DOCTORAL DISSERTATION———————————————————————–
Measurement of Neutrino and Antineutrino
Neutral-Current Quasielastic-like Interactions andApplications to Supernova Relic Neutrino Searches———————————————————————–

Yosuke ASHIDAHigh Energy Physics Group
Division of Physics and Astronomy
Graduate School of Science
Kyoto University

February 10, 2020

ABSTRACTMEASUREMENT OF NEUTRINO AND ANTINEUTRINO
NEUTRAL-CURRENT QUASIELASTIC-LIKE INTERACTIONS ANDAPPLICATIONS TO SUPERNOVA RELIC NEUTRINO SEARCHES

Neutrinos are a key messenger that carry valuable information about the supernova explosion.
In particular, discovery of supernova relic neutrinos (SRNs) would open up many paths toprecise studies of the supernova explosion mechanism. A barrier for the discovery of SRNs
is that one of the main backgrounds, atmospheric neutrino neutral-current quasielastic-like(NCQE-like) interactions, is not precisely measured nor predicted. In this thesis, a measurementof this channel using Super-Kamiokande data in the T2K experiment is presented. Signal event
candidates were selected based on nuclear de-excitation γ-rays. An application of the measured
results to the background estimation in an SRN search at Super-Kamiokande is also reported.
T2K has accumulated 14.94 × 1020 and 16.35 × 1020 protons-on-target exposures of theneutrino and antineutrino beams, respectively. The measured flux-averaged NCQE-like crosssections are:−38
⟨σν-NCQE ⟩ = 1.70 ± 0.17(stat.)+0.51
cm2 /oxygen,−0.38 (syst.) × 10
−38
⟨σν̄-NCQE ⟩ = 0.98 ± 0.16(stat.)+0.26
cm2 /oxygen,−0.19 (syst.) × 10

at flux-averaged energies of 0.82 GeV and 0.68 GeV for neutrinos and antineutrinos, respectively. These are the world’s most precise measurement results to date, and the antineutrino
result is the first measurement of this channel. Distributions in the kinematic regions of interest
for SRN searches are also studied for the first time.
The largest uncertainty in the NCQE-like measurement comes from modeling of the γ-rays
emitted from neutron-oxygen reactions. In order to provide experimental data, a measurement of γ-ray production via neutron-oxygen reactions with an 80 MeV neutron beam was
performed. Several γ-rays of various energies were observed and their production cross sections
were measured to ∼20% precision.
An SRN search was performed with a new estimation of the NCQE-like background basedon these T2K results and using a 2970.1-day data set from Super-Kamiokande. The new
estimation reduces the uncertainty from 100% to 60%. This improves the search sensitivity
by 12% compared to an analysis with a 100% uncertainty on the NCQE-like background. No
significant excess over the prediction was observed in the data spectrum, and an upper limiton the ν̄e flux was placed. The result is the world’s most stringent above 13.3 MeV in neutrinoenergy and a factor 3 to 30 above model predictions. The methods presented in this thesis areapplicable to SRN searches at other water Cherenkov detectors, such as SK-Gd and HyperKamiokande, and may help a future discovery of the SRN flux.

ACKNOWLEDGMENTS
My research life in the graduate school was full of fun and joy. This thesis has never been accomplished without huge supports from many people. I would like to oﬀer my humble appreciation
to all those people.
I would like to show a big appreciation to my supervisor Prof. Tsuyoshi Nakaya. He
introduced me this interesting research topic and has been supporting me throughout the
research. His thoughtful advices always stimulate my mind, leading to new ideas, and his keencomments motivate me to go and think deeper. I am sure that his manner is one of the goals
for physicits. I am grateful to Prof. Yusuke Koshio of Okayama University. Throughout myresearch project, from neutron experiments to supernova neutrino studies, he has always beenencouraging me. I would also like to thank my another supervisor, Prof. Roger Wendell. He
oﬀered me tremendous supports as an Super-Kamiokande expert as well as a convener in the
T2K-SK group. Not only in the research but he helped me a lot about the English things. I
always realize he is from US as I see his elegant English (I forget the fact since we usually talkin Japanese super naturally). My special thanks go to Dr. Tatsuya Kikawa. Sometimes he isa nice advisor, and sometimes like a friend.
My research life had started from the RCNP neutron project. Through this project I havemet many respectful researchers, and I am sure that the neutron experiment had given me
basis as a physicist. Prof. Gianmaria Collazuol from University of Padova is among the greatest
researchers. I would never forget an impact when I met him for the first time. His experimental
thoughts and techniques are so much beautiful and have always led the experiment successful. I
would like to appreciate great supports from Prof. Akira Konaka of TRIUMF. He always makescomments from the point of view that I could have never imagined. Talking with him, evenfor a brief moment, always leaves me mysterious but wonderful feelings. I would also like tothank fantastic students of this project, Hirotaka Nagata, Toshiaki Horai, Fabio Iacob, Corina
Nantais, Alice Maurel, Daisuke Fukuda, Masamitsu Mori, and Tetsuya Shirahige. Nagata-kun
is the first experimental partner with whom I spent a lot of fun and tough moments. We had
failed in many beam tests and had finally arrived at a small but unforgettable success. I would
say that the basic motivation that I continue research is to experience that moment again. I
would like to thank him about carrying many lead bricks for the experiments. Horai-kun is
the second experimental partner. He is very eager to learn many and I am always happy toteach him, and he is now a nice physicist that comes up with nice ideas and produces amazing
results. I would also like to acknowledge him about his mangas and board games we enjoyed
together. By the way, I should note that I don’t forget about Peace Maker.
Studies in the MUMON grounp taught me a lot including diﬃculty and importance ofbeam operation. Prof. Atsuko Ichikawa introduced me a topic about EMTs. She encouraged me
through her amazing ideas. I enjoyed discussion with her which sometimes gets heated. I would
like to thank Mr. Hajime Kubo. I was amazed at his careful works about MUMON and learned
many from him. My big appreciation also goes to people in the T2K beam group, especiallyto Prof. Ken Sakashita, Dr. Megan Friend, and Dr. Taku Ishida for their contributions to
the EMT studies. There are many students for this detector: Dr. Keigo Nakamura, Wataru
Uno, Kenji Yasutome, Nao Izumi, Takashi Honjo, and Takuya Kobata. Keigo-san is a strict
but in fact kind guy. I really thank him that he introduced me MUMON studies. Uno-kun
and Yasutome-kun are funny guys in Kyoto University. Uno-kun eats only tuna (maguro) in5sushi restaurants and Yasutome-kun never stops working in MUMON calibrations. Both areso patient about everything even though it is very tough and I want to be like that.
The main part in this thesis is based on the work in the T2K-SK group. This is thefirst physics analysis to me and I learned many things therein. Dr. Michael Wilking from
Stony Brook University and Prof. Kimihiro Okumura from the University of Tokyo gave lotsof thoughtful comments in meetings. I would like to show my special appreciation to Dr.
Ryosuke Akutsu who is a superposition of greatness and craziness in Kamioka. I asked him
many technical things and enjoyed many physics discussion with him. Fabio Iacob is one of mybestest friends who is trying to apply neutron tagging to the NCQE sample and worked hard
together on the RCNP beam tests. We spent many fun moments together and had many fruitful
discussions. His skill of drinking two glasses of cocktail at the same time, double traveling, hasimpressed me a lot.
As the final topic of the Ph.D research, I was dedicated to the SRN analysis. This work
would never been shown in this thesis without helps from many people. Dr. Yasuhiro Nakajima
of ICRR has been a very nice advisor. His careful comments and advices in meetings and daily
conversations showed me a right path. I would really like to thank Dr. Yuuki Nakano from
Kobe University for his kind help about the SK analysis. I feel sorry about always asking him
when I find unknowns, but he always answers kindly and very quickly. Dr. Sonia El Hedriof Laboratoire Leprince-Ringuet has been working together about the SRN analysis. I would
never forget hardworking weeks full of chats and meetings with her before the collaboration
meeting. Dr. Hiroshi Ito of ICRR is another guy who spent tough weeks on the analysis. We
discussed every day in Kamioka, leading to completion of the analysis. Alberto Giampaolo,
a student at Laboratoire Leprince-Ringuet, had been working really hard about the neutron
tagging.
I had many chances to stay in Tokai for the T2K works. Tokai is one of the best places
in Japan with delicious food, friendly people, and amazing onsen. In addition, I spent many
fun moments with staﬀs, postdocs, and students from many universities. I would also like tothank people in Kamioka where I spent about four months for the final analysis in this thesis.
Though Kamioka is a really isolated place, instead relations among people are really strong.
I enjoyed parties in Kenkyu-to and driving to Toyama for nice places with them. I also hada special tie with Okayama University and people there. Thanks to them I spent relaxed andfun moments. I would like to say thank you to all people in the T2K and Super-Kamiokande
collaborations.
I would like to thank my friends in the High Energy Physics group of Kyoto University,
Shun’ichi Akatsuka (ak-san), Yohei Noguchi (Y-nog), Ayami Hiramoto (Ayamin or Hiramotty),
Shunsuke Tanaka (Tanaka-kun), and Yoshie Nakanishi (YOSHIE). They are all very nice friends
and good researchers at the same time. I am very happy that we had many valuable coﬀee
breaks, fun drink parties, and pretty nice Karaoke nights together, and hope to have more. I
also thank all the past and current members of the lab group and secretarias in the department:
Kiseki-san, Shinohara-san, Kamiji-san, Kunigo-san, Tashiro-san, Nakagiri-san, Ko-san, Keigosan, Sanjana-san, Kubo-san, Hayashino-san, Uno-kun, Benjamin, Kawasaki-san, Ishiyamasan, Minamino-san, Hirota-san, Son-san, Nikhul, Nanjo-san, Ishino-san, Naito-san, Hirakisan, Fan-san, Monden-san, Yanagita-san, Yamamoto-san, Maeda-san, Suzuki-san, Tajima-san,Sumida-san, Hayashi-san, Skiguchi-san, Sasaki-san, Tanizawa-san, Nishikubo-san, Hiraokasan, Hirano-san, Okazaki-san, Adachi-san, Obara-san, Honda-san, Ajimi, Suzuki-san, Seki-san,

6
Ban-san, Okazaki-kun, Yoshida-kun, chan-Mori, KZ Nakamura-kun, Komine-kun, Yasutomekun, Kuniyoshi-kun, Abe-kun, Ikemitsu-kun, Odagawa-jokyo, Kuribayashi-kun, Tajima-kun,
Hatano-kun, Mino-san-black, Otsuka-kun, Kobayashi-kun, Sueno-kun, Sugashima-kun, Tanikun, Tsujikawa-kun, Fu-kun, Yohan, and Wan-kun. It was a great pleasure that I was a memberof this lab.
The works in this thesis have been achieved by supports from JSPS Young Scientist Fellowship (17J06141: “Search for supernova relic neutrinos by improving neutrino neutral current
cross section measurement”).
In the end, I would like to express my deepest appreciation to my family: Hiroshi Ashida(Dad), Chikako Ashida (Mom), and Mio Ashida (sister). They all support me patiently forvery long time. I learned from my Dad the pleasure of thinking, which is the most important
thing for research, when we tackled mathematical problems together in my childhood. I am soproud of my family. Thank you very much !!!!!

Contents
I

Introduction

1

1 Introduction
1.1 Supernova Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Supernova Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Galactic Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Insights into Fundamental Physics . . . . . . . . . . . . . . . . . . . . . .
1.1.4 Relation to Other Astronomical Objects . . . . . . . . . . . . . . . . . .
1.2 Neutrinos from Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . .
1.2.1 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Core-Collapse Supernovae and Neutrino Emission . . . . . . . . . . . . .
1.2.3 Observation of Neutrinos from SN1987A . . . . . . . . . . . . . . . . . .
1.3 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Neutrino Oscillation Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Galaxy Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Contributions from Failed Supernovae . . . . . . . . . . . . . . . . . . .
1.3.4 Shock Revival Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.5 SRN Flux Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Status of SRN Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Neutrino-Oxygen NCQE Interactions . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Neutrino-Nucleus Interactions . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2 NCQE Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.3 Previous NCQE Measurement in T2K . . . . . . . . . . . . . . . . . . .
1.6 Outline of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4
5
5
6
6
6
8
11
11
13
14
14
15
15
16
18
18
19
22
22

II Measurement of Neutrino- and Antineutrino-Oxygen Neutral25
Current Quasielastic-like Interactions
2 Measurement Overview
2.1 Measurement Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Neutral-Current Quasielastic Interactions . . . . . . . . . . . . . . . . . . . . . .
2.3 Signal Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27
27
27
29

3 T2K Experiment
3.1 Overview of T2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 J-PARC Accelerator and Neutrino Beamline . . . . . . . . . . . . . . . . . . . .
3.3 Near and Far Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Beam Monitoring with MUMON . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30
30
30
33
36
40

i

CONTENTS

ii

4 Super-Kamiokande
4.1 Overview of Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Detector Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Water Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Helmholtz Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Water and Air Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Data Acquisition System in SK-IV . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Front-End Electronics: QBEE . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Low Energy Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Vertex and Direction Reconstructions . . . . . . . . . . . . . . . . . . . .
4.6.2 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Cherenkov Angle Reconstruction . . . . . . . . . . . . . . . . . . . . . .
4.7 Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.2 Water Transparency Measurement . . . . . . . . . . . . . . . . . . . . . .
4.7.3 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41
41
42
43
43
43
45
46
46
46
48
49
50
50
52
53
55
55
55
56

5 Event Simulation
5.1 Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Nuclear De-excitation γ-rays and Detector Response . . . . . . . . . . . . . . . .
5.4 Neutrino Oscillation Eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58
58
59
60
62

6 Event Selection
65
6.1 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Selected Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7 Uncertainty Estimates
7.1 Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Primary-γ Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Secondary-γ Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 Oscillation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Summary of Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . .

79
79
81
82
84
86
86
88

8 Cross Section Results
8.1 Cross Section Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Flux-averaged NCQE-like Cross Sections . . . . . . . . . . . . . . . . . . . . . .
8.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 NC 2p2h Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.2 Comparison with Theoretical Models . . . . . . . . . . . . . . . . . . . .
8.3.3 Impact on Supernova Relic Neutrino Searches . . . . . . . . . . . . . . .
8.4 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89
89
93
94
94
94
96
99

CONTENTS

III

Studies towards Improvements of γ-ray Emission Model

iii

101

9 RCNP-E487 Experiment103
9.1 Experimental Motivation and Overview . . . . . . . . . . . . . . . . . . . . . . . 103
9.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.3 Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.4 Neutron Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
9.4.1 PSD and TOF Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
9.4.2 Detection Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9.4.3 Neutron Flux Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9.4.4 Flux Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.4.5 Neutron Beam Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
9.4.6 TOF Measurements in the Lanthanum-Bromide Scintillator . . . . . . . 113
9.5 De-excitation γ-rays from Neutron-Oxygen Reactions . . . . . . . . . . . . . . . 114
9.6 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.7 Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.7.1 Signal Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.7.2 Continuous Background Template . . . . . . . . . . . . . . . . . . . . . . 122
9.7.3 Fitting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.7.4 Cross Section Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.8 Summary and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

IV

Search for Supernova Relic Neutrinos

127

10 Signal and Background129
10.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
10.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
10.2.1 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
10.2.2 Muon Spallation and Lithium-9 . . . . . . . . . . . . . . . . . . . . . . . 130
10.2.3 Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.2.4 Accidental Background Events . . . . . . . . . . . . . . . . . . . . . . . . 134
10.3 Energy Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
11 Data Reduction
135
11.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
11.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
11.3 Second Reduction: Spallation Cut . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11.4 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
11.5 Fourth Reduction: Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . . 148
11.6 Reduction Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
12 Background Estimation
152
12.1 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
12.1.1 NCQE-like Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
12.1.2 CCQE-like Interaction and Pion Production . . . . . . . . . . . . . . . . 157
12.2 Lithium-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
12.3 Reactor Neutrino Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
12.4 Accidental Fake Coincidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

CONTENTS

iv

13 Results161
13.1 Selected Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
13.2 Model-independent ν̄e Flux Upper Limit . . . . . . . . . . . . . . . . . . . . . . 161
13.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
13.3.1 Comparison with Theoretical Predictions . . . . . . . . . . . . . . . . . . 164
13.3.2 Benefits of the T2K NCQE-like Results . . . . . . . . . . . . . . . . . . . 164
13.3.3 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

V

Summary169

14 Conclusion

171

Appendices

174

A Beam Studies with MUMON
175
A.1 Correlation between Proton and Muon Beams . . . . . . . . . . . . . . . . . . . 175
A.2 Correlation between Horn Current and Muon Beam . . . . . . . . . . . . . . . . 175
B Electron-Multiplier Tubes for MUMON
177
B.1 Concerns for the Current MUMON Detectors . . . . . . . . . . . . . . . . . . . 177
B.2 Electron-Multiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
B.3 First Prototype Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
B.4 Further Tests and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.4.1 New Divider Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.4.2 Test of PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.4.3 EMTs without Alkali/Sb . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
B.4.4 Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
C Supplements for the NCQE-like Analysis
197
C.1 Low Energy Background Cut Criteria . . . . . . . . . . . . . . . . . . . . . . . . 197
C.2 Study of Post-activity Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
C.3 Distributions at Each Selection Stage . . . . . . . . . . . . . . . . . . . . . . . . 198
C.4 Primary- and Secondary-γ Distributions . . . . . . . . . . . . . . . . . . . . . . 211
C.5 Properties of Nucleons in the NCQE Interaction . . . . . . . . . . . . . . . . . . 212
D Distributions for the Spallation Cut

216

E Future SRN Search Sensitivities

236

Bibliography236

List of Figures
1.1
1.2

An image of the Crab Nebula taken by NASA’s Hubble Space Telescope. . . . . 3Classification of supernovae based on their spectral properties and explosion
mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Schematic illustration of the explosion mechanism of core-collapse supernovae
assuming a neutrino-heating mechanism. Descriptions of each part with numbersin the parentheses are given in the text. . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Time evolution of the neutrino luminosity (top) and average energy (bottom) for
each neutrino flavor in a numerical simulation. Note that νx = 14 (νµ + ν̄µ + ντ + ν̄τ ). 11
1.5 Distribution of the energy and time of the neutrinos from SN1987A, observed in
the Kamiokande-II (12 events) and IMB (8 events) experiments. . . . . . . . . . 12
1.6 The CSFRD as a function of redshift (left), and the scaled IMF (right) for for
diﬀerent models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 SRN ν̄e fluxes from various theoretical models. . . . . . . . . . . . . . . . . . . . 16
1.8 Upper limits on the ν̄e obtained from searches in the Super-Kamiokande and the
KamLAND experiments. The black solid lines correspond to the maximum andminimum predictions in Nakazato model. . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Feynman diagrams for neutrino-nucleus interactions: (a) CC quasielastic scattering, (b) CC resonant single pion production, (c) CC coherent pion production,and (d) CC deep inelastic scattering. . . . . . . . . . . . . . . . . . . . . . . . . 20
1.10 Schematic drawings for the ν̄e ’s inverse beta decay by SRNs (top) and the NCQE
interaction by atmospheric neutrinos (bottom) in a pure or Gd-doped water
Cherenkov detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.11 Flux-averaged neutrino-oxygen NCQE cross section measured in T2K with a
3.01 × 1020 protons-on-target data. The black points correspond to the measured
value, with vertical and horizontal bars being the measured uncertainty andthe width of the neutrino flux, respectively. The red line corresponds to thetheoretical prediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1
3.2
3.3
3.4
3.5
3.6

Schematic view of the T2K experiment. . . . . . . . . . . . . . . . . . . . . . . . 30
Aerial view of the J-PARC. Note that “50 GeV” for MR is the original design
value, but the actual operation is with a 30 GeV setting. . . . . . . . . . . . . . 31
Schematic view of the J-PARC proton beam structure. . . . . . . . . . . . . . . 31
Schematic view of the T2K neutrino beamline. . . . . . . . . . . . . . . . . . . . 32
Experimental components after the primary neutrino beamline, including thesecondary neutrino beamline, the near detectors, and the far detector. . . . . . . 33
The νµ → νµ and νµ → νe probabilities as a function of neutrino energy (toptwo), and the neutrino flux in diﬀerent oﬀ-axis (OA) angle configurations (bottom). 34v

LIST OF FIGURES
Schematic illustration of INGRID. The whole structure is shown in the left panel
and each module is shown in the right panel. Each module consists of the irontarget plates and the tracking scintillator planes and is surrounded by the vetoscintillator planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 A neutrino beam profile measured by INGRID. The left and right panels correspond to the horizontal and vertical directions, respectively. . . . . . . . . . . .
3.9 Schematic illustration of ND280. The neutrino beam is incident from the left
side in the figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Schematic illustration of the T2K muon monitor. . . . . . . . . . . . . . . . . .
3.11 History of the accumulated POT and the J-PARC beam power over the T2K
Run 1−9 operation period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 INGRID and MUMON beam measurements of the event rate and beam directions over the T2K Run 1−9 operation period. . . . . . . . . . . . . . . . . . . .
3.13 Muon beam center in horizontal (top) and vertical (bottom) directions measured
by MUMON Si and IC in each J-PARC MR run. T2K was operated with nohorn current application in MR Run 41, showing the large error. . . . . . . . . .
3.14 Muon beam width in horizontal (top) and vertical (bottom) directions measured
by MUMON Si and IC in each J-PARC MR run. T2K was operated with nohorn current application in MR Run 41, showing the narrow beam. The beamwidth in RHC is smaller than that in FHC, which is attributed to diﬀerence inthe momentum of the parent hadrons. Since the parent hadrons are produced
by protons, the number of particles are likely to be larger when the negative
hadrons, which are the parents of antineutrinos, are made. Therefore, the momentum of each particle, including the negative hadron, is likely to be smaller
and accordingly those hadrons are easier to focus in RHC, contributing to thenarrower beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

3.7

4.1
4.2

Schematic illustration of the Super-Kamiokande detector. . . . . . . . . . . . . .
Cosmic-ray muon flux as a function of depth. The unit 103 hg/cm2 is equivalent
to km.w.e. The depth of SK is 2700 m.w.e. . . . . . . . . . . . . . . . . . . . . .
4.3 An example of the Cherenkov ring pattern in SK. Each pixel corresponds to the
PMT and the color scale denotes the detected charge amount. . . . . . . . . . .
4.4 Schematic illustration of the PMT support structure in SK. . . . . . . . . . . . .
4.5 Schematic cross sectional view of the SK 20 inch PMT (Hamamatsu R3600). . .
4.6 Quantum eﬃciency of the SK 20 inch PMT as a function of wavelength. . . . . .
4.7 Distributions of single photoelectron pulse height (left) and relative transit timewith 410 nm wavelength light at the single p.e. level (right) for the SK 20 inch
PMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Schematic diagram of the water circulation system in SK-IV (left) and the watertemperature as a function of the ID vertical position (right). . . . . . . . . . . .
4.9 Block diagram of the QTC and its surrounding parts. . . . . . . . . . . . . . . .
4.10 Block diagram of one QTC channel. . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 Timing chart for the QTC operation. . . . . . . . . . . . . . . . . . . . . . . . .
4.12 Probability density function for the timing residual (t − ttof − t0 ) obtained by the
LINAC calibration. Peaks at around 40 ns and 110 ns are the PMT after-pulses.
4.13 Vertex resolution as a function of electron energy in SK-IV. . . . . . . . . . . . .
4.14 Schematic illustration for definitions of dwall and eﬀwall. . . . . . . . . . . . . .

34
35
35
36
37
37

38

39
41
41
43
44
44
45

45
46
47
47
48
50
51
52

LIST OF FIGURES
4.15 Relation between the number of eﬀective hits (Neﬀ ) and the reconstructed visibleenergy (Erec ) for generated electrons in MC and the linear fitting result (top)and the ratio of the MC and the fit values (bottom). . . . . . . . . . . . . . . .
4.16 Distributions of opening angles by all three-hit combinations of the hit PMTs forthe e-like (left), µ-like (middle), and multiple-γ-like (right) event, respectively.
The blue lines and numbers indicate the most frequent values which are taken
as the reconstructed Cherenkov angles. . . . . . . . . . . . . . . . . . . . . . . .
4.17 Schematic illustration for the timing calibration (left) and the 2D distributionof the charge and timing (right). The QBin in the lower horizontal axis of theright panel is defined as: QBin = 5Q (0 < Q < 10) or QBin = 50 · log10 Q (10 <Q < 3981). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.18 Distributions of reconstructed energies for the diﬀerent energy settings in the
LINAC 2010 data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.19 The Neﬀ distribution as a function of time in the SK-IV period measured using
the decay electron sample. The blue and red dashed lines indicate the averageand ±0.5% deviated values, respectively. Here the eﬀect of the PMT gain shift
is corrected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1
5.2
5.3
5.4
6.1

6.2
6.3

6.4

6.5

6.6

6.7
6.8

T2K neutrino flux predictions at SK in the FHC (left) and RHC (right) modes.
Here the neutrino oscillations are not considered. . . . . . . . . . . . . . . . . .
NCQE cross sections by NEUT for neutrinos (left) and antineutrinos (right) on
all neutrons, all protons, and all nucleons inside oxygen. . . . . . . . . . . . . . .
Schematic drawing of the primary and the secondary γ-rays in the NCQE interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic drawing for the correction of oscillation eﬀects. . . . . . . . . . . . . .
Optimized cut values for dwall (top), eﬀwall (middle), and ovaQ (bottom), asa function of reconstructed energy for Run 8. Vertical bars represent the bin
width in the parameter scans. Red lines represent linear fits to each distribution
and used as cut criteria. The fitting regions for dwall and eﬀwall are explainedin the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distributions of ovaQ in FHC (left) and RHC (right) after the energy cut, thegood spill cut, the on-timing cut, the FV cut, the dwall cut, and the eﬀwall cut.
Two-dimensional Erec −θC distributions of each interaction mode and the beamunrelated events before the CC interaction cut together with the optimized cut
function (θC = 1.68 × Erec + 17.73) in FHC. . . . . . . . . . . . . . . . . . . . .
Two-dimensional Erec −θC distributions of each interaction mode and the beamunrelated events before the CC interaction cut together with the optimized cut
function (θC = 1.57 × Erec + 17.73) in RHC. . . . . . . . . . . . . . . . . . . . .
The Erec distribution of the MC beam neutrino and the beam-unrelated events
before the FV cut and after all cuts for the FHC (left) and RHC (right) modes.
The beam-unrelated backgrounds are reduced dramatically after the cuts bothin FHC and RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertex distributions for the selected events in FHC: X−Y (left) and R2 −Z (right).
Area filled with transparent gray and blue represent the ID and FV regions,
respectively. The red arrow in the left panel represents the beam direction. . . .
Distributions of the event timing (left) and its residual time from the spill timing(right) for the selected events in FHC. . . . . . . . . . . . . . . . . . . . . . . .
Observed event rate in each FHC run. . . . . . . . . . . . . . . . . . . . . . . .

vii

54

54

56
56

57
58
60
60
63

68
69

70

71

73

74
74
74

LIST OF FIGURES
Vertex distributions for the selected events in RHC: X−Y (left) and R2 −Z(right). Area filled with transparent gray and blue represent the ID and FV
regions, respectively. The red arrow in the left panel represents the beam direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Distributions of the event timing (left) and its residual time from the spill timing(right) for the selected events in RHC. . . . . . . . . . . . . . . . . . . . . . . .
6.11 Observed event rate in each RHC run. . . . . . . . . . . . . . . . . . . . . . . .
6.12 Distributions of Erec (top) and θC (middle), and their 2D scatter plot (bottom)
in the FHC sample. In the 2D plot, magenta dots represent the observed events.
6.13 Distributions of Erec (top) and θC (middle), and their 2D scatter plot (bottom)
in the RHC sample. In the 2D plot, magenta dots represent the observed events.
6.14 Kinetic energies of neutrons from the neutrino and antineutrino NCQE interactions in RHC obtained by MC. . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.15 The 2D distributions of the energy of neutrons from the ν-NCQE interaction in
FHC (left) and the ν̄-NCQE interaction in RHC (right) and θC obtained by MC.

viii

6.9

7.1

7.2
7.3

7.4
7.5

7.6

8.1

8.2

8.3

Total and each source uncertainties of the flux prediction at SK as a function ofneutrino energy for diﬀerent neutrino flavors in both FHC and RHC modes. The
solid line indicates the current uncertainty, while the dashed line corresponds tothe uncertainty in the tuning only with the thin target data. . . . . . . . . . . .
The Q2 distributions of ν-NCQE in FHC (left) and ν̄-NCQE in RHC (right) at
each selection stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(See only the lower part) Total and partial cross sections leading to the groundstate (15 O and 15 N) and the excited state (15 O∗ and 15 N∗ ) after the 16 O(ν, ν ′ )interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutrino- and antineutrino-oxygen NCQE interaction cross sections and thosewith γ-ray emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probabilities of an event being reconstructed in the current analysis window of
3.49−29.49 MeV as a function of the number of Cherenkov photons (NC ) in FHC
and RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK PMT relative gain with respect to April 2009 as a function of time. Diﬀerent
colors correspond to the PMT types with diﬀerent production periods. Clear
gain shift is observed over the operation period in every PMT type. . . . . . . .

75
75
75
76
77
78
78

80
81

82
83

84

87

Results of the pseudo experiments on the scale factors when the numbers of
the observed events are varied based on the statistical uncertainties: fν-NCQE =0.80 ± 0.08 and fν̄-NCQE = 1.11 ± 0.18. . . . . . . . . . . . . . . . . . . . . . . . 91
Results of the pseudo experiments on the scale factors when the numbers of thepredicted events are varied based on the systematic uncertainties: fν-NCQE =+0.29
0.80+0.24−0.18 and fν̄-NCQE = 1.11−0.22 . The dominant uncertainty source is thesecondary-γ emission model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
The measured neutrino- (left) and antineutrino- (right) oxygen NCQE-like crosssections in comparison with the NCQE cross sections predicted by NEUT. The
points are placed at the flux mean values, 0.82 GeV for neutrinos and 0.68 GeV
for antineutrinos, respectively. The vertical bars represent the statistical errors(shorter) and the quadratic sums of the statistical and systematic errors (longer).
The horizontal bars represent the upper and lower 1σ ranges of the fluxes. The
T2K fluxes for each neutrino beam mode are also shown together in an arbitrarynormalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

LIST OF FIGURES
8.4
8.5

8.6

8.7

8.8
8.9
9.1

ix

Neutrino (left) and antineutrino (right) NCQE cross sections on all nucleons inoxygen as a function of neutrino energy for six theoretical predictions. . . . . . . 95
Comparison of the flux-averaged NCQE-like cross sections by T2K and the fluxaveraged NCQE cross sections by various models for neutrinos (left) and antineutrinos (right). Solid line and transparent area represent the measured meanvalues and their 1σ uncertainties including both statistical and systematic ones,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Two-dimensional Erec −θC distributions for FHC (left) and RHC (right) respectively before the CC interaction cut and after all of the preceding cuts describedin Chapter 6. Magenta dots correspond to the observed data. . . . . . . . . . . . 97
The Erec distributions for θC ∈ [38, 50] degrees and θC ∈ [78, 90] degrees (topfour) and the θC distributions for Erec ∈ [3.49, 7.49] MeV and Erec ∈ [7.49, 29.49] MeV(bottom four). All are before the CC interaction cut and after all of the preceding
cuts described in Chapter 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Neutron capture eﬃciency as a function of Gd doping rate in SK. . . . . . . . . 99
Schematic illustration of the Hyper-Kamiokande detector. . . . . . . . . . . . . . 100

Schematic drawing of the RCNP facility and its neutron beamline. The dottedmagenta box represents a magnified experimental setup. . . . . . . . . . . . . . 104
9.2 Photograph of the setup for the γ-ray and fast neutron background measurementswith a water-filled target. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.3 Photograph of the setup for the neutron flux measurement. . . . . . . . . . . . . 105
9.4 The LaBr3 (Ce) energy spectra in QDC channel with various radioactive sources:
0.662 MeV from 137 Cs, 1.17 and 1.33 MeV from 60 Co, 1.46 MeV from 40 K,
2.22 MeV from 2 H, 2.61 MeV from 208 Tl, 4.44 MeV from 12 C, and 7.65 MeV
from 57 Fe. The S.E. and D.E. represent the single and double escape peaks ofthe corresponding photoelectric-absorption peak, respectively. Diﬀerent colors
correspond to diﬀerent measurements. . . . . . . . . . . . . . . . . . . . . . . . . 106
9.5 PSD parameter as a function of Qtotal value in QDC channel. The blue line
represents the neutron selection criterion. . . . . . . . . . . . . . . . . . . . . . . 108
9.6 Deposited energy in QDC channel in the BC-501A detector for all (black),neutron-like (blue), and γ-like (red) events. . . . . . . . . . . . . . . . . . . . . . 108
9.7 TOF distributions of all (black), neutron-like (blue), and γ-like (red) events
classified by PSD. The sharp peak around 3350 ch is due to the flash γ-rays. . . 109
9.8 Kinetic energy distribution of the neutron-like events reconstructed from the
TOF distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.9 Neutron detection eﬃciencies of the BC-501A calculated with SCINFUL-QMD.
The attenuation factor of 0.008 cm−1 from the previous study and the PMT light
output function from Satoh et al. are used. The bump around 20 MeV is due toan open of new reaction channels by carbon. . . . . . . . . . . . . . . . . . . . . 110
9.10 Neutron flux normalized by the detector covering solid angle and the incident
protons. The red bars indicate the peak region (72−82 MeV) used for the crosssection analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.11 Neutron beam profile measured by the BC-501A detector. The result is for the
peak region (72−82 MeV). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

LIST OF FIGURESx

9.12 Distributions of TOF (left) and the inferred kinetic energy (right) in the LaBr3 (Ce)detector. In the left panel, the on-timing (corresponding to 72−82 MeV in the
kinetic energy) and oﬀ-timing regions are indicated by the solid and dashed bars,
respectively. In the right panel, the red bars indicate the neutron energy regionused for the cross section analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.13 Energy spectra of the HPGe detector with and without water. The spectra in
the bottom panel focus on the region between 3 and 8 MeV. . . . . . . . . . . . 114
9.14 Energy spectra of the LaBr3 (Ce) scintillator with and without water without the
TOF cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.15 Energy spectra of the LaBr3 (Ce) scintillator with and without water with the
TOF cut selecting the on-timing and oﬀ-timing regions defined in Figure 9.12. . 115
9.16 Distribution of the ratio of the integrated tail part to the total in the CsI(Tl)waveform as a function of energy. The populations (a), (b), and (c) correspondto the γ-like, neutron-like, and pile-up events, respectively. . . . . . . . . . . . . 118
9.17 Schematic illustration of the continuous background caused by γ-rays from scattered fast neutron reactions with the surrounding materials for a water-filled
target (left) and an empty target (right). . . . . . . . . . . . . . . . . . . . . . . 119
9.18 Comparison of the spectra for the neutron energy region 72−77 MeV and 77−82 MeV(left) and comparison between the shape diﬀerence of these two and the nonwater spectrum for the 72−82 MeV region (right). . . . . . . . . . . . . . . . . . 119
9.19 Energy resolution as a function of the deposited energy in the LaBr3 (Ce). The
black points are data and the red line is the fitting√ to those data points. The
resolution curve function is: σE /E = p0 + p1/ E + p2/E (E [MeV]), wherep0 = (−1.89±0.81)×10−3 , p1 = (1.68±0.17)×10−2 , and p2 = (−2.47±0.91)×10−3 .120
9.20 Signal templates for each γ-ray peak in the LaBr3 (Ce) simulated by GEANT4.
The spectra smeared with the nominal and ±1σ resolutions by the resolution
curve are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9.21 An exponential fitting to the on-timing non-water spectrum for the continuous
background template. The region 3−6.5 MeV is removed in the fitting to avoid
the signal components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.22 Energy spectrum of the LaBr3 (Ce) scintillator after the TOF cut and subtractions of the non-water spectrum and the oﬀ-peak spectrum in a linear (top)and a log (bottom) vertical scale. Diﬀerent color spectra correspond to signal
and background: 7.12 MeV (gray), 6.92 MeV (brown), 6.32 MeV (magenta),
6.13 MeV (orange), 5.27 MeV (cyan), 4.44 MeV (green), 3.68 MeV (yellow),
2.30 MeV (violet), and continuous background (blue). . . . . . . . . . . . . . . . 124
10.1 Eﬀective neutrino interaction cross sections as a function of neutrino energy. . . 129
10.2 IBD cross section on a free proton as a function of ν̄e energy as calculated byStrumia and Vissani. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
10.3 Atmospheric neutrino flux at Kamioka from the HKKM2011 calculation: thevertical axis shown in linear (left) and log (right). Here the neutrino oscillation
is not taken into account. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
10.4 Decay scheme of 9 Li (left) and β spectra from its decay with a neutron emission(right). In the right panel, black one represents the total spectrum and theother color ones correspond to decay modes from diﬀerent excited states, andKn represents the emitted neutron kinetic energy. . . . . . . . . . . . . . . . . . 133
10.5 Reactor neutrino flux at SK for the SK-IV operation period. . . . . . . . . . . . 133

LIST OF FIGURES

xi

11.1 The Erec −gvtx distributions for the ν̄e signal MC (left) and data (right). Dashedgreen lines indicate the cut criteria, and events with gvtx > 0.5 are selected. . . . 136
11.2 The Erec −ovaQ distributions for the ν̄e signal MC (left) and data (right). Dashedgreen lines indicate the cut criteria, and events with ovaQ > 0.25 are selected. . 137
11.3 Two sample regions for the spallation cut. . . . . . . . . . . . . . . . . . . . . . 137
11.4 Muon types categorized by the muon fitter and their goodness. Variable types
which are used for the spallation likelihood calculation are shown in each region.
In the analysis, the corner-clipping muons are considered not to cause spallation. 138
11.5 Schematic of the variables, Ltran and Llong , for the spallation cut. The cylindricalshape represents the SK detector. . . . . . . . . . . . . . . . . . . . . . . . . . . 139
11.6 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) for the single through-going muons and 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.
The smoothing over the bins is performed for some distributions to mitigate thestatistical fluctuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
11.7 The spallation and random PDFs of dt (top left), Ltran (top right), Llong (middle
left), Qpeak (middle right), and Qµ (bottom) for the single through-going muonsand 7.49 < Erec < 9.49 MeV. For variables except for dt, the distributions arefor 0 < |dt| < 0.05 sec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
11.8 Distributions of the spallation likelihood for each muon type in the 7.49−9.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the rightside of the lines are removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
11.9 Schematic drawings of the definition of θsun and the cos θsun distribution. . . . . 144
11.10The eﬀwall distributions for the ν̄e signal MC (left) and data (right) after the
spallation cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
11.11Number of decay electrons after the pre-activity cut in the atmospheric neutrino MC sample from the 7.49 < Erec < 29.49 MeV region. Diﬀerent colors
correspond to the neutrino interaction types. . . . . . . . . . . . . . . . . . . . . 145
11.12The pilike distributions for the ν̄e signal (left) and atmospheric neutrino (right)
MC samples after the post-activity cut. Both samples are from the 7.49 < Erec <29.49 MeV region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
11.13The Q50 /N50 distributions for the ν̄e signal (left) and atmospheric neutrino(right) MC samples after the pilike cut. Both samples are from the 7.49 <Erec < 29.49 MeV region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
11.14The Cherenkov angle distributions for the ν̄e signal (left) and atmospheric neutrino (right) MC samples after the Q50 /N50 cut. Both samples are from the
7.49 < Erec < 29.49 MeV region. . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
11.15Number of hit PMTs in a 10 ns sliding time window for the neutron signal andbackground in the region [+2, +535] µs. The blue line and arrow indicate thepre-selection criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
11.16The signal eﬃciency and the mis-tag probability for the diﬀerent ten operation
periods. Diﬀerent colors correspond to the results from the diﬀerent data taking
periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
11.17Photograph of the Am/Be source embedded in the BGO scintillator. . . . . . . . 150
12.1 Background energy spectrum after all the reductions. Diﬀerent colors correspondto each background source. Shaded bars represent the total systematic error of
the background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

LIST OF FIGURES

xii

12.2 The Erec distributions for the θC region between 38 and 50 degrees obtained
from the T2K FHC (left) and RHC (right) samples. These are before the CC
interaction cut described in Chapter 6. . . . . . . . . . . . . . . . . . . . . . . . 154
12.3 Average of the number of tagged neutrons in the neutrino event as a function ofreconstructed Q2 in the T2K Run 1−9 FHC (left) and RHC (right) samples. . . 155
12.4 Number of tagged neutrons in the atmospheric neutrino MC sample for eachQ2 region. Top and bottom four correspond to neutrinos and antineutrinos,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
12.5 The Erec distributions in the 29.49−79.49 MeV region for data, the atmospheric
neutrino MC, and the scaled MC with the neutron tagging condition in the
19.49−29.49 region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
12.6 Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 7.49−9.49 MeV region. Dashed green lines represent the cut criteria, theright side of which is removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
13.1 Energy spectra of the observation and background prediction after all the reductions. Diﬀerent colors correspond to each background source. Shaded bars
represent the total systematic error of the background. . . . . . . . . . . . . . . 161
13.2 Result of the pseudo experiments on the number of signal events with statisticaland systematic variances for the 7.49−9.49 MeV region. . . . . . . . . . . . . . . 162
13.3 Model-independent ν̄e flux upper limit at 90% C.L. with a 2970.1-day data set
from SK-IV. The sensitivity in the current work is also shown. For comparisons,the upper limits by the KamLAND 2343 days, the SK-I/II/III spectrum analysis
with 2853 days, and the SK-IV neutron tagging analysis with 960 days and 2778
days are shown together. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
13.4 The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period witha 0.1% Gd doping for the neutrino energy region 13.29 < Eν < 21.29 MeV (left)
and 21.29 < Eν < 31.29 MeV (right). The predictions from the models explainedin Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
13.5 The 3σ sensitivity for the ν̄e flux as a function of Hyper-Kamiokande operation
period for the neutrino energy region 13.29 < Eν < 21.29 MeV (left) and 21.29 <Eν < 31.29 MeV (right). The predictions from the models explained in Chapter 1
are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
13.6 The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period witha 0.1% Gd doping for the neutrino energy region 13.29 < Eν < 21.29 MeV(left) and 21.29 < Eν < 31.29 MeV (right) for diﬀerent NCQE-like backgroundconditions. Note that assumptions on the background are diﬀerent from those in
Figure 13.4 as explained in the text. The predictions from the models explainedin Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
A.1 Horn scan points in FHC (left) and RHC (right) in the 2D HPS1−HPS2 plane.
Magenta boxes represent the points used for obtaining the correction functions.
The other points are used for the cross check after the correction. . . . . . . . . 175
A.2 Horn scan results in the FHC mode for the HPS1 (top) and HPS2 (bottom)
scans. The left and right panels give the results from Si and IC, respectively. . . 176
A.3 Horn scan results in the RHC mode for the HPS1 (top) and HPS2 (bottom)
scans. The left and right panels give the results from Si and IC, respectively. . . 176

LIST OF FIGURES

xiii

B.1 Ratio of the average signal yield of Si to that of IC (Ar) over the T2K operation.
Si sensors are replaced twice so far and the second replacement was conducted
for only half of 49 sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
B.2 Ratio of the average yield of odd-numbered Si sensors to that of even-numbered
Si sensors in certain periods in T2K Run 8. All sensors are the 2nd generation
ones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
B.3 Ratio of the average yield of odd-numbered Si sensors to that of even-numbered
Si sensors in certain periods in T2K Run 9. The odd-numbered sensors are the
3rd generation and the even-numbered ones are the 2nd generation. . . . . . . . 179
B.4 IC (Ar) yield for the 8th bunch at several beam intensities under a +250 kAhorn operation (left) and the ratio of the IC (Ar) to the Si center channels foreach bunch at 460 kW and +250 kA horn current (right). . . . . . . . . . . . . . 179
B.5 IC (He) signal waveform at 340 kW and +250 kA horn current, equivalent to
2.5 × 106 /cm2 per 80 ns (left), and IC (Ar) signal waveform at 480 kW and−250 kA horn current, equivalent to 2.3 × 106 /cm2 per 80 ns (right). . . . . . . 180
B.6 Schematic illustration of the signal multiplication in EMTs. . . . . . . . . . . . . 180
B.7 A photograph of EMTC3. The monitor radius is 8 mm. . . . . . . . . . . . . . . 182
B.8 Schematic diagram of the divider circuit of the prototype EMT. “K”, “P”, “DY”
and “GND” represent the cathode, anode, dynode, and ground, respectively. The
resistances R1 −R10 are 330 kΩ, and R11 is 160 kΩ. The capacitances are given
in Table B.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
B.9 Installation positions of the prototype EMTs overlaid with the IC sensor positions (left) and a zoom version focusing around the EMTs (right). Green squares
in the left panel indicate the 49 ch of the IC and solid magenta square corresponds
to the center channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
B.10 Examples of the EMTC3 (left) and C4 (right) waveform. Two tail parts (Tail-1
and Tail-2) are shown together in shaded bands. . . . . . . . . . . . . . . . . . . 184
B.11 Relative sizes of Tail-1 (left) and Tail-2 (right) to the 1st bunch signals. The
proton beam power and the horn current setting are 450 kW and +250 kA
respectively, corresponding to a muon flux of 3.2 × 106 /cm2 per 80 ns beam bunch.185
B.12 The normalized signal sizes of EMTC3 (left top), EMTC4 (right top), Si (leftbottom), and IC with Ar gas (right bottom) under the 450 kW beam power andthe +250 kA horn current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.13 Ratio of the muon flux at the EMT position for various proton beam widths tothat at beam width = (4, 4) mm obtained by the simulation. . . . . . . . . . . . 187
B.14 Beam intensity scan results for the Si center channel before (left) and after (right)
the beam width eﬀect correction. Diﬀerent colors represent diﬀerent scans, eachof which is summarized in Table B.4. . . . . . . . . . . . . . . . . . . . . . . . . 187
B.15 Beam intensity scan results for EMTC3 with −500 V (left) and −450 V (right)
applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.16 Beam intensity scan results for EMTC4 with −500 V (left) and −450 V (right)
applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.17 Signal yield of the Si center channel as a function of time. . . . . . . . . . . . . 190
B.18 Signal yield of the IC (Ar) center channel as a function of time. The yield jumps
seen in Period III and IV, marked with magenta circles, are due to calibration
work where the entire IC system is moved. . . . . . . . . . . . . . . . . . . . . . 191

LIST OF FIGURES

xiv

B.19 Signal yield of EMTC3 as a function of time. Two yield jumps are seen andseem to be synchronized with IC calibration work, although the cause is not
fully understood. After a short HV-oﬀ period during Period V, the yield changed.192
B.20 Signal yield of EMTC4 as a function of time. Other than the short periods justafter the HV is turned on, C4 shows stable performance. . . . . . . . . . . . . . 193
B.21 Pictures of the PMT and the divider circuit. . . . . . . . . . . . . . . . . . . . . 194
B.22 Example waveforms of one of the installed PMTs. The condition in the left panel
is 470 kW power, −250 kA horn current and −350 V applied, and that in theright panel is 40 kW, −250 kA, and −500 V. . . . . . . . . . . . . . . . . . . . . 195
B.23 Yield stability of the PMT with (left) and without (right) warming-up. . . . . . 195
C.1 Distributions of the number of decay-e after the candidate event for FHC events:
NC (left) and CC(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
C.2 Distributions of the number of decay-e after the candidate event for RHC events:
NC (left) and CC(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
C.3 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the FV cut in
FHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
C.4 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the dwall cut
in FHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
C.5 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the eﬀwall cut
in FHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
C.6 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the ovaQ cut
in FHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
C.7 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the CC interaction cut in FHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
C.8 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the FV cut in
RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
C.9 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the dwall cut
in RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
C.10 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the eﬀwall cut
in RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
C.11 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the ovaQ cut
in RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
C.12 Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the CC interaction cut in RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
C.13 Distribution of true Eν for each neutrino interaction (left) and the one focusing
on CCQE and CC 2p2h (right) in FHC. . . . . . . . . . . . . . . . . . . . . . . 210
C.14 Distribution of true Eν for each neutrino interaction (left) and the one focusing
on CCQE and CC 2p2h (right) in RHC. . . . . . . . . . . . . . . . . . . . . . . 210
C.15 The Erec distributions for the NCQE events broken down by the γ-ray type in
FHC (left) and RHC (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
C.16 The θC distributions for the NCQE events broken down by the γ-ray type in
FHC (left) and RHC (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
C.17 Nucleon kinetic energy after NCQE in FHC: neutron (left) and proton (right).
Each of them is area normalized. . . . . . . . . . . . . . . . . . . . . . . . . . . 212
C.18 Nucleon kinetic energy after NCQE in RHC: neutron (left) and proton (right).
Each of them is area normalized. . . . . . . . . . . . . . . . . . . . . . . . . . . 212

LIST OF FIGURES

xv

C.19 The 2D distributions of neutron energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in FHC. . . . . . . . . . . . . . . . 213
C.20 The 2D distributions of proton energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in FHC. . . . . . . . . . . . . . . . 213
C.21 The 2D distributions of neutron energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in RHC. . . . . . . . . . . . . . . . 214
C.22 The 2D distributions of proton energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in RHC. . . . . . . . . . . . . . . . 214
C.23 The Erec (left) and θC (right) distributions for neutrino-proton and neutrinoneutron NCQE interactions in FHC. The numbers of selected events for protons
and neutrons are 76.4 and 102.2, respectively. . . . . . . . . . . . . . . . . . . . 215
C.24 The Erec (left) and θC (right) distributions for antineutrino-proton and antineutrinoneutron NCQE interactions in RHC. The numbers of selected events for protons
and neutrons are 25.6 and 30.8, respectively. . . . . . . . . . . . . . . . . . . . . 215
D.1 The dt distributions of the missfit or poorly-fit muons for pre and post samples
and diﬀerent energy regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
D.2 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.218
D.3 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0.05 < |dt| < 0.5 sec.219
D.4 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0.5 < |dt| < 30 sec.220
D.5 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the stopping muons for 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec. . . . . . . . 221
D.6 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.222
D.7 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0.05 < |dt| < 0.5 sec.223
D.8 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0.5 < |dt| < 30 sec.224
D.9 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle right), and Qµ (bottom) of the corner-clipping muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.225
D.10 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 9.49 < Erec <11.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.226
D.11 Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 11.49 < Erec <19.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.227

LIST OF FIGURES

xvi

D.12 PDF distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak(middle right), and Qµ (bottom) of the single through-going muons for 7.49 <Erec < 9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| <0.05 sec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
D.13 PDF distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak(middle right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec <9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.229
D.14 Distributions of the spallation likelihood for each muon type in the 7.49−9.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the rightside of the lines are removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
D.15 Distributions of the spallation likelihood for each muon type in the 9.49−11.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the rightside of the lines are removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
D.16 Distributions of the spallation likelihood for each muon type in the 11.49−19.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the rightside of the lines are removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
D.17 Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 7.49−9.49 MeV region. Dashed green lines represent the cut criteria, theright side of which is removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
D.18 Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 9.49−11.49 MeV region. Dashed green lines represent the cut criteria, theright side of which is removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
D.19 Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 11.49−19.49 MeV region. Dashed green lines represent the cut criteria,
the right side of which is removed. . . . . . . . . . . . . . . . . . . . . . . . . . . 235
E.1 The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period witha 0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (topleft), 11.29 < Eν < 13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom
left), and 21.29 < Eν < 31.29 MeV (bottom right). The predictions from themodels explained in Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . 237
E.2 The 3σ sensitivity for the ν̄e flux as a function of Hyper-Kamiokande operation
period for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left), 11.29 <Eν < 13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left), and21.29 < Eν < 31.29 MeV (bottom right). The predictions from the models
explained in Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . . . . . 238
E.3 The 3σ sensitivity for the ν̄e flux as a function of HK-Gd operation period witha 0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (topleft), 11.29 < Eν < 13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom
left), and 21.29 < Eν < 31.29 MeV (bottom right). The predictions from themodels explained in Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . 239
E.4 The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period with a
0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left),
11.29 < Eν < 13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left),and 21.29 < Eν < 31.29 MeV (bottom right) for diﬀerent NCQE-like backgroundconditions. Note that assumptions on the background are diﬀerent from those in
Figure E.1 as explained in the text. The predictions from the models explainedin Chapter 1 are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

List of Tables
1.1

Best-fit values of the neutrino oscillation parameters from PDG2018. NH andIH represent the normal and inverted neutrino mass hierarchy, respectively. . . .

8

3.1

Summary on the T2K runs with the operation period, the operation mode, andthe accumulated POT for the good spills used in the analysis. . . . . . . . . . . 40

4.1
4.2

Properties of the five SK operation periods. . . . . . . . . . . . . . . . . . . . . 42
Summary of the SK triggers. The numbers in the second column are the numberof hit PMTs within a 200 ns window (N200 ). . . . . . . . . . . . . . . . . . . . . 49

5.1

Neutrino interaction parameter settings in NEUT for the nominal MC production. Errors of each parameter are also shown. Note that the definition of “NC
other” here is diﬀerent from “NC-other” elsewhere in this thesis. . . . . . . . . .
Probabilities of a remaining nucleus belonging to each excited state, (p1/2 )−1 ,(p3/2 )−1 , (s1/2 )−1 , and others, after the neutrino interaction. . . . . . . . . . . .
Excited states and γ-ray emission modes of 16 O proton hole (p3/2 )−1
and neutronp−1hole (p3/2 )n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Excited states and γ-ray emission modes of the proton hole (s1/2 )−1
in 16 O. The
pg.s. represents the ground state. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutrino oscillation parameters and their errors used in this analysis. These aretaken from the recent T2K result. . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2
5.3
5.4
5.5
6.1
6.2
6.3

6.4

7.1
7.2
7.3

Type of the NCQE event selections and their application targets. . . . . . . . .
Scan regions and intervals of each parameter. . . . . . . . . . . . . . . . . . . . .
Number of events after each cut in data and MC in FHC. Before the timing
cut, only the beam quality and detector condition cuts are applied. In thecolumn with “Total”, the sum of the ν-NCQE, ν̄-NCQE, NC-other, CC, andbeam-unrelated events is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of events after each cut in data and MC in RHC. Before the timing
cut, only the beam quality and detector condition cuts are applied. In thecolumn with “Total”, the sum of the ν-NCQE, ν̄-NCQE, NC-other, CC, andbeam-unrelated events is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . .

59
61
61
62
64
65
67

72

72

Uncertainties on the observed event rate in percent for each sample component
due to the systematic errors on neutrino flux prediction. . . . . . . . . . . . . . 79
Uncertainties on the observed event rate in percent for each sample component
due to the systematic errors on neutrino interaction model. . . . . . . . . . . . . 81
Uncertainties on the observed event rate in percent for each sample component
due to the systematic errors on primary-γ emission model. . . . . . . . . . . . . 83

xvii

LIST OF TABLES
7.4
7.5

8.1
8.2
9.1
9.2
9.3
9.4

xviii

Uncertainties on the observed event rate in percent for each sample component
due to the systematic errors on secondary-γ emission model. . . . . . . . . . . . 85
Summary of systematic uncertainties on the observed event rate in percent for
the FHC and RHC sample components. The fraction of each component, listed
as “Event fraction”, is shown together in percent. For the beam-unrelated events,
the total uncertainty entry represents the statistical uncertainty. . . . . . . . . . 88
Covariance of the neutrino and antineutrino cross sections for the statistical(systematic) error case. The unit of numbers is (10−38 cm2 /oxygen)2 . . . . . . . 93
Numbers of observed and predicted events for each region defined in the text. . . 97
Statistical and systematic uncertainties on the neutron flux in the energy regionof 72−82 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Energies, parent nuclei with their spin (J) and parity (π), and physics processesof the observed γ-ray peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Results of the first and second spectrum fittings. . . . . . . . . . . . . . . . . . . 123
Results of the γ-ray production cross sections. . . . . . . . . . . . . . . . . . . . 125

10.1 List of isotopes produced in the muon spallation at SK calculated by FLUKA.
The primary process is with 16 O except for the first three rows. . . . . . . . . . 132
11.1 Summary on the period and live time for diﬀerent SHE and AFT trigger conditions.135
11.2 Random and spallation event eﬃciencies by the present spallation cut for each
Erec region. The uncertainties come mainly from the statistics of the samples. . 143
11.3 The signal eﬃciency and the mis-tag probability in the current working points. . 149
11.4 Neutron tagging eﬃciencies in percent estimated by the Am/Be calibration bothin data and MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
11.5 Number of observed events after each cut in diﬀerent Erec regions. . . . . . . . . 151
11.6 Signal eﬃciencies at each reduction for diﬀerent energy regions. . . . . . . . . . 151
12.1 Summary of the background estimates in the SRN search. . . . . . . . . . . . . 152
12.2 Relative ratios of the flux-averaged events from the T2K flux to the atmospheric
neutrino flux from six models in Figure 8.4 to NEUT (the nominal model in theanalysis). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
12.3 Ratios of the number of the observation to that of the prediction in each Q2
region calculated from Figure 12.3. The number of the observation is the sum of
those from the FHC and RHC samples, and this is the same for the prediction
FHC
RHC
FHC
RHC
as well (Nobs = Nobs
+ Nobsand Npred = Npred+ Npred). . . . . . . . . . . . . 155
12.4 Summary of the NCQE background uncertainties for neutrinos and antineutrinos
for each energy region. The numbers are shown in percent. The numbers forantineutrinos are shown in parenthes. . . . . . . . . . . . . . . . . . . . . . . . . 157
12.5 Results of the Michel spectrum fitting for the neutron tagging conditions in eachenergy region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
12.6 Summary of the 9 Li eﬃciency in the spallation cut. The 9 Li eﬃciency is the
product of the weighted eﬃciency and the random event eﬃciency. . . . . . . . . 159
13.1 Summary of the 90% C.L. sensitivities and upper limits on the electron antineutrino flux in each energy region. Ēν represents the mean neutrino energy in theregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

LIST OF TABLES

xix

13.2 Comparison of the 90% C.L. upper limit on the ν̄e flux with the SRN theoreticalpredictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
B.1 Capacitances and stored charges for EMTC3 and EMTC4 when −500 V is applied.182
B.2 EMT output signal size per bunch at 460 kW beam intensity and +250 kA horncurrent (muon flux of 3.3 × 106 /cm2 per 80 ns beam bunch) with applied voltageof −500 V. The expected charge is 730 pC/bunch. . . . . . . . . . . . . . . . . . 184
B.3 Intensity resolution of each detector for spill and the first bunch only. The proton
beam intensity is 450 kW and the horn current is +250 kA. . . . . . . . . . . . . 185
B.4 Proton beam powers and applied voltages to the EMTs in the beam intensity
scans. The number of protons per kW at a repetition cycle of 2.48 sec is 5.3×1011
protons/spill/kW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.5 Beam conditions and high-voltages for EMTC3 and EMTC4 during each beam
exposure period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B.6 Total charge integration prior to EMT signal yield stabilization. The calculations
for Period III assume the charge per PMT is larger by 10% since a bit highervoltage (−505 V) was used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
C.1 Summary on the cut function parameters for dwall, eﬀwall and ovaQ in each run.197

Part I
Introduction

1Chapter 1
Introduction
Supernova explosions are one of the most dynamic phenomena in the universe and have beenplaying important roles in terms of physics and astrophysics. It is particularly important
to study the supernova via neutrino detections. In this chapter, first, supernovae and theirrelations with neutrinos are described, and followed by the descriptions on supernova relic neutrinos, which are neutrinos from all past supernovae. After describing the physics background,experimental searches for supernova relic neutrinos are explained, focusing on an importanceof the neutrino neutral-current quasielastic interaction, which is the main subject of this thesis.

1.1

Supernova Explosion

A star, whose mass is more than about eight times heavier than the Sun, ends its life by
an explosion, a kinetic energy of which reaches ∼1051 erg. This is one of the most energetic
phenomena in the universe, known as a supernova. It is estimated that supernovae occur a
few times a century in a galaxy [1, 2]. Many have been observed via optical surveys in many
galaxies over centuries. Figure 1.1 gives an image of the Crab Nebula, which was observed in1054 as a Type-II supernova. Despite these observations there remain many unknowns about
supernovae and their explosion mechanisms.

Figure 1.1: An image of the Crab Nebula taken by NASA’s Hubble Space Telescope [3].

3CHAPTER 1. INTRODUCTION

1.1.1

4

Supernova Types

Supernovae are classified by their spectral characteristics: Ia, Ib, Ic, and II, as shown in Figure 1.2. A supernova whose spectrum without hydrogen lines (the Balmer series) is classified
as Type-I, and that with those lines as Type-II. Type-I supernovae with intense silicon lines
are classified as Type-Ia. Among the other Type-I supernovae, those with and without heliumlines are Type-Ib and Type-Ic, respectively. Type-Ia supernovae are typically observed in older
elliptical galaxies that do not contain young stars, while the other types are observed only inthe region where star formations occur actively. This indicates that Type-Ia supernovae canoriginate from long-lived stars unlike the other types. The reason for this diﬀerence is related
to the explosion mechanisms as explained below.

Supernovae

no hydrogensiliconType-Ia

hydrogenno siliconheliumno helium

Type-Ib

Type-Ic

thermonuclear

Type-II

core-collapse

Figure 1.2: Classification of supernovae based on their spectral properties and explosion mechanisms.

The kinetic energy of supernovae reaches ∼1051 erg. Possible sources for such large energy
are the nuclear energy and the gravitational energy [4]. First, the explosion with release of thenuclear energy is explained. Assuming that drastic nuclear fusion reactions happen in a star
whose mass is similar to the Sun, the released energy (E) is:(E ∼ 3 × 10

51

M
Msun

)
erg,

(1.1)

where Msun = 1.989 × 1030 kg is the solar mass and M is the mass of the star. Here thefusion reactions from carbon to iron are assumed. This energy size is comparable to the scaleof energies of Type-Ia supernovae. This drastic fusion happens in a star which is supported bypressures of the Fermi gas degenerate electrons such as white dwarfs. This type of explosions is

CHAPTER 1. INTRODUCTION

5

called “thermonuclear supernovae”. Second, the explosion based on release of the gravitationalenergy is possible. When a star collapses by the gravity to leave a compact object with a masssimilar to the Sun, the released energy is:(E ∼ 3 × 10

53

M
Msun

)2 (

R
10 km

)−1
erg,

(1.2)

where R is the radius after the collapse and 10 km is a typical size of the neutron star. This gives
enough energy to explain the scale of the supernova explosion when ∼1% of the total released
energy is used as kinetic energy. This type is called “core-collapse supernovae”, 99% of whoseenergy is carried by neutrinos. The collapse by the gravitation is inevitable for the star which
is more massive than ∼10Msun and the lifetime of those stars is typically ≲107 years. This is
short compared to a typical lifetime of ∼1010 years for a star with ∼1Msun . The fact that only
Type-Ia supernovae are observed in elliptical galaxies indicate that these are the thermonuclear
supernovae, while the other types (Ib, Ic, and II) are the core-collapse supernovae. Thoughboth types of supernovae accompany the neutrino burst, much more neutrinos are emitted fromthe core-collapse supernovae. Therefore this thesis focuses on the core-collapse type.

1.1.2

Galactic Evolution

Supernovae are important phenomena that drive both the chemical and physical evolution of
the universe [5–7]. The explosion rate, properties of the stars that cause supernovae, and the
explosion properties are important to unravel the history of the universe and help to predict
its future evolution.
In the early phase, the universe was composed of only hydrogen and helium. On theother hand, the present universe is enriched with heavier elements. Explosive phenomena
such as supernovae are an important source for synthesizing heavy elements via two possible
paths. Since the star makes elements via its nuclear fusion inside itself, the explosion disperses
elements heavier than hydrogen and helium into the universe. This process, however, canproduce elements only up to iron, because the binding energy per nucleon takes its maximum
at iron nuclei. Another important process is the r-process [8,9], in which neutrons are captured
by light elements during the explosion leading to beta decay to produce heavier elements thaniron. The r-process requires a neutron-dominant environment, which is represented by theelectron-to-proton ratio (Ye ) to be Ye < 0.5. In supernovae, Ye = 0.3 ∼ 0.45 is expected 1 .

1.1.3

Insights into Fundamental Physics

All four forces (electromagnetic force, strong force, weak force, and gravitation) are involved in
the supernova dynamics, and all of them are essential. Therefore, to study the explosion mechanism leads to validation of the fundamental forces in the Standard Model of particle physics.
Currently the theoretical simulations do not perfectly succeed in modeling these explosions. It
has been argued that some fundamental theory might be insuﬃcient and hence some physics
beyond the Standard Model (BSM) could be required.

1

Some studies disfavor the r-process in supernovae because the neutron amount near the core decreases due
to inverse beta decay. Instead neutron star mergers are another favorable sites for the r-process since theysatisfy the neutron rich condition (Ye ∼ 0.1) while their rate is lower than supernovae.

CHAPTER 1. INTRODUCTION

1.1.4

6

Relation to Other Astronomical Objects

Supernovae are thought to be strongly related to other astronomical phenomena. Among them,
γ-ray bursts (GRBs) are of particular interest. A GRB is considered to be a highly relativistic
jet, and its energy reaches 1054 erg, making it the most luminous event in the universe. It isthought that some supernovae produce GRBs, and there have been some coincident observationsof a supernova and a GRB, such as SN1998bw+GRB980425 [10] and SN2001ke+GRB011121[11]. Since the rate of GRBs is ∼10 times less than supernovae, it is important to study
supernovae in detail for the GRB research. Other related objects are, for example, black holes
and pulsars (neutron stars rotating with a high frequency). Both of them are often made fromsupernova explosions.

1.2

Neutrinos from Core-Collapse Supernovae

Neutrinos are elementary particles with spin 1/2 and no electric charge, and have three flavors:
electron, muon, and tau corresponding to their charged lepton partners. They interact withmaterials only via weak forces (and gravity). It is thought that neutrinos play an essential rolein the supernova explosion and are an important messenger that carry diﬀerent information
about the supernova than electromagnetic radiation. In this section, the neutrino oscillation is
described first as an important property of neutrinos, and followed by the descriptions on the
explosion mechanism of the core-collapse supernova.

1.2.1

Neutrino Oscillations

It was believed that neutrinos are massless. However, the observation of neutrino oscillations[12,13] contradicts this, indicating that neutrinos have small but nonzero masses (<1 eV). Whenneutrinos have mass, their flavor eigenstates, |να ⟩ (α = e, µ, τ ), are expressed as superpositionof their mass eigenstates, |νi ⟩ (i = 1, 2, 3):|να ⟩ =∑

Uαi |νi ⟩,

(1.3)

i

where U is a 3×3 unitary matrix, referred to as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS)
matrix [14,15]. This matrix is expressed by four independent parameters, which are three mixing
angles (θ12 , θ23 , and θ13 ) and one complex phase (δCP ):





1
0
0
c13
0 s13 e−iδCPc12 s12 0  −s12 c12 0 
010
U =  0 c23 s23  iδCP
0 −s23 c23−s13 e
0
c13
0
0 1


c12 s13s12 c13s13 e−iδCPc13 s23  ,=  −s12 c23 − c12 s13 s23 eiδCP c12 c23 − s12 s13 s23 eiδCP
iδCP
iδCP
s12 s23 − c12 s13 c23 e
c12 s23 − s12 s13 c23 e
c13 c23(1.4)

where cij = cos θij and sij = sin θij . In case of sin δCP ̸= 0, the PMNS matrix contains
imaginary parts, which cause CP violation. In vacuum, the evolution of a mass eigenstate |νi ⟩after a traveling time t is derived from the Schrödinger equation:

CHAPTER 1. INTRODUCTIONi7d|νi (t)⟩ = H|νi (t)⟩ = Ei |νi (t)⟩,
dt

(1.5)

|νi (t)⟩ = exp(−iEi t)|νi ⟩,(1.6)

where H represents the Hamiltonian and Ei is the energy of the mass eigenstate. The flavor
eigenstate |να ⟩ at a time t can be written as:|να (t)⟩ =∑Uαi exp(−iEi t)|νi ⟩.

(1.7)

i

√
m2
m2
Since the masses of neutrinos are small, an approximation, Ei = p2i + m2i ≃ pi + 2pii ≃ p + 2Ei ,where pi and mi are the momentum and mass of the mass eigenstate respectively (pi ∼ p andEi ∼ E), can be used:()
im2i t|να (t)⟩ =Uαi exp(−ipt) exp −
|νi ⟩
2E
i
(
)
∑
im2i t†Uαi exp(−ipt) exp −=Uβi|νβ ⟩.
2E
i,β
∑

(1.8)

Then the να → νβ transition probability is calculated as:
P (να → νβ ) = |⟨νβ |να (t)⟩|2
=

=

(
)
2
im2i t†Uαi exp(−ipt) exp −
Uβi
2E
i,β

∑
∑

(

†
†
Uαi
Uβi Uαj Uβj
exp

i,j

=

∑

(

†
†
Uαi
Uβi Uαj Uβj
exp

i,j

= δαβ − 4∑i(m2i − m2j )t−2Ei∆m2ij L
−
2E

+ 2

∑
i>j

)

†
†
Re(UαiUβi Uαj Uβj) sin2i>j††
Im(UαiUβi Uαj Uβj
) sin

(

)

(

∆m2ij L4E)
∆m2ij L
,
2E

)

(1.9)

where ∆m2ij ≡ m2i − m2j is a mass-squared diﬀerence, t is replaced with a travel distance∑ †L = ct (neutrinos are relativistic), and the unitary condition ( i UαiUβi = δαβ ) had been used.
According to this equation, neutrino oscillation occurs only when at least two masses are notCHAPTER 1. INTRODUCTION

8degenerate (mi ̸= mj ) and there is nonzero mixing (U ̸= I). Neutrino oscillations in vacuum areparametrized by three mixing angles (θ12 , θ23 , and θ13 ), two mass-squared diﬀerences (∆m221
and ∆m232 ) 2 , and a CP phase (δCP ). The formalism needs to be modified for the case of
oscillations in matter [16, 17]. Over the past 20 years, the neutrino oscillation parameters havebeen measured with various sources: atmospheric, solar, reactor, and beam neutrinos. The
order of the mass eigenstates, ∆m232 > 0 or ∆m232 < 0, has not been determined. The former
is called the normal hierarchy (NH) and the latter the inverted hierarchy (IH). The NH isslightly favored by some experiments including T2K and Super-Kamiokande [18–20]. The CP
phase is not observed yet, though a recent T2K result excludes sin δCP = 0 with more than 2σconfidence [21]. Table 1.1 summarizes the most precise results of the oscillation parameters asof 2018 [22].
Table 1.1: Best-fit values of the neutrino oscillation parameters from PDG2018 [22]. NH andIH represent the normal and inverted neutrino mass hierarchy, respectively.
Oscillation parametersin2 θ12
sin2 θ23 (NH, Octant I)
sin2 θ23 (NH, Octant II)
sin2 θ23 (IH, Octant I)
sin2 θ23 (IH, Octant II)
sin2 θ13∆m212∆m232 (NH)∆m232 (IH)

1.2.2

Best-fit value
0.307 ± 0.013
0.417+0.025−0.0280.597+0.024−0.0300.421+0.033−0.0250.592+0.023−0.030(2.12 ± 0.08) × 10−2
(7.53 ± 0.18) × 10−5 eV2(2.51 ± 0.05) × 10−3 eV2(−2.56 ± 0.04) × 10−3 eV2Core-Collapse Supernovae and Neutrino Emission

In this section, the explosion mechanism of the core-collapse supernova (CCSN) is explained.
The neutrino-heating mechanism [4,23] is described here because it is widely accepted although
the mechanism is not completely confirmed and still being actively studied. Figure 1.3 showsa schematic view of the mechanism for explanation below.
(Steps 1−3) A star initially supports itself against the gravity with pressure produced by
nuclear fusion. The process begins with the hydrogen burning into helium (1). The temperatureand density increase due to nuclear fusion until it is high enough for helium fusion to occur.
Since hydrogen remains in the outer parts of the star avoiding the fusion, the star becomeslayered (2). Once the helium in the core is exhausted, the star contracts again, until thetemperature and density of the core become suﬃciently high for the fusion of more massive
nuclei. This sequence continues until the silicon burning in the core and the star structure
becomes multi-layered (3). The silicon burning produces nickel and iron group nuclei. Since
iron nuclei have the largest binding energy, nuclear fusion stops.
(Steps 4−7) As iron accumulates in the core of the star, the density and temperature of thecore become higher, increasing the Fermi energy of electrons therein. It promotes the electron
capture reaction (e− +p → νe +n) mainly on protons in iron. This causes lack of the degeneratepressure. In addition, at temperatures above ∼5 × 109 K, photodisintegration of iron nuclei
2∆m221 + ∆m232 + ∆m213 = 0

CHAPTER 1. INTRODUCTION

(1)

(2)

H

9

(3)

H
He

H
He
C,O
O,Ne,Mg
SiFe…

“accretion phase”
(8)

ν

(4)

Fe core“neutronization burst” “bounce & shock wave”“neutrino trapping”

(7)

(5)

νe

(6)

νe

νe
PNS
neutrinosphere

(9)

ν

(10)

ν

(11)

(12)

success

failure“shock stall & revival”

black hole

“explosion”

neutron staror
black hole

Figure 1.3: Schematic illustration of the explosion mechanism of core-collapse supernovae assuming a neutrino-heating mechanism. Descriptions of each part with numbers in the parentheses are given in the text.

CHAPTER 1. INTRODUCTION

10(γ + 56 Fe → 13α + 4n − 124.4 MeV) occurs. Since this is an endothermic reaction, the corepressure does not increase enough. These processes make the core unstable and become triggersof the gravitational collapse of the core (4). In this phase, the mean free path for neutrinos isdetermined by the interaction with nuclei, ∼109 cm, which is larger than the size of the ironcore. Therefore, the νe ’s produced from electron capture can initially escape from the core. The
surface where the neutrino is scattered last is called the “neutrinosphere”, which is represented
as dashed blue circles in Figure 1.3. The inner part of the core (“inner core”) falls with avelocity proportional approximately to the radius, while the outer part (“outer core”) falls
quasi-free with a velocity proportional to the inverse square of the radius. When the densityof the inner core reaches ∼1011 g/cm3 , the neutrinosphere becomes as large as the inner core.
Then electron neutrinos produced from electron capture are trapped (5). The collapse continues
until the inner core reaches nuclear density (∼1014 g/cm3 ). At that point, repulsive nuclear
forces halt the collapse and the core bounces. A shock wave (yellow waved circles in Figure 1.3)
is launched at the boundary between the two parts of the core. The shock wave propagates
outwards and interact with surrounding matter. Neutrinos are produced through the chargedcurrent interactions; however, these neutrinos are not emitted since they are trapped in theneutrinosphere. In the most inner part, a proto neutron star (PNS) is formed (6). Once theshock wave arrives at the neutrinosphere, the emission of neutrinos begins (7), and this emission(“neutronization burst”) continues until the shock wave arrives in the region with low matter
density. The duration of the neutronization burst is ≲10 ms.
(Steps 8−12) After the passage of the shock wave, matter (nucleons, electrons, and positrons)
falls on to the PNS. PNS is then heated to produce neutrinos. The falling matter is represented
by black arrows in panel (8). In this phase (“accretion phase”), neutrinos of all flavors areproduced via electron and positron capture (e− + p → νe + n, e+ + n → ν̄e + p) and pair production (e− + e+ → νe,µ,τ + ν̄e,µ,τ ). These are called the thermal neutrinos. The shock wave stalls
by losing its energy due to the pressure from the accretion materials, photodisintegration, andneutrino emission (9). In order for the star to explode, revival of the shock wave is required.
The revival is believed to be caused by neutrino-heating 3 . In this mechanism, matter behindthe shock wave is heated by absorption of neutrinos emitted from the PNS region and the shock
wave regains energy. If the shock wave has enough energy to blow oﬀ the outer layer of matter,an explosion happens. If not, the matter accretion to the PNS and neutrino emission continue
until a black hole is formed. In the case of an explosion, the PNS cools by emitting neutrinos
and becomes a neutron star or a black hole depending on the mass and the initial metallicityof the progenitor.
The energy of emitted neutrinos depends on the flavor. Neutrinos emitted from a deeper
layer whose temperature is higher are likely to have higher energy. Since ν̄x ’s experience only
neutral-current interactions, the corresponding neutrinosphere is smaller than those of νe ’s andν̄e ’s. Due to the neutron-rich environment in the PNS, the radius of ν̄e ’s neutrinosphere issmaller than the νe ’s one. A smaller neutrinosphere indicates that the corresponding neutrinos
have higher energy. Figure 1.4 shows the time evolution of the neutrino luminosity and theaverage energy for diﬀerent flavors obtained in a numerical simulation [24]. The sharp peak inthe νe plot in the figure corresponds to the neutronization burst. The order of average energies
is Eνe < Eν̄e < Eνx as expected.

3

Other scenarios include the shock revival caused by magnetic fields or convection.

CHAPTER 1. INTRODUCTION

11

Figure 1.4: Time evolution of the neutrino luminosity (top) and average energy (bottom) for
each neutrino flavor in a numerical simulation [24]. Note that νx = 14 (νµ + ν̄µ + ντ + ν̄τ ).

1.2.3

Observation of Neutrinos from SN1987A

There has only been one observation of neutrinos from a supernova so far. On February
23rd, 1987, the Kamiokande-II, IMB, and Baksan experiments observed neutrino emission
from SN1987A in the Large Magellanic Cloud [25–27]. Figure 1.5 shows the distribution of theenergy and time of neutrinos in the Kamiokande-II and IMB detectors. This event verifies thefundamental mechanism of the CCSNe while its power to constrain models is not strong due tosmall statistics. The total energy derived from SN1987A is consistent with the expectation in
Equation 1.2 [28,29]. In order to learn more about the supernova mechanism, detectors aroundthe world, including Super-Kamiokande, are watching the next supernova burst.

1.3

Supernova Relic Neutrinos

As mentioned above, the supernova explosion rate is rare (a few per century per galaxy);
however, neutrinos emitted from all past CCSNe are accumulated and form an integrated
flux. This flux is called the supernova relic neutrinos (SRNs) or diﬀuse supernova neutrino
background (DSNB). Detection of SRNs would provide valuable information on the supernova
rate and physics of the neutrino emission process. In this section, the theoretical prediction of
the SRN flux is reviewed based on Refs. [31, 32].
The number density of SRNs which were emitted at redshifts z ∼ z + dz and whose energies
at emission were Eν′ ∼ Eν′ + dEν′ is expressed as:

CHAPTER 1. INTRODUCTION





 

 
 
 

 





12

 






 

  

¾Ĥ

          

Figure 1.5: Distribution of time and energy of the neutrinos from SN1987A, observed in the
Kamiokande-II (12 events) and IMB (8 events) experiments. The figure is taken from Ref. [30].

dn′ (Eν′ ) = RCCSN (z)(1 + z)3

dt dN (Eν′ ) ′
dz
dEν ,
dz
dEν′

(1.10)

where RCCSN (z) represents the CCSN rate in a unit comoving volume at redshift z and t is
time and the quantities at the neutrino emission time is attached with the superscript prime
sign. The factor (1 + z)3 is multiplied to express the volume at the CCSN and dN (Eν′ )/dEν′ isthe neutrino number spectrum from each CCSN. The SRN number density at present is:dn(Eν′ ) =dn′ (Eν′ ).
(1 + z)3(1.11)The energy is also redshifted to Eν′ = (1 + z)Eν . Then the number density of SRNs that were
emitted at redshifts z ∼ z + dz and have energies Eν ∼ Eν + dEν at present is written as:
dt dN (Eν′ )(1 + z)dEν .
dn(Eν ) = RCCSN (z) dz
dz
dEν′(1.12)The relation between the redshift z and the time t is given by the Friedmann equation as:
dt
1
√
=
,
dz
H0 (1 + z) Ωm (1 + z)3 + ΩΛ

(1.13)

where H0 is the Hubble constant, and Ωm and ΩΛ are the matter density and the cosmologicalconstant, respectively. The SRN flux is then expressed using the relation dΦ(Eν )/dEν =c · dn(Eν )/dEν , where c is the speed of light, as:CHAPTER 1. INTRODUCTIONdΦ(Eν )
=c
dEν

∫ ∞
0

H0

13

√

dz
Ωm (1 + z)3 + ΩΛ

RCCSN (z)dN (Eν′ ).
dEν′(1.14)The number spectrum can be a function of the initial mass M and the metallicity Z of theprogenitor. In this case, the initial mass function ΨIMF (M ) and the metallicity distributionfunction ΨZF (z, Z) of the progenitor are used:∫ ∞dzdΦ(Eν )√
= c×dEν
H0 Ωm (1 + z)3 + ΩΛ0{∫ Mmax} ][∫ ZmaxdN (M, Z, Eν′ )ΨIMF (M )RCCSN (z)ΨZF (z, Z)dM dZ .
dEν′0
Mmin
(1.15)

There are various factors that aﬀect the SRN flux. Hereafter only electron antineutrinos are
considered since the signal in experimental searches is usually inverse beta decay as describedlater.

1.3.1

Neutrino Oscillation Eﬀects

The number spectrum of ν̄e is a mixture of spectra of all flavor neutrinos:
dNν̄e
dEν

= P̄eedNν̄0µdNν̄0edN 0+ P̄µe+ P̄τ e ν̄τ
dEν
dEν
dEν

dNν̄0edNν̄0x= P̄ee+ (1 − P̄ee )
,
dEν
dEν

(1.16)(1.17)∑
where P̄αe (α = e, µ, τ ) ( α P̄αe = 1) is the transition probability from ν̄α to ν̄e after the travel
through stellar envelopes and space. The superscript “0” represents the number spectrum at theinitial neutrino emission. With the PMNS matrix in Equation 1.4 and oscillation parametersin Table 1.1, this equation is transformed into:
dNν̄e
dEν

= |Ue1 |2

dNν̄1
dNν̄2
dNν̄3
+ |Ue2 |2+ |Ue3 |2
dEν
dEν
dEν

= cos2 θ12 cos2 θ13∼ 0.68 ·

dNν̄2
dNν̄3
dNν̄1
+ sin2 θ12 cos2 θ13+ sin2 θ13
dEν
dEν
dEν

dNν̄1
dNν̄2
dNν̄3
+ 0.30 ·+ 0.02 ·
,
dEν
dEν
dEν

(1.18)(1.19)(1.20)

Under the normal mass hierarchy, dNν̄1 /dEν ∼ dNν̄0e /dEν , dNν̄2 /dEν ∼ dNν̄0x /dEν , and dNν̄3 /dEν ∼dNν̄0x /dEν , then:CHAPTER 1. INTRODUCTION

14

dNν̄0edNν̄0xdNν̄e∼ 0.68 ·+ 0.32 ·
.
dEν
dEν
dEν

(1.21)

In contrast, under the inverted mass hierarchy, dNν̄3 /dEν ∼ dNν̄0e /dEν , dNν̄1 /dEν ∼ dNν̄0x /dEν ,and dNν̄2 /dEν ∼ dNν̄0x /dEν , then:dNν̄0x
dNν̄e
∼
.
dEν
dEν

(1.22)As described above, the emission rate and average energy of the supernova neutrino depend on
the flavor. Since the electron flavor neutrino has relatively lower energy than the muon and tau
flavor neutrinos as described above, the SRN flux becomes harder in the inverted hierarchy.

1.3.2

Galaxy Evolution

The supernova rate RCCSN (z) can be expressed by the cosmic star formation rate density(CSFRD) ρ̇∗ (z), mass of the stars produced in a unit time and a unit comoving volume, andthe initial mass function ΨIMF (M ) as:
RCCSN (z) = ζCCSN ρ̇∗ (z),∫ Mmax
ΨIMF (M )dM
Mmin
ζCCSN = ∫ 100M
,
sun
M
Ψ
(M
)dM
IMF
0.1Msun(1.23)(1.24)

where Mmin and Mmax are the minimum and maximum masses of the progenitor which produce
the SRN, respectively. For Mmax , 100Msun is frequently used. In Figure 1.6, CSFRD and
IMF predictions from diﬀerent models are shown. For CSFRD, model diﬀerence gets larger
for z > 0.5, and this leads to a diﬀerence in the low energy SRN flux as larger redshifts
correspond to lower energies. The IMF directly relates to the rate of heavy progenitors whichcause supernovae. Models which have a higher probability in the low mass, such as “Chabrier”
in the right panel of Figure 1.6, give the larger SRN flux. It is widely believed that stars heavier
than 10Msun always cause CCSNe. However, it depends on models for the region 8−10Msun .
The minimum mass in the integration in Equation 1.23 aﬀects the SRN flux prediction. As
expected, the lower minimum mass provides larger flux over energies. The combinations ofthese three show about 3 times diﬀerence in the number of events at most [31–33].

1.3.3

Contributions from Failed Supernovae

Some stars fail in the explosion to become black holes (“failed supernovae”). In this case, since
the accretion phase continues until black hole formation, more energetic neutrinos are emitted
in general. Therefore, the rate of progenitors that would become black holes aﬀects the SRN
flux. The galactic metallicity evolution is strongly related to the black hole formation. Anotherimportant factor is the equation-of-state (EOS) of the neutron star. It takes more time for the
PNS, whose EOS is stiﬀer, to become the black hole, then accordingly the neutrino emission
amount is larger.

CHAPTER 1. INTRODUCTION

15

•

•

o
MψIMF/∫100M
MψIMFdM(Mo• -1)
0.1Mo

10

Chabrier
SalpeterA
Salpeter

1
0.1
0.01
0.001

0.00010.1

1

M(Mo• )

10

100

Figure 1.6: The CSFRD as a function of redshift, ρ̇∗ (z) (left), and the mass distribution,∫ 100Msun
M ΨIMF (M )/ 0.1Msun
M ΨIMF (M )dM (right), for diﬀerent models [31, 32].

1.3.4

Shock Revival TimeAs explained in the section for the CCSN mechanism, the shock wave stalls once and revives
via neutrino-heating. The time between the stall and revival is used as a parameter in the
supernova study (“shock revival time”). Apparently the longer revival time leads to moreneutrinos because more matter falls on to the PNS. This eﬀect appears in the high energy
region of the SRN flux due to the high temperature of the PNS. The typical value of the revival
time is considered O(100) ms. For instance, Ref. [34] suggests 100−200 ms deduced from themass distribution of neutron stars and black holes, Ref. [35] suggests 300−400 ms based on
simulations, and there exists some studies suggesting even longer than 500 ms.

1.3.5

SRN Flux Predictions

Many models have been proposed to predict the SRN flux. Some of them are briefly reviewed
below and their ν̄e flux predictions are shown in Figure 1.7. There is nearly an order ofmagnitude diﬀerence in the flux depending on the model.
• Horiuchi+18 [36]: This model studies the eﬀect of the progenitor conditions on the explosion, especially focusing on the critical compactness, which determines if the star becomesa black hole or not. In Figure 1.7, the results with two values (0.1 and 0.5) are shown.
The smaller critical compactness corresponds to more black hole formation.
• Nakazato+15 [31, 37]: This model considers the redshift dependence of black hole formation and investigates the eﬀects of various eﬀects on the SRN flux, such as neutrino
oscillations, the star formation rate, the initial mass function, EOS of the neutron star,and the shock revival time. Two cases providing the largest and smallest fluxes are shownin Figure 1.7.
• Horiuchi+09 [38]: In this calculation, the CCSN rate is derived from the cosmic starformation history based on data [39]. The ν̄e spectrum per explosion is approximatedwith a Fermi-Dirac distribution. In Figure 1.7, the eﬀective neutrino temperature isassumed to be 6 MeV.

CHAPTER 1. INTRODUCTION

16• Lunardini09 [40]: This model considers failed supernovae which form black holes, separately from the explosions that form neutron stars. The explosion resulting in the blackhole contributes to the higher energy SRN fluxes.
• Ando+09 [41]: This is the first model that takes into account neutrino oscillations. The
normal mass hierarchy and oscillations in vacuum are assumed.
• Malaney97 [42]: This model considers the redshift evolution of the cosmic gas, as determined from observations of absorption lines in quasi-stellar objects.

SRN νe Flux [/cm2/sec./MeV]• Hartmann+97 [43]: This model calculates the flux using the chemical evolution of theuniverse. The information on the galactic halo and chemical evolution are obtained fromobservations of the Damped Ly α system.

Horiuchi+18 (ξ2.5,crit = 0.1)
Horiuchi+18 (ξ2.5,crit = 0.5)
Nakazato+15 (Max, IH)
Nakazato+15 (Min, NH)
Horiuchi+09
Lunardini09
Ando+03
Malaney97
Hartmann+97

10

1

10−1

10−2

10−3

5

10

15

20

25

30

35

40

45

50

νe Energy [MeV]

Figure 1.7: SRN ν̄e fluxes from various theoretical models [31, 36, 38, 40–43].

1.4

Status of SRN Searches

As explained in the previous section, there are many theoretical predictions of the SRN flux.
Observation of SRNs would provide constraints on theoretical uncertainties. So far the SRN
signature has never been detected despite enormous experimental eﬀorts towards the discovery.
Almost all experimental searches are performed using inverse beta decay (IBD) of electron
antineutrinos (ν̄e + p → e+ + n), since its cross section is the largest as explained in Chapter 10.

CHAPTER 1. INTRODUCTION

17

The world’s most sensitive searches have been performed in the Super-Kamiokande (SK) water
Cherenkov detector and the KamLAND liquid scintillation detector. At SK the first search was
conducted with 1496 live days and spectrum fitting with various backgrounds was performed.
It placed an upper limit on the SRN ν̄e flux in the energy region of Eν > 19.3 MeV [44]. Thissearch was updated with a higher statistics 2853-day data set and improved analysis techniques.
Here the analysis threshold was lowered to Eν > 17.3 MeV [45]. As described in Chapter 4, anelectronics upgrade made it possible to record more data after a primary trigger. This makes it
possible to tag a neutron from IBD. This can reduce a large amount of backgrounds, especiallymuon spallation events dominating the energy region Eν < 17.3 MeV, and then the searchwith the lower energy threshold has been achieved. In contrast to the spectrum analysis, theneutron tagging analysis suﬀers from lower statistics because of the low tagging eﬃciency inSK (about 20%). The first analysis with the neutron tagging technique using 960 day of data
showed comparable or better results compared to the KamLAND experiment in the region
below 16 MeV while the result above 16 MeV is still worse than the SK spectrum analysis [46].
KamLAND is tuned to measure the IBD signal using delayed coincidence, which requires thesignal be paired with a 2.2 MeV γ-ray from the neutron capture on hydrogen. Since the neutron
tagging eﬃciency is almost 100% in KamLAND and the energy threshold is lower, the searchsensitivity is competitive in the lower energy region though the detector size is 20 times smaller
than SK [47]. The upper limits on the ν̄e flux from both experiments are shown in Figure 1.8.

Figure 1.8: Upper limits on the ν̄e obtained from searches in the Super-Kamiokande and the
KamLAND experiments. The black solid lines correspond to the maximum and minimum
predictions in Nakazato model [31]. The figure is taken from Ref. [31].
This thesis focuses on the search at SK, especially with the neutron tagging analysis. Among
several background sources, the atmospheric neutrino interactions are dominant in the region
Eν > 14 MeV. Above ∼20 MeV the charged-current neutrino interaction, where the charged
lepton is produced in the final state, is the main background. This channel is measured inmany neutrino experiments because it is the signal in the neutrino oscillation analysis. Thenthe interaction models are studied with many experimental data. Prior to the work in this

CHAPTER 1. INTRODUCTION

18

thesis, data on the neutral-current interaction, which dominates as the main background source
around 14−20 MeV, was not suﬃcient. This thesis focuses on the neutral-current interaction,
especially the quasielastic channel (called “NCQE”), to improve the SRN search sensitivity.
More details on the neutrino interaction are given in the next section.

1.5

Neutrino-Oxygen NCQE Interactions

1.5.1

Neutrino-Nucleus Interactions

Neutrinos interact with materials via weak boson exchanges (“weak interaction”). Dependingon the weak boson type, W ± or Z 0 , the interaction is referred to as charged-current (CC) or
neutral-current (NC), respectively. In the energy region from sub-GeV up to 10 GeV, neutrinos
interact with nucleons inside nuclei. From an experimental point of view, since the detectormaterial is not usually free protons, nuclear eﬀects inside nuclei are important. Neutrinonucleus interactions are classified into several types as explained below. Feynman diagrams forthe neutrino-nucleus interactions are shown in Figure 1.9.
(Quasi)elastic scattering
The main channel below ∼1 GeV is (quasi)elastic scattering with a nucleon:
νl + N → l + N ′ ,(1.25)

νl + N → νl + N,

(1.26)

where l is the charged lepton and νl is the counterpart neutrino, and N is thenucleon. In the CC channel (Equation 1.25), the nucleon type (neutron or proton)
is flipped. In case of CC the channel is called CC quasielastic (CCQE) since theinteraction is not truly “elastic” due to momentum transfer for the charged lepton
production. Interactions of this type without a charged lepton (Equation 1.26) are
termed NC elastic.

Multi-nucleon scattering via meson exchange currents
Nucleons inside the nucleus are correlated to each other via meson exchange currents. More than one nucleon could take part in the interaction. In this case multiple
nucleons are scattered. The leading term is the case two nucleons are involved andis referred to as the two-particle-two-hole (2p2h) interaction.

Resonant meson production
Nucleons can be excited to the baryon resonance. These would then decay into
combinations of nucleons and meson(s). The dominant intermediate resonant stateCHAPTER 1. INTRODUCTION

19

in a few GeV region is ∆(1232), and this state decays mainly into a nucleon and apion:

νl + N → l + ∆(1232) → l + N ′ + π,

(1.27)

νl + N → νl + ∆(1232) → νl + N ′ + π.

(1.28)

Other baryon resonance states give diﬀerent final states which can be composed ofmultiple mesons or a radiative photon.

Coherent pion production
When neutrinos interact with entire nuclei (A) coherently and nuclei are virtually
excited, pions are produced from decays of the nuclei. The remaining nuclei are in
their ground states:

νl + A → l + A + π ± ,(1.29)

νl + A → νl + A + π 0 .

(1.30)

Deep inelastic scattering
In higher energy region (>5 GeV), neutrinos are likely to directly hit quarks inside
nucleons and this is referred to as deep inelastic scattering (DIS). The final statefrom DIS usually contains hadrons:

1.5.2

νl + N → l + N ′ + hadrons,(1.31)

νl + N → νl + N ′ + hadrons.

(1.32)NCQE Interactions

Hereafter water is assumed as a target material since the detector used in this thesis is SuperKamiokande. At Eν ≳ 200 MeV, the NC quasielastic nucleon knock-out (NCQE) process,ν(ν̄) + 16 O → ν(ν̄) + n + 15 O∗ ,(1.33)

ν(ν̄) + 16 O → ν(ν̄) + p + 15 N∗ ,(1.34)

CHAPTER 1. INTRODUCTION

νl

20

l

(a)

−

νl

W

W
n
νl

u
d
u

d
d
u

(c)
W

A

l

(b)

p

p
l

−

νl

π+
A

(d)
W

N

π+

u
u
u
u

d
u
u

−

d
++

Δ

l

d
u
u

p

−

N
hadrons

Figure 1.9: Feynman diagrams for neutrino-nucleus interactions [48]: (a) CC quasielastic scattering, (b) CC resonant single pion production, (c) CC coherent pion production, and (d) CC
deep inelastic scattering.

becomes dominant over the NC inelastic process without nucleon emission (ν(ν̄) + 16 O →ν(ν̄) + 16 O∗ ) 4 [49]. The residual nuclei then de-excite to the ground state with the emissionof γ-rays 5 . The out-going nucleons, especially neutrons, further interact with water insidethe detector, which produce γ-rays and additional neutrons in some cases. These neutrons
are then captured by hydrogen, emitting 2.2 MeV γ-rays. Pairs of the primary signal and the
2.2 MeV γ mimic the SRN signal, as schematically shown in Figure 1.10. In the figure, thecase for Gd-doped water is shown together, because SK has its upgrade plan to dope Gd as
mentioned in Chapter 8. In the SK-I/II/III analysis [45], a 100% uncertainty was assigned
to this channel 6 because of little data on the NCQE channel. Hence, measuring the NCQE
interaction with high accuracy is essential to understand the background to the SRN search.
There is a measurement of this channel by atmospheric neutrinos in SK [50]. However, it isdiﬃcult to make a feedback to the cross section model because the uncertainty is too large andthe atmospheric neutrinos contain both neutrinos and antineutrinos. In addition, the analysis
should contain the SRN contributions.
An artificial neutrino beam used in the T2K experiment has its peak around 600 MeV as
shown in Chapter 3, and this is similar to the spectrum of atmospheric neutrinos. Measurementswith the T2K beam can provide constraints on the NCQE background estimation in the SRN
search at water Cherenkov detectors.

4

This terminology is a nuclear physicist’s manner. In neutrino physics, these two are both called the NC
elastic interaction.
5
Since there is no branching fraction for hydrogen to emitting γ-rays with this interaction, only oxygen isconsidered here.
6
In the SK-IV analysis, only the accidental background was considered.

CHAPTER 1. INTRODUCTION

21

Supernova relic neutrino (IBD)
n

νe

Gd

H
or

(thermalized)

γ

p

γ
e+
(2.2 MeV)(~8 MeV)

Atmospheric neutrino (NCQE)
n

ν

Gd

H
or

(thermalized)

γ
γ

16O

γ

(2.2 MeV)(~8 MeV)Figure 1.10: Schematic drawings for the ν̄e ’s inverse beta decay by SRNs (top) and the NCQE
interaction by atmospheric neutrinos (bottom) in a pure or Gd-doped water Cherenkov detector.

CHAPTER 1. INTRODUCTION

1.5.3

22

Previous NCQE Measurement in T2K

σ (10-38 cm2)

In the T2K experiment, the neutron-oxygen NCQE interaction cross section was measured to−38
be 1.55+0.71
cm2 /oxygen with data from a 3.01 × 1020 protons-on-target−0.35 (stat. ⊕ syst.) × 10
exposure in the neutrino beam mode [51], as shown in Figure 1.11. In the measurement, theγ-ray signal from the NCQE interaction was successfully selected and the basic analysis method
was established. However, the measurement has large statistical and systematic uncertainties.
Another problem is that the systematic uncertainty regarding modeling of the γ-rays producedin neutron-oxygen reactions is estimated based only on theoretical models because there islimited experimental data in the energy of interest here. This may be highly model-dependentand dangerous. In addition, there is no measurement of the antineutrino NCQE cross section,
while both are present in similar proportions in the atmospheric neutrino flux. In order toestimate the atmospheric neutrino NCQE interaction precisely, both neutrino and antineutrino
interactions should be separately measured.

4
Ankowski NCQE cross section
Flux-averaged Ankowski NCQE cross section

3

T2K data
T2K ν flux

2

1

0
0

0.5

1
1.5
2
Neutrino Energy (GeV)

Figure 1.11: Flux-averaged neutrino-oxygen NCQE cross section measured in T2K with a
3.01 × 1020 protons-on-target data. The black points correspond to the measured value, withvertical and horizontal bars being the measured uncertainty and the width of the neutrino flux,
respectively. The red line corresponds to the theoretical prediction. The figure is taken from
Ref. [51].

1.6

Outline of This Thesis

In this thesis, a measurement of neutrino- and antineutrino-oxygen NCQE-like interactions in
the T2K experiment and its applications to the background estimation in an SRN search at
Super-Kamiokande are presented. The NCQE-like cross section results are the world’s mostCHAPTER 1. INTRODUCTION

23

precise measurements. The antineutrino result is the first measurement of this channel todate. In addition, distributions in the kinematic regions of interest for SRN searches arestudied for the first time. The background estimation method demonstrated in this thesis is
the first application of experimental data. With the T2K results, the uncertainties on the
NCQE background are reduced, and a better sensitivity in the SRN search is achieved. The
obtained upper limit on the ν̄e flux is the most stringent result to date. These are applicable forthe future water Cherenkov experiments as well. The thesis hereafter is organized as follows.
Part II describes a measurement of neutrino and antineutrino NCQE-like interactions on
oxygen in the T2K experiment. Chapter 2 gives an overview of the analysis. Chapters 3 and 4
explain the T2K experiment and the Super-Kamiokande detector, respectively. In Chapter 3,
beam monitoring with the muon monitor is highlighted, which is essential to stable data taking.
Details of the Monte Carlo simulation is explained in Chapter 5. The event selection for the
NCQE signal is described in Chapter 6 and followed by the estimation of uncertainties in
Chapter 7. Cross section results and discussions are given in Chapter 8.
In Part III (Chapter 9), studies for improvements of the modeling of γ-ray emission fromthe neutron-oxygen reaction are presented. This interaction is important to reduce the largest
uncertainty in the NCQE-like interaction measurement.
Part IV is tailored to the analysis of a search for supernova relic neutrinos with a 2970.1day data set from Super-Kamiokande. The signal and background and their simulations are
overviewed in Chapter 10, and the data reduction is explained in Chapter 11. Chapter 12
describes the background estimation in detail. Here the T2K results are applied to the NCQE
background estimation. The final search result is shown in Chapter 13.
The thesis is concluded in Chapter 14 with a summary of the obtained results presented inParts II, III, and IV.

Part II
Measurement of Neutrino- andAntineutrino-Oxygen Neutral-Current
Quasielastic-like Interactions

25

Chapter 2
Measurement Overview
2.1

Measurement Motivation

Precise measurement of the neutrino-oxygen NCQE interaction in the sub-GeV region benefits a variety of physics studies. As explained in Chapter 1, this interaction forms the main
background in SRN searches at water Cherenkov detectors. Currently the search sensitivity islimited by the large uncertainty of this interaction especially in the low energy region where
the SRN flux is expected to be high. Measuring the NCQE interaction with the T2K beamwould improve the situation since the T2K energy region is similar to that of atmospheric
neutrinos. When searching for dark matter in accelerator-produced neutrino experiments, as
proposed in Refs. [52, 53], the NC interaction rate should be estimated precisely since it is
the main background. Another motivation arises in the sterile neutrino search in accelerator
neutrino experiments [54–56]. The fact that the NC interaction is flavor-independent makes
it possible to search for a deficit in the NC event rate, which could be interpreted as transitions from active to sterile neutrinos. Furthermore, the NC measurement is important tounderstand the neutrino-nucleus interaction, from a standpoint diﬀerent from the CC measurements, such as strange quark contributions inside the nucleus, which is visible only in the NC
interaction [57–60]. The initial state of nucleons inside nuclei could be addressed through the
NC-induced γ-ray measurements.

2.2

Neutral-Current Quasielastic Interactions

The diﬀerential cross section of the neutral-current (NC) elastic interaction of a neutrino (anantineutrino) on a free nucleon can be written as follows [61]:dσ ν(ν̄)
M 2 G2F
=
dq 2
8πEν2

{

2
s−u
2 (s − u)A(q ) ± B(q )
+
c(q
)
M2
M4
2

2

}
,

(2.1)

where Eν denotes the initial (anti)neutrino energy, M = 0.938 GeV is the nucleon mass, GF
is the Fermi coupling constant, q = pν − p′ν is the four momentum transfer (pν and p′ν arefour momenta of in-coming and out-going (anti)neutrinos respectively), and s and u are theMandelstam variables (s − u = 4M Eν + q 2 , assuming mν = 0). The upper (lower) sign
corresponds to the neutrino (antineutrino) interaction. The factors A, B, and C are written
by using τ = −q 2 /4M 2 as below:
27

CHAPTER 2. MEASUREMENT OVERVIEW()[
m2
A(τ ) =
4τ + 2(1 + τ )|F̃A |2 − (1 − τ )|F̃V1 |2 + τ (1 − τ )|F̃V2 |2 + 4τ F̃V1 F̃V2
M
]
m2
1
2 2
2
2
−
{(F̃V + F̃V ) + |F̃A | + 4F̃A F̃p − 4τ |F̃p | } ,4M 2
B(τ ) = 4τ F̃A (F̃V1 + F̃V2 ),C(τ ) =

28

(2.2)
(2.3)

1
(|F̃A |2 + |F̃V1 |2 + τ |F̃V2 |2 ).
4

(2.4)

Here the form factors F̃Vi (i = 1, 2), F̃A , and F̃p are specific to NC interactions and are describedby the form factors for the charged-current (CC) interactions (FVi , FA , and Fp ):1
F̃V1,N = ± FV1 − 2 sin2 θW · FN1 ,2
1
F̃V2,N = ± FV2 − 2 sin2 θW · FN2 ,
2
F̃A

(
)−2
1 s
1
q2
=
(F ± FA ) = (∆s ± gA ) 1 − 2
,
2 A
2
MA

F̃p =

2M 2 F̃A,
m2π − q 2

(2.5)
(2.6)
(2.7)
(2.8)

where N = p and n correspond to proton and neutron with upper and lower signs respectively,
θW is the Weinberg angle (sin2 θW = 0.23117 in the present work), and mπ = 0.13957 GeV
is the charged pion mass. The axial-vector interaction part is described by the axial-vector
mass (MA ) and the axial-vector weak coupling constant (gA ). The strange quark contribution,∆s = FAs (1 − q 2 /MA2 )2 , appears in the NC interaction and this eﬀect diﬀers between protons
and neutrons. Furthermore FVi and FNi can be written by using the electric and magnetic formNfactors (GVE , GVM , GN
E , and GM ):FV1 =GVE + τ GVM
,
1+τ

(2.9)

FV2 =

GVM − GVE,
1+τ(2.10)

FN1 =N
GN
E + τ GM,1+τ(2.11)FN2 =N
GN
M − GE
.
1+τ

(2.12)

These electric and magnetic form factors are parametrized often in the dipole and BBBA05
methods [62]. In the neutrino-nucleus scattering, nuclear eﬀects such as the nucleon motion

CHAPTER 2. MEASUREMENT OVERVIEW

29

and its binding inside the nucleus should be considered. Further details about neutrino-nucleus
scattering theories can be found in Refs. [57, 63].
At Eν ≳ 200 MeV in neutrino-oxygen interactions, nucleons are likely to be knocked-out
oﬀ nuclei. This interaction is especially termed NC quasielastic (NCQE). After the neutrinooxygen NCQE interaction, the remaining nucleus is usually in its excited state:ν(ν̄) + 16 O → ν(ν̄) + n + 15 O∗ ,(2.13)

ν(ν̄) + 16 O → ν(ν̄) + p + 15 N∗ ,(2.14)···

These nuclei promptly relax to the ground state by emitting γ-rays in some cases, such as
15 ∗O → 15 O + γ and 15 N∗ → 15 N + γ. These γ-rays are available as a probe to measure the
NCQE interaction, as is done in the present work.

2.3

Signal Definition

In the present work, the neutrino- and antineutrino-oxygen flux-averaged cross sections aremeasured using nuclear de-excitation γ-rays as a signal with the T2K beams. In this work, thesignal is termed “NCQE-like” because the event selection may contain contributions from NC
two-particle-two-hole (2p2h) interactions, in which two nucleons are involved in the interaction
via meson exchange currents. Previous studies [50,51] may have also included such contributions
although the fact was not specifically addressed. Note that the measurement of this inclusive
process is still beneficial in terms of the motivations explained in the beginning of this chapter.

Chapter 3
T2K Experiment
In this chapter, components of the T2K experiment and data taking history are described.

3.1

Overview of T2K

The T2K experiment [64] has been designed for the precise measurement of neutrino oscillations.
T2K provides a variety of physics programs as well, including the neutrino cross section measurement which is the main focus of this thesis. In the experiment, neutrino and antineutrino
beams are produced by the J-PARC accelerator and directed towards the Super-Kamiokande(SK) detector. The near detectors are placed to measure (anti)neutrinos before their oscillations. The cross sectional schematic illustration of T2K is given in Figure 3.1. T2K has beenrunning since 2009 and its physics run is divided into nine periods (Runs 1−9).

^ƵƉĞƌͲ<ĂŵŝŽŬĂŶĚĞ

EĞĂƌĞƚĞĐƚŽƌƐ

Dƚ͘EŽŐƵĐŚŝͲ'ŽƌŽϮ͕ϵϮϰŵ:ͲWZ

Dƚ͘/ŬĞŶŽͲzĂŵĂϭ͕ϯϲϬŵϭ͕ϳϬϬŵďĞůŽǁƐĞĂůĞǀĞů

EĞƵƚƌŝŶŽĞĂŵϮϵϱŬŵ

Figure 3.1: Schematic view of the T2K experiment.

3.2

J-PARC Accelerator and Neutrino Beamline

Prior to the neutrino beamline
Figure 3.2 gives an aerial view of J-PARC. Neutrinos or antineutrinos are produced from proton beams. Protons are accelerated step-by-step in three accelerators at J-PARC: the linear
accelerator (LINAC) up to 400 MeV/c, the rapid cycling synchrotron (RCS) up to 3 GeV/c,and the main ring synchrotron (MR) up to 30 GeV/c.
30

CHAPTER 3. T2K EXPERIMENT

31

Figure 3.2: Aerial view of the J-PARC. Note that “50 GeV” for MR is the original design value,
but the actual operation is with a 30 GeV setting.

Primary neutrino beamline
Beams are extracted from the MR and passed to the neutrino beamline. Here proton beams
are bundled into eight bunches (six in T2K Run 1), each being approximately 58 ns wide andseparated by about 580 ns. The eight bunches are referred to as a spill. Each beam spill isdelivered with a repetition cycle of ∼3 sec. (2.48 sec. in the recent operation). The beam
structure is schematically viewed in Figure 3.3.
2~3 sec

Spill
Time

Zoom

581 nsec

58 nsec

4.1 µsec

Bunch
Time

Figure 3.3: Schematic view of the J-PARC proton beam structure [48].
The neutrino beamline is composed of the 54 m long preparation section, the 147 m longarc section, and the 37 m long final focusing section, as shown in Figure 3.4.

CHAPTER 3. T2K EXPERIMENT

32

N
Main Ring
Secondary beamline

ND280

e
lin

n
Preparatio
sectionFast extraction
to the neutrino beamlinemea

Decay volume

yb

50 100 m

ar

0

Final

Target focusing
station sectionnArecctios

Beam dump+ Muon monitorimPr

to Super-K

Figure 3.4: Schematic view of the T2K neutrino beamline [65].
There are various proton beam monitors equipped in the primary beamline. They are
explained briefly in the following.
• CT (current transformer): A CT is a 50-turn toroidal coil around a cylindrical ferromagnetic core. Five CTs are equipped to monitor the proton beam intensity.
• ESM (electro-static monitor): An ESM is composed of four segmented cylindrical electrodes, measuring the beam position with the beam-induced current in the top-bottom
and left-right sides. There are 21 ESMs equipped in total.
• SSEM (segmented secondary emission monitor): An SSEM is made of two 50 µm thicktitanium foils stripped in horizontal and vertical directions. Nineteen SSEMs measure
the beam position and width at each position in the primary beamline. In the physics
data taking, only the most downstream SSEM is used to minimize the beam loss.
• BLM (beam loss monitor): A BLM is a wire proportional counter filled with an Ar-CO2
gas mixture. Fifty BLMs are installed to monitor the beam loss.

Secondary neutrino beamline
Experimental components after the primary beamline are shown in Figure 3.5. After the final
focusing part, a baﬄe is placed as a collimator for the beam. The proton beam is injected onto
a graphite target. The optical transition radiation (OTR) monitor [66], an imaging detector
made of a foil and a camera, is located just upstream of the target and used to measure thebeam position and width. Charged hadrons, such as pions and kaons, are produced from theproton-target reactions, and then focused by magnetic fields generated by three electromagnetic
horns [67, 68]. Each horn is made of an aluminum conductor and produces a toroidal magnetic

CHAPTER 3. T2K EXPERIMENT

33

field inside the conductor. The applied current to the horns is 250 kA. Some hadrons will decay
into pairs of a muon (anti)neutrino and a muon in the 96 m long decay volume lying after
the target. The polarity of the horn current can be changed, allowing selection of the beam
property, which is either neutrino-dominant or antineutrino-dominant in its composition. The
former setting is referred to as forward horn current (FHC) mode and the latter as reverse horncurrent (RHC) mode. The muon monitor (MUMON) [69] is placed at the downstream of thebeam dump to measure the >5 GeV muons, which are outcomes of the pion and kaon decays.
MUMON gives the neutrino beam profile indirectly on a bunch-by-bunch basis and plays an
indispensable role for the experimental operation. Further details about MUMON are given
later in this chapter.

Figure 3.5: Experimental components after the primary neutrino beamline, including the secondary neutrino beamline, the near detectors, and the far detector [70].

3.3

Near and Far Detectors

In T2K, the far detector, Super-Kamiokande, is placed at 2.5◦ oﬀ-axis with respect to theproton beam direction at the graphite target. This provides a narrow-band flux and adjusts aflux peak being at the maximum oscillation probability, as shown in Figure 3.6.
At 280 m away from the graphite target, two near detectors are placed at on-axis and 2.5◦
oﬀ-axis, INGRID [71] and ND280 [72, 73], respectively. INGRID is composed of the fourteen
identical modules aligned in a cross formation: seven being laid horizontally and another sevenvertically, as shown in Figure 3.7, and measures a neutrino beam profile. Each module is madeof plastic scintillators and iron plates. The beam profile measured by INGRID is shown in
Figure 3.8. The other near detector, ND280, is a complex of several components as shown in
Figure 3.9, and measures neutrino event rate and spectrum before oscillations. The SuperKamiokande detector, a large water Cherenkov detector, is located 295 km away. Since it is
the main detector for the analyses in this thesis, it is described in detail in Chapter 4. Beamtiming information is shared between the beamline and the far detector via the GPS system.

CHAPTER 3. T2K EXPERIMENT

34

P(νµ→ νe)

P(νµ→ νµ)1
sin22θ23 = 1.0
sin22θ13 = 0.12∆m32 = 2.4 × 10-3 eV2

0.5

0.10

1

2

1

2

NH, δCP = 0
NH, δCP = π/2

IH, δCP = 0
IH, δCP = π/2

3

0.05

Φ295km
(A.U.)
νµ0
1

3

OA 0.0°OA 2.0°OA 2.5°

0.5

0
0

1

Eν (GeV)2

3

Figure 3.6: The νµ → νµ and νµ → νe probabilities as a function of neutrino energy (top two),and the neutrino flux in diﬀerent oﬀ-axis (OA) angle configurations (bottom).

~10m
1.5m

Designed
Beam center

Iron plates

Y
X

Veto planes

1.24mElectronics boxes

Tracking planes

Y
X

Z

Z

~10m

Figure 3.7: Schematic illustration of INGRID. The whole structure is shown in the left panel
and each module is shown in the right panel. Each module consists of the iron target plates
and the tracking scintillator planes and is surrounded by the veto scintillator planes.

CHAPTER 3. T2K EXPERIMENT

35

40 Horizontal
35
30
25
20
15

×103

Number of events

Number of events

×103
40

Vertical

35
30
25
20
15

10

10

5

5

0

0
-400
-200
0
200
400
-400
-200
0
200
400
Position from designed beam center[cm] Position from designed beam center[cm]Data for each module
Fitted Gaussian

Figure 3.8: A neutrino beam profile measured by INGRID. The left and right panels correspondto the horizontal and vertical directions, respectively.

Figure 3.9: Schematic illustration of ND280. The neutrino beam is incident from the left sidein the figure.

CHAPTER 3. T2K EXPERIMENT

3.4

36

Beam Monitoring with MUMON

In addition to the beam measurements by proton monitors and INGRID, MUMON is used tomonitor the muon beam intensity and direction. Only MUMON can monitor the beam on abunch-by-bunch basis at downstream of the graphite target, and then its stable operation andquick trouble shooting are essential to stable data taking.
MUMON consists of two arrays of detectors, silicon PIN photodiodes (Si; Hamamatsu
S3590-08) and ionization chambers (IC; Ar+N2 or He+N2 ) [69], and the Si array lies upstreamof the IC array. The schematic view is given in Figure 3.10. Each array covers a 150 × 150 cm2
region by 7×7 channels with a 25 cm interval between each. The sensor waveforms are sampledwith a 65 MHz Flash-ADC. The current MUMON has been running since the beginning of theT2K operation [74]. By May of 2019, T2K has accumulated data with 1.51 × 1021 POT in the
FHC mode and 1.65 × 1021 POT in the RHC mode. J-PARC has been increasing its beam
power throughout the experimental operation, as shown in Figure 3.11.

SiIC

muon beam

Figure 3.10: Schematic illustration of the T2K muon monitor.

Figure 3.12 shows the beam measurement results by MUMON and INGRID over the T2K
operation periods until May of 2019. The beam direction is stable within a 0.3 mrad requirement[74]. Figures 3.13 and 3.14 give the measured muon beam center and width by MUMON foreach MR operation period. The beam width is smaller in RHC than FHC due to diﬀerencein the kinematics of the parent hadrons. MUMON is also essential to understand the beam
properties such as relationships of muon beams with proton beams and horn conditions. These
measurements have been performed, contributing to the operation. The results can be foundin Appendix A. The current MUMON detectors have several issues with their performances
under the high intensity beam irradiation and these are investigated. In addition, a new detector
based on an electron-multiplier tube is studied for the future operation with further high power
beams [75, 76]. These studies are described in Appendix B.

CHAPTER 3. T2K EXPERIMENT

37[mrad][events/1e14 POT]

Figure 3.11: History of the accumulated POT and the J-PARC beam power over the T2K
Run 1−9 operation period.

1.8
1.6
1.4
1.2
1
0.8 Event rate
0.6
0.4
0.5

Horn250kA
Horn205kA
Horn-250kA

Horizontal beam direction

INGRID
MUMON

Vertical beam direction

INGRID
MUMON

Day

0

[mrad]

−0.5
−1
0.5
0
−0.5
−1

T2K Run1

T2K Run2

T2K Run3

Jan.2010-Jun.2010 Nov.2010-Mar.2011Mar.2012-Jun.2012

T2K Run5 T2K Run6

T2K Run7

T2K Run8

T2K Run9

T2K Run4

May.2014

Feb.2016-May.2016

Oct.2016-Apr.2017

Oct.2017-May.2018

Oct.2012-May.2013-Jun.2014

Oct.2014-June.2015

Day

Figure 3.12: INGRID and MUMON beam measurements of the event rate and beam directions
over the T2K Run 1−9 operation period.

CHAPTER 3. T2K EXPERIMENTSi X Center [cm]Horizontal Center
538

Si XXCenter+ Si
CenterIC XXCenter+ IC
Center

4
3
2
1
0
−1
−2
−3
−4
−5

Si Y Center [cm]

5

+MRSi
Center
SiRun#YYCenterIC YYCenter+ IC
Center

29 30 31 32 33 34 36 37 38 41 42 43 44 45 46 47 48 49 55 56 58 59 60 61 62 63 66 67 68 70 71 72 73 74 76 77 78 79

Vertical Center

4
3
2
1
0
−1
−2
−3
−4
−5

29 30 31 32 33 34 36 37 38 41 42 43 44 45 46 47 48 49 55 56 58 59 60 61 62 63 66 67 68 70 71 72 73 74 76 77 78 79

MR Run#Figure 3.13: Muon beam center in horizontal (top) and vertical (bottom) directions measured
by MUMON Si and IC in each J-PARC MR run. T2K was operated with no horn current
application in MR Run 41, showing the large error.

CHAPTER 3. T2K EXPERIMENT

39

Si X Width (FHC)Si X Width [cm]Horizontal Width
120

115

X Width (FHC)+ Si XICWidth(FHC)
Si X Width (RHC)X Width (RHC)+ IC XICWidth(FHC)+ Si X Width (RHC)+ IC X Width (RHC)

110

105

100

95

90

Si Y Width [cm]Vertical Width
135

130

+ Si Y Width (FHC)Run#
Y Width (FHC)+ IC MRYICSiWidth(FHC)
Y Width (RHC)IC Y Width (RHC)+ Si Y Width (RHC)+ IC Y Width (RHC)

29 30 31 32 33 34 36 37 38 41 42 43 44 45 46 47 48 49 55 56 58 59 60 61 62 63 66 67 68 70 71 72 73 74 76 77Si78
79
Y Width
(FHC)

125

120

115

110

105

100

29 30 31 32 33 34 36 37 38 41 42 43 44 45 46 47 48 49 55 56 58 59 60 61 62 63 66 67 68 70 71 72 73 74 76 77 78 79

MR Run#Figure 3.14: Muon beam width in horizontal (top) and vertical (bottom) directions measured
by MUMON Si and IC in each J-PARC MR run. T2K was operated with no horn current
application in MR Run 41, showing the narrow beam. The beam width in RHC is smaller
than that in FHC, which is attributed to diﬀerence in the momentum of the parent hadrons.
Since the parent hadrons are produced by protons, the number of particles are likely to belarger when the negative hadrons, which are the parents of antineutrinos, are made. Therefore,
the momentum of each particle, including the negative hadron, is likely to be smaller andaccordingly those hadrons are easier to focus in RHC, contributing to the narrower beam.

CHAPTER 3. T2K EXPERIMENT

3.5

40

Data Set

In the analysis, data from T2K Runs 1−9 with 14.94 × 1020 POT in the FHC mode and16.35 × 1020 POT in the RHC mode, which have passed the quality check based on the beamand detector conditions, are used. The detailed information of each run is summarized inTable 3.1 with the operation period, the operation mode (FHC or RHC), and the accumulated
POT.
Table 3.1: Summary on the T2K runs with the operation period, the operation mode, and theaccumulated POT for the good spills used in the analysis.
T2K Run#
1
2
3b
3c
4
5a

Operation Mode
FHC
FHC
FHC
FHC
FHC
FHC

5b

FHC

5c

RHC

6a

FHC

6b

RHC

6c
6d

RHC
RHC

6e

RHC

6f
7a
7b
7c
8
9a
9b
9c
9d
Total
Total

FHC
FHC
RHC
FHC
FHC
FHC
RHC
RHC
RHC
FHC
RHC

Start Date
End Date POT [×1019 ]23rd, Jan., 2010 26th, Jun., 2010
3.26
18th, Nov., 2010 11th, Mar., 2011
11.22
8th, Mar., 2012 22nd, Mar., 2012
2.17
8th, Apr., 2012
9th, Jun., 2012
13.82
19th, Oct., 2012
8th, May., 2013
35.97
21st, May., 2014 29th, May., 2014
0.66
29th, May., 2014
3rd, Jun., 2014
1.78
24th, Jun., 2014 26th, Jun., 2014
4th, Jun., 2014 24th, Jun., 2014
5.12
2nd, Nov., 2014
4th, Nov., 2014
12th, Jan., 2015 16th, Jan., 2015
1.03
25th, Feb., 2015 27th, Feb., 2015
4th, Nov., 2014 25th, Nov., 2014
13.04
29th, Nov., 2014 22nd, Dec., 2014
27th, Feb., 2015 12th, Mar., 2015
5.25
12th, Mar., 2015
1st, Apr., 2015
7.89
8th, May., 2015 20th, May., 2015
9.29
22nd, May., 2015
1st, Jun., 2015
1st, Jun., 2015
3rd, Jun., 2015
0.89
1st, Feb., 2016
3rd. Feb., 2016
0.89
3rd, Feb., 2016 18th, May., 2016
34.99
19th, May., 2016 27th, May., 2016
3.96
27th, Oct., 2016 12th, Apr., 2017
71.70
17th, Oct., 2017 22nd, Oct., 2017
2.04
22nd, Oct., 2017
6th, Dec., 2017
26.53
6th, Dec., 2017 22nd, Dec., 201710.25
9th, Mar., 2018 31st, May., 2018
51.10
149.38163.46

Chapter 4
Super-Kamiokande
In this chapter, the Super-Kamiokande detector, the detector simulation, the event reconstruction, and the detector calibrations are described. Descriptions in this chapter are importantalso for the SRN analysis in Part IV.

4.1

Overview of Super-Kamiokande

Super-Kamiokande (SK) is a cylindrical water Cherenkov detector, a schematic view of which isshown in Figure 4.1, and is located 1,000 m under Mt. Ikeno in Kamioka, Gifu of Japan. Thislocation provides an environment with a depth of 2700 m-water-equivalent (m.w.e.), where only
cosmic-ray muons with energies above 1.3 TeV can reach the detector. The cosmic-ray muon
flux as a function of depth is shown in Figure 4.2. At SK, the muon rate is about 2 Hz.
-3

10

-4

Crouch World Survey, 1987
Crookes and Rastin, 1973
Bergamasco et al., 1971
Stockel, 1969
Castagnoli et al., 1965
Avan and Avan, 1955
Randall and Hazen, 1951
Bollinger, 1950
Clay and Van Gemert, 1939
Wilson, 1938

Soudan 2
Minos

10

-5

10

-6

Intensity (cm-2 s -1 sr -1)

10

-7

10

-8

10

-9

10

IMB
-10

10

Gran Sasso
Homestake-11

10Super-Kamiokande

π,K-muonsνπ,K-muons + I µ

-12

10

ν

I µ = 2.17x10

-13

10

0

Figure 4.1: Schematic illustration of theSuper-Kamiokande detector [77].

2

4

-13

cm -2 s-1 sr -1

6

8

10

12

14

16

18

Depth (103 hg cm-2 )Figure 4.2: Cosmic-ray muon flux as a function of
depth [77]. The unit 103 hg/cm2 is equivalent tokm.w.e. The depth of SK is 2700 m.w.e.

41

CHAPTER 4. SUPER-KAMIOKANDE42

The detector structure is separated into two regions, the inner detector (ID) and the outerdetector (OD). The 20 inch and 8 inch photomultiplier-tubes (PMTs) are implemented to detect
Cherenkov light from charged particles in each region, respectively. The whole detector is filledwith 50 kton ultra pure water. A variety of physics programs are provided in SK: neutrino
oscillation measurements with atmospheric neutrinos, solar neutrinos, and accelerator neutrino
beams, searches for physical phenomena beyond the Standard Model such as proton decay anddark matter, and astronomical object studies via detections of neutrinos, for example, fromsupernovae and the Sun.
SK started its operation in April 1996 and has been running in five separate run periods
so far. The operation period for the first five years until July of 2001 is called “SK-I”, andsome bad PMTs were replaced with new ones during the shutdown after this period. It was
followed by the accident that nearly half of PMTs had been broken due to a chain reactionof shock wave. The operation was restarted as “SK-II” with approximately 5,000 ID PMTs.
Each PMT is protected by a fiber reinforced plastic cover to avoid further destructions. These
new PMTs were installed and data taking was resumed and continued until September of 2008.
This operation period is referred to as “SK-III”. The fourth stage of the SK operation, “SKIV”, started with the new electronics which enables to store data longer after a primary eventand then activates the neutron tagging analysis, as described later. In 2018, the SK tankunderwent the refurbishment. After the tank refurbishment work, the operation started andhas been running as of January 2020, which is termed as “SK-V”. The properties in each
operation period are summarized in Table 4.1. In the analyses in this thesis, data from SK-IV
are used, therefore the descriptions in the following part focus on the system in SK-IV.
Table 4.1: Properties of the five SK operation periods.
Phase
Start
End
Live time [days]
Number of ID PMTs
ID PMT coverage
Number of OD PMTs
PMT protection
Neutron tagging
Threshold [MeV]

4.2

SK-I
SK-II
SK-III
Apr., 1996 Oct., 2002 Jul., 2006
Jul., 2001 Oct., 2005 Aug., 2008
1496
791
548
11,146
5,182
11,129
40%
19%
40%
1,885
1,885
1,885
No
Yes
Yes
No
No
No
4.5
6.5
4.0

SK-IV
Sep., 2008
May., 2018
2970
11,129
40%
1,885
Yes
Yes
3.5

SK-V
Jan., 2019(running)
11,129
40%
1,885
Yes
Yes
3.5

Detection Principle

Observable in SK is Cherenkov light emitted from the charged particle passing through thedetector at a speed faster than the speed of light in water. The momentum threshold for
the Cherenkov radiation depends on the particle type, for example, 0.57 MeV/c for electrons,
118 MeV/c for muons, 156 MeV/c for charged pions, and 1051 MeV/c for protons. Cherenkov
photons are emitted in a cone shape with a half opening angle (θ), referred to as Cherenkov
opening angle which is related to the speed of the particle (β = v/c; v and c are the speeds ofthe charged particle and light, respectively) and the refractive index (n) as cos θ = 1/nβ. In
water (n ∼ 1.33) the Cherenkov angle is θ ∼ 42◦ for suﬃciently relativistic particles (β ∼ 1).

CHAPTER 4. SUPER-KAMIOKANDE43The Cherenkov photons then reach the wall and are detected by the PMTs, forming ringpatterns. The ring pattern looks diﬀerent by the particle type, the particle momentum, themultiplicity, and so on. For example, the electron-induced ring is likely to be fuzzier than the
muon-induced ring because of electromagnetic cascades. Figure 4.3 gives an example of theCherenkov ring observed in SK.

Super-Kamiokande IV
Run 77472 Sub 279 Event 285409251
18 -01-2 0:05:3 5:14
I nner : 1164 hi t s, 3559 pe
Out er : 1 hi t s, 1 pe
Tr i gger : 0x10000007
D_wal l : 436. 3 cm
Evi s: 394. 7 MeV
mu- l i ke, p = 556. 2 MeV/ cChar ge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

380

0 mu- edecays

304
228
152
76
0
0

500

1000

1500

2000

Times (ns)Figure 4.3: An example of the Cherenkov ring pattern in SK. Each pixel corresponds to the
PMT and the color scale denotes the detected charge amount.

4.3

Detector Components

4.3.1

Water Tank

The SK detector is subdivided into the ID and OD parts with a support structure between
them, which is shown in Figure 4.4. The ID measures 33.8 m in diameter and 36.2 m in height,
containing 32 kton water, and is instrumented with 11,129 20 inch PMTs on the wall supportedby the structure in Figure 4.4. The PMT coverage in the ID is about 40%. The OD region isabout 2 m thick between the support structure and the tank surface. There are 1,885 8 inch
outward-facing PMTs equipped on the back side of the ID wall. The OD is used to issue a vetofor the cosmic-ray muon events.

4.3.2

Photomultiplier Tubes

The 20 inch PMTs (R3600) were produced by Hamamatsu Photonics K.K. and optimized for theexperiment [77, 78]. The schematic view of the PMT is given in Figure 4.5. The photocathodeis made of bialkali (Sb-K-Cs) and the dynode is the 11-stage Venetian blind type. With a highvoltage application of ∼2000 V, the gain is about 107 . The quantum eﬃciency is wavelengthdependent as shown in Figure 4.6, being the most sensitive to around 360 nm (∼21%). The
single photoelectron (p.e.) distribution is clearly seen, as shown in the left panel of Figure 4.7.

CHAPTER 4. SUPER-KAMIOKANDE

44

Figure 4.4: Schematic illustration of the PMT support structure in SK [77].

~ 70000

cable length
φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure( 610 20 )

~ 720

(mm)

Figure 4.5: Schematic cross sectional view of the SK 20 inch PMT (Hamamatsu R3600) [77].

CHAPTER 4. SUPER-KAMIOKANDE

45

Quantum efficiency

The transit time spreads by about 2.2 ns, as shown in the right panel of the same figure. Afterthe accident in 2001, the fiber reinforced plastic (FRP) cover was installed to each ID PMT.
The acrylic surface of the cover is more than 96% transparent to light with wavelength above
350 nm.
The 8 inch PMTs are used in the OD. There are two types: 591 R1408 PMTs from the IMB
experiment [79] and 1,293 R5912 PMTs that were newly installed after the accident in 2001.

0.2

0.1

0

300

400

500

600

700

Wave length (nm)Figure 4.6: Quantum eﬃciency of the SK 20 inch PMT as a function of wavelength [77].

Figure 4.7: Distribution of single photoelectron pulse height (left) and relative transit timewith 410 nm wavelength light at the single p.e. level (right) for the SK 20 inch PMT [77].

4.3.3

Helmholtz Coils

To reduce the eﬀect of the geomagnetic field on the collection of photoelectrons in PMTs, 26
sets of Helmholtz coils are installed, around the water tank [80]. The currents of the Helmholtz
coils are monitored real time. The original magnetic field, which was measured before SK-I,
was ∼450 mG while the average field with the coil operation is 32 mG.

CHAPTER 4. SUPER-KAMIOKANDE

4.3.4

46

Water and Air Systems

12t/h

36t/h

60t/h

Temperature (degrees)

Water is one of the most essential parts in the experiment because the water quality aﬀects the
Cherenkov photon propagation. Water is originally taken from the two streams in the Kamioka
mine and then purified and circulated by a dedicated system. The purified water is circulatedwith a flow rate of 60 ton/hour. The left panel of Figure 4.8 shows a schematic diagram of thewater circulation system. With this system water is supplied in the bottom region and drainedin the top region. Usually water is well convecting below the vertical position of −11 m (theID center is set to the origin of the coordinate). In this region the temperature is then uniform;
however, it rises gradually above this level, as shown in the right panel of Figure 4.8. Thisvariance results in a 5% diﬀerence in the water transparency over the ID detector.

13.3
13.25
13.2
13.15
13.1
-15 -10 -5

12t/h

0

5

10 15

z (m)

Figure 4.8: Schematic diagram of the water circulation system in SK-IV (left) and the watertemperature as a function of the ID vertical position (right) [80].
In the low energy analysis, including the works reported in this thesis, reducing radioactive
impurities in the water, especially radon, is important. The radon concentration in the supply
water is reduced by the water purification system down to 1.83±0.31 mBq/m3 . In addition, theair purification system is being operated to prevent radon dissolving into the purified water [81].

4.4Data Acquisition System in SK-IV

As mentioned before, the front-end electronics was upgraded in SK-IV to QTC-Based Electronics with Ethernet (QBEE) [82]. Since then the SK has been operated with QBEE.

4.4.1

Front-End Electronics: QBEE

The main parts of the QBEE module are the QTC (charge-to-time converter) and TDC (timeto-digital converter). Eight QTCs are put on each QBEE board and each QTC processes datafrom three PMTs. The charge dynamic range is from 0.2 to 2500 pC, and each channel has
three diﬀerent gains, the relative ratios of which are 1 : 1/7 : 1/49, corresponding to the large,
medium, and small gains, respectively. Figure 4.9 shows a block diagram of the QTC for theCHAPTER 4. SUPER-KAMIOKANDE47

PMT signal readout and its surroundings. The block diagram for one QTC channel is shownin Figure 4.10.

Figure 4.9: Block diagram of the QTC and its surrounding parts [82].

Pedestal
DSC (Large)
DSC (Medium)
Discriminator (DSC)

CAL
LNA
protection
diode
impedanceadjusting

+

Input

DAC

Attenuator

Small

LNA

Termination
Resistor

MediumLarge

HITTimer Block

Charging Timer
Discharging
Timer

LPF
(delay)LPF

DSC Qtrg
Logic
VETO

VETO
Timer
Charging andDischarging Block
D

Q
Q
CLR

V/I
Converter
PMTSUMDAC

DSC

DSC Logic

Charging Timer

LPF

V/I

DAC

LVDS

Comparator

Discharging Timer

Charging and Discharging BlockLVDS

PMTSUM

LNA

DSC

DSC Logic

LPF

V/I
PMTSUM

Charging Timer

Discharging Timer
LVDS

Charging and Discharging Block

PMTSUM

Figure 4.10: Block diagram of one QTC channel [82].

The timing chart in the QTC operation is shown in Figure 4.11. After the QTC is triggeredby the discriminator, it opens a charge gate spanning 400 ns, and is followed by a discharge
gate with a 350 ns window. The time consumed for processing one signal is about 900 ns in
total.

CHAPTER 4. SUPER-KAMIOKANDE

48

Figure 4.11: Timing chart for the QTC operation [82].

4.4.2

Triggers

A variety of triggers are prepared in SK-IV, depending on the number of hit PMTs within a
200 ns time window, defined as N200 , and other special conditions. The trigger types are thesuper-low energy (SLE), low energy (LE), high energy (HE), super-high energy (SHE), outerdetector (OD), after-window (AFT), and T2K triggers. When N200 exceeds pre-determinedthresholds, which are summarized in Table 4.2, the corresponding trigger is issued. Dependingon the trigger type, a data taking window is diﬀerent. For example, the SHE trigger opens
a 40 µs window (5 µs before and 35 µs after the trigger timing, respectively) to store data.
The similar counting is conducted for the OD PMTs and the OD trigger is issued if N200 for
the OD PMTs exceeds 22. The AFT trigger is specially tailored to the neutron tagging andproduced when the SHE trigger is issued but the OD trigger is not, extending the data storing
window up to 535 µs from the SHE trigger point. The T2K trigger is made when the beam ison and stores data for about 1 ms 1 . In this thesis, data with the T2K triggers are used for the
NCQE-like measurement and data with the SHE+AFT triggers are used for the SRN search.

1

Even when the beam is oﬀ, the T2K trigger is sometimes issued to take data for the neutron tagging analysis
as explained later in Chapter 10.

CHAPTER 4. SUPER-KAMIOKANDE

49

Table 4.2: Summary of the SK triggers. The numbers in the second column are the number of
hit PMTs within a 200 ns window (N200 ).
Trigger Type
SLE
LE
HE
SHE
OD
AFT
T2K

4.5

Threshold34 → 31 (after May of 2015)47
50
70 → 58 (after September of 2011)
22 (in OD)
SHE + no OD
Beam onTime Window [µs][−1.5, +1.0][−5, +35][−5, +35][−5, +35][−5, +35][+35, +535][−500, +535]

Detector Simulation

Interactions and transport of particles, generation and propagation of Cherenkov photons inwater, and the PMT and electronics responses are simulated by a dedicated Monte Carlo (MC)package. Details can be found in Ref. [83].
The physics process is based on GEANT3 ver. 3.21 [84]. As mentioned in Chapter 9,
hadronic interactions are simulated by GCALOR [85,86]. For the low momentum (<500 MeV/c)pion interaction, a custom model [87] based on experimental data of the π-16 O interaction [88]and the π-p interaction [89] is implemented.
For the charged particles, Cherenkov photons are generated following the equation below:
d2 N
2πα
=
dxdλ
nλ2

(
1−

1
n2 β 2),(4.1)

where N represents the number of generated Cherenkov photons, λ is wavelength of the photon,
n is the refractive index, α is the fine structure constant, β is the velocity of the charged particle
in water in a unit of the speed of light in vacuum, and x is the traveling length. Since n
depends on various environmental factors, such as the wavelength, the water temperature, andthe water pressure, their measurement results are used in the simulation. Here only photons
whose wavelengths are between 300 and 700 nm (the PMT sensitive range) are generated.
The generated Cherenkov photons are then transported in water with the eﬀects of scatteringand absorption. The probability for each process is implemented depending on the watertransparency. The Rayleigh and Mie scatterings are taken into account here. At the wall of
the tank, the reflection of Cherenkov photons is implemented. Further details can be found in
Ref. [81].
The charge and timing responses of PMTs and the electronics are also simulated so that
the MC provides the same data structure as the observed data. This enables to compare theMC outputs directly to the observed data.

CHAPTER 4. SUPER-KAMIOKANDE

4.6

50

Low Energy Event Reconstruction

There are various types of reconstruction tools for the SK analysis. For the reconstruction of
low energy events (≲80 MeV), a dedicated tool is used 2 .

4.6.1

Vertex and Direction Reconstructions

The vertex position is reconstructed using the timing information of hit PMTs. Since low
energy electrons and positrons travel only a short distance, for example, ∼10 cm at 20 MeV,
the tracks are treated as point-like sources. The timing residual of each hit PMT is defined ast − ttof − t0 , where t is the hit timing, ttof is the time-of-flight (TOF) from the vertex position
to the hit PMT, and t0 is the time of the interaction which is treated as a free parameter. The
likelihood function is defined as:

L(x, t0 ) =Nhit∑

log P (t − ttof − t0 ),

(4.2)

i=1

where x represents the testing vertex position and P (t − ttof − t0 ) is the probability density
function of the timing residual for a single photoelectron signal which is extracted from the
LINAC calibration, as shown in Figure 4.12. With the maximum likelihood fitting based on
this, the vertex position and t0 are determined. The vertex resolution, a 1σ diﬀerence between
the true and reconstructed positions, as a function of electron energy is shown in Figure 4.13.

t – ttof – t0 [ns]Figure 4.12: Probability density function for the timing residual (t − ttof − t0 ) obtained by the
LINAC calibration. Peaks at around 40 ns and 110 ns are the PMT after-pulses.
The event direction is reconstructed using information on the Cherenkov ring pattern. Thisis performed by maximizing the following likelihood:2

Another tool made for proton decay and atmospheric neutrino analyses also treat events below 80 MeV.

Vertex Resolution (cm)CHAPTER 4. SUPER-KAMIOKANDE

51

250
SK-IV

200
150
100
50
0

5

7.5
10
12.5
15
True Electron Energy (MeV)

Figure 4.13: Vertex resolution as a function of electron energy in SK-IV. The figure is takenfrom Ref. [81].

L(d) =

N20∑

log f (cos θi , E) ×

i=1

cos θi,a(θi )(4.3)

where N20 is the number of hit PMTs within a 20 ns timing window around t − ttof − t0 = 0,
d is the event direction, f (cos θi , E) is the expected distribution of the opening angle between
the true event direction and the observed direction where E is the event energy, θi is thereconstructed event direction, and a(θi ) is the correction for the PMT acceptance. The angularresolution is 25◦ for the 10 MeV electrons.
With reconstructed event vertex and direction, two parameters which are used in the analysis
are defined, dwall and eﬀwall: dwall represents the distance from the reconstructed vertex tothe closest ID wall and eﬀwall is the distance from the reconstructed vertex to the ID wallas measured backward along the reconstructed direction. Schematic illustration for these twoparameters is given in Figure 4.14.
The fit quality parameters, gvtx and gdir , are obtained and used in the analysis. The vertex
quality parameter, gvtx , is defined as:∑
gvtx =∆ti− ()
ie 2 σ
i w∑
i wi
1

2

1
with wi = −
2

(

∆ti
ω

)2
,

(4.4)

where ∆ti = tres,i − t0 (tres,i : the timing residual of an event for the i-th hit PMT, t0 : the fit
value minimizing all tres,i ), and wi is the weight for the i-th hit PMT to reduce the dark noise.
The ω and σ are set to 60 ns and 5 ns, respectively. The summation above is conducted over all
hit PMTs, satisfying |∆ti | < 50 ns for the numerator and |∆ti | < 360 ns for the denominator.

CHAPTER 4. SUPER-KAMIOKANDE52

SK Outer Detector
SK Inner Detector

all

Reconstructedvertex

w
eff

dwall
Reconstructed
direction

Figure 4.14: Schematic illustration for definitions of dwall and eﬀwall.
The angular quality parameter, gdir , is evaluated by using the spatial uniformity of hit PMTs
based on the Kolmogorov-Smirnov test:

gdir =

maxi {∠uni (i) − ∠data (i)} − mini {∠uni (i) − ∠data (i)}
,
2π

(4.5)

where ∠data (i) is the azimuthal angle of the i-th hit PMT in data which is included in thesliding 50 ns window (N50 ) and ∠uni (i) = 2πi/N50 is the azimuthal angle of the i-th hit PMTin the toy simulation when the uniform distribution is assumed. The gvtx value increases as
the timing distribution becomes sharper, while gdir decreases as the space distribution becomes
more uniform. With these two parameters, a new quality parameter (ovaQ) is defined as
22
ovaQ = gvtx
− gdir. The larger ovaQ corresponds to sharper in time and more uniform in space
for an event. This is used to discriminate the low energy background.

4.6.2

Energy Reconstruction

For the energy reconstruction, the eﬀective number of hits (Neﬀ ), which is defined below, is
used.

Neﬀ =

N50 [
∑
i=1

Nall
Rcover(Xi + ϵtail − ϵdark ) ××× exp
Nnormal S(θi , ϕi )

(

ri
λrun

)

]
1
×
.
QEi

(4.6)

Here N50 is the number of hit PMTs within a 50 ns timing window. Other parameters are
explained in the following.
• Occupancy (Xi ): The energy reconstruction is conducted assuming the number of hits
in one PMT is single in the low energy region. This assumption breaks down at higher

CHAPTER 4. SUPER-KAMIOKANDE

53

energies. When a PMT detects multiple photons, the surrounding PMTs are likely tohave hits. The term Xi is used for estimating the multiple photoelectron eﬀect for thei-th PMT, defined as:
{
Xi =

(
log
3.0

1
1−xi

)
(xi < 1)(4.7)

(xi = 1)

where xi represents the ratio of the number of hit PMTs to the total number of PMTs ina 3 × 3 patch around the i-th hit PMT.
• Late hits (ϵtail ): Some Cherenkov photons arrive late due to scattering and reflection andthen are not detected during the 50 ns window. This is corrected by the term ϵtail .
• Dark noise (ϵdark ): The dark noise contribution is subtracted from the occupancy.
• Correction for the dead PMTs (Nall /Nnormal ): Some PMTs may not be working properly
depending on the period. This is corrected by the term Nall /Nnormal , where Nall and
Nnormal are the numbers of all and properly working PMTs, respectively.
• Correction for the PMT coverage (Rcover /S(θi , ϕi )): The eﬀective photocathode area isrepresented by S(θi , ϕi ) (θi : the incident angle, ϕi : the azimuth angle), and the acceptanceof the PMT is corrected by Rcover .
• Correction for the water transparency (ri /λrun ): The correction about the water transparency (λrun ) is added for the event located at distance ri from the i-th PMT to thevertex.
• Correction for the PMT quantum eﬃciency (1/QEi ): The last correction term is about
the quantum eﬃciency of PMTs.
The relation between the eﬀective number of hits and the reconstructed visible energy is shownin Figure 4.15. A linearity better than ±0.5% is achieved in the energy region 0−80 MeV. In
the analyses in this thesis, the eﬀect of the PMT gain shift over the SK-IV period (shown in
Chapter 7) is not corrected, but the systematic error regarding this is estimated.

4.6.3

Cherenkov Angle Reconstruction

A Cherenkov opening angle (θC ) for each event is reconstructed as the most frequently occurring
value in the distribution of opening angles by all three-hit (triplet) combinations of the hit PMTs
within a 15 ns timing window. The distributions of angles formed by the triplet hits are shownin Figure 4.16 for typical events. The Cherenkov angle is characterized by the event topology
and then used to identify the particle type. The electron and single γ-ray events tend to haveθC ∼ 42◦ , while the multiple-γ events have higher angles. In the current low energy region,
muons are not so relativistic as to have 42◦ but instead show lower angles.

(UHF>0H9@

CHAPTER 4. SUPER-KAMIOKANDE

54

80
70

MC generated
Fitted

60
50
40
30
20
10
0
0

100

200

300

400

500

600
Neff

Ratio

1.005
1.004
1.003
1.002
1.001
1
0.999
0.998
0.997
0.996
0.995
0

100

200

300

400

500

600
Neff

Figure 4.15: Relation between the number of eﬀective hits (Neﬀ ) and the reconstructed visibleenergy (Erec ) for generated electrons in MC and the linear fitting result (top) and the ratio of
the MC and the fit values (bottom).

10000

41.4°

2500

33.3°

e-likemu-like

8000

3000

gamma-like

2500

2000

87.3°
2000

6000

1500

1500

4000

1000

1000

2000

500

0
0

10

20

30

40

50

60

70

80 90
Degree

0
0

500

10

20

30

40

50

60

70

80 90
Degree

0
0

10

20

30

40

50

60

70

80 90
DegreeFigure 4.16: Distributions of opening angles by all three-hit combinations of the hit PMTs forthe e-like (left), µ-like (middle), and multiple-γ-like (right) event, respectively. The blue lines
and numbers indicate the most frequent values which are taken as the reconstructed Cherenkov
angles.

CHAPTER 4. SUPER-KAMIOKANDE

4.7

55

Detector Calibration

SK is calibrated in various ways. Here they are overviewed, and more details can be found in
Refs. [77, 80, 90, 91].

4.7.1

PMT Calibration

The absolute gain is applied to all PMTs in common to convert the number of photoelectrons
into the charge. The applied high-voltages to PMTs were determined at the beginning of
the SK-III using a Xe light source. A Ni-Cf source is used for the calibration. The absolute
gain is determined from the distribution of the average charge of single photoelectron to be
2.645 pC/p.e. in SK-IV.
The relative gains are measured using high and low intensity lights. The charge detectedby the i-th PMT (Qiobs ) in the high intensity measurement is expressed as:i
Qiobs ∝ Ihigh
× QE i × Gi ,

(4.8)

i
where Ihighis the light intensity seen from the i-th PMT, and QE i and Gi are the quantum
eﬃciency and the relative gain of the i-th PMT, respectively. In the low intensity measurement,
the number of observed hits (Nobs ) is expressed as:

i
i
Nobs
∝ Ilow
× QE i ,(4.9)

iwhere Ilowis the light intensity seen from the i-th PMT. Using Equations 4.8 and 4.9:

i
Qiobs
Ilow
G = i × i .
Nobs Ihighi(4.10)

Here the light attenuation and geometric eﬀects are all cancelled out. The measured relative
PMT gains fluctuate within 6%.
The relative timings of the PMTs are measured using a laser. A N2 laser beam is injectedfrom the center of the ID tank, as shown in the left panel of Figure 4.17. In the same figure,the two-dimensional plot of the timing versus charge is shown.

4.7.2

Water Transparency Measurement

The water transparency is measured in two ways. The absorption and scattering parameters
are independently measured using the N2 laser, and the eﬀective attenuation length is measured
using the decay electrons from cosmic-ray muons. The measured eﬀective attenuation lengthof photons in the water is around 140 m and is stable within 15% in SK-IV.

CHAPTER 4. SUPER-KAMIOKANDE

56

4 S&

WTPDSRIFDEOH          













7 QV











(QWULHV 






























4%LQ

Figure 4.17: Schematic illustration for the timing calibration (left) and the 2D distributionof the charge and timing (right). The QBin in the lower horizontal axis of the right panel isdefined as: QBin = 5Q (0 < Q < 10) or QBin = 50 · log10 Q (10 < Q < 3981). The figures aretaken from Ref. [80].

4.7.3Energy Calibration

The energy scale calibration is performed in three independent ways: LINAC [90], DT generator [91], and decay electrons.
An electron linear accelerator (LINAC) is equipped on the top of the SK tank. It injects
downward-going mono-energetic electron beams into the SK tank. The electron energy isavailable up to ∼19 MeV and is measured within a ±20 keV precision by a germanium detector.
Several positions are taken as injection points to study the position dependence. Figure 4.18
shows comparison of the LINAC data with the corresponding MC. The absolute energy isdetermined by LINAC with an accuracy better than 1%.

Data
MC

Figure 4.18: Distributions of reconstructed energies for the diﬀerent energy settings in the
LINAC 2010 data. The figure is taken from Ref. [92].

CHAPTER 4. SUPER-KAMIOKANDE

57

A deuterium-tritium (DT) neutron generator is used to provide a cross check in the energy
scale calibration. The 6.1 MeV γ-rays are isotropically emitted and used as a calibration point.
This is conducted every a few months. In the DT calibration, the direction dependence is alsomeasured and it is found that a directional bias is less than 1%. Another calibration source isdecay electrons from cosmic-ray muons. With this sample, the energy scale up to ∼60 MeV
can be calibrated.
Through the calibrations explained above, the absolute energy scale had been monitored
and found to be stable better than 1% in the SK-IV period, as shown in Figure 4.19. Notethat the PMT gain shift eﬀect is corrected here. This causes an additional a few % error on
the energy scale, as is explained in Chapter 7.

Effective hit

275
274
273
272
271
270
269
268
267
266
265 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Year

Figure 4.19: The Neﬀ distribution as a function of time in the SK-IV period measured using the
decay electron sample. The blue and red dashed lines indicate the average and ±0.5% deviatedvalues, respectively. Here the eﬀect of the PMT gain shift is corrected.

Chapter 5
Event Simulation
The MC simulation is essential to determine the selection criteria and to estimate the uncertainties. The simulation in this analysis considers the models of neutrino flux, neutrino interaction,
γ-ray emission, and detector response.

5.1

Neutrino Flux

As described in Chapter 3, the neutrino beam is produced from the proton reactions on thegraphite target, and this is simulated by FLUKA ver. 2011.2c.6 [93]. Here the proton beam
properties, such as energy, position, and width, reflect the measurement results by the ESM,
SSEM, and OTR. The hadron interaction cross sections are renormalized using data from theNA61/SHINE experiment [94–98], where the protons with the same energy are incident on thegraphite target and the kinematics of the out-going hadrons is measured. The experiments
were conducted with diﬀerent graphite target configurations: thin targets and the T2K replicatarget. In the present work, both data are used for the renormalization. Transport and decayof the particles are simulated by GEANT3 [84]. Figure 5.1 shows the flux predictions at SK
without neutrino oscillations.
T2K Run 1-9 Flux at SK (RHC)106

Flux [/cm2/50-MeV/1021-POT]

Flux [/cm2/50-MeV/1021-POT]

T2K Run 1-9 Flux at SK (FHC)

νµ
νµ
νe
νe

105

104

103

0

6

10

νµ
νµ
νe
νe

5

10

104
103
102

2

4

6

0

8
10
Eν [GeV]

2

4

6

8
10
Eν [GeV]Figure 5.1: T2K neutrino flux predictions at SK in the FHC (left) and RHC (right) modes.
Here the neutrino oscillations are not considered.

58

CHAPTER 5. EVENT SIMULATION

5.2

59

Neutrino Interaction

The neutrino-nucleus interaction and the final state interaction inside the nucleus are simulated by the neutrino event generator NEUT ver. 5.3.3 [99]. For the NCQE interaction, thespectral function model by Benhar et al. [100, 101] is used as the nucleon momentum distribution inside the nucleus, while the relativistic Fermi gas model by Smith-Moniz [102] is used
for the CCQE interaction. CC 2p2h interactions are simulated based on the model by Nieves
et al. [103], but the NC counterpart is not simulated since there is no calculation available in
the literature. To describe the vector form factor and the axial-vector form factor, BBBA05
and dipole parametrizations [62, 104] are used, respectively. For the single pion production
via baryon resonance, the Rein-Sehgal model [105] with some modifications is used. Deep inelastic scattering is simulated using the GRV98 parton distribution [106] corrected by Bodek
and Yang [107]. The nominal NEUT settings about neutrino interaction parameters in thisanalysis are summarized in Table 5.1. Here the errors of each interaction parameter, which areused later in the systematic error estimation, are also shown. Figure 5.2 gives the NCQE crosssection in NEUT for neutrinos and antineutrinos. The final state interactions are simulatedwith a cascade model [18,99]. Further details about the neutrino-nucleus interaction simulation
are given in Ref. [18].
Table 5.1: Neutrino interaction parameter settings in NEUT for the nominal MC production.
Errors of each parameter are also shown. Note that the definition of “NC other” here is diﬀerent
from “NC-other” elsewhere in this thesis.
Parameter
Mean value
Error
QE
2
Axial vector mass in QE (MA )1.21 GeV/c
0.18 GeV/c2
Fermi momentum for oxygen (pF O)
225.0 MeV/c 31.0 MeV/c
2p2h normalization for ν
1.0
1.0
2p2h normalization for ν̄
1.0
1.0
2p2h normalization carbon to oxygen
1.0
0.2
2p2h shape for oxygen
0.0
0.0
A
0.15
Form factor parameter in single pion production (C5 (0))
1.01
RES
2
Axial vector mass in resonance interaction (MA )0.95 GeV/c
0.15 GeV/c2
1
Non-resonant (Isospin = 2 ) background normalization
1.30
0.40
νe /νµ1.00.028284ν̄e /ν̄µ1.00.028284
CC DIS normalization
0.0
0.4
CC coherent normalization for oxygen
1.0
0.3
NC coherent normalization
1.0
0.3
NC1γ normalization
1.0
1.0
NC other normalization for far detector
1.0
0.3
BeRPA parameter A
0.59
0.118
BeRPA parameter B
1.05
0.21
BeRPA parameter D
1.13
0.1695BeRPA parameter E
0.88
0.352
BeRPA parameter U
1.20
0.1

cm2]

60

σNCQE [× 10σNCQE [× 10

2.5

-38

3

-38

cm2]

CHAPTER 5. EVENT SIMULATION

2.5
2

2
1.5

1.5
1
1

16

0.5
0
0

O(ν,ν'N)O(ν,ν'n)16O(ν,ν'p)16O(ν,ν'N)O(ν,ν'n)16O(ν,ν'p)
16

1

2

3

4

5

6

7

16

0.5
0
0

8 9 10Eν [GeV]

1

2

3

4

5

6

7

8 9 10Eν [GeV]Figure 5.2: NCQE cross sections by NEUT for neutrinos (left) and antineutrinos (right) on all
neutrons, all protons, and all nucleons inside oxygen.

5.3

Nuclear De-excitation γ-rays and Detector Response

The nuclear de-excitation γ-rays are simulated separately for the primary γ-rays from neutrinonucleus interactions and the secondary γ-rays from nucleon-nucleus interactions. The processes
are schematically shown in Figure 5.3. More details can be found in Ref. [104].

ν

16O

primary γ(NCQE interaction)n or psecondary γγ(nuclear reactions)γγ

Figure 5.3: Schematic drawing of the primary and the secondary γ-rays in the NCQE interaction.

After the neutrino-oxygen interaction, one of excited states is selected based on probabilities
calculated by Ankowski et al. [49]. The possible states are categorized into four: (p1/2 )−1 ,(p3/2 )−1 , (s1/2 )−1 , and others. According to the simple nuclear shell model, nucleons inside 16 O
belong to either of p1/2 , p3/2 , or s1/2 . The states of (p1/2 )−1 , (p3/2 )−1 , and (s1/2 )−1 are thesituation that a nucleon occupying either of p1/2 , p3/2 , or s1/2 is removed from the nucleus,
respectively. Probabilities for each state to be produced are summarized in Table 5.2. The
treatment of the others state is explained below.

CHAPTER 5. EVENT SIMULATION

61

Table 5.2: Probabilities of a remaining nucleus belonging to each excited state, (p1/2 )−1 ,(p3/2 )−1 , (s1/2 )−1 , and others, after the neutrino interaction.
Simple shell model
Ankowski et al. [49]This analysis(p1/2 )−1
0.25
0.158
0.158

(p3/2 )−1
0.50
0.35150.3515(s1/2 )−1
0.25
0.10550.4905others00.385-

The (p1/2 )−1 state corresponds to the ground state of 15 O (15 N) after a neutron (proton)knock-out, and therefore does not lead to any γ-ray emission.
The possible excited states and γ-ray emission modes for the (p3/2 )−1 state are summarizedin Table 5.3. Here Eex represents the excited energy level, J π is the spin and parity of theresidual nucleus, Eγ and Ep are energies of the emitted γ-ray and proton respectively, Rγ is theprobability of the residual nucleus to emit the γ-ray at each excited state, and Br(X∗ → Y + γ)
is the branching ratio for the residual nucleus (X = 15 N or 15 O) to de-excite to the ground stateof Y. The most likely modes are the emission of the 6.32 MeV γ-ray from 15 N or the 6.18 MeV
γ-ray from 15 O.
Table 5.3: Excited states and γ-ray emission modes of 16 O proton hole (p3/2 )−1
and neutronp−1hole (p3/2 )n .
Residual nucleus Eex [MeV]
15
N
6.32
9.93

15

O

10.70
6.18

Jπ
( 3 )−( 23 )−
2( 3 )−( 32 )−
2Eγ [MeV] Ep [MeV] Rγ [%]
6.32
100
5.30
15.3
6.32
4.9
7.30
2.1
9.93
77.6
0.5
6.18
100

Br(X∗ → Y + γ) [%]
86.2
1.1
0.3
0.1
5.4
6.9
100

There are more fractions to the emission of γ-rays with energies of >3 MeV from the (s1/2 )−1state. For the proton knock-out case, excited states and their branching ratios of the γ-ray
emission are measured or calculated as summarized in Table 5.4. From the analogy, the neutron
knock-out case is set to be identical in the nominal MC.
The others state includes all the other states whose excited energies are higher than anyof the three states above or which are aﬀected by other nuclear eﬀects such as short-range
correlation between nucleons. Since there is no data nor theoretical calculation on the γray emission from the others state, this state is integrated into (s1/2 )−1 at the nominal MC
production. The systematic uncertainty regarding this treatment is estimated later.
The interactions of particles produced in the neutrino interaction, the Cherenkov lightemission, and the PMT responses are simulated by the GEANT3-based dedicated package,
which is described in Chapter 4. Important for this analysis is the hadronic interaction parts,
especially the models of neutron reactions on oxygen. The hadronic interactions are basedon GCALOR [85, 86]. This implements MICAP for neutrons below 20 MeV and NMTC above
20 MeV, respectively. MICAP reads experimental cross sections from ENDF/B-V, while NMTCCHAPTER 5. EVENT SIMULATION

62

is based on the intra-nuclear cascade model. Details about these models can be found in
Refs. [85, 86] and references therein.
in 16 O. The g.s.
Table 5.4: Excited states and γ-ray emission modes of the proton hole (s1/2 )−1p
represents the ground state.
Residual nucleus Eex [MeV] J π( 1 )+
13
C
3.09( 23 )+
3.68( 21 )+
3.85
2
12
C
4.44
2+
14
N
g.s.
2+
4.92
0−
5.11
2−
5.69
1−

14

5.4

C

5.83

3−

6.20

1+

6.45

3+

7.03
g.s.
6.09
6.59
6.73

2+
2+
1−
0+
3−

6.90
7.01

0−
2+

7.34

2−

∗

Eγ [MeV] Rγ [%] Br(15 N → Y + γ) [%]
3.09
100
3.0
3.68
99.3
4.2
3.09
1.20
<0.1
4.44
100
5.8
6.7
4.92
97
5.0
5.11
79.9
<0.1
3.38
63.9
2.9
5.69
36.1
1.6
5.11
62.9
0.3
5.83
21.3
0.1
3.89
76.9
<0.1
6.20
23.1
<0.1
5.11
8.1
0.2
6.44
70.1
2.0
7.03
98.6
(6.6)
1.1
6.09
100
<0.1
6.09
98.9
<0.1
6.09
3.6
<0.1
6.73
96.4
0.4
6.09
100
<0.1
6.09
1.4
<0.1
7.01
98.6
(6.6)
6.09
49.0
2.8
6.73
34.3
2.0
7.34
16.7
1.0

Neutrino Oscillation Eﬀect

Unlike the NC interaction, the cross section and the final state of the CC interaction dependon the neutrino flavor, then neutrino oscillation eﬀects need to be considered. At the stage of
event selection described in Chapter 6, this eﬀect is corrected as shown in Figure 5.4, where
the oscillation probability at true neutrino energy is multiplied as weight to each MC event.
Although the oscillation probabilities of νµ → ντ and ν̄µ → ν̄τ are high, the CC cross sections ofντ (ν̄τ ) are negligible in the T2K energy region because the tau lepton mass is higher. Therefore,
contributions from tau (anti)neutrinos are negligible. The νµ → νµ and νµ → νe oscillation
probabilities are written as follows:

CHAPTER 5. EVENT SIMULATION

63

(–)

νµ

(–)

(–)

(–)

(–)

(–)

(–)

× P(νµ→νe; Eν)× P(νµ→νµ; Eν)× P(νµ→ντ; Eν)

(–)

(–)

νµ

(–)

× σCC(νe; Eν)/σCC(νµ; Eν) ~ 1

×1× σCC(ντ; Eν)/σCC(νµ; Eν)

wgte

wgtµ

wgtτ

νe

(–)

(–)

ντ

(–)

(–)

Figure 5.4: Schematic drawing for the correction of oscillation eﬀects.

()∆m232 [eV2 ] · L[km]P(νµ → νµ ; Eν ) ≃ 1 − (cos θ13 · sin 2θ23 + sin 2θ13 · sin θ23 ) · sin 1.267 ·,Eν [GeV](5.1)()∆m232 [eV2 ] · L[km]P(νµ → νe ; Eν ) ≃ sin2 2θ13 · sin2 θ23 · sin2 1.267 ·Eν [GeV]()∆m221 [eV2 ] · L[km]∆m232 [eV2 ] · L[km]2∓· JCP · sin δCP · sin 1.267 ·,(5.2)
4Eν [GeV]Eν [GeV]
4

JCP =

2

2

2

2

1
cos θ13 · sin 2θ12 · sin 2θ23 · sin 2θ13 · sin δCP ,
8

(5.3)

where L denotes the experimental baseline, 295 km, and Eν represents the neutrino energy. In
Equation 5.2, an upper and a lower sign corresponds to neutrino and antineutrino oscillations,
respectively. In the correction, the CC cross sections of νµ (ν̄µ ) and νe (ν̄e ) are assumed tobe the same, and later the systematic error of this assumption is evaluated. In addition, thekinematics diﬀerence between the final state electron and muon is not considered, because
this eﬀect is expected to be small. By using the equations above, the weight factor (wgtosc )multiplied to each MC event is obtained as follows:

wgtosc (Eν ) = P(νµ → νµ ; Eν ) + P(νµ → νe ; Eν ) ·σCC (νe ; Eν )σCC (νµ ; Eν )≃ P(νµ → νµ ; Eν ) + P(νµ → νe ; Eν )()∆m232 [eV2 ] · L[km]422= 1 − cos θ13 · sin 2θ23 · sin 1.267 ·.
Eν [GeV](5.4)

CHAPTER 5. EVENT SIMULATION64

The same oscillation probability is assumed for muon antineutrinos and so does the weightfactor. Oscillation parameters used in the analysis are taken from the recent T2K result [108],
as summarized in Table 5.5.
Table 5.5: Neutrino oscillation parameters and their errors used in this analysis. These aretaken from the recent T2K result [108].
Parametersin2 θ13
sin2 θ23∆m232 [×10−3 eV2 ]NominalError
0.0211±0.0008
0.541+0.027/−0.037
2.469+0.073/−0.071

Chapter 6
Event Selection
6.1

Selection Criteria

In the analysis, events are categorized into five: neutrino and antineutrino NCQE interactions(“ν-NCQE” and “ν̄-NCQE” respectively), all the other NC interactions (“NC-other”), CCinteractions, and beam-unrelated accidental backgrounds. Both NC-other and CC include
neutrino and antineutrino interactions. Note that this categorization is based on the primary
neutrino interaction type (before the final state interactions), that is, for example, an NC
pion production event where a pion is absorbed in the nucleus is categorized as the NC-otherinteraction. The first four are simulated and the beam-unrelated events are estimated using
the oﬀ-timing data, as described later. The cuts described in this chapter eﬀectively select thesignal-like events and reduce the other events. Table 6.1 summarizes the type of event selections
and their application targets (data and/or MC).
Table 6.1: Type of the NCQE event selections and their application targets.
No.
0
1
2
3
4
5
6

Selection
Energy window
Good spill selection
Timing cut
Decay-e cut
Fiducial volume cut
Low energy background cut
CC interaction cut

Application target
Data & MC
Data
Data
Data
Data & MC
Data & MC
Data & MC

Energy window
In this analysis, the energy window is set to 3.49−29.49 MeV in visible energy. The lower edge isdetermined by the SK energy threshold. The higher edge is settled because the Michel electron
background from the νµ and ν̄µ CC interactions increase while the NCQE signal decreases above
30 MeV.

65

CHAPTER 6. EVENT SELECTION

66

Good spill selection
Each spill is judged whether good for physics analysis or not based on the beam and SK detector
conditions. Only good spill data are used in the analysis.

Timing cut
In order to select beam-induced events, the reconstructed event timing is required to be within±100 ns with respect to the expected timing of each bunch (“on-timing”). Beam-unrelated
events are selected by applying the same energy and quality cuts but a diﬀerent timing cut
with a window [−500, −5] µs with respect to the beam spill (“oﬀ-timing”).

Decay electron cut
Since the signal events do not accompany a muon nor a pion, tagging these particles would
be a powerful cut. Here an electron or a positron from muon decay is focused. The required
minimum energy, Eth , for a charged particle, whose mass is m, to emit Cherenkov light in a
medium with a refractive index of n can be written as follows:
nmc2
Eth = √.
n2 − 1(6.1)

In water, n being 1.33, this “Cherenkov threshold” is 158.7 MeV for muons and 209.7 MeV
for pions while 0.768 MeV for electrons and positrons. Therefore, in case that the energy ofan out-going muon or pion is smaller while its decay product, an electron or a positron, haslarger energy than its Cherenkov threshold, SK detects signature of only these decay electronsor positrons (referred to as the “decay-e” events).
It is possible that the selected event is the decay-e from a preceding muon, then the preactivity is searched before the event. Here a 30 ns wide window is slid between 0.2 and 20 µs
before the event, and the number of hit PMTs within 30 ns (N30 ) is counted. Then, the event
whose maximum N30 is greater than 22 is rejected. This pre-activity cut is applied only for
data, because these events do not exist in the MC sample. The eﬀect on the signal eﬃciency
by the pre-activity cut is negligible.
The other possibility that the decay-e comes after the selected event is also checked, but
the signal-to-background ratio is not improved much, then the cut on this post-activity is notconsidered here.

Fiducial volume (FV) cut
There are lots of background events due to radioactive impurities in the detector material.
Since these backgrounds are expected to come mainly from the ID wall, dwall is required to belarger than 200 cm. This FV cut is usually applied in the SK analysis. Below 6 MeV thesebackgrounds increase considerably even after the FV cut, and then tighter cuts are required,as described next.

CHAPTER 6. EVENT SELECTION67

Low energy background cut
Cuts in the energy region below 6 MeV are tuned using three variables, dwall, eﬀwall, and ovaQ.
Cuts on these variables are optimized in five energy regions between 3.49 MeV and 5.99 MeV
with a 0.5 MeV bin and the optimization is performed separately for diﬀerent T2K run periods
because the beam power and the detector condition diﬀer from run to run. A figure-of-merit(FOM) to be maximized for the cut optimization is defined as:
Nsig
FOM = √
Nsig + Nbkg

MCbeam-unrelated(Nbkg = Nbkg
+ Nbkg),(6.2)

where Nsig represents the number of signal events by MC (ν-NCQE for FHC and ν̄-NCQE for
RHC respectively), while Nbkg represents the number of background events composed of theMCbeam-unrelated). Thebeam neutrino background (Nbkg) and the beam-unrelated background (Nbkg
FOM is calculated for each set of {dwall, eﬀwall, ovaQ} independently in the five lowest energy
regions, 3.49−3.99, 3.99−4.49, 4.49−4.99, 4.99−5.49, and 5.49−5.99 MeV. By scanning themultiple parameter sets, the optimized one is selected which maximizes the FOM. In the scan atemporary cut of θC ≥ 34◦ is applied to reduce CC events, while the cut for the CC events will
be optimized later 1 . Table 6.2 summarizes the scan regions and intervals of each parameter.
Table 6.2: Scan regions and intervals of each parameter.
Parameter min max
dwall [cm]200 320
eﬀwall [cm] 200 1200
ovaQ
0.20 0.30

interval
10
10
0.01

After calculating FOMs for each energy region in each run, distributions of the best cut valuesof dwall, eﬀwall, and ovaQ, as a function of energy are obtained. Results from Run 8 are shownin Figure 6.1 as an example. The results for the other runs are given in Appendix C. Each
distribution is fit by a linear function. As for the dwall and eﬀwall distributions, if the optimized
value is 200 cm (the FV cut criterion) in two successive bins, the region after the second 200 cm
bin is rejected from the fitting area. The fitting results are also shown in Figure 6.1. In theend, each parameter is required to be larger than the fit line, that is, the events in the upper
right portion in the figure are selected. Figure 6.2 gives the ovaQ distributions after the energy
cut, the good spill cut, the on-timing cut, the FV cut, the dwall cut, and the eﬀwall cut. Clear
separations between signal and background events are seen.

1

The eﬀect of this temporary treatment on the optimization is small.

CHAPTER 6. EVENT SELECTION

68

dwall [cm]Optimized dwall for Run 8
300
280
260
240
220
200
180
160
3.5

4

4.5

5

5.5
6
Erec [MeV]

effwall [cm]Optimized effwall for Run 8
1000
800
600
400
200
0
3.5

4

4.5

5

5.5
6
Erec [MeV]

ovaQ

Optimized ovaQ for Run 8
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
3.5

4

4.5

5

5.5
6
Erec [MeV]

Figure 6.1: Optimized cut values for dwall (top), eﬀwall (middle), and ovaQ (bottom), asa function of reconstructed energy for Run 8. Vertical bars represent the bin width in theparameter scans. Red lines represent linear fits to each distribution and used as cut criteria.
The fitting regions for dwall and eﬀwall are explained in the text.

69

Events/0.05

Events/0.05

CHAPTER 6. EVENT SELECTION

Data (T2K Run1-9 FHC)

100

ν -NCQEν -NCQE
NC-other

80

CC

Data (T2K Run1-9 RHC)

100

ν -NCQEν -NCQE
NC-other80

CC
Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60

60

40

40

20

20

0
−0.4

−0.2

0

0.2

0.4

0.6

0.8

ovaQ

0
−0.4

−0.2

0

0.2

0.4

0.6

0.8

ovaQ

Figure 6.2: Distributions of ovaQ in FHC (left) and RHC (right) after the energy cut, the good
spill cut, the on-timing cut, the FV cut, the dwall cut, and the eﬀwall cut.

CC interaction cut
A single charged particle with momentum large compared to its mass tends to have a Cherenkov
opening angle of ∼42◦ because it is almost relativistic. On the other hand, if the particle
momentum is lower, for example, ≲250 MeV for muons, the reconstructed Cherenkov angle
decreases. In this analysis, the low energy muons from the CC interaction still above theCherenkov threshold distribute below ∼35◦ , whereas their decay-e’s have ∼42◦ . These areseen in Figures 6.3 and 6.4 for FHC and RHC, respectively. To reduce the CC interaction
events, the cut criteria are tuned in the 2D Erec −θC plane. The two parameters (aopt andbopt ) of a linear function, θC = aopt × Erec + bopt , are determined by maximizing FOM. The
definition of FOM is the same as Equation 6.2. Here the selection is done by requiring an
event fulfilling θC ≥ a × Erec + b, and the combination of a and b which maximizes FOM istaken as an optimized one. The cut criteria are also shown in the figures. The large part of
the NCQE events locates above the functions, while the CC events are below them. Some
CC events remain after the cut and these could be due to, for example, multiple γ-rays via
neutron production, and similar population is seen also in the NC-other distribution. With
the optimized cut, the signal eﬃciency is 99% (99%) while 63% (58%) of the CC events are
removed in the FHC (RHC) sample.

CHAPTER 6. EVENT SELECTION

70

3

80
2.5

70
60

θC [degree]θC [degree]

ν-NCQE (FHC)90

ν-NCQE (FHC)

90

0.1

80
0.08

70
60

2

0.06
50

50
1.5

40

40
0.04

30

30

1

20

20

0.02

0.5
10

10
0

5

10

15

20

25

0

0

5

0.6

80
0.5
70
60

θC [degree]θC [degree]

NC1π (FHC)
90

10

15

20

25

90
80

0.05

70
0.04

60

0.4

50

50

0.03

0.3
40

40
30

0.02

30

0.2

20

20

0.01

0.1
10

10
0

5

10

15

20

25

0

0

5

10

15

20

25

0

Erec [MeV]

Erec [MeV]CC 2p2h (FHC)

90
0.35
80
0.3

70

θC [degree]

CCQE (FHC)θC [degree]0

Erec [MeV]
NC-other - NC1π (FHC)

Erec [MeV]

90
0.045
80

60

0.25

60

50

0.2

50

40

0.15

30

0.04

70

0.035
0.03
0.025

40

0.02

30

0.015

20

0.01

10

0.005

0.1
20
0.05

10
0

5

10

15

20

25

0

0

5

0.045
0.04

70

0.035

60

0.03

50

0.025

θC [degree]θC [degree]

CC-other (FHC)
90
80

10

15

20

25

0

Erec [MeV]
Beam-unrelated (FHC)

Erec [MeV]
90

0.24
0.22

80

0.2

70

0.18
60

0.16

50

0.14
0.12

40

0.02

40

30

0.015

30

0.08

20

0.01

20

0.06

10

0.005

10

0

0

0.1

0.04

0

5

10

15

20

25

Erec [MeV]

0.02
5

10

15

20

25

0

Erec [MeV]

Figure 6.3: Two-dimensional Erec −θC distributions of each interaction mode and the beamunrelated events before the CC interaction cut together with the optimized cut function (θC =1.68 × Erec + 17.73) in FHC.

CHAPTER 6. EVENT SELECTION

71

0.3

80
0.25

70
60

θC [degree]θC [degree]

ν-NCQE (RHC)90

ν-NCQE (RHC)

90

1.2
80
1

70
60

0.2

0.8

50

50
0.15

40
30

0.6

40
30

0.1

0.4

20

20
0.05

0.2
10

10
0

5

10

15

20

25

0

0

5

NC1π (RHC)

15

20

25

0

90

90

0.18

80

0.16

70

0.14

60

0.12

60

0.025

50

0.1

50

0.02

40

0.08

40

30

0.06

30

20

0.04

20

10

0.02

10

0

0

θC [degree]θC [degree]

10Erec [MeV]
NC-other - NC1π (RHC)

Erec [MeV]

0.035
80
0.03

70

0.015
0.01

0

5

10

15

20

25

0.005

5

10

15

20

0.07

80

0.06

70
0.05

θC [degree]

90

90

0.014

80

0.012

70
0.01

60

60
50

0.04

50

0.008

40

0.03

40

0.006

30

30
0.02

0.004
20

20
0.01

10
0

5

10

15

20

25

0.002

10
0

0

5

0.01

70
0.008

60
50

0.006

40

θC [degree]

CC-other (RHC)
90
80

10

15

20

25

90

0.14

80
0.12
70
60

0.1

50

0.08

40
0.004

30

0

Erec [MeV]
Beam-unrelated (RHC)

Erec [MeV]θC [degree]0

CC 2p2h (RHC)

CCQE (RHC)θC [degree]

25

Erec [MeV]

Erec [MeV]

0.06

30
0.04

20

20
0.002

10
0

0.02

10
5

10

15

20

25

Erec [MeV]

0

0

5

10

15

20

25

0

Erec [MeV]

Figure 6.4: Two-dimensional Erec −θC distributions of each interaction mode and the beamunrelated events before the CC interaction cut together with the optimized cut function (θC =1.57 × Erec + 17.73) in RHC.

CHAPTER 6. EVENT SELECTION

6.2

72

Selected Samples

Figure 6.5 shows the reconstructed energy distributions of the MC beam neutrino events andthe beam-unrelated events both before and after the cuts. The numbers of each interaction
and the beam-unrelated events are summarized in Tables 6.3 and 6.4, for the FHC and RHC
mode, respectively. After the cuts, the signal eﬃciency is more than 90%, while the backgroundis reduced by more than two orders of magnitude, and 204 events remain in the FHC sample
and 97 events remain in the RHC sample. The FHC sample has a high signal purity, while
the neutrino NCQE interaction forms ∼20% of the RHC sample because of the cross section
diﬀerence between neutrinos and antineutrinos. The observed and predicted numbers of selected
events agree well to each other both in the FHC and RHC modes at every selection stage.

Table 6.3: Number of events after each cut in data and MC in FHC. Before the timing cut,
only the beam quality and detector condition cuts are applied. In the column with “Total”,
the sum of the ν-NCQE, ν̄-NCQE, NC-other, CC, and beam-unrelated events is shown.
Observation
On-timing Total ν-NCQE
Timing cut
4595
Decay-e cut
4553
FV cut
831
896.8
190.7
dwall cut
735
791.4
190.0
eﬀwall cut
442
492.7
185.6
ovaQ cut
220
263.9
181.0
CC cut
204
238.4
178.6

Predictionν̄-NCQE NC-other
5.2
52.1
5.2
51.9
5.0
51.4
4.9
50.2
4.8
42.5

CC
24.9
24.8
24.6
24.1
8.9

Beam-unrelated
4357.54350.8
623.9
519.5
226.1
3.7
3.6

Table 6.4: Number of events after each cut in data and MC in RHC. Before the timing cut,
only the beam quality and detector condition cuts are applied. In the column with “Total”,
the sum of the ν-NCQE, ν̄-NCQE, NC-other, CC, and beam-unrelated events is shown.
Observation
Prediction
On-timing Total ν-NCQE ν̄-NCQE NC-other
Timing cut
3626
Decay-e cut
3597
FV cut
613
606.0
19.6
60.7
19.6
dwall cut
535
524.1
19.5
60.5
19.5
eﬀwall cut
282
279.4
19.1
58.7
19.3
ovaQ cut
101
101.8
18.5
57.0
18.7
CC cut
97
94.3
17.9
56.5
15.5

CC
5.7
5.7
5.6
5.5
2.3

Beam-unrelated
3746.93470.0
500.4
418.9
176.7
2.1
2.1

104

T2K Run 1-9 FHC
Beam-unrelated (before FV cut)

3

10

Beam-unrelated (after all cuts)
MC (before FV cut)

2

10

73

Events/MeV

Events/MeV

CHAPTER 6. EVENT SELECTION

104

T2K Run 1-9 RHC
Beam-unrelated (before FV cut)

3

10

Beam-unrelated (after all cuts)
MC (before FV cut)2

10

MC (after all cuts)

MC (after all cuts)

10

10

1

1

10−1

10−1

10−2

5

10

15

20

25

Erec [MeV]

10−2

5

10

15

20

25

Erec [MeV]

Figure 6.5: The Erec distribution of the MC beam neutrino and the beam-unrelated events
before the FV cut and after all cuts for the FHC (left) and RHC (right) modes. The beamunrelated backgrounds are reduced dramatically after the cuts both in FHC and RHC.
The data quality of the selected events is checked by seeing if there is no bias in the distributions of the event vertex and timing and the event rate. The vertex distributions in the
X−Y and R2 −Z coordinates, where X and Y correspond to the horizontal plane (R2 = X2 +Y2 )and Z corresponds to the vertical direction, for the FHC sample are shown in Figure 6.6. The
selected events distribute uniformly in both the horizontal and vertical coordinates. In the
figure, the beam direction is represented by a red arrow, and no bias on the event vertex withrespect to the beam direction is observed. The event timing and the residual timing from theexpected beam timing of the FHC sample are shown in Figure 6.7. The numbers of selected
events in eight bunches are comparable to each other and most events come within 50 ns fromthe expected beam timing. Figure 6.8 shows event rates in each FHC run in comparison to theoverall average rate of 1.37/1019 -POT. The event rate of each run is consistent with the overall
average. Corresponding data quality checks for the RHC sample are shown in Figures 6.9, 6.10,
and 6.11. The averaged event rate over the all RHC runs is 0.59/1019 -POT. No bias are seenin the position, timing, and event rate distributions.
Figures 6.12 and 6.13 show distributions of the reconstructed energy and Cherenkov angle
and their 2D scatter plots for the FHC and RHC samples, respectively. The observed Erec
distributions agree well with the predictions and clear contributions from ∼6 MeV γ-rays areobserved in both FHC and RHC modes. In the θC distribution of the FHC sample, the observed
data at high angles is below the expectation, while no such excess in the expectation is seenin the RHC distribution. A similar tendency was also observed in the previous analysis [51],while the statistical uncertainty was large. The high angle region is dominated by the multipleγ events, as explained in Chapter 4. These are caused mainly by fast neutron reactions on
nuclei inside the detector. The excess in the FHC sample may then be attributed to inaccurate
modeling of fast neutron reactions and the subsequent γ-ray emissions (secondary-γ). The
fact that the excess is seen in FHC while not in RHC, may be understood by diﬀerence inthe kinematics of out-going nucleons between neutrino and antineutrino interactions. Helicity
conservation produces more forward-going leptons in the final state and accordingly lower

74

20

Z [m]

Y [m]

CHAPTER 6. EVENT SELECTION

15

20
15

10

10

5

5

0

0

−5

−5

−10

−10

−15

−15

−20
−20

−15

−10

−5

0

5

10

15

−20
0

20

50

100

150

200

250

300

R2 [m2]X [m]Events/5-ns

Events/0.05-µ s

Figure 6.6: Vertex distributions for the selected events in FHC: X−Y (left) and R2 −Z (right).
Area filled with transparent gray and blue represent the ID and FV regions, respectively. The
red arrow in the left panel represents the beam direction.

10
10

1

1

−1

0

1

2

3

4

−200 −150 −100

5

−50

0

dt0 [µs]

50

100 150 200
Residual time [ns]19

Observed Event Rate [/10 POT]

Figure 6.7: Distributions of the event timing (left) and its residual time from the spill timing(right) for the selected events in FHC.
4
19

3.5

All Runs Rate: 1.37 [/10 POT]

3
2.5
2
1.5
1
0.5
0

1

2

3b

3c

4

5a

5b

6a

6f

7a

7c

8

9a

T2K FHC Run#

Figure 6.8: Observed event rate in each FHC run.

75

20

Z [m]

Y [m]

CHAPTER 6. EVENT SELECTION

15

20
15

10

10

5

5

0

0

−5

−5

−10

−10

−15

−15

−20
−20

−15

−10

−5

0

5

10

15

−20
0

20

50

100

150

200

250

300

R2 [m2]X [m]Events/5-ns

Events/0.05-µ s

Figure 6.9: Vertex distributions for the selected events in RHC: X−Y (left) and R2 −Z (right).
Area filled with transparent gray and blue represent the ID and FV regions, respectively. The
red arrow in the left panel represents the beam direction.

10

1

1

−1

10

0

1

2

3

4

−200 −150 −100

5

−50

0

dt0 [µs]

50

100 150 200
Residual time [ns]19

Observed Event Rate [/10 POT]

Figure 6.10: Distributions of the event timing (left) and its residual time from the spill timing(right) for the selected events in RHC.
2
1.8

19

All Runs Rate: 0.59 [/10 POT]

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

5c

6b

6c

6d

6e

7b

9b

9c

9d

T2K RHC Run#

Figure 6.11: Observed event rate in each RHC run.

Events/MeV

CHAPTER 6. EVENT SELECTION

76

50
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

40

NC-otherCC
Beam-unrelated (from off-timing data)

30

20

10

0

5

10

15

20

25

Events/2.7-degree

Erec [MeV]45
Data (T2K Run1-9 FHC)
ν -NCQE

40

ν -NCQE
NC-other

35

CC

30

Beam-unrelated (from off-timing data)

25
20
15
10
5
0
0

10

20

30

40

50

60

70

80

90

θC [degree]θC [degree]

90

3.5

80
3
70
2.5

60
50

2

40

1.5

30
1
20
0.5

10
0

5

10

15

20

25

0

Erec [MeV]

Figure 6.12: Distributions of Erec (top) and θC (middle), and their 2D scatter plot (bottom) in
the FHC sample. In the 2D plot, magenta dots represent the observed events.

Events/MeV

CHAPTER 6. EVENT SELECTION

77

22

Data (T2K Run1-9 RHC)
ν -NCQE

20ν -NCQE

18

NC-otherCC

16

Beam-unrelated (from off-timing data)

14
12
10
8
6
4
2
0

5

10

15

20

25

Events/2.7-degree

Erec [MeV]20

Data (T2K Run1-9 RHC)
ν -NCQE

18

ν -NCQE

16

NC-otherCC

14

Beam-unrelated (from off-timing data)

12
10
8
6
4
2
0
0

10

20

30

40

50

60

70

80

90

θC [degree]θC [degree]

90
1.6
80
1.4

70

1.2

60

1

50
40

0.8

30

0.6

20

0.4

10

0.2

0

5

10

15

20

25

0

Erec [MeV]

Figure 6.13: Distributions of Erec (top) and θC (middle), and their 2D scatter plot (bottom) in
the RHC sample. In the 2D plot, magenta dots represent the observed events.

CHAPTER 6. EVENT SELECTION

78

Events/5-MeV (area normalized)

momentum nucleons in the antineutrino interaction than the neutrino interaction, as shownin Figure 6.14. The lower momentum nucleons will undergo fewer nuclear reactions inside thewater to produce secondary γ-rays. Comparison of the ratio of the single-γ peak around 42◦
to the multiple-γ peak around 90◦ of the MC in Figures 6.12 and 6.13 shows that there are
relatively fewer events at high angles in the RHC sample. Figure 6.15 shows the 2D distributionsof the energy of neutrons from the (anti)neutrino NCQE interactions and θC obtained by MC.
The large contribution at high angles from the higher momentum neutrons is seen in the FHC
ν-NCQE distribution, while this is weaker in the RHC ν̄-NCQE distribution. The observationand prediction agree well to each other in the 2D scatter plots in Figures 6.12 and 6.13.

0.035

ν-n NCQE

0.03

ν-n NCQE

0.025
0.02
0.015
0.01
0.005
0
0

100 200 300 400 500 600 700 800 900 1000

En [MeV]Figure 6.14: Kinetic energies of neutrons from the neutrino and antineutrino NCQE interactions
in RHC obtained by MC.

0.35
80
0.3

70

θC [degree]θC [degree]ν-n NCQE (FHC)
90

90

70

0.12
0.1

0.25

60

50

0.2

50

0.15

30

0.14

80

60

40

ν-n NCQE (RHC)

0.08

40
0.06
30

0.1
20
10
0
0

0.04
20

100 200 300 400 500 600 700 800 900 1000

En [MeV]

0.05

10

0

0
0

0.02

100 200 300 400 500 600 700 800 900 1000

0

En [MeV]Figure 6.15: The 2D distributions of the energy of neutrons from the ν-NCQE interaction in
FHC (left) and the ν̄-NCQE interaction in RHC (right) and θC obtained by MC.

Chapter 7
Uncertainty Estimates√
Statistical errors
ontheobserved
eventsarecalculated
tobe
204/204 = 7.0% for the FHC√
sample and 97/97 = 10.2% for the RHC sample, respectively.
Systematic error in this analysis is composed of six parts: neutrino flux prediction, neutrino interaction model, primary-γ emission model, secondary-γ emission model, oscillation
parameters, and detector response. For the beam-unrelated events, only statistical errors are
considered as 3.0% in FHC and 3.9% in RHC. This is because they are part of the observed
data and then respond to detector uncertainties in the same way.

7.1

Neutrino Flux

Flux uncertainties are estimated for each neutrino flavor, operation mode, and neutrino energy
bin. Figure 7.1 shows the total and each source uncertainties of the flux prediction at SK as afunction of neutrino energy for diﬀerent neutrino flavors in both FHC and RHC modes [109].
The flux uncertainty is composed of hadronic interaction model, proton beam and neutrino
beam measurements, and horn and magnetic field measurements. The hadronic interaction
model is the dominant uncertainty. The hadronic interaction cross section is tuned by datafrom the NA61/SHINE experiment, as mentioned in Chapter 5, and the replica target data isused in this analysis in addition to the thin target data. This has improved the uncertainty
mainly at around the flux peak. The MC neutrino event is renormalized by the error size at
its flavor and energy, and the change in the number of selected events relative to the nominalcase is taken as the systematic error. Here the energy bins are treated as fully correlated. The
results are summarized in Table 7.1.

Table 7.1: Uncertainties on the observed event rate in percent for each sample component due
to the systematic errors on neutrino flux prediction.
FHC
RHC

ν-NCQE
6.7
7.0

ν̄-NCQE NC-other
8.6
7.3
6.4
7.0

79

CC
6.4
6.5

CHAPTER 7. UNCERTAINTY ESTIMATES

80

0.3

SK: Neutrino Mode, νµHadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Fractional Error

Fractional Error

SK: Neutrino Mode, νµΦ×E ν , Arb. Norm.

0.2

0.1

0.3

Hadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Φ×E ν , Arb. Norm.

0.2

0.1

0.0

0.0
10

1

10

10

1

Eν (GeV)
SK: Neutrino Mode, νeHadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Fractional Error

Fractional Error

SK: Neutrino Mode, νe

0.3

10

Eν (GeV)Φ×E ν , Arb. Norm.

0.2

0.4

0.3

Hadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Φ×E ν , Arb. Norm.

0.2
0.1
0.1

0.0

0.0
10

1

10

10

1

Eν (GeV)
SK: Antineutrino Mode, νµHadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Fractional Error

Fractional Error

SK: Antineutrino Mode, νµ0.3

Φ×E ν , Arb. Norm.

0.2

0.1

0.3

Hadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Φ×E ν , Arb. Norm.

0.2

0.1

0.0

0.0
10

1

10

10

1

Eν (GeV)
SK: Antineutrino Mode, νeHadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Fractional Error

0.3

10

Eν (GeV)

SK: Antineutrino Mode, νe

Fractional Error

10Eν (GeV)Φ×E ν , Arb. Norm.

0.2

0.1

0.4

0.3

Hadron Interactions

Material ModelingProton Beam Profile & Off-axis Angle

Number of Protons

Horn Current & Field

Replica Tuning Error

Horn & Target Alignment

Thin Tuning Error

Φ×E ν , Arb. Norm.

0.2

0.1

0.0

0.0
10

1

10

Eν (GeV)

10

1

10

Eν (GeV)Figure 7.1: Total and each source uncertainties of the flux prediction at SK as a function ofneutrino energy for diﬀerent neutrino flavors in both FHC and RHC modes. The solid line
indicates the current uncertainty, while the dashed line corresponds to the uncertainty in thetuning only with the thin target data.

CHAPTER 7. UNCERTAINTY ESTIMATES

7.2

81

Neutrino Interaction

The cross section model uncertainties are estimated by changing model parameters by their 1σerrors as summarized in Table 5.1. In addition, systematic uncertainties of nuclear eﬀects areevaluated by replacing the Fermi gas model with the spectral function model. The resulting
errors are shown as “Cross section model” in Table 7.2. Here the model uncertainty is notconsidered for the NCQE interaction, because the γ-ray is emitted isotropically and the detector
is 4π eﬃcient therefore the signal eﬃciency is unaﬀected by the cross section model uncertainty.
In contrast, the detector such as ND280 does not 4π acceptance, therefore, for example, thechange in Q2 due to the cross section model uncertainty, which aﬀects the out-going lepton
direction, clearly changes the number of selected events. Figure 7.2 shows the Q2 distributionsof the signal in FHC and RHC at each selection stage, in which no significant change is seen
throughout all stages. This supports that the NCQE signal is not aﬀected by the interaction
model uncertainty.
Table 7.2: Uncertainties on the observed event rate in percent for each sample component due
to the systematic errors on neutrino interaction model.

Events/0.02-(GeV/c)2 (area normalized)

RHC

T2K Run 1-9 FHC

0.04

No cutAfter FV cut

0.035

After dwall cut
After effwall cut

0.03

After ovaQ cut
After CC interaction cut

0.025
0.02
0.015
0.01

0

ν̄-NCQE NC-other CC
8.2
16.5
3.0
3.0
8.2
16.5
10.8
38.2
3.0
3.0
10.8
38.2

T2K Run 1-9 RHC

0.06

No cutAfter FV cut
After dwall cut

0.05

After effwall cut
After ovaQ cut
After CC interaction cut

0.04

0.03

0.02

0.01

0.005
0

ν-NCQE
3.0
3.0
3.0
3.0

Events/0.02-(GeV/c)2 (area normalized)

FHC

Cross section model
NC inelastic
Total
Cross section model model
NC inelastic
Total

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6
2

1.8

2
2

Q [(GeV/c) ]

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Q2 [(GeV/c)2]

Figure 7.2: The Q2 distributions of ν-NCQE in FHC (left) and ν̄-NCQE in RHC (right) at
each selection stage.

CHAPTER 7. UNCERTAINTY ESTIMATES

82

The NC inelastic interaction without nucleon knock-out, ν (ν̄) + 16 O → ν (ν̄) + 16 O∗ , isnot simulated in this analysis. However, the present selection may contain contributions fromthis process. Figure 7.3 shows the neutrino-oxygen NC cross sections leading to the groundstate (15 O, 15 N) and the excited state (15 O∗ , 15 N∗ ) calculated in Ref. [110]. Note that these
nuclei are produced by decay from the excited 16 O∗ after the NC inelastic scattering with nonucleon emission. This shows the sum of cross sections leading to 15 O∗ and 15 N∗ after the16O(ν, ν ′ ) interaction is increased from 6.7 × 10−42 cm2 at Eν = 50 MeV to 481 × 10−42 cm2
at Eν = 500 MeV while are saturated above Eν ∼ 200 MeV. On the other hand, Figure 7.4
shows the NCQE cross sections calculated in Ref. [49]. Comparing these two, the QE process
is dominant than the inelastic process without nucleon knock-out above Eν ∼ 200 MeV as
mentioned in Chapter 2. The former cross section is ∼40 times larger than the latter at
500 MeV, and is expected to be more in the higher energy region. In the T2K measurement, thedominant contributions come from neutrinos with >500 MeV (see Figure 5.1). With assumptionthat the detectable γ-ray emission rate from excited states after the inelastic interaction without
nucleon emission is comparable to that after the QE, a conservative 3% (≳ 1/40) error is
assigned. Similar is expected for the antineutrino case, so the same size error is assigned.
It is also possible that γ-rays are produced by the proton secondary reactions after the NC
interactions on hydrogen, ν(ν̄) + 1 H → ν(ν̄) + 1 H, though this process is not simulated in
the current analysis. The contributions from the proton-induced secondary-γ’s in the NCQE
interaction with oxygen are estimated and compared with the total, which result in ≲9%. Since
the composition of hydrogen in water is 1/9, the contribution size is ≲1% (negligible).

Figure 7.3: (See only the lower part) Total and partial cross sections leading to the groundstate (15 O and 15 N) and the excited state (15 O∗ and 15 N∗ ) after the 16 O(ν, ν ′ ) interactions [110].

7.3

Primary-γ Production

Primary-γ production is determined based on the spectroscopic strengths of the excited states,
therefore the uncertainties on these strengths may aﬀect the observed event rate. The results
are summarized in Table 7.3.
The calculation of the p3/2 strength is accomplished with a precision of 5.4% according to
Ankowski et al. [49]. To estimate the eﬀect of the p3/2 state, the spectroscopic strength of thisstate is increased by 5.4% with the changed amount absorbed by decrease of the strength of

CHAPTER 7. UNCERTAINTY ESTIMATES
4

ν-induced γ’sν̄-induced γ’s1038σ (cm2)3

83

O(ν, ν ! N )O(ν̄, ν̄ ! N )

16
16

2
1
0

0

0.5

1.0
Eν (GeV)

1.5

2.0

Figure 7.4: Neutrino- and antineutrino-oxygen NCQE interaction cross sections and those with
γ-ray emission [49].
the p1/2 state, which gives (p1/2 , p3/2 , s1/2 ) = (0.139, 0.3705, 0.4905). The uncertainty sizedue to this change is diﬀerent between ν-NCQE and ν̄-NCQE because the rate of out-goingneutrons is changed and accordingly the secondary-γ emission is aﬀected. This is more visible
in the FHC sample since the out-going neutron has larger eﬀect as explained in the previous
chapter. The error of the s1/2 state is included in that of the others state as explained below.
Note that an even conservative size change of this state does not produce any comparable error
1.
As mentioned in Chapter 5, there is no data nor theories on the γ-ray emission from theothers state. At the nominal MC production, this state is integrated into the (s1/2 )−1 state.
The error on this treatment is estimated by comparing the nominal case to an extreme case.
Since no significant deviation on the strength of p3/2 from the calculated strength is observedin the (e, e′ p) and (p, 2p) scattering experiments [49,111], the others state cannot be integrated
into the (p3/2 )−1 state. In contrast, it is possible for the others state to behave like the groundstate, (p1/2 )−1 , because no signal is produced from the ground state and then such situation
does not contradict any experiments. As an extreme case, the integration of others into (p1/2 )−1is selected as (p1/2 , p3/2 , s1/2 ) = (0.543, 0.3515, 0.1055). The diﬀerent treatment shows thedominant error in this source.
Table 7.3: Uncertainties on the observed event rate in percent for each sample component due
to the systematic errors on primary-γ emission model.

FHC

RHC

1

p3/2 changed
others integrated into (p1/2 )−1
Total
p3/2 changed
others integrated into (p1/2 )−1
Total

ν-NCQE ν̄-NCQE NC-other
0.1
3.3
3.1
11.0
10.1
5.1
11.0
10.6
6.0
0.8
1.8
2.6
12.2
11.3
2.3
12.2
11.4
3.5

CC
5.6
3.4
6.6
<0.1
0.5
0.5

This is clear that the diﬀerent treatment of the others state changes the nominal s1/2 strength by about
80% which produces the error of 5−10% level.

CHAPTER 7. UNCERTAINTY ESTIMATES

7.4

84

Secondary-γ Production

Pselected

Uncertainties regarding the secondary nuclear interaction and subsequent γ-ray emission are
considered. Contributions from the secondary γ-ray production are made mainly by neutrons(and some protons). In the previous analysis, the systematic error was estimated by replacing
part of GCALOR with the NEUT γ-ray emission model (Ankowski et al. [49]) [51, 104]. The
neutron energy boundary, where the neutron interaction changes from non-QE to QE (without
and with a nucleon knock-out respectively), was assumed to be 30 MeV. However, the recent
measurement, which is reported in Part III, shows that QE is not dominant even at 80 MeV.
Accordingly it may be dangerous to place such a boundary at the moment.
In this analysis, only the number of emitted Cherenkov photons is focused to estimate
the uncertainty about the secondary-γ production. First, the probability (Pselected ) of an event
being reconstructed in the 3.49−29.49 MeV energy region as a function of the number of emitted
Cherenkov photons is calculated using the MC samples. Calculated probabilities for the FHC
and RHC samples are shown in Figure 7.5. In both cases, events with Cherenkov photons
between 1000 and 5000 are likely to be reconstructed in the selected region.

0.9

FHC

0.8

RHC

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

2000

4000

6000

8000

10000

NC

Figure 7.5: Probabilities of an event being reconstructed in the current analysis window of
3.49−29.49 MeV as a function of the number of Cherenkov photons (NC ) in FHC and RHC.
The number of emitted Cherenkov photons (NC ) is composed of mainly three parts:
NC ≃ NCprimary-ν + NCsecondary-n + NCsecondary-p .

(7.1)

Here NCprimary-ν denotes contributions from the primary neutrino interaction while NCsecondary-nand NCsecondary-p are from the secondary neutron and proton reactions, respectively. The NCsecondary-nand NCsecondary-p are varied and the number of selected events are recalculated by using the probability distribution in Figure 7.5. The maximum fractional diﬀerence between the nominal andchanged settings is taken as the systematic uncertainty. The variation size is described in what
follows.

CHAPTER 7. UNCERTAINTY ESTIMATES

85

The secondary-γ emission consists of two processes: the nucleon-16 O reaction and the emission of nuclear de-excitation γ-rays. In Ref. [112], the proton-12 C data is fit to obtain constraints
on the nucleon-nucleus scattering. As a result of the fitting, a factor of 1.229 ± 0.075 is obtained
for scaling the intra-nuclear cascade cross section. To cover the whole region of the original
and corrected cross sections, Ref. [113] assigns a 30% error on the secondary interaction crosssection. Because diﬀerent nucleon and nucleus types are considered here, while the basic picture is expected to be similar and the eﬀect of the target diﬀerence in the neutrino-nucleus
interaction is measured to be less than 5% in Ref. [114], a conservative 40% error is assigned
for the nucleon-16 O reaction in this analysis.
In order to estimate the impact of γ-ray emission from fast neutron reactions on oxygen, amuon-induced spallation study in SK [115] is used. Since the selected sample therein should
contain contributions from such neutron reactions, and the measured energy distribution does
not diﬀer by more than 50% from the MC prediction, this number is taken as the error estimate.
In total, a 65% (∼ 40% ⊕ 50%) error is used to change the number of Cherenkov photons made by secondary nuclear interactions, that is, factors of 1.65 or 0.35 are multiplied toNCsecondary-n and NCsecondary-p . For further safety, the larger one of the two cases (±65%) is taken
as the systematic error. The resulting errors are shown in Table 7.4. The error sizes are similar
between FHC and RHC in NC while the error size in RHC is larger in CC. This is considered
due to the fact that the antineutrino CC interaction is likely to involve a neutron in the final
state. The larger uncertainty for the NC-other interaction than that for the NCQE interaction
may be understood by that the NC-other interaction has more neutrons in the final state, forexample, via pion production, and consequently the secondary-γ eﬀect is larger.
It should be noted that the current method considers only Cherenkov photons, therefore
the model dependence has been reduced from the previous analysis [51, 104]. The secondary-γ
model remains the dominant uncertainty source in this analysis.
The final state interaction (FSI) of nucleons may aﬀect the secondary γ-ray production.
Thus, the FSI cross section is changed by 30% in NEUT following Refs. [113, 116]. This
produces no more than a few % change to the selected number of events, so a 3.0% error is
assigned conservatively to all the interaction types in both modes.
Table 7.4: Uncertainties on the observed event rate in percent for each sample component due
to the systematic errors on secondary-γ emission model.

FHC

RHC

Secondary Cherenkov photons
Nucleon FSI
Total
Secondary Cherenkov photons
Nucleon FSI
Total

ν-NCQE ν̄-NCQE
13.2
13.1
3.0
3.0
13.5
13.4
13.3
12.8
3.0
3.0
13.6
13.1

NC-other
19.3
3.0
19.5
19.1
3.0
19.3

CC
17.3
3.0
17.6
21.2
3.0
21.4

CHAPTER 7. UNCERTAINTY ESTIMATES

7.5

86

Oscillation Parameters

As described in Chapter 5, the event rate of the CC interaction is corrected for neutrino oscillations. Then the eﬀect of uncertainties on the oscillation parameters, θ13 , θ23 , and ∆m232 , assummarized in Table 5.5, are considered. First, the two combinations which maximize and minimize the oscillation probability are taken as (sin2 θ13 , sin2 θ23 , ∆m232 ) = (0.0219, 0.504, 2.543×
10−3 eV2 ) and (0.0203, 0.568, 2.398 × 10−3 eV2 ), respectively. These produce errors of+3.7/−1.6% for FHC and +2.9/−2.1% for RHC. Second, the assumption of the same crosssections for νµ and νe (ν̄µ and ν̄e ) could produce an error. To estimate this error, the CC crosssection ratio of νµ and νe (ν̄µ and ν̄e ) is obtained at each energy bin and multiplied to each MC
event. The change from the nominal setting is taken as the systematic error. Event increases by
1.7% and 1.1% are obtained for FHC and RHC, respectively. In general, the CC cross sectionof νe (ν̄e ) is higher than that of νµ (ν̄µ ) especially in a lower energy region due to diﬀerencein the lepton mass. Totally 4.1% and 3.1% errors assigned for the CC event rate in FHC and
RHC, respectively.

7.6

Detector Response

Errors of each reduction parameter and cut criterion may change the observed event rate. The
estimation results are 3.4%, 3.4%, 2.0%, and 5.2% for ν-NCQE, ν̄-NCQE, NC-other, and CC,
respectively. Details of each item are explained below.

EnergyThe error on the absolute scale of the reconstructed energy is evaluated to be 1.5% (Figure 7
in Ref. [117]) by the LINAC [90] and DT [91] calibrations. To estimate an uncertainty comingfrom the absolute error, Erec is shifted by its error size, and a less than 1% change is seen in
the selected number of events. The resolution error is also evaluated by the calibrations to be
1.6%. This does not produce any sizable error. In total, a 1% error is assigned.

Vertex position and direction
The vertex position precision is estimated to be 5 cm in Ref. [117]. This may aﬀect the dwall
cut. A 5 cm change in dwall does not produce a more than 1% error in every interaction mode.
Since the eﬀect of the position resolution error is considered to be negligible, a 1% uncertainty
is assigned to the dwall cut.
As for the eﬀwall case, not only position error but also direction error needs to be considered.
Even a conservatively large error of the angular precision (3◦ ) does not lead to an error of larger
than 50 cm. A 50 cm change in eﬀwall produces a less than 1% error in the final event number.
Neither does resolution error arise a more than 1% error. Thus, 1% is used as the systematic
uncertainty regarding the eﬀwall cut.

Fit quality
Ref. [81] shows an estimation of the ovaQ error to be 1.5%. This causes a negligible size oferror in the end. The eﬀect of the ovaQ resolution error on the final result is also negligible.

CHAPTER 7. UNCERTAINTY ESTIMATES

87

Cherenkov opening angle
A 2◦ change of θC is applied and the diﬀerence from the nominal is checked. This can coverboth absolute and resolution error eﬀects. As a result, a smaller than 0.5% change is seen for
NCQE, while a 1% change for NC-other and a 4% change for CC are seen. This is reasonablebecause the CC events lie close to the CC interaction cut criteria in the Erec −θC plane, as
shown in Figures 6.3 and 6.4.

PMT gain shift
Over the T2K operation period (SK-IV), the SK PMT gain has been increasing continuously,
as shown in Figure 7.6. This aﬀects the eﬀective number of hit PMTs, and accordingly changes
the reconstructed energy. The size of such eﬀect on the reconstructed energy is at most a few
percent. Then, this eﬀect is taken into account as the systematic error, with a change of Erec by
5%. As a result, changes of 2% for ν-NCQE, 2% for ν̄-NCQE, 0.5% for NC-other, and 3% for
CC are found. The fact that a smaller change is seen in NC-other can be understood by that
NC-other events distribute almost uniformly in energy while NCQE events locate mainly in alower energy side where the PMT gain shift eﬀect is more critical. As for the other reconstructedparameters such as vertex and Cherenkov opening angle, the gain shift eﬀect is expected to be
negligible.

Dark noise charge peak w.r.t. April 2009

1.2

1.15

1992-1995 PMT
1996-1997 PMT
2003 PMT
2004 PMT2005 PMT

1.1

1.05

1

0.95
01/01/09

01/01/10

01/01/11

01/01/12

01/01/13

01/01/14

01/01/15

01/01/16

01/01/17

date

Figure 7.6: SK PMT relative gain with respect to April 2009 as a function of time. Diﬀerent
colors correspond to the PMT types with diﬀerent production periods. Clear gain shift isobserved over the operation period in every PMT type.

Accidental coincidence events
The accidental events due to the cosmic-ray muons would potentially aﬀect the selection. Thiseﬀect is checked by the SK trigger rate and found to be negligible.

CHAPTER 7. UNCERTAINTY ESTIMATES

7.7

88

Summary of Systematic Uncertainties

Table 7.5 summarizes the systematic uncertainties as well as the event composition fraction ofeach interaction mode. The dominant errors come from the primary- and secondary-γ emission
models. The total uncertainties on the NCQE signal are ∼20% in both FHC and RHC.
Table 7.5: Summary of systematic uncertainties on the observed event rate in percent for
the FHC and RHC sample components. The fraction of each component, listed as “Event
fraction”, is shown together in percent. For the beam-unrelated events, the total uncertainty
entry represents the statistical uncertainty.

FHC

RHC

Event fraction
Neutrino flux
Neutrino interaction
Primary-γ production
Secondary-γ production
Oscillation parameter
Detector response
Total error
Event fraction
Neutrino flux
Neutrino interaction
Primary-γ production
Secondary-γ production
Oscillation parameter
Detector response
Total error

ν-NCQE ν̄-NCQE
75.0
2.0
6.7
8.6
3.0
3.0
11.0
10.6
13.5
13.4
3.4
3.4
19.2
19.7
19.0
59.9
7.0
6.4
3.0
3.0
12.2
11.4
13.6
13.1
3.4
3.4
20.1
19.0

NC-other
17.8
7.3
8.2
6.0
19.5
2.0
23.3
16.5
7.0
10.8
3.5
19.3
2.0
23.4

CC Beam-unrelated
3.7
1.5
6.4
16.5
6.6
17.6
4.1
5.2
26.7
3.0
2.5
2.1
6.5
38.2
0.5
21.4
3.1
5.2
44.7
3.9

Chapter 8
Cross Section Results
8.1

Cross Section Extraction

FHC
RHC) are expressed
The number of observed events in the FHC and RHC samples (Dobs
and Dobs
as follows:

mode
mode
mode
mode
mode
mode
Dobs
= fν-NCQE Mν-NCQE+ fν̄-NCQE Mν̄-NCQE+ MNC-other+ MCC+ Dbeam-unrelated
,

(8.1)

mode
mode
where mode = FHC or RHC, Mν-NCQE
and Mν̄-NCQE
represent the number of neutrino and
mode
mode
mode
antineutrino NCQE interactions respectively, and MNC-other, MCC, and Dbeam-unrelated
are thoseof the NC-other interaction, the CC interaction, and the beam-unrelated events, respectively.
Here quantities from data are written with a capital D, while those from MC with a capital
M . The factors fν-NCQE and fν̄-NCQE are the measured quantities and serve to scale the NCQE
cross section predictions. The number of events by neutrino and antineutrino interactions arecalculated as below:

modeMν-NCQE

=

∑ ∫

NEUT
σν-NCQE(Eν )ϕmode(Eν )ϵmodeνν-NCQE (Eν )T dEν ,

(8.2)

NEUT
σν̄-NCQE(Eν )ϕmode(Eν )ϵmodeνν-NCQE (Eν )T dEν ,(8.3)

ν=νµ ,νemodeMν̄-NCQE=∑ ∫ν=ν̄µ ,ν̄emode
MNC-other=∑

ν=νµ ,νe ,ν̄µ ,ν̄e
mode
MCC

=

∑

∫
NEUT
σν-NC-other(Eν )ϕmode(Eν )ϵmodeνν-NC-other (Eν )T dEν ,

(8.4)

NEUT
σν-CC
(Eν )ϕmode(Eν )ϵmodeνν-CC (Eν )T dEν .

(8.5)

∫

ν=νµ ,νe ,ν̄µ ,ν̄e

Here σ NEUT expresses the NEUT cross section, ϕ is the flux, ϵ is the selection eﬃciency, T is
the number of target nucleons, and Eν is the neutrino energy. From Equation 8.1, the relations
below are obtained for each operation mode:
FHC
FHC
FHC
FHC
FHC
FHC
, (8.6)+ fν̄-NCQE Mν̄-NCQE= fν-NCQE Mν-NCQE− Dbeam-unrelated− MCC− MNC-other
Dobs
RHC
RHC
RHC
RHC
RHC
RHC
Dobs
− MNC-other− MCC− Dbeam-unrelated= fν-NCQE Mν-NCQE+ fν̄-NCQE Mν̄-NCQE. (8.7)89

CHAPTER 8. CROSS SECTION RESULTS

90

By transforming these, fν-NCQE and fν̄-NCQE can be written as below:fν-NCQE

RHC
FHC
XMν̄-NCQE− Y Mν̄-NCQE
=
,
FHC
RHC
RHC
FHC
Mν-NCQE
Mν̄-NCQE− Mν-NCQE
Mν̄-NCQE

(8.8)

RHC
FHC
XMν-NCQE− Y Mν-NCQE
,
FHC
RHC
RHC
FHC
Mν̄-NCQE
Mν-NCQE− Mν̄-NCQE
Mν-NCQE(8.9)

fν̄-NCQE =

FHC
FHC
FHC
FHC
X = Dobs− MNC-other− MCC− Dbeam-unrelated,(8.10)

RHC
RHC
RHC
RHC
= Dobs− MNC-other− MCC− Dbeam-unrelated.

(8.11)Y

Based on the number of the observed events, 204 in FHC and 97 in RHC, the scale factors arecalculated to be fν-NCQE = 0.80 and fν̄-NCQE = 1.11. Errors of these factors are evaluated bypseudo experiments generated according to random variations of the statistical and systematic
mode
uncertainties described in Chapter 7. Here statistical uncertainties are considered for Dobs
mode
(the eﬀect of the statistical uncertainty for Dbeam-unrelated
is negligible), and systematic uncermode
mode
mode
mode
tainties are considered for Mν-NCQE , Mν̄-NCQE , MNC-other, and MCC
. The pseudo experiments
are generated assuming Gaussian distributed errors, with means and variations as shown in
Tables 6.3, 6.4, and 7.5. All the errors are uncorrelated except for the primary- and secondaryγ uncertainties 1 . The primary-γ production error is considered to be fully correlated among
diﬀerent interaction types and operation modes. The secondary-γ production error is treatedin the same way. This is because the changes in γ-ray production rates are common for all theneutrino interaction types and T2K operation modes. Note that the primary-γ and secondary-γ
production uncertainties are uncorrelated. Distributions of the calculated scale factors for one
million pseudo experiments are shown in Figures 8.1 and 8.2, for the statistical and systematic
variation cases, respectively. The dominant error is the uncertainty of the secondary-γ emission
model. The scale factors have a weak negative correlation for variations of the statistical uncertainties but a strong positive correlation under the influence of the systematic uncertainties.
In the end, the scale factors are measured as follows:1fν-NCQE = 0.80 ± 0.08(stat.)+0.24−0.18 (syst.),(8.12)fν̄-NCQE = 1.11 ± 0.18(stat.)+0.29−0.22 (syst.).

(8.13)

Correlations from the flux and cross section parameters have a negligible impact on the final result andhave therefore been omitted here.

CHAPTER 8. CROSS SECTION RESULTS

91

50000

Statistical Error (ν)
nominal (0.80)

40000±1 σ (±0.08)
30000

20000

10000

0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

fν -NCQE

22000

Statistical Error (ν)

20000

nominal (1.11)

18000±1 σ (±0.18)

16000
14000
12000
10000
8000
6000
4000
2000
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

fν -NCQE

fν -NCQE

2
1.8
1000
1.6
1.4

800

1.2
600

1
0.8

400
0.6
Statistical Error

0.4

200
nominal (0.80, 1.11)

0.2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

fν -NCQE

Figure 8.1: Results of the pseudo experiments on the scale factors when the numbers of theobserved events are varied based on the statistical uncertainties: fν-NCQE = 0.80 ± 0.08 andfν̄-NCQE = 1.11 ± 0.18.

CHAPTER 8. CROSS SECTION RESULTS

92

20000
Systematic Error (ν )18000
nominal (0.80)

16000±1 σ (+0.24/-0.18)

14000
12000
10000
8000
6000
4000
2000
0
0

0.5

1

1.5

2

2.5

3

fν -NCQE

16000

Systematic Error (ν)

14000

nominal (1.11)

12000±1 σ (+0.29/-0.22)

10000
8000
6000
4000
2000
0
0

0.5

1

1.5

2

2.5

3

fν -NCQE

fν -NCQE

3
600
2.5
500
2

400

1.5

300

1

200
Systematic Error

0.5

100

nominal (0.80, 1.11)

0
0

0.5

1

1.5

2

2.5

3

0

fν -NCQE

Figure 8.2: Results of the pseudo experiments on the scale factors when the numbers of thepredicted events are varied based on the systematic uncertainties: fν-NCQE = 0.80+0.24−0.18 and.
The
dominant
uncertainty
sourceisthesecondary-γ
emissionmodel.
fν̄-NCQE = 1.11+0.29−0.22

CHAPTER 8. CROSS SECTION RESULTS

8.2

93

Flux-averaged NCQE-like Cross Sections

The predictions of the flux-averaged cross sections by NEUT for the neutrino and antineutrino
NEUT
NEUT
⟩ and ⟨σν̄-NCQE⟩) are calculated as below:
NCQE interactions (⟨σν-NCQE∫∑
ν=νµ ,νe∑NEUT⟨σν-NCQE
⟩ =

∫

∑
NEUT
⟩ =
⟨σν̄-NCQE

NEUTσν-NCQE(Eν )ϕν (Eν )dEν∫
= 2.13 × 10−38 cm2 /oxygen, (8.14)
ϕ
(E
)dE
ν
ν
ν
ν=νµ ,νe

ν=ν̄µ ,ν̄e∑

NEUT(Eν )ϕν (Eν )dEνσν̄-NCQE∫= 0.88 × 10−38 cm2 /oxygen. (8.15)
ϕ
(E
)dE
ν
ν
ν
ν=ν̄µ ,ν̄e

The nominal fluxes, ϕν = ϕFHC
and ϕν̄ = ϕRHC
, are used for neutrinos and antineutrinos in theνν̄
calculations above. Note that summation over muon and electron (anti)neutrinos means for theunoscillated fluxes in Figure 5.1, while the actual flux contains tau (anti)neutrinos which appear
due to the neutrino oscillation. This treatment is justified because the NCQE interaction is
flavor-independent. Here the integrations are conducted up to 10 GeV and the eﬀect from theregion above is negligible. The observed flux-averaged NCQE-like cross sections are obtainedby multiplying the scale factors to each of the NEUT cross sections:
NEUT−38⟨σν-NCQE ⟩ = fν-NCQE · ⟨σν-NCQE⟩ = 1.70 ± 0.17(stat.)+0.51
cm2 /oxygen,−0.38 (syst.) × 10
(8.16)NEUT−38⟨σν̄-NCQE ⟩ = fν̄-NCQE · ⟨σν̄-NCQE⟩ = 0.98 ± 0.16(stat.)+0.26
cm2 /oxygen.
−0.19 (syst.) × 10
(8.17)The measured NCQE-like cross sections are shown together with the predictions on NCQE from
NEUT in Figure 8.3. The measurement on neutrinos improves over the previous result with−38
the FHC Run 1−3 data, ⟨σν-NCQE ⟩ = 1.55+0.71
cm2 /oxygen [51]. The−0.35 (stat. ⊕ syst.) × 10
result on antineutrinos is the first measurement of this channel to date. Covariance matricesof the neutrino and antineutrino NCQE-like cross sections are calculated for both variations of
the statistical and systematic uncertainties as shown in Table 8.1.
Table 8.1: Covariance of the neutrino and antineutrino cross sections for the statistical (systematic) error case. The unit of numbers is (10−38 cm2 /oxygen)2 .
σν-NCQEσν̄-NCQEσν-NCQEσν̄-NCQE
0.030 (0.227) −0.005 (0.095)−0.005 (0.095)
0.025 (0.058)

3
2.5
total error

2stat. error

1.5

2
1.8
1.6
1.4
1.2

total error
stat. error

1
T2K Neutrino Data (Run1-9)
NEUT 5.3.3

1

NEUT 5.3.3 Flux-averaged

0.5
0
0

94

σNCQE [× 10-38 cm2]

σNCQE [× 10-38 cm2]

CHAPTER 8. CROSS SECTION RESULTS

T2K FHC ν Flux (Run1-9)

0.5

1

1.5

2

2.5
3
Eν [GeV]T2K Antineutrino Data (Run1-9)

0.8

NEUT 5.3.3

0.6

NEUT 5.3.3 Flux-averaged

0.4

T2K RHC ν Flux (Run1-9)

0.2
0
0

0.5

1

1.5

2

2.5
3
Eν [GeV]Figure 8.3: The measured neutrino- (left) and antineutrino- (right) oxygen NCQE-like crosssections in comparison with the NCQE cross sections predicted by NEUT. The points are placedat the flux mean values, 0.82 GeV for neutrinos and 0.68 GeV for antineutrinos, respectively.
The vertical bars represent the statistical errors (shorter) and the quadratic sums of the statistical and systematic errors (longer). The horizontal bars represent the upper and lower 1σ
ranges of the fluxes. The T2K fluxes for each neutrino beam mode are also shown together inan arbitrary normalization.

8.3

Discussion

8.3.1

NC 2p2h Interactions

Currently, there are no theoretical models nor experimental results available in the literature
about the NC 2p2h interaction, so this channel is not simulated in this analysis. Since the NC
2p2h interaction involves the multi-nucleon knock-out, not only multiple γ-rays but also thesecondary γ-rays from the recoil nucleons are expected. Therefore, if this process exists thenthe selection in this analysis likely to include such events. However, if the ratio of NC 2p2h
to NCQE cross sections is similar to the corresponding CC ratio, roughly 5−10% [103], thepresent measurement is not sensitive to these events.

8.3.2

Comparison with Theoretical Models

The measured NCQE-like cross sections are tied to NEUT as the underlying model about signal
and background, but it is interesting to compare these results with other theoretical predictions.
Five models from Ref. [118] are referred in comparison.
• Spectral Function (SF) [100, 101]: The SF describes a distribution of the momentum and removal energy of nucleons inside the nucleus, which provides a diﬀerent initialmomentum distribution of nucleons from the relativistic Fermi gas model [102].
• Relativistic Mean Field (RMF) [119–122]: The RMF makes use of the relativistic
distorted waves to describe the knocked-out particle.

CHAPTER 8. CROSS SECTION RESULTS

95• Superscaling (SuSA) [123, 124]: In the SuSA approach, the measured electron-nucleus
cross sections are used to predict the neutrino-nucleus cross sections.
• Relativistic Green’s Function (RGF) [122,125–127]: In this approach, the final stateinteractions are included using the relativistic Green’s function and a complex opticalpotential. Here two parametrizations, EDAI and “democratic”, are considered for the
optical potential.
• Relativistic Plane Wave Impulse Approximation (RPWIA) [122]: In the RPWIA,
the final state interactions between nucleons is neglected and the knocked-out particle isdescribed by the relativistic plane wave.

cm2]
-38

3

σNCQE [× 10σNCQE [× 10

-38

cm2]

The predictions of these models are shown in Figure 8.4. Due to diﬀerence in the available
energy range of the calculation values, the cross sections of some models are not shown in thefull range. The flux-averaged cross sections are calculated using each model prediction, and theresults are shown in Figure 8.5, together with the measurement results. Here the integration
ranges are diﬀerent following the cross section available range of each model but this eﬀect is
expected to be small since all the models are calculated up to at least 2 GeV where the T2K
flux gets attenuated enough. The measured result on neutrinos is consistent with all of themodels within the 1σ error, but the SF, RMF, and SuSA models lie outside the 1σ region for
antineutrinos. However, it should be noted that each model has its uncertainties and none ofthese models contains the NC 2p2h process.

2.5
2O(ν ,ν 'N) cross section
NEUT
SF
RMF
SuSA
RGF, EDAI
RGF, Democratic
RPWIA

1.8
1.6
1.4
1.2

16

1.5
1
0.5
0
0

2

0.5

1

1.5

2
2.5
Eν [GeV]1

O(ν,ν'N) cross section
NEUT
SF
RMF
SuSA
RGF, EDAI
RGF, Democratic
RPWIA

16

0.8
0.6
0.4
0.2
0
0

0.5

1

1.5

2

2.5
3
Eν [GeV]Figure 8.4: Neutrino (left) and antineutrino (right) NCQE cross sections on all nucleons inoxygen as a function of neutrino energy for six theoretical predictions.

CHAPTER 8. CROSS SECTION RESULTS

0

96

RPWIA

RPWIA

RGF, DEM

RGF, DEM

RGF, EDAI

RGF, EDAI

SuSA

SuSA

RMF

RMF

SF

SF

NEUT 5.3.3

NEUT 5.3.3

0.5

1

1.5

2

2.5

0

0.2

0.4

0.6

σν -NCQE [× 10-38 cm2]

0.8

1

1.2

1.4

σν -NCQE [× 10-38 cm2]

Figure 8.5: Comparison of the flux-averaged NCQE-like cross sections by T2K and the fluxaveraged NCQE cross sections by various models for neutrinos (left) and antineutrinos (right).
Solid line and transparent area represent the measured mean values and their 1σ uncertainties
including both statistical and systematic ones, respectively.

8.3.3

Impact on Supernova Relic Neutrino Searches

The present work can be used to estimate the NCQE-like background by atmospheric neutrinosin the SRN search, which is the main motivation of this thesis. The cross section results can beused directly, as is demonstrated in Part IV. However, this suﬀers from large uncertainties fromthe neutron multiplicity and γ-ray emissions that aﬀect the Cherenkov angle distribution, as
described in Chapter 12. If instead the number of events in the expected SRN signal region isused, most errors can be avoided. In the following, the current analysis samples are projected
onto the 2D Erec −θC plane, which is used in the SK SRN search. This is divided into four
regions: (1) Erec ∈ [3.49, 7.49] MeV and θC ∈ [38, 50] degrees, (2) Erec ∈ [7.49, 29.49] MeV
and θC ∈ [38, 50] degrees (3) Erec ∈ [3.49, 7.49] MeV and θC ∈ [78, 90] degrees, and (4)Erec ∈ [7.49, 29.49] MeV and θC ∈ [78, 90] degrees. The signal window of the SK SRN analysis
corresponds to region 2. Figure 8.6 gives the Erec −θC distributions from the FHC and RHC
samples before the CC interaction cut and after all of the preceding cuts. Table 8.2 summarizes
the numbers of observed and predicted events in each region calculated from Figure 8.6. The
diﬀerence between the observation and prediction in regions 3 and 4 in the FHC sample may be
attributed to the inaccurate modeling of the secondary-γ emission as explained in Chapter 6.
The Erec distributions for θC ∈ [38, 50] degrees and θC ∈ [78, 90] degrees for the FHC and
RHC samples are shown in the top four panels of Figure 8.7. Similarly, the θC distributions for
Erec ∈ [3.49, 7.49] MeV and Erec ∈ [7.49, 29.49] MeV are shown in the bottom four panels of thesame figure. Here also the FHC distributions from observation and prediction show discrepancies, which may be attributed to the modeling of the secondary-γ emission. These distributions
can be used to estimate the NCQE-like background to the SRN search by suitable weightingof the prediction to observation. This is more realistic with much larger statistics realized inHyper-Kamiokande and with high power beams in the upgraded J-PARC, which could provide
the NCQE-like background estimation better than a 10% precision as is explained later.

90

3.5

80
3
70
2.5

60
50

2

40

1.5

30

97

θC [degree]θC [degree]

CHAPTER 8. CROSS SECTION RESULTS

90
1.6
80
1.4

70

1.2

60

1

50
40

0.8

30

0.6

20

0.4

10

0.2

1
20
0.5

10
0

5

10

15

20

0

25

0

5

10

15

20

Erec [MeV]25

0

Erec [MeV]

Figure 8.6: Two-dimensional Erec −θC distributions for FHC (left) and RHC (right) respectively
before the CC interaction cut and after all of the preceding cuts described in Chapter 6.
Magenta dots correspond to the observed data.

Table 8.2: Numbers of observed and predicted events for each region defined in the text.
FHC
Observation
Prediction (total)
ν-NCQEν̄-NCQE
NC-otherCC
Beam-unrelated
RHC
Observation
Prediction (total)
ν-NCQEν̄-NCQE
NC-otherCC
Beam-unrelated

Region 1
47
41.1
34.8
1.1
3.4
0.8
1.0
Region 1
19
18.6
3.2
13.4
1.2
0.1
0.7

Region 2
16
20.4
10.7
0.3
5.7
3.6
0.1
Region 2
12
7.3
1.1
3.4
2.1
0.7
0.0

Region 3
18
30.8
24.4
0.6
4.6
0.7
0.5
Region 3
14
11.9
2.2
7.5
1.7
0.2
0.3

Region 4
40
73.8
49.6
1.3
19.3
3.6
0.0
Region 4
21
27.0
5.7
13.1
7.2
1.0
0.0

CHAPTER 8. CROSS SECTION RESULTS

98
78 ≤ θC < 90 degree
Events/MeV

Events/MeV

38 ≤ θC < 50 degree
Data (T2K Run1-9 FHC)

25

ν -NCQEν -NCQE

20

NC-other

Data (T2K Run1-9 FHC)

25

ν -NCQEν -NCQE

20

NC-otherCC

CC

Beam-unrelated (from off-timing data)

15

10

10

5

5

5

10

15

20

0

25
Erec [MeV]38 ≤ θC < 50 degree14

Events/MeV

0

Events/MeV

Beam-unrelated (from off-timing data)

15

Data (T2K Run1-9 RHC)
ν -NCQE

12ν -NCQE

10

NC-other

5

10

15

Data (T2K Run1-9 RHC)
ν -NCQE

12ν -NCQE

10

NC-otherCC

8Beam-unrelated (from off-timing data)

6

6

4

4

2

2

0

5

10

15

20

0

25
Erec [MeV]

Beam-unrelated (from off-timing data)

5

10

Data (T2K Run1-9 FHC)
ν -NCQE

30ν -NCQE
NC-other25

CC
Beam-unrelated (from off-timing data)

20

35

NC-otherBeam-unrelated (from off-timing data)

5

5
40

50

60

0
0

70 80 90
θC [degree]

CC

20

10

30

ν -NCQE

25

10

20

10

Data (T2K Run1-9 RHC)
ν -NCQE

16ν -NCQE

14

NC-other

12CC
Beam-unrelated (from off-timing data)

10

18

4

2

2
50

60

70 80 90
θC [degree]

70 80 90
θC [degree]

NC-otherCC
Beam-unrelated (from off-timing data)

6

40

60

10

4

30

50

ν -NCQE

12

8

20

40

ν -NCQE

14

6

10

30

Data (T2K Run1-9 RHC)

16

8

0
0

20

7.49 ≤ Erec < 29.49 MeV
Events/2.7-degree

Events/2.7-degree

3.49 ≤ Erec < 7.49 MeV
18

25
Erec [MeV]ν -NCQE

15

10

20

Data (T2K Run1-9 FHC)

30

15

0
0

15

7.49 ≤ Erec < 29.49 MeV
Events/2.7-degree

Events/2.7-degree

3.49 ≤ Erec < 7.49 MeV
35

25
Erec [MeV]78 ≤ θC < 90 degree

14

CC

8

20

0
0

10

20

30

40

50

60

70 80 90
θC [degree]

Figure 8.7: The Erec distributions for θC ∈ [38, 50] degrees and θC ∈ [78, 90] degrees (top four)and the θC distributions for Erec ∈ [3.49, 7.49] MeV and Erec ∈ [7.49, 29.49] MeV (bottom four).
All are before the CC interaction cut and after all of the preceding cuts described in Chapter 6.

CHAPTER 8. CROSS SECTION RESULTS

8.4

99

Future Prospects

Secondary-γ emission model
The current largest error source is the modeling of the secondary γ-ray emission. This could
be improved by incorporating experimental data on γ-rays from the neutron-oxygen reactions,which is described in Part III. As is explained in the next chapter, the experiment using an
80 MeV neutron beam achieved a 20% precision on the γ-ray production cross section. If
enough data points with similar sized errors are accumulated at diﬀerent neutron energies, thesecondary γ-ray uncertainty in the NCQE-like measurement can be reduced to less than 5%.
SK-Gd
SK has an upgrade plan to SK-Gd, which dissolves gadolinium-sulfate (Gd2 (SO4 )3 ) to enhance
the sensitivity to the neutron signal [128] utilizing the large neutron capture cross section ofgadolinium (49.7 kb) 2 . Figure 8.8 shows neutron capture eﬃciencies as a function of the Gd
doping rate in SK. With a 0.2% doping of Gd2 (SO4 )3 (corresponding to a 0.1% doping of Gd),a ∼90% capture eﬃciency is achieved. Since the Gd emits a few γ-rays whose energy sum is∼8 MeV (7.9 MeV with 80.5% and 8.5 MeV with 19.3% as branching fractions), the detection
eﬃciency is almost 100%, resulting in the 90% neutron tagging eﬃciency at a 0.1% Gd doping.

Capture eﬃciency on Gd [%]100

0.1% Gd 䠖~90%
capture efficiency=Gd2(SO4)3 100t

80

60

40

0.01% Gd 䠖~50%
capture efficiency=Gd2(SO4)3 10t

200.0001

0.001

0.01

0.1

1

Gd rate in water [%]Figure 8.8: Neutron capture eﬃciency as a function of Gd doping rate in SK.
There are many possible studies about the NCQE sample using neutron information. This
would help to study the relationship of neutrons, their transport in water, and the secondary-γ
production. Information on the neutron capture vertex would further constrain the kinetic
2

The neutron capture cross section of hydrogen is 0.33 b and that of oxygen is 0.19 mb.

CHAPTER 8. CROSS SECTION RESULTS

100

energy of neutrons from the NCQE interactions, by measuring the neutron flight length fromthe primary interaction vertex. Neutron information would also allow for the diﬀerential crosssection measurement by reconstructing Q2 as well as the ∆s measurement if the proton andneutron in the final state are discriminated. Finally, it may be possible to identify the NCQE
interaction resulting in the ground state by requiring no activity by the primary γ-ray. This
would reduce uncertainties on the initial state of nucleons inside the nucleus, which could
improve the sensitivity of searches for proton decay via p → νK + [129].
Hyper-Kamiokande
Hyper-Kamiokande (HK) is a successor of SK with a fiducial volume of ∼190 kton (∼8.4 times
larger than SK) [130, 131], as schematically illustrated in Figure 8.9. In HK, the photosensor is
expected to improve much over the SK one, then the higher neutron tagging eﬃciency (∼40%)
is expected. In the era of HK, J-PARC will be upgraded to serve a 1.3 MW proton beam (fromthe current 500 kW) as well as the magnetic horn current will increase to 320 kA (from thecurrent 250 kA) [76], yielding a ∼3 times more intense neutrino beam. HK is planned to beconstructed at 2.5◦ oﬀ-axis with respect to the J-PARC proton beam direction.

Figure 8.9: Schematic illustration of the Hyper-Kamiokande detector.
Since the oﬀ-axis angle is the same, a measurement similar to the current work but with∼25 times higher statistics is possible. With this condition, ≳100 times larger data sets bothon the FHC and RHC samples are obtained after the 5-year operation, which provides about1000 events with the neutron tagging in the SRN signal region (region 2 in the previous section).
In the SRN background estimation, as described in Chapter 12, the atmospheric neutrino flux
uncertainty needs to be considered, which is currently about 15%. This will be improved by a
new hadron interaction experiment (EMPHATIC) [132] down to as large as 5%. In the end, the
NCQE-like background would be estimated with a ∼10% accuracy. In addition, the neutron
kinematics after the NCQE interaction can be investigated with high statistics.

Part IIIStudies towards Improvements of γ-ray
Emission Model101

Chapter 9
RCNP-E487 Experiment
9.1

Experimental Motivation and Overview

As described in Part II, in addition to γ-rays produced from the neutrino-oxygen interaction,
γ-rays are emitted from the reactions by nucleons, mostly neutrons, knocked-out by the NCQE
interaction. Since the emission of these secondary γ-rays is isolated from the primary γ-ray emission due to the neutrino interaction by only less than O(100) ns, the primary- and secondary-γ’s
are reconstructed in the same event in SK. In the previous analysis, the uncertainty on thesecondary-γ emission rate was estimated by comparing two models, GCALOR [85, 86] and theγ emission model in NEUT [49]. In the estimation, the boundary between inelastic interactions
without nucleon knock-out and quasielastic nucleon knock-out interactions by neutrons was
set to 30 MeV in the neutron energy. The GCALOR was replaced with the latter model forneutrons with energies above 30 MeV, and variance was taken as a systematic error; however,setting such boundary is highly model-dependent. This has been improved in the present work,
as explained in Chapter 7, but there still remains a large uncertainty about the secondary-γ
model. Within GCALOR, the ENDF/B-V library [133] is used for simulating neutron reactions below 20 MeV and an intra-nuclear cascade model is used for energies above 20 MeV.
The latest update in the ENDF/B library, ENDF/B-VIII, includes new data from experiments,
but data on neutron reactions above 20 MeV is limited. The intra-nuclear cascade model isconsidered to be insuﬃcient for energies between 20 and 200 MeV, while it describes interactions above 200 MeV well [134, 135]. Furthermore, there is little data on the γ-ray production
from neutron-oxygen reactions. Therefore, providing experimental data on γ-ray production via
neutron reactions on oxygen is beneficial for the study of neutrino-oxygen NCQE interactions.
Basic concept of the experiment is to measure the γ-rays emitted from neutron reactions on
oxygen using neutron beams, a water target, and γ-ray detectors. Since data especially above
neutron energy of 20 MeV is insuﬃcient and the neutron energy from the NCQE interaction
ranges up to several hundred MeV as shown in Figure 6.14, three energies (30, 80, and 250 MeV)
were selected as the experimental points. The experiments are conducted at Osaka University’s
Research Center for Nuclear Physics (RCNP) [136–138] in Japan. The experiment with an
80 MeV beam is numbered as “E487” and that with 30 and 250 MeV beams as “E525” at
RCNP. In this thesis, results from the E487 experiment are presented 1 .

1Data taking of the E525 experiment was finished, and the analysis is now on-going.

103

CHAPTER 9. RCNP-E487 EXPERIMENT

9.2

104

Experimental Setup

The experiment was conducted in a 100 m long neutron beamline. A schematic drawing of theneutron beamline and the experimental setup is shown in Figure 9.1. Protons were accelerated
to a kinetic energy of 80 MeV by two cyclotrons, the K140 AVF cyclotron and the K400 ring
cyclotron. The proton beam was then injected onto a 10 mm thick lithium target, which is acompound of 92.5% nat Li and 7.5% 6 Li, producing a neutron beam via the 7 Li(p, n)7 Be reaction.
The proton beam size perpendicular to the beam direction was tuned to be smaller than thelithium target size then almost all the protons hit on the target. During the beam test, theenergy of protons was kept to be 80±0.6 MeV. The proton beam was accelerated in 200 ps widebunches, each being separated by 62.5 ns, and a chopper was set to pass one in nine bunches
to the lithium target. The beam current was tuned to be between a few and ∼100 nA after
the chopper. At downstream of the lithium target, a magnetic field bends charged particles,
which are produced from the proton-lithium reactions, towards a beam dump. The beams arethen composed almost only of neutral particles, which are neutrons and photons at the current
energy. A Faraday cup was placed at the beam dump and measured the proton beam current
throughout the beam time. A few particles that are not fully bent are stopped by an iron andconcrete collimator which is placed 4.5 m away from the target. The depth of the collimator is
1.5 m and its aperture is 10 × 12 cm2 .

~6 m

1.5 m

4.5 m

Neutron time-of-flight tunnel
Quadrupole magnet~~

Collimator~~

Secondary beam
(neutron or photon)

Li target

LaBr3(Ce), HPGe, CsI(Tl)(covered by Pb blocks)orBC-501A

Dipole magnet

Beam
Water target

Faraday cup

Proton beam

Figure 9.1: Schematic drawing of the RCNP facility and its neutron beamline. The dottedmagenta box represents a magnified experimental setup.
A cylindrical acrylic vessel, which is 20.0 cm in diameter and 26.5 cm in height, was placedon the beam axis as a target. This container is 0.5 cm thick along its barrel and 1.0 cm thickat its ends. Measurements were performed in both water-filled and empty conditions.
A Saint-Gobain B380 lanthanum bromide scintillator (LaBr3 (Ce)) was used to detect γrays. The crystal is cylindrical shape with 4.5 cm diameter and length. The LaBr3 (Ce) was
optically coupled to a Hamamatsu H6410 photomultiplier tube (PMT). The charge and time
data were read out by a VME 12-bit CAEN V792N QDC and a VME 12-bit CAEN V775N

CHAPTER 9. RCNP-E487 EXPERIMENT

105

TDC, respectively. The scintillator was placed upstream of the acrylic container to reduce
backgrounds from the neutrons that are scattered oﬀ materials, and shielded with lead bricks
on all sides except for the surface facing the acrylic target to lower backgrounds from theirradiated surrounding materials. Another γ-ray detector, an ORTEC GEM 20180-P highpurity germanium (HPGe) detector, was placed in a similar position to the LaBr3 (Ce) detector.
The detector uses a cylindrical coaxial crystal with a 55 mm (44 mm) in diameter (length) witha hole diameter (depth) of 9.2 mm (33.4 mm). The pulse height data from the HPGe detector
was read out by an MCA Kromek K102. No time data was recorded, hence, the HPGe wasused as a reference detector with a better energy resolution. The HPGe detector was covered
with lead bricks similarly to the LaBr3 (Ce) detector. A photograph of the setup for the γ-ray
measurement is given in Figure 9.2.

LaBr3(Ce)HPGeCsI

neutron beam

Figure 9.2: Photograph of the setup for the γ-ray and fast neutron background measurementswith a water-filled target.

neutron beam
BC-501A

Figure 9.3: Photograph of the setup for the neutron flux measurement.

CHAPTER 9. RCNP-E487 EXPERIMENT

106

Apart from the γ-ray measurements, dedicated measurements of the neutron beam and thebackground arising from fast neutrons were conducted. For the neutron beam measurement,
the acrylic target was replaced by an organic liquid scintillator, Saint-Gobain BC-501A 20LA32,
with coupled to a Hamamatsu H6527 PMT. The scintillator is a 5 inch diameter and a 8 inchlong cylindrical shape and was read out by the same QDC and TDC as the LaBr3 (Ce) detector.
The setup photograph is shown in Figure 9.3. Backgrounds at the LaBr3 (Ce) position from fastneutron hits were measured by an OKEN CsI(Tl) scintillator. The CsI(Tl) is cubic with a sizeof 3.5 × 3.5 × 3.5 cm3 and was coupled to a H6410 PMT. It was placed near the LaBr3 (Ce) andcovered with the lead bricks similarly. The waveform data were recorded by a 14-bit 250 MHz
CAEN DT5725 digitizer. Scattered neutron measurements were performed in parallel to themain measurements with both water-filled and empty configurations, as shown in Figure 9.2.
In all measurements, the proton beam current was monitored by the Faraday cup and used
for the normalization in the analysis.

9.3

Detector Calibration

Arbitrarily Normalized Counts

Energy calibrations of the LaBr3 (Ce), HPGe, and CsI(Tl) detectors were conducted using thephotoelectric-absorption peaks of the γ-rays from several isotopes: 137 Cs, 60 Co, 241 Am/Be,
57
Fe, and so on. These cover the energy range up to 8 MeV. The energy spectra taken with the
LaBr3 (Ce) are shown in Figure 9.4. The detector gains were monitored throughout the beamtime and no significant variations were observed.

0.662
1.17 & 1.33
104

2.22

4.44 & S.E. & D.E.

3

10

1.46

7.65 & S.E. & D.E.

2.61
2

10

10

500

1000

1500

2000

2500

3000

QDC Channel

Figure 9.4: The LaBr3 (Ce) energy spectra in QDC channel with various radioactive sources:
0.662 MeV from 137 Cs, 1.17 and 1.33 MeV from 60 Co, 1.46 MeV from 40 K, 2.22 MeV from2
H, 2.61 MeV from 208 Tl, 4.44 MeV from 12 C, and 7.65 MeV from 57 Fe. The S.E. and D.E.
represent the single and double escape peaks of the corresponding photoelectric-absorption
peak, respectively. Diﬀerent colors correspond to diﬀerent measurements.

CHAPTER 9. RCNP-E487 EXPERIMENT107

For the BC-501A energy calibration, recoil electrons from Compton-scattered γ-rays by a
Na source were used. The Compton-scattered γ-rays were tagged by the LaBr3 (Ce) detector
with diﬀerent geometrical settings, which allows for selection of the energy of recoil electrons
depending on the angles made by the BC-501A and LaBr3 (Ce) detectors and the 22 Na source.
The largest error on the energy scale comes from the geometrical uncertainty, but this resultsin less than a 0.1% systematic uncertainty in the neutron flux measurement as described in thenext section.
In order to identify neutron events separately from γ-rays in the BC-501A and CsI(Tl)detectors, pulse shape information is utilized. Separation capability in the BC-501A was checkedby an 241 Am/Be neutron source. As for the CsI(Tl) detector, the separation performance wastested with a 70 MeV fast neutron beam at Tohoku University’s Cyclotron and Radioisotope
Center [139].
22

9.4

Neutron Beam

In order to measure the γ-ray production cross section, a measurement of the neutron flux isnecessary. In the analysis, first, neutron-like events are selected using the pulse shape discrimination (PSD) technique in the BC-501A detector. Second, the kinetic energies of neutron-likeevents are inferred from their time-of-flight (TOF) between the lithium target and the detector.
Third, the kinetic energy distribution is converted into the flux by applying the neutron detection eﬃciency calculated using the Monte Carlo code, SCINFUL-QMD [140, 141]. The neutron
beam profile was also estimated with data from similar measurements at diﬀerent positions.

9.4.1

PSD and TOF Analyses

For events whose energy is within the QDC dynamic range, a PSD parameter is defined as:

PSD parameter =Qtail − Qped,
Qtotal − Qped

(9.1)

where Qtail is the integrated charge of the waveform for a pre-determined late-time window andQtotal is the charge of the entire waveform. The PSD parameter is larger for particles having
larger dE/dx, such as protons excited by neutrons, in the BC-501A [142]. The Qped represents
an oﬀset of the QDC module, which diﬀers channel to channel. The late-time window was
optimized by calibration data with neutrons from an 241 Am/Be source. The PSD parameter
distribution as a function of Qtotal is shown in Figure 9.5. Events with a PSD parameter larger
and smaller than 0.24 are treated as neutrons and γ-rays, respectively. The neutron ineﬃciency
by this selection was checked to be negligible by an 241 Am/Be calibration. Protons and heavier
particles, such as deuterons and alphas, induced by neutron reactions in the scintillator, areobserved in the large PSD parameter region. Figure 9.6 shows distributions of the depositedenergy in the BC-501A broken down by the neutron-like and γ-like events after PSD. Eventswith energy beyond the QDC dynamic range (∼4000 ch corresponding to ∼6.5 MeV) areselected as neutrons because contributions from γ-rays in this energy region is small.
The TOF distributions of neutron-like and γ-like events are reconstructed using TDC data.
Time-walk corrections are applied for both neutron-like and γ-like events separately when theevents are within the QDC dynamic range. A common correction is applied at high energies
above the dynamic range, where this eﬀect is expected to be small. Figure 9.7 shows TOF

CHAPTER 9. RCNP-E487 EXPERIMENT

108

CountsFigure 9.5: PSD parameter as a function of Qtotal value in QDC channel. The blue line
represents the neutron selection criterion.

240
all

220

Entries
Mean
RMS
total

200
180

γ-like4309281550
910.2

neutronEntries 346349
Mean
1723
RMS
919
gamma-ray
Entries
84579
Mean
1238
RMS
805.2

160
140
120
100
80
60
40
20
0
0

n-like
500

1000

1500

2000

2500

3000

3500

QDC Channel

Figure 9.6: Deposited energy in QDC channel in the BC-501A detector for all (black), neutronlike (blue), and γ-like (red) events.

CHAPTER 9. RCNP-E487 EXPERIMENT

109

Countsdistributions for the neutron-like and γ-like events after the time-walk corrections. The sharp
peak around 3350 ch corresponds to γ-rays emitted from the initial proton-lithium interaction(called the flash γ-rays). The small amount of neutron-like contamination in the flash-γ peakindicates that PSD is eﬀective. Neutron kinetic energies are reconstructed using their time
diﬀerence to the flash γ-ray peak and the distance between the lithium target and the BC501A. The result of the kinetic energy reconstruction is shown in Figure 9.8. The peak is seen
at 77 MeV and is consistent with the expectation from the beam setting.

all

10

Entries
Mean
RMS

3

neutronEntries 346349
Mean
2379
RMS
561.7

4309282379
615

flash-γ

gamma-ray
Entries
84579
total
Mean
2381
RMS
800.1
10

2

n-like10γ-like
500

1000

1500

2000

2500

3000

3500

TDC Channel

Figure 9.7: TOF distributions of all (black), neutron-like (blue), and γ-like (red) events classified by PSD. The sharp peak around 3350 ch is due to the flash γ-rays.

9.4.2

Detection Eﬃciency

The neutron detection eﬃciency of the BC-501A scintillator was calculated with a dedicatedMonte Carlo code, SCINFUL-QMD [140, 141], for each neutron energy bin. In the simulation,geometry, the energy threshold, the light attenuation inside the detector, and the PMT response
are set. The first four are taken from the geometrical survey, calibration data, and the previous
study with the same detector [143]. The PMT response is based on models in Refs. [144–146].
In the simulation 100,000 neutrons are generated in each of one hundred energies spanningfrom 0.1 MeV to 99 MeV, with a 1 MeV binning above 1 MeV. Figure 9.9 shows the estimatedneutron detection eﬃciencies with the nominal setting.

9.4.3

Neutron Flux Estimation

The neutron flux is obtained from the kinetic energy distribution divided by the detection
eﬃciency, as shown in Figure 9.10. The distribution is normalized by the detector solid angle
from the lithium target and the incident protons. The neutron flux in the peak region between
72 and 82 MeV is 1.71 × 1010 [/sr/µC]. This region is used for the cross section analysis later.

CHAPTER 9. RCNP-E487 EXPERIMENT

110

CountsnEkin {PSDparam>0.24}
18000
16000
14000

Ekin
Entries 346349
Mean
47.03
RMS
24.33

12000
10000
8000
6000
4000
2000
0
0

10

20

30

40

50

60

70

80

90

100

Kinetic Energy [MeV]

Detection Eﬃciency [%]Figure 9.8: Kinetic energy distribution of the neutron-like events reconstructed from the TOF
distribution.

50
45
40
35
30
25
20
15
10
5
0
0

20

40

60

80

100

Neutron Kinetic Energy [MeV]

Figure 9.9: Neutron detection eﬃciencies of the BC-501A calculated with SCINFUL-QMD.
The attenuation factor of 0.008 cm−1 from the previous study [143] and the PMT light output
function from Satoh et al. [144] are used. The bump around 20 MeV is due to an open of newreaction channels by carbon.

CHAPTER 9. RCNP-E487 EXPERIMENT

Neutron Flux [/sr/μC]

×10

111

6

3000

2500

2000

1500

1000

500

0
0

10

20

30

40

50

60

70

80

90

100

Kinetic Energy [MeV]

Figure 9.10: Neutron flux normalized by the detector covering solid angle and the incident
protons. The red bars indicate the peak region (72−82 MeV) used for the cross section analysis.

9.4.4

Flux Uncertainties

Table 9.1 summarizes the statistical and systematic uncertainties on the neutron flux in the
72−82 MeV region. The statistical uncertainty is less than 0.5%. Systematic uncertainties aredescribed in the following part.
Table 9.1: Statistical and systematic uncertainties on the neutron flux in the energy region of
72−82 MeV.
Error source
Size [%]
Statistical
0.5
Beam stability
1.4
Neutron selection
2.2
Detection eﬃciency by SCINFUL-QMD
10.0
Former bunch and environmental contamination
1.0
Kinetic energy reconstruction
1.0
Total
10.4

Beam stability
The flux measurement was conducted three times at the beginning, the middle, and the endof the beam test. Over the three measurements the flux was stable within a 1.4% fluctuation.
This is incorporated as a systematic error.
Neutron selection
The uncertainty of the neutron selection is estimated using the contamination of neutron-likeevents in the flash-γ peak in Figure 9.7. The flux is varied by the rate of remaining neutron-

CHAPTER 9. RCNP-E487 EXPERIMENT

112

like events to the total events in the flash-γ peak after PSD, and the diﬀerence is taken as asystematic error, resulting in 2.0%. In addition, the contamination of γ-ray events in the higher
energy data is extrapolated to the QDC overflow region using the distribution in Figure 9.6,
yielding a 0.8% contamination. In the end, the neutron selection error is taken to be the sum
in a quadrature of these two components, 2.2% in total.
Detection eﬃciency by SCINFUL-QMD
Physics modeling of SCINFUL-QMD is based on experimental data [140, 141], and a 10%
uncertainty is estimated for the region below 80 MeV in the previous studies [143]. Other
errors such as the energy calibration uncertainty and the PMT response model are checked tobe negligible. In total, a 10.0% uncertainty is assigned.
Other systematic errors
Systematic errors in the TOF measurement can result in uncertainties in the reconstructedkinetic energy and accordingly flux due to eﬃciency diﬀerences between energy bins. The timewalk correction error is found to have a negligible impact on the result. The TDC calibration
uncertainty leads to a 0.4 ns uncertainty in the TOF measurement. Uncertainties of the detectoralignment produce a 0.3 ns error, and the width of flash-γ peak incurs a further 1.1 ns. In total
a 1.2 ns error is assigned to the TOF measurement. This corresponds to a 1 MeV uncertainty
in the kinetic energy reconstruction and a 1% uncertainty in the flux.
Contaminations from the former beam bunches or environmental neutrons are estimated tobe less than 1% by comparing the event rate in the region between the flash-γ peak and theneutron peak in Figure 9.7.

9.4.5

Neutron Beam Profile

In order to reduce neutron backgrounds in the γ-ray detectors due to direct exposure to theneutron beam, a profile measurement was conducted ahead of the γ-ray measurements. In
the profile measurement, the BC-501A scintillator was shifted from the center to 20 cm perpendicularly oﬀ-axis in steps of 4 cm. The flux at each position was measured with the same
method as described above. The measurement results are shown in Figure 9.11. The flux at
20 cm away from the beam center is smaller than that at the beam center by more than twoorders of magnitude. This position is outside of the expected beam profile as determined by
the collimator (10 cm from the beam center), the γ-ray detectors were placed at 20 cm awayfrom the beam center. The neutron background at the position was measured with the CsI(Tl)scintillator as explained later.

Neutron Flux [/sr/μC]

CHAPTER 9. RCNP-E487 EXPERIMENT

10

113

10

10

9

10

8

0

0

1

4

2

8

3

4

12

5

16

20

6

Distance from Beam Center [cm]Figure 9.11: Neutron beam profile measured by the BC-501A detector. The result is for the
peak region (72−82 MeV).

9.4.6

TOF Measurements in the Lanthanum-Bromide Scintillator

To infer kinetic energies of neutrons which produce γ-rays observed in the LaBr3 (Ce) scintillator,
its timing information is used to perform a TOF analysis similarly to the BC-501A. The γray event timing is corrected for the time-walk eﬀect and the distance between the detector
and the acrylic target is considered in the reconstruction. Figure 9.12 shows both TOF andreconstructed kinetic energy distributions. The flux peak and width are consistent with theresult from the BC-501A detector.

On-timing (72–82 MeV)

Off-timing

CountsEventsnEkin
Ekin
Entries 450324
Mean
34.21
RMS
26.13

30000

25000

10

20000

3

15000

flash-γ
10000

5000

10

2

0
0

1500

2000

2500

3000

3500

10

20

30

40

50

60

70

80

90

100

Kinetic Energy [MeV]

TDC channel

Figure 9.12: Distributions of TOF (left) and the inferred kinetic energy (right) in the LaBr3 (Ce)detector. In the left panel, the on-timing (corresponding to 72−82 MeV in the kinetic energy)
and oﬀ-timing regions are indicated by the solid and dashed bars, respectively. In the rightpanel, the red bars indicate the neutron energy region used for the cross section analysis.

CHAPTER 9. RCNP-E487 EXPERIMENT

9.5

114

De-excitation γ-rays from Neutron-Oxygen Reactions

Normalized counts [/sr/μC]

Figures 9.13 and 9.14 show the observed energy spectra without the TOF cut by the HPGe and
LaBr3 (Ce) detectors, respectively. In both figures, the red and blue spectra correspond to theresults with a water-filled and an empty target, respectively. The vertical axes are normalizedwith the solid angle covered by the acrylic vessel from the lithium target and the incident
protons. Several energy peaks are observed in both detectors. The LaBr3 (Ce) spectra with the
TOF cut are shown in Figure 9.15. Here three spectra are shown: one with a water-filled target
and the on-timing cut applied, one with an empty target and the on-timing cut applied, andone with a water-filled target and the oﬀ-timing cut applied. Note that the oﬀ-timing spectrum
is normalized to the length of the on-timing window.

––– with water

2H (1+) [2.22 MeV]

105

16O (3–) [6.13 MeV] / S.E. / D.E.

––– without water

4

10

57Fe (1/2–) [7.63 MeV] / S.E. / D.E.
3

10

102

HPGe Spectrum
10

0

2

4

6

8

10

7

8

3000
12C (2+) [4.44 MeV] / S.E. / D.E.

15N (5/2+) [5.27 MeV] / S.E. / D.E.

2500

2000

1500
17O (5/2–) [3.84 MeV] / S.E.

1000

500
13C (3/2–) [3.68 MeV]

0

3

4

5

6

Energy [MeV]

Figure 9.13: Energy spectra of the HPGe detector with and without water. The spectra in thebottom panel focus on the region between 3 and 8 MeV.

Table 9.2 summarizes energies of the γ-rays of primary interest to the present measurement,
their parent nuclei with excited states, and the physics processes that produce them. Parent
nuclei are identified by the peak energy and the peak width. The γ-rays from nuclei with

CHAPTER 9. RCNP-E487 EXPERIMENT

115

Normalized Counts [/sr/µs]

3

×10
120

––– with water––– without water

100
80

LaBr3(Ce) Spectrum(w/o TOF cut)

60
40
20
0

2

3

4

5

6

7

8
Energy [MeV]

Figure 9.14: Energy spectra of the LaBr3 (Ce) scintillator with and without water without the
TOF cut.

Normalized Counts [/sr/µs]––– on-timing, with water
8000

15N (7/2+) [2.30 MeV] or 14N (0+) [2.31 MeV]7000––– on-timing, without water––– oﬀ-timing (normalized), with water

13C (3/2–) [3.68 MeV]

16O (3–) [6.13 MeV] / S.E. / D.E.

6000

LaBr3(Ce) Spectrum(w/ TOF cut)

5000
4000
2H (1+) [2.22 MeV]

3000

15N (3/2–) [6.32 MeV] / S.E. / D.E.

12C (2+) [4.44 MeV] / S.E. / D.E.

2000

15N (5/2+) [5.27 MeV] / S.E. / D.E.

1000
0

2

3

4

5

6

7

8
Energy [MeV]

Figure 9.15: Energy spectra of the LaBr3 (Ce) scintillator with and without water with the
TOF cut selecting the on-timing and oﬀ-timing regions defined in Figure 9.12.

CHAPTER 9. RCNP-E487 EXPERIMENT

116

Table 9.2: Energies, parent nuclei with their spin (J) and parity (π), and physics processes ofthe observed γ-ray peaks.
EnergyParent (J π )167.12 MeV
O(1− )
16
6.92 MeV
O(2+ )−
15
6.32 MeV
N( 23 )
16
6.13 MeV
O(3− )+
15
5.27 MeV
N( 25 )
12
4.44 MeV
C(2+ )−
13
3.68 MeV
C( 32 )
14
2.31 MeV
N(0+ )+
15
2.30 MeV
N( 27 )

Physics process
16
O(n, n′ )16 O∗
16O(n, n′ )16 O∗
16O(n, np)15 N∗
16O(n, n′ )16 O∗
16O(n, n′ )16 O∗ then 16 O∗ → 15 N∗ + p, or 16 O(n, np)15 N∗
16O(n, n′ )16 O∗ then 16 O∗ → 12 C∗ + α, or 16 O(n, nα)12 C∗
16O(n, α)13 C∗
16O(n, 2np)14 N∗
16O(n, np)15 N∗

shorter lifetime than the duration of motion after hits by incident particles are Doppler shifted
then the peak width of those γ’s becomes larger.
The 6.13 MeV γ-ray from the excited state of 16 O are clearly seen in both the HPGe and
LaBr3 (Ce) spectra. Inelastic scattering, (n, n′ ), is expected to produce this excited state. The
observed peak appears stronger in the spectrum without the TOF cut in Figures 9.13 and 9.14,
as there is a large contribution to this process from lower energy neutrons. On the other hand,the peak intensity is reduced relative to others in the spectrum with the on-timing TOF cut, asshown with the red spectrum in Figure 9.15. Although clear peaks are not observed, there seensome contributions above 6.5 MeV. Among possible peaks after neutron reactions on oxygen,the 6.92 MeV and 7.12 MeV γ-rays from 16 O after the (n, n′ ) scattering may be more likely tobe emitted, because they are from the excited states next and next-next to the 6.13 MeV state,
respectively. These peaks are added in the spectrum fitting as explained later.
The large bump around 5.8 MeV seen in the LaBr3 (Ce) spectrum with the on-timing cut
in Figure 9.15 is diﬃcult to explain only by the Compton edge of the 6.13 MeV γ-ray. It isconsidered due to the 6.32 MeV γ-ray from 15 N. This peak is thought to come from the direct
knock-out process, (n, np), because it is emitted dominantly when 15 N is created through thisprocess according to Refs. [111,147]. This is not seen clearly in the spectra without the TOF cut
in Figures 9.13 and 9.14 because other components from interactions of lower energy neutrons
which are likely to produce the 6.13 MeV γ’s may dominate. A similar process, (n, 2n), exists;
however, γ-rays from the state after this process are not observed clearly in this experiment.
The reason for this may be that a neutron is more likely to be paired with a proton inside thenucleus therefore the (n, np) process is more probable than the (n, 2n) process.
+In the HPGe spectrum (Figure 9.13), the 5.27 MeV γ-rays from 15 N( 25 ) are observed clearly.
It is less visible in the LaBr3 (Ce) spectrum without the TOF cut (Figure 9.14) because of theworse energy resolution. With the on-timing TOF cut, the 5.27 MeV γ peak, especially the
S.E. peak, is visible in Figure 9.15. Possible processes which produce this γ-ray are nucleon
knock-out, 16 O(n, np), deuteron flipping, 16 O(n, d), and nuclear decay from an excited state of16
O with proton emission after the inelastic process, 16 O∗ →15 N∗ + p. The present work does
not have an ability to distinguish the production processes, then an inclusive measurement
is performed. It is worth noting that the 16 O(n, np) cross section is predicted to be small at
60.7 MeV in a calculation [148] and the 6.32 MeV γ is the most likely if this direct process
happens as described above. Therefore, the 5.27 MeV γ-rays in this analysis might come fromthe (n, n′ ) process followed by decay with proton emission. The 4.44 MeV peak from 12 C(2+ )CHAPTER 9. RCNP-E487 EXPERIMENT

117

is also observed. Here the alpha knock-out, 16 O(n, nα) or decay of 16 O with alpha emission(16 O∗ →12 C∗ + α) (c.f. Ref. [148]) are potential processes contributing to this peak. As in
the 5.27 MeV case, these processes cannot be separated, thus an inclusive measurement is+conducted. In similar processes but with neutron emission, the 5.18 MeV γ-ray from 15 O( 12 )is expected, but was not observed in this experiment. This could be understood by the factthat the minimum excitation energy required for decay with neutron emission (15.66 MeV) is
higher than those for decay with proton emission (12.13 MeV) and decay with alpha emission(7.16 MeV).
The 3.68 MeV γ-rays are observed by both the HPGe and LaBr3 (Ce) detectors. This isconsidered to come from 13 C generated by (n, α) reactions with 16 O. Another peak observed
clearly is the one around 2.30 MeV. This is not so visible in the spectra without the TOF cut
due to the strong peak by 2.22 MeV γ-rays produced from thermal neutron capture. Thesethermal neutron induced events can be removed by the oﬀ-timing data, as explained in the+next section. There are two possibilities: the 2.30 MeV γ from 15 N( 72 ) and the 2.31 MeV
γ from 14 N(0+ ). These two cannot be separated by the LaBr3 (Ce) due to insuﬃcient energy
resolution.
Many peaks that are not from the fast neutron reactions on oxygen are also observed. Theseare explained below though are not of high interest for the purpose in this thesis. The 3.84 MeV
γ-rays seen in Figure 9.13 from 17 O are thought to arise from thermal neutron capture on 16 O.
In addition, there are several other peaks that cannot be attributed to neutron-oxygen reactions.
For instance, the 2.22 MeV and 7.63 MeV peaks are likely due to neutron capture on 1 H and
56
Fe, respectively. Other peaks such as the 1.46 MeV γ-ray from 40 K and the 2.61 MeV γ-ray
from 208 Tl can be made by a number of reactions with neutrons and materials in the beamline.
In this work, the production cross sections for nine peaks in Table 9.2 are measured with aspectrum analysis, which is explained later in this chapter. For the 2.30 MeV and 2.31 MeV
peaks, an inclusive cross section is measured. The spectrum analysis is performed for the peakneutron energy region, then the LaBr3 (Ce) spectra with the on-timing cut in Figure 9.15 are
used.

9.6

Background Estimation

Backgrounds are sorted into four: (1) fast neutron hits, (2) non-water backgrounds, (3) γ-rays
from thermal neutron capture and β’s, and (4) γ-rays from scattered fast neutron reactions.
Each background is explained in the following part.

Fast neutron hits
Neutrons reacting with the LaBr3 (Ce) are a potential background, which are either scatteredoﬀ the acrylic target or incident oﬀ-axis. The CsI(Tl) scintillator was used to measure thisbackground with its PSD capability. For this measurement, the PSD integration region was
optimized with figure-of-merit laid out in Ref. [139]. The same neutron energy region as the
cross section analysis, 72−82 MeV, is selected in the CsI(Tl) time data. The result is shownin Figure 9.16, where three populations are seen: (a) γ-rays, (b) neutrons, and (c) pile-up
events. The latter is due to events having multiple signals within one Flash-ADC time window.
The amount of such pile-up events is negligible compared to that of the γ-ray events. The
fast neutron background is estimated in each energy region between 1 and 8 MeV. Here theresult with an empty target is subtracted from that with a water-filled target. The resulting
contamination of neutrons is smaller than 1% in all energy regions. This is negligible comparedCHAPTER 9. RCNP-E487 EXPERIMENT

118

to the total systematic error. Even if the material diﬀerence between CsI(Tl) and LaBr3 (Ce)is considered, the fast neutron contamination rate is still negligible.

Figure 9.16: Distribution of the ratio of the integrated tail part to the total in the CsI(Tl)waveform as a function of energy. The populations (a), (b), and (c) correspond to the γ-like,neutron-like, and pile-up events, respectively.

Non-water background
Backgrounds arising from neutron reactions on other objects than water are estimated using
data with an empty target. They are seen as the blue spectrum in Figure 9.15 and subtracted
from the measurement with water in the acrylic vessel which is the red spectrum in the same
figure.

γ-rays from thermal neutron capture and β’s
The γ-rays emitted from thermal neutron capture and the electrons or positrons from beta
decay have much longer time scale than the beam repetition cycle (∼560 ns) and hence are
expected to distribute uniformly in time. The contributions from these can then be subtractedusing data in the oﬀ-timing region which is shown as the magenta spectrum in Figure 9.15.
The energy spectrum in the oﬀ-timing region is subtracted from that in the on-timing region
with normalization based on length of the time window in the left panel of Figure 9.12.

γ-rays from scattered fast neutron reactions
After subtraction of the non-water background and the oﬀ-timing background, continuous components remain in the spectrum. This is considered due to the γ-ray events that are producedby scattered neutron reactions with the surrounding materials, as depicted in Figure 9.17. If
this assumption is right, the continuous component is smaller in the spectrum with the TOF
cut selecting faster neutrons, because it takes time for the γ-ray to reach the detector fromthe emission point. To check this, the spectra from the diﬀerent timing regions, corresponding

CHAPTER 9. RCNP-E487 EXPERIMENT

119

to 72−77 MeV and 77−82 MeV in neutron kinetic energy, are compared as shown in the left
panel of Figure 9.18. Clear shape diﬀerence between the two spectra is seen. To further checkthe assumption, the spectrum with an empty target and the on-timing TOF cut is comparedwith the diﬀerence between the 72−77 MeV and 77−82 MeV spectra. Here the 77−82 MeV
spectrum is subtracted from the 72−77 MeV spectrum with an arbitrary scaling. The result
is given in the right panel of Figure 9.18. The shape of the two look similar. These make theassumption that the continuous background is made by the scattered neutrons reacting withthe surrounding materials plausible. The non-water spectrum with the on-timing cut is used
for the spectrum fitting later.

Neutrons

Target (Empty)

Neutrons

Target (Water)

gamma<50 cmgamma<50 cmLaBr3(Ce)

LaBr3(Ce)Figure 9.17: Schematic illustration of the continuous background caused by γ-rays from scattered fast neutron reactions with the surrounding materials for a water-filled target (left) andan empty target (right).

4000

Arbitrary scaled

Normalized counts [/sr/μC]

h_subtr_tof_on_72to77

77–82 MeV
72–77 MeV

3500
3000
2500
2000

2500

(72–77 MeV) – α × (77–82 MeV)
No-water, 72–82 MeV

2000

1500

α: arbitrary factor

1000

1500
1000

500

500
0

2

3

4

5

6

7

8

Energy [MeV]

0

2

3

4

5

6

7

8

Energy [MeV]

Figure 9.18: Comparison of the spectra for the neutron energy region 72−77 MeV and
77−82 MeV (left) and comparison between the shape diﬀerence of these two and the non-water
spectrum for the 72−82 MeV region (right).

CHAPTER 9. RCNP-E487 EXPERIMENT

9.7

120

Spectrum Analysis

In the previous section, the non-water and oﬀ-timing backgrounds are subtracted. Now theobserved spectrum is composed of signals (the γ-rays from neutron-oxygen reactions) and thecontinuous background. With signal and background templates, the observed data is fit to
extract the γ-ray production cross sections. The signal template is made by the simulation
based on a GEANT4 package [149], and the continuous background template is obtained fromthe on-timing non-water data.

9.7.1

Signal Templates

σE/E

In the GEANT4 simulation, the LaBr3 (Ce) detector and the acrylic target filled with water
are set, and γ-rays are generated randomly and isotropically in the water. The γ-rays are thendetected by the LaBr3 (Ce). The obtained spectrum is smeared with the detector resolution
which is obtained from the resolution curve below. The Gaussian fitting was conducted forseveral peaks, which are not Doppler shifted, and the resulting width (σE ) is plotted as afunction of energy (E [MeV]) in Figure 9.19. The data points are then fit to obtain a resolution
curve. The Doppler shift eﬀect should be considered for some peaks. It is known that its eﬀect
size is ∼1%. The 4.44 MeV peak is known to be Doppler shifted and its resolution obtained
from the Gaussian fitting to data, 1.09 ± 0.08%, is consistent with the calculated resolution
from the resolution curve in Figure 9.19 and the Doppler eﬀect, 1.14 ± 0.10%. Therefore, a 1%
is added to the resolution obtained by the curve in Figure 9.19 for the Doppler shifted peaks,
7.12, 6.92, 6.32, 4.44, 3.68, and 2.30 or 2.31 MeV. Note that the 2.30 MeV spectrum is used
for the 2.30 MeV and 2.31 MeV peaks since they are not discriminated in the LaBr3 (Ce). The
resulting signal templates are shown in Figure 9.20. Here the spectra with better and worse
resolutions by 1σ uncertainties of the resolution curve are shown together. For the peaks with
no Doppler shift, the eﬀect of this resolution uncertainty is large.

0.03

σE/E = p0 + p1/√E + p2/E

0.025

p0 = (–1.89 ± 0.81) × 10–3
p1 = (1.68 ± 0.17) × 10–2
p2 = (–2.47 ± 0.91) × 10–3

0.02

0.015

0.01

0.005

0
0

1

2

3

4

5

6
E [MeV]

Figure 9.19: Energy resolution as a function of the deposited energy in the LaBr3 (Ce). The
black points are data and the red√ line is the fitting to those data points. The resolution curve
function is: σE /E = p0 + p1/ E + p2/E (E [MeV]), where p0 = (−1.89 ± 0.81) × 10−3 ,p1 = (1.68 ± 0.17) × 10−2 , and p2 = (−2.47 ± 0.91) × 10−3 .

CHAPTER 9. RCNP-E487 EXPERIMENT

121

MC (6.92 MeV)
EventsEventsMC (7.12 MeV)
3000
nominal resolution

2500+1 σ (worse) resolution-1 σ (better) resolution

2000

3000

1500

1000

1000

500

500

3

4

+1 σ (worse) resolution-1 σ (better) resolution

2000

1500

0
2

nominal resolution

2500

5

6

7

0
2

8

3

4

5

6

Energy [MeV]EventsEventsnominal resolution

7000
nominal resolution

6000+1 σ (worse) resolution+1 σ (worse) resolution

5000-1 σ (better) resolution

2000

8

MC (6.13 MeV)

MC (6.32 MeV)
3000

2500

7

Energy [MeV]-1 σ (better) resolution

4000
1500
3000
1000
2000
500

1000

0
2

3

4

5

6

0
2

7

3

4

5

6

MC (4.44 MeV)
EventsEventsMC (5.27 MeV)
7000
nominal resolution

6000
5000

7

Energy [MeV]

Energy [MeV]
5000
4500

nominal resolution+1 σ (worse) resolution

4000+1 σ (worse) resolution-1 σ (better) resolution

3500-1 σ (better) resolution

3000

4000

2500
3000

2000
1500

2000

1000
1000
500
0

2

2.5

3

3.5

4

4.5

5

5.5

0

6

2

2.5

3

3.5

4

EventsEventsnominal resolution

4000+1 σ (worse) resolution

3500-1 σ (better) resolution5

MC (2.30 MeV)

MC (3.68 MeV)
5000
4500

4.5

Energy [MeV]

Energy [MeV]
9000
8000

nominal resolution

7000+1 σ (worse) resolution

6000-1 σ (better) resolution

3000
5000
2500
4000
2000
3000

1500

2000

1000

1000

500
0

1

1.5

2

2.5

3

3.5

4

Energy [MeV]

0
0.5

1

1.5

2

2.5

3

Energy [MeV]

Figure 9.20: Signal templates for each γ-ray peak in the LaBr3 (Ce) simulated by GEANT4.
The spectra smeared with the nominal and ±1σ resolutions by the resolution curve are shown.

CHAPTER 9. RCNP-E487 EXPERIMENT

9.7.2

122

Continuous Background Template

EventsAs described in the previous section, γ-rays from the scattered neutron reactions on the surrounding materials form the continuous background. The shape of this background is obtained
from the on-timing data with an empty target. In order to obtain a smooth shape template, theon-timing non-water spectrum is fit. Here the spectrum should contain some signal components
such as the 6.13 MeV and 4.44 MeV γ-rays due to the acrylic vessel, then the region between 3
and 6.5 MeV is removed in the fitting. The spectrum is well fit with an exponential function,
as shown in Figure 9.21. This fitting function is used as the continuous background template.

3000

Events = exp(p0 + p1 × Energy)

2500

p0 = 9.02 ± 0.02
p1 = –0.57 ± 0.01

2000

1500

1000

500

0

2

3

4

5

6

7

8

9

Energy [MeV]

Figure 9.21: An exponential fitting to the on-timing non-water spectrum for the continuous
background template. The region 3−6.5 MeV is removed in the fitting to avoid the signal
components.

9.7.3

Fitting Results

The fitting to the observed spectrum with the continuous background template and the eightsignal templates is performed. The χ2 is calculated by comparing the observed and predicted(= signal + background) spectra as below:()2
Niobs − Nipred
χ =
,
σi
i
i
∑
Nipred = f0 · Nibkg +fj · Nisig,j ,
2

∑

χ2i =

∑

(9.2)
(9.3)

j

where Niobs and Nipred represent the numbers of observed and predicted events in the i-th energybin, Nipred being the sum of background and signal events multiplied with the scale factors fj(j = 0, 1, · · · , 8, 0: background, 1−8: signal). The error for the i-th energy bin (σi ) considers
the statistical uncertainties of data and MC, the MC modeling error, and the energy resolution
error. The MC modeling is checked by γ-ray sources and the absolute diﬀerence in the number

CHAPTER 9. RCNP-E487 EXPERIMENT

123

of detected events between data and MC is found to be 3.4%, and this is taken as a systematic
error. The energy resolution error is taken as the maximum diﬀerence in the number of eventsin the bin between the nominal and either ±1σ as shown in Figure 9.20. The scale factors, fj ,are determined by minimizing the χ2 value. The fitting is performed in two steps. First, only
the high energy region, 5.5−7.3 MeV is fit, with the background and the 7.12 MeV, 6.92 MeV,
6.32 MeV, and 6.13 MeV signal spectra. In the second fitting, the scale for these four signals
are fixed while that for the background is varied in the best-fit ± 2σ region. The second fitting
is performed for the region including the low energy side, 2.2−7.3 MeV. The fitting results are
summarized in Table 9.3. The best-fit spectrum is shown together with the observed data in
Figure 9.22. The best-fit spectrum agree well with the observation in general, though there
seen some discrepancies around the 6.13 MeV and 5.27 MeV peaks. This is considered due tolarge resolution uncertainties of these two peaks as seen in Figure 9.20. The eﬀect on the crosssection of these deviations is smaller than the currently assigned systematic uncertainties.
Table 9.3: Results of the first and second spectrum fittings.
1st fitting
χ2 /ndf
138.33/51 ∼ 2.71
f0
0.055 ± 0.007
f1
0.16 ± 0.02
f2
0.19 ± 0.02
f3
0.90 ± 0.05
f4
0.78 ± 0.09

9.7.4

2nd fitting
χ2 /ndf
414.53/162 ∼ 2.56
f0
0.049 ± 0.001
f5
0.72 ± 0.03
f6
0.60 ± 0.02
f7
0.14 ± 0.02
f8
0.19 ± 0.02

Cross Section Results

The γ-ray production cross section (σγj ) for the j-th signal is calculated as:

σγj =

j
NMC,generated
Nfit= fj ×,j
ϕn · Tϵγ · ϕn · T

j
j
Nfit
= fj · NMC,detected
,

ϵjγ

j
NMC,detected=,
NMC,generated

(9.4)
(9.5)
(9.6)

where ϕn denotes the neutron flux [/sr/µC], T is the number of target oxygen nuclei per area[/cm2 ], ϵγ is the γ-ray detection eﬃciency, and NMC,generated (NMC,detected ) is the number ofgenerated (detected) events in the GEANT4 simulation. The generated events are 108 forevery peak and the number of the target oxygen is estimated to be 8.52 × 1023 /cm2 . The mean
free path for 77 MeV neutrons is about 30 cm estimated from the total neutron-water crosssection of ∼1 b [133]. This is longer than the target length of 24.5 cm then whole part of thetarget eﬀectively functions, requiring no correction.
The systematic uncertainty on the cross section is composed of errors regarding the spectrum
fitting, neutron flux, and target. The first two are given in the previous sections. For the6.13 MeV and 5.27 MeV peaks, the fitting uncertainties are larger due to larger resolution

Normalized Counts [/sr/µs]

CHAPTER 9. RCNP-E487 EXPERIMENT

124

7000

Data
Best-fit (χ2/ndf=414.5/162)

6000
5000
4000
3000
2000
1000
0

2

3

4

5

6

7

Normalized Counts [/sr/µs]

Energy [MeV]

DataBest-fit
103

102

2

3

4

5

6

7
Energy [MeV]

Figure 9.22: Energy spectrum of the LaBr3 (Ce) scintillator after the TOF cut and subtractionsof the non-water spectrum and the oﬀ-peak spectrum in a linear (top) and a log (bottom)
vertical scale. Diﬀerent color spectra correspond to signal and background: 7.12 MeV (gray),6.92 MeV (brown), 6.32 MeV (magenta), 6.13 MeV (orange), 5.27 MeV (cyan), 4.44 MeV(green), 3.68 MeV (yellow), 2.30 MeV (violet), and continuous background (blue).

CHAPTER 9. RCNP-E487 EXPERIMENT

125

errors, as explained above. In the water-filled measurement, ∼56% of neutrons do not reachthe back-face of the acrylic vessel, which is estimated from the mean free path and the target
length. This may lead to overestimate of the non-water background, since there is little neutron
deficit at the back-face in the non-water measurement. Since the back-face volume rate to thetoal vessel is ∼23% and the neutron flux at the center is ∼1.7 times larger than the barrel
position from Figure 9.11, the eﬀective contributions from the back-face to the total non-water
background is ∼29%. Contributions from the spectrum without water to that with water are
at most 50% in Figure 9.15. Therefore, the eﬀect of the back-face is estimated to be 8.1%(= 56% × 29% × 50%).
The cross sections for each γ-ray are summarized in Table 9.4. The result for the 2.30 MeV
and 2.31 MeV peaks is an inclusive cross section. In general, the measurement is performed
with better than 20% precisions. As explained above, the 7.12 MeV, 6.92 MeV, and 6.13 MeV
γ-rays originate from the inelastic scattering without nucleon knock-out. In addition, the5.27 MeV and 4.44 MeV γ-rays might come from the same process followed by proton andalpha emission, respectively. In contrast, the 6.32 MeV γ-ray is likely to be from the direct
knock-out (quasielastic) process. Then the current results indicate that the inelastic process
without nucleon knock-out exceeds the quasielastic nucleon knock-out process at 80 MeV.
Table 9.4: Results of the γ-ray production cross sections.
γ-ray energy [MeV]
7.12
6.92
6.32
6.13
5.27
4.44
3.68
2.30 + 2.31

9.8

cross section [mb]1.1 ± 0.1(fitting) ± 0.1(flux) ± 0.1(target)
1.3 ± 0.1(fitting) ± 0.1(flux) ± 0.1(target)
6.2 ± 0.3(fitting) ± 0.6(flux) ± 0.5(target)
5.4 ± 0.6(fitting) ± 0.6(flux) ± 0.4(target)
4.9 ± 0.2(fitting) ± 0.5(flux) ± 0.4(target)
4.1 ± 0.1(fitting) ± 0.4(flux) ± 0.4(target)
1.0 ± 0.1(fitting) ± 0.1(flux) ± 0.1(target)
1.3 ± 0.1(fitting) ± 0.1(flux) ± 0.1(target)

Summary and Prospects

In the E487 experiment at RCNP, several γ-ray peaks emitted from the neutron-oxygen reactions are observed, and their production cross sections are measured. The results indicate thatthe inelastic process without nucleon knock-out may be dominant over the quasielastic nucleon
knock-out process at 80 MeV. This contradicts the assumption that boundary of the transition
between these two interactions is 30 MeV used in the previous NCQE measurement [51]. Therefore, in this thesis, another method is used instead, as explained in Chapter 7. Furthermore,
the current ∼13% uncertainty in the NCQE measurement, as shown in Chapter 7, would be
reduced down to less than 5%, if the precision comparable to the E487 experiment (≲20%) isachieved at several energy points and those results are suitably incorporated in the simulation.
The measurement was improved with a HPGe detector by storing its time data in theE525 experiment. Similar spectrum analysis is performed to extract production cross sections
at neutron energies of 30 and 250 MeV. In the E525 experiment, better precision results are
expected thanks to higher energy resolution in the HPGe detector. Together with the resultsfrom the current work in this thesis, these cross section results will be implemented in the SK

CHAPTER 9. RCNP-E487 EXPERIMENT

126

simulation, and would help improve the systematic uncertainty in the NCQE-like measurement.
This improvements would also be valuable for the analysis utilizing the neutron information
especially in SK-Gd, including the SRN search reported in Part IV. The improved simulation
would be useful also in the future water Cherenkov experiments such as Hyper-Kamiokande.

Part IV
Search for Supernova Relic Neutrinos

127Chapter 10
Signal and BackgroundIn this part, a search for supernova relic neutrinos using an SK-IV 2970.1-day data set isreported. In the analysis, the NCQE-like cross section results from T2K are applied to theatmospheric neutrino background estimation, as described in Chapter 12.
In this chapter, the SRN signal and the background sources in the search are overviewed
and their MC simulations are explained.

10.1

SignalAll three flavor neutrinos are emitted from supernovae as explained in Chapter 1, but thedominant interaction in SK is inverse beta decay (IBD) of electron antineutrinos (ν̄e + p →e+ + n) in the energy region of the analysis (<30 MeV). Figure 10.1 shows eﬀective neutrino
cross sections, which are cross sections including the energy resolution and detector threshold
eﬀects, of various interaction channels as a function of neutrino energy. The second largest
cross section is smaller than IBD by more than two orders of magnitude, therefore only IBD isconsidered. In the analysis, pairs of a positron and a 2.2 MeV γ-ray from neutron capture onhydrogen are searched.

Figure 10.1: Eﬀective neutrino interaction cross sections as a function of neutrino energy [150].

129

CHAPTER 10. SIGNAL AND BACKGROUND

130

σIBD [×10–41 cm2]

In the simulation, events are produced uniformly in the positron energy, and the actual
spectra are obtained with renormalization by the parent ν̄e flux. In total nine SRN ν̄e fluxes
from seven models are referred, which are shown in Figure 1.7 in Chapter 1. IBD cross sections
are taken from Ref. [151] and shown in Figure 10.2.

9
8
7
6
5
4
3
2
1
0

0

5

10

15

20

25

30

35

νe Energy [MeV]

Figure 10.2: IBD cross section on a free proton as a function of ν̄e energy as calculated byStrumia and Vissani [151].

10.2

Background

Background sources are categorized into four: (1) atmospheric neutrino interactions, (2) muon
spallation, (3) reactor neutrino events, and (4) accidental background events.

10.2.1

Atmospheric Neutrinos

Atmospheric neutrinos are a major background in the search. The MC production of atmospheric neutrino events are based on flux prediction by the HKKM2011 model [152, 153] andthe neutrino interaction by NEUT ver. 5.3.6. The fluxes used in the analysis are shown in
Figure 10.3. In the figure, neutrino oscillations are not considered, but such eﬀect is appliedlater. The neutrino interaction model is the same as the one used in the NCQE-like measurement described in Chapter 5. However, the setting of spectroscopic factors is diﬀerent; The
others state is integrated into (p1/2 )−1 here, while it is integrated into (s1/2 )−1 in the NCQE-likeanalysis. The systematic error of this treatment is evaluated in the NCQE-like measurementin Chapter 7.

10.2.2

Muon Spallation and Lithium-9

SK is exposed to ∼2 Hz cosmic-ray muons, and high energetic muons break up oxygen nuclei inwater (“muon spallation”), producing electromagnetic and hadronic particles such as photons,
neutrons, and pions. These will subsequently undergo reactions with other nuclei via several
channels. Eventually the nuclei are in their excited states, which decay via many channels.

CHAPTER 10. SIGNAL AND BACKGROUND

131

Atmospheric Neutrino Flux (HKKM2011)

0.014

E2ν Φ [GeV/cm2/sec./sr]E2ν Φ [GeV/cm2/sec./sr]

Atmospheric Neutrino Flux (HKKM2011)

νµ
νµ
νe
νe

0.012
0.01
0.008

10−2

νµ
νµ
νe
νe

−3

10

10−4
−5

10
0.006

10−6

0.004

10−7

0.002
0
−1

0

1

2

3

4

5

log (Eν [GeV])
10

−1

0

1

2

3

4

5

log (Eν [GeV])
10

Figure 10.3: Atmospheric neutrino flux at Kamioka from the HKKM2011 calculation: thevertical axis shown in linear (left) and log (right). Here the neutrino oscillation is not taken
into account.
Energies of β’s and γ’s resulting from the decays range in the current analysis window. Some
decays form a combination of “β+n” which is the same as the ν̄e signal. Possible isotopes
and their visibilities in water are studied with the FLUKA simulation [93] in Refs. [154–156],and summarized in Table 10.1. The table categorizes isotopes into three: neutrons (the 1strow), isotopes whose decay contain a β (the 2nd−19th rows), and isotopes which are not likely
backgrounds standalone because they are stable, have very long lifetime, or decay without a β(the 20th−33rd rows). Even if the final state is not a “β+n” combination, when a β or γ forms
a coincidental pair with a neutron or fake hits, due to PMT noise or radioactive materials, thisbecomes a background to the search. Therefore, the muon spallation should be reduced. Since
the spallation endpoint in the energy is 20.6 MeV from the 14 B and 11 Li, the cut should be tuned
up to the periphery. In the analysis, the cuts are prepared for the region up to 19.49 MeV.
Details about the spallation cut are given in Chapter 11.
The β+n decay events are an irreducible background in the analysis. Among such isotopes
listed in the table, the 9 Li isotope is the most likely background due to its yield, lifetime, andenergy. The 9 Li decays into a β+n pair with a branching ratio of 50.8%, as shown in the left
panel of Figure 10.4. This is almost identical to the ν̄e ’s IBD event except that the β from9
Li is an electron and the neutron energy is higher than that from IBD. SK is not sensitive tothese diﬀerences, then the MC event production is performed by renormalizing the β+n event
made for the ν̄e signal. Potential systematic errors due to diﬀerence in the neutron energy
is covered by the Am/Be calibration since neutrons from the source have similar energies tothose from 9 Li. The β spectra from 9 Li for diﬀerent decay modes are shown in the right panelof Figure 10.4. The previous SK measurement result [115] is used as the 9 Li production rate:
0.86 ± 0.12(stat.) ± 0.15(syst.) kton−1 day−1 .

CHAPTER 10. SIGNAL AND BACKGROUND

132

Table 10.1: List of isotopes produced in the muon spallation at SK calculated by FLUKA [154].
The primary process is with 16 O except for the first three rows.
Isotope
n
N
17
N
16
N
16
C
15
C
14
B
13
O
13
B
12
N
12
B
12
Be
11
Be
11
Li
9
C
9
Li
8
B
8
Li
8
He
15
O
15
N
14
O
14
N
14
C
13
N
13
C
12
C
11
C
11
B
10
C
10
B
10
Be
9
Be
sum
18

Half-life[sec.]
0.624
4.173
7.13
0.747
2.449
0.01380.00860.01740.01100.02020.023613.8
0.0085
0.127
0.178
0.77
0.838
0.119

Decay mode

Yield
Primary process[×10−7 muon−1 g−1 cm2 ]
2030
−
18
β
0.02
O(n, p)
−
18
β n
0.59
O(n, n + p)
β − γ (66%), β − (28%)
18(n, p)−
β n0.02(π − , np)−−
β γ (63%), β (37%)
0.82(n, 2p)−β γ
0.02(n, 3p)+−β0.26(µ , p + 2n + µ− + π − )β−1.9(π − , 2p + n)β+1.3
(π + , 2p + 2n)−β12(n, α + p)
−
−
β
0.10
(π , α + p + n)−−
β (55%), β γ (31%)
0.81(n, α + 2p)
β −n
0.01
(π + , 5p + π + + π 0 )β+0.89(n, α + 4n)−
β n (51%), β − (49%)
1.9(π − , α + 2p + n)β+
5.8
(π + , α + 2p + 2n)β−13(π − , α + 2 H + p + n)−−
β γ (84%), β n (16%)
0.23(π − , 3 H + 4p + n)
351
(γ, n)
773(γ, p)
13(n, 3n)295(γ, n + p)
64(n, n + 2p)
19(γ, 3 H)225
(n, 2 H + p + n)792(γ, α)
105(n, α + 2n)174(n, α + p + n)
7.6(n, α + 3n)
77(n, α + p + 2n)24(n, α + 2p + n)
38(n, 2α)3015

CHAPTER 10. SIGNAL AND BACKGROUND

133
Li β spectrum (with n emission)

Normalized Events

9

0.014

Kn = 1.11 MeV
0.012

Kn = 0.76 MeV
Kn = 8.25 MeV

0.01

Kn = 8.78 MeV
0.008
0.006
0.004
0.002
0
0

2

4

6

8

10

12

14

β Energy [MeV]

Figure 10.4: Decay scheme of 9 Li (left) and β spectra from its decay with a neutron emission(right). In the right panel, black one represents the total spectrum and the other color ones
correspond to decay modes from diﬀerent excited states, and Kn represents the emitted neutron
kinetic energy.

10.2.3

Reactor Neutrinos

Reactor Flux [/0.01-MeV/SK-IV-Period]

Reactor neutrinos are the electron antineutrinos and then an irreducible background in theanalysis. Their contamination in the analysis is limited to the lowest energy bin. Reactor
neutrino flux is calculated using the database on Power Reactor Information System (PRIS)
from IAEA [157] with neutrino oscillations [158], and the event production is done with renormalization of the ν̄e signal MC. Figure 10.5 shows the reactor ν̄e flux at SK. It should be notedthat the reactors in Japan were oﬀ in large part of the SK-IV period.
8E+17

6E+17

4E+17

2E+17

0E+00

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

Neutrino Energy [MeV]

Figure 10.5: Reactor neutrino flux at SK for the SK-IV operation period.

CHAPTER 10. SIGNAL AND BACKGROUND

10.2.4134

Accidental Background Events

There are two types of accidental background events. First one is made by the combinationof a low energy event and a true neutron which is mainly produced from muon spallation.
This is referred to as the “accidental true background”. The other is the combination of a low
energy event and a fake event, such as PMT dark noise and radioactive events, which mimics
neutrons. This is referred to as the “accidental fake background”. It is diﬃcult to remove theformer background in the current analysis, then the strict spallation cut is applied as explainedin the next chapter. The latter can be separated from the signal (the true neutron) by applying
the neutron tagging as explained in Chapter 11.

10.3

Energy Window

The energy window in the analysis is set to 7.49−29.49 MeV, which is separated into four
regions as 7.49−9.49, 9.49−11.49, 11.49−19.49, and 19.49−29.49 MeV. This is determinedby the detector threshold and background types. As is explained in the next chapter, the SKenergy threshold was lowered from 9.49 MeV to 7.49 MeV by the SHE trigger improvement. The
lowest two bins (7.49−9.49 MeV and 9.49−11.49 MeV) are dominated by the muon spallation
backgrounds (9 Li) and the accidental fake background. The NCQE interaction becomes large inthe region 11.49−19.49 MeV, and the other interactions of atmospheric neutrinos are dominant
in the highest energy region.

Chapter 11
Data Reduction
11.1

Data Set

All data taken with the SHE+AFT trigger in the SK-IV period (see Chapter 4) are used forthe search. After rejection of suspicious periods or runs in terms of data quality, live time ofthe data set is 2970.1 days. The analysis energy (Erec ) window is determined depending on the
SHE trigger threshold, which was changed once from the 70 hits to the 58 hits. The former andlatter correspond to the 9.49 MeV and 7.49 MeV analysis thresholds, respectively. Neutrons
are searched in the window spanning from 2 µs after the SHE trigger until the end of the AFT
trigger time window. The AFT window length is diﬀerent depending on the operation period.
The trigger conditions in diﬀerent periods are summarized in Table 11.1.
Table 11.1: Summary on the period and live time for diﬀerent SHE and AFT trigger conditions.
Start Date
End Date
Live time SHE threshold
6th, Oct., 2008 22nd, Nov., 2008
25.0 days
70 hits
22nd, Nov., 2008
9th, Sep., 2011 869.8 days
70 hits
9th, Sep., 2011 31st, May., 2018 2075.3 days
58 hits

AFT window length
350 µs500 µs500 µsData reduction is performed in four steps: the first reduction removes trash data, the second
reduction focuses on removal of muon spallation events, the third reduction targets are mainly
the atmospheric neutrino backgrounds, and the fourth reduction is the neutron tagging to
remove the large accidental fake background.

11.2

First Reduction

Non-physics data cut
The normal runs, which are not test nor calibration runs, are used for physics analyses. Suchnormal runs are further reduced either if the run time is shorter than 5 minutes, the run started
less than 15 minutes after the high-voltage recovery, any hardware problem is reported, or event
distribution is strange due to detector problems. Some calibrations are not labeled as test runs
since they are conducted with periodical triggers during normal runs. Such calibration events
are removed from the analysis sample. The number of hits due to PMT noise is expected
to be smaller than that due to physical events. To eliminate PMT noise induced events,
135

CHAPTER 11. DATA REDUCTION

136

N (Q < 0.5 p.e.)/Nall < 0.55, where N (Q < 0.5 p.e.) and Nall represent the number of hit
PMTs with a charge larger than 0.5 p.e. and the number of all PMTs, is required. During theT2K operation, a special trigger is issued every 2.48 sec. and its time window is [−500, +535] µs.
This region is removed from the sample.

Cosmic-ray muon cut
Cosmic-ray muon events happen ∼2 Hz at SK. In many cases such events are expected to leavesigns in the OD, then the events are removed if the OD trigger is issued. Even if the OD trigger
is not issued, events with more than nineteen OD PMTs hit are removed. Some muons decay
into electrons to leave hits inside the ID. To eliminate this, events within 50 µs after muons are
removed. Spallation events caused by muons will be treated later.

Fiducial volume cut
There are many background events coming from the wall. To remove these, the fiducial volume(FV) cut is applied, which selects only events more than 200 cm away from the ID wall.

Fit quality cut

ð

1

g

vtx

1

g

vtx

Some events are poorly reconstructed, which occurs more often for background events. These
events are removed with goodness-of-fit parameters, gvtx and ovaQ. Figure 11.1 shows Erec −gvtx
distributions for the ν̄e signal MC and data after the non-physics run cut, the FV cut, andthe OD cut. Events with gvtx < 0.5 are rejected with keeping the signal eﬃciency >99.9%.
Figure 11.2 shows similar distributions for ovaQ after the gvtx cut. Events with ovaQ < 0.25
are removed and the signal eﬃciency is >99.9%.

0.9

0.06

0.8

0.8
0.05

0.7
0.6

0.04

0.5

0.3

0.02

0.2

νe MC

0.1

5
4

0.6

8

10

12

14

16

18

20

22

24

26
28
Erec [MeV]

3

0.4
2

0.3
0.2

0.01
0

6

0.7

0.5
0.03

0.4

0

SK-IV 2970.1 days

0.9

1

0.1
0

8

10

12

14

16

18

20

22

24

26
28
Erec [MeV]0

Figure 11.1: The Erec −gvtx distributions for the ν̄e signal MC (left) and data (right). Dashedgreen lines indicate the cut criteria, and events with gvtx > 0.5 are selected.

137

1
0.045
0.8

RYD4

ovaQ

CHAPTER 11. DATA REDUCTION

0.04
0.035

0.6

0.03
0.4

î



SK-IV 2970.1 days








0.025
0.2

0.02



0

0.015



−0.4

8

10

12

14

16

18

20

22

24



0.01

νe MC

−0.2



0.005

26
28
Erec [MeV]

0

−
−





















(UHF>0H9@

Figure 11.2: The Erec −ovaQ distributions for the ν̄e signal MC (left) and data (right). Dashedgreen lines indicate the cut criteria, and events with ovaQ > 0.25 are selected.

11.3

Second Reduction: Spallation Cut

After the first reduction, the dominant background is cosmic-ray muon spallation. Since there
is no reliable MC simulation that treats all spallation isotopes 1 , a data-driven method is takenin this analysis. Note that the 9 Li events are simulated, as explained in the previous chapter;
however, this MC does not contain the spallation production process therefore the eﬃciency
needs to be estimated. This is achieved by the data-driven method here. The basic idea is toinvestigate the events that are likely to be caused by the preceding muons.

–30 sec.

±0 sec.

Pre regionmuon+30 sec.

Post regiont
SHE eventFigure 11.3: Two sample regions for the spallation cut.
In order to study the correlation between the muon and the signal candidate (the SHEtriggered event), muon-like events are collected. The OD and HE triggers are required to
identify the muon, and its information, including the track, the number of tracks, and thedeposit energy along the track (dE/dx), are extracted by the muon fitter. Details about the1

There is the FLUKA package, but systematic uncertainties are not estimated well.

CHAPTER 11. DATA REDUCTION

138

1

it
misf
0.3%

d)
d)
fitte
fitte
1
1
>
=
(
(
ping
tiple
tiple
clip
mul
mul
4.6%
2.5%
4.1%

ping
stop
4.7%

le
sing
83.8%

dt, Ltran, Llong,
Qpeak, Qµ0.90.8dt, Ltran, Llong,
Qpeak, Qµ, Ntrack

No evidence for spallation production

muboy goodness

muon fitter can be found in Refs. [159–161]. For each SHE event, correlations with the muonsthat come within ±30 sec. from the SHE event are studied. Hereafter the region [−30, 0] sec.
is termed the pre region and the region [0, +30] sec. is termed the post region, which are
schematically shown in Figure 11.3. Then the muons in these two regions are compiled for all
SHE events to produce the pre and post samples, respectively.
The muon fitter classifies the muon type into six; The single through-going muons are theones with a single track that passes through the detector. These dominate the muon events(83.8%); When a single muon stops inside the detector, this is categorized as the stoppingmuons (4.7%); There are two categories for the multiple track muons, the event with one of
the tracks being fit properly (4.6%) and the event with more than one tracks being fit properly(2.5%). In this analysis, both are treated together as the multiple muons; The muons whose
track length is less than 7 m, usually traveling close to the edge of the ID, are called the cornerclipping muons (4.1%); The track information is not extracted properly due to the fitting failure
for the misfit muons (0.3%). The goodness-of-fit parameter is calculated, and the muons withthis goodness smaller than 0.4 are treated as the poorly-fit muons in this analysis. Figure 11.4
shows a 2D distribution of the muon type and the goodness obtained from the muon fitting to
the current 2970.1-day data set.

0.7
0.6
0.5
0.4
0.3
0.2

dt

0.1
0
0

1

2

3

4

5

6
muboy ID

6

×10
25

20

15

10

5

0

Figure 11.4: Muon types categorized by the muon fitter and their goodness. Variable types
which are used for the spallation likelihood calculation are shown in each region. In the analysis,
the corner-clipping muons are considered not to cause spallation.
Several variables for finding muon spallation events are calculated for the pre and post
samples: dt, Ltran , Llong , Qpeak , Qµ , and Ntrack . The variable dt represents the time diﬀerenceCHAPTER 11. DATA REDUCTION

139

between the SHE event and the muon. There are two variables regarding the geometricalinformation; Ltran is the distance between the SHE event vertex and the muon track, and
Llong is the distance from the point where the SHE event vertex is projected onto the track
to the place where dE/dx peaks along the muon track, as schematically shown in Figure 11.5.
The Qpeak is the maximum dE/dx value in the track, Qµ is the total deposit charge by themuon, and Ntrack is the number of muon tracks. Distributions of these variables are madefor the combinations of diﬀerent conditions on the muon type (single through-going, stopping,
multiple, corner-clipping, and missfit or poorly-fit), the SHE event energy region (7.49 < Erec <9.49 MeV, 9.49 < Erec < 11.49 MeV, and 11.49 < Erec < 19.49 MeV), and the dt region(0 < |dt| < 0.05 sec., 0.05 < |dt| < 0.5 sec., and 0.5 < |dt| < 30 sec.). The results for the
single through-going muons, 7.49 < Erec < 9.49 MeV, and 0 < |dt| < 0.05 sec. are shown in
Figure 11.6. Clear contributions from the spallation are seen as an excess in the pre sample
than the post sample in every distribution. The spallation events are more likely to populate
near the SHE event both in time and space and to be produced from the muons depositing
much energy in the detector. The distributions for other conditions are given in Appendix D.
The corner-clipping muons are judged not to produce spallation since no significant excess isseen in the pre sample.

muon track

position wheredE/dx is largest

Llong

SHE event

Ltran

Figure 11.5: Schematic of the variables, Ltran and Llong , for the spallation cut. The cylindricalshape represents the SK detector.
In order to discriminate the spallation events from the random events more eﬀectively, likelihood is calculated from these variables. For this, two probability density functions (PDFs), thespallation PDF (PDFispall ) and the random PDF (PDFirandom ), are prepared for each discriminating variable i. The post sample distribution is subtracted from the pre sample distribution
and the resulting distribution is area-normalized to produce the spallation PDF. For making
the random PDF, two dedicated samples are made, the “shuﬄed” post sample and the toy MC
sample. The shuﬄed post sample is obtained by shuﬄing Ltran and Llong among the muonsof each SHE event in the post region to achieve randomness. Since the other three variables

CHAPTER 11. DATA REDUCTION

50000

140

single (7.49 < Erec < 9.49 MeV)

single (7.49 < Erec < 9.49 MeV)
35000

pre
post

40000

pre
post

30000
25000

30000

20000
15000

20000

10000
10000
5000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

single (7.49 < Erec < 9.49 MeV)

Ltran [cm]single (7.49 < Erec < 9.49 MeV)

5

10

8000

pre
post

7000

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

6000

pre
post

104
103

5000

102

4000
10
3000
1

2000

10−1

1000
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (7.49 < Erec < 9.49 MeV)

pre
post

104
103
102
10
1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure 11.6: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) for the single through-going muons and 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec. The smoothing over thebins is performed for some distributions to mitigate the statistical fluctuation.

CHAPTER 11. DATA REDUCTION

141(Qpeak , Qµ , Ntrack ) are the muon properties, the random distributions are made by a toy MC
based on the muon measurements. Taking Ltran and Llong from the shuﬄed post sample and
Qpeak , Qµ , Ntrack from the toy MC sample and combining these two, the random sample isproduced. Then each distribution is area-normalized to serve as the random PDF. The ratiosof PDFispall to PDFirandom are multiplied to each other to make spallation likelihood (Lspall ) as:(
Lspall = log∏ PDFispalli)

PDFirandom.

(11.1)For the misfit and poorly-fit muons, only dt is used to calculate the spallation likelihood since theother variables are not reliable. For the multiple muons, the muon fit results only from the first
track are used, and the number of tracks is used. These are also summarized in Figure 11.4.
The PDF distributions for the single through-going muons, 7.49 < Erec < 9.49 MeV, and
0 < |dt| < 0.05 sec. are shown in Figure 11.7. The spallation likelihoods for the diﬀerent
muon types and 7.49 < Erec < 9.49 MeV are shown in Figure 11.8. In all distributions, thecontributions from spallation are clearly observed as an excess at high values of the spallation
likelihood in the pre sample. The cut criteria are determined separately for the muon types
and represented with dashed green lines in the figure. The SHE events with at least one muonin their pre region having likelihood larger than the threshold which is represented by the green
lines in the figure are removed. The distributions for other conditions are given in Appendix D.
The random and spallation event eﬃciencies in the spallation cut are estimated as follows.
The random event eﬃciency is estimated by calculating the spallation likelihood for the eventsin the toy MC sample and applying the cut criteria determined above. Since the data sample
at this stage is dominated by the spallation and solar neutrino events, the spallation eﬃciency
is estimated based on data by separating the solar events. This is performed in the cos θsun
distribution, where θsun is defined as the angle between the event direction and the direction
pointing to the Sun at the event timing as schematically shown in Figure 11.9. In this distribution, the event is categorized into two as the solar and non-solar events. The numbers of each
event are represented as Nsol and Nnonsol , respectively. The solar events populate in the region
close to cos θsun = 1, while the non-solar events distribute uniformly. Therefore, the number of
non-solar events (Nnonsol ) is obtained by fitting the region cos θsun < 0 with a constant. The
non-solar events are composed of the spallation and the atmospheric neutrino events. The contribution of the atmospheric neutrinos is negligible in the region Erec < 11.49 MeV but visible
above. The spallation eﬃciency (ϵspall ) is calculated as:
after
after
Nnonsol− Natm,beforebeforeNnonsol− Natm(11.2)

beforeafter
× ϵrandom ,= NatmNatm(11.3)

ϵspall =

after
after
beforebefore) represent the numbers of non-solar (atmospheric) and Nnonsol(Natmwhere Nnonsol(Natmneutrino) events before and after the spallation cut, respectively. The atmospheric neutrino
events are obtained by MC. Since the atmospheric neutrino events occur independent of the
beforeafter. The resulting eﬃis obtained by multiplying the random eﬃciency to Natmmuons, Natmciencies are summarized in Table 11.2. The random eﬃciency above 11.49 MeV is more than
80% while that below is about half.

CHAPTER 11. DATA REDUCTION

142

single (7.49 < Erec < 9.49 MeV)

0.1

spall
random

0.08

PDF

PDF

single (7.49 < Erec < 9.49 MeV)

spall
random

0.35
0.3
0.25

0.06
0.2
0.04

0.15
0.1

0.02
0.05
0
10−2

10−1

1

0
0

10
|dt| [sec.]

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]0.07

single (7.49 < Erec < 9.49 MeV)

spall
random

0.06

PDF

PDF

single (7.49 < Erec < 9.49 MeV)
1

spall
random

0.05
0.04

10−1

0.03
0.02
0.01
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]PDF

single (7.49 < Erec < 9.49 MeV)

spall
random
10−1

10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure 11.7: The spallation and random PDFs of dt (top left), Ltran (top right), Llong (middle
left), Qpeak (middle right), and Qµ (bottom) for the single through-going muons and 7.49 <Erec < 9.49 MeV. For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

CHAPTER 11. DATA REDUCTION

106

143

missfit or poorly-fit (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

single (7.49 < Erec < 9.49 MeV)

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

multiple (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30

−30

−20

−10

Lspall

0

10

20

30
LspallFigure 11.8: Distributions of the spallation likelihood for each muon type in the 7.49−9.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the right side of thelines are removed.

Table 11.2: Random and spallation event eﬃciencies by the present spallation cut for each Erecregion. The uncertainties come mainly from the statistics of the samples.
Erec region [MeV]
7.49−9.49
9.49−11.49
11.49−19.49

ϵrandomϵspall
0.478±0.014 0.077±0.001
0.549±0.016 0.098±0.001
0.827±0.010 0.101±0.001

CHAPTER 11. DATA REDUCTION

144

Sun

SK

θsun

Nsol
Nnonsol–101cosθsunFigure 11.9: Schematic drawings of the definition of θsun and the cos θsun distribution.

11.4

Third Reduction

Wall-originated event cut

Events/10-cm

Events/10-cm

In order to remove backgrounds coming from the wall further, the cut based on eﬀwall isapplied. Figure 11.10 shows the eﬀwall distributions for the ν̄e signal MC and data after the
spallation cut. Since the signal-to-background ratio becomes worse below 500 cm, the eventswith eﬀwall < 500 cm are removed. Signal eﬃciencies with this cut are about 92% in all Erecregions.

10000

νe MC

0.25

0.2

SK-IV 2970.1 days
8000

6000

0.15
4000

0.1

2000

0.05

0

500

1000

1500

2000

2500

3000

3500

4000

effwall [cm]

0

500

1000

1500

2000

2500

3000

3500

4000

effwall [cm]Figure 11.10: The eﬀwall distributions for the ν̄e signal MC (left) and data (right) after the
spallation cut.

CHAPTER 11. DATA REDUCTION

145

Pre-activity cut
When a decay electron from the muon makes the SHE event and the primary signature, suchas γ-rays by the neutrino interaction, is not high energetic enough to be triggered, this forms
a background in the search. In order to remove this background, the pre-activity is searchedin the time range [−5, 0] µs with respect to the SHE trigger by a 15 ns long timing window.
The maximum number of hits in this time window is required to be less than 12. This cut isapplied only to data since these pre-activity events do not exist in MC. The eﬃciency loss forthe signal by this cut is small (<0.1%).

Post-activity cut

EventsThere is another case that the triggered events may accompany decay-e’s. The post-activity
is searched similarly to the pre-activity search. Figure 11.11 shows the number of decay-e’s(Ndecay-e ) with all the preceding cuts in the atmospheric neutrino MC sample. Events with
Ndecay-e ≥ 1 are rejected. Many CCQE-like events are removed by this cut. The signal eﬃciency
loss is negligible.

900

CCQE-like
CC1π
CC-otherν -NCQEν -NCQE
NC1π
NC-other

800
700
600
500
400
300
200
100
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Ndecay-eFigure 11.11: Number of decay electrons after the pre-activity cut in the atmospheric neutrino
MC sample from the 7.49 < Erec < 29.49 MeV region. Diﬀerent colors correspond to theneutrino interaction types.

Pion and γ-ray cut
Fuzziness of the Cherenkov ring is characterized by the pilike parameter, which is defined asfollows using the triplet PMT distribution (see Figure 4.16):

pilike =N (peak ± 3◦ ),N (peak ± 10◦ )(11.4)

where N (peak ± 3◦ ) and N (peak ± 10◦ ) are the numbers of entries in the region of the peakvalue ±3 and ±10 degrees in the triplet PMT distribution, respectively. Some pions are quickly
captured by oxygen while electrons are likely to travel and scatter more, which leads to fuzzier

CHAPTER 11. DATA REDUCTION

146

1Events/0.005

Events/0.005

ring patterns. Another target here is the multiple-γ events mainly by the NC interactions.
Figure 11.12 shows the pilike distributions from the ν̄e signal and atmospheric neutrino MC
samples with all the preceding cuts. The events with pilike > 0.36 are removed with the signal
eﬃciency of ∼98%. Pion production events and NCQE events are removed eﬀectively.

νe MC

−1

10

10−2

102

CCQE-like
CC1π
CC-otherν -NCQEν -NCQE
NC1π
NC-other

10

10−3
10−4

1

−5

10

10−1

10−6
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pilike

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pilikeFigure 11.12: The pilike distributions for the ν̄e signal (left) and atmospheric neutrino (right)
MC samples after the post-activity cut. Both samples are from the 7.49 < Erec < 29.49 MeV
region.

Charge/Hit cut
The total charge stored in all PMTs of an event, Q50 , is calculated with a 50 ns time window.
The ratio of Q50 to the total number of hit PMTs, N50 , which is calculated with the same time
window, represents how concentrated the hits are then corresponds to fuzziness of the Cherenkov
ring 2 . Figure 11.13 shows the Q50 /N50 distributions of the ν̄e signal and atmospheric neutrino
MC samples after all the preceding cuts. The events with Q50 /N50 > 2 are removed with thesignal eﬃciency of ∼99%.

Cherenkov angle cut
Electron events tend to be reconstructed at θC ∼ 42◦ and mainly NC events are likely to
distribute at higher angles. Figure 11.14 shows the θC distributions from the ν̄e signal andatmospheric neutrino MC samples after all the preceding cuts. Less event above 85 degrees
is mainly due to the pilike cut. Events are required to satisfy 38◦ < θC < 50◦ . The signal
eﬃciency depends on the energy since lower energy events are more likely to have the wide
θC distribution due to more scatterings and then be removed. This cut accompanies a large
uncertainty in the atmospheric NCQE-like background estimation, as described in the next
chapter.
In the third reduction, the atmospheric neutrino events are reduced to less than 15% while theν̄e signal is kept with more than the 80−90% eﬃciency depending on the Erec region.
2

The ratio Q50 /N50 has correlation with pilike.

147

1

Events/0.5

Events/0.5

CHAPTER 11. DATA REDUCTION

νe MC

−1

10

10−2

102

CCQE-like
CC1π
CC-otherν -NCQEν -NCQE
NC1π
NC-other

10

10−3
1

10−4
−5

10

10−1

0

1

2

3

4

5

6

7

8

9

0

10

1

2

3

4

5

6

7

8

9

10

Q50/N50

Q50/N50

2.2

Events/2.7-degree

Events/2.7-degree

Figure 11.13: The Q50 /N50 distributions for the ν̄e signal (left) and atmospheric neutrino (right)
MC samples after the pilike cut. Both samples are from the 7.49 < Erec < 29.49 MeV region.

νe MC

2
1.8
1.6
1.4

80

CCQE-like
CC1π
CC-otherν -NCQEν -NCQE
NC1π
NC-other

70
60
50

1.2
40

1
0.8

30

0.6

20

0.4
10

0.2
0
0

10

20

30

40

50

60

70

80

90

θC [degree]

0
0

10

20

30

40

50

60

70

80

90

θC [degree]

Figure 11.14: The Cherenkov angle distributions for the ν̄e signal (left) and atmospheric neutrino (right) MC samples after the Q50 /N50 cut. Both samples are from the 7.49 < Erec <29.49 MeV region.

CHAPTER 11. DATA REDUCTION

11.5

148

Fourth Reduction: Neutron Tagging

Tagging neutrons from the ν̄e ’s IBD is a powerful technique to select signal. The idea is tosearch for a 2.2 MeV γ-ray from neutron capture on hydrogen, whose typical time-scale is∼200 µs, by investigating the later window. Because the amount of backgrounds, such as PMT
dark noise and radioactive events, is too many below 3.5 MeV, separating the 2.2 MeV signal
from these backgrounds relies on the neural network technique, based on the boosted decision
tree (BDT) [162]. In this section, the procedure and performance are explained briefly. Basic
descriptions about the neutron tagging method in SK can be found in Refs. [92, 163, 164].

Procedure

Entries

The primary events are simulated in MC as described in Chapter 10. For the neutron tagging
study, information about later hits are necessary. The PMT dark noise is simulated and convoluted in the region between the primary event timing and 18 µs later. The region after 18 µs
and up to 535 µs (385 µs for some periods) reflects hits from the dummy spill data, which aretaken with the T2K trigger when the beam is oﬀ. Since the PMT gain shift is observed, as described in Chapter 7, the dummy spill data are taken from 10 diﬀerent periods over SK-IV, andthe systematic error is estimated later. These extensions are added to both the ν̄e signal andatmospheric neutrino MCs. The tagging procedure is separated in two steps: the pre-selection
and the BDT selection.
First, a 10 ns sliding time window is used to look for a hit cluster in the region [+2, +535] µs(or [+2, +385] µs). If the number of hit PMTs in this 10 ns window (N10 ) exceeds seven,
N10 > 7, the cluster is kept as a 2.2 MeV γ-ray candidate. Figure 11.15 shows the N10
distributions of the neutron signal and background. To avoid a multiple counting of the same
2.2 MeV γ event, an additional search until 20 ns later is conducted, and additional clusters inthis window, are treated as the same event.

Neutron signal
Background

2

4

6

8

10

12

14

16

18

Number of hit PMTs within 10 ns (N10) / 533 μs

Figure 11.15: Number of hit PMTs in a 10 ns sliding time window for the neutron signal andbackground in the region [+2, +535] µs. The blue line and arrow indicate the pre-selection
criterion.

CHAPTER 11. DATA REDUCTION

149

After the pre-selection based on N10 , a multivariate analysis based on the BDT is performed.
In this analysis 22 variables are used: N10 , seven geometrical variables, seven PMT noise
related variables, and seven fitter related variables. They are described in more detail in
Refs. [92, 165, 166]. The BDT is trained with both the neutron signal and the dummy trigger
background samples.

Performance
The performance is evaluated using the MC sample that contains the neutron signals anddoes not contain them. Figure 11.16 shows a relation of the signal eﬃciency and the mis-tag
probability for the diﬀerent operation periods. The eﬃciencies in the current working points
are summarized in Table 11.3. The neutron tagging removes the accidental fake backgroundeﬀectively with keeping the signal eﬃciency as O(10)%.

Figure 11.16: The signal eﬃciency and the mis-tag probability for the diﬀerent ten operation
periods. Diﬀerent colors correspond to the results from the diﬀerent data taking periods.

Table 11.3: The signal eﬃciency and the mis-tag probability in the current working points.
Energy region
7.49−9.49 MeV
9.49−11.49 MeV
11.49−19.49 MeV
19.49−29.49 MeV

Signal eﬃciency
0.129
0.151
0.146
0.241

Mis-tag probability
2.08 × 10−4
4.06 × 10−4
3.51 × 10−4
5.27 × 10−3

Calibration with an Americium-Beryllium source
In order to check the neutron tagging method, calibrations with an Am/Be neutron source are
performed, following the procedure in Refs. [46, 163, 166]. The source is embedded in a 5 cm

CHAPTER 11. DATA REDUCTION

150

cubic bismuth germanate oxide (BGO) scintillator, as shown in Figure 11.17. Alpha decay
happens in an 241 Am, and is followed by a reaction of an alpha with a 9 Be, producing an
excited carbon and a neutron. The carbon then de-excites with emission of a 4.44 MeV γ-ray:
α + 9 Be →12C∗ + n,(11.5)C∗ →12

C + γ (prompt),(11.6)

12n + p → d + γ (delayed).

(11.7)The γ-ray from carbon decay is the prompt signal and the γ-ray from neutron capture is thedelayed signal in this calibration. The calibration is conducted twice in 2009 and 2016 andat diﬀerent positions inside the ID, A: (35.3, −70.7, 0.0) cm, B: (35.3, −1201.9, 0.0) cm, andC: (35.3, −70.7, 1500.0) cm in the coordinate where the ID center position is set to (0, 0, 0).
The measurements are compared with the MC expectations and the results are summarizedin Table 11.4. The observed eﬃciencies show good agreements in general with the predicted
eﬃciencies. The largest discrepancy between the data and MC results, 21% in 2009 at theposition A, is taken as a systematic uncertainty on the neutron tagging eﬃciency.

Figure 11.17: Photograph of the Am/Be source embedded in the BGO scintillator.

Table 11.4: Neutron tagging eﬃciencies in percent estimated by the Am/Be calibration bothin data and MC.
Year Position
A
2009
B
C
A
2016
B
C

Data
20.7 ± 0.4
23.2 ± 0.5
25.9 ± 0.6
18.1 ± 0.3
23.9 ± 0.5
25.6 ± 0.6

MC16.3 ± 0.1
21.1 ± 0.1
24.1 ± 0.2
15.2 ± 0.1
19.3 ± 0.1
23.3 ± 0.2

CHAPTER 11. DATA REDUCTION

11.6

151

Reduction Summary

The numbers of observed events in four Erec regions after each reduction are summarized inTable 11.5. Most events are reduced by the neutron tagging because of the very low probabilityof the accidental fake coincidence, as shown in Table 11.3. The reduction eﬃciencies are summarized in Table 11.6 for these energy regions. Total eﬃciencies are also shown with productsof each selection eﬃciency. Here the multiplication starts after the FV cut.
Table 11.5: Number of observed events after each cut in diﬀerent Erec regions.
Energy region [MeV]
fit quality cut
spallation cut
eﬀwall cut
pre-activity cut
post-activity cut
pilike cut
charge/hit cut
Cherenkov angle cut
neutron tagging

7.49−9.49 9.49−11.49 11.49−19.49 19.49−29.49
864437400598145226
609
69362
42420
17374
609
54966
35433
14776
551
54956
35422
14750
497
54956
35420
14743
479
49877
32750
14150
292
49377
32557
14077
255
23677
19767
11401
132
8
17
12
11

Table 11.6: Signal eﬃciencies at each reduction for diﬀerent energy regions.
Energy region [MeV]
fit quality cut
spallation cut
eﬀwall cut
pre-activity cut
post-activity cut
pilike cut
charge/hit cut
Cherenkov angle cut
neutron tagging
Total

7.49−9.49>0.9990.478
0.924>0.999>0.999
0.974
0.999
0.793
0.129
0.043

9.49−11.49 11.49−19.49 19.49−29.49>0.999>0.999>0.999
0.549
0.827
1
0.921
0.920
0.918
>0.999>0.999>0.999>0.999>0.999>0.999
0.978
0.982
0.980
0.998
0.995
0.989
0.852
0.909
0.952
0.151
0.146
0.241
0.064
0.099
0.204

Chapter 12
Background Estimation
As overviewed in Chapter 10, the background is sorted into four types. The background estimates are summarized in Table 12.1 and the spectrum is shown in Figure 12.1. In the lower
two energy bins, the main background sources are the 9 Li and accidental fake events, while theatmospheric neutrino events become large in the upper two energy bins.
Table 12.1: Summary of the background estimates in the SRN search.

EventsEnergy [MeV]
7.49−9.49 9.49−11.49
Atmospheric-ν (ν-NCQE)
1.2±0.9
1.3±1.0
Atmospheric-ν (ν̄-NCQE)
0.6±0.4
0.9±0.7
Atmospheric-ν (non-NCQE) 0.2±0.1
0.2±0.1
9Li
7.6±3.5
5.5±3.1
Reactor-ν
2.0±2.0
0.1±0.1
Accidental fake coincidence
4.9±2.0
8.0±3.0
Total
16.5±4.6
16.0±4.5

11.49−19.49
2.2±1.3
1.2±0.7
1.1±0.3
2.8±1.80
4.0±1.5
11.3±2.8

19.49−29.49
0.5±0.5
0.3±0.3
5.1±1.200
0.7±0.2
6.6±1.330

Atmospheric-ν (ν-NCQE)
Atmospheric-ν (ν-NCQE)
Atmospheric-ν (non-NCQE)
9
Li
Reactor-ν
Accidental fake coincidence

25

20

15

10

5

0

8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Figure 12.1: Background energy spectrum after all the reductions. Diﬀerent colors correspondto each background source. Shaded bars represent the total systematic error of the background.

152

CHAPTER 12. BACKGROUND ESTIMATION

12.1

153

Atmospheric Neutrinos

Backgrounds from the atmospheric neutrino interactions are estimated by MC, which is described in Chapter 10. This background is categorized into two: NCQE-like and the others.
Estimation of each is explained in the following part.

12.1.1

NCQE-like Interaction

Below 19.49 MeV, the dominant atmospheric neutrino background is made by the NCQE-likeinteractions. To estimate this background, the measurement in Part II is used. The MC predictions of neutrino and antineutrino NCQE-like interactions are renormalized by multiplying
the scale factors in Equation 8.12. This provides an inclusive estimation of the NCQE and NC
2p2h interactions. The errors of these factors are taken as cross section uncertainties.
There are two uncertainties about neutrino flux: the atmospheric neutrino flux uncertainty
and the uncertainty due to the flux diﬀerence between the T2K and atmospheric neutrinos. A
15% is taken as the former error from Refs. [152, 167]. The latter one arises from the fact thatthe scale factors above are measured in the T2K fluxes while the current focus is the atmospheric
neutrino flux and then the eﬀect of cross section model uncertainties is diﬀerent. To estimate
this uncertainty, the ratios of flux-averaged events in the T2K beam and atmospheric neutrino
fluxes for diﬀerent cross section models are calculated. The ratios, Rνi and Rν̄i for model i from
Figure 8.4 in Chapter 8, are defined as follows:∫ T2K iϕν σν-NCQE dEν
Rνi = ∫ ATM i,ϕν σν-NCQE dEν
∫Rν̄i = ∫(12.1)i
ϕT2K
σν̄-NCQE
dEν̄
ν̄
,
i
ϕATM
σν̄-NCQE
dEν̄ν̄(12.2)

where ϕT2K and ϕATM represent the T2K and atmospheric neutrino fluxes respectively, andiiσν-NCQE
and σν̄-NCQE
correspond to neutrino and antineutrino NCQE cross sections on oxygenfrom model i respectively. Table 12.2 summarizes the relative ratios to RνNEUT and Rν̄NEUT . The
maximum diﬀerences are taken as systematic errors, 5% for neutrinos and 7% for antineutrinos.
Table 12.2: Relative ratios of the flux-averaged events from the T2K flux to the atmospheric
neutrino flux from six models in Figure 8.4 to NEUT (the nominal model in the analysis).
Model (i)
NEUT
SF
RMF
SuSA
RGF, EDAI
RGF, Democratic
RPWIA

Rνi /RνNEUT
1
1.03
1.05
0.96
1.04
1.05
0.98

Rν̄i /RνNEUT
1
1.03
1.07
0.98
1.04
1.06
0.96

CHAPTER 12. BACKGROUND ESTIMATION

154

Uncertainties of the random event eﬃciencies in the spallation cut aﬀect the estimation of
the NCQE-like events. The errors are 3% for 7.49−9.49 MeV, 3% for 9.49−11.49 MeV, and 1%
for 11.49−19.49 MeV as shown in Table 11.2.
Since the Cherenkov angle distribution for the NCQE events is highly dependent on modelsof the neutrino interaction and the following secondary interaction, the uncertainty regarding
the Cherenkov angle cut needs to be considered. Figure 12.2 shows Erec distributions for the θCregion between 38 and 50 degrees obtained from the T2K FHC and RHC samples. The numbersof observed and predicted events are compared in each energy region. Since the statistics islimited, two samples are combined here. This treatment also gives similar proportions of theatmospheric neutrino and antineutrino NCQE interactions and hence is justified. The resulting
diﬀerences are 42% for 7.49−9.49 MeV, 50% for 9.49−11.49 MeV, 18% for 11.49−19.49 MeV,
and 84% for 19.49−29.49 MeV. These are taken as systematic uncertainties. Systematic errors
about the other third reduction cuts are estimated similarly to the NCQE-like cross section
analysis, as described in Chapter 7, and found to be as small as a few percent in total.

Events/MeV

Events/MeV

38 ≤ θC < 50 degree
Data (T2K Run1-9 FHC)

25

ν -NCQEν -NCQE

20

NC-other38 ≤ θC < 50 degree

14

Data (T2K Run1-9 RHC)
ν -NCQE

12ν -NCQE

10

NC-otherCC

CC

Beam-unrelated (from off-timing data)

15

8

Beam-unrelated (from off-timing data)

6
10
4
5
0

2
5

10

15

20

25
Erec [MeV]

0

5

10

15

20

25
Erec [MeV]

Figure 12.2: The Erec distributions for the θC region between 38 and 50 degrees obtained
from the T2K FHC (left) and RHC (right) samples. These are before the CC interaction cut
described in Chapter 6.
There are two systematic error sources in the neutron tagging: tagging eﬃciency and neutron
multiplicity. As for uncertainty on the tagging eﬃciency, 21% is employed in this analysis as the
maximum diﬀerence between the measured and predicted eﬃciencies in the Am/Be calibration,
as shown in Chapter 11. In this analysis, the number of neutrons is required to be one, therefore
the model uncertainty aﬀecting the neutron multiplicity has to be estimated. Here the recent
T2K measurement of the neutron multiplicity after neutrino interactions with the CC-dominantsamples at Super-Kamiokande are used [116]. Figure 12.3 shows the average of the number oftagged neutrons as a function of reconstructed Q2 . The ratios of the number of the observation
to that of the prediction in Figure 12.3 are calculated for each Q2 region. Here the sum of thenumbers from the FHC and RHC samples is used. The results are summarized in Table 12.3.
The numbers of tagged neutrons (Ntagged ) for these Q2 regions in the atmospheric neutrino MC
sample are shown in Figure 12.4. The number of events in the Ntagged = 1 bin is varied sothat the average of the number of tagged neutrons becomes the product of its original value

CHAPTER 12. BACKGROUND ESTIMATION

155

and the factors in Table 12.3. Here the events with Q2 > 3 GeV2 are treated together withthe events with 0.75 < Q2 < 3 GeV2 because the number of events in Q2 > 3 GeV2 is small.
The ratio of the number of events in the Ntagged = 1 bin after the variation to that before thevariation is multiplied to each event depending on its Q2 . Then the variance in the number of
selected events is evaluated. The resulting variances are approximately 40% for both neutrinos
and antineutrinos in every Erec region.

Figure 12.3: Average of the number of tagged neutrons in the neutrino event as a function ofreconstructed Q2 in the T2K Run 1−9 FHC (left) and RHC (right) samples [116].

Table 12.3: Ratios of the number of the observation to that of the prediction in each Q2 region
calculated from Figure 12.3. The number of the observation is the sum of those from the FHCFHCRHC
and RHC samples, and this is the same for the prediction as well (Nobs = Nobs
+ Nobsand
FHC
RHC
Npred = Npred + Npred ).
Q2 region
0.00−0.25 GeV2
0.25−0.50 GeV2
0.50−0.75 GeV2
0.75−3.00 GeV2

Nobs /Npred
0.65
0.72
0.51
0.82

Uncertainties on the NCQE-like background estimation is summarized in Table 12.4 forneutrinos and antineutrinos in diﬀerent Erec regions. The largest uncertainty comes from theCherenkov angle cut and the neutron multiplicity. The uncertainties are improved for the region
below 19.49 MeV from the previous 100% to 60−70%.

CHAPTER 12. BACKGROUND ESTIMATION

156

ν-NCQE (0.25 < Q2 < 0.5 GeV2)
EventsEventsν-NCQE (0 < Q2 < 0.25 GeV2)

10

10

1
1

10−1

10−1

10−2
0

10−2
1

2

3

4

5

6

0

1

2

Number of tagged neutrons

3

4

5

6

Number of tagged neutrons

ν-NCQE (Q2 > 0.75 GeV2)

EventsEventsν-NCQE (0.5 < Q2 < 0.75 GeV2)

1

1

10−1

10−2
−1

10

0

1

2

3

4

5

0

6

1

2

4

5

6

ν (0.25 < Q2 < 0.5 GeV2)
Eventsν (0 < Q2 < 0.25 GeV2)
Events3

Number of tagged neutrons

Number of tagged neutrons

10

1
1

10−1
−1

10

0

1

2

3

4

5

0

6

1

2

3

4

5

6

Number of tagged neutrons

Number of tagged neutronsν (Q2 > 0.75 GeV2)

EventsEventsν (0.5 < Q2 < 0.75 GeV2)
1

1

10−1

0

1

2

3

4

5

6

Number of tagged neutrons

0

1

2

3

4

5

6

Number of tagged neutrons

Figure 12.4: Number of tagged neutrons in the atmospheric neutrino MC sample for each Q2
region. Top and bottom four correspond to neutrinos and antineutrinos, respectively.

CHAPTER 12. BACKGROUND ESTIMATION

157

Table 12.4: Summary of the NCQE background uncertainties for neutrinos and antineutrinos
for each energy region. The numbers are shown in percent. The numbers for antineutrinos areshown in parenthes.
Energy [MeV]T2K cross section (in this thesis)
Atmospheric-ν flux
Flux diﬀerence
Spallation cut
Cherenkov angle cut
Other third reduction
Neutron tagging eﬃciency
Neutron multiplicity
Total (neutrino)
Total (antineutrino)

12.1.2

7.49−9.49 9.49−11.49 11.49−19.49+32/−25 (+31/−25)
15 (15)
5 (7)
3 (3)
3 (3)
1 (1)
42 (42)50 (50)18 (18)
3 (3)
3 (3)
3 (3)
21 (21)40 (39)41 (40)40 (40)+72/−69+77/−74+60/−57+71/−68+76/−74+60/−57

19.49−29.49

0 (0)84 (84)3 (3)41 (42)+102/−100+102/−101

CCQE-like Interaction and Pion Production

The other atmospheric neutrino backgrounds are dominated by the events with decay-e’s. The
Michel spectrum is well-known, hence the MC spectrum in the 29.49−79.49 MeV region is fit
by the observed spectrum in the same region. The fitting is done for the spectrum with theneutron tagging 1 . First, the spectrum shape is changed by smearing the spectrum, and thiseﬀect is found to be negligible. Second, the overall scaling of the spectrum is considered. In thefitting, χ2 is calculated for each energy bin between 29.49 and 79.49 MeV. The fitting is done
separately for diﬀerent neutron tagging criteria (BDT cut score) used in each Erec region, thatis, the scale factors are obtained for each Erec region. The results are summarized in Table 12.5.
This includes all uncertainties about the flux model, the cross section model, and selection cuts.
The results are consistent with each other among the diﬀerent Erec regions and accordingly the
BDT scores as well. The reason for much smaller values than the nominal is that the current
model may be inappropriate and this is consistent with the neutron multiplicity results fromT2K shown in Figure 12.3 where the number of tagged neutrons in data is much lower than thatin MC [116]. Figure 12.5 shows the result from the fitting for the neutron tagging condition in
the 19.49−29.49 MeV region.
Table 12.5: Results of the Michel spectrum fitting for the neutron tagging conditions in eachenergy region.
Energy region
7.49−9.49 MeV
9.49−11.49 MeV
11.49−19.49 MeV
19.49−29.49 MeV

1Scaling factor
0.383±0.138
0.377±0.122
0.388±0.125
0.361±0.084

The fitting before the neutron tagging gives a better precision, but instead the large neutron tagging errors
should be considered as shown in the NCQE-like background estimation.

Events/MeV

CHAPTER 12. BACKGROUND ESTIMATION

158

8

Data

7

ATMNU MC (nominal)
ATMNU MC (scaled ×0.361)

6
5
4
3
2
1
0
30

35

40

45

50

55

60

65

70

75

Erec [MeV]

Figure 12.5: The Erec distributions in the 29.49−79.49 MeV region for data, the atmospheric
neutrino MC, and the scaled MC with the neutron tagging condition in the 19.49−29.49 region.

12.2

Lithium-9

The 9 Li background is simulated using the ν̄e signal MC as described in Chapter 10. Systematic uncertainty sources are separated into five: the production rate and the first to fourth
reductions. In the analysis, the result in Ref. [115] is used as the production rate, which is
0.86 ± 0.12(stat.) ± 0.15(syst.) kton−1 day−1 (a 22% uncertainty in total). The uncertainty inthe first reduction is negligible. The second reduction error is explained below, and the third
reduction error is a few percent as described in the NCQE-like part. As the neutron tagging
uncertainty, 21% is taken from the Am/Be calibration.
The 9 Li eﬃciency in the spallation cut is estimated as follows. First, the spallation likelihood
is calculated in the same way as described in Chapter 11 for the pre and post samples, though
here dt is replaced with random numbers following the exp (−dt/τ ) where τ = 0.26 sec. (Li9lifetime). The resulting likelihood distributions for the 7.49−9.49 MeV region are shown in
Figure 12.6. Then the selection eﬃciencies for each muon type are averaged with weights
based on its fraction to the total muons to obtain “weighted eﬃciency”. The outcomes are
the eﬃciencies for one pair of an SHE event and a muon, then the random event eﬃciencies
in Table 11.2 are multiplied to reflect all the pairs. The resulting 9 Li eﬃciencies are 3.1% for
7.49−9.49 MeV, 4.1% for 9.49−11.49 MeV, and 13.1% for 11.49−19.49 MeV. Uncertainties
come from the statistical error of the sample and the random event eﬃciency. Table 12.6
summarizes the eﬃciency in each muon type and the eﬃciencies.
In total, systematic errors on the 9 Li background are 46% for 7.49−9.49 MeV, 56% for
9.49−11.49 MeV, and 64% for 11.49−19.49 MeV, respectively. There is no 9 Li event in theregion above 19.49 MeV.

CHAPTER 12. BACKGROUND ESTIMATION

106

missfit or poorly-fit (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

single (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

159

1
−20

−10

0

10

20

−30

30

−20

−10

0

10

20

Lspall106

stopping (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

multiple (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

30
Lspall

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

Lspall20

30
LspallFigure 12.6: Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 7.49−9.49 MeV region. Dashed green lines represent the cut criteria, the right side ofwhich is removed.
Table 12.6: Summary of the 9 Li eﬃciency in the spallation cut. The 9 Li eﬃciency is the productof the weighted eﬃciency and the random event eﬃciency.
Erec region [MeV]
misfit or poorly-fit muons
single though-going muons
stopping muons
multiple muonscorner-clipping muons
Weighted eﬃciency muonsRandom event eﬃciency
9
Li eﬃciency

7.49−9.49
00.059±0.027
0.170±0.126
0.106±0.011
00.065±0.023
0.478±0.014
0.031±0.011

9.49−11.49
0.025±0.002
0.059±0.039
0.468±0.253
0.037±0.012
00.074±0.035
0.549±0.016
0.041±0.019

11.49−19.49
0.068±0.005
0.135±0.064
0.758±1.471
0.112±0.027
00.158±0.088
0.827±0.010
0.131±0.073

CHAPTER 12. BACKGROUND ESTIMATION

12.3

160

Reactor Neutrino Background

Reactor neutrino background is estimated by renormalizing the ν̄e signal MC as describedin Chapter 10. The reactor neutrino events populate only in the lowest energy bin. In thisanalysis, a conservative 100% uncertainty is assigned for the reactor neutrino events. The eﬀectof this conservative error on the sensitivity is limited because the reactor neutrino backgroundrate is small.

12.4

Accidental Fake Coincidences

The accidental fake background spectrum is obtained by multiplying the mis-tag probabilities
in Table 11.3 to the observed spectrum before the neutron tagging. Since the estimation uses
data, only statistical uncertainties should be considered except for uncertainties on the mis-tag
probability. The statistical error is less than 1% for the region below 19.49 MeV and 9% for19.49−29.49 MeV. The time variation in the PMT gain has a critical impact on the mis-tag
probability 2 . Figure 11.16 shows the mis-tag probability as a function of the signal eﬃciency
for ten diﬀerent periods that cover the whole period of SK-IV. The errors due to this time
variation are 41% for 7.49−9.49 MeV, 37% for 9.49−11.49 MeV, 38% for 11.49−19.49 MeV,
and 26% for 19.49−29.49 MeV.

2This has no sizable impact on the signal eﬃciency in the neutron tagging because the signal has more hits.

Chapter 13
Results
13.1

Selected Events

EventsThe observed spectrum and the estimated background spectrum are shown in Figure 13.1. No
significant excess is observed in data over the background prediction in every energy region.

30

Data
Atmospheric-ν (ν-NCQE)
Atmospheric-ν (ν-NCQE)
Atmospheric-ν (non-NCQE)
9
Li
Reactor-ν
Accidental fake coincidence

25

20

15

10

5

0

8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Figure 13.1: Energy spectra of the observation and background prediction after all the reductions. Diﬀerent colors correspond to each background source. Shaded bars represent the total
systematic error of the background.

13.2

Model-independent ν̄e Flux Upper Limit

Since no significant excess is observed in the data spectrum, an upper limit on the ν̄e flux is
calculated using pseudo experiments as follows. The number of signal events, Nsig , is calculatedby the numbers of the observation and background (Nobs and Nbkg respectively) as Nsig =Nobs − Nbkg with random variations of the statistical and systematic uncertainties on Nobs and161

CHAPTER 13. RESULTS

162

Nbkg . The pseudo experiments are generated assuming Gaussian-shape errors with means andvariances summarized in Table 12.1, and performed separately for four Erec regions. Figure 13.2
shows the result on the 7.49−9.49 MeV region.

Events7.49 < Erec < 9.49 MeV
2500

Zero
N90

2000

1500

1000

500

0
−40

−30

−20

−10

0

10

20

30

40

50

60

Nobs - Nbkg

Figure 13.2: Result of the pseudo experiments on the number of signal events with statisticaland systematic variances for the 7.49−9.49 MeV region.

limit
The 90% C.L. upper bound on the number of signal (N10
) is calculated as the number, theintegration between zero and which contains 90% of the integration above zero, as shown in
Figure 13.2. Then the 90% C.L. upper limit on the ν̄e flux is calculated as:

ϕlimit
=
90

limit
N90
,
t · Np · σ̄IBD · ϵsig

(13.1)

where t is the live time [sec.], Np is the number of free protons, σ̄IBD is the IBD cross section[10−41 cm2 ] at a mean neutrino energy in the corresponding region (Ēν ), and ϵsig is the signal
eﬃciency. Note that the neutrino energy is obtained as Eν = Erec +1.8 MeV in IBD. The results
are shown in Table 13.1. For the sensitivity, a similar procedure is taken but by replacing thenumber of observed event (Nobs ) with the number of nominal background events which is shownin Table 12.1. In the pseudo experiments here, statistical uncertainties on the background areconsidered. The sensitivity results are also shown in the same table. In the table, the sensitivity
and upper limit per MeV are also shown. These are shown and compared with the previous
searches in Figure 13.3. The present analysis places the world’s most stringent upper limits in
the region above 12 MeV.

νe Flux Upper Limit [/cm2/sec./MeV]

CHAPTER 13. RESULTS

163

SK-IV 2970 days (This work)
Sensitivity (This work)
SK-IV 2778 days

102

SK-IV 960 days
SK-I/II/III 2853 days
KamLAND 2343 days

10

1

10−1
10

15

20

25

30

νe Energy [MeV]
Figure 13.3: Model-independent ν̄e flux upper limit at 90% C.L. with a 2970.1-day data set
from SK-IV. The sensitivity in the current work is also shown. For comparisons, the upper
limits by the KamLAND 2343 days [47], the SK-I/II/III spectrum analysis with 2853 days [45],and the SK-IV neutron tagging analysis with 960 days [46] and 2778 days [166] are shown
together.

CHAPTER 13. RESULTS

164

Table 13.1: Summary of the 90% C.L. sensitivities and upper limits on the electron antineutrino
flux in each energy region. Ēν represents the mean neutrino energy in the region.
Erec region [MeV]Eν (= Erec + 1.8) region [MeV]t [×108 sec.] ([days])
Np
σ̄IBD [×10−41 cm2 ] (Ēν [MeV])
ϵsig
sensitivity
N90
sensitivity
ϕ90[/cm2 /sec.]
sensitivity
dϕ90/dEν [/cm2 /sec./MeV]
limit
N90
ϕlimit[/cm2 /sec.]
90
2
dϕlimit90 /dEν [/cm /sec./MeV]

7.49−9.49
9.49−11.49 11.49−19.49 19.49−29.49
9.29−11.29 11.29−13.29 13.29−21.29 21.29−31.29
1.79 (2075.3)
2.57 (2970.1)
33
1.5 × 10 (22.5 kton FV)
0.72 (10.29) 1.05 (12.29) 2.17 (17.29) 4.92 (26.29)
0.043
0.064
0.099
0.204
9.1
8.8
6.4
4.4
109.2
34.1
7.8
1.1
54.6
17.1
1.0
0.1
5.2
10.5
7.8
9.2
62.1
40.8
9.4
2.4
31.0
20.4
1.2
0.2

13.3

Discussion

13.3.1Comparison with Theoretical Predictions

The 90% C.L. upper limits in this analysis are compared with theoretical predictions in Table 13.2. The current limits in the region above 13.29 MeV are a factor 3 to 30 above model
predictions, while those in the lower energy regions are even farther.
Table 13.2: Comparison of the 90% C.L. upper limit on the ν̄e flux with the SRN theoreticalpredictions.
Eν [MeV]
9.29−11.29
2
This work [/cm /sec.]
62.1
Horiuchi+18 [36] [/cm2 /sec.]
ξ2.5,crit = 0.1
1.47
ξ2.5,crit = 0.5
1.44
Nakazato+15 [31, 37] [/cm2 /sec.]
Maximum, Inverted hierarchy
0.95
Minimum, Normal hierarchy
0.41
Horiuchi+09 [38] [/cm2 /sec.]
2.23
2
Lunardini09 [40] [/cm /sec.]
1.01
2
Ando+09 [41] [/cm /sec.]
1.11
Malaney97 [42] [/cm2 /sec.]
0.52
2
Hartmann+97 [43] [/cm /sec.]
0.95

13.3.2

11.29−13.29
40.8

13.29−21.29
9.4

21.29−31.29
2.4

1.22
1.07

1.82
1.23

0.49
0.18

0.60
0.26
1.61
0.79
0.74
0.34
0.65

0.91
0.38
2.94
1.18
1.18
0.53
1.09

0.21
0.07
0.80
0.27
0.27
0.10
0.25

Benefits of the T2K NCQE-like Results

In this work, the NCQE-like background is estimated using the T2K results for the first time, as
demonstrated in Chapter 12. This provides more reliable estimation of this background than theCHAPTER 13. RESULTS

165

previous analyses that are based on the theoretical predictions. The uncertainty size is reduced
from 100% to 60−70% as shown in Table 12.4. With the T2K results, the search sensitivity(the upper limit) has been improved by 3% (2%) for the region 9.29 < Eν < 13.29 MeV and by
12% (10%) for the region 13.29 < Eν < 21.29 MeV in comparison to an analysis with a 100%
uncertainty.
The estimation with the T2K measurements is promising in terms of its possible improvements. As mentioned in Chapter 8, precisions of the NCQE cross section will be improved
with the RCNP results presented in Part III, more precise flux prediction, and larger statistics. Furthermore, the neutron tagging will be applicable to the NCQE sample and this would
avoid large uncertainty from the neutron multiplicity which is explained in Chapter 12. This is
more feasible in SK-Gd because of the higher neutron tagging eﬃciency. In the era of HyperKamiokande, thanks to its ∼8.4 times larger fiducial mass and the upgrade of J-PARC and theneutrino beamline as mentioned in Chapter 8, ∼1000 events are expected in the SRN signal
region in the Erec −θC phase space with the neutron tagging. This could provide the NCQE
background estimation with a precision better than 10%, avoiding large uncertainties due toneutron multiplicity and Cherenkov angle cut.

13.3.3Future Prospects

The 3σ sensitivities at SK-Gd and HK are evaluated with the same procedure as explained above
for the 90% C.L. sensitivities. In SK-Gd, since the γ-ray energy is ∼8 MeV, the search is free ofthe accidental fake background. Other than the accidental background, the same backgroundsources with the current systematic uncertainties are assumed and the absolute amount of eachbackground is scaled by live time. A 90% neutron tagging eﬃciency is assumed for SK-Gd.
For HK, the neutron tagging eﬃciencies twice better than those in SK with the same mis-tag
probabilities, shown in Table 11.3, are assumed, because the γ-ray energy is 2.2 MeV and thenHK also suﬀers from the large background by PMT dark noise and radioactive sources. Herethe other backgrounds than the accidental coincidences are scaled by live time and detector
mass and the same error sizes as the current analysis are assumed.
The results for SK-Gd are shown in Figure 13.4. Here the results only for the region Eν >13.29 MeV are presented, because the lower region is less promising. Models by Horiuchi+18
and Horiuchi+09 can be tested after 5−10 years of operation. The reach after the 10-year
operation is comparable or a bit worse compared to predictions by Lunardini09, Ando+09, andHartmann+97. However, the sensitivity is not enough to reach the predictions by Nakazato+15
and Malaney97. Note that the evaluations are based on the current background compositionand systematic uncertainties, but it is highly probable that the 9 Li background will be reducedwith improvements on the spallation cut and use of various neutron information, or understoodwell through the spallation measurement as demonstrated in Ref. [115]. This would help toachieve the better sensitivity and then test more models.
The results for HK are shown in Figure 13.5 also only for the region above 13.29 MeV in
neutrino energy. According to the results, HK can test most models except for the minimum
flux prediction by Nakazato+15, while it is not so far. Again note that if the 9 Li background isreduced or estimated more precisely, it is probable to test the whole region of the Nakazato+15
prediction.
As mentioned above, the situation about the 9 Li background will improve by using neutron
information. Once the 9 Li background uncertainty and its rate are reduced, the improved
measurements of the NCQE-like interactions in SK-Gd and HK would be much more beneficial.
Figure 13.6 shows the 3σ sensitivities in SK-Gd with a 0.1% Gd doping for diﬀerent conditions

166

SK-Gd (13.29 < Eν < 21.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.6

0.5

0.4

0.3

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]

CHAPTER 13. RESULTS

SK-Gd (21.29 < Eν < 31.29 MeV)

0.16

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.14
0.12
0.1
0.08
0.06

0.2
0.04
0.1
0.02
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

Year

10
Year

Hyper-Kamiokande (13.29 < Eν < 21.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.25

0.2

0.15

0.1

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]

Figure 13.4: The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period witha 0.1% Gd doping for the neutrino energy region 13.29 < Eν < 21.29 MeV (left) and 21.29 <Eν < 31.29 MeV (right). The predictions from the models explained in Chapter 1 are also
shown.

Hyper-Kamiokande (21.29 < Eν < 31.29 MeV)
0.035

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.03

0.025

0.02

0.015

0.05

0.01

1

2

3

4

5

6

7

8

9

10
Year

0.005

1

2

3

4

5

6

7

8

9

10
Year

Figure 13.5: The 3σ sensitivity for the ν̄e flux as a function of Hyper-Kamiokande operation
period for the neutrino energy region 13.29 < Eν < 21.29 MeV (left) and 21.29 < Eν <31.29 MeV (right). The predictions from the models explained in Chapter 1 are also shown.

CHAPTER 13. RESULTS

167

SK-Gd (13.29 < Eν < 21.29 MeV)

0.6

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.55
0.5
0.45
0.4
0.35
0.3

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]on the NCQE-like background. Here the non-NCQE background is scaled by live time withthe same systematic error as the analysis in this thesis and the amount of 9 Li background isreduced to 1/5 from the simple scaling by live time with a 10% uncertainty. The treatments of
the reactor and accidental backgrounds are the same as above for SK-Gd. Three conditions for
the NCQE-like background are considered: the absolute amount scaled by live time with 100%and 60% uncertainties, and the absolute amount reduced by 30% (×0.7) from the simple scaling
with a 40% uncertainty. The 100% and 60% error cases correspond to the previous and current
situations. Since the number of neutrons from atmospheric neutrinos seems smaller than the
MC prediction as shown in Chapter 12, the absolute background amount may be reduced in
the future, then the third case assumes the reduced NCQE-like background. With an improved
estimation of the NCQE-like background, models by Horiuchi+18, Lunardini09, Ando+09, andHartmann+97 can be tested in the 13.29−21.29 MeV region, while the reach with a 100% error
is not enough for these models. The benefits of improvements on the NCQE-like backgroundestimation are limited for the region above 21.29 MeV. The Michel spectrum fitting will be
improved with higher statistics in the future, providing prediction on the CCQE-like event ratewith better precision. All these improvements would help a future discovery of the SRN flux.
Further sensitivity results are given in Appendix E.

SK-Gd (21.29 < Eν < 31.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.14

0.12

0.1

0.08

0.25
0.2 –– NCQE 100% error

0.06–– NCQE 60% error
0.15–– NCQE×0.7 40% error
1

2

3

4

5

6

7

8

9

10
Year

0.04

–– NCQE 100% error–– NCQE 60% error–– NCQE×0.7 40% error
1

2

3

4

5

6

7

8

9

10
Year

Figure 13.6: The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period with a
0.1% Gd doping for the neutrino energy region 13.29 < Eν < 21.29 MeV (left) and 21.29 < Eν <31.29 MeV (right) for diﬀerent NCQE-like background conditions. Note that assumptions on
the background are diﬀerent from those in Figure 13.4 as explained in the text. The predictions
from the models explained in Chapter 1 are also shown.

Part V
Summary

169

Chapter 14
Conclusion
Supernova explosions are among the most powerful and complex phenomena in the universe,
and unraveling the details of the explosion and properties of the supernova itself would help
solve various mysteries in particle physics, nuclear physics, and astrophysics. There have beenfrequent observations of supernovae in optical surveys, though the observation via neutrinos
is limited to SN1987A. Supernova relic neutrinos (SRNs), if detected, would provide valuable
information about the supernova explosion mechanism as well as star formation history. The
atmospheric neutrino neutral-current quasielastic-like (NCQE-like) interactions are among thedominant background in SRN searches at water Cherenkov detectors. In this thesis, a measurement of the NCQE-like interaction with T2K neutrino and antineutrino beams based on nuclear
de-excitation γ-rays was presented, and its application to an SRN search at Super-Kamiokande
was also reported.
Beam monitoring with the muon monitor is essential to stable data taking in T2K, andthis has been achieved through various investigations. It helped T2K accumulate data with
14.94 × 1020 and 16.35 × 1020 protons-on-target exposures of the neutrino and antineutrino
beams, respectively. With these data sets, the flux-averaged NCQE-like cross sections were
measured as:−38⟨σν-NCQE ⟩ = 1.70 ± 0.17(stat.)+0.51
cm2 /oxygen,−0.38 (syst.) × 10
−38
⟨σν̄-NCQE ⟩ = 0.98 ± 0.16(stat.)+0.26
cm2 /oxygen,−0.19 (syst.) × 10

at flux-averaged energies of 0.82 GeV and 0.68 GeV for neutrinos and antineutrinos, respectively. Simultaneous treatment of both FHC and RHC data has resulted in similar sized errors
for the neutrino and antineutrino results. These are the world’s most precise measurement results to date, and the antineutrino result is the first measurement of this channel. The obtained
results were found to be consistent with currently available models within the precisions. Basedon distributions from the FHC and RHC samples, properties of γ-rays emitted from the secondary nuclear reactions were investigated. In addition, distributions in the kinematic regionsof interest for SRN searches were studied for the first time in this thesis. This has suggested an
importance of understanding the secondary-γ emission. Possible updates to the measurement
utilizing the neutron information were also discussed.
The largest uncertainty in the NCQE-like measurement comes from the modeling of γ-rays
emitted from neutron-oxygen reactions. Prior to the work in this thesis there was little dataon this interaction. In order to provide experimental data, a measurement of γ-ray production
171

CHAPTER 14. CONCLUSION172

via neutron-oxygen reactions with an 80 MeV neutron beam was performed at RCNP. In theexperiment, several γ-rays of various energies thought to come from neutron-oxygen reactions
were observed and their production cross sections were measured to ∼20% precision. The
results indicate that the current models used in the NCQE-like measurement are incomplete.
This experiment established the basic measurement method and suggests there is the potential
to reduce the secondary-γ uncertainty from 13% to less than 5% if similar measurements are
made with diﬀerent neutron energies. Additional measurements at neutron energies of 30 and
250 MeV were performed in the same facility and the data analysis is on-going towards themodel improvements together with the results obtained in this thesis.
An SRN search was performed using a 2970.1-day data set from Super-Kamiokande IV.
In order to remove a large amount of muon spallation background, a data-driven method wasdeveloped. The neutron tagging method was tuned based on the boosted decision tree techniqueand has removed huge accidental backgrounds. In the estimation of the atmospheric NCQElike background, the T2K results are used. This new estimation has reduced the uncertainty
from 100% to 60%, improving the search sensitivity by 12% compared to an analysis witha 100% uncertainty on the NCQE-like background. No significant excess over the prediction
was observed in the data spectrum, and an upper limit on the ν̄e flux was placed. The result
is the world’s most stringent above 13.3 MeV in neutrino energy, which is a factor 3 to 30
above model predictions. In future water Cherenkov detectors, such as SK-Gd and HyperKamiokande, which will have better background rejection power or a larger fiducial mass, the
NCQE-like background will become more important. The search sensitivities and the potential
to make constraints on SRN models at these detectors were also discussed. The methods
presented in this thesis are applicable to SRN searches at these detectors, and may help afuture discovery of the SRN flux.

Appendices173

Appendix A
Beam Studies with MUMON
A.1

Correlation between Proton and Muon Beams

Muon beams are aﬀected by proton beam properties such as intensity, position, and width.
These are studied and some of them are shown in Appendix B.

A.2

Correlation between Horn Current and Muon Beam

The horn current aﬀects the magnetic field and accordingly the muon beam. This eﬀect iscorrected in the measurement. In order to obtain the correction functions, the horn current
scans are performed both in FHC and RHC modes. The horn current is measured by two horn
power supplies (HPS1 and HPS2). The HPS1 measures the current for the horn-1, while the
HPS2 measures the current for the horns-2 and 3 (the current is separated into two). The scanpoints are shown in Figure A.1. The results in the FHC and RHC modes are shown Figures A.2
and A.3, respectively.
hornps[1]:hornps[0]
7

25.2

FHC

HPS2hornps[1][kA]

HPS2hornps[1][kA]

hornps[1]:hornps[0]
25.2

6

25

5

25

RHC

20
25
15

4

24.8

24.8
3

10
24.6

24.6
2

5
24.4

24.4

1

24.3

24.4

24.5

24.6

24.7

24.8

24.9

25

25.1
25.2
hornps[0]

0

24.2

24.4

24.6

24.8

25

25.2
hornps[0]0HPS1 [kA]

HPS1 [kA]

Figure A.1: Horn scan points in FHC (left) and RHC (right) in the 2D HPS1−HPS2 plane.
Magenta boxes represent the points used for obtaining the correction functions. The otherpoints are used for the cross check after the correction.

175

APPENDIX A. BEAM STUDIES WITH MUMON−9

IC Yield

Si Yield×10
32.6

Si, HPS1 scan

32.4
32.2

176

×10

−9

0.95

IC, HPS1 scan

0.94
0.93

32
0.92
31.8
0.91

31.6
31.4

0.9

p0 −4.855e−09 ± 1.405e−09

31.2
31

p1
24.3

24.4

24.5

24.6

24.7

24.8

p1

1.48e−09 ± 5.681e−11
24.9

25

25.1

p0

0.89
0.88

25.2

24.3

24.4

24.5

24.6

24.7

24.8

−5.938e−11 ± 9.275e−11
3.957e−11 ± 3.75e−12
24.9

×10
32.6
32.4

Si, HPS2 scan

32.2

25.1

25.2

HPS1 [kA]−9

IC Yield

Si Yield

HPS1 [kA]

25

×10

−9

0.95

IC, HPS2 scan

0.94

0.93

32
31.8

0.92

31.6
0.91
31.4

p0

3.398e−09 ± 1.617e−09

p1

1.147e−09 ± 6.526e−11p02.407e−10 ± 1.09e−10p12.745e−11 ± 4.396e−12

0.9

31.2
24.4

24.6

24.8

25

25.2

24.4

24.6

24.8

25

HPS2 [kA]

25.2

HPS2 [kA]

20.2

20

×10

−9

IC Yield

Si YieldFigure A.2: Horn scan results in the FHC mode for the HPS1 (top) and HPS2 (bottom) scans.
The left and right panels give the results from Si and IC, respectively.

Si, HPS1 scan

×10
0.62

−9

IC, HPS1 scan

0.615

19.8

0.61

19.6

0.605
0.6

19.4

19.2

24.2

24.4

24.6

p0 −2.061e−10 ± 3.358e−10

0.595

p0

6.834e−12 ± 1.034e−11

p1

0.59

p1

2.421e−11 ± 4.18e−1324.8

8.018e−10 ± 1.358e−11
25

25.2

24.2

24.4

24.6

24.8

25

×10
20.1
20

−9

Si, HPS2 scan

25.2

HPS1 [kA]
IC Yield

Si Yield

HPS1 [kA]
×10
0.62

−9

IC, HPS2 scan

0.615

19.9
19.8

0.61

19.7
0.605

19.6
19.5

p0

5.03e−09 ± 3.23e−10p15.935e−10 ± 1.306e−11

19.4
19.3

24.4

24.6

24.8

25

25.2

HPS2 [kA]

0.6

24.4

24.6

24.8

p0

1.739e−10 ± 1.004e−11p11.755e−11 ± 4.06e−13
25

25.2

HPS2 [kA]

Figure A.3: Horn scan results in the RHC mode for the HPS1 (top) and HPS2 (bottom) scans.
The left and right panels give the results from Si and IC, respectively.

Appendix B
Electron-Multiplier Tubes for
MUMON
B.1

Concerns for the Current MUMON Detectors

In the near future, J-PARC will strengthen its beam power up to 1.3 MW from the current
485 kW. In addition, the electromagnetic horn current is increased from 250 kA to 320 kA.
These will provide nearly tripled power beams. The current MUMON detectors are expected
to suﬀer from issues in such situation, which are observed even at present.
For Si sensors, the yield degradation is observed and this is considered due to radiation
damage. Figure B.1 shows a history of ratio of the average Si yield to the average IC (Ar) yieldover the T2K operation. It is found that the Si yield has been continuously degraded over theperiod. Note that Si sensors were replaced twice so far; the whole of 49 ch was replaced withnew ones (2nd generation) after MR Run 49, and the 24 ch were changed to the new ones (3rdgeneration) after MR Run 74 (the remaining 25 ch are the 2nd generation). The ratios of theyield sum of these 25 ch to that of 24 ch before and after the second replacement are shownin Figures B.2 and B.3. Just after the replacement, the new sensors show their yield decreasein a short period. This was reported from the studies in the first replacement. After the 3rd
generation sensor yield gets stable, the degradation rate of the 2nd generation is found to befaster than that of the 3rd generation.
For IC, the signal linearity is broken at high intensity due to the space charge eﬀect thatthe electric field inside the detector is distorted by lots of accumulated ions. This eﬀect ismore visible in the latter bunches because more ions are accumulated from the former bunches.
Figure B.4 shows that linearity response of IC (Ar) is broken above 400 kW. The feature forthe bunches 1 to 7, seen in the right panel of the figure, is attributed to the fact that the Si
detectors have longer decay time as shown later. The drop in the 8th bunch is due to the spacecharge eﬀect of IC (Ar). One solution to this issue would be change of the gas since ligher
ions will be sweeped faster and then no accumulation causing the space charge eﬀect happens.
However, the pileup becomes a problem instead when He gas is used, as shown in Figure B.5.
This is because contributions to signal not only from electrons but also from ions are visible.
Such pileup clearly aﬀects the bunch-by-bunch beam monitoring.

177

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

178+ Si/IC-Ar
Si/IC-Ar(FHC)(FHC)+ Si/IC-Ar
Si/IC-Ar(RHC)
(RHC)

Si/IC

Si/IC-Ar
36

Si 1st generation

Si 2nd generation

Si 3rd generation(Half are 2nd generation)

35

34

33

Bunch number change(6 → 8)IC HV increase(250 V → 270 V)

32

31

POT
30

FHC: 0.326e20 FHC: 6.317e20
RHC: 0.0e20
RHC: 0.0e20

FHC: 0.922e20
RHC: 7.558e20

FHC: 7.170e20 FHC: 0.205e20
RHC: 0.0e20
RHC: 8.887e20

29 30 31 32 33 34 36 37 38 41 42 43 44 45 46 47 48 49 55 56 58 59 60 61 62 63 66 67 68 70 71 72 73 74 76 77 78 79

MR Run#Figure B.1: Ratio of the average signal yield of Si to that of IC (Ar) over the T2K operation.
Si sensors are replaced twice so far and the second replacement was conducted for only half of
49 sensors.

Si Odd-Ch / Si Even-Ch

Odd# 24 ch: 2nd generation
Even# 24 ch: 2nd generation

1.05
1.04

1000

Si Odd/Even

Si Odd/Even

Si Odd-Ch / Si Even-Ch
1.06

1.06

400

Odd# 24 ch: 2nd generation
Even# 24 ch: 2nd generation

1.05
1.04

300

800
1.03

350

1.03

250
1.02

600

1.01

1.02

200
1.01

400

1
0.99

150
1

100

0.99

200
0.98

0

0.97

23, Feb.
09:00

50

0.98

02, Mar.
09:00

09, Mar.
09:00

16, Mar.
09:00

23, Mar.
09:00

30, Mar.
09:00

0

0.97

02, Apr.
21:00

06, Apr.
09:00

09, Apr.
21:00

Figure B.2: Ratio of the average yield of odd-numbered Si sensors to that of even-numbered Si
sensors in certain periods in T2K Run 8. All sensors are the 2nd generation ones.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

Si Odd-Ch / Si Even-Ch

1.06

140

Odd# 24 ch: 2nd generation
Even# 24 ch: 3rd generation

1.05
1.04

Si Odd/Even

Si Odd/Even

Si Odd-Ch / Si Even-Ch

179

120

1.06

220

Odd# 24 ch: 2nd generation
Even# 24 ch: 3rd generation

1.05
1.04

200
180

100
1.03

160

1.03

140

80

1.02
1.01

1.02

60

120

1.01

100

1

80

1

40
0.99

60

0.99

40

20

0.98

0.98

0

0.97

17, Oct.
09:00

18, Oct.
09:00

19, Oct.
09:00

20, Oct.
09:00

21, Oct.
09:00

20
0

0.97

22, Oct.
09:00

26, Oct.
09:00

02, Nov.
09:00

Si Odd/Even

Si Odd-Ch / Si Even-Ch
1.06

900

Odd# 24 ch: 2nd generation
Even# 24 ch: 3rd generation

1.05
1.04

800
700

1.03

600
1.02

500
1.01

400

1

300

0.99

200

0.98

100
0

0.97

09, Nov.
09:00

16, Nov.
09:00

23, Nov.
09:00

30, Nov.
09:00

07, Dec.
09:00

14, Dec.
09:00

21, Dec.
09:00

0.027

For only 8th bunch (+250 kA)
0.026

0.025

0.024

IC Center/Si Center

IC Center/CT5 [nC/(1012 protons/bunch)]

Figure B.3: Ratio of the average yield of odd-numbered Si sensors to that of even-numbered
Si sensors in certain periods in T2K Run 9. The odd-numbered sensors are the 3rd generationand the even-numbered ones are the 2nd generation.

0.033

At 460 kW & 250 kA operation
0.032
0.031
0.03
0.029

0.023

0.028

400 kW

0.022

0.021
0

0.027

5

10

15

20

25

30

CT5 [1012 protons/bunch]

0.026
0

1

2

3

4

5

6

7

8

9

Bunch#

Figure B.4: IC (Ar) yield for the 8th bunch at several beam intensities under a +250 kA horn
operation (left) and the ratio of the IC (Ar) to the Si center channels for each bunch at 460 kW
and +250 kA horn current (right).

180

ADC count
ADC

ADC count
ADC

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

Pileup

− 100

− 20

− 150
− 200

− 40

− 250
− 300

− 60

− 350
− 80

− 400
− 450

− 100

0

− 500
50

100

150

200

250

300

350

400

0

50

100

150

200

250

Sample (~15 ns/sample)

300

350

400

Sample (~15 ns/sample)

FADC sample (~15 ns/sample)

FADC sample (~15 ns/sample)

Figure B.5: IC (He) signal waveform at 340 kW and +250 kA horn current, equivalent to
2.5 × 106 /cm2 per 80 ns (left), and IC (Ar) signal waveform at 480 kW and −250 kA horncurrent, equivalent to 2.3 × 106 /cm2 per 80 ns (right).

B.2

Electron-Multiplier Tubes

de

n
dyn
ode

ano

3

2
dyn
ode

dyn
ode

1

Al

dyn
ode

For the reasons described above, a new detector for the muon monitoring is desired under the
future high intensity operation. Electron-multiplier tubes (EMTs) are one candidate as a new
detector. Secondary electron emission (SEM) monitors are usually radiation tolerant and their
response is fast, which are important for the muon monitor. Photomultiplier tubes (PMTs) are
one of the SEM detectors; however, the photocathode is not necessary for the muon detection.
Replacing the photocathode with another material, in the present work with aluminum, EMTs
are considered as a candidate. Indeed, PMTs are also tested but showed worse performance
than EMTs about their linearity and stability, as explained later in this chapter. The schematic
illustration of the signal multiplication is shown in Figure B.6. Secondary electrons are emitted
either at the aluminum cathode or at the dynodes when a muon passes through the detector.
Those secondary electrons are then accelerated and hit the downstream dynodes to produce
further secondary electrons.

e
e
e
μ

e
Δe,Al
Δμ,Al

δe,1
δμ,1

δe,2
δμ,2

δe,3
δμ,3

δe,n
δμ,n

Figure B.6: Schematic illustration of the signal multiplication in EMTs.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

181

The secondary emission eﬃciency is expressed by the number of emitted electrons over that ofincident particles and is specific to the type of material and the properties of incident particles
such as particle type and energy. In Figure B.6, ∆ and δ represent the secondary emission
eﬃciencies for aluminum and dynodes, respectively. Here a subscript “e” is used for electrons
and a subscript “µ” is used for muons as incident particles. The subscripts of δ represent thedynode numbers. The product of the secondary emission eﬃciencies of all dynodes gives thegain of the PMT:

G = δe,1 × δe,2 × · · · × δe,n =n∏δe,i .

(B.1)

i=1

For the muon monitor, the signal is generated mainly by muons and electrons (δ-rays) producedby muon hits. The energy of δ-rays is up to several hundred MeV according to the beamline
simulation [74]. The muons and δ-rays penetrate the EMT, while most secondary emission
electrons stop at the dynodes. The final output signal (Q) is expressed as follows:

Q = Qµ + Qe ,{Qµ = e · ϕµ ·Asur · ∆µ,Al ·{Qe = e · ϕe ·Asur · ∆e,Al ·n∏δe,i +

n−1
∑

i=1

i=1

n
∏

n−1
∑

δe,i +

i=1

i=1(
Ai · δµ,i ·

δe,j

j=i+1

(
Ai · δe,i ·

n
∏

(B.2)

)}

n
∏

δe,j

,

(B.3)

)}
,

(B.4)

j=i+1

where e represents the elementary electric charge (1.6 × 10−19 C), Asur and Ai are the areaof the aluminum cathode surface and each dynode surface [cm2 ] respectively, and ϕµ and ϕe
are the muon and δ-ray fluxes [/cm2 ]. The first terms in Eqs. B.3 and B.4 correspond to thesecondary electrons at the aluminum cathode, and the second terms correspond to those at thei-th dynode.

B.3

First Prototype Detectors

R
Two EMTs were made based on HAMAMATSU⃝
PMT R9880 by depositing aluminum on
the cathode, termed as EMTC3 and EMTC4. The reason why R9880 was selected is that it isshort enough for the installation space. Figure B.7 shows a picture of the EMTC3 sensor andFigure B.8 shows the divider curcuit diagram for EMTs. In the figure, the resistances R1 −R10
are set to 330 kΩ and R11 is set to 160 kΩ. This setting gives uniform voltage diﬀerences
between the dynodes. The capacitors, C1 −C11 , are put to compensate for the charge usedon the dynodes in the multiplication. To maintain linearity of the EMT response, suﬃcientcharge (usually 100−1000 times the consumed charge) should be stored in the capacitors. The
51 Ω damping resistances (R12 and R13 in the figure) are inserted to reduce waveform ringing,but these are not used this time so that the charged consumed in the earlier bunches can becompensated for quickly from the capacitors.
In the present work, two divider curcuits are made (C3 and C4). Table B.1 summarizes thecapacitances and stored charges in each capacitor in C3 and C4 when a negative bias −500 V is

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

16

182

mm

Figure B.7: A photograph of EMTC3. The monitor radius is 8 mm.

Signal Output

K

P

R12

R13

DY1 DY2 DY3 DY4 DY5 DY6 DY7 DY8 DY9 DY10

R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R11

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11
GND

Figure B.8: Schematic diagram of the divider circuit of the prototype EMT. “K”, “P”, “DY”
and “GND” represent the cathode, anode, dynode, and ground, respectively. The resistances
R1 −R10 are 330 kΩ, and R11 is 160 kΩ. The capacitances are given in Table B.1.
Table B.1: Capacitances and stored charges for EMTC3 and EMTC4 when −500 V is applied.

K-DY1 (C1 )DY1-2 (C2 )DY2-3 (C3 )DY3-4 (C4 )DY4-5 (C5 )DY5-6 (C6 )DY6-7 (C7 )DY7-8 (C8 )DY8-9 (C9 )DY9-10 (C10 )DY10-GND (C11 )EMTC3capacitance (nF) charge (µC)
10
0.48
10
0.48
10
0.48
15
0.35

EMTC4
capacitance (nF) charge (µC)
100
4.8
100
4.8
100
4.8
330
15.7
330
15.7
330
7.6

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

183

applied. Only C8 to C11 were used for EMTC3 and C6 to C11 for EMTC4, and other capacitors
were removed (represented as “-” in the table).
Both EMTs were installed at the downstream of the IC. The installation positions are shownin Figure B.9. The signal and high-voltage cables for the EMTs are the same ones as those for
the Si and IC sensors. The readout electronics is also the same but the attenuator module is
not used for the EMTs.

muon beam center
C3

C4

EMTC3

muon beam

26.5 cm

26.5 cm EMTC4

26.5 cm

26.5 cm

25 cm

Most downstream (behind ion chamber)

25 cm

Figure B.9: Installation positions of the prototype EMTs overlaid with the IC sensor positions(left) and a zoom version focusing around the EMTs (right). Green squares in the left panel
indicate the 49 ch of the IC and solid magenta square corresponds to the center channel.

Output charge
The expected charge for the prototype detectors can be calculated by using Eqns ??. To
simplify the case contributions from δ-rays are ignored and the area of each aluminum anddynode surface is assumed to be the same (A). The radius is 8 mm then the surface area is
A = 2.01 cm2 . It is assumed that particles are incident on the EMT perpendicular to thesurface and then the eﬀective surface area is not changed. In addition, the secondary emission
eﬃciencies for electrons of all dynodes (δe,i ) are assumed to be equal (δe ). At −500 V thetypical gain of R9880 is 5 × 103 and the number of dynodes is n = 10. Therefore the gain
per dynode is calculated to be δe ∼ 2.35. The secondary emission eﬃciencies for several GeV
muons, ∆µ,Al and δµ,i , are assumed to be 0.08. The normalied muon flux under the +250 kA= 1.09×105 /cm2 /1012 POT. At the proton beam power of 460 kW,
horn operation is ϕnormalizedµ
the number of protons is N = 3.0 × 1013 POT/bunch. The muon flux can be calculated as· N . With assumptions above the expected EMT charge is calculated to be
ϕµ = ϕnormalizedµ730 pC/bunch at 460 kW beam power and +250 kA horn current. This power is corresponding
to a muon flux of 3.3 × 106 /cm2 per 80 ns beam bunch. The measured charge outputs per
beam bunch for EMTC3 and C4 when −500 V was applied are shown in Table B.2. The
measurement result is found to be in a good agreement with the expectation. The diﬀerencein the output charge between C3 and C4 is compatible with the expected diﬀerence between
individual PMTs.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

184

Table B.2: EMT output signal size per bunch at 460 kW beam intensity and +250 kA horncurrent (muon flux of 3.3 × 106 /cm2 per 80 ns beam bunch) with applied voltage of −500 V.
The expected charge is 730 pC/bunch.
Bunch# EMTC3 charge [pC]
1
873.1
2
870.7
3
866.9
4
855.9
5
860.4
6
850.6
7
847.8
8
854.1
Average859.9

EMTC4 charge [pC]
784.9
787.3
788.6
787.9
797.0
795.5
798.5
797.7
792.2

Time response

ADC count

ADC count

Figure B.10 shows EMTC3 and EMTC4 waveform examples. The signal has a tail component
due to both the detector intrinsic property and reflections from cables and electronics modules.
These tails could aﬀect the performance of bunch-by-bunch basis beam monitoring. The ratioof the integration of the tail region to the integration of the 1st bunch region is calculated toevaluate the tail component fraction. This is done for two tail regions as shown in Figure B.10;
Tail-1 as earlier and Tail-2 as later tail parts. The tail sizes of the Si center channel, the IC
center channel, EMTC3, and EMTC4 are shown in Figure B.11. Here the beam intensity is
450 kW and the horn current setting is +250 kA. The EMTs show smaller tail sizes (∼1%) thanthe Si and IC sensors (a few %). This indicates that EMTs perform better than the current
detectors in terms of signal response.
0
−100
−200

0
−100
−200

−500

−600

−600

−700

−700

−800
−900
0

−400

Tail-2−500−300

Tail-1−400

Tail-2

Tail-1

−300

EMTC3
50

100

150

200

250

300

350

400

FADC sample (~15 ns/sample)

−800

EMTC4

0

50

100

150

200

250

300

350

400

FADC sample (~15 ns/sample)

Figure B.10: Examples of the EMTC3 (left) and C4 (right) waveform. Two tail parts (Tail-1
and Tail-2) are shown together in shaded bands.

Intensity resolution
Figure B.12 shows signal sizes normalized with the proton beam power for beam spill, from theSi center channel, the IC center channel, EMTC3, and EMTC4. The proton beam power andthe horn current are 450 kW and +250 kA, respectively. The intensity resolutions of C3 andAPPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

185

4000

IC (Ar)Tail-1

3500

6000

Tail-2

IC (Ar)

2500

4000

EMTC3
3000

1500

EMTC4

2000

EMTC4

Si

EMTC3

5000

3000

2000

Si

1000
1000

500
0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0
0

0.01

0.02

0.03

0.04

Ratio (Tail-1/1st-bunch)

0.05

0.06

0.07

0.08

Ratio (Tail-2/1st-bunch)

Figure B.11: Relative sizes of Tail-1 (left) and Tail-2 (right) to the 1st bunch signals. The proton
beam power and the horn current setting are 450 kW and +250 kA respectively, corresponding
to a muon flux of 3.2 × 106 /cm2 per 80 ns beam bunch.
C4 are 0.34% and 0.41% respectively. These of Si and IC are better than the EMTs (0.25%
and 0.24% respectively). Each detector resolution is summarized in Table B.3, including bothfor the 1st bunch only and for the spill. The statistical fluctuation eﬀect on each value isless than 0.01%. The eﬀect of noise due to the readout system such as cables and electronics
modules is evaluated by integrating the baseline before the beam spill to be less than 0.1%.
The EMTs show a bit worse resolution than the current detectors. However, a 1% uncertainty
on the intensity measurement for each of 49 ch sensors leads to an 0.06 mrad uncertainty inthe beam direction measurement, which is much smaller than the total precision of 0.28 mrad.
The current intensity measurement precision is limited by the readout system calibration (afew %), therefore the intensity resolution of the EMTs fulfills the requirements for the muon
monitor.
Table B.3: Intensity resolution of each detector for spill and the first bunch only. The proton
beam intensity is 450 kW and the horn current is +250 kA.
Detector
Spill (8 bunch sum)
EMTC3
0.34%
EMTC4
0.41%
Si center
0.25%
IC (Ar) center
0.24%First bunch
0.73%
0.78%
0.37%
0.33%

Linearity performance
Beam intensity scans were carried out to test the linearity response of the EMTs. In the scans,the beam power was tuned to be 13 kW, 50 kW, 150 kW, 260 kW, 340 kW, 400 kW, 460 kW,
and 500 kW, and the horn current was set to +250 kA. For the EMTs two diﬀerent voltages,−500 V and −450 V, were applied to study the space charge eﬀect. This occurs when thenumber of produced electrons is large, which causes the electric field distortion and accordingly
signal degradation. The scan conditions are summarized in Table B.4.
The signal yields are corrected for the horn current eﬀect (see Ref. ?? for details about therelationship between the muon flux and the horn current). In the intensity scans, the proton

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMONEMTC4.Q[0]/ct[4][0]htemp
Entries:
26956
Entries
26956
Mean:
29.67−11
Mean 2.967e
RMS 1.023e−13RMS:0.1023EMTC32500Counts

EMTC3.Q[0]/ct[4][0]Counts

186

3500

htemp
Entries:
26956
Entries
26956
Mean:
27.33−11
Mean 2.733e
RMS 1.114e−13
RMS:
0.1114

EMTC4

3000

2000

2500

1500

2000
1500

1000

1000
500

500

RMS/MEAN ~ 0.34 %
0

29.3

29.4

29.5

29.6

29.7

29.8

29.9
30
EMTC3.Q[0]/ct[4][0]

×10

−12

0

RMS/MEAN ~ 0.41 %
26.9

27

27.1

27.2

EMTC3/CT5 [pC/(1012 protons/spill)]

Si Center

CountsCounts

27.5

27.6
27.7
EMTC4.Q[0]/ct[4][0]

×10

−12

muic.Q[3][3][0]/ct[4][0]Entries:h 26956
Entries
26956
Mean:
Mean 797.4
797.4
RMS
1.961
RMS: 1.961

3000

Entries:htemp
26956
Entries
26956
Mean:
Mean0.02339
2.339e−11
RMS 5.537e−14
RMS: 0.0005537

IC (Ar) Center
3000
2500

2500

2000

2000
1500

1500

1000

1000

500

500

RMS/MEAN ~ 0.24 %RMS/MEAN ~ 0.25 %
0
788

27.4

EMTC4/CT5 [pC/(1012 protons/spill)]musi.Q[3][3][0]*1e12/ct[4][0]
3500

27.3

790

792

794

796

798

800

802

804

806

Si Center/CT5 [pC/(1012 protons/spill)]

0
23.15

23.2

23.25

23.3

23.35

23.4

23.45

×10
23.5
23.55 23.6
muic.Q[3][3][0]/ct[4][0]−12

IC (Ar) Center/CT5 [pC/(1012 protons/spill)]

Figure B.12: The normalized signal sizes of EMTC3 (left top), EMTC4 (right top), Si (leftbottom), and IC with Ar gas (right bottom) under the 450 kW beam power and the +250 kAhorn current.
beam position was kept within ±0.5 cm, monitored by SSEM19 and SSEM18. The eﬀect of
this fluctuation on the muon flux is less than 1%. The proton beam width changes as thebeam power changes, from 2 mm (1.5 mm) at the lowest power to 4.8 mm (4 mm) at thehighest power in the horizontal (vertical) direction. The eﬀect of this change on the muon
flux is corrected using MC simulation. For various conditions on the beam width, the muon
flux at the EMT position is simulated. The simulation result is shown in Figure B.13. The
measured yield is corrected by the ratio of the yield at the measured beam width to that at
the nominal condition of 4 mm in both horizontal and vertical directions. During the scans thebeam width was taken from SSEM18, since SSEM19 had some unreliable points at very low
beam intensities. The beam width was too narrow for the monitor sensitivity and beam profile
reconstruction was therefore not reliable at those points. The consistency between SSEM19
Table B.4: Proton beam powers and applied voltages to the EMTs in the beam intensity scans.
The number of protons per kW at a repetition cycle of 2.48 sec is 5.3 × 1011 protons/spill/kW.
Scan
I
II
III
IV

Beam power [kW]Applied HV [V]150, 260, 340, 400, 460−500
260, 340, 400, 460−450
13, 50−500, −450
500
−500

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

187

and SSEM18 was confirmed by other reliable points. In order to validate the width correction,
two diﬀerent beam widths, 2.6 mm (2.2 mm) and 4.2 mm (3.2 mm) for the horizontal (vertical)
direction, were tried at 150 kW (∼ 80 × 1012 protons/spill) in Scan I.
1.02
6
0.6

1

Flux ratio

Proton beam width (Y) [mm]corr_factor

0.98

4
0.4

0.96
2
0.2

0.94
0.2
2

0.4
0.6
4
6
Proton beam width (X) [mm]Figure B.13: Ratio of the muon flux at the EMT position for various proton beam widths tothat at beam width = (4, 4) mm obtained by the simulation.

0.87

Scan I

0.86

Scan II

0.85

Scan III

0.84

Scan IV

Si Center/CT5 [nC/(1012 protons/spill)]

0.88

0.83
0.82
0.81
0.8
0.79
0.78
0

w/o proton beam width correction
50

100

150

200

250

300

CT5 [1012 protons/spill]

0.88
0.87

Scan I

0.86

Scan II

0.85

Scan III

0.84

Scan IV

0.83
0.82

2%

Si Center/CT5 [nC/(1012 protons/spill)]

Figure B.14 shows the results from the Si center channel. The left panel shows the result
before the beam width correction and the right panel shows that after the correction. The horncurrent eﬀect is corrected in both results. At low intensities the plots are more scattered due
to a poor signal-to-noise ratio. This figure shows the beam width correction works properly. It
is more visible looking at the points at 150 kW in Scan I. The signal linearity is kept within±1% above 100 kW up to 4500 kW.

0.81
0.8
0.79
0.78
0

w/ proton beam width correction
50

100

150

200

250

300

CT5 [1012 protons/spill]

Figure B.14: Beam intensity scan results for the Si center channel before (left) and after (right)
the beam width eﬀect correction. Diﬀerent colors represent diﬀerent scans, each of which issummarized in Table B.4.

The scan results for EMTC3 and EMTC4 are shown in in Figures B.15 and B.16, respectively. The results are after the horn current and beam width corrections. In the figures, bothcases with −500 V and −450 V applied as high-voltage are shown. EMTC4 shows better linearity performance than EMTC3, because the capacitance used in the divider circuit for C4
was improved. Results with lowe voltage show better linearity, which indicates that the spacecharge eﬀect is more visible under the −500 V application. EMTC4 with −450 V applied showsAPPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

188

EMTC3

–500 V

34

32

28

26

17

EMTC3

–450 V

16

15

3.5%

30

EMTC3/CT5 [pC/1012 protons/spill]

36

6.5%

EMTC3/CT5 [pC/(1012 protons/spill)]as good linearity as Si up to 460 kW (muon flux of 3.3 × 106 /cm2 per 80 ns beam spill). To
further improve linearity response, the diﬀerent divider ratio can be changed.

14

13

12

0

50

100

150

200

0

250

50

100

150

CT5 [1012 protons/spill]

200

250

CT5 [1012 protons/spill]

30

26

24

EMTC4
0

50

100

150

200

250

CT5 [1012 protons/spill]–450 V

15

14

2%

28

EMTC4/CT5 [pC/(1012 protons/spill)]–500 V32

3.5%

EMTC4/CT5 [pC/(1012 protons/spill)]

Figure B.15: Beam intensity scan results for EMTC3 with −500 V (left) and −450 V (right)
applied.

13

12

EMTC4

11
0

50

100

150

200

250

CT5 [1012 protons/spill]

Figure B.16: Beam intensity scan results for EMTC4 with −500 V (left) and −450 V (right)
applied.

Yield stability
Signal stability <3% is required for the muon monitor. The prototype EMTs were exposedto the muon beam over the five data taking periods, as summarized in Table B.5. EMTC3
was installed before Period I. Since several tests including high-voltage and attenuation leveltunings were performed, therefore the stability before Period I is not shown here. EMT4 wasinstalled before Period II. There is about half a year beam oﬀ period between Periods II and
III, during which the EMT high-voltages were turned oﬀ. In the middle of Period V, a shortturn oﬀ of the high-voltage was conducted for one day.
Figures B.17, B.18, B.19 and B.20 show the yields as a function of time for the Si centerchannel, the IC center channel, EMTC3, and EMTC4. The horn current correction is applied.
The yield jumps are observed twice in EMTC3, the cause of which is still unknown, but theseappear as synchronized with unrelated IC calibration work. Both EMTC3 and C4 show drifts intheir yields in the initial high-voltage applications in Periods I and III for EMTC3 and Periods
II and III for EMTC4, respectively. This drift is considered due to the stabilization of thedynode materials such as alkali metals and antimony (Sb). PMTs usually require “warmingup” by irradiation with light for the initial stabilization; however, this is not possible for EMTsAPPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

189

Table B.5: Beam conditions and high-voltages for EMTC3 and EMTC4 during each beam
exposure period.
PeriodI (23, Feb., 2017 ∼ 30, Mar., 2017)
II (31, Mar., 2017 ∼ 12, Apr., 2017)
III (16, Oct., 2017 ∼ 22, Oct., 2017)
IV (22, Oct., 2017 ∼ 2, Nov., 2017)
V (2, Nov., 2017 ∼ 22, Dec., 2017)

Horn current [kA]
+250
+250
+250
−250
−250

HV [V]
−500
−500
−505
−505
−450

POT [×1018 ]
224.1
76.8
20.5
59.4
305.8

since they do not have a photocathode. The recommended warm-up output charge is several µA
for several minutes, which is equivalent to several mC. Table B.6 shows the integrated charge
before the EMT signal gets stable. The yields seem reasonable compared to the expected charge
for the PMT warming-up. For later irradiations both C3 and C4 stabilized after fewer incident
protons. This is thought to be due to stabilization of the dynode materials to some level by theformer irradiation. After the initial drift period, the yield is stable within ±1% excluding someperiods where the yield fluctuated due to changes in the EMT high-voltage and the proton
beam conditions. EMTs usually satisfies the requirement of <3% signal fluctuation.
Table B.6: Total charge integration prior to EMT signal yield stabilization. The calculations
for Period III assume the charge per PMT is larger by 10% since a bit higher-voltage (−505 V)
was used.
EMT number Period
C3
I
III
C4
II
III

POT amount [×1018 ]
∼70
∼13
∼50
∼13

Integrated charge [mC]
∼2.0
∼0.4
∼1.3
∼0.4

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

179.1

224.1

880

0
220
200
180
160

860

140

840

120
820

100
80

800

60

780

40
760

Si (Period I)

20
0

0

02, Mar.
09:00

09, Mar.
09:00

16, Mar.
09:00

23, Mar.
09:00

Si Yield (with HPS correction)

0.7

3.4

4.9

10.8

900

35

860

30

840

25

820

20

800

15

780

10
5

Si (Period III)

017, Oct.
09:00

18, Oct.
09:00

19, Oct.
09:00

20, Oct.
09:00

021, Oct.
09:00

43.2

60
840

50
820

40
800

30

780

20

760

10

Si (Period II)

006, Apr.
09:00

Si Yield (with HPS correction)
15.1

560

50
40
30

500

20
480

10

Si (Period IV)

0

213.2

261.0

02, Nov.
09:00

Time

305.8

250
540

200

520

150

500

100

50

Si (Period V)
023, Nov.
09:00

30, Nov.
09:00

70

520

Si Yield (with HPS correction)

16, Nov.
09:00

80

60

×1018 POT

09, Nov.
09:00

59.4

540

560

480

Time

proton beam setting

Time

169.4

09, Apr.
21:00

×1018 POT26, Oct.
09:00

125.7

90

70

860

22, Oct.
09:00

93.4

76.8

80

0
40

60.0

880

02, Apr.
21:00

20.5

×1018 POT

36.9

×1018 POT

30, Mar.
09:00

13.4

Si Yield (with HPS correction)

13.6

900

Time

880

760

Si Center/CT5 [pC/(1012 Si/CT5
protons/spill)]12[pC/10 ppp]

128.7

Si Center/CT5 [pC/(1012 Si/CT5
protons/spill)]12[pC/10 ppp]

91.1

×1018 POT23, Feb.
09:00

Si Center/CT5 [pC/(1012 Si/CT5
protons/spill)]12[pC/10 ppp]

Si Yield (with HPS correction)

49.0

Si Center/CT5 [pC/(1012 Si/CT5
protons/spill)]12[pC/10 ppp]

Si Center/CT5 [pC/(1012 Si/CT5
protons/spill)]12[pC/10 ppp]

0
900

190

07, Dec.
09:00

14, Dec.
09:00

21, Dec.
09:00

Time

Figure B.17: Signal yield of the Si center channel as a function of time.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

128.7

179.1

224.1

0

25.5

220
200

25

180

24.5

160
140

24

120
23.5

100

23

80

22.5

60
40

22

IC (Period I)

21.5

20
0

23, Feb.
09:00

02, Mar.
09:00

09, Mar.
09:00

16, Mar.
09:00

23, Mar.
09:00

IC Yield (with HPS correction)

0.7

3.4

4.9

10.8

30, Mar.
09:00

20.5

×1018 POT

26.5
26

30

25
24.5

20

24
23.5
23

10

Calibration work

IC (Period III)

22.5

0

17, Oct.
09:00

18, Oct.
09:00

19, Oct.
09:00

20, Oct.
09:00

IC Center/CT5 [pC/(1012 IC/CT5
protons/spill)]12[pC/10 ppp]

021, Oct.
09:00

43.2

22, Oct.
09:00

169.4

76.8

25.5

70

25

60

24

50

23.5

40

23

30

22.5

20

22

10

IC (Period II)

21.5

0

02, Apr.
21:00

06, Apr.
09:00

IC Yield (with HPS correction)
15.1

09, Apr.
21:00

Time

59.4

17.5

×1018 POT

IC (Period IV)
proton beam setting

60

16.5

50
16

40
15.5

30

Calibration work
20

15

10
14.5

0

26, Oct.
09:00

213.2

261.0

02, Nov.
09:00

Time

305.8

×1018 POT

IC (Period V)

300

17

250
16.5

200
16

150
15.5

100
15

50
14.5

0

16, Nov.
09:00

23, Nov.
09:00

30, Nov.
09:00

80
70

17

17.5

09, Nov.
09:00

80

24.5

IC Yield (with HPS correction)
125.7

60.0

×1018 POT

Time

93.4

36.9

0
50

40

25.5

IC Yield (with HPS correction)

13.6

26

Time

13.4

27

IC Center/CT5 [pC/(1012 IC/CT5
protons/spill)]12[pC/10 ppp]

91.1

×1018 POT0

IC Center/CT5 [pC/(1012IC/CT5
protons/spill)]12[pC/10 ppp]

IC Yield (with HPS correction)

49.0

IC Center/CT5 [pC/(1012 IC/CT5
protons/spill)]12[pC/10 ppp]

IC Center/CT5 [pC/(1012 IC/CT5
protons/spill)]12[pC/10 ppp]

0
26

191

07, Dec.
09:00

14, Dec.
09:00

21, Dec.
09:00

Time

Figure B.18: Signal yield of the IC (Ar) center channel as a function of time. The yield jumps
seen in Period III and IV, marked with magenta circles, are due to calibration work where theentire IC system is moved (see Ref. [74] for the calibration method).

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

49.0

EMTC3 Yield (with HPS correction)
91.1

128.7

179.1

224.1

×1018 POT

0180

12 protons/spill)]
EMTC3/CT5 [pC/(1012
EMTC3/CT5 [pC/10 ppp]

12 protons/spill)]
EMTC3/CT5 [pC/(1012
EMTC3/CT5 [pC/10 ppp]

0
33

160
32

140
120

31

100
30

80
60

29

40
28

20

EMTC3 (Period I)

13.6

192

EMTC3 Yield (with HPS correction)
36.9

33

60.0

76.8

×1018 POT

60
32

50
31

40
30

30
29

20

28

10

EMTC3 (Period II)00.709, Mar.
09:00

16, Mar.
09:00

23, Mar.
09:00

EMTC3 Yield (with HPS correction)
3.4

4.9

10.8

13.4

Time

20.5

×1018 POT
36

002, Apr.
21:00

30, Mar.
09:00

37

30

35

25
34

20
33

15
32

31

10
5

EMTC3 (Period III)06, Apr.
09:00

09, Apr.
21:00

EMTC3 Yield (with HPS correction)

0
40
35

Unknown jump

15.1

Time

59.4

24

×1018 POT
23.5

60

proton beam setting

Unknown jump

23

50

22.5

40

22

30

21.5
21

20

20.5
20

10

EMTC3 (Period IV)

017, Oct.
09:00

18, Oct.
09:00

19, Oct.
09:00

20, Oct.
09:00

0
12 protons/spill)]
EMTC3/CT5 [pC/(1012
EMTC3/CT5 [pC/10 ppp]

12 protons/spill)]
EMTC3/CT5 [pC/(1012
EMTC3/CT5 [pC/10 ppp]

002, Mar.
09:00

12 protons/spill)]
EMTC3/CT5 [pC/(1012
EMTC3/CT5 [pC/10 ppp]

23, Feb.
09:00

21, Oct.
09:00

43.2

0

22, Oct.
09:00

26, Oct.
09:00

Time

EMTC3 Yield (with HPS correction)
93.4

125.7

169.4

213.2

261.0

02, Nov.
09:00

Time

305.8

10.2

×1018 POT
10

220
200

9.8

180
160

9.6

140

9.4

120
9.2

100
80

9

60

8.8
8.6

HV turned off

40

EMTC3 (Period V)

20
0

8.4

09, Nov.
09:00

16, Nov.
09:00

70

23, Nov.
09:00

30, Nov.
09:00

07, Dec.
09:00

14, Dec.
09:00

21, Dec.
09:00

Time

Figure B.19: Signal yield of EMTC3 as a function of time. Two yield jumps are seen and seemto be synchronized with IC calibration work, although the cause is not fully understood. Aftera short HV-oﬀ period during Period V, the yield changed.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMONEMTC4 Yield (with HPS correction)
36.9

76.8

0

×1018 POT

30

60
29

50

40

28

30
27

20
26

25

10

EMTC4 (Period II)

006, Apr.
09:00

09, Apr.
21:00

EMTC4 Yield (with HPS correction)
15.1

3.4

4.9

10.8

13.4

20.5

33

30

32

25
31

20
30

15
10

29

5

EMTC4 (Period III)

28

0

59.4

0
60

50

proton beam setting

40
20.5

30

20

19.5

20

19

10

EMTC4 (Period IV)

43.2

18, Oct.
09:00

19, Oct.
09:00

20, Oct.
09:00

EMTC4 Yield (with HPS correction)
93.4

125.7

169.4

213.2

21, Oct.
09:00

261.0

22, Oct.
09:00

Time

305.8

×1018 POT

9.4

02, Nov.
09:00

Time

220
200

9.2

180
9

160
8.8

140

8.6

120
100

8.4

80
8.2

60

HV turned off

8
7.8

40

EMTC4 (Period V)20

026, Oct.
09:00

40
35

17, Oct.
09:00

21

18.5

EMTC4 Yield (with HPS correction)

×1018 POT

Time

×1018 POT

22
21.5

0.7

0

02, Apr.
21:00

12 protons/spill)]
EMTC4/CT5 [pC/(1012
EMTC4/CT5 [pC/10 ppp]

60.0

12 protons/spill)]
EMTC4/CT5 [pC/(1012
EMTC4/CT5 [pC/10 ppp]

13.6

12 protons/spill)]
EMTC4/CT5 [pC/(1012
EMTC4/CT5 [pC/10 ppp]

12 protons/spill)]
EMTC4/CT5 [pC/(1012
EMTC4/CT5 [pC/10 ppp]

0

193

0

09, Nov.
09:00

16, Nov.
09:00

23, Nov.
09:00

30, Nov.
09:00

07, Dec.
09:00

14, Dec.
09:00

21, Dec.
09:00

Time

Figure B.20: Signal yield of EMTC4 as a function of time. Other than the short periods justafter the HV is turned on, C4 shows stable performance.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

B.4

Further Tests and Prospects

B.4.1

New Divider Circuits

194

Since better linearity was observed with the lower voltage (−450 V) than the higher voltage(−500 V) in the first prototypes. Since this is considered due to the space charge eﬀect byelectron cloud, can be avoided if one uses another type of the divider circuit which provides
diﬀerent voltage fractions among dynodes and then possibly better linearity. Instead the gain
will be lowered and signal size becomes small.
This was in fact purchased from Hamamatsu and the new prototypes were made and installed in the muon monitor place together with C3 and C4. However, since the operation mode
after the installation was RHC and then muon flux is approximately 66% of that in FHC, thelinearity check up to the high intensity could not checked. This work is now left for the future.

B.4.2

Test of PMTs

The second prototype detectors contained PMTs with new divider circuits as mentioned above.
The pictures of the PMT and the divider circuit are shown in Figure B.21. Installed PMTs are
two: one with warming-up and the other without warming-up.

Divider Circuit

PMT

Figure B.21: Pictures of the PMT and the divider circuit.

The example waveforms for one of the PMTs (the one with warming-up) are shown in
Figure B.22. Two pictures correspond to diﬀerent conditions (beam power and applied high-APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

195

ADC

ADC

voltage): (470 kW,−250 kA) and (40 kW,−500 V). The horn current is the same for two as−250 kA. Although two cases should see similar sizes of output signal calculated from the beam
power and the gain, the waveform from the (470 kW,−250 kA) case observes saturated signal
but the other case does not. This is considered due to the cathode linearity condition. Whenthe in-coming yield is large and the resistivity is high, the voltage induced by the input is large,
which leads to worse yield eﬃciency. In case of EMTs, since the alminum whose resistivity is
suﬃciently low, such saturation was not observed. This saturation was observed in the other
PMT (without warming-up) and then not related to the warming-up. Figure B.23 shows theyield stability of the PMTs. Diﬀerent signal sizes are because of many diﬀerent high-voltage
trials. Regardless of the high-voltage values, the yields are continuously decreased in both.
This is considered due to the damage of the photo-cathode. In conclusion, PMTs are found
not suitable for the muon monitor detector.

− 30

− 50

− 40
− 100

− 50
− 150

− 60
− 200

− 70

− 80
0

− 250

470 kW, –350 V
50

100

150

200

250

300

350

0

400

40 kW, –500 V
50

100

150

200

250

300

350

400

Sample (~15 ns/sample)

Sample (~15 ns/sample)

Figure B.22: Example waveforms of one of the installed PMTs. The condition in the left panel
is 470 kW power, −250 kA horn current and −350 V applied, and that in the right panel is
40 kW, −250 kA, and −500 V.

EMTP8 Yield (with HPS correction)
12

4000

EMTP8/CT5 [pC/10 ppp]

12

EMTP7/CT5 [pC/10 ppp]

EMTP7 Yield (with HPS correction)
60
55

3500
50

3000
45

Different HV trials

2500

40

2000

35

60

4000
55

3500

50

3000

45
40

2500

Different HV trials

35

2000

30

1500

30

1500
25

25

1000

20

500

15

15

0

10

08, Mar.
09:00

22, Mar.
09:00

05, Apr.
09:00

19, Apr.
09:00

03, May.
09:00

17, May.
09:00

31, May.
09:00

1000

20

08, Mar.
09:00

500
0

22, Mar.
09:00

05, Apr.
09:00

19, Apr.
09:00

03, May.
09:00

17, May.
09:00

31, May.
09:00

Figure B.23: Yield stability of the PMT with (left) and without (right) warming-up.

APPENDIX B. ELECTRON-MULTIPLIER TUBES FOR MUMON

B.4.3

196

EMTs without Alkali/Sb

Usually alkali metals and Sb are put on the surface of dynodes to obtain high gain, but thesematerials are potentially sensitive to the radiation damage. Therefore EMTs without alkali/Sb
on the dynode surface are prepared and tested. Unfortunately the signal was not observed
because of the low gain (∼O(10)). This may be useful under the future intensity. In addition,
it needs to be done to change the current equipment that allows the voltage application only
up to 500 V, while the maximum voltage that can be applied to EMTs is 1000 V. This would
help the situation further.

B.4.4

Prospects

From the studies with the prototype detectors, EMTs are found to be a promising candidate
for the future MUMON. Before the actual installation, further tests of linearity and stability
performances need to be done. An electron beam test at Tohoku University’s Research Center
for Electron Photon Science was carried out to test EMTs towards the future installation. It
will be determined whether install EMTs as MUMON or not by seeing the results from thebeam test.

Appendix C
Supplements for the NCQE-like
Analysis
C.1

Low Energy Background Cut Criteria

The optimized cut functions for three parameters, dwall, eﬀwall, and ovaQ, are shown in Table C.1 for each T2K run. For the parameter param (: dwall, eﬀwall, and ovaQ), the linear
function param = pparam [0] + pparam [1] × Erec is used for the cut.
Table C.1: Summary on the cut function parameters for dwall, eﬀwall and ovaQ in each run.
Run# pdwall [0] pdwall [1] peﬀwall [0] peﬀwall [1] povaQ [0] povaQ [1]
1
523.5
−70.0
2087.7−332.0 0.3831 −0.042
2
477.7
−60.0
1934.0−300.0 0.4095 −0.048
3b
389.6
−40.0
2154.5−352.0 0.3641 −0.038
3c
386.3
−40.0
2154.5−352.0 0.3811 −0.042
4
539.2
−80.0
2035.7−332.0 0.3506 −0.036
5a
539.2
−80.0
2131.0−350.0 0.3866 −0.044
5b
539.2
−80.0
2131.0−350.0 0.3866 −0.044
5c
539.2
−80.0
1939.0−296.0 0.3906 −0.044
6a
539.2
−80.0
2100.6−344.0 0.3277 −0.032
6b624.0−100.02579.5−452.0 0.3726 −0.036
6c
624.0−100.02579.5−452.0 0.3726 −0.036
6d
624.0−100.02579.5−452.0 0.3726 −0.036
6e
624.0−100.02579.5−452.0 0.3726 −0.036
6f
539.2
−80.0
2134.5−352.0 0.3277 −0.032
7a
539.2
−80.0
1972.3−322.0 0.3401 −0.038
7b
539.2
−80.0
1840.2−290.0 0.3457 −0.032
7c
539.2
−80.0
1972.3−322.0 0.3401 −0.038
8
539.2
−80.0
1668.8−266.0 0.3771 −0.042
9a
539.2
−80.0
1793.1−288.0 0.3895 −0.048
9b
539.2
−80.0
1837.6−294.0 0.3911 −0.042
9c
539.2
−80.0
1837.6−294.0 0.3911 −0.042
9d
539.2
−80.0
1837.6−294.0 0.3911 −0.042

197

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

C.2

198

Study of Post-activity Cut

As described in Chapter 6, only the pre-activity cut is applied for the decay-e events. The
results on the post-activity is shown in Figures C.1 and C.2 for the FHC and RHC samples,
respectively. With the post-activity cut removing events with Ndecay-e > 0, the CC events
are reduced by nealy 10% and the NC1π and NC-other events are reduced by 5%, while theeﬃciency loss for the NCQE events is small.

C.3

Distributions at Each Selection Stage

Distributions from the FHC and RHC samples after each selection cut are shown in the following
pages.

Events (area normalized)

Events (area normalized)

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

ν-NCQE
ν-NCQE
NC1π
NC-other

1

10−1

10−2

10−3

0

199

CCQE
CC 2p2hCC-other

1

10−1

0.5

1

1.5

2

2.5

0

3

0.5

1

1.5

2

2.5

3

Ndecay-e

Ndecay-e

Events (area normalized)

Events (area normalized)

Figure C.1: Distributions of the number of decay-e after the candidate event for FHC events:
NC (left) and CC(right).

ν-NCQE
ν-NCQE
NC1π
NC-other

1

10−1

CCQE
CC 2p2hCC-other

1

10−2
10−1
10−3
0

0.5

1

1.5

2

2.5

3

Ndecay-e

0

0.5

1

1.5

2

2.5

3

Ndecay-eFigure C.2: Distributions of the number of decay-e after the candidate event for RHC events:
NC (left) and CC(right).

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

Data (T2K Run1-9 FHC)

700

ν -NCQEν -NCQE

600

NC-otherCC

500

Beam-unrelated (from off-timing data)

200

Data (T2K Run1-9 FHC)

120

ν -NCQEν -NCQE
NC-other100

CC
Beam-unrelated (from off-timing data)

80

400
60
300
40
200
20

100
0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

300
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

250

NC-other
CC

200

80

90

θC [degree]

Erec [MeV]

Beam-unrelated (from off-timing data)

Data (T2K Run1-9 FHC)

140

ν -NCQEν -NCQE

120

NC-otherCC

100

Beam-unrelated (from off-timing data)

80

150

60
100
40
50

0
200

20

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

220
Data (T2K Run1-9 FHC)200

ν -NCQE

180

ν -NCQE
NC-other

160

100
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

80

NC-other
CC

CC

140

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60

120
100

40

80
60

20

40
20
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90

50

80
40

70
60

30

50
40

20
30
20

10

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.3: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the FV cut in
FHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

Data (T2K Run1-9 FHC)600

ν -NCQEν -NCQE
NC-other500

CC
Beam-unrelated (from off-timing data)

400

201

Data (T2K Run1-9 FHC)

100

ν -NCQEν -NCQE
NC-other80

CC
Beam-unrelated (from off-timing data)

60
300
40
200
20

100

0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

200
Data (T2K Run1-9 FHC)
ν -NCQE

180

ν -NCQE

160

NC-other
CC

140

80

90

θC [degree]

Erec [MeV]

Beam-unrelated (from off-timing data)

120
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

100

NC-otherCC

80

Beam-unrelated (from off-timing data)

120
100

60

80
40

60
40

20

20
0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

180
Data (T2K Run1-9 FHC)
ν -NCQE

160

ν -NCQE
NC-other

140

100
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

80

NC-other
CC

CC

120

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60
100
80
40
60
40

20

20
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90
80

35

70

30

60

25

50
20
40
15
30
10

20

5

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.4: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the dwall cut in
FHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

300
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

250

NC-otherCC

200

Beam-unrelated (from off-timing data)

60
Data (T2K Run1-9 FHC)
ν -NCQE

NC-other
CC

40

30

100

20

50

10

5

10

15

20

0
0

25

ν -NCQE

50

150

0

202

Beam-unrelated (from off-timing data)

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

Data (T2K Run1-9 FHC)

100

ν -NCQEν -NCQE
NC-other

80

80

90

θC [degree]

Erec [MeV]CC
Beam-unrelated (from off-timing data)

60
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

50

NC-otherCC

40

Beam-unrelated (from off-timing data)

60
30
40

20

20

0
200

10

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

Data (T2K Run1-9 FHC)

100

ν -NCQEν -NCQE
NC-other80

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]60
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

50

NC-other
CC

CC

40

Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60
30
40

20

20

0
−0.4

10

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90
14
80
12
70
10

60
50

8

40

6

30
4
20
2

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.5: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the eﬀwall cut in
FHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

50
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

40

NC-otherCC
Beam-unrelated (from off-timing data)

30

203

45
Data (T2K Run1-9 FHC)
ν -NCQE

40

ν -NCQE
NC-other

35

CC

30

Beam-unrelated (from off-timing data)

25
20

20
15
10

10

5
0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

50
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

40

80

90

θC [degree]

Erec [MeV]

NC-otherCC
Beam-unrelated (from off-timing data)

40
Data (T2K Run1-9 FHC)
ν -NCQE

35

ν -NCQE
NC-other30

CC
Beam-unrelated (from off-timing data)

25

30

20
20

15
10

10
5
0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

100
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

80

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]NC-otherCC

35
Data (T2K Run1-9 FHC)
ν -NCQE

30ν -NCQE
NC-otherCC

25

Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60

20
15

40

10
20
5
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90

3.5

80
3
70
2.5

60
50

2

40

1.5

30
1
20
0.5

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.6: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the ovaQ cut in
FHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

50
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

40

NC-otherCC
Beam-unrelated (from off-timing data)

30

204

45
Data (T2K Run1-9 FHC)
ν -NCQE

40

ν -NCQE
NC-other

35

CC

30

Beam-unrelated (from off-timing data)

25
20

20
15
10

10

5
0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

50
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

40

80

90

θC [degree]

Erec [MeV]

NC-otherCC
Beam-unrelated (from off-timing data)

40
Data (T2K Run1-9 FHC)
ν -NCQE

35

ν -NCQE
NC-other30

CC
Beam-unrelated (from off-timing data)

25

30

20
20

15
10

10
5
0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

100
Data (T2K Run1-9 FHC)
ν -NCQEν -NCQE

80

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]NC-otherCC

35
Data (T2K Run1-9 FHC)
ν -NCQE

30ν -NCQE
NC-otherCC

25

Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60

20
15

40

10
20
5
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90

3.5

80
3
70
2.5

60
50

2

40

1.5

30
1
20
0.5

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.7: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the CC interaction
cut in FHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

Data (T2K Run1-9 RHC)

700

ν -NCQEν -NCQE

600

NC-otherCC

500

Beam-unrelated (from off-timing data)

205

Data (T2K Run1-9 RHC)

120

ν -NCQEν -NCQE
NC-other100

CC
Beam-unrelated (from off-timing data)

80

400
60
300
40
200
20

100
0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

300
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

250

NC-other
CC

200

80

90

θC [degree]

Erec [MeV]

Beam-unrelated (from off-timing data)

Data (T2K Run1-9 RHC)

140

ν -NCQEν -NCQE

120

NC-otherCC

100

Beam-unrelated (from off-timing data)

80

150

60
100
40
50

0
200

20

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

220
Data (T2K Run1-9 RHC)

200

ν -NCQE

180

ν -NCQE
NC-other

160

100
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

80

NC-other
CC

CC

140

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60

120
100

40

80
60

20

40
20
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90

40

80

35

70
30
60
25
50
20
40
15

30

10

20

5

10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.8: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the FV cut in
RHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

Data (T2K Run1-9 RHC)

600

ν -NCQEν -NCQE
NC-other500

CC
Beam-unrelated (from off-timing data)

400

206

Data (T2K Run1-9 RHC)

100

ν -NCQEν -NCQE
NC-other80

CC
Beam-unrelated (from off-timing data)

60
300
40
200
20

100

0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

200
Data (T2K Run1-9 RHC)
ν -NCQE

180

ν -NCQE

160

NC-other
CC

140

80

90

θC [degree]

Erec [MeV]

Beam-unrelated (from off-timing data)

120
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

100

NC-otherCC

80

Beam-unrelated (from off-timing data)

120
100

60

80
40

60
40

20

20
0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

180
Data (T2K Run1-9 RHC)
ν -NCQE

160

ν -NCQE
NC-other

140

100
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

80

NC-other
CC

CC

120

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60
100
80
40
60
40

20

20
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90

30

80
25

70
60

20

50
15
40
30

10

20
5
10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.9: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the dwall cut in
RHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

300
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

250

NC-otherCC

200

Beam-unrelated (from off-timing data)

60
Data (T2K Run1-9 RHC)
ν -NCQE

NC-other
CC

40

30

100

20

50

10

5

10

15

20

0
0

25

ν -NCQE

50

150

0

207

Beam-unrelated (from off-timing data)

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

Data (T2K Run1-9 RHC)

100

ν -NCQEν -NCQE
NC-other

80

80

90

θC [degree]

Erec [MeV]CC
Beam-unrelated (from off-timing data)

60
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

50

NC-otherCC

40

Beam-unrelated (from off-timing data)

60
30
40

20

20

0
200

10

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

Data (T2K Run1-9 RHC)

100

ν -NCQEν -NCQE
NC-other80

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]60
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

50

NC-other
CC

CC

40

Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

60
30
40

20

20

0
−0.4

10

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90
80
10
70
8

60
50

6
40
30

4

20
2
10
0

5

10

15

20

25

0

Erec [MeV]

Figure C.10: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the eﬀwall cut
in RHC.

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

25
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

20

NC-otherCC
Beam-unrelated (from off-timing data)

15

22

208

Data (T2K Run1-9 RHC)
ν -NCQE

20ν -NCQE

18

NC-otherCC

16

Beam-unrelated (from off-timing data)

14
12
10

10
8
6
5

4
2

0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

25
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

20

80

90

θC [degree]

Erec [MeV]

NC-otherCC
Beam-unrelated (from off-timing data)

15

20
Data (T2K Run1-9 RHC)
ν -NCQE

18

ν -NCQE

16

NC-otherCC

14

Beam-unrelated (from off-timing data)

12
10

10

8
6

5

4
2

0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

50
Data (T2K Run1-9 RHC)
ν -NCQEν -NCQE

40

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]NC-other

18
Data (T2K Run1-9 RHC)

16

ν -NCQEν -NCQE

14

NC-other
CC

CC

12

Beam-unrelated (from off-timing data)

30

Beam-unrelated (from off-timing data)

10
8

20
6
4

10

2
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90
1.6
80
1.4

70

1.2

60

1

50
40

0.8

30

0.6

20

0.4

10

0.2

0

5

10

15

20

25

0

Erec [MeV]

Figure C.11: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the ovaQ cut in
RHC.

22

Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

Data (T2K Run1-9 RHC)
ν -NCQE

20ν -NCQE

18

NC-otherCC

16

Beam-unrelated (from off-timing data)

14
12

20

209

Data (T2K Run1-9 RHC)
ν -NCQE

18

ν -NCQE

16

NC-otherCC

14

Beam-unrelated (from off-timing data)

12
10

10
8
8
6

6
4

4

2

2

0

5

10

15

20

0
0

25

10

20

30

40

50

60

70

Events/100-cm

Events/100-cm

22

Data (T2K Run1-9 RHC)
ν -NCQE

20ν -NCQE

18

NC-other
CC

16

80

90

θC [degree]

Erec [MeV]

Beam-unrelated (from off-timing data)

18
Data (T2K Run1-9 RHC)
ν -NCQE

16ν -NCQE
NC-other

14

CC

12

Beam-unrelated (from off-timing data)

14
10

12
10

8

8

6

6
4
4
2

2
0
200

400

600

800

1000

1200

1400

1600

0

1800

500

1000

1500

2000

2500

45
Data (T2K Run1-9 RHC)
ν -NCQE

40

ν -NCQE
NC-other

35

16
Data (T2K Run1-9 RHC)
ν -NCQE

14ν -NCQE
NC-other

12

CC

CC

30

3000

effwall [cm]
Events/0.05

Events/0.05

dwall [cm]Beam-unrelated (from off-timing data)

Beam-unrelated (from off-timing data)

10

25
8
20
6
15
4

10

2

5
0
−0.4

−0.2

0

0.2

0.4

0.6

0
−1

0.8

−0.8 −0.6 −0.4 −0.2

θC [degree]

0

0.2

0.4

0.6

0.8

1

cosθbeam

ovaQ
90
1.6
80
1.4

70

1.2

60

1

50
40

0.8

30

0.6

20

0.4

10

0.2

0

5

10

15

20

25

0

Erec [MeV]

Figure C.12: Distributions of Erec , θC , dwall, eﬀwall, ovaQ, and cos θbeam after the CC interaction cut in RHC.

Events/0.05-GeV (area normalized)

Events/0.05-GeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

25

T2K Run 1-9 FHC
ν-NCQE
ν-NCQE
NC-other
CC

20

15

10

5

0
0

1

2

3

4

5

6

7

8

9

0.3

CCQE

0.25

CC 2p2h

0.2
0.15
0.1
0.05
0
0

10

210

0.5

1

1.5

Eν [GeV]2

2.5

Eν [GeV]

Events/0.05-GeV (area normalized)

Events/0.05-GeV

Figure C.13: Distribution of true Eν for each neutrino interaction (left) and the one focusing
on CCQE and CC 2p2h (right) in FHC.

9

T2K Run 1-9 RHC
ν-NCQE
ν-NCQE
NC-other
CC

8
7
6
5
4
3
2
1
0
0

1

2

3

4

5

6

7

8

9

10

Eν [GeV]

0.45
0.4

CCQE

0.35

CC 2p2h

0.3
0.25
0.2
0.15
0.1
0.05
0
0

0.5

1

1.5

2

2.5

Eν [GeV]Figure C.14: Distribution of true Eν for each neutrino interaction (left) and the one focusing
on CCQE and CC 2p2h (right) in RHC.

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

C.4

211

Primary- and Secondary-γ Distributions

30
T2K Run1-9 FHC ν + ν NCQE
Primary-γ only

25

Secondary-γ only
Both primary- and secondary-γ

20

Events/MeV

Events/MeV

The neutrino and antineutrino NCQE events are broken down into the events with the primaryγ only, secondary-γ only, and both γ-rays. The resulting Erec and θC distributions for FHC and
RHC are shown in Figures C.15 and C.16. It is found from these that the secondary-γ events
contribute to the region with higher energy and Cherenkov opening angle.

T2K Run1-9 RHC ν + ν NCQE

12

Primary-γ only
Secondary-γ only

10

Both primary- and secondary-γ

8
15

6

10

4

5
0

2
5

10

15

20

0

25
Erec [MeV]

5

10

15

20

25
Erec [MeV]25

Events/2.7-degree

Events/2.7-degree

Figure C.15: The Erec distributions for the NCQE events broken down by the γ-ray type in
FHC (left) and RHC (right).

T2K Run1-9 FHC ν + ν NCQE
Primary-γ only
Secondary-γ only

20

Both primary- and secondary-γ

15

T2K Run1-9 RHC ν + ν NCQE
Primary-γ only

8

Secondary-γ only
Both primary- and secondary-γ

6
4

10

2

5
0
0

10

10

20

30

40

50

60

70 80 90
θC [degree]

0
0

10

20

30

40

50

60

70 80 90
θC [degree]

Figure C.16: The θC distributions for the NCQE events broken down by the γ-ray type in FHC(left) and RHC (right).

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

0.03
0.025

Properties of Nucleons in the NCQE Interaction

ν-n NCQE
ν-n NCQE

0.02
0.015
0.01

Events/5-MeV (area normalized)

Events/5-MeV (area normalized)

C.5

0.03

0.025

0.02

ν-p NCQE
ν-p NCQE

0.015

0.01

0.005

0.005
0
0

212

0
0

100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000

Ep [MeV]

En [MeV]

0.035
0.03
0.025

ν-n NCQE
ν-n NCQE

0.02
0.015
0.01

0.03
0.025

ν-p NCQE
ν-p NCQE

0.02
0.015
0.01
0.005

0.005
0
0

Events/5-MeV (area normalized)

Events/5-MeV (area normalized)

Figure C.17: Nucleon kinetic energy after NCQE in FHC: neutron (left) and proton (right).
Each of them is area normalized.

100 200 300 400 500 600 700 800 900 1000

En [MeV]00

100 200 300 400 500 600 700 800 900 1000

Ep [MeV]Figure C.18: Nucleon kinetic energy after NCQE in RHC: neutron (left) and proton (right).
Each of them is area normalized.

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

0.35
80
0.3

70

θC [degree]θC [degree]ν-n NCQE (FHC)9090

ν-n NCQE (FHC)
0.01

80
70

0.008

60

0.25

60

50

0.2

50

40

213

0.006

40

0.15

30

0.004

30
0.1

20

20

10
0
0

100 200 300 400 500 600 700 800 900 1000

0.05

10

0

0
0

0.002

100 200 300 400 500 600 700 800 900 1000

En [MeV]0

En [MeV]Figure C.19: The 2D distributions of neutron energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in FHC.

0.25

80
0.2

70
60

θC [degree]θC [degree]ν-p NCQE (FHC)9090

ν-p NCQE (FHC)
0.01

80
70

0.008

60
0.15

50
40

0.006

50
40

0.1
30
20

0.05

10
0
0

0.004
30
20

0.002

10
100 200 300 400 500 600 700 800 900 1000

Ep [MeV]000100 200 300 400 500 600 700 800 900 1000

0

Ep [MeV]Figure C.20: The 2D distributions of proton energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in FHC.

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

0.045

80

0.04

70

0.035

60

θC [degree]θC [degree]ν-n NCQE (RHC)
90

90

214

ν-n NCQE (RHC)
0.14

80
70

0.12

0.03

60

0.1

50

0.025

50

40

0.02

40

30

0.015

30

20

0.01

20

10

0.005

10

0

0
0

0.08
0.06
0.04

0
0

100 200 300 400 500 600 700 800 900 1000

0.02

100 200 300 400 500 600 700 800 900 1000

En [MeV]0

En [MeV]Figure C.21: The 2D distributions of neutron energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in RHC.

80

0.025

70
0.02

60

θC [degree]θC [degree]ν-p NCQE (RHC)9090

ν-p NCQE (RHC)
0.12

80
70

0.1

60
0.08

50

0.015

40

50
0.06

40
0.01

30
20

30

0.04

20
0.005

10
0
0

0.02

10
100 200 300 400 500 600 700 800 900 1000

Ep [MeV]000100 200 300 400 500 600 700 800 900 1000

0

Ep [MeV]Figure C.22: The 2D distributions of proton energy and Cherenkov angle for neutrino (left)
and antineutrino (right) NCQE interactions in RHC.

16
T2K Run 1-9 FHC

14

ν-p NCQE
ν-n NCQE

1210Events/2.7-degree

Events/MeV

APPENDIX C. SUPPLEMENTS FOR THE NCQE-LIKE ANALYSIS

8

18
16

T2K Run 1-9 FHC
ν-p NCQE

14

ν-n NCQE

12
10
8

6

6

4

4

2

2

0

215

5

10

15

20

0
0

25
30
Erec [MeV]

10

20

30

40

50

60

70 80 90
θC [degree]

6
T2K Run 1-9 RHC
ν-p NCQE

5

ν-n NCQE

4Events/2.7-degree

Events/MeV

Figure C.23: The Erec (left) and θC (right) distributions for neutrino-proton and neutrinoneutron NCQE interactions in FHC. The numbers of selected events for protons and neutrons
are 76.4 and 102.2, respectively.

5
T2K Run 1-9 RHC
ν-p NCQE

4

ν-n NCQE

3

3
2
2
1

1
0

5

10

15

20

25
30
Erec [MeV]

0
0

10

20

30

40

50

60

70 80 90
θC [degree]

Figure C.24: The Erec (left) and θC (right) distributions for antineutrino-proton andantineutrino-neutron NCQE interactions in RHC. The numbers of selected events for protons
and neutrons are 25.6 and 30.8, respectively.

Appendix D
Distributions for the Spallation Cut
Some histograms, PDFs, and likelihoods for the SRN spallation cut are shown in the following
pages. Figures D.17, D.18, and D.19 show the spallation likelihood of the 9 Li sample.

216

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

217

missfit or poorly-fit (7.49 < Erec < 9.49 MeV)

pre
post

25000

20000

15000

10000

5000

0
10−2

24000

10−1

1

10
|dt| [sec.]

missfit or poorly-fit (9.49 < Erec < 11.49 MeV)

pre
post

22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
10−2

10−1

1

10
|dt| [sec.]

missfit or poorly-fit (11.49 < Erec < 19.49 MeV)
12000

pre
post

10000
8000
6000
4000
2000
0
10−2

10−1

1

10
|dt| [sec.]

Figure D.1: The dt distributions of the missfit or poorly-fit muons for pre and post samples
and diﬀerent energy regions.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

50000

single (7.49 < Erec < 9.49 MeV)

218

single (7.49 < Erec < 9.49 MeV)
35000

pre
post

40000

pre
post

30000
25000

30000

20000
15000

20000

10000
10000
5000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

single (7.49 < Erec < 9.49 MeV)

Ltran [cm]single (7.49 < Erec < 9.49 MeV)

5

10

8000

pre
post

7000

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

6000

pre
post

104
103

5000

102

4000
10
3000
1

2000

10−1

1000
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (7.49 < Erec < 9.49 MeV)

pre
post

104
103
102
10
1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.2: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

50000

single (7.49 < Erec < 9.49 MeV)

single (7.49 < Erec < 9.49 MeV)

pre
post

40000

219

16000

pre
post

14000
12000
10000

30000

8000
20000

6000
4000

10000

2000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]single (7.49 < Erec < 9.49 MeV)

single (7.49 < Erec < 9.49 MeV)

pre
post

14000
12000

pre
post

5

10

104

10000

103

8000

102

6000

10

4000

1

2000

10−1

0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (7.49 < Erec < 9.49 MeV)
5

10

pre
post

104
103
102
10
1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.3: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0.05 < |dt| < 0.5 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

single (7.49 < Erec < 9.49 MeV)

50000

40000

single (7.49 < Erec < 9.49 MeV)

×10

3

pre
post

220

pre
post

900
800
700
600

30000

500
400

20000

300
200

10000

100
0
10−2

10−1

×10

3

1

0
0

10
|dt| [sec.]

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]single (7.49 < Erec < 9.49 MeV)

single (7.49 < Erec < 9.49 MeV)

800

pre
post

700

107

pre
post

106
5

600

10

500

104
103

400

102
300
10
200

1

100
0
−5000−4000 −3000−2000−1000

−1

10
0

1000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (7.49 < Erec < 9.49 MeV)
107

pre
post

106
5

10

104
103
102
10
1
−1

10

10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.4: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0.5 < |dt| < 30 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

stopping (7.49 < Erec < 9.49 MeV)

221

stopping (7.49 < Erec < 9.49 MeV)
1000

1400

pre
post

1200

pre
post

800

1000
600

800
600

400

400
200
200
0
10−2

10−1

1

10
|dt| [sec.]

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]stopping (7.49 < Erec < 9.49 MeV)

stopping (7.49 < Erec < 9.49 MeV)

180

pre
post

160
140

pre
post

103

102

120
100

10

80
1

60
40

10−1

20
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]stopping (7.49 < Erec < 9.49 MeV)

pre
post

103

102

10

1

10−1

10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.5: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the stopping muons for 7.49 < Erec < 9.49 MeV. For variables
except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

multiple (7.49 < Erec < 9.49 MeV)
18000

12000

pre
post

16000

222

multiple (7.49 < Erec < 9.49 MeV)

pre
post

10000

14000
8000
12000
10000

6000

8000
4000

6000
4000

2000

2000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

Ltran [cm]multiple (7.49 < Erec < 9.49 MeV)

multiple (7.49 < Erec < 9.49 MeV)

104

pre
post

2500

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

pre
post

103

2000

102

1500

10

1000

1
10−1

500

0
−5000−4000 −3000−2000−1000

0

10−2

1000 2000 3000 4000 5000

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]multiple (7.49 < Erec < 9.49 MeV)

22000

pre
post

103

×10
900 1000

30multiple (7.49 < Erec < 9.49 MeV)

pre
post

20000
18000

102

16000
14000
12000

10

10000
8000

1

6000
10−1

4000
2000

10

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

3

−2

0

Qµ [p.e.]

0
0

2

4

6

8

10
NtrackFigure D.6: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec < 9.49 MeV. For variables
except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

multiple (7.49 < Erec < 9.49 MeV)
18000

multiple (7.49 < Erec < 9.49 MeV)
5000

pre
post

16000

223

pre
post

4000

14000
12000

3000

10000
8000

2000
6000
4000

1000

2000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

Ltran [cm]multiple (7.49 < Erec < 9.49 MeV)
1800

multiple (7.49 < Erec < 9.49 MeV)
104

pre
post

1600

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

pre
post

103

1400
1200

102

1000
10

800
600

1

400

10−1

200
0
−5000−4000 −3000−2000−1000

0

10−2

1000 2000 3000 4000 5000

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]multiple (7.49 < Erec < 9.49 MeV)

104

×10
900 1000

30multiple (7.49 < Erec < 9.49 MeV)
35000

pre
post

103

pre
post

30000
25000

102

20000
10
15000
1
10000
−1

10

10−2

5000
×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]

0
0

2

4

6

8

10
NtrackFigure D.7: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec < 9.49 MeV. For variables
except for dt, the distributions are for 0.05 < |dt| < 0.5 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

multiple (7.49 < Erec < 9.49 MeV)

224

multiple (7.49 < Erec < 9.49 MeV)
70000

18000

pre
post

16000

pre
post

60000

14000

50000

12000
40000

10000

30000

8000
6000

20000

4000
10000

2000
0
10−2

10−1

1

0
0

10
|dt| [sec.]

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]multiple (7.49 < Erec < 9.49 MeV)

multiple (7.49 < Erec < 9.49 MeV)
6

10

50000

pre
post

40000

pre
post

5

10

104
103

30000

102
20000

10
1

10000
10−1
0
−5000−4000 −3000−2000−1000

0

10−2

1000 2000 3000 4000 5000

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]multiple (7.49 < Erec < 9.49 MeV)

×10

3

104

multiple (7.49 < Erec < 9.49 MeV)

1800

pre
post

5

10

×10
900 1000

3

0

pre
post

1600
1400

103

1200

2

1000

10

800

10

600
1
400
10−1
10

200
×10
200 400 600 800 10001200 1400 16001800 20002200 2400

3

−2

0

Qµ [p.e.]

0
0

2

4

6

8

10
NtrackFigure D.8: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec < 9.49 MeV. For variables
except for dt, the distributions are for 0.5 < |dt| < 30 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

clipping (7.49 < Erec < 9.49 MeV)

225

clipping (7.49 < Erec < 9.49 MeV)
80

700

pre
post

600

pre
post

70
60

500
50
400

40

300

30

200

20

100

10

0
10−2

80

10−1

1

10
|dt| [sec.]

00

Ltran [cm]clipping (7.49 < Erec < 9.49 MeV)

clipping (7.49 < Erec < 9.49 MeV)

pre
post

70

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

pre
post

103

60
102
50
10

40
30

1

20
10−1
10
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]clipping (7.49 < Erec < 9.49 MeV)

pre
post

103

102

10

1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.9: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the corner-clipping muons for 7.49 < Erec < 9.49 MeV. For variables
except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

single (9.49 < Erec < 11.49 MeV)

226

single (9.49 < Erec < 11.49 MeV)
30000

35000

pre
post

30000
25000

pre
post

25000

20000

20000
15000
15000
10000
10000
5000

5000
0
10−2

10−1

1

10
|dt| [sec.]

00

Ltran [cm]single (9.49 < Erec < 11.49 MeV)
6000

single (9.49 < Erec < 11.49 MeV)

pre
post

5000

pre
post

104
103

4000

102

3000

10

2000

1

1000

10−1

0
−5000−4000 −3000−2000−1000

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (9.49 < Erec < 11.49 MeV)
104

pre
post

103
102
10
1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.10: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 9.49 < Erec < 11.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

single (11.49 < Erec < 19.49 MeV)
18000

single (11.49 < Erec < 19.49 MeV)

pre
post

16000

227

14000

16000

pre
post

14000
12000

12000
10000
10000
8000
8000
6000

6000

4000

4000

2000

2000
0
10−2

10−1

1

10
|dt| [sec.]

00

Ltran [cm]single (11.49 < Erec < 19.49 MeV)

single (11.49 < Erec < 19.49 MeV)

pre
post

3000
2500

104

pre
post

103

2000

102

1500

10

1000

1

500

10−1

0
−5000−4000 −3000−2000−1000

0500 1000 1500 2000 2500 3000 3500 4000 4500 5000

1000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]single (11.49 < Erec < 19.49 MeV)
4

10

pre
post

3

10

102

10

1
10−1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.11: Distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak (middle
right), and Qµ (bottom) of the single through-going muons for 11.49 < Erec < 19.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

single (7.49 < Erec < 9.49 MeV)

0.1

spall
random

0.08

PDF

PDF

single (7.49 < Erec < 9.49 MeV)

228

spall
random

0.35
0.3
0.25

0.06
0.2
0.04

0.15
0.1

0.02
0.05
0
10−2

10−1

1

0
0

10
|dt| [sec.]

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]0.07

single (7.49 < Erec < 9.49 MeV)

spall
random

0.06

PDF

PDF

single (7.49 < Erec < 9.49 MeV)
1

spall
random

0.05
0.04

10−1

0.03
0.02
0.01
0
−5000−4000 −3000−2000−1000

01000 2000 3000 4000 5000

10−2

×10
900 1000

3

0

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]PDF

single (7.49 < Erec < 9.49 MeV)

spall
random
10−1

10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]Figure D.12: PDF distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak(middle right), and Qµ (bottom) of the single through-going muons for 7.49 < Erec < 9.49 MeV.
For variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

0.1

multiple (7.49 < Erec < 9.49 MeV)
PDF

PDF

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

spall
random

0.08

0.25

0.15

0.04

0.1

0.02

0.05

10−1

1

0
0

10
|dt| [sec.]

PDF

PDF

spall
random

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Ltran [cm]multiple (7.49 < Erec < 9.49 MeV)

spall
random0.05

multiple (7.49 < Erec < 9.49 MeV)

0.2

0.06

0
10−2

229

1

multiple (7.49 < Erec < 9.49 MeV)

spall
random

0.04

0.03

10−1

0.02

0.01

0
−5000−4000 −3000−2000−1000

0

10−2

1000 2000 3000 4000 5000

100

200

300

400

500

600

700

800

Qpeak [p.e.]

Llong [cm]multiple (7.49 < Erec < 9.49 MeV)
PDF

multiple (7.49 < Erec < 9.49 MeV)
PDF

×10
900 1000

3

0

spall
random0.8

spall
random

0.7
0.6
0.5

10−1
0.4
0.3
0.2
0.1
10−2

×10
200 400 600 800 10001200 1400 16001800 20002200 2400

30Qµ [p.e.]

0
0

2

4

6

8

10
NtrackFigure D.13: PDF distributions of dt (top left), Ltran (top right), Llong (middle left), Qpeak(middle right), Qµ (bottom), and Ntrack of the multiple muons for 7.49 < Erec < 9.49 MeV. For
variables except for dt, the distributions are for 0 < |dt| < 0.05 sec.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

single (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

230

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

multiple (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.14: Distributions of the spallation likelihood for each muon type in the 7.49−9.49 MeV
energy region. Dashed green lines represent the cut criteria. Events in the right side of thelines are removed.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (9.49 < Erec < 11.49 MeV)

106

pre
post

5

10

single (9.49 < Erec < 11.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

231

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (9.49 < Erec < 11.49 MeV)

106

pre
post

5

10

multiple (9.49 < Erec < 11.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.15: Distributions of the spallation likelihood for each muon type in the
9.49−11.49 MeV energy region. Dashed green lines represent the cut criteria. Events in theright side of the lines are removed.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (11.49 < Erec < 19.49 MeV)

106

pre
post

5

10

single (11.49 < Erec < 19.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

232

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (11.49 < Erec < 19.49 MeV)

106

pre
post

5

10

multiple (11.49 < Erec < 19.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.16: Distributions of the spallation likelihood for each muon type in the
11.49−19.49 MeV energy region. Dashed green lines represent the cut criteria. Events in
the right side of the lines are removed.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

single (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

233

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (7.49 < Erec < 9.49 MeV)

106

pre
post

5

10

multiple (7.49 < Erec < 9.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.17: Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 7.49−9.49 MeV region. Dashed green lines represent the cut criteria, the right side ofwhich is removed.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (9.49 < Erec < 11.49 MeV)

106

pre
post

5

10

single (9.49 < Erec < 11.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

234

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (9.49 < Erec < 11.49 MeV)

106

pre
post

5

10

multiple (9.49 < Erec < 11.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.18: Distributions of the spallation likelihood in the 9 Li sample for each muon typein the 9.49−11.49 MeV region. Dashed green lines represent the cut criteria, the right side ofwhich is removed.

APPENDIX D. DISTRIBUTIONS FOR THE SPALLATION CUT

106

missfit or poorly-fit (11.49 < Erec < 19.49 MeV)

106

pre
post

5

10

single (11.49 < Erec < 19.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

235

1
−20

−10

0

10

20

30

−30

−20

−10

0

10

20

Lspall106

stopping (11.49 < Erec < 19.49 MeV)

106

pre
post

5

10

multiple (11.49 < Erec < 19.49 MeV)

pre
post

5

10

104

104

103

103

102

102

10

10

1
−30

30
Lspall

1
−20

−10

0

10

20

30
Lspall

−30

−20

−10

0

10

20

30
LspallFigure D.19: Distributions of the spallation likelihood in the 9 Li sample for each muon type in
the 11.49−19.49 MeV region. Dashed green lines represent the cut criteria, the right side ofwhich is removed.

Appendix E
Future SRN Search Sensitivities
Figure E.1 gives results for SK-Gd with a 0.1% Gd doping. Here the same systematic errors
as the analysis in this thesis are assumed for the backgrounds except for the accidental background. Since the γ-ray energy is ∼8 MeV, SK-Gd is free of the accidental background. The
absolute amounts of the other backgrounds are scaled from the current analysis by live time.
As mentioned in Chapter 13, models by Horiuchi+18 and Horiuchi+09 can be tested and thereach after the 10-year operation is comparable or a bit worse compared to predictions by
Lunardini09, Ando+09, and Hartmann+97.
Figure E.2 gives results for Hyper-Kamiokande. The same systematic errors as the analysis
in this thesis are assumed; however, the twice better neutron tagging eﬃciencies with the samemis-tag probabilities are considered. Here the absolute background amount is obtained withscaling from the current analysis by live time and detector mass. Most models except for theminimum flux prediction by Nakazato+15 can be tested.
The case for Hyper-Kamiokande with a 0.1% Gd doping (called “HK-Gd” in this thesis)
is also considered. The amount of the NCQE-like background is considered to be 70% of
the nominal prediction by the MC multiplied with the scale factors from T2K. This is dueto that the current model may be inappropriate about the neutron multiplicity as shown in
Chapter 12 and it seems that the number of neutrons is smaller than the prediction. A 10%
systematic error is assumed for the NCQE-like background. For the non-NCQE background,a 10% systematic error is considered because the Michel spectrum fitting is expected to be
performed more precisely with higher statistics. The amount of the 9 Li background is assumed
to be scaled by the statistics from the current analysis, while the systematic error is assumed tobe 10%. There is no accidental background in HK-Gd. The results are shown in Figure E.3. All
the models can be tested by HK-Gd and advanced studies such as the spectrum measurement
are expected.
In order to see the benefits of the NCQE-like measurement, the sensitivities in SK-Gd with
diﬀerent NCQE-like conditions are evaluated as shown in Figure E.4. In this estimation, theamount of the 9 Li background is assumed to be 1/5 of the analysis in this thesis with scaling bylive time. This is because the better spallation cut is expected in SK-Gd. Three conditions for
the NCQE-like background are considered: the absolute amount scaled by live time with 100%and 60% uncertainties, and the absolute amount reduced by 30% (×0.7) from the simple scaling
with a 40% uncertainty. With an improved estimation of the NCQE-like background, models by
Horiuchi+18, Lunardini09, Ando+09, and Hartmann+97 can be tested in the 13.29−21.29 MeV
region, while the reach with a 100% error is not enough for these models.

236

SK-Gd (9.29 < Eν < 11.29 MeV)
Flux prediction [/cm2/sec./MeV]

22(Horiuchi+18) 0.72–0.73(Nakazato+15) 0.20–0.47(Horiuchi+09) 1.11
(Lunardini09) 0.51
(Ando+09) 0.56
(Malaney97) 0.26
(Hartmann+97) 0.47

20
18
16
14
12
10

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]APPENDIX E. FUTURE SRN SEARCH SENSITIVITIES

8

237

SK-Gd (11.29 < Eν < 13.29 MeV)
9

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.54–0.61(Nakazato+15) 0.13–0.30(Horiuchi+09) 0.81
(Lunardini09) 0.40
(Ando+09) 0.37
(Malaney97) 0.17
(Hartmann+97) 0.33

8
7
6
5
4
3

6
2

4

1

2
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

SK-Gd (13.29 < Eν < 21.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.6

0.5

0.4

0.3

10
Year

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]Year

SK-Gd (21.29 < Eν < 31.29 MeV)

0.16

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.14
0.12
0.1
0.08
0.06

0.2
0.04
0.1
0.02
1

2

3

4

5

6

7

8

9

10
Year

1

2

3

4

5

6

7

8

9

10
Year

Figure E.1: The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period with a
0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left), 11.29 < Eν <13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left), and 21.29 < Eν < 31.29 MeV(bottom right). The predictions from the models explained in Chapter 1 are also shown.

Hyper-Kamiokande (9.29 < Eν < 11.29 MeV)
Flux prediction [/cm2/sec./MeV]
10(Horiuchi+18) 0.72–0.73(Nakazato+15) 0.20–0.47(Horiuchi+09) 1.11
(Lunardini09) 0.51
(Ando+09) 0.56
(Malaney97) 0.26
(Hartmann+97) 0.4786

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]APPENDIX E. FUTURE SRN SEARCH SENSITIVITIES

4238

Hyper-Kamiokande (11.29 < Eν < 13.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.54–0.61(Nakazato+15) 0.13–0.30(Horiuchi+09) 0.81
(Lunardini09) 0.40
(Ando+09) 0.37
(Malaney97) 0.17
(Hartmann+97) 0.33

4
3.5
3
2.5
2
1.5
1

2
0.5
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

Hyper-Kamiokande (13.29 < Eν < 21.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.25

0.2

0.15

0.1

10
Year

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]Year

Hyper-Kamiokande (21.29 < Eν < 31.29 MeV)
0.035

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.03

0.025

0.02

0.015

0.05

0.01

1

2

3

4

5

6

7

8

9

10
Year

0.005

1

2

3

4

5

6

7

8

9

10
Year

Figure E.2: The 3σ sensitivity for the ν̄e flux as a function of Hyper-Kamiokande operation
period for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left), 11.29 < Eν <13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left), and 21.29 < Eν < 31.29 MeV(bottom right). The predictions from the models explained in Chapter 1 are also shown.

HK-Gd (9.29 < Eν < 11.29 MeV)
2.5

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.72–0.73(Nakazato+15) 0.20–0.47(Horiuchi+09) 1.11
(Lunardini09) 0.51
(Ando+09) 0.56
(Malaney97) 0.26
(Hartmann+97) 0.472

1.5

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]APPENDIX E. FUTURE SRN SEARCH SENSITIVITIES

1

239

HK-Gd (11.29 < Eν < 13.29 MeV)
0.9

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.54–0.61(Nakazato+15) 0.13–0.30(Horiuchi+09) 0.81
(Lunardini09) 0.40
(Ando+09) 0.37
(Malaney97) 0.17
(Hartmann+97) 0.33

0.8
0.7
0.6
0.5
0.4
0.3
0.2

0.5

0.1
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

HK-Gd (13.29 < Eν < 21.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.06

0.05

0.04

0.03

10
Year

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]Year

HK-Gd (21.29 < Eν < 31.29 MeV)

0.018

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.016

0.014

0.012

0.01

0.02

0.008

0.01

0.006
1

2

3

4

5

6

7

8

9

10
Year

1

2

3

4

5

6

7

8

9

10
Year

Figure E.3: The 3σ sensitivity for the ν̄e flux as a function of HK-Gd operation period with a
0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left), 11.29 < Eν <13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left), and 21.29 < Eν < 31.29 MeV(bottom right). The predictions from the models explained in Chapter 1 are also shown.

SK-Gd (9.29 < Eν < 11.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.72–0.73(Nakazato+15) 0.20–0.47(Horiuchi+09) 1.11
(Lunardini09) 0.51
(Ando+09) 0.56
(Malaney97) 0.26
(Hartmann+97) 0.47

16

14

12

10

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]APPENDIX E. FUTURE SRN SEARCH SENSITIVITIES240

SK-Gd (11.29 < Eν < 13.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.54–0.61(Nakazato+15) 0.13–0.30(Horiuchi+09) 0.81
(Lunardini09) 0.40
(Ando+09) 0.37
(Malaney97) 0.17
(Hartmann+97) 0.33

6

5

4

3
8

–– NCQE 100% error–– NCQE 100% error

6 –– NCQE 60% error

2 –– NCQE 60% error–– NCQE×0.7 40% error
1

2

3

4

–– NCQE×0.7 40% error
5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

SK-Gd (13.29 < Eν < 21.29 MeV)

0.6

Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.15–0.23(Nakazato+15) 0.05–0.11(Horiuchi+09) 0.37
(Lunardini09) 0.15
(Ando+09) 0.15
(Malaney97) 0.07
(Hartmann+97) 0.14

0.55
0.5
0.45
0.4
0.35
0.3

10
Year

3σ Sensitivity [/cm2/sec./MeV]

3σ Sensitivity [/cm2/sec./MeV]Year

SK-Gd (21.29 < Eν < 31.29 MeV)
Flux prediction [/cm2/sec./MeV](Horiuchi+18) 0.018–0.049(Nakazato+15) 0.007–0.021(Horiuchi+09) 0.080(Lunardini09) 0.027(Ando+09) 0.027(Malaney97) 0.010(Hartmann+97) 0.025

0.14

0.12

0.1

0.08

0.25
0.2 –– NCQE 100% error
0.15

0.06

–– NCQE 60% error–– NCQE×0.7 40% error
1

2

3

4

5

6

7

8

9

10
Year

0.04

–– NCQE 100% error–– NCQE 60% error–– NCQE×0.7 40% error
1

2

3

4

5

6

7

8

9

10
Year

Figure E.4: The 3σ sensitivity for the ν̄e flux as a function of SK-Gd operation period with a
0.1% Gd doping for the neutrino energy region 9.29 < Eν < 11.29 MeV (top left), 11.29 < Eν <13.29 MeV (top right), 13.29 < Eν < 21.29 MeV (bottom left), and 21.29 < Eν < 31.29 MeV(bottom right) for diﬀerent NCQE-like background conditions. Note that assumptions on the
background are diﬀerent from those in Figure E.1 as explained in the text. The predictions
from the models explained in Chapter 1 are also shown.

Bibliography[1] G. Tammann et al. The Astrophysical Journal Supplement, 92:487, 1994.
[2] R. Diehl et al. Nature, 439:45, 2006.
[3] https://www.nasa.gov/mission_pages/hubble/multimedia/crab_nebula.html, Picture of the Crab Nebula from NASA.
[4] M. Fukugita et al. Springer, ISNB 978-4-431-67029-2, 1994.
[5] C. Kobayashi et al. The Astrophysical Journal, 653:1145, 2006.
[6] Y. Hirai et al. The Astrophysical Journal, 814:41, 2015.
[7] Y. Hirai et al. The Astrophysical Journal, 855:63, 2018.
[8] E. M. Burbidge et al. Review of Modern Physics, 29:4, 1957.
[9] S. Woosley et al. The Astrophysical Journal, 433:229, 1994.
[10] T. J. Galama et al. Nature, 395:670, 1998.
[11] J. S. Bloom et al. The Astrophysical Journal, 572:L45, 2002.
[12] Y. Fukuda et al. Physical Review Letters, 81:1562, 1998.
[13] Q. R. Ahmad et al. Physical Review Letters, 87:071301, 2001.
[14] B. Pontecorvo. The Journal of Experimental and Theoretical Physics, 33:549, 1957.
[15] Z. Maki et al. Progress of Theoretical Physics, 28:870, 1962.
[16] L. Wolfenstein. Physical Review D, 17:2369, 1978.
[17] S. P. Mikheyev and A. Y. Smirnov. Nuovo. Cim. C, 9:17, 1986.
[18] K. Abe et al. Physical Review D, 96:092006, 2017.
[19] M. Jiang et al. Progress of Theoretical and Experimental Physics, 2019(5):053F01, 2019.
[20] M. G. Aartsen et al. arXiv:1902.07771 [hep-ex], 2019.
[21] K. Abe et al. arXiv:1910.03887 [physics.hep-ex], 2019.
[22] M. Tanabashi et al. Physical Review D, 98:030001, 2018.
[23] K. Kotake et al. Reports on Progress in Physics, 69:971, 2006.
241

BIBLIOGRAPHY

242[24] K. Nakazato et al. The Astrophysical Journal Supplement Series, 205:2, 2013.
[25] K. Hirata et al. Physical Review Letters, 58:1490, 1987.
[26] R. M. Bionta et al. Physical Review Letters, 58:1494, 1987.
[27] E. N. Alekseev et al. Journal of Experimental and Theoretical Physics Letters, 45:589,
1987.
[28] H. A. Bethe. Review of Modern Physics, 62:801, 1990.
[29] G. Pagliaroli et al. Astroparticle Physics, 31:163, 2009.
[30] K. Hirata et al. Physical Review D, 38:2, 1988.
[31] K. Nakazato et al. The Astrophysical Journal, 804:75, 2015.
[32] E. Mochida. Master Thesis [in Japanese], Tokyo University of Science, 2016.
[33] K. Nakazato et al. JPS Conference Proceedings, 14:010705, 2017.
[34] K. Belczynski et al. The Astrophysical Journal, 757:91, 2012.
[35] Y. Yamamoto et al. The Astrophysical Journal, 771:27, 2013.
[36] S. Horiuchi et al. Monthly Notices of the Royal Astronomical Society, 475, 2018.
[37] http://asphwww.ph.noda.tus.ac.jp/srn/, Nakazato SRN Flux.
[38] S. Horiuchi et al. Physical Review D, 79:083013, 2009.
[39] A. M. Hopkins and J. F. Beacom. The Astrophysical Journal, 651:142, 2006.
[40] C. Lunardini. Physical Review Letters, 102:231101, 2009.
[41] S. Ando et al. Astroparticle Physics, 18:307, 2003.
[42] R. A. Malaney. Astroparticle Physics, 7:125, 1997.
[43] D. H. Hartmann and S. E. Woosley. Astroparticle Physics, 7:137, 1997.
[44] M. Malek et al. Physical Review Letters, 90:061101, 2003.
[45] K. Bays et al. Physical Review D, 85:052007, 2012.
[46] H. Zhang et al. Astroparticle Physics, 60:41, 2015.
[47] A. Gando et al. The Astrophysical Journal, 745, 2012.
[48] T. Kikawa. Ph.D Thesis, Kyoto University, 2014.
[49] A. Ankowski et al. Physical Review Letters, 108:052505, 2012.
[50] L. Wan et al. Physical Review D, 99:032005, 2019.
[51] K. Abe et al. Physical Review D, 90:072012, 2014.

BIBLIOGRAPHY

243[52] P. deNiverville et al. Physical Review D, 86:035022, 2012.
[53] P. deNiverville et al. Physical Review D, 95:035006, 2017.
[54] P. Adamson et al. Physical Review Letters, 107:011802, 2011.
[55] P. Adamson et al. Physical Review D, 96:072006, 2017.
[56] K. Abe et al. Physical Review D, 99:071103(R), 2019.
[57] L. Alvarez-Ruso et al. New Journal of Physics, 16, 2014.
[58] L. A. Ahrens et al. Physical Review D, 35:785, 1987.
[59] A. A. Aguilar-Arevalo et al. Physical Review D, 82:092005, 2010.
[60] A. A. Aguilar-Arevalo et al. Physical Review D, 91:012004, 2015.
[61] C. H. Llewellyn Smith. Physics Reports, 3:261, 1972.
[62] R. Bradford et al. Nuclear Physics B Proceedings Supplements, 159:127, 2006.
[63] J. A. Formaggio. Review of Modern Physics, 84, 2012.
[64] K. Abe et al. Nuclear Instruments and Methods in Physics Research, Section A, 659:106–
135, 2011.
[65] K. Suzuki. Ph.D Thesis, Kyoto University, 2015.
[66] S. Bhadra et al. Nuclear Instruments and Methods in Physics Research, Section A, 703:45–
58, 2013.
[67] A. K. Ichikawa. Nuclear Instruments and Methods in Physics Research, Section A, 690:27–
33, 2012.
[68] T. Sekiguchi et al. Nuclear Instruments and Methods in Physics Research, Section A,
789:57–80, 2015.
[69] K. Matsuoka et al. Nuclear Instruments and Methods in Physics Research, Section A,
624:591–600, 2010.
[70] T. Hiraki. Ph.D Thesis, Kyoto University, 2015.
[71] K. Abe et al. Nuclear Instruments and Methods in Physics Research, Section A, 694:211–
223, 2012.
[72] P. A. Amaudruz et al. Nuclear Instruments and Methods in Physics Research, Section A,
696:1, 2012.
[73] N. Abgrall et al. Nuclear Instruments and Methods in Physics Research, Section A,
637:25, 2011.
[74] K. Suzuki et al. Progress of Theoretical and Experimental Physics, 2015(5):053C01, 2015.
[75] Y. Ashida et al. Progress of Theoretical and Experimental Physics, 2018(10):103H01,2018.

BIBLIOGRAPHY

244[76] K. Abe et al. arXiv:1908.05141 [physics.ins-det], 2019.
[77] S. Fukuda et al. Nuclear Instruments and Methods in Physics Research, Section A,
501:418, 2003.
[78] H. Kume et al. Nuclear Instruments and Methods in Physics Research, Section A, 205,
1983.
[79] R. Becker-Szendy et al. Nuclear Instruments and Methods in Physics Research, Section
A, 324:363, 1993.
[80] K. Abe et al. Nuclear Instruments and Methods in Physics Research, Section A, 737:253,
2014.
[81] Y. Nakano. Ph.D Thesis, The University of Tokyo, 2016.
[82] H. Nishino et al. Nuclear Instruments and Methods in Physics Research, Section A,
610:710, 2009.
[83] K. Hagiwara. Ph.D Thesis, Okayama University, 2019.
[84] R. Brun et al. Report No. CERNW5013, 1994.
[85] C. Zeitnitz and T. A. Gabriel. Proceedings of the International Conference on Monte
Carlo Simulation in High Energy and Nuclear Physics (MC93), 1993.
[86] C. Zeitnitz and T. A. Gabriel. Nuclear Instruments and Methods in Physics Research,
Section A, 349:106, 1994.
[87] M. Nakahata et al. Journal of the Physical Society of Japan, 55(11):3786, 1986.
[88] E. Bracci et al. CERN-HERA-72-01, 1972.
[89] A. S. Carroll et al. Physical Review C, 14:635, 1976.
[90] M. Nakahata et al. Nuclear Instruments and Methods in Physics Research, Section A,
421, 1999.
[91] E. Blaufuss et al. Nuclear Instruments and Methods in Physics Research, Section A, 458,
2001.
[92] H. Zhang. Ph.D Thesis, Tsinghua University, 2012.
[93] G. Battistoni et al. AIP Conference Proceedings, 896:31, 2007.
[94] K. Abe et al. Physical Review D, 87:012001, 2013.
[95] N. Abgrall et al. Physical Review C, 84:034604, 2011.
[96] N. Abgrall et al. Physical Review C, 85:035210, 2012.
[97] N. Abgrall et al. The European Physics Journal C, 76:84, 2016.
[98] N. Abgrall et al. The European Physics Journal C, 79:100, 2019.
[99] Y. Hayato. Acta Physica Polonica B, 40:2477, 2009.

BIBLIOGRAPHY

245[100] O. Benhar et al. Nuclear Physics A, 579:493, 1994.
[101] O. Benhar et al. Physical Review D, 72:053005, 2005.
[102] R. A. Smith and E. J. Moniz. Nuclear Physics, 43:605, 1972.
[103] J. Nieves et al. Physical Review C, 83:045501, 2011.
[104] K. Ueno. Ph.D Thesis, The University of Tokyo, 2012.
[105] D. Rein and L. M. Sehgal. Annals of Physics, 133(1):79, 1981.
[106] M. Gluck et al. The European Physical Journal C, 5, 1998.
[107] A. Bodek and U. K. Yang. AIP Conference Proceedings, 670, 2003.
[108] K. Abe et al. Physical Review Letters, 121:171802, 2018.
[109] T. Vladisavljevic. Ph.D Thesis, University of Oxford, 2019.
[110] E. Kolbe et al. Physical Review D, 66:013007, 2002.
[111] M. Leuschner et al. Physical Review C, 49:955, 1994.
[112] W. Y. Ma et al. Journal of Physics Conference Series, 888:012171, 2017.
[113] K. Abe et al. Physical Review D, 98:032003, 2018.
[114] K. Abe et al. Progress of Theoretical and Experimental Physics, 2019(9):093C02, 2019.
[115] Y. Zhang et al. Physical Review D, 93:012004, 2016.
[116] R. Akutsu. Ph.D Thesis, The University of Tokyo, 2019.
[117] K. Abe et al. Physical Review D, 94:052010, 2016.
[118] A. Ankowski et al. Physical Review C, 92:025501, 2015.
[119] C. J. Horowitz and B. D. Serot. Nuclear Physics A, 368:503, 1981.
[120] C. Maieron et al. Physical Review C, 68:048501, 2003.
[121] J. A. Caballero et al. Physical Review Letters, 95:252502, 2005.
[122] R. Gonzalez-Jimenez et al. Physical Review C, 88:025502, 2013.
[123] J. E. Amaro et al. Physical Review C, 71:015501, 2005.
[124] J. E. Amaro et al. Physical Review C, 73:035503, 2006.
[125] F. Capuzzi et al. Nuclear Physics A, 524:681, 1991.
[126] A. Meucci et al. Nuclear Physics A, 739:277, 2004.
[127] A. Meucci and C. Giusti. Physical Review D, 89:057302, 2014.
[128] J. Beacom and M. Vagins. Physical Review Letters, 93:171101, 2004.

BIBLIOGRAPHY

246[129] K. Abe et al. Physical Review D, 90:072005, 2014.
[130] K. Abe et al. arXiv:1109.3262 [physics.ins-det], 2011.
[131] K. Abe et al. Progress of Theoretical and Experimental Physics, 2015(5):053C02, 2015.
[132] T. Akaishi et al. arXiv:1912.08841 [physics.hep-ex], 2019.
[133] https://www.nndc.bnl.gov/exfor/endf00.jsp, ENDF/B Web Page.
[134] G. Cugnon et al. Nuclear Physics A, 620:4, 1997.
[135] A. Boudard et al. Physical Review C, 66:044615, 2002.
[136] T. Miura. Proceedings of 13th International Conference on Cyclotrons and their Applications, 1992.
[137] T. Saito. Proceedings of 14th International Conference on Cyclotrons, 1995.
[138] S. Ninomiya. Proceedings of 17th International Conference on Cyclotrons and their Applications, 2004.
[139] Y. Ashida et al. Progress of Theoretical and Experimental Physics, 2018(4):043H01, 2018.
[140] D. Satoh et al. JAEA-DATA/CODE, 2006-023, 2006.
[141] T. Kajimoto et al. Nuclear Instruments and Methods in Physics Research, Section A,
665, 2011.
[142] G. F. Knoll. Jhon Wiley & Sons, 2001.
[143] Y. Iwamoto et al. Nuclear Instruments and Methods in Physics Research, Section A, 804,
2015.
[144] D. Satoh et al. Journal of Nuclear Science and Technology, 43:7, 2006.
[145] J. K. Dickens. Technical Report ORTN-6436, 1988.
[146] N. Nakao et al. Nuclear Instruments and Methods in Physics Research, Section A, 362,
1995.
[147] H. Ejiri. Physical Review C, 48:1442, 1993.
[148] P. J. Dimbylow. Physics in Medicine and Biology, 25:637, 1980.
[149] S. Agostinelli et al. Nuclear Instruments and Methods in Physics Research, Section A,
506, 2003.
[150] G. Fogli et al. Journal of Cosmology and Astroparticle Physics, April 2005, 2005.
[151] A. Strumia and F. Vissani. Physics Letters B, 564, 2003.
[152] M. Honda et al. Physical Review D 83, 83:123001, 2011.
[153] http://www.icrr.u-tokyo.ac.jp/~mhonda/nflx2011/index.html, HKKM2011 Flux.

BIBLIOGRAPHY[154] S. W. Li and J. Beacom. Physical Review C, 89:045801, 2014.
[155] S. W. Li and J. Beacom. Physical Review D, 91:105005, 2015.
[156] S. W. Li and J. Beacom. Physical Review D, 92:105033, 2015.
[157] https://pris.iaea.org/pris/, IAEA PRIS Web Page.
[158] M. Baldoncini et al. Physical Review D, 91:065002, 2015.
[159] Z. Conner. Ph.D Thesis, Boston University, 1997.
[160] S. Desai. Ph.D Thesis, Boston University, 2004.
[161] K. Bays. Ph.D Thesis, University of California, Irvine, 2012.
[162] A. Hoecker et al. arXiv:physics/0703039, 2007.
[163] H. Watanabe et al. Astroparticle Physics, 31:320, 2009.
[164] T. Irvine. Ph.D Thesis, The University of Tokyo, 2014.
[165] Y. Zhang. Ph.D Thesis, Tsinghua University, 2015.
[166] L. Wan. Ph.D Thesis, Tsinghua University, 2018.
[167] M. Honda et al. Physical Review D, 75:043006, 2007.

247