A model independent determination of theπ 0 background in Super-Kamiokande in the T2K
νe appearance measurement.
Lauren Helen Victoria Anthony
Department of Physics
Oliver Lodge Laboratory
University Of Liverpool
A Thesis submitted for the degree ofDoctor of Philosophy
February 2020

To my friends and family in Toyama city,
whom I miss dearly
私が心から愛おしく思う富山市の友人や家族へ

Abstract
T2K is a long-baseline neutrino oscillation experiment which was designed to study
neutrino oscillation through the appearance of νe in a νµ beam, and measure the θ13
mixing angle. The νµ beam originates from an accelerator complex (JPARC) in Tokai,
East Japan. The far detector, Super-Kamiokande (Super-K) is a large scale Water
Cherenkov (WC) detector, located 1000 m underground in Kamioka, Weat Japan, andsits approximately 295 km from the neutrino beam source.
This thesis discusses the detector calibration techniques employed by Super-K alongside an unique physics analysis. Firstly the calibration technique is reported, with afocus on the derivation of water scattering and absorption coefficients and the improvements made to the existing analysis strategies. Also presented is a detailed report ofthe development and commissioning of a new light injection system, designed and built
in the UK, which was installed inside Super-K during the 2018 refurbishment period.
The analysis presented focuses on the development of a data driven prediction of theneutral current single π 0 (NC1π 0 ) background contribution to the νe oscillation analysis.
Next to the intrinsic νe component of the beam, NC1π 0 events contribute significantly
to the background contamination of the P (νµ −→ νe ) appearance signal.
The method presented uses a newly constructed NCπ 0 "hybrid" control sample,
used to calculate the 2-ring NCπ 0 selection and rejection efficiencies. The sample isconstructed using a combination of Super-K MC/data and T2K-SK beam MC/datafrom T2K Runs 1-9. The new method yields results competitive with the current T2K
prediction, and provides significantly reduced uncertainties. The new method predicts
the number of NC1π 0 related background events to be: N ν1R = 1.65 ± 0.23 events forν mode and N ν̄1R = 0.74 ± 0.16 events for ν̄ mode, from a T2K-data sample of 53
and 23 2-ring π 0 events respectively. This thesis also discusses the potential of applying
this method to a larger detector such as Hyper-Kamiokande (Hyper-K), which will be
the next generation WC detector with 8.4 times the fiducial volume of Super-K and anincrease in the provided protons on target (POT) by a factor of 10.

[a\Acknowledgements
I would like to begin by thanking my supervisor, Professor Neil McCauley for his support, encouragement and guidance throughout the PhD in both work and personalmatters. I know that I have been quite stubborn at times. I would especially like toexpress my deepest gratitude for the loan of his office in the run up to the end of the PhD.
I would also like to thank the staff at Liverpool University, especially those in theelectronics group and the workshop. Without their knowledge, skills and years of invaluable experience, our physics achievements wouldn’t be possible. I would especiallylike to thank my good friend George Simm who looked after me during my time spentpottering around the workshop. The four year supply of tea and Turkish delight was
highly appreciated, as was the time spent listening to me and occasionally let me win
at darts.
I was lucky enough to begin this journey with some friends from my undergraduatedays here in Liverpool, and with some new friends from the other side of the world. I
would like to express my appreciation of my fellow PhD classmates at Liverpool University; Heather, Tabitha, Vin and Adam, it has been a pleasure to take this journeywith you. Especially I would like express my appreciation of Tabitha and Heather for
their unwavering support, motivational pub breaks and nights in with Chinese food. I
could not have got through this and remained so calm without you.
During my LTA at Super-Kamoikande, I made some friends that became family. I
could not have asked for better students to share the experience with. I would like towish the best to, and express my gratitude to the SK-UK and XMASS students that
I shared my time with; Charles Simpson for the Karaoke memories, Alex Mason forbeing so supportive and always being willing to offer his help and advice, Alex Goldsack
for being my northern younger brother, Susanna Molina-Sedgewick for her late nightcompany during my (what seemed like endless) Super-K shifts, and Artur Sztuc for ourlong coffee and lunch breaks in Kenkyuto. I would like to thank Masako Ishikura, Yuko
Fujumura and Scott Locke for their friendship and help when I needed it most. You
guys truly helped me become the best possible version of myself. I would like to express
special thanks to Mitsuhiro "Mi-Chan" Shimada and Pub Pot Still: you were my homefrom home in Toyama city. Finally I would like to express my thanks to the ICRR
group for making me feel so welcome, with special mentions to Hide-san, Kameda-sanand Moriyama-san for your support, guidance and efforts, and your time, especiallyduring the commissioning of the UK calibration hardware.

iii

[a\

Finally I would like to thank my friends and family for their support and encouragement over my academic career, especially to my Dad and for proofreading my thesis,
and to my mother for listening to all my endless problems. I also appreciate her efforts
when trying to understand and explain my PhD and Super-K to her co-workers. To my
Grandmother Doreen and my uncle Martin (and late Granddad Brian), thank you foralways believing that I could do whatever I wanted in life.
I am eternally grateful to my very close friends; Lee Roberts for the motivational
Mexican food, the (almost) decade of unconditional support, and for the great (butharsh) grammatical corrections toward this thesis; Sam Powell for giving me literally
everything I could ever need; I really appreciate your time and patience, especially when
I was writing up - I know I was endlessly annoying; And finally, Nicola Hatchard andLide Vinas of Vines Vixens, for the years of emotional support, dancey dance fun andwine, and gin, and beer...

iv

[a\

Declaration
The work presented in this thesis is the work of the author, except as noted here andwhere the work of others has been cited.
In Chapter 4, the Korean Laser analysis software was originally developed by the
Korean Super-Kamiokande collaborators, and the PMT gain correction tables and plots
used during the authors efforts in updating the analysis were provided by the Super-K
collaboration. The author of thesis developed and adapted the analysis to include thecorrection tables, which had not been done by an analyst previously.
Chapter 6 discusses the development and commissioning of the UK light injection
system, which has been a collaborative effort. The author worked on all aspects ofthe system over the 4 year period of the PhD. The author performed all on-site tasks
which were required by the UK group; including extensive equipment testing; prototype
deployment, and all data taking. The author also lead the on-site installation of thesystem inside the Super-K detector during the refurbishment period, and worked heavily in the commissioning of the electronics, and operating the run control for all datataking periods for the system.
In Chapter 7, the construction of the 2018 primary sample and the analysis of both2018 primary and secondary samples were done by the author and used to develop
a new, model independent NC1π 0 background estimation method for T2K νe oscillation analysis however, the construction of the 2018 secondary sample was performed byThomas Mueller.
Lauren Helen Victoria Anthony

v

[a\

vi

Contents
1 The Neutrino
1.1

1

A brief history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Neutrinos within the Standard Model . . . . . . . . . . . . . . .

2

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

4

1.2.1

Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.3

Experimental Measurements . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.4

Current Status of Neutrino Physics . . . . . . . . . . . . . . . . . . . . .

10

1.4.1

Solar Neutrinos and the parameters ∆m221 and θ21 . . . . . . . .

11

1.4.2

12
14

1.4.4

Atmospheric Neutrinos and the parameters ∆m232 and θ23 . . . .
Reactor Neutrinos and the parameters ∆m221 , θ21 and θ13 . . . .
Accelerator neutrinos and the parameters ∆m232 and θ23 . . . . .

1.4.5

Supernova Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.4.6

Measurements of δCP and neutrino mass hierarchy . . . . . . . .

18

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

1.2

1.4.3

1.5

2 The Kamiokande Family

16

21

2.1

Kamioka Observatory: A Brief History . . . . . . . . . . . . . . . . . . .

21

2.2

The Super-Kamiokande Experiment . . . . . . . . . . . . . . . . . . . .

24

2.2.1

Cherenkov Light . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2.2.2

The Detector Structure . . . . . . . . . . . . . . . . . . . . . . .

27

2.2.3

Optical Separation of the Inner and Outer detector . . . . . . . .

29

2.2.4

DAQ and Electronics . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.2.5

Water Filtration System . . . . . . . . . . . . . . . . . . . . . . .

30

2.2.6

Super-K detector simulation . . . . . . . . . . . . . . . . . . . . .

31

2.3

2.4

The T2K Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.3.1

The Neutrino Beamline . . . . . . . . . . . . . . . . . . . . . . .

32

2.3.2

The Near Detector Complex . . . . . . . . . . . . . . . . . . . . .

35

2.3.3

The On-Axis detector: INGRID . . . . . . . . . . . . . . . . . . .

35

2.3.4

The Off-Axis detector: ND280. . . . . . . . . . . . . . . . . . .

36

The Hyper-Kamiokande Experiment . . . . . . . . . . . . . . . . . . . .

38

2.4.1

39

Hyper-K as a far detector . . . . . . . . . . . . . . . . . . . . . .
vii

CONTENTS

[a\

2.4.2
2.5

Physics Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

3 Calibration at Super-Kamiokande
3.1

3.2

3.3

3.4

43

Photon Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.1.1

Rayleigh and Mie Scattering . . . . . . . . . . . . . . . . . . . . .

44

3.1.2

Scattering and Absorption Measurements . . . . . . . . . . . . .

44

PMT Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

3.2.1

PMT High Voltage setting . . . . . . . . . . . . . . . . . . . . . .

47

3.2.2

Relative Gain Calibration . . . . . . . . . . . . . . . . . . . . . .

47

3.2.3

Absolute Gain Calibration . . . . . . . . . . . . . . . . . . . . . .

48

Energy Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.3.1

LINAC Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.3.2

DT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4 The Super-K Laser Calibration System

53

4.1

The Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

4.2

The Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4.3

Online Data Taking and Monitoring . . . . . . . . . . . . . . . . . . . .

57

4.3.1

Auto-calibration Process . . . . . . . . . . . . . . . . . . . . . . .

57

4.3.2

Super-K Laser System Monitoring . . . . . . . . . . . . . . . . .

57

Derivation of Absorption and Scattering Coefficients . . . . . . . . . . .

59

4.4.1

Time variation of water coefficients . . . . . . . . . . . . . . . . .

62

4.4.2

Implementation of Number of Hit Correction . . . . . . . . . . .

64

4.4.3

Results and Conclusion . . . . . . . . . . . . . . . . . . . . . . .

66

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

4.4

4.5

5 The Super-Kamiokande Refurbishment

71

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

5.2

The Motivation : SK-Gd . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

5.3

Preparation : Gadolinium Compatibilityty Testing . . . . . . . . . . . .

73

5.3.1

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

5.3.2

Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .

74

5.4

General Refurbishment Tasks . . . . . . . . . . . . . . . . . . . . . . . .

74

5.5

Calibration Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.5.1

PMT Response . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.5.2

Super-K Water Laser Hardware Replacement . . . . . . . . . . .

78

5.5.3

Installation of UK light injection system . . . . . . . . . . . . . .

80

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

5.6

viii

CONTENTS[a\

6 The UK Light Injection System

81

6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

6.2

The Light Source and Electronics . . . . . . . . . . . . . . . . . . . . . .

82

6.2.1

System stability studies . . . . . . . . . . . . . . . . . . . . . . .

86

6.3

Prototype deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

6.4

The Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

6.4.1

The Optical Fibres . . . . . . . . . . . . . . . . . . . . . . . . . .

87

6.4.2

The Bare fibre . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

6.4.3

The Diffuser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

6.4.4

The Collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

6.4.5

The Optics Plate . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

Commissioning of UK System . . . . . . . . . . . . . . . . . . . . . . . .

91

6.5.1

On-site preparation . . . . . . . . . . . . . . . . . . . . . . . . . .

91

6.5.2

Installation procedure . . . . . . . . . . . . . . . . . . . . . . . .

95

6.5.3

First data using UK fibres and optics . . . . . . . . . . . . . . . .

98

6.5.4

Installation of the electronics . . . . . . . . . . . . . . . . . . . .

98

6.5.5

Final Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.5

6.6

Future Hyper-Kamiokande calibration system . . . . . . . . . . . . . . . 102

6.7

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7 A Model Independent Measurement of the NC1π 0 rate at Super-K

105

7.1

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.2

Neutrino Interactions at T2K . . . . . . . . . . . . . . . . . . . . . . . . 106

7.3

7.4

7.5

7.2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2.2

Elastic and Quasi-Elastic Interactions . . . . . . . . . . . . . . . 108

7.2.3

Deep-Inelastic Scattering

7.2.4

Single Pion Production . . . . . . . . . . . . . . . . . . . . . . . . 108

7.2.5

NC1π 0 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.2.6

Final State Interactions . . . . . . . . . . . . . . . . . . . . . . . 112

7.2.7

NC1π 0 Measurements . . . . . . . . . . . . . . . . . . . . . . . . 113

7.2.8

Characteristics of the NC1π 0 background at Super-K . . . . . . . 116. . . . . . . . . . . . . . . . . . . . . . 108

Estimation of π 0 rejection efficiency at Super-K . . . . . . . . . . . . . . 118
7.3.1

The Hybrid-π 0 control sample . . . . . . . . . . . . . . . . . . . . 118

7.3.2

Properties of the Hybrid π 0 sample . . . . . . . . . . . . . . . . . 121

7.3.3

The Hybrid-π 0 sample construction procedure . . . . . . . . . . . 122

The 2-ring NC1π 0 sample . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4.1

Selection stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.4.2

Selection Parameter Distributions . . . . . . . . . . . . . . . . . . 131

7.4.3

Remaining efficiencies of the 2-ring NC-hybrid-π 0 samples . . . . 139

Comparison of the 2013 and 2018 two ring NC-hybrid-π 0 samples . . . . 142
ix

CONTENTS

[a\

7.6

Estimating the single-ring contamination of the NC1π 0 using the NChybrid-π 0 sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.7

7.6.1

Benefits of a model independent measurement . . . . . . . . . . . 147

7.6.2

The νe Appearance Selection . . . . . . . . . . . . . . . . . . . . 147

7.6.3

Remaining efficiencies of νe appearance background selection . . 154

NC1π 0 Prediction in T2K-SK MC and Data . . . . . . . . . . . . . . . . 156
7.7.1

Predicted number of events and NC1π0 sample purity . . . . . . 156

7.7.2

Comparison Between Model Independent and Official T2K Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

7.8

Background Estimation for Hyper-Kamiokande . . . . . . . . . . . . . . 162

7.9

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8 Conclusions

167

8.1

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

8.2

Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

8.3

Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Bibliography

172xList of Figures
1.1

The standard model of particle physics. . . . . . . . . . . . . . . . . .

1.2

The normal and inverted mass hierarchies. The normal hierarchy is shown3

on the left, and can exist in nature if mν3 > mν2 > mν1 . Alternatively
the inverted hierarchy shown on the right exists in the case that mν2 >mν1 > mν3 [14].

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

9

1.3

Summary of neutrino sources and the range of energies covered [15]. . .

10

1.4

Muon neutrino and tau neutrino flux vs. electron neutrino flux. The
bands represent CC (charged current), NC (neutral current) and ES (elastic scattering) flux measurements. The dashed line represents the total
8 B solar neutrino model as predicted by the SSM [21].

1.5. . . . . . . . . .

12

Results from Super-K: The ratio of FC data events to FC MC events vs.
reconstructed L/Eν . The points show the ratio of observed data to MC
expectation under the no-oscillation condition. The dashed lines show
the expected shape for νµ ↔ ντ oscillation at ∆m2 = 2.2 × 10−3 eV2 [23]

1.6

13

Results from Super-K: Zenith angle distributions of µ-like and e-likeevents for both sub-GeV and multi-GeV data sets. The hatched region
represents the MC expectation for no oscillation normalised to data livetime with statistical errors. The bold line is the best fit expected for νµ↔ ντ oscillations. [23] . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

Results from KamLAND showing the ratio of the observed ν̄ spectrum
to the expectation for no oscillation vs L/E [24] . . . . . . . . . . . . . .

1.8

14

15

Results from Daya-Bay. The upper plot displays the background subtracted positron energy observed at the far detector site and the derived
expectation at the near detector site both with and without oscillation.
The lower plot displays the ratio of the spectra at both sites to the nooscillation case [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.9

15

The 90% confidence level region for |∆m232 | and sin2 θ23 phase space displayed by measurements from a number of experiments. [33]. . . . . . .
xi

16

LIST OF FIGURES[a\

1.10 Time sequence of events from SN-1987a centred about 07:35:35 UT 23rd
February 1987. The dashed lines represent muon events in units of p.e
and the solid lines represent the low energy electron events in units of hit
PMTs [35] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.11 The 90% confidence interval of the δCP measurement for normal and inverted hierarchies. The values were obtained by joint analysis of neutrino
and antineutrino oscillations in appearance and disappearance channels
at T2K [38].

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

18

2.1

Schematic of the Kamiokande detector. . . . . . . . . . . . . . . . . . . .

22

2.2

Schematic of Super-Kamiokande, showing the detector structure, tank
top electronics huts and control room [47].

2.3. . . . . . . . . . . . . . . .

23

Image of Super-Kamiokande in the water filling stage during the fullreconstruction phase in 2006. . . . . . . . . . . . . . . . . . . . . . . . .

24

2.4

Diagram displaying Cherenkov light cone [48].

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

25

2.5

Example of electron ring (left) and muon ring (right) as seen in Super-K.

26

2.6

Schematic and photograph of the 20 inch Hamamatsu PMT used in the
ID.

2.7

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

27

Photographs of the 8 inch Hamamatsu PMTs with the waveshifting plates
that are used in the OD.

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

28

2.8

Schematic of the Super-K supermodule structure [47]. . . . . . . . . . .

28

2.9

Schematic of the T2K experiment. The neutrino beam is produced at
J-PARC to the far detector, Super-Kamiokande.

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

2.10 Schematic of primary and secondary beamline at T2K.
2.11 Simplified diagram of the T2K experiment [56] .

31. . . . . . . . .

32. . . . . . . . . . . . .

33

2.12 Plot of the predicted flux at different off-axis angles [58].

. . . . . . . .

34

2.13 Predicted neutrino and anti-neutrino flux at ND280 and Super-K [64]. .

35

2.14 Schematic of INGRID on-axis detector and individual INGRID modules[55]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.15 Schematic of ND280.

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

2.16 Schematic of the P0D detector [65].

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

36
37
38

2.17 Illustration of first single Hyper-Kamiokande tank in Japan [67].

. . . .

39

2.18 Prediction of the neutrino and anti-neutrino flux at Hyper-K [67].

. . .

40

2.19 Comparison of past, current and future nucleon decay experiments. [67].

40

3.1

Diagram displaying Rayleigh and Mie scattering [69]. Rayleigh scattering
consists of both forward and backwards going symmetric scattering in
relation to the direction of incoming light whilst Mie scattering consistsof symmetric backwards going, and asymmetric forwards going scattering. 44
xii

LIST OF FIGURES

[a\

3.2

Current optical calibration at Super-K. The five horizontal light injection
points are denoted by B1-B5 which are not used in the analysis. The
labels B1 to B5 also is used to denote the 5 regions that the barrel is split
into during this analysis. Schematic adapted from [47] . . . . . . . . . .

3.3

45

Plot of typical fitted water coefficient functions used in SK-MC. Datataken in 2009. This plot shows the points for absorption, asymmetricscattering and symmetric scattering. [51]. . . . . . . . . . . . . . . . .

46

3.4

High Voltage calibration using a scintillator ball [51] . . . . . . . . . . .

47

3.5

Relative gain calibration using timing calibration system [51] . . . . . .

48

3.6

Ni ball with contained 252Cf source [51]. . . . . . . . . . . . . . . . . .

49

3.7

Schematic of LINAC calibration [71] . . . . . . . . . . . . . . . . . . . .

50

3.8

Energy reconstruction of events generated by the LINAC [71] . . . . . .

51

3.9

DT calibration [70]

51

4.1

Cartoon of injector positions, spacing and fibre entry points to the detector.

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

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

54

4.2

The light tight optical switch box has one input fibre from the. . . . . .

55

4.3

Injector flanges, fully assembled injector and face on view of mounted
hardware. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4.4

Full view of injector mounting in detector barrel wall.

56

4.5

Example of day by day monitoring including the total charge collected. . . . . . . . . .

in Super-K and the monitor PMT data. . . . . . . . . . . . . . . . . . .
4.6

58

Detector divided into five barrel positions. Light is injected vertically andthe number of hits and charge are measured at each of the five positions,for each wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7

59

Timing distribution histograms for light injected from the NT (TOP) injector. Histograms are the hits/event vs. corrected time of flight withing
the scattered hit region. In order left to right of the eight images, NT,
B1 - B5 and finally the bottom right two are measured position combined
histograms of charge/event vs. corrected time of flight for all PMTs andhits/event vs. corrected time of flight in the scattered hit region. Specificexample is for 337 nm laser.

4.8. . . . . . . . . . . . . . . . . . . . . . . .

60

The left hand image is the original N/Q histogram before the dark hits
are subtracted from the signal region. The right hand image is the same
N/Q histogram with dark hits subtracted and then re-binned into a 200
bin histogram in preparation for comparing to the water laser MC. The
scattered hit region can be seen to be enclosed between the two blacklines.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii

61

LIST OF FIGURES

[a\

4.9

Data MC comparison with data in black and MC in red. It’s clear thatthe reflected peak at the NT position is not fit well with the MC. From
top to bottom the positions are NT, B1 - B5. . . . . . . . . . . . . . . .

62

4.10 Scattering and absorption coefficients for all five wavelengths before analysis improvements.

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

63

4.11 Symmetric scattering coefficient for 337 nm and 445 nm wavelengths,with RMS/mean time variation.

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

64

4.12 official plots of PMT gain increase for each PMT batch as a function ofSuper-K run number [72]. . . . . . . . . . . . . . . . . . . . . . . . . . .

65

4.13 official plots of PMT production year vs. Z position in the detector [72].

66

4.14 Gain corrected Symmetric scattering coefficient for 337 nm and 445 nm
wavelengths, with RMS/mean time variation for the SK-IV period (2009- 2018). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

4.15 Gain corrected scattering and absorption coefficients for all five wavelengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1

Diagram of neutron tagging with gadolinium (left), and capture efficiency
as a function of Gd concentration (right) [73].

5.2

67

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

72

Absorption and transmittance spectra for soak tests of the PMMA diffuser sample. The pure water tests correspond to panels a) and b) andGd solution samples correspond to panels c) and d). . . . . . . . . . . .

5.3

75

Image from the refurbishment of myself and Artur Sztuc taking PMT
dynode direction measurements. Photograph taken by M.Nakahata.

. .

77

. . . . . . .

78

5.4

Image of the replaced injectors and the alignment method.

6.1

Full system architecture including the electronics which sit outside thetank and the optical connections from the electronics to the opticalsources at positions B1 - B5.

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

6.2

Circuit diagram of pulser board circuit layout.

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

6.3

The motherboard can accommodate four pulser boards per side. The
pulser board here has three 200 µm core fibres coupled to the LED.

82
83

. .

84

6.4

Pre potting of monitor PMT with all 19 channels connected.

. . . . . .

85

6.5

Photodiode monitor board. . . . . . . . . . . . . . . . . . . . . . . . . .

85

6.6

Prototype deployment setup. The deployment was performed inside alight tight tent. The right image shows the deployment method andposition inside the detector.

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

86

6.7

Prototype injector plate, diffuser and collimator. . . . . . . . . . . . . .

86

6.8

Event display of collimator data after one day of submersion in Super-K[77]. The hit pattern is expected to be an uniform circle.

6.9. . . . . . . .

87

Diffuser enclosures and diffuser pieces before assembly . . . . . . . . . .

88

xiv

LIST OF FIGURES[a\

6.10 Schematic of collimator including the GRIN lens mount and mounting
sleeve [78].

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

89

6.11 Technical drawings of the optics plate provided by Warwick University.

90

6.12 Image displaying the stainless steel "spacer" piece which extends theheight of the PMT structure rail.

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

91

6.13 Photographs of fibre reeling procedure. The left image shows the required
length of fibre laid out and secured together with chemical resistant cableties. The right image shows the length of bundled fibre wound onto thesmaller black reel and the remaining length stored individually on theoriginal reels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

6.14 Image displaying the signal testing of one of the installed collimators.
The top image shows a clear signal. The bottom image confirms the
expected narrow circular beam spot. . . . . . . . . . . . . . . . . . . . .

93

6.15 Image displaying the signal testing of one of the installed diffuser coupledwith the custom built LED fibre tester. The upper images displays adiffuser that passes the pressure testing. The lower image displays adiffuser that failed. It can be seen that there is a non-uniform light
output across the diffuser, which is strongest around the outer edge. . .

94

6.16 The left image displays the injector plate being assembled whilst thecentral image shows the completed assembly. The right image shows the
stenciled black sheet sitting on the injector plate.

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

94

6.17 Process of feeding the fibre reels through the calibration port into SK totheir storage inside the PMT structure.

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

95

6.18 Attachment of the plate to the detector structure in the ID. . . . . . . .

96

6.19 Final attachment and re-attaching the black sheet. . . . . . . . . . . . .

96

6.20 The full fibre connection process, beginning on the left with the connection itself and on the right, the potting and attachment to the inside of
the PMT structure between the ID and OD.

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

97

6.21 The final confirmation of the signal along the whole length of fibre including fibre connection. Left to right shows the illuminated bare fibre,
collimator and diffuser.

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

98

6.22 Event displays for position B1. From left to right: Bare fibre, collimator,
diffuser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

6.23 Map of routed cables after integration of UK electronics with Super-K
trigger and DAQ systems. Also shown is the layout of the electronics
huts in the experimental area on the top of the tank.

. . . . . . . . . . 100

6.24 Signal form to trigger board channels 8 and 16. A, B, C and D are continuous signals which select the channel to trigger. Channel is triggered
when NIM trigger signal comes along. . . . . . . . . . . . . . . . . . . . 100
xv

LIST OF FIGURES[a\

6.25 Occupancy event displays for position B2. From left to right: collimator,bare fibre, diffuser [78].
7.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Total neutrino and anti-neutrino CC cross sections divided by the neutrino energy as a function of energy for various interaction modes as predicted by NUANCE [80]. The interaction modes include; Quasi-Elastic(QE), Resonant (RES) and Deep-Inelastic Scattering (DIS). Figures from[15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.2

Resonant π 0 production on a proton via delta resonance as shown inEquation 7.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.3

Resonant π 0 production on a neutron via delta resonance as shown inEquation 7.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.4

Coherent π 0 production as shown in Equation 7.13.

7.5

Diagram of the π 0 −→ γ γ decay, where θ is the opening angle between
the gammas.

7.6. . . . . . . . . . . 111. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Feynman diagram displaying charge exchange interaction between a π 0
and a proton, where the π 0 changes into a π + .

. . . . . . . . . . . . . . 112

7.7

The NC1π 0 cross section measurements [15].

. . . . . . . . . . . . . . . 114

7.8

The expected and observed reconstructed π 0 energy measured by the
P0D. The expectation for each sample is normalised to the observed number of events [96].

7.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Schematic showing the two cases of π 0 decay which can lead to misidentification [98].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.10 Event displays of two separate simulated π 0 events which demonstrate
the cases of mis-identification (left) and positive identification (right). . 117
7.11 Schematic drawing showing the construction of the primary hybrid-π 0sample for data (Left) and MC (right).

. . . . . . . . . . . . . . . . . . 119

7.12 Schematic drawing showing the construction of the secondary hybrid-π 0sample for data (Left) and MC (right).

. . . . . . . . . . . . . . . . . . 119

7.13 Momentum distributions of the extracted e-like rings taken from the SK
atmospheric neutrino for data (Left) and MC (right).

. . . . . . . . . . 123

7.14 Momentum distributions of the extracted decay electron rings taken fromthe SK decay electron data for data (Left) and MC (right). . . . . . . . 124
7.15 True momentum distributions of 1st, or high energy (left) and 2nd, or
lower energy, (right) decay gammas from true T2K-MC kinematic. . . . 124
xvi

LIST OF FIGURES[a\

7.16 The schematic describes the T2K-MC neutrino event which produces two
gammas, and the single electron like event extracted from SK-atmospheric
neutrino data in their respective frames. Between the first and third diagram, the angles between the neutrinos and gammas (θ, Θ and φ) are
the same as between the corresponding neutrino, electron and gamma.
The kinematics of the electron like event have not changed however the
direction of the gamma and neutrino have changed.

. . . . . . . . . . . 126

7.17 True momentum distributions of the 1st (top) and 2nd (bottom) decay
gammas overlaid with the momentum distributions of the matched elike events from Super-K atmospheric neutrino data and MC (primary
sample).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.18 True momentum distributions of the 2nd decay gammas overlaid with themomentum distribution of the matched decay electron events (Secondary
sample).
7.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

π 0 momentum distribution comparison for SK data (left) and MC (right)
overlaid with the true π 0 momentum from true T2K kinematics.

. . . . 128

7.20 Figure containing event displays of a real e-like event from atmosphericν data (b), it’s corresponding simulated MC gamma (a) and the merged
hybrid-π 0 event from the primary data sample (c). . . . . . . . . . . . . 130
7.21 The "wall" distribution of the primary (left) and secondary (right) MCMC and data-MC samples. The selection criteria is displayed by the pinkarrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.22 The visible energy distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by thepink arrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.23 The OD hit distribution of the primary (left) and secondary (right) MCMC and data-MC samples. The selection criteria is displayed by the pinkarrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.24 The number of ring distribution of the primary (left) and secondary(right) MC-MC and data-MC samples. Events with only two rings are
selected. The selection criteria is displayed by the pink arrows. . . . . . 135
7.25 The PID distributions of the primary (left) and secondary (right) MCMC and data-MC samples. The top two histograms show the PID of thefirst particle in the two ring sample and the bottom two histograms show
the PID of the second particle in the two ring sample. Events which havean electron like PID are selected by setting the reconstructed particle
code to 2. The selection criteria is displayed by the pink arrows.

. . . . 136

7.26 The decay electron distributions of the primary (left) and secondary(right) MC-MC and data-MC samples. The selection criteria is displayedby the pink arrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
xvii

LIST OF FIGURES[a\

7.27 Standard π 0 mass distribution of the primary (left) and secondary (right)
hybrid-π 0 samples along the standard two ring event selection. The pinkarrows represent the π 0 mass cut threshold. . . . . . . . . . . . . . . . . 137
7.28 Fit region of the standard π 0 mass distribution of the primary (left) andsecondary (right) hybrid-π 0 samples along the standard two ring π 0 event
selection, including the Gaussian fit. . . . . . . . . . . . . . . . . . . . . 138
7.29 Fit region of the standard π 0 mass distribution of the primary (left) andsecondary (right) hybrid-π 0 samples along the standard two ring π 0 event
selection.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.30 The remaining efficiencies of the two ring NC-h-π 0 sample, for primary(left) and secondary (right) samples. For each sample the selection efficiency is shown alongside the ratio of MC/data.
7.31. . . . . . . . . . . . . 140

Standard π 0 mass distribution of the primary hybrid-π 0 samples along thestandard two ring π 0 event selection, for the 2013 (left) and 2018 (right)
hybrid-π 0 samples. The error bars for each bin represent the statisticalerror from the electron data. The pink arrows represent the π 0 mass cut
threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.32 Hybrid π 0 remaining efficiency along the two ring event selection for 2013
(left) [104] and 2018 (right) primary samples. The tops plots show the remaining efficiency and the bottom plots show the MC-to-data remaining
efficiency ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.33 Hybrid π 0 remaining efficiency along the two ring event selection for2013 (left) [104] and 2018 (right) secondary samples. The tops plotsshow the remaining efficiency and the bottom plots show the MC-to-dataremaining efficiency ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.34 The visible energy distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by thepink arrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.35 The number of ring distribution of the primary (left) and secondary(right) MC-MC and data-MC samples. The selection criteria is displayedby the pink arrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.36 The PID distributions of the primary (left) and secondary (right) MCMC and data-MC samples. Events which have an electron like PID are
selected by setting the reconstructed particle code to 2. The selection
criteria is displayed by the pink arrows. . . . . . . . . . . . . . . . . . . 149
7.37 The decay electron distributions of the primary (left) and secondary(right) MC-MC and data-MC samples. The selection criteria is displayedby the pink arrows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

7.38 The reconstructed neutrino energy of the primary (left) and secondary(right) MC-MC and data-MC samples.
xviii. . . . . . . . . . . . . . . . . . 151

LIST OF FIGURES[a\

7.39 Left: Oscillated νe CCQE signal and right: the (νµ )NC1π 0 backgroundwith only FCFV cuts applied. The π 0 rejection cut is indicated by the
red lines, where all events above the lines are rejected. [101] . . . . . . . 151
7.40 Electron to π 0 likelihood (ln(Lπ0 /Le )) vs. FiTQun π 0 mass from the dedicated π 0 fitter for the NC-h-π 0 samples. The events are fully contained
within the fiducial volume, no other cuts have been applied. Events above
the red line are rejected.
7.41. . . . . . . . . . . . . . . . . . . . . . . . . . 152

Electron to π 0 likelihood (ln(Lπ0 /Le )) vs. FiTQun π 0 mass from thededicated π 0 fitter for the single ring NC-h-π 0 samples. All cuts until thereconstructed neutrino energy have been applied. Events above the redline are rejected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.42 The remaining efficiencies over the νe event selection stages for primary(left) and secondary (right) samples. For each sample the selection efficiency is shown alongside the ratio of MC-MC/data-MC.

. . . . . . . . 154

7.43 The left histograms show the reconstructed invariant π 0 mass of the 2ring π 0 events seen in each analysis channel. The top two histograms
show the invariant mass before the final selection stage, and the bottom
two plots show the invariant mass after the final selection stage (mass in
the range of 85 and 185 MeV/c2 ). The right plots show the mass for ν
data (FHC) and the left plots show ν̄ data (RHC). . . . . . . . . . . . . 157
7.44 The histograms show the reconstructed π 0 momentum of the 2-ring π 0events seen in each analysis channel, along the full 2-ring π 0 event selection. The left histogram shows the MC and data for runs 1-9 (FHC) andthe right histogram shows the MC and data for runs 5-9 (RHC). . . . . 158

xix

LIST OF FIGURES

[a\

xx

List of Tables
1.1

Table of neutrino properties within the standard model under the assumption that neutrinos are massless. . . . . . . . . . . . . . . . . . . .

4

1.2

Table of current best-fit values for the neutrino oscillation parameters [6]. 10

2.1

Table of Cherenkov energy threshold values in Super-K [49]. . . . . . . .

26

4.1

Summary table of Super-K laser wavelengths and types. . . . . . . . . .

55

4.2

Summary of the RMS/mean variation over the SK-IV period for thesymmetric and asymmetric scattering parameters and the absorption coefficient, over all wavelengths. . . . . . . . . . . . . . . . . . . . . . . . .

6.1

68

Table of channel connections to motherboards, the position and opticalsource. C = Collimator, B = Bare fibre, D = Diffuser. . . . . . . . . . . 101

7.1

Table of neutrino interactions at where α corresponds to e, µ and τ , andp and n correspond to protons and neutrons. Typical interactions at T2K
take α corresponding to e and µ. . . . . . . . . . . . . . . . . . . . . . . 106

7.2

Table of NC1π 0 /CC cross-section measurements using the ANL and Gargamelle
bubble chamber experiments, the BML and CERN PS spark chamber experiments and the most recent K2K and SciBooNE neutrino experiments.
The NUANCE predictions are also included for comparison. . . . . . . . 115

7.3

Absolute cross section of NC1π 0 interactions on mineral oil made by the
MiniBooNE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.4

cross section of NC1π 0 interactions on water as measured by the P0D at
T2K. Results are taken from [96]. Table adapted from [97] . . . . . . . . 116

7.5

Table of comparison between previous and new hybrid samples, including
the construction year, neutrino event generator version (NEUT), size ofthe data (in days), PMT gain correction (GainCor) application, SKDetSim, and reconstruction algorithm (APFit and fiTQun) versions. . . . . 121

7.6

Table of abbreviations used for each selection stage. Stage 0 is used only
to calculate the number of events contained within the true fiducial volume132
xxi

LIST OF TABLES

[a\

7.7

Table of π 0 mass peak position extracted through a Gaussian fit between
the limits of 85 and 185 MeV/c2 , for the 2018 hybrid π 0 samples. . . . . 139

7.8

Remaining efficiencies along all 2-R event selection stages for the Primaryh-π 0 samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.9

Remaining efficiencies along all 2-R event selection stages for the secondary h-π 0 samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.10 Table of remaining efficiency for the 2018 two ring hybrid-π 0 samples andthe overall efficiency as calculated using Equations 7.16 - 7.19. . . . . . . 141
7.11 Table of π 0 mass peak position for the 2013 and 2018 hybrid π 0 samples. 143
7.12 Table of remaining efficiency for the two ring hybrid-π 0 samples . . . . . 144
7.13 Remaining efficiencies along all νe event selection stages for the Primaryh-π 0 samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.14 Remaining efficiencies along all νe selection stages for the secondary h-π 0samples .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.15 Table of remaining efficiency for the νe event selection, including theoverall efficiency of the νe background . . . . . . . . . . . . . . . . . . . 155
7.16 Table of sample abbreviations and definitions of samples containing 2-ring
π 0 ’s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.17 Table of predicted number of 2-ring π 0 like events in T2K-SK data using
T2K-SK MC, with 14.94×1020 POT in ν mode and 16.35×1020 POT inν̄ mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.18 Table of events in MC 2-ring π 0 sample before scaling MC to data. . . . 159
7.19 Comparison table of the NC1π 0 background events in the νe and ν̄e analyses alongside the total number of events in the samples from the current T2K analysis.The percentage background contribution take the total number of events from the official analysis in both cases. The official
numbers are adapted from [79]. . . . . . . . . . . . . . . . . . . . . . . . 162
7.20 Comparison of the fiducial mass and POT in ν and ν̄ modes for T2K and
T2HK. The numbers are calculated using information from [67] . . . . . 163
7.21 Summary of scale factors and predicted number of events in Hyper-K. . 164
7.22 Table of predicted number of 2-ring π 0 like events in theoretical T2K-HK
data using scaled T2K-SK MC, and scaled POT. . . . . . . . . . . . . . 164

xxii

Chapter 1

The Neutrino"I’m learning about magic, Gaia,
energy, and the roots system."Willow - Lessons

This chapter introduces the neutrino and tells the story of its discovery and its
importance in the current world of physics. Firstly, a brief history of the neutrino will
be discussed, followed by its properties and its place in nature. The focus will thenmove on to the studies that Super-Kamiokande (Super-K) and T2K have been involvedin which have led to several discoveries and turning points in neutrino physics.

1.1

A brief history

The neutrino was first postulated by Wolfgang Pauli in 1930 to explain the violation ofseveral laws, including the energy laws, that he observed via the continuous β spectrum
from the nuclear β-decay of Radon. Pauli proposed that the solution was held in theexistence of a new particle: a weakly interacting "neutron" which was to be emitted
along with the β particle in the decay [1].
The "neutron" was to have the following properties; have a spin of 1/2, would obey
the exclusion principle; would not travel at the speed of light (therefore letting themdiffer from light quanta), and would have a mass on the same order of magnitude as
the electron. Pauli himself doubted the existence of this new particle but none the less,addressed a letter to the Tubingen conference "Radioactive Ladies and Gentlemen" toexplain his observation. Two years later in 1932, James Chadwick discovered the neutron, as we now know it, and in 1933 the neutral particle that Pauli postulated wasnamed as the neutrino, by Enrico Fermi, who himself developed the theory of β decay.
In Fermi’s theory, the neutrino was denoted by νe , and the β decay process as:n −→ p + e− + ν̄e
1

(1.1)

CHAPTER 1. THE NEUTRINO[a\Such a theory suggested that the e− and νe pair are spontaneously produces by the
nucleus, similarly to the spontaneous emissions of photons. It also lead to possibility ofdetecting neutrinos via [2]:ν̄e + p −→ e+ + n,

(1.2)

which in 1956, Frederick Reines and Clyde Cowan confirmed by observing inverse βdecay via nuclear reactor anti-neutrinos. The second flavour of neutrinos was discoveredin 1962 by Leon Lederman, Melvin Schwartz and Jack Steinberg by impacting protons
on a beryllium target using the Brookhaven Alternating Gradient Synchrotron. Theyobserved the muon neutrino νµ from the decay of pions produced by bombarding theberyllium target [3]:π ± −→ µ± + ν̄µ(1.3)

The first evidence for the existence of the third neutrino flavour was observed in 1975
through the discovery of the tau (τ ) lepton [4]. In 1989, it was discovered that there
must be three neutrino flavours, after LEP at the Stanford Linear Collider measured the
decay of the Z 0 gauge boson. The first observation of the tau neutrino interaction wasmade by the DONUT (Direct Observation of NU Tau) collaboration in 2001 throughthe decay of charmed mesons, produced by a high energy beam [5].

1.1.1

Neutrinos within the Standard Model

The standard model of particle physics encapsulates our knowledge and best understanding of the elementary particles, and the forces which govern them. It is the unified
theory that defines the building blocks of nature. Figure 1.1 displays the 17 constituentsand their groupings 1 . The standard model describes the scenario in which matter iscomposed of 12 fermions, each which have half integer spin. Any interactions that afermion may undergo, are mediated by gauge bosons which have integer spin. Fermionsare further subdivided into two groups; leptons and quarks, which each exist in three
generations.
There are three generations of quarks. Each quark carries a fractional charge ofthe electron charge, and a "color" charge, which is related to the strong force. Quarks
can interact via any of the three fundamental forces; the strong, the weak and theelectromagnetic. The forces are mediated by the gauge bosons; the gluon, W ± and Z 0
and photon respectively. Quarks combine to form Hadrons; colourless, integer particles
which can be broken down into two families; baryons and mesons. Baryons consist of
three quarks, for example, the proton, with a combination of (uud) and the neutron
1

Image sourced from http://higgstan.com/particle-image.
2

CHAPTER 1. THE NEUTRINO[a\Figure 1.1: The standard model of particle physics(ddu). Mesons consist of two quarks which form a a quark, anti-quark pair, such as¯ The focus of the analysis section of
the pion (π + ) which has the combination (ud).
this thesis will be on the π 0 , which has an unusual composition. It is formed by asuper-position of two quark - anti-quark pairs:
π0 =uū − dd¯2

(1.4)

The π 0 has a mass of 134.9770±0.0005MeV/c2 and a mean lifetime of 8.52±0.18
× 10−17 s [6]. As will be discussed later, it primarily decays into two photons with abranching ratio of 98.82 ± 0.03%.
Finally, leptons exist in both charged and uncharged, neutral form; the e− , µ−and τ − are negatively charged and interact via the electromagnetic force. Each have aneutral, neutrino counterpart; the νe , νµ , and ντ [7]. In the standard model, neutrinos
are massless, carry zero charge and have a helicity of -1 for a ν and +1 for a ν̄, meaning
neutrinos are "left handed" and anti-neutrinos are "right handed". The helicity of aparticle is defined by the ratio ms /s, or the z component of the spin divided by themagnitude of the spin. Neutrinos interact via the weak interaction, which is selected by
3

CHAPTER 1. THE NEUTRINO[a\the helicity properties described as above. Due to the Dirac2 neutrino being massless,the "handedness" or helicity is a fixed quantity. The helicity can also be referred toas the chirality for particles that do not have mass. Even though the discovery of the
Higgs boson in 2012 was proof of the success of the standard models predictions [8],the evidence of neutrino oscillation suggests that neutrino have non-zero mass, which is
not predicted by the standard model. A table of properties of the neutrino under theassumptions of the standard model can be seen in table 1.1.
Property
mass
chargespinhelicity
force

value
0
0
1
2

-1 (ν)
weak

Table 1.1: Table of neutrino properties within the standard model under the assumptionthat neutrinos are massless.

As discussed, within the standard model neutrinos are considered to be massless, lefthanded and distinct from antineutrinos. There are extensions to the standard modelin which a heavier, right-handed neutrino is introduced. These neutrinos are known
as "Majorana" neutrinos are are considered to be their own antiparticle. Such an
addition required an extension to the standard model through the addition of a term to
the standard model Lagrangian. These heavier, right-handed neutrinos are thought tointroduce a small mass to the left-handed neutrinos.

1.2

Neutrino Oscillations

It was B.Pontecorvo who proposed the theory of neutrino oscillation, in 1957 [9]. He
postulated that, it was possible for neutrinos to oscillate between ν −→ ν̄. In 1962,
the observation of the existence of two types of neutrinos was made, which lead tothe proposition of neutrino flavour oscillation by Z. Maki, M. Nakagawa and S. Sakata[10]. Neutrino oscillations were observed in 1998 and are a result of transitions between
neutrino flavours [11] and the mixing of flavour and mass states. Oscillations happen as
neutrinos travel from a source. Each mass state acquires a phase and since each state
represents a different mass, the phases are slightly different. Hence, as the neutrino
travels away from the source, the mass states become out of phase with each other andthe resulting interference causes the wave-function to evolve into one which comprisesof a combination of all three flavour states [12]. The oscillations are thus a function of
the mixing angles, the distance traveled from the source and the neutrino energy. The
2

Dirac neutrinos are defined as neutrinos which are distinct from their antineutrinos.
4CHAPTER 1. THE NEUTRINO[a\fact that these oscillations occur means that at least two of the neutrino masses must
be non-zero, whilst it still remains possible for the lightest neutrino mass to be zero.

1.2.1

Formulation

There are three flavours of neutrino, νe , νµ and ντ , thus the neutrino has flavour andmass eigenstates, which can be denoted as: |να i = {|νe i , |νµ i , |ντ i} for the flavour
eigenstates, and |νi i = {|ν1 i , |ν2 i , |ν3 i} for the mass eigenstates. Even though neutrinos propagate their mass eigenstates in a vacuum, they can only be observed in theirflavour eigenstate. Neutrino oscillations happen under the assumption that neutrinos
are massive particles with flavour eigenstates which are a linear superposition of themass eigenstates. The mixing of the flavour and mass eigenstates can be described byequations 1.5 and 1.6|να i =

X∗
Uαi
|νi i ,

(1.5)

Uαi |να i ,

(1.6)

i

|νi i =

X
i

Where U is the unitary "PMNS" (Pontecorvo-Maki-Nakagawa-Sakata) matrix. The
existence of non-zero off-diagonal elements implies that a neutrino of one flavour isin fact a combination of multiple mass states. The "PMNS" mixing matrix can beparameterised as below:c12 c13e−iδ s13

s12 c13Uαi ≡  −s12 c23 − e−iδ c12 s23 s13

c12 c23 − e−iδ s12 s23 s13

s12 s23 − e−iδ c12 c23 s13−c12 s23 − e−iδ s12 c23 s13s23 c13  · P,
c23 c13(1.7)

Where sij and cij correspond to sin θij and cos θij , where θij are the mixing angles,and δ is the Dirac CP-violating (Charge Parity) phase which is directly observable. This
phase arises from the differences in the oscillation rates between two states with opposite
starting points, thus making the order in time in which events take place necessary to
predict the oscillation rates. If the neutrinos are Majorana as briefly described in theprevious section, the additional phases α13 and α23 are included in the matrix P [13],however these do not affect the physics of neutrino oscillations. In this case the matrix
P can be written as:


1

0

α21

P =  0 ei 2

0

0

e

0



0


,

α
i 231

(1.8)

Where P reduces to the identity matrix when neutrinos are considered to be of the5CHAPTER 1. THE NEUTRINO[a\

Dirac type, which is assumed for the following derivation.
It can be shown that the PMNS matrix is a product of 3 rotation matrices The
parameters contained in each can be measured in 3 different sectors: Atmospheric,reactor/accelerator and solar. The matrix can be dissected as follows:(Atmospheric - ∆m223 , θ23 ) (Reactor/Accelerator - ∆m231 , θ13 )

z


}|
0

1

Uαi =  0 c23
0 −s23(Solar - ∆m2 , θ12 )

}|
{z
}| 12
{



0
c13
0 e−iδ s13
c12 s12 0 s23  010
  −s12 c12 0  .
c23−e−iδ s13 0
c13
0
0 1
{ z
 

(1.9)

In order to determine the possibility of neutrino oscillation, we begin with the neutrino in its initial state in a vacuum at a time t = 0:|Ψ(t = 0)i = |να i =

3
X

∗
Uαi
|νi i ,

(1.10)

i=1

and consider that the Schrodinger equation should be used to determine the temporal
evolution of the neutrino flavour eigenstates, where H is the Hamiltonian:id|νi (t)i = H |νi (t)i .
dt(1.11)

We can assume the plane wave approximation:|νi (t)i = e−iEi t |νi i(1.12)

and by substituting this equation (1.12) into equation 1.10, we find that the time
evolution state of the neutrino is:|Ψ(x, t)i =

X

∗
Uαi
|νi i e−ipν ·xν ,(1.13)iwhere pν and xν correspond to the neutrino 4-momentum and 4-positions respectively. We can make the assumption that the mass of the neutrino is negligible orthat there is no mixing. As the neutrino is relativistic, the neutrino momentum can be
described as follows:
pν =

q
m2
Ei2 − m2i ∼ Ei + i
2Ei(1.14)

leading to an approximation of the energy of the ith eigenstate, Ei , to be:
Ei ' |pν | +6m2i,
2 |pν |

(1.15)

CHAPTER 1. THE NEUTRINO[a\where mi is the mass of the ith eigenstate and c = ~ = 1. From here, we derive thefollowing wave function:|Ψ(x, t)i =Xm2−i 2|pi |∗Uαi|νi i eν.

(1.16)i

The wave-function to describe the flavour eigenstate can be derived by substituting
Equation 1.6 into Equation 1.16, where x denotes the distance propagated by the neutrino, α denotes the initial neutrino flavour and β denotes the flavour state that theneutrino may be observed in after propagating the distance x:|Ψ(x, t)i =

XX
i

m2

−i 2|pi | x

∗
Uαi
e

ν

Uβi |νβ i .

(1.17)β

From here we take the probability that the neutrino in initial state α is observed inflavour state β after traveling a distance of L in km is:
P (α → β) = |hνα |νβ (L)i|2(1.18)


"
#
m2
m2
X
X
i
i L
−i
L
−i
∗
∗
P (α → β) = 
Uαj e 2|pν | Uβj 
Uαi e 2|pν | Uβi .

(1.19)

ji

Due to the mass of the neutrino being negligible, we can approximate p ' E andcontinue our assumption that the neutrino travels at the speed of light (c = 1), thus:
P (α → β) =

X

∗
∗ i
e
Uαi
Uαj Uβi Uβj

2
m2
i −mj
2E

L

.

(1.20)

ij

We can take the difference m2i −m2j to be ∆m2ij in eV 2 , and express the mass-squared
differences as:∆m221 = m22 − m21 ,(1.21)∆m231 = m23 − m21 ,(1.22)

and use the unitarity of the PMNS matrix to express the oscillation probability as:∆m2ij L∗P (α → β) =δαβ − 4Re UαiUαj Uβi Uβj sin2
4E
i>j
!
X
∆m2ij L∗∗
+2
Im Uαi Uαj Uβi Uβj sin
.
2E
X


∗

!
+
(1.23)

i>j

Considering the oscillation probability from an experimental point of view, we canshow the disappearance probability in the νµ beam in the Japanese long baseline acceler7

CHAPTER 1. THE NEUTRINO[a\ator neutrino experiment, T2K, from which data is used in this thesis. The experimentwill be discussed in detail in chapter 2, section 2.3:
4

2

2

P (νµ → νµ ) ' 1 − cos θ13 sin 2θ23 sin∆m232 L,
1.27
E

(1.24)and similarly for a νe beam:
222

P (νµ → νe ) ' sin 2θ13 sin θ23 sin∆m213 L
1.27.
E

(1.25)The oscillation amplitude can be given by:
LOSC =πE,
1.27∆m213(1.26)

where 1.27 is unit-less and arises from the reduction of the constants ~ and c3 3 . In
order to measure flavour oscillations, the neutrino requires the time to oscillate at least
once, which leads to the requirement of LL
osc ∼ 1. The distance, L and the energy E canbe controlled experimentally in order to maximise the oscillation at the far detector,
in the case of T2K, the L is the distance between J-PARC (Japan Particle Accelerator
Complex) and Super-K, the far detector. From Equation 1.20, the conclusion can be
drawn that the non-zero mass of the neutrino can be proven by neutrino oscillation.
The antineutrino oscillation probability can also be derived and yields the same result
as seen in Equation 1.23 but with an inverted sign in front of the 3rd term. By measuring any possible asymmetry between neutrino and antineutrino oscillation probabilities,
the δCP phase can be estimated.
This probability derivation of neutrino oscillation is for oscillations which occur
within a vacuum. The oscillation probabilities are influenced by the presence of electrons and nucleons in matter as the neutrino propagate through that matter. The νeand ν̄e can interact via the neutral and charged currents die to the presence of electrons
in the matter however, µ and τ (anti)neutrinos only interact via neutral current. Thisphenomenon is known as the matter effect, or the MWS effect, names after Mikheyev,
Smirnov and Wolfenstein. The MWS effect can be parameterised as follows, by considering the excess potential Ve for the νe which arise due to the perturbation of the
Hamiltonian due to charged current interactions:√
Ve = ± 2GF ne(1.27)

Where GF is the Fermi coupling constant and ne is the number density of electrons.
The neutral current potentials for the νµ and ντ can be considered to be the sameand therefore ignored. The MWS effect effects neutrino and antineutrino oscillations
3 ∆m2 c3 L=
4~E

GeV fm
4~c

2

2

L GeV
L GeV
× ∆m
≈ 1.27 × ∆meV2 km E
eV2 km E

8

CHAPTER 1. THE NEUTRINO[a\differently which leads to differences in the oscillation probabilities.

1.3

Experimental Measurements

Now that it is known that neutrinos are not massless, the next step is to determine themass ordering. There are two orderings, or, "hierarchies" which are: Normal hierarchy,
where mν3 > mν2 > mν1 or, Inverted hierarchy, where mν2 > mν1 > mν3 . Confirming
the neutrino mass hierarchy can determine whether the neutrino is it’s own antiparticle
and give insight into why the present day universe is matter dominated, and if the four
governing forces were once unified. Figure 1.2 displays the differences between normal
and inverted mass hierarchies for the neutrino mass states. The value δCP , the Charge
and Parity violating component of the oscillation matrices, can also give insight into
why the universe is heavily matter dominated. Accelerator neutrino experiments aremost sensitive to CP violation and therefore the δCP .

Figure 1.2: The normal and inverted mass hierarchies. The normal hierarchy is shownon the left, and can exist in nature if mν3 > mν2 > mν1 . Alternatively the inverted
hierarchy shown on the right exists in the case that mν2 > mν1 > mν3 [14].

The current best known values for the oscillation parameters can be seen in table1.2. A full review of the current status of the measurements can be found in the 2018
Particle Data Group Review [6].
9CHAPTER 1. THE NEUTRINO[a\Parameterm221
m231(23)m231(23)
sin2 θ12
sin2 θ23
sin2 θ23
sin2 θ13
sin2 θ13
δCP /πδCP /πHierarchy
NormalInverted
NormalInverted
NormalInverted
NormalInverted

best-fit
7.27 [10−5 eV2 ]2.56 [10−5 eV2 ]2.54 [10−5 eV2 ]
0.297
0.425
0.589
0.02150.0216
1.38
1.31

3σ
[6.93 - 7.96] [10−5 eV2 ][2.45 -2.69] [10−5 eV2 ][2.42 - 2.66] [10−5 eV2 ][0.250 - 0.354][0.381 - 0.615][0.384 - 0.636][0.0190 - 0.0240][0.0190 - 0.0242]
2σ : (1.0 - 1.9)
2σ : (0.92 - 1.88)

Table 1.2: Table of current best-fit values for the neutrino oscillation parameters [6].

1.4

Current Status of Neutrino Physics

Current neutrino studies cover a wide energy range and a wide range of sources. A
summary of the neutrino sources can be seen in Figure 1.3, which describes each neutrino
source as a function of its cross section and energy range. This section will focus on
the sources which are studied by the Kamiokande experimental family and those which
contribute to the neutrino oscillation measurements.

Figure 1.3: Summary of neutrino sources and the range of energies covered [15].

10CHAPTER 1. THE NEUTRINO

[a\

1.4.1

Solar Neutrinos and the parameters ∆m221 and θ21

Solar neutrino are produced by the Sun, with a flux on earth of approximately 6 ×1020 cm2 s−1 . As shown in Figure 1.3, their energy is on the order of 1 MeV. Solar
neutrinos are produced via thermonuclear reactions in the Suns core 4 .
The first experiment to observe solar neutrinos was the chlorine based Homestake
experiment in South Dakota in the 1960s [16]. The experiment was led by Raymond
Davis Jr and was designed to detect νe from the sun via inverse β decay. The first
results from the experiment were published in 1968 and stated that the observed solar neutrino rate was significantly less than that predicted by the standard solar model(SSM). The discrepancy became known as the solar neutrino problem. In 1989 the water
Cherenkov Kamiokande experiment [17] reported that their observed 8 B solar neutrino
flux was a factor of 2 smaller than predicted by the SSM. Kamiokande was sensitive toneutrinos of a higher energy (on the order of 10 MeV) than Homestake and was alsoable to measure the direction of the incoming solar neutrinos, and could therefore reconstruct the directional relationship between the neutrinos and the Sun, resulting in aclearer signal. From here, more experiments began working towards unravelling the solar
neutrino problem, including the GALLium Experiment (GALLEX)/Gallium Neutrino
Observatory (GNO) [18] and the Soviet-American Gallium Experiment (SAGE)[19]. In
the 1990s these experiments confirmed the Kamiokande result. The results were also
confirmed by Super-K through taking data between 1996 and 2001.
In 2002, the Sudbury Neutrino Observatory (SNO) measured the total active solar
neutrino flux and νe flux [20], making the first model-independent measurement of thenon νe component of the 8 B solar neutrino flux at a 5.3σ level. The observation of
the solar neutrino flux rewarded Prof. Koshiba (Kamioka observatory) and Raymond
Davis, Jr. with the Nobel Prize in 2002. The heavy water5 Cherenkov detector observedhigh energy solar neutrinos via charged current (CC), neutral current (NC) and elastic
scattering (ES) interactions.
νe + d −→ p + p + e− (CC)

(1.28)

να + d −→ p + n + να (N C)(1.29)

να + e− −→ να + e− (ES)(1.30)

Where α corresponds to e, µ, τ .
4Thermonuclear reaction which produces solar neutrinos: 4p −→ He + 2e+ + 2νe + fusion energy
The neutrino target is 1000 tonnes of 99.92% isotropically pure D2 O contained within a 12 m
diameter acrylic vessel.
511

CHAPTER 1. THE NEUTRINO[a\

SNO showed that flavour change was possible between νe to νµ and ντ and therefore
solved the solar neutrino problem whilst providing evidence of neutrino oscillations.
Figure 1.4 shows the results from SNO where the total neutrino flux is summed over all
flavours and is consistent with SSM.

Figure 1.4: Muon neutrino and tau neutrino flux vs. electron neutrino flux. The bands
represent CC (charged current), NC (neutral current) and ES (elastic scattering) flux
measurements. The dashed line represents the total 8 B solar neutrino model as predictedby the SSM [21].
The plot shows the νµ + ντ flux Φµτ vs the νe flux Φe . These results confirm thatthe flux Φµτ is non-zero and shows strong evidence for solar νe flavour conversion. The
oscillation parameters which drive solar neutrino flavour conversion are those of ∆m221
and θ21 .

1.4.2

Atmospheric Neutrinos and the parameters ∆m232 and θ23

Atmospheric neutrinos are decay products of hadronic showers which result in collisionsof cosmic rays in the upper atmosphere. When the cosmic ray interacts with the upper
atmosphere, pions are produced which decay into µ and νµ , which decay into e and νe .
Atmospheric neutrino experiments measure the neutrino flux ratio, R:R=νµ + ν̄µνe + ν̄e(1.31)

Underground experiments such as Kamiokande, Irvine-Michigan-Brookhaven (IMB)[22] and Super-K are able to measure the atmospheric neutrino fluxes due to their rockoverburden which acts as shielding from cosmic rays. It was Kamiokande that initially
12CHAPTER 1. THE NEUTRINO[a\measured a deficit in the muon like events from cosmic rays compared to predictions.
This was followed by results from the IMB experiment which reported a similar anomaly.
In 1998, Super-K made the measurement of νµ disappearance [23] and the asymmetry
between the number of neutrinos entering the detector through the upper atmosphere,
travelling 10-20 km before interacting, and those entering after passing a distance of up
to 13,000 km through the earth. The phenomena became known as up-down asymmetry,
and the measurement showed that flux of upward going neutrinos was approximately
half of that of the down going flux. Figure 1.5 shows at high L/Eν , there is a deficit
in the muon neutrino flux which is consistent with oscillation prediction shown by thedashed line.

Figure 1.5: Results from Super-K: The ratio of FC data events to FC MC events vs.
reconstructed L/Eν . The points show the ratio of observed data to MC expectation
under the no-oscillation condition. The dashed lines show the expected shape for νµ ↔
ντ oscillation at ∆m2 = 2.2 × 10−3 eV2 [23]Figure 1.6 shows the zenith angle distributions of µ-like and e-like events for both
sub-GeV and multi-GeV data sets. The results show that the zenith angle distributionsof µ-like events and the observed R value differ significantly from the best predictions
under the no-oscillation hypothesis, showing that the data from Super-K are in good
agreement with two flavour νµ ↔ ντ oscillations. This result, combined with that from
SNO were consistent with neutrino oscillation theory. The deficit in µ like events hinted
at a larger value of θ23 .

13

CHAPTER 1. THE NEUTRINO[a\Figure 1.6: Results from Super-K: Zenith angle distributions of µ-like and e-like events
for both sub-GeV and multi-GeV data sets. The hatched region represents the MC
expectation for no oscillation normalised to data livetime with statistical errors. The
bold line is the best fit expected for νµ ↔ ντ oscillations. [23]1.4.3

Reactor Neutrinos and the parameters ∆m221 , θ21 and θ13

As briefly mentioned in section 1.1 Frederick Reines and Clyde Cowan were the first to
observe reactor neutrinos through the inverse β decay. Reactor neutrino experiments
measuring neutrino oscillation parameters often face some difficulties due to the limitations of the source to detector distances. Experiments often cannot see neutrino
oscillations however, they are able to derive limits on parameter measurements such as
θ13 , which the French experiment Chooz placed a limit on in 1999 despite being unable
to observe neutrino oscillations in a ν̄e sample [24]. The source to detector issues arise
due to the antineutrino flux decreasing rapidly as a function of distance (L). Other reactor neutrino experiments include the Kamioka Liquid Scintillator AntiNeutrio Detector(KamLAND) [25], the history of which will be briefly discussed in chapter 2.
KamLAND is located in Kamioka, in the same mine which is home to the Kamiokande
experimental family. The detector consists of 1 kton of ultra-pure liquid scintillator contained within a 13 m diameter transparent balloon suspended in non-scintillating oil.
The flux averaged baseline of KamLAND allowed for a sensitivity to measuring the ∆m221
and θ21 parameters: KamLAND successfully observed neutrino oscillations by detecting
antineutrinos from 53 Japanese power reactor units over a 2 year period between 2002
and 2004. Results from KamLANDs observations can be seen in Figure 1.7. The plots
shows the ration of the observed ν̄ spectrum to the expectation for no oscillation vs L/E.
Over the years, shorter baseline reactor neutrino experiments have been able to
make the best measurement of θ13 and ruled out the no-oscillation hypothesis. Numer14

CHAPTER 1. THE NEUTRINO[a\Figure 1.7: Results from KamLAND showing the ratio of the observed ν̄ spectrum tothe expectation for no oscillation vs L/E [24]ous experiments around the globe have contributed to the result including Daya Bay[26] in China, the upgrade of Chooz, Double Chooz [27] and Reactor Experiment for
Neutrino Oscillation (RENO) [28] in South Korea whom all published results in 2012
stating their results were consistent with Oscillation theory. Figure 1.8 shows the result
from Daya-Bay, indicating that the far and near detector site spectra are in agreementwith oscillation predictions.

Figure 1.8: Results from Daya-Bay. The upper plot displays the background subtracted
positron energy observed at the far detector site and the derived expectation at the neardetector site both with and without oscillation. The lower plot displays the ratio of thespectra at both sites to the no-oscillation case [29].
15CHAPTER 1. THE NEUTRINO

[a\

1.4.4

Accelerator neutrinos and the parameters ∆m232 and θ23

Accelerator neutrinos are produced by colliding protons on a nuclear target, from whichmesons are produced and in turn decay into neutrinos. Often in long baseline experiments study νµ which are decay products of the π ± produced by the proton-target
collision. Accelerator neutrino production is discussed in more detail in chapter 2,
section 2.3. Accelerator neutrino experiments are most sensitive to CP violation, neutrino oscillation via νµ disappearance and νe appearance by measuring the mixing angle
θ13 . Accelerator neutrino experiments are typically composed of both "near" and "far"detectors which are located at a given distance from the beam which maximises thepossibility of measuring the target neutrino oscillation parameters.
The first accelerator experiment to observe νµ disappearance with results consistent
with oscillation theory was K2K [30] in Japan, where beam neutrinos were sent from the
KEK accelerator facility in Tokai, Japan to the far detector Super-K, which is locatedapproximately 250 km away. Following K2K, between 2003 and 2012, the Main Injector
Neutrino Oscillation Search (MINOS) [31] experiment confirmed νµ disappearance via
the observation of νµ produced by the NuMI beam at Fermilab. The Tokai-to-Kamioka(T2K) experiment was the next iteration of the Japanese accelerator experiments andwas the first to be "off-axis"6 . T2K began taking data in 2010 and was the first experiment to observe neutrino oscillations through νe appearance in a νµ beam in 2013 [32].
Alongside T2K’s observation of neutrino oscillation, the experiment has also improved
the precision in other measurements of oscillation parameters such as ∆m232 and θ23 .

Figure 1.9: The 90% confidence level region for |∆m232 | and sin2 θ23 phase space displayedby measurements from a number of experiments. [33].

Figure 1.9 shows the 90% confidence region for the |∆m232 | and sin2 θ23 phase space6

where the far detector is offset from the beam axis by a small angle
16

CHAPTER 1. THE NEUTRINO[a\for both atmospheric and accelerator neutrino experiments. Jiangmen Underground
Neutrino Observatory (JUNO) [34], located in China, will be the next generation inreactor neutrino experiments. JUNO designed to be a multi-purpose liquid scintillator
experiment with the goal of determining neutrino mass hierarchy and precisely measuring the oscillation parameters sin2 θ12 and ∆m221 , via the observation of reactor neutrinos
from various power stations in China. It is expected to begin operation in the next 2
years.

1.4.5

Supernova Neutrinos

On February 23rd 1987, the Kamaiokande-II and the IMB experiment made the firstand only direct observation of supernova neutrinos, from a supernova in the Large
Magellanic Cloud, which is now known as SN-1987a. Kamiokande-II observed an event
burst, which can be seen in Figure 1.10.

Figure 1.10: Time sequence of events from SN-1987a centred about 07:35:35 UT 23rd
February 1987. The dashed lines represent muon events in units of p.e and the solidlines represent the low energy electron events in units of hit PMTs [35]In order to confirm that this was observation was a genuine neutrino burst, datain the period of February 9th to 25th was analysed. No other such behaviour wasobserved during that period and so the collaboration confirmed that the results were
genuine. This was the first direct observation of a supernova in neutrino astronomy andconfirmed predictions made by the supernova collapse model. The conclusions impacted
the solar neutrino analysis at the time, by the findings that the lifetimes of the νe andν̄e must be greater than 105 years/γ where γ is equal to the ratio of the neutrino energy
to the neutrino mass. The result ruled out neutrino decay being the explanation for thesolar neutrino problem [35].
17CHAPTER 1. THE NEUTRINO[a\

As will be further discussed in Chapter 5, Super-K is undergoing an upgrade motivated to improve the tagging of supernova neutrinos through the addition of gadolinium
sulphate (Gd2 (SO4 )3 ) to the pure water [36]. Such an addition will allow Super-K, over
several years, to detect the DSNB (Diffuse SuperNova Background) neutrino signal.
These supernova neutrinos are currently detected through neutron tagging on hydrogen[37] where the signal is a 2.2 MeV γ ray. With the addition of Gd and the enhancement
to the signal which it provides, neutrinos will be able to be tagged via the 8 MeV γ
cascade.

1.4.6

Measurements of δCP and neutrino mass hierarchy

In the current universe, there is an imbalance of matter and antimatter. Such anobservation implies that the Charge-Parity (CP) symmetry may be violated. So far,
CP violation has been observed through the weak interactions of quarks, however thelevel is too low to fully explain the state of the current universe. The value of δCP
is a complex phase arising from the quantum mixing of neutrinos, thus providing asource of CP violation in the lepton sector. This CP violating phase can be measured
through the comparison of the P(νµ −→ νe ) and P(ν̄µ −→ ν̄e ). Although there are no
direct measurements of δCP or the neutrino mass hierarchy, the larger than expectedvalue of θ13 has enabled current accelerator neutrino experiments to constrain the δCPparameter. By comparing the aforementioned oscillation probabilities, results from T2K
suggest that δCP 6=0 or π, which is currently the strongest constraint on this parameter.

Figure 1.11: The 90% confidence interval of the δCP measurement for normal andinverted hierarchies. The values were obtained by joint analysis of neutrino and antineutrino oscillations in appearance and disappearance channels at T2K [38].

18CHAPTER 1. THE NEUTRINO[a\Figure 1.11 shows the T2K prediction of the allowed range for δCP for the normal
and inverted mass hierarchy scenarios at a 90% confidence level It is clean that there
are only small allowed regions for the value of δCP .
A new generation of accelerator neutrino experiments are currently being built tofocus on the δCP and mass hierarchy measurements, including the accelerator neutrino
experiments Tokai-to-Hyper-Kamiokande (T2HK) [39] in Japan, and the Deep Underground Neutrino Experiment (DUNE) [40] in the US. Both experiments are expected to
begin operation between 2025 and 2027. The T2HK (WC) and DUNE (Liquid Argon)
experiments each use a different detector medium, providing different sensitivities todifferent neutrino interaction channels which should prove complimentary (and competitive) to each other.
Looking further in to the future, there is the possibility of a dual tank scenario forHyper-Kamiokande, where a second tank will be constructed in Korea, thus extending the baseline such the second detector will sit at the second oscillation maximum.
The addition will form the Tokai-to-Hyper-Kamiokande-Korea (T2HKK) [41] where themain physics goal will be probing of non-standard interactions (NSI) in neutrino propagation. Non-standard interactions (NSI) of neutrinos can be studied through neutral
current (NC) and charged current (CC) interactions. The NC NSI should affect theneutrino propagation in matter whilst CC NSI should affect the neutrino detection andproduction. Neutrino NSI’s can cause degeneracies in determining oscillation parameters such as δCP and the mass hierarchy [42]. This new generation of experiments work
towards higher precision oscillation parameter measurements and measuring δCP and
neutrino mass hierarchy whilst attempting to resolve the degeneracies in determining
these parameters. With the larger data sets that will become achievable with thesefuture experiments, the determination of whether leptonic CP violation is larger thanin the quark sector [43].

1.5Summary

Neutrino oscillation measurements are made by studying a number of sectors whichhave been discussed in this chapter:• Solar neutrinos: via neutrinos from the Sun• Atmospheric neutrinos: via cosmic-ray interactions with the atmosphere• Reactor neutrinos: via nuclear reactors• Accelerator neutrinos: via proton accelerators
19

CHAPTER 1. THE NEUTRINO[a\

As many of the current and past neutrino experiments have better sensitivity tocertain elements of the PMNS matrix than others, the oscillation parameters have beenmeasured by a range of different experiments over the years. For example, Super-K,
MINOS, T2K and NOνA [44] are sensitive to, and have measured the atmospheric parameters, ∆m232 and θ23 . Reactor experiments such as Daya Bay, Double Chooz andReno are capable and have made the more precise measurement of θ13 . The |∆m232 | andsin2 θ23 parameters were initially measured by atmospheric neutrino experiments suchas Super-K which measured νµ disappearance. When accelerator neutrino experiments
began producing controlled sources of νµ , these parameters could be better constrained.
T2K currently holds the best measurement of sin2 θ23 and the best prediction of the valueof δCP , where the current official result excludes δCP = 0 at a 3σ level. Extensions to theneutrino oscillation matrix are also studied through the search for "Majorana" neutrinos, as briefly discussed in Section 1.2, Subsection 1.2.1. If neutrinos are Majorana thenadditional α parameters can be introduced into the oscillation matrices. Experiments
such as SNO+ search for Majorana neutrinos through neutrino-less double β decay.
From the mid 2020’s, a new generation of neutrino experiments will be emerging
which promise better constraints on the δCP parameter and the neutrino mass ordering.
The T2HK, DUNE and JUNO experiments each have the common goal of observing
supernova neutrinos alongside precise measurements of the neutrino oscillation parameters. As each of the experiments will use a different detector medium (pure water,
liquid Argon and liquid Scintillator respectively), each will have different sensitivities
to various neutrino interaction channels, allowing for a wide range of complimentarymeasurements and a promising future for neutrino oscillation measurements.

20

Chapter 2

The Kamiokande Family"Power. I have it. They don’t.
This bothers them."
Buffy - Checkpoint

2.1

Kamioka Observatory: A Brief History

In the picturesque mountain village of Higashi-Mozumi, Kamioka-cho, Japan, is Kamioka
Observatory. This research facility is home to a number of neutrino physics experiments,
including KamLAND and the Nobel prize winning Kamiokande experiments. Hidden
within this once active mining village, is the Kamioka mine, in the heart of Mt Ikeno.
Historically, Kamioka mine provided rich sources of zinc and lead, however in 1981 theMitsui mining company commenced a collaboration with the University of Tokyo and began a new journey in the construction of this neutrino observatory and the Kamiokande
detector.
Kamioka Underground observatory began with the Kamiokande detector. Located1000 m underground, was a 3000 ton water Cherenkov detector, originally designed by
Prof. Koshiba, to search for and observe proton decay signals. The detector was a cylindrical container of approximately 3000 tons of pure water with 16 m height and 15.6 m
diameter. A schematic can be seen in Figure 2.11 . Construction was completed in 1983
and in 1984 discussions began between the Kamiokande collaboration and members of
the University of Pennsylvania, who took over the Homestake experiment that same
year. It was in 1985 that Kamiokande underwent an upgrade to Kamiokande-II andmembers of several American institutes joined the collaboration. During the upgrade,
the American group provided new, improved electronics whilst the Japanese group upgraded water purification measures [45]. These upgrades would allow for the detection
1

Image sourced from http://www-sk.icrr.u-tokyo.ac.jp/sk/news/2017/02/SN1987A-en.html

21

CHAPTER 2. THE KAMIOKANDE FAMILY[a\of astrophysical and solar neutrinos with a 10 MeV energy threshold. Also running concurrently, between 1982 and 1991, was the IMB experiment. IMB was an 8700 tonnewater Cherenkov detector which, like Kamiokande, was designed to study nucleon decay.
Over the coming years, US members of IMB joined the Japanese collaboration, bringing
with them the 8 inch Photomultiplier tubes (PMTs) which would later be installed in
the Super-Kamiokande outer detector. The Kamiokande-II experiment began operationin 1986 and, as if it was fate, received signals from supernova (SN) 1987a [35], followedby the observation of solar neutrinos two years later. IMB also observed SN 1987a andthe joint observation provided the first test of standard Supernova theory with respect
to neutrino production during core collapse.

Figure 2.1: Schematic of the Kamiokande detector.
After the decommissioning of the Kamiokande detector, the reactor antineutrino
experiment KamLAND [25] found its home within the original Kamiokande cavern.
KamLAND was designed for the detection of reactor neutrinos and began taking data
in 2002. After Kamiokande-II discovered the solar neutrino and atmospheric neutrino
problems, Super-Kamiokande was proposed to address them. Excavation of the cavity took place between 1991 and 1994, and the detector construction followed between
1994 and 1996. At the beginning of 1996, the construction of Super-Kamiokande wascompleted, water filling began and Kamioka Observatory was established. The SuperKamiokande detector, like its predecessor Kamiokande, has a rock overburden of 1000 m(2700 m water equivalent) such that cosmic ray muons with energies below 1.3 Tev can22

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

not penetrate. In April 1996, operation of this next generation water Cherenkov detectorbegan. With its larger size, Super-Kamiokande was tailored toward the observation ofsolar and atmospheric neutrinos. A schematic of the Super-Kamiokande detector canbe seen in figure 2.2. In 1999 the K2K [30] (KEK to Kamioka) long baseline neutrino
experiment was formed, and by 2004, was completed with Super-Kamiokande taking
the role of far detector for the accelerator based experiment. K2K’s goal was to study
neutrino oscillation using a neutrino beam with well understood systematics, whilst
confirming the atmospheric neutrino measurements [46].

Figure 2.2: Schematic of Super-Kamiokande, showing the detector structure, tank top
electronics huts and control room [47].

Super-Kamiokande continued its far detector role throughout both the K2K experiment and the T2K experiment which began in 2009. By 2015, Super-K had received
a Nobel Prize; the second for an experiment associated with Kamioka observatory. Although the success story sounds somewhat smooth, Super-Kamiokande didn’t go without its setbacks. In 2001 the detector suffered a devastating accident caused by an imploding PMT which sent a shockwave through the detector, resulting in mass implosionof the majority of the PMTs. The detector was restored by 2002 and began operation in
the SK-II phase with a PMT coverage of only half that of SK-I. Reconstruction began
in 2005 where full PMT coverage was recovered and in 2006, the SK-III phase began.
An image of Super-K in 2006, taken during the filling stage can be seen in Figure 2.3.
After some electronics upgrades in 2008, the longest running Super-Kamiokande phasebegan as SK-IV.

23

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.3: Image of Super-Kamiokande in the water filling stage during the full reconstruction phase in 2006.

2.2

The Super-Kamiokande Experiment

In Super-K, neutrino events are detected via the charged particles produced during theirinteractions with atoms in the pure water inside the detector. The resulting signal isthe emission of Cherenkov radiation in which a light cone is produced, projecting a ring
shaped hit pattern on the detector wall. The Cherenkov light is detected by Photomultiplier tubes (PMTs), which are evacuated tubes (often glass tubes) which collect lightand convert it into an output charge signal. Cherenkov light enters the PMT throughthe input window and excites electrons inside the PMT’s photocathode. Photoelectrons are then emitted into the vacuum via the photoelectric effect. The photoelectrons
are accelerated and focused onto the first of multiple "dynodes" (secondary-emissive
electrodes), where they are multiplied via secondary electron emission. This process of
secondary emission is repeated over all successive dynodes until the final dynode. There
are up to 19 dynodes over which the photons are multiplied by up to 108 times. The
secondary electrons which have been multiplied and emitted are collected by the PMT
anode. The following subsection describes Cherenkov light production and how it isobserved inside the Super-K detector.

2.2.1

Cherenkov Light

Cherenkov radiation is produced when a particle travels through a medium at a speed
that is greater than the speed of light in that medium, and radiates photons. Cherenkov
24

CHAPTER 2. THE KAMIOKANDE FAMILY[a\radiation does not come from the charged particle ( e± , µ± and τ ± ) itself, but from theatoms in the detector medium. The atoms in the vicinity of the charged particle tracks
are polarised. For fast particles (those with a speed greater than the speed of lightin the medium), there is a symmetry of polarised atoms around the particle track andthese particles that receive the electromagnetic boost produce radiation in the form ofphotons of the wavelength peaked at approximately 400 nm in water, in order to returnto their normal state. A Cherenkov light cone is produced by a cascade of photons that
constructively interfere with each other, where the constructive interference increases
with radiation intensity. The opening angle of the Cherenkov cone, θ, with respect tothe trajectory of the incident particle is defined by Equation 2.1:
cosθ =

1
βn

(2.1)

The particle propagates through the medium with speed βc. The speed of lightin the medium is equal to c/n, where n is the refractive index of light in the medium.
Figure 2.4 demonstrates the Cherenkov light cone production within a detector, and it’sdetection by a photodetector array. In the case of Super-K, the array is approximately
11,000 photomultiplier tubes (PMTs).

Figure 2.4: Diagram displaying Cherenkov light cone [48].
The Cherenkov opening angle θ in water can be calculated using the refractive index
of water, n = 1.34 and β, which can be approximated to β 1 as the particles measured inSuper-K are ultra-relativistic singly charged particles. The Cherenkov angle is therefore
approximately 42◦ . The peak PMT response 2 of Super-K PMTs is between 300-500 nm
making them ideal for the detection of radiation of peak wavelength 400 nm. As the
Cherenkov radiation is produced in the form of a cone shape, the observed Cherenkov
signal inside the detector is in the shape of a ring, which represents a cross-section of
the cone as it reaches the array of PMTs on the detector wall. Figure 2.5 displays on theleft, a signal from an incident electron, and on the right, a muon which both produced
Cherenkov radiation.
2

The wavelength band with the highest quantum efficiency
25

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.5: Example of electron ring (left) and muon ring (right) as seen in Super-K.
The events are observed as a single ring "electron-like" and "muon-like" events.
Electron and muon type rings differ somewhat in appearance and are therefore distinguishable. The differences in the ring appearance arise from the properties of theparticles themselves. Muons are not highly ionising and have a large mass, therefore
they do not often scatter, and thus the Cherenkov ring is clearly defined. Electrons on
the other hand are much lighter and scatter more often.The electrons associated with
the T2K beam also have a tendency to shower due to the neutrino energies. Electrons
therefore producing a "fuzzy" appearing ring. The threshold energy values for e± , µ±and τ ± can be seen in Table 2.1.
Particlee±µ±τ±

Threshold Energy [MeV]
0.767
157.4
209.7

Table 2.1: Table of Cherenkov energy threshold values in Super-K [49].

The energy and the momentum of the particle which produced the rings can bereconstructed using the information collected by the illuminated PMTs.
ID PMTsThe ID PMTs were developed by Hamamatsu, specifically for the Kamiokande experiments. Professor Koshiba from the University of Tokyo approached Hamamatsu withthe task of creating a large PMT which could easily capture Cherenkov light and havea high photoelectron collection efficiency. The result was a 20 inch (50 cm) glass-bulb
PMT with a hemispherical light input window, and Venetian-blind type dynode of 75 ×
75 mm. This type of dynode creates an electric field that can easily collect electrons. It
is most often used in PMTs with a large diameter which collect direct "head on" light,
26

CHAPTER 2. THE KAMIOKANDE FAMILY[a\and provides a wide field of view, making this type of PMT ideal for use in Cherenkov
detectors. Each of the ID PMTs is covered by a protective acrylic cover to prevent
mass PMT implosion, after the devastating accident where thousands of PMTs weredestroyed. Super-K has 40% PMT coverage in the ID with a distance of approximately
70 cm between the centre of one PMT to the next. A schematic of the ID PMT can beseen in Figure 2.6.

Figure 2.6: Schematic and photograph of the 20 inch Hamamatsu PMT used in the ID.

OD PMTsThe OD contains 1885 8 inch Hamamatsu PMTs: many of which were originally usedin the IMB experiment. They are mounted onto the outer side of the dividing PMT
structure, and point outwards towards the barrel wall. Each of the OD PMTs are surrounded by acrylic wavelength-shifting (WS) plates which are approximately 60 cm2 ,1.3 cm thick and doped with 50 mgL−1 of bis-MSB (bis-(o-methylstyryl)-benzene),
which is a wavelength shifter and is commonly used in liquid scintillator experiments[50]. Images of the OD PMTs and the WS plates can be seen in Figure 2.7. The plates
are used to enhance light collection efficiency by absorbing UV light and re-radiating
photons in the blue-green wavelength region, thus, better matching the sensitivity of
the PMTs [47]. By using the wavelength-shifting plates, the light collection efficiency isimproved by a factor of approximately 1.5.

2.2.2

The Detector Structure

Encapsulated within the 38m diameter, 41m tall stainless steel tank is 50 kton of ultrapure water and a buoyant PMT housing structure, optically separating the inner andouter detectors (ID and OD). The PMT housing structure is a cylinder comprised of anumber of superstructures, each holding 12, 20 inch Hamamatsu PMTs. In total there
27

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.7: Photographs of the 8 inch Hamamatsu PMTs with the waveshifting plates
that are used in the OD.

are approximately 11000 ID PMTs as well as approximately 2000, 8 inch Hamamatsu
OD PMTs, many of which were originally used in the IMB experiment.
The PMT barrel structure consists of 38 towers, 37 of these towers contain fullsupermodules which are 4 PMTs wide, while 1 tower is only 2 PMTs wide. Each tower
is 17 supermodules in height, where each supermodule is 3 PMTs deep. To keep the ID
and OD areas optically separate, layers of black sheet and Tyvek (see Subsection 2.2.3)
are fitted around each PMT in the ID and OD respectively, more information about
these materials can be found in the following sub section. A schematic of the detector
and supermodule structure can be seen in Figure 2.8.

Figure 2.8: Schematic of the Super-K supermodule structure [47].
28CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Although the OD contains many PMTs, it was designed and optimised for use as acalorimeter and veto counter, rather than a particle tracker. The primary role of the OD
is to identify incoming cosmic rays and atmospheric neutrino interactions that involve
particles exiting the ID. The region also acts as a shield against neutrons and γ rays
originating from the mine cavity walls. For further shielding, a layer of concrete resides
between the cavity wall and the stainless steel tank, which was filled in after construction
to decrease the radioactive contamination from the surrounding rock. Occasionallyvery high energy events in the TeV range occur and saturate the ID. In these cases,
the OD can be used for rough reconstruction of such events. The OD also allows theseparation between stopping (muons that stop inside the ID) and cosmic ray throughgoing muons (muons which pass through the detector) which are used in atmospheric
neutrino oscillation analysis.
Geomagnetic Field
Inside the detector there is an average magnetic field of 450 mG with an inclinationof 45◦ with respect to the horizon at the detector site. The Earths magnetic field cancause issues with PMT sensitivity, as the strength and direction of the field can deflect
photoelectrons and systematically bias the PMT efficiency and timing. In order tocompensate for the magnetic field, there are 26 coils on the detector wall, 14 horizontal
coils to cancel the vertical geomagnetic field and 12 vertical coils to cancel the horizontal
geomagnetic field [47]. With compensation coils on and an 100 mG field is applied
parallel to the dynode plate of the 20 inch PMTs [51], the magnetic field is reduced toapproximately 50 mG.

2.2.3

Optical Separation of the Inner and Outer detector

The inner and outer detectors are optically separated by the PMT structure. For full
separation and to further enhance light collection in the OD, the barrel structure is fully
covered with a white reflective material called Tyvek. The space between PMTs in the
ID is covered with "black sheet". The reflective properties of the Tyvek and black sheet
are included in the Super-K simulation software.
Tyvek
Tyvek is a thick and resilient paper like material with high reflectivity (approximately80%) in the wavelength range in which the OD PMTs are most sensitive. Lining thevolume with (white only) Tyvek allows multiple reflections of Cherenkov light, minimising the effects of any dead PMTs, which is essential due to the rather sparse coverageof the OD PMTs. Even though certain resolutions are reduced, the overall detection
efficiency is increased. A second type of "black-white" (BW) Tyvek is used to line theouter part of the ID-OD separation structure. It covers all space between the OD PMTs
29

CHAPTER 2. THE KAMIOKANDE FAMILY[a\and WS plates. The white side of the (BW) Tyvek faces the OD volume and the blackside faces into the dead space between the ID and OD PMTs, optically separating thetwo volumes.
Black SheetBlack sheet is a reflective plastic sheet which covers the structure around the 20 inch
PMTs in the ID. This acts as the first layer of optical separation between the ID and
OD and is also used to mask metal surfaces. The black sheet layers can also be seen in
Figure 2.8

2.2.4

DAQ and Electronics

Signals of the arrival times and charges of the PMT signals from the ID and OD PMTs
are processed by Charge-to-time Converter (QTC) Based Electronics with Ethernet(QBEE) modules. The QBEEs consist of several components, each with specific tasks.
They include components which; convert charge to time and, convert multiple hit times
to digital signals. Using QBEEs provides high-speed signal processing and allows forthe integration of the charge and the recording of the time of every PMT signal. This
information is sent to online computers where a software trigger filters high, low andsuper low energy events via the number of hits received within a 200 ns time window.
[51] The QBEEs are located in 4 electronics huts in the Super-K experimental areaon the top of the Super-K tank. A central electronics hut houses various trigger andreadout modules which are connected to the 4 other electronic huts.

2.2.5

Water Filtration System

The water used in Super-K is sourced from natural water found near the mine. It
undergoes purification via a dedicated water purification system comprised of meshparticle filters to remove dust and other particles. The water is then passed through aheat exchanger to reduce PMT dark noise levels and reduce the likelihood of bacteria
growth. Any remaining bacteria are killed by a UV sterilizer. Heavy ions are removed
and the water passes through a reverse osmosis system and a tank which removes otherparticulates. Any dissolved gas in the water is removed, since radon gas is a large
source of background for solar neutrino events in the MeV range. Dissolved oxygen isalso removed as it encourages bacteria growth. The water then passes through an ultrafilter which removes particles as small as 10 nm. Finally any remaining radon dissolvedin the water is removed by a degasifier. The purified water is continuously recirculated
whilst the detector is in operation. Understanding the water quality and properties isessential for detector calibration as the water quality affects photon propagation in thedetector. The water temperature which is stable at approximately 13.6 ◦ C, is monitored
daily by thermometers which are permanently installed in the tank in eight positions30

CHAPTER 2. THE KAMIOKANDE FAMILY[a\in both the ID and OD volumes. Absorption and scattering coefficients are measured
daily using a laser calibration system, which is described in Chapter 3. Specifics of the
hardware and water coefficient analysis can be found in Chapter 4.

2.2.6

Super-K detector simulation

The Super-K detector simulation software (SKDetSim) is a GEANT3 [52] based program, with neutrino interaction information based on the neutrino interaction model,
NEUT [53]. SKDetSim is used to produce the official Monte Carlo data sets for physics
and calibration analyses. It also allows the production of user specific Monte Carlo simulations. Both neutrino interactions and background events are simulated in order tocompare the data to the simulated expectation. Firstly the type of neutrino-interaction
is chosen and the particles generated in via that interaction can be simulated. The
types of particles produced via specific interaction are defined by neutrino generator
codes (NEUT). The software takes an input kinematics file (often a vector file in text
format) and simulates the particles inside the detector using s series of FORTRAN
codes. Simulations can be produced for all detector phases from SK-I to SK-V byloading specific detector simulation libraries including detector calibration coefficients,
which are built into SKDetSim and based on data from various calibration sources.

2.3

The T2K ExperimentT2K is a long-baseline neutrino oscillation experiment which was designed to reveal themysteries of the neutrino by measuring the now well-known mixing angle θ13 , via theobservation of νe appearance in a νµ beam. Other physics goals include measurementsof neutrino oscillation parameters via νµ disappearance studies, achieving better sensitivity toward θ13 [54], and the precision measurement of sin2 2θ23 and ∆m223 . Since thediscovery of the larger than expected value of θ13 , T2K’s goals have shifted towards theinvestigation of CP violation through constraining the δCP parameter. A schematic of
the T2K experiment can be seen in Figure 2.9.

Figure 2.9: Schematic of the T2K experiment. The neutrino beam is produced at JPARC to the far detector, Super-Kamiokande.

31

CHAPTER 2. THE KAMIOKANDE FAMILY

[a\

2.3.1

The Neutrino Beamline

Neutrinos are produced artificially at J-PARC (Japan Proton Accelerator ResearchComplex) in Tokai, Ibaraki prefecture. J-PARC consists of three accelerators: a linear accelerator (LINAC) which accelerates a H − beam to 400 MeV, a rapid-cycling
synchrotron (RCS) where the beam is converted to H + , and the main ring (MR) synchrotron. The RCS accelerates the proton beam to 3 GeV, after which a fraction of hebeam is delivered to the MR. In the MR, the proton beam is accelerated to 30 GeV
and extracted into the primary beamline. Each proton beam spill is 5µs and consistsof eight proton bunches. To ensure stability, the beam itself is monitored by a series ofbeam monitors which measure the intensity, position and any losses of the beam. The
approximate number of protons on target (POT) per run is O of 1020 . A schematicof the neutrino beamline can be seen in Figure 2.10. One T2K run typically spans amaximum period of approximately 2-3 months per year and run at a beam power of approximately 400 - 500 kW. Inside each run, "beam spills" are selected based on physics
and hardware selection criteria, where each beam spill must contain > 1011 protons witha spill cycle of approximately 0.5 Hz. Each individual run contains O 1022 POT withthe total integrated T2K POT between 2010 and 2019 is equal to 3.4 × 2021 .

Figure 2.10: Schematic of primary and secondary beamline at T2K.
The proton beam from the secondary beamline is focused toward a graphite target
to produce predominantly π ± and a small number of K ± . The mesons are focused bythree 2.1 T magnetic horns, and from there decay into neutrinos [55]. The beam can be
operated under two conditions; forward horn current (FHC) and reverse horn current(RHC). Under the FHC condition, a positive horn current of I = 250 kA is used, which
selects predominantly π + and K + . To operate under the RHC condition, the sign of thehorn current is inverted and π − and K − are selected. This configuration allows for the
production of a neutrino beam to be produced under FHC mode and an antineutrino
to be produced under RHC mode. The mesons produced finally travel through a 96 m
decay volume during which time they decay into neutrinos/antineutrinos. Any hadrons
with energy < 5 GeV are absorbed by a beam dump placed at the end of the decay
32

CHAPTER 2. THE KAMIOKANDE FAMILY[a\volume. Equations 2.2 and 2.3 demonstrate FHC and RHC modes respectively.
π + −→ µ+ + νmu ; K + −→ µ+ + νmu (F HC)(2.2)

π − −→ µ− + ν̄mu ; K − −→ µ− + ν̄mu (RHC)(2.3)

Off-axis Beam
The beamline was designed such that the neutrino energy spectrum at Super-K could
be tuned by changing the off-axis angle. The beam centre is 2.5◦ off axis relative tothe near detector ND280, and Super-K, producing a narrow beam flux peaked at approximately 0.6 GeV. At this fixed off-axis angle, the mean neutrino beam energy is
reduced such that the mean L/E of the beam placed Super-K very close to the firstneutrino oscillation maximum, thus maximizing the oscillation probability at the baseline of 295 km. A simplified diagram of T2K and the off-axis configuration can be seenin figure 2.11 and the prediction of the neutrino beam flux at different off-axis angles
can be seen in Figure 2.12. Also shown in Figure 2.12 is the neutrino energy versus thepion momentum for various angles between the pion and neutrino directions.

Figure 2.11: Simplified diagram of the T2K experiment [56] .
The outgoing neutrino energy can be written as:Eν =m2π − m2µ2 (Eπ − pπ · cos θ)(2.4)

Where mπ , Eπ and pπ are the mass, energy and 3-momenta of the pion, and mµ is
the mass of the muon and θ is the angle between the pion direction and the neutrino.
By differentiating equation 2.4, it can be shown that there is a maximum neutrino,(Eν )max energy for a given neutrino emission angle:
33

CHAPTER 2. THE KAMIOKANDE FAMILY[a\(Eν )max =m2π − m2µ2Eπm sin2 θν(2.5)

Thus showing that for a pion energy which is greater than or less than the maximum
pion energy Eπm , the energy of the neutrino is less than (Eν )max . Due to this, the rangeof possible neutrino energies decreases with a large emission angle θ, and so even witha wide range of pion energies, the range of neutrino energies will be narrow [57].

Figure 2.12: Plot of the predicted flux at different off-axis angles [58].

The off-axis technique reduces the neutrino flux and also reduces the rate of highenergy non-Charged Current Quasi Elastic (non-CCQE) events which risk being misidentified and reconstructed as lower energy CCQE events. Reducing the number ofwrongly-reconstructed events at the first oscillation maximum reduces background contamination to the νe appearance signal.

Neutrino Beam Flux
The beam flux is predicted by using a series of simulations and models. Proton interactions on a target are modeled by FLUKA 2008 [59, 60], a simulation of the secondary
beamline is generated using GEANT3 [52]; and particles that exit from the surrounding material are modeled using GCALOR [61]. Finally, the hadron interaction models
are tuned using data from the NA61 and SHINE experiments [62, 63]. In the coming
years, T2K will undergo an upgrade which will increase the beam power and increase
the neutrino flux at Super-K. The current neutrino and anti-neutrino flux predictions
can be seen in figure 2.13.

34

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.13: Predicted neutrino and anti-neutrino flux at ND280 and Super-K [64].

2.3.2

The Near Detector Complex

The neutrino energy spectrum, flavour content and interaction rates of the neutrino
beam are measured by the near detector complex, which sits downstream of the secondary beamline and the graphite target. The complex consists of an "on-axis" detector,
Interactive Neutrino Grid (INGRID), that monitors the on-axis beam profile and intensity, and an "off-axis" detector, ND208, that measures neutrino interactions, the datafrom which is used to tune flux and interaction models that are fed into the oscillation
analysis. As this analysis focuses on making a model independent measurement of theνe sample contamination, the focus will be on the components of the near detector complex which are used to tune some of the models which the νe appearance analysis andthe NCπ 0 background measurement depends upon.

2.3.3

The On-Axis detector: INGRIDINGRID is composed of 16 identical INGRID modules arranged in a cross shape, witha detector for muons and protons placed in the centre. The detector and the individual
modules can be seen in Figure 2.14. Each INGRID module consists of alternating
layers of scintillator and iron plates whilst the central proton module is made from only35

CHAPTER 2. THE KAMIOKANDE FAMILY[a\the scintillator material. The detector covers an approximate area of 10 m × 10 m andmeasures the centre of the on-axis beam. There are two supplementary INGRID modules
placed on the horizontal aspect (shoulders) of the cross which are used to measure theaxial asymmetry of the beam. INGRID sits within the near detector complex in thesame plane as the beam, whilst the off-axis detector sits 2.5◦ off axis from the beam on
the top of the near detector suite, directly above INGRID.

Figure 2.14: Schematic of INGRID on-axis detector and individual INGRID modules
[55].

2.3.4

The Off-Axis detector: ND280

ND280 (near detector that is 280 m from the production target house), is used to predict
the neutrino interactions at Super-K. The complex consists of a series of detectors andtrackers placed 2.5◦ off-axis to the beam. It sits within a 0.2 T magnet, which throughthe bending of charged particles makes for better determination of kinematics of said
particles entering the complex. The most upstream end of the detector includes a π 0
detector (POD) and further downstream is a tracker comprised of three time projection
chambers (TPCs) and two fine grained detectors (FGDs), all surrounded by an electromagnetic calorimeter (ECal) for detecting γ rays. Side Muon Range Detector (SMRD)
panels are placed around the detector which measures high angle muons that exit fromthe sides of the off-axis detector, and also vetoes cosmic ray muons and events frominteractions which occur within the surrounding materials. A schematic of the ND280
complex can be seen in Figure 2.15.

36

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.15: Schematic of ND280.
The π 0 Detector: P0D
The The π 0 Detector, or P0D is designed to specifically measure the π 0 cross-section
on water, with the focus being on the NCπ 0 production as, NCπ 0 interactions are oneof the highest contributors of background to the νe appearance analysis. A schematicof the detector can be seen in figure 2.16. Although the POD is able to make this measurements, the results do not contribute to the oscillation analysis due to the limitationin statistics and therefore large uncertainties on the measurements.
The P0D itself is comprised of layers of scintillator bars, brass, lead and water suspended in High Density Polyethylene (HDPE) bags. The scintillator bars are triangularpolystyrene bars threaded with Wavelength Shifting (WS) fibres. Layers of scintillator
bars are formed by placing the bars together whilst alternating their orientation. The
scintillation light collected from the subject particles is read out by attaching an Hamamatsu Multi-Pixel Photon Counter (MPPC) to the end of the WLS fibres. The otherend of the MPPC is attached to electronic readout boards [66]. The scintillator layers
are arranged with alternating orientation. The alternation between horizontal and vertical layers allows for 3D particle track reconstruction. The P0D is further subdivided
into four modules which constitute the upstream and central ECals and the upstream
and central water targets. The upstream and central water targets provide the target
medium for interactions. The regions are comprised of 13 (12 for the central target)
layers of repeating patterns of scintillator layers, brass and HPDE bags, whilst both
ECals are identical. Internal interactions are vetoed by the ECal regions, allowing forcontainment of the particles which exit the target regions. As discussed in Chapter 7,
section 7.2.5, the P0D can be operated under two configurations, Water-in and water37

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.16: Schematic of the P0D detector [65].
out. During the water-in stage, the HPDE bags are filled in order to measurements of
the interactions on water. For operation in the water-out configuration, the bags are
drained.
Events are reconstructed in the P0D through simulations of all near detectors. The
neutrino beam flux is estimated through beam MC, which is propagated through theentire detector geometry. The behaviour within the WS fibres, MPPCs and scintillator
bars is simulated using GEANT4 [52]. The full analysis uses a combination of global
and local detector simulations. More information on the P0D and the reconstruction
can be found here [65].

2.4

The Hyper-Kamiokande ExperimentHyper-K will be the next generation water Cherenkov detector, located only 8 km fromSuper-K in the Tochibora mine, Kamioka-cho. With Hyper-K’s larger dimensions of;
68 m diameter, 72 m height, and 257.8 kton mass (188.4 kton fiducial volume), it boasts
a rich neutrino research program. The current single cylindrical tank design can be seenin Figure 2.17.

38

CHAPTER 2. THE KAMIOKANDE FAMILY[a\

Figure 2.17: Illustration of first single Hyper-Kamiokande tank in Japan [67].
Similar to Super-K, Hyper-K will use 20 inch Hamamatsu PMTs, however the PMT
dynode type will be changed to the "box and line" type. The newly developed PMTs
have high resolution and high efficiency, improving single photon detection by a factorof 2, and single photon timing by 2 ns. The new Hamamatsu R12860 PMTs should be
able to amplify faint signatures such as those from neutrons associated with neutrino
interactions and nuclear de-excitation gammas. It is expected that the photocoverage
will be between 20 - 40% with the possibility of using some "mPMT" (multi PMT)
modules alongside the 20 inch PMTs to increase photocoverage.

2.4.1

Hyper-K as a far detector

Hyper-K will be the far detector for T2K and operate under a similar configuration
to T2K currently, as T2HK. It is predicted that the neutrino beam power will be approximately 1.3 MW and will deliver a POT O 1022 over a 10 year period, providing
an increase of a factor of 10 over the current T2K POT. As well as the detector complex ND280, there will be an "intermediate Water Cherenkov (WC) detector" placed
approximately 1-2 km from the J-PARC beamline. The intermediate detector will further reduce systematic errors which Hyper-K requires in physics analysis. The WC
type of detectors are proven to be able to identify particles with high accuracy andwill provide the ability to directly measure neutrino interaction cross-sections on waterwith the same solid angle acceptance as the far detector. With this addition, numerous
particle samples that are considered background in physics analyses can be measured.
Such samples include pure νµ -CC, νe -CC and NCπ 0 samples. The measurement of the39CHAPTER 2. THE KAMIOKANDE FAMILY[a\

CCπ 0 and kaon production in neutrino interactions will also be available, which arebackgrounds in nucleon decay searches.

Figure 2.18: Prediction of the neutrino and anti-neutrino flux at Hyper-K [67].
Figure 2.18 shows the prediction of the neutrino and antineutrino flux at Hyper-K.

2.4.2

Physics Goals

One of Hyper-K’s main physics goals is the measurement of CP violation in the lepton
sector [50]. The combination of the size of the detector and the high power off-axis beam
will enable previously challenging physics studies to become accessible. A detector massof at least O(102 ) kton is necessary in order to accumulate O(103 ) νe signal events fromthe J-PARC neutrino beam, which is required to measure effects of CP violation to an
accuracy of a few percent.

Figure 2.19: Comparison of past, current and future nucleon decay experiments. [67].
The scale of Hyper-K will also aid other studies, such as; neutrino oscillation including the determination of the mass hierarchy; the θ23 octant; the search for proton
decay; the observation of cosmic ray neutrinos; and the potential to observe supernova
neutrinos. Hyper-K is expected to improve the current bounds set by Super-K for avariety of non-standard neutrino properties, including the possible presence of sterile
40CHAPTER 2. THE KAMIOKANDE FAMILY[a\neutrinos and non-standard interactions of neutrinos with matter. Figure 2.19 shows acomparison of limits on the rates of nucleon decay for several key modes. It shows that,over 10 years of exposure, Hyper-K is sensitive to nucleon lifetimes that are predictedby modern grand unified theories.

2.5

Summary

Both Super-K and T2K have contributed substantially to neutrino physics in the previous two decades with Super-K making the first direct measurement of supernova neutrinos and T2K providing the best constraints on the δCP parameter. Hyper-K will be
the next generation in water Cherenkov detectors and will have approximately 8.4× thevolume of Super-K. The construction is due to begin in the early 2020’s and operation
begin in the mid 2020’s. The larger detector size and increase in statistics should allow
Hyper-K to make measurements of neutrino mass hierarchy and δCP alongside being
supernova ready.

41

CHAPTER 2. THE KAMIOKANDE FAMILY

[a\

42

Chapter 3

Calibration at Super-Kamiokande"It’s only our methods that differ; we
use the latest in scientific technology
and state of the art weaponry and you,if I understand correctly, poke themwith a sharp stick."
Maggie Walsh - A New Man

There are two categories of calibration; those which calibrate the underlying detector properties such as PMT gain and the water properties, and physics calibrations
such as those for vertex resolution and energy scale. A comprehensive calibration program provides a quantitative measurement of the detector performance, response anddetector-related systematic uncertainties which are required for physics analyses. SuperKamiokande employs numerous detector calibration techniques that allow continuousand periodic calibration of the detector properties. Extensive detector calibration allows
many parameters to be well defined, thus improving the overall quality of data. This
chapter provides an overview of techniques used in calibrating the inner detector, with afocus on the photon propagation calibration technique which the author was responsible
for.

3.1

Photon Propagation

It is important to monitor and understand water properties in a large scale detector,
since the water properties could potentially change with depth. Photon propagation
is influenced largely by the water properties, whilst the Particle Identification (PID) isalso affected. Changes in water quality and transparency can be signs of contamination.
By making measurements of scattering and absorption coefficients, one can distinguishbetween the presence of atomic and molecular contamination of the water.
43

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE

[a\

3.1.1

Rayleigh and Mie Scattering

Rayleigh and Mie scattering are types of elastic scattering, where the scattered lightis polarised and the incident and scattered light is of the same wavelength. Rayleighscattering primarily relates to light scattered from particles that have a diameter of1approximately 10th of the incident light wavelength λ and varies as a function of λ−4 ,whilst Mie scattering has little to no wavelength dependence. This type of scattering
primarily relates to scattering of light off particles with a diameter greater than theincident light wavelength [68]. Figure 3.1 displays the patterns of Rayleigh and Mie
scattering.

Figure 3.1: Diagram displaying Rayleigh and Mie scattering [69]. Rayleigh scattering
consists of both forward and backwards going symmetric scattering in relation to thedirection of incoming light whilst Mie scattering consists of symmetric backwards going,
and asymmetric forwards going scattering.

In the following section, 3.1.2, these scattering types have been combined to form
symmetric αsym and asymmetric αasy scattering coefficients. The symmetric scattering
coefficient consists of contributions from both Rayleigh and symmetric (backwards) Mie
scattering, whereas the asymmetric scattering coefficient consists of only forward Mie
scattering.

3.1.2

Scattering and Absorption Measurements

Scattering and absorption parameters are measured by vertically injecting a collimatedlaser beam into the tank over five wavelengths. Figure 3.2 shows the current systemand each of the seven light injection points; "Top", "Bottom" and "B1 - B5" (Barrel
positions 1 - 5). The horizontal injectors at B1-B5 are not used in the analysis, but thesame notation is used for the five regions that the detector is divided into during theanalysis of the vertically injected light. This system and the data analysis method is
described in full detail in Chapter 4.

44

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

Figure 3.2: Current optical calibration at Super-K. The five horizontal light injection
points are denoted by B1-B5 which are not used in the analysis. The labels B1 to B5
also is used to denote the 5 regions that the barrel is split into during this analysis.
Schematic adapted from [47]The timing and spatial distributions of the injected light are measured and comparedto Monte Carlo (MC) simulations, allowing the extraction of absorption and scattering
coefficients as a function of time [51]. The total number of scattered photons andthe shape of the timing distributions are used to tune the symmetric and asymmetricscattering, and the absorption parameters for the calibration MC. Equation 3.1 describes
the water transparency, Lλ , as a function of the absorption and scattering amplitudes;
asymmetric scattering αasy , symmetric scattering αsym and absorption αabs .
L(λ) =

1αabs (λ) + αsym (λ) + αasy (λ)(3.1)

The symmetric scattering can be described as 1 + cos2 θ, where θ is the scatteredphoton angle. The asymmetric scattering increases linearly between cosθ = 0 to 1, andno scattering occurs for cosθ 6 0. Equations 3.2 to 3.5 describe the scattering andabsorption parameters, and an absorption amplitude based on experimental data.
αabs = P0 ×

αsym =

P1+ C, λ = 464nm
λ4

(3.2)

P1
P5
× (1 + 2 )
4
λ
λ

(3.3)

αasy = P6 × (1 +P7× (λ − P8 )2 )
λ4
45

(3.4)

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

C = P0 + P2 × (λ P3) , λ 6 464nm
500

(3.5)

Where P0 - P8 are fitting parameters. The second term, C in equation 3.2 is theabsorption amplitude at λ = 464 nm based on experimental data. The value C inequation 3.5 is the absorption amplitude for λ 6 464 nm. These fitting parameters thatcan be found in [51] are used to calculate the values for 1/αabs , 1/αsym and 1/αasy
which are calculated to be 4.02 × 102 , 1.76 × 102 and 9.89 × 103 respectively. For
each of the five wavelengths, the three α parameters are fitted with polynomials which
generate the wavelength dependent curves in Figure 3.3.

Figure 3.3: Plot of typical fitted water coefficient functions used in SK-MC. Data taken
in 2009. This plot shows the points for absorption, asymmetric scattering and symmetricscattering. [51]The fit functions for the scattering and absorption coefficients, obtained from datafrom April 2009, are used in SKDetSim as the default water tuning for SK-IV. Based on
this calibration method, for a wavelength value of λ = 400 nm, the water transparency,
Lλ , in Super-K is approximately 120m.

3.2

PMT Response

Event energy and position reconstruction is performed using timing and charge information which is provided by the PMTs inside Super-K. The PMT charge can be parameterised by two factors: its quantum efficiency (QE) and the PMT gain. The gain is
the conversion factor between the number of photo electrons (p.e) on the PMT cathode46

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\and the charge in pico Coulombs (pC) output by the PMT. The QE is defined here as
the ratio of the collected p.e’s to the number of photons incident on the cathode. To
understand these properties, calibrations must be performed with respect to the PMT
QE and the gain.

3.2.1

PMT High Voltage setting

The PMTs must be calibrated such that their output charge per number of incident
photons is relatively uniform over all PMTs. To achieve this, the high voltage setting
for each PMT is adjusted by recording its response to an isotropic light source. The
Isotropic light source is a scintillator ball, into which light from a Xenon (Xe) lamp
enters through an optical fibre. Figure 3.4 displays the schematic of the calibration
method.

Figure 3.4: High Voltage calibration using a scintillator ball [51]Between the phases SK-II and SK-III, 420 PMTs were calibrated before installation which act as a reference point for the PMTs inside the detector that weren’t precalibrated. These PMTs are highlighted in red in Figure 3.4 and are used to accountfor geometrical differences within the detector. The HV setting for each PMT is thentuned such that its charge output matches that of the pre-calibrated PMTs in the same
geometrical location.

3.2.2

Relative Gain Calibration

The gain of the PMTs drifts over time and can cause artificial changes in the observed
amount of collected charge per event. The gain is a conversion factor between the output
charge from the PMTs and the observed number of photo-electrons. The relative timingof PMTs is necessary for accurate event reconstruction, and the monitoring of detector
medium properties is essential for enabling correct PID during analysis. The relative47

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

Figure 3.5: Relative gain calibration using timing calibration system [51]gain calibration of the PMTs is performed using a constantly deployed diffuser ball,through which a light source is sent via an optical fibre. The light source is a nitrogenlaser which has its wavelength modified by a dye, such that the wavelength of theemitted photons is shifted to correspond to the PMT response region. A diagram ofthe experimental set up can be seen in Figure 3.5. The system produces light pulses of
two intensities; a high-intensity flash of light which illuminates all PMTs simultaneouslywith multiple photons, providing an observed charge value Qobs (i); and a low-intensity
pulse which illuminates only a small percentage of PMTs, required to simulate single
photon hits. The PMT gain G(i) is shown in Equation 3.6.
G(i) ∝

Qobs (i), i = P M T id
Nobs (i)(3.6)

The low-intensity pulse provides a hit threshold Nobs (i). As the light source is not
moved, the geometrical acceptance and quantum efficiency cancel out.

3.2.3

Absolute Gain Calibration

Absolute gain conversion is performed using a nickel (Ni) source in the form of a sphericalball, inserted into the tank during Ni calibration periods. The Ni ball emits a stablesource of single photo-electrons, via isotropically emitting a 9 MeV gamma cascade fromneutron capture 58Ni(nγ) 59N, where the neutrons are emitted from a 252Cf source within
the ball. The low intensity γs produce approximately 0.004 p.e/PMT, ensuring that over
99% of the hits produce an occupancy1 of 1 p.e/PMT. The Ni calibration provides asingle p.e and charge distribution over all ID PMTs which when averaged, provides a1

Occupancy is defined as the number of p.e generated by a PMT divided by the total number of p.ecollected by all PMTs
48

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

Figure 3.6: Ni ball with contained 252Cf source [51]conversion between the charge to single p.e. Once the p.e is determined, a calculation of
the corresponding charge is performed and compared to the threshold of the electronics.
In the most recent phase of Super-K, SK-IV, the conversion factor between pC to p.e
is 2.658 pC/p.e. As observed in numerous experiments that use PMTs, the PMT gain
in Super-K increases over time. The reason for this occurrence has not been identified
however in physics analyses, a run by run gain correction is applied to the data.

3.3

Energy Scale

Due to WC detectors being primarily sensitive to high energy neutrino events, thedetection and measurement of low energy events is somewhat hindered. For example, ahigh energy event in Super-K can be easily detected by the characteristics of the observed
Cherenkov radiation and the large number of hit PMTs. For low energy events, thenumber of hit PMTs is very low, where roughly only six photo-electrons are collected,
thus only a few PMTs receive single photo-electron hits. The number of hit PMTs
must be translated into a measurement of energy. To achieve this, the energy for low
energy events in Super-K is determined by absolute energy scale calibration using alinear accelerator (LINAC) and a deuterium-tritium neutron generator (DT) [70].

3.3.1

LINAC Calibration

The LINAC, or LINear ACcelerator has been permanently installed in the Super-K experimental area since 1996. It is a commercial LINAC which was originally built in 1978
for use in hospitals for medical purposes. A schematic of the LINAC calibration can beseen in Figure 3.7. The LINAC produces an accelerated electron beam, whose direction
is steered by a series of magnets. The energy of the beam is measured and calibratedusing a germanium detector with keV level resolution. The number of electrons entering
the transportation tube is tuned using a collimator in order to exclude multi-electron
events. The beam position in Super-K is dictated by the length of the beam pipes used[71]. The black points on Figure 3.7 display the usual positions where LINAC data is49

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

Figure 3.7: Schematic of LINAC calibration [71]taken. Data taking is performed over a two week period with electron ranges between
4.4 MeV to 18 MeV, which matches the range of the low energy solar neutrinos, forwhich such an energy scale calibration is necessary. The data are used to determine theenergy scale, energy resolution and angular resolution of the detector. Reconstruction
likelihoods are also built for the reconstruction of low energy electrons, in order to checkdata quality and cut criteria.
LINAC data was taken five times over the SK-IV period. Calibration analysis results
are used to set the absolute energy scale in Super-K MC detector simulation. The
MC extrapolates the calibration to the entire energy, volume and direction ranges,
thus providing an absolute energy scale calibration. The LINAC has limitations, inthat the electron beam always enters the tank in the same downward direction andso the measurements cannot accommodate for an angular dependence. The direction
dependence and detector mapping is checked using a DT (deuterium-tritium) source.

3.3.2

DT Calibration

The DT source is used to fill in the gaps left by the LINAC calibration and provides
a cross-check of the energy scale. The DT generator creates 14.2 MeV neutrons via
16

N(n,p) 16O 2 in the water inside Super-K. Approximately 72% of the 16N decays are

via the βγ process and approximately 28% are via a pure β decay. This particular 16N
decay is dominated by an electron with a maximum energy of 4.3 MeV and a γ ray of 6.3
MeV, which matches well to the energy range of low energy solar neutrinos mentioned in
Section 3.3.1. The DT source is lowered into the detector at several different calibration
ports and data is taken at each position. The 16N is created in situ by lowering the
2 16

N has a halflife of 16N is approximately 7.13 s
50

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\

Figure 3.8: Energy reconstruction of events generated by the LINAC [71]DT source into the detector and firing the source, producing approximately 3 million
neutrons which interact with Oxygen and travel a distance of approximately 10 - 15 cm.
The source is then automatically withdrawn by a distance of 2m in order to allow the16

N to decay without any interference from the calibration source itself. A schematicof the DT calibration procedure can be seen in Figure 3.9. The DT data taking periodspans approximately three days and is repeated several times per year. During years
when LINAC data is taken, DT data is taken before and after the LINAC calibration
period.

Figure 3.9: DT calibration [70]The creation of 16N in this way allows for events to be created which have a wellknown energy distribution. Since 16N decays isotropically, measurements of systematic51

CHAPTER 3. CALIBRATION AT SUPER-KAMIOKANDE[a\components can be made which are not easily measured by the LINAC, such as directional dependence of the energy scale.

3.4

Summary

A comprehensive calibration system allows for a better understanding of the detector
response and therefore detector simulation. Great calibration efforts have been madeat Super-K over the years which have allowed bother Super-K and T2K to reach their
desired physics goals.

52Chapter 4

The Super-K Laser Calibration
System"In every generation there is a chosen
one"
Giles - Season 1 and 2 narration

The calibration procedure for photon propagation was briefly described in chapter
3, section 3.1. The equipment and analysis from here is referred to as "The Super-K
laser calibration system". This chapter describes in full, the system hardware, analysis
flow and derivation of water coefficients inside Super-K. The author of this thesis has
been the "water laser" expert for the period of November 2016 - February 2019, during
which time the author was based on-site at Super-K. The author performed all necessary
hardware and system maintenance alongside software updates and maintenance. The
methods and software used to derive the water coefficients were originally developedby the Korean Super-K group and had minimal development over the period spanning2009 to 2016. The author maintained and built upon the existing tools and made major
improvements to the water coefficient derivation methods and documentation.
If anyone asks why I know so much FORTRAN77 and PAW. This is why. Welcome
to the 90s.

4.1

The Laser System

Laser injection fibres are placed at 8 locations along the vertical and horizontal ID barrel
region. Figure 4.1 shows the injector positions inside the detector. The first injector
to be installed was the oldest top injector (OT) in 1999, which was lowered down acalibration port into the detector and was not physically attached to the inside of thedetector. In 2002, as part of the SK-II upgrade, injectors were installed at seven more53

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\positions inside the detector; five on the barrel wall with 6 m spacing (B1 - B5), oneon the tank bottom (BT) and one on the tank top (NT). The OT injector was removed
in 2018 during the most recent refurbishment. Laser light is injected into the detector
at five wavelengths, at each injector position: however, only the new top (NT) injector
data is used to derive the water coefficients. The barrel injectors B1-B5 are not used
for analysis however the same labels are used to define the five equal regions that thedetector is divided into during the analysis of the vertically injected light. From thelight injected vertically the scattering and absorption coefficients can be measured, as
shown in Figure 4.1. Derivation of the water coefficients is described in Section 4.4.

Figure 4.1: Cartoon of injector positions, spacing and fibre entry points to the detector.

There are four Laser Diodes and one Nitrogen dye laser in the system which sit
outside the tank on top of the detector, alongside all electronics. Table 4.1 lists the
wavelengths and laser types. The lasers are situated on the tank top close by to the
OT injection entry port. There is one fibre bundle output from the laser box whichcontains seven individual outputs. There are five 1 mm core fibres which are fed into
two system monitor PMTs, and two monitor avalanche photodiodes (APDs) with one
spare output. The last two outputs are 200 µm core fibres, one of which is the input
into the detector and one is spare. The Super-K input fibre is connected to a step54

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

Wavelength (nm)
337
375
405
445
473

Laser Type
Nitrogen
Diode
Diode
Diode
Diode

Table 4.1: Summary table of Super-K laser wavelengths and types.

motor inside an "optical switch box" which is controlled by a dedicated networked PC.
There are eight output fibres from the optical switch box which correspond to the eight
injector positions. The inside of the optical switch box can be seen in Figure 4.2.

Figure 4.2: The light tight optical switch box has one input fibre from the.

The control script registers the physical location of the switch and has the distances
between each fibre output hard coded. The user or automated control inputs the desired injector position and the script communicates with the step motor and converts
the input to a physical distance by which to move.

55

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM

[a\

4.2

The Optics

An example of the light injector hardware which is installed inside the tank can be seenin Figure 4.3. Each position has two stainless steel injector casings which are mounted
into stainless steel mounts.

Figure 4.3: Injector flanges, fully assembled injector and face on view of mounted hardware.

Each mounting plate has a black PVC surround attached, which has an inner red
PVC coating. This absorbs any off-axis light and avoids excess noise in neighbouring
PMTs. The fibres are pre-inserted into a protective stainless steel flange. During assembly and before introducing the fibre flange into the main injector body, Nitrogen gas is
injected into the stainless steel enclosure in order to prevent condensation on the quartz
glass window. The window is in place to ensure that the fibre end is not exposed towater. The flanges can be seen in Figure 4.3 along with a face on view of the assembled
and mounted hardware.

Figure 4.4: Full view of injector mounting in detector barrel wall.
Figure 4.4 shows the full injector and mount installed at one of the horizontal barrel
positions.
56

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM

[a\

4.3

Online Data Taking and Monitoring

During normal data taking, calibration data is taken automatically for all continuously
running calibration sources. The "auto-calibration" program cycles through each of
the calibration sources including each Super-K laser system wavelength and position
alongside other sources which are not mentioned here.

4.3.1

Auto-calibration Process

The auto-calibration process is an automated program which loops through multiple
calibration sources during normal physics data taking. A "normal" Super-K run isof a maximum length of 24 hours. During online data analysis all bad channels aremasked (i.e dead PMTs), the data is reformatted and the various calibration source
events are separated from the main reformatted data. Each set of calibration eventsare programmed to occur in calibration source specific time window, which is used toseparate each sources events into their own data files. To distinguish the laser calibration events from the physics events the NIM trigger signals for the calibration eventsare duplicated and sent to a dedicated "calibration" QBEE, therefore each calibration
event will include a a calibration specific flag which is checked in the data. During the
SK-IV period, the cycle length of the auto-calib process was 3.6s, therefore, the time
between one event from the NT injector to the next of the same wavelength is 3.6s.
During "test" data taking, the auto-calibration process is usually disabled.

4.3.2

Super-K Laser System Monitoring

System monitoring is performed on a run by run basis. At the end of each normal
Super-K run, the water laser monitoring software automatically reads in the collected
monitor PMT information, the total collected charge in the detector and the total number of events collected, from the output data files which were reduced in the online
process. Figure 4.5 shows the monitor information for the NT injector displayed over
the whole of the SK-IV period, and over the course of one year. These plots are checked
daily by the experts in order to identify any abnormal behaviour and make short term
corrections to the system when necessary. When instabilities in the system are spottedhere and accounted for, they lead to the long term improvement of the system, which
can clearly be seen by the bottom plot of the SK-IV period.

57

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

Figure 4.5: Example of day by day monitoring including the total charge collected inSuper-K and the monitor PMT data.

58

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM

[a\

4.4

Derivation of Absorption and Scattering Coefficients

Water scattering and absorption coefficients are derived from the laser calibration databy comparing data to a large set of calibration Monte Carlo (MC) files which are generated for each laser wavelength, with every combination of scattering and absorption
factors within a range defined by a data reference period. A χ2 best fit method is thenapplied in order to extract the best fit water coefficients. Firstly, timing distribution
histograms are created from the reduced data for light injected from the NT injector.
The detector is split into five barrel regions, as can be seen in Figure 4.6. Histograms ofthe number of hits/event vs. corrected time of flight within the scattered hit region are
created for each wavelength, as measure at each barrel position. The barrel positions
are defined within the analysis code.

Figure 4.6: Detector divided into five barrel positions. Light is injected vertically andthe number of hits and charge are measured at each of the five positions, for eachwavelength.

Figure 4.7 displays the timing distributions as measured at all positions in the detector using light injected by the 337 nm laser. The combined information for each barrel
position is also shown. The charge/event vs. corrected time of flight for all PMTs isdisplayed for all positions alongside the hits/event vs. corrected time of flight in the
scattered hit region. The scattered hit region is the region outside of a 2 m radius of theinjector, and outside of the beam spot. Dark noise regions can be seen as highlighted
in blue, with the wavelength region labelled. The scattered light region can be seenin the left hand broad peak on all histograms and the reflected region is the smaller
right hand peak. As can be seen, the reflected light peak increases as a function of
Z and eventually it becomes increasingly difficult to distinguish between the scattered
59

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\and reflected hits. After dark hit subtraction, the selected signal region is highlighted
in green on the bottom left histograms.

Figure 4.7: Timing distribution histograms for light injected from the NT (TOP) injector. Histograms are the hits/event vs. corrected time of flight withing the scattered hit
region. In order left to right of the eight images, NT, B1 - B5 and finally the bottom
right two are measured position combined histograms of charge/event vs. corrected
time of flight for all PMTs and hits/event vs. corrected time of flight in the scattered
hit region. Specific example is for 337 nm laser.

The next step is to normalise the data to account for fluctuations in the laser intensity. This is done by dividing the number of hits (N) by the total charge (Q) in thedetector, to produce N/Q histograms. These histograms can be seen in figure 4.8. The
left image displays the original N/Q histogram before the dark hits are subtracted from60

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\the signal region. The right image is the same N/Q histogram with dark hits subtracted,
however it has been re-binned into a 200 bin histogram in preparation for comparing to
the water laser MC. The fast response region (rising of the first peak) and the reflectedpeak (second peak) and not reproduced will with the MC, so only certain bins from theN/Q distributions are used to calculate χ2 in the data MC comparison. The region of
selected bins is contained between the two black lines on each histogram.

Figure 4.8: The left hand image is the original N/Q histogram before the dark hits are
subtracted from the signal region. The right hand image is the same N/Q histogramwith dark hits subtracted and then re-binned into a 200 bin histogram in preparation forcomparing to the water laser MC. The scattered hit region can be seen to be enclosed
between the two black lines.

Figure 4.9 shows the data MC comparison with data in black and MC in red, whichclearly shows that the reflected peak at the NT position is not fit well with the MC.
The χ2 value is calculated by comparing the data to MC and extracting the best fit
parameters. The water coefficients are calculated from here.

61

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

Figure 4.9: Data MC comparison with data in black and MC in red. It’s clear that thereflected peak at the NT position is not fit well with the MC. From top to bottom thepositions are NT, B1 - B5.

4.4.1

Time variation of water coefficients

The water coefficients are presented as daily and monthly averages depending upon thetime period of interest. An average value is calculated since the coefficient measurements
themselves have no error assigned, so the error on the time variation of the coefficients
becomes the statistical error on the average. Extra data selections are applied whencalculating such time variation. The event selections are to ensure that only reliabledata is used; for example, "bad" laser events are removed corresponding to events whichyielded a total charge in the detector of less than 400 p.e. Run time and event rate
are also included in the data selection. Selecting runs with greater than 200 events per
run acts as an indirect cut on run time. This number of events corresponds generally
to runs of less than 3 h. Data with an event rate outside of the range of 60 to 180
events per hour is removed. The final cut is on badly fitted data, where data with a χ2
value of greater than 300 is removed. Figure 4.10 shows the time variation of the water
coefficients as displayed by a 30 day average over the SK-IV period.
62

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

Figure 4.10: Scattering and absorption coefficients for all five wavelengths before analysis improvements.

63

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

It is interesting to note that over the period, the symmetric scattering coefficientincreases which is not a reflection on the physical water coefficient but on a missing
piece of the analysis which will be discussed in the next section.

4.4.2

Implementation of Number of Hit Correction

Over time the gain of the PMTs in the detector changes. The reason for this is not clear,
however similar behaviour is observed in other experiments using PMTs. On average
this change is approximately 2 % per year. The time variation of the gain has been monitored and accounted for on a run by run basis in the more recent detector simulation
libraries; however it had not been accounted for in the water laser analysis. Effects ofthis are reflected in an artificial increase in the symmetric scattering coefficient. Figure
4.11 shows the time variation of this coefficient for wavelengths 337 nm and 445 nm anddemonstrates the effect on the uncorrected data in the analysis. After the correction isapplied, it was expected that the RMS/mean variation would decrease and little to no
increase in the coefficient over time would be seen.

Figure 4.11: Symmetric scattering coefficient for 337 nm and 445 nm wavelengths, with
RMS/mean time variation.

When applying the gain correction to the data, charge and hit corrections weredone separately. The charge correction was applied by an official gain correction program which was applied when reprocessing the raw data into a readable format. This
program uses a table of data of run number and gain increase per PMT inside the detector. Information is present for each PMT production year batch. When applied tothe data, the charge collected per PMT is recalculated accordingly based on the gainincrease specific to that PMT and its production year. Figures 4.12 and 4.13 show
the official plots of PMT production year vs. Z position in the detector, and the gainincrease for each PMT batch as a function of Super-K run number.

64

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

The correction to the number of hits was done during the process of generating
the data histogram files. When building the correction into the data analysis, it was
important to make a prediction about how much change was expected in the numberof hits collected in the detector. The prediction was made by using the two plots in
Figures 4.13 and 4.12. Figure 4.13 shows the several PMT batches as a function of Z.
Most of the PMTs on the bottom of the tank (inside the vertical laser injector beamspot) were manufactured in 2005, thus, the predicted change was calculated based on
the 2005 data set in yellow in Figure 4.12, and a hit correction factor developed by the
low energy working group [49].

Figure 4.12: official plots of PMT gain increase for each PMT batch as a function ofSuper-K run number [72].

The chosen period to make the prediction was 2009 to 2015, suggesting that the
PMT gain would increase by approximately 10 % during this time. This change wasmultiplied by a conversion factor of C = 0.226, derived by the low energy group, whichstates that the effective number of hits increases by 22.6 % as PMT gain increases by
100 % (which is independent of production year). The predicted change over the given
period was predicted to be 2.26 %.
The hit gain correction was applied using the following equations:1
1 + (C × G(i))(4.1)

G(i, run) − G(i, ref )G(i, ref )(4.2)

Ncor =

G(i) =

Here Ncor = the corrected number of hits. The timing distribution histograms areweighted with this value. G(i) is the gain factor calculated based on PMT production
year information, where (i) is the production year index. G(i, run) is run specific gain
65CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\

Figure 4.13: official plots of PMT production year vs. Z position in the detector [72].
correction factor obtained from the official gain correction tables, and G(i, ref ) is areference gain value defined in the data analysis software.

4.4.3

Results and Conclusion

The increase in the number of hits in the data was calculated to be 2.3 %. Figure 4.14
shows the symmetric scattering coefficient after the gain correction has been applied.
For easy observation of the correction effect, the plot shows again only wavelengths
337 nm and 445 nm wavelengths.

Figure 4.14: Gain corrected Symmetric scattering coefficient for 337 nm and 445 nm
wavelengths, with RMS/mean time variation for the SK-IV period (2009 - 2018).

The results agree with the prediction, showing no artificial increase over time. The
RMS/mean time variation is also significantly reduced by approximately 1 % in both66

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\cases. A full collection of corrected water coefficients can be seen in Figure 4.15.

Figure 4.15: Gain corrected scattering and absorption coefficients for all five wavelengths.

67

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM[a\Table 4.2 displays a summary of the RMS/mean variation over the SK-IV period
for the symmetric and asymmetric scattering parameters and the absorption coefficientvalues for all 5 wavelengths are shown. The RMS/mean is defined as the RMS value ofthe data over the SK-IV period divided by the mean of the data points points over the
SK-IV period. The attenuation length is not included here as it is a sum of the scattering and absorption coefficients, and is not used in analyses. After the introductionof the hit correction to the data, the RMS/mean variation over time for the scattering
coefficients has significantly decreased over all wavelengths as expected, whilst the variation of the absorption coefficient has increased in most cases.

Coefficient
Symmetric

AsymmetricAbsorption

λ (nm)
337
375
405
445
473
337
375
405
445
473
337
375
405
445
473

Old RMS/mean (%)
1.5
1.5
1.6
3.9
1.4
16.6
18.1
13.7
8.3
16.3
8.7
9.2
6.2
5.6
2.2

New RMS/mean (%)
0.7
0.6
0.7
2.2
0.8
13.4
17.8
14.8
6.6
14.4
11.4
10.7
6.2
5.8
2.7

Difference (%)
-0.8
-0.9
-0.9
-1.7
-0.6
-3.2
-0.4
-1.1
-1.7
-1.9
+2.7
+1.5
± 0.0
+0.2
+0.5

Table 4.2: Summary of the RMS/mean variation over the SK-IV period for the symmetric and asymmetric scattering parameters and the absorption coefficient, over all
wavelengths.

The table of RMS/mean variation can be used to scale scattering and absorption
coefficients within SKDetSim for the SK-IV period. The water coefficients are tuned
within SKDetSim to a period of known stability. This study provides a data driven estimation of the variation over the period which includes the PMT gain variation over time.

68CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM

[a\

4.5

Summary

After the gain correction was applied to the SK-IV phase, the data no longer displays an
artificial increase in scattering lengths over time as predicted. The correction provides
a more accurate derivation of the scattering and absorption coefficients and a central
value for the period which will be used as a reference point for future MC generations,and has already been used for feasibly studies for the newly developed calibration system which is discussed in Chapter 6.
The Super-K light injection system has some shortcomings in that even though thesystem provides five barrel injector positions that were intended to measure any depth
dependence of the water, the data is not suitable for the analysis. This is due to the sizeof the beam spot being large. Each of the beam spots projected onto the vertical barrel
wall from the horizontally injected light overlap such that it is difficult to isolate thelight in these five regions. In order to perform the analysis for the depth dependenceof the water coefficients, numerous PMTs outside of the beam spot must be excluded
from the analysis thus reducing the statistics significantly. For this reason a new andimproved system is required to make these measurements. A system which provides
significantly narrower beam profiles which do not overlap with each other. The systemthat has been developed is the UK light injector which will be discussed in detail in
Chapter 6.

69

CHAPTER 4. THE SUPER-K LASER CALIBRATION SYSTEM

[a\

70

Chapter 5

The Super-Kamiokande
Refurbishment"There are no dead students here.
This week."
Principal Snyder - Out of Mind, Out
of Sight

Here begins the story of how the Super-Kamiokande detector became my 2018 summer vacation home.

5.1

Introduction

After the successful phase of SK-IV which ran from 2008 - 2018, Super-K began the
upgrades for the next phase, SK-Gd (Super-K-Gadolinium). The upgrade began with afull refurbishment of the detector, with the aim to assess the toll that ultra-pure watertakes on the detector and to repair it as necessary. The detector hardware also required
some modifications to make every component Gadolinium safe. This chapter provides
an overview of the motivations behind the refurbishment and a brief summary of manyof the refurbishment tasks that the author took part in.

5.2

The Motivation : SK-Gd

The Super-K upgrade commenced in the summer of 2018, when the detector was officially shut down on May 31st at 9:01am. Super-K-Gd, or, SK-Gd will see the gradualaddition of water soluble gadolinium sulphate (Gd2 (SO4 )3 ) up to final concentration of
0.2%. Gadolinium has a large thermal neutron capture cross-section, with an intrinsic
8 MeV gamma cascade, which is above the detector threshold, and therefore easier todetect than the 2.2 MeV signal from neutron tagging on hydrogen.

71

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\

The addition of Gd will open the doors to some previously un-achievable physics forSuper-K, which is currently hindered by backgrounds. One of the most important andimpressive prospects, is that SK-Gd should be able to make the world’s first observationof the diffuse supernova neutrino background (DSNB) [73]. Neutrinos from the DSNB
can aid in unravelling the mysteries of star formation history in the universe. Reactor neutrinos and atmospheric neutrinos are the dominant background sources below
10 MeV and above 30 MeV respectively, leaving the 10 MeV - 30 MeV energy window
open for DSNB measurements [74]. Currently Super-K searches for DSNB neutrinos bydetecting both prompt positron signals and by coincidence detection of positrons and delayed 2.2 MeV gammas from protons which capture neutrons. Due to the poor efficiency
of detecting 2.2 MeV signals using Cherenkov light, such measurements are constrainedby backgrounds. Background reduction is performed by identifying the 2.2 MeV gamma
ray signal produced via thermal neutron capture on hydrogen. Tagging of the events
which produced neutrons allows for significant background reduction by reducing thenumber of decay electrons produced by muons below Cherenkov threshold in the data
samples.
The addition of 0.2% (Gd2 (SO4 )3 ) into Super-K should significantly improve thedetection difficulties discussed [75]. Due to gadolinium’s high thermal neutron capture
cross section of 49,000 barns (approximately 5 orders of magnitude larger than the neutron capture on protons), Super-K will be able to observe the 2 signals from inverse
Beta decay via the prompt positron signal and the delayed signal from the emission ofa gamma cascade of 8 MeV which can easily be detected using Cherenkov light. At
the Gd concentration of 0.1% - 0.2%, the goal of 90% efficiency for neutron capture isachievable. The neutron tagging efficiency with the intended Gd concentration can beseen in Figure 5.1.

Figure 5.1: Diagram of neutron tagging with gadolinium (left), and capture efficiency
as a function of Gd concentration (right) [73].

72CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\

The EGADS detector facility (Evaluating Gadolinium’s Action on Detector System),is a 200 ton cylindrical water tank located in its own cavern in Kamioka mine. EGADS
was constructed in 2010 and built to assess the addition of Gd to pure water and theit’s effects on the detector itself. EGADS took data with a pure water fill in 2013.
This run lasted approximately 6 months until the end of 2013, when refurbishment
work began to fully prepare the tank for Gd filling. In November 2014, (Gd2 (SO4 )3 )was first introduced into the detector and filling was completed by April 2015 [76].
During Super-K’s refurbishment period EGADS continued running, ensuring Kamioka
observatory was supernova live.

5.3

Preparation : Gadolinium Compatibilityty Testing

Before the loading of Gd, the testing of the compatibility of Super-K hardware with Gd
was essential, for both conservation of equipment integrity and for maintaining water
quality. During 2017 and 2018, hardware soak tests were performed. Test subjects
included any new system hardware, replacement hardware to existing systems and any
existing equipment that would continue its service during the SK-Gd phase. Any existing equipment which was found to be unsuitable was replaced with a compatible
alternative, and in some cases, the equipment was redesigned and fabricated from amore suitable material. This section will describe the soak tests performed for calibration equipment exclusively.

5.3.1

MethodAll compatibility soak tests were conducted in the Super-K clean room area. Gd solution was prepared using 500 ml of SK pure water, to 1g of (Gd2 (SO4 )3 ) powder. The
solution was left to fully dissolve for 1-3 days before the addition of the subject material.
Equipment from the current Super-K water laser system was tested along with a small
number of OD calibration related items. For each set of soak tests, a control sampleof Gd solution was made to account for any potential changes in Super-K pure watertransparency. In partnership with the Gd soak tests, a series of soak tests in Super-K
pure water were conducted, also with corresponding control samples.
Test subjects were cleaned using Super-K pure water or ethanol. The cleaning procedure was repeated 3 times for each piece of equipment before introduction to the Gd
solution. The test period was between 3-6 months, with some special cases requiring ashorter test period due to time constraints or unusual water transparency results leading
to further long term monitoring of the samples. During the test period, soak samples
were checked by eye to identify any changes in the appearance of the test subject. Alleye examinations were done without disturbing the sample, by keeping the test bottle
73CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\sealed. Metallic subjects were examined for the presence of rust, coloured plastics were
examined for leaching of dye into the water and other subjects were examined for any
test subject specific changes in appearance.
After terminus of the test period, the pure water and Gd soak samples were analysed using an UV-VIS spectrometer. In order to assess the status of the spectrometer,
sample spectra measurements of percentage transparency and absorption were taken,
firstly with an empty chamber, and secondly with only an empty cuvette. The cuvettedimensions were kept constant at 2 × 1 × 5 cm. Sample spectrum measurements weretaken 3 times to ensure stability. All measurements were taken after the minimum bulb
warming period of 1h for equipment stability. Percentage transparency and absorption
spectra were taken for all soak samples. Each day that measurements of soak samples
were taken, the spectra for the control samples were taken in order to account for fluctuations in the spectrometer’s bulb performance. During measurement taking, soak sample
spectra were compared to the control sample in real time to check for any abnormalities.

5.3.2

Spectrum Analysis

Spectrum analysis was conducted outside of the lab. All soak sample spectra werecompared to the control sample and ratios between the sample spectra and control
sample were taken. This allowed closer analysis of where unusual behaviour was seenin the spectrum region. Example spectra can be seen in Figure 5.2. The subject test
material here is a cylindrical piece of PMMA (Poly(methyl methacrylate)) provided fortesting by the UK calibration group. More information about the material itself canbe found in Section 6.2. Panels a) and b) in Figure 5.2 show comparisons between
the SK water control sample and SK water soaked samples. Panels c) and d) show
comparisons between the Gd control sample and the Gd solutions containing the test
soak samples. Differences in spectra are clear in both SK and Gd soak samples. All
spectra agree well with each other at wavelengths above approximately 275 nm. In theregion of 200 - 275 nm there is clear disagreement. Some disagreement was expected
due to abnormalities in the test subject in the intermediate examinations of the subject
by eye. It could be clearly seen that excess suspended PMMA particles had transferredto the water in both cases. The spectra in panel d) show a significant decrease at
approximately 275 nm which corresponds to the intrinsic absorption peak of gadolinium.

5.4

General Refurbishment Tasks

There are too many general refurbishment tasks to discuss in full, however the in-tankstory begins with preparations for the maintenance tasks. Firstly came the arduous
task of cleaning the detector and preparing all surfaces for Tyvek replacement and74

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\

Figure 5.2: Absorption and transmittance spectra for soak tests of the PMMA diffuser
sample. The pure water tests correspond to panels a) and b) and Gd solution samples
correspond to panels c) and d).

maintenance. OD PMT replacements also began as soon as the top of the OD became
accessible. With every water drain, the work progressed further into the detector andwork in the ID also began. Over the course of the refurbishment PMTs in both the ID
and OD were replaced. Before the OD PMT’s were replaced, the PMTs to be introduced
were tested and the voltages required recorded so that they could be matched to a retired PMT, and take its place. Approximately 1/3 of the dead ID PMTs were replacedwith Hyper-K box and line PMTs (see Section 2.4) in order to test their true response
inside the detector. Approximately 136 ID PMTs and 213 OD PMTs were replaced.
Tyvek replacement was a relentless task which continued until the end of summer. All
black-white Tyvek (which covered the OD side of the supermodule) floor Tyvek at thebarrel bottom was replaced and all wall Tyvek was rehung.
One of the most important, if not the most important, goals of the refurbishment
work was to find and repair the water leak. Failure to find and seal the leak would
jeopardise the Gd loading schedule. In order to prevent any future leaks, all weld
75

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\lines and support features on the OD barrel wall were sealed with a poly-urea basedsealant. Once the leak was found, it was sealed during filling, and the water level was
meticulously monitored.

5.5

Calibration Tasks

During the refurbishment there were a number of calibration tasks specifically undertaken by the Super-K calibration group. These tasks included replacement of originalcalibration sources, installation of new systems and taking measurements of PMT and
detector properties. Such measurements would yield results that would work towards
the improvement of detector calibration, simulation and physics analyses. Measurements which could affect physics analyses are those of magnetic field and PMT dynodedirection. It is known that there are some non-uniformities in PMT response. If these
non-uniformities can be understood, then the effect that the detector structure has on
physics events that occur near the detector wall can also be understood. Such calibrations aid the studies for expansion of the fiducial volume selection used in physics
analysis.

5.5.1

PMT Response

The ID PMTs are not azimuthally symmetric and therefore show some non-uniformities
in their response. By knowing the residual magnetic field and the PMT dynode direction, it is possible to deduce the effect that the magnetic field has on the PMTs. A moreaccurate simulation of PMT response can be made by implementing the measurementsof both factors into the Super-K detector simulation.
Magnetic Field Measurements
In order to specifically the magnetic field inside the detector, there were two prerequisites: firstly confirming that the compensation coils on the outer OD wall provide
enough magnetic field correction, and secondly, providing a full magnetic field map ateach PMT position. The measurements will aid an estimation of any magnetic field
induced change in PMT response. The work was based upon the last related study in2005, which deduced that there are typical maximum changes of 40 % in PMT gain
at a magnetic field of 100 mG [54], 2.3 ns change in transit time and a 15 % change
in efficiency. With the compensations coils off, the magnetic field in the detector isapproximately 460 mG. With coils on, this should be reduced to less than 100 mG in
module.
The measurement method involved two people in Super-K’s infamous inflatable boat.
One person was to hold the magnetic field sensor (3 axis magnetometer and 3 axis ac76

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\celerometer) in place in front of the centre of the PMT acrylic cover, with the second person taking the measurements with a data recording interface. After the measurements,
the data was backed up and transferred for offline analysis. During daily refurbishment
shifts, the compensation coils were turned off, thus all magnetic field measurements weretaken during evening shift after all personnel had exited the tank. Approximately 29%
of PMTs were measured which was sufficient to deduce the compensation coil ability.
The new measurements provided seven times more data than previously. On average
the magnetic field was found to be reduced to approximately 33 mG.

PMT Dynode Direction Measurements
PMT dynode direction measurements were taken on the same days as magnetic fieldmeasurement, usually during the day shift. The procedure was similar to that of themagnetic field measurements, where, using a camera, a team of 2 people in the inflatableboat (which became more and more uncomfortable over the days) took photographs ofevery individual PMT. A photograph of the dynode measurements being taken can beseen in Figure 5.3. As shown here, the equipment was simply a camera on an extendable
rod held by one person, which was remotely controlled by the other person using a tablet.

Figure 5.3: Image from the refurbishment of myself and Artur Sztuc taking PMT dynodedirection measurements. Photograph taken by M.Nakahata.

Before these measurements, only half of the PMT dynode directions were known.
77CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT[a\

Having a measurement of every dynode direction aids in understanding the PMTs asymmetrical response with respect to the dynode direction, thus provides a better error
estimation of each individual PMTs gain, efficiency and transit time and the impactthat these properties have on Super-K.

5.5.2

Super-K Water Laser Hardware Replacement

Preparation for the replacement of the Super-K laser system hardware began in November 2017 when all optical fibres and injectors were tested, and all degraded fibres identified so they could be replaced. Over the next year and a half, soak tests of all current
and new materials were performed. Any failed materials were replaced. New fibres werereeled onto smaller fibre reels that were a suitable size to fit in the calibration port.
Replacement work started on June 4th 2018 with the replacement of the NT injector,
which was the first injector to become accessible. The procedure for the replacements
was as follows. For each of the injectors that were to be replaced, the new injectors weretaken into the tank and the work area set up in the ID. In order to check the conditionof the fibre behind the injector body, the PVC injector casing was then removed fromits metal support structure and the fibre removed from the main stainless steel body.
The new injector body was prepared by inserting a new replacement rubber O ring
between the main injector body and the fibre flange. Nitrogen gas was pumped into thenew main injector body and the fibre inserted. The newly assembled injector body wasreattached to the metal support structure and the process was then repeated for thesecond (spare) injector of the pair. After the injectors were replaced, the beam direction
was adjusted by mounting a laser pointer to the PVC casing. The final replacement
injector and the beam alignment method can be seen in Figure 5.4.

Figure 5.4: Image of the replaced injectors and the alignment method.
Optical fibres were replaced for injector positions B1 A, B4 B and B5 A. The new
fibres were routed along the pre-existing fibre route and then introduced to the target
injector via the OD, through the PMT superstructure.
78

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT

[a\

79

CHAPTER 5. THE SUPER-KAMIOKANDE REFURBISHMENT

[a\

5.5.3

Installation of UK light injection system

The UK calibration group have designed and built a new light injection system, which
is described in full detail in Chapter 6. Installation of the UK light source was done
alongside the replacement of the Korean injector hardware. The fibre routing and preparations were done in a similar way to the Super-K water laser hardware replacement
work. In depth details about the installation procedure specifically, are described in
Section 6.5.

5.6

Summary

Over the summer of 2018 Super-K underwent a successful refurbishment after the longest
phase of SK-IV. The measurements from the calibration work will be fed into the SuperK detector simulation with the aim to expand the fiducial volume selection in physics
analyses. New calibration sources were also introduced which will help to further improve the understanding of the underlying detector properties such as the depth dependence of the water quality, which will be discussed in the following chapter.

80

Chapter 6

The UK Light Injection System"Everything I put in the groundwithers and dies."
Drusilla - School Hard

The author of this thesis has been the "water laser" expert for the period of November 2016 - February 2019, during which time the author was based at Super-K. Throughthe role, the author focused on developing the Super-K laser data analysis as describedin Chapter 4 whilst performing a large amount of hardware based tasks. The work
provided the author with the necessary skills required for testing, installing, runningand taking data with the UK Light Injection (LI) system. This chapter describes the LI
system in detail, from early testing, to the installation inside the detector; which waslead by the author; and the observation of the first calibration events.

6.1

Introduction

The water scattering and absorption coefficients in Super-K are measured using theSuper-K laser injection calibration system described in Chapter 3, Section 3.1, andChapter 4. Since the UK group joined Super-K, we have been heavily involved in thecalibration group and have been working toward introducing an entirely new UK developed system which produces calibration events with multiple beam diameters. The
UK LI system was initially developed for Hyper-K, however with Super-K undergoing alarge refurbishment in summer 2018, we were provided with an unmissable opportunity
to install the first UK designed and built hardware into the Super-K detector. Over the
past five years, the calibration system has been developing for Hyper-K’s needs, alongside being tailored toward Super-K’s requirements. The UK system can be used tocalibrate several different detector properties, unlike the current Super-K system. The
UK system can measure both scattering and absorption parameters at various depths
within the detector, and measure PMT properties. Such a goal requires the ability to81

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\produce light pulses of known emission time and intensity from a known location insidethe detector, whilst also providing beam profiles of different opening angles. The UK
system was designed to be installed at five barrel wall positions in the detector, withthree different optical sources mounted at each position, providing fifteen new calibration channels to the detector.

6.2

The Light Source and Electronics

The LI system architecture can be seen in Figure 6.1. The electronics and light sources
sit outside of the tank in the experimental area and consist of two motherboards poweredby a VME crate which have a total of sixteen LED "pulser" boards connected (eightto each motherboard). The pulser boards are coupled to three optical fibres each. The
system also includes one monitor PMT requiring a 5 V supply, one optical power meterwith pico-watt sensitivity which is used to calibrate the monitor PMT, and a control
laptop used to set the LED light intensities.

Figure 6.1: Full system architecture including the electronics which sit outside the tankand the optical connections from the electronics to the optical sources at positions B1- B5.

The current setup at Super-K uses sixteen LED pulser boards, or channels, mounted
onto motherboards that control which channel to send an electronic signal to. There82

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

are two motherboards, each with eight channels. Fifteen channels deliver light into thedetector and one channel is dedicated to a separate system for internal calibration purposes. This channel delivers light to an on-board monitoring system. A circuit diagramof the LED pulser board can be see in Figure 6.2. The electronics system has been
designed to be modular; allowing for the mother and daughter boards to be designed
independently. This allows for further development of the system without redesigning
the motherboards.

Figure 6.2: Circuit diagram of pulser board circuit layout.
The light pulses are produced by 435 nm LEDs mounted onto the pulser boards, thesignals to which are controlled by FPGA (Field Programmable Gate Array) firmware.
The pulse time, profile and intensity of the light pulses are controlled by on-board integrated circuits. The pulse production is controlled by custom written firmware that canbe used in several modes, including an automated mode and a "self trigger" mode. The
firmware has been designed so that it can be integrated with Super-K NIM (Nuclear
Instrumentation Module) triggers.
Each LED is coupled to three short 1mm core optical fibres by a custom 3D printed
coupler. The first fibre connection is to the monitor PMT channel, the second to afibre that delivers light into the detector and the third is prepared to be connected toa dedicated on-board photodiode monitor in the future. The fibre connections can beseen in Figure 6.3. The monitor PMT is a 2 inch Hamamatsu photosensor module with
an effective range of 230 nm to 700 nm and a peak response at approximately 400 nm.
The signal from the LED is recorded by the PMT and the information is sent to a dedicated QBEE channel. The monitor charge information will be used as a normalisation
factor when deriving the water coefficients. A 3D printed box houses the monitor PMT
to ensure there is no light exposure. Figure 6.4 shows the monitor PMT inside thecustom built box. There are nineteen input monitor channels (1 mm core fibres) which
83CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

are bundled together and held in place against the PMTs quarts covered photocathodeby a 3D printed holder. The removable holder allows the fibres to be replaced easily
if necessary. Fifteen fibres are coupled to LEDs that deliver light to the detector, thesixteenth is connected to the LED board for the system monitor and the remaining
three channels are spare. The spare channels are provided for use by other calibration
systems at Super-K.

Figure 6.3: The motherboard can accommodate four pulser boards per side. The pulser
board here has three 200 µm core fibres coupled to the LED.

The sixteenth "monitor" channel is dedicated to the calibration of the monitor PMT
itself. Unlike the fifteen detector channels, the monitor channel signal is fed into theoptical power meter. All sixteen channels have a fibre prepared for the future connection
to a photodiode monitor board (PMD). A photo of the PMD is displayed in Figure 6.5.
Each PMD has four channels, with the system requiring 4 PMDs in total: two permotherboard. The PMDs monitor the light output from all sixteen LED channels toprovide a safey check against any incorrect pulser behaviour. It can independently shut
down a channel if it is emitting light when it was not requested to do so, thus preventing
any light leak into the detector.

84

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.4: Pre potting of monitor PMT with all 19 channels connected.

Figure 6.5: Photodiode monitor board.

85

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM

[a\

6.2.1

System stability studies

Stability measurements are required as real time pulse monitoring is vital for understanding each pulse fully, and will allow for a more accurate calibration. Measurementsthat rigorously test the stability of the system have been carried out over the past several years at both Liverpool and Sheffield University. Test details are out of the scopeof this thesis, however the author worked on testing previous iterations of the board
design.

6.3

Prototype deployment

In January 2018 the prototype light injector and electronics were tested at Super-K.
The prototype plate and optics can be seen in Figure 6.7.

Figure 6.6: Prototype deployment setup. The deployment was performed inside a lighttight tent. The right image shows the deployment method and position inside thedetector.

The plate was deployed from the tank top into Super-K via a calibration port which
was previously used as part of the Super-K laser system. The plate was lowered into
the detector through the calibration port until it was level with the bottom of the port.
If the plate was sitting lower than the port, there would be a risk of shadowing the top
PMTs in the ID and introducing an un-simulated reflective surface inside the detector.
A schematic of the deployment and an image of the test setup can be seen in Figure
6.6. The original diffuser and collimator designs used in this deployment can be seen in
Figure 6.7.

Figure 6.7: Prototype injector plate, diffuser and collimator.
86

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

An event displays for the collimator data can be seen in Figure 6.8. There is a clear
deviation from the intended circular beam shape. The development of the beam spots
tail was investigated and determined to be a misalignment between the fibre and thelens which reduces the opening angle of the light.

Figure 6.8: Event display of collimator data after one day of submersion in Super-K[77]. The hit pattern is expected to be an uniform circle.

The results of the January 2018 deployment led to the revised and more robust
design of the collimator described in Section 6.4.4.

6.4

The Optics

As discussed in Chapter 3, Section 3.1, the current Super-K water laser system injects
light from an optical fibre with a standard opening angle of approximately 4 degrees.
The new UK system is comprised of three optics, each with a different opening angle,
thus allowing for a wider range of calibration measurements to be made. The three
optics are mounted together within one stainless steel optics plate,.

6.4.1

The Optical Fibres

Long fibres are used to connect the electronics on top of the Super-K tank, outside thedetector, to the injector plate inside the detector. The fibres are 70 m long, 200 µm coreThor Labs step index fibres, similar to those used in the current Super-K system. The
diffuser and collimator housed in the injector plate are connected to the long fibres via a
20 cm fibre which attached in Warwick university during construction. For consistency,
87

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\there is also a 20 cm bare fibre secured within the optics plate which is also connected
to a 70 m fibre.

6.4.2

The Bare fibre

The bare fibres are used only for reference and are not for analysis purposes. They
can however be used to perform crosschecks between the UK and Super-K systems bycomparing the position, size and total p.e of the events. The bare fibres themselves are
200 µm core Thor Labs step index fibres. The fibres are the same as the 20 cm fibres
which were connected to the diffusers and collimators during construction. The barefibres are screwed into the optics plate via a cut off FC connector. The free end of the
20 cm fibre is connected to the 70 cm fibre which exits the detector. The 70 m to 20 cm
fibre connection was made inside the detector during installation.

6.4.3

The Diffuser

The wide angled beam, or diffuser, allows measurements of PMT characteristics andwater coefficients. Such measurements include PMT gain evolution over time, PMT
timing calibration and derivation of light attenuation length in water, as well as potentially being able to monitor any potential changes in the water absorption coefficient.
The diffuser provides an easy way to illuminate anywhere from several hundred to one
thousand PMTs with only a single light pulse. This characteristic is useful for PMT
timing calibration, as when installed inside the tank, the output light has know origin,time and wide opening angle. Another design feature is that the exiting photons has notime dependence as a function of angle. As the emitted light has various path lengths
between the injector position and each hit PMT, any uniform change in the absorption
parameter is reflected in the distance the light travels, which can be measured by thedifference in time between the light entering the tank and it being detected by a PMT.

Figure 6.9: Diffuser enclosures and diffuser pieces before assembly
The diffuser itself is a Poly(methyl methacrylate) (PMMA) ball. The ball is a half
spherical piece of acrylic resin which contains suspended PMMA particles. The inten88

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\tion is that the injected photons are able to bounce between PMMA particles within theball, such that the photons exiting the ball will be distributed evenly across the tankand be uniformly distributed over an angle of 45 degrees. The PMMA ball is housed
within a water tight enclosure for two reasons: to ensure that no PMMA will leach into
the water and so that the integrity of the material is maintained. The housing wasdeveloped due to the diffuser ball samples failing the soak tests performed at Super-K.
As explained in Chapter 5, the soak tests showed that it is possible for the suspended
PMMA to be lost to the water sample, thus changing the appearance of the diffuser balland decreasing the concentration of PMMA. Figure 6.9 shows the diffuser balls (right)
and enclosures (left) before assembly. The optical fibre is coupled to the flat rear side ofthe diffuser ball using a stainless steel flange which is inserted into the enclosure. Water
tight seals were made with chemical and water resistant epoxy resin.

6.4.4

The Collimator

The collimator, or narrow angle beam, uses a graded index (GRIN) lens coupled to abare fibre to reduce the opening angle of the beam of injected light. A schematic of thecollimator design can be seen in Figure 6.10. This design was created after the prototype
deployment described in Section 6.3 and encases the optical fibre and coupled GRIN
lens inside a water tight, stainless steel cylindrical mounting sleeve. In order to reducethe chances of misalignment between the GRIN lens and fibre, the GRIN lens is heldin place by spring loading the end of the ferrule in the fibre FC connector. The GRIN
lens itself sits within a lens mount, where an HAFC connector is drilled to accept thelens through the centre of the aperture. The design includes a 2.35 diameter aperture
to reduce any off-axis background light. The sapphire glass end cap can be screwed
into place on the mounting sleeve. All drilled holes are sealed with epoxy to ensure
water-tightness.

Figure 6.10: Schematic of collimator including the GRIN lens mount and mounting
sleeve [78].

The benefits of including a narrow angled beam in the system is that it provides aprecise target on the detector wall. Water scattering lengths can be measured by the89CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\charge collected by PMTs hit outside of the target beam spot, and by measuring thelight level as a function of path length through the detector. The absorption coefficient
can be measured oppositely by monitoring the light collected by hit PMTs inside thetarget beam spot. When a number of collimators are installed at various points, at equal
spacing on the detector walls, there should be no overlap between the beam spots. Thisposes a large improvement over the Super-K light injectors as the characteristics of the
UK system should allow for localised measurements of the absorption and scattering
coefficients in the water, and the derivation of any depth dependence of the water
coefficients, which is currently un-achievable. Due to the target beam spot being smaller
than that of a bare fibre, there is less exclusion of hit PMTs outside of the target spot,
allowing for higher statistics in water calibration data.

6.4.5

The Optics Plate

The optics plate was designed to be easily attached to the Super-K PMT structureusing a simple kinematic mount, allowing for tuning of the pointing direction during
installation. Due to the slightly different positioning of the optics plates on the PMT
structures in SK, two sizes of plate were designed in order for there to be no interference
between the structure itself and the optical fibres connected to the optics. Technicaldrawings of the plate designs can be seen in Figure 6.11.

Figure 6.11: Technical drawings of the optics plate provided by Warwick University.
Such differences in position arise from the positioning of the Korean laser injectors.
Each of the five barrel injectors are not on the equivalent PMT rails on each structure,as three injectors are on the higher rail of the two, and two injectors are on the lower rail.
Differences in association with the PMTs themselves mean that the lower rails include
a "spacer" (short cylindrical piece of metal) which raises the rail in order to eradicate
any interference between the structure and the PMTs. The taller plate, fabricated toaccommodate for the spacers is an extra 2.5 inches in height compared to the shortplate in order to accomodate for the PMT structure rail. The shorter length plate wasdesigned for use on the standard PMT structure. Figure 6.12 shows the stainless steel
90

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\tubing which raises one of the two rails on the PMT structure.

Figure 6.12: Image displaying the stainless steel "spacer" piece which extends the heightof the PMT structure rail.

The plate is secured to the PMT structure using an existing bolt. The bolt was
simply removed, slotted through the "L" bracket on the plate and reattached to thestructure.

6.5

Commissioning of UK System

During the summer of 2018, the optics were deployed inside Super-K at five positions
on the detector wall in line with the Super-K injectors. The UK optical fibres were also
run alongside the pre-existing calibration fibres. The installations were done over thecourse of three months as each position became accessible during the water drain. The
hardware was installed in two parts, with work being done inside both the ID and OD
on floating floors.

6.5.1

On-site preparation

In preparation for the refurbishment, there were several preparation tasks required forthe new hardware. The first component to arrive on site were the optical fibre. The
fibres were bundled together in sets of 3 (one fibre per optic), and wound onto a new reelsuitable to fit through the calibration port on the Super-K tank top, where the fibres
would be fed either into or out of the tank. The amount of fibre wound onto the new reelwas calculated based on technical drawings of the detector. The length was equal to the
distance from the injector location to the tank top fibre storage location, plus an extra
91CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

2 m to account for any potential miscalculation, or differences in injector location foundupon entering the tank. The remaining fibre length was wound onto the original fibrereels for storage. For the top three barrel positions, bundles of three or four fibres were
wound on to a single smaller reel, however, for the bottom two positions, two separate
smaller reels were used due to the fibre wound reels diameter exceeding the diameter ofthe calibration port. Figure 6.13 shows the fibre reeling process, fibre storage method
and the smaller (black) reels, which were cut for feeding through the calibration port.
For the barrel positions B3 to B5, both ends of the fibres were transferred onto thesmaller reels due to unforeseen shipping issues which posed some constraint when fibre
routing could be done. The fibres for the remaining three positions were stored on
the top of the tank until the installation date and fed through the port to the storage
location on top of the tank during the installation.

Figure 6.13: Photographs of fibre reeling procedure. The left image shows the required
length of fibre laid out and secured together with chemical resistant cable ties. The
right image shows the length of bundled fibre wound onto the smaller black reel and theremaining length stored individually on the original reels.

Upon their arrival, each of the optics were tested in the laboratory to confirm that
there had been no damage during transit. All the optics were assembled at Warwick
university. The remaining testing was broken down into three simple points. Firstly,
confirming signals through the connected short fibres using a custom made red LED
fibre tester. Secondly, confirming that the stainless steel enclosures (for the diffuser)
and mounting sleeves (for the collimator) were fully intact. Finally, the sealing epoxy
on all equipment was investigated for and degradation or cracks. The signals for thebare fibre and collimator were tested by observing the beam spot on blank paper. This
test can be seen in Figure 6.14.
92

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.14: Image displaying the signal testing of one of the installed collimators. The
top image shows a clear signal. The bottom image confirms the expected narrow circularbeam spot.
The diffusers were more closely checked than the collimators. Not only was theoutput signal confirmed, but also the light distribution over the PMMA ball. Any nonuniformity in light coverage suggested a failure during pressure testing or degradationof epoxy integrity causing the enclosure to no longer be water tight. Testing of the
diffuser with the LED fibre tester can be seen in Figure 6.15. Another sign of pressure
test failure is condensation on the glass cover of the enclosure. There were two cases offailed pressure testing with regards to the diffusers. In the first case, there was a watermark on the diffuser ball itself, causing non-uniform light coverage and in the second
case, the epoxy had deteriorated. An image of the non-uniform light coverage from oneof the diffusers can also be seen in Figure 6.15. Both diffusers were sent back to the UK
for refurbishment and further pressure testing. After fully testing all the equipment,each piece that passed during onsite preparation was cleaned with ethanol and the full
optics plate assembled.
The optics plates were rigorously cleaned before full assembly. Figure 6.16 shows oneof the injector plates being assembled in the lab. Each component was cleaned by handusing ethanol, before cleaning in a sonic bath also of ethanol. Each plate was carefully
assembled in advance and sealed in plastic after cleaning. Before each installation, theoptics were attached to the plate and wrapped in protective packaging ready for the
installation shift. The final task was to cut a piece of black sheet to fix over the plate,which was required to reduce the amount of visible reflective surface.
93CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.15: Image displaying the signal testing of one of the installed diffuser coupledwith the custom built LED fibre tester. The upper images displays a diffuser that passes
the pressure testing. The lower image displays a diffuser that failed. It can be seen that
there is a non-uniform light output across the diffuser, which is strongest around theouter edge.

Figure 6.16: The left image displays the injector plate being assembled whilst the central
image shows the completed assembly. The right image shows the stenciled black sheet
sitting on the injector plate.

94CHAPTER 6. THE UK LIGHT INJECTION SYSTEM

[a\

6.5.2

Installation procedure

Before the installation of the optics plate, the optical fibres for two barrel positions wereintroduced to the tank. This was done in a team of two people, one inside the tank andone on the tank top. The small black reel that can be seen in Figure 6.13 was fed fromthe top of the tank down a calibration port to the receiving person inside the tank. The
calibration port location used was that closest to the PMT structure where the injector
plate would be installed. This is the same port through which the Super-K fibres enter
the tank. The reels were stored within a PMT structure which was accessible both fromthe OD barrel gondola and from the OD top at the time. The remaining three sets offibres which had had both ends transferred to smaller reels had both ends stored in thesame PMT structure. All fibre reels were secured with rope. A length of rope was left
secured to a metal post in the OD top which would be tied to the reels that would later
be fed up through the calibration port. Figure 6.17 shows the fibre entry procedure.
From left to right; feeding of the fibre reel into the tank, location of the fibre port in
the OD top region, passing the fibres from the OD top into the OD barrel and finallythe storage location in the PMT structure in the OD barrel.

Figure 6.17: Process of feeding the fibre reels through the calibration port into SK totheir storage inside the PMT structure.

As stated earlier in Section 6.5, there were two teams required for the installation.
The optics plate was installed within the inner detector using a small island of floating
floor which was anchored to the PMT structure. Firstly the black sheet surrounding
the PMTs was pulled back to uncover the intended injector position. The fixing bolt
was then removed, the injector plate put into position and a longer bolt introduced,
which was a suitable length that could be safely and securely tightened. Figure 6.18
shows the plate attachment process. After the plate had been adjusted such that it
was sitting parallel with the support rail, the short fibres attached to the optics werepassed through to the OD installation group. Before the black sheet could be recovered,95

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\the optics were tested using the LED fibre tester. Once the signal was confirmed, theoriginal black sheet was reattached, to the PMTs and the plates black sheet stapled tothe original. The final attachment before and after the black sheet was reattached canbe seen in Figure 6.19. It can be seen by this image that the plate has been alignedwith the rail, and the plate black sheet has been cleanly attached to the original black
sheet.

Figure 6.18: Attachment of the plate to the detector structure in the ID.

Figure 6.19: Final attachment and re-attaching the black sheet.
Whilst the ID team were attaching the plate, the OD team confirmed the signal of
the 70 m fibre which in the cases of positions B1 and B2, was on the top of the SK tank,96

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\and in the remaining three cases, on a reel stored inside one of the PMT structures
close to the top of the OD. All fibres were routed using the OD gondola and followed
the pre-existing fibre run. The fibres were then loosely cable tied into place. Once thissignal was confirmed, the OD team cleaned the fibre ends with ethanol and performed
the fibre connection of the short optics fibres to the 70 m fibre. The connection was
done inside a stainless steel box which was potted using a "poly-urea" resin. Just before
potting, the signal from the tank top end of the fibre through to the optics in the ID was
confirmed. Once confirmed, the fibres were potted and left on a supporting table forthree hours until cured. After curing, the box was moved to a supporting rail inside the
PMT structure and secured using chemical resistant cable ties. Figure 6.20 shows thefibre connection and potting procedure. The left two images show the fibre connections
being made inside the box and the right two images show resin being poured and thebox being transferred and secured to the space inside the PMT structure.

Figure 6.20: The full fibre connection process, beginning on the left with the connection
itself and on the right, the potting and attachment to the inside of the PMT structure
between the ID and OD.

Finally the signal was tested once more and the target PMT on the opposite sideof the tank was noted. Figure 6.21 shows the signal confirmation along the whole fibre
length after all final fibre connections and potting. The image shows the illuminatedbare fibre, the collimator and the diffuser. The target PMT was decided by attaching alaser pointer in the spare hole in the optics plate. The target reference was determinedby the first installation, such that the remaining four positions were tuned to point at
the equivalent PMT at each level. Such a measurement is required for producing MC
for this calibration system.

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CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.21: The final confirmation of the signal along the whole length of fibre including
fibre connection. Left to right shows the illuminated bare fibre, collimator and diffuser.

6.5.3

First data using UK fibres and optics

The first data taken for the newly installed fibres and beam optics was taken in November 2018, for positions B1 and B2 only, during partial fill. Due the fibre running in thesummer, the only fibres accessible from the top of the tank were the two top positions.
The data was taken in air with the intention that it could be compared to laboratory
data taken in air in the UK. As the electronics had not been commissioned at this time,
all data was taken using the Super-K 445 nm laser as the light source. The goal of thetest was to confirm the signal from each of the optics. Event displays of the first light
can be seen in Figure 6.22. The data shown is from the injector position B1, taken
in November 2018. The images from left to right show the bare fibre, collimator anddiffuser. From observation of the event displays, the beam profiles can be characterised
as expected.

6.5.4

Installation of the electronics

The full commissioning of the electronics was done in February 2019 by members of
University of Liverpool, Kamioka Observatory and Sheffield University. During the fullcommissioning, the new electronics were integrated with the Super-K NIM trigger lines
and the DAQ. Firstly, before any connections to Super-K, each of the sixteen pulser
boards and the nineteen monitor PMT signals were tested in self trigger mode. Suchtests allowed the confirmation that all equipment was behaving as expected and that98

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.22: Event displays for position B1. From left to right: Bare fibre, collimator,
diffuser.

there had been no damage in transit. Alongside testing the electronics, other preparations included; bundling all BNC and LEMO cables that were required to integrate thenew electronics with the pre-existing calibration system. A schematic of the electronics
hut layout and the UK cable routing can be seen in Figure 6.23.
The NIM control and trigger signals are sent to the pulser board via official Super-K
calibration trigger scripts, which were been modified to trigger the UK electronics. Eachcalibration VME crate in the central hut has an hexadecimal address attached to it.
The script selects the address of the new UK VME crates and selects which channel
to fire by sending a binary control trigger signal. The control signals are indicated by
the red arrows in Figure 6.23 which go from the central hut to the VME crate whichcontains the motherboards.
These signals are also sent from the central hut to the allocated QBEE in hut 1.
Due to the QBEE being unable to accept a continuous signal, the binary signals passthrough a discriminator which takes the constant signal and latches it to make a shortpulse. This allows us to determine which channel was fired at what time in the calibration data. Also due to the nature of the QBEE, the monitor PMT signal is attenuated
so the QBEE isn’t saturated. Trigger information is also sent to the allocated periodic
trigger QBEE in hut 4 which tags events as calibration/periodic events allowing them
to be removed from data used for physics analysis. An illustration of the trigger method
can be seen in Figure 6.24. The red lines show the four continuous control signals thatin the first case, selects channel 16 and fires this channel with the NIM trigger signal,
when control signal D is changed, channel 8 is selected and fired when the next trigger
signal is received. There is no communication between the trigger control scripts andthe system firmware. It is only the pulse width and intensity that is controlled by thelaptop currently. For this period, the pulse with remained constant, however, in time,some communication between the laptop and the Super-K trigger will be established.

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CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Figure 6.23: Map of routed cables after integration of UK electronics with Super-K
trigger and DAQ systems. Also shown is the layout of the electronics huts in theexperimental area on the top of the tank.

Figure 6.24: Signal form to trigger board channels 8 and 16. A, B, C and D arecontinuous signals which select the channel to trigger. Channel is triggered when NIM
trigger signal comes along.

After all connections had been made and tested and the group were satisfied thatthe DAQ was receiving the triggers sent to the new electronics, connections to the optics were made. All 15 channels were connected to the motherboards but only selectedchannels were used to take data. Table 6.1 shows the optics connected to the fist eightchannels on motherboard 2. These optics were prioritised due to their locations in thetank and the importance of them in later analysis. Collimator data at positions B1, B3
and B5 was taken first due to the positions being the two extremes in the z axis andthe central position, between which it would be expected to see the z dependence of in100

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\water coefficients. Bare fibres at B2 and B4 were used as these two positions would see
no overlap in beam spots or scattering onto the tank top and bottom. Diffuser data
was taken for position B3 as this is the central position would provide the most uniform
PMT coverage.

Channel
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Motherboard
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1

Light source
B1 C
B2 C
B3 C
B4 C
B5 C
B2 B
B3 D
B4 B
B1 B
B3 B
B5 B
Monitor PMT
B1 D
B2 D
B4 D
B5 D

Table 6.1: Table of channel connections to motherboards, the position and opticalsource. C = Collimator, B = Bare fibre, D = Diffuser.

The final stage of the February 2019 installation was to confirm that the calibration
events could be extracted from Super-K data for later analysis. This was done with a lotof help from the team members from ICRR. There were however some remaining tasks
that couldn’t be solved during this period such as integration with the auto-calibration
system and correct mapping of the T2K veto system connections.

6.5.5

Final Commissioning

In July 2019 the final commissioning of the system took place. During this period the
setup of the electronics was changed slightly, with the addition of a ribbon cable toconnect the motherboard and slave motherboard together so the boards could communicate with each other. This allowed for the addition of only one extra digit in theoriginal three digit binary code which selects the channel to fire, such that the code
now selects the board and channel on that board, reducing the required number ofcode combinations. After the modification, trigger scripts were written for individual
channels and the intensity for each of the optics was tuned based on the observed total photo-electrons (p.e) in Super-K, and the intensities hard coded into the firmware.
101

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\

Data was taken for all optics and distributed between the UK students. The final task
was to integrate the optics with the auto-calibration system, which was done in two
parts. Firstly, only the B1 collimator was be added to the loop of calibration sourcesin order to confirm the systems compatibility, and to confirm that adding new sources
did not disturb the auto-calibration process. The second stage was to incorporate thecollimators and diffusers to the program which was done in February 2020.

Figure 6.25: Occupancy event displays for position B2. From left to right: collimator,bare fibre, diffuser [78].

Occupancy event displays from the final commissioning can be seen in figure 6.25,
for the collimator, bare fibre and the diffuser.

6.6

Future Hyper-Kamiokande calibration system

Like Super-K, Hyper-K has a rich physics program, which varies over a wide energy
scale of several MeV to a few hundred GeV, meaning that calibrations for various physics
analyses are essential. The majority of calibration devices and systems developed forHyper-K are somewhat based on Super-K’s long running successful calibration methods.
The newly built UK system was developed under the same concept: potentially proving
beneficial for Super-K and Hyper-K alike, after some tailored changes, which can be
determined after a number of years running as part of the overall Super-K calibration
system. The commissioning techniques in Hyper-K will be based on those learned over
the Super-K tank open and commissioning periods as described in this chapter.
As the scale of Hyper-K is much greater than that of Super-K, there will be anincreased number of light injection points and an increased number of fibre deployment
ports. Rather than a single entry point into the Hyper-K tank, there will be at least
seven entry points with approximately four fibre lines run through each port. Other
modifications include the potential addition of Laser Diodes (LDs) alongside the LEDs,
as LDs have a little to no wavelength variation as opposed to an LED. LDs are also
more monochromatic and allow for a narrower pulse width. Such characteristics provide,102

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM[a\analysis wise, a more understandable and reliable light source, allowing for a reduction
in systematic errors when deriving water scattering and absorption parameters. Other
possibilities are to use lasers similar to those used for the Super-K system. Along sidethese differences, graded index fibres will be used in order to maintain fast light pulses
over the 100 m scale of Hyper-K, a requirement which step index fibres would struggle
to provide.
The deployment of the system in the Super-K detector was an invaluable experienceand is guiding the UK calibration group to make further improvements to the system.
The UK group is currently undergoing a review of the equipment and the installation
procedure to tailor it towards commissioning within Hyper-K. Valuable knowledge wasgained from the experience about all aspects of the system, most importantly withrespect to the optics. To provide a few examples, the underwater fibre connection procedure can be improved to make for a cleaner connection and also provide a reduction inmaterials required. The optics themselves could be improved by lowering the mechanical tolerances allowed for the mounting plates to ensure uniformity in any protrusionof the collimator mounting sleeves over all plates. Also related is the diffuser enclosure,although this is likely to still be required, the size could be reduced and the sealing
process could be improved.
Almost all of the calibration sources used in Super-K will be developed for HyperK’s requirements and eventually deployed in the detector. Due to the larger scale ofHyper-K, automated systems are preferred, where calibration sources should be placedat chosen locations in the tank. Methods used in Super-K must be further refined inorder to be used in Hyper-K, for example, fixed rails and wire guides are necessary toreplace the drop lines (manual deployment through tank top calibration ports) used inSuper-K for systems such as the TQ and Xe balls (see Chapter 3). Like all other sources
at Super-K that will be used in Hyper-K, the UK light injection system will also require
some tuning. The next several years of data taking in Super-K, and the lessons learned
will be invaluable for the refinement of the system for Hyper-K.

6.7

Summary

The newly installed UK light injection system has been fully integrated into the Super-K
detector and the analysis of the data taken to the current date is ongoing at a number ofuniversities in the UK. The author is working on integrating all diffuser and collimator
optics into the automated calibration system which is in operation during each normal
run. The data will be used to measure any potential depth dependence inside thedetector. Not only will this improve the understanding of the water coefficients in thedetector, it will be used to monitor the coefficients during gadolinium loading towards
the SK-Gd upgrade.
103

CHAPTER 6. THE UK LIGHT INJECTION SYSTEM

[a\

104

Chapter 7

A Model Independent Measurementof the NC1π 0 rate at Super-K"I’m all for spurty knowledge"
Buffy - The Freshman

7.1

Motivation

Two of T2K’s main goals are the searches for the mixing angle θ13 via νµ → νe neutrino
oscillation, and for CP violation. In the νe neutrino oscillation analysis, NC1π 0 events
one of the most dominant sources of background, second to the intrinsic νe componentof the beam, at approximately 2.5% [79]. The background originates from specificallyNC1π 0 events, which are π 0 events produced via neutral current interactions. Currently
the NC1π 0 background estimation in the T2K νe appearance analysis is highly model
dependent. Neutrino interaction cross-section and flux models are used in T2Ks neardetector (ND) fits, introducing complex uncertainties and model dependencies. The
detector systematic component of the uncertainty on the 2-ring NC1π 0 sample can be
determined using a control sample which is constructed using Super-K data and Monte
Carlo (MC) and event kinematics from T2K beam data and MC. By calculating the π 0rejection and selection efficiencies in this way, the differences in the detector response between data and MC are incorporated into the efficiencies and their uncertainties. Thesesystematic uncertainties are then fed into the oscillation analysis, thus providing moreaccurate efficiencies and uncertainties. The method therefore provides a more accurate
measurement of the νe appearance signal, and reduces the NC1π 0 related backgroundthrough improving the selection and rejection efficiencies. This chapter discusses thecharacteristics of the NC1π 0 background as seen in Super-K and how the systematic
error on π 0 rejection at Super-K has been performed over the years.

105CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K

[a\

7.2

Neutrino Interactions at T2K"I don’t understand how all thishappens."
Anya - The Body

The current measurement, which neutrino experiments strive to make, is that ofthe δCP parameter and the mass hierarchy. Eventually cross-section uncertainties will
become the main factor which limits the achievable measurement precision of these parameters. In order to achieve the required precision, the neutrino-nucleus cross-sections
must be understood in detail. This includes the initial and final state interactions inside
the nucleus through which the initial outgoing particle from the interaction traverses.
Both initial and final state interactions are complex, and often the final state changes
based on intermediate interactions with other nuclei.

7.2.1

Introduction

As stated in Section 1.1.1, neutrinos interact via the weak force, where the gauge bosons
are the W+ /W− for charged current (CC) and the Z0 for neutral current (NC) interactions, therefore, the neutrino interactions must be determined by the observed particles
produced by the interactions. Table 7.1 describes the typical neutrino interaction modes
expected at T2K.
Interaction type
Charged current quasi-elastic
Charged current single π 0Charged current single π +Neutral current quasi-elastic
Neutral current single π 0Charged current single π ±Abbreviation
CCQE
CC1π 0CC1π +
NCQE
NC1π 0NC1π ±

Interaction
να + n → α− + pνα + n → α− + p + π 0να + n → α− + n + π +να + n(p) → να + n(p)να + n(p) → να + n(p) + π 0να + n(p) → να + p(n) + π − (π + )Table 7.1: Table of neutrino interactions at where α corresponds to e, µ and τ , andp and n correspond to protons and neutrons. Typical interactions at T2K take α
corresponding to e and µ.

The peak energy at T2K is at approximately 0.6 GeV and is dominated by quasielectric interactions and those which produce a pion. Below 2 Gev, the dominant interaction modes are the quasi-electric, and the second dominant modes are those where
the neutrino excites a nucleon into a resonant state, where, for example, through ∆baryon production. This resonant particle can decay into numerous states producing
many combinations of nucleons and mesons. At an energy greater than 2 GeV, deep
inelastic scattering dominates the neutrino-induced interactions. Figure 7.1 shows the106CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\cross sections for neutrino and anti-neutrino CC interactions as a function of neutrinoenergy [15].

Figure 7.1: Total neutrino and anti-neutrino CC cross sections divided by the neutrinoenergy as a function of energy for various interaction modes as predicted by NUANCE[80]. The interaction modes include; Quasi-Elastic (QE), Resonant (RES) and DeepInelastic Scattering (DIS). Figures from [15].

Neutrino experiments including T2K, use simulations and event generators based on107CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\theoretical models to predict the neutrino-nucleon interactions. The most commonlyused include NEUT [53], GENIE [81], NuWro [82] and NUANCE [80]. T2K and SuperK specifically uses the NEUT event generator to simulate neutrino-nucleon interactions.
All analysis performed by the author in Section 7.3.1 onward is based on the theoreticalmodels within the NEUT event generator.

7.2.2

Elastic and Quasi-Elastic Interactions

Elastic and quasi-elastic interactions are the dominant modes of interactions in theapproximate energy range of 0.1 - 1.5 GeV, where the neutrino scatters elastically fromthe original nucleon. Charged current quasi-electric (CCQE) interactions take placewhen the neutrino interacts with a neutron inside the nucleus, leaving the outgoing
nucleon to be different from the original; producing a charged lepton and proton in the
final state. Neutral current (NC) elastic interactions correspond to the case in which
the neutrino interacts with a nucleon and produces a neutrino and the same type of
nucleon in the final state. As the focus of the analysis performed by the author is on
the neutral current single π 0 (NC1π 0 ), the focus of the neutrino theory will shift towards
interactions which firstly produce a single pion in the final state at T2K.

7.2.3

Deep-Inelastic Scattering

At higher energies above 1.5 GeV, deep-inelastic scattering (DIS),να + q −→ q + N 0 + hadrons,(7.1)

is the dominant neutrino scattering mechanism. Such interactions are found in thehigh energy end of the neutrino energy distribution at T2K. During DIS interactions,the neutrino interacts with quarks inside a nucleus, denoted by q and N respectively ininteraction 7.1. During the interaction, a large mount of momentum is transferred to
the nucleus resulting in the nucleus breaking and hardonic showers following.

7.2.4

Single Pion Production

There are two main processes which result in production of a single pion in the final
state; resonant production, which is dominant at higher energy neutrino interactions,and coherent pion production through coherent scattering.
Resonant Production
At higher neutrino energies, neutrinos can induce a resonant state in the target nucleon. During the resonant production process, the neutrino interacts with a single
nucleon within a nucleus, resulting in baryon resonance which decays to a nucleon and108

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\a meson, most commonly, a pion, in order to return to the ground state. Resonant
production takes place in both cases of CC and NC interactions. There are seven single pion resonant states in total, three charged current (Equations 7.2 - 7.4) and four
neutral current (Equations 7.5 - 7.8).

να + p −→ α− + p + π +(7.2)

να + n −→ α− + p + π 0(7.3)

να + n −→ α− + n + π +(7.4)

να + p −→ να + p + π 0(7.5)

να + n −→ να + n + π 0(7.6)

να + p −→ να + p + π +(7.7)

να + n −→ να + p + π −(7.8)

The event generators used to simulate resonant production mechanisms are based on
the Rein-Sehgal model [83], which describes single pion production via 18 ∆ resonances
below 2 GeV.
Coherent Production
Due to the nature of the nuclear target in the coherent production mechanisms, an extra
neutrino interaction mode is introduced compared to resonant production mechanisms.
In the resonant production case, when the neutrino interacts with the nucleus, the nucleus recoils but is left intact. For coherent pion production there is little energy transfer
between the incident neutrino and the nucleus and so the scattering neutrino leaves theoriginal nucleus intact and a forward-going pion is produced. The small scattering angle
with respect to the incident neutrino is dictated by the low momentum transfer requiredfor coherent scattering. The two mechanisms for coherent pion production can be seenin equations 7.9 and 7.10, where N corresponds to the target nucleus. The Rein-Sehgal
coherent model [84] is used by the event generators to simulate coherent interactions.
να + N −→ να + N + π 0
109

(7.9)

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\να + N −→ να + N + π +(7.10)In the following subsections, the focus will shift to specifically the NC1π 0 interactions
and measurements.

7.2.5

NC1π 0 Interactions

Long baseline neutrino experiments suffer somewhat from background induced by NC1π 0interactions. In T2K the NC1π 0 contributes to the background contamination whenmeasuring the P (νµ −→ νe ) appearance signal. The π 0 dominantly decays via themode π 0 −→ γ γ, which produces electron/positron pairs which emit further photons
via Bremsstrahlung radiation, forming an electromagnet shower. Inside the Super-K
detector, the Cherenkov rings produced by photons and electrons appear to be almost
identical, resulting in a mis-identification of one of the Cherenkov rings from the decay,
when it is missed by the reconstruction algorithm. In this situation, the signal νe CCQE
events and the NC1π 0 events are indistinguishable. As this analysis focuses on a model
independent measurement of this background contribution, its characteristics and its
reduction methods will be discussed in more detail in Section 7.2.8.
There are two processes that dominate NC1π 0 production: resonant production andcoherent scattering. Equations 7.11 and 7.12 show explicitly the NC1π 0 productions via
delta resonance, where the decay produces a nucleon and a π 0 with no other mesons in
the final state. The Feynman diagrams which illustrate resonant π 0 production can beseen in Figures 7.2 and 7.3. Equation 7.13 is an example of π 0 production via coherent
scattering, where in the example case, the neutrino interacts coherently with an Oxygen
atom and very little energy is exchanged. The nucleus is left in its ground state and aforward going π 0 is produced [85]. This type of production can be seen in Figure 7.4.
In both production cases, if there is sufficient momentum transfer, there is a possibility
that other mesons such as kaons may be produced. Such events are rare due to the peakaverage neutrino energy of T2K. If such rare decays happened, it is likely that the only
meson visible in Super-K would be the π 0 .

να + p −→ να + p + π 0(7.11)

να + n −→ να + n + π 0(7.12)

να + 16O −→ να + 16O + π 0(7.13)

110

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.2: Resonant π 0 production on a proton via delta resonance as shown in Equation 7.5.

Figure 7.3: Resonant π 0 production on a neutron via delta resonance as shown inEquation 7.6.

Figure 7.4: Coherent π 0 production as shown in Equation 7.13.

111

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.5: Diagram of the π 0 −→ γ γ decay, where θ is the opening angle between the
gammas.

7.2.6

Final State Interactions

The interaction modes discussed in the previous subsections describe the scenario where
the neutrino interacts with a single nucleon, however, the target nucleon will mostoften reside inside a nucleus. The cross-section of these interactions is affected by thepresent nuclear matter, meaning that there is an uncertainty on the identification of aninteraction when the identification is based on the final hadronic state. It is not possible
to isolate the initial interaction type from the final state interaction, as both initial andfinal states are complex. After an interaction occurs within a nucleus, the outgoingparticle must travel the length of the parent nucleus, therefore the outgoing particles
can scatter, be absorbed, or re-interact with dense nuclear matter. Other hadrons may
also be emitted which were not associated with the initial interaction. To demonstratethese effects, Figure 7.6 shows a case where initially a π 0 was produced which interacts
with a proton within the nucleus, undergoing a charge exchange : π 0 + p −→ π + +n. The interaction results in the initial π 0 becoming a π + , which is not associated with
the initial interaction. These processes are knows as final state interactions (FSI).

Figure 7.6: Feynman diagram displaying charge exchange interaction between a π 0 anda proton, where the π 0 changes into a π + .

FSI are a significant source of uncertainty on cross-section measurements and areimportant to understand. Though the current understanding of these effects is limited,112

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\cascade models are used within event generators to simulate FSI. Such models allow
each hadron at the interaction vertex to propagate through the nuclear matter within
the nucleus independently. The probability of any potential interactions is simulated
along with any by-products until the hadron has exited from the nucleus. It is possible
also for a neutrino to interact with a pair of nucleons inside the nucleus, which are known
as 2p-2h, or "two-particle two-hole" interactions. These interactions are significantly
different than single nucleon interactions and require different models and an additionof a factor to account for the electro-weak coupling strengths.

7.2.7

NC1π 0 Measurements

There are few measurements of the absolute NC1π 0 cross-section, as demonstrated in
Figure 7.7. Neutral current (NC) interactions are challenging to measure at neutrino
experiments due to the proton being the only charged particle produced during theinteraction. Two scenarios exist for the proton; the first is that it does not leave thenuclear environment due to final state interactions, the second is that, if it does leave
the nuclear environment, its energy is too low to be reconstructed. These factors resultin the majority of measurements for such channels to be the ratio of NC/CC crosssections, which were measured by bubble chamber experiments.
The first published measurements of the NCπ 0 to CC channel cross section ratio
was made by ANL in 1974 [86, 87], and the Gargamelle bubble chamber experiments.
It was also Gargamelle which produced the first NCπ 0 cross section measurement which
was not represented as a ratio, made in 1978 by measuring neutrinos on a C3 H8 CF3 Br
target [88]. The first two sections of Table 7.2 give a summary of the current measurements for multiple experiments, including the ANL and Gargamelle measurements.
Also included are the measurements from the BNL [89, 90] and CERN PS [91] sparkchamber experiments. The prediction from the NUANCE [80] event generator is included for comparison.
After the turn of the century, the K2K and SciBooNE neutrino experiments mademeasurements of the NC/CC inclusive cross sections in 2005 [92] and 2010 [93] respectively. The inclusive measurements do not suffer from the limitations that non inclusive
measurements do, due to the production of easily reconstructed charged pions producedby NC deep inelastic scattering. The K2K experiment was the first to make this measurement on water before the measurement was made at T2K. The results from K2K
and SciBooNE can be seen in the third section of Table 7.2. In 2010, MiniBooNE
measured the absolute NCπ 0 interaction cross section on CH2 mineral oil for both νµand ν̄µ neutrino modes [94]. Later, ArgoNEUT made a measurement of the NCπ 0 /CC
inclusive cross section was measured on Argon [95]. A summary of the MiniBooNE
measurements can be seen in Table 7.3.
113

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.7: The NC1π 0 cross section measurements [15].

114CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\
Experiment
ANL
ANL
NUANCE
Gargamelle
Gargamelle
CERN PSBNLBNLNUANCEK2K
SciBooNE

TargetH2
H2
free nucleon
C3 H8 CF3 Br
C3 H8 CF3 Br
Al
AlAl
free nucleon
H2 O
C3 H8

NC/CC ratioσ νµ p → νµ pπ 0  /σ (νµ p → µ− pπ + )σ νµ p → νµ pπ 0  /σ (νµ p → µ− pπ + )σ νµ p → νµ pπ 0 /σ (νµ p → µ− pπ + ) σ νµ N → νµ N π 0 /2σ νµ n → µ− pπ 0σ νµ n → νµ nπ 0σ νµ N → νµ N π 0  /2σ νµ n → µ− pπ 0 σ νµ N → νµ N π 0  /2σ νµ n → µ− pπ 0 σ νµ N → νµ N π 0  /2σ νµ n → µ− pπ 0 σ νµ N → νµ N π0 /2σ νµ n → µ− pπ 0σ NClπ 0  /σ(CC incl. )σ NClπ 0 /σ(CC incl. )Value
0.51 ± 0.25 [86]0.09 ± 0.05 [87]0.20 [80]0.45 ± 0.08 [88]see figure, (b) 7.7 [15]0.40 ± 0.06 [91]0.17 ± 0.04 [89]0.248 ± 0.085 [90]0.41 [80]0.064 ± 0.001 ± 0.007 [92]0.077 ± 0.005 ± 0.005 [93]Table 7.2: Table of NC1π 0 /CC cross-section measurements using the ANL andGargamelle bubble chamber experiments, the BML and CERN PS spark chamber experiments and the most recent K2K and SciBooNE neutrino experiments. The NUANCE
predictions are also included for comparison.

Experiment
MiniBooNE

TargetCH2

Eν GeV
0.81
0.66

Measurement
σ(νµ NCπ 0 )σ(ν̄µ NCπ 0 )Total cross section (× 10−40 cm2 /nucleon)
4.76 ± 0.05 (stat.) ± 0.76 (sys.) [94]1.48 ± 0.05 (stat.) ± 0.23 (sys.) [94]Table 7.3: Absolute cross section of NC1π 0 interactions on mineral oil made by the
MiniBooNE

As the number of absolute NC1π 0 and NC/CC ratio cross section measurements
increases, the understanding of these types of interactions grows. Better understanding
will lead to improvements in the current models through testing based on increased data
samples. Oscillation analyses would largely benefit due to the potential reduction inmodel uncertainties.

NC1π 0 Production and Measurement at T2K
Oscillation analysis at T2K takes into account flux and cross section models and arange of near detector fits. NC1π 0 production is measured in the near detector ND280(described in Chapter 2) and in the dedicated Pi0 Detector (P0D). The P0D is designed
at aid the understanding of the π 0 background at Super-K, through measuring the π 0rate on a water target:νµ + N −→ νµ + N + π 0 + X(7.14)

Although the POD is able to make this measurements, the results do not contributeto the oscillation analysis due to the limitation in statistics.
115

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

The π 0 Rate Measurement T2K
The π 0 rate at T2K is measured using the P0D under two operation conditions, water-in(with the detector filled with water) and water-out (when the detector is drained). Using
the two conditions allows for the extraction of interactions which occurred on water.
The most recent publication stating the π 0 rate at T2K was in 2018 which yielded theresults found in Table 7.4 with 2.64 × 1020 protons on target (POT) for the water-in
configuration and 3.49 × 1020 POT for the water-out configuration [96].

P0D configurationwater-inwater-out
on water

Expected
433
290
157

Observed
324 ± 33(stat) ± 88(sys)246 ± 26(stat) ± 61(sys)157 ± 41(stat) ± 69(sys)Ratio
0.79 ± 0.08 ± 0.20
0.85 ± 0.09 ± 0.21
0.68 ± 0.26 ± 0.44

Table 7.4: cross section of NC1π 0 interactions on water as measured by the P0D at
T2K. Results are taken from [96]. Table adapted from [97]

Alongside the systematic errors on the measurements in Table 7.4, a flux systematic error of 12% is included. The measurement is statistically limited and subject toadditional systematic errors introduced by the π 0 selection itself.

Figure 7.8: The expected and observed reconstructed π 0 energy measured by the P0D.
The expectation for each sample is normalised to the observed number of events [96].

The π 0 energy spectrum of the expected and observed reconstructed π 0 ’s in the P0D
can be seen in Figure 7.8. The expected compositions for each distribution are shown.

7.2.8

Characteristics of the NC1π 0 background at Super-K

It is possible for the two decay gammas to be misidentified as an electron-like event
when only one Cherenkov ring is reconstructed by the event reconstruction algorithm,
leading to the π 0 being classified as a single ring shower event; the signature of a νesignal event. This mis-identificaiton can occur in the cases described below.
• One of the two decay gammas has a very low energy and is not detected (E2 <<E1 ) (Figure 7.9a).
116

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\• One of the gammas is boosted in the same direction as the second and the angularseparation between the two gammas is small, such that the two rings overlap(Figure 7.9b).

Figure 7.9: Schematic showing the two cases of π 0 decay which can lead to misidentification [98].

Two examples of simulated π 0 events as seen inside the Super-K detector can be seenin Figure 7.10. The left event displays the case where there has been an asymmetricenergy decay where E2 = 113 MeV and E1 = 785.1 MeV. The hit location of the second
photon can be seen only via the blue MC truth ring. Such a decay resembles an e-likering and is likely to be mis-identified. The event display on the right shows an event
which clearly can be classified as a π 0 event. Both Cherenkov rings are visible and caneasily be separated.

Figure 7.10: Event displays of two separate simulated π 0 events which demonstrate thecases of mis-identification (left) and positive identification (right).

The study of neutrino induced NC1π 0 interactions helps not only to reduce thesystematic uncertainty on the P (νµ −→ νe ) measurement, but also lead to improvements
117

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\in the MC simulations of the interactions. Further measurements of the NC1π 0 crosssection will provide additional data to constrain the flux and cross section models which
are fed into T2K’s oscillation analysis.

7.3

Estimation of π 0 rejection efficiency at Super-K

For many years, MC only was used to study π 0 identification and rejection, however it is
not sufficient when calculating the rejection efficiencies. This is due to differences in thedetector response between data and MC, such as the distribution of scattered light. The
rejection of π 0 events can be performed by identifying two ring events and investigating
the electron to π 0 (e− -π 0 ) using event reconstruction algorithms. However, when oneof the rings from a π 0 event is missed, it can be mis-identified, and therefore identified
an electron signal. The rejection efficiency is at it’s smallest for the case where one ofthe π 0 decay gammas has a large fraction of the total energy of the event.
In order to calculate the systematic error relating to both the higher and lower energy Cherenkov rings, a control sample is constructed which is known as the "hybrid-π 0 "sample. This sample consists of "primary" and "secondary" samples which are used toestimate the systematic uncertainties for the higher and lower energy rings respectively.
Data-MC and MC-MC hybrid samples are constructed in both cases and the detection
efficiencies are calculated and compared. The difference between the two samples provides an estimated of the associated systematic error.

7.3.1

The Hybrid-π 0 control sample

The hybrid control sample is constructed in several stages. Firstly the hybrid data-MC
sample is generated. The data-MC sample consists of one Cherenkov ring from Super-K
data and one simulated gamma-ray event. The two events are merged at hit level toform a composite π 0 event. An hybrid MC-MC sample is also constructed to study the
expected properties of the hybrid data-MC sample. In order to estimate the systematic
error with respect to the higher and lower energy rings separately, "primary" and "secondary" samples are constructed. The primary sample is constructed by replacing thehigher energy ring by an electron-like (e-like) event from Super-K atmospheric neutrino
data/MC, and generating a simulated gamma-ray to replace the lower energy ring. Figure 7.11 illustrates the construction procedure for the data-MC and MC-MC primary
hybrid-π 0 samples.
The secondary hybrid-π 0 sample is constructed in a similar way to the primary
sample however, in this case for 1/3 of the sample, the lower energy gamma is replacedwith a Michel (decay) electron event from a cosmic-ray Muon decay from data or MC.
118

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.11: Schematic drawing showing the construction of the primary hybrid-π 0sample for data (Left) and MC (right).

Figure 7.12: Schematic drawing showing the construction of the secondary hybrid-π 0sample for data (Left) and MC (right).

An illustration of the construction procedure can be seen in Figure 7.12. This section
describes the construction procedure of the hybrid control samples. Firstly the algorithm
used to reconstruct the event information during the sample construction, APFit will
be described, followed by a second reconstruction algorithm, fiTQun, which is applied
to the sample after it is constructed.
The APFit reconstruction algorithm
The original reconstruction algorithm to be used at Super-K is APFit. The software isa single iteration fitter which reconstructs events in several steps, beginning with thevertex reconstruction which is based on the corrected timing information of the hits
inside the detector. The number of rings is then determined in a number of stages [99].
The first ring is found based on the charge distribution with respect to the interaction
vertex, and then subsequent rings are determined using a Hough-transformation and are
selected by an optimised likelihood function, which also rejects fake candidates. Fake
119

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\candidates are classed as those which have an opening angle of < 15◦ . The PID ofeach ring is determined through the ring pattern and opening angle of the rings. Eachparticle is classified as a showering particle (e± , γ) or a non-showering particle (π ± ,µ± ). The photo electron (p.e) distributions are calculated along with an assumptionof the particle type. The likelihood of electron and muon assumptions are calculated
based on the expected p.e distribution. Once the number of rings and PID assumptions
are determined, the ring separation part of the reconstruction extracts the fraction of
p.e’s in each PMT due to each ring and confirms the particle PID and contributes
to the momentum reconstruction. The final stage is the momentum reconstruction,
which is estimated using the total sum of p.e’s within a 70◦ half opening angle from thereconstructed ring direction. The number of p.e’s is then collected for each PMT andis corrected for light attenuation in the water [100].

The fiTQun event reconstruction algorithm
FiTQun is a likelihood based fitting algorithm developed for Super-K. It uses a likelihood based approach to event reconstruction by comparing the observed PMT hit charge
and time information with a PDF (Probability Density Function), which is constructed
for specific event kinematics [101]. The likelihood function is therefore a product of
the PDFs, evaluated at the measured value, and is also a function of the particle parameters. The final reconstructed values of the event track parameters are those which
maximise the the value of the likelihood function. FiTQun applies many reconstruction
hypotheses when determining the reconstructed particle type and particle compositionof the subevents. For example, PID is performed by comparing the best fit likelihoodsfor different particle types including, electron, muon and charged pion.
FiTQun includes tailored fitters such as the single-ring fitter which is used for: electron, muon and charged pion hypotheses, and a dedicated pi0 fitter used for identifying
the second ring from a neutral pion decay [102]. The final particle PID is the one which
maximised the value of the likelihood function. To perform electron, muon or pion
selection using fiTQun, the negative log likelihoods for, for example, electron - muon,
are compared and desired particle type selected based on the fraction of the total momentum that the event possesses based on an electron like hypothesis. The π 0 fitting
hypothesis is based on two of the standard electron-hypothesis tracks. The electronhypothesis tracks are produced via photon conversion, thus the vertices start somewhat
downstream of the π 0 vertex itself. This distance is fitted on an event-by-event basis.
The single track electron hypothesis fit is used to identify the first track. To identify
the second track, a π 0 likelihood function is evaluated with 100 uniformly distributed
choices of the direction for the second track. The chosen track is the one that returns
the lowest value of the negative log likelihood [102].
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[a\

7.3.2

Properties of the Hybrid π 0 sample

Currently the official analysis library used by the joint T2K-SK (or Super-K Long Baseline) analysis group uses an older detector library released in 2014 ("14c") and thesystematic errors on π 0 rejection efficiency are estimated using the previously most recent hybrid-π 0 sample, constructed in 2013, which was constructed using a detector
library released in 2013 ("13a"). There are minimal differences between the two detector libraries, hence the hybrid sample was not updated to use the 14c library. Future
T2K-SK analysis will use a newer library released in 2016 ("16c"), in which numerous improvements have been made upon the previous libraries. By reconstructing the
hybrid-π 0 sample using the newer "16c" library, the systematic error on the π 0 rejection
efficiency can be updated. The differences between the detector libraries include theuse of a newer version of SKDetSim with built in PMT gain correction and updated
versions of the reconstruction algorithms.
Building a new hybrid sample for future oscillation analyses using the newer detector libraries improves the previous hybrid-π 0 analysis, and therefore improves the
input parameters for the oscillation analysis. The main difference between the new andprevious samples is that the updated detector library includes the time dependant PMT
gain correction (GainCor) discussed in Chapter 4, Section 4.4.2. This provides a moreaccurate simulation of detector response: previously the increase in measured charge
due to the time dependent PMT gain increase was accounted for by scaling the charge
relative to time during the hybrid sample construction. Improvements also include an
updated energy scale, use of a more recent version of the APFit 1 algorithm used forvalidating the construction of the sample and most importantly, increased statistics.
The same neutrino event generator (NEUT [53]) is used for all samples.
Sample
2013
2018

NEUT
5.3.2
5.3.2

Data (days)
1294.72867.19

GainCorNo
Yes

SKDetSimv11.90v13.90

APFit
13a
16c

fiTQunv4r0
v6r0

Table 7.5: Table of comparison between previous and new hybrid samples, including theconstruction year, neutrino event generator version (NEUT), size of the data (in days),
PMT gain correction (GainCor) application, SKDetSim, and reconstruction algorithm(APFit and fiTQun) versions.

The 2013 hybrid sample uses data between October 2008 and November 2012, withapproximate live time of 1294.7 days. The new samples uses Super-K data between
October 2008 and April 2017, with a total livetime of 2867.19 days, a 45% increase inlivetime compared to the 2013 sample. A detailed breakdown of the updates since the1

The more recent version of APFit used is the version corresponding to detector library used for the
SK-MC construction.
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CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\last hybrid-π 0 sample construction can be seen in Table 7.5. The new sample provides
a more accurate representation of the detector response and a better understanding of
the event charge information. Based on the increase in statistics alone, it is expectedthat there will be a significant reduction in the statistical errors on the event sample
efficiencies derived using the new sample when compared to the previous samples.

7.3.3

The Hybrid-π 0 sample construction procedureStage 1: Single ring e-like event selection from atmospheric ν data and MC
The primary hybrid-π 0 sample constructions begins by extracting single ring e-like event
information from Super-K atmospheric ν data and MC. In this sample, the information
is taken from the April 2017 reduction, which spans the period of October 2008 andApril 2017. The event information is used to replace the higher energy decay gamma(the gamma with an energy > 60 MeV) in the primary sample and any lower energy
gammas in the secondary sample which have an energy > 60 MeV, which in this case,corresponds to approximately 2/3 of the secondary sample. The secondary sample will
be discussed in more detail in the following construction stages. The events are extracted
based on the following selection criteria:• The number of hits within a hit cluster in the OD is < 16
• Visible energy > 30 MeV• Number of rings = 1• The ring is electron like as defined by the reconstruction algorithm• There are 0 decay electrons (Michel electrons)• Goodness of APfit = 0.6
No fiducial volume (FV) cut is applied during this selection to ensure that the sample contains events which occur outside of the default fuducial volume. The fiducial
volume is defined as the distance between the reconstructed event vertex and the innerdetector wall, where the default FV definition is that this distance to be greater than
2 m. The total number of events selected from Super-K data is equal to 7491 and thetotal number selected from Super-K MC is equal to 467419. The number of MC events
is equalled to data such that each data and MC samples have equal number of events; inthis case, 7491. The number of events in MC is equalled to data by simply taking 7491
events of the MC sample at random. This is to reduce possible bias due to differencesin the samples. The momentum distributions for the extracted e-like events can be seenin Figure 7.13.

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Figure 7.13: Momentum distributions of the extracted e-like rings taken from the SK
atmospheric neutrino for data (Left) and MC (right).

Stage 2: Decay electron event selection from atmospheric ν data and MC
The second construction stage is specific to the secondary sample. Here decay electron
events are used to replace the lowest energy gammas which have an energy of < 60 MeV,
which in this case corresponds to 1/3 of the sample. The decay electron data and MC
used is that where an e-like event produced by a muon which decays inside the Super-K
detector, also known as a decay electron or Michel electron. The reason that only afraction of the sample is constructed using decay electron data is due to the numberof lower energy e-like rings available from the atmospheric data: There are not enoughsuitable low energy events in the atmospheric data to produce a full secondary sample,
thus the lowest energy rings are replaced with decay electron events. The decay electron
events for the hybrid data-MC sample are selected from the data spanning the whole
SK-IV period of October 2008 to May 2018. In this part of the sample construction,
the total number of events extracted is equal to 210844. The decay electron MC events
that are used to construct the MC-MC sample are generated using SKDetSim and are
based on the reconstructed kinematics from data events. The decay electron momentum
distributions can be seen in Figure 7.14.
Stage 3: Extraction of true π 0 kinematics from T2K-MC
In the third stage, all true NC1π 0 kinematics are extracted from T2K-MC by selecting
any neutral current neutrino interactions which contain π 0 production. The extracted
events are specifically only true π 0 ’s in their final state. No other events above Cherenkov
threshold are extracted. The kinematics are taken from the νµ → νµ (no oscillation)
channel where there is only one π 0 in the final state (after nuclear interactions inside
Oxygen) of a neutral current interaction, where the π 0 decays into two gammas. Unlike
during the extraction of e-like events, there are no other selection cuts applied. In this123CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.14: Momentum distributions of the extracted decay electron rings taken fromthe SK decay electron data for data (Left) and MC (right).

sample, a total of 152335 π 0 vectors were extracted. The momentum distribution of thetwo decay gammas from the extracted π 0 events can be seen in Figure 7.15.

Figure 7.15: True momentum distributions of 1st, or high energy (left) and 2nd, or
lower energy, (right) decay gammas from true T2K-MC kinematic.

Stage 4: Ring matching and generating the lower energy decay gamma
In order to combine the data (MC) and MC (MC) event information, it is necessary
in the case of both primary and secondary samples, to pair each of the e-like rings
with a gamma whilst maintaining the neutrino interaction kinematics. With respect
to the primary sample, the higher energy gammas vectors from all π 0 events extracted
from T2K-MC are matched with an e-like candidate ring from the SK data (MC). With
respect to the secondary sample, the lowest energy gamma is matched to an atmospherice-like candidate from SK data (MC) for for 2/3 of the sample. For the remaining 1/3 of124

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\the sample, the gamma is matched to a decay electron event. The best matching ringis defined as the one that satisfies the directional conditions of the neutrino interaction,
and whose reconstructed energy is closest to that of the true MC gamma. Ideally the
number of available atmospheric e-like events would be greater than the number ofhigher energy gammas from the π 0 interactions. As the number of e-like events is only
approximately 5 % of the number of those gammas, it is required that the e-like events
must be reused in order for all gammas to be matched. For the case of the secondary
sample, there are sufficient decay electron events such that it is not necessary to resuse
any events when constructing that specific part of the sample. For the part of the sample
which uses Super-K atmospheric events, the reusage method is applied. It is unlikelythat each event could be exactly matched, so three degrees of freedom are introducedin this construction stage. Based on these degrees of freedom, the e-like ring with theclosest energy to the gamma for which it will be matched is chosen.
1. The matching of the e-like rings vertex to the original event vertex from T2K-MC
kinematics is not required.
2. It is assumed that the detector is symmetric around the z axis. The T2K π 0system is rotated about to match the e-like event ring direction, hence assumingthat the highest energy gamma from the π 0 decay is symmetric around φ, pointing
in the z direction.
3. Is is assumed that the physics is unchanged when the system is rotated, hence
the rotated system conserves the angle between the π 0 decay gamma and theatmospheric ν e-like ring
When reproducing the kinematics of the neutrino interaction in the π 0 in the hybrid sample event, the π 0 vectors are converted to match the direction of the selected
e-like events. This conversion takes place with two rotational transformations. Firstly
a rotation about the central (z) axis if the Super-K detector is performed and secondly,
a rotation about the ν beam axis is performed. The azimuthal freedom about the beamaxis is allowed for the physics aspects, as we assume azimuthal freedom of the neutrino
interactions about the ν beam. Due to the possibility of the event direction pointing
toward the detector wall, this is not always an ideal assumption for the matching process. To accommodate for this, it is assumed that the detector response is symmetric
about Super-K’s central axis.
Figure 7.16 demonstrates the allowed rotations of the system whilst preserving theoriginal kinematics of the neutrino interaction. The angles between the neutrinos andgammas (θ, Θ and φ) in the first of the three schematics are the same as between thecorresponding neutrino, electron and gamma. During the matching process, the kinematics of the electron like event from Super-K data are preserved and the corresponding125

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\gamma is matched whilst preserving the original kinematics. The resulting composite
hybrid π 0 event is a transformation around the z-axis of the detector and the neutrino
beam direction.

Figure 7.16: The schematic describes the T2K-MC neutrino event which produces two
gammas, and the single electron like event extracted from SK-atmospheric neutrino datain their respective frames. Between the first and third diagram, the angles between theneutrinos and gammas (θ, Θ and φ) are the same as between the corresponding neutrino,
electron and gamma. The kinematics of the electron like event have not changed however
the direction of the gamma and neutrino have changed.

When two rings in each event are matched, the kinematics are validated and either
zero or two solutions are found. In the case that there are zero solutions, the event isdisregarded and the suitability of the next event is analysed. This matching process isrepeated until a valid candidate is found. Such a process ensures the conservation of
the scattering angles of the π 0 and the gamma, relative to the ν beam direction. In thecase that solutions are found, one solution is chosen at random and the electron withthe best matching reconstructed energy (closest energy to the true gamma energy) is
chosen. A comparison of the momentum distributions of the matched 1st and 2nd gammas to their respective e-like rings for both data-MC and MC-MC primary samples canbe seen in Figure 7.17. Figure 7.18 shows the equivalent plots for the secondary sample
where the decay electron event is matched. Any differences between the SK-data/MCand the T2K-MC feed into the overall systematic uncertainties in the final samples.

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Figure 7.17: True momentum distributions of the 1st (top) and 2nd (bottom) decay
gammas overlaid with the momentum distributions of the matched e-like events fromSuper-K atmospheric neutrino data and MC (primary sample).

Figure 7.18: True momentum distributions of the 2nd decay gammas overlaid with themomentum distribution of the matched decay electron events (Secondary sample).

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Figure 7.19: π 0 momentum distribution comparison for SK data (left) and MC (right)
overlaid with the true π 0 momentum from true T2K kinematics.

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Finally in this stage, for the primary sample, the lower energy gamma corresponding
to the given decay is simulated using SKdetSim, based on the e-like ring vertex. For thesecondary sample, the higher energy gamma is simulated. In this new hybrid sample,
the simulation takes into account the time dependant PMT gain variation. In order
to avoid double counting of dark hits after the merging of the data (MC) e-like ringand the MC (MC) gamma, the simulation is performed without PMT dark noise. The
simulated lower energy gamma is then merged with it’s higher energy data (MC) e-likecounterpart to create a hybrid π 0 event. The π 0 momentum distributions for the 1st
and 2nd gammas for the SK data and MC sample overlaid with the true π 0 momentum
from T2K-MC kinematics can be seen in figure 7.19.
Stage 5: Combining Super-K and T2K-MC event information
In the final construction step, the two rings are merged to form the composite event.
The Super-K event for the data-MC and MC-MC samples are merged with their MC
simulated counterparts primary and secondary hybrid-π 0 samples. Figure 7.20 shows
an example of a primary hybrid-π 0 data-MC event. The simulated gamma is displayedby image a) and the Super-K e-like event which has replaced the higher energy gamma
in the event is displayed in image b). The composite hybrid data-MC event can be seenin image c). The APFit and fiTQun algorithms are applied to the final samples.

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Figure 7.20: Figure containing event displays of a real e-like event from atmospheric ν
data (b), it’s corresponding simulated MC gamma (a) and the merged hybrid-π 0 eventfrom the primary data sample (c).

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[a\

7.4

The 2-ring NC1π 0 sample

The selection efficiency of the 2-ring NC1π 0 sample can be obtained by applying the
2-ring NC1π 0 event selection criteria to the data-MC and MC-MC the hybrid NC1π 0samples. An efficiency for each data-MC and MC-MC sample for both primary andsecondary samples is derived, and four efficiencies combined to estimate an overall 2ring NC1π 0 selection efficiency. The selection efficiency which will be referred to as the"remaining efficiency" and its systematic error will be used within the calculation toderive the NC1π 0 related background in Super-K to the νe appearance analysis at T2K
which is discussed in Section 7.6.1.

7.4.1

Selection stages

There are six selection stages used to select 2-ring π 0 events. The selection criteria are
based on the reconstructed event information and are as follows;
1. The events are fully contained in the reconstructed fiducial volume
2. Visible energy is greater than 30 MeV based on an e-like event hypothesis
3. Two rings are identified by the ring counting algorithm
4. Both rings are identified as e-like by the PID algorithm
5. There are no decay electrons (Michel electrons)
6. The standard π 0 mass is between 85 and 185 Mev/c2
A summary of these selection stages and abbreviations can be seen in Table 7.6.
Stage 0 (FVV) is used only to calculate the number of events contained within the
TRUE fiducial volume (the distance between the true event vertex and the inner detector wall is greater than 200 cm) and is used for normalisation at each selection stage
when calculating the remaining efficiencies. The event selection stages 1 - 6 use thereconstructed event information. It is useful to note that stage 5 is applied due tolegacy reasons. As the sample is constructed under the condition that there are no
decay electrons present, this selection stage is not necessarily required.

7.4.2

Selection Parameter Distributions

The following sub sections describe the cut parameter distributions along all stages of the
2-ring NC-h-π 0 sample for MC-MC and data-MC parts of both primary and secondary
samples. Due to the nature of the construction of the hybrid sample and the differences
between the number of electron-like rings used in the sample construction, and thenumber of true NC1π 0 kinematics extracted from T2K-MC, many of the electron likerings are reused to create the full hybrid event sample.
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Selection stage
0
1
2
3
4
5
6

Abbreviation
FVV
FCFV
Evis
2-ringe-likeNo dcyeinv.mass

Information type
Truth
Reconstructed
Reconstructed
Reconstructed
Reconstructed
Reconstructed
Reconstructed

Table 7.6: Table of abbreviations used for each selection stage. Stage 0 is used only to
calculate the number of events contained within the true fiducial volume

The statistical errors for both samples therefore are calculated by taking into account√the event re-usage factor. This changes the statistical error from N , where N is equal√
to the total number of events, to N 1n + N 2n2 . . . N xnx , where N becomes to Nx . The
number of the event is denoted by x, and nx corresponds to the number of times thatevent x was re-used during the sample construction, thus the statistical error becomes afunction of the event number and it’s re-usage factor [103]. As Only 2/3 of the secondary
sample is created using e-like rings from Super-K atmospheric data, the errors for thesecondary sample are calculated in two parts. The 1/3 of the sample which uses decay
electrons to replace the lower energy gamma does not require the error modification,
thus the reusage method is not applied and the error is the standard statistical error.
The re-usage function is applied to 2/3 of the sample. The two data sets are then
combined, thus preserving the two error calculation methods on a bin by bin basis.
Fully contained in the fiducial volume (FCFV)The first stage in the selection process is to discard any event which have a reconstructedvertex outside of the fiducial volume (FV) and keep only events which are fully contained
within the volume. The FCFV selection is defined by three parameters; the distance
between the ID detector wall and the reconstructed vertex, the number of hits per
event in the OD and the visible energy of the event. The first requirement is that thereconstructed vertex of the event is at a distance of greater than 200 cm from the ID
wall (Figure 7.21), the second criteria is that there are less than 16 hits in an event
cluster in the OD (Figure 7.23) and the final constraint is that the visible energy of theevent must be greater than 30 MeV (Figure 7.22).
The visible energy value itself is defined as the momentum of the particle based onan electron like hypothesis. The cut value for the 2-ring π 0 selection is equal to thatwhich is included in the standard FCFV selection. It is labelled as an individual stage
as other samples require a visible energy cut which is different to the cut in the FCFV
selection.

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Figure 7.21: The "wall" distribution of the primary (left) and secondary (right) MC-MCand data-MC samples. The selection criteria is displayed by the pink arrows.

Figure 7.22: The visible energy distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by the pink arrows.

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Figure 7.23: The OD hit distribution of the primary (left) and secondary (right) MCMC and data-MC samples. The selection criteria is displayed by the pink arrows.

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Number of ring distribution

The number of ring distributions along the FCFV selection for all samples is shownin Figure 7.24. The 2-ring sample is defined by selecting only events which have tworeconstructed rings. The NC1π 0 sample contains predominantly two ring events. Thereis some difference in the number of events after FCFV cuts in the secondary sample due
differences in the statistics of the data-MC and MC-MC components of the sample.

Figure 7.24: The number of ring distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. Events with only two rings are selected. The selection
criteria is displayed by the pink arrows.

Particle ID distribution

It is required that both rings in the two ring sample have an electron like PID. The
PID distributions of both rings in the primary and secondary samples can be seen in
Figure 7.25. The PID of the particles are defined by ID codes provided by the fitter.
The codes follow the convention of: 1 = gamma, 2 = electron, 3 = muon. It is useful
to note that the gamma hypothesis is labelled but not implemented into APFit, and is
not part of the particle reconstruction therefore all reconstructed gammas have an e-like
PID. In order to select an electron like PID for each of the two reconstructed ring, thering number is selected and for that ring, a code of "2" is selected. The 2-ring sample isdominated by electron like rings as expected due to the construction process, however
there is a small fraction of events are tagged with a muon like PID after reconstruction.
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Figure 7.25: The PID distributions of the primary (left) and secondary (right) MC-MCand data-MC samples. The top two histograms show the PID of the first particle in thetwo ring sample and the bottom two histograms show the PID of the second particle in
the two ring sample. Events which have an electron like PID are selected by setting thereconstructed particle code to 2. The selection criteria is displayed by the pink arrows.

Decay electron distribution

Due to the hybrid NC1π 0 sample construction procedure, e-like events from Super-K
atmospheric data and MC are extracted under the constraint that there are no decay
electron sub events present. This is reflected in the decay electron distribution shownin Figure 7.26, where clearly there are no decay electrons present for almost 100% of
events along the 2-ring, e-like event selection. The decay electron rejection cut ensuresthat, even after pre-definition that there are zero decay electrons present in the sample,
no events events that are reconstructed as decay electrons will be present in the sample.
This possibility is displayed in the left histogram in Figure 7.26. The primary data-MC
sample contains a (negligible) number of decay electron events after reconstruction.
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Figure 7.26: The decay electron distributions of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by the pink arrows.

Invariant mass distribution
The π 0 mass is calculated by using the reconstructed momentum for each electron
like ring and the opening angle between the two rings. The calculation that gives
the standard invariant π 0 mass can be seen in Equation 7.15. The final selection stage
constrains the mass of the π 0 to be between 85 and 185 MeV/c2 . The mass distributions
and cut threshold can be seen in Figure 7.27.
mπ0 = E(1) · E(2) − (1 − cosθ)(7.15)

Figure 7.27: Standard π 0 mass distribution of the primary (left) and secondary (right)
hybrid-π 0 samples along the standard two ring event selection. The pink arrows represent the π 0 mass cut threshold.

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Before the final selection stage, and by convention, the π 0 mass peak is extracted
individually for all four samples by fitting the distribution with a Gaussian function
between 85 and 185 MeV/c2 . The mass and its error correspond to the mean, and it’s
uncertainty given by the fit. The expected peak is at approximately 135 MeV/c2 whichcorresponds to the rest mass of a π 0 . The mass peaks for all samples within the fit
region, including the Gaussian fit are shown in Figure 7.28. The comparison between
data-data and data-MC samples within the fit region is shown in Figure 7.29.

Figure 7.28: Fit region of the standard π 0 mass distribution of the primary (left) andsecondary (right) hybrid-π 0 samples along the standard two ring π 0 event selection,
including the Gaussian fit.

A summary of the peak values of the mass distributions can be seen in Table 7.7.
Both primary and secondary MC-MC and data-MC samples agree well with each other,showing an MC/data ratio of approximately 1 in both cases.
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Figure 7.29: Fit region of the standard π 0 mass distribution of the primary (left) andsecondary (right) hybrid-π 0 samples along the standard two ring π 0 event selection.

Sampleprimary data-MC
primary MC-MC
MC-MC/data-MC
secondary data-MC
secondary MC-MC
MC-MC/data-MC

π 0 mass peak (MeV/c2 )136.8 ± 0.1
137.3 ± 0.1
1.003 ± 0.001
135.3 ± 0.1
136.8 ± 0.2
1.001 ± 0.001

Table 7.7: Table of π 0 mass peak position extracted through a Gaussian fit between thelimits of 85 and 185 MeV/c2 , for the 2018 hybrid π 0 samples.

7.4.3

Remaining efficiencies of the 2-ring NC-hybrid-π 0 samples

The remaining efficiencies after the two ring event selection for primary (p) and secondary (s) MC-MC and data-MC samples are denoted as ∈ (p, s)M C and ∈ (p, s)data ,and their errors as δ∈ (p, s)M C and δ∈ (p, s)data respectively. The error on each efficiency is the statistical error. In the case of both samples, the statistical error includes
the event reusage factor which was described in Section 7.4 Subsection 7.4.2.
The remaining efficiencies for all samples along the 2-ring π 0 selection are shown in
Figure 7.30. The MC-MC and data-MC samples agree with each other to within statistical error along each selection stage. A summary table of the remaining efficiencies along
all selection stages of the MC-MC and data-MC samples for the primary sample can beseen in Table 7.8, and for the secondary sample, in Table 7.9. It should be noted that it
is possible for the remaining efficiency to exceed 1, as demonstrated in Figure 7.30. In
this case, more events have been reconstructed inside the fiducial volume by the reconstruction algorithm than the number of events contained within the true fiducial volume.
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Figure 7.30: The remaining efficiencies of the two ring NC-h-π 0 sample, for primary(left) and secondary (right) samples. For each sample the selection efficiency is shown
alongside the ratio of MC/data.

Selection
FVV
FCFV
Evis
2-ringe-likeNo dcyemπ0∈ (p)M C (%)
100
101.81101.81
67.61
64.85
64.84
63.44

δ ∈ (p)M C (%)
N/A
0.30
0.30
0.99
1.00
1.00
1.00

n.ev
110636112635112635
74799
71746
71740
70190

∈ (p)data (%)
100
101.44
101.44
66.99
63.43
63.41
62.02

δ ∈ (p)data (%)
N/A
0.27
0.27
1.02
1.02
1.02
1.03

n.ev
106890108425108425
71609
67802
67782
66290

Table 7.8: Remaining efficiencies along all 2-R event selection stages for the Primaryh-π 0 samples .

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Selection
FVV
FCFV
Evis
2-ringe-likeNo dcyemπ 0∈ (s)M C (%)
100
100.19100.19
66.24
64.11
64.09
62.84

δ ∈ (s)M C (%)
N/A
0.12
0.12
1.34
1.35
1.35
1.36

n.ev
107074107282107282
70921
68640
68626
67286

∈ (s)data (%)
100
99.86
99.86
64.77
62.16
62.14
60.89

δ ∈ (s)data (%)
N/A
0.09
0.09
1.25
1.24
1.24
1.25

n.ev
98848
98709
98709
64027
61448
61423
60190

Table 7.9: Remaining efficiencies along all 2-R event selection stages for the secondaryh-π 0 samples .

Sampleprimary data-MC
primary MC-MC
secondary data-MC
secondary MC-MC
2-R NC1π 0

Remaining efficiency (%)
62.0 ± 1.0
63.4 ± 1.0
60.9 ± 1.3
62.8 ± 1.4
62.38 ± 1.25

Table 7.10: Table of remaining efficiency for the 2018 two ring hybrid-π 0 samples andthe overall efficiency as calculated using Equations 7.16 - 7.19.

The overall remaining efficiency of the sample is calculated by taking the weighted
mean of the four efficiency measurements:Pni
i=1 σi2 2¯ = Pn 1 σxi
i=1 σi2(7.16)and the errors are calculated by adding in quadrature the spread:nsσ2i =1 X
(i − ¯)n−1

(7.17)

i=1

and the uncertainty on the weighted mean:.
s

1Pn(7.18)q(sσ2i ) + (wσ¯i 2 )(7.19)wσ¯i 2 =δ =2i=1 iThe overall remaining efficiency for the two ring NC1π 0 sample is (62.4% ± 1%)(table 7.10)
141

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[a\

7.5

Comparison of the 2013 and 2018 two ring NC-hybridπ 0 samples

In order to assess the differences and expected improvements in the new NC-h-π 0 sample, the 2013 and 2018 samples are be compared. As discussed in Subsection 7.3.2, the2018 sample should provide numerous improvements over the 2013 sample including thein-built gain correction during construction, and a 45% increase in statistics. When comparing the old and new samples, it is expected that there will be a reduction in statisticalerror on the selection efficiencies and thus a reduction in the associated systematic error
on the sample. It is also anticipated that the 2018 sample will show a better data to MC
agreement and selection efficiencies. An increase in selection efficiency would suggestthat the application of the gain correction provides a better understanding of the collected charge information inside the detector and therefore, a more accurate PID ability.
Firstly, the π 0 mass distribution and fitted peak value for both 2013 and 2018 samples are compared, along with the relative differences between the data-MC and MC-MC
samples in both cases. Figure 7.31 shows the standard π 0 mass distributions for eachcase. The 2013 samples are displayed in the left hand panels of the figures, and the2018 samples on the right. The mass distribution displayed contains the same data as
Figure 7.27, however it has been rebinned into 10 MeV bins and the x-axis extended forcomparison with the distributions from the official 2013 sample. It can be seen from
Figure 7.31 that there has been a reduction in the statistical errors in the 2018 sample when compared to the 2013 sample. It can be argued that the agreement between
data-MC and MC-MC samples has decreased somewhat based on this representationof the samples, however the fluctuations observed are also compatible with statisticalfluctuations. A more appropriate determination of the agreement between data-MC
and MC-MC samples is to calculate the ratio of MC-MC/data-MC for the fitted mass
peaks for all samples.
The summary of the fitted mass peaks and relative differences between data-MC
and MC-MC samples for all cases can be seen in Table 7.11. It is clear from the initial2013 values of the mass peak that there is a noticeable difference between the data-MC
and MC-MC samples, which is summarised by calculating the ratio of the mass peaks
for all samples. The ratio between the 2013 primary and secondary mass peaks show
fluctuations of approximately 12% and 6% respectively. The fluctuations between the2013 data-MC and MC-MC samples is larger than observed in the 2018 primary andsecondary samples, showing fluctuations of 3% and 1% respectively. It is also worthy
to note that the mass peaks derived from the 2018 sample are much closer to the true
π 0 mass of 135MeV/c2 .

142

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Figure 7.31: Standard π 0 mass distribution of the primary hybrid-π 0 samples along
the standard two ring π 0 event selection, for the 2013 (left) and 2018 (right) hybrid-π 0samples. The error bars for each bin represent the statistical error from the electron
data. The pink arrows represent the π 0 mass cut threshold.

Year
2013

2018

Sampleprimary data-MC
primary MC-MC
MC-MC/data-MC
secondary data-MC
secondary MC-MC
MC-MC/data-MC
primary data-MC
primary MC-MC
MC-MC/data-MC
secondary data-MC
secondary MC-MC
MC-MC/data-MC

π 0 mass peak (MeV/c2 )141.0 ± 0.2
139.4 ± 0.2
0.988 ± 0.002
137.2 ± 0.2
136.4 ± 0.2
0.994 ± 0.002
136.8 ± 0.1
137.3 ± 0.1
1.003 ± 0.001
135.3 ± 0.1
136.8 ± 0.2
1.011 ± 0.002

Table 7.11: Table of π 0 mass peak position for the 2013 and 2018 hybrid π 0 samples.

The second comparison to make is that between the remaining efficiencies along the
2-ring π 0 sample selection. Table 7.12 shows the comparison between the remaining
efficiencies for both 2013 and 2018 samples, and the relative differences between the143CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

MC-MC and data-MC samples. By convention, the relative efficiency of the 2-ringsamples for both 2013 and 2018 samples, and their errors can calculated using Equations
7.20 and 7.21. Table 7.12 shows the relative differences between all samples and theirerrors. There has been a reduction in systematic error with respect to both primaryand secondary samples in the 2018 sample construction, which was expected due to theincrease in statistics. It is also clear that in the case of the secondary 2018 sample,
there has been an increase in the relative difference between the data-MC and MCMC samples which is possibly due to the increased ability in PID ability after the gain
correction. The full remaining efficiency of the selection for both 2013 samples can beseen in Figure 7.32 for the primary samples and Figure 7.33 for the secondary samples.
Is it clear that there has been a reduction in statistical error over all stages of the 2018
samples.
Year
2013

2018

Sampleprimary dataprimary MC(MC-data)/datasecondary datasecondary MC(MC-data)/dataprimary dataprimary MC(MC-data)/datasecondary datasecondary MC(MC-data)/data

Remaining efficiency (%)
61.2 ± 1.5
62.7 ± 1.5
2.4 ± 3.5
61.2 ± 1.9
62.1 ± 2.1
1.3 ± 4.7
62.0 ± 1.0
63.4 ± 1.0
2.3 ± 2.3
60.9 ± 1.3
62.8 ± 1.4
3.2 ± 3.0

Table 7.12: Table of remaining efficiency for the two ring hybrid-π 0 samples

R(p, s) =∈ (p, s)M C
δR(p, s) =∈ (p, s)data∈ (p, s)M C − ∈ (p, s)data∈ (p, s)data˙δ ∈ (p, s)M C 2
δ ∈ (p, s)data 2) +()(∈ (p, s)M C∈ (p, s)data(7.20)

s(7.21)For direct comparison, the associated systematic errors on the the 2-ring π 0 samples
are calculated in the same way as in the official hybrid-sample technical notes [104], using
the relative difference between the MC-MC and data-MC samples for both primary andsecondary constructions. The calculation for the total associated systematic error isdetermined using equation 7.22.
δ∈ =pR(p)2 + δR(p)2 + R(s)2 + δR(s)2

144(7.22)

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.32: Hybrid π 0 remaining efficiency along the two ring event selection for 2013
(left) [104] and 2018 (right) primary samples. The tops plots show the remaining efficiency and the bottom plots show the MC-to-data remaining efficiency ratio.

By using the traditional associated systematic error calculation, it is shown that
there has been an absolute decrease of 1.0% in systematic error, and fractional decreaseof approximately 18% from 6.5% in 2013 [104] to 5.5% in 2018.

145

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.33: Hybrid π 0 remaining efficiency along the two ring event selection for 2013
(left) [104] and 2018 (right) secondary samples. The tops plots show the remaining
efficiency and the bottom plots show the MC-to-data remaining efficiency ratio.

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[a\

7.6

Estimating the single-ring contamination of the NC1π 0using the NC-hybrid-π 0 sample"Listen, some prophecies are-are a bit
dodgy.
They’re-they’re mutable."
Giles - Prophecy Girl

7.6.1

Benefits of a model independent measurement

Oscillation analysis and the related background estimations at T2K rely heavily on fluxand cross section models. As discussed in Subsection 7.2.5, there are a limited numberof measurements of the NC1π 0 cross-section, therefore neutral current interactions are
not the most well understood. The NC1π 0 production and rate is measured by the P0D
at T2K (see Subsection 7.2.7) in order to aid the understanding of the π 0 related backgrounds however, these measurements rely on flux systematics, which, in the most recent
P0D analysis, introduce a systematic error of 12%. Until the number of NC1π 0 crosssection measurements increases, and the model predictions can be improved, there will
be large model induced uncertainties introduced to related measurements. Even though
the P0D makes measurements of the NC1π 0 cross-section on water, the far detector
systematics still remain to be accounted for in detail. Providing a model independentmeasurement of the NC1π 0 related background to the νe oscillation analysis signal canbe performed by, using a combination of Super-K and T2K MC and data, thereby including detector systematics, such as the detectors response to scattered light. Thismethod can significantly reduce the measurements dependence on model induced uncertainties. This section discusses the method used to estimate the fraction of NC1π 0events in a 2-ring sample, which have only a single reconstructed ring, and can therefore
be identified as an e-like event. Following this selection, the method used to calculate amodel independent prediction of the NC1π 0 background will be shown in Section 7.7.
In order to estimate the fraction of π 0 events that can be considered background inthe νe appearance analysis, the official T2K π 0 rejection cut is applied to the hybrid π 0samples. As the selection described in the following section uses two fitters; APFit andfiTQun which have been described in Subsection 7.3.1

7.6.2

The νe Appearance Selection

An estimate of the fraction of π 0 ’s from an NCπ 0 sample, which leak into the νe appearance sample, can be evaluated by applying the official T2K νe appearance selection
to both the primary and secondary hybrid samples. The selection criteria is as follows:147

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

1. Fully contained in the fiducial volume
2. Visible energy is greater than 100 MeV
3. One ring is identified by the ring counting algorithm
4. The ring is identified as electron-like by the PID algorithm
5. There are no decay electrons
6. The reconstructed neutrino energy is < 1.25 GeV
7. The event is not a π 0 based on the electron - π 0 likelihood ratio and the π 0 mass
Fully Contained in the Fiducial Volume (FCFV)The FCFV cut used is the standard APFit selection used in the 2-ring π 0 selection. See
Section 7.4, Subsection 7.4.2 for the parameter distributions.
Visible Energy distribution
The visible energy distribution is the same as that presented in the FCFV selection in
Section 7.4 Subsection 7.4.2. Figure 7.34 shows the distribution with the cut threshold
shifted to 100 MeV.

Figure 7.34: The visible energy distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by the pink arrows.

Number of ring distribution
The νe sample is defined by selecting only events which have a single reconstructed ring.
The parameter distribution is the same as that presented in Section 7.4, Subsection 7.4.2.
The number of ring distributions along the FCFV selection for all samples is shown in
Figure 7.35 with the single ring selection displayed.
148

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.35: The number of ring distribution of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by the pink arrows.

Particle ID distribution
It is required that the single ring has an e-like PID as determined by the reconstruction
algorithm. The PID distributions for both the primary and secondary samples can beseen in Figure 7.36. The PID of the particles are defined by ID codes provided by thefitter, which follow the same convention discusses in Section 7.4, Subsection 7.4.2. Inorder to select an electron like PID for the single-ring event, a code of "2" is selected.

Figure 7.36: The PID distributions of the primary (left) and secondary (right) MC-MCand data-MC samples. Events which have an electron like PID are selected by setting
the reconstructed particle code to 2. The selection criteria is displayed by the pinkarrows.

149

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Decay electron distribution

The decay electron distribution along the single ring, e-like selection can be seen in
Figure 7.37.

Figure 7.37: The decay electron distributions of the primary (left) and secondary (right)
MC-MC and data-MC samples. The selection criteria is displayed by the pink arrows.

Reconstructed neutrino energy (RecνE)

During the selection, a cut is placed on the reconstructed neutrino energy at RecνE <1.25 GeV, as above this energy, the intrinsic νe background component of the beam isdominant [105] over the oscillation signal. The reconstructed neutrino energy, RecνE, iscalculated using the equation for the exact reconstructed energy under the assumptionthat a CCQE neutrino interaction took place (Equation 7.23). The variables are defined
as follows, in order of appearance: mn = mass of the neutron, V = nuclear binding
16
potential which takes
q into account that the neutron is bound. In this case, for O, V

= 27 MeV. El =p2l + m2l is the lepton energy, mp = proton mass, ml = lepton massand finally, cosθνl = cosine of the beam direction [106].

RecνE =

2(mn − V )El − m2l − (mn − V )2 + m2p2(mn − V − El + pl cosθνl )150(7.23)

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.38: The reconstructed neutrino energy of the primary (left) and secondary(right) MC-MC and data-MC samples.

The π 0 rejection cut
The π 0 rejection cut is based on the dedicated fiTQun π 0 fitter. The cut is definedas: the electron - π 0 likelihood ratio is > 175 - 0.875 × fiTQun π 0 mass. The cut isparameterised by (y = ae x + be ) in ln(Lπ0 /Le ) v.s. reconstructed π 0 mass phase space.
Figure 7.39 shows the official log-likelihood ratios used to define the rejection cut inboth the oscillated νe CCQE (Charged Current Quasi-Elastic) signal and the NC1π 0background [101]. All events above the red line are rejected.

Figure 7.39: Left: Oscillated νe CCQE signal and right: the (νµ )NC1π 0 backgroundwith only FCFV cuts applied. The π 0 rejection cut is indicated by the red lines, where
all events above the lines are rejected. [101]151CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.40 shows the equivalent 2D distributions for the NC-hπ 0 sample. Figure7.41 displays a 2D distribution along the reconstructed neutrino energy selection. The
high statistics band above the red line represents the π 0 candidate region, which is
rejected based on the official π 0 rejection cut. The region below the red line represents
the electron event candidate region, which is classed as the signal region in the νeappearance analysis. Even though though the hybrid sample is constructed using only
true NC1π 0 kinematics, there is still a reasonably populated electron candidate region
based on these distributions. These events correspond to single ring π 0 events and form
the T2K background to the νe appearance signal.

Figure 7.40: Electron to π 0 likelihood (ln(Lπ0 /Le )) vs. FiTQun π 0 mass from thededicated π 0 fitter for the NC-h-π 0 samples. The events are fully contained within thefiducial volume, no other cuts have been applied. Events above the red line are rejected.

152

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.41: Electron to π 0 likelihood (ln(Lπ0 /Le )) vs. FiTQun π 0 mass from thededicated π 0 fitter for the single ring NC-h-π 0 samples. All cuts until the reconstructed
neutrino energy have been applied. Events above the red line are rejected.

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[a\

7.6.3

Remaining efficiencies of νe appearance background selection

The remaining efficiencies along the νe event selection for primary (p) and secondary(s) MC-MC and data-MC samples can be seen in Figure 7.42. A summary table of
the remaining efficiencies along all selection stages for the primary sample can be seenin Table 7.13, and for the secondary sample, in Table 7.14. As the final stage in theselection rejects π 0 ’s, this remaining efficiency represents the percentage of events in thepure NC-hπ 0 sample which pass the νe appearance event selection, and can be considered background in the analysis. The remaining efficiency can be inverted to give an
estimate of the π 0 rejection efficiency.

Figure 7.42: The remaining efficiencies over the νe event selection stages for primary(left) and secondary (right) samples. For each sample the selection efficiency is shown
alongside the ratio of MC-MC/data-MC.

After the νe selection is applied to the NC-hπ 0 sample, the percentage of events
that remain is equal to, in the primary case 5% and in the secondary case 2%. These
percentages can be given as an estimate of the percentage of NCπ 0 events which can beconsidered background in the νe selection. If the remaining efficiencies are considered154

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\
Selection stage
FVV
FCFV
Evis
1-ringe-likeNo dcyeErec
π 0 rej∈ (p)M C (%)
100
101.81101.77
30.87
30.59
30.59
24.42
4.40

δ ∈ (p)M C (%)
N/A
0.30
0.30
0.53
0.53
0.53
0.46
0.21

n.ev
110635112635112588
34148
33844
33843
27019
4872

∈ (p)data (%)
100
101.44101.38
30.77
30.49
30.48
24.36
4.93

δ ∈ (p)data (%)
N/A
0.27
0.30
0.54
0.54
0.54
0.47
0.14

n.ev
106890108425108369
32892
32590
32578
26040
5274

Table 7.13: Remaining efficiencies along all νe event selection stages for the Primaryh-π 0 samples .

Selection stage
FVV
FCFV
Evis
1-ringe-likeNo dcyeErec
π 0 rej∈ (s)M C (%)
100
100.19100.02
29.17
28.74
28.73
22.74
1.73

δ ∈ (s)M C (%)
N/A
0.12
0.039
0.37
0.37
0.37
0.32
0.04

n.ev
107074107282107095
31232
30771
30763
24350
1848

∈ (s)data (%)
100
99.86
99.61
30.25
29.80
29.80
23.54
2.03

δ ∈ (s)data (%)
N/A
0.09
0.16
0.37
0.37
0.37
0.32
0.05

n.ev
98848
98709
98459
29904
29464
29452
23275
2002

Table 7.14: Remaining efficiencies along all νe selection stages for the secondary h-π 0samples .

inversely as the π 0 rejection efficiency, then the rejection efficiency can be estimatedto be approximately 95% in the primary case and 98% in the secondary case. The
final remaining efficiencies after the νe selection, and the overall efficiency of the νebackground estimation is shown in Table 7.15. The calculation of the overall efficiency
is the same as presented in Section 7.3.1, Subsection 7.4.3. The final efficiency for the
single ring e-like sample is 2.04% ± 2.15%. Due to the differences between the primaryand secondary samples, the uncertainty is dominated by the disagreement rather thanany statistical difference.
Sampleprimary data-MC
primary MC-MC
secondary data-MC
secondary MC-MC
1-R e-likeRemaining efficiency (%)
4.9 ± 0.1
4.4 ± 0.2
2.0 ± 0.1
1.7 ± 0.1
2.0 ± 2.2

Table 7.15: Table of remaining efficiency for the νe event selection, including the overall
efficiency of the νe background155

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[a\

7.7

NC1π 0 Prediction in T2K-SK MC and Data

In order to predict the number of π 0 events seen in the T2K beam data, the two-ring
π 0 selection, as described in Subsections 7.3.1, 7.4.1 and 7.6.2, are applied to the T2K
beam MC. To make this prediction, the MC has been re-weighted using the official
T2K oscillation parameters, flux tuning [107] and cross-section models, T2K BANFF[108] event-by-event weighting and fixed Neutrino Interaction Working Group (NIWG)
parameters [109]. The MC is also scaled to the data by the number of Protons on Target(POT). The 2-ring sample in the T2K beam MC is used to calculate the purity of theNC1π0 sample.
This study uses T2K beam data from runs 1-9. Run 1-9 data was collated whilst
the beam run ran in forward horn current (FHC), producing a neutrino (ν) beam. The
data which the beam was operated in reverse horn current (RHC) mode, producing
anti-neutrinos (ν̄) is contained in runs 5-9. Predictions of the observed events are madeusing both neutrino (ν) and anti-neutrino (ν̄) mode data and scaled to 14.94×1020 POT
and 16.35×1020 POT respectively.

7.7.1

Predicted number of events and NC1π0 sample purity

By applying the 2-ring π0 selection to the T2K-SK MC over all oscillation channels, thepredicted number of 2-ring NC1π0 events (and events contained from other channels)
can be calculated. Figure 7.43 shows the π0 invariant mass for ν (left) and ν̄ (right)
data. The top plots display data and MC along the 2-ring π0 event selection before theπ0 mass cut. At this stage in the selection there is very little background contribution
to the NC1π0 sample outside of the final selection region of 85 to 185 MeV/c2 , withthe majority of the small background coming from CC interactions. The momentum
distribution along the full selection can be seen in Figure 7.44. A list of abbreviations
and definitions can be seen in Table 7.16.
Based on the background region in the top two histograms in Figure 7.43, the theNC-other contribution to the 2-ring π0 sample can be considered a part of the NC1π0signal. The NC-other sample consists of multi-π events and events from complex interactions which produce particles via delta resonance, such as single kaons. When theseinteractions occur inside the Super-K detector, there is a high probability that the only
observable particle is the π 0 .

156

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.43: The left histograms show the reconstructed invariant π 0 mass of the 2-ring
π 0 events seen in each analysis channel. The top two histograms show the invariant
mass before the final selection stage, and the bottom two plots show the invariant mass
after the final selection stage (mass in the range of 85 and 185 MeV/c2 ). The right plotsshow the mass for ν data (FHC) and the left plots show ν̄ data (RHC).

Abbreviation
Osc ν̄e CC
Osc νe CCνµ ν̄µ CC
B-νe cc
NC1π
NC-othSampleν̄e signal : CC interactions in oscillated ν̄e sample
νe signal: CC interactions in oscillated νe sample
νµ + ν̄mu CC interactions
Beam νe CC interactions
All NC1π’s from NC interactions over all data
All other NC interactions over all data

Table 7.16: Table of sample abbreviations and definitions of samples containing 2-ring
π 0 ’s.

157

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

Figure 7.44: The histograms show the reconstructed π 0 momentum of the 2-ring π 0events seen in each analysis channel, along the full 2-ring π 0 event selection. The left
histogram shows the MC and data for runs 1-9 (FHC) and the right histogram shows
the MC and data for runs 5-9 (RHC).

158

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

NC1π 0 Purity
A summary of the contents of the T2K-SK 2-ring sample can be seen in Table 7.17.
Mode
ν
ν̄

Oscν̄e CC
0.881
0.054

Oscνe CC
0.881
0.054

νµ ν̄µ CC
0.352
0.087

B-νe CC
0.197
0.092

NC1π
43.49822.657NC-oth
5.384
2.537

NM C
51.19425.480

NDAT A
53
23

Table 7.17: Table of predicted number of 2-ring π 0 like events in T2K-SK data using
T2K-SK MC, with 14.94×1020 POT in ν mode and 16.35×1020 POT in ν̄ mode.

The purity, p of the NC1π 0 sample can be calculated using the predicted number of
events within the 2-ring π 0 selection:p=

Ns
Ns + B(7.24)

Where Ns is the number of signal events and B is the number of background events.
Equation 7.24 can be further simplified by considering that the denominator, Ns + B,
the sum of the signal and background events, to be equal to the number of events inthe 2-ring MC sample, NM C . In this case, NM C = Ns + B and Ns = NN C1π + NN Coth .
The predicted ν mode NC1π 0 purity is calculated to be 95.5%, and 98.9% for ν̄ mode.
NN C1π + NN Coth
NM C

(7.25)pν =43.498 + 5.348= 0.9548
51.498(7.26)pν̄ =22.657 + 2.537= 0.9888
25.480(7.27)

p=

The uncertainty on the purity is calculated using the number of events in the 2-ring
π 0 MC sample after the events before being scaled to data.

Table 7.18 contains theC , the number of events considered signal, N M C ,total number of 2-ring π 0 sample, NTMOTs

the purity and the uncertainty on the purity, δp.
Mode
ν
ν̄

MCNT OT
53869
52472

MCNs
51432
51884

pν(ν̄) %
95.48
98.88

δpM C %
0.09
0.05

Table 7.18: Table of events in MC 2-ring π 0 sample before scaling MC to data.

Signal and background estimation using the NC-hybrid-π 0 samples
As this is a model independent and data driven measurement, the prediction of thenumber of single-ring and 2-ring events in the 2-ring sample selection will be calculated
159

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\using the overall efficiencies of the single-ring and 2-ring NC-h-π 0 samples. The overall
efficiencies can be found in Section 7.3.1, Subsection 7.4.3, Table 7.10 and Subsection
7.6.2, Table 7.15 respectively. Firstly, the number of 2-ring events is calculated as the
product of the efficiency of the 2-ring hybrid sample selection, 2R , and the number ofπ 0 events within the data sample selection, which currently unknown:
N2R = 2R · Nπ0 .

(7.28)

Similarly, the number of single ring events that are considered background can be
written as:
N1R = 1R · Nπ0 ,(7.29)

where 1R is the efficiency of the single-ring hybrid-NCπ 0 sample. The number of
2-ring π 0 events is considered the signal in this analysis, thus, N2R can be assumed tobe equal to Ns . Rearranging Equation 7.25 and substituting into equation 7.28 lets thenumber of π 0 events within the data sample selection can be written as:
Nπ0 =pM C · NDAT A.
2R(7.30)As Nπ0 takes an unknown value, Equation 7.30 can be substituted into Equation
7.31 to achieve the equation which predicts the number of single-ring events that passthe 2-ring π 0 selection.
N1R =

1R
· p · NDAT A
2R(7.31)The number of number of single-ring events that pass the 2-ring π 0 selection for theν sample is defined as N ν1R and for the ν̄ sample, N ν̄1R . Substituting the numbers
into equation 7.31 yields the background contribution to be approximately 1.65 events,
or 3.1% of the 2-ring π 0 sample in the ν mode case. In the ν̄ case, the contribution
is 0.74 events, or 3.4% of the 2-ring sample. The associated uncertainty on δN ν1R andδN ν̄1R can be calculated by adding the uncertainties on all variables in quadrature.
The uncertainties on the efficiencies and purity have already been obtained, and theuncertainty √on NDAT A is taken to be the statistical error, therefore the fractional error
is equal to

NDAT A
NDAT A .

As the uncertainty on the purity is negligible, at less that 1%, it

can be neglected when calculating the uncertainty on the NCπ 0 background estimation.
The background contribution and uncertainties in terms of number of events are
therefore:N ν1R = 1.7 ± 14.0% −→ 1.7 ± 0.2 eventsN ν̄1R = 0.7 ± 21.0% −→ 0.7 ± 0.2 events
The uncertainties can further be broken down into the systematic and statistical160

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\components:
δN1R =s2
δ21R + δ22R + δNDAT|{z} | {z A}
systematic(7.32)

statistical

The final result obtained for the number of events contributing to the single-ringbackground contributions are as follows, the uncertainties are quoted in terms of percentage:
N ν1R = 1.7 ± 2.5% (sys) ± 13.8% (stat)N ν̄1R = 0.7 ± 2.5% (sys) ± 20.9% (stat)
The result is statistics dominated due to the limitations of T2K and the the current
POT.

7.7.2

Comparison Between Model Independent and Official T2K Predictions

The current prediction for the T2K event rates for Run 1-9 (ν mode) and Run 5-9 (ν̄)
can be found in [79]. The events represented in Table 7.19 are from the "Asimov A"
data set. Asimov A data sets uses nominal values of oscillation parameters which can befound in [110], whilst all other oscillation parameter values correspond to those closest
to the T2K best fit for Run 1-9d. In the Asimov A case, normal hierarchy is fixed andδCP = -1.601. More information about the T2K data set can be found here [79].
Table 7.19 shows a comparison of the NC1π 0 background events in the νe and ν̄eanalyses alongside the total number of events in the samples from the current T2K
analysis. The "official" method is that employed by T2K, the "new" method is theone developed in this analysis. The same number of total events is used to make thepercentage background prediction for both official and new methods. There is currently
no direct calculation of the uncertainty on the NC1π 0 background contribution in T2K
oscillation analysis as the uncertainties are tied within the theoretical and model dependent uncertainties. The uncertainties on the NC1π 0 production itself arise fromareas including; single pion production, multi-pion production, deep inelastic scattering
production and final state interaction uncertainties. Taking into account these factors,
the uncertainty on the π 0 rate depends on the π 0 cross-section and the kinematics.
The official values quoted in Table 7.19 are the NC1π 0 rates obtained by the VALOR
analysis for T2K runs 1-9 [79]. The quoted uncertainties on the official NC1π 0 background events are an estimate calculated by the author of this thesis, and are basedon the the results in [79]. The uncertainty is a combination of the central values ofthe flux, cross-section and detector acceptance uncertainties. The flux uncertainties are
161

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\(post-near detector fits) approximately 5%, the NC cross-section uncertainty is approximately 30% and the detector acceptance uncertainty is approximately 19% [79].

MethodOfficialNew

Analysis
νeTotal events
74.4 ± 6.6 (sys)ν̄e17.1 ± 1.2 (sys)

νe

N/A

ν̄e

N/A

NC1π 01.8 ± 35.9%
1.8 ± 0.7 events
0.7 ± 35.9%
0.7 ± 0.3 events
1.7 ± 14.0%
1.7 ± 0.2 events
0.7 ± 21.0%
0.7 ± 0.2 events

Background (%)
2.5
4.1
2.2
4.3

Table 7.19: Comparison table of the NC1π 0 background events in the νe and ν̄e analyses
alongside the total number of events in the samples from the current T2K analysis.The
percentage background contribution take the total number of events from the official
analysis in both cases. The official numbers are adapted from [79].

The background estimation obtained by the new, model independent method is consistent with the official prediction. The uncertainty on the new estimate is significantly
smaller than than the estimated uncertainty on the official prediction, even when including the dominant statistical error. This method has almost completely removed any
model dependence in the uncertainties on the prediction, as the systematic error fromthe hybrid-π 0 sample comes mainly from the Super-K detector.
With respect to the prediction of the percentage background coming from misidentified NC1π 0 events, the background contribution to the νe sample would decreaseby the new method, however in the ν̄e case, the contribution would increased. The absolute differences are approximately 0.2% in both cases. It would be possible to further
break down the systematic uncertainty on the new method by considering the characteristics of the π 0 spectrum and calculating the rejection efficiency and it’s uncertainty over
several momentum bins. As this method is currently limited by statistics for T2K, thefollowing section investigates the validity of the new method for a much larger detector
with higher POT, such as Hyper-K.

7.8

Background Estimation for Hyper-Kamiokande

If a long-baseline neutrino experiment like T2K provided a higher POT and had a larger
far detector, an investigation could be performed to confirm whether the backgroundestimation method in this analysis would be still largely dominated by statistics, oralternatively would become dominated by systematic uncertainties. It is predicted that162

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\the uncertainties would switch from being statistically dominated to being dominatedby detector systematics, encompassed within the π 0 selection efficiencies provided by ahybrid control sample.
The fiducial volume of the Hyper-K detector will be 8.4 times larger than that ofSuper-K, with significantly higher POT. A scale factor can be calculated by taking into
account the increase in POT and fiducial mass, allowing for a projection of the NCπ 0
related background to be made for Hyper-K.
Firstly, a prediction of the POT is calculated. The current T2K beam power, P= 1.3 MW (= 1.3 × 106 J s−1 ). The current MR energy, E = 30 GeV 2 (= 48.07 ×
10−10 J) and the general operation time for particle accelerators is approximately, t= 107 s year−1 . The predicted beam operation time for T2HK (Tokai-to-Hyper-K) is
approximately 10 years. The total POT during the run period can be calculated using
equation 7.33:
P OT =

P ·t
E(7.33)

A comparison of the POT in ν mode, ν POT, and ν̄ mode, ν̄ POT, of T2K and
T2HK can be seen in Table 7.20. The calculation of the POT for T2HK is based on an
expected ratio of 1:3 for ν:ν̄ beam modes.
Experiment
T2K
T2HK

Massf (kton)
22.5
188.4

ν POT (1021 )
1.494
6.762

ν̄ POT (1021 )
1.635
20.29

Table 7.20: Comparison of the fiducial mass and POT in ν and ν̄ modes for T2K and
T2HK. The numbers are calculated using information from [67]The number of predicted background π 0 events and the statistical related uncertainties can be scaled to make a prediction for Hyper-K. The number of events that can beconsidered as background in the Hyper-K analysis can be calculated as follows. Firstly
the number of events, N, generally can be calculated using Equation 7.34, where Φ isequal to the neutrino flux.

N = Φ · P OT · M assf

(7.34)The scale factor required to calculate the projection for Hyper-K can be calculatedby dividing the number of events predicted for Hyper-K, NHK by the number of events
predicted by this method for T2K, NT 2K . The neutrino flux is assumed to be the same2

1 GeV = 1.6021773 × 10−10 J
163

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\for T2K and Hyper-K therefore the Φ term cancels.
scale factor}|{z
M assf HK
HK
T 2K P OTHKN=N··P OTT 2K M assf T 2K

(7.35)The scale factor must be calculated for both ν and ν̄. The scale factors can be seenin Equations 7.36 and 7.37.
N ν HK = N ν T 2K · 37.90(7.36)N ν̄ HK = N ν̄ T 2K · 103.87(7.37)The predicted fraction of beam time that will run in ν̄ mode is three times larger
than the time running in ν mode, which is reflected in the differences in the scale factors,
thus during the T2HK beam time, there will be much higher statistics of ν̄ data thanprovided by T2K compared to ν data. A summary of the scale factors, the projection
HK ), and the predicted number of single ringof the number of 2-ring π 0 events (NDAT
AHK ) can be seen in Table 7.21. The
events which leak into the νe appearance sample (N1R

numbers from T2K can also be seen here, which take the same notation style as thosefor Hyper-K.
Mode
ν
ν̄

Scale factor
37.90
103.87

T 2K
N1R
1.65
0.74

HK
N1R
62.54
76.86

T 2K
NDAT
A
53
23

T 2K (%)
δNDAT
A
13.74
20.85

HK
NDAT
A
2008.702389.01

HK
δNDAT
A (%)
2.23
2.05

Table 7.21: Summary of scale factors and predicted number of events in Hyper-K.

It is assumed that the systematic errors associated with the hybrid sample remainunchanged when calculating the projection for Hyper-K. It is also assumed that the
purity of the samples would remain the same and the uncertainty unchanged if it isassumed that the MC fake data set for Hyper-K is generated with the same statistics.
The number of events within the 2-ring π 0 MC sample can be scaled in a similar way
to the number of events in T2HK data by scaling the number of events in the MC by
the increase in POT for the ν and ν̄ samples individually. Table 7.22 presents a scaled
version of the Table 7.17 in Subsection 7.7.1.
Mode
ν
ν̄

Oscν̄e CC
33.3905.690

Oscνe CC
33.3905.690

νµ ν̄µ CC
13.3419.037

B-νe CC
7.466
9.556

NC1π
1648.574
2353.382

NC-oth202.689263.518

NM C
1940.253
2646.608

NDAT A2008.702389.01

Table 7.22: Table of predicted number of 2-ring π 0 like events in theoretical T2K-HK
data using scaled T2K-SK MC, and scaled POT.

164

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\

The predicted background contribution for Hyper-K is the following:
HK = 62.5 ± 3.3 % −→ 62.5 ± 2.1 events
N ν1R
HK = 76.9 ± 2.7 % −→ 76.9 ± 2.1 eventsN ν̄1R

When the errors is broken down into the statistical and systematic components,theresult is:
HK = 62.5 ± 2.5 (sys) ± 2.2 (stat)
N ν1R
HK = 76.9 ± 2.5 (sys) ± 2.1 (stat)N ν̄1R

With a larger detector and increased statistics, the uncertainties on the measurement
provided by this method have significantly decreased and the uncertainty has shiftedfrom being statistically dominated to systematics dominated.

7.9

Summary

Currently there is no official uncertainty quoted on the NC1π 0 related component of
the background to the νe appearance signal, as all of the related uncertainties are tied
within the theoretical uncertainties, making this specific uncertainty troublesome to extract. An uncertainty can be estimated by taking into account the flux, detector andcross-section uncertainties, which provides an overall uncertainty of approximately 36%,
which is dominated by the uncertainty from the NC cross-section model.
Developing a data-driven and model independent method of determining the NC1π 0
related background has provided a competitive prediction which is consistent with thevalue predicted by the official T2K oscillation analysis, and provides a significantly
reduced uncertainty. Comparing the ν beam mode (FHC) results, it can be seen thatthe error bars are significantly reduced:
New: N ν1R = 1.7 ± 0.2 events
Official: N ν1R = 1.8 ± 0.7 events
By removing model dependencies from this measurement, the complex uncertainties
somewhat simplify and become easier to understand. The systematic component now
comes from the construction of the hybrid control sample and therefore from detector
systematics such as event reconstruction, rather than from flux and nuclear interaction
uncertainties. This is reflected in the reduction in uncertainty from approximately 36%
to 14% in the FHC case.
If a larger detector such as Hyper-Kamiokande is considered, one can discuss theeffects that the newly derived method would have on the current oscillation analysis.
165

CHAPTER 7. A MODEL INDEPENDENT MEASUREMENT OF THE NC1π 0 RATE AT SUPER-K[a\Hyper-K strongly predicts that with the increased detector volume and statistics, itwill be able to make some of the most precise measurements of the neutrino oscillation
parameters. For Hyper-K to reach it’s goals, a reduction on the statistical uncertainties,
and systematic uncertainties on the neutrino flux and cross-section contributions to theoscillation analysis is required. It is somewhat difficult to reduce the NC cross-section
uncertainties due to there being very few experimental measurements of the NC crosssection itself. By making a model independent measurement of the NC1π 0 related
background, direct dependence on the neutrino flux and cross-section models are isremoved, therefore largely reducing the related uncertainty. When taking this into
consideration alongside the existence of a larger detector such as Hyper-K, it can beshown that the uncertainty on the NC1π 0 measurement becomes negligible due to theincrease in statistics, and therefore would also be a viable method for use in the future.
For ν mode, the Hyper-K prediction is as follows:
HK = 62.5 ± 2.1 events
N ν1R

166

Chapter 8

Conclusions"You think you know who you are,what’s to come,You haven’t even begun."Tara/The first Slayer - Restless

8.1

Summary

As Super-K undergoes the addition of gadolinium to the detector, the daily monitoringof the water quality at numerous locations along the depth (z positions) of the detector
become increasingly important. The UK designed and built light injection system was
successfully installed inside the Super-K detector over the summer 2018 refurbishment
period. Between November 2018 and July 2019, the first full sets of data were taken andhave been analysed by members of the UK team. The new system is able to provide
measurements of the water properties at 5 locations along the z axis of the detector.
It is not expected that the water transmittance would change after the gadolinium isintroduced however, any issues with the water due to contamination of poor circulation
could be derived.
After stable and continuous running for an extended period of time, and the introduction of real time run-by-run derivations of the water coefficients, the information
could be built into the Super-K detector simulation software, SKDetSim. This addition
would allow the simulation of more realistic detector response, by simulating any true
daily and run-by-run variations in the water quality. The system would therefore also
be used for monitoring purposes, with the aim of integration into the daily shift checks.
The current Super-K laser injection system has been continuously running for approximately 10 years, and is providing daily analysis of the water coefficients. The daily
analysis has been updated and improved via the implementation of a hit correction factor to take into account the PMT gain variation over time. The data is now corrected
on a run-by-run basis, thus improving the overall derivation of the water coefficients167

CHAPTER 8. CONCLUSIONS[a\and the run by run monitoring. The derived RMS/mean time variation is also available
for the "SK-IV" period and has been used in feasibility studies for the UK LI systemcapabilities. The Super-K system will continue running alongside the UK LI system as
the system provides a well understood output which is fully integrated with the Super-K
DAQ.
This thesis also presented an analysis to provide a detector systematic error on the
2-ring NC1π 0 sample in Super-K. The control sample created to provide the detector
systematic error was used to develop a new data-driven measurement of the NC1π 0
component of the background events to νe appearance analysis at T2K.
The NC1π 0 contributes significantly to background contamination when measuring
the P (νµ −→ νe ) appearance probability by T2K. The π 0 dominantly decays via themode π 0 −→ γ γ. Inside the Super-K detector, the Cherenkov rings produced by photons
and electrons appear to be almost identical, resulting in a mis-identification if one of theCherenkov rings from the decay is missed by the reconstruction algorithm. Rejection ofπ 0 events can be performed by identifying two ring events and investigating the electron
to π 0 (e− -π 0 ) separation using event reconstruction algorithms. However, when one of
the rings from a π 0 event is missed, the event can be identified as an electron signal.
In order to calculate the systematic error on both the higher and lower energy
rings, a control sample is constructed which is known as the "hybrid-π 0 " sample. This
sample consists of "primary" and "secondary" samples which are used to estimate thesystematic uncertainties for the higher and lower energy rings respectively. Data-MC
and MC-MC hybrid samples are constructed and the detection efficiencies calculated
and compared. The difference between them provides the estimation of the systematic error. As part of this analysis, the hybrid sample has been updated and has been
constructed using updated detector libraries, which includes the time dependent PMT
gain correction. This introduces a more accurate simulation of the detector response
and understanding of the event charge information. The sample also contains increased
statistics, leading to a reduction in statistical error. The associated systematic errors
on the 2-ring NC-h-π 0 sample have been updated and compared and can be seen below,
where δ∈2013 and δ∈2018 correspond to the errors for the 2013 and 2018 samples respectively:δ∈2013 = 6.5%
δ∈2018 = 5.5%
Using the traditional associated systematic error calculation, it is shown that there
has been an absolute decrease of 1.01% in the associated systematic error and relative
decrease of approximately 18%. The update has also made a significant impact on the168CHAPTER 8. CONCLUSIONS[a\overall statistical errors associated with the selection efficiencies for both primary andsecondary data-MC and MC-MC samples. A summary can be found in Table 7.12 in
Chapter 7.
Current estimates of NC1π 0 related events which contaminate the νe appearance signal are based on model predictions and a range of near detector fits at T2K, resulting
in complex uncertainties which are troublesome to extract via the oscillation analysis.
The quoted error on the official background contribution in this thesis is an estimatebased on the official flux, detector reconstruction related and cross-section models, whichis equal to approximately 36%, with the dominant contribution coming from the NC
cross-section model. This analysis has developed a data-driven background estimation
method, with significantly reduced and simplified uncertainties that have little to no
direct dependence on model induced uncertainties. The new method uses the 2-ring
NC1π 0 selection and rejection efficiencies combined with NC1π 0 sample purity predictions from T2K-SK MC and data. The calculation has been made using data from T2K
runs 1-9 scaled to a total of 14.94×1020 POT in ν mode and 16.35×1020 POT in ν̄ mode.
The final estimation of the NC1π 0 related background contribution in terms of thenumber of events and relative to the official predictions are as follows:
New: N ν1R = 1.7 ± 0.2 events
Official: N ν1R = 1.8 ± 0.7 eventsfor ν mode and,
New: N ν̄1R = 0.7 ± 0.2 events
Official: N ν̄1R = 0.7 ± 0.3 eventsfor ν̄ mode.
Results for both ν and ν̄ modes are consistent with the current number of eventsin the T2K analysis, showing an 11% deviation from the official νe prediction and 5%
deviation in the νe case. This method has almost completely removed any model dependence in the uncertainties on the prediction, as the systematic component of theerror originates from the hybrid-π 0 sample which comes purely from the Super-K detector reconstruction. By removing the model induced uncertainties, the uncertainty
on the prediction has reduced from approximately 36% in the official ν and ν̄ cases toapproximately 14% and 21% respectively with the new method. Currently for T2K thismethod is limited by statistics, resulting in the uncertainties being dominated by thestatistical component. The systematic uncertainty provided by the new method could
be further broken down by considering the characteristics of the π 0 spectrum and calculating the systematic uncertainty on the rejection efficiency over several momentum169

CHAPTER 8. CONCLUSIONS[a\bins. The systematic uncertainties on the rejection efficiencies should also be made ona momentum bin by bin basis.

8.2

OutlookThe new method already provides a competitive measurement and uncertainty on theNC1π 0 related background contribution to the νe appearance analysis: however for alarger detector and higher number of POT, this method will become more valuable. The
fiducial volume of the Hyper-K detector will be 8.4 times larger than that of Super-K
and the POT will increase by a factor of 10. By considering these factors, a projection
was made for Hyper-K by scaling the number of predicted background NC1π 0 eventsand the number of events in the data by the scale factors derived in Chapter 7, Section
7.8. The projection for Hyper-K yields the following results:

HK = 62.5 ± 3.3 % −→ 62.5 ± 2.1 events
N ν1R
HK = 76.9 ± 2.7 % −→ 76.9 ± 2.1 eventsN ν̄1R

It was assumed that the systematic component of the uncertainty which is provided
by the hybrid sample would remain unchanged for Hyper-K and the uncertainty on thesample purity would also be negligible. With the increase in POT and therefore statistics, the statistical error component becomes comparable to the systematic component.
The uncertainty on this same measurement with this new method for Hyper-K predicts
a further reduction in uncertainty in greater than 10% over ν and ν̄ samples.

This analysis has developed a new data-driven background estimation method withpromising results, which in time can be further improved. For example, it is likelythat Hyper-K will use potentially more complex reconstruction algorithms which could
provide more accurate vertex and energy reconstruction. The detector simulation will
be influenced by the upgrades of the many calibration systems, from which the data
provided can be fed into the reconstruction algorithms, thus providing a more accurate
understanding of the detector response.

170

CHAPTER 8. CONCLUSIONS

[a\

8.3

Final Remarks

In conclusion, the current T2K oscillation analysis does not provide a direct uncertainty
on the NC1π 0 related background due to complex model dependencies. The expected
uncertainty based on the flux, detector reconstruction and NC cross-section models predicts an uncertainty of approximately 36%, where the NC cross-section uncertainty itself
is approximately 30%. The data-driven measurement method developed in this thesis
provides a viable alternative method that can be used to make the background prediction with a highly simplified uncertainty, which does not rely on the (rarely measured)
NC cross-section. The new method is consistent with the official prediction and reduces
the uncertainty on the measurement by greater than 10% in both ν and ν̄ cases. It
also is capable of providing an absolute (and simplified) uncertainty on the background
prediction using a well understood control sample.

171

CHAPTER 8. CONCLUSIONS

[a\

172

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