Doctoral Dissertation
博士論文

A Study of Neutrons Associated with Neutrino andAntineutrino Interactions on the Water Target atthe T2K Far Detector(T2K 後置検出器における水標的でのニュートリノ及び反ニュートリノ反応に伴う中性子の研究)

A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2019
令和元年 12 月博士 (理学) 申請

Department of Physics, Graduate School of Science, The Universityof Tokyo
東京大学大学院理学系研究科物理学専攻

Ryosuke Akutsu
阿久津良介

Abstract
Neutrons production associated with neutrino interactions on water target in an energy region from sub-GeV up to a few GeV will be utilized to improve the physics
program of neutrino experiments employing water Cherenkov detectors. To thisaim, a precise prediction of such neutrons by Monte Carlo (MC) simulation is essential. However, current prediction is highly dependent on simulations due to large
uncertainties related to the modeling of neutrino interactions in nuclear medium,hadronic final-state interactions in nuclei, and secondary interactions in detector
medium. Therefore, it is worth studying these neutrons with beam neutrinos andevaluating the validity of simulations.
This thesis presents the first measurement of neutrons associated with neutrino
interactions in water for accelerator neutrinos and antineutrinos at the T2K far detector.
The Tokai-to-Kamioka (T2K) experiment is a long-baseline ν oscillation experiment in Japan. A primarily νµ (ν̄µ ) beam is produced at the J-PARC with a peakenergy of 0.6 GeV, and is detected by the Super-Kamiokande far detector, which is a
50 kton water Cherenkov detector located 295 km away from the beam source. The
observed beam-neutrino events at the far detector can be used to study the neutron
production.
In this thesis, the data collected at the far detector until 2018 are analyzed
to measure neutrons associated with neutrino interactions on water target. By
using Charged Current νµ and ν̄µ enriched samples, mean neutron multiplicity ismeasured with a total systematic uncertainty of ∼8%. The measured mean neutron multiplicity is 1.00 ± 0.17 (stat.) +0.07−0.08 (syst.) for the ν-mode operation and+0.10
1.40 ± 0.26 (stat.) −0.11 (syst.) for the ν̄-mode operation. The equivalent expectation by the reference simulation is 1.50 (2.14) for the ν-mode operation (ν̄-mode
operation), The deviation from the expectation is 2.75 σ (2.69 σ) for ν-mode operation (ν̄-mode operation) based on the total error of the measured value.
By using the measurement result, impact of uncertainty regarding the neutron
production on a particular physics analysis is estimated based on experimental data
for the first time, in context of Hyper-Kamiokande atmospheric neutrino oscillation
analysis. From the estimation, this measurement provides the first demonstrationthat understanding of the neutron production is essential to utilize those neutrons infuture experiments. As several experimental studies will be carried out, it is expectedthat a satisfactory level of understanding of those neutrons will be obtained.

iStatement of Originality
This thesis and the results presented in it were produced as a result of my own
original and independent research. However, this thesis contains the works that I
performed as well as the works done by the past and present T2K collaborators. In
a large experiment such as T2K, any analyses cannot be performed by a person andare always performed as part of the experiment. Indeed, the primary analysis of
this thesis was performed within the T2K collaboration, with the works done by theother collaborators. In the following, this statement clarifies my contributions.
Chapter 1 presents an overview of neutrino physics associated with the primary
analysis of this thesis based on both experimental and theoretical works, and gives
the motivation of this thesis by reviewing relevant works. All the works done byothers have been cited.
Chapter 2 and 3 describe an overview of the T2K experiment and the near detectors and the far detector to provide appropriate information in order to performthe primary analysis of this thesis. These chapters summarize the works done by thepast and the present collaborators, and relevant documents have been cited.
Chapter 4 presents simulations used for this thesis. Almost all the works aredone by others and relevant documents have been cited. However, I implemented
neutron production processes into the far detector simulation, SKDETSIM, based on
the work done by Tsui Ka Ming (ICRR, now Liverpool). He developed an interface
which connects SKDETSIM with Gean4. I also made improvements on SKDETSIM
such that systematic uncertainties on nucleon secondary interaction cross sections in
HETC and MICAP can be studied. This is completely and independently done bymyself.
Chapter 6 describes neutron tagging algorithm. Although the Super-Kamiokande
collaboration has their own neutron tagging algorithms, the algorithm, that I developed newly and independently, is diﬀerent from them. I wrote the codes of myalgorithm from scratch. Moreover, part of my developments have been included
into those algorithms. However, a recent study on random noise of the far detector’s photosensors done by T. Mochizuki (ICRR, now graduated) within the HyperKamiokande collaboration is adopted to this thesis. This Chapter also presents ananalysis of low-energy neutron calibration. The analysis method presented in thisthesis is based on the past Super-Kamiokande collaborators, and relevant documents
have been cited. However, the estimation method of systematic uncertainty using
the calibration data, which is presented in Chapter 8, was newly and independentlyiideveloped by myself in a completely diﬀerent way compared to the past works doneby the Super-Kamiokande collaboration. The eﬀects of the far detector time variations were estimated by myself for the first time.
Chapter 7 describes the first application of neutron tagging to T2K data. This
thesis uses the T2K data collected until 2018, which correspond to the Run 1-9 datataking periods. The data used in this thesis consist of two sets: primary neutrino
interaction and neutron tagging. For the data set of primary neutrino interaction,
part of the data was prepared by myself through the expert work of the data reduction, and the remaining data were prepared by the others. On the other hand, forthe data set of neutron tagging, all the data were prepared by myself. The figure,tables, analysis methods presented in this chapter were produced by myself.
Chapter 8 presents the primary analysis of this thesis. In the first part, all theworks related to MC simulations are done by myself, which includes the generation of
the alternative Monte Carlo (MC) sets: GENIE and NuWro. I independently built
a framework which enables full GENIE and NuWro MC sets for the first time at
the far detector. For the neutron measurement part, I independently performed all
the works from the generation of Monte Carlo events up to estimation of systematic
uncertainties. However, for the systematic error estimation I used the works done by
the T2K-beam working group for the neutrino beam fluxes, the T2K-neutrino interaction working group (NIWG) for the neutrino interaction cross sections, the T2K
neutrino oscillation analysis groups for neutrino oscillation parameters, the T2K-SK
working group for the neutrino event selection and the neutrino event reconstruction, the Super-Kamiokande collaboration for the discrepancy of the gain increaseof photosensor between data and detector simulation. Although I used these inputs,
all the methods to propagate these error inputs are developed by myself.
Chapter 9 summarizes this thesis, describes an impact of neutron production
uncertainty based on the measurement result presented in Chapter 8, and presents
future prospects. I made the estimation of the impact utilizing the atmospheric neutrino oscillation analysis tool, Osc3++, developed by R. Wendell (Kyoto) and otherpast Super-Kamiokande collaborators. In addition, in this estimation, I used an improved atmospheric neutrino oscillation analysis method developed by P. Menendez(UAM, now IFIC), which exploits information about tagged neutrons.
The primary analysis of this thesis, measurement of neutron associated with neutrino interactions in water, was oﬃcialized on 4 December 2019, and is now an oﬃcial
result of the T2K collaboration. The primary analysis is documented as the T2K
technical note-371 and is credited to the T2K collaboration.

iii

Acknowledgement
First of all, I would like to express my sincere gratitude to my supervisor, Dr. Kimihiro Okumura, for all his supports. His generosity and patience for letting me were
essential for completing my Ph.D.
I also would like to thank Dr. Yasuhiro Nakajima and Dr. Roger Wendell, without whom I would likely still be a Ph.D student. I cannot express how much I canappreciate your helps.
I want to oﬀer my thanks to Dr. Kevin McFarland. My very hard but quite
fruitful neutron studies were initiated by your comment. Although there were communications between us only during collaboration meetings, your comments always
polished my analysis and were always essential to complete it.
I am grateful to the members of the T2K-SK group. Dr. Mike Wilking wasalways interested in my study and gave me very sharp comments, which greatly
trained me. I was always helped by Dr. James Imber, Dr. Xiaoyue Lee, Dr. Cris
Vilela, and Tomoyo Yoshida for the T2K-SK data reduction work. Cris also helped
me for statistics, and answered to my stupid questions. Dr Shoei Nakayama gently
educated me as the T2K-SK data reduction worker, and I was saved from my catastrophic presentation skill by his education.
I would like to thank all people who supported my research in T2K. In particular,
I would like to thank Dr. Mark Hartz, Dr Akira Konaka, Dr. Kendall Mahn, and Dr.
Stephen Dolan. With kind help from Mark, I was able to report the measurement
result inside T2K in the 2019 summer meeting, which was essential to finish writing
up this thesis in time. Beyond T2K, Mark and Akira gave me great opportunity to
study neutrons in context of Hyper-K. Kendall kindly helped me when I was reallystruggling to find out the concrete strategy. Stephen gave me a lot of useful comments when working on systematics regarding nucleon FSI.
I must thank all the member of the Kamioka observatory as I spent all the time asa Ph.D. student. In particular, I am grateful to Dr. Koichi Ichimura, Dr. Takatomi
Yano, Dr. Makoto Miura, Dr. Christopher Bronner, and Dr. Motoyasu Ikeda. Also,
I want to thank people who made my life in Kamioka enjoyable: Dr. Tomonobu Tomura, Dr Byeongsu Yang, Dr. Keishi Hosokawa, Dr. Guillaume Pronost, Dr. Yuki
Nakano, Dr. Naoya Oka, Dr. Yusuke Suda, Dr. Masatoshi Kobayashi, Dr. Asato
Orii, and Akira Takenaka. Working around Mozumi, with Yutaro Sonoda, Toshiki
Mochizuki, Kohei Okamoto, and Nobuyuki Kato, was vital to survive my life in thelast two years. Discussion with Takumi Suzuki about a very wide topics also greatly
helped to refresh my mind. I would like to oﬀer special thanks to Artur Stuz as aiv

Kamioka member. Since you have started living in Kamioka, my life in Kamioka
drastically changed, and I really enjoyed Hida-Furukawa and Takayama with you.
Thanks to your passion for onsen, I came to like onsen. I also must oﬀer my thanks
to the Kamioka machines for finishing quite CPU intensive works in time.
I would like to thank people in RCCN: Dr. Tsui Ka Ming (now Liverpool),
Chieko Mashima, Dr. Yasuhiro Nishimura (now Keio), Dr. Morihiro Honda, Dr.
Kajita Takaaki, Dr Takuya Tashiro, Junjie Xia, and Seungho Han. The work on the
SK-Gd simulation done by Ka Ming was one of key ingredient for my research.
I would like to thank the T2K-SK neutroner: Yosuke Ashida and Fabio Iacob. I
was able to enjoy discussion about neutrons with you and drinking during T2K andSK collaboration meetings. I would not forget what Fabio said in Paris when we saw
electric kick board.
I want to thank T2K-SK Canada members: Dr. Shimpei Tobayama, Dr. Sophie
Berkman, Corina Nantais, Trevor Towstego. The Minouchi-BBQ party was one ofgreat fun during the T2K collaboration meeting, and I learned about beef a lot.
I would like to thank my family and my friends for many support. Thanks tohelps from my family, I was able to concentrate on my research in Kamioka.
Finally, I would like to thank my wife, Risako, for her continual support and encouragement over the past four years. I would not have made what I have achieved
without you.

v

Contents
Abstracti

Acknowledgementiv

1 Introduction
1.1 Neutrino physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 A brief history of neutrino physics . . . . . . . . . . . . . . . .
1.1.2 Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . .
1.2 Neutrons associated with ν-nucleus interactions on water . . . . . . .
1.2.1 Neutron productions . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Benefits of utilization of neutrons . . . . . . . . . . . . . . . .
1.2.3 Current status of prediction of neutrons . . . . . . . . . . . .
1.3 Research motivation . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
2
2
5
14
17
17
19
23
25
26

2 The T2K experiment27
2.1 Neutrino beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.1 J-PARC proton beam line . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Neutrino beam line . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.3 Oﬀ-axis approach . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Near detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.1 On-axis near detector . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.2 Oﬀ-axis near detector . . . . . . . . . . . . . . . . . . . . . . . 36
3 Far detector Super-Kamiokande
40
3.1 Cherenkov radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Detector design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Experimental phases . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.2 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3 Outer detector . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Water and air purification . . . . . . . . . . . . . . . . . . . . 45
3.3 Data acquisition for SK-IV . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.1 DAQ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.2 T2K data acquisition at the far detector . . . . . . . . . . . . 47

vi

CONTENTS

3.4

Detector calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Adjustment of high-voltage setting . . . . . . . . . . . . . . .
3.4.2 Relative gain calibration . . . . . . . . . . . . . . . . . . . . .
3.4.3 Absolute gain calibration . . . . . . . . . . . . . . . . . . . .
3.4.4 Measurement of relative quantum eﬃciency . . . . . . . . . .
3.4.5 Timing calibration . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 Measurement of water properties with laser light . . . . . . .
3.4.7 Time variation of water transparency . . . . . . . . . . . . . .
3.4.8 Position dependence of water transparency . . . . . . . . . . .
3.4.9 Measurement of reflectivity for PMT and black sheet . . . . .

49
49
50
50
51
52
53
56
58
60

4 Event simulation
62
4.1 T2K neutrino beam flux . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Neutrino interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Hadronic final-state-interactions (FSI) . . . . . . . . . . . . . 68
4.3 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Hybrid neutron MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5 Summary of MC sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5 Data reduction
76
5.1 Good spill selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 FC event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 Event classification . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4 Data reduction summary . . . . . . . . . . . . . . . . . . . . . . . . . 86
6 Neutron tagging
90
6.1 Definitions of tagging eﬃciency and background event rate . . . . . . 90
6.2 Initial selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3 Neural network classification . . . . . . . . . . . . . . . . . . . . . . . 98
6.3.1 The 14 feature variables . . . . . . . . . . . . . . . . . . . . . 100
6.3.2 Network training . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.4 Application to Americium-Beryllium calibration data . . . . . . . . . 110
6.4.1 Experimental setup and data taking . . . . . . . . . . . . . . . 111
6.4.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.4.3 MC simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4.4 Data-MC comparison . . . . . . . . . . . . . . . . . . . . . . . 114
6.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.5 Correction for detector time variation eﬀects . . . . . . . . . . . . . . 121
6.5.1 SK time variations . . . . . . . . . . . . . . . . . . . . . . . . 122
6.5.2 Regeneration of MC with time variations . . . . . . . . . . . 123
6.5.3 Correction of the time variation eﬀects . . . . . . . . . . . . . 129
6.5.4 Statistical uncertainties . . . . . . . . . . . . . . . . . . . . . 132

vii

CONTENTS

7 First application of neutron tagging to T2K data
135
7.1 Prediction of event rate . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2 Definition of analysis sample . . . . . . . . . . . . . . . . . . . . . . . 136
7.3 Event selection for data collected until 2018 . . . . . . . . . . . . . . 139
7.4 Quality checks for tagged neutrons . . . . . . . . . . . . . . . . . . . 146
7.5 Distributions related to tagged neutrons . . . . . . . . . . . . . . . . 158
7.5.1 Muon kinematics dependence . . . . . . . . . . . . . . . . . . 159
7.5.2 Kinematics of tagged neutrons . . . . . . . . . . . . . . . . . . 164
8 Measurement of mean neutron multiplicity
168
8.1 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.2 Analysis strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.3 Systematic uncertainties on tagging eﬃciency . . . . . . . . . . . . . 176
8.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.3.2 Neutrino cross sections . . . . . . . . . . . . . . . . . . . . . 178
8.3.3 Neutrino beam fluxes . . . . . . . . . . . . . . . . . . . . . . . 180
8.3.4 Pion FSI/SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.3.5 Nucleon FSI . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
8.3.6 Nucleon SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
8.3.7 µ− and π − captures on oxygen . . . . . . . . . . . . . . . . . . 189
8.3.8 Detector response for ν events . . . . . . . . . . . . . . . . . . 191
8.3.9 Oscillation parameters . . . . . . . . . . . . . . . . . . . . . . 192
8.3.10 ν vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.3.11 Simulation of PMT gain increase . . . . . . . . . . . . . . . . 194
8.3.12 Detector response to 2.2 MeV γ rays . . . . . . . . . . . . . . 198
8.3.13 Total systematic uncertainties . . . . . . . . . . . . . . . . . . 206
8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
9 Summary and outlook

217

A Implementation of neutron productions by µ− /π − captures

238

B Distribution of NN input variables

240

C True neutrino energy spectra

245

viii

List of Figures
1.1
1.2

1.3
1.4

1.5

1.6
1.7

1.8

1.9

Feynman diagrams of neutrino interaction vertices . . . . . . . . . . .
Experimental constraints on δCP , sin2 θ13 , and sin2 θ23 by T2K. 2D
confidence intervals for δCP vs sin2 θ13 for NH (top), 2D confidence
intervals for δCP vs sin2 θ23 with reactor constraint for NH (middle),
1D confidence intervals on δCP with reactor constraint for both NH
and IH (bottom). In the bottom figure, the error bars represent 3 σ
allowed regions. Figure taken from [1]. . . . . . . . . . . . . . . . . .
Size of matrix elements for the CKM matrix (left) and the PMNS
matrix (right). Figure taken from [2]. . . . . . . . . . . . . . . . . .
Probabilities of νµ → νe and ν̄µ → ν̄e oscillations for the NOvA experiment’s setup (left) and the observed electron appearance events forthe ν- and ν̄-beam operations (right). Figure taken from [3]. . . . . .
Eﬀective cross section for SRN and water, which includes energy resolution and detector threshold eﬀect based on Super-Kamiokand II.
Figure taken from [4]. . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental limits on SRN flux at 90% C.L. with flux predictions.
Figure taken from [5]. . . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic drawing of neutron productions by primary ν̄-nucleon
interaction inside oxygen nucleus, hadronic-final-state interactions inside the nucleus, and hadronic secondary interactions in water. In thiscase, the primary reaction ν̄ℓ + p → ℓ+ + n + π − is used. . . . . . . .
An example of neutron multiplicity using true CCQE ν (cyan) and ν̄(orange) interactions in water. The left, middle, right correspond toneutron multiplicities after primary interaction, after FSI, and afterSI, respectively. T2K beam neutrino flux is assumed. . . . . . . . . .
Distribution of tagged neutron multiplicity for diﬀerent ν interaction
channels in the SK atmospheric multi-GeV e-like sample assuming a
70% tagging eﬃciency, which corresponds to the full configuration of
SK-Gd. Figure taken from [6]. . . . . . . . . . . . . . . . . . . . . . .

ix

3

12
13

14

16
16

17

18

19

LIST OF FIGURES

1.10 An example of MC simulation study on energy correction by counting
number of tagged neutrons for the atmospheric neutrino samples incase of the SK-Gd’s full configuration, in which a 70% neutron tagging eﬃciency is expected to be achieved. Green colored histograms
represent true neutrino energies. Red and blue lines correspond to
lepton energies and corrected lepton energies by counting the numberof tagged neutrons, respectively. Figure taken from [7]. . . . . . . .
1.11 Sensitivities to δCP assuming true normal MH (right) and wrong MH
rejection as a function of true sin2 θ23 for the atmospheric neutrino
oscillation analyses at Hyper-Kamiokande. Black lines correspond tothe conventional analysis method developed by the SK collaboration
based on lepton energy. Magenta lines correspond to the improved
analysis method in which case an energy correction and a better event
selection using tagged neutrons are applied with an assumption of a
70% neutron tagging eﬃciency. Estimation for systematic uncertainties regarding neutron tagging (but, very rough) is taken into accountfor the magenta lines. Figure taken from [7]. . . . . . . . . . . . . .
1.12 Expected SRN flux as a function of positron energy for diﬀerent redshift at Super-Kamiokande. Figure taken from [8]. . . . . . . . . . .
1.13 Expected positron energy spectrum at SK-Gd with an exposure of
10 years (left). The red, blue, and magenta lines represent the SRN
signal, the atmospheric NCQE events, and the atmospheric CC decay
electron events, respectively. A revised version of the LMA model [9]is used for the SRN flux. For the decay electron events, a reduction
by a factor of five is assumed and is planned to be achieved by neutron tagging. Figure taken from [10]. Distribution of true distancefrom ν interaction to n capture vertices (right). The orange and green
correspond to the inverse β decay signal of SRN and the NCQE atmospheric neutrino background, respectively. . . . . . . . . . . . . .
1.14 Mean neutron multiplicities as a function of visible energy for heavy
water, measured by using atmospheric neutrinos at the SNO experiment. MC expectations are made from a combination of GENIE [11]and Geant4 [12]. The error bars of the data represent statistical errors
and the envelopes of the MC expectations correspond to the assigned
systematic uncertainties. Note that no systematic uncertainties due
to hadronic SI are taken into account for the error envelopes. Figure
taken from [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.15 Distribution of measured apparent velocity for neutron candidates by
the MINERvA experiment. The ν̄-mode of NuMI neutrino beam produced at Fermlab and a hydrocarbon target are used as neutrino
source and target material, respectively. The data are shown withstatistical error only and the gray bands represent the assigned systematic errors on the MC expectations. The MC expectations areproduced by a combination of GENIE [11] and Geant4 [12]. Figure
taken from [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x

20

21
22

22

23

24

LIST OF FIGURES

1.16 Proton multiplicity for CC νµ interactions on a C8 H8 target with 0 pionin the final state, measured by the T2K experiment. Only protons withkinetic energies above 500 MeV are considered. The error bars of thedata include both statistical and systematic uncertainties. Solid andbroken lines represent predictions by diﬀerent MC simulations withuses of various models. Figure taken from [15]. . . . . . . . . . . . .
2.1
2.2
2.3
2.4

25

A schematic view of the T2K experiment. . . . . . . . . . . . . . . .
A schematic drawing of the neutrino beam line. Figure taken from [16].
A schematic drawing of the neutrino beamline. Figure taken from [17].
A cross-sectional view of the secondary beamline. Figure taken from[16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Muon neutrino flux at the SK for operation of diﬀerent horn currents.
Figure taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Neutrino energy from two-body decay of pion in Lab. frame as afunction of parent pion energy for diﬀerent oﬀ-axis angles. T2K uses
an oﬀ-axis angle of 2.5◦ . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Survival probability of moun neutrinos with a baseline of 295 km(top) and neutrino beam fluxes at 295 km away from neutrino production target for three diﬀerent oﬀ-axis angles (bottom). Figure taken
from[17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 A schematic drawing of the near detector complex. Figure taken from[16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 INGRID on-axis detector. The direction of the beam neutrinos isparallel with the z-axis. Figure taken from [16] . . . . . . . . . . . .
2.10 A schematic diagram of the INGRID module. Figure taken from [16]2.11 A simplified schematic view of ND280. Figure taken from [16]. . . .
2.12 A schematic cross sectional view of P̸ OD. Figure taken from [16]. . .
2.13 A schematic drawing of TPC. Figure taken from [16]. . . . . . . . .

27
29
30

3.1
3.2

40

3.3
3.4
3.5

3.6
3.7

A schematic view of the Super-Kamiokande. Figure taken from [16].
An unrolled event display of a typical single-ring muon-like data eventof the T2K beam neutrino. Each dot corresponds to a PMT and color
represents the number of observed photoelectrons. . . . . . . . . . .
A schematic drawing of a super-module instrumented with the ID and
OD PMTs. Figure taken from [18]. . . . . . . . . . . . . . . . . . . .
A cross-sectional view of an ID PMT. Figure taken from [18]. . . . .
The wavelength dependence of the quantum eﬃciency of R3600 20inch PMT (left). Distribution of the transit time of R3600 20-inch
PMT (right). Figures taken from [18]. . . . . . . . . . . . . . . . . .
A schematic drawing of the online data process. Figure taken from[19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic drawing of the data acquisition at SK. The spill interval
and the width of one spill has been changed from 3.5 s and ∼3 µs to
2.4 s and ∼5 µs, respectively. Figure taken from [20]. . . . . . . . . .
xi

30
31

33

33
34
35
35
36
38
39

42
43
44

44
47

48

LIST OF FIGURES

3.8

The measured single-p.e. distribution in unit of pC. Figure taken from[21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 An example of the TQ distribution for an ID PMT. The horizontal
axis is the observed charge (pC) binned into the Q bin whose binning
is a linear scale up to 10 pC, and then becomes a log scale. The verticalaxis represents the observed timing with the TOF correction from thediﬀuser ball and the laser firing timing. In the vertical axis, larger
values correspond to earlier timing. Figure taken from [21]. . . . . .
3.10 Timing resolution as a function of observed charge in p.e. The PMT
hit timing of ID is modeled by an asymmetric Gaussian function whoseparameters depend on observed charge. The σt and σt′ are the timing resolutions for before and after the peak timing of the function,
respectively. Figure taken from [21]. . . . . . . . . . . . . . . . . . .
3.11 A schematic drawing of the laser calibration system for the measurement of the water properties (left). Distributions of the TOFsubtracted hit timings for the five diﬀerent tank regions (right). Figures taken from [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Typical fitted amplitudes. The points present the data taken in April
2009. The black, blue, red, and violet lines correspond to the fitted
functions of total amplitude, symmetric scattering, asymmetric scattering, and absorption, respectively. Figure taken from [21]. . . . . .
3.13 Time variations of the fitted amplitudes for various wavelengths. The
violet, black, and cyan correspond to the amplitudes of symmetricscattering, asymmetric scattering, and light absorption. Three laser
units were replaced during this data taking period, and the black
vertical lines represent the time when the replacement was conducted.
Figure taken from [21]. . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Typical ln Qave distribution (left) and the relation between the relative absorption amplitude and the eﬀective attenuation length (right).
In the left, the slope of the fitted linear function corresponds to theeﬀective attenuation length. The left and right side figures taken from[22] and [23], respectively. . . . . . . . . . . . . . . . . . . . . . . . .
3.15 A typical vertical position z dependence of the water temperatureinside the tank. Figure taken from [23]. . . . . . . . . . . . . . . . .
3.16 Time variation of the measured αT BA with the daily calibration using
Xe light source (blue) and the monthly nickel calibration (red). Figure
taken from [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 A schematic drawing of the setup for the reflectivity measurement of
the black sheets. Figure taken from [21]. . . . . . . . . . . . . . . . .
4.1
4.2

A schematic of the geometrical setup considered in the FLUKA simulation of the proton injection. Figure taken from [17]. . . . . . . . .
Beam neutrino non-oscillated fluxes for the FHC (left) and RHC(right) modes. These fluxes are used for event simulation at the far
detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii

51

53

53

55

56

57

58
59

60
61
63

64

LIST OF FIGURES

4.3

4.4
4.5
4.6

4.7
4.8
4.9
5.1
5.2

5.3

5.4

5.5

5.6

5.7

Cross-sections for interactions calculated by NEUT 5.3.2. Left andright correspond to νµ and ν̄µ . The gray histograms represent T2K
fluxes, which are shown with arbitrary units. Figure taken from [24].
A schematic drawing of hadronic final-state-interactions by an intranuclear cascade model. Figure taken from [25]. . . . . . . . . . . . . .
A schematic drawing of hadronic final-state-interactions. Figure takenfrom [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cross sections of free N -N scattering used in NEUT and GCALOR.
The left and right plots corresponds to pp scattering and pn scattering,
respectively. The cross sections are retrieved from GCALOR. . . . .
Summary of neutron-nucleus reactions considered in MICAP. Figure
taken from [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The macroscopic cross section for water used in MICAP. . . . . . . .
A schematic diagram of the procedure that merges noise PMT hits ofdummy spill data into simulated PMT hits. . . . . . . . . . . . . . .
A schematic drawing of the flow of the FC event selection. Figure
taken from [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The goodness G(x, t) as a function of t for a MC event consisting a
primary muon and a decay-electron (black dots). The vertical brokenlines represent the true particle creation time. The orange solid lines
denote the peak time of the subevents. The blue and green curves represent the threshold used for selecting subevent peaks. Figure takenfrom [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cherenkov emission profile for electron (left) and muon (right) withinitial momenta of 1000 MeV/c. The vertical axes represent the distance traveled from the initial position of the particle. The horizontal
axes show the cosine of the angle between the particle direction andthe photon emission direction. Figure taken from [28]. . . . . . . . .
Two-dimensional distribution of single-ring ln(Le /Lµ ) and reconstructed
momentum under electron hypothesis for electrons (left) and muons(right). The distributions are made from particle gun MC events simulated by SKDETSIM. The solid lines indicate the cut criterion for
single-ring electron and muon separation. Figure taken from [29]. . .
A schematic drawing of the flow for performing the Multi-ring fit forthe case where the best first-ring fit is electron’s one. Figure takenfrom [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance of the fiTQun single-ring fit. Top left, top right, bottom left, and bottom right figures show momentum resolution, vertex
resolution, direction resolution, and misidentification probability as
a function of true momentum. The definitions of these values aredescribed in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability of the event rate measured by INGRID (top) and the beam
directions measured by the INGRID and MUMON (middle and bottom). Figure taken from [30]. . . . . . . . . . . . . . . . . . . . . . .
xiii

65
68
70

70
72
72
74
78

82

83

84

85

86

87

LIST OF FIGURES

5.8

Accumulated POT as a function of date. The red and orange lines
correspond to the FHC Run 1-9 POT and the RHC Run 5-9 POT,
respectively. The green line represents the ineﬃciency of beam good
spill at the far detector and its scale is shown by the right side of thisfigure. Figure taken from [31]. . . . . . . . . . . . . . . . . . . . . . 88
5.9 Cumulative number of FC events as a function of accumulated POT
at the far detector for FHC mode (left) and RHC mode (right). The
blue lines correspond to the Run 1-9 data. The red lines represent
expectation of constant FC event rates which are obtained from theobserved FC events and the accumulated POT. Figure taken from [31]. 89
5.10 Distribution of the time diﬀerence from the expected arrival time at
the far detector, ∆T0 , for the Run 1-9 FC events. The vertical dashedlines represent fitted bunch center positions. Figure taken from [31].
89
6.1
6.2

6.3

6.4

6.5
6.6
6.7

6.8

Distribution of kinetic energies for electrons which are produced by
the Compton scattering of 2.2 MeV γ rays . . . . . . . . . . . . . . .
Example of event display of a ν event (MC) which have two true
neutron captures on hydrogen. The PMT hits after 18 µs from theprimary event trigger are shown. The red and blue dots correspondto PMT being hit by true 2.2 MeV γ ray and noise. . . . . . . . . .
Example of raw PMT hit time distribution of a ν event (MC) which
has two true neutron captures on hydrogen nucleus. The red and blue
correspond the PMT hits simulated in MC and extracted from dummy
spill data, respectively. In the red histogram, spikes around +190 µs
and +250 µs are due the two neutron captures. . . . . . . . . . . . .
Distribution of time diﬀerence from the first hit (µs) for dummy spill
data which were taken in the beam oﬀ period between the Run 6 andRun 7. For each individual PMT, the time diﬀerences are computed,
but are filled into this histogram. The cyan solid curve is the best
result of a χ2 fit of the distribution to a function consisting of two
exponential + an asymmetric gaussian + a constant functions. Theorange dashed line shows the fitted constant function. . . . . . . . .
Distribution of true distance from ν interaction vertex to neutron capture vertex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic drawing of the calculation of PMT hit clusters using a
10 ns sliding timing window. . . . . . . . . . . . . . . . . . . . . . .
Distribution of N 10pvx for the true neutron events (left) and backgrounds events (right), respectively. The green arrows show the lower
cut position of N 10pvx . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutron tagging eﬃciency as a function of N 10pvx threshold (left)
and number of accidental background events per ν event as a functionof N 10pvx threshold (right). Note that the threshold used for thisanalysis is N 10pvx = 7. . . . . . . . . . . . . . . . . . . . . . . . . . .

xiv

92

93

94

95
95
96

97

97

LIST OF FIGURES

6.9

Example of typical PMT hits of a signal MC event and a backgroundMC event. The signal (background) event has 10 (8) PMT hits anda NN output value of 0.9906 (0.0007). The hits of signal event (background event are enclosed by pink hollow squares (cyan hollow circles).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.10 Distribution of the distance between the true and reconstructed vertices (left). The arrow shows the 68 percentile of the distribution.
Distribution of true distance from the generation point of 2.2 MeV γ
ray to the vertex of the first Compton scattering (right). . . . . . . . 99
6.11 A schematic drawing of opening angle defined by 3 hits. . . . . . . . 103
6.12 Array of one-dimensional PDF of 3 hits Cherenkov angle distribution
for the signal (left) and background (right) events. For a given N 10nvx ,the corresponding horizontal slice is used to calculate llrCAng. In
the left and right plots, N 10n denotes N 10nvx . . . . . . . . . . . . . 104
6.13 Distributions of the 14 feature variables, which are fed into the NN.
Red and blue distributions correspond to true neutron events andaccidental background events, respectively. All the distributions arearea normalized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.14 Linear correlation matrices for true neutron events (top) and accidental background events (bottom). . . . . . . . . . . . . . . . . . . . . 107
6.15 Area normalized distribution of the neural network output. . . . . . 109
6.16 The left and right figures shows background event rate (number ofbackground events per ν event) and tagging eﬃciency as a function of
the neural network output threshold, respectively. The vertical green
arrow shows the position of the threshold which is determined to be
0.886 by setting background event rate to 0.02. . . . . . . . . . . . . 109
6.17 Neutron tagging eﬃciency as a function of reconstructed ν interaction
vertex position inside the SK tank (left). Background event rate as afunction of reconstructed ν interaction vertex position inside the SK
tank (right). R2 is defined as X 2 + Y 2 , where X and Y are x and ypositions of reconstructed ν interaction, respectively. Green dashedlines represent the fiducial volume used in the primary analysis of thisthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.18 The Americium-Beryllium source and BGO crystal scintillator. . . . 111
6.19 Distributions of potot for the center (top left), Z+15 m (top right),
and Y-12 m (bottom). The events inside the regions surrounded byarrows are selected as the prompt events related to 4.4 MeV γ rays.
113
6.20 Kinetic energy spectra of neutrons produced by 9 Be(α, n)12 C reactions. The broken line peaked around 3 MeV corresponds to the delayed neutrons of the signal reaction: α +9 Be →∗12 C + n. Figure
taken from [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

xv

LIST OF FIGURES

6.21 Distributions of the 14 input variables before the NN classification.
The MC distribtions are shown by stacked histograms consisting of thetrue signal events (blue) and the true background events (pink). The
dots corresponds to the data. Green bands represent the statisticalerrors of the MC. All the distributions are normalized by the numberof the selected prompt events. . . . . . . . . . . . . . . . . . . . . . 116
6.22 Distributions of the 14 input variables after the NN classification. The
MC distribtions are shown by stacked histograms consisting of the truesignal events (blue) and the true background events (pink). The dots
corresponds to the data. Green bands represent the statistical errorsof the MC. All the distributions are normalized by the number of theselected prompt events. . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.23 Distribution of capture time after the primary selection for the three
data taking positions. The top left, top righ, bottom correspond tothe center, the Z+15 m, and the Y-12 m data taking positions, respectively. The fitted background component is subtracted. All the
distributions are normalized by the number of the selected prompt
events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.24 The fitted neutron tagging eﬃciency (left) and the fractional diﬀerencewith respect to the MC’s ones. In the left plot, green and blue points
correspond to the MC and the data, respectively. In the right plot, thegreen dashed line represents the average of the fractional diﬀerences.
The horizontal axes represent the three data taking positions. . . . . 120
6.25 Fitted neutron tagging eﬃciency of the data at the center position forvarious potot cut values. In the left plot, lower cut value is varied while
keeping upper cut value. On the other hand, in the right plot, upper
cut value is varied while keeping lower cut value. In the left (right)
plot, each color represents the corresponding fixed upper (lower) cut
value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.26 The time variations of the ID PMT gain (top), the attenuation lengthof the water measured by using decay electrons (middle), the TBA
measured by the auto Xe light (bottom). For the PMT gain, thevertical axis represents the relative PMT gain with respect to theaverage value in Apr. 2009. The green bands show the Run 1-9 datataking periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.27 The average number of PMT hits of the dummy spill data. The green
bands show the Run 1-9 data taking periods. . . . . . . . . . . . . . 123
6.28 Neutron tagging eﬃciency after the primary selection as a functionof time. The top panel and bottom panel correspond to the FHC
and RHC 1Rνµ MC samples, respectively. The error bars represent
the MC statistical errors. The green bands show the Runs 1-9 datataking periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xvi

LIST OF FIGURES

6.29 Background event rate after the primary selection as a function oftime. The top panel and bottom panel correspond to the FHC and
RHC 1Rνµ MC samples, respectively. The error bars represent the
MC statistical errors. The green bands show the Runs 1-9 data taking
periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.30 Comparison of the N 10pvx distributions between the diﬀerent MC regeneration points. The left and right plots represent the true neutron
and background events, respectively. The green bands show the Runs
1-9 data taking periods. . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.31 Neutron tagging eﬃciency after the NN classification as a functionof time. The top panel and bottom panel correspond to the FHC
and RHC 1Rνµ MC samples, respectively. The error bars represent
the MC statistical errors. The green bands show the Runs 1-9 datataking periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.32 Background event rate after the NN classification as a function oftime. The top panel and bottom panel correspond to the FHC and
RHC 1Rνµ MC samples, respectively. The error bars represent the
MC statistical errors. The green bands show the Runs 1-9 data taking
periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.33 Comparison of the NN output distributions between the diﬀerent regeneration points. Left and right correspond to the true neutron andaccidental background events, respectively. The arrow shows the cut
position of the NN output. . . . . . . . . . . . . . . . . . . . . . . . 128
6.34 The fitted tagging eﬃciency (left) and the POT weighted averages.
The top panel and bottom panel correspond to the FHC and RHC
1Rνµ samples. The solid curves and broken lines correspond to thebest fit results and POT weighted average, respectively. The green
bands show the Run 1-9 data taking periods. . . . . . . . . . . . . . 130
6.35 The fitted background event rate (left) and the POT weighted averages. The top panel and bottom panel correspond to the FHC and
RHC 1Rνµ samples. The solid curves and broken lines correspond tothe best fit results and POT weighted average, respectively. The green
bands show the Run 1-9 data taking periods. . . . . . . . . . . . . . 131
6.36 Fraction of POT which is computed by dividing the total accumulated
POT of each individual MR run by the total Runs 1 − 9 POT. The
green bands show the Run 1-9 data taking periods. . . . . . . . . . . 132
6.37 Correlation matrices for the parameters of the tagging eﬃciencies (left)
and the background rates (right). In the left side, “TagEﬀ FHC”,“TagEﬀ RHC”, “FVar 1”, and “FVar 2” correspond to εF0 HC , εRHC,
0
a1 , a2 , respectively. In the right side, “BRate FHC”, “BRate RHC”,“FVar 1” correspond to B0F HC , B0RHC , b1 , respectively. These paramters
are defined in Equation 6.5.3. The matrices are derived from the corresponding covariance matrices calculated by MINUIT. . . . . . . . . 133
6.38 Distribution of the fractional errors obtained by throwing the parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
xvii

LIST OF FIGURES

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

Fraction of the neutron captures which happened inside ID as a function of Dwall for the three diﬀerent ν event generators. The left andright correspond to the FHC and RHC 1Rνµ samples, respectively.
Dwall is the nearest distance between the ν vertex and ID wall. The
analysis cuts (better selection) described in this section are applied
except for the FV cut. . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Fraction of the neutron captures which happened outside the ID as
a function of Dwall cut value (i.e. fiducial volume) for the three
diﬀerent ν event generators. The left and right correspond to the FHC
and RHC 1Rνµ samples, respectively. Dwall is the nearest distance
between the ν vertex and ID wall. The analysis cuts (better selection)
described in this section are applied except for the FV cut. . . . . . 138
Neutron tagging eﬃciency (top) and background event rate (bottom)
as a function of Dwall for the three diﬀerent ν event generators. Dwall
is the nearest distance between the ν vertex and ID wall. The rightand left side plots are for the FHC and RHC 1Rνµ samples, respectively. The analysis cuts (better selection) described in this section
are applied except for the FV cut. . . . . . . . . . . . . . . . . . . . 139
Distributions of the variables used in the 1Rνµ selection for the FHC
mode. The vertical axes represent the number of observed neutrino
events. The selection criteria and their order are described in Section 7.2. The arrows indicate the cut positions. All the MC distributions are normalized by the Run 1-9 POT. . . . . . . . . . . . . . . . 140
Distributions of the variables used in the 1Rνµ selection for the RHC
mode. The vertical axes represent the number of observed neutrino
events. The selection criteria and their order are described in Section 7.2. The arrows indicate the cut positions. All the MC distributions are normalized by the Run 1-9 POT. . . . . . . . . . . . . . . . 141
Number of ν events (top) and the corresponding selection eﬃciencies
from the FCFV cut (bottom) for each selection stage. The left andright side plots correspond to the FHC and RHC 1Rνµ samples, respectively. The MC expectations are normalized by the Run 1-9 POT.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Number of tagged neutrons (top) and the corresponding selection efficiencies from the FCFV cut (bottom) for each selection stage. The
left and right side plots correspond to the FHC and RHC 1Rνµ samples, respectively. The MC expectations are normalized by the Run
1-9 POT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Distribution of the NN output for the Run 1-9 data overlaid with thecorresponding MC distribution. The left and right side plots correspond to the FHC and RHC 1Rνµ samples, respectively. The MC
expectations are normalized by number of observed tagged neutrons. 146

xviii

LIST OF FIGURES

7.9

Cumulative number of tagged neutrons as a function of accumulated
POT. The left and right side plots are for the FHC and RHC 1Rνµsamples, respectively. The solid lines correspond to expectation which
is derived from the number of observed tagged neutrons and Run 1-9
POT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.10 Two dimensional distribution of reconstructed neutron capture vertex
distributions of the Run 1-9 data. The top and bottom figures show
the distribution of the vertical vertex position versus the square of theradial distance and the vertex distribution projected onto the horizontal plane of the inner detector, respectively. The left and right sideplots are for the FHC and RHC 1Rνµ samples, respectively. The blacksolid lines represent the inner detector wall. The yellow broken lines
represent the fiducial volume used in this analysis. The red arrows
represent the beam direction in the SK coordinate. . . . . . . . . . . 148
7.11 Distributions of the reconstructed neutron capture vertex for the Run
1-9 data. The left and right side figures correspond to the FHC and
RHC 1Rνµ samples, respectively. The top figures show the distribution of the distance from the reconstructed vertex to the closest ID
wall. The middle figures show the distribution of the square of theradial distance in the SK ID. The bottom figures show the distribution of the vertical position in the SK ID. All the MC distributions
are normalized by the number of observed tagged neutrons of the Run
1-9 data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.12 Cumulative distribution functions of the reconstructed neutron capture vertex distributions for the Run 1-9 data. The left and right sideplots correspond to the FHC and RHC 1Rνµ samples, respectively.
The top figures show the distribution of the distance from the reconstructed vertex to the closest inner detector wall. The middle figures
show the distribution of the square of the radial distance in the SK ID.
The bottom figures show the distribution of the vertical position in
the inner detector. The broken lines are the corresponding cumulative
distributions function of the MC distributions. . . . . . . . . . . . . 151
7.13 Distributions of test statistics produced by random throws for the
Dwall of the tagged neutrons of the FHC 1Rνµ sample. The top left,
top right, and bottom figures correspond to distributions of KS, CVM,
and AD test statistics, respectively. The green arrows show the valuesof the test statistics obtained by the Run 1-9 FHC 1Rνµ data sample. 152
7.14 Time diﬀerence between ν event and neutron capture. Left and rightare for the FHC and RHC 1Rνµ samples, respectively. The solid lines
correspond to the best fit results of the binned log likelihood fit. . . 155
7.15 Distributions of the fitted τ , µS , µB of the toy MCs. The left and rightpanels correspond to the FHC and RHC 1Rνµ samples, respectively.
The top, middle, and bottom figures represent the fitted τ , µS , andµB . The magenta arrows show the true values used for the generationof the toy MC. The green arrows represent the data fit results. . . . 157
xix

LIST OF FIGURES
7.16 Distribution of minimum L obtained by the toy MC fits. Left andright are for the FHC and RHC 1Rνµ samples, respectively. The
green arrows show the minimum L obtained by the data fit. . . . . . 158
7.17 Distribution of tagged neutron multiplicity for the Run 1-9 FHC (left)
and the Run 5-9 RHC data (right). Note that the accidental backgrounds are included in the tagged neutrons. The MC expectations
are normalized by the Run 1-9 POT. . . . . . . . . . . . . . . . . . . 159
7.18 Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed muon momentum. The left and right side plots are for the
FHC and RHC 1Rνµ samples, respectively. The expected numbers
are normalized by the Run 1-9 POT. . . . . . . . . . . . . . . . . . . 160
7.19 Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed muon transverse momentum. The left and right side plots
are for the FHC and RHC 1Rνµ samples, respectively. The expected
numbers are normalized by the Run 1-9 POT. . . . . . . . . . . . . . 161
7.20 Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed neutrino energy. The left and right side plots are for the FHC
and RHC 1Rνµ samples, respectively. The distributions are normalized by the Run 1-9 POT. . . . . . . . . . . . . . . . . . . . . . . . . 162
7.21 Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of the reconstructed negative four momentum transfer squared. The left andright side plots are for the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized by the Run 1-9 POT. . . . . . . . . 163
7.22 Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of the cosineof the angle between the reconstructed muon and beam directions.
The left and right side plots are for the FHC and RHC 1Rνµ samples,
respectively. The distributions are normalized by the Run 1-9 POT. 164
7.23 Distribution of the reconstructed neutron travel distance which is defined as the distance between the ν intraction and neutron capture
vertices. The left and right correspond to the FHC and RHC 1Rνµsamples, respectively. The distributions are normalized by the Run
1-9 POT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.24 Distribution of the reconstructed longitudinal travel distance, whichis the travle distance projected onto the beam direction. The left andright correspond to the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized by the Run 1-9 POT. . . . . . . . . 165
7.25 Distribution of the reconstructed transverse travel distance, which is
the travel distance perpendicular to the beam direction. The left andright correspond to the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized by the Run 1-9 POT. . . . . . . . . 166
xx

LIST OF FIGURES

7.26 Distribution of cosine of the actual angle which is the angle between
the beam direction and reconstructed momentum direction. The left
and right plots are for the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized by the Run 1-9 POT. . . . . . . . . 166
7.27 Distribution of cosine of the inferred angle which is the angle between
the inferred direction and reconstructed momentum direction. The left
and right plots are for the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized by the Run 1-9 POT. . . . . . . . . 167
8.1

8.2

8.3

8.4

8.5

8.6

8.7

Distribution of true neutron multiplicity before SI for three diﬀerentMonte Carlo ν event generators. The left and right correspond to the
FHC and RHC 1Rνµ samples, respectively. . . . . . . . . . . . . . . 169
Distribution of kinetic energy for neutrons (top left), protons (topright), π + (bottom left), and π − (bottom right) which have left thetarget nucleus, but have not undergone their secondary interactions
in detector. The FHC 1Rνµ samples are used for these hadrons. All
the distributions are normalized by 1021 POT. . . . . . . . . . . . . . 170
Distribution of kinetic energy for neutrons (top left), protons (topright), π + (bottom left), and π − (bottom right) which have left thetarget nucleus, but have not undergone their secondary interactions
in detector. The RHC 1Rνµ samples are used for these hadrons. All
the distributions are normalized by 1021 POT. . . . . . . . . . . . . . 171
Mean neutron captures as a function of incident kinetic energy for neutrons, protons, and π ± . Orange and cyan lines correspond to expectation of SKDETSIM and Geat4.10.1 with an option of FTFP BERT HP,
respectively. In SKDETSIM, GCALOR is used to simulate hadrons
except only for pions with momenta below 500 MeV/c, and NEUT
simulates pions for the momentum region. These hadrons are generated by the particle guns of the two simulations. . . . . . . . . . . . 172
Distribution of true neutron multiplicity for the FHC 1Rνµ sample(left) and the RHC 1Rνµ sample (right). Filled histograms and solidlines correspond to true neutron multiplicity before SI and after SI,
respectively. All the distributions are normalized by the Run 1-9 POT. 173
Distribution of true neutron multiplicity for the three popular ν event
generators, NEUT, NuWro, and GENIE. All the contributions fromneutrino interactions, hadronic FSI and SI are included in the multiplicities. The left and right plots correspond to the FHC and RHC
1Rνµ samples, respectively. The secondary interactions of the hadrons
produced by the generators are common among the three generators.
(i.e. the identical detector simulation is used). All the distributions
are area normalized. . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
True travel distance of neutron captures per incident hadron as afunction of initial momentum for n, p, π + , π − . The Z-axes show thenumber of neutron captures. . . . . . . . . . . . . . . . . . . . . . . 174

xxi

LIST OF FIGURES

8.8

Distribution of true distance between ν interaction and neutron capture vertices for the NEUT, NuWro, and GENIE. The left and rightplots correspond to the FHC and RHC 1Rνµ samples, respectively.
The secondary interactions for the hadrons produced by the generators are common among the three generators. All the distributions
are normalized by 1021 POT. . . . . . . . . . . . . . . . . . . . . . . 174
8.9 Mean neutron multiplicity as a function of true Q2 . The left and rightcorrespond to the FHC and RHC 1Rνµ samples, respectively. The
error bars represent the MC statistical uncertainties. . . . . . . . . . 175
8.10 Relation between true Q2 and reconstructed Pt . The left and rightcorrespond to the FHC and RHC 1Rνµ samples, respectively. The
Z-axes show the number of neutrino events normalized by 1021 POT
The black lines represent the mean reconstructed Pt at each true Q2bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.11 Neutron tagging eﬃciency as a function of true distance from ν interaction and neutron capture vertices for the FHC (left) and RHC(right) 1Rνµ samples. . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.12 Fractional change in the average tagging eﬃciency due to ±1 σ variations of each individual parameter for the FHC (top) and RHC (bottom) 1Rνµ samples. The blue and red bars correspond to ±1 σ variations, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.13 Fractional uncertainties on the ν beam fluxes. The uncertainties aretaken from TN-354 [33] . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.14 Fractional change in the total average tagging eﬃciency. Right andleft are for the FHC and RHC 1Rνµ samples, respectively. As the 1Rνµsamples are dominantly composed by the νµ and ν̄µ fluxes, only thesystematic parameters of these fluxes have therefore visible variations.
The blue and red bars correspond to ±1σ variations, respectively. . . 181
8.15 Fractional changes in the average neutron tagging eﬃciency due topion FSI/SI uncertainty. Top and bottom figures are for the FHC
and RHC 1Rνµ samples, respectively. The horizontal axes represent
the parameter sets described in Table 8.3. . . . . . . . . . . . . . . . 183
8.16 Fractional change in the average tagging eﬃciency for the FHC (left)
and RHC (right) 1Rνµ samples. The blue and red bars correspond to±1 σ variations, respectively. . . . . . . . . . . . . . . . . . . . . . . 184
8.17 Distribution of the true distance from ν interaction and neutron capture vertices for the total neutrons (top) and the tagged neutrons(middle). Neutron tagging eﬃciency as a function of the true distance(bottom) (i.e. middle/top). The right and left side plots correspondto the FHC sample and RHC 1Rνµ samples, respectively. All the distributions are normalized by 1021 POT. The histograms filled by thecolors are made from the nominal MC, whereas the pink and green
solid lines are made from the regenerated MC with the ±30% variationof the Bertini’s total free N-N cross sections, respectively. . . . . . . 186

xxii

LIST OF FIGURES

8.18 Comparison of ENDF/B microscopic total cross section between different versions. MICAP use a thinned version V and thus, there
are diﬀerence between the MICAP’s one and version V (formatted
in ENDF-6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.19 Distribution of the true distance between the true distance between
the ν interaction and neutron capture vertices. The histograms filledby the colors and solid lines are made from the nominal MC and regenerated MC with the ENDF/B-VIII0, respectively. The left and rightplots are for the FHC sample and RHC 1Rνµ samples, respectively. . 188
8.20 Mean true distance between generation and neutron capture positions
for the MICAP’s thinned ENDF/B-V and ENDF/B-VIII0 versions.
These are made from results of neutron particle gun MC of the detector
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.21 Fraction of interaction channel of oxygen nucleus for the MICAP’s
thinned version V (left) and ENDF/B-VIII0 (right). . . . . . . . . . 189
8.22 Comparison of the diﬀerent simulation of neutron productions by the
distribution of true distance between the ν interaction and neutron
capture vertices. The left and rights plot are for the FHC and RHC
1Rνµ samples, respectively. In the plots, “Nominal ”corresponds tothe nominal MC generated with G4MuonMinusCaptureAtRest, whereas“CHIPS ”corresponds to the regenerated MC with G4QCaptureAtRest
instead. All the distributions are normalized by 1021 POT. . . . . . . 190
8.23 The distributions of true distance between the ν interaction and neutron capture vertices for the three diﬀerent models of the neutron productions by π − capture. The left and right plots are for the FHC and
RHC 1Rνµ samples, respectively. In the plots, “Nominal ”corresponds
to the nominal MC generated with G4PiMinusAbsorptionAtRest,
whereas “CHIPS ”and “BERT ”correspond to the regenerated MCwith G4QCaptureAtRest and G4PiMinusAbsorptionBertini, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.24 Fractional uncertainties on each event category which are derived fromthe uncertainty on the detector response. The left and right plots arefor the FHC and RHC 1Rνµ samples, respectively. . . . . . . . . . . 192
8.25 Fractional change in the average tagging eﬃciency for the FHC (left)
and RHC (right) 1Rνµ samples. . . . . . . . . . . . . . . . . . . . . 192
8.26 Distribution of the single photo-electron of the SK-III type PMTs usedin SKDETSIM (left) and Relation between relative number of PMT
hits and relative PMT gain for the data derived from various calibrations and MC (right). In left side plot, the green filled histogram
corresponds to the nominal gain and the blue and red lines correspondto +8% and +16% gain from the nominal value, respectively. . . . . 195

xxiii

LIST OF FIGURES

8.27 Comparison of the α = 1.0 and α = 1.6 cases for the tagging eﬃciency(top) and background rate (bottom) after the NN classification. The
filled circles and open triangles are for the regenerated MCs with α =1.0 and α = 1.6, respectively. These plots are for the FHC 1Rνµsample, but same tendency is also found for the RHC 1Rνµ sample. . 196
8.28 Tagging eﬃciency after the NN classification as a function of time for
α = 1.6. The solid curves and broken lines correspond to the best fit
results and POT weighted averages, respectively. The top and bottom
plots correspond to the FHC and RHC 1Rνµ samples, respectively. . 197
8.29 QE dependence of N 10pvx shape. The distributions are made fromneutron particle gun MC events which are generated by varying QE. 199
8.30 N 10pvx distribution of the data taken at the center position of the
Am/Be calibration. Both the data and MC distributions are normalized by number of prompt events. . . . . . . . . . . . . . . . . . . . 200
8.31 N 10pvx shape of the data taken at the detector center position of
the Am/Be calibration (left) and its ratio to the corresponding MC(right). The shape of the data shown in left panel was obtained bysubtracting scaled accidental background of the background data fromthe N 10pvx distribution shown in Figure 8.30. . . . . . . . . . . . . . 200
8.32 N 10pvx Calculated χ2 by comparing N 10pvx shape between data ad MC(left). The solid curve is fitted χ2 obtained by a least square fit witha quadratic function. Relative number of selected true 2.2 MeV γ
candidates in the primary selection as a function of relative QE withrespect to the default value (right). The error bars are the MC statistical errors. The solid line is obtained by fitting a linear function to thepoints and is used in order to propagate the QE diﬀerence estimatedby the shape fit to the neutron tagging eﬃciency. . . . . . . . . . . . 201
8.33 Distribution of capture time after the primary selection for the three
data taking positions. The top left, top right, bottom correspondto the center, the Z+15 m, and the Y-12 m data taking positions,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.34 Distribution of capture time after the neural network classification
for the three data taking positions. The top left, top right, bottom
correspond to the center, the Z+15 m, and the Y-12 m data taking
positions, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.35 Ratio of the fitted relative eﬃciency between the data and MC. . . . 205
8.36 Dwall of the data taking positions (left) and the assignment of the
Dwall dependent error on the relative eﬃciency (right). In the rightside plot, δεN N is the fractional error of the relative eﬃciency between
the data and MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8.37 Fractional variation in the average tagging eﬃciency for each individual systematic source. The total variations are calculated by adding
each uncertainty in quadrature. The blue and red lines correspond to
the uncertainties of the FHC and RHC 1Rνµ samples, respectively. . 208

xxiv

LIST OF FIGURES

8.38 Tagging eﬃciency as a function of reconstructed muon transverse momentum in comparison with equivalent eﬃciency estimated by GENIE
and NuWro MCs. The bands shows the ±1σ envelope of the total
systematic uncertainty. The left and right figures show the FHC and
RHC 1Rνµ samples, respectively. . . . . . . . . . . . . . . . . . . . . 208
8.39 Averaged neutron tagging eﬃciency of the FHC and RHC 1Rνµ samples in comparison with equivalent eﬃciency estimated by GENIE and
NuWro MCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.40 Measured mean neutron multiplicity as a function of reconstructedmuon transverse momentum for the Run 1-9 FHC and RHC 1Rνµsamples. The left and right figures correspond to the FHC and RHC
samples, respectively. The color bands represent the equivalent expectations which are obtained the NEUT-based MC. The widths ofthe bands correspond to the size of the MC statistical error of the
expectations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8.41 Measured mean neutron multiplicity averaged over reconstructed muontransverse momentum for the Run 1-9 FHC and RHC 1Rνµ samples.
All the observed tagged neutrons and ν events in the 1Rνµ samples
are integrated over Pt before calculating this multiplicity. The color
bands represent the equivalent expectations which are obtained theNEUT-based MC. The widths of the bands correspond to the size of
the MC statistical error of the expectations. . . . . . . . . . . . . . . 212
8.42 Mean neutron multiplicity as a function of reconstructed muon transverse momentum in comparison to the equivalent expectations of theNEUT-, NuWro-, and GENIE-based MCs. The left and right figures
show the FHC and RHC 1Rνµ samples, respectively. . . . . . . . . . 213
8.43 Mean neutron multiplicity averaged over Pt for the Run 1-9 data withthe three diﬀerent expectations. All the observed tagged neutrons andν events in the 1Rνµ sample are integrated over Pt before calculating
the multiplicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.44 Number of neutron captures produced by post-FSI neutrons (blue),
protons (red), π + (yellow), and π − (green) of the 1Rνµ sample. The
left and right corresponds to the FHC and RHC smaples, respectively. 214
8.45 Distribution of reconstructed distance for the Run 1-9 FHC 1Rνµ sample (left) and the Run 1-9 RHC 1Rνµ sample (right). Solid lines
correspond to the nominal MC expectations based on NEUT. Greenenvelops correspond to a ±30 % variations in the Bertini’s total crosssections used for the nucleon SI in GCALOR. Orange envelopes represent the nominal MC expectation with the ±30% variations in the total nucleon SI cross sections and the diﬀerences among NEUT, NuWro,
and GENIE. All the MC distributions are normalized by the Run 1-9
POT. The data are shown with the statistical uncertainties only. . . 216

xxv

LIST OF FIGURES

9.1

9.2

Impact of the observed 40% discrepancy in neutron production to thesensitivity to δCP using the atmospheric neutrinos at Hyper-Kamiokande.
The exposure time is assumed to be five years of one tank of 258 ktonwith a 40% photocoverage. Black lines correspond to the conventional
analysis method developed by the SK collaboration based on reconstructed lepton energy. Magenta lines correspond to the improved
analysis method in which case an energy correction and a better event
selection using tagged neutrons are applied with an assumption of a
70% neutron tagging eﬃciency. White magenta bands represent thesystematic variations in the magenta line due to an overall ±40% error
on neutron production. Solid (Dashed) lines correspond to the casewhere the χ2 is computed assuming normal (inverted) mass hierarchy. The lower (upper) side corresponds to the overall -40% (+40%)
variation in neutron multiplicity. The setting of oscillation parametervalues are as follows: ∆m221 =7.65 ×10−5 eV2 , ∆m232 =2.5 ×10−3 eV2 ,sin2 θ23 =0.575, sin2 θ12 =0.309, sin2 θ13 =0.0219, δCP =4.189 rad, Mass
Hierarchy = normal.
. . . . . . . . . . . . . . . . . . . . . . . . . . 220
Comparison of vertex resolution of n captures between SK and SKGd. In SK, only neutron capture by hydrogen nucleus can happen,
whereas ∼80% of neutrons will be captured by gadolinium in the fullconfiguration of SK-Gd. . . . . . . . . . . . . . . . . . . . . . . . . . 221

A.1 Neutron multiplicity (top) and kinetic energy distribution (bottom).
Left and right correspond to µ− and π − captures on oxygen nucleus, respectively. All the figures are obtained by by generating 5 MeV µ− andπ − . G4MuonMinusCaptureAtRest (G4PiMinusAbsorptionAtRest) isused for the µ− (π − ) capture. . . . . . . . . . . . . . . . . . . . . . . 239
A.2 Distribution of the true distance from ν interaction vertex to neutron
capture vertex before and after the implementation of the µ− and π −capture on 16 O. Left and right figures are for the FHC and RHC 1Rνµsamples, respectively. The distributions are normalized to 1021 POT. 239
B.1 Distributions of the NN input variables before the NN classification(i.e. just after the primary selection) for the Runs 1-9 FHC 1Rνµsample in comparison to the corresponding MC disributions. All the
MC distributions are normalized by the number of observed neutron
candidates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
B.2 Distributions of the NN input variables after the NN classification for
the Runs 1-9 FHC 1Rνµ sample in comparison to the corresponding
MC disributions. All the MC distributions are normalized by the
number of observed tagged neutrons. . . . . . . . . . . . . . . . . . . 242

xxvi

LIST OF FIGURES

B.3 Distributions of the NN input variables before the NN classification(i.e. just after the primary selection) for the Runs 1-9 RHC 1Rνµsample in comparison to the corresponding MC disributions. All the
MC distributions are normalized by the number of observed neutron
candidates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
B.4 Distributions of the NN input variables after the NN classification for
the Runs 1-9 RHC 1Rνµ sample in comparison to the corresponding
MC disributions. All the MC distributions are normalized by the
number of observed tagged neutrons. . . . . . . . . . . . . . . . . . . 244
C.1 Distributions of true neutrino energy for each reconstructed muontransverse momentum of the FHC 1Rνµ sample. The bin edges of thetransverse momentum is summarized in Table 8.13. . . . . . . . . . . 246
C.2 Distributions of true neutrino energy for each reconstructed muontransverse momentum of the RHC 1Rνµ sample. The bin edges of thetransverse momentum is summarized in Table 8.13. . . . . . . . . . . 247

xxvii

List of Tables
1.1
2.1
4.1
5.1
5.2

6.1

6.2

7.1

7.2

Summary of the current measurements of neutrino mixing angles andsquared mass diﬀerences. Values taken from [34] with 2019 update. .

10

The parameters of the machine design of the J-PARC Main Ring forthe fast extraction. [16] . . . . . . . . . . . . . . . . . . . . . . . . . .

29

Summary of MC simulation models used in GCALOR. The energies
are given by kinetic energy. . . . . . . . . . . . . . . . . . . . . . . .

71

Summary of the good spill selection at the far detector for the Run
1-9 data. Numbers taken from [31]. . . . . . . . . . . . . . . . . . .
Accumulated POT of each Run for the Run 1-9 data taking. FHC and
RHC correspond to the ν- and ν̄-modes beam operation, respectively.
The numbers are derived from Table 1 in [31]. . . . . . . . . . . . .

77

87

Neutron tagging eﬃciency and background event rate, which is number of tagged background events per ν event, after the primary selection and after the NN classification, respectively. These numbers
are obtained by using the FHC and RHC 1Rνµ samples which areused for the primary analysis of this thesis. Note that the SK time
variation eﬀects are not included here. The eﬀects will be consideredin Section 6.5, and the corrected numbers can be found in Table 6.2.
Errors represent MC statistical uncertainties. . . . . . . . . . . . . . 110
Tagging eﬃciencies and background event rates with and without thecorrection of the time variation eﬀect. The numbers for the nominal
are same as summarized in Table 6.1. . . . . . . . . . . . . . . . . . 132
Parameters used for calculation of oscillation probabilities. The valuesof ∆m221 and sin2 θ12 are from [35]. The value of sin2 θ13 is from [34].
The values of the other parameters are based on the results of a T2K
neutrino oscillation analysis using the data taken until 2018 [36]. . . . 136
Expected numbers of tagged neutrons Ntag and ν events N1µ passing
each selection stage in comparison to the FHC data taken in Run 1-9.
The expected numbers are normalized by the Run 1-9 POT. . . . . . 144

xxviiiLIST OF TABLES

7.3

7.4

7.5

7.6

7.7

7.8

Expected numbers of tagged neutrons Ntag and ν events N1µ passing
each selection stage in comparison to the RHC data taken in the Run
5-9. The expected numbers are normalized by the Run 5-9 POT. . . 144
Summary of selection eﬃciencies from the FCFV cut for the FHC
1Rνµ sample. Expected numbers are compared to the data taken in
the Run 1-9 data. The errors on the data are binomial statisticalerrors and are calculated by Bayesian approach with a flat prior. . . 145
Summary of selection eﬃciencies from the FCFV cut for the RHC
1Rνµ sample. Expected numbers are compared to the data taken in
the Run 5-9 data. The errors on the data are binomial statisticalerrors and are calculated by Bayesian approach with a flat prior. . . 145
p -values of Dwall, R2 , Z, and combined R2 + Z obtained by the KS,
CVM, AD tests using toy MC for the tagged neutrons of the Run 1-9
FHC and RHC 1Rνµ samples. . . . . . . . . . . . . . . . . . . . . . 153
Summary of the results of the bin log likelihood fit to the capture
time distribution. The expected τ , µS , and µB are obtained from anexperimental result [37], Table 7.2, and Table 7.3, respectively. Itshould be noted that the fitted µS can diﬀer from the expectation,
because this analysis does aim to measure µS itself. . . . . . . . . . . 155
Expected and observed numbers of ν events with tagged neutrons =0, = 1, ≥ 2 and their fractions compared to the Run 1-9 FHC and
RHC data. For the expectation, the backgrounds are included. The
expectations are normalized by the Run 1-9 POT. . . . . . . . . . . 159

8.1
8.2
8.3
8.4

List of parameters which describe uncertainties on neutrino cross sections178
True ν energy binning of the beam fluxes for their systematic parameters.180
π FSI/SI 1 σ parameter sets. . . . . . . . . . . . . . . . . . . . . . . . 182
List of parameters which describe the nucleon final state interactions
in GENIE. Numbers taken from [38]. . . . . . . . . . . . . . . . . . . 184
8.5 Categorization of the 1Rνµ events for the systematic uncertainty on
the detector response. The reconstructed energy is computed as inEquation 7.5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.6 List of nominal values and 1 σ intervals of the parameters used for theoscillation probability calculation. Taken from Table 7 in [36]. . . . . 193
8.7 Fractional change in the total average tagging eﬃciencies for ±1 σvariations of each oscillation parameter. . . . . . . . . . . . . . . . . 193
8.8 Fractional changes in the average neutron tagging eﬃciency due tothe artificial vertex shifts . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.9 POT weighted total average tagging eﬃciency and background rate forthe α = 1.0 and α = 1.6 cases. X represents either tagging eﬃciency
or background event rate. Note that the numbers for α = 1.0 are thesame as listed in Table 6.38. . . . . . . . . . . . . . . . . . . . . . . . 198
8.10 Relative eﬃciency of the Am/Be calibration. εP S and εN N is thefitted neutron tagging eﬃciencies of the primary selection and NNclassification, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 204
xxix

LIST OF TABLES

8.11 Summary of fractional uncertainty of the average neuron tagging efficiency for each individual systematic source. All the estimations ofthses numbers are detailed in Sections 8.3.2- 8.3.12. . . . . . . . . . 207
8.12 Summary of the numbers used to calculate the measured mean neutron
multiplicities. The numbers for All Pt are used to compute the mean
neutron multiplicity averaged over Pt . Note that Ntag and N1µ are theresults of the Run 1-9 observation. The background event rate b is thesame value as summarized in Table 6.2 . . . . . . . . . . . . . . . . . 210
8.13 Summary of the measured mean neutron multiplicities of the Run 1-9
data in comparison to the expected numbers. For the expected numbers which are derived from the NEUT-based MC, the errors are theMC statistical uncertainties. For the data results, the first errors andsecond errors represent the statistical and systematic uncertainties,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
9.1

Summary of the number of neutrino events and tagged neutrons for
the Runs 1-9 POT with the following oscillation parameter values:∆m221 =7.53 ×10−5 eV2 , ∆m232 =2.452 ×10−3 eV2 , sin2 θ23 =0.532, sin2 θ13 =0.0212,
δCP =-1.885, Mass Hierarchy = normal. All the expectations are normalized to the Run 1-9 POT. . . . . . . . . . . . . . . . . . . . . . . 218

1

Chapter 1
Introduction
In the universe neutrinos are the second most dominant particles and their nature
has not been fully understood yet. The remains of the unknown natures are notdue to lack of study, but instead because of the significant feature of neutrinos thatthey interact extremely weakly with other particles. Although this feature still keeps
neutrinos mysterious, it allows neutrinos to deliver unique information about theuniverse to us, which can not be obtained from other particles. In order to address
such information, first of all neutrino interactions with matter need to be understood
well.
This chapter begins with a brief history of neutrinos. Following this, neutrino
oscillations and supernova relic neutrinos are described, which motivates the primary
analysis of this thesis. Then, neutrons associated with neutrino interactions in water
are introduced, and the motivation of the primary analysis and a thesis overview are
given.

1.1

Neutrino physics

Neutrinos are accommodated by the Standard Model of particle physics that describes the fundamental forces between particles, except for the gravitational forces,
and the elementary particles. In the original Standard Model, neutrinos are described as spin 1/2 massless Dirac fermions and have three flavors: νe , νµ , and ντ .
Each neutrino flavor has an associated charged lepton, which forms the three lepton
generations, and electron, muon, and tau correspond to the first, second, and third
generations, respectively. Neutrinos only interact with other particle via the weakinteraction which separately conserves each generation’s lepton number.

1.1.1

A brief history of neutrino physics

Neutrinos were originally postulated as “neutrons” by W. Pauli in 1930 [39] to remedy an apparent violation of energy conservation observed in β-decay. The modern
neutron was discovered by J. Chadwick in 1932. In 1934, a theory of β-decay inwhich the neutrinos proposed by Pauli are included was developed by E. Fermi.
However, it took another 22 years to prove the existence of neutrinos suggested by
2

CHAPTER 1. INTRODUCTION

Palui and Fermi. The first detection of neutrinos was made by C. Cowen and F.
Reins in 1956 [40] and they detected ν¯e produced in a nuclear reactor via inverse βdecay. Three years later, R. Davis and S. Harmer reported that νe and ν̄e are distinct
particles [41].
In late 1950s, the Fermi’s theory, which included only the vector component of
the weak interaction, was modified. In 1956, T. Lee and C. Yang suggested that theparity of the weak interaction is not conserved [42]. Indeed, the parity violation was
experimentally confirmed by C. Wu [43] and other experimentalists [44] in 1957. In
1958, M. Goldhaber et al. proved that neutrinos are always emitted with the same
helicity from the electron capture processes [45]. In order to account for these experimental results, V-A theory was proposed by Sudarshan and Marshak, Feynman
and Gell-Mann [46, 47] in 1958.
In the original V-A theory only one species of neutrino had been recognized, andonly distinction was made between neutrinos and antineutrinos (i.e. νe and ν̄e ). In
1962, the AGS experiment at Brookhaven National Laboratory generated the firstneutrino beam, and observed a second type of neutrino, the muon neutrino νµ , bydetecting muons produced in νµ Charged-Current (CC) interactions [48].
In the late 1960s, the electroweak theory was established by A. Salam, S. Glashow
and S. Weinberg [49, 50, 51]. The electroweak theory is combined with the Quantum
Chromodynamics theory [52, 53], and the combined theory is known as “the Standard Model” of particle physics today. In the Standard Model, three gauge bosons,
W ± and Z 0 , which are the mediators of the weak interaction, are predicted. Interactions which are accompanied by the W ± bosons are regarded as CC interactions,whereas Neutral-Current (NC) interactions are interactions in which Z 0 boson is involved as the mediator. Figure 1.1 shows the vertices of CC and NC interactions.
Electron neutrinos and muon neutrinos were observed via CC interactions, and NC
interactions had never been observed before 1973. In 1973, the Gargamelle bubble
chamber at CERN confirmed the existence of NC interactions.

(a) Charged Current interaction(b) Neutral Current interaction

Figure 1.1: Feynman diagrams of neutrino interaction vertices
When the third charged lepton, τ , was discovered at SLAC in 1975 [54], a third
generation of neutrino, ντ , was expected to exist. In 1989, the number of neutrino generations which are lighter than half the mass of Z 0 boson was determined3

CHAPTER 1. INTRODUCTION

to be three by the Mark II experiment at the SLC [55] and other experiments at
LEP [56, 57, 58], and existence of ντ was strongly indicated. Finally ντ was discovered by the DONUT experiment at Fermilab in 2001 [59].
These results established the nature of neutrinos as the particles of the Standard
Model; In the Standard Model, νe , νµ , and ντ are neutral left-handed fermions, interact with matter only by the weak interactions, and are massless. However, thediscovery of neutrino oscillation showed that neutrinos do have non-zero mass.
History of neutrino oscillation is very closely related to the “solar neutrino problem”. However, neutrino oscillation was discovered by the observation of the atmospheric neutrinos.
The first indication of neutrino oscillation came from this problem. It was thoughtthat neutrinos might be utilized to probe environments in which other particles can
not penetrate. An attempt was made by R. Davis and J. Bahcall to study nuclear
reactions occurring in the sun and test Bahcall’s solar model, which is referred to as
the standard solar model. To this aim, in 1968 Davis measured the electron neutrino
flux from the sun at Homestake [60], and the observed flux was about three timesmaller than the prediction of the standard solar model [61]. It was suspected thateither there was a problem with the model or a problem with the measurement basedon this discrepancy. However, in 1989 Kamikande [62] also observed a deficit of electron neutrino flux compared to the solar model with a direction information, which
was consistent with the Homestake observation. The directional information which
was unavailable at the Homestake experiment proved that electron neutrinos definitely come from the sun, but the measured flux was still smaller than the prediction.
Observations of helioseismology showed agreement with the solar model’s predictions
by the early 1990s, whereas results from SAGE [63], GALLEX [64], and GNO [65]neutrino experiments still showed consistent results with the Homestake experiment.
The answer to this solar neutrino problem was provided by Super-Kamiokande [66]and SNO [67]. Super-kamiokande precisely measured the flux of 8 B solar neutrinos
only for the elastic scattering (ES) reaction by using a water target in 1998. In 2001,
SNO detected all the three interactions, CC, ES, and NC, using a heavy water target
to measure the total flux of 8 B solar neutrinos. The measured total flux by SNO withthe constraint on ES from Superk-Kamiokande was consistent with the prediction of
the standard solar model. Also, SNO translated the measured fluxes of CC, ES, andNC interactions into the flux of νµ and ντ under hypothesis of neutrino oscillations.
The resultant flux of νµ and ντ was above 5.3 σ from zero, which corresponds totransition between flavors.
The first observation of neutrino oscillations was obtained from atmospheric neutrinos. When primary cosmic rays, mostly protons, interact with nuclei in the atmosphere, (anti) muon and electron neutrinos are produced dominantly by pion andmuon decays. A flux ratio of (νµ + ν̄µ )/(νe + ν̄e ) is expected to be ∼2 around at
1 GeV of neutrino energies. However, Kamiokande observed about two times smaller
than the expectation [68, 69]. Similar results were also reported by the IMB [70] andSoudan-2 experiments [71]. In 1998, Super-Kamiokande [72] measured zenith angle
dependent fluxes of νe + ν̄e and νµ + ν̄µ separately. The zenith angle is a good proxy4

CHAPTER 1. INTRODUCTIONof the distance that an incoming neutrino has traveled from its generation point.
As will be described later, neutrino oscillation depends on the distance, and thus
the zenith angle dependent fluxes are suitable to study neutrino oscillation. Boththe observed electron neutrino and muon neutrino fluxes were consistent with the
hypothesis of νµ → ντ oscillation, which became the discovery of neutrino oscillation.
In 2006, the νµ → ντ oscillation was supported by the K2K long baseline neutrino
experiment which used a muon neutrino beam [73]. K2K observed a deficit of thebeam muon neutrinos, which is consistent with the observation of the atmospheric
neutrinos by SK. Both SK and K2K observed the deficits of muon neutrinos by detecting muon neutrinos. Direct observation of νµ → ντ was made by OPERA [74] in
2014.

1.1.2

Neutrino oscillations

Neutrino oscillation was originally proposed by B. Pontecorvo in a context of ν ν̄ oscillations in 1957 [75] although such oscillation has never been observed. In
1962, a full theory of two flavor oscillations was developed by Maki, Nakagawa and
Sakata [76]. In the following, the standard three flavor neutrino oscillations aredescribed.
The formalization of the theory of neutrino oscillations is built on the fact thatthe flavor eigenstates of the weak interaction, |να ⟩ (α=e,µ,τ ), are diﬀerent from themass eigenstates, |νi ⟩ (i=1,2,3). The flavor eigenstates in which neutrinos are always
created are related to the mass eigenstates that neutrinos propagate as:|να ⟩ =3∑∗Uαi
|νi ⟩,(1.1.1)i=1where Uαi are the elements of the 3×3 unitary matrix referred to as the PontecorvoMaki-Nakagawa-Sakata (PMNS) or Maki-Nakagawa-Sakata (MNS) matrix. In themodern parametrization [77], the matrix can be expressed in terms of four matricesas:
Ue1 Ue2 Ue3
U = Uµ1 Uµ2 Uµ3 Uτ 1 Uτ 2 Uτ 3




c13
0 s13 e−iδCPc12 s12 0100αα −s12 c12 0 × diag(1, ei 221 , ei 231 ),010= 0 c23 s23  
0 −s23 c23
0
0 1−s13 eiδCP 0
c13(1.1.2)where cij =cos θij and sij =sin θij . The U is parameterized by three mixing angles (θ12 ,5

CHAPTER 1. INTRODUCTION

θ23 , θ13 ), a Dirac CP-violating phase (δCP ), and two Majorana CP-violating phases(α21 ,α31 ), where CP stands for charge-parity. The Majorana CP-violating phases or
the last matrix in the equation have physical meaning only if neutrinos are Majorana
particle whose antiparticle is its own particle. It has not been shown whether or
not neutrinos are Majorana particles yet. Whilst the Majorana nature of neutrinos
is unknown, the Majorana CP-violating phases do not aﬀect neutrino oscillation
probability that can be studied experimentally since this probability depends on
U ∗ U , in which case these phases are cancelled out.
Neutrino oscillations in vacuum
Neutrinos experimentally observed are created as the flavor states. Consider the time
evolution of a neutrino which is produced in a flavor state |να ⟩, in vacuum. Using
the relation between the flavor eigenstates and the mass eigenstates, the state of theneutrino propagating in vacuum after time t, |να (t)⟩, can be written as (in naturalunits where c and ℏ are set to 1):|να (t)⟩ = e−iĤt |να ⟩∑ −iE t ∗=e i Uαi |νi ⟩,(1.1.3)iwhere Ĥ is the free particle Hamiltonian, Ei is the total energy of i-th mass state.
The transition probability to flavor state |νβ ⟩ at time t is given as:
P (να → νβ ) = |⟨νβ |να (t)⟩|2∑ ∗∗ −i(Ei −Ej )t=
Uβi Uβi Uαj Uβje.

(1.1.4)i,j

In the ultra-relativistic limit as is the case in neutrino oscillation experiments, thefollowing approximation can be done:
√
√
∆m2ij
2
2
,
Ei − Ej = pi + mi − p2ȷ + m2j ≈2E(1.1.5)where mi is the mass of i-th mass eigenstate, E = |p| is the neutrino energy in whichcase dependence of pk and pℓ is neglected, p is the neutrino momentum, and∆m2ij = m2i − m2j .

(1.1.6)

Also, in this case the approximation t ≈ L is applicable, where L is the distance6

CHAPTER 1. INTRODUCTION

that the neutrino traveled from its creation point. The transition probability can be
written in terms of the neutrino energy E and the propagation length L:

P (να → νβ ) =∑∆m2ij L∗∗Uαi Uβi Uαj Uβj exp(−i
).
2E

i,j

(1.1.7)It may be instructive to express this as follows:

P (να → νβ ) = δαβ − 4
+2

∑

[ ∗
] 2 ∆m2ij L∗
Re UαiUβi Uαj Uβj
sin (
)
4E
i>j

∑

[ ∗
]
∆m2ij L∗Im UαiUβi Uαj Uβj
sin(
).
2E
i>j

(1.1.8)From the above equation and Equation 1.1.2, it can be seen that the probability canbe described by the three mixing angles, the CP-violating phase δCP , and the squared
mass diﬀerences. In addition, the probability varies
periodicallywith a phase which
[
]
2

∆m L

2

is proportional to ∆m2ij L/E (≃ 1.27 × Eij eVGeVkm in SI units), by which thephenomenon of this transition between flavor eigenstates is referred to as neutrino
oscillation. It is worth noting that oscillations between diﬀerent flavor eigenstates canhappen only if the following two conditions are satisfied. One of the two condition isthat the mixing matrix U is not diagonal, which means that the flavor eigenstates are
diﬀerent from the mass eigenstates. The other one is that at least one of the masses
is diﬀerent from others. Therefore, existence of neutrino oscillations is regarded as
evidence of non-zero mass of neutrino.
For antineutrinos, the relation between the flavor and mass eigenstates is givenas:|ν̄α ⟩ =3∑

Uαi |ν̄i ⟩.

(1.1.9)i=1

By following the same procedure as neutrinos, the oscillation probability is obtained
as follows:

P (ν̄α → ν̄β ) = δαβ − 4

∑

Re

[

i>j

∑

∗
∗
Uαi
Uβi Uαj Uβj]∆m2ij L
sin (
)
4E
2

]
[ ∗
∆m2ij L∗−2
Im Uαi Uβi Uαj Uβj sin(
).
2E
i>j

(1.1.10)The only diﬀerence between neutrinos and antineutrinos can be seen in the sign of7

CHAPTER 1. INTRODUCTION

the third term from the above equation and Equation 1.1.10. If α=β, the product,∗∗
Uαi
Uβi Uαj Uβj, becomes a real number. Thus, P (να → νβ ) = P (ν̄α → ν̄β ) since
the third term vanishes. On the one hand, for α ̸= β, oscillation probability diﬀers
between neutrinos and antineutrinos unless δCP = 0 or π. Therefore, the value ofδCP can be studied only via transition between diﬀerent flavors (called “neutrino
appearance”).
As will be discussed later, it is practically suﬃcient to consider two flavor oscillations in many cases. The mixing matrix defined in Equation 1.1.2 reduces to a single
rotation matrix as follows:(U=)
cos θ sin θ.
− sin θ cos θ(1.1.11)

Accordingly, the oscillation probability given by Equation 1.1.8 reduces to()
2
1 − sin2 2θ sin2 1.27∆m L(α = β)E()
P (να → νβ ) =.
2
sin2 2θ sin2 1.27∆m L
(α =
̸ β)
E

(1.1.12)

Neutrino oscillations in matter
When neutrinos propagate a dense matter such as the Sun and the Earth, the neutrino oscillation probability in vacuum is modified since they can interact with thematter via the weak interactions. This eﬀect is known to be Mikheyev-SmirnovWolfenstein (MSW) eﬀect [78, 79].
Propagation of neutrinos in matter is aﬀected by eﬀective potentials due to theforward CC and NC interactions. Since the NC interaction is independent on neutrino flavor, the resultant eﬀect of the NC reaction is a common phase factor among
the flavor states, and does not aﬀect the vacuum oscillation probability. However,since only electrons and not muons and taus are contained in ordinary matter, theCC interaction aﬀects electron neutrinos, whereas the other neutrino flavors do notundergo the interaction. This asymmetry introduces an additional potential VCC
which aﬀects only electron neutrinos:√
VCC = ± 2GF ne ,(1.1.13)

where GF is the Fermi coupling constant and ne is the number density of electrons in
the matter. In the equation, the positive and negative signs are applied to neutrinos
8CHAPTER 1. INTRODUCTION

and antineutrinos, respectively.
In order to see how the matter eﬀect modifies the vacuum oscillation probability,
for simplicity, consider a case of two flavor oscillations between νe and νx in a constantmatter, where νx is either νµ or ντ . In this case, the oscillation probabilities of P (νe →νx ) and P (νe → νe ) are obtained by replacing ∆m2 and sin2 θ in Equation 1.1.12
with ∆m2M and sin2 θM , respectively. ∆m2M and sin2 θM are given as:
sin 2θ
sin 2θM = √sin2 2θ + (cos 2θ − A/∆m2 )2√22∆mM = ∆m sin2 2θ + (cos 2θ − A/∆m2 )2 ,(1.1.14)(1.1.15)√
where A = 2 2GF ne E. Note that for A → 0, sin 2θM and ∆m2M reduce to thevacuum ones. From the above equation, it can be seen that the mixing angle andmass splitting are changed from the vacuum case by the matter eﬀect.
Thanks to the matter eﬀect, maximal mixing, sin θM = 1, can occur even for avery small vacuum mixing angle if the resonance condition is satisfied:cos 2θ =A.
∆m2(1.1.16)

It is worth noting that the sign of A depends on neutrinos or antineutrinos. In
addition, the condition is sensitive to the sign of ∆m2 . Therefore, for positive valueof cos 2θ, the resonance eﬀect only happens for neutrinos if ∆m2 > 0, whereas it only
happens for antineutrinos if ∆m2 < 0. In other words, the resonance eﬀect can beutilized to determine the sign of ∆m2 .
A full treatment of the matter eﬀect within three flavor oscillations can be seenin [80].
Experimental status of neutrino oscillation parameters
The mixing angles θ12 , θ13 , θ23 , the Dirac CP-violating phase δCP , and the neutrino
masses of the Standard Model need to be determined experimentally. Neutrinos oscillation experiments are sensitive to the angles, the phase, and the squared massdiﬀerences ∆m221 and ∆m232 . Table 1.1 summarizes the current measurement resultsfrom various experiments. In the table, Normal hierarchy (NH) and Inverted hierarchy (IH) refer the ordering of neutrino eigen masses:

NH : m3 > m2 > m1 ,IH : m2 > m1 > m3 .

9

CHAPTER 1. INTRODUCTION
Table 1.1: Summary of the current measurements of neutrino mixing angles andsquared mass diﬀerences. Values taken from [34] with 2019 update.
ParameterValuesin2 θ21

0.307±0.013

sin2 θ13(2.18±0.07)×10−2

sin2 θ23

0.536+0.023−0.028 (IH)+0.0190.512−0.022 (NH)0.542+0.019−0.022 (NH)∆m212

(7.53±0.18)×10−5 eV2∆m223(−2.55±0.04)×10−3 eV2 (IH)
(2.444±0.034)×10−3 eV2 (NH)In reality, the relation, |∆m223 | >> ∆m221 , is hold as shown in the table. Since
the oscillation periods of neutrino oscillation probability depend on ∆m2ij L/E, only
oscillation parameters of interest can be studied experimentally by choosing relevantbaseline L and neutrino energy E through the leading oscillation eﬀect. In such case,the two flavor oscillations can be adopted, and a set of relevant mixing angle andsquare mass diﬀerence is extracted according to Equation 1.1.12.
In the following, the past and current neutrino oscillation experiments are briefly
summarized.
θ12 , ∆m212 :These parameters are related to the solar neutrino oscillations and havebeen measured by solar neutrino experiments[64, 65, 63, 81, 23, 82]. The
preferred solution by these experiments, so called LMA solution [83], wasconfirmed by the KamLAND experiment [84], which uses a liquid scintillator to detect ν̄e produced in distant nuclear reactors.

θ23 , |∆m223 |:Atmospheric neutrinos and accelerator neutrinos are sensitive to theseparameters. SK [85] and IceCube [86] have used atmospheric neutrinos
while T2K [87, 88, 89], NovA [90, 91, 92], K2K [73], and MINOS [93] uses
accelerator based neutrinos.

θ13 , ∆m2ee :10CHAPTER 1. INTRODUCTION

In 2011, the first indication of non-zero value of θ13 was reported by
T2K [94] which uses artificial νµ and ν̄µ beams. Non-zero value of θ13
was measured in 2012 by nuclear reactor oscillation experiments: Daya
Bay [95], RENO [96], and Double Chooz [97]. T2K also measured nonzero θ13 with a significance of more than 7 σ in 2014 [98]. In these reactor
experiments, two neutrino mass splitting |∆m231 | and |∆m232 | needs to betaken into account, and these mass splitting can be studied via an eﬀectivesquared mass diﬀerence: ∆m2ee ≃ cos2 θ12 |∆m231 | + sin2 θ12 |∆m232 |.

δCP :The value has not been precisely measured yet so far and been still largely
unknown. From an experimental point of view, measurements of νµ → νeand ν̄µ → ν̄e oscillations are the only possible way to study the parameter. T2K and NOνA which are ongoing experiments are designed to besensitive to the parameter.
Importance of precision measurement of remaining neutrino oscillation
parameters
Neutrino oscillations have been studied and related parameters have been measured
by many experiments. However, the value of δCP , mass hierarchy (MH), and theoctant of θ23 have not been understood yet.
One of questions which can not be answered by the Standard Model is the imbalance of matter (baryon) and antimatter (antibaryon) in the universe. To explain thisasymmetry, in 1967 A. Sakharov proposed a set of three necessary conditions, one ofwhich requires that in a theory both C- and CP-symmetries are violated [99]. The
Standard Model contains such CP violation in the Cabbibo-Kobayashi-Masakawa(CKM) matrix [100, 101], which describes mixing between up- and down-type quarks.
In the quark sector, the first CP violation was observed in measons via neutral K decays [102], and recently CP violation in baryons was discovered [103]. However, it is
known that these observations of CP violation within the framework of the Standard
Model are not suﬃcient to account for the matter and antimatter asymmetry, which
naturally requires there be a theoretical model “beyond the Standard Model”. Froma theoretical point of view, non-zero value of δCP would motivate a model, which
includes a heavy right-handed Majorana neutrino, has oﬀered a scenario called “leptogenesis” [104]. In leptogenesis, first a lepton asymmetry is generated by the heavy
neutrino decays if CP violation exists in the lepton sector, and the lepton asymmetry turns into the observed baryon asymmetry. Therefore, measurement of δCP isimportant to understand the matter-antimatter asymmetry.
Thanks to relatively large value of θ13 , a possibility for probing δCP has been
opened. Among the current generation of neutrino oscillation experiments, T2K
and NOvA have ability to study δCP . In 2019, T2K reported an indication of near11

CHAPTER 1. INTRODUCTION

maximal violation by excluding δCP = 0 with a significance of 3 σ [1] as shown in
Figure 1.2. On the other hand, however, the NOvA’s best estimation of δCP prefers
CP conservation although statistical significance is very weak [105].

Figure 1.2: Experimental constraints on δCP , sin2 θ13 , and sin2 θ23 by T2K. 2D confidence intervals for δCP vs sin2 θ13 for NH (top), 2D confidence intervals for δCP vssin2 θ23 with reactor constraint for NH (middle), 1D confidence intervals on δCP withreactor constraint for both NH and IH (bottom). In the bottom figure, the error
bars represent 3 σ allowed regions. Figure taken from [1].
Although the theoretical framework of mixing is similar between the neutrino andquark sectors, the matrix elements are very diﬀerent between the CKM and PMNS
matrices. Figure 1.3 visualizes the matrix elements of the two matrices, and clear
diﬀerence can be seen. To account for this diﬀerence, theoretical models have been
built [106, 107, 108, 109].

12

CHAPTER 1. INTRODUCTION

Figure 1.3: Size of matrix elements for the CKM matrix (left) and the PMNS matrix(right). Figure taken from [2].
In addition, from a theoretical point of view, understanding of the correct MH
together with the neutrino mixing would provide information about how the neutrino
mixing and masses are generated [110]. Thus, it is important to know the correct
MH and the octant of θ23 as well as δCP . T2K, NOvA, and Super-Kamiokande aresensitive to MH due to the Earth’s matter eﬀect. Although statistical significanceis still not suﬃcient, all the three experiments prefer NH. For the octant of θ23 ,in both T2K and NOvA, the probabilities of νµ → νe and ν̄µ → ν̄e oscillations(called “bi-probability”) can be sensitive to a term which is proportional to sin 2θ23 .
Measurements of bi-probability distinguishes between the lower octant (θ23 < 45◦ )and the upper octant (θ23 > 45◦ ). NOvA has weakly preferred the upper octant witha significance of 1.6 σ by comparing observed electron appearance events between
the ν- and ν̄- modes of the beam neutrinos [105]. Figure 1.4 shows the measurement
results by NOvA.

13

CHAPTER 1. INTRODUCTION

Figure 1.4: Probabilities of νµ → νe and ν̄µ → ν̄e oscillations for the NOvA experiment’s setup (left) and the observed electron appearance events for the ν- andν̄-beam operations (right). Figure taken from [3].

1.1.3Supernova Relic Neutrinos

Neutrinos have oﬀered themself as a probe to study the universe since the detection of the neutrinos [111, 112] from SN1987A, which is a core collapse supernova
that occurred in the Large Magellanic Cloud. When the evolution of stars withmass of M ≳ 8M⊙ reach to the final stages, core collapse supernovae eventuallyoccur, which releases typical energies of O(1053 ) ergs. Since ∼99 % of the released
energy is carried away as neutrino burst during a core-collapse explosion, detecting
and studying these neutrinos experimentally may provide vital information to understand the mechanism of supernova explosion. Although the neutrino burst provides
unique and interesting information, there has been no neutrino burst detected since
SN1987, because expected supernova explosion rate in our galaxy is very small, ≲ 3
per century [113, 114]. However, neutrinos emitted from all the past core-collapse
supernovae should still exist at present because of the fact that neutrinos only weaklyinteract with matter. Indeed, flux of such neutrinos has been theoretically predicted
and these neutrinos are called “supernova relic neutrinos” (SRN) and are referred toas “diﬀuse supernova neutrino background” (DSNB). Detailed experimental studies
on SRN would provide information about the evolution of the universe.
The SRN flux is a superposition of each of all the past supernovae by taking into
account the redshift eﬀect by the expansion of the universe and the cosmochemical
evolution. The diﬀerential SRN flux with respect to energies of SRN at the Earth isgiven by [115, 116]:

14

CHAPTER 1. INTRODUCTION

dϕ
=c
dEν

∫ ∞
RSN (z)(1 + z)
0dN (Eν′ ) dt
dz,
dEν
dz

(1.1.17)

where RSN is the core-collapse supernova rate at redshift z, Eν′ is defined as Eν (1+z),
and dN (Eν′ )/dEν is the number spectrum emitted by one supernova explosion, wherea neutrino received at energy Eν was emitted at a higher energy Eν′ . The cosmic
time t is related to the redshift z by Friedmann equation as follows:√dz= −H0 (1 + z) Ωm (1 + z)3 + ΩΛ ,dt

(1.1.18)

where H0 is the Hubble constant, Ωm and ΩΛ are the cosmic matter density andcosmological constant, respectively.
From an experimental point of view, large water Cherenkov detector is suitable to study SRN. Since typical average energy of SRN ranges from ∼10 MeV to∼20 MeV [117, 118], SRN interacts with water via various reaction channels:

Inverse β decay (IBD): ν̄e + p(free) → e+ + n
Electron elastic scattering: νe + e− → ν + e−
CC interaction with oxygen: νe +16 O → e− +16 F , ν̄e +16 O → e+ +16 N
NC interaction with oxygen: νx +16 O → νx + γ + X,

where x denotes all neutrino flavors (e, µ, τ ) and X represents residual nuclei. Figure 1.5 shows the cross-sections for these interaction channels as a function of neutrino energy. As shown in the figure, the cross section of IBD is almost two orders ofmagnitude larger than those of the other reactions below 30 MeV. Therefore, SRN isdominantly detected through the IBD reaction.

15

CHAPTER 1. INTRODUCTION

Figure 1.5: Eﬀective cross section for SRN and water, which includes energy resolution and detector threshold eﬀect based on Super-Kamiokand II. Figure takenfrom [4].
Present status of SRN searches
There have been many experimental SRN searches [119, 120]. However, SRN has
never been observed. Super-Kamiokande [121, 122] and KamLAND [123] have set
stringent upper limits on the SRN flux. Figure 1.6 shows a SRN flux prediction
in comparison with the experimental limits. Although SRN flux prediction depends on theoretical model or assumption, the current experimental limits are close
to prediction. Future experiments such as SK-Gd [124], Hyper-Kamiokande [125],
JUNO [126], the Jinping neutrino experiment [127] may reach to various predictions,and thus aim to discover SRN.

Figure 1.6: Experimental limits on SRN flux at 90% C.L. with flux predictions.
Figure taken from [5].

16CHAPTER 1. INTRODUCTION

1.2

Neutrons associated with ν-nucleus interactions on water

Neutrons associated with neutrino interactions on water target are expected to be ofvalue to various important physics analyses: measurement of neutrino oscillations,
SRN searches, and nucleon decay searches. It has also been suggested that information about these neutrons will improve neutrino oscillation analyses [128]. Indeed, innear future experiments employing water Cherenkov detectors such as SK-Gd [124]and Hyper-Kamiokande [125], utilization of such neutrons are planned in order toimprove their physics analyses.
In this section, production of neutrons related to ν interactions on water target
is outlined. Following this, benefits to physics analyses are described, and the current status of experimental studies on neutrons associated with ν interactions are
overviewed, which emphasises the importance of the primary analysis presented inthis thesis.

1.2.1

Neutron productions

Figure 1.7: A schematic drawing of neutron productions by primary ν̄-nucleon interaction inside oxygen nucleus, hadronic-final-state interactions inside the nucleus,
and hadronic secondary interactions in water. In this case, the primary reaction
ν̄ℓ + p → ℓ+ + n + π − is used.
When a neutrino interaction happens in water, the interaction often produce one ormore neutrons. These neutrons are produced via three processes:• Primary ν-nucleon interaction in nuclear medium,- e.g. ν̄ℓ + p → ℓ+ + n• Hadronic final-state-interaction (FSI) inside the target nucleus.
- e.g. p + p → p + n + π +17

CHAPTER 1. INTRODUCTION• Hadronic secondary interaction (SI) in water.
- e.g. n +16 O → n + n +15 O∗

Figure 1.7 shows a schematic drawing of neutron production by these three processes.
These neutrons are quickly thermalized and then are captured by hydrogen nucleus,
after which single 2.2 MeV γ ray is produced. By detecting this γ ray, the T2K far
detector can tag neutrons of any energy. Details of the neutron tagging at the far
detector will be described in Chapter 6.
For neutrino energies from sub-GeV up to several GeV, neutrinos scatter oﬀ a nucleon inside the target nucleus via various reaction channels. The resultant number ofneutrons produced in the primary ν-nucleon interaction depends on interaction channel and whether it is neutrino or antineutrino. In the primary interaction, hadrons
such as protons and charged pions as well as neutrons are also produced inside thetarget nucleus, and these hadrons have a considerable probability to undergo interaction inside the nucleus before they escape from it. This hadronic interaction
inside nucleus is referred to as Hadronic final-state-interaction (FSI). After leaving
the target nucleus, they propagate across the detector volume of an experiment, andthey can interact with the detector’s medium, which is known as hadronic secondaryinteraction (SI).

Figure 1.8: An example of neutron multiplicity using true CCQE ν (cyan) andν̄ (orange) interactions in water. The left, middle, right correspond to neutron
multiplicities after primary interaction, after FSI, and after SI, respectively. T2K
beam neutrino flux is assumed.
Figure 1.8 shows an example of contribution from each process to neutron multiplicity in case of Charged Current quasi-elastic (CCQE) neutrino and anti-neutrino
interactions on water target. In this case, neutrinos produce a proton, whereas antineutrinos produce a neutron as follows:νℓ + n → ℓ− + p(1.2.1)ν̄ℓ + p → ℓ+ + n.

(1.2.2)18

CHAPTER 1. INTRODUCTION

The outgoing nucleons undergo FSI by they leave the target nucleus, and additional
neutrons can be produced even for protons. For instance, a proton’s FSI can produce
a neutron via a single-pion production reaction: p + p → p + n + π + . As anotherexample, a π − produced by a single-pion production reaction of a neutron’s FSI isoften absorbed by a nucleon pair before it escapes from the nucleus, and the absorption can produce multiple neutrons. Due to the eﬀects of FSI, neutron multiplicity
is modified after FSI from that of the primary interaction as shown in the middle
panel of the figure. Once particles produced in both the primary ν interaction and
FSI leave the target nucleus, they undergo SI in water when propagating throughthe detector. In case of SI, negative muons produced in the primary neutrino interactions also contribute to the neutron production since these muons lose energies
and are eventually captured on nuclei if they do not decay. As a consequence of SI,
neutrons are further produced, which is illustrated in the right panel of Figure 1.8.

1.2.2

Benefits of utilization of neutrons

As explained above, the eﬀects of FSI and SI largely modify the neutron multiplicityof the primary ν interaction. However, neutron multiplicity is still clearly diﬀerent
between neutrinos and antineutrinos even after FSI and SI. This diﬀerence, for instance, can be exploited to distinguish between neutrinos and antineutrons. Since
water Cherenkov detectors are not magnetized (or can not be magnetized due topresence of photosensors), it is diﬃcult to perform a ν-ν̄ separation although thisis very important in order to improve sensitivities to the MH determination andδCP measurement. Similar diﬀerence in neutron multiplicity is also seen between
CC interactions and NC interactions as shown in Figure 1.9, which is expected to
be useful to reject one of main backgrounds for the MH determination by using theatmospheric neutrinos at SK.

Figure 1.9: Distribution of tagged neutron multiplicity for diﬀerent ν interaction
channels in the SK atmospheric multi-GeV e-like sample assuming a 70% tagging efficiency, which corresponds to the full configuration of SK-Gd. Figure taken from [6].

19CHAPTER 1. INTRODUCTION

Another way to utilize neutrons is about an improved energy estimation of neutrinos. It is desirable to reconstruct energies of neutrinos as precise as possible forany measurements of neutrino oscillations, because eﬀects of neutrino oscillations
depend on neutrino energy. In a water Cherenkov detector, only charged leptons
and pions produced in ν interactions can be detected for most cases, and the energy
which is transferred to the hadonic system at the primary ν interaction can not be
seen. The resultant reconstructed neutrino energy is therefore highly biased, whichsmears eﬀects of neutrino oscillations. Since the number of neutrons produced in FSI
and SI are correlated with the unseen energy, estimate of neutrino energy is expected
to be improved by counting these neutrons. Potential of such energy reconstruction
has been studied in the context of the atmospheric neutrino analyses at SK-Gd [7].
Figure 1.10 demonstrates a significant improvement on the energy reconstruction of
the atmospheric neutrinos. This idea can be applied to the atmospheric neutrino
oscillation analyses in Hyper-Kamiokande, and a large improvement on the sensitivities to the δCP measurement and the MH determination has been expected as shownin Figure 1.11.

Figure 1.10: An example of MC simulation study on energy correction by counting
number of tagged neutrons for the atmospheric neutrino samples in case of the SKGd’s full configuration, in which a 70% neutron tagging eﬃciency is expected to beachieved. Green colored histograms represent true neutrino energies. Red and bluelines correspond to lepton energies and corrected lepton energies by counting thenumber of tagged neutrons, respectively. Figure taken from [7].

20CHAPTER 1. INTRODUCTION

Figure 1.11: Sensitivities to δCP assuming true normal MH (right) and wrong MH rejection as a function of true sin2 θ23 for the atmospheric neutrino oscillation analyses
at Hyper-Kamiokande. Black lines correspond to the conventional analysis method
developed by the SK collaboration based on lepton energy. Magenta lines correspondto the improved analysis method in which case an energy correction and a better
event selection using tagged neutrons are applied with an assumption of a 70% neutron tagging eﬃciency. Estimation for systematic uncertainties regarding neutron
tagging (but, very rough) is taken into account for the magenta lines. Figure takenfrom [7].
Neutrons can also be utilized for neutrino astronomy and an improvement is expected in searching for SRN. As was mentioned in Section 1.1.3, IBD is the signal
reaction of SRN in a water Cherenkov detector, and it can be eﬃciently identified
by employing a coincidence of the prompt signal of e+ and the delayed signal ofn. In practice, this coincidence is made by requiring one tagged neutron for eachreconstructed prompt event. To obtain an insight into an early stage of the universe,
region of neutrino energies used for SRN search needs to be lowered as much as
possible as shown in Figure 1.12. One of main background sources is produced byatmospheric neutrinos via NC quasi-elastic (NCQE) reaction: ν +16 O → ν +15 O∗ +nand ν +16 O → ν +15 N ∗ + p. The residual nuclei emit gamma rays according tode-excitation modes, which can mimic the prompt signal of SRN and the out-going
nucleons produce neutrons via their FSI and SI. Therefore, the atmospheric NCQE
background is an irreducible background even if one tagged neutron is required asshown in the left panel of Figure 1.13. However, energies of neutrons are quite
diﬀerent between the SRN and the atmospheric NCQE background. Neutrons produced by the SRN’s IBD reaction have energies below a few MeV, whereas thoseof the NCQE background have much higher energies, more than several hundreds
MeV, which results in a clear diﬀerence in the distance traveled of neutron fromthe primary ν interaction position as shown in the right panel of Figure 1.13. Further reduction of the atmospheric NCQE background may be achieved by exploiting
this diﬀerence. Since the peak energy is similar between the T2K neutrinos and theSuper-Kamiokande atmospheric neutrinos [129], studying the neutron travel distanceby the T2K beam neutrinos may be useful.
21

CHAPTER 1. INTRODUCTION

Figure 1.12: Expected SRN flux as a function of positron energy for diﬀerent redshift
at Super-Kamiokande. Figure taken from [8].

Figure 1.13: Expected positron energy spectrum at SK-Gd with an exposure of 10
years (left). The red, blue, and magenta lines represent the SRN signal, the atmospheric NCQE events, and the atmospheric CC decay electron events, respectively.
A revised version of the LMA model [9] is used for the SRN flux. For the decay electron events, a reduction by a factor of five is assumed and is planned to be achievedby neutron tagging. Figure taken from [10]. Distribution of true distance from νinteraction to n capture vertices (right). The orange and green correspond to theinverse β decay signal of SRN and the NCQE atmospheric neutrino background,respectively.
Alongside the utilization of distance information for SRN searches, a possibility ofsimilar utilization of neutron kinematics has been studied for estimation of neutrino
direction and further ν-ν̄ separation in atmospheric neutrino oscillation analyses.
22

CHAPTER 1. INTRODUCTION

Figure 1.14: Mean neutron multiplicities as a function of visible energy for heavy
water, measured by using atmospheric neutrinos at the SNO experiment. MC expectations are made from a combination of GENIE [11] and Geant4 [12]. The error
bars of the data represent statistical errors and the envelopes of the MC expectations
correspond to the assigned systematic uncertainties. Note that no systematic uncertainties due to hadronic SI are taken into account for the error envelopes. Figure
taken from [13].

1.2.3

Current status of prediction of neutrons

Utilization of neutrons associated with neutrino interaction in water is able to produce promising improvements on various physics analyses as described above. In
order to realize such improved analyses, the multiplicity and the kinematics of suchneutrons need to be precisely understood with satisfactory control of related systematic errors. The SK collaboration has made only measurement of those neutrons
by using the atmospheric neutrinos [130]. However, the measurement result does
not have systematic uncertainty and, in addition, it is not compared with any MC
predictions.
Although target material is not water, it is worth mentioning existing measurements of equivalent or similar neutrons to know the status of experimental studies
on neutrons related to ν-nucleus interactions. The SNO collaboration has measured
neutrons in the heavy water by using the atmospheric neutrinos [13]. As shown in
Figure 1.14, the agreement between the data and their reference simulation varies
over the visible energy and the analysis samples. In some regions overpredictions areseen despite the very large systematic uncertainties on the MC predictions. In the
MINERvA experiment [131], a post-FSI enriched neutron sample in which neutrons
produced in hadronic SI are reduced by applying analysis cut is prepared for the23

CHAPTER 1. INTRODUCTION
antineutrino enriched mode of NuMI beam with a peak energy of ∼3 GeV produced
at Fermilab. By using the sample, neutron kinematics and multiplicity for antineutrino interaction on a hydrocarbon target are measured, and are compared between
the data and their simulations [14]. A 15% overall overestimate was seen in theirreference simulation, but further overestimates were found in a region of low energy
deposition by neutron candidates as shown in Figure 1.15.

Figure 1.15: Distribution of measured apparent velocity for neutron candidates
by the MINERvA experiment. The ν̄-mode of NuMI neutrino beam produced atFermlab and a hydrocarbon target are used as neutrino source and target material,
respectively. The data are shown with statistical error only and the gray bands
represent the assigned systematic errors on the MC expectations. The MC expectations are produced by a combination of GENIE [11] and Geant4 [12]. Figure takenfrom [14].
Both SNO and MINERvA made their MC predictions by a combination of two
MC simulations: GENIE [11] which simulates primary neutrino interaction and subsequent hadronic FSI and Geant4 [12] which handles simulation of particle propagation in detector medium (i.e. hadronic SI). For this combination, the SNO’s resultshows a large prediction uncertainty and the MINERvA’s data show overprediction.
Thus, it may be interesting to refer to another experimental study whose MC predictions are made from diﬀerent MC simulations. The MiniBooNE experiment hasstudied NCQE (“NCE” in their paper) reaction with a mineral oil target [132], andtheir data have shown a ∼30% of overprediction which is produced by two MC simulations: NUANCE [133] for primary neutrino interaction and FSI and GCALOR [134]for hadronic SI. Thus, MC simulations used in neutrino oscillation experiments utilizing atmospheric neutrinos and accelerator based neutrinos ranging from sub-GeV
up to several GeV tend to overpredict.
Since the production process of protons related neutrino interactions are almost
24CHAPTER 1. INTRODUCTION

the same as neutrons, it is worth discussing the current status of prediction of proton
multiplicity. Figure 1.16 shows the proton multiplicity with kinetic energies above
500 MeV for a C8 H8 target, measured by the T2K experiment [15]. As shown in the
figure, the data shows less protons compared to several MC predictions, in which
NEUT [135] and NuWro [136] are used for their simulation of the primary neutrino
interactions and the FSI.

Figure 1.16: Proton multiplicity for CC νµ interactions on a C8 H8 target with 0pion in the final state, measured by the T2K experiment. Only protons with kinetic
energies above 500 MeV are considered. The error bars of the data include both
statistical and systematic uncertainties. Solid and broken lines represent predictions
by diﬀerent MC simulations with uses of various models. Figure taken from [15].
Another overprediction has been seen for both neutrino and antineutrino interactions on a liquid argon target in the ArgoNeut experiment at Fermilab [137], whichis mentioned in Ref. [138].

1.3

Research motivation

In Section 1.1.2 and Section 1.1.3, neutrino oscillations, SRN, and their experimental status were described, and further improvement on these experimental studies
needs to be done. To this aim, information about neutrons associated with neutrino
interactions in water will be useful for various physics analyses. In order to utilize
such information, these neutrons need to be precisely measured and that information
can be used to improve MC predictions. However, as will described in Section 8.1,
currently used MC simulations in neutrino oscillation experiments utilizing atmospheric neutrinos and accelerator based neutrinos produce diﬀerent predictions ofneutron production for water. In addition, no quantitative comparison of neutron
multiplicity for water has been made although non-negligible diﬀerence in neutron
multiplicity and proton multiplicity have been seen for diﬀerent target materials as
was described above. It is therefore quite valuable to measure those neutrons forwater and understand how much level of agreement between data and simulations
25

CHAPTER 1. INTRODUCTION

can be realized. For this purpose, a well understood neutrino source is required.
T2K beam neutrino has advantages compared to other neutrino source such asatmospheric neutrinos:• well known and peaked energy,• well known neutrino flavour composition,• known neutrino direction,• two separate neutrino- and antineutrino-enriched fluxes.
Also, the SK far detector is capable of tagging neutrons on an event-by-event basis
by detecting γ rays produced from neutron captures on hydrogen nucleus. Thus,
T2K is suitable for studying those neutrons, and the primary analysis of this thesispresents the first measurement of neutrons associated with neutrino interactions inwater for accelerator based neutrinos and antineutrinos.

1.4

Thesis overview

This thesis presents the first study on neutrons associated with neutrino interactions
on water target for accelerator based neutrinos and antineutrinos using the data collected at the SK far detector of the T2K experiment.
An overview of the T2K experiment and a detail of the SK far detector are described in Chapter 2 and Chapter 3, respectively. Following this, simulations of theT2K beam neutrinos at the SK far detector are overviewed in Chapter 4. The data
reduction and reconstruction of neutrino event at the far detector are the subjects
of Chapter 5.
The original and independent works done by the author of this thesis are described from Chapter 6. Chapter 6 details the development of the neutron tagging
algorithm and related analyses. The first application of the neutron tagging techniqueto accelerator neutrinos for water target is presented in Chapter 7. In Chapter 8,
a measurement of mean neutron multiplicity associated with neutrino interactions
in water is described, and the summary of this thesis and an outlook are given in
Chapter 9 .

26

Chapter 2
The T2K experiment
The Tokai-to-Kamioka (T2K) experiment is a long baseline neutrino oscillation experiment in Japan [16]. It was originally designed to achieve the following goals:• A precision measurement of ∆m223 and sin2 θ23 with an accuracy of δ(∆m223 ) ∼10−4 eVand δ(sin2 2θ23 ) ∼0.01 by studies on muon neutrino disappearance.
• Observation of electron neutrino appearance from a muon beam neutrino if
sin2 2θ13 > 0.008.

The precision measurements of ∆m223 and sin2 θ23 have been successfully done [139],
although the accuracy continues to improve. The observation of νe appearance has
also been achieved [98] in the νµ dominant mode, whereas ν̄e appearance has not been
observed yet in the ν¯µ mode. Since the value of θ13 has been measured by reactor
based experiments, a possibility to probing δCP has been opened. Indeed, T2K is
now moving to make a constraint on δCP , and has excluded the CP-conserving values(δCP = 0, π) with a 90% C.L. for the first time [140, 139]. In addition, studies onthe ν-nucleus interactions are also studied by the intensive beam neutrinos.

Figure 2.1: A schematic view of the T2K experiment.
Figure 2.1 shows a schematic layout of the T2K experiment. Predominantly muon
neutrino and antimuon neutrino beams are produced at J-PARC (Japan Proton
27

CHAPTER 2. THE T2K EXPERIMENT

Accelerator Research Complex) facility. They are detected by the INGRID and
ND280 near detectors placed ∼280 m downstream from the production target of theneutrino beams before the beam neutrinos oscillate and the Super-Kamiokande far
detector located 295 km further away after they oscillate. The near-far comparison of
the detected neutrinos is the vital input to measure neutrino oscillation parameters.
INGRID sits at the beam center to monitor the beam neutrinos. ND280 and SK are
placed on an oﬀ-axis angle of 2.5 ◦ with respect to the beam center, which enables
utilizing a relatively narrow band neutrino flux with a peak energy of 0.6 GeV. T2K
has started taking physics data since January 2010.
This chapter describes the T2K beamlines, the oﬀ-axis beam method, and theT2K near detectors. Since the primary analysis of this thesis does use the data
accumulated at the SK far detector only, details in SK will be described in Chapter 3.

2.1

Neutrino beam

The T2K neutrino beam [17] is produced at J-PARC in Tokai, Ibaraki, Japan. T2K
adopts the oﬀ-axis approach to produce a narrow band muon neutrino beam witha minimal contamination of electron neutrinos and with a peak energy of 0.6 GeV.
This beam configuration is determined in order to maximumize the oscillations ofmuon neutrinos at SK. The neutrino beam is produced by using two beam-lines:
the J-PARC proton beam line and the neutrino beam line. In this section, first an
overview of these beam lines are provided. Following this, the oﬀ-axis approach is
described.

2.1.1

J-PARC proton beam line

A 30 GeV kinetic energy of proton beam is generated by the J-PARC proton beamline which consists of three accelerators: a linear accelerator (LINAC), a rapid cycling
synchrotron (RCS), and the main ring (MR) synchrotron. The generation of the
30 GeV proton beam begins with LINAC by which an H− beam is accelerated up
to a kinetic energy of 400 MeV. The accelerated H− beam is navigated to the RCS
injection where an proton beam is created from the conversion of the H− beam bycharge-stripping foils. The proton beam is then accelerated up to 3 GeV in kinetic
energy by RCS whose the number of bunches are two per cycle. About 5% of thesebunches are supplied to the MR to further accelerate the proton beam up to 30 GeV.
For the T2K neutrino beamline which will be described in the following section, theaccelerated protons are extracted as a spill which consists of eight proton bunches
at the fast extraction point in MR and are supplied to the neutrino beamline.
Table 2.1 summarizes the machine design parameters of MR for the fast extraction
mode. The beam power has been gradually increased. The continuous operation witha beam power of 480 kW was successfully achieved in 2018 [30]. Also, in 2018 thebeam power of single shot reached to 520 kW [141], which is the highest beam powerat the present moment.
28

CHAPTER 2. THE T2K EXPERIMENT
Table 2.1: The parameters of the machine design of the J-PARC Main Ring for the
fast extraction. [16]Circumference
Beam power
Beam kinetic energy
Beam intensity
Spill cycle
Number of bunches
RF frequency
Spill width

2.1.2

1567 m∼750 kW30 GeV∼3×1014 p/spill∼0.5 Hz
8/spill
1.67-1.72 Hz∼5 µs

Neutrino beam line

Figure 2.2: A schematic drawing of the neutrino beam line. Figure taken from [16].
The neutrino beamline consists of the primary and secondary beamlines as shown in
Figure 2.2. In the primary beam line, the proton beam extracted from MR is directed
toward Kamioka, and is transported through a series of beam monitors in the final
focusing section: five current transformers (CTs), 21 electrostatic monitors (ESMs),
19 segmented secondary emission monitors (SSEMs) and 50 beam loss monitors(BLMs). Figure 2.3 shows the locations of these monitors.

29

CHAPTER 2. THE T2K EXPERIMENT

Figure 2.3: A schematic drawing of the neutrino beamline. Figure taken from [17].
By using these monitors, the beam intensity, position, profile, and loss are measured. In particular, CT5, which is placed on the most downstream, is used tomeasure Protons-On-Target (heareafter called “POT”) on a buch-by-bunch basis.
The measured POT is directly used to determine the beam neutrino flux.
Figure 2.4 shows a schematic drawing of the secondary beamline. Upon the injection from the primary beamline, the proton beam impinges a target ,which is a91.4 cm long corresponding to 1.9 interaction length, 2.6 cm diameter and 1.8 g/cm3
graphite rod, to produce secondary hadrons which are focused by three magnetic
horns.

Figure 2.4: A cross-sectional view of the secondary beamline. Figure taken from [16].

The magnetic horns are operated with a 250 kA pulsed current whose polarity
can be either positive or negative and are used to guide those secondary hadrons to
a decay volume. The +250 kA operation predominantly focuses on π + and K + to
produce a muon neutrino enriched beam as follows:
π + → µ + + νµK + → µ + + νµ .
30

CHAPTER 2. THE T2K EXPERIMENTIn the -250 kA operation, on the one hand, π − and K − are focused on to create ahigh purity of muon antineutrino beam via the decays :π − → µ− + ν̄µK − → µ− + ν̄µ .
A maximum filed of 1.7 T is produced in the ±250 kA operation. The configurations of neutrino and antineutrino enriched beam are called forward-horn-current(hereafter called “FHC)” or reverse-horn-current (hereafter called “RHC”) modes,
respectively. Figure 2.5 shows an illustration of eﬀects on the beam flux at SK forthe operation with diﬀerent horn currents, and the 250 kA operation increases thebeam flux at the SK by a factor of ∼17 at the peak energy compared to the case of
0 kA operation.

Figure 2.5: Muon neutrino flux at the SK for operation of diﬀerent horn currents.
Figure taken from [17].
Once the secondary hadrons are guided to the decay volume whose length is about
96 m, either muon neutrinos or muon antineutrinos are predominantly produced depending on the polarity of the horn magnets. However, there is a contaminationof wrong-sign neutrinos which are produced by imperfect horn focusing, subsequentmuon decays and another decay mode of the kaons:31CHAPTER 2. THE T2K EXPERIMENTµ+ → e+ + νe + ν̄µ and K + → π 0 + e+ + νe for FHCµ− → e− + ν̄e + νµ and K − → π 0 + e− + ν̄e for RHC
The length of the decay volume is determined to maximize the conversion rate frommeason to muon neutrino, while minimizing the contamination of electron neutrinosin the beam. At the end of the decay volume, there is a beam dump which is madeof 3.2 m long of graphite and 2.4 m long of iron. The protons, secondary hadrons,
and measons below momenta of ∼5 GeV/c are absorbed by the beam dump.
A muon monitor [142, 143] is placed just downstream of the beam monitor inorder to measure the beam intensity and direction on a bunch-by-bunch basis. Sincemuons are dominantly produced along with neutrinos from the two-body pion decay, these beam properties can be monitored by measuring the distribution profileof these muons. In addition, a detector consisting of nuclear emulsion is locatedjust downstream of the muon monitor, by which the absolute flux and momentum
distribution of those muons are measured.

2.1.3

Oﬀ-axis approach

ND280 and SK do not sit on the beam center, instead these detectors are placedon 2.5 ◦ oﬀ-axis from the beam center. This approach is referred to as the “oﬀaxis configuration” [144]. It utilizes the fact that, in the laboratory frame, theenergies of neutrinos produced from the two-body decay of pions do depend only
weakly on the energies of the parent pions in a energy region above scattering angle
dependent threshold. This can be quantitatively explained by considering the energy
conservation of the relativistic kinematics of the two-body pion decay, and the energyof outgoing neutrino Eν in the laboratory frame is given as:Eν =m2 − m2√π 2 µ 2,2(Eπ − Eπ − mπ cos θ)(2.1.1)

where mπ is pion mass, mµ , is muon mass, Eπ is the parent pion energy, and θ
is the scattering angle of the outgoing neutrino with respect to the parent pion’s
momentum direction. Figure 2.6 shows Eν for diﬀerent θ, and the weak dependenceon Eπ can be clearly seen above some Eπ , which depends on θ.

32

CHAPTER 2. THE T2K EXPERIMENT

Figure 2.6: Neutrino energy from two-body decay of pion in Lab. frame as a functionof parent pion energy for diﬀerent oﬀ-axis angles. T2K uses an oﬀ-axis angle of 2.5◦ .

By exploiting the eﬀect of oﬀ-axis, a quasi-monochromatic neutrino beam flux canbe produced. However, such beam intensity quickly decreases as the oﬀ-axis angle
increases. The 2.5 ◦ oﬀ-axis angle of T2K is therefore determined by considering abalance between beam intensity and beam energy spread while keeping a peak energyof ∼0.6 GeV for the oscillation maximum at SK. Figure 2.7 shows an illustration, in
which the 2.5 ◦ oﬀ-axis maximize the T2K’s sensitivity to the oscillation maximum.

Figure 2.7: Survival probability of moun neutrinos with a baseline of 295 km (top)and neutrino beam fluxes at 295 km away from neutrino production target for three
diﬀerent oﬀ-axis angles (bottom). Figure taken from[17].

2.2Near detectors

The T2K near detector complex, which is located 280 m downstream from the production target of the beam neutrinos, is used to monitor the profile of the neutrino
beam and measure neutrino interaction rates in order to constrain uncertainties in33

CHAPTER 2. THE T2K EXPERIMENT

the measurements of neutrino oscillations. As shown in Figure 2.8, the near detector complex consists of two detectors: an on-axis detector, Interactive Neutrino
Grid (INGRID), and an oﬀ-axis detector, Near Detector at 280 m (ND280). In thissection, each component of these detectors is described.

Figure 2.8: A schematic drawing of the near detector complex. Figure taken from
[16].

2.2.1

On-axis near detector

INGRID is a separate array of iron and scintillator detector placed on the on-axis.
The detector is designed to daily monitor the beam direction and intensity using
neutrino interactions on its iron target. Also, the beam direction can be accurately
measured within 0.4 mrad. INGRID consists of 16 identical modules as shown in
Figure 2.9. The cross shape of INGRID whose center corresponds to the beam
center is formed by 14 modules. The remaining two modules are separately placedon oﬀ-axis directions and used to check the axial symmetry of the neutrino beam.

34

CHAPTER 2. THE T2K EXPERIMENT

Figure 2.9: INGRID on-axis detector. The direction of the beam neutrinos is parallelwith the z-axis. Figure taken from [16]An INGRID module is made of 9 iron plates and 11 tracking scintillator planes.
These iron plates and tracking planes are arranged in a sandwich structure and aresurrounded by veto scintillator planes as shown in Figure 2.10. Each iron plateserves as a neutrino target and the total iron mass of one module is 7.1 ton. Eachtracking plane consists of 24 scintillator bars. Also, each of veto plane is made of
22 scintillator bars which are diﬀerent from the ones used in the scintillator plane.
For both of the scintillator plane and veto plane, a wave-length shifting fiber (WLS)
is inserted to each scintillator bar for light collection. The signal from a WLS are
read out by an multi-pixel photon counter (MPPC) [145, 146] attached to the endof WLS.

Figure 2.10: A schematic diagram of the INGRID module. Figure taken from [16]INGRID is calibrated by using cosmic ray data. The measured mean light yield
which is larger than 10 p.e./cm for MIP tracks satisfies the requirement.
35

CHAPTER 2. THE T2K EXPERIMENT

2.2.2

Oﬀ-axis near detector

ND280 is a large, fine grained, and magnetized oﬀ-axis detector. Since the detector
is placed on the same oﬀ-axis as SK, it is designed to achieve the following goals inorder to accurately predict event rates at SK:• Measure the energy spectrum of νµ to predict the event rate at SK.
• Measure the νe component which is the main background in νe appearance
search at SK.
• Measure the cross sections of νµ interactions to reduce systematic uncertainties
on ν-nucleus interaction models.

The detector design is determined by considering these requirements.

Figure 2.11: A simplified schematic view of ND280. Figure taken from [16].
ND280 is composed of a series of specialized detectors: 2 Fine Grained Detectors(FGDs), 3 gaseous Time Projection Chambers (TPCs), and a π 0 detector (P̸ OD).
These subdetectors are contained in a metal frame container and are surroundedby Electromagnetic Calorimeters (ECals), which are contained within a magnet instrumented with side muon range detector (SMRD). Figure 2.11 shows a schematic
drawing of ND280. To magnetize these detectors, a magnet (UA1) is used.
UA1 Magnet
36

CHAPTER 2. THE T2K EXPERIMENTThe ND280 detecor uses the magnet which was previously used in the UA1
experiment. The magnet provides a horizontally oriented dipole magnetic
field of 0.2 T and consists of water-cooled aluminium coils and a 850 ton
flux return yoke.
Side Muon Range Detector (SMRD)
The SMRD [147] detector is incorporated into the yoke of the magnet
surrounding ND280 and consists of 440 scintillator modules which are
inserted into the 1.7 cm air gaps between 4.8 cm thick steel plates inside
the yoke. It is purposely used to measure the momenta of muons escaping
from the inner detectors at a large angle with respect to the neutrino
beam. Also, it can act as a veto for entering particles such as cosmic raymuons and particles produced by beam-related events that happen in thecavity walls and iron of the magnet.
Pi -Zero detector (P̸ OD)
Since the π 0 produced in the neutral current interaction on water νµ +N →
νµ + N + π 0 + X can mimic the signal event of νe appearance at SK,P̸ OD [148] is designed to measure this process. The detector consistsof three components: the central section, “upstream ECal”, and “central
ECal”. The central section is made of alternating scintillator plane, brass
sheets, and water bags as show in Figure 2.12. The water bags can be filledwith water or empties, which enable us to perform a subtraction method
to extract the cross-section of the interaction process. The upstream ECaland central ECal are used to veto events entering from outside and consistof alternating scintillator planes and lead sheets and have not water bags.
Each scintillator plane is made of two perpendicular arrays of triangular
scintillator bars, each of which has a hole filled with a WLS fiber. The
signal from a WLS fiber is read out by a MPPC attached to one end.
P̸ OD has 40 scintillator plates with 10,400 readout channels and 50 waterbags. The total detector mass is 16.1 ton and 13.3 ton for the water-in
configuration and water-out configuration, respectively.

37

CHAPTER 2. THE T2K EXPERIMENT

Figure 2.12: A schematic cross sectional view of P̸ OD. Figure taken from [16].
Time Projection Chamber (TPC)
Three TPCs [149] are separately placed just downstream of P̸ OD. TPCs
are designed to have good resolution in reconstruction of charged particle
tracks, momentum determination, and particle identification such thatthe event rate of muon and electron neutrinos as a function of energy canbe measured.
Each TPC has an inner box filled with an argon based drift gas, which iscontained within an outer box that holds CO2 as an insulating gas. An
11.5 mm pitch copper strip pattern is accurately formed on the inner box
panels such that an uniform electric field of around 280 V/cm is producedin the active volume of TPC. The magnetic field by the UA1 magnet isroughly parallel to the electric field. Figure 2.13 schematically shows a
simplified TPC.
The argon atoms are ionized as charged particles traverse TPCs. The ionization electrons produced along the trajectories of those charged particles
drift away from the central cathode towards one of the readout planes.
Upon reaching the readout plane, the drifting electrons enter an amplification region by an electric filed of 27 kV/cm over a distance of 128 µm
and are read out by bulk micromegas detectors [150].

38

CHAPTER 2. THE T2K EXPERIMENT

Figure 2.13: A schematic drawing of TPC. Figure taken from [16].
Fine Grained Detector (FGD)
The two fine grained detectors (FGDs) [151] have two functionalities: target mass of neutrino interaction and reconstruction of charged particle
tracks. The outer dimension of FGDs are 2300 mm in width, 2400 mm inheight, 365 mm in depth with 1.1 ton of target material. FGDs are madeof layers of scintillator bars which are arranged in the direction perpendicular to the beam direction. Each scintillator bar has the dimension
with a width of 9.61 mm, a height of 9.61 mm, and a depth of 1864.3 mm
and has a WLS fiber whose one end is connected to a MPPC. The scintillator bars are arranged into modules, each of which contains a layer of
192 scintillator bars in the horizontal direction glued to 192 bars in thevertical direction.
The first FGD consists of 15 scintillator modules, whereas the second FDG
has 7 scintillator modules and 6 water target modules. By comparing theneutrino interaction rates between FGDs, cross sections on carbon andwater can be measured.
Electromagnetic calorimeter (ECal)
ECal [152] is a lead-scintillator sampling electromagnetic calorimeter, whichsurrounds the inner detectors: P̸ OD, TPCs, and FDGs. It is utilized tocomplete the event reconstruction of the inner detectors fully by detecting
photons and charged particles, which escape from the inner detector, andmeasuring the energies and directions of them. In particular, ECal plays
a key role to reconstruct π 0 produced by ν interaction inside the innerdetectors.

39

Chapter 3
Far detector Super-Kamiokande
Super-Kamiokande (SK) [18] is a 50 kton scale water Cherenkov detector located in
Gifu Prefecture, Japan. SK consists of two key components: a tank filled with 50 ktonof ultra pure water and roughly 13,000 photomultiplier tubes (PMT). When charged
particles traverse the water, the Cherenkov light emitted by the charged particles is
detected by the PMTs. In order to suppress the cosmic ray muon background, thedetector is placed in the Kamioka mine under near the top of Mt Ikenoyama with
1000 m of overburden (2700 meter water equivalent). Figure 3.1 shows a diagram of
the SK detector. SK started its operation in April 1996 with the primary purposes
to search for nucleon decay and observe neutrinos from a variety of sources: solar
neutrinos, astrophysical neutrinos, atmospheric neutrinos, and accelerator neutrinos.
SK has also been used as the T2K far detector since January 2010. In this chapter,first the operation principle of the detector is described. Following this, the remaining
parts describe the detector design and detector calibration.

Figure 3.1: A schematic view of the Super-Kamiokande. Figure taken from [16].

40CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

3.1

Cherenkov radiation

Water Cherenkov detectors utilize the Cherenkov light emitted in the water to detect charged particles. When an object travels faster than the speed of sound, ashock wave is produced. Analogously, an electromagnetic shock wave referred to as“Cherenkov radiation” is produced if a charged particle traverses a dielectric medium
faster than that of the phase velocity of light in the medium [153]:
v≥

c
,
n

(3.1.1)

where v is the velocity of the charged particle, c is the speed of light in vacuum,and n is the refractive index of the medium. In Cherenkov radiation, photons are
emitted as a cone with an opening angle θC called “Cherenkov angle” with respect
to the direction of the motion of the charged particle:cos θC =1,nβ(3.1.2)where β = v/c. The number of emitted photons per unit travel distance per unit
wavelength of a charged particle with the electric charge z is given as:
d2 N
2πz 2 α
=
dxdλ
λ2

(
1−

1
2 2
nβ

)
,

(3.1.3)where α ≃ 1/137 is the fine structure constant.
In the environment of SK, the refractive index of the water is ∼1.34 in a wave
length region where the photosensors used for SK are sensitive. The momentum
threshold for Cherenkov radiation is calculated to be approximately 0.57 MeV/c for
an electron, 118 MeV/c for a muon, 156 MeV/c for a charged pion and 1052 MeV/c
for a proton. Cherenkov light is emitted with the θC ∼42◦ for a charged particle
moving with β ≃ 1.

3.2

Detector design

The SK detector is made of a cylindrical stainless-steel tank with the diameter of
39 m and a height of 42 m. The tank is filled with 50 kton of ultra pure water anda cylindrical PMT supporting structure that optically separates the tank into twoconcentric cylinders: the inner detector (ID) and the outer detector (OD). ID has acylindrical volume containing 32 kton of the water with 33.8 m in diameter and 36.2 m
in height, and is used as the main detector. OD surrounding ID has a cylindricalshell volume with the thickness for the barrel side of 2.2 m and the thickness for the41CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

top and bottom sides of 2.5 m. OD serves as an active veto counter for incoming
particles such as cosmic ray muons originating from outside of the detector. OD isalso used as a passive shield against neutrons and gamma rays which emanate fromthe surrounding rock. The PMT supporting structure defining ID is made of “supermodule” frames whose dimensions are 2.1 m in height, 2.8 m in width and 0.55 m
in thickness. Each of the super-modules houses twelve 20-inch PMTs for ID and
two 8-inch PMTs for OD as shown in Figure 3.3. The inner side of the supporting
structure is mounted with 11,129 inward-facing 20-inch PMTs and the outer side ismounted with 1,885 8-inch outward-facing PMTs. This detector design “ID and OD
installed with PMTs” enables SK to be used as a Cherenkov-ring imaging detector.
Figure 3.2 shows an event display of a “muon-like” event induced by T2K beam
neutrinos. As shown in Figure, a clear ring which is produced by Cherenkov lightemitted by the muon candidate can be found.

Super-Kamiokande IV
T2K Beam Run 0 Spill 952106
Run 66831 Sub 410 Event 96851432
10-05-18:18:33:08
T2K beam dt =1879.5 ns

Inner: 2949 hits, 8030 pe
Outer: 3 hits, 2 pe
Trigger: 0x80000007
D_wall: 709.7 cm
mu-like, p = 1024.6 MeV/c

Charge(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
790
1 mu-e
decay

632
474
316
158
0
0

500

1000

1500

2000

Times (ns)Figure 3.2: An unrolled event display of a typical single-ring muon-like data event of
the T2K beam neutrino. Each dot corresponds to a PMT and color represents thenumber of observed photoelectrons.
Since the performance of the PMTs depend on magnetic field, 26 sets of horizontal
and vertical Helmholtz coils line the inner wall of the tank. In the operation of thesecoils, the residual magnetic field is measured to be about 50 mG on average.

42CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.3: A schematic drawing of a super-module instrumented with the ID and
OD PMTs. Figure taken from [18].

3.2.1

Experimental phases

The fourth-phase of SK(IV) started in September 2008 by upgrading its readout
electronics [154, 19], and the T2K experiment began in Jan. 2010. Since this thesis
is related only to SK-IV, this phase is described in the following.

3.2.2

Inner detector

In ID, 11,129 Hamamatsu R3600 20-inch PMTs, which were developed for the SK[155], are used. Figure 3.4 shows a schematic drawing of a PMT. All the PMTs
are evenly placed 70 cm from each other on the wall of ID, which realizes that 40%of the surface area of ID is covered by the photocathodes. This enables detecting
Cherenkov photons emitted by charged particles with a high eﬃciency and with anexcellent resolution for observed geometrical pattern of PMT signals. The remaining
60% of the surface area is covered with black polyethylene sheets (hereafter called“black sheets”) to prevent light leaks between ID and OD.

43

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.4: A cross-sectional view of an ID PMT. Figure taken from [18].
Photocathodes which are composed of a bialkali (Sb-K-Cs) material are sensitive
to photons in a wavelength region from 300 nm to 600 nm and have the quantum
eﬃciency (QE) with a maximum value of 22% around at 390 nm as shown in theleft panel of Figure 3.5. When a photon reaches the photocathode of an ID PMT,a photoelectron (p.e.) is produced in accordance with the quantum eﬃciency. The
p.e. is then amplified by the 11-stage dynodes inside the PMT with a gain of 107 at
a supply high-voltage ranging from 1700 V to 2000 V. The collection eﬃciency for ap.e. at the first dynode is higher than 70%. The right panel of Figure 3.5 shows thetransit time spread (TTS) of the PMTs for a p.e. signal and the TTS is evaluatedto be ∼2.2 ns. The dark rate for the SK-IV is about 6 Hz on average when setting
threshold on the signal to ∼0.25 p.e.

Figure 3.5: The wavelength dependence of the quantum eﬃciency of R3600 20-inch
PMT (left). Distribution of the transit time of R3600 20-inch PMT (right). Figures
taken from [18].
In 2001, SK had an accident by which about half of the ID PMTs were broken due
to the implosion of an ID PMT. After the accident, PMT cases which are made of44

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

a fiber reinforced plastic shell (FRP) at the base and an acrylic case were developed
to protect implosions as happened in the accident. All the PMTs are encased by the
FRP shell with an acrylic front window.

3.2.3

Outer detector

In OD, 1,885 8-inch PMTs [156] are evenly distributed on the inner surface of OD.
Since the primary role of OD is to veto entering backgrounds such as cosmic raymuons, the ability of light collection need to be enhanced. For this purpose, reflectiveRsheets made of Tyvek⃝
whose reflectivity is about 90 % at the wavelenght of 400 nm
are used to cover all the surface of OD. Also, each of the OD PMTs is attached to a
50 cm square acrylic plate which absorbs ultraviolet light and remits the light withblue-green wavelengths that the PMT can detect.

3.2.4

Water and air purification

The underground water in the mine is utilized to supply the 50 kton of the ultra
pure water inside the detector. Many impurities such as tiny dust, ions, radioactive
isotopes, and bacteria are contained in the underground water. Those impurities
attenuate Cherenkov light emitted by light absorption or scattering before the lightreaches the PMTs of the detector. In addition, the radioactive isotopes originatingfrom the uranium or thorium produce electrons and gamma-rays by their decay
chains, which aﬀect low energy analyses such as neutron tagging. Therefore, theunderground water needs to be purified as much as possible before injecting it to thedetector. The water purification system of SK basically consists of nine sequential
processes as follows:
1. Water filter is used to remove large particles in the water.
2. Heat exchanger cools the water down to 13 ◦ C to prevent variations in the darknoise of the SK PMTs, water convection inside the tank, and the growth ofbacteria.
3. UV light is used to kill bacteria in the water.
4. Metalic and carbonate ions and 218 Po and the daughter nuclei are removed byion exchanger.
5. Radon-less air is dissolved into the water to improve the capability of the radon
removal for later process.
6. Organic compounds down to a molecular weight of 100 are removed by a highperformance membrane.
7. Dissolved radon and oxygen gases are removed in vacuum de-gasifier system.
8. Ultra filter removes small particles with size down to 10 nm.

45CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

9. Remaining radon and oxygen dissolved in the water are further removed bymembrane de-gasifier.
The purification processes suppress the radon concentration to a level of 10−3 Bq/m3
and enable the attenuation length of the water inside the inner detector to reachabout 90 m.
As the SK experimental area is surrounded by the rock in the mine, the concentration of radon contained in the air housing the experimental area is naturally
very high. Therefore, the radon, which emanates from the rock, can contaminate
the water in the detector, and needs to be removed. In order to reduce the radon
concentration, the rock surrounding the experimental area is covered with a mineguard (polyurethane). In addition, radon-free air produced in a hut outside of themine by using compressors and activated charcoal filters is continuously provided tothe experimental area.

3.3

Data acquisition for SK-IV

3.3.1

DAQ system

Once photoelectron is produced in a PMT by incident photon(s), the photoelectronis amplified through the dynodes inside the PMT and then is outputted as an analog
signal. The analog signal is fed into a charge-to-time converter (QTC) which is acustom ASIC purposely designed for SK-IV [157]. If the signal from a PMT exceeds
the threshold of a build-in discriminator in QTC (hereafter called “hit”), then QTC
integrates the charge of the signal over the following 400 ns, and produces a squarewave pulse whose front edge corresponds to the time when the input signal exceeded
the threshold and the width of the pulse is proportional to the integrated charge ofthe input signal. After integrating the charge of an input signal over 400 ns, QTC
discharges the integrated charge with a constant current in the next ∼400 ns, which
results in the total processing time of 900 ns for a hit. The output pulse of QTCis then digitized by a time-to-digital converter (TDC). The digitized data from the
TDCs are eventually sent to readout front-end PCs by using Ethernet which enables
the needed high rate of data transfer.
There are 20 front-end PCs to collect digitized information of all the ID and
OD PMTs. Each front-end PC collects the digitized PMT hits from 30 ID and
20 OD fron-end boards QBEEs (QTC-Based Electronics with Ethernet), and thensorts the information of these PMT hits in order of time. The time-ordered PMT
hit information from all the front-end PCs is then sent to another group of PCs,
called Marger PCs, in order to make a time-order list of the PMT hits. Using thelist, Margers apply a set of software triggers to select event candidates by using thevariable N200 which is the number of PMT hits in a 200 ns time window. When
N200 exceeds the threshold of a trigger type, the trigger is issued to select an event
candidate. For each event candidate, a time window is defined around the time thetrigger is issued, and all the PMT hit information inside the window is sent to asingle Organizer PC. The Organizer PC collects all the event candidates from all the46

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Marger PCs, and writes them on disks. The data written on disks are eventuallyused in physics analyses in oﬄine. Figure 3.6 shows a schematic drawing of the flowof the online data processing.

Figure 3.6: A schematic drawing of the online data process. Figure taken from [19].

3.3.2

T2K data acquisition at the far detector

As was described above, all the PMT hits are continuously sent to online PCs. The
software trigger program running on online PCs is then applied to these hits to extract events. In order to avoid possible biases by the software trigger in online, first,
PMT hits induced by the T2K beam neutrinos are stored on disks based on theabsolute arrival time of the T2K beam neutrinos, and later the same software trigger
program used in online is applied to the stored hits to extract events in oﬄine.
Since the SK DAQ buﬀer can hold all the PMT hit information for a few second,
T2K beam spill information needs to be available at SK before the buﬀer resets the
temporally stored hit information. To make this possible, beam spill information
containing spill timing data is transferred from the Neutrino beam-line at J-PARC
to the SK control room via a VPN network in real-time, which is then immediately sent back to the J-PARC side to check for data corruption. For each beam
spill, the absolute time when the first bunch of the spill arrives at the graphite target in the secondary beamline is measured by using the GPS system at J-PARC.
Then, the absolute arrival time of a T2K beam spill at SK is calculated by adding
the neutrino time-of-flight of 985.134 µs to the absolute time measured at J-PARC(295.336 km÷299792.458 km/s = 985.134 µs, where 295.336 km is the distance fromthe target of the proton beam to the SK detector center). The transferring timeof the spill information is also monitored by measuring the round trip time (RTT)
between Tokai-Kamioka-Tokai. The typical RTT is 30-50 ms, which is short enoughto save the PMT hit information for each individual beam spill. Figure 3.7 showsa schematic drawing of the data acquisition using the beam arrival timing. A time
window of ±500 µs from the absolute beam arrival time is defined on a spill-by-spillbasis, and all the PMT hits within the windows are stored on disks. The extraction of events from the PMT hits in the 1 ms time windows and classification of the47

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

extracted events will be described in Section 5.2.

Figure 3.7: A schematic drawing of the data acquisition at SK. The spill interval
and the width of one spill has been changed from 3.5 s and ∼3 µs to 2.4 s and ∼5 µs,
respectively. Figure taken from [20].
Since the events induced by the T2K beam neutrinos are identified based ontiming information, the absolute time needs to be precisely determined. The absolute
time of a PMT hit is calculated based on the GPS clock. One pulse per second (1PPS)
signal from the GPS receiver is sent from the main entrance to a local time clock(LTC) by an optical fiber with a length of about 1.8 km. Both all of QBEEs andthe LTC are synchronized by a 60 kHz trigger clock which is distributed by a masterclock module. The synchronization enables calculating the time diﬀerence between
the 1PPS signal and the PMT signals recorded by the QBEE modules. The TDC
count of QBEE is reset to 0 when QBEE receives a 60 kHz trigger. Therefore, theabsolute time of each PMT hit TAbs (PMT hit) can be obtained by using both of the
TDC count of the QBEE and the LTC count as follows:

TAbs (PMT hit) = TAbs (GPS 1PPS)+ (LTC count(60 kHz trigger) − LTC count(GPS 1PPS)) /LTC frequency+ TDC count/TDC frequency+ 10008 ns(3.3.1)− 972.1 ns,
where the factor +10008 ns accounts for the propagation of the 1PPS through theoptical fiber and the factor −972.1 ns takes into account timing delay due to various
sources:• Time delay due to internal processing in LTC.
• Time delay due to internal processing in TDC.
• Diﬀerence in arrival time of trigger between LTC and QBEE.
48

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE• PMT’s transit time and propagation time between PMT and signal cable.
The timing delay from each source is determined by calibration measurements [20].
For this determination of the absolute PMT hit time, the stability of the GPS
system at SK is essential. In order to stably obtain the timing information from the
GPS system, SK is equipped with two independent GPS modules (called “GPS1”and “GPS2”). In addition, a rubidium clock is installed, which is auxiliarily used
if the timings of the two GPS modules are inconsistent. The GPS1 and GPS2 areconsistent with each other within 200 ns. From comparisons with the Rb clock,however, the GPS2 shows more stable operation than that of the GPS1, and theGPS2 is used as the default clock. In the case where neither the GPS1 nor GPS2
works properly, the Rb clock is used for the absolute arrival time of the beam spills
at SK.

3.4

Detector calibration

Since the precision of a measurement depends on how well the detector used in themeasurement is calibrated, calibration works are the vital component in experiment.
In this section, the procedures of the calibrations conducted in SK are summarizedbased on [21].
In SK, event is reconstructed using the timing and observed charge of PMTs.
Therefore, timing and observed charge responses of PMT need to be well calibrated
for each individual PMT. In addition, the optical properties of the water and othermaterials used in the detector need to be measured. The resultant PMT’s responses
and optical properties are also used as the ingredients for building the detector
simulation.

3.4.1

Adjustment of high-voltage setting

The high-voltage setting for each individual PMT is adjusted so that all the PMTs
produce approximately the same amount of charge for a given light intensity. For thisadjustment, an isotropic light source was placed at the center of the detector. Since
the shape of the detector is cylindrical, there is no position from which the distance
between the light source and each PMT is the same. This makes the light attenuationeﬀect in the water to be diﬀerent on each PMT, and thus each PMT can not receive
the same amount of light from a light source. In order to avoid the eﬀect of thediﬀerent in distance light attenuation, pre-calibrated reference 420 PMTs are used.
All the ID PMTs including these reference PMTs are grouped based on geometrical
relation with respect to the light source. For each group, PMTs, which belong to it,
receive geometrically the same light intensity. The high-voltage of PMTs are thenadjusted so that all the PMTs in the group observe the same charge as the reference
PMTs.

49

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

3.4.2

Relative gain calibration

After determining the high-voltage setting for each PMT, all the PMTs produce
roughly the same charge for a given light intensity, but each PMT still has residual
variation in its PMT gain. This is regarded as the relative gain and is measured withcalibration using a nitrogen-laser-driven dye laser. The laser is located roughly at thecenter position of the inner detector and emits light isotropically. In order to avoid
the diﬀerence between the PMTs due to the SK tank’s cylindrical geometry, two setsof measurement are conducted. In the first measurement, the laser is operated at
a high intensity so that every PMT receive multiple photons. For each individual
PMT, average observed charge Qobs
is measured and is expressed as follows:i
Qobs∝ IH × ai × εQE × Gi ,i

(3.4.1)

where IH is the light intensity, ai is the angular acceptance of i-th PMT, εQE and
Gi denote the quantum eﬃciency and gain of i-th PMT, respectively.
In the second measurement, the light intensity is set to a low intensity IL suchthat only a few ID PMTs are hit by single flash. This low intensity enables making areasonable assumption that each PMT hit is made by single photon and the hit does
negligibly depend on the PMT gain. Therefore, the number of hits for each PMT
counted in the second measurement can be expressed as:
Niobs ∝ IL × ai × εQE(3.4.2)Using Equation 3.4.1 and 3.4.2, a quantity which is proportional to gain can beobtained for each PMT:
Gi ∝

Qobs
i
Niobs

(3.4.3)

The relative gain can be obtained by averaging the quantity over all the ID PMTs,
since the proportional constant is common among all the ID PMTs. After obtaining
the relative gain for each PMT, distribution of the relative gain is made using all the
ID PMTs. From that distribution, the diﬀerence in the gain across all the ID PMTs
has a standard deviation of 5.9%. The obtained relative gain is used to accurately
convert observed charge to number of observed p.e. on a PMT-by-PMT basis whendata is analyzed.

3.4.3

Absolute gain calibration

When photons reach the photocathode of a PMT, p.e. are produced by the photoelectric eﬀect and the PMT eventually observes charge. The absolute gain relates
the produced p.e. within observed charge, and is called single-p.e. distribution. To
50CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

convert observed charge to produced p.e. (or equivalently detected photons) andperform detector simulation, the single-p.e. distribution needs to be measured.
A nickel source, which contains a 252 Cf source providing neutrons, is utilized tocreate the single-p.e. distribution. The nickel source emits γ rays isotropically withtotal energy of ∼9 MeV via the reaction of 58 Ni(n;γ)59 Ni. In this measurement thenickel source is placed at the central position of ID and the γ rays are detected by all
the ID PMTs. The observed number of p.e. is 0.004 per event on average for each
PMT, meaning that more than 99% of produced PMT hits are due to a single-p.e.
The observed charges of all the PMT hits produced by the nickel source are used tomake the single-p.e. distribution by considering the relative gain diﬀerence among
all the ID PMTs described in the previous subsection. Figure 3.8 shows the observed
charge distribution.
From the charge distribution, the average of the charge is obtained and then the
average is used as the conversion factor from pC to single-p.e. The conversion factor
is found to be 2.658 pC/p.e. and is used to obtain the single-p.e. distribution which
is used for the detector simulation.

Figure 3.8: The measured single-p.e. distribution in unit of pC. Figure taken from
[21].

3.4.4

Measurement of relative quantum eﬃciency

QE is diﬀerent between the ID PMTs, and thus relative variation in the quantum
eﬃciency (called “relative QE”) needs to be measured for each individual ID PMT.
As expressed in Equation 3.4.2, number of hits for a PMT is proportional to its QE
when the intensity of a light source is low enough. The same nickel source as usedin the measurement of the single-p.e. distribution is therefore used for relative QE
determination. In order to measure the relative QE, the light intensity, the lightpropagation in water, and the geometrical acceptance need be taken into account,which is not easy in an analytic way. A detector simulation of the nickel calibration
51

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

is therefore performed by simulating the γ rays emitted from the nickel source. In
the simulation, a common QE value is used among all the ID PMTs to predict the
number of hit for each PMT. In addition, convection is artificially set such that thewater quality is uniform across ID. The simulated number of hits are then comparedto the data for each individual PMT and the resulting ratio between the simulationand the data is regarded as the relative QE. The relative QE obtained for each PMT
is tabulated and is used for detector simulation.

3.4.5

Timing calibration

Since event reconstruction such as determination of vertices and track directions ofparticles produced by the T2K beam neutrinos aggressively utilizes timing of PMT
hit. Time response, which is the time interval from the time, that photons reacha PMT, to the time, when the signal of the PMT is registered as a hit, needs tobe precisely calibrated. The time response can diﬀer between the ID PMTs, which
originates from diﬀerences in the transit time of the PMTs, the lengths of the PMT
signal cables, and the processing time of the readout electronics. In addition, a hit isregistered when the analog signal of a PMT exceeds the threshold of hit discriminator,
and the time to cross the threshold depends on the pulse height of the signal whichis correlated with the observed charge of the signal. Therefore, the time response
can also vary depending on the observed charge.
To calibrate the time response for each PMT, a nitrogen laser is used to injecta fast enough pulsed laser light a diﬀuser ball placed near the center position of ID.
The timing of the laser light injection is provided by using a 2-inch monitor PMT.
The laser light is flashed by varying its intensity. For each PMT hit, the timing of
the fired laser, which is obtained from the monitor PMT, and time-of-flight (TOF)from the diﬀuser ball are subtracted. Using the TOF subtracted timings and theobserved charges of the PMT hits, a two-dimensional distribution (hereafter called“TQ distribution”) is made for each ID PMT as shown in Figure 3.9. In the TQ
distribution, the observed charges in pC are divided into 180 bins defined as Q bins
in order to obtain the observed charge dependence of the time response. The peaktiming and standard deviation are obtained for each Q bin at which an asymmetric
Gaussian function is fitted to the corresponding timing distribution. Once the timing
distributions are fitted for all the Q bins, the obtained peak timing and standard
deviations are fitted by a combination of polynomial functions. The resulting fit
parameters are stored as TQ-map for each PMT and are used to correct hit timing
as a function of the observed charge on a PMT-by-PMT basis.

52

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.9: An example of the TQ distribution for an ID PMT. The horizontal axis
is the observed charge (pC) binned into the Q bin whose binning is a linear scale up
to 10 pC, and then becomes a log scale. The vertical axis represents the observed
timing with the TOF correction from the diﬀuser ball and the laser firing timing. In
the vertical axis, larger values correspond to earlier timing. Figure taken from [21].
The PMT timing resolution is also evaluated by using the same calibration data
as for the TQ-map production above. All the PMT hits from all the ID PMTs arecorrected by their TQ-maps, and the TQ-corrected hits are used to produce residual
timing distribution for each Q bin. In each Q-bin, the residual timing distribution isfitted with an asymmetric Gaussian function to extract σt and σt′ which are timing
resolutions for before and after the peak timing of the residual timing distribution,
respectively. Figure 3.10 shows the resultant timing resolution as a function of theobserved charge, which is used for the detector simulation.

Figure 3.10: Timing resolution as a function of observed charge in p.e. The PMT
hit timing of ID is modeled by an asymmetric Gaussian function whose parameters
depend on observed charge. The σt and σt′ are the timing resolutions for before andafter the peak timing of the function, respectively. Figure taken from [21].

3.4.6

Measurement of water properties with laser light

In the detector, the water attenuates Cherenkov light by scattering and absorbing
the light. The light whose wavelength is λ after traveling a distance l is attenuated53

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

exponentially as exp(−l/L(λ)). L(λ) is the light attenuation length of the water andis characterized by Equation 3.4.4.

L(λ) =

1
αsym (λ) + αasym (λ) + αabs (λ),(3.4.4)

where αsym (λ), αasym (λ), and αabs (λ) are amplitudes for symmetric scattering, asymmetric scattering, and absorption, respectively. The αsym (λ) parameter is modeled
based on the Rayleigh scattering and symmetric component of the Mie scatteringand has an angular dependence of 1 + cos θ2 , where θ is angle between the incoming
and the scattered directions of a photon. The αasym (λ) parameter consists of theasymmetric Mie scattering which has a cos θ dependence only for forward direction
and has no amplitude for backward direction (i.e. 0 for cos θ <0). αabs (λ) takes into
account the eﬀect of light absorption.
Each amplitude separately and the sum of thereof (a.k.a L(λ)) need to be precisely measured in order to accurately reconstruct an event and perform detector
simulation. If the fraction of these amplitudes is diﬀerent between data and simulation, it can make diﬀerent observed light pattern even for same attenuation length.
This is done by a calibration using an apparatus which can inject collimated laser
light.
The calibration setup is shown in the left panel of Figure 3.11. In this calibration, a collimated laser light is vertically injected from the detector top to bottom.
The direct light of the laser light is detected by the PMTs located around the target
position of the laser beam. On the one hand, the scattered light by the water and thereflected light by the bottom PMTs and the black sheet are detected by the PMTs
positioned on the top and barrel regions of ID. As the timing of light associatedwith the laser beam has a spacial dependence, the detector is vertically divided into
five regions as schematically shown in the left panel of the figure: B1, B2, B3, B4,
and B5. Then, for each region TOF-subtracted distribution, which is PMT hit time
distribution after subtracting time-of-flight from the beam target position to each hit
PMT, is made. A typical TOF-subtracted distribution is shown in the right panelof the figure. As shown in the panel, the broad structures of the PMT hits in earlier timing are produced by the scattered photons, whereas the peaks after 1800 ns
originate from the photons reflected by the PMTs and the black sheets.

54

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.11: A schematic drawing of the laser calibration system for the measurementof the water properties (left). Distributions of the TOF-subtracted hit timings forthe five diﬀerent tank regions (right). Figures taken from [21].
In order to extract the scattering and absorption amplitudes, the left region
enclosed by two lines in the right panel of Figure 3.11 is used. Since the total
number of scattered photons and the shapes of the distributions in the region are
sensitive to these amplitudes, a number of MC sets are generated by varying theseamplitudes, and then a χ2 fit is performed. This procedure is performed for fivediﬀerent wavelengths ranging from 365 nm to 445 nm. Figure 3.12 shows typical
amplitudes obtained by the χ2 fit.

55

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.12: Typical fitted amplitudes. The points present the data taken in April
2009. The black, blue, red, and violet lines correspond to the fitted functions of
total amplitude, symmetric scattering, asymmetric scattering, and absorption, respectively. Figure taken from [21].

3.4.7Time variation of water transparency

The amplitudes of the light absorption and the light scattering extracted using thecollimated laser light described above are continuously monitored. The time dependencies of these coeﬃcients are shown in Figure 3.13. As shown in the figure,
relatively large time variations in the absorption and the asymmetric scattering amplitudes are seen, which causes a time variation in the light attenuation length of thewater. Since the asymmetric scattering coeﬃcient is about one order of magnitude
smaller than that of the absorption, the time variation of the light attenuation lengthis dominated by the light absorption.

56

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.13: Time variations of the fitted amplitudes for various wavelengths. The
violet, black, and cyan correspond to the amplitudes of symmetric scattering, asymmetric scattering, and light absorption. Three laser units were replaced during thisdata taking period, and the black vertical lines represent the time when the replacement was conducted. Figure taken from [21].
In order to relate the variation of absorption with the attenuation length, decayelectrons from cosmic ray muons are utilized. By using these electrons, an attenuation length averaged over the Cherenkov photon spectrum and the wavelength
dependence of the PMT’s QE (hereafter called “eﬀective attenuation length” in thissubsection) can be measured.
To measure the eﬀective attenuation length, first a deacy-e event sample is prepared as follows:• Select cosmic ray muons which stop inside the inner detector.
• For each selected muon, deacy-electron is searched for, and the time diﬀerence
between the primary muon and the decay-electron, ∆t, is within a time window:
3 µs < ∆t < 8 µs.
• The nearest distance from the reconstructed vertex of the decay-electron to the
ID wall is > 2 m.
• The distance between the reconstructed decay-electron vertex and the stopping
position of the primary muon is < 2.5 m.
After applying the cuts, there are about 1,500 decay-electron events per day [158].
To obtained the eﬀective attenuation length, the azimuthal symmetry of Cherenkov
radiation with respect to the momentum direction of a charged particle is exploited.
With this symmetry, it is extracted by using distance from reconstructed decayelectron vertex to hit PMT position and observed charges. Each deacy-electron eventin the sample has a number of PMT hits, and a distance r from the reconstructed its
57

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

vertex to each individual hit PMT position is calculated. Once r is calculated for all
the PMT hits in the sample, they are filled into a histogram with bins of r. Then,the distribution of the logarithm of the mean observed charge, ln Qave , in bins of r is
calculated. The left panel of Figure 3.14 shows a typical ln Qave as a function of r.

Figure 3.14: Typical ln Qave distribution (left) and the relation between the relative
absorption amplitude and the eﬀective attenuation length (right). In the left, theslope of the fitted linear function corresponds to the eﬀective attenuation length.
The left and right side figures taken from [22] and [23], respectively.
Since the slope of ln Qave distribution corresponds to the eﬀective attenuation
length, a linear function is fitted. The measured eﬀective attenuation length is thenconverted to a scaling factor that scales the nominal absorption amplitude used in
the detector simulation. The relationship between the eﬀective attenuation lengthand the scaling factor is obtained by generating electrons with diﬀerent absorption
amplitudes in the detector simulation. The right panel of Figure 3.16 shows theobtained relation.

3.4.8

Position dependence of water transparency

The ultra pure water is supplied from the bottom part of the tank, and is returned to
the water circulation system in the top region. This water flow makes a temperature
gradient with respect to the vertical direction in the detector tank. Figure 3.15 showsa typical vertical dependence of the water temperature in the tank.

58

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.15: A typical vertical position z dependence of the water temperature inside
the tank. Figure taken from [23].
As shown in the figure, the region with a vertical position z below -11 m does nothave clear temperature variation, whereas for z >-11 m the temperature monotonically increases as a function of z. The temperature variation introduces a vertical
position dependence of the light attenuation length, which causes an asymmetry of
PMT’s hit probability between the top and bottom regions. The vertical position
dependence of the light attenuation length is modeled using the nickel calibration
data obtained by monthly data taking and the real-time calibration data using thelight produced by a Xe lamp. In the nickel calibration, the asymmetry of the PMT
hit probability is quantified as follows:

αT BA =

< Ntop > − < Nbottom >,< Nbarrel >(3.4.5)where < Ntop >, < Nbottom >, and < Nbarrel > are the mean hit rates of the PMTs
located on the top, bottom, and barrel regions of the inner detector, respectively. In
the case of the Xe calibration, the mean hit rates are replaced with the corresponding
mean observed charges. Figure 3.16 shows the measured αT BA s by the nickel and Xe
calibrations, and there is a 3∼5 % level of asymmetry.

59

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

Figure 3.16: Time variation of the measured αT BA with the daily calibration using
Xe light source (blue) and the monthly nickel calibration (red). Figure taken from[21].
In order to account for the observed asymmetry, a vertical position dependence ofthe light absorption is modeled by introducing a time dependent parameter β(t) into
the detector simulation. The β(t) parameter converts the measured αT BA into thestrength of the vertical position dependence. The resultant absorption coeﬃcient,which depends on wavelength λ, time t, and vertical position z in the detector, isgiven as:{αabs (λ, t)(1 + β(t)Z) (for Z ≥ −11m)
αabs (λ, Z, t) =αabs (λ, t)(1 − β(t)11) (for Z ≤ −11m)(3.4.6)

The relation between the β and αT BA is derived by comparing the nickel calibration
data and the corresponding MC samples, which are generated by varying the βparameter. The relation is found to be [159]:
β = (−0.164αT2 BA − 3.676αT BA ) × 10−3 .

3.4.9(3.4.7)

Measurement of reflectivity for PMT and black sheet

The reflectivity of the ID PMT surfaces is also tuned by using the same laser calibration used for the extraction of the amplitudes of the water attenuation length as
described in Section 3.4.6. The reflectivity is parametrized in an inclusive way as thecomplex refractive index of the PMT’s photocathode: nreal + inimag . Using the rightregion shown in Figure 3.11, nreal and nimag are extracted similarly to the fitting of
the absorption and scattering coeﬃcients.
The reflectivity of the black sheets is also measured and is tuned. For this tuning, an in situ measurement is conducted as schematically drawn by Figure 3.17.
As shown in the figure, laser light is injected toward the black sheet attached to60

CHAPTER 3. FAR DETECTOR SUPER-KAMIOKANDE

the experimental apparatus by varying incident angle at three wavelengths: 337 nm,
400 nm, and 420 nm. Then, the observed charges of the PMT hits due to the reflected
light Qref are measured. The laser light is also injected without the black sheet tomeasure the intensity of the direct light, and the observed charges for the direct light
Qdir are measured. The reflectivity of the black sheets is then tuned by using theratio between Qref and Qdir .

Figure 3.17: A schematic drawing of the setup for the reflectivity measurement of
the black sheets. Figure taken from [21].

61Chapter 4
Event simulation
In order to measure physical quantity of interest, measurement often needs “eﬃciency correction”. In general, eﬃciency is dependent on particular experimental
configuration such as performance of event reconstruction and analysis sample used
for the measurement. As a consequence, it is often impossible to express eﬃciency
in closed form. Similarly, expectation which includes eﬀect of detector response can
not be expressed analytically in many cases. Therefore, these quantities are obtained
from results of Monte Carlo (MC) simulations.
This chapter describes MC event simulation at the T2K far detector which mainly
consists of two parts: simulation of neutrino interactions in water and detector simulation for the particles produced in the neutrino interaction simulation. Section 4.1
overviews the simulation of the T2K beam neutrino fluxes which produces vital input to perform simulation of neutrino interactions. Following this, simulation of
ν-nucleus interaction and detector simulation are described in Section 4.2 and Section 4.3, respectively. Then, modifications on the detector simulation which enables
performing analyses with neutron tagging is described in Section 4.4. Section 4.5
summarizes the MC sets used for the primary analysis of this thesis.

4.1

T2K neutrino beam flux

The prediction of the T2K neutrino beam fluxes begins with the simulation of an
upstream part of the primary proton beamline as shown in Figure 4.1. Protons witha kinetic energy of 30 GeV are injected to the target, which is simulated including
the hadronic interactions by FLUKA [160]. The particles which have left the target material are stored with their kinetic information, and these particles are fed
into another simulation JNUBEAM which is a Geant3 [161] based simulation with
GCALOR for hadronic interactions.

62

CHAPTER 4. EVENT SIMULATION

Figure 4.1: A schematic of the geometrical setup considered in the FLUKA simulation of the proton injection. Figure taken from [17].
In JNUBEAM, the geometrical setup of the horn and decay volume is considered.
Particles are propagated through the setup, and these particles are simulated until
they interact or decay. In order to save computational time, directions of neutrinos
produced from particle decays are artificially set to either the far detector directionor the direction from its production point to a randomly selected point in the neardetector plane. In the primary proton simulation by FLUKA and JNUBEAM, truth
information such as the kinematics of the initial proton, full interaction chain of theneutrinos, the kinematics of the neutrinos, and the probability density in the decay
phase-space are stored. Using the saved information, the neutrino flux and energy
spectrum are made from the simulated events by weighting.
For the weighting in the hadron interactions which happen inside the target, several external measurements are used to accurately predict the flux. Since the flux prediction strongly depends on yields of pions and kaons, the results of pion and kaon differential yields for same proton energy as T2K measured by NA61/SHINE [162] [163]are used. In addition, other experimental data [164] [165] are also used to tune theregion where the data of NA61/SHINE do not cover. Figure 4.2 shows the predictionof T2K fluxes at the far detector.

63

CHAPTER 4. EVENT SIMULATION

Figure 4.2: Beam neutrino non-oscillated fluxes for the FHC (left) and RHC (right)
modes. These fluxes are used for event simulation at the far detector.
Recently the NA61/SHINE published the hadron yields for a replica target of
the target used in T2K [166], and the analysis to use the results inside T2K has
completed. In this thesis, the fluxes tuned by using the measurement of the replicatarget [31] are therefore used.

4.2

Neutrino interaction

In the energies of the T2K beam neutrinos up to 30 GeV, neutrinos interact with
nucleus, and a variety of reactions can occur in very diﬀerent ways depending onenergy. For instance, a neutrino can interact with whole an atomic nucleus coherently, whereas it can interact with a constituent quark inside a nucleus. Due to thecomplexity of neutrino interactions in the energy region, interaction cross sections
are calculated by MC technique. In addition, since neutrino interaction often happen
inside a nucleus, resultant outgoing particles are also produced inside the nucleus.
Therefore, rescattering of these particles inside the nucleus needs to be taken into
account.
In T2K, both neutrino interaction and subsequent rescattering of particles produced by the interaction are simulated by NEUT MC event generator [135]. In
NEUT, the following processes are considered:
CC/NC (quasi-) elastic scattering
CC multi nucleons scattering
CC/NC single meason production
CC/NC coherent scattering
CC/NC deep inelastic scattering
Figure 4.3 shows the CC cross sections for neutrinos and antineutrinos, calculated
by NEUT. In the figure, “MEC” and “RES” corresponds to CC multi nucleons scattering and CC single meason production, respectvely. CC deep inelastic scattering
is divided into “Multi-pi” and “DIS”.
64

CHAPTER 4. EVENT SIMULATION

Figure 4.3: Cross-sections for interactions calculated by NEUT 5.3.2. Left and rightcorrespond to νµ and ν̄µ . The gray histograms represent T2K fluxes, which are shownwith arbitrary units. Figure taken from [24].
Elastic and quasi-elastic scattering
NC elastic scattering is a process in which an incoming neutrino scatters oﬀ a target
nucleon. The reaction is given as:νℓ + N → νℓ + N(4.2.1)

where νℓ is either neutrino or antineutrino and N is either neutron or proton. In
this process, only momentum is transferred to the target nucleon and no additional
particles are produced.
In case of CCQE reaction which was mentioned in Section 1.2.1, a W boson is
exchanged between an incoming neutrino and a target nucleon. Consequently, theneutrino and the target nucleon are converted to a charged lepton and other nucleon,
respectively. In neutrino energies below ∼1.5 GeV, CCQE is the dominant interaction process.
Since nucleon is not an elementary particle and an extended object, calculationof such interactions is diﬃcult. For this calculation, the Llewellyn Smith model [167]is used for free protons. The model contains a set of parameters which need to be
determined experimentally. Most of the parameters are accurately determined byexperimental data for β-decay and electron-nucleus scattering. The axial form factor in the model which characterizes the axial charge distribution inside nucleon has
a parameter called MAQE . Since MAQE can not be determined by those experimental
data, it is set to 1.2 GeV/c2 based on the results of K2K [168] and MiniBooNE [169].
For bound nucleon in nucleus, Fermi motion, Pauli blocking, and a nuclear screening eﬀect are taken into account. Fermi motion is the initial movement of the target
nucleon inside the nucleus before it interacts with neutrino and the relativistic Fermi
gas (RFG) model [170] is used. Pauli blocking forces the out-going nucleon to haveits momentum above the Fermi surface. Since the mediator of a weak interaction
propagates through the nuclear medium, there is a screening eﬀect on the propagator
65CHAPTER 4. EVENT SIMULATION

due to long-range correlations between the nucleons inside the nucleus. This eﬀect
is taken into accunt by the random phase approximation [171, 172].
Multi-nucleon interaction (2p2h)
The CCQE reaction for bound nucleon described above is modeled under an assumption. In the assumption, direct correlation among nucleons in the target nucleus isignored, and an incoming neutrino interacts with a bound nucleon without consideration of such direct correlation. However, the results of the νµ and ν̄µ CCQE
interaction for a carbon target by MiniBooNE [169, 173] suggest that existence of aninteraction process (hereafter called “2p2h”) in which an incident neutrino interacts
with two nucleons simultaneously as a result of such direct correlation.
In NEUT, the 2p2h interaction modeled by Ref. [171, 174] is implemented. In thissimulation, a neutrino interacts with a pair of nucleons inside the target nucleus asfollows:
ν + N + N ′ → ℓ + N ′′ + N ′′′ ,(4.2.2)where N and N ′ is the incoming pair and N ′′ + N ′′′ is the outgoing pair. In NEUT,
the incoming np pair is allowed for both neutrino and antineutrino interactions andis selected with a probability of 31 . If the selected incoming pair is not np, thennn and pp pairs are selected for neutrino interaction and antineutrino interaction,
respectively.
Single meason production
Once the center of mass energy in a neutrino-nucleon interaction exceeds the massof a delta baryon, the interaction can produce a baryon resonance excitation. The
subsequent baryon decay produces a single meason as follows:ν + N → ℓ + N∗ → ℓ + N′ + m(4.2.3)where N and N ′ are the nucleon in the initial and the final state, respectively, N ∗ isthe intermediate baryon resonance, ℓ is the outgoing lepton, and m is a meson such
as π, K and η. In this reaction, any interaction channel is allowed if it conserves
electric charge. For instance, single pion production has three CC neutrino interaction channels:
νℓ + n → ℓ− + p + π 0 ,−(4.2.4)

νℓ + n → ℓ + n + π ,(4.2.5)

νℓ + p → ℓ − + p + π + ,(4.2.6)66+

CHAPTER 4. EVENT SIMULATION

three CC antineutrino interaction channels:ν̄ℓ + p → ℓ+ + n + π 0 ,−ν̄ℓ + p → ℓ + p + π ,+−ν̄ℓ + n → ℓ + n + π ,+(4.2.7)(4.2.8)(4.2.9)and four NC neutrino (antineutrino) interaction channels:ν̄ℓ + p → ν¯ℓ + p + π 0 ,(4.2.10)+ν̄ℓ + p → ν¯ℓ + n + π ,(4.2.11)ν̄ℓ + n → ν¯ℓ + n + π ,(4.2.12)0−ν̄ℓ + n → ν¯ℓ + p + π .

(4.2.13)

It is worth noting that in case of CC interaction channels antineutrinos produce
more neutrons compared to neutrinos. In NEUT, this reaction is simulated by theRein and Sehgal s model [175] with some modifications and is considered for W <2 GeV/c2 , where W is the invariant mass of the hadronic final state.
Coherent pion production
Coherent pion production reaction is also considered in NEUT, in which an incoming
neutrino interacts with entire an oxygen nucleus producing a pion:να +16 O → ℓα +16 O + π.

(4.2.14)

The outgoing lepton ℓα is a charged lepton for CC interaction while it is a neutrino for
NC. The charge of the pion is the same charge as the incoming weak-current. Since
four momentum transfer to hadronic system is low and the incoming momentum iscarried by the pion produced, outgoing lepton and resultant pion tend to be peakedin forward direction. The simulation is performed according to the model by Rein
and Sehgal [176].
Deep inelastic scattering
Once hadronic invariant mass W exceeds 1.3 GeV/c2 , NEUT considers deep inelastic
scattering (DIS), in which case an incoming neutrino interacts with a constituent
quark in the target nucleon, and then hadrons are produced. The nucleon structure
function used in NEUT is a model based on the GRV98 [177] for the parton distribution function, with the corrections in the low Q2 region by Bodek and Yang [178].
67

CHAPTER 4. EVENT SIMULATION

Since the DIS interaction has an overlap with the single pion production describedearlier for W < 2 GeV/c2 , only the processes producing more than one pion are considered in this region in order to avoid the overlap. In a region of W above 2 GeV/c2 ,production of heavier mesons such as K and η are taken into account and the outgoing hadrons in the final state are modeled based on PYTHIA/JETSET [179].

4.2.1

Hadronic final-state-interactions (FSI)

After primary neutrino interactions described above, the outgoing hadrons producedin the interactions may eventually exit the target nucleus by propagating throughnuclear medium. The outgoing hadrons have considerable chance to undergo reinteraction with the nuclear medium, which is known to be hadronic final-stateinteractions (FSI) as was mentioned in Section 1.2.1. These hadrons have theirkinematics altered, can be absorbed, can produce more hadrons via FSI. Therefore,
the resultant particles which just left the target nucleus are often diﬀerent from theparticles produced in the primary neutrino interaction.

Figure 4.4: A schematic drawing of hadronic final-state-interactions by an intranuclear cascade model. Figure taken from [25].
In most neutrino event MC simulations including NEUT, FSI is simulated withinframework of an intranuclear cascade model since modeling of FSI is quit diﬃcult. The concept of intranuclear cascade model was proposed by R. Serber in
l947 [180]. Then, a statistical calculation of cascade model based on his idea wasmade by M. Goldberger [181], and in 1958 most complete computation of the M.
Goldberger calculation using MC technique was performed by N. Metropolis etal. [182, 183]. Currently widely adopted framework of cascade model was established by H. Bertini [184, 185].
Within cascade model, hadrons are treated as classically, and are linearly propagated through the nucleus from their generation points in finite steps. At each step,
interaction probabilities are calculated for all the allowed reactions by taking into
68

CHAPTER 4. EVENT SIMULATION

account local nuclear density. Then it is determined whether or not an interaction
happens at the step based on the calculations. This hadron transportation continues
until hadrons exit the nucleus. Figure 4.4 shows a schematic drawing of intranuclear
cascade model.
In the NEUT’s cascade model, hadron FSI is simulated as follows. When a νinteraction happens, its interaction position inside the target nucleus is determinedbased on the Woods-Saxon nuclear density profile [186]. If the primary ν interaction was not DIS, then the hadrons produced in the interaction share the above
interaction position as their production positions. In case of DIS, the production
positions of hadrons are shifted due to the eﬀect of formation zone. The concept was
originally introduced by [187] and applied to hadron production for the first timeby [188]. The distance between the primary ν interaction and the hadron production vertices is parametrized by p/µ2 , where p is the momentum of the hadron andµ2 is a free parameter. The value of µ2 is estimated based on the results of the SKAT
experiment [189]. From the production position, each hadron is transported linearlythrough the nucleus step-by-step. Each step has a size of xstep = RN /100 [190],
where RN is the size of the nucleus. This size is chosen to be small enough to beable to approximate constant nuclear density. For each step, the probability that a
hadron passes a distance x (hereafter called “free path”) without any interaction is
calculated as:
P (λ) = e−x/λ ,(4.2.15)

where λ = (σρ)−1 is the mean free path and σ is the total interaction cross sectionsand ρ is the nuclear density. By generating a random number, the free path at a
step is sampled as follows:
x = −λ ln(ξ),(4.2.16)

where ξ is a random number distributed uniformly between 0 and 1. If xstep > x, thenan interaction happens. Otherwise, the hadron is linearly transported to the next
step. When an interaction occurs, the Pauli blocking eﬀect is taken into account,which requires the nucleon after the interaction to have a momentum larger than the
Fermi momentum. If the requirement is not satisfied, the interaction is withdrawn,
and the hadron moves to the next step. This transportation between steps is repeateduntil the hadron disappears by an interaction or it escapes from the nucleus.
For pion FSI, the model by Oset et al [191] is used for calculating cross sectionsof elastic scattering, single charge exchange, absorption. In a momentum region
above 500 MeV/c, pions have high enough energies to produce multiple hadrons or
perform double charge exchange. These reactions are modeled based on the resultsof fits to the data of pion scattering oﬀ from free proton and deuteron compiled69CHAPTER 4. EVENT SIMULATIONby [192].The model in NEUT has been tuned using various pion-nucleon and pionnucleus data [26]. Figure 4.5 shows the tuned cross sections calculated by for π ± -12 C
scattering.

Figure 4.5: A schematic drawing of hadronic final-state-interactions. Figure takenfrom [26].
For nucleon FSI, the interaction probabilities are calculated based on the freenucleon-nucleon scattering by [193]. Elastic scattering, single pion production, anddouble pion production are considered. The cross sections are also used in GCALOR [134]by which hadronic interactions in the detector simulation are simulated. Figure 4.6
shows the cross sections used in NEUT and GCALOR.

Figure 4.6: Cross sections of free N -N scattering used in NEUT and GCALOR. The
left and right plots corresponds to pp scattering and pn scattering, respectively. The
cross sections are retrieved from GCALOR.

4.3

Detector simulation

The resultant particles of NEUT, which are leptons and hadrons escaping from thenucleus, are fed into a detector simulation called SKDETSIM in order to simulate
the detector response to these particles. SKDETSIM is a GEANT3 [161] based MC
simulation and simulates particle interactions and decays including generation and70

CHAPTER 4. EVENT SIMULATION

propagation of Cherenkov photons by considering the geometry of the SK detector. In
addition, PMT’s response to generated Cherenkov light and resultant response of theelectronics are simulated. The detector parameters used in SKDETSIM such as thewater property are tuned by using various calibration data described in Section 3.4.
Output of SKDETSIM is formatted in the same as real data, and thus same analysis
chain can be applied to both real data and output of SKDETSIM.
Hadronic interaction processes are simulated by GCALOR package [134], with an
exception for charged pions below 500 MeV/c for which NEUT is used. GCALOR
is a collection of diﬀerent MC simulation models, which is summarized in Table 4.1.
Note that in the energy region associated with the primary analysis of this thesis(also, most of the T2K beam neutrinos), FLUKA is not called in GCALOR.
Table 4.1: Summary of MC simulation models used in GCALOR. The energies are
given by kinetic energy.
Criteria
Hadrons > 10 GeV
Hadrons < 10 GeV
Neutrons < 20 MeV

MC simulation package
FLUKA [194]HETC [195, 196]
MICAP [197]For nucleons with an energy below 3.5 GeV and charged pions with an energy
below 2.5 GeV, HETC (High Energy Transport Codes) uses NMTC (Nucleon Meson
Transport Code) [198] which uses an intranuclear cascade evaporation model basedon Bertini [185, 193]. The simulation procedure of the model is divided into two
steps: fast cascade and subsequent evaporation of particles. In the first step, acascade simulation is performed in a similar way described in Section 4.2.1. Afterthe first step, the residual nucleus can be altered from the target nucleus before thecascade process, and can emit particles when deexciting. The evaporation process
is handled by EVAP-4 [199] which is based on a MC calculation [200]. In thisintranuclear cascade evaporation model, a nuclear density profile is used for bothprotons and neutrons [184]. It consists of three concentric sphere regions in order toapproximate a charge distribution obtained from electron scattering data [201].
For neutron energies below 20 MeV, MICAP (Monte Carlo Ionization Chamber
Analysis Package) [202] is adopted. It uses ENDF/B-V (Evaluated Nuclear Data
File version B) which consists of neutron scattering cross sections modeled basedon experimental data. Various neutron-nucleus reactions are considered by MICAP
and are summarized in Figure 4.7. Figure 4.8 shows the macroscopic cross section ofwater which is used to calculate interaction probability in MICAP. Within MICAP
thermalization of neutrons and neutron capture are simulated.

71

CHAPTER 4. EVENT SIMULATION

Figure 4.7: Summary of neutron-nucleus reactions considered in MICAP. Figure
taken from [27].

Figure 4.8: The macroscopic cross section for water used in MICAP.
Emission and propagation of Cherenkov photons in water are handled by custom
codes. Attenuation of Cherenkov light in water due to absorption, Rayleigh scattering, and Mie scattering are taken into account. Light reflection by PMT, blacksheet,R
and Tyvek⃝
are also considered. The timing and charge response of the SK PMTs
and the subsequent response of electronics are simulated.

72

CHAPTER 4. EVENT SIMULATION

4.4

Hybrid neutron MC

As was described in the beginning of this chapter, MC simulation of the far detector mainly consists of two parts: simulation of neutrino interactions in water anddetector simulation. The currently used MC sets in T2K (called “14a T2K-SK MCsets”) do not include suﬃcient information in order to perform analyses which use
information about neutron tagging. In addition, some neutron productions had notbeen simulated in SKDETSIM. Therefore, it was modified for the primary analysis of
this thesis. As a result, another MC sets (hereafter called “hybrid neutron MC sets”)
were generated by using the modified SKDETSIM. In the following, modifications
made for hybrid neutron MC are described.
For very low energy analysis such as neutron tagging, PMT hits related to low
energy random background sources (e.g. radioactive decay products) have nonnegligible impacts. However, an accurate simulation of these background sources
is extremely diﬃcult. Indeed, they have never been simulated in SKDETSIM. Although they can not be simulated easily, the PMT hits originating from them (hereafter called “noise hits”) can be obtained from T2K dummy spill data. Since T2K
dummy data is taken with the T2K trigger during T2K beam-oﬀ periods, the datacontains noise hits produced by all the low energy background sources in the far
detector as well as the dark noise of the ID PMTs. Thus, the first modification is
to merge noise PMT hits into simulated ones which originate from neutrino interactions. This was done by author [203] and is as follows:• In SKDETSIM, the energy threshold of the neutron simulation is reduced to10−4 eV, which enables simulating 2.2 MeV γ ray emitted by neutron capture
on hydrogen nucleus.
• The record time of PMT hit information is extended up to +535 µs from trigger
time, because thermal neutron capture has a capture time constant of ∼200 µs.
• The dark noises of the ID PMTs are simulated only until +18 µs, after which
the PMT hits of dummy spill data are merged into the simulated hits which
are produced by particles originating from neutrino interaction.
Figure 4.9 shows a schematic diagram describing how noise PMT hits of dummy
spill data are added to simulated PMT hits. The +18 µs at which noise PMT hits
in dummy spill data are started to be merged with simulated hits is chosen due tothe fact that PMT hit by PMT’s after pulse has not been implemented in SKDETSIM. For the ID PMTs, PMT hits are also produced by their after pulses, which are
peaked around +15 µs later after primary hits due to neutrino interactions. Since
after pulses are not simulated, they may produce additional background events inthe neutron tagging only for real data if a time region before ∼15 µs is included. Inorder to avoid such possible background events which can not be modeled by dummy
spill data, the value of +18 µs is determined.
73

CHAPTER 4. EVENT SIMULATION

Figure 4.9: A schematic diagram of the procedure that merges noise PMT hits ofdummy spill data into simulated PMT hits.
In addition to the above modification, another modification was made in SKDETSIM. Neutron productions by µ− and π − captures on oxygen nucleus had never been
simulated although contribution from these captures to total number of neutrons associated with neutrino interactions is not negligible. To implement neutron productions by these captures, Geant4.9.6 is used since these productions are not available in
SKDETSIM. Technically G4MuonMinusCaptureAtRest and G4PiMinusAbsorptionAtRest
which are the classes of Geant4.9.6 and are used as the default models, are directly called from SKDETSIM via an interface which connects SKDETSIM with
Geant4.9.6. The resultant neutron multiplicity, their energy spectrum, and impact
on the analysis samples used in the primary analysis of this thesis are summarizedin Appendix A.

4.5

Summary of MC sets

The primary analysis of this thesis uses three hybrid neutron MC sets, each of which
consists of simulated events for both FHC and RHC modes. The first set is generated
based on NEUT and used as “default MC set” by which MC expectations and neutron
tagging eﬃciency are calculated. For the other two sets, GENIE [11] and NuWro [136]are used as alternative MC ν event generators in order to study dependence of ν
event generators on neutron tagging algorithm and compare neutron productions
by neutrino interactions and FSI between the three generators. Although ν event
generator is diﬀerent for each MC set, the same detector simulation, SKDETSIM, isused for all the three sets.
The procedure of the MC generations is tricky due to very diﬀerent energy scale
between primary neutrino interactions (O(1) GeV) and γ rays from neutron captures(O(10−2 ) GeV). Since the beginning of the T2K data taking in January 2010, the far
detector has been stably running, although there have been several time variations in
74

CHAPTER 4. EVENT SIMULATION

the detector. For primary neutrino interactions, eﬀects of the detector time variations
are negligibly small, whereas these eﬀects can not be ignored for neutron tagging.
Therefore, the detector simulation was run twice for each MC set in order to take
into account the time variation eﬀects. The first run was done with the same set ofthe detector parameters (or “generation point”) as used for the generation of the 14a
T2K-SK MC set (i.e. oﬃcial T2K MC), which ensures that there is no systematic
diﬀerent in the part of primary neutrino interactions between the hybrid MC andthe 14a T2K-SK MC sets. For the second run, diﬀerent set of detector parameters
was used, which were chosen in terms of neutron tagging. The generation point wasdetermined by considering the following two factors. To take into account the time
variations, one of the best representative generation point may be the point of a T2K
Run where 50% of POT for the primary analysis of this thesis was accumulated. In
addition, since the hybrid neutron MC uses dummy spill data to model noise PMT
hits for neutron tagging, the limited statistics of dummy spill data needs to be taken
into account. The generation point for the second detector simulation was chosen
to be the far detector DAQ run#74222 which is in December 2015. Accordingly,
the PMT hits of the dummy spill data taken from Nov. 2015 to Feb. 2016 wereadded to the simulated PMT hits of the second simulation. In case of the firstdetector simulation, its generation point is in August 2009. More details in the MC
productions can be found in [204].
Note that in the analysis of this thesis the results of the first simulation areused for the neutrino event selection described in Section 7.2 and computing the
MC expectation for quantities that use reconstructed muon kinematics, whereas theresults of the second simulation are used only for the neutron tagging related.

75

Chapter 5
Data reduction
This chapter describes the data reduction of the T2K beam neutrinos at the SK far
detector. The selection of the beam data is described in Section 5.1. Extractionof “events” induced by the T2K beam neutrinos, and the subsequent classificationon the extracted events are overviewed in Section 5.2. Then, Section 5.3 describes
neutrino event reconstruction. Information about the data taking until 2018 and thedata set used for this analysis is summarized in Section 5.4.

5.1

Good spill selection

The reduction processes of the T2K event at the far detector begins with the selectionof “good spills” by requiring the following conditions on a spill-by-spill basis. Only
good spills are used for physics analyses. The criteria [20] are as follows:
1. DAQ alive
The DAQ of the far detector must be running when taking the beam data.
2. Bad subrun cut
The subrun of a spill collected should not be a bad subrun. A subrun is aunit of the far detector data, which roughly corresponds to one minute longof data taking. Each subrun is determined whether or not the subrun issuitable for physics analyses based on various information regarding thedetector status. In order to assign good or bad to a subrun, the samedefinition used for the SK atmospheric analyses is utilized. Bad subruns
are primarily caused by flashing PMTs that emit light from internal corona
discharge inside.
3. Incomplete data/GPS error cut
Since the rates of dark noise hits of the ID and OD PMTs are approximately constant for ∼1 ms window which is equivalent to a T2K window,
the number of hits within the ± 500 µs of a spill is required to be greaterthan 4,8000 and 6000, respectively. The cut intends to reject the casewhere part of the detector is not working properly. These thresholds are76CHAPTER 5. DATA REDUCTION

determined based on looking at dummy spill data in which the beam
neutrino data are not included. The threshold for the OD hits has beenchanged from 6000 to 5400 during the Run 1-9 data taking periods mainly
due to increase of number of dead-OD PMTs. In addition, the GPS system at the far detector is required to be stable by imposing the conditionon the GPS time stamp: |GPS1 − GPS2 − oﬀset| < 100 ns.
4. Special data block cut
Information about all the PMT hits is recorded by the DAQ system of the
far detector in a unit of 17 µs long data block. The pedestal block which
stores the pedestal data for all the channels of the front-end electronics
module and TDC rest block which is for resetting some counters in the
TDC chips are generated once per 4096 and 65536 blocks, respectively.
These special blocks are mandatory for the data taking of the DAQ system, which causes an unavoidable loss of spills. The cut criterion is thata spill does not contain a special data block.
5. Pre-activity cut
The final cut is designed to reject event produced by non-T2K beam neutrinos such as electrons by decays of cosmic-ray muons. The cut therefore
require no activities in the 100 µs before the beam arrival timing in order
to avoid contamination of such events in the beam window.
Table 5.1 summarizes the good spill selection at the far detector for the Run 1-9
data. The overall ineﬃciency of the spills during the Run 1-9 data taking periods is∼1% as shown in the table.
Table 5.1: Summary of the good spill selection at the far detector for the Run 1-9
data. Numbers taken from [31].
Number of spills

Ineﬃciency

Beam good spills(1) DAQ alive(2) Bad subrun cut(3) Incomplete data/GPS error cut(4) Special data block cut(5) Pre-activity cut

20,122,743
20,085,525
20,039,874
20,030,596
20,014,244
19,915,932

0%0.18 %
0.23%
0.05%
0.08%
0.49 %

Total SK good spills
Total POT (×1020 )

19,915,932
31.2836

1.03%
-

77

CHAPTER 5. DATA REDUCTION

5.2

FC event selection

As was described in Section 3.3.2, a ± 500 µs time window surrounding the expected
time called “T2K window” are defined for each beam spill. The information about
all the PMT hits in a T2K window is stored. Then later “events” induced by theT2K beam neutrinos are extracted and classified. In the following, the selection of
the fully-contained (FC) events which is the primary sample of the T2K analyses is
described.

5.2.1

Event classification

The software trigger program of the DAQ system is used to extract events containedin a T2K window by searching for clusters of PMT hits. In this program, the variable
N200 which is number of PMT hits in a 200 ns sliding time window is calculated forthe ID and OD PMT hits separately. The trigger thresholds of the ID and OD PMThits are set to 47 hits, which roughly corresponds to a 5 MeV electron, and 22 hits,
respectively. If either the ID’s N200 or the OD’s N200 exceeds the thresholds, a trigger
is issued. For each issued trigger, the PMT hits within a time window from -5 µs to< +35 µs surrounding the trigger time is defined as an event.
All the events extracted from T2K windows are then classified into five types of
events: calibration events, OD events, Low Energy (LE) events, flasher events, andFC events. The classification is sequentially performed. Figure 5.1 schematicallyshows the flow of the classification.

Figure 5.1: A schematic drawing of the flow of the FC event selection. Figure takenfrom [20].
The flow of the classification is as follows:
1. Rejection of calibration events78

CHAPTER 5. DATA REDUCTION

An event is required not to be a calibration event by checking a flag which
identifies calibration events.
2. OD events classification
NHITAC is calculated, where NHITAC is the number of OD PMT hits inthe largest hit cluster. If NHITAC > 15, then the event is classified as an
OD event.
3. LE events classification
PE300 is computed, where PE300 is the total charge of the ID PMT hits
within a 300 ns window. If PE300 < 200 p.e. which roughly corresponds toa 20 MeV electron, then the event is classified as a LE event. In addition,
further reduction of LE events which are likely to be caused by radioactive
decay products is performed. For such LE events, a very large fraction ofPE300 is occupied by a single hit PMT. To detect such events, PEMAX
is calculated, where PEMAX is the maximum charge of a PMT hit used
for the calculation of PE300. If PEMAX/PE300 > 0.5, then the event isclassified as a LE event.
4. Rejection of flasher events
Sudden flashing PMT which emits light from its internal corona discharge
can produce an event mimicking a FC event. Events caused by such PMTs
called “flasher PMTs” are referred to as “flasher” events. Flasher events
tend to have broader distribution of PMT hit timing compared to that ofneutrino events. Also, flasher PMT tends to repeatably produce flasher
events with similar geometrical pattern of PMT hit charge among them.
By using the above two features, flasher events are distinguished fromneutrino events.
The broader feature is parameterized by MIN100 which is the minimum
number of hits in a sliding 100 ns window from +300 ns to +800 ns after
the trigger timing of the event.
Flasher events tend to have larger MIN100 than that of neutrino events
due to its broader feature. If MIN100 >20, then the event is classified asa flasher event.
Geometrical distribution of PMT hit charge is used to construct astatistical test (hereafter called “flasher scan”), and flasher events which
are produced by same flasher PMTs are rejected by the test. To thisaim, the ID wall is divided into 1450 regions called “patches”, each ofwhich contains 6 or up to 9 PMTs. For each patch, the total charge iscomputed. In addition, a database which consists of atmospheric neutrino
data collected at the far detector is used to perform flasher scan. For atested event, which will be judged as a flasher event or a FC event, theprocedure of flasher scan are as follows. (1) A number of scanned events
are sampled from the database to form a statistical ensemble; (2) The
above total charges are calculated for the test event and all the sampled
79

CHAPTER 5. DATA REDUCTION

events; (3) For each combination of a scanned event and the tested event,a Pearson correlation coeﬃcient r and Kolmogorov-Smirnov distance d
are calculated by using the total charges calculated above. Note that if
a scanned event is similar to the tested events, then r and d tend to belarge and the small, respectively. (4) The highest 10 rs and and smallest
10 ds are picked up, and a likelihood function is constructed. (5) If thelikelihood exceeds a threshold, then the tested event is classified as a
flasher event.
After this selection, the selected FC events are passed to event reconstruction.

5.3

Event reconstruction

After the FC event selection described above, event reconstruction is performed, inwhich number of particles contained in a FC event, their particle types, and theirkinematics are reconstructed based on information about time and charge of PMT
hit. At the far detector, this event reconstruction is done by a maximum likelihood
based algorithm, called “fiTQun”. The basics of fiTQun was originally developedin the MiNiBooNE experiment [205]. The main feature of fiTQun makes full useof both “unhit” PMTs and “hit” PMTs inside the SK ID (i.e. all the ID PMTs).
Since fiTQun employs maximum likelihood technique, the event reconstruction isequivalent to find the best particle hypothesis. However, neutron tagging is out of
scope of fiTQun, and it is fully separated from fiTQun. The algorithm of the neutron
tagging is described in Chapter 6.
The event reconstruction by fiTQun is divided into four steps:
1. Event vertex pre-fitting,
2. PMT hit clustering (finding subevents),
3. Single-ring fit,
4. Multi-ring fit.
In the following, thees steps are briefly described. Details of fiTQun can be foundin [28].
Vertex pre-fitting and finding subevents
Since a FC event contains PMT hit information in ∼40 µs, the event reconstruction
begins to divide an event into “subevents” by clustering PMT hits in time. For
instance, in case of a νµ CCQE reaction, a muon is created and produces PMT
hits via Cherenkov radiation. Then, the muon eventually decays, and the resultant
electron also produce PMT hits after a time scale of ∼2 µs from the creation of theparent muon on average. Therefore, in this case there are well separated two PMT
hit clusters in time, each of which forms a subevent.
80

CHAPTER 5. DATA REDUCTION

To define subevents, first the subevent algorithm performs a quick fit to roughly
estimate the vertex of a event, which is done by finding the vertex position x andthe vertex time t that maximize the following metric, called “goodness”:

G(x, t) =

PMT
∑hits
i

(

1
exp −
2

(

i
Tres
σ

)2 )
,

(5.3.1)iiiwhere Tres
is residual time defined as Tres
= ti − t − |RPMT− x|/cn , ti is hit timeiof i-th hit PMT, RPMT is the position of i-th hit PMT, cn is the group velocity oflight in water, and σ is set to 4 ns. Form the above equation, it can be found thatmaximization of goodness is equivalent to minimize residual time.
After obtaining the vertex position x̂ and time t̂ which maximize goodness,
subevents are searched for. Consider the example of the above νµ CC reaction,in which case there are a muon and a decay-electron. For the PMT hits inducedby the muon, their residual time may distribute around zero when using x̂ and t̂.
At zeroth-order approximation, it is reasonably assumed that the vertex positions of
the second and later subevents are close to the first one. Under the assumption, in
this case the residual time of PMT hits induced by the decay-electron can distributenear zero if t̂ is changed to a suitable value. Therefore, subevents can appear as
large peaks in goodness by scanning goodness with respect to t while keeping x̂.
Figure 5.2 shows an example of the scanned goodness with respect to t for an event
which contains a muon and a decay-electron. As shown in the figure, two clear peaks
can be found, which corresponds to two subevents.
Since the number of subevents is a good proxy for the number of decay-electrons
in an event, the number of decay-electrons is computed by using the number ofsubevents. The number of decay-electrons calculated in this way is used to make theanalysis samples of the primary analysis in this thesis.

81

CHAPTER 5. DATA REDUCTION

Figure 5.2: The goodness G(x, t) as a function of t for a MC event consisting a
primary muon and a decay-electron (black dots). The vertical broken lines represent
the true particle creation time. The orange solid lines denote the peak time of thesubevents. The blue and green curves represent the threshold used for selecting
subevent peaks. Figure taken from [28].
Sing-ring and Multi-ring fits
Once an event is divided into subevents, next process is applied to each subevent.
Since fiTQun employs a maximum likelihood algorithm to reconstruct particles contained in an event, for each subevent the following likelihood function given a particle
hypothesis is constructed:
unhit

hit

i

j

L(x) = Π Pi (unhit|x) Π {(1 − Pi (unhit|x))}fq (qj |x)ft (tj |x),(5.3.2)where x parametrizes a hypothesis, which includes particle type, vertex, direction,and momentum. The likelihood function defined in the above equation mainly consists of two diﬀerent kinds of PMTs: “unhit PMT” and “hit PMT”. Unhit PMTs
are PMTs that did not have a real hit, whereas hit PMTs are PMTs which did havea hit. In the above equation, the index i and j run over unhit PMTs and hit PMTs,
respectively. The unhit probability P (unhit|x) that is the probability not to make a
hit for a given hypothesis x is calculated for each individual PMT. For unhit PMTs,
only the unhit probability is considered. On the one hand, for hit PMTs, in addition
to the hit probability P (unhit|x) which can be computed from the unhit probability,
probability for observed timing t and charge q are considered. The charge likelihood
fq (qj |x) is the probability density for observing qj at j-th PMT for a given hypothesis
x. Similarly, the timing likelihood ft (tj |x) is the probability density for observing a
hit by j-th PMT at tj for a given hypothesis.
It may be worth explaining how fiTQun gains the ability that enables performing
particle identification. The presence of fq (qj |x) in the above equation means thatthe likelihood function takes into account the charge pattern of a subevent in the
SK tank. To construct fq (qj |x) , predicted charge is computed for each PMT, which82

CHAPTER 5. DATA REDUCTION

consists of the direct light due to Cherenkov radiation and the indirect light fromlight scattering in water and light reflection by the ID wall and the ID PMT surfaces. The prediction of the direct light strongly depends on given hypothesis, anduses Cherenkov emission profile which describes the average number of Cherenkov
photons emitted per unit track length per unit solid angle by a particle with an
initial momentum. Figure 5.3 shows the Cherenkov emission profile for an electron
and a muon. As shown in the figure, electron produces broader angular distribution
than that of muon, which is caused by the fact that electrons tend to undergo more
multiple electromagnetic scattering compared to muons. Therefore fiTQun can perform a particle identification with an excellent performance by exploiting diﬀerencein emission of Cherenkov photons among diﬀerent particle types.

Figure 5.3: Cherenkov emission profile for electron (left) and muon (right) withinitial momenta of 1000 MeV/c. The vertical axes represent the distance traveledfrom the initial position of the particle. The horizontal axes show the cosine of theangle between the particle direction and the photon emission direction. Figure takenfrom [28].
The maximization of the likelihood function begins with “single-ring fit” which
considers a particle track. The current single-ring fit supports three diﬀerent particle
hypotheses: electron, muon, and charged pion. For each particle hypothesis, the likelihood function is maximized to obtain the best estimates of parameters x describing
the particle track. In practice, the maximization is performed by minimizing −lnL.
Once the best parameters are obtained for all the single-ring hypotheses, the particle
type is determined by the minimized −lnL.
For instance, the particle identification (PID) between electron and muon is performed based on the likelihood ratio ln(Le /Lµ ), where Le and Lµ are the maximized
likelihood function with respect to single-ring electron and muon hypotheses, respectively. Figure 5.4 shows distribution of ln(Le /Lµ ) for electron events and muon
events. As shown in the figure, the likelihood ratio is well separated around at zero,but there is a clear reconstructed momentum dependence. Therefore, in this case83CHAPTER 5. DATA REDUCTION

PID is practically performed as follows:e−like if ln(Le /Lµ ) > 0.2 × p1R−e [MeV/c]
PID =




,

(5.3.3)µ−like otherwise

where p1R−e is the reconstructed momentum under single-ring electron hypothesis.
In a similar way, other PID such as µ v.s. charged pion is performed.

Figure 5.4: Two-dimensional distribution of single-ring ln(Le /Lµ ) and reconstructed
momentum under electron hypothesis for electrons (left) and muons (right). The
distributions are made from particle gun MC events simulated by SKDETSIM. The
solid lines indicate the cut criterion for single-ring electron and muon separation.
Figure taken from [29].
Since in the energies of the T2K beam neutrinos, a primary ν-nucleon interaction
often results in production of more than one visible charged particles which radiate
Cherenkov photons. Therefore, after the single-ring fits, fiTQun moves to trying
to find additional particle tracks by performing the “Mluti-ring” fit in which event
hypothesis consisting of more than 1 particle track is considered.
Among the Multi-ring fits, a dedicated fit is performed for π 0 . π 0 almost always
decays into two γ rays, and these γ rays produce electromagnetic shower via a pair
production of e− and e+ after they traveled some distance. Therefore, π 0 is observed
as the two electromagnetic shower like tracks which originate from the decay vertexof the π 0 . As a consequence, in π 0 hypothesis common vertex position and time areused for the two tracks.
Except for π 0 fit, a generic Multi-ring fit is performed only for the first subvent.
The Multi-ring fit begins with two-ring hypotheses, and increase the number ofparticle tracks (or Cherenkov rings) one-by-one. During the fit, the two hypotheses,
electron-ring hypothesis and “upstream-track π + ” hypothesis, are considered. The
first one treats Cherenkov ring produced by electron or γ ray (i.e. “shower-like”),
whereas that of charged pion or muon (i.e. “non-shower-like”) is fitted by the otherone.
Figure 5.5 shows the flow of the generic Multi-ring fit for an example in whichcase the best single-ring hypothesis is electron’s one. As shown in the figure, the84CHAPTER 5. DATA REDUCTION

Multi-ring fit tries all the possible combinations of the two hypotheses for a given
number of particle tracks. However, the number of tracks considered is increased
by one-by-one. In this case, first, an electron ring or a π + ring is added, and thebest two-ring hypothesis is obtained. If the likelihood ratio between the −lnL of
the best two-ring hypothesis and that of the best single-ring hypothesis exceeds acertain threshold, the two-ring hypothesis is accepted, and another particle track is
added in order to move to three-ring hypothesis. By following similar procedure, thealgorithm continues to add a ring one-by-one up to six rings. Since this Multi-ring
fit often contains fake rings, each ring found in the above procedure is refitted to
improve the fit result and obtain the final result.

Figure 5.5: A schematic drawing of the flow for performing the Multi-ring fit for thecase where the best first-ring fit is electron’s one. Figure taken from [28].
Basic performance
As will be mentioned in Section 7.2, the analysis samples used in the primary analysisof this thesis, called “1Rνµ samples”, are based on single-ring µ-like events and contain a high fraction of CCQE interaction described in Equation 1.2.2. Therefore, it
may be interesting to see the performance of the single-ring fit using muons produced
by CCQE interaction. Figure 5.6 summarizes the resolutions of vertex position, momentum, and direction and misidentification probability that a true single-ring muonis misidentified as a single-ring electron. For the vertex resolution, first distributionof distance between true and reconstructed vertices is made. Then, the 68 percentileof the distribution is defined as the vertex distribution. Similarly, the direction
resolution is estimated from distribution of angle between true and reconstructed
directions. In case of the momentum resolution, first distribution of fractional variation from true momentum is made, and is fitted by a Gaussian. The fitted σ of theGaussian is regarded as the momentum resolution. Misidentifiaction probability is
estimated by following the criterion of electron-muon separation in Equation 5.3.3.
Although the performance is dependent on the true momentum, it is good enough tostudy lepton kinematics dependence on the neutron production. Indeed, the primary
analysis of this thesis measures such kinematics dependence in Chapter 8.

85

CHAPTER 5. DATA REDUCTION

Figure 5.6: Performance of the fiTQun single-ring fit. Top left, top right, bottom
left, and bottom right figures show momentum resolution, vertex resolution, direction
resolution, and misidentification probability as a function of true momentum. The
definitions of these values are described in text.

5.4

Data reduction summary

This section summarizes the T2K data used in this thesis.
T2K started physics data taking in January 2010 and has finished the nine datataking periods: Run 1-9. The Run 9 period ended on May 2018. Although the Run
10 period has started on November 2019, it has not been finished yet. Therefore, theprimary analysis in this thesis uses all the data collected until 2018 which correspondto 14.938×1020 POT for FHC mode and 16.346×1020 POT for RHC mode. Table 5.2
summarize the Run 1-9 accumulated POT.

86

CHAPTER 5. DATA REDUCTION
Table 5.2: Accumulated POT of each Run for the Run 1-9 data taking. FHC and
RHC correspond to the ν- and ν̄-modes beam operation, respectively. The numbers
are derived from Table 1 in [31].

Run1
Run2
Run3
Run4
Run5
Run6
Run7
Run8
Run9
Total

FHC POT (×1019 )
3.26
11.22
15.99
35.96
2.44
1.92
4.84
71.69
2.04
149.38RHC POT (×1019 )
5.12
35.46
34.98
87.88
163.46

During the data taking periods, the quality of the beam neutrinos was continuously monitored. Figure 5.7 shows the stability of the neutrino beam monitored by
the INGRID and MUMON detectors over time. As shown in the figure, the measured
beam direction is better than the requirement of 0.4 mrad. In addition to the stable
operation in the near detector side, the far detector also operated stably, which resulted in a small constant loss of the beam spills. Figure 5.8 shows the accumulated
POT at the far detector as a function of date overlaid with the far detector’s ineﬃciency of the beam spills.

Figure 5.7: Stability of the event rate measured by INGRID (top) and the beam
directions measured by the INGRID and MUMON (middle and bottom). Figure
taken from [30].

87CHAPTER 5. DATA REDUCTION

Figure 5.8: Accumulated POT as a function of date. The red and orange lines
correspond to the FHC Run 1-9 POT and the RHC Run 5-9 POT, respectively. The
green line represents the ineﬃciency of beam good spill at the far detector and its
scale is shown by the right side of this figure. Figure taken from [31].
After the good spill selection and the FC event selection which are described in
Section 5.1 and Section 5.2, respectively, there are 1252 (582) FC events for FHC(RHC) mode. Figure 5.9 shows the cumulative number of FC events as function of
accumulated POT in comparison to an expectation of constant event rate which isderived from the observed FC events and the accumulated POT. As shown in the figure, the cumulative FC events increases linearly as the accumulated POT increases.
Contamination of FC events induced by atmospheric neutrinos is also evaluated byusing the atmospheric neutrino data collected at the far detector. For the Run 1-9
data taking periods, the number of FC events induced by the atmospheric neutrinos
is expected to be 0.512 [31].
Since the event extraction at the far detector is performed based on the expectedbeam arrival time, the FC events should hold the timing structure of beam spill
which has eight bunches with an interval of 581 ns between bunches. Therefore, thetime diﬀerence from the expected beam arrival timing, ∆T0 , is studied. To calculate ∆T0 , two factors, which aﬀect ∆T0 on an event-by-event basis, are taken into
account, one of which is diﬀerence in neutrino flight length from the beam target
at J-PARC to ν interaction vertex position among the FC events. Due to the large
detector volume of the far detector, diﬀerence in the flight length results in a time
diﬀerence of O(10ns) depending on ν interaction vertex position in the detector. In
order to consider this eﬀect, a plane which passes through the detector center and isperpendicular to the beam direction is adopted as a virtual target of the far detector,
and then the time-of-flight of incoming neutrino from this plane to reconstructed νvertex is considered. Also, time delay due to light propagation in water depends onemission position in the detector. Therefore, diﬀerence in light propagation in wateris also taken into account. In addition to these two eﬀects, the constant time delay

88

CHAPTER 5. DATA REDUCTION

due to the DAQ system described in Section 3.3.2 is considered. Figure 5.10 showsthe ∆T0 distribution of the Run 1-9 FC events with the above timing corrections.
As shown in the figure, the eight bunches structure can be clearly seen.

Figure 5.9: Cumulative number of FC events as a function of accumulated POT
at the far detector for FHC mode (left) and RHC mode (right). The blue lines
correspond to the Run 1-9 data. The red lines represent expectation of constant FC
event rates which are obtained from the observed FC events and the accumulated
POT. Figure taken from [31].

Figure 5.10: Distribution of the time diﬀerence from the expected arrival time at thefar detector, ∆T0 , for the Run 1-9 FC events. The vertical dashed lines represent
fitted bunch center positions. Figure taken from [31].

89Chapter 6
Neutron tagging
Since the primary analysis of this thesis aims to measure neutrons, the algorithm used
for tagging neutrons needs to be independent on the modeling of neutron production
as much as possible. To achieve this, a neutron tagging algorithm was developed
for the primary analysis, which consists of two selection stages: the primary neutron
candidate selection and the neutral network (NN) classification. In the following,
first the definitions of neutron tagging eﬃciency and accidental background event
rate which characterize the performance of the algorithm are given in Section 6.1.
Then, Section 6.2 and Section 6.3 detail the primary selection and the NN classification, respectively. A validation of the developed algorithm using a low-energy
neutron calibration data is described in Section 6.4. Section 6.5 ontlines the correction to the algorithm due to the SK detector time variation eﬀects.
In a water target, neutrons associated with neutrino interactions are quickly thermalized after they are produced, and are eventually captured by a hydrogen nucleus
or an oxygen nucleus. The cross sections of thermal neutron captures for hydrogenand oxygen nuclei are 0.33 barns [206] and 0.17×10−3 barns [207], respectively. Thus,
almost all of the thermal neutrons are captured by hydrogen nucleus.
A neutron capture on hydrogen nucleus results in the production of a single
2.2 MeV γ ray which is equal to the binding energy of a deuteron as follows:n + H → d + γ (2.2 MeV).

(6.0.1)In SK, the 2.2 MeV γ rays produce Compton scattered electrons which emit Cherenkov
photons. By detecting these phtons as PMT hits, neutrons can be tagged. The neutron tagging is therefore equivalent to identify the γ rays.

6.1

Definitions of tagging eﬃciency and background
event rate

The neutron tagging algorithm is applied to ν events on an event-by-event basis. Fora ν event, the algorithm searches for neutrons from +18 µs to +513 µs after ν inter90

CHAPTER 6. NEUTRON TAGGING
action. Since the neutron caputre time constant is ∼200 µs, about 92% of neutrons
are therefore contained in the search region.
The algorithm finds neutron candidates which consist of true neutron eventsand accidental background events. The true neutron events are produced by the
Cherenkov photons originating from the 2.2 MeV γ rays, whereas the background
events are caused by accidental coincidences of noise PMT hits. Since the noise hitsstem from random background sources such as PMT’s dark noise and radioactive
decay products, the background events do not depend on detail of primary neutrino
interaction.
The performance of the algorithm are characterized by “neutron tagging eﬃciency” and “background event rate” defined as follows:

tagging eﬃciency =Selected Candidates which are true neutrons
All neutron captures(6.1.1)

background rate =Selected Candidates which are backgrounds
Total neutrino events(6.1.2)For the tagging eﬃciency, the denominator includes the neutron captures which happen outside the SK ID as well as the neutron capture occurred inside ID. Therefore
neutrons escaping from ID need to be considered and will be discussed in Section 7.2.
In addition, neutron captures occurred outside the search window are included into
the denominator. The background event rate does not depend on the detail of ν interactions such as the kinematics of the outgoing lepton. Once the rate is estimated,
we can subtract the background events of the neutron tagging in the real data byusing the number of observed ν events. Such subtraction will be done to measureneutrons in Chapter 8.4.

6.2

Initial selection

In the first stage of the algorithm (hereafter called “primary selection”), neutron
candidates are searched. The primary selection is a very simple selection based on
number of PMT hits.

91CHAPTER 6. NEUTRON TAGGING

Figure 6.1: Distribution of kinetic energies for electrons which are produced by theCompton scattering of 2.2 MeV γ rays
Once a neutron capture on hydrogen nucleus happens, a single 2.2 MeV γ ray isemitted by the reaction 6.0.1. Then, the γ ray produces one or more recoil electrons
via Compton scattering. However, number of PMT hits produced by these Compton
scattered electrons is extremely small since their kinetic energies are very low asshown in Figure 6.1. A typical MC ν event display for the PMT hits, which are usedin this neutron tagging algorithm, is shown by Figure 6.2. From this figure, it canbe seen that indeed true 2.2 MeV γ rays produces extremely small PMT hits (redcolored dots).

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CHAPTER 6. NEUTRON TAGGING

Figure 6.2: Example of event display of a ν event (MC) which have two true neutron
captures on hydrogen. The PMT hits after 18 µs from the primary event trigger are
shown. The red and blue dots correspond to PMT being hit by true 2.2 MeV γ ray
and noise.
In order to extract the signal of 2.2 MeV γ ray, the primary selection performs avery simple selection based on number of PMT hits by clustering PMT hits in time.
Figure 6.3 shows a typical distribution of PMT hit timing of a ν event. As shown in
the figure, the PMT hits related to these γ rays tend to be buried under noise PMT
hits. Thus, the primary selection begins with a reduction of the noise hits, which
utilizes a characteristic of the noise hits. From a recent study of the PMT hits in the
dummy spill data, the noise hits have a large time correlated component as shownin Figure 6.4. This component has successive hits probably due to scintillation lightemitted from the ID PMT’s glass. The correlated component can be removed by
imposing a cut on time diﬀerence between hits. The cut is applied to each individual
PMT as follows:• Sort hits in increasing order by its recorded time,• Compute time interval between two successive hits sequentially from the first
hit,

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CHAPTER 6. NEUTRON TAGGING

Figure 6.3: Example of raw PMT hit time distribution of a ν event (MC) which
has two true neutron captures on hydrogen nucleus. The red and blue correspond
the PMT hits simulated in MC and extracted from dummy spill data, respectively.
In the red histogram, spikes around +190 µs and +250 µs are due the two neutron
captures.
• If time diﬀerence is shorter than 3 µs, then the two hits used for the calculationof the time diﬀerence are identified as the time correlated hits, and thus bothhits are removed.

The width of 3 µs was determined empirically, because this cut removes the hits
originating from 2.2 MeV γ rays as well as noise hits. In the primary selection, thiscut results in about 60% reduction of background events while keeping ∼90% of
2.2 MeV γ events compared to the case of the absence of this cut. After this noise
hits reduction, the primary selection moves to the next step, in which clusters of
PMT hits in time are searched for.
As a Compton scattered electron produced by 2.2 MeV γ ray can be treated as apoint source of Cherenkov photons, PMT hits associated with the γ ray are ideallywell clustered in time. However this is not the case in practice, because distanceof light traveled from the emission point to hit PMT position is diﬀerent among
these hits. In order to make these hits clustered in time, subtraction of time-of-flight(TOF) need to be done for each individual hit. Although the TOF calculation fromneutron capture position is an ideal way for this purpose, in reality this is impossible,
because the capture position is unknown. The TOF is computed from ν interaction
vertex reconstructed by fiTQun which was mentioned in Section 5.3. As shown in
Figure 6.5, most of the neutrons are captured within 2 m away from the ν interaction
vertex. In addition, the vertex resolution of fiTQun is good enough in comparison
to the 2 m scale as was shown in Figure 5.6. The use of the fiTQun vertex as analternative of neutron capture vertex is therefore a good approximation.
94

CHAPTER 6. NEUTRON TAGGING

Figure 6.4: Distribution of time diﬀerence from the first hit (µs) for dummy spill data
which were taken in the beam oﬀ period between the Run 6 and Run 7. For eachindividual PMT, the time diﬀerences are computed, but are filled into this histogram.
The cyan solid curve is the best result of a χ2 fit of the distribution to a function
consisting of two exponential + an asymmetric gaussian + a constant functions. Theorange dashed line shows the fitted constant function.

Figure 6.5: Distribution of true distance from ν interaction vertex to neutron capture
vertex.
After subtracting TOF from all PMT hits by using reconstructed ν interaction vertex, the TOF subtracted hits are sorted in increasing order by the residual
time. Then, number of PMT hits in a 10 ns sliding timing window (hereafter called“N 10pvx ”) is computed as schematically shown in Figure 6.6. Also, the capture time
t0 of the cluster is calculated as the time of the first hit in the N 10pvx hits. A
95

CHAPTER 6. NEUTRON TAGGING

Figure 6.6: A schematic drawing of the calculation of PMT hit clusters using a 10 ns
sliding timing window.
N 10pvx cluster is selected as a neutron candidate if it passes the following criteria:• N 10pvx ≤ 50,• N 200 ≤ 200,
• Time diﬀerence from previous candidate’s t0 ≥ 20 ns,• N 10pvx ≥ 7,
where N 200 is the number of PMT hits in the 200 ns surrounding t0 . The first two
cuts intend to remove high energy activities such as decay electrons from cosmic
ray muons. The third one is used in order to avoid double counting of a 2.2 MeV
γ ray (i.e. true neutron). The performance of the primary selection is dominantly
determined by the last cut.
To evaluate the performance of the primary selection, for MC events, each neutron candidate is judged whether it is a true neutron or not based on MC truth
information about true neuron capture time ttrue [203]. If |t0 − ttrue | < 100 ns, thenthe candidate is regarded as a true neutron. Otherwise, it is identified as a background event.
Figure 6.7 shows neutron tagging eﬃciency and background event rate as a function of lower threshold on N 10pvx . Lowering the threshold makes the eﬃciency higher
linearly, whereas the background rate increases exponentially at the same time asshown in Figure 6.8. Although almost all the background events selected in the primary selection will be rejected in the NN classification, too many background eventsin the primary selection result in a large amount of contamination in true 2.2 MeV γ
events, which causes a large contamination of the background events in the observed
neutrons. In addition, neutron candidates with small N 10pvx hits do not have strong
enough discrimination power between 2.2 MeV γ and background events in the NN
classification. The lower threshold of the last cut was therefore chosen to be 7 byconsidering the above two factors. With this threshold, a ν event has ∼3 background96

CHAPTER 6. NEUTRON TAGGING

events after the primary selection, which can be seen in the left panel of Figure 6.8.

Figure 6.7: Distribution of N 10pvx for the true neutron events (left) and backgrounds
events (right), respectively. The green arrows show the lower cut position of N 10pvx .

Figure 6.8: Neutron tagging eﬃciency as a function of N 10pvx threshold (left) andnumber of accidental background events per ν event as a function of N 10pvx threshold(right). Note that the threshold used for this analysis is N 10pvx = 7.

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CHAPTER 6. NEUTRON TAGGING

6.3

Neural network classification

Figure 6.9: Example of typical PMT hits of a signal MC event and a backgroundMC event. The signal (background) event has 10 (8) PMT hits and a NN output
value of 0.9906 (0.0007). The hits of signal event (background event are enclosed bypink hollow squares (cyan hollow circles).
After the primary selection, there is still a large contamination of background eventsin true neutron events. Thus, these background events need to be eﬃciently removed
while keeping true neutron events as much as possible. Since there is no visible
diﬀerence between signal events and background events as shown in Figure 6.9, sucheﬃcient reduction of background events is achieved by employing an artificial neuralnetwork (NN) technique. The second selection of the neutron tagging algorithm istherefore the classification of the candidates selected in the primary selection by aNN.
In this classification, a set of 14 feature variables are fed into the NN to produce
the output of the NN which reflects how likely that particular set of variables is tobelong to the candidate labeled as “signal/background”. By using the output, thefinal selection is done on a candidate-by-candidate basis.
In order to compute the 14 variables, first, neutron capture vertex is reconstructed
for each candidate selected in the primary selection. The reconstruction is performedby using N 10pvx hits. As was explained in the previous section, 2.2 MeV γ ray can betreated as point-like source of Cherenkov photons, which leads us to expect that the98

CHAPTER 6. NEUTRON TAGGING

spread of the residual time computed from true neutron capture position is minimum.
Thus, the capture vertex rncap is defined as follows:
 v
u
 u
rncap = argmin  t
r


∑
1

(τi (r) − τ̄ (r))2  ,N 10pvx i=1
N 10pvx(6.3.1)whereτi = ti − T OFi (r),r is trial vertex, ti is hit time of i-th hit, T OFi (r) is TOF of i-th hit computed fromr, and τ̄ (r) is the average of the residual time. The left panel of Figure 6.10 shows
the distribution of the distance between the true and reconstructed vertices, and theresolution is estimated to be about 134 cm from the distribution. Since 2.2 MeV
γ rays travel ∼20 cm on average before they undergo the first Compton scattering
as shown in the right panel of the figure, the distance between the true and reconstructed vertices is broadened.

Figure 6.10: Distribution of the distance between the true and reconstructed vertices(left). The arrow shows the 68 percentile of the distribution. Distribution of true
distance from the generation point of 2.2 MeV γ ray to the vertex of the first Compton
scattering (right).
After the vertex reconstruction, a new set of PMT hits within a 10 ns windowusing the reconstructed capture vertex is computed. Then, the 14 variables are calculated by using only the newly computed PMT hits and the capture vertex, whichmeans that all the variables do not explicitly include any information regarding
primary ν event such as reconstructed distance between ν interaction and neutron
capture vertices. Such information is highly dependent on the modeling of neutron
production (or particular MC simulations), and thus is likely to introduce a dependence of the modeling of the neutron production into the NN. The neutron tagging
99

CHAPTER 6. NEUTRON TAGGING

algorithm used in the primary analysis of this thesis has been purposely designed to
avoid such model dependence and therefore diﬀers from algorithms used in other SK
analyses. As this primary analysis aims to measure neutron itself, a maximum eﬀort
needs to be made in order to minimize such model dependence as much as possible.
The 14 variables therefore characterize diﬀerences in geometrical and time spreadsof the hits, and position of reconstructed capture vertex in ID between true neutron
and background events. The robustness of the neutron tagging algorithm, which
describes how strongly the algorithm depends on a particular MC simulation, will
be mentioned in the context of the systematic uncertainty on the neutron tagging
eﬃciency in Section 8.3.13.

6.3.1

The 14 feature variables

In the following, the 14 feature variables used for the NN classification are described.
All the 14 feature variables are shown in Figure 6.13. Figure 6.14 shows the linear
correlations between the variables for signal and background events.

1. Number of hits in 10 ns: N 10nvx
This is the same number of PMT hits which are calculated by using thereconstructed neutron capture vertex as mentioned above. The remaining
13 feature variables are computed using the reconstructed capture vertex
and the N 10nvx PMT hits except for N 300S.
2. Number of hits in 300 ns: N 300S
The PMT hits of signal events are tightly clustered in the residual timing
computed from the reconstructed capture vertex, whereas those of background events tend to be broadly distributed. For instance, Cherenkov
photons emitted by β particles produced in decay chain processes of radon
may not be tightly distributed in the residual timing since the TOF subtraction is done from reconstructed neutron capture vertex rather thanthe production vertex. This diﬀerence is taken into account by considering N 300 which is the number of PMT hits in the ±150 ns surrounding
the capture time t0 of the candidate event. N 300S is defined as N 300 N 10nvx .
3. Number of clustered hits: N cS
It is known from studies on background events that the PMT hits ofbackground events tend to be geometrically clustered compared to thoseof signal events. This tendency is parametrized by the number of clustered
PMT hits N c. To calculate this variable, first hit vector which is definedas the unit vector from the reconstructed n capture vertex to hit PMT
position is computed for each PMT hit of the candidate event. Then,for each hit angles between its hit vector and the other’s hit vectors arecalculated. If a hit has an angle less than 14.1 ◦ , then the hit is regarded100CHAPTER 6. NEUTRON TAGGING

as a clustered hit. This calculation is conducted for all the PMT hits ofthe candidate event. If the cumulative number of clustered hits is morethan 3 hits, then the cumulative number is assigned to be N c. Otherwise,
N c is set to 0. N cS is defined as N 10nvx - N c.
4. Standard deviation of hit timings: tSD
Although the GMT hits of candidate events are clustered in a 10 NSF
window, spread of hit timings in the window still diﬀers between signal
and background events. T od is calculated as the standard deviation of
the residual time of N 10nvx PMT hits.
5. Minimum standard deviation of hit timings: tSDM in6
Ideally PMT hits of signal events consist of PMT hits related to 2.2 MeV
γ rays from neutron captures on hydrogen nucleus only. However noise
hits can contaminate signal events. In order to consider the eﬀect by suchcontamination, another standard deviation is calculated by using all thepossible combinations of 6 hits in the PMT hits of a candidate event.
Then, the minimum value is defined as tSDM in6.
6. Nearest distance to the ID wall: nDwall
Reconstructed vertex of background events tends to be distributed near
the ID wall. This tendency is considered by nDwall which is the closest
distance from the reconstructed vertex of a candidate event to the ID wall.
7. Closest distance to the ID wall along particle direction: nT wall
The PMT hits of signal events are produced by Compton scattered electron originating from 2.2 MeV γ rays, which means that these hits havea directionality because of the nature of Cherenkov radiation. On theother hand, background events do not have such directionality since they
are caused by accidental coincidences of noise hits. This diﬀerence distinguishes between signal and background events even if they have identicalvalue of nDwall and is parametrized by nT wall which is the closest distance from the reconstructed capture vertex to the nearest ID wall along
the candidate’s direction. The direction is reconstructed as the average of
hit vectors of the candidate.
8. Geometrical acceptance of PMT: lnAccp
The ID PMTs have an angular dependence on detecting photons. In addition, photons emitted by charged particles are attenuated by the lightabsorption and scattering of the water. Therefore, probability to hit i-th
ID PMT by a photon emitted at an ID position r depends on the geometrical relation between the emitted position and the hit PMT position,and can be expressed as:a (r)Pi (r) = ∑all ID iPMTsi

101

ai (r),(6.3.2)

CHAPTER 6. NEUTRON TAGGING

where
(
)
|r − Ri |F (θi )exp −,ai (r) ≡LAtt|r − Ri |2
θi is the PMT zenith angle of the photon, F (θi ) is the angular dependenceof the PMT detection eﬃciency, Ri is the position of i-th PMT, and LAtt isthe light attenuation length of the water. The angular acceptane, which is
obtained from a simulation of optical photons by the detector simulation,is given as:
F (θ) = 0.21 + 0.52 cos θ + 0.39 cos2 θ − 0.13 cos3 θ(6.3.3)

The PMT hits of signal events are produced by photons emitted aroundreconstructed capture vertex, whereas it may not be the case for background events. This diﬀerence is taken into account by lnAccep which
is a likelihood calculated by using the above hit probability.
N 10nvx∑1
lnAccep =− log10 Pi (rncap ).
N 10nvx i(6.3.4)In the above equation, the factor 1/N 10nvx is adopted in order to take into
account diﬀerent N 10nvx value among candidate events.
9. Hypothesis testing of Cherenkov angle: llrCAng
For a candidate event, the Cherenkov opening angle can be defined using
arbitrary 3 hits as schematically shown in Figure 6.11. Since the PMT
hits of signal events are produced by Compton scattered electrons originating from 2.2 MeV γ rays, the opening angles of signal events tend to be∼42 ◦ which corresponds to the opening angle of the Compton scatteredelectrons. On the one hand, those of background events are expected not
to have such angular dependence.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.11: A schematic drawing of opening angle defined by 3 hits.
To make use of this diﬀerence, a log likelihood ratio, llrCAng, is constructed as:llrCAng =N∑

ln LBkg. (θCi ) − ln LSig. (θCi ),(6.3.5)iwhere N is all the possible combinations of 3 hits using the candidate’s
N 10nvx PMT hits, θCi is the opening angle of i-th 3 hits combination,and LBkg. and LSig. are the N 10nvx dependent probability density functions (PDFs) of the opening angle for background and signal events, respectively. Figure 6.12 shows the pre-calculated PDFs. As shown in the
figure, the signal PDF has the clear peak around at ∼ 42◦ .
10. Geometrical anistropy of hits: βℓ
The diﬀerence in the geometrical spreads of the PMT hits between signal
and background events are further utilized. Since this diﬀerence originatesfrom diﬀerent angular distribution of PMT hits, the angular distribution
can be used to separate the signal and background events. Although thetrue angular distribution is not known, it can be approximately obtained
as a linear combination of orthogonal spherical harmonics. Therefore, thecoeﬃcients of the linear combination are used as the feature variables.
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CHAPTER 6. NEUTRON TAGGING

0.02
N10n>=160.018
N10n =15

0.016
N10n =140.014
N10n =13

0.012
N10n =120.01
N10n =110.008
N10n =100.006
N10n = 90.004
N10n = 80.002
N10n<= 7

0

10

20

30

40

50

60

70

80

90

0

3 hits combination Cherenkov angle (deg)0.02
N10n>=160.018
N10n =15

0.016
N10n =140.014
N10n =13

0.012
N10n =120.01
N10n =110.008
N10n =100.006
N10n = 90.004
N10n = 80.002
N10n<= 7

0

10

20

30

40

50

60

70

80

90

0

3 hits combination Cherenkov angle (deg)Figure 6.12: Array of one-dimensional PDF of 3 hits Cherenkov angle distribution forthe signal (left) and background (right) events. For a given N 10nvx , the corresponding
horizontal slice is used to calculate llrCAng. In the left and right plots, N 10n
denotes N 10nvx .

104

CHAPTER 6. NEUTRON TAGGING

The coeﬃcients are given as:
N 10nvx N 10nvx
∑ ∑
2
βℓ =
P (cos θij ),N 10nvx (N 10nvx − 1) i=1 j=i+1 ℓ(6.3.6)

where θij is the angle between the i-th and j-th hit vectors and Pℓ are
Legendre polynomials. This parametrization had been used in the SNO
experiment [208] in the context of separation of CC-NC interactions for
the SNO’s solar neutrino analysis. β1 , β2 , β3 , β4 and β5 are adopted asa part of the feature variables, because the correlations among them are
diﬀerent between signal and background events. The diﬀerence in thecorrelation is shown in Figure 6.14.

105

CHAPTER 6. NEUTRON TAGGING

Figure 6.13: Distributions of the 14 feature variables, which are fed into the NN. Red
and blue distributions correspond to true neutron events and accidental background
events, respectively. All the distributions are area normalized.

106

CHAPTER 6. NEUTRON TAGGING

100tSDMin6

80

tSD
β5

60

β4
β3

40

β2

20

β1

0

llrCAnglnAccep-20

nTwall-40

nDwall

-60

N300S
NcS
N10n

-80
-100
N10 NcS N30 nDw nTw lnAc llrCAβ 1 β 2 β 3 β 4 β 5 tSD tSD
Minn0S all all cep ng
6100

tSDMin6

80

tSD
β5

60

β4
β3

40

β2

20

β1

0

llrCAnglnAccep-20

nTwall-40

nDwall

-60

N300S
NcS
N10n

-80
-100
N10 NcS N30 nDw nTw lnAc llrCAβ 1 β 2 β 3 β 4 β 5 tSD tSD
Minn0S all all cep ng
6

Figure 6.14: Linear correlation matrices for true neutron events (top) and accidental
background events (bottom).

107

CHAPTER 6. NEUTRON TAGGING

6.3.2

Network training

The MLP neural network implemented in the TMVA package [209] which is a feedforward multilayer perceptron is used. In general, this kind of NN have a few hyper
parameters that have to be set by user such as layer architecture. In addition, choiceof such parameters is arbitrary, so that these parameters need to be determined
empirically. The setting of the NN used in this algorithm was determined after trying
a variety of parameter settings. The layer architecture and activation function of the
NN were chosen to be 14:11:8:4:1 and hyperbolic tangent, respectively. The NN
training and testing processes were done by back propagation algorithm with 650
training cycles and a training rate of 0.001.
Although the NN is applied to the 1Rνµ samples which are used in the primary
analysis of this thesis, the samples used for the training and testing were made from
FCFV (Fully Contained Fiducial Volume) ν events in order to make the NN robust.
In order to prepare the samples, the same FCFV cut described in Section 7.2 wasapplied to half of the second hybrid neutron MC ν events, after which 800,000 true
2.2 MeV γ events and 2,200,000 background events were randomly extracted fromthe FCFV events. These extracted events were used for the training and testingprocesses with a one to three ratio for the signal events and the background events.
No behaviour of overtraining was found during the training process.
Figure 6.15 shows the NN output distributions for true neutron and background
events. As shown in the figure, true neutron and background events peak aroundat the NN output = 1 and = 0, respectively. In order to select a final event whichis referred to as “tagged neutron” hereafter, a threshold on the NN output needs
to be determined.√ In this determination, one can not utilize any model dependent
metric such as S/ S + B, because number of neutrons (here it is S) strongly depend
on a particular simulation that is used for this determination. As the background
events depend only on number of ν events used for the neutron tagging, the cut
threshold was determined by setting the background event rate, which is number oftagged background events per ν event, to 0.02 as shown in Figure 6.16. consequently,
the value of the determined threshold on NN output is 0.886, and neutron tagging
eﬃciency is ∼20%.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.15: Area normalized distribution of the neural network output.
Although there is no strong reason for the value of 0.02 chosen, this low background event rate enables us to have high purity tagged neutron samples for theneutron measurement in Chapter 8. As it will be described in Section 7.3, the fraction of the background events in the detected neutrons is estimated to be less than
10% for both the FHC and RHC 1R νµ samples, which are summarized in Table 7.2
and Table 7.3. It should be noted that this determination of the threshold enables
us to subtract the backgrounds contained in the real data by using only the numberof observed ν events, which means that any systematics varying ν event rate do notaﬀect the background subtraction.

Figure 6.16: The left and right figures shows background event rate (number ofbackground events per ν event) and tagging eﬃciency as a function of the neuralnetwork output threshold, respectively. The vertical green arrow shows the positionof the threshold which is determined to be 0.886 by setting background event rate
to 0.02.
The performance of the neutron tagging algorithm before and after the NN classification is summarized in Table 6.1. Figure 6.17 shows the neutron tagging eﬃciency
109

CHAPTER 6. NEUTRON TAGGING

and background event rate in bins of reconstructed ν interaction vertex.
Table 6.1: Neutron tagging eﬃciency and background event rate, which is numberof tagged background events per ν event, after the primary selection and after the
NN classification, respectively. These numbers are obtained by using the FHC and
RHC 1Rνµ samples which are used for the primary analysis of this thesis. Note that
the SK time variation eﬀects are not included here. The eﬀects will be considered in
Section 6.5, and the corrected numbers can be found in Table 6.2. Errors represent
MC statistical uncertainties.

After primary selection

After NN classification

Tagging eﬃciency (%)

Acc. Bkg. rate

FHC

33.29±0.30

3.55±0.02

RHC

33.71±0.17

3.51±0.02

FHC

19.89±0.23(2.10±0.67)×10−2

RHC

20.04±0.13(1.98±0.44)×10−2

Figure 6.17: Neutron tagging eﬃciency as a function of reconstructed ν interaction
vertex position inside the SK tank (left). Background event rate as a function ofreconstructed ν interaction vertex position inside the SK tank (right). R2 is definedas X 2 + Y 2 , where X and Y are x and y positions of reconstructed ν interaction,
respectively. Green dashed lines represent the fiducial volume used in the primary
analysis of this thesis.

6.4

Application to Americium-Beryllium calibration data

The neutron tagging algorithm described in the previous section can be validated by acalibration which exploits an Americium-Beryllium (Am/Be) radioactive source. The
110

CHAPTER 6. NEUTRON TAGGING

first study using the source [210] was done during the SK-III phase to demonstratefeasibility of neutron tagging in a water Cherenkov detector.
241

Am of the Am/Be source emits α particles, and these particles interact with
Be. One of reaction channels produces a prompt signal of 4.4 MeV γ ray and adelayed neutron as follows:9

α +9 Be →∗12 C + n∗12

C → C + γ (4.43 MeV)

(6.4.1)

The calibration uses the reaction channel as the signal process to search for neutrons.
The Am/Be source has an intensity of 97 µCi of 241 Am. Since this signal reaction
occurs as the dominant reaction channel with a probability of ∼62%, the source
provides the signal prompt 4.4 MeV γ rays with a frequency of 87 Hz.

6.4.1

Experimental setup and data taking

In this calibration, the Am/Be source is embedded into BGO crystal scintillators,
which enables detecting the 4.4 MeV gamma rays as the prompt events and thus
the delayed neutrons can be searched for by using the detected 4.4 MeV γ events.
Figure 6.18 shows the Am/Be source with the BGO scintillators.

Figure 6.18: The Americium-Beryllium source and BGO crystal scintillator.
In the analysis of this section, the calibration data set taken in Dec. 2016 is used.
The Am/Be source was put at three diﬀerent ID positions:• Center : Am/Be source position (35.3, -70.7, 0) [cm]111

CHAPTER 6. NEUTRON TAGGING• Z+15 m : Am/Be source position (35.3, -70.7, 1500.0) [cm]• Y-12 m : Am/Be source position (35.3, -1201.9, 0.0) [cm].

The data were taken at each position with SHE (Super High Energy) trigger which
can be issued by the scintillation light of BGO scintillators produced by prompt
4.4 MeV γ rays. Following a SHE trigger in which case PMT hit information until
the first 35 µs is stored, another trigger (called “AFT” trigger) is issued, by which
the information about the PMT hits after the 35 µs is stored until +835 µs. The
835 µs record length of PMT hit information allows us to study the time spectrumof the tagged neutrons in detail.
Since the composition of the noise hits in the calibration is diﬀerent from thatof ν events which is modeled by the T2K dummy spill data, due to the presenceof the BGO scintillators, a dedicated accidental background data was taken at thecenter position with the Am/Be source by a random trigger. The PMT hits of the
background data are used for the corresponding simulated events of this calibration.

6.4.2

Data reduction

The calibration data are processed to extract the events related to the prompt 4.4
MeV γ rays by requiring the following conditions:
1. An event issued by SHE trigger has a AFT trigger.
2. Time diﬀerence from the previous SHE + AFT triggered event is longer than
1.5 µs.
3. Total charge of PMT hits (potot) is in the accepted region.
The first cut ensures that the delayed neutrons can be searched for until +835 µs
and the second one avoids contamination of the delayed neutron from the previous
prompt event. The third cut intends to select the prompt events which are producedby the scintillation light of 4.4 MeV γ rays. Figure 6.19 shows the distributions ofpotot for the three data taking positions with an indication of the accepted regions.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.19: Distributions of potot for the center (top left), Z+15 m (top right), andY-12 m (bottom). The events inside the regions surrounded by arrows are selected
as the prompt events related to 4.4 MeV γ rays.

6.4.3

MC simulation

Corresponding MC events are simulated by generating neutrons at the same datataking positions. Ideally a precise MC which can simulate both all the γ rays emitted
from the Am/Be source and the scintillation light of BGO scintillator is needed toperform a full event simulation. However, such MC is not available at the present
moment and is quite challenging to make. Therefore, only the delayed neutronsof the signal reaction are simulated by considering their kinetic energy spectrum.
Figure 6.20 shows the kinetic energy spectrum of the delayed neutrons used in thisanalysis.

113

CHAPTER 6. NEUTRON TAGGING

Figure 6.20: Kinetic energy spectra of neutrons produced by 9 Be(α, n)12 C reactions.
The broken line peaked around 3 MeV corresponds to the delayed neutrons of thesignal reaction: α +9 Be →∗12 C + n. Figure taken from [32].
After simulating these neutrons including subsequent 2.2 MeV γ rays producedby neutron capture on hydrogen nucleus, the PMT hit information of the backgrounddata taken with a random trigger is injected into these simulated events.

6.4.4

Data-MC comparison

For the data, the neutron tagging algorithm is applied to the prompt events which
passes through all the three cuts described in Subsection 6.4.2. On the other hand,in the case of the MC the algorithm is applied to all the simulated events, and thus
the number of prompt events is equal to the number of simulated events for the MC.
The algorithm is applied to both the data and the MC from +18 µs to +835 µs
after the initial trigger. Since the production position of the delayed neutrons is thesame as the Am/Be source location which is known, for each data taking position thelocation of the source is used to seach for neutron candidates. In the analysis of thisM ax
calibration, an additional variable, N200
, is calculated when applying the algorithm
M ax
to both the data and MC. N200 is the maximum number of PMT hits in a 200 ns
sliding timing window from +18 µs to +835 µs in a prompt event. This variable isused to avoid a second scintillation light event following the primary scintillation
light which is produced by γ rays emitted from the Am/Be source [211, 203]. The
M ax
cut condition for N200
is given as:

M ax• N200< 50

If a prompt event does not satisfy the above condition, the event is rejected, and is
not used in the following comparison between the data and the MC.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.21 and 6.22 show the distributions of the NN’s 14 input variables before
and after the NN classification, respectively. As shown in the figures, almost all thebackground events are removed by the NN classification. In addition, the data showsa good agreement with the MC.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.21: Distributions of the 14 input variables before the NN classification.
The MC distribtions are shown by stacked histograms consisting of the true signal
events (blue) and the true background events (pink). The dots corresponds to thedata. Green bands represent the statistical errors of the MC. All the distributions
are normalized by the number of the selected prompt events.

116

CHAPTER 6. NEUTRON TAGGING

Figure 6.22: Distributions of the 14 input variables after the NN classification. The
MC distribtions are shown by stacked histograms consisting of the true signal events(blue) and the true background events (pink). The dots corresponds to the data.
Green bands represent the statistical errors of the MC. All the distributions arenormalized by the number of the selected prompt events.
The capture time distribution can be used to study the capture time constant andthe neutron tagging eﬃciency by a fit. The fit function is obtained by considering the117CHAPTER 6. NEUTRON TAGGING

following factors. In principle, this calibration can address neutron tagging eﬃciency
by using the number of selected prompt events and the number of tagged neutrons
as follows:
ndelaytagging eﬃciency = prom ,N(6.4.2)where ndelay is the number of tagged true delayed neutrons and N prom is the numberof selected prompt 4.4 MeV γ events. Since there are remaining accidental background events even after the NN classification, the contribution from the remaining
background events to the tagged neutrons needs to be taken into account. The background events are caused by accidental coincidences of noise PMT hits. Therefore,
the time dependence of the background events is reasonably assumed to be a constant over time. Thus, the fit function at each data taking position consists of an
exponential function and a constant function as follows:[]
1 −t/τ
1f (t; τ, ε, b) = N × ε e+b,τ
820 − 20

(6.4.3)where τ is capture time, N is number of selected prompt events, ε is tagging eﬃciency,
and b is background event rate. Since the capture time should be the same among
the three data taking positions, τ need to be treated as a common parameter among
the three positions. Then, the fit parameters τ , ε, and b are obtained by minimizinga χ2 given as:
(
)2
∑
∑
E
−
O
(τ,
ε
,
b
)
i,j
i,j
i
i
,
χ2 =
Ei,j
i
j

(6.4.4)

where i runs over the three diﬀerent data taking positions, j represents bin numberof capture time distribution, E is number of observed events, and O is number of
expected events.
The minimization is done by the MINUIT algorithm. The resultant τ is 207.7±3.2µs for the data and 202.3±3.5 µs for the MC, and is consistent between the data andthe MC. Also, both of the two fitted τ s are consistent with an external measurement
result of 204.8±0.4 µs [37]. Figure 6.23 shows the capture time distributions of thedata with the fit results in comparison with the corresponding MC.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.23: Distribution of capture time after the primary selection for the three
data taking positions. The top left, top righ, bottom correspond to the center, theZ+15 m, and the Y-12 m data taking positions, respectively. The fitted backgroundcomponent is subtracted. All the distributions are normalized by the number of theselected prompt events.
Since the fit extracts the neutron tagging eﬃciency as well as the capture time
constant, the eﬃciency is also compared between the data and the MC. In Figure 6.24, the left and right plots show the fitted neutron tagging eﬃciency and therelative diﬀerence from the MC’s ones, respectively. As shown in the figure, theeﬃciency of the data is systematically lower than that of the MC for all the threepositions. Possible reason for this systematic disagreement is discussed in the remaining part of this section.

119

CHAPTER 6. NEUTRON TAGGING

Figure 6.24: The fitted neutron tagging eﬃciency (left) and the fractional diﬀerencewith respect to the MC’s ones. In the left plot, green and blue points correspond to
the MC and the data, respectively. In the right plot, the green dashed line represents
the average of the fractional diﬀerences. The horizontal axes represent the three datataking positions.

6.4.5

Discussion

As was shown in the above, the data showed the systematically lower neutron tagging
eﬃciency compared to the MC although the extracted capture time constant wasconsistent with each other. To understand the discrepancy, it is worth noting thediﬀerence in the selection of the prompt events between the data and the MC. The
prompt events of the data are selected by assuming that the events around the peak in
the potot distribution shown in Figure 6.19 are produced by signal prompt 4.43 MeV
γ rays, whereas that of the MC is equal to all the simulated events, each of which
has a delayed neutron. If the assumption made only for the data is not correct, thenthere may be fake prompt events, in which there are no signal delayed neutrons.
Existence of such fake prompt events can lower the data’s eﬃciency as follows:
ndelaytagging eﬃciency = prom,
N+B

(6.4.5)where B is the number of fake prompt events.
In order to confirm whether or not such fake prompt events exist only in the data,
the data’s neutron tagging eﬃciency was evaluated by varying the cut values of the
potot. If the assumption that the events around the peak in the potot distribution
are due to prompt 4.4 MeV γ rays is true, then the eﬃciency may not change as thecut values on potot are varied.
Figure 6.25 shows the fitted neutron tagging eﬃciency of the data as a functionof the lower cut value (ql) and the upper cut value (qh). As shown in the figure,both lowering ql and raising qh resulted in decrease of the fitted tagging eﬃciency,
which strongly indicates that a non-negligible amount of fake prompt event is likely
to contaminate the selected true prompt 4.4 MeV γ rays only for the data.
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CHAPTER 6. NEUTRON TAGGING

Figure 6.25: Fitted neutron tagging eﬃciency of the data at the center position forvarious potot cut values. In the left plot, lower cut value is varied while keeping
upper cut value. On the other hand, in the right plot, upper cut value is varied
while keeping lower cut value. In the left (right) plot, each color represents thecorresponding fixed upper (lower) cut value.
In addition to the fake prompt events, there is likely to be another systematic
source which can also lower the data’s neutron tagging eﬃciency. The delayed neutrons in Equation 6.4.1 are produced inside the Am/Be source surrounded by the
BGO scintillator crystals. It is known that neutrons can be captured on the nuclei
contained in the sealing metal of the Am/Be source and the BGO crystals. If such
absorption happens, then the prompt 4.4 MeV gamma rays are not accompanied by
the delayed neutrons. Therefore, these two eﬀects only for the data might be theprimary cause that can explain the systematically lower tagging eﬃciency of the datacompared to that of the MC.

6.5

Correction for detector time variation eﬀects

The primary analysis in this thesis uses the FHC and RHC data taken until 2018 tomeasure neutrons. This data taking (hereafter called “Run 1-9” data taking) periods
spanned the nine years; The Run 1 data taking started in Jan. 2010 and the Run 9
data taking ended in May 2019. Although the operation of the SK was stable enoughin terms of ν event reconstruction during the data taking periods, there were known
time variations, which may have non-negligible impacts on low energy analyses suchas the neutron tagging, and this has never been quantitatively studied. As these variations are likely to aﬀect the nominal neutron tagging eﬃciencies and backgroundrates estimated around Dec. 2015, which are summarized in Table 6.1, the nominal
values need to be corrected for this data taking period properly. Note that the eﬀects
are negligibly small, so that no significant impact on primary neutrino events havebeen seen during the Run 1-9 data taking periods [31].
In this section, first, a short introduction to the SK time variations consideredis given. Following this, the procedure for the correction and the results are detailed. Note that the systematic uncertainty related to the following correction will
be described in Section 8.3.11.
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CHAPTER 6. NEUTRON TAGGING

6.5.1

SK time variations

As described in Section 6.2, the neutron tagging algorithm uses only ∼10 PMT
hits, which means that either increase or decrease of just one PMT hit due to any
time variations of SK may give a visible impact on the performance of this algorithm.
During the Run 1-9 data taking periods, such time variations had been observed: thegain of the ID PMTs, the light attenuation length, the hit probability of top-bottom
asymmetry (TBA) inside the ID.

Figure 6.26: The time variations of the ID PMT gain (top), the attenuation lengthof the water measured by using decay electrons (middle), the TBA measured by theauto Xe light (bottom). For the PMT gain, the vertical axis represents the relative
PMT gain with respect to the average value in Apr. 2009. The green bands show
the Run 1-9 data taking periods.
Figure 6.26 shows these time variations. As shown in the top panel, the gain of
the ID PMT has been continuously increasing over time, depending on the ID PMT
production years. The middle and bottom panels show the time variations in the122CHAPTER 6. NEUTRON TAGGING

attenuation length and the TBA of the water, which were described in Section 3.4.
Their time evolution is diﬀerent from that of the PMT gain as shown in these panels,
but has still a visible variation from the beginning of the T2K data taking in Jan.
2010.
As was mentioned in Section 4.4, the background events of the neutron tagging
algorithm, which are caused by random noise PMT hits, are modeled by using theT2K dummy spill data. Therefore, the time dependence of the dummy spill dataalso needs to be taken into account. Figure 6.27 shows the time evolution of theaverage number of PMT hits for the data taken during the beam-oﬀ periods. From
the figure, a large variation mainly due to the PMT gain’s increase can be seen.

Figure 6.27: The average number of PMT hits of the dummy spill data. The green
bands show the Run 1-9 data taking periods.
Since the above time variations aﬀect the probability for making PMT hit, there
may be non-negligible impact of these variations on the performance of the neutron
tagging. In the following parts of this section, Subsection 6.5.2 describes the stabilityof the performance over the Run 1-9 data taking periods, and the eﬀect of these time
variations in the neutron tagging is taken into account as a correction in Section 6.5.3.
Note that the corrected numbers summarized in Table 6.2 will be used for the primary
analysis of this thesis to measure neutrons.

6.5.2

Regeneration of MC with time variations

In order to incorporate the eﬀect of the time variations into the nominal tagging
eﬃciency and background event rate, the time evolution of PMT hits produced byboth true neutron and background sources need to be traced. This can be done, but
the way to trace the evolution is diﬀerent between true neutron events and background events. As the background events are modeled by the dummy spill data, its
time evolution can be evaluated by utilizing the pre-existing dummy spill data. On
the one hand, the case of 2.2 MeV γ ray is conducted by the detector simulation.
The procedure of tracing the time evolution is therefore equivalent to regenerate thehybrid neutron MC at various time points.
For each regeneration point, SKDETSIM is rerun on the output of the NEUT
used for the production of the nominal hybrid neutron MC with appropriate dummy
123CHAPTER 6. NEUTRON TAGGING

spill data, PMT gain, water attenuation length, and TBA. The regeneration points
are determined by considering the statistics of both the MC and the dummy spill
data. In order to maximize available number of regeneration points, only MC events
which pass the 1Rνµ analysis cuts described in Section 7.2 are used. After the cuts,
there are about 240,000 MC events. As one event of the dummy spill data is used
for two MC events due to diﬀerent record length of PMT hits, 120,000 dummy spill
events are needed at each regeneration point. To obtain available number of regeneration points, the events of the pre-existing dummy spill data are sorted in increasingorder by time and then, are binned by every 120,000 events. Each bin is treated as
one regeneration point and the representative time of a regeneration point is definedas the time when the 60,000-th event (i.e. 50 percentile) is recorded in the bin. The
resultant number of regeneration points are 128 in total. The first and last points
are in Sep. 2009 and Oct. 2017, respectively.
For each regenerated MC, the neutron tagging eﬃciency and background event
rate are evaluated by using the identical neural network described in Section 6.3 andthe results of the ν event reconstruction (i.e. fiTQun) of the nominal MC. Note that
retraining NN and ν event reconstruction are very CPU intensive work and are notfeasible to be done for each regenerated MC in a realistic time scale.
Figure 6.28 and 6.29 show the time evolution of the tagging eﬃciency and background event rate after the primary selection, respectively. As shown in the figures,
after the primary selection, both the tagging eﬃciency and background rate areclearly and monotonically increasing over time, which indicates that the dominanteﬀect comes from the increase of the PMT gain. Since the neutron candidates are
selected by N 10pvx in the primary selection, it may be interesting to check the timedependence of the N 10pvx distribution. Figure 6.30 shows the comparison of theN 10pvx distributions between the first, nominal, and last regeneration points. As
shown in the figure, the distribution of the true neutron events are clearly shifted tohigher value, whereas that of the background events is relatively flat over N 10pvx compared to the true neutrons.

124

CHAPTER 6. NEUTRON TAGGING

Figure 6.28: Neutron tagging eﬃciency after the primary selection as a function oftime. The top panel and bottom panel correspond to the FHC and RHC 1Rνµ MC
samples, respectively. The error bars represent the MC statistical errors. The green
bands show the Runs 1-9 data taking periods.

Figure 6.29: Background event rate after the primary selection as a function of time.
The top panel and bottom panel correspond to the FHC and RHC 1Rνµ MC samples,
respectively. The error bars represent the MC statistical errors. The green bands
show the Runs 1-9 data taking periods.

125

CHAPTER 6. NEUTRON TAGGING

Figure 6.30: Comparison of the N 10pvx distributions between the diﬀerent MC regeneration points. The left and right plots represent the true neutron and background
events, respectively. The green bands show the Runs 1-9 data taking periods.
The tagging eﬃciency and background rate after the NN classification are shownin Figure 6.31 and 6.32, respectively. It is interesting to notice that the time evolution
is very diﬀerent between the primary selection and NN classification for both the true
neutrons and background events.

126

CHAPTER 6. NEUTRON TAGGING

Figure 6.31: Neutron tagging eﬃciency after the NN classification as a function oftime. The top panel and bottom panel correspond to the FHC and RHC 1Rνµ MC
samples, respectively. The error bars represent the MC statistical errors. The green
bands show the Runs 1-9 data taking periods.
After the NN classification, the time variation of the tagging eﬃciency become
smaller compared to the primary selection as shown in the figure. Although the sizeof the variation is small, the time variation seems to have a weak quadratic structure
which is likely to have a peak around Aug. 2013. A possible explanation for thisstructure may be due to a result of competition by two eﬀects: an increased PMT
hits of the true neutron events and a larger contamination of the noise PMT hits.
The first eﬀect increase the absolute number of true neutron events selected in the
primary selection and enhances the discrimination power of the NN between the true
neutron and background events, which results in higher tagging eﬃciency after the
NN classification. On the contrary, the second one may degrades the discrimination
power, because some input variables of the NN utilize the diﬀerence in the geometricalspreads of the PMT hits, which causes lower tagging eﬃciency. The probability thatthe noise hits contaminate a true neutron event increases as the number of noise PMT
hits increase due to the increase of the ID PMT gain. The eﬀect of the degradationis therefore expected to become larger as time proceeds.
In case of the background event rate after the NN classification, on the one hand,the value is linearly decreasing over time as opposed to that of after the primary
selection. In this case, contamination of PMT hits originating from 2.2 MeV γ rays
is negligible, so that the backgrounds tend to be more “background-like” over time.
Comparison of the NN output distributions between the three diﬀerent points
are shown in Figure 6.33. As shown in the figure, the distributions of the true andbackground events are shifted to “neutron-like” and “background-like”, respectively.

127

CHAPTER 6. NEUTRON TAGGING

Figure 6.32: Background event rate after the NN classification as a function of time.
The top panel and bottom panel correspond to the FHC and RHC 1Rνµ MC samples,
respectively. The error bars represent the MC statistical errors. The green bands
show the Runs 1-9 data taking periods.

Figure 6.33: Comparison of the NN output distributions between the diﬀerent regeneration points. Left and right correspond to the true neutron and accidental
background events, respectively. The arrow shows the cut position of the NN output.
128

CHAPTER 6. NEUTRON TAGGING

6.5.3

Correction of the time variation eﬀects

The time evolution of both the tagging eﬃciency and background event rate is likely
to be smooth on average as it can be seen in Figure 6.31 and Figure 6.32. The time
evolution during the Run 1-9 data taking periods is therefore extrapolated by a fit to
the regenerated MCs and then, the fit result is used to correct the nominal tagging
eﬃciency and background event rate.
The eﬀect of the time variations is probably common among the FHC and RHC
1Rνµ samples, because there is no reason which diﬀerentiates the two samples interms of the detector time variations. Thus, it is assumed that the eﬀect is common
between the two samples, so that there are common parameters which characterize
the time evolution of the two samples. The tagging eﬃciency and background event
rate as a function of time are parameterized as follows:[]ε(t) = ε0 1 + a1 × (t − t0 ) + a2 × (t − t0 )2 ,(6.5.1)

B(t) = B0 [1 + b1 × (t − t0 )] ,(6.5.2)where t0 is the time where the nominal MC is generated, a1 , a2 and b1 account for
the time evolution and are common parameters between the two samples, and ε0 and
B0 are the tagging eﬃciency and background event rate at t0 , respectively.
The tagging eﬃciencies and background event rates of the regenerated MCs as
well as that of the nominal MC are fitted by Equation 6.5.1 and 6.5.2, respectively.
The χ2 used for this fit is given as:
∑

∑

i

j

FHC/RHC Nregeχ2 (θ) =(rege− XiExp (tj ; θ)
Xi,j
rege
δXi,j

)2

where

εF0 HC εRHC 0θ (for tagging eﬃciency) =  a1 
a2

B0F HCθ (for background rate) =  B0RHC  ,
b1


129

,

(6.5.3)

CHAPTER 6. NEUTRON TAGGINGX denotes tagging eﬃciency or background event rate, X Exp is expected value, X rege
is value evaluated by regenerated MC, δX is statistical error of X rege , i runs over the
FHC and RHC samples, j runs over the regeneration points including the nominal
generation point, and tj is the representative time of j-th regeneration point. It
should be noted that the FHC and RHC samples are fitted simultaneously. The
minimization of the χ2 fits are done by the MINUIT algorithm [212] implemented in
the ROOT Minuit2 libraries.
After this fit, the best fit results are used to correct the nominal tagging eﬃciency
and background event rate. The correction is performed by considering the diﬀerent
accumulated POT among the MR runs of Run 1-9 as a T2K Run consists of several
MR (Main Ring) runs. The corrected numbers are the POT weighted average givenas:∑MR runs
X

Run1−9=i

POTi × X Best (tMi )∑MR runs
i

POTi

,

(6.5.4)

where i runs over the MR runs of the Run 1-9, POTi is the total accumulated POTof i-th MR run, X Best is either tagging eﬃciency or background event rate evaluatedby the best fit parameters, and tM
i is the time when the accumulated POT of i-th
MR run reaches 50 percentile. Figure 6.34 and 6.35 show the best fit results andFigure 6.34: The fitted tagging eﬃciency (left) and the POT weighted averages. The
top panel and bottom panel correspond to the FHC and RHC 1Rνµ samples. The
solid curves and broken lines correspond to the best fit results and POT weighted
average, respectively. The green bands show the Run 1-9 data taking periods.

130

CHAPTER 6. NEUTRON TAGGING

Figure 6.35: The fitted background event rate (left) and the POT weighted averages.
The top panel and bottom panel correspond to the FHC and RHC 1Rνµ samples.
The solid curves and broken lines correspond to the best fit results and POT weighted
average, respectively. The green bands show the Run 1-9 data taking periods.
the POT weighted averages of the tagging eﬃciency and background event rate. The
χ2 /n.d.f for the best fit was obtained to be 258.3/254 and 263.7/255 for the tagging
eﬃciency and background event rate, respectively. These reasonable value of the
reduced χ2 are consistent with the assumption that the time variation eﬀects arecommon between the FHC and RHC samples.
Table 6.2 summarizes the tagging eﬃciencies and background rates before andafter the correction. Although the same time evolution is assumed between the FHC
and RHC 1R νµ samples, the size of the time variation eﬀect is diﬀerent. Thisdiﬀerence arises from the diﬀerent data taking periods between the FHC and RHC
modes. Figure 6.36 shows the POT weights used for the calculation of the averages.
For the FHC sample all the Run 1-9 data taking periods contribute the calculation,
whereas only the data taking periods after 2014 contribute to the calculation of the
RHC sample. Note that the corrected numbers will be used to derive the central
values for the neutron measurement described in Chapter 8.

131

CHAPTER 6. NEUTRON TAGGING
Table 6.2: Tagging eﬃciencies and background event rates with and without thecorrection of the time variation eﬀect. The numbers for the nominal are same assummarized in Table 6.1.

Tagging Eﬃciency (%)

FHC
RHC

Nominal
19.89
20.40

Corrected
20.09
20.37

(Cor. - Nom.)/Nom. (%)
+0.98
-0.16

Background rate

FHC 2.10×10−2
RHC 1.98×10−2

2.02×10−2
1.94×10−2

-3.83
-2.44

Figure 6.36: Fraction of POT which is computed by dividing the total accumulated
POT of each individual MR run by the total Runs 1 − 9 POT. The green bands show
the Run 1-9 data taking periods.

6.5.4

Statistical uncertainties

The statistical errors on the POT weighted averages need to be considered. As the
FHC and RHC 1Rνµ samples are simultaneously fitted, there are correlations among
the fit parameters. The left and right panels of Figure 6.37 show the correlation
matrices for the fit parameters of the tagging eﬃciency and background rate, respectively. As shown in the figure, the FHC and RHC parameters are correlated, whichmeans that the POT weighted averages are also correlated.
In order to estimate the statistical errors on the averages with the correlations,random throws of the fit parameters are performed using the fit results. The throws
are done assuming that the fit parameters are treated as a multivariate Gaussian
whose covariance matrix is the one calculated by MINUIT. For each random throw,
POT weighted average is computed for the fit parameters which are sampled fromthe Gaussian using the Cholesky decomposition and then, fractional diﬀerence fromthe POT weighted average for the best fit parameters is calculated.
The random throws were repeated by 200,000 times separately for the tagging
132

CHAPTER 6. NEUTRON TAGGING

eﬃciency and background event rate, respectively. The resultant distributions of
the fractional diﬀerences are made and are shown in Figure 6.38. The resulting 1σerror is computed from the 68% area surrounding the peak of the distribution as in
the figure and is estimated to be less than 0.05% and 0.3% for the eﬃciency andbackground rate, respectively. Note that the statistical error of each regenerate MC
is about ∼1% and ∼3% for the tagging eﬃciency and background rate, respectively,
which means that the correction of the time variations by the fit eﬀectively increases
MC statistics.

Figure 6.37: Correlation matrices for the parameters of the tagging eﬃciencies (left)
and the background rates (right). In the left side, “TagEﬀ FHC”, “TagEﬀ RHC”,“FVar 1”, and “FVar 2” correspond to εF0 HC , εRHC
, a1 , a2 , respectively. In the0right side, “BRate FHC”, “BRate RHC”, “FVar 1” correspond to B0F HC , B0RHC ,b1 , respectively. These paramters are defined in Equation 6.5.3. The matrices arederived from the corresponding covariance matrices calculated by MINUIT.

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CHAPTER 6. NEUTRON TAGGING

Figure 6.38: Distribution of the fractional errors obtained by throwing the parameters.

134

Chapter 7First application of neutron
tagging to T2K data
Since the beginning of the first data taking in January 2010, T2K has finished thedata taking until Run 9 which ended in May 2018. The collected data has been used
for both the neutrino oscillation analyses and the studies on neutrino-nucleus scattering. However, neutrons associated with neutrino and antineutrino interactions inwater had never been studied until the primary analysis of this thesis was performed.
In this chapter, the first application of neutron tagging to the T2K data is presented. Prediction of event rate at the far detector is overviewd in Section 7.1, andthe selection criteria of the 1Rνµ sample used in the primary analysis is describedin Section 7.2. Following this, the results of the event selection for the T2K datacollected until 2018 is summarized in Section 7.3. Section 7.4 describes the data
quality checks in terms of neutron tagging. A set of comparisons between the data
and the MC predictions for the detected neutrons is given in Section 7.5.

7.1

Prediction of event rate

The observed neutrino events and the tagged neutrons accompanying the primary
neutrino events are compared with the corresponding predictions. For a neutrino
flavor which is created as να at J-PARC and is detected as νβ at the far detector
due to neutrino oscillation, the expected number of neutrino events in bins of someobservables Θ such as reconstructed neutrino energy, Nν (Θ), is given as:∫Nν (Θ) = C Φ(Eν )σ(Eν )Pνα →νβ (Eν )ϵ(Eν )U (Eν , Θ)dEν ,(7.1.1)
where C takes into account the target volume, Eν is the true energy of the incoming
neutrino, Φ(Eν ) is the incoming neutrino flux, σ(Eν ) is the neutrino interaction crosssection, Pνα →νβ (Eν ) is the neutrino oscillation probability, ϵ(Eν ) is the detection
eﬃciency by the far detector, U (Eν , Θ) describes how a neutrino with an energy ofEν is reconstructed in Θ.
Similarly, the expected number of tagged neutrinos accompanying the expected
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
neutrino events Nν (Θ) is as follows:∫
Nntag (Θ) = C

Φ(Eν )σ(Eν )Pνα →νβ (Eν )ϵ(Eν )U (Eν , Θ) × Y (Eν )εntag (Eν )dEν ,(7.1.2)where εntag (Eν ) is the neutron tagging eﬃciency and Y (Eν ) is the inclusive neutron yield which includes all the contributions from primary ν-nucleon interactions,hadronic FSI inside oxygen nucleus, and hadronic SI in water.
These calculations are performed based on MC simulations described in Chapter 4. In practice, MC simulations are performed without the eﬀect of neutrino
oscillation by using “nominal” beam fluxes and neutrino interaction cross sections.
Then, later the oscillation eﬀect and other eﬀects such beam flux tunings and corrections of neutrino interaction cross sections are taken into account by assigning aproper weight on an event-by-event basis. This scheme enables saving computationaltime.
In order to compute the oscillation probability, the neutrino oscillation parameters in Table 7.1 are used throughout in the remaining part of this thesis except in
Section 8.3.9, where systematic uncertainty on neutron tagging eﬃciency due to uncertainties on oscillation parameters is described. Prob3++ [213] is used to calculate
the oscillation probability by considering the Earth’s matter eﬀect based on [80].
Since the current T2K oscillation analyses do not use information about neutron
tagging, the results of the analyses are applicable for the primary analysis of thisthesis.
Table 7.1: Parameters used for calculation of oscillation probabilities. The valuesof ∆m221 and sin2 θ12 are from [35]. The value of sin2 θ13 is from [34]. The values ofthe other parameters are based on the results of a T2K neutrino oscillation analysis
using the data taken until 2018 [36].
Parameter
∆m221
∆m232
sin2 θ12
sin2 θ23
sin2 θ13
δCP
Mass hierarchy

7.2

value
7.53 × 10−5 eV22.452 × 10−3 eV2
0.304
0.532
0.0212−1.885
NH

Definition of analysis sample

The primary analysis in this thesis aims to study and measure neutrons associatedwith neutrino interactions on water target. It is therefore important to use ν event
136

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
sample which is well known, studied, and established in terms of neutrino interaction
cross sections and neutrino fluxes.
The FHC and RHC 1R νµ samples used for the T2K neutrino oscillation analyses [140] are suitable for this purpose. The samples mainly consist of CCQE interaction described in Equation 1.2.2 and contain a high purity of νµ and ν̄µ events for
the FHC and RHC modes, respectively. Since the selection criteria of these samples
were optimized by considering uncertainties on cross sections and fluxes [214, 215],
the same selection criteria are adopted for this thesis except for the definition of thefiducial volume (FV).
The same criteria are used for both the FHC sample and the RHC sample andare given as:
1. Fully-contained in the SK ID and reconstructed inside the fiducial volume which
is defined by Dwall > 2 m,
2. Number of rings found is one,
3. The ring is identified as a muon-like,
4. Reconstructed momentum > 200 MeV/c,
5. Number of tagged decay electrons is ≤ 1,
6. Not charged pions like,
where Dwall is the closest distance between the ν vertex and the ID wall. It should
be noted that the FV used for the oscillation analyses is defined as Dwall >50 cm
and T owall > 250 cm, where T owall is the nearest distance from the ν vertex to the
ID wall along the particle direction.
The current FV used for the T2K oscillation analyses has been optimized to their
sensitivity. However, this analysis aims to measure neutrons associated with neutrino
interactions on water target rather than oscillation parameters. Thus, the FV of thisanalysis needs to be determined in terms of neutron tagging.
Neutrons escape from the ID volume depending on their energies and their production points inside ID, and the fraction of these neutrons is dependent on MC
simulations. Figure 7.1 shows this fraction as a function of Dwall reconstructed by
the fiTQun vertex (i.e. reconstructed ν interaction vertex position) for three diﬀerent MC neutrino event generators: NEUT, NuWro, and GENIE. It becomes rapidly
low when Dwall < 1 m and the diﬀerence between the generators also becomes large
for all the three event generators. As this analysis uses the whole FV to measureneutrons (i.e. neutron tagging eﬃciency is averaged over FV), the fraction of escaping neutrons as a function of fiducial volume also needs to be considered, and this isshown in Figure 7.2. As shown in the figure, the fraction of the escaping neutrons
over the whole FV is less than 0.5% when setting the Dwall cut value to 2 m.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
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Figure 7.1: Fraction of the neutron captures which happened inside ID as a functionof Dwall for the three diﬀerent ν event generators. The left and right correspondto the FHC and RHC 1Rνµ samples, respectively. Dwall is the nearest distance
between the ν vertex and ID wall. The analysis cuts (better selection) described inthis section are applied except for the FV cut.

Figure 7.2: Fraction of the neutron captures which happened outside the ID as afunction of Dwall cut value (i.e. fiducial volume) for the three diﬀerent ν event
generators. The left and right correspond to the FHC and RHC 1Rνµ samples,
respectively. Dwall is the nearest distance between the ν vertex and ID wall. The
analysis cuts (better selection) described in this section are applied except for the
FV cut.
In addition, the neutron tagging eﬃciency and the background rate need tobe taken into account, because these are position dependent in ID. As shown in
Figure 7.3, the tagging eﬃciency becomes very low below at Dwall < 2 m region,
whereas the background event rate does not. Based on the escaping neutrons from ID
and the position dependence of the performance of the neutron tagging, the fiducial
volume used for this analysis was defined as Dwall > 2 m only.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.3: Neutron tagging eﬃciency (top) and background event rate (bottom) as
a function of Dwall for the three diﬀerent ν event generators. Dwall is the nearest
distance between the ν vertex and ID wall. The right and left side plots are for
the FHC and RHC 1Rνµ samples, respectively. The analysis cuts (better selection)
described in this section are applied except for the FV cut.

7.3

Event selection for data collected until 2018

This section summarizes the results of the event selection for the Run 1-9 data. In theremaining part of this section, for all the MC expectations related to neutron tagging,the correction to the time variation eﬀects described in Section 6.5 is considered.
The 1Rνµ cuts described in Section 7.2 are applied to the FC samples of the FHC
and RHC Run 1-9 data. Figure 7.4 and 7.4 show the distributions of the variables
used in the 1Rνµ selection for FHC and RHC, respectively. As shown in the figures,the data show a good agreement with the corresponding MC expectations at eachselection stage. This can be clearly seen in Figure 7.6, which summarizes the numberof ν events at each selection stage and the resultant selection eﬃciency from the first
selection, the FCFV cut. From this figure, it can be found that the MC expectations
well reproduce the observations for the neutrino events. On the one hand, however,the MC expectation has overpredicted the tagged neutrons for all the selection stages
as shown in Figure 7.7.

139

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.4: Distributions of the variables used in the 1Rνµ selection for the FHC
mode. The vertical axes represent the number of observed neutrino events. The
selection criteria and their order are described in Section 7.2. The arrows indicate
the cut positions. All the MC distributions are normalized by the Run 1-9 POT.
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.5: Distributions of the variables used in the 1Rνµ selection for the RHC
mode. The vertical axes represent the number of observed neutrino events. The
selection criteria and their order are described in Section 7.2. The arrows indicate
the cut positions. All the MC distributions are normalized by the Run 1-9 POT.
141

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.6: Number of ν events (top) and the corresponding selection eﬃciencies
from the FCFV cut (bottom) for each selection stage. The left and right side plots
correspond to the FHC and RHC 1Rνµ samples, respectively. The MC expectations
are normalized by the Run 1-9 POT.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.7: Number of tagged neutrons (top) and the corresponding selection eﬃciencies from the FCFV cut (bottom) for each selection stage. The left and rightside plots correspond to the FHC and RHC 1Rνµ samples, respectively. The MC
expectations are normalized by the Run 1-9 POT.
Table 7.2 and Table 7.3 summarize the observed numbers in comparison to thecorresponding Run 1-9 MC expectations for the FHC and RHC 1Rνµ samples, respectively. The eﬃciencies from the FCFV cut for both ν events and tagged neutrons
are also summarized in Table 7.4 and Table 7.5, respectively. As described in thetables, the diﬀerence in the selection eﬃciency of the tagged neutrons between thedata and the MC prediction is yielded at the single-ring cut for both the FHC and
RHC samples. Since most of the NC and CC non-QE events are removed by thiscut, the diﬀerence could indicate that the fraction of tagged neutrons regarding NC
and CC non-QE interactions is diﬀerent between the data and MC expectations.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
Table 7.2: Expected numbers of tagged neutrons Ntag and ν events N1µ passing eachselection stage in comparison to the FHC data taken in Run 1-9. The expected
numbers are normalized by the Run 1-9 POT.
CCQE
νµ

CCQE
ν̄µ

CCNQ
νµ

CCNQ
ν̄µ

CC
νe /ν̄e

NC
ν/ν̄

Total

Acc.
bkg.

Data

FCFV

N1µ
Ntag

175.90
44.72

11.41
5.71

297.98314.35

12.33
12.22

87.96
29.31

197.36166.29782.95572.59

N/A
14.26

801
537

Nring = 1

N1µ
Ntag

152.80
30.80

10.24
4.95

57.90
29.86

3.20
3.10

63.88
14.13

36.53
20.62

324.55103.46

N/A
6.05

336
85

µ-likeN1µNtag

150.75
30.48

10.17
4.93

55.04
27.76

3.14
3.05

0.04
0.01

16.78
10.29

235.93
76.52

N/A
4.42

232
51

Pµ ≥0.2GeV/c

N1µ
Ntag

150.64
30.47

10.17
4.93

55.01
27.74

3.14
3.05

0.04
0.01

16.59
10.23

235.59
76.43

N/A
4.41

231
51

Ndecay−e ≤ 1

N1µ
Ntag

149.07
29.43

10.05
4.85

34.71
19.86

2.88
2.77

0.04
0.01

16.12
9.57

212.87
66.49

N/A
4.02

210
48

Not π ± -like

N1µ
Ntag

147.68
29.05

10.00
4.83

33.81
19.45

2.85
2.75

0.04
0.01

7.74
4.11

202.12
60.20

N/A
3.88

201
44

Table 7.3: Expected numbers of tagged neutrons Ntag and ν events N1µ passing eachselection stage in comparison to the RHC data taken in the Run 5-9. The expected
numbers are normalized by the Run 5-9 POT.
CCQE
νµ

CCQE
ν̄µ

CCNQ
νµ

CCNQ
ν̄µ

CC
νe /ν̄e

NC
ν/ν̄

Total

Acc.
bkg.

Data

FCFV

N1µ
Ntag

39.84
12.30

59.91
25.79

95.49
103.62

44.30
42.14

26.69
14.77

92.82
72.44

359.05271.06

N/A
6.78

361
224

Nring = 1

N1µ
Ntag

32.01
7.35

55.60
22.94

17.04
9.59

12.29
11.32

17.60
7.06

16.54
9.34

151.07
67.61

N/A
2.83

159
51

µ-like

N1µ
Ntag

31.81
7.31

54.99
22.74

16.38
9.09

12.02
11.14

0.01
0.00

7.26
4.76

122.46
55.05

N/A
2.27

126
39

Pµ ≥0.2GeV/c

N1µ
Ntag

31.81
7.31

54.96
22.73

16.37
9.09

12.02
11.14

0.01
0.00

7.19
4.72

122.35
54.99

N/A
2.27

126
39

Ndecay−e ≤ 1

N1µ
Ntag

31.40
7.09

54.33
22.35

10.57
6.36

11.06
10.20

0.01
0.00

6.97
4.48

114.33
50.48

N/A
2.12

112
34

Not π ± -like

N1µ
Ntag

31.17
7.01

53.91
22.20

10.37
6.23

10.89
10.07

0.01
0.00

3.25
1.87

109.61
47.39

N/A
2.03

110
33

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
Table 7.4: Summary of selection eﬃciencies from the FCFV cut for the FHC 1Rνµsample. Expected numbers are compared to the data taken in the Run 1-9 data.
The errors on the data are binomial statistical errors and are calculated by Bayesian
approach with a flat prior.

FCFVExpected
N1µ
Ntag

N1µ

Data
Ntag

1.000

1.000

1.000

1.000
0.158 (+0.017−0.016 )Nring = 1

0.415

0.187

0.419 (+0.018−0.018 )µ-like

0.301

0.138

0.290 (+0.017−0.016 )0.095 (+0.014−0.013 )Pµ ≥0.2GeV/c

0.301

0.138

0.288 (+0.017−0.016 )0.095 (+0.014−0.013 )Ndecay−e ≤ 1

0.272

0.120

0.262 (+0.016−0.016 )0.089 (+0.014−0.012 )Not π ± -like

0.258

0.109

0.251 (+0.016−0.016 )0.082 (+0.014−0.012 )Table 7.5: Summary of selection eﬃciencies from the FCFV cut for the RHC 1Rνµsample. Expected numbers are compared to the data taken in the Run 5-9 data.
The errors on the data are binomial statistical errors and are calculated by Bayesian
approach with a flat prior.

FCFVExpected
N1µ
Ntag

N1µ

Data
Ntag

1.000

1.000

1.000

1.000
0.228 (+0.032−0.029 )Nring = 1

0.421

0.254

0.440 (+0.028−0.027 )µ-like

0.341

0.206

0.349 (+0.027−0.026 )0.174 (+0.029−0.026 )Pµ ≥0.2GeV/c

0.341

0.206

0.349 (+0.027−0.026 )0.174 (+0.029−0.026 )Ndecay−e ≤ 1

0.318

0.189

0.310 (+0.026−0.025 )0.152 (+0.028−0.024 )Not π ± -like

0.305

0.178

0.305 (+0.026−0.025 )0.147 (+0.028−0.024 )As a summary of the event selection for the Run 1-9 data, after all the selection
stages, there are 201±14 (110±10) neutrino events in the FHC (RHC) 1Rνµ data
sample when 202.12 (109.61) events are expected. On the other hand, for the tagged
neutrons 44±6.6 (33±5.7) tagged neutrons are observed in the FHC (RHC) 1Rνµdata sample, whereas the expected number of tagged neutrons is 64.08 (49.42). It
should be noted that in order to obtain these expected numbers, the values of “Total”
needs to be added to the value of “Acc. bkg.” in Table 7.2 and Table 7.3 since theformer and the latter correspond to tagged true neutron events and accidental background events, respectively. These errors on the observation represent the Poisson
statistical errors.
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
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7.4

Quality checks for tagged neutrons

In the previous section, the first application of neutron tagging to the T2K data waspresented, and for the tagged neutrons there is a relatively large discrepancy between
the data and the MC expectations. However, such discrepancy could be caused by
diﬀerent behaviour of the neutron tagging algorithm between the data and the simulated events if such diﬀerence exists. Therefore, several studies were performed tocheck whether or not the neutron tagging algorithm does work properly for the data.
In the following, the first part mentions the observed response for the NN classification and the stability of neutron tagging over the Run 1-9 data taking periods.
The subsequent parts describe the studies on the distributions associated with thereconstructed neutron capture vertex and the neutron capture time distribution.
NN output distribution and tagged neutron rate
Figure 7.8 shows the observed distribution of NN output in comparison to the equivalent MC distribution. As shown in the figure clear peaks can be found around 0 and
1, which supports that the neural network does work and does distinguish between
true neutron events and accidental backgrounds events. The distributions of the NN
input variables before and after the NN classification can be found in Appendix B.

Figure 7.8: Distribution of the NN output for the Run 1-9 data overlaid with thecorresponding MC distribution. The left and right side plots correspond to the
FHC and RHC 1Rνµ samples, respectively. The MC expectations are normalized bynumber of observed tagged neutrons.
Figure 7.9 shows the cumulative number of tagged neutrons as a function of
accumulated POT. Since the cumulative numbers are assumed to be proportional
to accumulated POT, the assumption needs to be validated. If the assumption was
not reasonable enough, there would be a non-negligible time variation in neutron
tagging. To validate this assumption, a Kolmogorov-Smirnov (KS) test is performed.
In order to perform the test, an estimate of tagged neutron rate (i.e. number of tagged
neutrons/POT) is needed to construct the null hypothesis. This is done based on theobserved tagged neutrons, and thus the resulting rate is 0.295/1019 POT (0.202/1019
POT) for the FHC (RHC) sample. The observed KS distance, which is the maximum146

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
distance of the cumulative distribution function between the data and the data driven
expectation, is 0.115 and 0.044 for the FHC and RHC samples, respectively. Using
the KS distances, the KS p -value which is the probability obtaining the KS distanceunder the constant tagged neutron rate is estimated to be 63.4% and 75.1% for
the FHC and RHC samples, respectively. It is concluded from the result that theobserved cumulative distribution function is consistent with the assumption of theconstant tagged neutron rate.

Figure 7.9: Cumulative number of tagged neutrons as a function of accumulated
POT. The left and right side plots are for the FHC and RHC 1Rνµ samples, respectively. The solid lines correspond to expectation which is derived from the numberof observed tagged neutrons and Run 1-9 POT.
Neutron capture vertex distributions
As the neutron tagging algorithm reconstructs neutron capture vertex for each tagged
neutron, vertex for the observed tagged neutrons can be studied. Figure 7.10 shows
the two-dimensional distributions of the reconstructed neutron capture vertex for
R2 -Z and X-Y . As shown in the figure, the observed distributions are likely to be
distributed uniformly or are likely not to be clustered at a particular region.

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Figure 7.10: Two dimensional distribution of reconstructed neutron capture vertex
distributions of the Run 1-9 data. The top and bottom figures show the distributionof the vertical vertex position versus the square of the radial distance and the vertex
distribution projected onto the horizontal plane of the inner detector, respectively.
The left and right side plots are for the FHC and RHC 1Rνµ samples, respectively.
The black solid lines represent the inner detector wall. The yellow broken lines
represent the fiducial volume used in this analysis. The red arrows represent thebeam direction in the SK coordinate.
Since the neutron tagging algorithm has a position dependence in the detector
as shown Figure 7.3, shape of distribution associated with the reconstructed capture
vertex is therefore determined by the dependence. In other words, diﬀerence in such
shape between the data and the MC may indicates a bias in the neutron tagging
algorithm if it exists. Therefore, there diﬀerent statistical tests for shape comparison
between two histograms was performed to quantify the level of agreement between
the data and the MC.
For this test, one-dimensional distributions of the capture vertex, Dwall, R2 , andZ, are used. The Dwall distribution may be useful to check if there is a bias for thediscrimination of accidental backgrounds events, because most of these background
events are populated on the inner detector wall. The R2 and Z distributions canbe utilized to validate the position dependence of the neutron tagging algorithm.
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
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Figure 7.11 shows the Dwall, R2 , and Z distributions for the Run 1-9 data.

Figure 7.11: Distributions of the reconstructed neutron capture vertex for the Run
1-9 data. The left and right side figures correspond to the FHC and RHC 1Rνµsamples, respectively. The top figures show the distribution of the distance from thereconstructed vertex to the closest ID wall. The middle figures show the distributionof the square of the radial distance in the SK ID. The bottom figures show the
distribution of the vertical position in the SK ID. All the MC distributions arenormalized by the number of observed tagged neutrons of the Run 1-9 data.
As shown in the figure, statistics of each bin content for all the distributions is
not large enough to make a normal approximation, which means that in general there
is no unique way to quantify the agreement between two histograms (i.e. the data
and the MC). The agreement is therefore evaluated by three diﬀerent non-parametric
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
methods:• Kolmogorov-Smirnov (KS) test
• Cramer-von-Mises (CVM) test
• Anderson-Darling (AD) test

The test statistic for each test is derived from Ref. [216], and is given as:
TKS = max|Eiobs − Eiexp |i

TCVM =k[]2
1 ∑ obs
exp
obs(ni + nexp
)
E
−
E
i
i
i
4 i=1
kmax −1

TAD =∑i=kmin(7.4.1)

exp
[
]2
(nobs
i + ni )exp
obs
Ei − Ei,(Eiobs + Eiexp )(2 − Eiobs − Eiexp )where ni is number of tagged neutrons of i-th bin, kmin and kmax are the first bin andthe last bin where either histogram has non-zero counts, Ei is empirical cumulative
distribution function and is defined as follows∑i

j=1 njEi = ∑All bins .
nj
j=1

In order to derive the above test statistics, all the MC distributions are normalized
to the number of observed tagged neutrons, since the eﬀect of statistical fluctuations
on the shape comparison is taken into account by random throws in the following
procedure.
The CVM and AD tests use the sum of the squared diﬀerence between the two
cumulative distribution functions, whereas the KS test uses the maximum diﬀerence.
The AD test is similar to the CVM test, but it is designed to be sensitive to the tailsof a cumulative distribution function. It is therefore more sensitive to the Dwall andR2 distributions compared to the other tests, because these distributions have tailstructure.
Figure 7.12 shows the cumulative distribution functions of Dwall, R2 , Z for the
Run 1-9 data.

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T2K DATA

Figure 7.12: Cumulative distribution functions of the reconstructed neutron capture
vertex distributions for the Run 1-9 data. The left and right side plots correspond to
the FHC and RHC 1Rνµ samples, respectively. The top figures show the distributionof the distance from the reconstructed vertex to the closest inner detector wall. The
middle figures show the distribution of the square of the radial distance in the SK
ID. The bottom figures show the distribution of the vertical position in the innerdetector. The broken lines are the corresponding cumulative distributions functionof the MC distributions.
For each test and each vertex distribution, p -value, which is probability observing
the test statistic under the null hypothesis by statistical fluctuation, is calculated as
an upper tail probability of the test statistic distribution. The p -value is calculated
from toys which are generated by random throws. The procedure to generate thetoys is as follows:151CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

obs• Sample Ntag
tagged neutrons from the nominal MC distribution of interest,
obs
where Ntag is number of observed tagged neutrons (i.e. 44 and 33 for the FHC
and RHC 1Rνµ samples, respectively).

• Make a finely binned histogram using the sampled tagged neutrons.
• Make a cumulative distribution function from the histogram made just above.
• Compute test statistic of interest by using the cumulative distribution functionsof the nominal MC and toy MC.
• Repeat 10,000 times.

Using generated toys, distribution of test statistic is made. Figure 7.13 shows example of the test statistic distribution made from the toys for Dwall distribution of theFHC 1Rνµ sample.

Figure 7.13: Distributions of test statistics produced by random throws for the Dwallof the tagged neutrons of the FHC 1Rνµ sample. The top left, top right, and bottom
figures correspond to distributions of KS, CVM, and AD test statistics, respectively.
The green arrows show the values of the test statistics obtained by the Run 1-9 FHC
1Rνµ data sample.
152

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATAThe p -value is then estimated by Equation 7.4.2.
∫ +∞p − value =(7.4.2)F (T ) dT,
TData

where TData is the test statistic obtained by the data, F (T ) is the probability density
function made from the generated toys. In addition to the p -values for Dwall, R2 ,and Z, a combined p -value of R2 + Z is also considered. This may address thevalidity of the neutron tagging algorithm across the volume of the inner detector.
As the p -values for R2 and Z are treated as independent, the Fisher’s method
can be employed to evaluate the combined p -value. In this case the method uses a
χ2 which follows a chi-square distribution with four degrees of freedom and is defined
as follows.

χ2Fisher = −2 ln PR2 − 2ln PZ ,(7.4.3)where PR2 and PZ are the p -value of the R2 and Z distributions, respectively. The
combined p -value is therefore calculated as the upper tail probability of the chisquare distribution.
Table 7.6 summarizes the p -values for the Dwall, R2 , Z, and combined R2 + Z
distributions for all the tests performed. As shown in the table, there have been no
significantly small p -values.
Table 7.6: p -values of Dwall, R2 , Z, and combined R2 + Z obtained by the KS,
CVM, AD tests using toy MC for the tagged neutrons of the Run 1-9 FHC and RHC
1Rνµ samples.
Beam mode
FHC

RHC

SampleDwall
R2Z
R2 + Z

KS
49.6%
82.6%
5.1%
53.1%

CVM
33.3%
75.0%
3.0%
41.8%

AD
27.9%
69.0%
2.9%
43.0%

Dwall
R2
Z
R2 + Z

37.1%
94.3%
32.9%
88.3%

18.4%
89.8%
28.8%
84.6%

19.8%
86.1%
29.0%
85.3%

Neutron capture time distributions
The neutron tagging algorithm tags the accidental backgrounds as well as the true
neutrons. The correlation of the time diﬀerence from the neutrino interaction is dif153

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
ferent between the true neutrons and backgrounds, because the true neutrons havean exponential time structure with the capture time of about 200 µs, whereas the
backgrounds have a flat time structure. The capture time distribution is therefore
useful to validate the neutron tagging. In addition, in principle the expected numberof backgrounds described in Table 7.2 and 7.3 can be checked by the observed distributions. In order to extract these quantities, the observed distributions are fitted
by a function consisting of an exponential and a constant components defined by
Equation 7.4.4.

f (t; τ, µS , µB ) = µS

exp(−t/τ )1+ µB,[exp(−18/τ ) − exp(−513/τ )]513 − 18

(7.4.4)

where τ is capture time, µS is number of tagged true neutrons, and µB is number oftagged backgrounds. As the number of observed tagged neutrons are 44 and 33 for
the FHC and RHC 1Rνµ sample, respectively, a Gaussian χ2 fit is not relevant to
extract τ , µS , and µB . A binned Poisson negative log likelihood is therefore used forthe fit and is defined in Equation 7.4.5.
L = −lnL(τ, µS , µB )=5∑Ei − Oi + Oi ln(Oi /Ei ),(7.4.5)

i=1

where

Ei =

∫ ti +45
ti −45f (t; τ, µS , µB ) dt,

is number of expected tagged neutrons and Oi is number of observed tagged neutronsin i-th bin. The likelihood is minimized by the MINUIT algorithm.
Figure 7.14 shows the observed capture time distributions with the fitted functions. Table 7.7 summarizes the numbers obtained from the fit, which include thefitted τ , µS , and µB . The fitted τ and µB for the FHC (RHC) 1Rνµ sample are 39.4
± 22.6 (155.9 ± 38) and 20.0 ± 6.1 (2.7×10−6 ± 5.4), respectively. As shown in
the table, these fitted numbers diﬀer from their expectations, but the diﬀerence isobtained probably due to the small statistics.

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T2K DATA

Figure 7.14: Time diﬀerence between ν event and neutron capture. Left and rightare for the FHC and RHC 1Rνµ samples, respectively. The solid lines correspond tothe best fit results of the binned log likelihood fit.
Table 7.7: Summary of the results of the bin log likelihood fit to the capture time
distribution. The expected τ , µS , and µB are obtained from an experimental result [37], Table 7.2, and Table 7.3, respectively. It should be noted that the fitted µS
can diﬀer from the expectation, because this analysis does aim to measure µS itself.
Beam mode

FHC

RHC

Parameter
τ
µS
µB
-lnL
χ2 /ndf

Fit results
39.4 ± 22.6
24.0 ± 6.4
20.0 ± 6.1
0.743
0.948/(5-3)

Expected
204.8 ± 0.4 µs
60.2 (Can be diﬀerent)
3.9
N/A
N/A

τ
µS
µB
-lnL
χ2 /ndf

155.9 ± 38
33.0 ± 5.7
2.7×10−6 ± 5.4
1.610
0.809/(5-3)

204.8 ± 0.4 µs
47.4 (Can be diﬀerent)
2.0
N/A
N/A

A study using toy MC fits is done in order to confirm whether or not the data fit
results can be described by the small statistic. The procedure is as follows:• Set true τ , µS , and µB of toy MC :– τ : 204.8 µs– µS : 44-3.9 (33-2.0) for the FHC (RHC) 1Rνµ sample– µB : 3.9 (2.0) for the FHC (RHC) 1Rνµ sample• Generate tagged true neutrons and background events by Poisson distributions
with mean value of the true µS and µB above, respectively. For each generated
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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
neutron (background event), its capture time is sampled from an exponentialfunction with the true τ (a flat function).
• Make capture time distribution from the generated tagged true neutrons andbackground events.
• Fit the capture time distribution made above to extract τ , µS , and µB in thesame way as the data fit.
• Repeat 30,000 times.
Using the fitted parameters of the toy MCs, distributions for these parameters areconstructed, and can be used to know how precisely these parameter are fitted forthis small statistics. Figure 7.15 shows the distributions for the fitted parameters incomparison to the data fit results. As shown in the figure, the binned log likelihood
fit does not extract the parameters well for this small statistics, and thus the fitted
parameters are not distributed as Gaussian.
From this results, the results of the data fit are reasonably explained due to thesmall statistics of the Run 1-9 data. In order to quantify the results of the data fit,
goodness-of-fit (GoF) is evaluated using the minimum L distribution. Distribution of
the minimum L can be also made using the toy MC fit results as shown in Figure 7.16.
Then, the GoF is obtained as an upper tail probability of the distribution and isestimated to be be 59.2% and 31.9% for the FHC and RHC samples, respectively.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.15: Distributions of the fitted τ , µS , µB of the toy MCs. The left and rightpanels correspond to the FHC and RHC 1Rνµ samples, respectively. The top, middle,
and bottom figures represent the fitted τ , µS , and µB . The magenta arrows show
the true values used for the generation of the toy MC. The green arrows represent
the data fit results.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.16: Distribution of minimum L obtained by the toy MC fits. Left and rightare for the FHC and RHC 1Rνµ samples, respectively. The green arrows show theminimum L obtained by the data fit.

7.5

Distributions related to tagged neutrons

Although this analysis aims to measure mean multiplicities, it may be interesting
to know the agreement regarding tagged neutrons between the data and the MC
expectations. A variety of distributions related to tagged neutrons for the Run 1-9
data are therefore overlaid with the corresponding MC expectations.
The MC expectations are made with flux tuning, correction of cross sections,and oscillation probabilities calculated from the oscillation parameters which aresummarized in Section 7.1, and then are normalized by the Run 1-9 POT (14.938 ×
1021 POT and 16.346 × 1021 for the FHC and RHC expectations, respectively).
Figure 7.17 shows the tagged neutron multiplicities. The number of ν events withtagged neutrons = 0, = 1, ≥ 2, and their fractions are summarized in Table 7.8. It
may be interesting to notice the fact that in both of the FHC and RHC data, themaximum tagged neutrons is 2 while the MC expectation has lager tagged neutrons.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
Figure 7.17: Distribution of tagged neutron multiplicity for the Run 1-9 FHC (left)
and the Run 5-9 RHC data (right). Note that the accidental backgrounds are included in the tagged neutrons. The MC expectations are normalized by the Run 1-9
POT.

ntag= 0

Expected
ntag= 1 ntag≥ 2

ntag= 0Datantag= 1ntag≥ 2

FHC

eventsfraction

153.70
0.76

36.16
0.18

12.26
0.06

162.000.81 (0.06)

34.00
0.17 (0.03)

5.00
0.02 (0.01)

RHC

eventsfraction

72.64
0.66

27.29
0.25

9.68
0.09

83.00
0.75 (0.08)

21.00
0.19 (0.04)

6.00
0.05 (0.02)

Table 7.8: Expected and observed numbers of ν events with tagged neutrons = 0, =1, ≥ 2 and their fractions compared to the Run 1-9 FHC and RHC data. For the
expectation, the backgrounds are included. The expectations are normalized by the
Run 1-9 POT.

7.5.1

Muon kinematics dependence

As neutron productions in FSI and SI depend on the energy transfer from incoming
neutrino to hadronic system at neutrino interactions, it may be interesting to checkmean tagged neutron multiplicity as a function of kinematic variables which are correlated with the energy transfer.
Figure 7.18 shows the mean tagged neutron multiplicity as function of the reconstructed muon momentum.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.18: Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed muon
momentum. The left and right side plots are for the FHC and RHC 1Rνµ samples,
respectively. The expected numbers are normalized by the Run 1-9 POT.
Figure 7.19 shows the mean tagged neutron multiplicity as function of the reconstructed muon transverse momentum.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.19: Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed muontransverse momentum. The left and right side plots are for the FHC and RHC 1Rνµsamples, respectively. The expected numbers are normalized by the Run 1-9 POT.
Since the 1Rνµ samples have a high purity of CCQE interaction events, thereconstructed neutrino energy calculated by assuming CCQE interaction is a good
approximation to its true energy. Thus, the neutrino energy dependence of the tagged
neutrons are also studied. The reconstructed energy is calculated by Equation 7.5.1.
2(Mn − Vnuc )Eµ − m2µ /2 + Mn Vnuc − Vnuc
/2 + (Mp2 − Mn2 )/2
Rec,
Eν CCQE =Mn − Vnuc − Eµ + Pµ cos θbeam(7.5.1)

where Mn (Mp ) is the neutron (proton) mass, Vnuc is the binding energy of the neu161

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA
tron in oxygen (taken to be 27 MeV), mµ is the mass of muon, Pµ is the reconstructed
momentum under muon hypothesis, Eµ is its total energy, and θbeam is the angle between the neutrino beam direction and the reconstructed lepton direction.
Figure 7.20 shows the mean tagged neutron multiplicity as function of the reconstructed neutrino energy.

Figure 7.20: Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of reconstructed neutrinoenergy. The left and right side plots are for the FHC and RHC 1Rνµ samples,
respectively. The distributions are normalized by the Run 1-9 POT.
Once the reconstructed neutrino energy is obtained, it is also possible to computethe reconstructed four momentum transfer squared by Equation 7.5.2.

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CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA()
Rec
2
Q2CCQE= 2EνRec
CCQE Eµ − pµ cos θbeam − mµ .

(7.5.2)

Figure 7.21 shows the mean tagged neutron multiplicity as function of the reconstructed four momentum transfer squared.

Figure 7.21: Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of the reconstructed negative four momentum transfer squared. The left and right side plots are for the FHC
and RHC 1Rνµ samples, respectively. The distributions are normalized by the Run
1-9 POT.
Figure 7.22 shows the mean tagged neutron multiplicity as function of the cosineof the angle between the reconstructed muon and beam directions.
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T2K DATA

Figure 7.22: Number of tagged neutrons (top), number of ν events (middle), andaverage number of tagged neutrons (bottom) as a function of the cosine of the angle between the reconstructed muon and beam directions. The left and right sideplots are for the FHC and RHC 1Rνµ samples, respectively. The distributions arenormalized by the Run 1-9 POT.

7.5.2

Kinematics of tagged neutrons

In principle, as will be mentioned in Section 8.1, travel distance, which is the distribution of distance between ν interaction and neutron capture vertices, contains
information regarding number of post-FSI hadrons (i.e. hadron multiplicities) andtheir energy distributions. Distributions of reconstructed distances are therefore
checked.
Figure 7.23 shows the distribution of reconstructed travel distance. In addition
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T2K DATA

Figure 7.23: Distribution of the reconstructed neutron travel distance which is defined as the distance between the ν intraction and neutron capture vertices. The
left and right correspond to the FHC and RHC 1Rνµ samples, respectively. The
distributions are normalized by the Run 1-9 POT.
to the reconstructed travel distance above, it may be interesting to check both longitudinal distance and transverse distance, which are the distance projected onto thebeam direction and the distance perpendicular to the beam direction, respectively.
Figures 7.24 and 7.25 show the distributions of the longitudinal and transverse distances, respectively.

Figure 7.24: Distribution of the reconstructed longitudinal travel distance, which is
the travle distance projected onto the beam direction. The left and right correspondto the FHC and RHC 1Rνµ samples, respectively. The distributions are normalized
by the Run 1-9 POT.
If the direction from ν vertex to neutron capture vertex is interpreted as themomentum direction of a tagged neutron, the momentum direction of neutron canbe reconstructed:
rncap − rν int,
dˆrec =
|rncap − rν int |where rncap and rν int. are the reconstructed ν vertex and neutron capture vertex,165

CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATA

Figure 7.25: Distribution of the reconstructed transverse travel distance, which is thetravel distance perpendicular to the beam direction. The left and right correspondto the FHC and RHC 1Rνµ samples, respectively. The distributions are normalized
by the Run 1-9 POT.
respectively.
Using the reconstructed momentum direction of tagged neutron, two angularvariables can be studied. The first one is cosine of the actual angle which is the angle
between the beam and reconstructed momentum directions, which may address themomentum directions of the hadrons leaving the target nucleus with respect to thebeam direction. Figure 7.26 shows the distribution of cosine of the actual angle.

Figure 7.26: Distribution of cosine of the actual angle which is the angle between the
beam direction and reconstructed momentum direction. The left and right plots arefor the FHC and RHC 1Rνµ samples, respectively. The distributions are normalized
by the Run 1-9 POT.
The other angule is cosine of the inferred angle which is the angle between theinferred and reconstructed momentum directions. The inferred direction can be calculated by assuming that all the ν events observed are due to true CCQE interaction
and the tagged neutron is associated with the outgoing nucleon of CCQE interaction,and is given as:

166CHAPTER 7. FIRST APPLICATION OF NEUTRON TAGGING TO
T2K DATAEν CCQE b − P1µdˆinf = Rec,|Eν CCQE b − P1µ |Rec

where EνRec
CCQE is reconstructed neutrino energy defined in Equation 7.5.1, b is thebeam direction, and P1µ is the reconstructed µ momentum.
Figure 7.27 shows the distribution of cos(dˆrec · dˆinf ).

Figure 7.27: Distribution of cosine of the inferred angle which is the angle between
the inferred direction and reconstructed momentum direction. The left and rightplots are for the FHC and RHC 1Rνµ samples, respectively. The distributions arenormalized by the Run 1-9 POT.
As was shown by the distributions regarding the reconstructed distances andangular variables above, the shapes of the observed distributions do not agree wellwith those of the corresponding MC distributions. In case of the angular variables
shown in Figure 7.26 and Figure 7.27, relatively large deficits in the forward region
can be seen, although the statistical uncertainties are still large. This may indicatethat there might be non-negligible diﬀerence in either or both of the kinematics ofhadrons after FSI and their secondary interactions in water between the data andthe simulations.
As a conclusion, in general the distributions related to the neutrino events show
good agreement between the data and the MC predictions. On the other hand, theobserved distributions associated with tagged neutrons show that the MC prediction
tends to produce more tagged neutrons than that of the data. It is worth notingthat the neutron tagging algorithm does work properly for both the data and the
MC predictions as described in Section 7.4.

167

Chapter 8
Measurement of mean neutron
multiplicity
The primay aim of this thesis is to measure neutrons associated with neutrino interactions on water target with a proper systmatic uncertainty, and make a quantitative
comparison between experimental data and simulations. Both the neutron tagging
algorithm described in Chapter 6 and the result of its application to the T2K data
accumulated until 2018 presented in Chapter 7 are the ingredients to this aim.
In this Chapter, first the production of those neutrons are described using MC
simulations in Section 8.1. Following this, Section 8.2 describes the strategy of thisanalysis, and a series of extensive studies on systematic uncertainties on this neutron mesurement is summarized in Section 8.3. Finally Section 8.4 presents themeasureent result, and a discussion on the result is given in Section 8.5.

8.1

Simulation studies

As was introduced in Section 1.2.1, neutrons related to neutrino interactions in water, which are measured in this thesis, are produced via three sequential processes:
primary ν-nucleon interaction in nuclear medium, hadronic FSI inside the target
nucleus, and hadronic SI in water. In practice, current scheme to simulate the three
processes uses two separate MC simulations, which has been adopted in neutrino
oscillation experiments for both atmospheric and accelerator neutrinos.

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Figure 8.1: Distribution of true neutron multiplicity before SI for three diﬀerentMonte Carlo ν event generators. The left and right correspond to the FHC and
RHC 1Rνµ samples, respectively.
For the first two processes, MC simulation called “ν event generator” is used.
Modern neutrino oscillation experiments and ν-nucleus interaction experiments haveused several generators such as GENIE [11], NEUT [135], and NuWro [136]. These
generators consider almost same primary interaction channels, but diﬀerences in
adopted interaction model, treatment of nuclear eﬀect, and implementation methodby itself make diﬀerent simulation results. Figure 8.1 shows neutron multiplicities
after primary interactions and FSI for the FHC and RHC 1Rν samples, which areused for this analysis. As shown in the figure, a large diﬀerence is seen between
GENIE and the others, which mainly originates from diﬀerent way of simulating
FSI. Both NEUT and NuWro perform their FSI simulation within framework ofcascade model by tracking hadrons inside the target nucleus on basis of microscopic
interaction cross-section, whereas GENIE uses a cascade-like model, “hA”, in which
particle tracking is not conducted and the simulation of FSI is performed by single
MC calculation (i.e. single throwing of random number) in accordance with a look-up
table.

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Figure 8.2: Distribution of kinetic energy for neutrons (top left), protons (top right),
π + (bottom left), and π − (bottom right) which have left the target nucleus, but havenot undergone their secondary interactions in detector. The FHC 1Rνµ samples areused for these hadrons. All the distributions are normalized by 1021 POT.

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Figure 8.3: Distribution of kinetic energy for neutrons (top left), protons (top right),
π + (bottom left), and π − (bottom right) which have left the target nucleus, but havenot undergone their secondary interactions in detector. The RHC 1Rνµ samples areused for these hadrons. All the distributions are normalized by 1021 POT.
The diﬀerence in the neutron multiplicity between NEUT and NuWro is marginal
between them. However, they have a visible diﬀerence in distribution of kinetic energy of neutron. Figure 8.2 and 8.3 show distributions of kinetic energy for post-FSI
hadrons including neutrons, which just escaped from the target nucleus and do notundergo their SI in water, for the FHC and RHC 1Rνµ samples. As shown in the
figures, NuWro predicts post-FSI nucleons with lower energies compared to NEUT.
In a water Cherenkov detector, neutrons after all the three processes are detected
and they are indistinguishable in terms of production process. Since neutron production by SI strongly depends on energies of post-FSI hadrons, prediction of resultant
neutron multiplicity after all the processes is also aﬀected by diﬀerence in kinetic
energies as shown in Figure 8.4.
The figure also shows diﬀerence between SKDETSIM and Geat4.10.1 with an option of FTFP BERT HP. Although both simulations adopt same SI’s simulation scheme
based on the Bertini’s cascade model, the results are diﬀerent since the details in thetreatment and implementation methods of the model diﬀers between them. Alongside the energy and simulation dependencies on the neutron production in SI, inorder to understand the dominant contribution to the neutron production by SI, it
is helpful to notice that the number of post-FSI π ± is much less than that of postFSI nucleons in the 1Rνµ samples. Therefore, according to the MC expectations,
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
neutrons and protons mainly contribute to the neutron production by SI in thisanalysis.

Figure 8.4: Mean neutron captures as a function of incident kinetic energy for neutrons, protons, and π ± . Orange and cyan lines correspond to expectation of SKDETSIM and Geat4.10.1 with an option of FTFP BERT HP, respectively. In SKDETSIM,GCALOR is used to simulate hadrons except only for pions with momenta below
500 MeV/c, and NEUT simulates pions for the momentum region. These hadrons
are generated by the particle guns of the two simulations.
In a region of neutrino energies ranging from Sub-GeV up to several GeV, many
neutrons are produced in SI. Figure 8.5, for instance, shows the neutron multiplicities
before and after SI of the 1Rν samples and more than half of the total neutrons areproduced in SI, on average. The diﬀerence in the neutron multiplicity after the SI
among the three event generators is also shown in Figure 8.6. Even after SI, NuWro
still predicts similar neutron multiplicity to NEUT, whereas GENIE predicts moreneutrons than the other generator. Nevertheless, there is still remaining experimentally visible diﬀerence between the three generators. In a water Cherenkov detector,
energy of neutron can not be measured, because neutrons can only be detected by using gamma rays emitted from neutron capture on nuclei. However, thanks to neutron
capture, any energies of neutrons can be detected, and the distance from primary νinteraction vertex to neutron capture vertex can be reconstructed for each neutron
capture. Since the distance is correlated with energies of post-FSI hadrons as shownin Figure 8.7, the distance, therefore, has information about the diﬀerence in primaryν interactions and FSI among three generators as shown in Figure 8.8. Moreover,the distance would be an important input to the modeling of the two processes if SI
could be simulated precisely or constrained experimentally very well.

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Figure 8.5: Distribution of true neutron multiplicity for the FHC 1Rνµ sample (left)
and the RHC 1Rνµ sample (right). Filled histograms and solid lines correspond totrue neutron multiplicity before SI and after SI, respectively. All the distributions
are normalized by the Run 1-9 POT.

Figure 8.6: Distribution of true neutron multiplicity for the three popular ν event
generators, NEUT, NuWro, and GENIE. All the contributions from neutrino interactions, hadronic FSI and SI are included in the multiplicities. The left and rightplots correspond to the FHC and RHC 1Rνµ samples, respectively. The secondaryinteractions of the hadrons produced by the generators are common among the three
generators. (i.e. the identical detector simulation is used). All the distributions arearea normalized.

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Figure 8.7: True travel distance of neutron captures per incident hadron as a functionof initial momentum for n, p, π + , π − . The Z-axes show the number of neutron
captures.

Figure 8.8: Distribution of true distance between ν interaction and neutron capture
vertices for the NEUT, NuWro, and GENIE. The left and right plots correspond to
the FHC and RHC 1Rνµ samples, respectively. The secondary interactions for the
hadrons produced by the generators are common among the three generators. All
the distributions are normalized by 1021 POT.

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8.2

Analysis strategy

In this analysis, a set of mean neutron multiplicities are measured rather than multiplicity distributions. As was described in Section 6.3, typical neutron tagging
eﬃciency of the neutron tagging algorithm is ∼20%. In addition, all the neutrons
produced in hadronic FSI (Final State Interactions) and hadronic SI (Secondary Interactions) as well as primary ν interactions are included in the observed neutronsat SK.
When a neutrino interaction happens inside a nucleus, hadrons are produced by
the interaction within the nucleus. These hadrons interact with nucleons in the nucleus before they leave it. These interactions are referred to as hadronic FSI. Once
those hadrons exit the nucleus in which they are produced, they propagate throughdetector mediums (i.e. water for the SK far detector) and interact with these mediums, which is referred to as hadronic SI.
The predictions for FSI and SI strongly depend on the hadron multiplicities andthe energy distributions of the hadrons produced in primary ν interaction, whichmeans that one can not extract the neutrons produced at a particular process ofinterest without any assumption (i.e. introducing model dependence). Thus, themeasured neutrons in this analysis includes all the contributions from three processes and is performed in a minimal model dependent way.

Figure 8.9: Mean neutron multiplicity as a function of true Q2 . The left and rightcorrespond to the FHC and RHC 1Rνµ samples, respectively. The error bars represent the MC statistical uncertainties.
Neutron multiplicity is expected to become large as the four momentum transfer
squared Q2 to the hadronic system at the primary ν-nucleus interaction increases,
as shown in Figure 8.9. Since the direction of beam ν is known, reconstructedmuon transverse momentum Pt , which is a good indicator of Q2 , can be calculated.
Figure 8.10 shows the relation between true Q2 and reconstructed Pt . As shown inthis figure, a clear positive relation can be seen. This analysis therefore measures themean neutron multiplicity as a function of Pt using the FHC and RHC 1Rνµ samples
as follows:

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY()
Ntag,i − b × N1µ,i1M̄i = ×,εiN1µ,i(8.2.1)∑N1µ,iwhere i represents i-th Pt bin, Ntag,i =j=1 mij , N1µ,i is number of observed
1Rνµ events, mij is number of tagged neutrons of j-th 1Rνµ event, b is accidental
background event rate of the neutron tagging, and εi is neutron tagging eﬃciency.
Neutron tagging eﬃciency and accidental background event rate are defined in Equation 6.1.1 and Equation 6.1.2, respectively.
The relation between the transverse momenta and the true neutrino energies canbe found in Appendix C.

Figure 8.10: Relation between true Q2 and reconstructed Pt . The left and rightcorrespond to the FHC and RHC 1Rνµ samples, respectively. The Z-axes show thenumber of neutrino events normalized by 1021 POT The black lines represent themean reconstructed Pt at each true Q2 bin.

8.3

Systematic uncertainties on tagging eﬃciency

This analysis aims to measure neutrons in the less model dependent way by following
Equation 8.2.1. Estimates of systematic uncertainties on the neutron tagging eﬃciency and the background event rate is therefore important. However, the estimatesneed to be done only for the tagging eﬃciency.
As the background event rate of the neutron tagging algorithm is estimated by
T2K dummy spill data, there is no systematics regarding simulations, and only thetime variation eﬀect needs to be considered, which has been taken into account in
Section 6.5. Thus, this section describes the estimates of systematic uncertainties on
the neutron tagging eﬃciency.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

8.3.1

Overview

In the following, the sources of systematics considered are mainly categorized bysimulations associated with neutrons and others. As was described in Section 6.2,
the tagging algorithm uses ν interaction vertex to search for neutron candidates,
which introduces dependence on distance between ν interaction and neutron capture
vertices into the neutron tagging eﬃciency. This dependence is shown in Figure 8.11,
and the eﬃciency goes down as the distance increases. As it can be found fromthe figure shown, systematics, which eﬀect the shape of the true distance, causesa variation in the eﬃciency. Therefore, the uncertainties on neutrino interaction
cross sections, neutrino fluxes, nucleon and pion FSI/SI, µ− and π − captures on
oxygen nucleus, and oscillation parameters, which are associated with the simulationsof neutrons, are taken into account. The uncertainty on the 1Rνµ event selection
described in Section 7.2 is also considered, because it can aﬀect the shape of the
distance distribution.

Figure 8.11: Neutron tagging eﬃciency as a function of true distance from ν interaction and neutron capture vertices for the FHC (left) and RHC (right) 1Rνµ samples.

Other systematic sources which are reconstruction error of ν vertex, simulationof the PMT gain increase over time, and detector response for 2.2 MeV γ rays. In
addition, the statistical errors of the MC events are taken into account on top of the
SK time variations described in Section 6.5.4.
In the following parts, the systematic uncertainties regarding these sources are
estimated for the tagging eﬃciency as a function of the reconstructed muon transverse
momentum and the tagging eﬃciency averaged over the transverse momentum.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

8.3.2

Neutrino cross sections

The systematic variations on the tagging eﬃciency due to uncertainties regarding
the neutrino interaction cross sections are studied. The inputs to the uncertainties
associated with the neutrino interactions are the same as used in the cross section
analyses at the T2K near detectors. The following uncertainties are considered basedon the works done by the T2K neutrino interaction working group [217]. The parameters which account for the uncertainties on neutrino interactions are categorized
by true interaction modes. Table 8.1 summarizes the parameters considered. In thetable, “shape ”parameter have kinematic dependence and “norm ”parameter is normalization parameter.
Table 8.1: List of parameters which describe uncertainties on neutrino cross sections
ParameterpO
F
OEB
MACCQE
2p2h
RES
CA5
MARES
BGRES
A
CC other
CC coherent
NC coherent
NC otherRadiative corrections

Interaction catergories applied
CCQE
CCQE
CCQE
2p2h
CC/NC1π
CC/NC1π
CC/NC1πCC other
CC coherent
NC coherent
NC other
CC νe

Type
shape
shape
shape
norm
shape
shape
shape
shape
norm
norm
norm
norm

Nominal value and 1σ error
225 ± 31 MeV/c
27 ± 9 MeV
1.2 ± 0.41 GeV/c2
1.0 ± 1.0
1.01 ± 0.12
0.95 ± 0.15 GeV/c2
1.3 ± 0.2
0.0 ± 0.4
1.0 ± 0.3
1.0 ± 0.3
1.0 ± 0.3
1 ± 0.03

For CCQE interaction, its uncertainty is described by the axial mass MACCQE ,O
Fermi momentum of oxygen nucleus pO
F , and binding energy of oxygen nucleus EB .
The uncertainty on 2p − 2h interaction is taken into account by an overall normalization parameter.
For single pion interactions, their uncertainties are described by the parameterswhich vary the axial mass MARES , I = 1/2 continuum background (i.e. isospin BG),
RES
and axial form factor CA5.
There are normalization parameter and energy dependent parameter to accountfor the uncertainties on CC coherent and CC other interactions, respectively. The
uncertainties regarding NC coherent and NC other interactions are separately treatedby two independent normalization parameters.
The eﬀect of Bremsstrahlung from electron as the final state lepton is also considered and is treated by a normalization parameter.
The uncertainty on each individual parameter is propagated to the tagging efficiency by reweighting the nominal MC on an event-by-event basis. The weights
applied are generated by a T2K software package (T2KReWeight v1r23). Figure 8.12
shows the resultant fractional variations in the tagging eﬃciency. As shown in the
figure, all the parameters considered have very small impacts. Since the uncertainties
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
regarding these parameters are commonly applied to both the denominator and thenumerator in Equation 6.1.1, these are largely cancelled out for the tagging eﬃciency.

Figure 8.12: Fractional change in the average tagging eﬃciency due to ±1 σ variationsof each individual parameter for the FHC (top) and RHC (bottom) 1Rνµ samples.
The blue and red bars correspond to ±1 σ variations, respectively.
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
The total systematic uncertainty due to the cross section parameters are computed by adding each fractional variation in quadrature as follows:√∑
max{|δεi (+1σ)|, |δεi (−1σ)|}2
δεXSec =(8.3.1)i

The resultant systematic variation in the average neutron tagging eﬃciency is estimated to be ∼0.2% as shown in Table 8.11.

8.3.3

Neutrino beam fluxes

The ν beam fluxes are binned by true ν energy and the fractional uncertainty of eachindividual bin is treated as a systematic parameter. The binning is summarized inTable 8.2. Figure 8.13 shows the fractional uncertainties on the beam fluxes. The
dominant contribution to the 1Rνµ samples comes from the energy region ranging
from sub-GeV to a few GeV where the corresponding uncertainties are about less than
8%. In order to estimate the systematic uncertainties regarding these parameters,
Table 8.2: True ν energy binning of the beam fluxes for their systematic parameters.
Beam mode

Flux type
νµ

FHC

ν̄µ
νe
ν̄e
νµ
ν̄µ

RHC

νe
ν̄e

True ν energy bin edges (GeV)
0.0, 0.4, 0.5, 0.6, 0.7, 1.0,
1.5, 2.5, 3.5, 5.0, 7.0, 30.0
0.0, 0.7, 1.0, 1.5, 2.5, 30.0
0.0, 0.5, 0.7, 0.8, 1.5, 2.5,
4.0, 30.0
0.0, 2.5, 30.0
0.0, 0.7, 1.0, 1.5, 2.5, 30.0
0.0, 0.4, 0.5, 0.6, 0.7, 1.0,
1.5, 2.5, 3.5, 5.0, 7.0, 30.0
0.0, 2.5, 30.0
0.0, 0.5, 0.7, 0.8, 1.5, 2.5,
4.0, 30.0

Number of bins
11
5
7
2
5
11
2
7

fractional change in the tagging eﬃciency is computed for ±1 σ variations of eachindividual parameter. The computation is done by reweighting the nominal MC onan event-by-event basis. Figure 8.14 shows the resulting fractional changes in the
total average eﬃciencies. As shown in the figure, the size of all the variations areless than 0.8%.

180CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.13: Fractional uncertainties on the ν beam fluxes. The uncertainties aretaken from TN-354 [33]Figure 8.14: Fractional change in the total average tagging eﬃciency. Right andleft are for the FHC and RHC 1Rνµ samples, respectively. As the 1Rνµ samples are
dominantly composed by the νµ and ν̄µ fluxes, only the systematic parameters ofthese fluxes have therefore visible variations. The blue and red bars correspond to±1σ variations, respectively.
Although the correlations among the flux parameters are studied well, these are
ignored, because the impacts of all the parameters on the tagging eﬃciency are
marginal. The total fractional uncertainties on the eﬃciency are estimated by adding
each parameter variation linearly as follows. In the case of the average tagging
eﬃciency, it is estimated to be less than 0.38%, which is summarized in Table 8.11,
and is very small.
∑(8.3.2)
δεFlux =max{|δεi (+1σ)|, |δεi (−1σ)|}.
i

8.3.4

Pion FSI/SI

Uncertainties on pion FSI/SI aﬀect final states (i.e. visible topology) in SK, because
the processes of QE scattering, absorption, and charge exchange (CX) can alter energy deposition, number of visible particles, etc. These uncertainties can vary the181CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
composition of the 1Rνµ samples, which results in variations in neutron tagging eﬃciency. Since both pion FSI and SI are handled by the same cascade model in NEUT
described in Section 4.2.1, the FSI and SI uncertainties are propagated by varying a
set of systematic parameters of the model.
The NEUT’s cascade model is divided into two pion energy regions. In eachregion, the microscopic cascade interaction probabilities are scaled via the following
systematic parameters. In the low energy region (pion momentum pπ < 500 Med/c),
FSIABS, FSIQE, and FSICX consider uncertainties on the interaction probabilities
for the absorption, QE scattering including CX, and the branching fraction of CX,
respectively. In the above pπ > 500 MeV/c region, pions have enough energy to
produce hadrons and the pion absorption becomes smaller. Thus, uncertainties on
the QC scattering, the inelastic processes, CX in the high energy region are treatedby FSIQEH, FSIQEH, and FSICX, respectively.
These parameters are constrained by various experimental pion scattering data
and a 1-σ surface in the parameter space is constructed from the constraint. Fromthe surface, 16 sets of the parameters are chosen, and used to evaluate the systematic uncertainties on neutron tagging eﬃciency. Table 8.3 summarizes the 16 sets.
The detail of the procedure to derive the 16 sets can be found in [218]. For each
Table 8.3: π FSI/SI 1 σ parameter sets.
Comment
NominalPar. set number
0

FSIQE
1.0

FSIQEH
1.8

FSIINEL1FSIABS
1.1

FSICX
1.0

FSICXH
1.8

Had. Prod. Up

15
16
17
18
19
20
21
22

0.6
0.6
0.7
0.7
1.4
1.3
1.5
1.6

1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1

1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5

0.7
0.7
1.6
1.6
0.6
0.7
1.5
1.6

0.5
1.6
0.4
1.6
0.6
1.6
0.4
1.6

2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3

Had. Prod. Down

23
24
25
26
27
28
29
30

0.6
0.6
0.7
0.7
1.4
1.3
1.5
1.6

2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3

0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5

1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1

0.5
1.6
0.4
1.6
0.6
1.6
0.4
1.6

1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3

parameter set, event-by-event weights are generated, and are used to reweight thenominal MC events. Fractional errors for neutron tagging eﬃciency are computedfor each parameter set by the reweighting. Figure 8.15 shows the fractional errors
for the average tagging eﬃciency.
All the 16 sets represent the 1 σ uncertainty of the model. The systematic uncertainties due to pion FSI/SI are therefore computed as the RMS of the fractional
errors, and are estimated to be less than 0.2% for the average tagging eﬃciency as
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
shown in Table 8.11.

Figure 8.15: Fractional changes in the average neutron tagging eﬃciency due topion FSI/SI uncertainty. Top and bottom figures are for the FHC and RHC 1Rνµsamples, respectively. The horizontal axes represent the parameter sets described inTable 8.3.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

8.3.5

Nucleon FSI

Uncertainties associated with nucleon FSI are estimated by using a GENIE MC. In
the case of GENIE, nucleon FSI is simulated by a data-driven model called hA. It
simulates the charge exchange, elastic scattering, inelastic scattering, and absorption.
Table 8.4: List of parameters which describe the nucleon final state interactions in
GENIE. Numbers taken from [38].
Parameter name
xN
mf p
xN
cex
xN
el
N
xinel
xN
abs

Description
Fractional error
Total rescattering probability±20%
Charge exchange probability±50%
Elastic reaction probability±30%
Inelastic reaction probability±40%
Absorption probability±20%

Figure 8.16: Fractional change in the average tagging eﬃciency for the FHC (left)
and RHC (right) 1Rνµ samples. The blue and red bars correspond to ±1 σ variations,
respectively.
N
NN
The uncertainties on these processes are parameterized by xN
mf p , xcex , xel , xinel ,and xNabs , respectively. The first parameter alter the total interaction probability,
whereas the others vary the fraction of the corresponding interaction process. Table 8.4 shows the 1 σ errors of the parameters.
These errors are propagated by reweighting the nominal GENIE MC on an eventby-event basis. Figure 8.16 shows the resulting fractional change in the average tagging eﬃciency for ±1 σ variations of a parameter of interest. Total systematic uncertainties on the tagging eﬃciencies are estimated by adding the fractional changes
in quadrature. As described in Table 8.11, the estimated uncertainties are ∼1%.

8.3.6

Nucleon SI

Uncertainties regarding nucleon SI aﬀect the distance from ν interaction and neutron
capture vertices directly. As was mentioned in Section 6.2, in the primary selection184

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
neutron candidates are searched using ν interaction vertex. In the first step of theselection, the vertex is alternatively used as the true neutron capture’s one, which
introduce a weak correlation between the two vertices. Thus, uncertainties regarding
nucleon SI can vary the neutron tagging eﬃciencies through the correlation.
The simulation of nucleon SI is handled by GCALOR [134] in SKDETSIM as
described in Section 4.3. For the energies of the T2K beam neutrinos, nucleons are
simulated by HETC [195][196] and MICAP [197] codes in GCALOR. Protons are
simulated by HETC only. In the case of neutrons, HETC and MICAP are called forabove and below 20 MeV kinetic energy regions, respectively.
In the following parts, uncertainties regarding HETC and MICAP are described
separately. As the results of the MICAP simulation should be fully correlated withthat of HETC, the total systematic uncertainties regarding nucleon SI are calculated
by adding the resulting fractional variations due to HETC and MICP linearly, andetimated to be ∼7% as shown in Table 8.11.
Nucleon SI in high energy region
In HETC, the interaction probability as well as interaction channel is calculated
based on the Bertini’s free nucleon-nucleon cross sections [185]. Thus, uncertainties
on the cross sections can directly vary the distance between ν interaction and neutron
capture vertices, and result in variations in the neutron tagging eﬃciency. Figure 4.6
show the total free nucleon-nucleon cross sections used in HETC.
An experimental constraint on the cross sections by nucleon-oxygen scatteringin the T2K energy region may be an ideal input to be propagated to the neutron
tagging eﬃciency. However, there is no such experimental data. A conservative
error assignment on the cross sections is therefore made based on an analysis ofworld experimental data of proton-carbon scattering [219]. In that analysis, thetheoretical cross sections of carbon were calculated by NEUT which uses the same
Bertini’s cross sections [135] as used in HETC. The calculated cross sections werecompared to several theoretical calculations as well as the data. The comparison
showed that the total Bertini’s cross sections need to be varied by ±30% in order
to cover both the other calculations and the data. Based on the comparison, we
determined to assign a 30% error on the total Bertini’s cross section as the input of
the systematic uncertainty regarding HETC.
In order to propagate the cross section error to the neutron tagging eﬃcienciesof the 1Rνµ samples, the nominal hybrid neutron MC described in Section 4.5 wasregenerated varying the total cross section by ±30%.
The left panel of Figure 8.17 shows distribution of true distance from ν interaction
vertex and neutron capture vertex for total neutrons. As shown in the figure, the ±30% errors have large impacts on the normalization of the distribution (i.e. number of
total neutrons), and vary the total number of neutrons by +6/ − 9% and +10/ − 15%
for the FHC and RHC 1Rνµ samples, respectively. In addition, the shape of the
distribution is also largely varied. Similar variations are seen for the tagged neutrons
as shown in the middle panel of the figure. Since the eﬀects of the uncertainty on
the cross sections are similar between the total and tagged neutrons, most of the185

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
variations in the total and tagged neutrons are therefore largely cancelled out whencalculating the neutron tagging eﬃciency. The resultant neutron tagging eﬃciency
is shown in the right panel of Figure 8.17. The systematic uncertainty due to theBertini’s cross sections are estimated to be less than 6.7% for the average neutron
tagging eﬃciency.

Figure 8.17: Distribution of the true distance from ν interaction and neutron capture
vertices for the total neutrons (top) and the tagged neutrons (middle). Neutron
tagging eﬃciency as a function of the true distance (bottom) (i.e. middle/top).
The right and left side plots correspond to the FHC sample and RHC 1Rνµ samples,
respectively. All the distributions are normalized by 1021 POT. The histograms filledby the colors are made from the nominal MC, whereas the pink and green solid lines
are made from the regenerated MC with the ±30% variation of the Bertini’s total
free N-N cross sections, respectively.
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
Neutron SI in below 20 MeV region
The remaining part describes the systematic uncertainties regarding the cross section
for the neutrons whose kinetic energy is below 20 MeV.
Neutrons in this energy region are simulated by MICAP which utilizes the ENDF/B (Evaluated Neutron Data Files version B) cross section data to calculate theinteraction probabilities and resulting interaction channel. The MICAP program
uses a thinned ENDF/B version V in which version the number of data points are
reduced from its original version. The original version was released more than 20
years ago, whereas there have been several version updates with visible changes fromthe version V. The version VIII0 is the latest one as of this moment. Figure 8.18
shows comparison of the microscopic total cross sections. As shown in the figure, themicroscopic total cross sections of hydrogen nucleus has changed slightly from thethinned version V used for MICAP and the relative changes from MICAP are lessthan 2.5%. On the one hand, there are clear diﬀerences between the two versions,which mainly comes from the absorption cross sections.

Figure 8.18: Comparison of ENDF/B microscopic total cross section between diﬀerent versions. MICAP use a thinned version V and thus, there are diﬀerence between
the MICAP’s one and version V (formatted in ENDF-6).
There are relatively large diﬀerences between two versions especially for oxygen
nucleus in the figure shown. The uncertainties on the cross section used for MICAP
are therefore assigned as the diﬀerences between the two versions. In order to estimate the impacts of the cross section diﬀerences, the ENDF/B-VIII0 cross sections
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
needed to be implemented to SKDETSIM. The original MICAP code was modified
and a new code was developed in order to replace the MICAP’s cross sections with
the ENDF/B-VIII0’s ones.
After the modifications, the nominal hybrid neutron MC was regenerated with
the ENDF/B-VIII0’s ones. Figure 8.19 shows the distribution of the true distance
between the ν interaction and neutron capture vertices for the nominal and regenerated MCs.

Figure 8.19: Distribution of the true distance between the true distance between theν interaction and neutron capture vertices. The histograms filled by the colors andsolid lines are made from the nominal MC and regenerated MC with the ENDF/BVIII0, respectively. The left and right plots are for the FHC sample and RHC 1Rνµsamples, respectively.
As shown in the figure, the shapes of the distributions are relatively similar, but
the normalization (i.e. number of total neutrons) diﬀers between the two MCs. The
reason for the variation (i.e. similar shape and diﬀerent normalization) is explained
as follows. The origin of the similar shapes come from the fact that in this energy
region the mean distance from the generation point to the capture position is very
short and is less than 35 cm as shown in Figure 8.20. Thus, the cross section differences do not result in a large variation in the distance and alter the shape of the
distributions of the 1Rνµ samples slightly. For the diﬀerence in the normalization,
the fraction of the disappearance interaction of oxygen nucleus in which there is no
out-going neutron is largely diﬀerent between the two versions and the version VIII0
has clearly higher fraction as shown in Figure 8.21. In the regenerated MC withthe version VIII0, number of neutrons which disappear before thermalization and
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
neutron capture by hydrogen nucleus therefore increased compared to the nominalMC.
The systematic uncertainties due to the cross sections used for MICAP are assigned as the diﬀerences between the nominal and regenerated MCs and are estimatedto be less than 0.2% for the average tagging eﬃciency.

Figure 8.20: Mean true distance between generation and neutron capture positions
for the MICAP’s thinned ENDF/B-V and ENDF/B-VIII0 versions. These are madefrom results of neutron particle gun MC of the detector simulation.

Figure 8.21: Fraction of interaction channel of oxygen nucleus for the MICAP’s
thinned version V (left) and ENDF/B-VIII0 (right).

8.3.7µ− and π − captures on oxygen

The uncertainties on neutron productions by the µ− and π − captures on oxygen nucleus are considered. As was described in Section 4.4, in the nominal hybrid neutron
MC G4MuonMinusCaptureAtRest and G4PiMinusAbsorptionAtRest simulate theseproductions, respectively. Although these simulation codes are the default models
189

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITYin Geant4.9.6, Geant4.9.6 also provides alternative models. The uncertainties onthese production are therefore taken into account by taking the diﬀerences between
models.
In the case of the µ− capture, the alternative model is CHIPS (Chiral Invariant
Phase Space) which is derived from a non-perturtative theory of QCD. The nominal hybrid neutron MC was regenerated by replacing G4MuonMinusCaptureAtRest
with G4QCaptureAtRest which is the class in CHIPS codes. Figure 8.22 shows the
distribution of the true distance between ν interaction and neutron capture vertices
for G4MuonMinusCaptureAtRest and G4QCaptureAtRest. As shown in the Figure,the diﬀerence is marginal and thus, the resulting fractional variations in the tagging
eﬃciency are also small and is estimated to be less than 1.5% for the average tagging
eﬃciency.

Figure 8.22: Comparison of the diﬀerent simulation of neutron productions by the
distribution of true distance between the ν interaction and neutron capture vertices. The left and rights plot are for the FHC and RHC 1Rνµ samples, respectively. In the plots, “Nominal ”corresponds to the nominal MC generated with
G4MuonMinusCaptureAtRest, whereas “CHIPS ”corresponds to the regenerated MCwith G4QCaptureAtRest instead. All the distributions are normalized by 1021 POT.

For the π − capture, in addition to CHIPS, there is another alternative model
which is a similar cascade model to HETC. The uncertainty regarding the π captureis therefore assigned from the diﬀerences between G4PiMinusAbsorptionAtRest,
G4QCaptureAtRest, and G4PiMinusAbsorptionBertini. These diﬀerences are obtained by regenerating the nominal MC in the same way as the case of µ− capture.
Figure 8.23 shows the resulting distribution of the true distance between the ν interaction and neutron capture vertices for the three MCs. The average tagging eﬃciency
varied by ∼1% due to the diﬀerences as shown in Table 8.11.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.23: The distributions of true distance between the ν interaction and neutron capture vertices for the three diﬀerent models of the neutron productions by
π − capture. The left and right plots are for the FHC and RHC 1Rνµ samples,
respectively. In the plots, “Nominal ”corresponds to the nominal MC generated
with G4PiMinusAbsorptionAtRest, whereas “CHIPS ”and “BERT ”correspond to
the regenerated MC with G4QCaptureAtRest and G4PiMinusAbsorptionBertini,
respectively.

8.3.8

Detector response for ν events

Uncertainty on the detector response which aﬀects the selection eﬃciency of the 1Rνµevents may vary the shape of the true neutron travel distance, which cases systematic
variation on the tagging eﬃciencies. As such uncertainty has been estimated in thefrom of the covariance matrix described in [220], the covariance matrix is therefore
used. In the covariance matrix, the 1Rνµ events are categorized based on the interaction modes, neutrino flavor, and reconstructed neutrino energy as summarizedin Table 8.5. Figure 8.24 shows the uncertainty regarding the selection eﬃciency of
the 1Rνµ events for each event category. Fractional changes in the tagging eﬃcienTable 8.5: Categorization of the 1Rνµ events for the systematic uncertainty on thedetector response. The reconstructed energy is computed as in Equation 7.5.2
Beam mode
FHC

RHC

True event categoryνµ /ν̄µ CCQE
νµ /ν̄µ CCNQνe /ν̄e CC
NC

Reco. ν energy bin edges (GeV)
0.0, 0.4, 1.1, 30.0
0.0, 30.0
0.0, 30.0
0.0, 30.0νµ /ν̄µ CCQE
νµ /ν̄µ CCNQνe /ν̄e CC
NC

0.0, 0.4, 1.1, 30.0
0.0, 30.0
0.0, 30.0
0.0, 30.0

Number of bins
4
1
1
1
4
1
1
1

cies are computed for 1 σ variation of each individual event category by reweighting
191

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.24: Fractional uncertainties on each event category which are derived fromthe uncertainty on the detector response. The left and right plots are for the FHC
and RHC 1Rνµ samples, respectively.
the nominal MC on event-by-event basis. Figure 8.25 shows the resulting fractionalchanges. The systematic uncertainties due to the detector systematics are evaluatedin the same manner as the flux uncertainties and are estimated to be less than 0.4%
for the average tagging eﬃciency, which are described in Table 8.11.

Figure 8.25: Fractional change in the average tagging eﬃciency for the FHC (left)
and RHC (right) 1Rνµ samples.

8.3.9

Oscillation parameters

The uncertainties on the oscillation probabilities are considered. As the neutrons are
not used in the oscillation analyses for the Run 1-9 data, the measured oscillation
parameters using the data can be used as the input of the systematics regarding theoscillation probabilities. Table 8.6 summarizes the 1 σ uncertainties on the oscillation
parameters used for the oscillation probability calculation. In order to estimate theimpacts on the tagging eﬃciency, oscillation probability is re-calculated for the nominal MC on an event-by-event basis by varying ±1 σ for each individual parameterand then, fractional variations in the eﬃciency are computed. As shown in Table 8.7,
the systematic variations due to the oscillation parameters are very small.
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
Table 8.6: List of nominal values and 1 σ intervals of the parameters used for theoscillation probability calculation. Taken from Table 7 in [36].
Parametersin2 θ13
sin2 θ23∆m223 10−3 eV2
δCP

Nominal value

1 σ interval

0.02120.532
2.452−1.885[0.0225,0.0323][0.495,0.562][2.382,2.523][-2.460,-1.187]

The total systematic uncertainty due to the oscillation parameters is calculatedby the same way as the flux uncertainties using Equation 8.3.2 since the know correlation between the parameters are ignored. As shwon in Table 8.11, the estimateduncertainties on the average tagging eﬃciency are ∼0.2%.
Table 8.7: Fractional change in the total average tagging eﬃciencies for ±1 σ variations of each oscillation parameter.
sin2 θ13+1σ/−1σsin2 θ23+1σ/−1σ∆m223+1σ/−1σδCP+1σ/−1σFHC-0.00%/+0.00%+0.12%/-0.01%-0.01%/+0.05%-0.00%/+0.00%

RHC-0.00%/+0.00%+0.08%/-0.01%+0.05%/-0.03%+0.00%/-0.00%

8.3.10ν vertex

The neutron tagging uses ν vertex to select the neutron candidates, which was mentioned in Section 6.2. The uncertainties on the resolution and shift for the ν reconstructed vertex may aﬀect the performance of the selection. These uncertainties havebeen studied using cosmic ray muons and these studies are summarized in [221] andin [220]. The estimated resolution and shift errors are 2.5 cm and 5 cm, respectively.
In order to propagate these errors to the neutron tagging eﬃciency, three artificial
vertex shifts are added to the nominal MC on an event-by-event basis as follows:• Isotropic shift : add isotropic 2.5 cm vertex shift.
• Forward shift : add 5 cm vertex shift along the particle momentum direction.
• Backward shift : add 5 cm vertex shift along the opposite direction to theparticle momentum direction.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
The vertex resolution error is taken into account by the first shift, whereas the vertex
shift error is considered by the last two shifts. The tagging eﬃciency is computed foreach individual shift and then, the fractional change in the eﬃciency is evaluated.
Table 8.8 summarizes the resulting fractional change in the average tagging eﬃciency.
The total systematic uncertainties regarding these vertex errors are computed by
Table 8.8: Fractional changes in the average neutron tagging eﬃciency due to theartificial vertex shifts

FHC

Resolution error
Isotropic shift-0.07%

RHC-0.06%

Shift error
Forward shift Backward shift
0.26%-0.11%
0.22%-0.22%

adding the variations by the resolution and shift errors in quadrature. The estimateduncertainties are ∼0.3%, which are described in Table 8.11.

8.3.11

Simulation of PMT gain increase

The SK time variations described in Section 6.5 aﬀect both the neutron tagging
eﬃciency and the background event rate. The eﬀects of the time variations are estimated and have been corrected to the nominal values by utilizing the simulation for
2.2 MeV γ rays and T2K dummy spill data for the background events, respectively.
However, there is a non-negligible systematic uncertainty associated with the simulation of the PMT gain increase. It should be noted that this is related only to thesimulation of 2.2 MeV γ rays and thus, there is no such uncertainty on the accidental
background events which are modeled by T2K dummy spill data.
As shown in Figure 6.26, the PMT gain has continuously increased, which makes
the hit probability higher as time proceeds. In SKDETSIM, the increase of the gain
is simulated by scaling charge of the hit PMT Q while keeping the threshold on the
charge. The scaling is performed as follows:)(
G(t) − G0
,
Q× 1+
G0

(8.3.3)where G(t) is the PMT gain at time t and G0 is the average of the PMT gain
measured in Oct. 2008.
Thus, this way to simulate charge of PMT hit naturally increase number of PMT
hits for a given fixed energy deposition as the gain increases as shown in the left sidepanel of Figure 8.26.
194

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.26: Distribution of the single photo-electron of the SK-III type PMTs usedin SKDETSIM (left) and Relation between relative number of PMT hits and relative
PMT gain for the data derived from various calibrations and MC (right). In left sideplot, the green filled histogram corresponds to the nominal gain and the blue andred lines correspond to +8% and +16% gain from the nominal value, respectively.
In the neutron tagging, what is the most important in the detector simulation isto reproduce the time evolution of the number of PMT hits rather than PMT gain
itself. If the number of PMT hits as a function of PMT gain diﬀers between the data
and the MC, then it causes a systematic variation in the neutron tagging eﬃciency.
It can be assumed from the studies on the various calibration data performed in SK
that the relative number of PMT hits are proportional to the relative PMT gain.
The proportional constant has been estimated to be 0.226 based on the calibration
data [222]. For the detector simulation, on the other hand, the proportional constantevaluated from the gain simulation is ∼1.6 times smaller compared to the data. The
right panel of Figure 8.26 shows the linear relation obtained by the calibration datain comparison with that of MC. The disagreement of the proportional constant istherefore interpreted as the systematic uncertainty regarding the gain simulation.
In order to account for the disagreement, an extra scaling factor α is introduced
into the gain simulation as follows:)(
G(t) − G0.
Q× 1+α×G0(8.3.4)

Then, additional MC regeneration with α = 1.6 was performed in the same way as
described in Section 6.5.2. It should be noted that the case of α = 1.0 is the sameas what was done in Section 6.5.
Figure 8.27 shows the comparison of the neutron tagging eﬃciency and the background event rate between the α = 1.0 and α = 1.6 cases. As shown in the figure,the eﬃciency clearly diﬀers between the two cases, whereas there is no visible variation for the background event rate. This is as expected, because the extra scaling is
195

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
applied only to the simulation of 2.2 MeV γ rays and the contamination of the PMT
hits produced by the γ rays in the background events is marginal.

Figure 8.27: Comparison of the α = 1.0 and α = 1.6 cases for the tagging eﬃciency(top) and background rate (bottom) after the NN classification. The filled circles andopen triangles are for the regenerated MCs with α = 1.0 and α = 1.6, respectively.
These plots are for the FHC 1Rνµ sample, but same tendency is also found for the
RHC 1Rνµ sample.
Following the procedure detailed in Section 6.5.3, the tagging eﬃciencies of theregenerated MCs with α = 1.6 are fitted and then the POT weighted average of thetagging eﬃciency is computed. Figure 8.28 shows the fit result and the resultant
average. Even for the case of α = 1.6, the fit function defined in Equation 6.5.1 wasapplicable, which produced an acceptable χ2 /n.d.f = 275.7/254.
Table 8.9 summarizes the POT weighted averages for both of the two cases. The
diﬀerence between the two cases is then assigned as the systematic uncertainty due
to the simulation of the PMT gain increase. The resultant systematic unertainty on
the average tagging eﬃciency is ∼2% as shown in Table 8.11.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.28: Tagging eﬃciency after the NN classification as a function of time for
α = 1.6. The solid curves and broken lines correspond to the best fit results and
POT weighted averages, respectively. The top and bottom plots correspond to the
FHC and RHC 1Rνµ samples, respectively.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
Table 8.9: POT weighted total average tagging eﬃciency and background rate forthe α = 1.0 and α = 1.6 cases. X represents either tagging eﬃciency or background
event rate. Note that the numbers for α = 1.0 are the same as listed in Table 6.38.
α = 1.0

α = 1.6(Xα=1.6 − Xα=1.0 )/Xα=1.0

20.09
20.37

20.48
20.86

+1.98%+2.40%

2.02 ×10−2
1.94 ×10−2

0.00%
0.00%

Tagging Eﬃciency (%)

FHC
RHC

# acc. bkg./ν event

FHC 2.02×10−2
RHC 1.94×10−2

8.3.12Detector response to 2.2 MeV γ rays

Uncertainty regarding the detector response for 2.2 MeV γ rays is estimated using
the Am/Be low energy neutron calibration data described in Section 6.4. Since
in principle the calibration enables estimating neutron tagging eﬃciency, ideally,
direct comparison of tagging eﬃciency between data and MC is desirable to address
systematics regarding detector response for 2.2 MeV γ rays.
As was discussed in Subsection 6.4.5, however, such direct comparison needs
estimations of both the contamination of fake prompt events in which there is no
signal delayed neutrons and neutron absorption by the geometry of the calibration,
because these eﬀects cause a systematic decrease of neutron tagging eﬃciency only
for the data. In order to estimate these eﬀects, a precise MC which can simulate
both γ rays from the Am/Be source and scintillation light of the BGO scintillator
is needed, but is not available at the present moment and is quit challenging to be
made. Therefore, a novel method which can avoid those eﬀects was newly developed
for this analysis. In this method, systematic uncertainties on the primary selection
and NN classification of the neutron tagging algorithm are separately estimated.
N 10pvx primary selection
As was described in Section 6.2, the primary neutron candidate selection is a simple
selection based on N 10pvx which is number of PMT hits in a 10 ns timing window.
The performance of the primary selection strongly depends on PMT hit yield, andthus diﬀerence in PMT hit yield between the data and MC can be systematics
regarding the primary selection. The PMT hit yield diﬀerence was estimated bycomparing the shape of N 10pvx distribution between the data and the MC, because
the shape should not be aﬀected by the eﬀects of the fake prompt events and theneutron absorption.
In order to compare the shape and quantify the resulting shape diﬀerence, PMT
hit yield needs to be parametrized for MC. In SKDETSIM, parametrization of PMT
hit yield is not trivial, but quantum eﬃciency QE (so called COREPMT) which is
not true quantum eﬃciency of PMT and is an overall scaling factor of PMT hit
probability is employed as an eﬀective parameter. Figure 8.29 demonstrates that198

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
the QE parameter can vary shape of N 10pvx distribution. Figure 8.30 shows the

Figure 8.29: QE dependence of N 10pvx shape. The distributions are made fromneutron particle gun MC events which are generated by varying QE.
N 10pvx distribution of the data taken at the detector center position. As shown in
the plot, the distribution is dominated by the accidental background events selectedin the primary selection, and the accidental background component needs to be
subtracted for the shape comparison.
As the background data of the calibration was taken with the Am/Be source anda periodic trigger, the N 10pvx distribution of the background data should be same as
the accidental background component of the signal calibration data. The backgroundsubtraction can be done by scaling the N 10pvx distribution of the background databy the number of prompt events, because the accidental background events do notdepend on whether or not prompt event is true 4.4 MeV γ ray event. Figure 8.31
shows the shape of the accidental background subtracted N 10pvx distribution of thedata for the center position.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.30: N 10pvx distribution of the data taken at the center position of the
Am/Be calibration. Both the data and MC distributions are normalized by numberof prompt events.

Figure 8.31: N 10pvx shape of the data taken at the detector center position of the
Am/Be calibration (left) and its ratio to the corresponding MC (right). The shapeof the data shown in left panel was obtained by subtracting scaled accidental background of the background data from the N 10pvx distribution shown in Figure 8.30.
A χ2 fit for the shape of N 10pvx distribution is performed to address the PMT
hit yield of the data. For this fit, a set of MC was generated by varying the QE
parameter and then χ2 is calculated by comparing the shape of N 10pvx distributionsof the data and MCs. The best fit point of the QE value was estimated by a leastsquare fit of a quadratic function to the calculated χ2 as shown in the left panel of
Figure 8.32. As shown in the plot, the calculated χ2 values seem not to be smooth.
This is due to the statistical fluctuation of the MC, because the available statistics ofthe MC is limited by the background data statistics. Since the fitted χ2 curve may
change slightly due to the MC statistical fluctuation, the 1σ fractional uncertainty
on the PMT hit yield σQE is conservatively assigned as:
200

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITYσQE =QE+1σ − QEN om,
QEN om

(8.3.5)where QE+1σ is the +1 σ QE value estimated by the fitted χ2 curve and QEN om isthe nominal QE value.
The assigned σQE is 1.9% and is propagated to neutron tagging eﬃciency ofthe primary selection. There is a linear relation between relative tagging eﬃciency
and relative QE with respect to the nominal value as shown in the right panel of
Figure 8.32. Using the relation, propagation of the uncertainty on the PMT hit yieldis done and the resulting variation in the tagging eﬃciency is estimated to be 2.8%.

Figure 8.32: N 10pvx Calculated χ2 by comparing N 10pvx shape between data ad MC(left). The solid curve is fitted χ2 obtained by a least square fit with a quadratic
function. Relative number of selected true 2.2 MeV γ candidates in the primary
selection as a function of relative QE with respect to the default value (right). The
error bars are the MC statistical errors. The solid line is obtained by fitting a linear
function to the points and is used in order to propagate the QE diﬀerence estimatedby the shape fit to the neutron tagging eﬃciency.
Neural network classification
The uncertainty on the NN classification is estimated from the diﬀerence in relativeeﬃciency between the data and MC. The relative eﬃciency is the eﬃciency from theprimary selection and is given as:

relative eﬃciency =Selected true neutrons in NN classification
Selected true neutrons in primary selection(8.3.6)

The relative eﬃciency does not depend on number of selected prompt events, whichmeans that possible contamination of the fake prompt events can be avoided. In
addition, the eﬀect of neutron absorption by the geometry of this calibration should
be same between the denominator and numerator. Thus, the relative eﬃciency is201

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
not aﬀected by those eﬀects.
Both the numerator and the denominator in Equation 8.3.6 can be statisticallyobtained from the capture time distributions after the primary selection and NNclassification, respectively. In order to obtain the numerator and the denominator,
a Gaussian χ2 fit to the capture time distributions is performed by modifying Equation 6.4.3 as follows:()∑ ∑ Ei,j − Oi,j (τ, εi , bi ) 2 ( 204.8 − τ )2
χ =
+
,
Ei,j
0.4
i
j
2

(8.3.7)

Figure 8.33 and 8.34 show the capture time distributions with the best fit curves
for the primary selection and NN classification, respectively. As shown in the plots,
fraction of the accidental backgrounds significantly diﬀer between the primary selection and NN classification. In the case of the primary selection the huge background
events aﬀect extracting τ due to its statistical fluctuation, whereas τ is well extracted
in the NN classification. This can potentially cause diﬀerence in fitted τ between
the primary selection and NN classification, but τ should be same between them. In
addition, such diﬀerence may cause a systematic bias in relative eﬃciency. In orderto stably fit τ , the penalty term (204.8 − τ /0.4)2 is added to the χ2 in the equation. The constraint 204.8 ± 0.4 µs comes from an external experiment result [37].
The fitted τ is 204.8 ± 0.4 µs and 204.9 ± 0.4 µs for the primary selection and NNclassification, respectively.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.33: Distribution of capture time after the primary selection for the three
data taking positions. The top left, top right, bottom correspond to the center, theZ+15 m, and the Y-12 m data taking positions, respectively.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.34: Distribution of capture time after the neural network classification for
the three data taking positions. The top left, top right, bottom correspond to thecenter, the Z+15 m, and the Y-12 m data taking positions, respectively.
Once the fit is performed, in practice the relative eﬃciency can be obtained by
dividing fitted ε of the NN classification by the primary selection’s one. Table 8.10
summarizes the relative eﬃciencies obtained by the fit for the data and MC. Using
the numbers summarized in the table, the ratio of the relative eﬃciency between
the data and MC is computed and is treated as the systematics regarding the NN
classification. Figure 8.35 shows the calculated ratio.
Table 8.10: Relative eﬃciency of the Am/Be calibration. εP S and εN N is the fitted
neutron tagging eﬃciencies of the primary selection and NN classification, respectively.
Relative eﬃciency εN N /εP S
Center Z+15m
Data 0.742
0.483

Y-12m
0.658

MC

0.646

0.719

204

0.516

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.35: Ratio of the fitted relative eﬃciency between the data and MC.
In order to evaluate the impact of the uncertainty of the NN classification on theneutron tagging eﬃciency, the uncertainty needs to be propagated properly to theeﬃciency. As was mentioned in Section 7.2, the neutron tagging eﬃciency depends
on Dwall of the ν vertex (i.e position of the ID), which is shown in Figure 7.3. Since
the calibration data was taken at three diﬀerent positions in the inner detector,a Dwall dependent NN classification error can be adopted by dividing up the ID
volume based on the three data taking positions. The inner detector volume isdivided into three regions based on the Dwall of the data taking position in sucha way that the volume between the neighbor two data taking positions is equallydivided. Figure 8.36 shows the Dwall of the three data taking positions and thedivided volume with the assigned systematics regarding the NN classification.
The Dwall dependent uncertainty is propagated by reweighting the nominal MC
on an event-by-event basis as follows:mtrue→ mtrue× (1 + δεN N (Dwall)),ii(8.3.8)where mtrue
is number of tagged true neutrons of i-th ν event, δεN N (Dwall) isithe Dwall dependent systematics regarding the NN classification. Full correlation
among the three regions is assumed for a conservative estimate of the systematics onthe tagging eﬃciency when propagating the source errors. The resulting fractionalvariation in the averaged neutron tagging eﬃciency is estimated to be 3.51%.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.36: Dwall of the data taking positions (left) and the assignment of the
Dwall dependent error on the relative eﬃciency (right). In the right side plot, δεN N
is the fractional error of the relative eﬃciency between the data and MC.
Total systematic uncertainty
In the previous parts, the systematic uncertainty on the tagging eﬃciency due tothe primary selection and NN classification was estimated to be 2.8% and 3.5%,
respectively. The total systematics regarding the detector response for 2.2 MeV γ
rays is obtained by adding those two uncertainties in quadrature and is estimated to
be 4.4%.

8.3.13

Total systematic uncertainties

The total systematic uncertainty on the neutron tagging eﬃciency is evaluated byadding each fraction variation described in the previous sections in quadrature.
The estimated fractional uncertainty on the averaged eﬃciency is +6.74/-7.70% and+7.22/-8.09% for the FHC ad RHC 1Rνµ samples, respectively.
The RHC 1Rνµ sample is a ν̄ CCQE interaction enriched sample and thus there
are more neutrons produced in the ν interactions and hadron FSI. These neutrons
tend to have higher energy than neutrons produced by hadron secondary interactions
and are more aﬀected by the variation of the nucleon SI described in Section 8.3.6.
The relatively larger uncertainty of the RHC sample compared to the FHC’s one
therefore comes from this diﬀerence.
The fractional uncertainty on the averaged eﬃciency for each individual error
component is summarized in Table 8.11 and is visualized in Figure 8.37. The neutron
tagging eﬃciency with the estimated total systematic uncertainty is also comparedwith the eﬃciencies evaluated by using the GENIE- and NuWro-based MCs. Figure 8.38 and 8.39 show the tagging eﬃciency as a function of Pt and the tagging
eﬃciency averaged over Pt , respectively. As shown in the figures, the estimated total
systematics covers the diﬀerence in the tagging eﬃciencies between the three MCs.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
Table 8.11: Summary of fractional uncertainty of the average neuron tagging eﬃciency for each individual systematic source. All the estimations of thses numbers
are detailed in Sections 8.3.2- 8.3.12.
Source neame

Fractional uncertainty (%)
FHCRHCν cross section

±0.16

±0.23

ν beam flux

±0.37

±0.30

π FSI/SI

±0.25

±0.10

Nucleon FSI

±1.20

±0.94

Nucleon SI(GCALOR)

+4.00
-5.82

+4.96
-6.61

µ− /π − captures on 16 O

±1.89

±0.71

Oscillation probability

±0.17

±0.14

MC statistics

+0.03
-0.03

+0.05
-0.05

Detector response for ν events

±0.38

±0.23

Detector response for 2.2 MeV γ

+4.47
-4.47

+4.47
-4.47

ν event vertex

±0.27

±0.23

PMT gain simulation

+1.98
-0.00

+2.41
-0.00

Total

+6.74
-7.70

+7.22
-8.09

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.37: Fractional variation in the average tagging eﬃciency for each individual
systematic source. The total variations are calculated by adding each uncertainty inquadrature. The blue and red lines correspond to the uncertainties of the FHC and
RHC 1Rνµ samples, respectively.

Figure 8.38: Tagging eﬃciency as a function of reconstructed muon transverse momentum in comparison with equivalent eﬃciency estimated by GENIE and NuWro
MCs. The bands shows the ±1σ envelope of the total systematic uncertainty. The
left and right figures show the FHC and RHC 1Rνµ samples, respectively.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.39: Averaged neutron tagging eﬃciency of the FHC and RHC 1Rνµ samples
in comparison with equivalent eﬃciency estimated by GENIE and NuWro MCs.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

8.4

Results

This section describes the measurement results. Two types of the mean neutron
multiplicities are measured:• Mean neutron multiplicity as a function of reconstructed muon transverse momentum Pt• Mean neutron multiplicity averaged over Pt

These mean neutron multiplicities, M̄i , are measured following Equation 8.2.1. The
statistical errors√are evaluated from the square root of the number of observed tagged
neutrons (i.e.
Ntag ) and the systematic uncertainties come from the systematics
regarding the neutron tagging eﬃciency described in Section 8.3. The total uncertainty of the measured mean multiplicity is calculated by adding the statistical andsystematic errors in quadrature.
Table 8.12 summarizes the definition of binning of Pt and numbers used for themeasurements.
Table 8.12: Summary of the numbers used to calculate the measured mean neutron multiplicities. The numbers for All Pt are used to compute the mean neutron
multiplicity averaged over Pt . Note that Ntag and N1µ are the results of the Run
1-9 observation. The background event rate b is the same value as summarized inTable 6.2
Beam mode

FHC

RHC

Pt bin

Ntag

N1µ

ε

b × N1µM̄δ M̄stat. (%)δ M̄syst. (%)δ M̄tot. (%)+7.050−10.457+8.042−9.277+9.253−8.296+7.278−8.505+6.737−7.703+41.339−42.054+25.861−26.272+35.551−35.314+42.936−43.161+17.846−18.232+6.496−8.057+7.284−8.394+8.199−9.818+13.103−9.216+7.219−8.088+42.527−42.793+28.329−28.635+38.147−38.527+60.632−59.912+19.910−20.2410.00 <Pt < 0.25

8

55

0.204

1.056

0.618

±40.733

0.25 <Pt < 0.50

20

94

0.203

1.805

0.954

±24.579

0.50 <Pt < 0.75

10

41

0.193

0.787

1.164

±34.325

Pt ≥ 0.75

6

11

0.190

0.211

2.768

±42.315

All Pt

44

201

0.199

3.860

1.004

±16.5250.00 <Pt < 0.25

7

38

0.213

0.705

0.777

±42.028

0.25 <Pt < 0.50

15

46

0.205

0.853

1.500

±27.3770.50 <Pt < 0.75

8

22

0.194

0.408

1.783

±37.255

Pt ≥ 0.75

3

4

0.186

0.074

3.926

±59.199

All Pt

33

110

0.202

2.040

1.396

±18.555

Figure 8.40 and 8.41 shows the measurement results of the mean neutron multiplicity as a function of the reconstructed µ transverse momentum Pt and the mean
neutron multiplicity averaged over Pt for the Run 1-9 FHC and RHC 1Rνµ samples.
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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY
Table 8.13 summarizes the measured mean neutron multiplicities in comparison to
the equivalent expectations which are derived from the NEUT-based MC. As shownin Figure 8.41, the measured mean multiplicity averaged over Pt shows a tendency
that the RHC sample has higher mean multiplicity than that of the FHC sample.
Since in general CC ν̄µ interactions produce more neutrons compared to CC νµ interactions (e.g. CCQE interaction) in the neutrino energies of this analysis, theobserved tendency is consistent with the expectation.
The deviation from the NEUT expectation is -2.75 σ (-2.69 σ) for the FHC (RHC)
1Rνµ sample based on the total error of this measurement.

Figure 8.40: Measured mean neutron multiplicity as a function of reconstructedmuon transverse momentum for the Run 1-9 FHC and RHC 1Rνµ samples. The left
and right figures correspond to the FHC and RHC samples, respectively. The color
bands represent the equivalent expectations which are obtained the NEUT-based
MC. The widths of the bands correspond to the size of the MC statistical error of
the expectations.
Table 8.13: Summary of the measured mean neutron multiplicities of the Run 1-9
data in comparison to the expected numbers. For the expected numbers which arederived from the NEUT-based MC, the errors are the MC statistical uncertainties.
For the data results, the first errors and second errors represent the statistical andsystematic uncertainties, respectively.

Pt binExpected

FHC
Measured

Expected

RHC
Measured

0.0 - 0.25 (GeV/c)
0.25 - 0.5 (GeV/c)
0.5 - 0.75 (GeV/c)> 0.75 (GeV/c)

1.22 ± 0.02
1.33 ± 0.02
1.77 ± 0.04
2.75 ± 0.12

+0.04
0.62 ± 0.25 −0.06+0.08
0.95 ± 0.23 −0.09+0.11
1.16 ± 0.40 −0.10+0.20
2.77 ± 1.17 −0.24

1.76 ± 0.02
2.05 ± 0.02
2.36 ± 0.03
3.41 ± 0.08

0.78 ± 0.33 +0.05−0.06
1.50 ± 0.41 +0.11−0.13
1.78 ± 0.66 +0.15−0.18
3.93 ± 2.32 +0.51−0.36

Averaged over Pt

1.50 ± 0.02

1.00 ± 0.17 +0.07−0.08

2.14 ± 0.02

1.40 ± 0.26 +0.10−0.11

The measurement results are also compared with the expectations of the GENIEand NuWro-based MCs as well as the NEUT’s one as shown in Figures 8.42 and211

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.41: Measured mean neutron multiplicity averaged over reconstructed muontransverse momentum for the Run 1-9 FHC and RHC 1Rνµ samples. All the observed
tagged neutrons and ν events in the 1Rνµ samples are integrated over Pt before
calculating this multiplicity. The color bands represent the equivalent expectations
which are obtained the NEUT-based MC. The widths of the bands correspond to
the size of the MC statistical error of the expectations.
8.43. Although the statistical errors of the measurement results are large, it can beunderstood from the figure that in the region below Pt < 0.75 GeV/c the measured
mean multiplicities are smaller compared to the expectation. It should be noted that
this tendency observed is common to both of the FHC and RHC 1Rνµ samples andbetween the three diﬀerent MCs. As small Pt corresponds to small four momentum
transfer squared Q2 at the primary ν interaction, the results may indicate that thesimulation used for making the expectations overpredict neutrons in the small Q2
region.

212

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.42: Mean neutron multiplicity as a function of reconstructed muon transverse momentum in comparison to the equivalent expectations of the NEUT-,
NuWro-, and GENIE-based MCs. The left and right figures show the FHC and
RHC 1Rνµ samples, respectively.

Figure 8.43: Mean neutron multiplicity averaged over Pt for the Run 1-9 data withthe three diﬀerent expectations. All the observed tagged neutrons and ν events in
the 1Rνµ sample are integrated over Pt before calculating the multiplicity.

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CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

8.5

Discussion

In the previous section, the measurement result of this analysis showed a relatively
large discrepancy between data and simulations although the statistical error of thedata is still large. In the following, possible causes of the discrepancy are discussed.
This analysis measure neutrons produced in the three processes: the primaryν-nucleon interaction in nuclear medium, hadronic FSI inside oxygen nucleus, andhadronic SI in the detector medium. Since this analysis can not address a particularneutron production process of interest because of the detection method, it is therefore
hard to reveal the origin of the observed discrepancy by this measurement only.
However, it is worth noting following points:• About half of the neutrons are produced in hadronic SI as shown in Figure 8.1,
which indicates that systematic uncertainty regarding the SI may aﬀect theMC expectations in a visible way.
• As shown in Figure 8.2, the number of post-FSI charged pions, which have left
the target nucleus and have not undergone SI in water, is much smaller thanthat of post-FSI nucleons. Thus the contribution to the neutron production in
SI from the post-FSI charged pins are expected to be also small. By using theenergy distributions of the post-FSI hadrons (shown in Figure 8.2) and averageof number of neutron captures produced in hadron SI as a function of initial
hadron energy (shown in Figure 8.7), the number of neutrons produced in SI for
each post-FSI hadron and its energy are obtained and are shown in Figure 8.44.
As shown in the figure, in both the FHC and RHC samples the contributions
from the post-FSI nucleons are much larger than those of the post-FSI charged
pions. Therefore, the post-FSI nucleons dominantly contribute to the neutron
production in the hadronic SI.

Figure 8.44: Number of neutron captures produced by post-FSI neutrons (blue),
protons (red), π + (yellow), and π − (green) of the 1Rνµ sample. The left and rightcorresponds to the FHC and RHC smaples, respectively.

214

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY• The neutron production by the nucleon SI is handled by the GCALOR which
is based on Bertini’s style cascade model. The cross-section of the Bertini’s free
N -N scattering on 16 O may have large uncertainty, and such large uncertainty
vary the total number of neutrons, the number of tagged neutrons, and theresultant distance from ν interaction to n capture vertices. Indeed, the ±30% uncertainty on the cross-section assigned in Subsection 8.3.6 varies the total
number of neutrons by ∼10 %. Also, it should be noted that there has alreadybeen visible diﬀerence in the neutron productions by the SI as was shown in
Figure 8.4.
• In addition, modeling of ν interactions and hadronic FSI is largely diﬀerent
between the three ν event generators used in this analysis: NEUT, NuWro,
and GENIE. This also results in diﬀerent true distance distribution as well as
diﬀerent total number of neutrons.

If these variations are put together into one prediction, then the nominal MC expectations based on NEUT have a large prediction uncertainty. For instance, Figure 8.45
shows the distribution of the observed reconstructed distance from ν interaction to n
capture vertices in comparison with the corresponding MC distribution. In the figure, the green envelopes correspond to the nominal MC expectations with the ±30% variations in the Bertini’s total free N -N cross sections. A visible variation canbe seen in the first two bins in which the data shows a relatively large discrepancy.
The diﬀerences among NEUT, NuWro, and GENIE are also included into the orange
envelopes by combining the variations due to the ±30 % nucleon cross section error
in quadrature. Although the orange envelopes, which reflect the uncertainties on theν interactions, the hadronic FSI and the nucleon SI, are relatively large, the envelops
seem not to cover the data in the first bin. Since short distance corresponds to nucleons in a low energy region as shown in Figure 8.7, the data could indicate that theMC simulations used in this analysis overpredict neutrons in a low energy region.
It may be interesting to recall that as mentioned in Subsection 1.2.3, MINERvA’s
measurement of neutrons associated with antineutrino interactions on a hydrocarbon target has shown a ∼25 % overprediction in a low apparent velocity region forneutron candidates.

215

CHAPTER 8. MEASUREMENT OF MEAN NEUTRONMULTIPLICITY

Figure 8.45: Distribution of reconstructed distance for the Run 1-9 FHC 1Rνµ sample(left) and the Run 1-9 RHC 1Rνµ sample (right). Solid lines correspond to thenominal MC expectations based on NEUT. Green envelops correspond to a ±30 %
variations in the Bertini’s total cross sections used for the nucleon SI in GCALOR.
Orange envelopes represent the nominal MC expectation with the ±30% variationsin the total nucleon SI cross sections and the diﬀerences among NEUT, NuWro, andGENIE. All the MC distributions are normalized by the Run 1-9 POT. The data areshown with the statistical uncertainties only.

216

Chapter 9
Summary and outlook
Since the discovery of neutrino oscillation, remarkable eﬀorts have been made in thelast two decades to study the nature of neutrinos. However, the value of δCP and
the neutrino mass ordering (the sign of ∆m231 ) are still unknown although these areespecially important. The value of δCP would provide information to explain theorigin of the matter-antimatter asymmetry in the universe. Also, determination of
the neutrino mass hierarchy (MH) may helps to understand the patterns of mixing
and masses between the particles of the Standard Model.
To understand the remaining unknowns of nature, building larger detectors withadvanced detection technology and further improvements to analysis methods areneeded. Indeed, possibility of such improvement on analysis has been studied infuture experiments adopting water Cherenkov detectors such as SK-Gd [124] andthe Hyper-Kamiokande [125] and the experiments plan to utilize neutrons associatedwith ν interactions in water for their main physics analyses. In order to utilize suchneutrons, predicting the production of these neutrons precisely by a MC simulation
is key. Current MC simulations, however, produce diﬀerent predictions due to large
uncertainties on ν-nucleon interactions in nuclear medium, hadronic FSI in nuclei,
and hadronic SI in detector medium. In addition, no extensive study has been madefor water. Therefore, it is quite worth studying those neutrons and evaluating thevalidity of the simulations by using well understood neutrino source.
In the T2K experiment, primarily νµ and ν̄µ beams with a peak energy of 0.6
GeV are produced, which enables us to study such neutrons with a well understoodν source. In this thesis, neutrons associated with ν interactions on a water target
using accelerator neutrinos and antineutrinos were studied for the first time. For
this study, a neutron tagging algorithm which does not depend explicitly on themodeling of neutron production was developed, and was applied to the T2K beam
neutrino data accumulated at the SK far detector until 2018, which corresponds to
1.4938×1021 POT for the FHC mode and 1.6346×1021 POT for the RHC mode.
After applying the 1Rνµ selection to the T2K FC neutrino events, the observed
neutrino events agreed well with the corresponding expectations. On the one hand,for the tagged neutrons, the observation showed less tagged neutrons than expected.
Table 9.1 summarizes the number of observed neutrino events and the number of217

CHAPTER 9. SUMMARY AND OUTLOOKtagged neutrons with the corresponding expectations. Since the neutron production
Table 9.1: Summary of the number of neutrino events and tagged neutrons for
the Runs 1-9 POT with the following oscillation parameter values: ∆m221 =7.53
×10−5 eV2 , ∆m232 =2.452 ×10−3 eV2 , sin2 θ23 =0.532, sin2 θ13 =0.0212, δCP =-1.885,
Mass Hierarchy = normal. All the expectations are normalized to the Run 1-9
POT.
Number of ν events
Expected Observed

Number of tagged n
Expected observed

FHC 1Rνµ202.12

201

64.08

44

RHC 1Rνµ109.61

110

49.42

33

depends on the four momentum transfer squared Q2 to the hadronic system at the
primary ν-nucleus interaction, the mean neutron multiplicity as a function of reconstructed transverse muon momentum Pt , which is a good indicator of Q2 , wasmeasured by using ν events and tagged neutrons with a systematic uncertainty of ∼8%. It should be noted that the transverse momentum can be reconstructed only forbeam neutrinos, because their incoming directions are known. The measured mean
neutron multiplicity averaged over Pt is:Runs 1 − 9 FHC 1Rνµ sample : 1.00 ± 0.17 (stat.)+0.07−0.08 (syst.) neutrons/ν event
Runs 5 − 9 RHC 1Rνµ sample : 1.40 ± 0.26 (stat.)+0.10−0.11 (syst.) neutrons/ν event,whereas the corresponding expectations of the NEUT-based MC are:
FHC 1Rνµ sample : 1.50 ± 0.02 (stat.) neutrons/ν event
RHC 1Rνµ sample : 2.14 ± 0.02 (stat.) neutrons/ν event.
The deviation from the expectation is 2.75 σ (2.69 σ) for the FHC (RHC) sample
based on the total error of the measured value.
Since this analysis showed a discrepancy of ∼40% between the observation and theprediction, it may be helpful to evaluate how much this 40% discrepancy in neutron
production aﬀects a particular physics analysis. As an improved analysis method,which utilizes those neutrons aggressively, has been developed [7], such impact isestimated by comparing sensitivity to δCP between the conventional and improved
analysis methods, in context of Hyper-Kamiokande atmospheric ν oscillation analysis. The conventional analysis method is detailed in [85, 223, 224].
218

CHAPTER 9. SUMMARY AND OUTLOOKHyper-Kamiokande is a next generation underground experiment employing water Cherenkov detector and will be build on the successful operation of SuperKamiokande. Although an option of two-tanks is being considered, a 258 kton tankwith 40% photocoverage is adopted as the baseline design [125]. In this design,for high-energy neutrinos such as atmospheric neutrinos, the detector performanceof Hyper-Kamiokande is expected to be roughly the same as Super-Kamiokande’s
one [125], which means that the number of expected atmospheric neutrino eventsat Hyper-Kamiokande can be obtained by scaling the equivalent numbers at SuperKamiokande by exposure. On the other hand, thanks to the higher detection eﬃciency of single-photoelectron signal of a photosensor newly developed for HyperKamiokande, neutron tagging eﬃciency has been evaluated to be ∼70% even forneutron capture by hydrogen nucleus [125]. In addition, an option of gadolinium
loading is also being considered, in which case neutron tagging eﬃciency is expected
to be higher than 70%. Therefore, the following impact study is done by scaling
the equivalent sensitivity of Super-Kamiokande by exposure, and assuming a 70%
neutron tagging eﬃciency as was adopted in the previous work [7].
To obtain the equivalent sensitivity, the pre-existing analysis framework developed by the Super-Kamiokande collaboration [85] is used. In this analysis framework,
the sensitivity is evaluated by a χ2 defined as:

2

χ =2

∑
n

(
En (1 +∑iOn
fni ϵi ) − On + On ln∑
En (1 + i fni ϵi ))+∑ ( ϵi )2i

σi,(9.0.1)
where En and On are the number of expected and observed neutrino events of n-th
bin and fni represents the systematic variation in En due to a systematic uncertainty corresponding to ϵi . This treatment of systematic errors is based on the pullmethod [225]. In order to find the best oscillation parameter, the above χ2 is minimized over the systematic error parameters at each value of δCP , which is equivalent2= 0 for every ϵi .
to solve ∂χ∂ϵiIn order to estimate the impact of the observed 40% discrepancy in neutron production, the sensitivity defined in the above equation is computed three times at
each oscillation parameter point for the improved analysis method [7], which enables improved estimation of neutrino energy and better sample selection in termsof separations of ν-ν̄ and CC-NC interactions. The first computation is done for thenominal atmospheric MC set, which is used for developing the improved method,
without any consideration of systematic uncertainty on neutron production. In theremaining calculations, neutron production error is taken into account by treating
the 40% diﬀerence as an inclusive error on neutron production. Two fake data sets
are therefore generated varying the neutron multiplicity of the nominal MC set by±40% on an event-by-event basis, and sensitivity is calculated for each fake data
set. The resultant diﬀerence in the sensitivity between the first calculation and theother calculations is interpreted as the systematic variations in the sensitivity due toneutron production uncertainty. Figure 9.1 shows the resultant variations in com219

CHAPTER 9. SUMMARY AND OUTLOOK

parison to the sensitivity of the conventional analysis method, which does not use
information about tagged neutrons, and demonstrates that the 40% discrepancy canyield non-negligible systematic variations in a particular pysics analysis. It should
be noted that this is the first estimation of impact of neutron production uncertainty
based on experimental data.

Figure 9.1: Impact of the observed 40% discrepancy in neutron production to thesensitivity to δCP using the atmospheric neutrinos at Hyper-Kamiokande. The exposure time is assumed to be five years of one tank of 258 kton with a 40% photocoverage. Black lines correspond to the conventional analysis method developedby the SK collaboration based on reconstructed lepton energy. Magenta lines correspond to the improved analysis method in which case an energy correction anda better event selection using tagged neutrons are applied with an assumption of
a 70% neutron tagging eﬃciency. White magenta bands represent the systematic
variations in the magenta line due to an overall ±40% error on neutron production.
Solid (Dashed) lines correspond to the case where the χ2 is computed assuming normal (inverted) mass hierarchy. The lower (upper) side corresponds to the overall-40% (+40%) variation in neutron multiplicity. The setting of oscillation parametervalues are as follows: ∆m221 =7.65 ×10−5 eV2 , ∆m232 =2.5 ×10−3 eV2 , sin2 θ23 =0.575,
sin2 θ12 =0.309, sin2 θ13 =0.0219, δCP =4.189 rad, Mass Hierarchy = normal.
As shown in Figure 9.1, a considerable reduction of prediction uncertainty on
neutron production needs to be done. To this aim, understanding of the observed
discrepancy may be the first step by similar measurement with higher data statistics
since the measurement presented in this thesis is statistically limited. Such measurement can be realized in near future by SK-Gd. In the SK-Gd experiment, thesame measurement can be performed with improved reconstruction of the neutron
capture vertex and with much higher neutron tagging eﬃciency. Figure 9.2 shows an
expected vertex resolution in SK-Gd. As shown in the figure, the vertex resolution of220

CHAPTER 9. SUMMARY AND OUTLOOK

neutron capture is expected to be almost twice better than that of the current one,which allows us to address more detailed information about the neutron kinematics. In addition, the tagging eﬃciency of SK-Gd is expected to be higher than 70%.
Since T2K has planed to extend its data taking until 2026 [226] and the initial Gdloading to SK will happen in 2020, SK-Gd will be able to conduct the same neutron
measurement with significantly improved precision.

Figure 9.2: Comparison of vertex resolution of n captures between SK and SK-Gd.
In SK, only neutron capture by hydrogen nucleus can happen, whereas ∼80% of
neutrons will be captured by gadolinium in the full configuration of SK-Gd.
ANNIE (Accelerator Neutrino Neutron Interaction Experiment) [227, 138] is an
ongoing experiment at Fermilab, in which a Gd-doped water Cherenkov detector isused to measure neutrons related to neutrino interactions from the Booster Neutrino Beam with a peak energy of 0.7 GeV. Future results from ANNIE will be very
useful to validate the measurement result of this analysis. As a long-term project,
E61 [125, 228] which is an intermediate water Cherenkov detector used for the longbaseline neutrino oscillation program of the HK is also planed to perform similar
measurement. The experiment will enable us to study the neutron production by
a Gaussian neutrino flux, which has never been realized. Such Gaussian neutrino
beam will significantly reduce systematic uncertainties related to primary ν-nucleus
interactions, and thus a more accurate measurement would be realized.
Although these experiments will produce crucial inputs to build a precise MC
simulation for the utilization of neutrons to various important physics analyses,
these experiments cannot disentangle the complicated neutron production processes:
the primary ν-nucleon interactions in nucleus, hadronic FSI inside the nucleus, andhadronic SI in water. To understand the neutron production and build MC simulation, disentanglement of these processes is quite important and at least the contribution from SI has to be isolated. One way to achieve this is to measure neutron
221

CHAPTER 9. SUMMARY AND OUTLOOK

productions by hadronic SI in water using hadron beams. Such such idea has been
proposed, and possible measurement is being included into the plan of a test water
Cherenkov experiment at CERN [229].
By combining eﬀorts from all of these future experiments, we would be able toutilize neutrons associated with ν interactions in water for various important physics
analyses including precision measurements of neutrino oscillations and SRN searches.
It is my humble wish that this measurement will be useful to accelerate experimental
studies and development of simulations for these neutrons.

222

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237

Appendix A
Implementation of neutron−−
productions by µ /π captures
Neutron productions by µ− and π − captures on oxygen nucleus had never been simulated. For the primary analysis of this theis, these captures are implemented to
SKDETSIM using Geant4.9.6.
Technically G4MuonMinusCaptureAtRest and G4PiMinusAbsorptionAtRest which
are the classes of Geant4.9.6 and are used as the default models, are directly calledfrom SKDETSIM via an interface which connects SKDETSIM with Geant4.9.6. The
neutrons produced by these simulation codes are modeled based on both theory andexperimental data. The neutron multiplicity and kinetic energy distribution of theµ− and π − captures are shown in Figure A.1. Figure A.2 shows the distributionof the true distance between the ν interaction and neutron capture positions before and after the implementation. As shown in the plots, these captures produce a
non-negligible number of neutrons depending on the distance. The total number ofneutrons in the samples used for the analysis which also be mentioned in Section 7.2
are increased by 16% and 10% for the FHC and RHC cases, respectively.

238

APPENDIX A. IMPLEMENTATION OF NEUTRON PRODUCTIONS
BY µ− /π − CAPTURES

Figure A.1: Neutron multiplicity (top) and kinetic energy distribution (bottom). Left and right correspond to µ− and π − captures on oxygen nucleus, respectively. All the figures are obtained by by generating 5 MeV µ− and π − .
G4MuonMinusCaptureAtRest (G4PiMinusAbsorptionAtRest) is used for the µ− (π − )capture.

Figure A.2: Distribution of the true distance from ν interaction vertex to neutron
capture vertex before and after the implementation of the µ− and π − capture on
16
O. Left and right figures are for the FHC and RHC 1Rνµ samples, respectively.
The distributions are normalized to 1021 POT.

239

Appendix B
Distribution of NN input variables
The distributions of the NN input variables before the NN classification (i.e. justafter the primary selection) and after the NN classification are cheked as shown in
Figure B.1 to B.4. All the distributions of the MC are normalized to the numberof observed neutron candidates in order to validate whether or not the shape of thedata agree with the equivalent MC’s one.

240

APPENDIX B. DISTRIBUTION OF NN INPUT VARIABLES

Figure B.1: Distributions of the NN input variables before the NN classification (i.e.
just after the primary selection) for the Runs 1-9 FHC 1Rνµ sample in comparison
to the corresponding MC disributions. All the MC distributions are normalized by
the number of observed neutron candidates.

241

APPENDIX B. DISTRIBUTION OF NN INPUT VARIABLES

Figure B.2: Distributions of the NN input variables after the NN classification for
the Runs 1-9 FHC 1Rνµ sample in comparison to the corresponding MC disributions.
All the MC distributions are normalized by the number of observed tagged neutrons.

242

APPENDIX B. DISTRIBUTION OF NN INPUT VARIABLES

Figure B.3: Distributions of the NN input variables before the NN classification (i.e.
just after the primary selection) for the Runs 1-9 RHC 1Rνµ sample in comparison
to the corresponding MC disributions. All the MC distributions are normalized by
the number of observed neutron candidates.

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APPENDIX B. DISTRIBUTION OF NN INPUT VARIABLES

Figure B.4: Distributions of the NN input variables after the NN classification for theRuns 1-9 RHC 1Rνµ sample in comparison to the corresponding MC disributions.
All the MC distributions are normalized by the number of observed tagged neutrons.

244Appendix C
True neutrino energy spectra
In Chapter 8, mean neutron multiplicity as a function of reconstructed muon transverse momentum Pt is measured. Distribution of true neutrino energy is diﬀerent
among the diﬀerent Pt regions. Figure C.1 to C.2 show the distribution of true
neutrino energy for each Pt bin for the FHC and RHC 1Rνµ samples, respectively.

245

APPENDIX C. TRUE NEUTRINO ENERGY SPECTRA

Figure C.1: Distributions of true neutrino energy for each reconstructed muon transverse momentum of the FHC 1Rνµ sample. The bin edges of the transverse momentum is summarized in Table 8.13.

246

APPENDIX C. TRUE NEUTRINO ENERGY SPECTRA

Figure C.2: Distributions of true neutrino energy for each reconstructed muon transverse momentum of the RHC 1Rνµ sample. The bin edges of the transverse momentum is summarized in Table 8.13.

247