cherenkov threshold energy in water, for common charged
particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.2

SK inner detector PMT specification [73].

. . . . . . . . . . . . .

31

3.3

Summary of QTC ranges in the new DAQ system [12]. . . . . . .

32

3.4

Summary of trigger types used in the SK software trigger. . . . .

33

3.5

Summary of SK run periods. ”Implosion Covers” refers to theprotective plastic covers used to prevent an implosion incident.
OD-SEG refers to the segmentation of the OD with Tyvek® . . . .

36

The absolute gain conversion from the single photoelectron toobserved output PMT charge (pC). . . . . . . . . . . . . . . . . .

43

The final event rates, reduction efficiencies and background contamination after the fully contained reduction steps. Shown for
SK-I to SK-IV. SubGeV refers to events with a visible energy below
1.3 GeV and Multi GeV refers to events with a visible energy above
1.3 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

The final event rates, reduction efficiencies and background contamination after the partially contained reduction steps. Shown
for SK-I to SK-IV. . . . . . . . . . . . . . . . . . . . . . . . . . .

83

The final event rates after the UPMU reduction steps. Shown for
SK-I to SK-IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

Summary of the uncertainties in the background contamination
estimation for UPMU events between −0.1 < cos θ < 0. . . . . . .

88

3.1

4.1

6.1

6.2

6.3
6.4

xxvi

7.1

A summary of the FC sub-GeV event sample criteria. . . . . . . . 100

7.2

A summary of the FC multi-GeV event sample criteria. . . . . . . 101

7.3

The number of observed and expected events for each eventclassification. The MC events has been normalised by the data
live time assuming neutrino oscillations with ∆m232 = 2.4×10−3 eV2and sin2 θ23 = 0.5. Sub-GeV multi-ring interactions are not usedin the present analysis. . . . . . . . . . . . . . . . . . . . . . . . . 102

7.4

Sample purity broken down by neutrino flavour assuming neutrino
oscillations with ∆m232 = 2.4 × 10−3 eV2 and sin2 θ23 = 0.5. SubGeV multi-ring interactions are not used in the present analysis.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.5

The energy/momentum and zenith binning for each event type. . 104

7.6

Summary of the systematic uncertainties associated with data
reduction for different event topologies. . . . . . . . . . . . . . . . 109

8.1

Model of the Earth used in the analysis. . . . . . . . . . . . . . . 113

8.2

The values of the fixed standard oscillation parameters in the NSI
analyses and their uncertainties. . . . . . . . . . . . . . . . . . . . 116

8.3

Constraints on εeτ for the current analysis and the previous SK
result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.4

Constraints on ετ τ for the current analysis and the previous SK
result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

9.1

Specifications of the 50cm Hamamatsu R12860-HQE PMT. Values
taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

10.1 The percentage of detected hits with 2 or fewer reflections forvarious attenuation lengths. Values are also shown for different
values of edge reflectivity. . . . . . . . . . . . . . . . . . . . . . . 149
10.2 The dimensions of the four WLS samples which had their absorption and emission spectra measured. . . . . . . . . . . . . . . . . . 155
10.3 The dimensions of the WLS plates used for the efficiency measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.4 The refractive indices for the WLS plates along with the fractionof light captured in air and in water. . . . . . . . . . . . . . . . . 165
10.5 The best fit η and ρ parameters for each plate. . . . . . . . . . . . 166

xxvii

10.6 Thickness and opacity of different Tyvek samples, values takenfrom Dupont datasheets. Values are given as averages and numbers
vary slightly depending on the standard used to measure theproperties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.7 The expected effective photocoverage for various WLS plates.
Assuming (η ,ρ) = (0.32, 0.7). All plates have reflective edges
and a PMT photocoverage of 0.28% is assumed. . . . . . . . . . . 180
A.1 The best fit systematic errors for the best fit point in the threeflavour εµτ fit. The systematic errors shown here are related
to the neutrino flux. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j . . . 187
A.2 The best fit systematic errors for the best fit point in the threeflavour εµτ fit. The systematic errors shown here are related to
the neutrino interaction. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j . . . 188
A.3 The best fit systematic errors for the best fit point in the threeflavour εµτ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-I and SK-II. 189
A.4 The best fit systematic errors for the best fit point in the threeflavour εµτ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-III and SK-IV.190
A.5 The best fit systematic errors for the best fit point in the twoflavour εµτ − ετ τ fit. The systematic errors shown here are related
to the neutrino flux. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j . . . 191
A.6 The best fit systematic errors for the best fit point in the twoflavour εµτ − ετ τ fit. The systematic errors shown here are related
to the neutrino interaction. The final column shows the estimated
1σ uncertainty and the penultimate column shows the best fit j .

192

A.7 The best fit systematic errors for the best fit point in the twoflavour εµτ − ετ τ fit. The systematic errors shown here are related
to the detector performance, event selection and reconstruction.
The ”σ” column shows the estimated 1σ uncertainty and the ”Fit”
column shows the best fit j . Uncertainties are shown for SK-I and
SK-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

xxviiiA.8 The best fit systematic errors for the best fit point in the twoflavour εµτ − ετ τ fit. The systematic errors shown here are related
to the detector performance, event selection and reconstruction.
The ”σ” column shows the estimated 1σ uncertainty and the ”Fit”
column shows the best fit j . Uncertainties are shown for SK-III
and SK-IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
A.9 The best fit systematic errors for the best fit point in the εee −εeτ − ετ τ fit. The systematic errors shown here are related to
the neutrino flux. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j . . . 195
A.10 The best fit systematic errors for the best fit point in the εee −εeτ − ετ τ fit. The systematic errors shown here are related to theneutrino interaction. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j . . . 196
A.11 The best fit systematic errors for the best fit point in the εee −εeτ − ετ τ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-I and SK-II. 197
A.12 The best fit systematic errors for the best fit point in the εee −εeτ − ετ τ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-III and SK-IV.198

xxix

Chapter 1
Thesis Overview
The discovery of neutrino oscillations has proven that neutrinos have a nonzero mass which is unaccounted for in the Standard Model of particle physics.
Many models of neutrino mass naturally include some form of phenomenologicallyallowed interactions which are not included in the Standard Model; suchinteractions are called non-standard interactions. If present, non-standard
interactions can affect the production, detection and propagation of neutrinos
through matter. The analyses carried out in this thesis aim to search for sub
dominant effects in neutrino oscillations which may be due to non-standard
interactions with matter in the Earth.
This thesis begins with an introduction to neutrino masses and oscillation theory,
as well as an overview of the current experimental status, in Chapter 2. The
theories of standard oscillations as well as standard and non-standard matter
effects are presented. The neutrino data used in this thesis comes from theSuper-Kamiokande experiment.
Super-Kamiokande (Super-K) is an underground water Cherenkov detector which
has been running since 1996. Data has been collected in four distinct phases SKI, SK-II, SK-III and SK-IV. A detailed description of the Super-Kamiokande
detector and its four phases are given in Chapter 3. The detector’s calibration
is outlined in Chapter 4. The analyses in this thesis compare the expected
atmospheric neutrino flux to the observed flux, where the expected flux is given
by a Monte Carlo (MC) simulation described in Chapter 5.
Super-Kamiokande is built under ∼ 1 km of rock in order to reduce backgrounds
1

from cosmic rays. The level of cosmic rays reaching the detector are reducedby five orders of magnitude compared to a detector located on the surface.
While backgrounds are significantly reduced, they still make up the overwhelming
majority of triggered events. Efforts must be taken to reduce the large amountof background events keeping only the neutrino events. This data reduction
is carried out regularly with occasional changes in the data reduction steps
depending on the detector’s configuration. In SK-IV it was found that somehigh energy events were being misclassified because they left a crosstalk signal in
the veto region. I was a member of a data reduction taskforce which implemented
the most recent changes to the data reduction, in particular I was in charge of
implementing a crosstalk selection cut. The details of the data reduction as wellas the implementation of the crosstalk cut are found in Chapter 6.
Chapter 7 details the event selection and binning of the events as well as theformulation of the χ2 . Searches are then carried out for non-standard interactionsin the νµ − ντ and νe − ντ sectors which are explained in Chapter 8. I performed
the analysis and extended the existing Super-K oscillation analysis framework toallow for the calculation of non-standard oscillation probabilities.
In order to increase the physics sensitivity, Super-Kamiokande have decided to
add Gadolinium to the ultrapure water in the tank. Gadolinium loaded water
improves the ability to detect neutrons which can reduce backgrounds as wellas increase the detector’s ability to separate neutrinos events from antineutrino
events. Super-K shut down in the middle of 2018 ending the run of SK-IV. I had
the amazing opportunity to enter the tank and take part in the refurbishmentof the detector in preparation for Gadolinium doping. Getting to see the insideof the detector was a valuable experience which gave me a good understandingof the detector setup. The knowledge was useful for the development of SuperKamiokande’s successor Hyper-Kamiokande.
Hyper-Kamiokande is a large underground water Cherenkov detector withroughly eight times the fiducial mass of Super-Kamiokande. While both tanks
are water Cherenkov detectors, which use similar technologies, complications arise
when designing the larger detector. Hyper-Kamiokande will have an improved
sensitivity to neutrino oscillation parameters and nucleon decays in addition to
the increased capability of supernovae observation. The improved sensitivity
requires backgrounds to remain low, many of which are removed by an outerdetector. The design of the Hyper-Kamiokande detector is described in Chapter 9.
Chapter 10 describes the study and design of the Hyper-Kamiokande detector,2and in particular the outer detector. I developed the analytic simulation of the
WLS plates and carried out significant development of the outer detector in
WCSim. The hardware measurements and R&D were carried out by me and othermembers of the Edinburgh Hyper-K group. This thesis ends with a summary
chapter, detailing the conclusions from the various studies and outlook to futurestudies.

3Chapter 2
Introduction
The neutrino is the most abundant massive particle in the universe. There
are many sources of neutrinos, both natural and manmade: the Sun, cosmic
ray interactions in the Earth’s atmosphere, supernovae, nuclear reactors andaccelerators. Each source of neutrinos has their own characteristic flavour andenergy spectrum, allowing the study of various physics phenomena. Neutrinos
interact only via the weak force and their very small cross section makes themdifficult to detect. For this reason, detectors with large target volumes and low
levels of background must be used.
In the late 1960s the Homestake experiment [64] measured the solar neutrino
flux and observed a solar neutrino flux which was much lower than thatpredicted by the Standard Solar Model. Kamiokande [84], SAGE [7] and SuperKamiokande [81] later confirmed the deficit. This problem became known as
the solar neutrino anomaly. Another anomaly was later found in the flux ofatmospheric neutrinos. The atmospheric neutrino flux is expected to have a(νµ /νe ) ratio of 2 for neutrino energies below 1 GeV (see Section 5.1) while
the Kamiokande [83], IMB [49] and Soudan [39] experiments measured a value
roughly two thirds of this, indicating an excess in νe or a deficit in νµ (or both).
This was known as the atmospheric neutrino anomaly and was solved by SuperKamiokande [85] when they found that the measured neutrino flux had a zenith
angle dependence for νµ which was consistent with νµ → ντ oscillation. In 2002
the solar neutrino problem was solved when SNO [30] measured the total solar
neutrino flux with a detector which was sensitive to νe , νµ and ντ . The total solar
neutrino flux measured by SNO was consistent with the Standard Solar Model4

prediction and solar neutrino oscillation νe → νµ /ντ was confirmed.
Since the first evidence of neutrino oscillations, much progress has been made in
determining the precise values of neutrino oscillation parameters. The precisionof neutrino oscillation experiments now allows us to look for sub-leading effects,
such as non-standard neutrino interactions, and to achieve a better understandingof this mysterious particle.

2.1Standard Model

The Standard Model of particle physics is a mathematical framework which
describes the behaviour of subatomic particles. The model incorporates all known
elementary particles and three of the four known fundamental forces. The model
includes fermions, matter particles with half integer spin, and bosons, forcecarrying particles with integer spin. There are 12 fermions which are madeup of six quarks and six leptons; the fermions are grouped together into three
generations of increasing mass. The three fundamental forces in the Standard
Model are the electromagnetic, weak and strong forces. The electromagnetic force
is mediated by the massless photon and the weak nuclear force is mediated bymassive W + , W − and Z 0 bosons; the photon and W/Z bosons collectively mediate
the electroweak interaction. The strong interaction is mediated by masslessgluons. A schematic diagram of the Standard Model is shown in Figure 2.1.
The interactions in the Standard Model are defined by gauge symmetries. The
gauge group of the Standard Model is SU (3)×SU (2)×U (1) where SU (2)×U (1) isthe electroweak group and SU (3) is the strong gauge group. The Higgs field [100]interacts with the gauge fields which results in spontaneous symmetry breaking
causing the weak bosons and charged fermions to gain mass. The Higgs field also
gives rise to a massive, spin-0 boson, the Higgs boson.
Neutrinos do not interact via the electromagnetic or strong interactions whichmeans they rarely interact with matter, making them difficult to detect. Weakinteractions are called charged current (CC) if they are mediated by a W ± boson,and neutral current (NC) if they are mediated by the Z 0 boson. The three
generations of neutrino are νe , νµ and ντ which are defined by the flavour of thecharged lepton associated with their charged current interactions. While the SM
is a very successful theory, with many successful experimental predictions, it does5

Standard Model of Elementary Particles
three generations of matter(fermions)III≃1.28 GeV/c²≃173.1 GeV/c²0charge

⅔

⅔

⅔

0

spin

½

u

c

½

QUARKSupcharm≃4.18 GeV/c²

0

−⅓

−⅓

0

d

½

s

½

b

strangebottomphoton≃0.511 MeV/c²≃105.66 MeV/c²≃1.7768 GeV/c²≃91.19 GeV/c²

−1

−1

e

½

<1.0 eV/c²0½νeelectronneutrino

μ

½

muon
<0.17 MeV/c²
0
½

νμ
muon
neutrino

τ

0

0
½

ντ
tau
neutrinoZ1

tau<18.2 MeV/c²

H0

Z boson≃80.39 GeV/c²
±1
1

higgs

γ

1

down

−1

0

gluon

≃96 MeV/c²

electron

LEPTONS

top

−⅓
½

g

1

≃4.7 MeV/c²½

Figure 2.1

t½≃124.97 GeV/c²

W

W bosonSCALAR BOSONS≃2.2 MeV/c²

VECTOR BOSONS

II

mass

GAUGE BOSONS

I

interactions / force carriers(bosons)

A summary showing the fermions and bosons in the Standard Model.
Taken from [1].

not yet include a way to generate neutrino mass or allow neutrino oscillations.

2.2

Neutrino Oscillations

Neutrinos are produced in various charged-current (CC) weak interaction processes, associated with a charged lepton. The three charged leptons means there
are three neutrino flavours: electron neutrino (νe ), muon neutrino (νµ ) and tau
neutrino (ντ ). The type of neutrino is determined either by the charged lepton
associated with a neutrino’s creation or the detected charged lepton resulting
from a neutrino CC interaction. In the late 1950s Pontecorvo [144] predicted aphenomenon that would cause neutrinos to change flavour in a process known
as neutrino oscillation. The oscillation is caused by the interference of different
massive neutrinos. In 1962 Maki, Nakagawa and Sakata [126] first introduced amodel with the mixing of different neutrino flavours. Neutrino oscillation has been
observed by atmospheric [85], solar [29] and reactor [21, 41] neutrino experiments.
The discovery of neutrino oscillation proves that neutrinos have a non-zero mass,
directly contradicting the assumption made in the Standard Model.

62.2.1

Neutrino Oscillation Theory

Neutrinos are in one of three flavour eigenstates at production and detection:|νe i, |νµ i or |ντ i. During propagation however, the neutrino is made up of asuperposition of three mass eigenstates: |ν1 i, |ν2 i or |ν3 i. The transformation
between flavour and mass bases is described by the Pontecorvo-Maki-NakagawaSakata (PMNS) unitary mixing matrix:
  
 
νe
Ue1 Ue2 Ue3
ν1
  
 
νµ  = Uµ1 Uµ2 Uµ3  ν2  .
ντUτ 1 Uτ 2 Uτ 3
ν3

(2.1)

Equation 2.1 shows that a neutrino flavour eigenstate is a superposition of mass
eigenstates which can be written in the form:|να i =

3X∗
Uαi
|νi i ,

(2.2)

i=1

where να represents a neutrino of flavour α = e, µ or τ . U is the PMNS matrixand νi represents the neutrino mass eigenstate where i = 1, 2 or 3. The PMNS
matrix is the product of three independent rotation matrices with rotation angles
θ12 , θ13 and θ23 and a complex phase δcp :






1
0
0
cos θ130 sin θ13 e−iδcpcos θ12 sin θ12 0




U = 0 cos θ23 sin θ23  010 − sin θ12 cos θ12 0 .
0 − sin θ23 cos θ23− sin θ13 eiδcp 0
cos θ13
0
0
1
(2.3)

2.2.2

Neutrino Oscillations in a Vacuum

Let us now consider the propagation of neutrinos. The massive neutrino states
are eigenstates of the Hamiltonian and their time evolution is governed by the
Schrödinger equation:d(2.4)
i |Vi (t)i = H |Vi (t)i .
dt

7Equation 2.4 suggests that the neutrino mass states evolve in time as plane waves:|Vj (t)i = e−iEj t |Vj i ,(2.5)

where Ej are the energy eigenvalues.
When a neutrino is created, with a definite flavour state α, at time t = 0
equations 2.2 and 2.5 give us the time evolution of the neutrino:|Vα (t)i =X∗ −iEj te|Vj i .
Uαj

(2.6)

j

The mass states can be written in terms of flavour states by using the unitarityof the mixing matrix. The time evolution equation (Equation 2.6) then can be
rewritten in terms of flavour states:|Vα (t)i =

X X
∗
(
Uαj
Uβj e−iEj t ) |Vβ i .
β=e,µ,τ

(2.7)

jEquation 2.7 shows that, assuming a non-diagonal mixing matrix, a neutrino
created with a definite flavour then propagates as a superposition of flavour states.
The amplitude of the transition from neutrino flavour α to β is given by:

X

∗
Uαj
Uβj e−iEj t .

(2.8)

∗
∗ −i(Ej −Ek )t
UαjUβj Uαk Uβk
e
.

(2.9)

Aνα →νβ ≡ hνβ |να (t)i =j

The transition probability is then given by:Pνα →νβ = |Aνα →νβ |2 =Xj,kAt ultrarelativistic energies, the energy eigenvalue, Ej , can be approximated byignoring higher order terms of the Taylor expansion:q
E = (p~2 + m2 )s
m2
= p~ 1 +p~2(2.10)(2.11)

8

= p~(1 +m2
m4++ ...)
2p~2 8p~4(2.12)

m2.
2p~2(2.13)' p~ +The Ej − Ek term that appears in the transition probability then becomes:
Ej − Ek = (~p +

∆m2jk
m2j
m2
,
) − (~p + k ) =
2Eν
2p~2
2p~2

(2.14)

where Eν ≈ |~p|, neglecting the neutrino mass contribution, and ∆m2jk = m2j −m2k .
Neutrino experiments do not typically measure the neutrino propagation time,
but rather the distance between the source and detector. Neutrinos travel close
to the speed of light so substituting t with propagation distance L and settingc = 1, Equation 2.9 becomes:
Pνα →νβ = |Aνα →νβ |2 =

X
j,k

∗
∗
Uαj
Uβj Uαk Uβkexp(−i

∆m2jk
L).
2E

(2.15)

This shows that neutrinos can change flavour as they propagate throughspace, with an oscillation phase determined by the energy of the neutrino,
the propagation length and the mass squared differences. The amplitude ofoscillations is governed by the mixing matrix. The mixing parameters and masssquared differences are physical constants so in order to probe neutrino oscillations
experiments must vary the neutrino energy or travel distance.
The antineutrino oscillation probability is derived in the same way except thatthe complex conjugate of the mixing matrix is used instead. If the mixing matrix
is real ( δcp = 0) then the transition probabilities are the same for neutrinos andantineutrinos, otherwise they differ.

Two Flavour Approximation
Neutrino experiments are not always sensitive to three flavour neutrino mixing,in this case a two flavour model can be used. The two flavour model is simpler
and has fewer parameters. In the two flavour case the mixing matrix U reduces9to a 2×2 unitary mixing matrix:U=!
cos θ sin θ,− sin θ cos θ(2.16)

where θ is the mixing angle. Since two flavours are considered there is only one
mass squared difference ∆m2 = m22 − m21 . Here the flavour states can be written
as:
!
!
!
να
cos θ sin θν1=.
(2.17)
νβ− sin θ cos θν2In this case, Equation 2.15 becomes:
Pνα →νβ = sin2 (2θ) sin2 (

∆m2 L
),
4E

(2.18)

when α 6= β, and the survival probability becomesPνα →να = 1 − sin2 (2θ) sin2 (

∆m2 L
).
4E

(2.19)In this discussion, and throughout this thesis, natural units h̄ = c = 1 are used.
Numerically, for ∆m2 in eV 2 , L in km and E in GeV , a factor of 1.267 is usedin the oscillation frequency. We can see from Equation 2.19 that the oscillation
2L= π so oscillation experiments can choose a baseline
maximum occurs when ∆m
2E
and neutrino energy range to be sensitive to different values of ∆m2 . Figure 2.2
shows the two flavour neutrino survival probability as function of flight length.

2.2.3

Neutrino Oscillations in Matter

The previous section described neutrino oscillations in a vacuum, however whenneutrinos propagate through matter the oscillation behaviour changes. L.
Wolfenstein [160] proposed that neutrinos propagating in matter are subject toa potential due to coherent forward elastic scattering with electrons, protons
and neutrons. The Feynman diagrams for charged current (CC) and neutral
current (NC) scattering in matter are shown in Figures 2.3a and 2.3b. The
NC and CC introduce new potentials VN C and VCC into the Hamiltonian
respectively. Neutrino oscillations arise due to the phase difference between the10

P(να → να)

1

0.8

0.6

0.4

0.2

0
10

Figure 2.2

102

3

Two flavour survival probability of να as a function of propagation
length. The black curve represents Eν = 1 GeV, the red curve isEν = 10 GeV and the blue curve for Eν = 100 GeV. This is for
maximal mixing θ = π/4 and ∆m2 = 2.56 × 10−3 eV2 .

νee−νe,νµ ,ντνe,νµ ,ντ

W

Z

e−

νe

(a)

Charged current

Figure 2.3

104
L [km]

10e− ,p,n(b)e− ,p,nNeutral current

Feynman diagrams of the elastic coherent forward scatteringinteractions that neutrinos undergo through propagation in a
medium. The flow of time is left to right.

mass eigenstates, in matter the phase difference can be affected by the totalenergy of the mass eigenstate.
Neutral current scattering is the same for all of the neutrino flavours, Section 2.2.4
describes the scenario where this may not be the case. The neutral current
11interactions add the same phase to all neutrino flavours so the phase differenceis unaffected, however electron neutrinos (and antineutrinos) undergo additionalcharged current interactions on the electrons in matter. These interactions add
a flavour dependent phase to electron neutrinos. The additional potential VCC isgiven by:√
VCC = ± 2GF Ne ,(2.20)

where GF is the Fermi coupling constant and Ne is the number density of electrons
in the matter, the plus (minus) sign is for neutrinos (antineutrinos). In 1985
Mikheev and Smirnov introduced resonant flavour transitions which can occur
when neutrinos propagate through a medium of varying density. This resonanttransition was used to explain the flavour transition of neutrinos leaving the sun
and is known as the MSW effect [129].
In order to see the effect we can consider the simple case of two flavour oscillations
where one of the neutrinos is an electron neutrino, a constant mass density is
assumed.
The Hamiltonian in a vacuum in the mass basis is

Hvac =

m21
2E

0

0

!
(2.21)

m22
2E

and the mixing matrix is defined as

νe
νβ

!
=

cos θ sin θ− sin θ cos θ

!

!
ν1
.
ν2

(2.22)The Hamiltonian then is transformed to the flavour basis using the mixing matrix
such that the vacuum Hamiltonian becomes

Hvac → U Hvac U †(2.23)and the Schrödinger equation in the flavour basis becomes

12

νe
νβ

d
i =
dt

!
= U Hvac U †

νe
νβ

!

∆m2
=
4E

− cos 2θ sin 2θ
sin 2θ cos 2θ

!

νe
νβ

!
.

(2.24)

Following the arguments from the previous section, the transition probability
would be:∆m2 L
P(νe →νβ ) = sin2 2θ sin2 ()(2.25)
4E
Now we add the potential from the matter, affecting only νe :Hmat =

!
VCC 0
0 0

(2.26)

When adding this potential we can shift the matrix by a multiple of the identity
and the Schrödinger becomes

d
i =
dt

νe
νβ

!

νe
= [U Hvac U +Hmat ]
νβ

!

†

where
A≡

∆m2
=
4E

!
!
− cos 2θ + A
sin 2θ
νe,sin 2θ
cos 2θ − Aνβ(2.27)

2EVCC
.
∆m2

(2.28)

It is convenient to write Equation 2.27 in this form as the traceless matrix can beeasily diagonalised to get the effective mixing angle θm and mass splitting ∆m2m .
The effective parameters are

sin 2θm ≡sin 2θ
sin 2θ + (cos 2θ − A)22(2.29)

sin2 2θ + (cos 2θ − A)2 .

(2.30)

and∆m2m ≡ ∆m2

q13

Equation 2.24 then becomes

d
i =
dt

νe
νβ

!

∆m2m
=
2E

− cos 2θm sin 2θm
sin 2θm cos 2θm

!

νe
νβ

!
.

(2.31)

It can be seen that in the case of a vanishing matter potential the effective
parameters reduce to their vacuum values. In the case when A = cos 2θ theeffective mixing angle is maximal (π/4) and the effective mass squared splitting
is minimised, this condition is called the MSW resonance condition.
It should also be noted that while vacuum neutrino oscillations are not sensitive tothe sign of the mass squared splitting ∆m2 , Equation 2.30 shows that the effective
mass splitting in matter does have a term (cos 2θ − A)2 which is dependent on thesign of the mass splitting. For this reason matter effects can be used to resolve
the sign of the mass splitting.

2.2.4

Non-Standard Neutrino Interactions

Non-standard neutrino interactions (NSI) were first considered by Wolfenstein [160, 161] and are now a natural part of most neutrino mass models [130,137]. In order to study NSIs in a model independent way, phenomenologicallythey can be described with an effective four fermion Lagrangian√0
LN SI = −2 2GF εfαβf C (ν α γ µ PL νβ )(f γµ PC f 0 ),(2.32)

0where GF is the fermi constant, εfαβf C are the NSI strength parameters, α, β =e, µ, τ , P is the chiral projector and C = L, R. Neutrino NSIs can be CC-likeor NC-like, if f 6= f 0 in Equation 2.32 then the interaction is CC-like, whereas if
f = f 0 then the interaction is NC-like and the NSI parameters are then definedas εfαβC ≡ εfαβf C . Figure 2.4 shows a diagram of an NC-like NSI interaction.
Charged current NSIs affect the production and detection of neutrinos whereas
neutral current NSIs affect the propagation of neutrinos through matter. The CC
NSI parameters are constrained by at least an order of magnitude better thanthe NC parameters and will not be discussed further in this thesis.
To describe neutrino propagation with NSIs the matter potential in Section 2.2.3

14

Figure 2.4

να

νβ

f

f

A pseudo-Feynman diagram of a neutral-current non-standard
neutrino interaction. α is the initial neutrino flavour, β is the final
neutrino flavour and f is a first generation fermion (e, u or d). The
flow of time is left to right.

is modified to:
1 + εee εeµ εeτ√A ≡ 2GF Ne  εµe
εµµ εµτ  .
ετ eετ µ ετ τ(2.33)As neutrinos propagate through the Earth we cannot distinguish between NSI
interactions on left and right handed fermions so the effective NSI parameters
are defined as εfαβ = εfαβL + εfαβR . As the Earth contains electrons, up and downquarks, the effective NSI parameters in Equation 2.33 are defined asεαβ ≡X Nf fε ,Ne αβ
f =e,u,d(2.34)

where Nf is the number density of the fermion f .
Including the NSIs, the effective Hamiltonian for neutrino propagation throughmatter becomes:





0
0
0
1 + εee εeµ εeτ
√
1 



Hef f =
U 0 ∆m221
0  U † ± 2GF Ne  εµe
εµµ εµτ  , (2.35)
2E
0
0
∆m231
ετ e
ετ µ ετ τ15where the first term is the vacuum component and the second term is the mattercomponent. The 1 in the matter matrix corresponds to the standard matter
effect on electron neutrinos and the plus (minus) sign corresponds to neutrinos(antineutrinos).
If the diagonal components of the NSI matrix (εαα ) are different from each other,
then the NC scattering amplitude is different for the different neutrino flavours,
this is known as lepton non-universality. If the off diagonal elements (εαβ where
α 6= β) are non-zero then we get flavour-changing neutral currents (FCNC). In
general the off-diagonal elements are complex with εαβ = ε∗βα but for the workin this thesis the complex phase was not considered. The diagonal parameters
can cause a matter induced mass squared difference which could create additional
resonances even if neutrinos had zero mass, while the off-diagonal parameters playa role similar to the mixing angles where even in the absence of vacuum mixing
there could be matter induced mixing. Lastly the complex phases of the offdiagonal NSI elements could introduce a new source of CP violation. These causesome non-trivial degeneracies in neutrino oscillation parameter measurements.

2.3

Experimental Status

Many experiments have observed neutrino oscillations and their complimentarymeasurements give us a clearer picture of the overall mechanism. This section
summarises the latest values of the neutrino oscillation parameters.

2.3.1

Standard Oscillations

The parameters θ23 and ∆m232 are referred to as the atmospheric mixing
parameters, which are measured by looking for νµ disappearance (by oscillationto ντ ). These parameters are measured by atmospheric neutrino experiments
such as Super-K [18] and IceCube [5] as well as accelerator neutrino experiments
such as T2K [90], NOvA [23] and MINOS [24]. Figure 2.5 shows contours for the
68% and 90% confidence region of these parameters. The mixing angle has beenmeasured to be near maximal and one of the remaining questions is whether
the mixing angle is less than or greater than π/4. Another open question is
the sign of the mass splitting ∆m232 . The sign of the mass-squared splitting is
resolved by matter effects (see Section 2.2.3) which are a sub-leading effect in16|∆ m232| (10-3 eV2/c4)

atmospheric neutrino oscillations. In principle, atmospheric neutrinos travelling
upwards traverse the diameter of the Earth and can be used to resolve the mass
hierarchy. Super-K’s atmospheric neutrino data shows a preference for the normal
hierarchy (ν3 > ν2 ) [113].
3.6
3.4
3.2

68%CL (-2 ∆ ln L = 2.3)
90%CL (-2 ∆ ln L = 4.61)
T2K best-fit

3
2.8
2.6
2.4
2.2

Super-K MINOS+
T2K NOvA IceCube

2
1.8
0.3

Figure 2.5

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

sin2 θ23

The 68% and 90% confidence regions for the sin2 θ23 -|∆m232 | plane,assuming normal mass hierarchy. Contours from NOvA [26],MINOS [24], SK [158] and IceCube [3] are included. Taken
from [16].

The parameters θ12 and ∆m221 are measured by solar and reactor neutrino
experiments. In 2002 the SNO solar neutrino experiment measured the flux ofsolar neutrinos via NC interactions and found a non e-like component to theneutrino flux [31] due to oscillations to νµ and ντ . Since then, measurementsfrom Super-K [15] and KamLAND [20] as well as global analyses [10] have greatly
constrained these parameters. The electron density in the sun is very large sounlike with atmospheric neutrinos, solar neutrinos are subject to large matter
effects and the sign of ∆m221 is known.
Figure 2.6 shows the allowed region for the ν1 − ν2 neutrino oscillation parameter
space. As solar neutrinos propagate through the earth, a regeneration of νeis expected due to the matter effect. In 2014 Super-K measured a day-night
asymmetry in solar neutrino events [148], this affects the solar experiment’s
measured mass splitting, preferring a lower value. The mass splitting measured
in this way does not agree well with KamLAND.
The mixing angle θ13 was the last to be measured. While accelerator νeappearance can give limits on this parameter, the best measurements come fromreactor ν e disappearance measurements. In 2003 the CHOOZ reactor experiment17

Figure 2.6

A plot of the allowed ν1 − ν2 neutrino oscillation parameter region.
Solar experiments are shown in green with contours showing 15σ, KamLAND (reactor) is shown in blue and the red shows the
combined analysis results. The filled regions indicate the 3σ region.
The overlaid red lines show the contours for day-night asymmetry.
Taken from [17].

found no evidence of ν e oscillation and set an upper limit sin2 θ13 < 0.15 at 90%
CL [42]. A decade later, short baseline reactor experiments Daya Bay [41], Double
CHOOZ [21] and RENO [32] independently reported values of sin2 2θ13 ≈ 0.1 andT2K observed electron neutrino appearance in their muon beam [14], giving a best
fit value of sin2 2θ13 ≈ 0.14.
The remaining unknowns in the standard neutrino oscillation parameters, inparticular δCP , will be tackled by the Hyper-K experiment and are discussed
further in Chapter 9.

2.3.2

NSI Parameters

Solar and atmospheric neutrino oscillations are described very well by thestandard oscillation framework so the NSI are at most a sub leading effect. It
is important to note that NSI parameters are usually measured by setting all
NSI to zero except for the parameters of interest. NSI parameters can be highly
18

Table 2.1 Three flavour oscillation parameters from a 2019 global analysis [71].
For normal ordering ∆m23l ≡ ∆m231 > 0 and for inverted ordering∆m23l ≡ ∆m232 < 0. The best fit point was with normal hierarchy.

Parametersin2 θ12
sin2 θ23
sin2 θ13∆m221
10−5 eV 2∆m23l
10−3 eV 2

Best Fit ±1σ
Normal Hierarchy Inverted Hierarchy
0.310+0.013−0.0120.582+0.015−0.0190.02240+0.00065−0.00066
7.39+0.21−0.20+2.525+0.033−0.0310.310+0.013−0.0120.582+0.015−0.0190.02263+0.00065−0.00066
7.39+0.21−0.20−2.512+0.034−0.031

correlated so this must be taken into consideration when interpreting results.
The solar neutrino survival probability is expected to increase with decreasingenergy, this is because of the transition from matter dominated oscillations at
higher energies to vacuum oscillations at lower energies. Figure 2.7 shows the
expected survival probabilities for various different scenarios. While both sides ofthe spectrum have been measured, the spectrum up-turn has yet to be measured.
Various analyses have found a slightly better agreement with small NSI than
the standard oscillation scenario [77, 142]. This is due to the lack of observed
spectrum upturn in solar neutrino survival probability [131] as well as the tension
in the mass splitting, which is eased with the addition of NSI.
When looking at NSI in solar neutrinos it is common to reduce the Hamiltonian
to an effective 2×2 matrix. This is done by rotating to a specific basis and using
the one mass scale dominance approximation ∆m231 → ∞ resulting in a system
where the third eigenstate decouples from the system [33, 123, 130].
The νe survival probability then becomes:

P (νe → νe ) = c413 Pef f + s413 ,(2.36)

where sij = sin(θij ), cij = cos(θij ). Pef f can be calculated using the effective 2×2

19

8

7

Brx (pep)

KL ( Be)

0.7

Brx (pp)0.8

Borexino ( B)Super-K
SNO

7Brx ( Be)

0.5

pp

〈Pee 〉 = ΦCC / ΦNC

0.6

0.4
0.3
0.2
0.1
0.1

0.5

Standard

NSI-upSterileNSI-dw

1

2

3

5

7

10

14

Eν [MeV]Figure 2.7

The expected survival probability of solar neutrinos for various
physics scenarios, including data from solar neutrino experiments.
All scenarios use sin2 θ13 = 0.022. The standard oscillations use(sin2 θ12 , ∆m221 ) = (0.31, 7.5 × 10−5 eV 2 ). The single additional
sterile neutrino uses (sin2 θ12 , ∆m221 , sin2 2α, ∆m201 ) = (0.31, 7.5 ×
10−5 eV 2 , 0.005, 1.2 × 10−5 eV 2 ). NSI on up quarks scenario uses
(sin2 θ12 , ∆m221 , εuD , εuN ) = (0.30, 7.25 × 10−5 eV 2 , −0.22, −0.30) andthe NSI on down quarks scenario uses (sin2 θ12 , ∆m221 , εdD , εdN ) =(0.32, 7.35 × 10−5 eV 2 , −0.12, −0.16). Taken from [127].

Hamiltonian:∆m221
Hef f =
4E

!
!
X Nf
− cos 2θ12 sin2θ12
cos2 θ13 A 0++ANe
sin2θ12 cos 2θ1200
f =e,u,d!
−εfD εfN,
εfN∗ εfD(2.37)√
where A = 2GF Ne and the diagonal, εD and off-diagonal, εN , parameters are
related to the NSI parameters, εαβ by [130]:εD = c13 s13 <[eiδCP (s23 εeµ + c23 εeτ )] − (1 + s213 )c23 s23 <(εµτ )c2s2 − s213 c223
− 13 (εee − εµµ ) + 23(ετ τ − εµµ )
22(2.38)20

andεN = c13 (c23 εeµ − s23 εeτ ) + s13 e−iδCP [s221 εµτ − c223 ε∗µτ + c23 s23 (ετ τ − εµµ )]. (2.39)

An analysis of solar neutrino and KamLAND experiments [127] obtained foundthe best fit points on the diagonal and off-diagonal NSI parameters (εuD , εuN ) =(−0.22, −0.3) and (εdD , εdN ) = (−0.12, −0.16) for up quarks and down quarks
respectively. A global oscillation analysis [88] found that large negative values ofεee ≈ -4 are compatible with the oscillation data.
The standard oscillation framework describes the νµ disappearance of atmospheric
neutrinos quite well, and large NSI in the νµ − ντ sector would be incompatible
with high energy atmospheric neutrino data. For this reason, atmospheric
neutrinos can provide tight constraints on the µ − τ parameters. In 2011 a
Super-K [133] two flavour analysis resulted in the following constraints at the
90% C.L.
dV
|εdV
|εdV
(2.40)µτ | < 0.011 ,µµ − ετ τ | < 0.049.
Recently, IceCube carried out a three flavour analysis using their most recent
DeepCore data and obtained the constraint [6]:−0.0067 < εdVµτ < 0.0081(2.41)

at 90% C.L.
A generalised NSI potential involves different parameters for different charged
fermions in matter (e,u and d). The Earth has a reasonably consistent matter
profile with the neutron to electron ratio Yn = 1.012 in the mantle and 1.137 in
the core and an average of 1.051 all over the Earth. Earth’s matter is neutral
which means that the proton to electron ratio Yp = 1. For this reason atmospheric
neutrinos which traverse the Earth can be parameterised with a single εαβ as seenin Equation 2.34. In the sun, the chemical composition varies significantly andYn varies from 1/2 in the centre to 1/6 at border of solar core [130] so it is notpossible to have a common parameter accounting for all of the different fermions
so only one fermion is considered at a time.
Bounds from accelerator neutrinos come from νµ → νµ and ν̄µ → ν̄µ channels.
To first approximation εµτ , εµµ and ετ τ are the relevant NSI parameters. The
MINOS experiment, with a long baseline of 730 km obtained the bound [25] at21

the 90% C.L.:−0.067 < εdVµτ < 0.023.

(2.42)In addition to reactor and accelerator neutrino experiments, measurements of
NSI parameters are made by various neutrino scattering experiments in which
neutrino interactions with matter could be significantly affected. Bounds for NSI
parameters are usually for specific fermions and the handedness of the fermions, so
comparison of various bounds involve some assumptions. For example, althoughneutrino oscillation experiments measure an overall NSI strength, this number isoften converted to assume all NSI only occurs on down quarks for the purposeof comparison. For a recent review of neutrino NSI status, the reader is referredto [72].

22

Chapter 3
The Super-Kamiokande Detector
Super-Kamiokande (SK) is a 50 kton underground water Cherenkov detector
located in Kamioka mine under Mt Ikeno, Gifu Prefecture, Japan [82]. The
experiment began taking data in April, 1996 with four distinct running periods
SK-I (1996-2001), SK-II (2003-2005), SK-III (2006-2008) and SK-IV (2008-2018).
The location within Kamioka mine results in an overburden of 1 km which reduces
the backgrounds from cosmic ray interactions in the atmosphere by five orders ofmagnitude. A sketch of the detector site is shown in Figure 3.1.
The physics program of SK consists of searches for nucleon decay and dark matter,as well as observation of neutrinos from different sources: the sun, cosmic ray
interactions in the atmosphere, supernovae and accelerator neutrinos produced
at the J-PARC [108] facility in Tokai, Japan [9].

3.1

Cherenkov Radiation

Cherenkov radiation [56] is emitted when a relativistic charged particle passes
through an optically transparent medium with a velocity greater than the local
phase velocity of light. The particle polarises the medium along its trajectory
forming wavelets which are in phase with one another (see Figure 3.2). As theparticle passes, the displaced electrons return to their normal positions emitting
coherent radiation [112]. The emission is cylindrically symmetrical along theparticle track, resulting in a cone of light.

23

Figure 3.1

A sketch of the Super-Kamiokande detector site under Mt Ikeno.
Taken from [82].

Figure 3.2

A diagram showing Cherenkov light production by a charged particle.

The angle of emission relative to the particle track is given bycos θc =

1
,
βn

(3.1)

where θc is the Cherenkov angle, n is the refractive index of the medium andβ = v/c is the speed of the charged particle relative to the speed of light invacuum. For water, n = 1.33 giving θc = 41° for ultra-relativistic particles.
Table 3.1 shows the minimum energy required by different particles in order to24emit Cherenkov radiation, when β = 1/n.
Table 3.1 The Cherenkov threshold energy in water, for common charged
particles.

Particle

Cherenkov Energy Threshold (MeV)electronmuon
pion
proton

0.77
160
211
1420

When the Cherenkov cone is projected onto the surface of the detector, the lightof the cone appears as a ring. Electrons undergo electromagnetic showering, via
Bremsstrahlung radiation and pair production, giving a fuzzy ring. The thicknessof the ring depends on the length of the track where the charged particle wasable to produce Cherenkov radiation. If a particle emits Cherenkov radiation
while leaving the detector, then the ring is completely filled in. The energy ofelectron-like events is reconstructed by counting the overall number of photoelectrons. Muons generally do not cause electromagnetic showers and so they
produce sharper rings. Such events are referred to as muon-like. Figure 3.3
shows example event displays for e-like and µ-like events.

(a)Figure 3.3

e-like event(b)µ-like event

A typical event display for an electron-like event [left] and muon-likeevent [right]. The blue dots represent a low number of photons andthe red dots represent a larger number of photons.

The number of Cherenkov photons per unit wavelength (λ) per unit path length25

is expressed by
2πz 2 α2πz 2 α 2
d2 N
1
=
)
=
(1
−
sin θcdλdx
λ2
β 2 n2 (λ)
λ2

(3.2)

where z is the particle’s charge in units of the electron charge and α is the finestructure constant. It can be seen from Equation 3.2 that Cherenkov radiation
is typically produced at blue/UV wavelengths. Though the 1/λ2 dependence
continues to shorter wavelengths the emitted light is absorbed by the water.
For electrons and muons, roughly 340 photons are emitted per centimetre in awavelength range of 300-600 nm.

3.2

Detector Design

Figure 3.4

A schematic view of the Super-Kamiokande support structure for the
inner detector. Taken from [82].

The SK detector [82] consists of a large stainless-steel tank with a height of 41.4 m
26

and a diameter of 39.3 m. SK is filled with 50 ktons of ultra pure water and issplit up into two optically separated regions referred to as the inner detector (ID)and the outer detector (OD). A 36.2 m tall, 33.8 m diameter cylindrical support
structure splits the tank into ID and OD volumes. Both sides of the support
structure hold photomultiplier tubes (PMTs) and are lined with a lightproof
material to ensure optical separation between the two regions.
The inside of the structure, the ID, contains 32 ktons of water and this serves
as the target volume for neutrino interactions. Roughly 40% of the ID’s surface
area is covered by inward-facing photocathodes each with a diameter of 50 cm, inthe form of 11,129 Hamamatsu R3600 PMTs [95]. The remaining surface area iscovered with opaque black polyethylene terephthalate sheets to stop light getting
through. Figure 3.5 shows a picture of the ID.

Figure 3.5

A picture of the Super-K inner detector taken in July 2018.
The detector was being drained and refurbished. Photo taken by
Nakahata-san.

The outer region, the OD, serves as a shield for γ-rays and neutrons from thesurrounding rock as well as a veto for incoming charged particles. The OD
side of the support structure is instrumented with 1,885 outward-facing 20 cm
Hamamatsu R1408 PMTs [94]. Each PMT was preassembled with a 60 cm x 60
cm x 1.3 cm wavelength shifting plate (WLS) [50]. The WLS plates are squareacrylic plates doped with 50 mg/L of bis-MSB. Each plate has a machined hole inthe centre for the PMT to be mounted and the edge of the hole is angled such thata good optical coupling can be achieved by physical contact. The WLS plates,
together with the PMTs, were originally used in the IMB experiment [50, 58].
27

Figure 3.6

A picture of the Super-K outer detector taken in July 2018. The
detector was being drained and refurbished.

The OD (see Figure 3.6) was designed to be used as a veto and the design waschosen such that light collection is maximised. The time resolution requirementsof the OD are relatively modest since only the total number of hits in a window ofO(100) ns needs to be known to act as a veto. The inner surface of the OD is linedwith a custom material made up of Tyvek® [68] which faces the OD volume, a
25 µm thick central layer of low-density polyethylene (LDPE) and a 25 µm thicklayer of black LDPE. This custom lining material reflects light coming from theOD volume side while absorbing any light coming from the dead space between
the ID and OD. The outer surface of the OD volume is lined with Tyvek® 1073B.
This material has a measured reflectivity value around 80% for λ =340 nm rising
to about 90% above 400 nm [82]. The reflective material on either side of the
OD allows Cherenkov light to reflect multiple times enhancing the light collection
and the overall detection efficiency.
In 2006 new sheets of Tyvek® were added in order to optically separate the end
caps of the OD and the barrel region of the OD. The OD segmentation, shown in
Figure 3.7, greatly increases the ability to recognize a partially contained event
instead of mistaking it for an incoming charged particle.

28

Figure 3.7

3.3

Schematic diagram showing the optical separation of the end caps
and barrel regions of the OD.

Photomultiplier Tubes

The ID PMTs were designed by Hamamatsu in collaboration with KamiokaNDE
collaborators and further improved for use in SK [154]. The R3600 PMT consistsof a bialkali (Sb-K-Cs) photocathode, chosen due to its spectral sensitivity to blue
light and its low thermionic emission. The PMT is sensitive to the predominant
wavelengths in the Cherenkov spectrum and has a peak quantum efficiency of
22 % at 390 nm. Figure 3.9 shows the Cherenkov spectrum in water, the sharp
cut-off is due to the reduced transparency of water below 300 nm.
The ID PMTs have a uniform gain of 107 at a high voltage ranging from 1500 V
to 2000 V; Table 3.2 lists the main characteristics of the ID PMTs. The large ID
PMTs are sensitive to the earth’s magnetic field as it affects the propagation of
the electrons within the tube. Hence, SK has 26 Helmholtz coils surrounding thedetector to counteract the earth’s magnetic field, reducing the typical value from
450 mG to 50 mG.
Intrinsically the OD PMTs have a worse timing resolution (13 ns). Factoring in
the fluorescence decay constant (4 ns) and the propagation time in the plate, theeffective time resolution is around 15 ns.

29

Figure 3.8

A schematic diagram of the 50 cm SK ID PMT, taken from [82].
All measurements are in mm.

Figure 3.9

Plot showing the relative Cherenkov spectrum through pure waterin addition to the quantum efficiency of the R3600 PMT. Taken
from [136].

3.4

Electronics and Data Acquisition

From 1996-2009 the ID PMT signals were processed by custom electronics
modules called analogue timing modules (ATM) which contained charge-to-30

Figure 3.10

Relative transit time distribution for the SK ID PMT tested with
410 nm light source at single photon level. Taken from [82].
Table 3.2 SK inner detector PMT specification [73].

Shape

Hemispherical

Photocathode diameter
Window material
Quantum efficiency
Dynode structure
Gain
Dark current
Dark pulse rate
Transit time
Transit time spread
WeightPressure tolerance

50 cm
Bialkali (Sb-K-Cs)
22% at λ=390 nm
11 stage Venetian blind
107 at ∼ 2000 V
200 nA at 107 gain
3 kHz at 107 gain
90 ns at 107 gain
2.2 ns (1σ) at single photoelectron level
13 kg
6 kg/cm2

analogue (QAC) and time-to-analogue (TAC) converters [107]. In August 2008,
the electronics and data acquisition (DAQ) systems were upgraded. The thresholdfor a PMT hit was set to 0.25 photoelectrons. The dynamic range was from0∼ 450 pC (0.2 pC resolution) for charge and -300∼ 1000 ns (0.4 ns resolution)
for time. The OD PMTs were connected to a system consisting of charge-to-time
converters which output a timing signal with a width proportional to the overallcharge.
Figure 3.11 shows a diagram of the upgraded DAQ. The upgrade included
replacing the old front-end electronics modules with new ones called QTC-based
electronics with ethernet (QBEE) [163]. The signals from ID and OD PMTs
go through a QTC which has three dynamic ranges which are summarized inTable 3.3. The analogue to digital conversion is carried out for each range
separately but the one used is the highest resolution range that is unsaturated.
31

Figure 3.11

Schematic view of the new data acquisition system [163].

Table 3.3 Summary of QTC ranges in the new DAQ system [12].

Range

Measuring Region [pC]

Resolution [pC]

Small
MediumLarge

0∼ 51
0∼ 3570∼ 2500

0.1
0.7
4.9

The output of the QTC is fed into a time-to-digital (TDC) converter whichmeasures the width of the pulse. The digitized time and width are then sent
to a field-programmable gate array (FPGA) for processing. The time resolutionof the QBEE board, for signal heights similar to that expected for single photons,
is 0.3 ns. This is better than the 2.2 ns intrinsic time resolution of the SK ID
PMTs.
Another big improvement comes from the ability to quickly process the PMT
signals. The processed information is sent to merger PCs for sorting and merging,and the data is then scanned by a customizable software trigger. Prior to theupgrade a hardware trigger was used; the deadtime after the hardware trigger
was initiated made the detection of decay electrons, from stopping muons, lessefficient. SK has several different trigger configurations: OD : OD trigger detects charged particles in the OD.
 SLE : Super low energy for lower energy solar neutrinos.

32

Table 3.4 Summary of trigger types used in the SK software trigger.

TriggerThreshold [Hits/200 ns]

Event Time Window [µs]

OD
SLE
LE
HE
SHE
AFT

22
34
47
50
58
SHE and no OD–-0.5→1.0
-5→35
-5→35
-5→35
35→535

 LE : Low energy trigger for solar and supernova neutrino events.
 HE : High energy trigger for atmospheric neutrino events.
 SHE : Special high energy with a slightly higher threshold.
 AFT : If the SHE trigger is unaccompanied by an OD trigger then the after

trigger records an additional 500 µs of data, to look for possible neutron
captures.
When the number of hits in a sliding 200 ns time window reaches a preset
threshold, a trigger is issued and the hits in the event time window are recorded.
The OD trigger counts only the PMT hits in the OD while other triggers count thehits in the ID. The current trigger types used in SK are summarized in Table 3.4.

3.5

Water System

The 50 ktons of water used in the detector is sourced from the mountain it sits
in, and is constantly circulated through a water purification system. The watermust be cleared of small particles in order to ensure a high attenuation length for
the Cherenkov light; the measured attenuation length is 120 m at a wavelength of
400 nm. The water purification system also removes radioactive materials fromthe water which would otherwise introduce a low energy (∼ MeV) background.
The system, shown in Figure 3.12, is made up of the following components
 1 µm Mesh Filters : Removes dust and particles which would affect thetransparency of water and possibly be a source of radon.
 Heat Exchanger : Cools down the water, to roughly 13° C, to suppress

the growth of bacteria. The lower temperature also results in lower PMT
33

Figure 3.12

A schematic diagram of the water purification system used inSK [82].

dark noise levels. This also removes heat which is generated by the PMTs
and reduces the convection and turbulence in the tank.
 Cartridge Polisher : Removes heavy ions which would otherwise affectthe water transparency, some of these ions are also radioactive. Originallyan ion exchanger was included in the water purification system but the resin
was found to be a significant radon source and was removed. The resistivityof the water, after it passes through the cartridge polisher, increases fromaround 8 MΩcm to 18 MΩcm.
 UV Steriliser : Any bacteria which survive the heat exchanger are thenkilled by the UV light.
 Radon Reduced Air Dissolving System : This tank dissolves radon-

reduced air into the water which increases the radon removal efficiency ofthe vacuum degasifier.
 Reverse Osmosis : Removes particulates.
 Vacuum Degasifier : Removes dissolved gasses from he water. Dissolved

radon gas introduces a low energy background and dissolved oxygen34

encourages bacteria growth. The removal efficiency of radon gas, after
passing through the vacuum degasifier, is estimated to be around 96%.
 Ultra Filter : The ultra filter is made up of hollow membrane filters whichremove very small particles. The typical number of particles above 0.2 µm
in diameter in the water is reduced from 1000 particles/cc to 6 particles/cc.
 Membrane Degasifier : The membrane degasifier is made up of 30

hollow fibre membrane modules and a vacuum pump. Radon-reduced air is
supplied as a purge gas. The membrane degasifier removes radon with anefficiency of 83%.

The water is circulated at a rate of roughly 50 ton/hour in a closed cycle system.
After passing through the water purification system, the attenuation length 1 forlight with a wavelength of 420 nm is approximately 100 m which is roughly twiceas large as the longest particle track length in the detector. The purified water
has a typical radon concentration of 0.4 ± 0.2 mBq m-3 .

3.6

Air Purification

The air in the mine has a high concentration of radon which is emitted by thesurrounding rock. Mine air typically has radon concentrations of 2000-3000 Bq
m-3 in the warmer months and 100-300 Bq m-3 in the cooler months 2 . In order toreduce the radon levels, air from outside the mine is passed through a purification
system and then pumped into the mine. The air purification system, shown in
Figure 3.13, is made up of compressors, filters, driers and 8 m3 of activatedcharcoal. The final set of charcoal filters are cooled to -40° C to increase theradon removal efficiency. The air purified by this system is referred to as radonreduced air and has a radon concentration of ∼ 3 mBq m-3 .
The radon-reduced air is pumped into the gap between the top of the water
surface and the top of the tank and kept at a slight overpressure in an attempt
1

The attenuation length is dependent on the wavelength of light and is not constant. Changes
in the water transparency result in a varying attenuation length over time.
2
The annual variation in radon concentrations in the air is due to the flow of air throughthe mine. From May to October, wind tends to flow out of the mine carrying the radon-rich airfrom deep within the mine past the experimental area. From November to April, wind tends
to flow into the mine and has a relatively short path length in the mine before reaching theexperimental area [82].

35Figure 3.13

A schematic diagram of the air purification system used in SK [82].

Table 3.5 Summary of SK run periods. ”Implosion Covers” refers to theprotective plastic covers used to prevent an implosion incident. ODSEG refers to the segmentation of the OD with Tyvek .

®

Phase

SK-I

SK-II

Start
End
Live days
ID PMTsOD PMTs
Implosion Covers
OD-SEG
Photo-coverage
DAQ
Trigger

Apr 1996
Jul 2001
1489.2
11,146
1,885
No
No
40%
ATM
HardwareJan 2003
Oct 2005
798.6
5,182
1,885
Yes
No
19%
ATM
Hardware

SK-III

SK-IV

Jun 2006 Aug 2008
Aug 2008 Jun 2018
518.1
3235.3
11,12911,129
1,885
1,885
Yes
Yes
Yes
Yes
40%
40%
ATM
QBEE
Hardware Software

SK-V
Jan 2019––
11,129
1,885
Yes
Yes
40%
QBEE
Softwareto reduce radon-rich air from entering the detector. The SK dome, having air
pumped in from outside the mine, typically has radon concentrations of ∼ 40
mBq m-3 .

3.7

Run Periods

SK started data-taking in 1996 and, since then, there have been five distinct
detector phases which are summarized in Table 3.5.
SK-I The first data-taking period started in April 1996, with an ID photocoverage of 40%. After a run comprising of 1489.2 live days of data, thedetector was stopped for maintenance in July 2001. During the refillingof the detector, an ID PMT imploded causing a chain implosion which
destroyed roughly half of the PMTs in the inner and outer detectors.
36

SK-II After the implosion disaster, the PMTs were redistributed evenly throughout the detector. The photocoverage in this run period was 19%. The
ID PMTs were each covered with an acrylic cover at the front and afibreglass reinforced plastic (FRP) cover in the back, to prevent anotherchain implosion incident. The second SK run period started in January
2003 and ran until October 2005. During this run period 798.6 live days ofdata was collected.
SK-III During the second run period, more PMTs were manufactured and after
SK-II the photocoverage was restored to 40%. At this point additional
Tyvek® sheets were put in place to optically separate the endcaps andbarrel region of the OD. The SK-III phase began in June 2006 and endedin August 2008, collecting 518.1 live days of data.
SK-IV In August 2008, the electronics and data acquisition (DAQ) system were
upgraded allowing for continuous data recording and better reconstruction
and detection of decay electrons. The SK-IV period ended in June 2018,with a total of 3235.3 live days of data.
SK-V In June 2018, the SK tank was opened up for refurbishment and upgrades
to enable it to be loaded with Gadolinium (Gd). Water systems toappropriately deal with Gd have been installed. Works were also carriedout in order to stop the tank from leaking. SK started taking data again
in January 2019. Gd is expected to be dissolved into the detector in June
2020 with an initial concentration of 0.02% Gd2 (SO4 )3 , increasing to 0.2%
by October 2020.

37

Chapter 4
Detector Calibration
The SK detector is continuously calibrated and monitored so as to understandits performance and ensure consistency when there are changes in hardware orwater quality. The calibration procedures also prevent systematic errors fromarising due to a particle’s position and direction in the tank. Three calibration
procedures are carried out related to: PMT response, water transparency andenergy scale. These are described in this chapter.

4.1

PMT Calibration

The two main characteristics that determine a PMT’s ability to detect photons
are the quantum efficiency and the collection efficiency of photoelectrons. The
combination of these two properties is referred to as the QE of a PMT. The
purpose of the PMT calibration is to understand the QE, gain and timing responseof each PMT.
Understanding the QE is crucial for low energy events, such as solar neutrinos,
which mainly leave single photoelectron hits in the detector. The gain of a PMT
is the conversion between the number of photoelectrons and the output charge(in pC). High energy events, for example upward going muons, give multiple
photoelectrons in the same PMT. Consequently, good knowledge of the gain is
important.Calibrations are carried out in order to know the QE and the gain foreach individual PMT.

38

4.1.1High Voltage Setting

The high voltage (HV) applied to each PMT needs to be adjusted such that the
charge output for a single photoelectron is the same for all PMTs. To achievethis, an isotropic light source is placed in the centre of the ID. There are several
factors affecting how much light makes it to each PMT. Since the SK tank is notspherically symmetric, twice as many photons reach the closest PMTs comparedto those furthest away. In addition, the way in which photons propagate in thewater together with water quality and reflections in the ID need to be considered.
This further complicates the calculation of expected intensities.

Figure 4.1

A schematic view of the pre-calibration setup. Taken from [12].

To simplify the HV calibration, the HV values for 420 PMTs were individually
determined, prior to installation, in the system shown in Figure 4.1. Light froma Xe lamp was passed through a UV filter which then fed into three opticalfibres. Two of the optical fibres led to avalanche photodiode (APD) modules,
which monitored the intensity of the light, and the third optical fibre went intoa scintillator ball. The scintillator ball is an acrylic ball, 5 cm in diameter,
containing 15 ppm of POPOP1 as a wavelength shifter and 2000 ppm of MgO
as a diffuser. Two 5 cm PMTs were mounted in the pre-calibration system tomeasure the light intensity of the scintillator ball. The PMT was placed in aµ-metal box to shield it from the Earth’s magnetic field. The HV value for each
PMT was then adjusted so that the observed ADC counts for all of the PMTs
matched.
The 420 PMTs were then placed in the detector to serve as references forother PMTs. The HV of each PMT is set so that the observed charge
matches the average of the reference PMTs matching its geometric relationship
1

POPOP is a wavelength shifter alternatively called 1,4-bis(5-phenyloxazol-2-yl) benzene.

39

to the scintillator ball. An example of PMT groups with identical geometric
relationships to the light source can be seen in Figure 4.2.

(a)Position of reference PMTs

Figure 4.2(b)Example of grouped PMTs

The position of the reference ID PMTs in red [left] and examples of
how PMTs with a similar geometric relationship are grouped [right].
Taken from. Taken from [12].

The scintillator ball is a permanent fixture in the ID and is used for constantmonitoring of the ID PMT gain.

4.1.2

Relative Gain

The relative gain calibration is carried out in order to understand the differencesin the response of individual PMTs. This calibration is performed with a nitrogenlaser-driven dye laser fed into an optical fibre attached to a diffuser ball. The
overall intensity of the light is controlled by a filter wheel, consisting of neutral
density filters, placed between the dye laser and the optical fibre. The diffuserball is then used at various positions in the ID.
The first part of this calibration uses high intensity flashes where each PMT
receives multiple photons, producing an average charge, Qobs (i) in the ith PMT.
40

The value of Qobs (i) is estimated by the equation:

Qobs (i) ∝ IS × a(i) × qe (i) × G(i)(4.1)

where IS is the average intensity of the light flash, a(i) is the acceptance angleof the ith PMT, qe (i) is its QE and G(i) is its gain. The second part of thiscalibration uses low intensity flashes where a small number of PMTs are hit ineach event, such hits are likely to be single-pe hits. The quantity measured hereis the number of times the ith PMT records a hit (above a threshold) Nobs (i).
The value of Nobs (i) is estimated from:

Nobs (i) ∝ IW × a(i) × qe (i) × G(i),(4.2)

where IW is the average intensity of the light flash.
The ratio of Equation 4.1 and Equation 4.2 yields the gain of each individual
PMT:

G(i) ∝

Qobs (i).
Nobs (i)(4.3)

The gain of each PMT is normalised to the average gain over the detector to givethe relative gain. The light source is not moved between the two measurements so
the acceptance and the QE of each PMT cancel each other out. The normalisation
also cancels out the intensity ratio IS /IW . The relative gain is used as a finecorrection factor, in the conversion between the observed charge and the numberof photoelectrons, for each individual PMT. The high voltage calibration ensuresthat Qobs (i) for each PMT was the same, so we deduce that the differences ingain are due to the differences in QE for each PMT.

4.1.3

Absolute Gain

The absolute gain calibration uses the charge distribution of single photoelectron
signals to convert the observed charge into the number of photoelectrons. Thiscalibration is carried out by placing a 252 Cf source into a ball made of NiO andpolyethylene. This source has a half-life of 2.654 years and 3.09% of its decays

41are via spontaneous fission [116]. The emitted neutrons thermalize and captureon the nickel, resulting in gamma emissions from 2 to 9 MeV [109]. The Cf-Niball is placed in the centre of the tank where the stable, isotropic, low intensity
light results in an average of ∼ 50 PMT hits per event, 99% of which are single
photoelectron hits. Figure 4.3 shows the total single photoelectron response of
the detector. The effect of dark noise was reduced by taking data when no signal
was expected (off-time) and subtracting it from the data taken when a signal was
expected (on-time).

Figure 4.3

The single photoelectron charge distribution for the Cf-Ni source in
SK-III, taken from [12]. The solid line shows the data with normal
PMT gain and a 0.25 photoelectron threshold, the dashed line shows
the data with double the gain and half the threshold. The dotted line
shows a linear extrapolation.

The charge of the single photoelectron peak is averaged and the value is set as thepC per photoelectron conversion factor. The conversion factors for the different
SK run periods are shown in Table 4.1. A long-term increase in PMT gain causes
the conversion factor to change over time, the reason for this increase is currently
unknown but is accounted for in the various physics analyses.

4.1.4

Timing Calibration

There are several factors which affect the timing response of the readout channels:
differences in the transit time of PMTs, the length of PMT signal cables as well as
42

Table 4.1 The absolute gain conversion from the single photoelectron to observed
output PMT charge (pC).

Figure 4.4

Run Period

Absolute Gain (pC / pe)

SK-I
SK-II
SK-III
SK-IV

2.055
2.297
2.243
2.645

A schematic diagram showing the time calibration system. Taken
from [12].

the signal processing. Time-walk refers to an effect where the signal pulse heightvaries the time response even when PMTs receive light at the same time. Timewalk occurs because the rise time of a larger signal is faster than that of a smaller
one, as a result larger signals appear sooner (see Figure 4.5). Understanding thetiming response of each readout channel allows for the precise reconstruction of43

event vertices and particle directions.

Figure 4.5

A diagram showing the time-walk effect. A larger signal has a fasterrise time, thus reaching the threshold sooner than a smaller signal
starting at the same time.

The time calibration system, shown in Figure 4.4, uses a nitrogen laser as theinitial light source. The nitrogen laser emits 0.4 ns (FWHM) pulses of light witha wavelength of 337 nm through to a dye which shifts the wavelength to 398 nm
and shortens the pulse to 0.2 ns. An optical filter varies the intensity of the light
before an optical fibre injects the light into a MgO diffuser ball (see Figure 4.6) inthe centre of the tank. The nitrogen laser’s light is monitored by a Hamamatsu
H2431-50 PMT [93], which has a 0.37 ns TTS, to define the injection time of thelight.
The time response for each channel is measured as a function of the output charge.
After correcting for the time of flight (TOF) between the diffuser ball and the hit
PMTs, a 2D time versus charge (TQ) plot is created for each readout channel. A
polynomial function is then fit to the data to create a lookup table referred to as
the TQ-map. Figure 4.7 shows an example TQ distribution.

44

Figure 4.6

Figure 4.7

4.2

Cross-section of the MgO diffuser ball. Taken from [12].

Time vs charge for readout channel 00010. Qbin refers to theamount of charge (pC) of each hit, which are binned in a linear scale(0.2 pC/Qbin) from 0 to 10 pC and a log scale (50log(pC)/Qbin)from 10 to 3981 pC. The timing (T) has been corrected for TOF,
the larger T corresponds to earlier hits. The plot is referred to as
a TQ distribution and the fitted polynomial (black line) is known as
the TQ-map. Taken from [12].

Water Calibration

The propagation of photons in the ID must be well understood in order toaccurately simulate the detector. The water calibration system measures theabsorption and scattering in the water (water quality) as well as the reflection oflight at the ID wall.

45

4.2.1

Absorption and Scattering

Figure 4.8

A diagram showing the real-time water quality calibration system.
The analysis splits up the PMTs into 5 barrel regions and thetop. The blue circle indicates the laser target used for the TOF
calculations. Taken from [12].

The water transparency measurement represents the combined effect fromabsorption, Rayleigh scattering and Mie scattering [128]. Rayleigh scattering
occurs when the dimensions of the target are smaller than wavelength of incident
light; when the dimensions of the target are larger than the wavelength of incident
light, Mie scattering occurs. For the purposes of this calibration, the scattering
will be split up into symmetric and asymmetric components. The symmetriccomponent consists of Rayleigh and symmetric Mie scattering, described by ascattering angle distribution intensity of 1 + cos2 θ. The asymmetric component
consists of forward Mie scattering where the probability of scattering increases
linearly from cos θ = 0 to cos θ = 1, for cos < 0 there is no scattering.
The intensity of light, of wavelength λ, in water decreases according tolI(λ) = I0 (λ)e− L(λ) ,

(4.4)
46

Figure 4.9

SK-MC typical fitted functions for the absorption and scattering
coefficients. The circles are data points obtained in April 2009 andthe lines show the fitted functions. The solid black line shows thetotal sum of the dotted lines. Taken from [12].

where I0 (λ) is the initial light intensity, I(λ) is the intensity at a distance l andL(λ) is the attenuation length.
The attenuation length in the SK simulation (SK-MC) is defined as:

L(λ) =

1,αabs (λ) + αsym (λ) + αasym (λ)(4.5)

where αabs (λ), αsym (λ) and αasym (λ) are the coefficients for absorption, symmetricand asymmetric scattering respectively.
A nitrogen laser is fed through an optical fibre which injects light into the ID (seeFigure 4.8). The absorption and scattering coefficients are adjusted in the SK-MC
until there is agreement with the laser data (see Figure 4.9). Laser data is taken
at several wavelengths ranging from 337 to 473 nm every 6 seconds during normal
data-taking in order to continuously measure the water transparency which varies
with time and wavelength.

47

4.3

Energy Calibration

The calibrations detailed in the previous sections convert the observed PMT
charge to the number of photoelectrons, but we still need to understand how
many photoelectrons to expect for a particle of a given energy. The various
neutrino analyses require an accurate energy determination so it is important tounderstand the absolute energy scale. To calibrate this, four methods covering awide range of particle momenta are used: Track length of high energy stopping muons (1 ∼ 10 GeV/c).
 Cherenkov angle of low energy stopping muons (200 ∼ 500 MeV/c).
 Invariant mass of π 0 produced by neutrino interactions (∼ 130 MeV/c).
 The endpoint of the decay spectrum for Michel electrons from stopped

muons (momentum of decay electron) (50 MeV/c).

The accuracy of the absolute energy scale is determined by comparing theobserved data with the Monte Carlo (MC) simulation for each calibration source.
The difference between the data and MC is combined with the time variation of
the energy scale and considered as a systematic uncertainty.

4.3.1

Range of Stopping Muons

The kinetic energy of stopping muons can be determined from the muon track
length: L(m) ∼ 4.5 × Eµ (GeV ). The track length of stopping muons isreconstructed from the distance between the entry point at the ID boundary
and the decay electron vertex. The vertex resolution for stopping muons anddecay electrons is better than 50 cm.
For this calibration, muons which fit the following criteria are selected:
 Muon’s entry point must be on the top cap of the ID.
 Muon’s direction must be downwards (cos θ > 0.94).
 One decay electron event must be detected after the muon has stopped.

48

 Reconstructed muon track must be between 7 and 30 m (1.5 to 7 GeV).

The muon momentum loss per cm is ∼ 2.3 MeV/c. Comparisons between the MC
and data show agreement in the absolute energy scale within 0.7%, 1.1%, 2.0%
and 2.2% for SK-I to SK-IV respectively.

4.3.2

Cherenkov Angles of Stopping Muons

The momentum of low energy muons (< 400 MeV/c) can be calculated using theequation:11=
cos θC =
nβ
n

s
1+

m2
,
p2

(4.6)

where θC is the Cherenkov angle, n is the refractive index of water, m is the known
muon mass and p is the estimated particle momenta. As the momentum increases
the Cherenkov angle converges to a single value which is why this method of
calibration can only be used at low momenta. Figure 4.10 shows the relationshipbetween muon momentum and Cherenkov angle.
For this calibration, muons which fit the following criteria are used: Muon’s entry point must be on the top cap of the ID.
 Muon’s direction must be downwards (cos θ > 0.9).
 One decay electron event must be detected after the muon has stopped.
 Total number of photoelectrons in the ID must be less than 1500 (750 for

SK-II).
Comparisons between the MC and data show agreement in the absolute energy
scale within 0.7%, 1.3%, 2.1% and 2.1% for SK-I to SK-IV respectively.

4.3.3

Invariant Mass of Neutral Pions

The neutral pions used in this calibration are produced by neutral current
atmospheric neutrino interactions in the detector. The neutral pions then decay
49

Figure 4.10

The energy calibration using low-energy stopping muons withreconstructed Cherenkov opening angles. The upper plots show
the reconstructed momentum (left) and reconstructed opening angle(right) for data (black circles) and MC (black lines). The lower
plots show the reconstructed momentum versus opening angle fordata (left) and MC (right). All plots are made using SK-II data
and MC. Taken from [143].

into two γ-rays. The invariant mass of the neutral pion can be reconstructed inevents with two showering-type Cherenkov rings using the following equation:
Mπ20 = 2Pγ1 Pγ2 (1 − cos θ)(4.7)

where the Pγ1 and Pγ2 are the momenta of the two γ-rays and θ is the opening
angle. The π 0 events must satisfy this following criteria:
 Event must have two electron-like Cherenkov rings
 Decay electron, from a stopping muon, must not be detected (rejects

charged current backgrounds)
50Figure 4.11

The invariant mass distribution of reconstructed neutral pions for2520 days of SK-IV live time. The black circles represent data andthe red lines represent the MC. The MC has been normalised to thelive time of the data.

 Reconstructed vertex must be within the fiducial volume (> 2 m away fromthe ID wall)
Although π 0 events are easily identified, the detection efficiency decreases withincreasing momentum. A π 0 with a higher momentum would result in a smaller
opening angle between the decay γ-rays which results in overlapping rings. The
second reason for the decrease in efficiency is that an asymmetric decay may resultin one of the γ-rays not having enough energy to be properly reconstructed. A
Gaussian function is used to fit the invariant mass distribution (see Figure 4.11)
for the data and MC. Comparisons between the MC and data show agreement inthe π 0 mass within 0.7%, 1.3%, 0.3% and 1.7% for SK-I to SK-IV respectively.

51

Figure 4.12

4.3.4

Momentum of decay electrons for data (black dots) and MC (bluehistogram). The MC has been normalised to the live time of thedata.

Decay Electrons

Decaying cosmic muons produce an electron, also called a Michel electron, which
is visible in the detector in the majority of events2 . The expected spectrumof these Michel electrons is well understood and the endpoint can be used forcalibrations for energies around 50 MeV.
Decay electron events are selected using the following criteria:
 The event must occur between 2 to 8 µs after a stopping cosmic muon.
 Must have more than 60 (30 for SK-II) PMT hits in a 50 ns window. This

rejects muon capture events.
 The vertex fit goodness must be larger than 0.5.
 Reconstructed vertex must be within the fiducial volume (> 2 m away fromthe ID wall).
Sometimes µ− capture on a proton and there is no decay electron, this process does notoccur for µ+ . Roughly 20% of µ− capture on 16 O in Super-K [149].
252

In Figure 4.12, the observed decay electron momentum spectrum is compared tothe expected spectrum (MC) which show agreement in the absolute energy scale
within 0.6%, 1.6%, 0.8% and 1.6% for SK-I to SK-IV respectively.

4.3.5

Energy Scale Summary

Figure 4.13

The energy scale deviation at various momenta for SK-IV. Taken
from [110].

The several different sources of calibration yielded uncertainties at different
energy ranges; the combined overall uncertainty is estimated to be 0.88%, 0.55%,
1.79% and 2.19% for SK-I to IV respectively. Figure 4.13 shows a summary of
the absolute energy scale calibration for SK-IV. The energy scale is monitored
over time using stopping muons and decay electrons, the fluctuation of absoluteenergy scale is estimated to be 0.74%, 1.60%, 2.08% and 0.39% for SK-I to SK-IV
respectively.
Decay electrons and stopping muons are used to monitor the variation of theenergy scale over time due to changes in water quality. Figure 4.14 shows thevariation in reconstructed momenta over time. The uncertainty in energy scale
added in quadrature with the uncertainty over time results in an overall estimateduncertainty of 1.1%, 1.7%, 2.7% and 2.3% for SK-I to SK-IV respectively.

53

Figure 4.14

The Super-K average reconstructed particle momentum since 1st
April 2006. The plots on the left show the reconstructed momentum
for decay electrons and the plots on the right show the reconstructedmuon momentum per unit track length. From top to bottom theplots are shown for SK-I, SK-II, SK-III and SK-IV respectively.
The dotted and dashed lines represent a 1% and 2% variation
respectively. Taken from [143].

54

Chapter 5
Atmospheric Neutrino Monte Carlo
Simulation
The physical properties of atmospheric neutrinos are studied by comparing theobserved data to the predictions made using Monte Carlo (MC) simulations. To
be confident that the differences between the data and MC are due to real physics
effects, it is important that the simulation is realistic.
There are three main parts to the SK atmospheric neutrino MC simulation: theatmospheric neutrino flux reaching the SK detector, the neutrino interactions in
the detector target volume (water) and the response of the detector to the final
state particles produced in the neutrino interaction.

5.1

Atmospheric Neutrinos

The analysis performed in this thesis was carried out on atmospheric neutrinos.
Primary cosmic rays, mainly made up of protons, constantly bombard theEarth interacting with nuclei in the atmosphere. The interactions result in the
production of secondary cosmic rays such as pions and kaons in hadronic showers.
Mainly pions are produced, which then decay into muons:

π + → µ + + νµ ,π − → µ− + ν µ .

(5.1)

55

Figure 5.1

Diagram of neutrino production in the Earth’s atmosphere. The
typical height of neutrino production is 15 km above the ground.
Taken from [115].

Electrons are then produced from the decay of muons which do not reach theground:µ+ → e+ + νe + ν µ ,µ− → e− + ν e + νµ .

(5.2)

The neutrinos resulting from the pion and muon decays make up the majority
of atmospheric neutrinos. From the decays in Equations 5.1 and 5.2 it can beseen that the decay of a pion results in two muon neutrinos for every electron
neutrino. This holds true for lower energy neutrinos around 1 GeV as most of
the parent muons decay before reaching the ground. Above 1 GeV the fractionof cosmic muons reaching the ground before decaying starts to increase, leading
to an increase in the muon neutrino to electron neutrino ratio, this can be seenin Figure 5.2.
Atmospheric neutrinos are constantly created around the earth so the flight lengthof the neutrino, before being detected, ranges from 10 ∼ 104 km. The energy rangeof the atmospheric neutrinos detected, spans 10−1 ∼ 103 GeV.

56

Figure 5.2

5.2

Neutrino flux ratios from various atmospheric neutrino calculations.
Taken from [104].

Atmospheric Neutrino Flux

Since neutrino analyses at SK compare the observed to the expected neutrino flux
it is important to accurately predict the expected flux of atmospheric neutrinos.
In order to understand the flux, the initial cosmic ray flux and the hadronic
showers that they produce must be understood.
Several models which predict the neutrino flux from the primary cosmic ray flux
exist. The models will be referred to as the Honda flux [103–106], the Fluka
flux [47] and the Bartol flux [45]. The SK atmospheric neutrino analysis uses the
Honda flux as the primary flux model; the Fluka and Bartol fluxes are used toestimate the systematic uncertainties on the Honda calculation. An additionalmodel, the Volkova flux [157], is used for energies above 10 TeV which is the57

cut-off energy for the Honda calculation.
The neutrino flux calculation uses a primary cosmic ray flux model based on
measurements taken by the Alpha Magnetic Spectrometer (AMS) [34, 35] andthe Balloon-borne Experiment with a Superconducting Spectrometer (BESS) [92,150]. A factor is applied to the primary cosmic ray flux above 10 TeV such thatthe model agrees with emulsion chamber data. Figure 5.3 shows the primarycosmic ray model used in the Honda calculation.

Figure 5.3

A compilation of primary cosmic ray observations from various
experiments. The green dashed line shows an initial calculated flux,
the green dotted line includes corrections to bring the model into
agreement with data above 10 TeV. The solid pink line is the Honda
flux model [102]. The various points represent data taken by different
experiments at solar minimum. See Ref [104] for further details.

Variations in solar wind have noticeable effects on the flux of low energy cosmic
rays. There is more than a factor of two difference in the flux of primary cosmic
rays around 1 GeV between solar maximum (periods with high solar activity) andsolar minimum (periods with low solar activity); This effect reduces to ∼10% at∼10 GeV.
The primary cosmic ray flux is also affected by the Earth’s geomagnetic field(east-west effect [124]). Lower energy cosmic rays are deflected away from Earthresulting in a low energy cut-off in the flux. The majority of primary cosmic
rays are protons, the geomagnetic field deflects the positively charged particles
58

Figure 5.4

The (calculated) zenith angle dependence of the atmospheric
neutrino flux of neutrinos reaching Kamioka. θ is the incoming
neutrino direction, where cos θ = 1 for vertically downward-goingneutrinos and cos θ = -1 for vertically upward-going neutrinos.
Taken from Ref [106].

Figure 5.5

The (calculated) azimuthal angle dependence of the atmospheric
neutrino flux of 1 GeV neutrinos reaching Kamioka. Taken from
Ref [106].

towards the east resulting in an excess of observed cosmic rays arriving fromthe west. Similar to the east-west asymmetry, the slightly higher than averagemagnetic field around Kamioka results in a slight up-down asymmetry in theneutrino flux, the effects of the geomagnetic field become negligible for cosmic
rays above 10 GeV. Figure 5.5 shows the east-west asymmetry and Figure 5.4
shows the up-down asymmetry of the neutrino flux at Kamioka.

59

Primary cosmic rays interact with nuclei in the atmosphere producing secondary
particles. The secondary particles consist mainly of pions and kaons which thendecay into muons and neutrinos. Muons approaching from the horizon have alonger path length to decay into neutrinos resulting in a peak in the neutrino flux
near the horizon (see Figure 5.4). The density of Earth’s atmosphere is given by
the US Standard Atmosphere 1976 model [44] and the geomagnetic field is basedon the International Geomagnetic Reference Field [2].
Figure 5.6 shows the total atmospheric neutrino flux reaching Kamioka. Thispart of the MC simulation ignores neutrino oscillation.

Figure 5.6

5.3

The atmospheric neutrino flux reaching Kamioka [left] and the flux
ratios [right] calculated using various models. ”This Work” refers
to the Honda 2011 calculation. Taken from Ref [106].

Neutrino Interactions

Knowledge of the energy and direction of the neutrino are crucial to the SK
physics program. Neutrinos are not observed directly, rather the products of theneutrino’s interaction in water are observed. Therefore, it is important to simulate
the neutrino interactions with nuclei in water and the surrounding rock. To
simulate such interactions SK uses a neutrino event generator called NEUT [96].
Interactions with atomic electrons are neglected as the interaction cross sectionis three orders of magnitude smaller than that of atomic nuclei.
NEUT first simulates the initial interaction between the neutrino and the target60

nucleon. Any produced hadrons are then propagated through the nucleus where
additional interactions are simulated. If a neutrino interacts with a particle byexchanging a W ± boson then the interaction is classified as charged current (CC).
CC interactions produce a charged lepton with the same flavour as the incoming
neutrino. These interactions produce a signal of the neutrino flavour making
them important in the oscillation analyses. Alternatively, a neutrino can interact
with a particle by exchanging a Z 0 boson, such events are referred to as neutral
current (NC) events. NC events are considered a background as the incoming
neutrino flavour can not be determined.
The five main types of interaction simulated in NEUT are:
 Quasi-elastic scattering: ν + N → l + N 0
 Meson exchange current: ν + N N ∗ → l + N 0 N 0∗
 Single meson production: ν + N → l + N 0 + meson Coherent pion production: ν +16 O → l +16 O + π Deep inelastic scattering: ν + N → l + N 0 + hadrons

where ν is neutrino or antineutrino, N and N ∗ are initial nucleons, N 0 and N 0∗
are outgoing nucleons and l is the outgoing lepton. Contributions to the total
neutrino cross section with nucleons can be seen in Figure 5.7.

Figure 5.7

NEUT simulation cross sections for neutrinos [left] and antineutrinos [right] compared to experiment data [75]. Contributions fromdifferent interaction modes shown. Taken from Ref [111].

61

5.3.1

Elastic Scattering

Neutrinos can undergo a NC interaction with nucleons elastically scattering offof them with no change in the system except momentum transfer. A similar CC
version of this interaction converts the incoming neutrino into a charged lepton
and the incoming nucleon changes in order to conserve charge, this is referred toas charged current quasi-elastic (CCQE) scattering.

Figure 5.8

The charged current quasi-elastic cross sections for muon neutrinos[left] and muon antineutrinos [right]. Solid lines show the calculated
cross sections for free target nucleons and the dotted line shows
the calculated cross sections for bound target nucleons (protons inoxygen). The points represent data from several experiments. Taken
from Ref [96].

The quasi-elastic scattering simulation is based on the Llewellyn-Smith model [125]for free nucleons and the relativistic Fermi gas model [152] is used for boundnucleons. Figure 5.8 shows the calculated cross sections compared to data fromseveral experiments.

5.3.2

Meson Exchange Current

The quasi-elastic scattering interaction described in Section 5.3.1 ignores any
correlations between nucleons in the nucleus so that the neutrino interacts with asingle nucleon only. However, including such correlation effects would mean that aneutrino can interact with multiple nucleons in a meson exchange current (MEC)
process. This is supported by the tension between existing models and data fromexperiments such as MiniBooNE [28]. NEUT simulates the MEC process using amodel by Nieves et al. [135]. Although effects between bound nucleons should be62

present in all types of interactions, NEUT only simulates the effect for this CC
process.

5.3.3

Single Meson Production

The dominant hadron production mechanism below a hadronic invariant mass of
2.0 GeV/c2 is single meson production. This process produces a meson via the
decay of an intermediate baryon resonance as shown in Equation 5.3
ν + N → l + N∗
N ∗ → N 0 + meson,(5.3)

where N is the initial nucleon, N ∗ is the baryon resonance and N 0 is the outgoing
nucleon. NEUT assumes one meson is generated by the decay of the resonance.
The simulation of this process is based on Rein and Sehgal’s model [146].

5.3.4

Coherent Pion Production

Coherent pion production occurs when a neutrino interacts with a nucleus asa whole, the nucleus remains the same with a very small momentum transferfrom the neutrino and a pion is produced with the same charge as the exchanged
boson. As there is a small momentum transfer to the nucleus, the outgoing lepton
and pion will be very forward-going with respect to the initial neutrino direction.
Coherent pion production is simulated in NEUT using a modified version of theRein and Sehgal model [147].

5.3.5

Deep Inelastic Scattering

At high neutrino energies where the energy of a neutrino is much larger thanthe mass of a nucleon (Eν >> mN ) the dominant scattering process is deep
inelastic scattering (DIS). In this process the particle interacts with the quarks
inside a nucleon, breaking it up, resulting in a number of final state hadrons.
NEUT simulates this interaction for hadronic systems with an invariant mass
higher than 1.3 GeV/c2 . The nucleon structure used for this interaction is takenfrom the parton distribution function GRV98 [87] with corrections by Bodek and63

Figure 5.9

The total charged current neutrino (upper) and antineutrino (lower)
cross sections. Lines show the models used and the points represent
data from several experiments. Taken from Ref [96].

Yang [51] which give better agreement with experimental data in the low q2
region.
As there is an overlap in the invariant mass (W) ranges used for single pion
production (W ≤ 2 GeV/c 2 ) and DIS (W > 1.3 GeV/c2 ) a precaution is taken
in order to avoid double counting. NEUT calculates the probability of generating
more than one pion when W < 2 GeV/c2 . Figure 5.9 shows the total CC
cross sections including quasi-elastic scattering, single meson production and DIS
processes.

5.3.6

Nuclear Effects

Once NEUT has simulated the neutrino interaction with bound nucleons theresulting hadrons may interact within the nucleus (16 O in SK). NEUT simulates
the propagation of pions, kaons, η-mesons and nucleons using cascade models
until the hadrons are either absorbed or leave the nucleus.
For neutrino energies larger than 1 GeV the pion production cross section is large,
as is the pion-nucleon interaction cross section. The pion’s interaction within the
nucleus must be understood in order to relate the observed final state particles
in the detector to the initial neutrino interaction.

64

Pions in the NEUT simulation can interact in several different ways; NEUT
considers the interaction of pions, elastic scattering, charge exchange, absorption
and multiplication in the nuclear medium. The probabilities for each type ofinteraction have been tuned using measurements from scattering experiments.
Figure 5.10 shows the results of a NEUT simulation compared to experimentdata. Similar cascade models and tuning is carried out in order to simulatekaons, η-mesons and nucleons leaving the nucleus (see Reference [96] for moredetails).

Figure 5.10

5.4

NEUT simulation of π-12 C scattering compared to experiment
data [38, 43, 80, 114, 122] for π + [left] and π − [right]. Taken
from Ref [65].

Detector Simulation: SKDETSIM

The final stage of the MC simulation is to simulate the final state particles’
interaction in the detector volume and the detector response. The particles
resulting from the neutrino and nuclear interactions from NEUT are propagatedinto a custom GEANT3-based [53] detector simulation called SKDETSIM.
The particles’ interaction with water, their decays, Cherenkov photon production
and propagation are all simulated by GEANT. The hadronic interactions are
simulated by GCALOR [86] except for pions below 500 MeV/c where the NEUT
cascade model is used instead.
The propagation of Cherenkov photons is dependent on the transparency of thewater. The photons can either be absorbed or undergo Rayleigh or Mie scattering.
The calibration described in Section 4.2 is used to model the photon propagationin the simulation. Absorption and reflection in detector surfaces is modelled using65

calibration measurements [12]. The response of the PMTs is simulated using thecalibration measurements described in Chapter 4.

66

Chapter 6
Event Selection
The trigger system of SK fires 106 times per day. Approximately 10 atmospheric
neutrinos, 20 solar neutrinos and 10 beam neutrinos are expected to be detectedeach day. Figure 6.1 shows an atmospheric neutrino event on the SK event
display. The majority of triggers are due to cosmic muons passing through thetank and low energy radioactive decays. In order to filter out candidate neutrino
interactions, the data undergoes several reduction steps.

Figure 6.1

An atmospheric neutrino event, detected in SK-V, shown on an
event display1 .

1As the Super-K event display shows events at a rate of 0.3 Hz, observing a neutrino eventon screen is unlikely. The author of this thesis was fortunate enough to observe this event ”live”

67There are four main event classifications which can be seen in Figure 6.2: fullycontained (FC), partially-contained (PC) and upward-going muons (UPMU),
which are separated into stopping and through-going events. FC events havea neutrino interaction vertex inside the fiducial volume of the detector and all
secondary particles remain in the ID. PC events also have an event vertex inside
the fiducial volume but secondary particles exit the ID and enter the OD. UPMU
events are muons produced by neutrino interactions in the surrounding rock whichthen enter the tank. Rock muons are also produced above the detector but are
indistinguishable from cosmic muons so this sample is restricted to upwards-going
muons.

Fully Contained

Figure 6.2

Partially Contained

Upward-going(stopping)Upward-going(through-going)

Different event classifications in Super-K. The dashed lines show
the neutrino path whereas the solid lines show the path of secondary
particles.

The process of removing background events from the data is referred to as data
reduction. Each class of events has its own reduction process which will be
explained in this chapter. The reduction process is applied to the full SK datasetwith many of the cuts being applied to all of the SK periods, however someof the cuts are tuned such that the rejection power is similar between running
periods. The main differences arise in reduction steps involving the ID during
SK-II. During this period the photocoverage was roughly half of that in otherperiods so the cuts are half of their typical values.
The cuts stated in this chapter indicate the requirements for an event to remain in
the data sample. Events not satisfying the cuts shown are rejected. For each stepof the data reduction, an efficiency calculation is carried out. The reduction
efficiency is estimated by applying the reduction to simulated atmospheric
neutrino events and determining the percentage which survive the cuts. The
values for the reduction efficiency quoted in this chapter apply to SK-IV. However,as it showed up in real-time.

68similar values were found the other SK periods.

6.1

Fully-Contained Reduction

The FC reduction is divided into five stages, FC1 to FC5. If an event passes thecriteria for a reduction stage it then moves on to the next reduction stage. This
staged approach optimises the processing time.

6.1.1

FC1

This reduction step is used to filter out obvious high energy backgrounds suchas cosmic muons as well as the low energy backgrounds such as radioactivity or
solar neutrinos.
The first step in this stage of the reduction removes low energy events and ensuresthat there is enough activity in the ID, the criteria for this is:
1. Total number of photoelectrons in the inner detector in a sliding 300 ns
time window must be larger than 200 (100 for SK-II).
The next step is to use OD information to remove events consistent with anincoming cosmic muon or an exiting particle. The following cuts are applied:

2. The number of OD PMTs hit must be larger than 0.
3. The number of OD hits in a time window -500 ns to +300 ns must be ≤ 50
(55 for SK-IV).

Cut 2 ensures that the OD is functioning correctly. At the start of SK-IV the OD
electronics boards had been changed and the gains of the PMTs had also changed.
This cut was tuned to reject similar muon energies as previous SK periods.
This reduction step reduces the event rate from 106 events per day to 2,500 events
per day. The reduction efficiency for this step is estimated to be 100%.

69

6.1.2FC2This reduction step is designed to remove electrical noise as well remaining highenergy backgrounds. Events due to electrical noise typically have the majority ofcharge deposited in one PMT. To remove these events the following cut is applied:
4. The number of photoelectrons from any single PMT should be less thanhalf of the total number of photoelectrons in the ID in that event.
Some fully contained events with a high enough energy can cause hits in the OD
through ID-OD crosstalk, this is discussed further in Section 6.4. The following
cuts are applied to tighten cut 3, removing cosmic muon events while allowing
very high energy events which may leak current into the OD.
5. One of the following conditions must be satisfied(a) The number of photoelectrons in the ID is larger than 100,000 (50,000
for SK-II).
(b) The number of OD hits in a time window -500 ns to +300 ns must be≤ 25 (30 for SK-IV).
This reduction step reduces the event rate to 500 events per day. The efficiency
for this step is estimated to be 100%.

6.1.3

FC3

The third stage of reduction is designed to target specific types of background
events and so the cuts are more complicated than the first two reduction stages.
The first step in this stage of the reduction is to remove very high energy
cosmic muons with energies Eµ ≥ 1 TeV. At this energy the muons undergo
Bremsstrahlung [117]. The photon produced in this process may then undergo
pair conversion. The resulting shower of particles will give a large number of hits
in a short time. The following cut removes these ”hard” muon events:
6. The number of OD PMTs hit within a 500 ns sliding time window must be
less than 40.
70

If the ID contains more than 231 photoelectrons spread out over at least 1000
tubes a fitter is used to look for a through-going muon. The fitter finds two
clusters in the OD, corresponding to the entry and exit points, separated by areasonable travel time. After the fitter has been applied the following cut is used
to remove through-going muons:
7. One of the following conditions must be satisfied(a) The goodness of fit must be less than 0.75.
(b) Less than 10 hit OD PMTs in each PMT cluster (< 8 m radius fromentry/exit point) in the 800 ns time window.
Similar cuts are used to remove stopping-muons which have an entry point but
no exit point. The cuts used are:
8. One of the following conditions must be satisfied(a) The fitter must not find an entry point (goodness of fit < 0.0).
(b) Less than 10 hit OD PMTs in the PMT cluster (< 8 m radius fromentry point) in the 800 ns time window.
The next cut removes remaining low energy backgrounds by applying a time-offlight (TOF) fitter to obtain an event vertex. All hits are TOF corrected and theevent must then satisfy the criterion:

9. The number of hits in the ID in a sliding 50 ns time window must be larger
than 50 (25, for SK-II).

The following cuts are used to remove PMT flasher events [165]. These are
events where electrical discharge inside the PMT causes light to be emitted into
the tank. The time distribution of the hits is typically longer in flasher events so
the following criteria are used to reject them:

10. For (SK-I) one of the two conditions must be satisfied(a) The minimum number of hits in the ID in a 100 ns sliding time window
between +200 ns→+700 ns must be less than 10.
71

(b) The above cut is relaxed to 15 if the total number of hits in the ID islarger than 800.
11. For (SK-II to SK-IV)(a) The minimum number of hits in the ID in a 100 ns sliding time window
between +200 ns→+700 ns must be less than 20.
The final cut used to remove flasher events is to require the goodness of the
TOF vertex fitter to be larger than 0.4. This cut removes low-energy flasher
events which may pass the other criteria. The wide time distribution of flasher
events would be difficult to fit to a single vertex position often resulting in a poor
goodness of fit.
As the rate of low-energy triggers is high, the coincidence rate of cosmic muons
with these is significant. Such coincidence muons allow these events to pass thelow energy cuts as there is light deposited into the ID by the muon. Additionally,
these events are not removed by the high energy cuts as the low energy trigger
occurred before the OD activity. Such events are removed using the following
criteria:
12. One of the following conditions must be satisfied(a) The number of hits in the OD between +300 ns and +800 ns must be
less than 20.
(b) The number of photoelectrons in the ID between +300 ns and +800 ns
must be less than 5,000 (2,500 for SK-II)
The final cut applied in this reduction stage is used to reject a type of cosmic
muon background. The Super-K PMT cables go up the sides of the Super-K tankin bundles and are fed through 12 (4 large and 8 small) cable holes at the top.
Due to the size of the cable bundles it is possible for muons to pass through somedead regions in the OD where they would not be detected and could appear as
fully contained events. Such muons are referred to as cable muons. In an effort
to remove this kind of background large scintillators were placed above each of
the four large cable holes (the smaller holes are dealt with in FC5). The following
cuts are then applied:
13. One of the following conditions must be satisfied
72

(a) The veto counter (scintillator) must not register any hits(b) The entry point given by the stopping muon fitter must be more than
4 m away from the large cable holes.
14. For SK-IV additional tighter cuts are applied.
conditions must be satisfied

One of the following(a) The goodness of fit must be less than 0.4(b) The total number of photoelectrons in the ID must be less than 4,000(c) cos(θ) ≥ −0.6 where θ is the muon’s zenith angle(d) The entry point must be at least 2.5 m away from the nearest cable
hole.
This reduction step reduces the event rate to ∼50 events per day and has an
estimated efficiency of 99.8%.

6.1.4

FC4

The fourth reduction stage is designed to remove the flasher events which havesurvived the previous cuts. The light pattern of flasher events are quite similarand so they can be removed using a pattern recognition algorithm which divides
the tank into a grid of 1,450 4 m2 patches. For any two events, A and B, aparameter r is calculated:NA
B
B
1 X (QAi − hQ i) × (Qi − hQ i)
r=
N i
σAσB

(6.1)

where N is the number of patches, Qi is the number of photoelectrons in patch iand σ is the standard deviation of Qi . A second parameter is calculated, for these
two events, which compares the time distribution of the hits using KolmogorovSmirnov[151] test. A third parameter finds out if the flashing tubes (tubes withthe highest number of photoelectrons) in both events are closer than 75 cm. These
three parameters are combined into a single likelihood function. Events whichhave a likelihood value above a tuned cut are rejected.
This reduction step reduces the event rate to ∼32 events per day. The efficiency
for this step is estimated to be 99.6%.
73

6.1.5

FC5

The final fully contained reduction step aims to remove remaining muon
backgrounds and flasher events. The first background is referred to as an invisible
muon. These events contain a muon below the Cherenkov threshold which enters
the tank and decays into an electron that is above Cherenkov threshold. Suchdecay electrons can appear as fully contained events. To remove this topology
the following cut is applied:

15. One of the following conditions must be satisfied(a) The total number of photoelectrons must be larger than 1000 (500 for
SK-II).
(b) Less than 5 OD PMTs must be hit in a sliding 200 ns time window
between -9000 ns and +200 ns.
(c) When the distance between two OD clusters is less than 0.5 m, cut 15b
plus the number of OD tubes hit between -200 ns and 300 ns must be
less than 10.

For a muon to reach the fiducial volume it must be above the Cherenkov thresholdin the OD so some light is expected. Cut 15 allows events where there isinsignificant early OD activity or events where the electron is above the Michelelectron energy.
The next cut targets the remaining coincidence muon events, which are removedby the following criteria:

16. One of the following conditions must be satisfied(a) Less than 20 OD PMTs must be hit in a sliding 200 ns time window
between +300 ns and +2100 ns.
(b) The total number of photoelectrons in the ID must be larger than 300(150 for SK-II).

This cut scans over a longer time range and removes events with significant late
OD activity if the event was triggered by the SLE trigger.

74

For SK-IV a new cut was introduced to remove muons which travel through theeight smaller cable holes not covered by a veto counter. In addition to cut 14 in
FC3 the following criteria is also applied:

17. Less than 4 OD tubes hit in an 8 m radius from the reconstructed entry
point in a 200 ns sliding time window between -500 ns and +300 ns.

Lastly some tighter cuts are applied to remove flasher events. The cuts appliedare:18. One of the following conditions must be satisfied(a) The time of flight goodness of fit must be less than 0.4.
(b) The minimum number of photoelectrons in a sliding 100 ns time
window between +200 ns and +700 ns must be less than 6.

For SK-II and SK-IV the following additional cuts are applied:
19. Both of the following conditions must be satisfied(a) The time of flight goodness of fit must be larger than 0.3.
(b) The minimum number of photoelectrons in a sliding 100 ns time
window between +200 ns and +700 ns must be ≥ 6.
This reduction step reduces the event rate to ∼20 events per day. The reduction
efficiency for this step is estimated to be 99.9%.

6.1.6

FC Data Sample

Only events passing FC1 to FC5 are considered for further analysis. In order forthe events to be used in the atmospheric neutrino analyses the following criteria
must be satisfied:

20. All of the following conditions must be satisfied(a) The visible energy must be above 30 MeV.
75

(b) Less than 16 (10 for SK-II) hits in cluster of OD hit PMTs.
(c) The reconstructed neutrino vertex must be at least 2 m away from thetank walls.

These final criteria are expected to remove the majority of the remaining low
energy background events. The final event rate after all of the selection criteria
is around 8 events per day with a reduction efficiency of 98.5%.
The events in the FC data sample are then scanned by eye in order to tag
any remaining cosmic muon or flasher backgrounds. These backgrounds are
not removed from the data sample, they are only tagged to give an estimateof background contamination. Table 6.1 shows a summary of the FC reduction
throughout the various SK phases.
Table 6.1 The final event rates, reduction efficiencies and backgroundcontamination after the fully contained reduction steps. Shown for
SK-I to SK-IV. SubGeV refers to events with a visible energy below
1.3 GeV and Multi GeV refers to events with a visible energy above
1.3 GeV.

Phase

Event Rate
[Day−1 ]Efficiency
[%]

Data
SK-I
SK-II
SK-III
SK-IV

6.2

8.26±0.07
8.28±0.10
8.41±0.13
8.14±0.09

99.25
99.95
99.62
99.19

Background [%]Flashers
Cosmics
Sub Multi Sub MultiGeV GeV GeV GeV
0.1
0.4
0.1
0.1

0.5
0.2
0.2
0.1

0.2
0.2
0.3
0.1

0.3
0.2
0.3
0.1

Partially Contained Reduction

Just as with the FC reduction, the PC reduction is divided into five stages, PC1
to PC5. If an event passes the criteria for a reduction stage it then moves on to
the next reduction stage. PC events, by definition, cause light in the OD and so
the PC reduction steps are very different to the FC reduction.

766.2.1

PC1

The cuts in this reduction step are quite basic and aim to remove through-going
muons and low energy backgrounds. Firstly, the total number of photoelectrons
in the inner detector must be larger than 1000 (500 for SK-II).
Partially contained muons must travel at least 2 m through the ID in order toreach the OD, this corresponds to a momentum loss of around 500 MeV/c. The
1000 photoelectron cut corresponds to a muon momentum loss of 310 MeV/c.
The next cut aims to remove through-going muon events with multiple clusters
in the OD by requiring
1. The RMS of OD hit times must be less than 260 ns (170 ns for SK-II).
For SK-I and SK-II a simple clustering algorithm is applied and the following cut
is applied
2. The number of clusters in the OD must be 1.
Since SK-III the OD has been segmented and through-going muons became easierto remove by requiring that
3. There must be less than 10 hit OD tubes in either endcap.
4. One of the following conditions must be satisfied(a) The number of OD hit tubes in both of the endcaps must be less than
25.
(b) The number of OD hit tubes in the barrel portion of the OD shouldbe less than 70.
A variable, ODRmean , the average distance between all hit pairs, is introduced.
The value is defined as
ODRmean =

1

N
−1
X

Npair i=1|~
xi − x~j |.

(6.2)

The following cut is then applied:77

5. If the number of OD hits in a 500 ns time window is less than 20, thenODRmean must be less than 2100 cm.
This reduction step reduces the event rate to 20,000 events per day.

6.2.2

PC2

The second stage of reduction aims to reduce some of the muon backgrounds.
Firstly, events must pass the following criteria:

6. One of the following conditions must be satisfied(a) The number of OD hit tubes in the endcaps must be less than 20.
(b) The number of OD hit tubes in the endcaps must be less thanMAX(NAs )The parameter MAX(NAs ) is defined as

M AX(N As ) = eα−β×N As(6.3)

where (α, β) = (5.8, 0.023) for N As < 75 and (4.675, 0.008) otherwise.
A clustering algorithm is then used to apply the following cut

7. The second highest charge cluster in the OD must have 10 hit tubes or less.

This reduction step reduces the event rate to 8000 events per day.

6.2.3

PC3

Similarly to the FC3 cut, this reduction step is designed to remove flasher eventsusing the broad timing distribution of these events. This cut requires that

8. One of the following conditions must be satisfied78

(a) The minimum number of hit ID PMTs in a sliding 100 ns window from+300 ns to +800 ns must be less than 14.
(b) The number of hit ID PMTs in the same sliding time window is lessthan 9 if the overall number of hit ID PMTs is less 800.

6.2.4

PC4

This stage of the reduction makes use of an event reconstruction algorithm.
Events are fitted and classified as: stopping muons, through-going muons,multiple muons or corner clipping muons. The following cuts are then applied
9. If the event is classified as a through-going muon then it must pass 4 out of
the following 5 criteria. If it is classified as a stopping muon then it shouldpass 4 out of the 5 criteria, including cut 9b. For other event classifications
only 2 of the following 5 criteria need to be passed.
(a) The angle between the reconstructed muon direction and the vector
between the vertex and the centre of the highest OD charge cluster
must be less than 90°.
(b) A similar cut to above is applied using the earliest saturated ID PMT
instead of the centre of the highest charge OD cluster.
(c) The reconstructed muon track length must be less than 1750 cm(d) The goodness-of-fit must be less than 0.52.A good fit indicates a cosmic
muon.
(e) The distance between the entry point and the corner of the tank mustbe at least 3 m
For stopping muons the following criteria is also applied
10. One of the following conditions must be satisfied:(a) The number of OD hits within 8 m of the entry point in a fixed 500 ns
time window must be less than 10.
(b) The goodness-of-fit must be less than 0.5.
Finally, low energy events are removed by requiring that79

11. The total number of photoelectrons in the ID must be at least 2900.
This final cut corresponds to a muon momentum of roughly 500 MeV/c whereas
a muon must have a momentum roughly 700 MeV/c in order to reach the OD.

6.2.5

PC5

The cuts in PC5 are more complex and aim to remove remaining muon
backgrounds. In this reduction step there are two types of cuts: hard cuts andsoft cuts. If an event fails a hard cut then it is rejected, however events areallowed to fail only one soft cut.
The hard cuts are:
12. All of the following conditions must be satisfied:(a) All of the following criteria must be satisfied:i. The distance between the highest and second highest charge OD
clusters must be at most 20 m apart.
ii. The number of photoelectrons in the second highest charge OD
cluster must be less than 10.
iii. There must be no more than one OD cluster with more than 9 hit
OD tubes.
(b) All of the following criteria must be satisfied:i. One of the endcaps must have less than 7 OD hit tubes.
ii. One of the endcaps must have less than 10 photoelectrons.
iii. The difference between the averaged hit time in each OD endcap
is multiplied by the speed of light and divided by 40 m. This value
must be less than 0.75 or larger than 1.5. This checks to see if thetime difference is consistent with a vertical muon passing throughthe endcaps.
(c) The angle between the Cherenkov ring direction and the vector
between the vertex and the OD cluster should be less 90° for either of
the two fitters used in this cut.
(d) If there is a veto counter hit then the dot product between the muon
direction and the vector between the vertex and the veto counter mustbe larger than -0.8.
80(e) The distance between the reconstructed vertex and the edge of the ID
must be larger than 1.5 m

Cut 12a removes through-going muons based on the clustering of OD hits.
Through-going muons sometimes pass through the edge of the ID and travel
vertically downwards. Such events are difficult to reconstruct so they may still
appear in the sample, cut 12b removes such events. Stopping muons should betravelling in the opposite direction of the OD charge cluster whereas PC eventsshould have a small angle between the muon direction and the vector between thevertex and the OD cluster. Cut 12c ensures that the angle is small and removes
stopping muons. Unlike FC events, it is possible for a PC event to hit a vetocounter, cut 12d requires that muon direction is not ant-parallel to the vector
between the vertex and the veto counter. Cut 12e removes muons that clip thecorner of the tank.
The soft cuts are:

13. All but one of the following conditions must be satisfied(a) Both of the following conditions must be satisfied:i. The number of OD hits within an 8 m radius of either the entry
or exit points must be less than 5.
ii. The difference between the averaged hit time in the entry and exit
points is multiplied by the speed of light and divided by the muontrack length. This value must be less than 0.75 or larger than
1.5. This checks to see if the time difference is consistent with avertical muon passing through the entry and exit points.
(b) The number of hit tubes in the highest charge cluster should be lessthan 10 or the number of hit tubes in the second largest cluster shouldbe less than 17.
(c) The number of OD hit PMTs within an 8 m radius of the entry pointshould be less than 10.
(d) If the stopping muon goodness-of-fit is larger than 0 then bothconditions must be satisfied:i. A 42° angle cone in the ID, facing the entry point, should containless than 60% of the total number of photoelectrons in the ID.

81

ii. The total number of hit OD tubes within an 8 m radius of theentry point should be less than 7.
(e) If the reconstructed vertex of both fitters agree within 15 m then thenumber of OD hit tubes within an 8 m radius of the entry point shouldbe less than 7.
(f) The angle between the reconstructed muon direction and the vector
between the vertex and the centre of the highest OD charge cluster
must be less than 90°. This cut was also used in PC4.
(g) If the track length is estimated to be larger than 15 m then anothertrack length is calculated using the visible energy and a loss of
2 MeV/cm. This visible energy track length should be larger than
the reconstructed track length minus 15 m.
(h) If the visible energy is above 25 GeV then there must be at least 1
decay electron.

The stopping muon fitter takes the earliest cluster in the ID as the estimatedentry point. For PC events the fitting doesn’t do so well (as the vertex is far
from the wall) but if the goodness of fit is above 0, cut 13d is applied to remove
stopping muons.
While most of the corner clipping muons have been removed in PC2 and PC3,
some remain. These corner clipping muons leave a small cluster in the ID
which can sometimes be reconstructed as an event originating in the tank. The
reconstructed track length is often large so cut 13g is used to reject them. Highenergy neutrinos (above 25 GeV) mainly interact through DIS interactions andso hadrons (mainly pions) are produced which then decay to electrons. Cut 13h
is applied to remove cosmic muons which don’t satisfy this criteria.

6.2.6

PC Data Sample

After the reduction process, just as with the FC sample, further cuts are applied
to create a final dataset.

14. The visible energy must be above 350 MeV.
15. More than 15 (9 for SK-II) hits in cluster of OD hit PMTs.
82

16. The reconstructed neutrino vertex must be at least 2 m away from the tankwalls.
The final rate after these selection criteria is ∼1 event per day. The events in the
PC data sample are scanned by eye in order to tag any remaining cosmic muon
background. Table 6.2 shows a summary of the PC reduction throughout thevarious SK phases.
Table 6.2 The final event rates, reduction efficiencies and backgroundcontamination after the partially contained reduction steps. Shown
for SK-I to SK-IV.

Phase

Event Rate [Day−1 ]Data

Efficiency [%]Background [%]Cosmics

SK-I
SK-II
SK-III
SK-IV

0.66±0.02
0.65±0.04
0.62±0.03
0.66±0.02

80.98
74.80
88.80
86.30

0.2
0.7
1.8
0.6

6.3

Upward-going Muon Reduction

6.3.1

Charge Cuts

The first cuts applied in the UPMU reduction are charge cuts. Low energy
events are removed by requiring that the total number of photoelectrons in the
inner detector is larger than 6000 (3000 for SK-II). This corresponds to a muon
momentum of 1 GeV/c and a track length of 3.5 m. Extremely high energy eventssaturate the electronics to the point where the muon fitter does not work. Such
events are removed by requiring that the total number of photoelectrons in the
inner detector must be less than 1,750,000 (800,000 for SK-II).

6.3.2

Zenith Angle Cuts

The next set of cuts make use of seven different event fitters, each specialising in
the fitting of stopping muons, through-going muons and very high energy muons
with Bremsstrahlung.

83

Several muon fitting algorithms are applied sequentially to select upward-going
events. For each algorithm, if the goodness of fit is above a threshold, the event
is saved for a classification of upward-going or horizontal-going. If the event isclassified as downward-going and satisfies the goodness of fit threshold, then theevent is rejected. In the case where the goodness of fit threshold is not satisfied,the event is neither saved nor rejected and another muon fitting algorithm isapplied.
This process continues until all of the fitting algorithms have been used. If noneof the fitting algorithms gives a goodness-of-fit above the threshold then the eventis rejected. If one of the fitting algorithms classifies an event as horizontal-going
then the event is saved. To keep only the upward-going muons the events must
pass the following zenith cut: cos θ < 0.
More information about the algorithms, fitters and thresholds used for thisreduction step can be found in Reference [66].

6.3.3

Eye ScanThe final step of the UPMU reduction is to have two independent researchers use
a visual display and reject background events that have been misclassified. The
efficiency of this reduction step is estimated to be close to 100% with roughly
half of the events reaching this stage being rejected.

6.3.4

UPMU Data Sample

Finally, the UPMU events are separated into stopping and through-going muons
samples. The stopping muon samples must satisfy the following criteria to be
used in the analysis:

1. Fitter must classify the event as a stopping muon.
2. The fitter momentum must be at least 1.6 GeV/c (7 m track length
equivalent).
3. There must be less than 10 (16 for SK-II) hit OD tubes within 8 m of thefitter exit point.

84

Through-going muons must satisfy the following criteria in order to be used in
the analysis:
4. All of the following criteria must be met(a) Fitter must classify the event as a through-going muon.
(b) The distance between the ID entry and exit points must be at least
7 m.
(c) At least 10 (16 for SK-II) OD PMTs must be hit within 8 m of thefitter exit point.
Table 6.3 shows a summary of event rates after the UPMU reduction.
Table 6.3 The final event rates after the UPMU reduction steps. Shown for
SK-I to SK-IV.

6.3.5

Phase

Event Rate [Day−1 ]
Data

SK-I
SK-II
SK-III
SK-IV

1.41±0.03
1.33±0.04
1.49±0.05
1.45±0.03

Background Estimation for Upward-going Muons

Cosmic muons undergo multiple Coulomb scattering and can be reconstructed
as upward-going muons (from neutrino interactions). The mis-classification ofcosmic muons can also occur for horizontal muons which can also be reconstructed
as upward-going. For this reason, most of the backgrounds are concentrated in
the most horizontal zenith angle bin (−0.1 < cos θ < 0).
Background contamination is estimated by extrapolating to the downward-goingregion with cos θ > 0. Figure 6.3 shows the zenith and azimuth angles for stopping
and through-going muon samples in SK-IV. Clusters can be seen in the downwardgoing (cos θ ≥ 0) region at azimuth angles 120°, 180° and 270°. These clusters inazimuth angle correspond to regions of the surrounding rock which are relatively
thin.
The muon samples are split into two distinct azimuthal regions. Region (1) isrelatively thick mountain rock and region (2), where 60° < φ < 310°, represents
85

(a)

Figure 6.3

stopping muons(b)through-going muonsDistributions of the zenith angle vs azimuth angle for stopping muonsand through-going muons. Taken from [143].

the region with the relatively thin mountain rock. Figure 6.4 shows the azimuth
distribution of stopping and through-going muon events.

(a)Figure 6.4

stopping muons(b)through-going muonsAzimuth angle distributions for stopping muons and through-going
muons in SK-IV. Region (1) indicates a muon path through a thicker
mountain region and region (2) indicates a muon path through athinner mountain region. Taken from [143].

Figure 6.5 shows the zenith angle distributions for the muon sample with regions(1) and (2) normalised by the coverage of the azimuth angle. It is clearly seenthat the distribution is mostly flat for region (1) while for region (2) there is anexponential increase in the number of events as the zenith angle increases up to86

downward-going events. A fit of the empirical functionf (cos θ) = p0 + ep1 +p2 ×cos θ ,(6.4)

to the zenith angle distribution shown in Figure 6.5, where p0 is fixed to theaverage of the events in region (1). Background contamination is then estimated
using
Z 0
Nbackground =ep1 +p2 ×cos θ .

(6.5)

cos θ

The uncertainties on the estimated number of background events are evaluatedby modifying parameters p0 , p1 and p2 within their allowed regions. Thesebackground uncertainties are summarised in Table 6.4.

(a)Figure 6.5

stopping muons(b)through-going muons

Background estimation for stopping (left) and through-going (right)
muons in SK-IV. The plots show the zenith angle distributions forthe muons. The black and white points show the data for regions(1) and (2) respectively. Region (1) indicates a muon path througha thicker mountain region and region (2) indicates a muon paththrough a thinner mountain region. A function is fitted (blacksolid line) to the data and used to estimate the background. Taken
from [143].

87

Table 6.4 Summary of the uncertainties in the background contamination
estimation for UPMU events between −0.1 < cos θ < 0.

6.3.6

Event Type

SK-I

SK-II

SK-III

SK-IV

Stopping
Through-going Non-Showering
Through-going Showering

16%
11%
18%

21%
15%
14%

20%
19%
24%

17%
14%
20%

Through-going Showering MuonsFinally, the UPMU through-going sample is split into showering and nonshowering samples. Muons at significantly high energies (above a few hundred
GeV) lose energy through radiative processes such as Bremsstrahlung, electronpositron pair production as well as photo-nuclear interactions. It can be seenin Figure 6.6 that around 1 TeV, the radiative losses are roughly equal to theionisation losses.

Figure 6.6

The average energy loss per meter water equivalent for muons inrock (green) and sea water (black) as a function of muon energy.
The contributions of the different processes are shown separately forwater. This plot was generated using MUSIC,a muon propagation
simulator. Taken from [98].

88Factors such as the water transparency and PMT acceptance affect the overallcharge collected by PMTs. This introduces variations in the charge collected perunit track length for muons in the tank. Other considerations such as longer track
lengths allowing for more light to be scattered into the projected Cherenkov conealso affect the non-uniformity.
These factors are used to correct the charge per unit track length for muonsand to calculate the expected value of the corrected charge for a non-showeringmuon. Figure 6.7 shows that while a non-showering muon has a relatively
uniform corrected energy loss per unit track length, showering muons have large
deviations. The χ2 from the fit is analysed and cuts applied to select showering
events. The event is classified as a showering event if χ2 ≥ 50 and ∆(Q), or ifχ2 < 50 and ∆(Q) > 4.5 − 0.08χ2 ; ∆(Q) is the difference between the correctedcharge and the expected non-showering muon charge.

(a)Figure 6.7

Non-showering muons(b)Showering muons

dE/dX distribution for an MC non-showering muon vs showeringmuon. Both muons have the same entry and exit point. Taken
from [66].

For more details on the χ2 analysis, the charge correction and the overall UPMU
reduction, the reader is referred to Reference [66].

89

6.4

ID OD Crosstalk Cuts

In addition to detection of photons or a PMT’s dark rate, a PMT may sometimes
register a charge if a nearby PMT registers a large enough charge; this is a process
known as crosstalk. In Super-K this process occurs between nearby PMTs in the
ID as well as between PMTs in the ID and OD. It is not clear whether this is dueto the proximity of the PMTs themselves or if it is due to the proximity of thecables or other electronics.
Since the start of SK-IV it has been observed that FC events which deposit alarge amount of charge in the ID were being mis-classified as PC events due to thelarge number of PMTs hit in the OD. These FC events have an OD hit patternsimilar to that of the ID, an example of such an event can be seen in Figure 6.8.
The crosstalk hits are all low charge hits which can be seen in the FC OD hit
distributions in Figure 6.9.

Figure 6.8

A Super-K event display showing an FC e-like event with crosstalk
between the ID and OD. The coloured circles represent hit PMTs, thelarge unfolded cylinder is the ID and the smaller unfolded cylinder
in the upper right corner is the OD.

900.10GeV-1.33GeV

1.33GeV-20GeVFC Data

700

FC Data
250

FC MC

600

FC MC
200

500
150

400
300

100

200
50
100
0
0

0.5

1

1.5

2

2.5
3
3.5
4
Charge of OD hits [p.e]

0
0

0.5

1

1.5

20GeV-100GeV

2

2.5
3
3.5
4
Charge of OD hits [p.e]100+GeV70
60

FC Data

6

FC Data

FC MC

5

FC MC

50
4
40
3
30
2

20

1

10
00

0.5

1

Figure 6.9

6.4.1

1.5

2

2.5
3
3.5
4
Charge of OD hits [p.e]

00

0.5

1

1.5

2

2.5
3
3.5
4
Charge of OD hits [p.e]Histograms showing the number of photoelectrons for each hit OD
PMT in the FC data sample. Blue lines show the MC scaled bylivetime to the data (red).

Selecting a Cut

In order to deal with this issue the Super-K calibration laser data was takenusing the setup mentioned in Section 4.1.2. The laser data is taken periodicallywith variable light intensity and should have little OD activity, making it ideal
to study the crosstalk. Figure 6.10 shows an example laser event with many OD
hits.
In order to differentiate the crosstalk hits from real OD hits, laser events werecompared to PC events. The first step was to investigate the charge and time
information of the OD hits. Charge distributions from the laser data as well as the
charge information shown in Figure 6.9 show two key things. Firstly, assumingthat there is enough charge to cause crosstalk, the crosstalk hit is always low incharge (< 0.5 photoelectrons) regardless of the amount of charge in the ID PMTs.
Secondly, a higher ID charge increases the probability of crosstalk occurring.
The hit time distributions for the crosstalk events in Figure 6.11 show a delay
91

Figure 6.10

A Super-K event display showing a laser event with crosstalk
between the ID and OD. The coloured circles represent hit PMTs,
the large unfolded cylinder is the ID and the smaller unfolded
cylinder in the upper right corner is the OD.

Figure 6.11

The time distribution of PMT hits for a PC MC event on the left
and an FC crosstalk event on the right. The top and bottom plotsshow ID and OD hits respectively.

92

between ID hits and OD hits of roughly 100 ns which is not seen in PC events.
To further investigate this time difference, OD hit times are compared to the hit
times of nearby ID PMTs. This is defined as any ID PMT that is less than 90 cm
away from the OD PMT. Nearly all of the OD PMTs are installed in the middleof four ID PMTs facing the opposite direction meaning they have four nearby
ID PMTs. The time difference is defined as the time between an OD hit andits most recent nearby ID PMT hit. Nearby ID PMTs were chosen because theimage in the OD is similar to that of the ID in these events, indicating that thephenomenon occurs close to the front end.

Laser Data

0.018

PC MC

0.016

PC Data

0.014

FC MC

0.012
0.01
0.008
0.006
0.004
0.002
0
0

Figure 6.12

50

100

150

200

250

300

350 400 450 500
Time Difference [ns]A plot showing the time difference between OD hits and nearby ID
hits for PC MC in blue, PC data in red and laser data in black.
The histograms were normalised by area.

Figure 6.12 shows a clear difference in the time difference variable between the
crosstalk events and PC events, making it a good variable to use to discriminate
between crosstalk and photons or dark noise. The final step was to look at
distributions of the time difference versus charge so as to avoid removing real hits
as much as possible. Figure 6.13 shows the distribution of the time difference
versus the number of photoelectrons for each hit for laser data as well as PC MC.
The chosen cut removes any OD hit which is less than 0.2 photoelectrons andarrives more than 50 ns after its most recent nearby ID PMT hit. A criteria whichis too loose would keep many crosstalk hits and a criteria which is too strict would93

remove genuine hits left in the OD by PC events. This cut was chosen to reject
as many crosstalk hits as possible while keeping the PC reduction efficiency at
an acceptable level.

Figure 6.13

Plots showing the number of photoelectrons for each OD hit vs thetime difference between the hit OD tube and its nearby ID tubes.
The left plot is for the laser data and the right plot is for PC MC.

The rejection power of the cut was estimated by comparing the shape of the OD
hit distributions for laser data (see Section 4.1.2) and FC MC, which can be seenin Figure 6.14. The difference between the integral of the two distributions was
taken as the number of crosstalk hits. A comparison before and after the cut
shows a reduction in the excess area by 97.3%.

Laser Data
6

10

Laser Data

70000

PC MC
PC Data
FC MC

PC MC
60000

PC Data
FC MC

50000

5

10

40000
30000

104

20000
10000

0

0.5

1

1.5

(a)

Figure 6.14

2

2.5

3
3.5
4
OD Hit Charge [pe]Before Cut

0
0

0.5

1

1.5

(b)

2

2.5

3
3.5
4
OD Hit Charge [pe]After CutOD hit distributions for FC MC (magenta), PC MC (blue), PC
data (red) and laser data (black). The histograms have been scaled
down to the laser data using the region 0.8→1.2 pe. The left plotshows the OD hit distributions before the crosstalk cut is applied,
the right plot shows the distributions after the cut has been applied.

The crosstalk cut is implemented before the reduction, to mask any hits satisfying
the cut criteria. The PC reduction efficiency was then recalculated and anegligible drop in the reduction efficiency, by 0.03%, was found.
94

6.5

Event Reconstruction

The selected neutrino events are reconstructed in order to get the neutrino flavour,
momentum, direction and interaction vertex. A brief discussion of the event
reconstruction is given in this section, for a more detailed description the reader
is referred to References [143, 156].
FC and PC events occur inside the tank and both can be reconstructed in thesame way. To determine the event vertex, an initial simple point fit is used.
All photons are assumed to come from a single point and the timing residual
distribution of hit PMTs is constructed for each tested vertex. The position
which gives the best goodness-of-fit, determined by a Gaussian fit to the data, isselected as the event vertex. The general direction is then estimated by taking
the charge-weighted vector sum of directions from the vertex to each PMT.
With a preliminary vertex and direction, the next step is to find the brightest
Cherenkov ring. The charge distribution is given as a function of Cherenkov angle,
npe (θ). The edge of the ring θedge is taken as the angle where the second derivativeequals zero after the peak of the distribution. A goodness-of-fit parameter isdefined as:

R θedgeQ(θedge ) =0

npe (θ)dθ(θedge − θexp )2
dnpe (θ)]θ=θedge )2 × exp(−),× ([sin θedge
dθ
2σ 2

(6.6)

where θexp is the expected Cherenkov angle calculated from the particle momentum, deduced from the total charge contained in the Cherenkov cone, and σ isthe uncertainty of the angle determined from the solid angle of the ID PMT atthe edge of the ring. The first, second and third terms in Equation 6.6 prefer
Cherenkov rings with a large number of photoelectrons, sharp edges2 and edges
close to the expected value. The parameter Q(θedge ) is maximised by varying θedge
and the initial direction. A more precise vertex can now be found by recalculating
the timing residual distribution. For PMTs inside the Cherenkov ring, photons
are assumed to be emitted along the particle track, for PMTs outside of the ring
photons are still assumed to be emitted from a single point. The goodness-of-fit
test is carried out including these effects and a new vertex is found.
2This second term is removed for unphysical Cherenkov cones (θedge > 43°).

95

42 deg. ring(possible center)

center(most probable)

Figure 6.15

hit PMT

Cherenkov ring

An illustration of the basic principle of ring-finding.
from [143].

Taken

The PMTs which were found to be in the Cherenkov ring are tagged and used tosearch for additional rings using the Hough transform method [63]. A sphericalcoordinate system, centred at the vertex position, is defined. Figure 6.15 shows
the basic principle of the ring-finding technique. Virtual Cherenkov rings arecentred at the position of each hit PMT. The point(s) where multiple virtual
rings overlap indicates the direction of a potential Cherenkov cone. A likelihood
method is used to determine if the newly found rings are consistent with
Cherenkov rings. Each previously found Cherenkov ring is fixed and this stepis run iteratively for up to five rings or until no new rings have been found.
The detected Cherenkov rings must then be classified as e-like or µ-like.
The expected light distribution for electrons is diffuse due to Bremsstrahlung
scattering (resulting in electromagnetic showers) allowed by its low mass. For
typical muon energies in Super-K, muons do not cause electromagnetic showers
and produce sharp rings. Also, the Cherenkov angle is smaller for muons which
are not highly relativistic. These differences are used to compute a PID likelihood;a cut on the likelihood classifies rings as e-like and µ-like. The PID likelihood
distribution is shown in Figure 6.16, approximately 1% of events are misclassified.
There is now a particle type associated with each ring and a momentum canbe calculated for each particle. The momentum is largely dependent on theamount of charge collected by the PMTs within a 70° cone centred on theparticle’s direction. Corrections to the charge are calculated by considering PMT

96

Super Kamiokande IV 1096.7 days : Monitoring

200

e-like 2457

muon-like 2412

180
160
140
CCQE muon

120
100
80
60
40
20
0
-10

Figure 6.16

-8

-6

-4

-2

0

2

4

6

8

10

PID likelihood sub-GeV 1ring (FC)PID likelihood distribution for single-ring FC events with visibleenergy less than 1.33 GeV. The black points are data from 1097
days of SK-IV, the red histogram is the MC and the shaded green
region is the MC CCQE νµ events.

acceptance and the attenuation of light in water. The final momentum is thenestimated by combining the total corrected charge with the particle type.

97

Chapter 7
Neutrino Oscillation Analysis
The neutrino oscillation analysis described in Chapter 8 is carried out by
weighting the SK MC on an event by event basis for different values of oscillation
parameters. The MC is brought into agreement with the data by minimising theχ2 . This chapter describes the dataset, event classification and event binning usedin the analysis. The formulation of the χ2 is then shown followed by a descriptionof the key systematic uncertainties in the analysis.

7.1

Dataset and Event Classification

In this section, the datasets used in this analysis are summarised. The analysis
uses the FC, PC and UPMU data from SK-I up until SK-IV, totalling 5,326 daysof live time. Simulation samples corresponding to an exposure of 500 years foreach SK period are used to predict the unoscillated neutrino flux.
To increase the sensitivity to oscillation effects, the three event topologies: FC,
PC and UPMU are further divided into sub-samples based on the reconstructedparticle information. The sub-samples are then divided into bins of reconstructed
momentum and zenith angle. There are a total of 520 bins.
All events are required to have a visible energy above 30 MeV (which removes
low energy background events). The visible energy is the reconstructed kinetic
energy above the Cherenkov threshold, for each observed ring, taking into accountthe type of particle emitting the light. Events are also required to have a98

reconstructed vertex more than 2 m away from the closest point on the ID wall.
Events are then further divided by the number of observed rings, the lepton
flavour, the visible energy and the number of decay Michel electrons (electrons
from muon decay as defined in Section 4.3.4).
The detected Cherenkov rings are all classified as e-like or µ-like by a particle
identification (PID) likelihood algorithm. The PID algorithm takes into accountthe sharpness of the edges of the ring as well the angular distribution of light (seeSection 6.5).
Fully contained events are divided into sub-GeV events if they have a visibleenergy below 1.33 GeV; events with a visible energy above this threshold are in themulti-GeV category. The main background in FC sub-GeV e-like sample is NC-π 0
events. Typically, the π 0 → γγ decay results in a two-ring signal. However, if the
decay is highly asymmetric, one photon may be undetected resulting in a single
ring. Alternatively, the signals from the two photons can overlap resulting in asingle ring. To reduce this type of background a specialised π 0 fitting algorithm
is used [46]. The algorithm enforces the two photon hypothesis and reconstructs
a second ring. A selection is then made based on the π 0 invariant mass, thefractional momentum of the second ring as well the difference between the π 0likelihood and electron likelihood.
Once the π 0 events have been selected, the remaining e-like events are divided
according to the number of decay electrons found. CCQE νe are not expected
to have any decay electrons whereas CCQE νµ events are expected to have asingle decay electron if the muon is not absorbed. Table 7.1 summarises the FC
sub-GeV selection.
A likelihood function is used to select multi-GeV multi-ring e-like (MME) events.
The MME likelihood function uses four variables: the PID likelihood, the fractionof momentum of the most energetic ring, the number of decay electrons and the
distance between the neutrino interaction vertex and any decay electrons. The
likelihood cut significantly increases the purity of CC νe and ν̄e events while
reducing the background from CC νµ and ν̄µ .
In order to increase the sensitivity to the mass hierarchy, multi-GeV e-like eventsare further separated into neutrino and antineutrino samples. For single-ring
events this is done by considering CC single pion (CC1π ± ) events, where the99Table 7.1 A summary of the FC sub-GeV event sample criteria.

SampleNumberof rings

Momentum MeV/c(invariant mass MeV/c2 )Number of
decay electrons

Single-ringe-like 0-decay
Single-ringe-like 1-decay
Single-ringµ-like 0-decay
Single-ringµ-like 1-decay
Single-ringµ-like 2-decay
π 0 0-decay

1

> 100

0

1

> 100

≥1

1

> 100

0

1

> 100

1

> 100

≥2

(85 − 215)

02pion is below the Cherenkov threshold. The CC1π ± interaction is:να + N → lα− + N 0 + π +(7.1)

ν̄α + N → lα+ + N 0 + π − .

(7.2)

For neutrino interactions, the produced π + decays into a µ+ which then decays
into a positron, which can be detected. The detection efficiency for decay electrons
is 88% (68%) for Sub-GeV (Multi-GeV) stopping muons. For antineutrinos, theproduced π − mesons mostly get absorbed by oxygen nuclei and no decay electron
is detected. For multi-ring e-like events, the neutrino/antineutrino separation
is carried out by applying a likelihood cut. The likelihood uses the number ofrings, the number of decay electrons and the transverse momentum. Table 7.2
summarises the FC multi-GeV selection.
PC events are separated into OD stopping and OD through-going. All PC eventsare classified as OD through-going unless in a 500 ns sliding time window theamount of photoelectrons in the OD is less than two thirds of the expectedvalue given the potential track length. UPMU events are divided into stopping
and through-going where through-going is further subdivided into showering andnon-showering muons. The criteria for the UPMU classification is detailed in
Section 6.3. The samples are then binned into bins of momentum/visible energy
and zenith angle separately for each SK running phase. Table 7.4 shows the100Table 7.2 A summary of the FC multi-GeV event sample criteria.

SampleNumberof rings

Cuts

Single-ringe-like νeSingle-ringe-like ν̄eSingle-ringµ-likeMulti-ringe-like νeMulti-ringe-like ν̄eMulti-ringµ-likeMulti-ringe-like other1

One or more decay electrons.

1

No decay electrons

1≥2

Highest momentum ring e-like. Pass MME
likelihood. Pass νe likelihood.
Highest momentum ring e-like. Pass MME
likelihood. Pass ν̄e likelihood.
Most energetic ring has visible energy above
600 MeV. Momentum above 600 MeV/c
Most energetic ring e-like. Fails MME likelihood.

≥2
≥2
≥2

sample purity broken down by neutrino flavour and Table 7.5 shows the detailed
binning information for each sample. After the selection process, there are 13 FC
samples, 2 PC samples and 3 UPMU samples. Table 7.3 shows the number of
events in each sample for both data and normalised MC.

7.2

Analysis Method

The atmospheric neutrino MC is reweighted with different oscillation parameterassumptions and the data is then fitted to the weighted MC. The data is binned
into energy and zenith angle bins which are detailed further in Section 7.1. The
fit uses a binned χ2 method assuming Poisson statistics.

7.2.1

Definition of χ2

For n bins of data, the likelihood can be defined as [132]:
L(E, O) =nY
e−Ei E Oi
i

i=1

Oi !

,

(7.3)

101

SampleFC Sub-GeV
e-like, Single-ring
0 decay-e
1 decay-eµ-like, Single-ring
0 decay-e
1 decay-e
2 decay-e
π 0 -likeSingle-ring
Two-ring
Multi-ring

Data

MC

10294
1174

10266.1
1150.7

2843
8011
687

2824.38008.7
687.0

578
1720
1682

571.8
1728.4
1624.2

FC Multi-GeV
Single-ringνe -likeν̄e -likeµ-likeMulti-ringνe -likeν̄e -likeµ-like
Other

705
2142
2565

671.3
2193.72573.8

907
745
2310
1808

915.5
773.8
2294.01772.6PC
Stopping
Through-going

566
2801

570.0
2889.91456.41448.95035.31231.04900.41305.0

UPMU
Stopping
Through-goingNon-showering
Showering

Table 7.3 The number of observed and expected events for each eventclassification. The MC events has been normalised by the data live
time assuming neutrino oscillations with ∆m232 = 2.4 × 10−3 eV2 andsin2 θ23 = 0.5. Sub-GeV multi-ring interactions are not used in thepresent analysis.

where Ei is the expected number of events in each bin and Oi is the observed102SampleFC Sub-GeV
e-like, Single-ring
0 decay-e
1 decay-eµ-like, Single-ring
0 decay-e
1 decay-e
2 decay-e
π 0 -likeSingle-ring
Two-ring
Multi-ring

CC νeSample Purity [%]CC ν¯e CC νµ + ν¯µ CC ντ

NC

71.7
80.5

24.8
1.9

0.2
10.8

0.0
0.1

3.3
6.7

4.1
0.1
0.0

1.3
0.0
0.0

75.9
97.2
97.9

0.1
0.0
0.1

18.6
2.7
2.0

9.6
6.7
29.4

3.3
2.5
4.7

1.5
1.1
34.2

0.0
0.0
0.0

85.6
89.7
31.8

FC Multi-GeV
Single-ringνe -likeν̄e -likeµ-likeMulti-ringνe -likeν̄e -likeµ-like
Other

62.1
54.6
0.3

9.0
37.2
0.1

10.0
0.9
99.2

3.3
1.0
0.2

15.6
6.3
0.2

55.7
53.1
2.7
27.5

10.2
27.0
0.4
2.9

11.7
4.1
91.3
34.8

4.0
2.2
0.5
4.9

18.4
13.6
5.1
29.9

PC
Stopping
Through-going

8.4
0.6

3.2
0.3

82.9
97.8

1.0
0.7

4.5
0.6

0.8

0.3

98.6

0.0

0.3

0.2
0.1

0.1
0.0

99.6
99.8

0.0
0.0

0.1
0.1

UPMU
Stopping
Through-goingNon-showering
Showering

Table 7.4 Sample purity broken down by neutrino flavour assuming neutrino
oscillations with ∆m232 = 2.4 × 10−3 eV2 and sin2 θ23 = 0.5. Sub-GeV
multi-ring interactions are not used in the present analysis.

number of events in each bin. The χ2 is then given by the log likelihood ratio:nX
L(E, O)Oi
χ ≡ −2log=2(Ei − Oi + Oi log ).
L(O, E)
Ei
i=1
2

(7.4)
103

SampleEnergy binscos θz bins

FC Sub-GeV
e-like, Single-ring
0 decay-e
5 e± momentum 10 in [−1, 1]
1 decay-e
5 e± momentumµ-like, Single-ring
0 decay-e
5 µ± momentum 10 in [−1, 1]
1 decay-e
5 µ± momentum 10 in [−1, 1]
2 decay-e
5 µ± momentum0
π -likeSingle-ring
5 e± momentum
Two-ring
5 π 0 momentum
Multi-ring
FC Multi-GeV
Single-ringνe -likeν̄e -likeµ-likeMulti-ringνe -likeν̄e -likeµ-likeOther
PC
Stopping
Through-going
UPMU
Stopping
Through-goingNon-showering
Showering

4 e± momentum 10 in [−1, 1]
4 e± momentum 10 in [−1, 1]
2 µ± momentum 10 in [−1, 1]
3 visible energy
3 visible energy
4 visible energy
4 visible energy

10 in [−1, 1]
10 in [−1, 1]
10 in [−1, 1]
10 in [−1, 1]

2 visible energy
4 visible energy

10 in [−1, 1]
10 in [−1, 1]

3 visible energy

10 in [−1, 0]
10 in [−1, 0]
10 in [−1, 0]

Table 7.5 The energy/momentum and zenith binning for each event type.

104

The uncertainties are assumed to be uncorrelated and are included in each binusing the ”pull approach” [74]. For example, if the true value of the CCQE crosssection is larger than the nominal value, the number of expected events in a
CCQE bin would increase. Including the effect of systematic uncertainties, thenumber of expected events in each bin Ei becomes:
Ei → Ei (1 +mXfji j ),

(7.5)

j

where m is the total number of systematic uncertainties, j is the variation of thej-th systematic uncertainty and fji is the fractional change of the event rate in
the i-th bin due to a 1σ variation in the j-th systematic uncertainty. For eachsystematic error, the data and MC are brought into best agreement by fitting j ,requiring that ∂χ2 /∂j = 0. In order to constrain the range of j , a quadratic
penalty term
m
X
j
(7.6)
( sys )2 ,σjjis added to Equation 7.4. This term prevents the systematic uncertainty fromstraying too far from its prior range, allowing it to vary reasonably to come into
agreement with the data. Including the penalty term, the resulting χ2 definitionis:χ2 = 2nX
i=1m(Ei − Oi + Oi log

X j
Oi
)+
( sys )2 .
Ei
σj
j

(7.7)

As the fit is performed, the expected number of events in each bin varies withdifferent parameter assumptions. The variation is not a uniform scaling across allbins, rather each bin is affected differently. This means that the best fit values are
determined by the shape of the distributions rather than total number of events.

7.3

Systematic Uncertainties

The analyses in this thesis use 162 systematic uncertainty parameters. The
systematic errors are related to the neutrino flux model, neutrino interactions,
event reduction and reconstruction. This sections details the key systematic105

errors. A detailed description of other errors and their estimation can be foundin References [132, 143].

7.3.1

Atmospheric Neutrino Flux

The uncertainty in the absolute atmospheric neutrino flux is estimated by Honda
et al. [104] by considering the uncertainties in the primary cosmic ray flux, thehadronic interaction model (δσ ), pion production (δπ ), kaon production (δK ) and
air density (δair ). The contributions of δπ and δσ are taken as the absolutenormalisation error while δK and δair are considered as separate systematics
because of their relationship with the incoming neutrino’s direction. Figure 7.1
shows the systematic uncertainty on the flux normalisation as a function ofneutrino energy. An additional independent systematic is estimated using thedifference between the Honda flux [103–106], the Fluka flux [47] and the Bartol
flux [45], in order to account for the differences in the flux models above 10 GeV.
Atmospheric neutrinos mainly come from pions produced in the atmosphere forneutrino energies up to 10 GeV. Above a few tens of GeV, kaons contributesignificantly to the neutrino flux, for neutrino energies above 100 GeV the flux
is mainly produced from kaons. The uncertainty on the neutrino flux, caused by
K/π production ratio, is estimated to be 5% for neutrino energies below 100 GeV
and 20% above 1 TeV, with a linear increase in the uncertainty for neutrinoenergies between 100 GeV and 1 TeV. This uncertainty is deduced from the K/πratio measurement, with 3% accuracy, by the SPY experiment [40].
The neutrino path length depends on the production height in the atmosphere,
which in turn depends on the density of the atmosphere. The uncertainty in thedensity is estimated to be 10%, by comparing US-standard 76 [44] and MSISE90 [97] models for the atmosphere. The resulting variation in production heightis propagated through the oscillation probability calculation. This uncertainty
is less important for upward-going neutrinos which have a very long path length(compared to the atmospheric production height) but becomes more importantfor downward-going and horizontal neutrinos.
In addition to the absolute flux, an uncertainty is estimated for the ν̄/ν ratio.
The antineutrino to neutrino ratio depends on the ratios of positive to negative
charged pions/kaons produced in the atmosphere. This uncertainty is estimatedby comparing ν̄/ν ratios between the Honda [106], Fluka [47] and Bartol [45] flux106

Relative Uncertainty

0.30

δ tot
δπ
δK
δσ
δair

0.25
0.20
0.15
0.10
0.05

Absolute normalization (%)

0

10

1

10

1

10

2

10
E ν (GeV)

3

35
30
25
20
15
10
5
0
10−1

Figure 7.1

0

10

102

103
104
Eν(GeV)The calculated uncertainty of the neutrino flux normalisation
including contributions from the hadronic interaction cross section(δσ ), pion production (δπ ), kaon production (δK ) and air density(δair ) (top). The uncertainty on the flux normalisation as a functionof energy taking only contributions from the hadronic interaction
model and pion production (bottom), taken from Ref [143].

models.
The Sun’s activity affects the primary cosmic ray flux. Solar activity has an 11
year cycle [79]. The uncertainty in the neutrino flux is estimated by taking thevariation in the neutrino flux caused by a ±1 year variation in the solar cycle.
This estimated uncertainty of solar activity is 20%, 50%, 20%, 10% for SK-I to
SK-IV respectively.
The neutrino oscillation probability is dependent on the amount of mattertraversed. The atmospheric neutrino analyses make use of density data from107νμ�/ νμ� double ratioνe/ νe double ratio

1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5 −110

1Figure 7.2

10

102

103
Eν(GeV)

1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5 −1
10

1

10

102

103
Eν(GeV)The anti-neutrino/neutrino double ratio for ν̄e /νe (left) and ν̄µ /νµ(right). The solid black line shows the ratio between the Honda andFluka ratios while the dashed red line shows the ratio between the
Honda and Bartol ratios. Taken from Ref [143].

the Preliminary Earth Reference Model (PREM) [69]. However, the chemicalcomposition of the Earth’s core affects the electron density. The Core is assumed
to be made of iron and nickel, these elements have an electron density lower thanlighter elements. The difference in electron density is used as an uncertainty on
the Core’s electron density.

7.3.2

Neutrino Interaction

The uncertainties related to neutrino interactions are the same for each of the
SK running periods. This section highlights key systematic uncertainties related
to the different types of neutrino interactions.
There are three key uncertainties estimated for the CCQE interaction. In addition
to the absolute CCQE interaction cross section, uncertainties are estimatedfor the cross section ratios ν̄/ν and (νµ + ν̄µ )/(νe + ν̄e ). These uncertainties
are estimated by taking the difference between the Fermi-gas model [152] andthe Nieves model [134]. The difference between the models is taken as a 1σuncertainty.
Quasi-elastic scattering and single meson production depend on the axial vector
mass MA which appears in the cross section as −1.3/(1 − Q2 /MA2 )2 [89]. The
axial vector mass is set to 1.21 GeV/c and has a 10% uncertainty [89] so theuncertainty is estimated by taking the ratio of the Q2 spectrum with MA set to1.21 GeV and 1.1 GeV.

108

DIS cross section calculations agree with experimental measurements within 5%
for neutrino energies above 10 GeV [143], so a 5% uncertainty is used for the
total cross section. Below 10 GeV, there is a larger additional uncertainty whichis estimated by comparing the default model (GRV98 [87] with corrections by
Bodek and Yang [51]) and the CKMT [55] model.
The uncertainty on the NC/CC ratio is estimated to be 20% [18].

7.3.3

Event Selection and Reconstruction

The uncertainties related to the event selection and reconstruction are independent for each of the SK running periods due to differences in the detector
configuration. This section highlights key systematic uncertainties related to theevent selection.
The first set of key systematic uncertainties arise from the data reduction. The
data reduction, detailed in Chapter 6, uses several cuts to remove backgrounds
and classify events into FC, PC and UPMU topologies. The distributions of eachcut variable used for the event selection process are compared for data and MC,
the difference is taken into account as a systematic uncertainty in the reduction
efficiency. These uncertainties are summarised in Table 7.6. The uncertainties
for stopping and through-going muons are considered to be correlated.
Table 7.6 Summary of the systematic uncertainties associated with data
reduction for different event topologies.

Event Classification

Systematic Uncertainty [%]SK-I SK-II SK-III SK-IV

FC
PC
UPMU Stopping
UPMU Through-going

0.2
2.5
0.7
0.5

0.2
4.8
0.7
0.5

0.8
0.5
0.7
0.5

0.3
1.0
0.5
0.3

In addition to the reduction uncertainty, systematic uncertainties also arise fromthe separation of event topologies.Events are separated into fully and partiallycontained samples by the number of hit PMTs in an OD cluster. The systematic
uncertainty associated with the FC/PC separation is estimated by comparing theobserved and MC distributions of the number of PMTs in an OD cluster. The
uncertainty is estimated to be 0.6%, 0.5%, 0.9% and 0.38% for SK-I to SK-IV
respectively.
109

Partially contained events are separated into stopping and through-going samples
by the energy deposit in the outer detector. This uncertainty is estimated bycomparing the number of photoelectrons in the OD for data and MC. Thisestimation is also carried out separately for different OD regions (top, bottom
and barrel) as the regions are calibrated separately.
Very high energy upwards through-going muons accompanied by radiativeemission are classified as showering samples. They are identified by checking
the deviation of energy deposit from the expected constant energy loss. The restof the through-going muon sample is classified as non-showering. This uncertainty
is estimated by comparing the ∆(Q) distributions, mentioned in Chapter 6, fordata and MC. The estimated uncertainty is 3.4%, 4.4%, 2.4% and 3.0% for SK-I
to SK-IV respectively.
The next set of systematic uncertainties arise from the event reconstruction which
includes particle identification, identification of rings and the detection of decay
electrons. The particle identification process involves cuts on a likelihood ratio,
the uncertainties are estimated by comparing the distributions of the likelihood
ratio e/π + for the FC data and MC. Uncertainties range from 0.1% to 0.4%,
depending on the event category, and are estimated for single-ring and multi-ring
events separately. Multiple rings are iteratively searched for and a likelihood
cut is applied in order to select rings. The likelihood distribution is compared
between FC data and MC in order to estimate the uncertainty. The uncertainty isdifferent for each event category and ranges from 0.3% to 2.8%. The uncertaintyof the decay electron tagging efficiency is estimated by comparing the detection
efficiency in stopping cosmic muon data and MC. The uncertainty is estimatedto be 0.8% across all energies.
Lastly there is an uncertainty associated with the energy calibration. As discussed
in Section 4.3.5, several calibration sources are used to estimate the uncertainty
on the energy scale, differences in the detector configuration result in different
uncertainties for each SK period. The estimated uncertainty of the absoluteenergy scale is 1.1%, 1.7%, 2.7% and 2.3% for SK-I to SK-IV respectively.

110

Chapter 8
NSI in Atmospheric Neutrinos
As discussed in Chapter 2, the effective Hamiltonian for neutrino propagation
through matter is:





0
0
0
1 + εee εeµ εeτ
√
1 



U 0 ∆m221
Hef f =
0  U † ± 2GF Ne  εµe
εµµ εµτ  , (8.1)
2E
0
0
∆m231
ετ e
ετ µ ετ τwhere U is the PMNS mixing matrix, Ne is the electron number density along theneutrino’s path length and the plus (minus) sign is for neutrinos (antineutrinos).
The first term in Equation 8.1 is the vacuum term and is energy dependent, thesecond term includes standard and non-standard matter effects and depends only
on the fermion density. In the µ − τ sector there are two quantities of interest:
the flavour-changing NC parameter εµτ which allows matter induced νµ → ντtransitions and the non-universal ετ τ − εµµ parameter which allows for different
NC scattering amplitudes for the two neutrino flavours. In the e − τ sector,
contributions from εµα can be ignored and matter induced flavour transitions
are allowed via εeτ . Different NC scattering amplitudes are then considered bysimultaneously considering εee and ετ τ . In this chapter, a measurement of thesequantities is made using 5,326 days of Super-K data, 2,519 of which are from
SK-IV.
While the analyses in this thesis use the full numerical calculation for oscillation
probabilities, insight can be gained for individual parameters using approximate
111

formulae. Assuming ∆m221 , θ12 and θ13 are zero, the νµ survival probability inconstant matter density can be expressed as [130]:

P (νµ → νµ ) = 1 − P (νµ → ντ ) = 1 − sin2 2θef f sin2 [ζwheresin2 2θef f ≡

∆31 L
],
2

| sin 2θ23 ± 2ηµτ |2,
ζ2qζ ≡ | sin 2θ23 ± 2ηµτ |2 + [cos 2θ23 + (ηµµ − ητ τ )]2 ,

(8.2)

(8.3)

(8.4)

εαβ Ve
,
∆ij

(8.5)

√
2GF Ne ,(8.6)∆ij ≡ ∆m2ij /2E

(8.7)

ηαβ ≡

Ve ≡

and the plus (minus) sign is for normal (inverted) hierarchy. For antineutrinos thesign of Ve changes. It can be seen in the above equations that the NSI εαβ term
only appears in terms with the mass splitting which means that the oscillation
probability is invariant under the simultaneous transformation εαβ → −εαβ and∆m231 → −∆m231 . For maximal mixing (θ23 = 45°) the oscillation probability is
no longer dependent on the sign of the difference between ετ τ and εµµ , but only
its absolute value.
Equations 8.2 and 8.3 show how the effective mixing angle and mass splitting
vary. A larger fermion density, larger NSI parameter strength or a high neutrinoenergy all result in an increase in the effective mass splitting and a reduced
effective mixing angle as ζ > 1.
In this analysis neutrinos oscillation probabilities are calculated for MC eventson an event-by-event basis as they propagate through the Earth. Atmospheric
neutrinos pass through various densities of matter before reaching the detector.
The Earth is modelled as a sphere of radius 6371 km with a simplified versionof the preliminary reference Earth model (PREM) [69]. Figure 8.1 shows thedifference in Earth layer densities for the simple and full model. Table 8.1 shows
the density layers used; the atmosphere is modelled as a vacuum. No change in112

3

Density [g/cm ]Crust
MantleOuter Core
Inner Core

12

10

8

6

Full PREM
4

Simplified PREM
0

1000

2000

3000

4000

5000

6000

Depth [km]

0
2000
4000
6000
Distance from center of the Earth [km](a)Figure 8.1(b)

The density of the Earth versus the depth (left). The black line shows
the full measured values of the PREM model and the red line shows
the values used in the analysis. The right plot shows the different
density layers of the Earth.

the analysis sensitivity was found with the full model but the computation timeincreased dramatically. Hence, the simplified model is used for the results here.
Table 8.1 Model of the Earth used in the analysis.

RegionRmin [km]Rmax [km]density [g/cm3 ]Inner core
Outer core
Mantle
Crust

0
1220
3480
5701

1220
3480
5701
6371

13.0
11.3
5.0
3.3

8.1

NSI in the µ − τ Sector

8.1.1

Oscillation EffectFigure 8.2 shows the calculated νµ survival probability contours as a function of
zenith angle and neutrino energy for different values of the µ − τ NSI parameters.
The discontinuities, in the lower zenith regions, in the plots show neutrinos

113

(a)

(εµτ , ετ τ − εµµ )=(0,0)(c) (εµτ , ετ τ − εµµ )=(0.0,0.2)

Figure 8.2(b)(εµτ , ετ τ − εµµ )=(0.2,0.0)(d)(εµτ , ετ τ − εµµ )=(0.2,0.2)

Oscillation contours showing the νµ survival probability for different
values of µ − τ NSI parameters. Oscillation probabilities calculatedusing full three-flavour equations with all other NSI set to zero. The
horizontal axis shows the energy and the vertical axis shows thezenith angle. The top left plot shows standard oscillation only, top
right shows standard plus flavour-changing neutral currents. The
bottom left plot shows standard plus lepton non-universality andthe bottom right plot includes flavour-changing neutral currents andlepton non-universality.

passing through the core of the Earth. The strength of NSI depends on theamount of matter traversed and is energy independent. However, the standard
oscillation term in Equation 8.1 is energy dependent so the relative strength of
NSI is expected to depend on the neutrino energy. The effects of NSI can be114divided into three energy regions: low, medium, high. The boundaries of theseregions depend on the matter density and the value of ε. A conservative ε ∼ O(1)√results in a matter term 2GF Nf ε ∼ 1×10−13 eV which is used to give the energy
ranges below.
At low energies (Eν < 1 GeV), the eigenvalue of the vacuum term ∆m232 /2Eν√is much larger than matter eigenvalue 2GF Nf ε so oscillations between νµ →ντ are mostly governed by two flavour vacuum oscillations. In this region thecontribution from NSI is not significant. The neutrinos in this energy region are
in the FC Sub-GeV sample, which is expected to show no change when NSI isconsidered.
The middle energy region (1 < Eν < 30 GeV) is where the decreasing vacuum
term becomes comparable to the matter term. In this energy region vacuum
oscillations no longer dominate and are altered by matter oscillations. Non-zeroεµτ increases the effective mass splitting which increases the oscillation frequency;
for the larger effective mass splitting the oscillation maximum is expected at
higher neutrino energies or shorter path lengths, compared to vacuum oscillations.
The neutrinos in this energy region are in the FC Multi-GeV, PC and UPMUstopping samples, which are expected to show an excess of νµ for significant path
lengths when NSI is considered.
At high energies (Eν > 30 GeV) the vacuum term significantly suppresses νµ → ντtransitions while εµτ increases the effective mass splitting. In this energy regionνµ → ντ transitions will be driven by εµτ if the neutrino’s path length, throughthe Earth, is sufficiently long. The non-universal term is also expected to havean effect in this energy region. When ετ τ − εµµ is non-zero, the effective mixing
angle decreases, suppressing transitions even further. The neutrinos in this energy
region are in the UPMU through-going sample.

8.1.2

Analysis

The analysis is carried out in two parts. First, fits are performed with thestandard three-flavour oscillation formalism extended to allow for a non-zerovalue of εµτ . A scan is made in steps of εµτ . For each point the value of the χ2
is calculated (see Chapter 7). In the second step εµτ is considered along with the
diagonal NSI elements εµµ and ετ τ along with two-flavour standard oscillations.
For this, a value of χ2 is determined for each grid point in the two dimensional
115

space εµτ and ετ τ − εµµ .

Figure 8.3

The allowed standard oscillation parameter regions. Solid lines show
allowed regions when including NSI and the dotted lines show theregions without NSI. Taken from [133].

The previous Super-K atmospheric neutrino NSI analysis [132, 133] showedthat the allowed regions for the standard oscillation parameters do not change
significantly when NSI are considered (see Figure 8.3). For this reason, the valuesof the standard oscillation parameters are fixed to those in the latest publishedresults from Super-K [18], shown in Table 8.2. The uncertainty on the standard
oscillation parameters is propagated to the systematic errors.
Table 8.2 The values of the fixed standard oscillation parameters in the NSI
analyses and their uncertainties.

Parameter∆m232 [×10−3 eV2 ]∆m221 [×10−5 eV2 ]sin2 θ23
sin2 θ12
sin2 θ13
δCP [rad]Value
Normal Hierarchy Inverted Hierarchy
2.5+0.13−0.20
7.65±0.18
0.5875+0.031−0.0640.309±0.014
0.0219±0.0012
4.19

2.5+0.13−0.20
7.65±0.18
0.575+0.036−0.0730.309±0.014
0.0219±0.0012
4.19

Prior to carrying out the analysis in this chapter, a sensitivity study was
performed. Rather than fitting data to MC, the study compares MC to MC.
116

The study confirmed that when there is zero NSI, the fitting algorithm gives abest fit point with zero NSI to a good precision. Such a test is necessary toconfirm that there is no bias in the fitting algorithm as well as to ascertain whatlevel of NSI would be detectable in Super-K.

8.1.3

Limit on εµτ from three-flavour fit

For the three-flavour fit all standard oscillation parameters are set to their best fit
from the latest Super-K results shown in Table 8.2. The values of ∆m232 and θ23
are set to the most recent best fit Super-K results, normal hierarchy is assumed.
The scanned parameter space in εµτ is from -0.06 to 0.06 in steps of 0.01 (121points). The best calculated χ2 versus εµτ is shown in Figure 8.4. The minimum
χ2 is found for εµτ = −0.023. The minimum χ2 is 568 for 519 degrees of freedom.
The 90% C.L. limit is:−0.033 < εµτ < −0.003 .

(8.8)

The systematic uncertainties and their j values at the best fit point aresummarised in Tables A.1 to A.4 in Appendix A.
The zenith angle distributions for the best fit point do not differ largely from thebest fit with the standard oscillation formalism for most of the sub-samples. The
only samples which shows a difference is the most upward-going zenith angle binsin the UPMU showering sample.

8.1.4

Limit on µ − τ NSI parameters from two-flavour fit

For the two-flavour fit ∆m221 , θ12 and θ13 are all set to zero. The values of ∆m232
and θ23 are set to the most recent best fit Super-K results, normal hierarchy isassumed. The scanned parameter space in εµτ is from -0.06 to 0.06 in steps of
0.01 (121 steps) and in ετ τ − εµµ from -0.5 to 0.5 in steps of 0.0125 (81 steps).
The minimum χ2 is found for (εµτ , ετ τ − εµµ ) = (-0.029, 0.075). The minimum
χ2 is 571.352 for 518 degrees of freedom.
The 90% C.L. limits are:

117

∆χ2
12
10
8
6
4
2
0
−0.04

Figure 8.4

−0.03

−0.02

−0.01

0

0.01

εµτ

0.02

∆χ2 distribution as a function of εµτ . The three flavour standard
oscillation parameters are fixed and all other NSI parameters are set
to zero. The three horizontal lines correspond to the 68%, 90% and
99% C.L. defined by ∆χ2 = 0.99, 2.71, 6.63 respectively.

−0.046 < εµτ < 0.019(8.9)−0.050 < ετ τ − εµµ < 0.138(8.10)The systematic uncertainties and their j values at the best fit point aresummarised in Tables A.5 to A.8 in Appendix A.
The zenith angle distributions for the best fit point do not differ largely fromthe best fit with the standard oscillations formalism for most of the sub-samples.
The samples which show the most difference are the most upward-going zenith
angle bins in the UPMU and PC sub samples. Figure 8.5 shows the zenith angle
distribution for the best fit point and standard oscillation (no NSI) for the UPMU
stopping and showering samples.
Figure 8.6 shows the allowed regions of the NSI parameters (εµτ , ετ τ − εµµ ). The
three contours correspond to the 68%, 90% and 99% confidence level regions
defined by χ2 = χ2min + 2.30, 4.61 and 9.21 respectively. Figures 8.7 and 8.8 showthe χ2 = χ2min distributions for εµτ and ετ τ − εµµ respectively.
118

Up-μ
� ShoweringUp-μ� Stopping

400

200

200

0
1.3

0
1.5

0.7

0.5

-1

-0.5

εττ-εµµ

Figure 8.50

cos zenith

cos zenith

The zenith angle distribution for the UPMU stopping sample (left)
and the UPMU showering sample (right). The black points show thedata, the red line shows the best fit standard oscillation parametersfrom [18] and the blue case shows the best fit NSI result from thetwo flavour fit.

0.4

0.2

0

−0.2

−0.4
−0.06

Figure 8.6

−0.04

−0.02

0

0.02

0.04

εµτ

0.06

Allowed NSI parameter region assuming two-flavour standard
oscillations with NSI in the µ − τ sector. The horizontal axis showsεµτ and the vertical axis shows (ετ τ - εµµ ). ∆m232 and θ23 are
fixed while ∆m221 , θ12 and θ13 are set to zero. The three contours
correspond to the 68%, 90% and 99% C.L. defined by ∆χ2 = 2.30,
4.61 and 9.21 respectively. The star represents the best-fit point for
the NSI parameters.

119

∆χ2
25

20

15

10

5

0
−0.06

∆χ2

Figure 8.7

−0.04

−0.02

0

0.02

0.04

εµτ

0.06

∆χ2 distribution as a function of εµτ . ∆m232 and θ23 are fixed while∆m221 , θ12 and θ13 are set to zero. (ετ τ - εµµ ) is integrated out. The
three horizontal lines correspond to the 68%, 90% and 99% C.L.
defined by ∆χ2 = 2.30, 4.61 and 9.21 respectively.

30
25
20
15
10
5
0
−0.2

Figure 8.8

−0.15

−0.1

−0.05

0

0.05

0.1

εττ-εµµ0.15

0.2∆χ2 distribution as a function of (ετ τ - εµµ ). ∆m232 and θ23 are
fixed while ∆m221 , θ12 and θ13 are set to zero. εµτ is integrated out.
The three horizontal lines correspond to the 68%, 90% and 99% C.L.
defined by ∆χ2 = 2.30, 4.61 and 9.21 respectively.

120

8.1.5

Discussion

The best fit value of εµτ is negative and the 90% C.L. obtained from the threeflavour fit is entirely in the negative region. This result is driven by the mostupward-going bin in the UPMU showering sample where there is a slight deficit in
the number of events. This can be understood by considering that the effective
neutrino oscillation frequency increases. For neutrinos of a fixed energy, thismanifests as a shorter oscillation length. Above 30 GeV, the oscillation lengthis greater than the diameter of the Earth and εµτ shortens the oscillation length
enough to allow oscillations for the most upward-going neutrinos. Below thisenergy the oscillation length is short enough that standard and NSI terms cancause oscillations which makes it difficult to discriminate between standard and
NSI oscillations in the lower energy samples.
The lower energy UPMU stopping and PC samples constrain the value of ετ τ −εµµ
and the best fit point is positive. Negative values of ετ τ − εµµ result in a larger
excess which causes an asymmetry in the constraints. The three-flavour εµτanalysis results in a tight constraint which is relaxed when ετ τ − εµµ is included.
The result of the three-flavour fit can be directly compared to IceCube’s NSI
result [6] in which all NSI parameters were set to zero except for εµτ . IceCube
studied neutrinos with energies in the range 6 - 56.2 GeV. IceCube, as well asother experiments, use a convention which assumes all NSI comes from interaction
with d quarks so as to easily compare with neutrino scattering experiments. In
order to compare results the NSI parameters in this analysis have to be divided
by 3 (neutral earth matter has 3 times as many d quarks as electrons). The
IceCube limit on εµτ at 90% C.L. (using d quark normalisation) is:−6.7 × 10−3 < εµτ < 8.1 × 10−3 ,(8.11)

while the limit from this study at 90% C.L. (using d quark normalisation) is:−1.1 × 10−2 < εµτ < −1 × 10−3 .

(8.12)The three flavour fit neglects any non-universal diagonal NSI couplings and theintroduction of this coupling relaxes the constraint. The two flavour analysis
including flavour-changing neutral currents and non-universal parameters can becompared to a previous Super-K study carried out more than a decade ago. The
121

analysis presented here uses a dataset 2.5 times the size of the last atmospheric
neutrino NSI zenith angle study which was carried out in 2009 with 2288 daysof data [133]. In addition to the larger dataset, this analysis includes positive
and negative values of εµτ , whereas the past study included only positive values.
The two flavour fit results from this study are consistent with the past result
albeit with slightly tighter constraints. Furthermore the analysis binning, MC
and systematic uncertainties have all changed since the last analysis was carriedout. The constraints on the µ − τ NSI parameters at 90% C.L. are:|εµτ | < 3.3 × 10−2

(8.13)|ετ τ − εµµ | < 1.5 × 10−1

(8.14)

for the previous analysis while the results from this analysis are:−4.5 × 10−2 < εµτ < 1.9 × 10−2

(8.15)−5.1 × 10−2 < ετ τ − εµµ < 1.4 × 10−1 .

(8.16)

The first difference between the past and current analysis is the asymmetricbounds. The past results were symmetric in εµτ due to the analytical expression
used to calculate the oscillation probabilities, resulting in symmetric bounds
about zero. This analysis uses a full numerical calculation which shows thedifference between positive and negative values of εµτ . Additionally, the mixing
angle was maximal, in the past analysis, which results in positive-negative
symmetry in ετ τ − εµµ . NSIs affect the effective mixing angle and mass splitting
so the key difference between the new and past result comes from the difference instandard oscillation parameters. Although shifted, the current bounds are tighter
than previous bounds. Sensitivity is still limited by a lack of statistics. The slight
improvement expected from the statistical update is confirmed by carrying out
the two-flavour analysis on SK-I and SK-II data. The 90% C.L. regions using
only SK-I and II data are:−5.7 × 10−2 < εµτ < 2.6 × 10−2

(8.17)−1.1 × 10−1 < ετ τ − εµµ < 1.7 × 10−1 .

(8.18)The SK atmospheric data is already described very well by the standard122

oscillation formalism and this tightly constrains the allowed NSI regions. The
constraints obtained from this analysis are consistent with past results and no
significant signal of non-standard neutrino interactions was found.

8.2

NSI in the e − τ Sector

8.2.1

Oscillation EffectSimilarly to the νµ − ντ sector, the effects of NSI in the νe − ντ sector can bedivided into three energy regions: low, medium, high.
At low energies (Eν < 1 GeV), the eigenvalue of the vacuum term ∆m232 /2Eν√is much larger than matter eigenvalue 2GF Nf ε so oscillations between νµ →ντ are mostly governed by two flavour vacuum oscillations. In this region thecontribution from NSI is not significant. The neutrinos in this energy region are
in the FC Sub-GeV sample, which is expected to show no change when NSI isconsidered.
In the middle energy region (1 < Eν < 15 GeV), νµ → ντ transitions can beaffected by ετ τ as discussed in Section 8.1.1. A non-zero εeτ can affect transitions
between νe and ντ . Effects from εeτ are expected to manifest as an upward-goingexcess in νe resulting from ντ → νe transitions. In principle, νe could oscillate toνµ or ντ . However this contribution is negligable due to the lack of high energy
νe flux (see Figure 5.2); the νµ /νe flavour ratio increases with neutrino energy,
especially so for steeper zenith angles.
The effect of εeτ overlaps with the effect of non-zero θ13 as both are expected toinduce ντ → νe transitions, this will be discussed further in Section 8.2.3.
At high energies (Eν > 15 GeV) the νe atmospheric neutrino flux is significantly
reduced so transitions from νe to other neutrinos, which would manifest as a
deficit, can be neglected. However, transitions from ντ → νe driven by εeτ would
result in an excess of νe . The effects of ετ τ discussed in Section 8.1.1 also apply
here.
In summary, the νe − ντ NSI parameters can be constrained by higher energy(Eν > 1 GeV) neutrinos. The νµ samples constrain the ετ τ parameter and νesamples constrain the εeτ parameter.
1238.2.2

Limits On εeτ and ετ τAll standard oscillation parameters are set to their best fit from the latest Super-K
results shown in Table 8.2. Normal hierarchy is assumed. The scanned parameter
space in εeτ is from -1.5 to 1.5 in steps of 0.025 (121 steps), in ετ τ is from -1.0 to
1.0 in steps of 0.025 (81 steps), and in εee from -4 to 4 in steps of 0.5 (17 steps).
The minimum χ2 is found for (εee , εeτ , ετ τ ) = (0.0, -0.025, 0.075). The minimum
χ2 is 568 for 517 degrees of freedom.

1

1

εττ

1

εττ

εττ

The parameters εeτ , ετ τ and εee are highly correlated so the limits on εeτ andετ τ are shown for fixed values of εee ; the nature of the correlation is discussed in
Section 8.2.3. The NSI allowed contour regions are shown in Figure 8.9.

0.5

0.5

0.5

0

0

0

−0.5

−0.5

−0.5

−1

−0.5

0.5

1

−1
−1.5

1.5

εeτ

ee = -4

−1

−0.5

(b)

1

εττ

εττ

(a)

0

0

0.5

1

−1
−1.5

1.5

εeτ

ee = -3

1
0.5

0.5

0

0

0

−0.5

−0.5

−0.5

−0.5

0

0.5

1

−1
−1.5

1.5

εeτ

−0.5

(e)

1

εττ

εττ

(d) ee = -1

−1

0

0.5

1

−1
−1.5

1.5

εeτ

ee = 0

1
0.5

0.5

0

0

0

−0.5

−0.5

−0.5

−1

−0.5

(g)

0

0.5

ee = 2

Figure 8.9

1

1.5

εeτ

−1
−1.5

−1

−0.5

(h)

0

0.5

ee = 3

1

1.5

εeτ

0

0.5

1

εeτ

1.5

1

εeτ

1

εeτ

ee = -2

−0.5

0

0.5

1.5

ee = 1

1

0.5

−1
−1.5

−1

(f )
εττ

−1

−0.5

1

0.5

−1
−1.5

−1

(c)
εττ

−1
−1.5

−1
−1.5

−1

−0.5

(i)

0

0.5

1.5

ee = 4

Allowed NSI parameter regions in εeτ − ετ τ plane for fixed values of
εee . The contours represent the 68%, 90% and 99% C.L. defined by∆χ2 = 2.30, 4.61, 9.21 respectively.

The systematic uncertainties and their j values at the best fit point aresummarised in Tables A.9 to A.12 in Appendix A.
124

The zenith angle distributions for the best fit point do not differ largely fromthe best fit standard oscillations for most of the sub-samples. The only samples
which shows a difference is the most upward-going zenith angle bins in the UPMU
showering sample.

8.2.3

Discussion

The results are presented as contours in the εeτ − ετ τ plane for fixed values of εee .
The shape of the contours is explained as follows. If εµα = 0, an approximation
justified by experimental constraints, then the matter component of the neutrino
propagation Hamiltonian is:
1 + εee 0 εeτ√
Hmatter = 2GF Ne  0
0 0 .
ετ e0 ετ τ

(8.19)

Following Reference [76], the diagonalisation of Equation 8.19 results in

Hmatter = Odiag(λe0 , 0, λτ 0 )O† ,(8.20)

where




cos β
0 e−iφeτ sin β


O=
0
1
0
.
cos β
−eiφeτ sin β 0(8.21)

νµ0 = νµ ,(8.22)

νe0 = cos βνe + e−iφeτ sin βντ ,(8.23)

ντ0 = −eiφeτ sin βνe + cos βντ .

(8.24)In this new basis,

125

The eigenvalues from the diagonalisation are:√r
1 + εee + ετ τ
1 + εee − ετ τ 2
λe0 = 2GF Ne (+ () + |εeτ |2 ,22r√
1 + εee + ετ τ
1 + εee − ετ τ 2
λτ 0 = 2GF Ne (− () + |εeτ |2 ,2
2

(8.25)(8.26)and the matter angles are:tan 2β =2|εeτ |,
1 + εee − εeτφeτ = arg(εeτ )/2.

(8.27)(8.28)In the case that λe0 and λτ 0 dominate over the vacuum terms, νµ oscillation
would be suppressed in matter in clear conflict with the data. A hierarchicalstructure where one of the matter eigenvalues is comparable to the vacuum mass
splitting and the other eigenvalue much larger decouples one state and allows
vacuum oscillations to occur between the remaining two states. In the case that
λe0 >> ∆m232 /2E ∼ λτ 0 , νe0 decouples from the system and the vacuum term
drives νµ → ντ0 oscillations.
The size of λτ 0 is strongly constrained by atmospheric neutrinos and it canbe assumed that λτ 0 << ∆m232 /2E otherwise the νµ disappearance probability
would not exhibit the characteristic energy dependence observed in atmospheric
neutrinos. In the limit λτ 0 = 0 the three NSI parameters satisfy a parabolic
relationship:ετ τ =|εeτ |2.
1 + εee(8.29)The parabolic curve presents itself in the χ2 distributions in Figure 8.9 with ετ τextending to negative values when 1 + εee is negative and positive values when
1 + εee is positive. The low energy (Eν < 1 GeV) data sample has negligable
matter effects and would be best fit by vacuum oscillation parameters, however
the effective mixing angle and mass splitting in matter are constrained by highenergy datasets. The need to keep the preferred vacuum parameters consistent
between the high and low energy data, constrains the effective mixing angle andmass splitting which translates to a constraint on the NSI  parameters; this is
the reason for the cut-offs in the parabolic shape.

126

There is a positive-negative symmetry in εeτ which is broken in the case of anon-zero θ13 . εeτ can cause an excess of upward-going νe which oscillate fromντ , a similar effect is caused by θ13 and the standard matter effect. The energy
and zenith angle regions of the expected excess coincide for θ13 and εeτ , shownin Figure 8.10. An expansion of the Hamiltonian equation with NSI shows that
θ13 terms appear with terms depending on arg(εeτ ) breaking the positive-negative
symmetry [76].
The standard matter effect is dependent on the sign of the matter term and thesign of the mass splitting: an excess of νe is observed for neutrinos and normal
hierarchy, or ν̄e for antineutrinos and inverted hierarchy. A larger atmospheric
neutrino flux and interaction cross section, compared to antineutrinos, results inasymmetric constraints on εeτ .
Table 8.3 Constraints on εeτ for the current analysis and the previous SK result.

εee

SK NSI 2011

New Result

1.5
0.0
-1.5

|εeτ | < 0.54|εeτ | < 0.39
|εeτ | < 0.24

-0.75 < εeτ < 0.325-0.225 < εeτ < 0.225-0.1 < εeτ < 0.125

Table 8.4 Constraints on ετ τ for the current analysis and the previous SK result.

εee

SK NSI 2011

1.5 -0.09 < ετ τ < 0.15
0.0 -0.09 < ετ τ < 0.21
-1.5 -0.15 < ετ τ < 0.09

New Result-0.05 < ετ τ < 0.35
-0.075 < ετ τ < 0.15
-0.075 < ετ τ < 0.125

These results can be compared to the previous Super-K NSI zenith angle
analysis [132, 133]. This analysis uses the full three-flavour standard oscillations
extended to include NSI, whereas the past result was achieved using two-flavour
standard oscillations. This limitation resulted in symmetric constraints on the
NSI parameters. The three-flavour standard oscillation, including standard
matter effects, have imposed tighter constraints on positive values of εeτ . Anotherkey difference is the scanned range of εee . In the former analysis, the range wasdetermined by considering the allowed range of εdee given by CHARM data [62].
The range was extended in this analysis to include (large) values of εee consistent
with global oscillation data discussed in Section 2.3.2.
127

(a)

θ13 = 0(c)εeτ = 0.2

Figure 8.10(b) standard oscillations(d)εeτ = -0.2

Oscillation contours showing the νµ → νe oscillation probability
for different values parameters. Oscillation probabilities calculatedusing full three-flavour equations with all other NSI set to zero.
The horizontal axis shows the energy and the vertical axis shows
the zenith angle. The top left plot shows standard oscillation only,
top right shows standard plus flavour-changing neutral currents.
The bottom left plot shows standard plus lepton non-universality
and the bottom right plot includes flavour-changing neutral currents
and lepton non-universality. Normal hierarchy has been assumed.

Comparisons of the new and past results are shown in Tables 8.3 and 8.4. The
new constraints on εeτ and ετ τ are somewhat looser than the past result, which is
expected due to the assumed standard oscillation parameters. The past analysis
fixed (∆m232 , sin2 θ32 ) to (2.1 × 10−3 eV2 , 0.5) which was the best fit point for128

SK atmospheric neutrino data at the time. It should be noted that while thestandard oscillation parameter assumptions affect the allowed ranges of the NSIparameters, the minimum χ2 values for different standard oscillation parameterassumptions are larger than those for the best fit point so the allowed region for
the NSI parameters is not expected to significantly differ if the standard oscillation
parameters are allowed to vary.
This is the first attempt at searching for NSI in the e − τ sector in atmospheric
neutrinos, accounting for three-flavour standard oscillations. Although no signalof NSI was found, constraints have been obtained for εeτ and ετ τ for various valuesof εee . The atmospheric neutrino data is explained well by standard νµ → ντoscillation so ετ τ is constrained tightly. However, large values of εeτ and εee arestill compatible with the data.

129

Chapter 9Hyper-Kamiokande
Hyper-Kamiokande is a next-generation large water Cherenkov detector which
will succeed Super-K. The physics program includes precise measurement of
neutrino oscillation parameters, measurement of CP violation in the lepton
sector, neutrino cross section measurements, searches for exotic oscillation
scenarios, solar neutrino day/night asymmetry measurements and spectrum
upturn, supernovae detection and diffuse supernova background measurements
as well as nucleon decay searches.
The Hyper-Kamiokande detector will be located in the Tochibora mine of the
Kamioka Mining and Smelting Company in Gifu, Japan under Nijuugo mountain.
This gives an overburden of 650 m of rock or 1,750 meters-water-equivalent(m.w.e). The site is located 8 km south of the Super-Kamiokande site and the
J-PARC [78] neutrino beamline is directed such that both of the detectors will
have the same 2.5° off-axis angle.
This chapter is intended to give the reader a brief summary of the key componentsof the Hyper-Kamiokande detector relevant to this thesis. For a more detailed
description, see Reference [17].

9.1

Physics Goals

In the next sections, the physics program of Hyper-K is outlined. For more details
refer to the Hyper-K design report [17].

130Figure 9.1

9.1.1

An illustration of a Hyper-Kamiokande cylindrical tank.
from [17].

TakenLong Baseline and Atmospheric Neutrinos

In a similar way to T2K [11], Hyper-K will use a beam of neutrinos produced
at the J-PARC [108] facility in Tokai, Japan. The neutrinos are produced byaccelerating protons and colliding them on a graphite target. The collisions
typically produce pions which then decay to give muon neutrinos. The far
detector will be 295 km away from the beam production point, at an off-axis
angle of 2.5°. This gives Hyper-K the same baseline and off-axis angle as SuperK. The energy spectrum of the neutrino beam varies with off-axis angle At anangle of 2.5° the energy spectrum peaks at roughly 600 MeV which corresponds
to the oscillation maximum for a baseline of 295 km.
The near detector is used to measure the flux and direction of the neutrino beam,
together with the contamination from electron neutrinos or wrong sign neutrinos.
Another key purpose of the near detector is to make measurements of neutrino
interaction cross sections. Figure 9.2 shows the ND280 near detector complex [13]currently used for the T2K experiment; this near detector suite will be upgraded131

Figure 9.2

The ND280 near detector complex with the INGRID on-axis detector(left) and the ND280 off-axis detectors (right). Taken from [17].

in preparation for T2K-II [8, 19] and will then be used for Hyper-K. A model ofthe planned ND280 upgrade is shown in Figure 9.3.

yxSuper-FGD

Figure 9.3z

HA-TPCA diagram of the upgraded ND280 detector where the TOF detectors
have not been drawn. Two High-Angle TPCs (yellow) with ascintillator detector ”Super-FGD” (grey) will be installed in the most
upstream portion of the detector (left). The three (orange) TPCs andtwo (green) FGDs make up the tracker system in the downstream
portion in the current ND280 detector and will remain after the
upgrade. Taken from [19].

Planned upgrades to the J-PARC main ring will see the beam power increase
from 500 kW to 1.3 MW in time for Hyper-K data-taking [78]. Hyper-K willcollect many events and have smaller statistical uncertainties, compared to T2K.
132

Near detector systematics need to be lowered to around 1-2% for Hyper-K
physics measurements. Current uncertainties on the estimated neutrino flux at
Super-K are roughly 6%, with half of this coming from flux and cross section
uncertainties [16]. One of the key limitations comes from the difference intarget material; T2K uses two scintillator targets, one of which is made up
of 40% water. ND280 compares the interaction rate on the two targets anduses a subtraction analysis to constrain the neutrino interaction cross section inwater and so additional uncertainties arise (from the subtraction), compared tomeasurements taken on pure water. A further limitation comes from differencesin the acceptance of the near and far detectors. Upgrades to ND280 will increase
the fiducial mass and angular acceptance of the detector, the addition of a timeof-flight (ToF) detector will also improve the reconstruction of backward-going
events.

Figure 9.4

A conceptual design of the IWCD detector facility [164].

These limitations will be addressed by the implementation of a complementary
additional ”near” detector called the intermediate water Cherenkov detector(IWCD) [17]. Figure 9.4 shows a conceptual design of IWCD. IWCD can measureinteractions in water with the same angular acceptance as the far detector, thisremoves the need for extrapolation. A key feature of IWCD will be its off-axis
133

spanning technique. The detector will be able to span various off-axis angles
from 1-4°, taking advantage of the angle dependent energy spectrum propertiesof the beam. The detector will also be loaded with gadolinium which will enable
separation of neutrino and antineutrino events and improve event classification
by tagging neutrons.

Figure 9.5

Reconstructed neutrino energy distribution for several values of δCP(top) and the difference in reconstructed neutrino energy distribution
from the case of δCP . The plots are for the νe appearance modefor neutrinos (left) and antineutrinos (right). Normal hierarchy isassumed and sin2 θ13 = 0.1. Taken from [17].

The main goal of the long baseline program is the measurement of CP violationin the lepton sector. The CP violating phase δCP , is measured by comparing theoscillation probabilities of neutrinos (νµ → νe ) and antineutrinos (ν̄µ → ν̄e ). The
J-PARC neutrino beam can be run in neutrino or antineutrino mode, allowing forseparation of neutrino and antineutrino events, which makes the measurement ofδCP possible. Figure 9.5 shows how the reconstructed νe energy spectrum varies
with different values of δCP . The long baseline program will also make precise
measurements of the neutrino oscillation parameters θ13 , θ23 and ∆m232 . Figure 9.6
shows that after 10 years, Hyper-K is expected to exclude CP conservation witha significance of 3σ (5σ) for 76% (57%) of the phase space.
Due to the relatively short path length, the sensitivity of the long baseline
program alone to the mass hierarchy is limited. Atmospheric neutrinos however,traverse the earth and the contribution from the matter effect results in an surplus
134Figure 9.6

Expected significance, for a single Hyper-K tank running for 10
years, to exclude CP conservation (δCP = 0). Normal hierarchy
is assumed with sin2 θ13 = 0.1 and sin2 θ23 = 0.5. Taken from [17].

of νe appearance for the normal hierarchy whereas the increase is seen in ν̄e forthe inverted hierarchy. Figure 9.7 shows how the oscillated flux differs from theunoscillated flux for different values for θ13 and δCP .
The strong matter effects in the atmospheric neutrino data will be complemented
by the precise knowledge of baseline and narrow energy region that enables T2HK
to precisely measure θ23 . Thus, combining the beam and atmospheric neutrinos
increases Hyper-K’s sensitivity to the oscillation parameters.

9.1.2

Solar Neutrinos

Measurements of solar neutrinos enable determination of the neutrino oscillation
parameters between mass eigenstates ν1 and ν2 . The allowed region for the ν1 −ν2neutrino oscillation parameter space can be seen in Figure 2.6. The mixing angle
measured by solar and reactor neutrino experiments are in agreement, however
there exists a 2σ tension in the mass squared splitting ∆m221 between Super-K
and KamLAND [118]. Super-K measured a day-night asymmetry in the numberof observed solar neutrinos [148]. This results in a value of ∆m221 lower than the
global best fit (which is dominated by KamLAND [20]). Hyper-K is expected
to measure the day-night asymmetry to more than 5σ significance. Due to a135

Figure 9.7

Upward-going oscillated νe flux relative to the non-oscillated flux
as a function of neutrino energy. Thick solid lines indicate thetotal flux whereas the thin line, dashed line and dotted line indicate
the contribution from the solar term, interference term and the θ1 3
resonance term respectively. The top two plots show the effect of theθ23 octant. The top right plot and bottom left plot show the effect of
δCP . The bottom right plot is for inverted hierarchy the resonanceis not seen in this sample but is seen in ν̄e instead. Taken from [17].

transition from vacuum oscillations below 2 MeV to matter effects in the Sun
above 5 MeV, lower energy solar neutrinos are expected to show an increase inνe survival probability which is called solar spectrum upturn. The shape of thisupturn spectrum can distinguish between regular matter oscillations and more
exotic models [127]. Hyper-K will be able to measure the spectrum upturn, withrespect to a flat survival probability, to 3σ (5σ) significance with a low energy
threshold of 4.5 MeV (3.5 MeV).

9.1.3

Supernova Neutrinos

A core collapse supernova is the ultimate fate of massive stars between 8 and 50
solar masses. The star fuses elements until it reaches nickel and iron, after which
no energy can be released from fusion. Once the core passes the Chandrasekhar
limit of 1.4 M the electron degeneracy pressure can no longer sustain thegravitational pressure and the core begins to collapse [57]. The supernova begins
with a prompt neutronisation burst phase in which a burst of electron captures(p + e− → n + νe ) emit νe with very high luminosity. The following accretion andcooling phases produce neutrinos and antineutrinos of all three types. Neutrinos
136interact weakly with matter so the majority (99%) of the energy released fromthe supernova is carried away by neutrinos.
In 1987, 25 neutrinos from supernova SN1987a, were detected by Kamiokande [101],
IMB [91] and Baksan [36]. The supernova occurred in the Large Magellanic Cloud(LMC) galaxy roughly 50 kpcs away. The neutrino observations confirmed thebasic model of core collapse supernovae and the detection of more supernova
neutrinos will provide further inputs to improve supernova models.

Figure 9.8

The expected number of supernova neutrino events, for each neutrino
interaction, as a function of the distance to the supernova. The
figure is for a single Hyper-K tank and the bands for eachline indicate the variation based on the assumption of neutrino
oscillation parameters. Taken from [17].

Supernova neutrinos undergo different interactions in water, the main interactionin Hyper-K will be the detection of electron antineutrinos undergoing inverse beta
decay (ν̄e + p → e+ + n). The advantage of Hyper-K as a supernova detector
comes from the very large detector volume, Figure 9.8 shows the expected event
rate as a function of the distance to the supernova. For a supernova occurring at
a distance of 50 kpcs, in the LMC, 2,200 to 3,600 neutrino events are expected.
Neutrinos and antineutrinos from all of the past core collapse supernovae are137

expected to be present throughout the universe. These neutrinos are calledsupernova relic neutrinos (SRN) or diffuse supernova background (DSNB) [48].
The detection of DSNB will give a better insight into the history of the universe as
well as the rate of core collapse supernovae and heavy element synthesis. HyperK will look for the DSNB in an energy range of 16-30 MeV. The shape of the
DSNB energy spectrum can provide important information about the history ofstar formation.

9.1.4

Proton decay

Figure 9.9

A comparison of the experimental limits on the rates of nucleon
decay and projected limits for Hyper-K (10 years, single tank)and DUNE. Ranges of theoretical predictions also shown. Taken
from [17].

The goal of the original Kamiokande experiment, the predecessor of Super-K,
was to search for proton decay, this was also a major goal of the Super-K
experiment and now Hyper-K. Proton decay is a key prediction of many grandunified theories (GUTs) [67, 121] with predictions of the proton lifetime being
longer than 1030 years. Due to the large detector mass, Hyper-K will be able toprobe proton lifetimes up to ∼ 1035 years. Figure 9.9 shows the 90% C.L. limits
set by Super-K and various other experiments as well as the expected lifetime
sensitivity of Hyper-K and DUNE [22].
The p → e+ π 0 is the golden channel for water Cherenkov detectors as there isno invisible energy and the two body decay should result in a very small total138

momentum. The decay would cause three Cherenkov cones, one from the positron
and the other two from the pion decay to two photons. Hyper-K will select the
proton decay events by looking for 2 or 3 e-like rings (the 2 photons from pion
decay may produce rings close enough to be reconstructed as a single ring). For
3-ring events, two of the rings with the invariant mass closest to the mass of π 0will be selected as the π 0 candidate and a further cut on the π 0 mass is applied.
Finally, the invariant mass of the three rings is required to be consistent with theproton mass and the total momentum is less than 100 MeV/c for a free proton
enriched sample; for a bound proton enriched sample the total momentum should
be between 100 and 250 MeV/c. Figure 9.10 shows the expected number of eventsand backgrounds for this search.

Figure 9.10

9.2

The total momentum of events passing the p → e+ π 0 event
selection criteria except the momentum cut (left) with solid verticallines indicating the momentum cuts. The reconstructed invariant
mass of events passing the p → e+ π 0 event selection criteria
except the invariant mass cut (right), for free (top) and bound(bottom) protons. The hatched regions in the plots indicate theatmospheric neutrino background whereas the black dots represent
the sum of proton decays and background. All plots are for a 10
year exposure of a single Hyper-K tank with an assumed proton
lifetime of 1.7x1034 years. Taken from [17].

Detector Design

The Hyper-Kamiokande tank will have a height of 73 m and a diameter of 69 m
making it 273 ktons. It is divided into two optically separated volumes, an innercylinder will form the ID, and a larger cylinder which encapsulates the ID will139

serve as the veto region (OD). The tank will be filled with ultrapure water.
The OD will have a lateral depth (along the cave barrel walls) of 1 m and a 2 m
depth from the top and bottom cave walls. Similar to Super-K, Hyper-K will
mount PMTs on either side of a PMT support frame which is roughly 60 cm
wide. Accounting for the deadspace in the PMT support frame, the total volumeof the ID is 230 ktons. If we assume only events with a reconstructed vertex
2 away from the ID walls are used, this would mean a total fiducial volume of
191 ktons which is eight times larger than Super-K (22.5 kton).
Up to 40% of the ID surface will be instrumented with 50 cm Hamamatsu R12860HQE PMTs (see Table 9.1) while the OD will be instrumented with up to 0.28%
photocoverage 8 cm PMTs coupled to wavelength shifting plates, which will be
discussed in Chapter 10. PMTs will be tested to ensure that they have a suitablepressure tolerance and acrylic covers will be placed on top of the ID PMTs toprevent a chain implosion event.
In order to increase physics sensitivities, there is an option to build a second
Hyper-K tank in South Korea six years after the first tank [145].

9.3

Photosensors

Figure 9.11

A picture of the 50 cm Hamamatsu R12860-HQE box-and-line
PMT. Taken from [17].

The Hyper-Kamiokande inner detector will have up to 40% of its surface covered
with 50 cm Hamamatsu R12860-HQE PMTs (see Figure 9.11). These PMTs
have been newly developed for Hyper-K with several improvements over the
existing 50 cm R3600 PMTs used in Super-K. The PMTs’ properties and their
140

Figure 9.12

Thesinglephotoelectron transit
time distribution of
the Hyper-K PMT(blue) and Super-K
PMT (black). Taken
from [17].

Figure 9.13

Thesinglephotoelectron charge
distribution of theHyper-K PMT (blue)
and Super-K PMT(black).
Taken
from [17].

improvements are discussed in detail in Reference [17].
The improvements include: Higher quantum efficiency:

Improvements to the photocathode haveresulted in a QE of 30% at 390 nm for the Hyper-K PMTs, compared to apeak QE of 22% for the Super-K PMTs.

 Higher collection efficiency: In the area covered by a 46 cm diameter,

Super-K PMTs have a CE of 73%, Hyper-K PMTs have a CE of 95%.
Outside of the 46 cm region the CE of Super-K PMTs drops below 50%
while for the Hyper-K PMTs it is 87%. This increase in collection efficiency
is achieved by optimising the glass curvature and focusing electrode as well
as changing the dynode structure. Photoelectrons could sometimes miss thefirst dynode in the Venetian Blind dynode structure used in the Super-K
PMTs. The Box-and-Line dynode used in the Hyper-K PMTs makes useof a wide box as the first dynode which collects nearly all of the emitted
photoelectrons (see Figure 9.14).
 Better time resolution:

Figure 9.12 shows the transit time spread for
the Super-K and Hyper-K PMTs and a clear improvement, by a factorof two, can be seen. The time resolution for single photoelectron signals
is 4.1 ns (FWHM). The left region of the transit time distribution has aresolution of 1.1 ns (σ) .
141

Figure 9.14

A sketch of the Venetian Blind dynode structure used in Super-K
PMTs (left) and the Box-and-Line dynode structure used in HyperK PMTs (right). Taken from [138].

The improvements to the photosensor have resulted in a single photon detection
efficiency two times better than that of the Super-K PMTs. A figure showing therelative single photon detection efficiency as a function of position angle on the
PMT is shown in Figure 9.15. It is worth noting that the increase in sensitivity
has also increased the PMT’s dark rate. The dark noise hits, resulting fromthermionic emission from the photocathode, vary with temperature and PMT
voltage. The dark noise for the Hyper-K PMTs have been measured, in air, tobe 8.3 kHz at 15° C this is double the rate of Super-K PMTs which have a darknoise rate of 4.2 kHz. Efforts are being made to reduce the dark noise in order
to increase the sensitivity of low energy physics analyses. Another concern for
low energy studies is the radioactive contaminants in PMT glass. Radioactive
contamination in the glass has been measured and the concentration of 40 K has
been reduced by an order of magnitude compared to the glass used in Super-K
PMTs. A summary of the PMT’s properties are shown in Table 9.1.
Some portion of the ID may be instrumented with other types of PMT which may
increase the physics capabilities of Hyper-K. One of the designs for alternative
PMTs is the Multi-PMT (mPMT). The mPMT, shown in Figure 9.16, consistsof 19 7.7 cm PMTs housed in an acrylic 50 cm dome. The dome acts as apressure-tolerant vessel and contains all of the readout electronics inside. There
are several advantages to this design. The increased number of PMTs will improve
the granularity and the smaller PMTs have a much lower dark rate so the overall
module will have less noise than a typical 50 cm PMT. Another advantage comesfrom the fact that the PMTs are angled such that they are perpendicular to thetangent of the surface of the dome, this increases directionality information which142

Table 9.1 Specifications of the 50cm Hamamatsu R12860-HQE PMT. Values
taken from [17].

Property
Shape
Hemispherical
Photocathode area
50 cm (20 inch) diameter
Bulb material
Borosilicate glass (3 mm thickness)
Photocathode material
Bialkali (Sb-K-Cs)
Quantum efficiency
30% at λ = 390 nm typical
Collection efficiency
95% at 107 gain
Dynode structure
10-stage box-and-line
Gain
107 at 2000 V
7
Dark pulse rate
8 kHz at 10 gain at 13° C (after stabilising)
Weight9 kg (without cable)
Volume61,000 cm3
Pressure tolerance
1.25 MPa waterproof

Figure 9.15

Relative single photon detection efficiency as a function of theposition on the photocathode. The PMT centre is at a position
angle of 0° and the PMT edges are at ±90°. The black lines show
the average measured values for of four Super-K PMTs whereas theblue lines show the measured value of a Hyper-K PMT. Scans weretaken along perpendicular lines and the results are shown in thedashed and solid lines. Taken from [17].

may be useful in reconstructing event vertices and directions.

143

Stainless steel ring
PPS vessel
Stainless steel backplate

Acrylic dome

PMT holder

Optical gel

Reflector
PMT

PMT support matrix

Daughter board

High voltage

Main board

Scintillator panel
50 cm

Figure 9.16

9.3.1

A conceptual drawing of a multi-PMT with 19 7.7 cm PMTs
outward-facing PMTs, on each side, for the ID and OD. The PMTs
are enclosed in a 50 cm acrylic vessel and readout electronics areembedded inside. Taken from [17].

Electronics

The dark noise and time resolution requirements for Hyper-K are stricter thanSuper-K because the B&L PMTs have twice the performance of the Super-K
PMTs. The charge and timing information for any PMT signal above 0.25
photoelectrons will be read out and stored, a software trigger then goes overthe stored hit information to select events. The current design uses the same
electronics system for both the ID and OD.
One of the key changes in the Hyper-K electronics system is that the frontend
electronics module will be housed in a water-tight, pressure-tolerant housing andplaced in the PMT support structure in the water. The reason for this comesfrom the size of Hyper-K. Hyper-K will have up to 60,000 PMTs (ID + OD) andif the frontend electronics modules are located on the roof of the tank, as is thecase for Super-K, then the structure would need to be designed to support theweight of the cables which is expected to be roughly 1 kton. The cables must also
be longer than those in Super-K which reduces the signal amplitude and reduces
the signal quality. Placing the frontend modules in the water allows for shorter
cable lengths and significantly reduces the weight that must be supported by the
PMT support structure.

144

9.4

Detector Simulation

The Hyper-Kamiokande detector is simulated using an open source1 Geant4 [27]simulation called WCSim (Water Cherenkov Simulation). This simulates thegeometry, physics and electronics response of user-defined water Cherenkov
detector configurations.
The Hyper-Kamiokande inner detector volume along with the HQE B&L PMTs
are simulated. The PMT simulation includes the dark noise rate, timing
resolution as well as an overall photon detection efficiency. The outer detector is
not currently included in the official WCSim release. Development efforts for theouter detector implementation in WCSim are outlined in Chapter 10.
Geant4 is used to propagate particles through the detector volume, calculating
any energy loss due to physics interactions. Any particles resulting frominteractions of the initial particle are also tracked. Photons which reach thesensitive regions of our simulated detector have quantum efficiency and collection
efficiency cuts applied in order to register a hit. The code then uses the SK-I (ora user defined) electronics scheme to digitise the hits.
The output of WCSim stores the vertex and energy information of the initial
particles as well as the true and digitised hits (in a window) for all hits in each
event. The hit information can then be used to inform design efforts or tune
and test the event reconstruction algorithms used for Hyper-K: fitQun [156] andBONSAI [153]. Both of these event reconstruction algorithms are used in Super-K
and SKDETSIM but have been adapted to work with Hyper-K and WCSim.

1

The WCSim package is available at https://github.com/WCSim/WCSim.

145

Chapter 10
Hyper-Kamiokande Outer Detector
The Hyper-K outer detector will use outward-facing PMTs to veto incoming
charged particles. Super-K’s OD has a 1% photocoverage of 20 cm PMTs, thesame photocoverage for Hyper-K would scale up to 6,700 20 cm PMTs. The
Hyper-K OD has a thickness of 1 m around the barrel and 2 m from the top andbottom caps, while the Super-K OD has a 2 m depth in the barrel and endcap
regions. This means that, compared to Super-K, incoming charged particles (inthe barrel regions) produce less light and the light is less spread out; for thisreason, an OD design with a finer granularity than that of Super-K is preferred.
Increasing the number of 20 cm PMTs greatly increases the cost of the OD but
the finer granularity can be achieved in a cost effective manner by using smaller
PMTs. As well as reduced costs, the 8 cm PMTs being considered have a darkcount rate of 100 Hz, much lower than the 2 kHz rate of the 20 cm PMTs.
Keeping the same photocoverage with 8 cm PMTs would mean nearly 50,000
PMTs in the OD. To reduce this number, a detailed optimisation of the reflective
materials on the OD walls together with additional wavelength shifting plates
has been proposed [17]. This will increase the effective photocoverage in the OD,
allowing us to reduce the 1% photocoverage (of PMTs) while maintaining highlight collection. So the OD will have 0.28% coverage of 8 cm PMTs which equates
to 13,300 PMTs.
Another possible method to increase the light collection is the use of a Winston
Cone [159]. This is a reflective parabolic surface which can be coupled to a PMT
to collect light and reflect it towards the PMT surface. Winston cones have beenused in the spherical detectors SNO [52] and Borexino [37]. The major flaw with146

this method of light collection is that photons which travel parallel to the PMT
surface would be blocked by the reflector, reducing the light collected by these
PMTs. Hyper-K is not a spherically symmetric detector, and the shadowing oflight would complicate the reconstruction of events, for this reason they weredeemed unsuitable for use in the OD.
Each PMT will be coupled to a wavelength shifting (WLS) plate in order toincrease the light collection. The wavelength shifting plates absorb photons
between 280 and 400 nm where the majority of Cherenkov light is produced,
and emit photons at longer wavelengths. The emitted photons have a random
direction and wavelengths between 410 and 460 nm which closely matches the
QE of the PMTs. Roughly one photon is emitted for each photon absorbed by
the wavelength shifter [162]. The light emitted in the plate is trapped by totalinternal reflection if the angle of incidence, with respect to the plate surface, islarge enough.
This chapter covers the R&D work that has been undertaken in order tounderstand and optimise the wavelength shifting plate design and the effectof reflective materials on the OD walls. Comparisons are made between threedifferent WLS plates: EJ-286 made by Eljen [155], a plate made by Kuraray [119]and a plate which is used in Super-K. Simulations of the OD and improvements
to the reflectors are also discussed.

10.1

Simulating Plate Response

A 2D analytical simulation was developed in order to model the response of a
WLS plate. The simulation creates a square with a circle cut out of the middle.
The square represents the plate while the circle in the middle represents the PMT.
Photons are generated randomly and uniformly across the plate. Each photon
has a randomly generated direction sampled uniformly from 0 to 2π in the planeof the plate. The photons are then propagated through the plate until they reachthe plate edge, at which point they are either reflected or killed. When a photon
reaches the PMT it is stored as a detected hit.
The simulation is run in two different modes. The first mode assumes no reflectors
around the edge of the plate. In this case, a photon reaching the edge is reflectedwith an angle of reflection equal to its angle of incidence if the angle of incidence147

is larger than the critical angle. The second mode assumes that a reflector, suchas aluminised Mylar tape, is used around the plate edges. In this case photons
reaching the edge are reflected.

PMT
Figure 10.1

Photonproduction
point

WLS

A diagram showing a side view of a PMT+WLS setup. the redlines show photons reaching the PMT directly while the purple lines
show light reaching after being internally reflected from the top andbottom of the plate.

There are several key simplifications in this simulation. The first is that the
thickness of the plate is ignored. The angle range at which a photon can be totallyinternally reflected from the top and bottom of the plate is larger than the angles
that would result in a photon reaching the PMT directly (without reflecting offof the top and bottom). This is shown in Figure 10.1. While no major effectis expected to result from this simplification, a full 3D Geant4 simulation of theplates is being developed.
The second simplification is to limit the maximum number of reflections. In thecase of reflective edges, given enough reflections, the simulation will eventuallydetect every simulated photon. In a realistic situation, photons will be attenuated.
Hence, we do not expect photons to survive a large number of reflections.
Figure 10.2 shows the expected number of reflections for various attenuation
lengths. Nominally the maximum number of reflections is set to two. Table 10.1
shows the percentage of detected hits which arrive in two or fewer reflections,for various attenuation lengths. The simulation uses the refractive indices ofthe plate and surrounding medium only to calculate attenuation losses, not theoverall light capture factor. The refractive indices used are 1.58 for the Eljen
sample which is made of PVT and 1.49 for the Kuraray and Super-K samples
which are made of PMMA.
Figure 10.3 shows the expected efficiency of a simulated plate with the contribution of 0, 1 and 2 reflections. Figures 10.4 and 10.5 show heatmaps of theplate efficiency without and with reflective edges. The simulation predicts a large
increase in the light collection with the addition of reflective material aroundthe edges of the plate. The contribution of the reflective edges increases as the148Table 10.1 The percentage of detected hits with 2 or fewer reflections for various
attenuation lengths. Values are also shown for different values ofedge reflectivity.

Attenuation Length [m]Detected Hits With 2 or Fewer Reflections [%]Edge Reflectivity: 1
0.9
0.8

1
2
3
4

100
96
91
86

100
97
93
89

100
98
95
92

3

160

×10

No Attenuation
Att Length 1m
Att Length 2mAtt Length 3mAtt Length 4m

140
120
100
80
60
40
20
0
0

Figure 10.2

1

2

3

4

5

6

7

8
9
10
Number of Reflections

A distribution showing the number of reflections it took before aphoton was detected in the simulation. The simulation is for a
23 cm square plate with 90% reflective edges and a refractive index
of 1.58. The plate was simulated in air. The different colouredlines show various attenuation lengths.

distance between the light source and the PMT increases, flattening out theefficiency curve.
The simulation allows us to understand the plate response at any point using
only geometric arguments, essentially giving an acceptance at any point in theplate.

149

Plate Efficiency

1

PMT Radius
Full Efficiency
0 Reflections
1 Reflection
2 Reflections

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

Figure 10.3

10.2

2

4

6

8

10

12

14
16
Radial Distance [cm]Distribution showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate with reflective edges andno attenuation. The black circles show the overall efficiency while
the blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively. 100% edge
reflectivity and perfect coupling between the PMT and plate areassumed.

Plate Shapes

The size of the WLS plate determines the overall detection efficiency. A platethat is too large will not increase light collection as light will be attenuated in
the plate before reaching the PMT. Similarly, the shape of the WLS plate may
have an effect on the overall light collection. In order to investigate the possible
effects, the simulation was run for square, rectangle and circle plates.
All plates have the same zero reflection contribution, which is given by:sin−1 (RP M T /x)/π,(10.1)

where RP M T is the PMT radius and x is the distance of the photon from thePMT centre. The reflected contributions vary between the different plate shapes.
Figure 10.7 shows the expected efficiency for a 23×46 cm rectangular WLS plate.
The rectangular plate shows a similar behaviour to the square plate, the 1 and 2
reflection contributions increase with radial distance. The circle plate, shown in150

Figure 10.4

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

Heatmaps showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate without reflective edges andno attenuation. The top left plot shows the overall efficiency andthe top right plot shows the contribution from 0 reflections. The
bottom left and right plots show the contribution 1 and 2 reflections
respectively.

Figure 10.6, is different as the one reflection contribution decreases with increasingradial distance and there is no contribution from 2 or more reflections. This isbecause the light is reflected at large enough angles such that it is not collectedby the PMT.
The poor reflection of the circle plate naturally leads to the idea of a plate shapethat focuses the reflected light onto the PMT without allowing it to ”miss” thePMT. The simplest version of this idea is to have square or rectangular plates
constraining the path of the light and ensuring that it heads for the PMT. Anotherpossibility is a triangular plate, this plate design will be referred to as a petal
design. Diagrams of the petal designs are shown in Figures 10.8 and 10.9. The
151

Figure 10.5

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

Heatmaps showing the efficiency of a simulated WLS plate. The
simulation is for a 23 cm square plate with reflective edges andno attenuation. The top left plot shows the overall efficiency andthe top right plot shows the contribution from 0 reflections. The
bottom left and right plots show the contribution 1 and 2 reflections
respectively.

petal designs are being investigated further.

10.3

Absorption and Emission Spectra

There are two key properties of wavelength shifters which are used to characterise
them: absorption and emission. Wavelength shifters absorb light over a rangeof wavelengths with the absorption length depending on the wavelength of the152Plate Efficiency

1

PMT Radius
Full Efficiency
0 Reflections
1 Reflection
2 Reflections

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

Plate Efficiency

Figure 10.6

2

4

6

8

10
Radial Distance [cm]Distribution showing the efficiency of a simulated WLS plate.
The simulation is for a 23 cm circle plate with reflective edges
and no attenuation. The black circles show the overall efficiency
while blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively.

1

PMT Radius
Full Efficiency
0 Reflections
1 Reflection
2 Reflections

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

Figure 10.7

2

4

6

8

10

12

14
16
Radial Distance [cm]Distribution showing the efficiency of a simulated WLS plate. The
simulation is for a 23x46 cm rectangle plate with reflective edges
and no attenuation. The black circles show the overall efficiency
while blue squares, red triangles and magenta rhombuses show thecontribution from 0, 1 and 2 reflections respectively.

absorbed photon. This absorption spectrum varies between wavelength shifting
dopants so it must be understood in order to compare various wavelength shifting
153

PMT

Figure 10.8

A diagram showing an example rectangle petal design, the image
on the right shows possible light reflections.

PMT

Figure 10.9

A diagram showing an example triangle petal design, the image on
the right shows possible light reflections.

samples. The ideal wavelength shifter (for use in Hyper-K) will be one that has
high absorption in the Cherenkov wavelength range. The Cherenkov spectrum
decreases as (1/λ2 ) and below 300 nm there is significant absorption in the water
so the ideal range of plate absorption is 300 to 400 nm.
Once a photon has been absorbed, light is emitted in a range of wavelengths.
Typically, the emitted light has a higher wavelength and is independent of theenergy of the absorbed light. To maximise the light detection capabilities, theemission spectrum of the WLS plate should match the quantum efficiency rangeof the PMTs.
This section describes the spectra measurements for each candidate sample.
154

Table 10.2 The dimensions of the four WLS samples which had their absorption
and emission spectra measured.

SampleHeight [cm]Width [cm]Depth [cm]EljenSuper-K
Kuraray
Sheffield

1.0
1.0
1.0
1.0

1.2
1.0
1.0
1.0

1.3
1.3
1.3
0.5

In addition to the three commercial samples Eljen, Kuraray and Super-K, theabsorption and emission spectra was measured for a non-commercial sample.
This was made for Sheffield University and does not come in the form of a WLS
plate. The Sheffield sample was measured in order to determine its suitability of
as a wavelength shifter. Table 10.2 summarises the dimensions of each sample
measured.

10.3.1

Measuring Emission

Ex = Excitation

Em = Emission

Beam Splitter
SampleXe Lamp

Monochromator(Ex)
Monochromator(Em)
PMT (Ex)PMT (Em)
Processing

Figure 10.10

A diagram of the emission spectrum measurement setup.

The emission spectrum measurement is made using a JASCO FP-6500 spectrofluorometer [59] which has the ability to emit and to measure light of precise
wavelengths. Figure 10.10 shows a diagram of the setup. Light emitted from axenon lamp is passed through a monochromator for wavelength selection. The
light is then split by a beam splitter so the intensity of the incident light can bemeasured. The light then passes through the wavelength shifting sample where
155

500
600
450
500
400

400

350

300

Excitation Wavelength [nm]Excitation Wavelength [nm]

it is absorbed and fluorescent light is emitted. The emitted light passes througha monochromator and its intensity is measured by a PMT. This setup allows us
to determine the emission spectrum for different wavelengths of incident light.

420

1

400

10−1

380

10−2

360

10−3

340
10−4

200

300

320
10−5

100
250

300
0
250

300

350

(a)

Measured Intensity

Figure 10.11

400

450
500
550
600
Emission Wavelength [nm]400 420 440 460 480 500 520 540 560 580
Emission Wavelength [nm]

(b)

10−6

Normalised Intensity

2D emission spectrum for the SK WLS sample. Left plot showsthe emission intensity for different excitation wavelengths andthe right plot shows the intensity normalised for each excitation
wavelength.

For each sample, the measured excitation wavelengths spanned 220 nm to 500 nm
and the emission wavelengths from 220 nm to 600 nm. Figure 10.11 shows the 2D
emission spectrum for the Super-K WLS Sample. The intensity of the excitation
light is stable but is not uniform over the entire wavelength range so what mattersis the relative intensity of the emitted wavelengths for each specific excitation
wavelength. Figure 10.11b shows that when the emission spectrum is normalisedby the area for each excitation wavelength bin, the emission spectrum is consistentover any wavelength that can excite the WLS.
The emission spectrum is obtained by selecting an excitation wavelength andchecking the normalised intensity of emitted wavelengths. An excitation
wavelength of 350 nm is chosen as this results in maximal absorption for allof the WLS samples tested. Figure 10.12 shows the emission spectrum for thefour WLS samples.
The emission spectra for the Eljen and Sheffield samples have a peak which is
closer to the PMT QE peak compared to SK and Kuraray samples. The widthof the emission spectrum of Eljen and Sheffield samples is also preferred as they
do not emit much light at longer wavelengths.
156

0.3

SK Emission
Kuraray Emission
Sheffield Emission

0.8

PMT QE

Normalised Emission

Eljen Emission
1

0.25
0.2

0.6

0.15

0.4

0.1
0.2

0.05
0
200

250

Figure 10.12

10.3.2

300

350

400

450

500
550
600
Emission Wavelength [nm]0The measured emission spectrum for four WLS samples. The
excitation wavelength for these measured values is 350 nm. The
dotted brown line shows the QE of the ETEL PMT which is takenfrom Reference [70].

Measuring Absorption

Monochromator
Beam Splitter

SampleProcessing

Monochromator
PMT
Monochromator
Reference
Deuterium/
Halogen
Lamp
PMT

Figure 10.13

A diagram of the absorption spectrum measurement setup.

The absorption measurements are taken using a JASCO V-550 spectrophotometer [60]. The spectrophotometer emits light which is split using a beam splitterand directed towards two optically separated PMTs. There is a space for materials
to be placed between the light and the PMT. One of the paths has no sample in
the path, the detected light for this PMT serves as a reference. The WLS samples
are then placed, one at a time, in the second holder. The difference between the157signals of the two PMTs gives an overall absorbance for the sample. A diagramof the setup is shown in Figure 10.13
The absorbance, A, is given by:
A = log10 (

Φt
),
Φi

(10.2)

where Φt is the intensity of light transmitted by the sample and Φi is the intensityof light incident on that sample. The absorbance of a material is related to thetransmittance, T, by the equation:

A = −log10 T.

(10.3)The transmittance tells us the fraction of light that has been transmitted throughthe sample, this can be used along with the sample thickness to calculate theattenuation length. The attenuation length is given by

λ=

−L
,
log(T )

(10.4)

where L is the thickness of the sample.
The candidate 8 cm PMTs have different expose heights and curvatures, a higher
expose height allows for thicker plates without covering up too much of the PMTs
active area. Depending on the PMT used, the final WLS plates in Hyper-K could
be either 0.6 or 1.3 cm thick. For this reason, the attenuation length was used to
calculate the probability of absorption for each thickness. Figures 10.14 and 10.15
show the absorption probabilities for the four WLS samples for the full and half
thickness plates respectively.
All of the samples tested have good absorption in the between 200 and 400 nm,
this is ideal for Cherenkov detectors as the majority of the photons produced havea wavelength in this region. The Kuraray sample has a slight dip in absorption
around 300 nm and the SK sample absorbs less than all other samples above
300 nm. After ∼400 nm the ideal WLS sample should have a low probability ofabsorption. This is because these are the wavelengths at which light is emitted.
The better transmittance will result in better propagation throughout the plate.
The transmittance of the SK sample is not as good as the Eljen or Kuraray158

Probability of Absorption at 1.3cm

Eljen Absorption

1

SK Absorption
Kuraray Absorption
Sheffield Absorption

0.8

0.6

0.4

0.2

0
200

Probability of Absorption at 0.6cm

Figure 10.14

300

400

500

600

700
800
Absorption Wavelength [nm]The measured absorption spectrum for four WLS samples. The
vertical axis shows the probability of absorption at 1.3 cm.

Eljen Absorption

1

SK Absorption
Kuraray Absorption
Sheffield Absorption

0.8

0.6

0.4

0.2

0
200

Figure 10.15

300

400

500

600

700
800
Absorption Wavelength [nm]The measured absorption spectrum for four WLS samples. The
vertical axis shows the probability of absorption at 0.6 cm.

sample. The poor transmittance of the Sheffield sample is because of the plastic
used. The Eljen plate is made from PVT, the Kuraray and Super-K plates use
PMMA and the Sheffield sample is made with Polystyrene.

159

10.4

Plate Efficiency Measurement

In these measurements, a PMT is coupled to a WLS plate and measurements
are taken at several points across the plate along one axis. The detected light isthen compared to that of the PMT alone. Each wavelength shifter has a curved
circular hole cut out of the centre so they can be mounted onto a PMT withthe base of the plate sitting close to the measured edge of the photocathode (seeFigure 10.16). The hole is curved such that it follows the shape of the PMT bulb
(see Figure 10.1). The efficiency measurements were carried out using a 3 inch
ETEL 9320KFLB [70] domed PMT with an active diameter of 78 mm (3”) witha blue-green sensitive bialkali photocathode.

Figure 10.16

A closeup picture of the curved WLS hole before the plate ismounted onto a PMT.

Various plate sizes and shapes were measured, the dimensions of each plate
are summarised in Table 10.3. Two measurement setups were used. Initially,measurements were taken using the two Eljen plates using relatively slow shaping
electronics which led to a relatively large background from dark counts thatneeded to be subtracted. Subsequently, the setup was improved by making use
of faster amplifiers and DAQ electronics, allowing faster data taking with less160

SetupFibre guiding the
UV LED signal

PMT

WLS

• 3“ PMT (93Shifter Plate• UV LED @ 3• A pulser pro
with rate: ~ 1• A fibre is use
the PMT.
• Neutral Dens
• Tube of ~ 8m
filter to constr• We collected
the WLS plat

Figure 10.17

A picture of the efficiency measurement setup.

background. All plates were retested with this setup.
Table 10.3 HK
The
the WLS plates used for the efficiency
PD dimensions
WG - 24 May of
2018measurements.

10.4.1

Plate

Height [cm]Width [cm]Depth [cm]Eljen Small
Eljen Large
Kuraray
SK Square
SK Circle
SK Rectangle Petal

23
30
25
21
21
5

23
50
25
21
21
18

1.3
1.3
1.3
1.3
1.3
1.3

First Setup

Light from a 370 nm ultraviolet LED is guided, via an optical fibre, into a large
light-tight dark box where the measurements are taken. The end of the fibre is161fed into a collimator which results in a spot size of ±0.5 cm. A pulse generator
generates a 10 kHz signal which triggers the LED. The LED is pulsed in such a
way that the majority of signals are single photoelectron signals. The signal fromthe PMT is then amplified by an ORTEC 4890 preamplifier and then an ORTEC
570 amplifier [141] giving an amplification factor of 100. The amplified signal
is then read by an ORTEC EASY-MCA [140] multi-channel analyser (MCA)
connected to a computer. The measurement of each individual point was taken
for 20 minutes, which corresponds to 107 triggers. The MCA is triggered by adelayed copy of the signal that generates the LED pulse. On receipt of a trigger
the MCA generates a gate that extends at least 0.5 µs beyond the start of thepulse. In addition to this, the amplifier shaping time is ∼1 µs. This means thatthe gate is quite wide and stray light in the dark box must be accounted for in
the analysis. Measurements showed that one hour after opening the box, thebackground rate reduced by an order of magnitude so there was a one hour wait
between the measurements of each point.
PMT

Ortec 4890
PreampOrtec 570
Amplifier

MCA

PC

LED boxPulser

Gate

Generator

Figure 10.18

A Block diagram of the electronic readout chain.

The procedure for measuring a plate is to first take a measurement at the centreof the PMT and gradually move the fibre towards the edge of the plate. For eachpoint two runs were taken, one with the LED off followed by a run with the LED
on. The LED off measurement is used to subtract the background. Once all of
the points on all of the plates are measured, the measurements are repeated withMylar wrapped around the edges. After the WLS and reflector measurements
were taken, the measurements were repeated with Tyvek® underneath the plates
in addition to the aluminised edges. It was found that placing Tyvek beneaththe plate did not increase the efficiency. This suggests all of the initial light isabsorbed in the plate, see Figure 10.14.
The signal region is defined as all of hits above the valley (55 counts), see
162

(a)

Figure 10.19

LED ON(b) LED OFF

The MCA spectra when the LED is turned on (left) and turnedoff (right). The measurement was taken with the LED positioned
at the centre of the PMT.

Figure 10.19. For each point, the number of counts is converted to a hit rate
and the dark count (background) measurement is subtracted from the LED on
measurement. All rates are then divided by the measured rate at the centre of
the PMT to give a relative efficiency.

10.4.2

Second Setup

For the second setup the same LED, collimator, optical fibre and PMT are used.
A pulse generator generates a 10 kHz signal which triggers the LED, the LED ispulsed in such a way that the majority of signals are single photoelectron signals.
The signal from the PMT is amplified (and inverted) by a custom built fast
amplifier with a gain of 20 and a shaping time of O(1 ns). The amplified signal
is then read by a CAEN DT5742 [54] waveform digitiser, with a sampling rateof 5 GHz, connected to a computer. The waveform for each trigger (gate andsignal) is saved.
The procedure for measuring a plate is largely the same as the first setup with two
exceptions. The background rate after opening the box was found to be negligible(as the timing window is less than 100 ns) so LED off measurements did not need
to be taken for each point. This also means that it was not necessary to wait
before taking a subsequent measurement. Instead, several LED off measurements
were taken, opening and closing the box after each measurement. The averageof the LED off measurements was used as the background rate. Once all of thepoints on all of the plates are measured, the measurements are repeated with
163

reflective edges around each plate. The reflective edges used in this setup are
different from that used in the first setup. The first setup used a removable
aluminised jacket where the WLS plate could easily be placed in and taken out
of. For the second setup, reflective foil tape was stuck to the edges of the plates.

Voltage [mV]The whole waveform was saved for this setup so the signal selection was done ona trigger by trigger basis in analysis scripts. For each trigger, a hit was registeredif the registered voltage exceeded 10 mV for 4 ns. These values correspondto a typical signal observed for measurements taken at the PMT centre, see
Figure 10.20. The signal selection criteria results in 0.1% of triggers registering
a hit when the LED is off.

35
30
25
20
15
10
5
0
−5
−50

Figure 10.20

10.5

0

50

100

150
Time [ns]A typical waveform for the amplified PMT signal in the second
setup.

Fit To Data

The simulation assumes that all of the photons that arrive in fewer than 2
reflections are detected when in reality there are several factors affecting theoverall efficiency of the plate. Two key factors affecting the efficiency of the plate
are the losses through the top and bottom as well as the coupling of the plate to
the PMT. In order to address this, an overall scaling factor η will be used to scale
the simulation down to the measured result. The reflective edges in the simulationreflect all of the photons received, so another parameter ρ will be used to model
the lower reflectivity of the edges by scaling down reflected contributions. The
164

Table 10.4 The refractive indices for the WLS plates along with the fraction oflight captured in air and in water.

Plate

Refractive Index

Capture Air

Capture Water

Eljen
Kuraray

1.58
1.49

0.77
0.74

0.54
0.45

simulation results are used to model the WLS plate using the equationXη×(
ρi × Mi ),(10.5)iwhere η is the inherent efficiency of the plate, ρ is the reflectivity of the edges
and Mi is the model contribution for i number of reflections.
Several factors are contained in the η parameter. The most obvious contribution
comes from the losses through the top and bottom of the plate. The loss throughthe top and bottom can be calculated by first working out the solid angle:Ω = 2π(1 − cos θC ),(10.6)

where θC is the critical angle. From this we calculate the fraction of a hemisphere
covered by the solid angle giving the percentage of light lost. The fraction of light
captured by the plate is

1 − Ω/2π = 1 − (2π(1 − cos θC ))/2π = cos θC .

(10.7)

The critical angle is dependent on the refractive index of the material used aswell as the refractive index of the surrounding medium. Table 10.4 shows the
expected fraction of captured light for the Eljen and Kuraray plates. It can beseen that from the effect of refractive index alone, the capture difference between
the Eljen and Kuraray plates is roughly 4% for measurements in air, whereas formeasurements in water it is 20%.
The other main contribution to the η parameter comes from the difference in the
PMT QE at 370 nm and the average QE over the WLS emission wavelengths.
A small contribution may be present if the quantum yield of the WLS plate isdifferent from 1. The uniformity of the PMT’s angular response may also effectthe result, however the efficiency at the centre of the PMT and the sides has been165

measured to be 95%.

10.5.1Results

For the measurements taken with the setup mentioned in Section 10.4.1 only twoplates were measured. The model was fit to the small square Eljen plate as wellas the larger rectangular Eljen plate. Figures 10.21 and 10.22 show the efficiency
plots for the small and large plates respectively. It can be seen that the additionof reflective material around the edges clearly improves the plate response andincreases the efficiency. The best fit η parameter is 46% for the small plate while
the large plate has a lower value of 32%, Table 10.5 shows the best fit values foreach plate. The lower efficiency of the large plate may be because the larger plate
can better constrain the reflectivity (ρ) parameter as the data points are taken
at further distances where reflection contributions are significant. However, thetwo Eljen plates are visually different and it is also possible that there is somevariation in production quality. In order to check the validity of the model, thebest fit parameters for the large plate were used to model the small plate and themodel is in reasonable agreement with the data, see Figure 10.23.
Table 10.5 The best fit η and ρ parameters for each plate.

Plate
Eljen Square
Eljen Square
Eljen Square (with constraint on η)
Eljen Rectangle
Eljen Rectangle

Reflector?
No
Yes
Yes
No
Yes

η [%]

ρ [%]

31±2 28±3
46±2 44±332
70±1
32±1 96±6
32±1 70±3

For the setup mentioned in Section 10.4.2 the efficiency plots show a similar shape
to the previous measurements however the efficiency relative to the PMT centre
is much lower. Figure 10.24 shows the measured efficiency for the Eljen andKuraray plates without reflective edges. The Eljen plate has a higher efficiency
than the Kuraray plate which is expected, considering that the spectra shown in
Section 10.3 more closely match the PMT’s QE range. However when reflective
material is added to the edges, the Kuraray plate performs better than the Eljen
plate, this can be seen in Figure 10.25. Interpretation of this result is limited asmeasurement data of the Eljen plate with aluminised edges is not good quality
and must be retaken.

166

Figure 10.21

The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for WLS plate withreflective edges and the pink dots represent measurements on
the WLS plate without reflective edges. The red and blue lines
show the fitted model for the reflective and non reflective edges
respectively. This plate is the Eljen 23×23×1.3 cm plate.

Figure 10.22

The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for WLS plate withreflective edges and the pink dots represent measurements on
the WLS plate without reflective edges. The red and blue lines
show the fitted model for the reflective and non reflective edges
respectively. This plate is the Eljen 30×50×1.3 cm plate.

167

Efficiency

Figure 10.23

The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for WLS plate withreflective edges and the pink dots represent measurements on
the WLS plate without reflective edges. The red and blue lines
show the fitted model for the reflective and non reflective edges
respectively. This plate is the Eljen 23×23×1.3 cm plate but themodel uses the best fit point of the larger 30×50×1.3 cm plate.

1

Eljen Square
Kuraray Square

10− 1

0

Figure 10.24

2

4

6

8
10
Radial Distance [cm]The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for the Eljen square andthe blue dots represent measurements on the Kuraray plate. The
plates do not have reflective material around the edges.

168

Efficiency

1

Eljen Square (Mylar)
Kuraray Square (Mylar)
SK Square (Mylar)

10− 1

0

Efficiency

Figure 10.25

2

4

6

8
10
Radial Distance [cm]The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for the Eljen square andthe blue dots represent measurements on the Kuraray plate andthe red dots represent the SK plate. The plates have reflective
material around the edges.

SK Circle (Mylar)

1

SK Square (Mylar)
SK Rectangle Petal (Mylar)

10− 1

0

Figure 10.26

2

4

6

8
10
Radial Distance [cm]The efficiency vs radial distance from the centre of the PMT.
Black dots represent the measurements for a square, the blue dots
for a circle and the red dots for a rectangular petal. All shapes are
made from the SK WLS plate. The plates have reflective material
around the edges.

Circle and petal shapes were cut out of a Super-K OD plate and measurements
were carried out at several radial distances. As can be seen in Figure 10.26, the169expectations from the simulation agree with the measured data. The efficiencyof the circle shape drops off with increasing distance as the edges of the plate
reflect light around the PMT. The efficiency of the petal shape is higher than thesquare or circle shapes as light is directed towards the PMT.

10.6

WCSim Simulation

In order to study the performance of the OD, the WCSim simulation software
was extended to include an outer detector region. This is still an ongoing
effort and the latest version is available at https://github.com/mahditaani/
WCSim/tree/prod/ODWithWLS. The key additions to WCSim are outward-facing
sensitive PMTs, WLS plates, an extended water volume and Tyvek walls. The
photocoverage, OD thickness and Tyvek reflectivity are user-defined. Figure 10.27
shows a visualisation of the Hyper-K detector in WCSim including the OD.
The simulation is improved by inputting measured values for the properties of the
OD materials. All measurements described in the chapter are used in WCSim.

Figure 10.27

Visualisation of the Hyper-K OD. The figure on the left showsa zoomed out image of the outer detector, blue squares show the
WLS plates and red circles show the OD PMTs. ID PMTs havebeen turned off to easily see the OD. The image on the right showsa zoomed in image of a single WLS plate.

170

10.7

Tyvek

Tyvek is used as a reflector in the Super-K OD as it is cheap, durable andvery reflective. A significant contribution to the light collection comes from thereflections allowed by Tyvek so it must be well understood in order to optimise the
OD design. To study the effects of Tyvek, the WCSim simulation software (seeSection 9.4) is used. Measurements of various Tyvek samples are also describedin this section.

10.7.1

Simulations

To understand the effects of Tyvek in the OD, WCSim was used to simulate
the OD with various configurations. The Tyvek on the outermost wall of theOD (cave) is treated separately from the innermost wall (structure) in order tounderstand the importance of the reflectors on either side.
One thousand 1 GeV muons are simulated, each particle is generated outsideof the OD and enters the OD with a direction perpendicular to the cave wall
(directed towards the centre of the tank). The OD has a thickness of one metre
and a PMT photocoverage of 0.42% (20,000 3 inch PMTs). Each PMT is coupled
to a 50×50 cm WLS plate. To remove any differences expected from various WLS
plates, the attenuation length in the plates is set to 1 mm for all wavelengths.
This means that the plates absorb photons but the emitted photons do not reachthe PMT, so the numbers shown here are very conservative.
There are several Geant4 parameters which can be tuned for reflective surfaces.
Constants for specular spike (RSS ), specular lobe (RSL ), backscatter (RBS ) and
Lambertian (RL ) can be set. The sum of these constants equals one and they
indicate the fraction of reflected light which will be reflected with their respective
angular distributions.
To see the effect of the reflectivity, simulations were carried out fixing the values of
RSL = 0.75 and RL = 0.25. Figure 10.28 shows the averaged light collection as afunction of Tyvek reflectivity. Large increase in light collection are observed withincreasing reflectivity. It can be clearly seen that reflectors are required on bothsides of the OD as light collection is greatly increased with multiple reflections.
To see the effect of specular versus diffuse reflection, the absolute reflectivity
171

0.8

Tyvek Reflectivity (Cave)

Tyvek Reflectivity (Cave)

103

1

1
103

0.8

0.6

0.6

102

0.4

0.4

0.2

0.2
102

0
0.2

(a)

0.4

0.6

0.8

1

Tyvek Reflectivity (Structure)

Number Of PMTs Hit

Figure 10.28

0

0.2

0.4

0.6

0.8

1

(b)

Number of Photoelectrons

Tyvek Reflectivity (Structure)

The average number of photoelectrons detected (right) and theaverage number of hit PMTs (left) per event, for a 1 GeV
incoming muon with various Tyvek reflectivity.

70
1

68

0.8

66
64

0.6

62

0.4

Specular Lobe Fraction (Cave)0

Specular Lobe Fraction (Cave)

0

10

158
1

156
154

0.8
152
150

0.6

148

0.4

60

0.2

146
144

0.2
58

0

56
0

0.2

0.4

0.6

0.8

1

Specular Lobe Fraction (Structure)(a)Number Of PMTs Hit

Figure 10.29

142
0

140
0

(b)

0.2

0.4

0.6

0.8

1

Specular Lobe Fraction (Structure)

Number of Photoelectrons

The average number of photoelectrons detected (right) and theaverage number of hit PMTs (left) per event, for a 1 GeV
incoming muon with various Tyvek specular lobe contributions.

was fixed to 75%. Figure 10.29 shows the light collection for varying degrees ofspecular reflection with the remainder of the reflection being diffuse. A modest
increase in light collection is expected for more specular reflections though thisis much smaller than the effect of the reflectivity. Materials more reflective than
Tyvek do exist, however for the 50,000 m2 required for Hyper-K such options are172

prohibitively expensive.

Measurements

Reflectivity [%]10.7.2

99.5
99
98.5
98
97.5
97
96.5
96
95.5
250

300

350

400

450

500

550

600

650

Wavelength [nm]Figure 10.30

The absolute reflectivity of the Spectralon reference sample.

Considering the large difference in the expected light collection caused by
Tyvek reflectivity, precise measurements of the reflectivity are required. Thisis measured using a JASCO V-650 spectrophotometer [61] with an integrating
sphere attachment. The use of an integrating sphere removes the need to model
the Tyvek reflection angles as it receives light for all reflected angles (not includingbackscatter). Measurements of the Tyvek reflectivity can be compared to areference sample with a known absolute reflectivity. The reference sample used inthese measurements is Spectralon [120], a highly reflective diffuse material withreflectivity values provided by Labsphere. The reflectivity of the reference sample
is shown in Figure 10.30.
Several samples have been measured. In Super-K there are two different forms of
Tyvek used, the Tyvek used on the innermost wall of the OD has a layer of black
polyethylene to aid optical separation of the ID and OD. The Tyvek used on theoutermost wall does not have this black layer, the two samples will be referred
to as SK Black Tyvek and SK Tyvek respectively. Note that the actual Tyvek
layer is of the same type for both of these materials. In addition to the two SK
samples, 1073B and 1082D Tyvek have also been measured. Figure 10.32 shows
the reflectivity as a function of wavelength for each of the measured samples.
173

1082D

Reflectivity [%]Figure 10.31

1073BD

A picture of two Tyvek samples, 1082D on the left and 1073B on
the right.

100
90
80
70
60
50
40
30

SK Black Tyvek
SK Tyvek
1073B
1082D

20
10
0
250

300

350

400

450

500

550

600

650

700

Wavelength [nm]Figure 10.32

The absolute reflectivity of several Tyvek samples.

Tyvek is made of randomly layered polyethylene fibres and measurements showthat the reflectivity increases for thicker samples, as Tyvek is not completely
opaque. Table 10.6 shows the thickness and opacity for different versions of Tyvek.
Figure 10.31 shows a photo of two samples, and the thinner sample (1073B) is
visibly more translucent. 1082D Tyvek is currently the thickest available Tyvek
and is clearly preferred to the other tested samples. Figure 10.33 shows thereflectivity for 1082D Tyvek and the Tyvek used in Super-K. The fibre structureof Tyvek also causes a slight positional dependence so measurements were taken
174

Reflectivity [%]

100
90
80
70
60
50
40
30

SK Tyvek position 1
SK Tyvek position 2
1082D position 1
1082D position 2

20
10
0
250

300

350

400

450

500

550

600

650

700

Wavelength [nm]Figure 10.33

The absolute reflectivity of Super-K Tyvek (without black PE
layer) in black and 1082D in blue. The solid and dashed lines
represent measurements taken at slightly different positions.

at various positions to give an idea of the variation.
Table 10.6 Thickness and opacity of different Tyvek samples, values taken from
Dupont datasheets. Values are given as averages and numbers varyslightly depending on the standard used to measure the properties.

Tyvek Version

Thickness [µm]Opacity [%]

1073B
1073D
1085D
1082D

178
211
267
275

91
96
96
97

The clear dependence on the thickness of Tyvek indicates a potential benefit
to joining together layers of Tyvek. The bonding of Tyvek must be carefully
considered; a simple lamination using heat would ruin the structure of Tyvek
possibly reducing its reflective performance. Daya Bay [41] uses a form of multilayered Tyvek bonded together with a layer of polyethylene in the middle, however
samples of this Tyvek are currently unavailable. As a proof of concept, the Tyvek
samples were bonded together using two basic methods: ultrasonic welding andglue. For the first method, samples were clamped together before being ultrasonicwelded at the edges. For the second method, HT-Seal F119 sealant [99] wasapplied between layers and clamps held the sample together for one day, to cure.
Figure 10.34 shows the reflectivity as a function of wavelength for the multi-layer
175

ultrasonic samples. Increasing the number of layers clearly shows an increase inreflectivity, especially in the most important 300-350 nm region. Figure 10.35
shows the same plots for the glued samples. Figure 10.36 shows a glued multilayer sample and a spot where the glue seeps through, the region where the glue
seeps through will be referred to as a dark spot. Using the glue, the increase was
not as large and was worse when measured on a dark spot.

Reflectivity [%]The 1082D Tyvek was not available when multi-layered samples were being madeso the sample was simply folded in half to give an idea of what to expect withmulti-layered 1082D. Figure 10.37 shows the absolute reflectivity for the folded
1082D sample. A clear increase in reflectivity can be seen, though this increaseis not as large for shorter wavelengths.

100
90
80
70
60
50
40
30
SK Black 1 Layer

20

SK Black 2 Layers (ultrasonic)

10
0
250

SK Black 3 Layers (ultrasonic)

300

350

400

450

500

550

600

650

700

Wavelength [nm]Figure 10.34

10.8

The absolute reflectivity of Super-K Tyvek with multiple layers.
The first layer has black PE backing and the remaining layers arebonded around the edges via ultrasonic welding.

Discussion

The study shows that a 2D simulation can reasonably model the performance of a
WLS plate. The performance of three commercial WLS plates has been measured
as well as different plate shapes. The absorption spectra for the Kuraray, Eljen
and Sheffield samples as well as the emission spectra for the Eljen and Sheffieldsamples are improvements over the plates used in SK.

176

Reflectivity [%]

100
90
80
70
60
50
40
30
SK Black 1 Layer

20

SK Black 2 Layers (glue)
SK Black 3 Layers (glue)

10

SK Black 3 Layers (glue) (dark spot)

0
250

300

350

400

450

500

550

600

650

700

Wavelength [nm]Figure 10.35

The absolute reflectivity of Super-K Tyvek with multiple layers.
The first layer has black PE backing and the remaining layers arebonded together using glue.

Dark Spot
Figure 10.36

A picture of a multi-layer Tyvek sample, joined using glue. The
spotted region in the middle is referred to as the ”dark spot”.

While the measurements showed that the Kuraray plate outperforms the Eljen
plate, the measured Eljen properties are more suited for use in a water-Cherenkov
detector. The refractive index of the Eljen plastic is 1.58 compared to Kuraray’s
1.49. This means that a larger fraction of the light will be trapped in the Eljen
plate, increasing its efficiency. The measured absorption and emission spectra

177

Reflectivity [%]

100
90
80
70
60
50
40
30
20

1082D Tyvek

101082D Tyvek Folded

0
250

300

350

400

450

500

550

600

650

700

Wavelength [nm]Figure 10.37

The absolute reflectivity of 1082D Tyvek. The black line shows
the values for a single layer of 1082D and the blue lines shows
the reflectivity for the same sample folded in half (two layers).

also show a preference for the Eljen plate as the emission for the Eljen plate moreclosely matches the PMT’s QE and the absorption spectrum in the Kuraray plate
has a dip around 300 nm, which is not seen in the Eljen plate. It should be notedthat the absorption is maximal for 370 nm which is the wavelength of light usedin this study so no effect from the worse absorption is expected. To see the effectof the absorption a future study can be done with the Cherenkov photons emitted
by cosmic muons. Another key factor is the refractive index which may result ina 20% difference in light collection even if all other factors were the same.
The difference in the expected and measured efficiencies may be caused by anumber of factors. The coupling of the plate to the PMT may be different between
the two plates, although we did take efforts to make sure that the holes were thesame. Also the setup was changed and so the measurements need to be retaken
and verified.
The effect of plate shapes has been studied and the simulations and measurements
favour a petal design. These shapes have a higher efficiency because they directly
guide light to the PMT. While petal shapes prove to be more efficient than othershapes, it should be noted that the petal shapes have a lower overall area so they
may result in less light being captured compared to a square with more area. A
study should be carried out to see what sized petals would compare to a squareof a particular size.
178

While reflective material beneath the plate did not make a difference in thesestudies it may make a difference if the WLS plates were thinner. Halving the
thickness of the plates and adding reflective material below may reflect photons
which haven’t been absorbed giving them twice the travel distance. A future
study can be done with thinner plates and reflective materials below.
This study did not include the effect of the attenuation length, for large plates theattenuation length becomes very important. In a future study the attenuation
length of each sample should be measured and the simulations should be rerun
to get a better calculation of the acceptance angles across the plate. This would
remove the need to limit reflections in the simulation as well as directly relating
the fitted ρ parameter to the reflectivity of the edges of the plate.

10.8.1

Combined WLS Results

The measurements of the WLS plate properties can be combined to give an overall
effective photocoverage. The efficiency measurements in Section 10.4 are takenwith a 370 nm wavelength LED light source, in air. The final setup will use
Cherenkov photons and will be in water. Several steps are taken to convert thelab measurements to the expected values for Cherenkov photons in water.
First, the quantum efficiency of the PMT is convolved with the measured emission
spectrum. The quantum efficiency of the PMT at 370 nm is maximal (30%), theaveraged quantum efficiency for the whole plate is ∼22% . This means thateven if every emitted photon reaches the PMT, the amount of detected lightfrom a point on the plate should be roughly two thirds of the value obtained
from measurements at the centre of the PMT. Also, the absorption in the plates
is maximal at 370 nm, however the light in the OD will be Cherenkov lightwhich follows a spectrum. In order to account for this, the measured absorption
spectrum is convoluted with the Cherenkov spectrum to get an idea of the amountof light absorbed by the plate. Combining these factors gives the expected
efficiency for Cherenkov photons hitting the plate. A separate convolution of
the PMT quantum efficiency with the Cherenkov spectrum is used to estimate
the response of the PMT to Cherenkov light.
These numbers assume that every photon emitted by the plate reaches the PMT;
including the efficiency measurements gives a more realistic response accounting
for propagation in the plate. Lastly a factor is used to account for the difference
179expected from going from air to water. The difference in medium alters theamount of emitted photons which are trapped in the plate by total internalreflection so this factor can be included as an overall scaling factor. The
air→water scaling factor is given by cos(θwater )/ cos(θair ) where θ is the criticalangle for plates in the respective medium. This factor is 70% for Eljen and 60%
for Kuraray/Super-K, as the higher refractive index of the Eljen plate traps more
light than the other two plates.
Table 10.7 The expected effective photocoverage for various WLS plates.
Assuming (η ,ρ) = (0.32, 0.7). All plates have reflective edges anda PMT photocoverage of 0.28% is assumed.

PlateSize (L×L cm)

Photocoverage [%]Light increase [(WLS+PMT)/PMT]

Eljen
KuraraySK
Eljen
Kuraray
SK

50
50
50
40
40
40

0.73
0.67
0.67
0.59
0.62
0.56

2.6
2.4
2.4
2.1
2.2
2.0

Plates are simulated in various sizes and the best fit values of η and ρ are appliedin order to estimate the expected efficiency. Table 10.7 shows the effective
photocoverage for different WLS plates. The lowest expected increase, from a
40×40 cm Super-K plate would result in a doubled effective photocoverage withlarger plates producing further increases in light collection.

10.8.2Tyvek

The Tyvek simulation studies show that it is important to have reflectors on bothsides of the OD and the type of reflection is much less important than the overall
reflectivity. The reflectivity of Tyvek is related to its thickness, with thicker
samples showing a higher reflectivity. Simple bonding methods have shown an
increase in Tyvek reflectivity though further tests need to be carried out in orderto determine the stability of such methods in ultrapure water. Tests would alsoneed to be carried out with the bonded samples in water to get a more realistic
value for the reflectivity. Ultimately, when tested under the same conditions,Tyvek 1082D [68] has a higher reflectivity than the Tyvek used in Super-K andbonding two layers shows a further increase.

18010.8.3

Next Steps

The light collection has been studied independently for WLS plates and Tyvek.
In the final OD design, there will be some interplay between the two components.
High reflectivity Tyvek allows multiple reflections in the OD but this effect will
be dampened by the WLS plates. Future studies will include both components
in order to optimise the size of the plates. The optimisations to individualcomponents of the OD has been achieved but the overall performance of the
OD must be tested with cosmic muons and low energy background sources. A
detector veto efficiency must be obtained and final changes to the OD design
should maximise it. There may be some physics capability in the OD if theincreased light collection can give a good enough estimate of the deposited energy.
Events which stop in the OD may be selected and treated as contained events.
Also, various forms of OD segmentation can be studied. It is seen in Chapter 6that the cosmic muon veto efficiency is increased by segmenting the barrel andendcap regions, this study has yet to be carried out for Hyper-K.

181

Chapter 11
Conclusions and Outlook
In this thesis two searches for non-standard interactions were carried out using
atmospheric neutrinos. The large range of neutrino energies and a significant
pathlength through matter make atmospheric neutrinos a good source to search
for matter effects. This study includes a statistical update of more than twice
the data since the last SK NSI zenith analysis; further improvements comefrom more precise measurements of standard neutrino oscillation parameters andimprovements to the simulation and event reconstruction.
The search in the µ − τ sector looked for flavour-changing neutral current
interactions between νµ and ντ driven by εµτ and lepton non-universality drivenby (ετ τ − εµµ ). The search was carried out with a two-flavour analysis, decouplingfrom νe and the following constraints were obtained at 90% C.L.:−0.046 < εµτ < 0.019(11.1)−0.050 < ετ τ − εµµ < 0.138(11.2)

These constraints slightly improve over past SK results and are consistent withresults from IceCube [4]. No evidence of NSI was found.
The search in the e − τ sector looked for flavour-changing neutral current
interactions between νe and ντ driven by εeτ and lepton non-universality driven
by ετ τ . This analysis improves over the past SK NSI analysis by including full
three-flavour standard neutrino oscillations with more precise standard oscillation182

parameter assumptions. The parameters εeτ and ετ τ are highly correlated to εeeso constraints are obtained for several values of εee . While the new constraints
are somewhat looser than the past result, this is expected from the difference inassumed standard oscillation paramaters. Asymmetric bounds result from theinclusion of three-flavour standard oscillations and standard matter effects. No
evidence of NSI is found.
Non-standard interactions affect the oscillation probabilities of neutrinos andanti-neutrinos separately and improvements to the NSI allowed region can be
expected from improvements in neutrino/antineutrino separation. Currently theatmospheric neutrino analyses statistically separate neutrinos and antineutrinos
for electron-like samples; a statistical separation of muon-like samples has beendeveloped though it has not yet been included in the atmospheric analysis
framework. Implementation of the νµ /ν̄µ separation may not improve NSI
constraints for Super-K as the contained events have a relatively low energy,
however the selection could be implemented in Hyper-K to improve NSI
constraints. Additional separation power will come from SK-Gd. Gadolinium will
be added to the ultrapure water and antineutrino interactions will be individuallytagged from the final state particles. This method of tagging requires that theneutrino interaction takes place inside the tank which excludes the highest energy
samples, thus improved constraints can be expected only for the non-universality
NSI parameter.
The NSI analyses were carried out using binned datasets which results in some lossof information. A significant portion of the dataset lies in a region where slightly
varying the energy or zenith angle drastically alters the survival probability.
A future maximum likelihood analysis could use the unbinned data to extract
more information and perhaps increase the precision of the oscillation parametermeasurements.
Future improvement in the analysis could come from the treatment of thesystematic uncertainties. In the current analysis, the systematic uncertainties
are assumed to be uncorrelated. This simplifies the fitting procedure, but a more
complete treatment of the uncertainties would require adding correlation terms
to the χ2 calculation [74].
Further improvements to NSI measurements can be expected from the Hyper-K
experiment. In addition to the increased statistics, the larger Hyper-K tank(s)will be able to contain higher energy neutrino events Eν > 10 GeV; the high183

energy neutrinos are potentially subject to matter NSI effects and, in SuperK, muons created from these neutrinos leave the tank resulting in the inability
to accurately reconstruct the incoming neutrino energy. At the time of writing
this thesis, no dedicated Hyper-K atmospheric neutrino MC exists. The expected
detector performance is evaluated using Super-K atmospheric neutrino MC scaled
up to account for the extra detector volume. This approach does not account for
the higher energy muon events which would be fully contained in Hyper-K but
are partially contained in Super-K. In order to determine a reasonable Hyper-K
sensitivity to NSI parameters, a full Hyper-K atmospheric neutrino MC must be
developed.
Another improvement can be expected from the combination of long baseline
and atmospheric neutrino data in Hyper-K. The long baseline measurements canbe taken as “vacuum” parameters as matter effects are negligible for such short
pathlengths. The atmospheric neutrinos will be subject to standard and nonstandard matter effects and tensions between the two datasets could indicate
new physics. Assuming the same systematic errors as SK-IV and scaling up the
SK-IV MC to the exposure expected for a single Hyper-K tank running for 10
years, the constraint on εµτ and ετ τ − εµµ could improve by a factor of two. This
does not include improvements to neutron tagging or the higher energy contained
events.
Hyper-K is expected to start taking data in 2028 and this thesis covers theoverall Hyper-K design and the development of the Hyper-K outer detector. The
key components used to maximise the light collection in the outer detector are
wavelength shifting plates, to increase the effective photocoverage and Tyvek, toallow for more light to be reflected onto the photosensors.
Wavelength shifting plates from multiple manufacturers have been tested,characterised and compared. The efficiency of the plates has been studied forvarious plate shapes. Designs which optimise the plate performance per unit
area have been found. The studies in this thesis show the improved efficiency atfixed distances from the PMT, further studies are required in order to compare
efficiencies of entire plates rather than the efficiencies at fixed radial distances.
Clear improvements can be seen when plate edges are aluminised and squareplates are preferred over circular ones.
Simulation studies of the Hyper-K outer detector have found that reflective edges
on both sides of the OD are necessary to maximise light collection and the184reflectivity of the materials is much more important than the type of reflection(specular, diffuse etc.). Different versions of Tyvek have been compared and theirreflectivity has been measured. Improvements have been found when joining
together layers of Tyvek via ultrasonic bonding at the seams. Further studies
are required to test the stability of bonded materials in ultrapure water (andgadolinium-loaded water) and effects on the water transparency should be carriedout. Measurements of reflective materials should also be carried out in water to
see a realistic measurement of reflectivity.

185

Appendix A
Systematic Uncertainties

186

Table A.1 The best fit systematic errors for the best fit point in the three-flavour
εµτ fit. The systematic errors shown here are related to the neutrino
flux. The final column shows the estimated 1σ uncertainty and thepenultimate column shows the best fit j .
SampleFlux normalisation

Eν < 1Eν > 1(νµ + ν̄µ )/(νe + ν̄e )ν̄e /νeν̄µ /νµUp/down ratio

Horizontal/vertical ratio

K/π ratio in flux calculation
Neutrino path length
Sample-by-sample
Matter Effects< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
PC< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeVPC

FC Multi-GeV
PC + Stopping UP-µe-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likeFit Value [%]

σ [%]

13.33
6.81
0.09
-1.12
1.68
1.59
3.36
-1.39
0.23
2.94
-1.96
-0.03
-0.08
-0.28
-0.20
-0.13
-0.43
-0.18
-0.05
-0.10
-0.05
-0.08
-0.05
-0.05
0.02
0.02
0.06
0.29
0.39
0.29
0.67
0.48
0.29
0.27
0.58
0.31
0.35
-7.89
-0.97
-6.39
-0.50
0.49

25
15
2
3
5
5
5
8
2
6
15
0.1
0.3
1.1
0.8
0.5
1.7
0.7
0.2
0.4
0.2
0.3
0.2
0.2
0.1
0.1
0.3
1.4
1.9
1.4
3.2
2.3
1.4
1.3
2.8
1.5
1.7
10
5
5
5
6.8

187

Table A.2 The best fit systematic errors for the best fit point in the three-flavour
εµτ fit. The systematic errors shown here are related to the neutrino
interaction. The final column shows the estimated 1σ uncertainty
and the penultimate column shows the best fit j .

SampleMA in QE
Single π production; Axial coupling
Single π production; CA5
Single π production; Background
CCQE cross section
CCQE ν̄/ν ratio
CCQE µ/e ratio
DIS cross section
DIS model comparisons
DIS Q2 distribution (high W)
DIS Q2 distribution (low W)
Coherent π production
NC/CCCC ντ cross section
Single π production; π 0 /π ± ratio
Single π production; ν̄i /νi (i = e; µ)NC fraction from hadron simulation
π ± decay uncertainty

Meson exchange current∆m221 [139]sin2 (θ12 ) [139]sin2 (θ13 ) [139]Fit Value [%] σ [%]e-like 0-decayµ-like 0-decay
e-like 1-decayµ-like 1-decayµ-like 2-decay

-0.46
-4.50
-3.08
-8.75
6.44
9.29
0.72
-2.13
3.01
7.78
-5.92
-9.34
12.88
-10.59-20.98-11.22
-0.69
-0.19
-0.26
-1.31
-0.29
-1.82
-1.66
0.02
0.33
0.19

10
10
10
10
10
10
10
5
10
10
10
100
20
25
40
10
10
0.6
0.8
4.1
0.9
5.7
10
2.4
4.6
5.4

188

Table A.3 The best fit systematic errors for the best fit point in the three-flavour
εµτ fit. The systematic errors shown here are related to the detector
performance, event selection and reconstruction. The ”σ” column
shows the estimated 1σ uncertainty and the ”Fit” column shows thebest fit j . Uncertainties are shown for SK-I and SK-II.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-I
Fit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

-0.01
0.03
-0.11
3.54
-16.34
6.52
0.01
0.04
0.01
0.02
0.07
0.01
3.59
3.79
-0.82
0.43
0.13
0.07
0.13
0.69
0.32
0.65
0.84
0.58
0.76
-0.04
-0.03
-0.03
-0.03
0.22
0.05
0.46
0.21
-6.46
1.39
0.25
-0.10
-0.07
-0.00
0.06
0.40
7.37
10.75
-3.48
-12.46
0.99
1.66
1.69
2.94
2.58
2.21
1.28
-3.27
-1.78

SK-II
Fit
σ

0.2
0.01
0.2
2.4 -3.43 4.8
0.6
0.08
0.5
7
-5.90 9.4
23
-2.51
13
46
-3.37
19
0.1
0.07
0.4
0.4
0.07
0.4
0.1
0.05
0.3
0.2
0.12
0.7
0.5 -0.00 0.2
0.1 -0.00 0.3
13
-5.16
38
12
3.75
11
2
-0.08
2
2.3 -1.09 1.3
0.7 -1.92 2.3
0.4 -1.42 1.7
0.7 -0.59 0.7
3.7 -2.17 2.6
1.7 -1.42 1.7
3.5 -3.18 3.8
4.5 -6.86 8.2
3.1 -1.59 1.9
4.1 -0.67 0.8
0.23 0.23 0.66
0.18 0.18
0.5
0.19 0.08 0.24
0.19 0.09 0.26
3.1
3.47
6
0.66 1.44
2.5
6.5
5.60
9.7
2.9
2.25
3.9
6
-1.23 3.8
3.3
1.11
2.8
0.6
0.24
0.6
0.7 -0.09 0.7
0.5 -0.07 0.5
0.4 -0.01 0.6
0.9
0.14
1.3
1.5
0.82
2.3
3.4 -4.79 4.4
16
-2.86
21
18
-3.52
14
18 -15.83 14
7.2
6.99
7.9
9
6.90
10
9.2
9.65
14
16
7.59
11
14
11.03
16
12
6.76
9.8
5.6 -2.69 4.4
10
-0.91
10
20
20.23
50

189

Table A.4 The best fit systematic errors for the best fit point in the three-flavour
εµτ fit. The systematic errors shown here are related to the detector
performance, event selection and reconstruction. The ”σ” column
shows the estimated 1σ uncertainty and the ”Fit” column shows thebest fit j . Uncertainties are shown for SK-III and SK-IV.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-IIIFit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

0.07
-0.01
-0.14
-14.48-0.35-15.66
0.12
0.12
0.09
0.42
-0.00
-0.01
-0.98
0.77
0.23
0.81
1.05
0.46
0.21
0.46
0.35
0.46
0.91
0.39
0.74
-0.05
-0.04
-0.06
-0.06
3.48
1.91
1.80
0.99
-4.98
1.36
0.74
0.16
0.11
0.03
0.95
-0.99
2.84
-4.38
1.47
0.03
0.40
0.95
0.74
3.62
1.24
1.66
1.62
0.86
2.70

SK-IV
Fit
σ

0.8
0.70
1.3
0.5 -0.78
1
0.9
0.00 0.02
29-0.73 8.5
12
-1.61 6.8
87 -26.65 40
0.5 -0.01 0.02
0.5 -0.01 0.02
0.4 -0.05 0.09
1.8 -0.27 0.49
0.2 -0.00 0.02
0.7 -0.00 0.08
27
2.62
18
11
0.49
12
2
-1.46
2
2.3 -0.95 1.6
3
-1.79
3
1.3 -0.60
1
0.6 -0.36 0.6
1.3 -0.60
11-0.71 1.2
1.3 -1.13 1.9
2.6 -1.37 2.3
1.1 -0.54 0.9
2.1 -1.43 2.4
0.26 0.12 0.28
0.19 0.10 0.22
0.31 0.16 0.35
0.3
0.16 0.35
9.5 -2.26 4.2
5.2 -0.86 1.6
4.9 -1.78 3.3
2.7 -0.86 1.6
5.3 -2.30
3
2.4 -0.74 2.1
1.3 -0.14 0.4
0.7
0.08
0.5
0.5
0.05
0.3
0.4 -0.11 0.6
2-0.17 1.7
2.8 -1.48 1.5
2.4
3.21
3
20
-9.77
17
24
2.12
17
24
-1.10
24
7.7
2.47
6.8
6.3
5.21
4.6
4.9
3.40
3
24
14.71
13
8.2 19.24
17
11
27.16
24
5.9 -0.74 5.6
10
1.39
10
20
0.63
10

190

Table A.5 The best fit systematic errors for the best fit point in the two-flavourεµτ − ετ τ fit. The systematic errors shown here are related to theneutrino flux. The final column shows the estimated 1σ uncertainty
and the penultimate column shows the best fit j .
SampleFlux normalisation

Eν < 1Eν > 1(νµ + ν̄µ )/(νe + ν̄e )ν̄e /νeν̄µ /νµUp/down ratio

Horizontal/vertical ratio

K/π ratio in flux calculation
Neutrino path length
Sample-by-sample
Matter Effects< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
PC< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeVPC

FC Multi-GeV
PC + Stopping UP-µe-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likeFit Value [%]

σ [%]

14.36
6.22
-0.46
-2.02
2.35
2.57
3.69
-1.24
0.07
2.42
-2.18
-0.01
-0.03
-0.10
-0.07
-0.05
-0.16
-0.06
-0.02
-0.04
-0.02
-0.03
-0.02
-0.02
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
-8.61
-0.16
-5.80
-1.57
-0.71

25
15
2
3
5
5
5
8
2
6
15
0.1
0.3
1.1
0.8
0.5
1.7
0.7
0.2
0.4
0.2
0.3
0.2
0.2
0.1
0.1
0.3
1.4
1.9
1.4
3.2
2.3
1.4
1.3
2.8
1.5
1.7
10
5
5
5
6.8

191

Table A.6 The best fit systematic errors for the best fit point in the two-flavourεµτ − ετ τ fit. The systematic errors shown here are related to theneutrino interaction. The final column shows the estimated 1σ
uncertainty and the penultimate column shows the best fit j .

SampleMA in QE
Single π production; Axial coupling
Single π production; CA5
Single π production; Background
CCQE cross section
CCQE ν̄/ν ratio
CCQE µ/e ratio
DIS cross section
DIS model comparisons
DIS Q2 distribution (high W)
DIS Q2 distribution (low W)
Coherent π production
NC/CCCC ντ cross section
Single π production; π 0 /π ± ratio
Single π production; ν̄i /νi (i = e; µ)NC fraction from hadron simulation
π ± decay uncertainty

Meson exchange current∆m221 [139]sin2 (θ12 ) [139]sin2 (θ13 ) [139]Fit Value [%] σ [%]e-like 0-decayµ-like 0-decay
e-like 1-decayµ-like 1-decayµ-like 2-decay

-1.45
-4.60
-3.14
-9.34
6.36
8.61
2.75
-1.74
2.92
6.94
-5.94
-11.91
14.50
3.11-23.68-11.19
-2.28
-0.18
-0.25
-1.26
-0.28
-1.75
-1.01
-0.00
0.29
0.68

10
10
10
10
10
10
10
5
10
10
10
100
20
25
40
10
10
0.6
0.8
4.1
0.9
5.7
10
2.4
4.6
5.4

192

Table A.7 The best fit systematic errors for the best fit point in the two-flavourεµτ − ετ τ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-I and SK-II.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-I
Fit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

-0.01
0.03
-0.12
3.28
-17.11
2.15
0.01
0.06
0.01
0.03
0.08
0.02
3.54
3.75
-0.77
0.54
0.16
0.09
0.16
0.87
0.40
0.82
1.06
0.73
0.96
-0.05
-0.04
-0.04
-0.04
0.39
0.08
0.82
0.36
-5.93
1.44
0.26
-0.10
-0.07
-0.01
0.08
0.36
7.27
12.02
-3.41
-12.47
1.09
1.51
1.55
2.69
2.35
2.02
1.26
-3.41
-1.95

SK-II
Fit
σ

0.2
0.01
0.2
2.4 -3.45 4.8
0.6
0.07
0.5
7
-6.37 9.4
23
-2.73
13
46
-4.64
19
0.1
0.09
0.4
0.4
0.09
0.4
0.1
0.07
0.3
0.2
0.15
0.7
0.5
0.00
0.2
0.1
0.00
0.3
13
-4.15
38
12
3.53
11
2
-0.03
2
2.3 -1.06 1.3
0.7 -1.88 2.3
0.4 -1.39 1.7
0.7 -0.57 0.7
3.7 -2.13 2.6
1.7 -1.39 1.7
3.5 -3.11 3.8
4.5 -6.70 8.2
3.1 -1.55 1.9
4.1 -0.65 0.8
0.23 0.25 0.66
0.18 0.19
0.5
0.19 0.09 0.24
0.19 0.10 0.26
3.1
3.78
6
0.66 1.57
2.5
6.5
6.11
9.7
2.9
2.46
3.9
6
-0.99 3.8
3.3
1.14
2.8
0.6
0.24
0.6
0.7 -0.10 0.7
0.5 -0.07 0.5
0.4 -0.01 0.6
0.9
0.16
1.3
1.5
0.78
2.3
3.4 -4.84 4.4
16
-2.47
21
18
-3.45
14
18 -15.85 14
7.2
6.86
7.9
9
6.75
10
9.2
9.46
14
16
7.43
11
14
10.81
16
12
6.62
9.8
5.6 -2.71 4.4
10
-0.99
10
20
20.41
50

193

Table A.8 The best fit systematic errors for the best fit point in the two-flavourεµτ − ετ τ fit. The systematic errors shown here are related to thedetector performance, event selection and reconstruction. The ”σ”
column shows the estimated 1σ uncertainty and the ”Fit” column
shows the best fit j . Uncertainties are shown for SK-III and SK-IV.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-IIIFit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

0.08
-0.01
-0.14
-15.03-0.44-24.27
0.14
0.14
0.11
0.51
-0.00
-0.00
-0.86
0.71
0.25
0.82
1.08
0.47
0.22
0.47
0.36
0.47
0.93
0.39
0.75
-0.06
-0.04
-0.07
-0.07
3.32
1.82
1.71
0.94
-4.75
1.37
0.74
0.16
0.11
0.03
0.93
-1.02
2.80
-3.42
1.51
0.06
0.48
0.86
0.67
3.28
1.12
1.50
1.56
0.75
2.76

SK-IV
Fit
σ

0.8
0.73
1.3
0.5 -0.78
1
0.9
0.00 0.02
29-1.24 8.5
12
-1.84 6.8
87 -32.57 40
0.5 -0.01 0.02
0.5 -0.01 0.02
0.4 -0.04 0.09
1.8 -0.24 0.49
0.2 -0.00 0.02
0.7 -0.00 0.08
27
2.65
18
11
0.23
12
2
-1.39
2
2.3 -0.87 1.6
3
-1.62
3
1.3 -0.54
1
0.6 -0.32 0.6
1.3 -0.54
11-0.65 1.2
1.3 -1.03 1.9
2.6 -1.25 2.3
1.1 -0.49 0.9
2.1 -1.30 2.4
0.26 0.11 0.28
0.19 0.08 0.22
0.31 0.13 0.35
0.3
0.13 0.35
9.5 -1.90 4.2
5.2 -0.72 1.6
4.9 -1.49 3.3
2.7 -0.72 1.6
5.3 -1.94
3
2.4 -0.70 2.1
1.3 -0.13 0.4
0.7
0.08
0.5
0.5
0.05
0.3
0.4 -0.12 0.6
2-0.25 1.7
2.8 -1.52 1.5
2.4
3.17
3
20
-8.46
17
24
2.15
17
24
-1.14
24
7.7
2.58
6.8
6.3
5.08
4.6
4.9
3.32
3
24
14.37
13
8.2 18.79
17
11
26.53
24
5.9 -0.83 5.6
10
1.14
10
20
0.76
10

194

Table A.9 The best fit systematic errors for the best fit point in the εee −εeτ −ετ τfit. The systematic errors shown here are related to the neutrino
flux. The final column shows the estimated 1σ uncertainty and thepenultimate column shows the best fit j .
SampleFlux normalisation

Eν < 1Eν > 1(νµ + ν̄µ )/(νe + ν̄e )ν̄e /νeν̄µ /νµUp/down ratio

Horizontal/vertical ratio

K/π ratio in flux calculation
Neutrino path length
Sample-by-sample
Matter Effects< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
PC< 400 M eV
< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeVPC

FC Multi-GeV
PC + Stopping UP-µe-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like0-decay µ-likee-likeµ-like0-decay µ-likee-likeµ-likee-likeµ-likee-likeµ-likeFit Value [%]

σ [%]

13.55
6.83
0.04
-1.11
1.96
1.68
3.39
-1.61
0.22
3.01
-3.57
-0.02
-0.07
-0.26
-0.19
-0.12
-0.40
-0.17
-0.05
-0.10
-0.05
-0.07
-0.05
-0.05
0.02
0.02
0.05
0.24
0.32
0.24
0.54
0.39
0.24
0.22
0.48
0.25
0.29
-11.16
-0.82
-6.37
-0.25
0.24

25
15
2
3
5
5
5
8
2
6
15
0.1
0.3
1.1
0.8
0.5
1.7
0.7
0.2
0.4
0.2
0.3
0.2
0.2
0.1
0.1
0.3
1.4
1.9
1.4
3.2
2.3
1.4
1.3
2.8
1.5
1.7
10
5
5
5
6.8

195

Table A.10 The best fit systematic errors for the best fit point in the εee − εeτ −ετ τ fit. The systematic errors shown here are related to the neutrino
interaction. The final column shows the estimated 1σ uncertainty
and the penultimate column shows the best fit j .

SampleMA in QE
Single π production; Axial coupling
Single π production; CA5
Single π production; Background
CCQE cross section
CCQE ν̄/ν ratio
CCQE µ/e ratio
DIS cross section
DIS model comparisons
DIS Q2 distribution (high W)
DIS Q2 distribution (low W)
Coherent π production
NC/CCCC ντ cross section
Single π production; π 0 /π ± ratio
Single π production; ν̄i /νi (i = e; µ)NC fraction from hadron simulation
π ± decay uncertainty

Meson exchange current∆m221 [139]sin2 (θ12 ) [139]sin2 (θ13 ) [139]Fit Value [%] σ [%]e-like 0-decayµ-like 0-decay
e-like 1-decayµ-like 1-decayµ-like 2-decay

-0.56
-4.42
-3.04
-8.73
6.41
9.10
0.64
-2.06
3.00
8.46
-5.79
-8.09
12.60
-12.22-20.88-11.22
-0.79
-0.18
-0.24
-1.25
-0.27
-1.73
-1.61
0.02
0.32
0.16

10
10
10
10
10
10
10
5
10
10
10
100
20
25
40
10
10
0.6
0.8
4.1
0.9
5.7
10
2.4
4.6
5.4

196

Table A.11 The best fit systematic errors for the best fit point in the εee − εeτ −ετ τ fit. The systematic errors shown here are related to the detector
performance, event selection and reconstruction. The ”σ” column
shows the estimated 1σ uncertainty and the ”Fit” column shows thebest fit j . Uncertainties are shown for SK-I and SK-II.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-I
Fit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

-0.01
0.01
-0.10
3.67
-16.27
6.17
0.01
0.04
0.01
0.02
0.07
0.01
3.58
3.78
-0.83
0.44
0.14
0.08
0.14
0.72
0.33
0.68
0.87
0.60
0.79
-0.04
-0.03
-0.03
-0.03
0.23
0.05
0.48
0.22
-6.52
1.39
0.25
-0.09
-0.07
0.00
0.05
0.41
7.45
10.52
-3.50
-12.14
0.97
1.71
1.75
3.04
2.66
2.28
1.30
-3.29
-1.78

SK-II
Fit
σ

0.2
0.01
0.2
2.4 -3.46 4.8
0.6
0.08
0.5
7
-5.80 9.4
23
-2.47
13
46
-3.43
19
0.1
0.07
0.4
0.4
0.07
0.4
0.1
0.05
0.3
0.2
0.12
0.7
0.5 -0.00 0.2
0.1 -0.00 0.3
13
-5.06
38
12
3.72
11
2
-0.10
2
2.3 -1.09 1.3
0.7 -1.93 2.3
0.4 -1.42 1.7
0.7 -0.59 0.7
3.7 -2.18 2.6
1.7 -1.42 1.7
3.5 -3.18 3.8
4.5 -6.87 8.2
3.1 -1.59 1.9
4.1 -0.67 0.8
0.23 0.23 0.66
0.18 0.17
0.5
0.19 0.08 0.24
0.19 0.09 0.26
3.1
3.46
6
0.66 1.44
2.5
6.5
5.60
9.7
2.9
2.25
3.9
6
-1.25 3.8
3.3
1.11
2.8
0.6
0.24
0.6
0.7 -0.09 0.7
0.5 -0.07 0.5
0.4 -0.01 0.6
0.9
0.13
1.3
1.5
0.80
2.3
3.4 -4.76 4.4
16
-2.97
21
18
-3.54
14
18 -15.55 14
7.2
6.99
7.9
9
6.93
10
9.2
9.71
14
16
7.63
11
14
11.10
16
12
6.80
9.8
5.6 -2.68 4.4
10
-0.93
10
20
20.24
50

197

Table A.12 The best fit systematic errors for the best fit point in the εee − εeτ −ετ τ fit. The systematic errors shown here are related to the detector
performance, event selection and reconstruction. The ”σ” column
shows the estimated 1σ uncertainty and the ”Fit” column shows thebest fit j . Uncertainties are shown for SK-III and SK-IV.
SampleFC reduction
PC reduction
FC/PC separation
PC stopping/through-going separation (barrel)
PC stopping/through-going separation (bottom)
PC stopping/through-going separation (top)Non-ν background µ − like

Non-ν background e−like

Fiducial Volume
Ring separation

PID 1-ring

PID Multi-ringMulti-ring likelihood selection
Energy calibration
Up/down asymmetry energy calibration
Up-µ reduction
Up-µ stopping/through-going separation
Up-µ stopping energy cut
Up-µ through-going path cut
Up-µ Through-going showering separation
Up-µ stopping BG subtraction
Up-µ non-showering BG subtraction
Up-µ showering BG subtraction
νe /ν̄e separation
Sub-GeV 1-ring π 0 selection

Sub-GeV 2-ring π 0
Decay-e tagging
Solar activity

SK-IIIFit
σ

Sub-GeV
Multi-GeV
Sub-GeV 1-ring 0-decay
PC
Sub-GeV
Multi-GeV
Multi-GeV 1-ring e-like
Multi-GeV Multi-ring e-like< 400 M eV
< 400 M eV
> 400 M eV
> 400 M eV
Multi-GeV
Multi-GeV
Multi-ring Sub-GeV
Multi-ring Sub-GeV
Multi-ring Multi-GeV
Multi-ring Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
Sub-GeV
Sub-GeV
Multi-GeV
Multi-GeV
e-likeStopping
Through-going

100 < Pe < 250 MeV/c
250 < Pe < 400 MeV/c
400 < Pe < 630 MeV/c
630 < Pe < 1000 MeV/c1000 < Pe < 1330 MeV/ce-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-likee-likeµ-like

0.07
-0.01
-0.13
-14.21-0.34-16.64
0.11
0.11
0.09
0.41
-0.00
-0.01
-0.98
0.73
0.22
0.80
1.05
0.45
0.21
0.45
0.35
0.45
0.91
0.38
0.73
-0.05
-0.04
-0.06
-0.06
3.47
1.90
1.79
0.99
-5.03
1.36
0.74
0.16
0.11
0.03
0.95
-0.99
2.87
-4.56
1.45
0.26
0.41
0.97
0.76
3.70
1.26
1.69
1.62
0.86
2.70

SK-IV
Fit
σ

0.8
0.70
1.3
0.5 -0.78
1
0.9
0.00 0.02
29-0.53 8.5
12
-1.59 6.8
87 -27.05 40
0.5 -0.01 0.02
0.5 -0.01 0.02
0.4 -0.05 0.09
1.8 -0.27 0.49
0.2 -0.00 0.02
0.7 -0.00 0.08
27
2.57
18
11
0.42
12
2
-1.48
2
2.3 -0.95 1.6
3
-1.78
3
1.3 -0.59
1
0.6 -0.36 0.6
1.3 -0.59
11-0.71 1.2
1.3 -1.13 1.9
2.6 -1.37 2.3
1.1 -0.53 0.9
2.1 -1.42 2.4
0.26 0.12 0.28
0.19 0.10 0.22
0.31 0.16 0.35
0.3
0.16 0.35
9.5 -2.25 4.2
5.2 -0.86 1.6
4.9 -1.77 3.3
2.7 -0.86 1.6
5.3 -2.35
3
2.4 -0.74 2.1
1.3 -0.14 0.4
0.7
0.09
0.5
0.5
0.05
0.3
0.4 -0.11 0.6
2-0.15 1.7
2.8 -1.49 1.5
2.4
3.20
3
20
-9.96
17
24
2.11
17
24
-0.85
24
7.7
2.46
6.8
6.3
5.24
4.6
4.9
3.42
3
24
14.82
13
8.2 19.38
17
11
27.36
24
5.9 -0.73 5.6
10
1.35
10
20
0.65
10

198

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