Development of Neutron Tagging Algorithm
and Search for Supernova Relic Neutrino
in SK-Gd Experiment

September, 2023
Masayuki Harada

Graduate School of
Natural Science and Technology(Doctor’s Course)
OKAYAMA UNIVERSITY

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OKAYAMA UNIVERSITY

Abstract
Graduate School of Natural Science and Technology
Doctor’s Course
Doctor of Philosophy
Development of Neutron Tagging Algorithm
and Search for Supernova Relic Neutrino
in SK-Gd Experiment
by Masayuki Harada
Observing neutrinos originating from supernovae is vital for deciphering the explosion
mechanisms of core-collapse supernovae. Specifically, detecting supernova relic neutrinos (SRNs) can elucidate these mechanisms as well as the cosmic star formation
history. The predominant signal within the SRN energy region corresponds to theinverse-beta decay (ν̄e + p → e+ + n).
The Super-Kamiokande experiment, currently the most sensitive neutrino detector
for the SRN energy region, has introduced the delayed coincidence method to the event
selection using a neutron capture signal. This improvement has resulted in a more
stringent upper limit. For the first discovery of SRN, the SK-Gd experiment was
proposed in 2004. In the SK-Gd experiment, the SRN signal efficiency is significantly
improved by loading gadolinium (Gd) in the detector tank. Gd has the largest crosssection for the thermal neutron capture among natural elements and emits a total of
about 8 MeV gamma rays during the thermal neutron capture. This key advantage
strengthens the correlation between the prompt positron and delayed neutron signal
with enhanced neutron detection efficiency.
The SK-Gd experiment with about 0.011% mass concentration of Gd started inJuly 2020 and operated until May 2022. At first, an algorithm for detecting theneutron signal in SK-Gd is newly introduced. The algorithm is evaluated by the newly
constructed Monte-Carlo simulation and neutron source measurement. Consequently,
the neutron tagging efficiency is estimated to be 40.2%, with an uncertainty of 8.7%.
After that, the initial search was conducted using data from 552.2 days SK-Gd
operation. This analysis employed the newly constructed neutron detection algorithm
and Monte Carlo simulation. After eliminating the major background events, theremaining were consistent with the expected background within 1.1σ according to thep-value test across all investigated energy bins. In the absence of an SRN signal inthis search, the observed and expected upper limits of SRN fluxes were respectively
extracted to be 0.3–32.3 and 0.3–49.2 cm−2 sec−1 MeV−1 , depending on the energy
bins. These limits are commensurate with the most stringent limit determined by thesearch result in a pure-water phase of Super-Kamiokande.
For prospects, pragmatic improvements to the detector and analysis are contemplated for the SK-Gd experiment. The future sensitivity of the SK-Gd experiment is
examined by assuming these enhancements. To demonstrate a potential approach forextracting physics parameters from the SRN flux, the formation rate of black holes
and heavy neutron stars are highlighted.

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Acknowledgements
I would like to express my gratitude to all those who supported me. First of all, I
would like to express my sincere gratitude to my adviser, Prof. Yusuke Koshio, forgiving me the great opportunity to study neutrino physics. I have learned a lot ofthings, not only physics but also the attitude toward research. We discussed physics,
analysis, and so on. He not only taught me but also often had discussions. Also, hegave me several opportunities to visit European countries and the US and attend andmake presentations at several conferences. Also, he introduced me to delicious foodsin each country we went to. All of those experiences are wonderful and made me growas a researcher. This thesis would never be without his kind comments and detailed
suggestions.
I will never forget to thank those who worked with me on the analysis, Prof.
Masayuki Nakahata, Prof. Hiroyuki Sekiya, Prof. Yasuhiro Nakajima, Dr. Guillaume
Pronost, Dr. Alberto Giampaolo, Dr. Hiroshi Ito, and Dr. Sonia El Hedri. Their advice was always accurate and made me realize new insights. I owe my gratitude to thewater team who operated the first Gd loading with me, Prof. Hiroyuki Sekiya, Prof.
Yasuhiro Nakajima, Prof. Motoyasu Ikeda, and Prof. Kiseki Nakamura. I learned alot from the hard work of everyone on site. I will never forget the days when I continued to knock on the pipe (and the impression when Nakajima-san found a yura-yuraswing machine). I would like to thank Dr. Yuuki Nakano. He told me so much knowledge about low-energy physics analysis in SK. Not only that, he invited me to dinnerand parties many times. A special gratitude I give to Dr. Takatomi Yano. We hadmany chances to discuss about Am/Be calibration analysis. I feel sorry that I was notable to go to Kamioka for calibration during the COVID period. But he took a lot of
calibration data and shared me. I also would like to thank the people who worked withme in Kamioka, Sonoda-san, Akutsu-san, Takenaka-san, Okamoto-san, Imaizumi-kun,
Chen-kun, Okada-kun, Nagao-kun, Han-kun, Shibata-kun, Izumiyama-kun, Shinokikun, Miki-kun, Kanemura-san, Watanabe-kun, Shimizu-kun, Kaneshima-kun, Kashiwagisan, Yoshida-kun, Tomiya-kun, Shima-san, Shigeta-san, Kochi-kun, and Kaminagasan. Although the Kamioka site is really isolated from the city, I had a pretty fun
moment in Kamioka thanks to them. We enjoyed a lot of parties in Kenkyu-to, anddriving to Toyama to have nice food with them. Especially, I was able to refresh myself by having many online drinking parties with colleagues in the same grade. I would
like to say thank you to all Super-Kamiokande collaborators. All the people kindly
lectured me when I had a question about even the basics of analysis, computing, etc.
I am grateful to the supernova theorists, Prof. Yudai Suwa, Prof. Ken’ichiro
Nakazato, Prof. Kosuke Sumiyoshi, Prof. Shunsaku Horiuchi, and Dr. Masamitsu
Mori. They have given me great theoretical insights since I started studying thesupernova by joining the nuLC group.
I would thank the people who often had parties. Kaito Hagiwara, Yosuke Ashida,
Hirotaka Nagata, and Toshiaki Horai. We had a number of times of the online andoffline parties. Hagiwara-san is my first colleague who did the same research. We had
a lot of discussions about the Geant4 and SKG4. That time was fun, like playing agame. Ashida-san told me about essential things of the SRN analysis. In addition
to giving me advice about research, we enjoyed some things like parties and playing
games. Nagata-san is a really kind and sincere person. Even though we were not in
the lab during the same period, he talked to me a lot. Horai-san is the only colleague
in the same grade. He had always taken care of deadlines and tasks of our homework
and assignments. My attitude towards life as a PhD was very much based on him.

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I would like to offer my special thanks to my friends at Okayama University,
Wataru Hosoda, Yuji Kogame, Shotaro Nakano, and Takeshi Takahashi. We madesome trips and on/off-line parties even after they graduated and went away from
Okayama and were under a severe situation with COVID. They are the only friends
with whom I can talk about research and physics other than researchers. I will neverforget our graduate trip to Italy.
I would like to express my sincere gratitude to my club activity members of ‘Five
Stars’ and ‘Perfetto Partita.’ The time spent playing basketball and playing withthem was very relaxing.
I would like to thank everyone who worked with me at Okayama University,
Hino-san, Sakai-san (Sakee-shi), Nakanishi-san, Shiraishi-kun, Tano-san, Tada-san,Takeya-kun, Higashi-kun, and Homma-san. Of course, I also would like to express
my gratitude to all the past members of the lab. group and secretaries, Shintarosan, Xu-san, Fukuda-san, Hagiwara-san, Yamasu-san, Takahira-san, Nakamura-san,Horai-san, Okada-kun (Oka-D), Wenjie, Kitagawa-kun, Tanaka-kun, and Shikaraskun. I am very happy that I could join this group. I am also particularly grateful forthe kind support to those who have previously or currently belonged to the Astrophysics Laboratory, Prof. Makoto Sakuda, Prof. Hirokazu Ishino, Ou-san, Pretam,
Mandeep, Kida-san, Komatsu-san, Hidehira-san, Sudo-san, Tanaka-san, Yanagisawakun, Toda-kun, Nakao-kun, Nakajima-kun, Takase-kun, Nagano-kun, Kazehaya-kun,
Doi-kun, Ishizaka-kun, Koeda-san, and Nagatsuna-san.
I owe my gratitude to my local friends, Kazuki Abe and Kaori, Jun’ichi Sakamoto,Kohei Yamasaki, Hiroyoshi Yamaoka, and Atsushi Nara. They gave me a lot of
valuable time without research. That made me relax and have a fun time other than
the research activity.
In addition, am grateful to everyone who involved me. I was able to enjoy myresearch life during the doctoral period and write this thesis without feeling tired
because of the support of my colleagues, including many professors, researchers, andfriends. The years I spent with everyone were extremely fulfilling and enjoyable.
The works in this thesis have been achieved with support from the JSPS Young
Scientist Fellowship (JP20J20189: “Search for Supernova relic neutrinos in SuperKamiokande experiment”).
At the end of acknowledgment, I would like to express my deepest gratitude to myfamily. In particular, my parents and my sister. They always supported me for a longtime. Finishing this thesis wouldn’t have been possible without all of you. Thank youvery much!

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Contents
1 Introduction
1.1 Supernova Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Explosion Types and Mechanism Overview . . . . . . . . . . .
1.1.2 Explosion Mechanism of Core-Collapse Supernova . . . . . . .
1.1.3 Neutrinos from Core-Collapse Supernovae . . . . . . . . . . . .
Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . .
Neutrino Emission from Core-Collapse Supernova . . . . . . . .
Neutrinos Observation from SN1987A . . . . . . . . . . . . . .
1.2 Diffuse Supernova Neutrino Background . . . . . . . . . . . . . . . . .
1.2.1 Formulation of SRN Flux . . . . . . . . . . . . . . . . . . . . .
1.2.2 Contribution to the SRN flux . . . . . . . . . . . . . . . . . . .
Neutrino Oscillation Effects . . . . . . . . . . . . . . . . . . . .
Modeling of Galaxy Evolution . . . . . . . . . . . . . . . . . . .
Other Contributions to the SRN Flux . . . . . . . . . . . . . .
1.2.3 Flux Predictions . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Current Status of SRN Search . . . . . . . . . . . . . . . . . . . . . . .

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2 Super-Kamiokande
2.1 Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Super-Kamiokande Detector . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 History of SK phase . . . . . . . . . . . . . . . . . . . . . . . .
SK-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK-VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 ID PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 OD PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Compensation Coils . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Water and Air purification system . . . . . . . . . . . . . . . . . . . .
2.3.1 Water purification . . . . . . . . . . . . . . . . . . . . . . . . .
Water system at SK-IV . . . . . . . . . . . . . . . . . . . . . .
Water system from SK-V . . . . . . . . . . . . . . . . . . . . .
2.3.2 Air purification system . . . . . . . . . . . . . . . . . . . . . . .
2.4 Electronics and Data Acquisition . . . . . . . . . . . . . . . . . . . . .
2.4.1 Electronics and DAQ from SK-IV . . . . . . . . . . . . . . . . .
2.4.2 Software Trigger . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Simulation
3.1 Simulation for High-Energy Neutrino Event . . . . . . . . . . . . . . .
3.1.1 Atmospheric neutrino flux . . . . . . . . . . . . . . . . . . . . .
Primary cosmic-ray . . . . . . . . . . . . . . . . . . . . . . . . .
Hadronic interaction . . . . . . . . . . . . . . . . . . . . . . . .
Neutrino Flux at the SK . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . .
Elastic and Quasi-elastic Scattering . . . . . . . . . . . . . . . .
CC Meson Exchange Interaction . . . . . . . . . . . . . . . . .
Single Meson Production . . . . . . . . . . . . . . . . . . . . .
Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . .
Coherent pion production . . . . . . . . . . . . . . . . . . . . .
3.2 Simulation for the IBD-like Event . . . . . . . . . . . . . . . . . . . . .
3.2.1 DSNB Signals MC creation . . . . . . . . . . . . . . . . . . . .
3.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Particle tracking . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Optical Photon Emission and Tracking . . . . . . . . . . . . . .
3.3.3 PMT response . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Event Reconstruction
4.1 Low Energy Event Reconstruction . . . . . . . . . . . . . . . . . . . .
4.1.1 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Effective hit calculation . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . .
4.1.5 Cherenkov angle reconstruction . . . . . . . . . . . . . . . . . .
4.2 Muon Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 PMT hit selection . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Initial Entry Point . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Event classification . . . . . . . . . . . . . . . . . . . . . . . . .
Corner-clipping muons . . . . . . . . . . . . . . . . . . . . . . .
Stopping muons . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiple muons . . . . . . . . . . . . . . . . . . . . . . . . . . .
Classification summary . . . . . . . . . . . . . . . . . . . . . . .

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5 Detector Calibration Measurement
5.1 ID Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 High-Voltage determination . . . . . . . . . . . . . . . . . . . .
5.1.2 Relative Gain Measurement . . . . . . . . . . . . . . . . . . . .
5.1.3 Absolute Gain Measurement . . . . . . . . . . . . . . . . . . . .
5.1.4 Relative QE measurement . . . . . . . . . . . . . . . . . . . . .
5.1.5 Timing Response Calibration . . . . . . . . . . . . . . . . . . .
5.2 Photon tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Water Transparency Measurement . . . . . . . . . . . . . . . .
5.2.2 Top-Bottom Asymmetry Measurement . . . . . . . . . . . . . .
5.2.3 Photon Reflection on the Material Surface . . . . . . . . . . . .
Reflection on PMT Surface . . . . . . . . . . . . . . . . . . . .
Reflection on Black Sheet . . . . . . . . . . . . . . . . . . . . .
5.3 Energy Scale Calibration using LINAC . . . . . . . . . . . . . . . . . .

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6 Development of Neutron Tagging in SK-Gd
6.1 Neutron Tagging Algorithm . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Neutron Tagging in Pure Water . . . . . . . . . . . . . . . . . .
6.1.2 Neutron Tagging in SK-Gd . . . . . . . . . . . . . . . . . . . .
6.1.3 Delayed Neutron Search . . . . . . . . . . . . . . . . . . . . . .
Injection of Realistic Noise into MC . . . . . . . . . . . . . . .
Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cut-based neutron selection . . . . . . . . . . . . . . . . . . . .
6.1.4 Neutron Tagging Efficiency . . . . . . . . . . . . . . . . . . . .
6.1.5 Misidentification rate . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Americium-Beryllium Calibration . . . . . . . . . . . . . . . . . . . . .
6.2.1 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Source structure . . . . . . . . . . . . . . . . . . . . . . . . . .
Data taking . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 AmBe MC simulation . . . . . . . . . . . . . . . . . . . . . . .
Primary Particles . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameter tuning for BGO scintillator . . . . . . . . . . . . . .
MC production procedure . . . . . . . . . . . . . . . . . . . . .
6.3 Neutron Tagging Efficiency Evaluation
with AmBe Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Prompt event selection . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Neutron Signal Search . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Tagging Efficiency Estimation . . . . . . . . . . . . . . . . . . .
6.4 Discussion on Tagging Efficiency Measurement . . . . . . . . . . . . .
6.4.1 Random neutron intensity . . . . . . . . . . . . . . . . . . . . .
6.4.2 Probability of prompt event from neutron . . . . . . . . . . . .
6.4.3 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Systematic Uncertainty Extraction . . . . . . . . . . . . . . . . . . . .
6.5.1 Prompt event selection . . . . . . . . . . . . . . . . . . . . . . .
6.5.2 Delayed event selection . . . . . . . . . . . . . . . . . . . . . . .
Vertex reconstruction goodness . . . . . . . . . . . . . . . . . .
Direction reconstruction goodness . . . . . . . . . . . . . . . . .
Reconstructed energy . . . . . . . . . . . . . . . . . . . . . . .
Vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3 MC simulation settings . . . . . . . . . . . . . . . . . . . . . .
Gd concentration . . . . . . . . . . . . . . . . . . . . . . . . . .
Gamma-ray emission model of neutron capture on Gd . . . . .
Neutron excited state fraction . . . . . . . . . . . . . . . . . . .
Neutron energy spectrum of the first excited state . . . . . . .
6.5.4 Position Dependence . . . . . . . . . . . . . . . . . . . . . . . .
6.5.5 Total Systematic Uncertainty . . . . . . . . . . . . . . . . . . .
6.6 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Neutron Tagging Efficiency . . . . . . . . . . . . . . . . . . . .
6.6.2 Time variation . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Search for Diffuse Supernova Neutrino Background in SK-Gd
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7.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2 Signal Energy Window . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 Overview of Background Events . . . . . . . . . . . . . . . . . . . . . . 108
7.3.1 Radioisotope Decays from Muon Spallation and Lithium-9 . . . 108
Isotopes accompanied by neutron . . . . . . . . . . . . . . . . . 108
7.3.2 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.3 Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3.4 Accidental Coincidence background . . . . . . . . . . . . . . . . 114
7.4 MC Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 Event reduction
115
8.1 First Reduction: Pre-cut . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.1.1 Nonphysical Event and Invalid Triggered Event Cut . . . . . . 115
8.1.2 Cosmic-ray muon-induced event cut . . . . . . . . . . . . . . . 115
8.1.3 Fiducial volume cut . . . . . . . . . . . . . . . . . . . . . . . . 116
8.1.4 Fit-quality cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.1.5 Trigger Requirement . . . . . . . . . . . . . . . . . . . . . . . . 116
8.2 Second Reduction: Spallation Cut . . . . . . . . . . . . . . . . . . . . 117
8.2.1 1-ms cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.2.2 Multiple Spallation Cut . . . . . . . . . . . . . . . . . . . . . . 119
8.2.3 Neutron Cloud Cut . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.2.4 Spallation Likelihood Cut . . . . . . . . . . . . . . . . . . . . . 122
Spallation variables . . . . . . . . . . . . . . . . . . . . . . . . . 122
PDF and Likelihood . . . . . . . . . . . . . . . . . . . . . . . . 124
8.2.5 Spallation Box Cut . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.2.6 Spallation Cut Efficiency Estimation . . . . . . . . . . . . . . . 127
Efficiency for random event . . . . . . . . . . . . . . . . . . . . 128
Efficiency for solar neutrino event . . . . . . . . . . . . . . . . . 128
Spallation remaining rate . . . . . . . . . . . . . . . . . . . . . 129
Efficiency for the Lithium-9 . . . . . . . . . . . . . . . . . . . . 130
ROC curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Efficiencies above 16 MeV . . . . . . . . . . . . . . . . . . . . . 132
8.3 Third Reduction: Positron Event Selection . . . . . . . . . . . . . . . . 133
8.3.1 Cherenkov angle . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.3.2 Ratio of charge over the number of hits . . . . . . . . . . . . . 134
8.3.3 Pion likeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.3.4 Pre-PMT activities and post-PMT activities . . . . . . . . . . . 135
8.3.5 Remaining Radioactivity cut using Effective wall distance . . . 136
8.3.6 Systematic Uncertainty Estimation with LINAC data . . . . . 137
Cherenkov angle . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Pion likeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
q50/n50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.3.7 Reduction summary . . . . . . . . . . . . . . . . . . . . . . . . 139
8.4 Forth Reduction: Neutron Tagging . . . . . . . . . . . . . . . . . . . . 139
8.4.1 Neutron misidentification rate . . . . . . . . . . . . . . . . . . . 140
8.4.2 Neutron tagging efficiency . . . . . . . . . . . . . . . . . . . . . 142
8.4.3 Tagged neutron multiplicity . . . . . . . . . . . . . . . . . . . . 142
8.5 Reduction Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.5.1 Optimization of Spallation Cut Criteria . . . . . . . . . . . . . 142
8.5.2 Signal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 143

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9 Background Estimation
147
9.1 Atmospheric neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.1.1 NCQE event . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Neutrino flux and flux shape . . . . . . . . . . . . . . . . . . . 148
Cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Neutron tagging efficiency and neutron multiplicity . . . . . . . 149
Spectrum shape of the observed event . . . . . . . . . . . . . . 149
Total systematic uncertainty . . . . . . . . . . . . . . . . . . . 152
9.1.2 Non-NCQE like interactions . . . . . . . . . . . . . . . . . . . . 153
9.2 Lithium-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.3 Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.4 Accidental Fake background . . . . . . . . . . . . . . . . . . . . . . . . 155
9.5 Expected Background Spectrum . . . . . . . . . . . . . . . . . . . . . . 156
10 Results
159
10.1 Search Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10.2 Upper Limit Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.2.1 Upper limit on the number of signal events . . . . . . . . . . . 161
10.2.2 Flux Upper Limit Calculation . . . . . . . . . . . . . . . . . . . 162
11 Discussion and Conclusion
165
11.1 Future Prospects on the SRN Search . . . . . . . . . . . . . . . . . . . 165
11.2 Future Sensitivity Calculation . . . . . . . . . . . . . . . . . . . . . . . 166
11.3 Limitation to the Failed Supernova Rate . . . . . . . . . . . . . . . . . 168
11.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A Theoretical prediction of SRN flux with integrated bins

173

B Spallation Distributions
175
B.1 Neutron cloud distributions . . . . . . . . . . . . . . . . . . . . . . . . 175
B.2 PDF distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
B.3 ROC Curves for each energy bin . . . . . . . . . . . . . . . . . . . . . 186
B.4 Correlation between Spallation and Li9 efficiency . . . . . . . . . . . . 187
C Third Reduction Cut Variables
189
C.1 Effective wall distance distribution . . . . . . . . . . . . . . . . . . . . 189
C.2 Third reduction variables in LINAC data . . . . . . . . . . . . . . . . . 190
C.2.1 Cherenkov Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 190
C.2.2 Cherenkov Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 191
C.2.3 Pion likeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

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List of Figures
1.1
1.2

Classification of the supernovae by these spectra. . . . . . . . . . . . .
Schematic of CCSN explosion procedure. Explosion proceeds from thesmaller number. Neutrino-heating is assumed to be the mechanism forshockwave revival. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Typical theoretical calculation of timing development of neutrino luminosity and average energy [1]. . . . . . . . . . . . . . . . . . . . . . .
1.4 Timing and energy distribution of neutrinos observed by KamiokandeII and IMB experiments. The figure is taken from [2]. . . . . . . . . .
1.5 CSFRD distribution as a function of redshift. This plot is taken from [3].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Difference of neutrino number spectrum of CCSN with 30M⊙ and Z =0.02 for a progenitor depending on the shock revival time. The left,
central, and right plots show the spectra corresponding to νe , ν̄e , andνx (νµ , ν̄µ , ντ , ν̄τ ). This figure is sourced from [3]. . . . . . . . . . . . .
1.7 Summary of modern theoretical prediction of SRN flux [4, 5, 6, 7, 8, 3,
9, 10, 11, 12, 13, 14, 15, 16]. . . . . . . . . . . . . . . . . . . . . . . .
1.8 Effective cross-section including the resolution and threshold effect ofcertain detectors for each process below 60 MeV. This plot is takenfrom [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9 Upper limits on ν̄e flux from SK, KamLAND, and the Borexino experiment [18]. This figure is taken from [19]. . . . . . . . . . . . . . . . .
1.10 Upper limits on ν̄e flux from the SK [20]. . . . . . . . . . . . . . . . .
2.1

Schematic of view of the SK detector (cutaway view). This figure istaken from [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Overall schematic of SK (Left) and magnified to each face of the support
structure (Right)[22]. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Image of the shockwave prevention case for 20-inch PMT . . . . . . . .
2.4 Overview of Hamamatsu R3600 used for SK ID PMT [22]. . . . . . .
2.5 Wavelength dependence of QE (top), distribution of relative transit
time (bottom left), and ADC charge count distribution(bottom right)
for Hamamatsu R3600 PMT [22]. . . . . . . . . . . . . . . . . . . . .
2.6 Relationship between ID PMT and OD PMT [23]. . . . . . . . . . . .
2.7 Schematic view of compensation coils wounding the SK tank [24]. . . .
2.8 Schematic diagram of the water purification system in SK-IV. This
figure is taken from [25]. . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Schematic of SK-Gd water system. This figure is taken from [26]. . . .
2.10 Schematic of the DAQ system with QBEE[27]. . . . . . . . . . . . . .
2.11 Schematic of the DAQ system with QBEE[28]. . . . . . . . . . . . . .
3.1

Illustration of atmospheric neutrino production.

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

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3.2
3.3

3.4
3.5

3.6

3.7

Comparison between HARP data and the theoretical calculations of
JAM and DPMJET-III for the cross-section of pion production. The
figures are taken in [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Comparison of muon flux between the theoretical calculations and experimental data. Dashed line represents the sum of the error in thecalculation and observation at Mt. Tsukuba (blue squares), at Mt.
Norikura(red triangles) using the BESS detector, and at CERN using
the L3 detector(black circles). Results from the DEIS experiment [30]and MUTRON experiment [31] are presented as well. The figure istaken from [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Zenith angle dependence of atmospheric neutrino flux, averaged over
all azimuthal angles, for Kamioka. Here the θ is the zenith direction ofcoming neutrinos. The figure is taken from [29]. . . . . . . . . . . . . 36
Comparison of the atmospheric neutrino flux for some calculations:
Honda prediction(solid red), previous Honda model(blue dotted-dashedline) [33], Bartol model[34], and the Fluka model[35]. The figure istaken from [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Cross-section of CCQE scattering of muon neutrino (left panel) andanti-muon neutrino (right panel). Lines denote the NEUT calculation
for the free target (solid) and the bound target(dashed). Data points
are taken from ANL (crosses), BNL (triangles), SKAT (stars), Serpukhov (asterisks), and GGMs (circles). The figures are taken from [36]. 38
Comparison between measured data from ANNRI experiment and MC
with ANNRI-Gd model. This figure was taken from [37]. . . . . . . . 41

4.1

PDF distribution for the PMT hit timing residuals. Additional peaks
surrounding 30 and 100 ns are caused by late pulse, which is caused by
the photoelectrons reflected at the dynode and further incidence. . . .
4.2 Vertex resolution as a function of true electron energy for SK-I, II, III,
IV by dotted, dot-dashed, dashed, and solid lines, respectively. This
figure is taken from [38]. . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Energy dependence of the directional resolution. This plot was takenfrom [39]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Illustration of the definition of ∠iuniform and ∠idata . Blue circles exhibit
the PMT hits, and gray circles indicate the expected point if the hits
are equally distributed at an azimuthal angle. . . . . . . . . . . . . .
4.5 Definition of the incident angle θ and ϕ. This plot is referred from [40].
4.6 S(θ, ϕ) distribution for barrel PMTs (left) and top and bottom PMTs
(right). The plots are taken from [40]. . . . . . . . . . . . . . . . . . .
4.7 Illustration defining the calculation of θ. Circles comprise unit vectors
from the reconstructed vertex to the three PMT hits. . . . . . . . . .
4.8 Example of θ distribution of three-hits combinations for electron-, andmuon-like events. Plots are taken from [41]. . . . . . . . . . . . . . . .
4.9 Illustration of muon categories for single-through (top, left), stopping(top, right), multiple (bottom, left), and corner-clipping (bottom, right)
muons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Illustration of the concept for the counting of Nnn with the case of
Nnn = 5 in the central PMT. . . . . . . . . . . . . . . . . . . . . . . .
4.11 Flowchart of Muboy about the direction reconstruction with a part ofevent classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.12 Histogram of typical dQ/dx distribution for considering the length
along the muon track as the horizontal axis. This figure is takenfrom [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.13 Muon types and reconstruction goodness. The term ‘single’ represents
the single-through muons. . . . . . . . . . . . . . . . . . . . . . . . . .
Positions of the Standard PMTs (left) and schematic of the groupingof the PMTs (right). Red points indicate the location. The figures aretaken from [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Appearance of the Ni-Cf source geometry. The figures are taken from [43].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Charge distribution taken using Ni-Cf source used in SK-III. The figures
are taken from [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Hit rate distribution as a function of PMT positions measured in SKVI. Top: barrel PMTs, with the z-position of PMTs plotted in the horizontal axis. Bottom: two plots indicate top (left) and bottom (right)
PMTs, where the horizontal axis denotes the square of the radial distance on the x-y plane. Black points indicate the data, and red points
display MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Schematic view of the timing calibration system. The figures are takenfrom [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Typical scatter plot of the timing and the charge. For the vertical axis,
larger (smaller) T corresponds to the earlier (later) hits. The figures
are taken from [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 Timing distribution and the function resulting from the fitting for the
Qbin = 14. The figures are taken from [43]. . . . . . . . . . . . . . . .
5.8 Distribution of timing resolution as a function of the charge, measured
during in SK-IV. The figures are taken from [43]. . . . . . . . . . . .
5.9 Schematic of the laser measurement system. The analysis uses PMTs
pertaining to five segmented barrel regions B1-B5 and the top. The
figures are taken from [43]. . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Best-fitted timing distribution of data and MC for each PMT region
in SK-IV measurement. The circle with the black line represents thedata, and the red line indicates the MC. Both are normalized by total
observed photoelectrons. The top panel represents the PMTs at the
top of the ID wall, whereas the second-to-bottom panels correspond to
the five segmented barrel regions B1–B5, as displayed in Figure 5.9.
The region between the two blue-solid lines on the left-hand side wasused to fit the attenuation coefficients. The region between the twoblue-solid lines on the right-hand was utilized in the PMT reflection
measurement. The figures are taken from [43]. . . . . . . . . . . . . .
5.11 Distributions of the coefficient as functions of the wavelength. Eachpoint represents the Best-fitted coefficients for each laser wavelengthand interaction. Red, blue, and magenta points and the lines represent
the αabs , αsym , and αasym , respectively. Circles (triangles) and solid(dot-dashed) lines of the Geant4-based (GEANT3-based) simulation
result are described in Section 3.3. . . . . . . . . . . . . . . . . . . . .

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5.12 Variation of the TBA during the SK-V and SK-VI, taken by the Ni-Cf
source and Xe light source (top), and differences of TBA between bothmeasurements and between data and MC for Ni-Cf source measurement (bottom). Thick dotted-dashed line indicates the 0.5% difference
region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.13 Schematic of a laser light injector to measure black sheet reflectivity.
The figure is taken from [43]. . . . . . . . . . . . . . . . . . . . . . . .
5.14 Comparison between laser data and MC in the black sheet measurement. The three left panels show the ratio of the charge between reflected and direct incident light, and the right panels show the ratio
between data and MC for the left plots, for the wavelength at 337 nm(top), 400 nm (middle), and 420 nm (bottom). The figure is takenfrom [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of the procedure of noise production. The contents
with the blue characters and lines are simulated in the detector MC,
while those with red characters and lines are appended later. . . . . .
6.2 Illustration of the primary selection. Dashed line indicates the N200
threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Distribution of the gvtx (left) and gdir (right) for signals from neutron
capture on Gd (magenta) and proton (cyan), and noise (gray) candidates. The red arrows show the cut criteria. These distributions arenormalized by area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Distributions of the dprompt for the signal from neutron capture on Gd(magenta) and proton (cyan), and noise (gray) candidates. Red arrow
indicates the threshold. These distributions are area-normalized. . . .
6.5 Distributions of the reconstructed energy for the signal from neutron
capture on Gd (magenta) and proton (cyan), and noise (gray) candidates. Red arrow indicates the cut criteria. These distributions arenormalized by area. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Capture time distribution of the neutron MC and the fitting result. .
6.7 Time variation of ϵmis . Black-dotted line denotes the weighted meanvalue for the entire period, and the gray-shaded region indicates thestandard deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Major final state of 13 C. A de-excitation from the second excited state
was not observed in the Kamioka AmBe source. . . . . . . . . . . . .
6.9 Appearance of the Am/Be source (left) and the four pieces of BGO
scintillator crystals (right). . . . . . . . . . . . . . . . . . . . . . . . .
6.10 Appearance and schematic of 1BGO geometry (left) and 8BGO geometry (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 Illustration of measurement points. Orange squares exhibit measurement points, and the darker blue circle denotes calibration holes, wherex = −1237, 35.3, 1080 cm ∼ −12, 0, +12 m. . . . . . . . . . . . . . . .
6.12 Kinetic energy spectrum of the emitted neutron from each state, calculated as the combination referring measurements of Guarrini andMalaroda [44], and ISO8529-1 [45]. . . . . . . . . . . . . . . . . . . .
6.13 Correlation between scintillation time constant for each component
with BGO temperature. This figure is taken from [46]. . . . . . . . .
6.14 QISMSK distribution of the AmBe MC with 8BGO at the center point
for various scintillation yield parameters. . . . . . . . . . . . . . . . .

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6.15 QISMSK distribution of the 8BGO at center point data with some lightyield setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.16 Correlation between yield and QISMSK in MC. Black circles denotethe MC peak and its deviation for each yield setting in Figure 6.15.
Red line indicates the QISMSK peak for the data in Figure 6.14. . . .
6.17 QISMSK distribution for the data and best-fitted MC; n0 , n1 , and n2
MC indicates the MC simulation for each excited state of 12 C. . . . .
6.18 QISMSK distributions for center data (top left), (X= −12 m, Z=−12 m) data (top right), and (X= +12 m, Z= 0 m) data (bottom)
obtained by 8BGO AmBe measurement; arrows indicate the thresholdcriteria for each source position. . . . . . . . . . . . . . . . . . . . . .
6.19 Distribution of the number of delayed candidates passing N200 ≥ 25. .
6.20 Distributions of neutron selection variables. Each color-filled histogram
exhibits the MC, and solid point represents the data, which is alignedwith the statistical error. Red arrow indicates the cut criteria for neutron selection. These distributions are normalized by the number ofprompt events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.21 Capture timing distributions for measured data (left) and MC simulation (right). Dotted line only displayed in the data plot represents theflat component evaluated by exponential fitting. . . . . . . . . . . . .
6.22 Illustration of emission of the random neutron. . . . . . . . . . . . . .
6.23 The probability of thermal neutron capture in the SK with AmBe
source geometry for 8BGO (top) and 1BGO (bottom). These probabilities were calculated based on the result of the five million neutron
MC, which uses ENDF.VII.1 as a nuclear data library [47]. . . . . . .
6.24 QISMSK cut criteria and the data-MC difference in the neutron tagging
efficiency as a function of the higher side (left) and lower side (right).
6.25 QISMSK cut criteria and the data-MC difference in neutron tagging
efficiency. Color depicts the difference between data and MC from thenominal criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.26 Distribution of gvtx for data and MC. Solid green line indicates thesmeared cut threshold. Both plots are normalized by area. . . . . . .
6.27 Distribution of gdir for data and MC. Solid green line indicates thesmeared cut threshold. Both plots are normalized by area. . . . . . .
6.28 Distribution of reconstructed energy for data and MC. Solid green line
denotes the smeared cut threshold. Both plots are normalized by area.
6.29 Distribution of the distance between reconstructed delayed event vertex
and the source position for data and MC. Solid green line denotes thesmeared cut threshold. Both plots are normalized by area. . . . . . .
6.30 Correlation between the time constant and Gd mass concentration(left), and the Gd capture fraction and Gd mass concentration (right).
6.31 Neutron kinetic energy spectra from the first state of 12 C based on ISO(black) and measured (red). . . . . . . . . . . . . . . . . . . . . . . .
6.32 Neutron tagging efficiency for each measured point. . . . . . . . . . .
6.33 Neutron tagging efficiency as a function of the surrounding BGOs. Efficiency without BGO (0BGO) is only estimated by MC because it
cannot be estimated for actual data. . . . . . . . . . . . . . . . . . . .
6.34 Neutron tagging efficiency as a function of the surrounding BGOs. . .

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7.1

7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.1

Correlation between end-point energies and half-lives (left) and thatbetween half-lives and yield (right) for spallation isotopes detected in
the DSNB search window and generated by cosmic-ray muons in water. Red circles in both figures represent undergoing beta decay withneutrons. For the isotopes undergoing decay with neutrons, the yield
includes the fraction of decay with neutrons. The fraction of these plots
referred from [48]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Decay scheme of 9 Li based on PDG [49]. . . . . . . . . . . . . . . . .
True and reconstructed electron kinetic energy for the β-decay of 9 Li.
Illustration of decay electron background. In the figure, the decay electron from an invisible muon produced via CCQE interaction of atmospheric neutrino is displayed. . . . . . . . . . . . . . . . . . . . . . . .
Illustration of the visible muon and pion background. In the figure, thevisible muon and the decay electron produced via the CCQE interactionof atmospheric neutrino are displayed. . . . . . . . . . . . . . . . . . .
Illustration of the electron background event via CCQE interaction of
the atmospheric electron neutrinos. . . . . . . . . . . . . . . . . . . .
Illustration of the NCQE background event. . . . . . . . . . . . . . .
Activities of Japanese reactor from Apr. 2018 to Sep. 2022; dashedline indicates 100% operation time. . . . . . . . . . . . . . . . . . . .
Expected neutrino energy flux from Japanese reactors at the SK site,
considering the neutrino oscillation effect. . . . . . . . . . . . . . . . .

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114

Reconstruction goodness and reconstructed energy distribution for data(left) and signal MC (right). Vertical magenta line exhibits the energy
threshold of 7.49 MeV, and the horizontal magenta line presents thegvtx threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.2 Illustration of muon concept for the spallation. . . . . . . . . . . . . . 118
8.3 Minimum distance between the SHE event and the low-energy event
within ±60 s, obtained from the SHE event and randomized vertex(left) and the subtracted distribution (right). . . . . . . . . . . . . . . 119
8.4 Number of neutrons after muons for pre (black) and post (red) samples. 120
8.5 Time difference between muons and the SHE event. Each color exhibits
the number of neutrons after muons. . . . . . . . . . . . . . . . . . . 120
8.6 Distance between neutron cloud position and the SHE event. Eachpanel exhibits the difference in Nncloud . . . . . . . . . . . . . . . . . . 121
8.7 Illustration of definition for the variables used in the neutron cloud cut. 121
8.8 Two-dimensional distribution of ∆x , ∆y , and ∆z . Left column represents the pre-samples, and right column indicates the post-samples.
Magenta lines indicate the cut criteria. These are clouds with Nncloud ≥10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.9 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud ≥ 10. . . . . . . . . . . . . . . . . . 124
8.10 Illustration for variables related to spatial correlation . . . . . . . . . . 125
8.11 Random (red) and spallation (blue) PDFs for dt (top, left), ℓt (top,right), ℓl (middle, right), Qres (middle, right), and Qµ (bottom). Thesemuons belong to the single through-going muons with the dt region of
0–0.05 s and the ℓt region of 0–300 cm. . . . . . . . . . . . . . . . . . 126

xix
8.12 Spallation likelihood distributions of pre (blue) and post (red) samples, for misfit (top, left), stop (top, right), single through-going with
dt = 0–0.05 sec (middle, left), and ℓt = 0–200 cm (middle, right), andmultiple muons with dt = 0–0.05 sec (bottom left), and ℓt = 0–100 cm(bottom, right). These findings correspond to the reconstructed energy
in the 8–10 MeV region. . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.13 Schematic of definition of θsun and cos θsun . . . . . . . . . . . . . . . . 129
8.14 Correlation between εrandom and εsolar . . . . . . . . . . . . . . . . . . 129
8.15 ROC curve representing the correlation between spallation remaining
rate and random event efficiency for 8–10 MeV region. . . . . . . . . . 131
8.16 Correlation between spallation remaining rate and lithium-9 event efficiency for 8–10 MeV region. . . . . . . . . . . . . . . . . . . . . . . . 131
8.17 Mis-reconstruction of the Cherenkov ring owing to the multiple Cherenkov
ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.18 Distribution of the Cherenkov angle. Color plot describe the type of
atmospheric neutrino interaction, and black line denotes the DSNB signal MC assuming the Horiuchi+09 flux model [10]. These are obtained
from the events after only passing the first reductions. . . . . . . . . . 134
8.19 Distribution of the q50/n50 with the linear (left) and logarithmic (right)
for the vertical axis. Color plot exhibits the type of atmospheric neutrino interaction, and black line denotes the DSNB signal MC assuming
the Horiuchi+09 flux model [10]. These are made from the events after
passing only the first reductions. . . . . . . . . . . . . . . . . . . . . . 134
8.20 Distribution of Lpion . Color plot denotes the type of atmospheric neutrino interaction, and black line exhibits the DSNB signal MC assuming
the Horiuchi+09 flux model [10]. These are made from the events after
passing only the first reductions. . . . . . . . . . . . . . . . . . . . . . 135
max . Color plot exhibits the type of atmospheric neu8.21 Distribution of Npre
trino interaction. These are made from the events after passing only
the first reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.22 Distribution of Ndecay-e with the linear (left) and logarithmic (right) for
the vertical axis. Color plot exhibits the type of atmospheric neutrino
interaction. These are made from the events after passing only the first
reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.23 Illustration of definition of deff . . . . . . . . . . . . . . . . . . . . . . . 137
8.24 Comparison of deff after 1st reduction between data and MC. . . . . . 137
8.25 Comparison of Cherenkov angle distribution between data and MC(top) and the data/MC ratio (bottom) for the E =12 MeV LINAC run. 138
8.26 Comparison of Lpion distribution between data and MC (top) and thedata/MC ratio (bottom) for the E =12 MeV LINAC run. . . . . . . . 139
8.27 Comparison of q50/n50 distribution between data and MC (top) andthe ratio of data/MC (bottom) for the E =12 MeV LINAC run. . . . . 140
8.28 Distribution of ϵmis as a function of the cut criteria for the dprompt (left)
and the Edelayed (right). Color for the left (right) plot exhibits the cut
criteria of Edelayed (dprompt ). . . . . . . . . . . . . . . . . . . . . . . . 141
8.29 Time variation of ϵmis . Black-dotted line depicts the weighted meanvalue for the entire period, and the gray-shaded region indicates thestandard deviation. Horizontal axis represents the same factor as thatin Figure 6.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

xx
8.30 Distribution of number of tagged neutrons for the IBD MC and atmospheric neutrino MC, after first to third reductions, in the signal energy
region. Histograms of atmospheric neutrino MC are stacked with eachother. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.31 Signal efficiency as a function of kinetic energy Erec . . . . . . . . . . . 143
9.1

Total cross-section for neutrino (left) and antineutrino (right) for 16 O(ν, ν ′ N)
interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.2 Average of the number of tagged neutrons in the T2K CC-dominantsamples, as a function of reconstructed Q2 , for FHC (left) and RHC(right). Plots are taken from [41], and the original work was done by[50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9.3 Neutron multiplicity distribution for Q2 < 0.25 GeV2 (upper left),
Q2 = 0.25–0.5 GeV2 (upper right), Q2 = 0.5–0.0.75 GeV2 (bottom
left), and Q2 = 0.75–3.0 GeV2 . . . . . . . . . . . . . . . . . . . . . . . 150
9.4 Illustration of the NCQE interaction and subsequent nuclear interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.5 Reconstructed Cherenkov angle distribution in the T2K FHC (left) andRHC (right) measurements. These plots are recited from [51]. . . . . 151
9.6 Weighting factor εν(ν̄) of neutrino (left) and antineutrino (right), each
2 MeV bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.7 Weighting factor εν+ν̄ each 2 MeV bin. . . . . . . . . . . . . . . . . . 153
9.8 Energy distribution before and after reweighting by εν+ν̄ , after the third
reduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.9 Energy spectrum in the side-band region of 31.49–79.49 MeV for thereconstructed kinetic energy. . . . . . . . . . . . . . . . . . . . . . . . 154
9.10 χ2 distribution as a function of the scaling factor. . . . . . . . . . . . 154
9.11 Expected background spectrum with these total systematic uncertainties (hatched) for each 2 MeV bin. Dotted-dashed red line denotes the
expected SRN signal based on [10]. . . . . . . . . . . . . . . . . . . . 156
9.12 Expected background spectrum with these total systematic uncertainty(hatched) for each merged bin (hatched). Dotted-dashed red line portrays the expected SRN signal based on [10]. . . . . . . . . . . . . . . 157
10.1 Observed and expected background spectrum with these total systematic uncertainties (hatched) with linear scale (top) and logarithmic(bottom). The dot-dashed red line shows the expected SRN signal
based on [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.2 Toy MC result for calculating the p-value for each energy bin above
11.49 MeV (bottom, right). Red line exhibits the actual observed eventin this analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
limit .
10.3 Nsig distribution for Erec = 9.49–11.49 MeV bin as an example of N90
limit
The region between Nsig = 0 and Nsig = N90 contains 90% of thetotal of Nsig > 0 events. . . . . . . . . . . . . . . . . . . . . . . . . . . 162

xxi
10.4 Upper limits on the ν̄e flux. Solid lines denote the observed upper
limit for SK-IV (blue), SK-VI (red), and KamLAND (green), respectively. Dot-dashed lines represent the expected sensitivity based on
the expected background for SK-IV (black) and SK-VI (yellow). Grayshaded region represents the range of the modern theoretical expectation. The expectation drawn in the figure includes DSNB flux models[15, 16, 14, 12, 11, 10, 9, 3, 8, 6, 5, 4, 52]. Ando+03 model was updatedin [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.1 Expected future sensitivity for 9.3–11.3 MeV (left) and 11.3–13.3 MeV
energy bins with various background conditions, such as nominal case(black), and further higher neutron tagging efficiency (red), 70% of
NCQE background (green), 50% of the error on the NCQE background(blue), 50% of the error on the 9 Li (Orange), 50% of the CCQE background and their error (Magenta). Thick-dotted line denotes the most
optimistic theoretical expected flux. In the 9.3–11.3 MeV region, thetheoretical expectation is excluded from this figure as it is smaller than
the sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.2 Expected future sensitivity for 13.3–17.3 MeV (left) 17.3–25.3 MeV(middle), and 25.3–31.3 MeV (right) energy bins with the same assumption as Figure 11.1; colors represent the assumptions listed inTable 11.1. Two thick-dotted lines exhibit the range of model expectations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
11.3 Event rate spectra of DSNB ν̄e for SK 22.5 kton water per year. The
EOS model is assumed to be (a) Togashi EOS, (b) LS220 EOS, (c) Shen
EOS, respectively. Colors correspond to the remnant types and mass
hierarchy of the neutrino oscillation. These plots are sourced from [53]. 168
11.4 Two-dimensional map of the DSNB ν̄e flux as a function of fBH andfHNS in normal mass hierarchy. Dotted-dashed line reports the 3σ
expected sensitivity derived from the 10 years of future SK-Gd operation. These are estimated as the integrated flux for the neutrino energy
13.3 < Eν < 31.3 MeV (top) and 17.3 < Eν < 31.3 MeV (bottom) with
distinct EOS models such as Togashi EOS (left), LS220 EOS (middle),
and Shen EOS (right), respectively. . . . . . . . . . . . . . . . . . . . 170
11.5 Distributions with the same manners as Figure 11.4, in case of inverted
mass hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
11.6 3σ detectable areas on the fBH -fHNS plane assuming NH for three distinct EOS models in the energy range of 13.3–31.3 MeV (left) and
17.3–31.3 MeV (right) according to the future flux limit at 10 year of
the SK-Gd observation. . . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.7 Distributions with the same manners as Figure 11.6 but assuming IH. 171
B.1 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud = 2. . . . . . . . . . . . . . . . . . . 175
B.2 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud = 3. . . . . . . . . . . . . . . . . . . 175
B.3 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud = 4-5. . . . . . . . . . . . . . . . . . 176

xxii
B.4 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud = 6-9. . . . . . . . . . . . . . . . . .
B.5 Two-dimensional distribution of log |dt| and ∆l for the pre-sample (left)
and the post-sample (right). Magenta lines are cut criteria in this plane.
These are for clouds with Nncloud ≥ 2. . . . . . . . . . . . . . . . . . .
B.6 Two-dimensional distribution of ∆x , ∆y , and ∆z . The left column
shows the pre-samples and the right column shows the post-samples.
Magenta lines are cut criteria. These are clouds with Nncloud = 2. . .
B.7 Two-dimensional distribution of ∆x , ∆y , and ∆z . The left column
shows the pre-samples and the right column shows the post-samples.
Magenta lines are cut criteria. These are clouds with Nncloud = 3. . .
B.8 Two-dimensional distribution of ∆x , ∆y , and ∆z . The left column
shows the pre-samples and the right column shows the post-samples.
Magenta lines are cut criteria. These are clouds with Nncloud = 4-5. .
B.9 Two-dimensional distribution of ∆x , ∆y , and ∆z . The left column
shows the pre-samples and the right column shows the post-samples.
Magenta lines are cut criteria. These are clouds with Nncloud = 6-9. .
B.10 Two-dimensional distribution of ∆x , ∆y , and ∆z . The left column
shows the pre-samples and the right column shows the post-samples.
Magenta lines are cut criteria. These are clouds with Nncloud ≥ 2. . .
B.11 Random (blue) and spallation (red) PDFs for dt (top), and ℓt (second from the top to bottom). ℓt PDF distributions are separated forthe muon with dt region of 0–0.05 sec (second from top), 0.05–0.5 sec(third from top), and 0.5-60 sec (bottom). These muons belong to thestopping (left) and multiple (right) muons. . . . . . . . . . . . . . . .
B.12 Random (blue) and spallation (red) PDFs for ℓl with dt region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec (bottom), and ℓt regionof 0–300 cm (left), 300–1000 cm (middle), and more than 1000 cm(right). These muons belong to the single through-going muons. . . .
B.13 Random (blue) and spallation (red) PDFs for Qres with dt region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec (bottom), and ℓt regionof 0–300 cm (left), 300–1000 cm (middle), and more than 1000 cm(right). These muons belong to the single through-going muons. . . .
B.14 Random (blue) and spallation (red) PDFs for Qmu with dt region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec (bottom), and ℓt regionof 0–300 cm (left), 300–1000 cm (middle), and more than 1000 cm(right). These muons belong to the single through-going muons. . . .
B.15 ROC curve for each 2 MeV bin below 16 MeV. . . . . . . . . . . . . .
B.16 Correlation between spallation remaining rate and 9 Li efficiency foreach 2 MeV energy bin below 16 MeV. . . . . . . . . . . . . . . . . . .

176
176
177
178
179
180
181

182

183

184

185
186
187

C.1 deff wall distribution for the data (black) and MC (blue). Each panel
show the reconstructed energy E for E > 8 MeV (left-top), E >10 MeV (right-top), E > 12 MeV (left-middle), E > 14 MeV (rightmiddle), E > 16 MeV (left-bottom), and E > 20 MeV (right-bottom).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

xxiiiC.2 Reconstructed Cherenkov angle distribution for LINAC data (black)and MC (blue). For each plot, the lower panel shows the ratio ofdata over MC. For the LINAC position, figures show the z = −12 m(top), z = 0 m (middle), and z = 12 m (bottom). For the LINAC
energy, figures show the E = 8 MeV (left), E = 12 MeV (middle), andE = 15 MeV (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
C.3 Ratio of charge over number of hits in 50 ns distribution for LINAC
data (black) and MC (blue). For each plot, the lower panel shows
the ratio of data over MC. For the LINAC position, figures show thez = −12 m (top), z = 0 m (middle), and z = 12 m (bottom). For
the LINAC energy, figures show the E = 8 MeV (left), E = 12 MeV(middle), and E = 15 MeV (right). . . . . . . . . . . . . . . . . . . . . 191
C.4 Pion likeness distribution for LINAC data (black) and MC (blue). For
each plot, the lower panel shows the ratio of data over MC. For the
LINAC position, figures show the z = −12 m (top), z = 0 m (middle),
and z = 12 m (bottom). For the LINAC energy, figures show theE = 8 MeV (left), E = 12 MeV (middle), and E = 15 MeV (right). . . 192

xxv

List of Tables
1.1

Best-fitted neutrino oscillation parameters. These values are taken by[54]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.1
2.2
2.3

The detector situation for each observation period of SK. . . . . . . .
Detectable dynamic range and charge resolution for each range. . . . .
Threshold for each type of trigger in SK-VI . . . . . . . . . . . . . . .

25
31
32

4.1
4.2

Parameter settings for the reconstructed energy calculation in SK-VI.
Charge thresholds for ID PMT corresponding to the number of ID PMT
hits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nnn thresholds for ID PMT corresponding to the number of ID PMT
hits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.3

52
53

6.1
6.2
6.3

Summary of thermal neutron capture on 155 Gd and 157 Gd [37] . . . . 78
Summary of neutron selection variables. . . . . . . . . . . . . . . . . . 80
Summary of selection and reduction efficiency for the neutron eventand background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.4 Parameters determined from the measurements, including the rise timeparameters and resolution scale parameter. . . . . . . . . . . . . . . . 89
6.5 Summary of capture time constant and neutron tagging efficiency for
the DATA and MC for each BGO geometry. Errors only include only
statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.6 Summary of contents in the calculation for the tagging efficiency of 4.4
MeV gamma-ray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.7 Break down the contents in the calculation of random neutron intensity. 95
6.8 Summary of the contents of the dummy prompt event. . . . . . . . . . 97
6.9 Summary of contents in dummy prompt event. . . . . . . . . . . . . . 97
6.10 Summary of excited state fraction and neutron tagging efficiency . . . 103
6.11 Summary of systematic uncertainty on AmBe measurement. . . . . . . 105
6.12 Summary of neutron tagging efficiencies for the DATA and MC for each
BGO geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.1
7.2

Trigger conditions and live-time during SK-VI. . . . . . . . . . . . . . 107
Summary of the muon spallation products in the water. This table istaken from Ref. [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1

AFT trigger efficiency calculated using 2 MeV energy bins. These values
are calculated by considering the average of the entire SK-VI period. .
Cut criteria of neutron cloud cut. The signature (+) in the multiplicity
column signifies equal or more than the value. . . . . . . . . . . . . .
Summary of cut criteria of spallation box cuts for each reconstructedenergy E region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the cut efficiency of spallation cut above 16 MeV. . . . .
LINAC positions and target energies used in the evaluation . . . . . .

8.2
8.3
8.4
8.5

117
122
128
132
138

xxvi
8.6
8.7

Summary of the cut criteria and efficiencies. . . . . . . . . . . . . . .
Summary of the signal efficiencies at each cut stage for energy E =8–16 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8 Summary of the signal efficiencies at each cut stage for the Erec =7.49–15.49 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9 Summary of the signal efficiencies at each cut stage for Erec =15.49–
23.49 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.10 Summary of the signal efficiencies at each cut stage for Erec = 23.49–
29.49 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1
9.2
9.3

140
143
145
145
145

T2K over the predicted by
Ratio of the number of observed neutrons Nobs
T2K
2
MC Npred in each Q region. . . . . . . . . . . . . . . . . . . . . . . . 150
Break down the systematic uncertainty on the NCQE interaction events.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Breakdown of the expected background events and these systematic
errors at each merged bin. . . . . . . . . . . . . . . . . . . . . . . . . 156

10.1 Breakdown the event reduction and signal efficiency at each merged bin. 159
10.2 Summary table of upper limits, sensitivity. . . . . . . . . . . . . . . . 162
11.1 Assumptions for calculating future sensitivity. Titles about color indicate the line color for each panel shown in Figure 11.1. . . . . . . . . 167
A.1 Summary of model projections of average flux and obtained sensitivity
in each bin. The future sensitivity in SK-VII represents the magenta
line in Figure 11.1. The unit of each value is cm−2 sec−1 MeV−1 . . . . 173

1Chapter 1

Introduction
Massive stars, with a gravitational mass exceeding about eight solar masses, end
their life in an intense explosion known as a Supernova. Supernova is one of the mostdynamic phenomena in the universe, and the energy released at the explosion is about1053 erg. Consequently, supernovae are pivotal in the fields of astrophysics and particle
physics. Contemporary theory suggests that a large part of this formidable explosion
energy is emitted via neutrinos, rendering their detection crucial for deciphering thephysics of supernovae.
In this chapter, the initial section presents a discussion on the supernova explosion and the consequent emission of neutrinos. After that, supernova relic neutrinos,
which constitute an integrated flux of neutrinos originating from past supernovae, areintroduced. Finally, the past experimental approach utilized in the detection of supernova relic neutrinos, culminating with a summary of the current status of sensitivity
toward these neutrinos, is outlined.

1.1Supernova Explosion

Supernova is predicted to occur a few times in our galaxy [55]. The light emission
from a supernova, reaching approximately 1051 erg, is primarily observable via optical surveys. Despite numerous observations of supernovae across various galaxies,
significant mysteries persist surrounding supernovae and their underlying explosion
mechanisms.

1.1.1

Explosion Types and Mechanism Overview

Supernovae can be categorized based on their optically observed spectra, including
types Ia, Ib, IIP, and IIL, as illustrated in Figure 1.1. A supernova devoid of hydrogenlines (Balmer series) in its spectrum is classified as Type-I, whereas those featuring
such lines are designated as Type-II. Those exhibiting silicon lines within the Type-I
supernova category are further classified as Type-Ia. The explosion mechanism ofthese supernovae is attributed to thermo-nuclear interactions.
The supernovae with weak silicon lines are classified as either Type-Ib or Type-Ic,
contingent upon the presence of a helium line. Type-II supernovae are differentiatedbased on their light curves. A supernova displaying a stable period in its light curve isdesignated Type-IIP (Plateau), whereas a linearly decreasing light curve characterizes
a Type-IIL (Linear) supernova. The explosion mechanism for supernovae apart from
Type-Ia is attributed to the core collapse of the star, leading to the nomenclature’Core-Collapse Supernova’ (CCSN). The neutrino emitted via this mechanism is focused on in this thesis as the explosion is accompanied by enormous neutrino emission.

2

Chapter 1. Introduction

Hydrogen line

No

Yes

Light curve

Silicon line
Yes

No
PlateaulinearHelium line

Type-Ia

Yes

No

Type-Ib

Type-Ic

Type-IIP

Type-IIL

Core-Collapse

Thermo-nuclear

Figure 1.1: Classification of the supernovae by these spectra.

The kinetic energy propelling an explosion emanates from two primary sources.
The first pertains to the energy derived from nuclear fusion. Assuming a rapid nuclear
fusion reaction transitioning from carbon atoms to iron atoms within a star of mass
M , the energy released, represented as Enuc , can be expressed as follows:!
M
51
Enuc ∼ 2 × 10 erg
,
(1.1)
M⊙
where M⊙ denotes the solar mass1 . The second source of energy is gravitational.
Assuming a star of radius R contracts to a final radius Rf , comparable to the size ofa neutron star (∼ 10 km), the gravitational energy Eg can be calculated as follows:Eg ∼ 3 × 1053 erg

M
M⊙

!2

!
Rf
10 km

(1.2)

Type-Ia supernovae are fueled by nuclear fusion reactions, whereas core-collapse
supernovae are driven by gravitational energy.

1.1.2

Explosion Mechanism of Core-Collapse Supernova

This section describes the mechanism through which a star concludes its life witha CCSN explosion. Figure 1.2 illustrates a schematic view of the CCSN explosion
process.
The formation of stars commences when the interstellar medium condenses due
to gravity, forming a core. Surrounding materials are continuously accreted to thecore, causing it to grow. Simultaneously, the gravitational energy from the accretedmaterials is converted into thermal energy, resulting in increasing internal pressure.
When the central temperature of the star reaches T ≈ 105 K, the radiation spectrum
1M⊙ ∼ 1.9884 × 1030 kg

3

1.1. Supernova Explosion

bears an optical range. Stars in this stage are referred to as primitive stars. Once thetemperature surpasses T > 107 K, the conditions are favorable for nuclear fusion andthe subsequent production of heavier elements. Hereinafter, the progenitor mass ofthe star constrains the maximum mass of the created element. In instances where thestar mass M > 8M⊙ , neon and magnesium serve as the fuel for nuclear fusion, suchas 1.3. If the density exceeds 4 × 109 g/cm3 , magnesium occurs electron capture,
which results in a decreased electron density (as indicated in stages (1) and (2) inFigure 1.2).
Mg+ e− −−→ 24Na + νe

24

(1.3)

As the density continues to rise, the generated nuclei start to capture electrons.
Na + e− −−→ 24Ne + νe

24

(1.4)

−

Ne + e −−→

24

(1.5)

−

24

(1.6)

24

24

F + e −−→

F + νeO + νeThe decrease in electron density reduces the electron degeneracy pressure, triggering a gravitational contraction at the central core (as depicted in stage (3) in Figure 1.2). Eventually, the mass density of the central core becomes sufficiently denseto cause a gravitational collapse. If M > 12M⊙ , magnesium undergoes nuclear fusion
under nondegenerate pressure, culminating in the creation of the Iron nucleus ( 56Fe).
Given that 56Fe is the most stable nucleus formed in this process, further nuclear
fusion to create heavier elements does not take place. Consequently, the iron corestops providing energy, and gravitational force is counterbalanced by electron degeneracy pressure. The temperature becomes sufficiently high to create the iron core, andhigh-energy photons disintegrate the nucleus in a process called photodisintegration.
Fe + γ −−→ 13 α + 4n − 124.4 MeV(1.7)

α + γ −−→ 2p + 2n − 28.3 MeV

(1.8)

56

As this reaction progresses, the electron density diminishes. The photodisintegration process is activated at the T ∼ 5 × 109 K, and the internal core achieves athermodynamic equilibrium between nuclear fusion and the photodisintegration. The
continuous contraction and rising temperature eventually lead to the core collapse of
the iron core, accompanied by explosive photodisintegration.
The collapse halts when the density reaches ∼ 1014 g/cm3 due to nuclear forces,
resulting in the creation of an outward shockwave ((5) in Figure 1.2). This shockwave
heats the surrounding material and dissipates its energy. Following the passage ofthe shockwave, a proto-neutron star (PNS) forms within the core. The PNS is anincredibly dense object with an inner core packed with neutron-rich nuclei and freeneutrons. The gravity acting on the PNS is offset by the neutron degeneracy pressure, yielding a radius of ∼ 10 km. The material remaining after the passage of theshockwave collapses onto the PNS (as depicted in stage (7) in Figure 1.2). Although
the shockwave is considered the engine of the supernova explosion, it eventually stalls
due to energy loss from the accretion of the surrounding matter. This shockwave
was believed to be revived through a neutrino-heating mechanism (as indicated in(8) in Figure 1.2) [56]. In this mechanism, the matter behind the shockwave absorbs
neutrinos emitted from the PNS, reenergizing the shockwave. Although only simple
neutrino transportation does not revive the shockwave [57], recent studies proposethat the shockwave instability and the convection in the progenitor may accelerate

4

Chapter 1. Introduction

the neutrino-heating [58, 59].
As the outer layer of a star is weakly bound to the core, the shockwave ejects theouter layer, leaving a neutron star after the explosion (as displayed in stage (9) in
Figure 1.2). Although the gravity of a neutron star is balanced by the degeneracypressure of neutrons, stars with M > 12M⊙ can occasionally exceed the neutron
degeneracy pressure, referred to as the Tolman-Oppenheimer-Volkoff limit. In suchcases, these stars ultimately form a black hole.
(1)

(2)

H
He

⋯

(4)

(3)

H
He
C,O
O,Ne,Mg
Si

Gravitational
Contraction

Fe(5)
Neutrino
SphereFe core(6)
Shockwave

PNS

νe

νe

(7)

νe

(9)

(8)
Accretion

νν

Figure 1.2: Schematic of CCSN explosion procedure. Explosion proceeds from the smaller number. Neutrino-heating is assumed to be themechanism for shockwave revival.

51.1. Supernova Explosion

1.1.3

Neutrinos from Core-Collapse Supernovae

Neutrinos are fundamental particles, possessing no electric charge and a spin of 1/2,
making them fermions. They are categorized into three leptonic flavors: electron,
muon, and tau, including their antiparticles. They only interact with matter via
weak forces (and gravity) due to their lack of charge and minuscule masses. This
characteristic plays a pivotal role in the mechanism of supernova explosions. Thissection first elucidates the neutrino oscillation, a key property of neutrinos, before
detailing the mechanisms and neutrino emissions from Core-Collapse Supernovae.
Neutrino Oscillations
The discrepancy between the observed and the expected flux of neutrinos was a longstanding mystery because neutrino was first believed to be mass-less. However, thisassumption of mass-less was contradicted, and the mystery was resolved by observing
a key characteristic of neutrinos, known as Neutrino Oscillation[60, 61]. This evidence
suggests that neutrinos possess extremely minute masses below 1 eV. The theory ofneutrino oscillation was first proposed by Pontecorvo[62, 63] for neutrinos and antineutrinos, and has since been further developed quantitatively[64, 65]. This theory
demonstrates the transition of neutrino types by assuming that the neutrino flavor
eigenstates differ from their mass eigenstates and that the flavor state eigenstate comprises a mix of three types of mass eigenstates. Initially, the fundamental concept ofneutrino oscillation in a vacuum is discussed, as material affects neutrino oscillation
until it is observed. The impact of the material will be discussed later in this section.
In a vacuum, the neutrino flavor state eigenstates |να ⟩ (α = e, µ, τ ) are correlated
linearly with three types of neutrino mass eigenstates |νi ⟩ (i = 1, 2, 3):|να ⟩ =

3
X

∗
Uαi
|νi ⟩

(1.9)

i=1

Here, U represents the 3×3 matrix called Pontecorvo-Maki-Nakagawa-Sakata(PMNS)
matrix [64]. PMNS matrix can be usually described by three unitary matrices asfollows:




c13
0 s13 e−iδCPc12 s12 0100 −s12 c12 0 ,
0 c23 s23  
010(1.10)−iδCP
001
0 −s23 c23−s13 e0c13where the sij = sin θij and cij = cos θij denote the sine and cosine of mixing angle θij
between two distinct mass eigenstates, and δCP represents the charge-parity violatingphase of the CP asymmetry for the lepton sector.
The evolution of the flavor eigenstate over time is described with the energy eigenvalue of each eigenstate for νi as follows:|να (t)⟩ =

3
X
i=1

∗ −iEi tUαie|νi (t = 0)⟩ ,(1.11)

6

Chapter 1. Introduction

and the probability amplitude, Aνα →νβ (t), when a neutrino is produced at a time
t = 0 with the state, is detected at the time t can be described as
Aνα →νβ (t) ≡ ⟨νβ |να (t)⟩X
∗ −iEj t=⟨νβ |Uαj
e
|νj ⟩
j

=

X X

=

X X

=

X

j

j

∗ −iEj t⟨νβ |Uαje
Uγj |νγ ⟩γ=e,µ,τ
∗UαjUγj e−iEj t ⟨νβ |νγ ⟩γ=e,µ,τ
∗UαjUβj e−iEj t .

(1.12)j

Therefore, the flavor oscillation probability Pνα →νβ (t) is expressed as
2Pνα →νβ (t) = Aνα →νβ (t)


!∗
X
X
∗
∗
=
Uαj
Uβj e−iEj t UαkUβk e−iEk t
j

k

=

XX

=

X

j

∗
∗ −i(Ej −Ek )t
UαjUβj Uαk Uβk
e

k
∗
∗
+
Uαj
Uβj Uαj UβjjX∗∗ −i(Ej −Ek )te.
UαjUβj Uαk Uβk(1.13)

j̸=k

In the case that neutrino moves relativistically, the energy difference between twoenergy eigenstates Ei and Ej is denoted as follows:qq
Ei − Ej = p2i − m2i − p2j − m2j
!
!
m2j
m2i
≃ pi 1 + 2 − pj 1 + 2(1.14)
2pi
2pj
m2i − m2j.
=
2E

(1.15)

Here E ∼= |pi | = |pj | represents the neutrino energy of relativistic neutrinos. Withthe transportation distance L = ct, Equation 1.13 can be rewritten as!
XX∆m2jk L∗∗∗∗tPνα →νβ (t) =Uαj Uβj Uαj Uβj +Uαj Uβj Uαk Uβk exp −i
2E
j
j̸=k
X
X
∗
∗
∗
∗
=
Uαj Uβj Uαj Uβj +UαjUβj Uαk Uβk
j

−2

X

j̸=k
∗
∗
Uαj
Uβj Uαk Uβk
sin2

j̸=k

+i

X

∗
∗
Uαj
Uβj Uαk Uβk
sin

j̸=k

= P1 + P2 − 2P3 + iP4 ,!
∆m2jk L4E
∆m2jk L!

2E
(1.16)

7

1.1. Supernova Explosion
where ∆mjk is defined as ∆m2jk = m2j − m2k . P1 and P2 are summarized as
P1 + P2 =

XX
j

=

∗
∗
Uαj
Uβj Uαk Uβk

k

X

∗
(Uαj
Uβj )

X

j

∗
(Uαk Uβk
)

k
2

=

X

∗
Uαj
Uβj

j

(1.17)= δαβ ,

where the δαβ denotes Kronecker delta. Moreover, P3 and P4 can be transformed as
!
2 L
X
∆m
jk
∗
∗
∗
∗
P3 =
(Uαj
Uβj Uαk Uβk+ UαkUβk Uαj Uβj) sin24Ej>k!
X∆m2jk L∗∗=2
Re[UαjUβj Uαk Uβk] sin2(1.18)
4Ej>k!
X∆m2jk L
∗
∗
∗
∗
P4 =
(Uαj Uβj Uαk Uβk − Uαk Uβk Uαj Uβj ) sin
2E
j>k
!
X
∆m2jk L∗∗.
(1.19)= −2i
Im[UαjUβj Uαk Uβk
] sin
2E
j>k

Finally, Pνα →νβ (t) can be denoted using Equations 1.16, 1.17, 1.18, and 1.19 as
Pνα →νβ (t) =δαβ − 4X∗∗] sin2
Re[UαjUβj Uαk Uβk

i>j

+2

X
j>k

∗
∗
] sin
Im[UαjUβj Uαk Uβk!
∆m2jk L4E!
∆m2jk L2E.

(1.20)

From Equation 1.20, it is clear that the neutrino oscillation occurs if any mass eigenstate differs from other states.
From now on, we consider the scenario where neutrinos interact with surrounding
matter. The oscillation effect of neutrinos changes when propagating through matter due to the interactions between neutrinos and matter. This effect is called the
Mikheyev-Smirnov-Wolfenstein (MSW) effect [66, 67, 68], or simply the matter effect.
All three generations of neutrinos undergo neutral-current coherent scattering with
protons, neutrons, and electrons. In addition, only electron-type neutrinos are affectedby the charged-current coherent interaction with abundant electrons in matter. Therefore, the neutral-current interaction does not impact the manifestation of neutrino
oscillation for each flavor since the neutral-current interaction happens in all flavors
with equal probability. Conversely, charged-current interaction influences oscillation
by adding potential VCC to only electron-type neutrinos:√
VCC = ± 2GF ne ,(1.21)

8

Chapter 1. Introduction

where the GF denotes the weak-coupling constant, and ne indicates the number density of electrons in the matter; the ± symbol represents the charge of neutrinos, i.e.,
the positive sign corresponds to neutrinos, while the negative sign corresponds to theanti-neutrinos.
Assuming a two-flavor oscillation νe → νµ , a Hamiltonian can be expressed as
∆m2M
H=
4Eν



− cos(2θM ) sin(2θM ),sin(2θM ) cos(2θM )(1.22)

where ∆m2M denotes the square difference of the effective mass with considering matter
effect, θM symbolizes the effective mixing angle, and Eν represents neutrino energy.
Both ∆m2M and θM are expressed using mixing angle θ and mass difference ∆m2
between νe and νµ asq
2
2(1.23)∆mM = ∆m sin2 2θ + (cos 2θ − x)2
sin2 2θM =sin2 2θ

sin2 2θ + (cos 2θ − x)2√
2 2GF Ne Eν
(x ≡
),
∆m2

(1.24)(1.25)In the case of the two-flavor oscillation of νe → νµ , the survival probability Pνe →νe
and transition probability Pνe →νµ can be expressed as
!
2 L
∆m
M
Pνe →νe = 1 − sin2 2θM sin2,
(1.26)
4E
!
2 L
∆m
M
Pνe →νµ = sin2 2θM sin2.
(1.27)
4E
In the study of neutrino oscillation in a vacuum, six parameters need to be considered: three mixing angles (θ12 , θ23 , θ13 ), two mass-splitting parameters (∆m221 =m22 − m21 , ∆m232 = m23 − m22 ), and a CP violating phase parameter δCP . These areextensively measured primarily through reactor, atmospheric, solar, and long-baseline
neutrino experiments.
θ12 and ∆m221 are measured from solar and reactor neutrino observations, bySuper-K[69], SNO[70], and KamLAND[71] experiments. θ23 and ∆m232 are exploredfrom νµ disappearance measurement by the atmospheric and long-baseline neutrino
experiment such as Super-K[72, 73], T2K[74, 75], NOvA[76, 77] experiments, and soon. θ13 is measured by the reactor experiment such as KamLAND[71], DayaBay[78],Double Chooz[7] experiment, and so on.
The current best-fitted parameters are summarized in Table 1.1 [54].
Neutrino Emission from Core-Collapse Supernova
This section describes the neutrino emissions from CCSN. As described in 1.1.1, an
energy surmounting to E ∼ 1053 erg is emitted from CCSN, with approximately
99% of this energy propagated out by neutrinos. The interaction responsible for theneutrino production varies with the time sequence of CCSN, so here, the emission
processes are described in accordance with this sequence.
1. At the commencement of the collapse
As the core contracts, the Fermi energy of its electrons increases. During this9

1.1. Supernova Explosion
Table 1.1: Best-fitted neutrino oscillation parameters. These values
are taken by [54].

2sin θ12sin2 θ23
sin2 θ13
δCP [deg]∆m221 [/10−5 eV]∆m232 [/10−3 eV]

Normal ordering
0.304 ± 0.012
0.573+0.016−0.0200.02219+0.00062−0.00063
197+27−24
7.42+0.21−0.20+2.517+0.026−0.028Inverted ordering
0.304+0.013−0.0120.575+0.016−0.0190.02238+0.00063−0.00062
282+26−30
7.42+0.21−0.20−2.498 ± 0.028

stage, neutrinos are created by electron capture (Equations 1.3–1.6, and 1.28)
and the photodisintegration (Equations 1.7 and 1.8), which collectively cause thecore to collapse. Initially, after the collapse, the density of the core is relatively
low, allowing neutrinos to escape freely ((3) in Figure 1.2).
e− + A(N, Z) ←→ νe + A(N + 1, Z − 1).

(1.28)

2. Neutrino Trapping
As density increases, the core becomes opaque to the neutrinos. Despite neutrinos having extremely high transparency in the matter, their escape fromthe dense core is delayed due to coherent scattering. When density reachesρ ∼ 1012 g/cm3 , the time scale of neutrinos leaving the core becomes equivalent
to the time scale of the core collapse. The optical thickness τ of the materials
outside the core radius r is defined for the neutrino mean free path lmfp as
Z ∞

1

r

lmfp

τ=

dr.

(1.29)

This formulation implies neutrinos require τ times longer to diffuse than totravel straight forward. The sphere with a radius where τ = 2/3 is specificallytermed the ‘Neutrino Sphere.’ This serves as the boundary of the region where
neutrinos truly interact with matter.
When the density of the core reaches nuclear density, ρ ∼ 1014 g/cm3 , contraction ceases due to the resistance offered by neutron degeneracy pressure, andthe core starts to expand–an event termed ‘core-bounce.’ The expanding core
collides with the outer layers still contracting, which generates a shockwave.
The remaining central core stabilizes and forms a PNS ((4) in Figure 1.2).
3. Neutronization burst
The shockwave heats the core materials, causing nuclei to decompose into nucleons due to photodisintegration (1.7). As the electron capture interaction exhibits
a significantly larger cross-section for nucleons than for nuclei, electron capture
processes proceed rapidly. The electron capture of nuclei can be expressed ase− + p −→ νe + n.

(1.30)

This process can be summarized as the ‘neutronization’ of the core. The neutronization burst lasts for about 1 ms, during which the neutrino luminosity
escapades to 1053 erg s−1 . Given the short duration, the energy emission is≲ 1051 erg, less than 1% of the total energy emission ((6) in Figure 1.2).

10Chapter 1. Introduction
4. PNS Cooling
Post explosion, matter from the outer layers accretes onto the PNS, converting
gravitational energy into thermal energy. This energy is subsequently emitted
as the neutrinos via the following processes, eventually cooling the PNS.
e + +n ←→ ν̄e + p,
e − +e+ ←→ νX + ν̄X ,e± + N ←→ e± + N + νX + ν̄X ,N + N ←→ N + N + νX + ν̄X ,(1.31)γ ←→ νX + ν̄X ,±γ + e ←→ e± + νX + ν̄X .
These processes result in the creation of all types of neutrinos.
Figure 1.3 presents a typical theoretical calculation of the time evolution of theneutrino luminosity and the average energy [1]. The sharp peak caused by the neutronization burst is clearly visible. A complex timing structure persists for the first
1 second, followed by a simpler structure representing the PNS cooling phase. Several analytical approaches focusing on this cooling phase have recently been proposed
based on theoretical expectations-[79, 80, 81].

Figure 1.3: Typical theoretical calculation of timing development of
neutrino luminosity and average energy [1].

Neutrinos Observation from SN1987A
To date, only a single recorded observation of neutrinos from a supernova. In total,
24 neutrinos were concurrently observed by the Kamiokande-II, IMB, and Baksan
experiments [82, 83, 84], during a supernova event dubbed SN1987A, which occurred1.2. Diffuse Supernova Neutrino Background11

in the Large Magellanic Cloud. Figure 1.4 displays the energies of observed neutrinos
as a function of the observed time, recorded by the Kamiokande-II (12 events) andIMB (8 events) experiments. The total energy and timeframe of neutrino emission
derived from SN1987A were confirmed to align with theoretical expectations [85].
Although the theory of supernovae was corroborated, it proved challenging to delve
into the fundamental physics and constrain of the supernova model due to the limited
statistical data. Several next-generation neutrino detectors exist worldwide, includingSuper-Kamiokande, all on the lookout for the next nearby supernova burst to gain
insight into the mechanics of supernovae.

Figure 1.4: Timing and energy distribution of neutrinos observed by
Kamiokande-II and IMB experiments. The figure is taken from [2].

1.2

Diffuse Supernova Neutrino Background

Presumably, neutrinos from all past CCSNe compose the background flux of our universe. This is called ‘Diffuse Supernova Neutrino Background (DSNB)’ or ‘Supernova
Relic Neutrinos (SRNs). ’ Observing this flux could provide us with variable information, not only on the explosion mechanism of CCSN but also on the history of starformation in our universe. This section outlines the theoretical prediction of the SRN
flux based on Ref. [3].

1.2.1

Formulation of SRN Flux

The number density of SRNs at present, which are emitted at redshift z ∼ z + dz
with energies Eν′ ∼ Eν′ + dEν′ , where Eν′ denote the energy at emission timing, can be
described as
dt dN (Eν′ ) ′′dn(Eν ) = RCCSN (z) dz
dEν ,
dz
dEν′

(1.32)

where RCCSN (z) denotes the CCSN rate in unit volume at redshift z, dN (Eν′ )/dEν′denotes the number density of neutrinos from each CCSN, and the variables with aprime sign represent the quantities at the neutrino emission period. The energy isredshifted to Eν′ = (1 + z)Eν and the redshift z is related to the time t based on the12Chapter 1. Introduction

Friedmann equation as
dt
1
p
,
=
dz H0 (1 + z) Ωm (1 + z)3 + ΩΛ

(1.33)

where H0 denotes the Hubble constant, Ωm and ΩΛ indicate the matter density andcosmological constant, respectively. Using the redshift evolution of the CCSN rate
RCCSN (z) and dN (Eν′ )/dEν′ , the flux of SRNs dΦ(Eν )/dEν can be denoted as:dΦ(Eν )
=c
dEν

Z ∞
0

dz
dN (Eν′ )p.
RCCSN (z)dEν′H0 (1 + z) Ωm (1 + z)3 + ΩΛ

(1.34)As the number density of neutrino emission depends on the metallicity Z and theinitial mass M of each progenitor, the SRN flux can be expressed according to [3] asfollows:
Z ∞dΦ(Eν )RCCSN (z)
p
dz
=c
dEν
H0 (1 + z) Ωm (1 + z)3 + ΩΛ0,(1.35)Z MmaxZ ZmaxdN (M, Z, Eν′ )ψIMF (M )ψZF (z, Z)
dM dZ
×
dEν′
Mmin
0
where the ψZF (z, Z) and the ψIMF (M ) represent the metallicity function and the initial
mass function of the progenitor (IMF), respectively. These are normalized as follows:
Z Mmax
ψIMF (M )dM = 1,
Mmin
Z ZmaxψZF (z, Z)dZ = 1.

(1.36)(1.37)

0

Although the flux is formed by all flavors of neutrinos and anti-neutrinos, hereafter,
only electron anti-neutrinos are considered because the experiment generally searches
through the SRN signal as the inverse beta decay of electron anti-neutrinos.

1.2.2

Contribution to the SRN flux

As discussed earlier, the SRN flux comprises various theories, parameters, and models
on neutrinos and galactic cosmology. This section describes the modeling of compositions for SRN flux.
Neutrino Oscillation Effects
The number spectrum of ν̄e , which forms the detection target of SRN for the neutrino
detector, is influenced by the matter effect of neutrino oscillation up to the surface ofthe explosion, and the spectrum is a combination of all flavors, such as:dNν̄0µdNν̄edNν̄0edNν̄0τ
= P̄ee+ P̄µe+ P̄τ e
Eν
Eν
Eν
Eν
0
0
dNν̄e
dNν̄x
= P̄
+ (1 − P̄ ),EνEx

(1.38)

13

1.2. Diffuse Supernova Neutrino Backgroundwhere P̄αe represents the probability that a neutrino with flavor α is converted todNν̄0αPthe electron type (α = e, µ, τ ), satisfying α P̄αe = 1, andindicates the initialEν
number spectrum as a function of M , Z, and Eν when the neutrinos are created in the
supernova, and P̄ = P̄ee denotes the survival probability of ν̄e after traveling throughstellar envelopes and space. As discussed in Section 1.1.3, using the PMNS matrix ofEquation 1.10, the Equation 1.38 can be transformed into:
dNν̄e
dNν̄1
dNν̄2
dNν̄3
= |Ue1 |2+ |Ue2 |2+ |Ue3 |2
dEν
dEν
dEν
dEν
dNν̄1
dNν̄2
dNν̄3
= cos2 θ12 cos2 θ13+ sin2 θ12 cos2 θ13+ sin2 θ13
,
dEν
dEν
dEν

(1.39)

where the Uei (i = 1, 2, 3) denotes the corresponding matrix element noted in Equation 1.10, and dNν̄i /dEν denotes the number spectrum of i-type neutrinos. According to Ref. [86], the lowest energy eigenstate corresponds to ν̄e , and other states inthe supernova core are assumed to be mixtures of the remaining types. Therefore,dNν̄i /dEν can be approximated as dNν̄1 /dEν ∼ dNν̄0e /dEν , dNν̄2 /dEν ∼ dNν̄0x /dEν ,and dNν̄3 /dEν ∼ dNν̄0x /dEν in case of normal hierarchy. These relations result in thefollowing approximation in Ref. [3]:dNν̄edNν̄0edNν̄0x∼ 0.68+ 0.32
.
dEν
dEν
dEν

(1.40)

Comparing with Equation 1.38, P̄ ∼ 0.68 for the normal hierarchy is obtained. In contrast, under the inverted hierarchy, the dNν̄i /dEν can be transformed as dNν̄1 /dEν ∼dNν̄0x /dEν , dNν̄2 /dEν ∼ dNν̄0x /dEν , and dNν̄3 /dEν ∼ dNν̄0e /dEν , based on which
Equation 1.38 can be rewritten asdNν̄edNν̄0x∼,dEν
dEν

(1.41)

where the terms with sin2 θ13 is neglected owing to its negligibly small value. This
results in P̄ = 0, indicating a complete transition. At this instant, the approximation
assumes that the stellar density profiles are not sufficiently steep and do not consider
the breaking of adiabaticity owing to the shockwave propagation. Furthermore, theneutrino-neutrino collective effect in the dense core is neglected.
Modeling of Galaxy Evolution
As described in Equation 1.35, the SRN flux depends on RCCSN (z), and it can be
expressed by a cosmic star formation rate density (CSFRD) (ρ̇∗ (z)) and the IMF
ψIMF (M ) as follows:
R MmaxM

min
RCCSN (z) = ρ̇∗ (z) × R 100M⊙

ψIMF (M )dM

0.1M⊙ M ψIMF (M )dM,(1.42)

where Mmin and Mmax denote the minimum and maximum masses of the progenitor
causing CCSN, respectively. The CSFRD ρ̇∗ (z) denotes the mass density of the star

14

Chapter 1. Introduction

formation for all galaxies at given z and is obtained fromZ ∞ρ̇∗ (z) =Ṁ∗ (M∗ , z)ϕ(M∗ , z)dM∗ ,(1.43)

0where the Ṁ∗ (M∗ , z) indicates the star formation rate of a galaxy (SFR), M∗ denotes
the stellar mass, and ϕ(M∗ , z) represents the stellar mass function (SMF). The measured data and the results obtained using model CSFRD are comparatively presented
in Figure 1.5 as a function of the redshift. According to [3], the differences between
each model increase for z > 0.5, corresponding to the lower energy region of the SRN
flux.

Figure 1.5: CSFRD distribution as a function of redshift. This plot
is taken from [3].

The metallicity of the progenitor affects both star formation and evolution. According to [3], the relation between ψZF (z, Z) and the SFR and SMF can be describedasR M∗ (z,Z)
Z Z
Ṁ∗ (M∗′ , z)ϕSMF (M∗′ , z)dM∗′
ψZF (z, Z ′ )dZ ′ = 0 R ∞,(1.44)′′′
00 Ṁ∗ (M∗ , z)ϕSMF (M∗ , z)dM∗
where M∗ (z, Z) denotes the stellar mass of a galaxy with metallicity Z at redshift z.
Other Contributions to the SRN Flux
The shockwave stalling duration, called the ‘shock revival time,’ affects the SRN flux.
As described in Section 1.1.3, a shockwave is generated during CCSN. Although theshockwave typically stalls only once, it is revived by a specific mechanism. This
revival time is estimated to be O(100) ms from the core bounce. A longer revival
time increases the neutrino emission and neutrino energy because more material isaccreted onto the core, and a significant amount of gravitational energy is released.
The variations in the neutrino number spectra from CCSN with some assumed revival
time are shown in Figure 1.6. The effect is critical for larger energy regions.

1.2. Diffuse Supernova Neutrino Background15

Figure 1.6: Difference of neutrino number spectrum of CCSN with
30M⊙ and Z = 0.02 for a progenitor depending on the shock revival
time. The left, central, and right plots show the spectra corresponding
to νe , ν̄e , and νx (νµ , ν̄µ , ντ , ν̄τ ). This figure is sourced from [3].

The formation of black holes is correlated with the SRN flux. Stars that fail to
explode and become black holes are called ‘failed supernovae.’ In the case of failed
supernovae, the matter accretion continues until black hole formation, and generally,requires a longer period than the standard CCSN scenario. Therefore, the rate ofprogenitors forming black holes contributes to the SRN flux, especially in the higher
energy region. Furthermore, the evolution of galactic metallicity is connected to theblack hole formation rate.
Another significant contribution related to the failed supernovae to the SRN flux
arises from the Equation-Of-State (EOS) of the progenitor and neutron star. A stiffer
EOS results in a larger maximum mass of neutron stars and more substantial massaccretion, leading to a longer black hole formation time. Recent observations [87, 88]
indicate that many stars form binaries with companion stars. These binary interactions, strongly affecting the CCSN rate, especially due to mass transfers and mergers,
must be considered. It is a combined effect of the increasing and decreasing massive
star and black hole-forming star.

1.2.3

Flux Predictions

Various SRN flux predictions have been proposed thus far. In this section, several ofthem are reviewed. The corresponding ν̄e fluxes are summarized in Figure 1.7. The
difference among these flux predictions is approximately one order of magnitude.
• Hartmann+97 [16]To calculate the SRN flux, this model considers the cosmic chemical evolution
in the calculation of the SRN flux. The evolution models are obtained fromobservations of a damped Ly α system.
• Malaney+97 [15]This model calculates the flux, including the redshift evolution of the cosmic
gas, based on the observations of the absorption lines.
• Kaplinghat+00 [14]This calculation aims to minimize the dependence of any model on SRN flux bydirectly associating the supernova rate and its evolution with the observationof the metal enrichment history [89]. This model adopts conservative values forother uncertain parameters to establish a robust upper bound on the SRN flux.

16

Chapter 1. Introduction• Ando+03 [12]This model considers a realistic neutrino oscillation into account for the first timeand uses a numerical SRN spectrum [90] instead of the Fermi-Dirac distribution.
In addition, the normal hierarchy and a vacuum oscillation are considered forthe oscillation. The SRN flux displayed in Figure 1.7 is an updated version
released at the NNN2005 conference [13].
• Lunardini09 [11]This model is the first model that accounted for the failed supernova rate to
the SRN flux and separately considered the SRN flux originating from the failed
supernovae rather than the neutron star-forming supernovae. As such, the flux
from the failed supernovae contributes to the higher energy side and tends tobe more luminous than the nominal supernovae.
• Horiuchi+09 [10]This calculation procedure of this model determines the CCSN rate based on
the cosmic star formation history from the data [91] and cross-checks the various astrophysics and CCSN neutrino emission parameters at that instant. As
depicted in Figure 1.7, the effective ν̄e temperature is assumed to be 6 MeV.
• Galais+10 [9]This research conducted comparative analytical solutions and numerical simulations, suggesting that the shockwave introduces significant modifications to
the SRN flux. Consequently, the flux evaluated upon considering the shockwave
effects is lower than that obtained without considering its effect.
• Nakazato+15 [3]This model considers the black-hole forming failed supernovae, including thecosmic metallicity evolution for the first time. In addition, the model investigates various effects on the SRN flux, such as the CSFRD, shock revival time,and EOS. As observed in Figure 1.7, two predictions estimated with varying
combinations of CSFRD, shock revival time, and EOS were accounted as thelargest and smallest fluxes.
• Horiuchi+18 [8]This model introduces critical compactness, which is a threshold for whether
the core will become a neutron star or a black hole. The SRN flux assuming thecritical compactness ξ2.5,crit = 0.1, is depicted in Figure 1.7.
• Kresse+20 [6]With state-of-the-art simulation, this model considers black hole formation alongwith the contributions from the helium stars to the SRN flux.
• Tabrizi+20 [5]This model considers the effect of additional neutrino transformation inducedby the neutrino decay [92] to the nominal neutrino oscillation theory of it in a
vacuum and the MSW effect, based on the Horiuchi+18 model[8].
• Horiuchi+21 [4]This model assesses the impact of the binary interaction of progenitors forming binary systems, such as mass transfer and mergers, on the SRN flux. In
Figure 1.7, the SRN flux in the case of the envelope parameter αλ, which determines the difficulty of unbinding the envelope, to be standard αλ = 0.1 isshown.

17

DSNB νe Flux [/cm2/sec/MeV]

1.3. Current Status of SRN SearchHoriuchi+21 (Extrapolated, α λ =0.1, NH)
Tabrizi+20 (NS+BH, NH)

10

Kresse+20 (High, NH)
Horiuchi+18 (ξ2.5,crit= 0.1)

Nakazato+15 (Max, IH)
Nakazato+15 (Min, NH)
Galais+10 (NH)1

Horiuchi+09 (6 MeV, Max)
Lunardini09
Ando+03 (updated at NNN05)
Kaplinghat+00
Malaney97−1

10

Hartmann+97

10−2
10−3
10−4

10

20

30

40

50
60
70
νe Energy [MeV]

Figure 1.7: Summary of modern theoretical prediction of SRN
flux [4, 5, 6, 7, 8, 3, 9, 10, 11, 12, 13, 14, 15, 16].

1.3

Current Status of SRN Search

Observation of the SRN can provide valuable information to support and enhance
the theoretical understanding of supernovae and neutrino physics. Despite concerted
efforts by neutrino experiments worldwide to detect the SRN, it is yet to be definitively
identified. As discussed in Section 1.2, most experiments searched the positron signal
via inverse-beta decay (IBD) of electron antineutrinos, as its cross-section is the largest
in the O(10) MeV region (Figure 1.8).
Globally, the Super-Kamiokande (SK) Water Cherenkov experiment and the KamLAND Liquid Scintillator experiment provide the most stringent upper limit on the
SRN flux. For the SK, the first search was performed over 1496 days of live time byfitting the spectrum for various backgrounds and the spectrum shape of each signal
model [93]. The search is limited to the neutrino energy region of Eν > 19.3 MeV
to prevent noise contamination from the large background from the muon spallation
events. This search was updated with a longer exposure of 2853 days and a loweredenergy threshold of Eν > 17.3 MeV by updating the analysis techniques [94]. Since

18

Chapter 1. Introduction

Figure 1.8: Effective cross-section including the resolution andthreshold effect of certain detectors for each process below 60 MeV.
This plot is taken from [17].

2008, an electronics upgrade has enabled longer recording periods after a primary
trigger, as described in Chapter 2. This improvement has facilitated the tagging ofa neutron from IBD interaction and the reduction of large backgrounds in the lowenergy region, especially muon spallation events, which dominate in the energy regionof Eν < 17.3 MeV. Consequently, the first energy binned search with the energy
threshold lowered to Eν > 13.3 MeV was performed for 960 days [48]. The resultof Eν < 17.3 MeV is practically inferior to the KamLAND results [19] owing to thelower statistics associated with the lower neutron tagging efficiency in SK, which isapproximately 20%. Similarly, due to lower statistics in the energy region above 17.3
MeV, the limit was also inferior to the spectral analysis result of the combination of
SK-I, II, and III.
The SRN search for SK during the pure water period was completed in 2021 witha live time of 2970 days along with neutron tagging [20]. The result is comparablewith KamLAND results [19] in the region of Eν < 17.3 MeV and the SK spectral
analysis results [94] observed at Eν > 17.3 MeV. In addition, the upper limits fromthe SK spectral analysis were also calculated for the modern SRN flux models over
5823 days of live time without neutron tagging. The result showed that the Totani+95
model [95] and the most optimistic prediction of the Kaplinghat model [14] could be
excluded with above a 90% confidence level (C.L.). The upper limits on the ν̄e flux
from the experiments are displayed in Figures 1.9 and 1.10.

1.3. Current Status of SRN Search

Figure 1.9: Upper limits on ν̄e flux from SK, KamLAND, and theBorexino experiment [18]. This figure is taken from [19].

Figure 1.10: Upper limits on ν̄e flux from the SK [20].

19

21

Chapter 2

Super-Kamiokande
The Super-Kamiokande (SK) detector is the world’s largest underground water Cherenkov
detector[22].

2.1

Detection Principle

When a charged particle passes through a dielectric medium with a refractive index
of greater than 1, at a velocity surpassing the speed-of-light within the medium, anelectromagnetic shock, termed ‘Cherenkov radiation,’ transpires.
v>

c
,
n

(2.1)

where v denotes the velocity of the charged particle and n indicates the refractive
index of the medium. The energy of the radiation light prevails in the optical region,and it is emitted in the cone shape with the half angle θC , which is calculated ascos θC =

1
,
nβ

(2.2)

where β represents the ratio of the velocity of charged particles to the speed of light ina vacuum; n of the ultrapure water in the SK is ∼ 1.33. Thus, the θC for an electronis ∼ 42◦ because the speed of the electron can be approximated to the speed of light.
In contrast, heavier particles such as muons and charged pions travel at speeds lower
than electrons owing to their mass. Thus, the θC tends to be smaller than that ofelectrons. Based on Equation 2.1, β for the charged particles exhibit a minimum speedwith Cherenkov emission (βthr ):βthr =

1
,
n

(2.3)

Therefore, a threshold Ethr exists for the minimum energy of the charged particle(called ‘Cherenkov threshold’), expressed as
mc2
Ethr = mc2 γ = p,
1 − 1/n2(2.4)

where γ denotes Lorentz factor, γ = (1 − β 2 )−1/2 , and m indicates the mass of thecharged particle.
The number of emitted photons N can be expressed in the form of a derivative ofunit length L and photon wavelength λ as


d2 N
1
1
= 2πα 1 − 2 2
,
(2.5)
dLdλ
n β
λ2

22

Chapter 2. Super-Kamiokande

where α indicates the fine-structure constant. Thus, the number of Cherenkov photons
for the SK can be estimated to reach hundreds per centimeter.

2.2

Super-Kamiokande Detector

2.2.1

Detector Overview

The SK detector is situated at a depth of 1,000 m (2,700 m water equivalent) beneath
Mt. Ikenoyama in Gifu Prefecture, Japan. Owing to the 1,000 m of overburden
above the detector, the cosmic-ray muon background is diminished by a factor of
10−5 relative to the mountain’s surface. The detector comprises a cylindrical tankwith a 39.3 m diameter and 41.4 m height. The tank accommodates 50 kilotons
of ultrapure water, serving as both the target material and dielectric medium for
Cherenkov radiation. The layout of the detector is depicted in Figure 2.1.

Figure 2.1: Schematic of view of the SK detector (cutaway view).
This figure is taken from [21].

The water tank of the SK is optically partitioned into an inner tank (ID) andan outer tank (OD), with approximately 60 cm width of a stainless steel structure
separating the ID and the OD. The ID has a diameter of 33.8 m and a height of 36.2 m,with a total water mass of approximately 32.5 kilotons. Additionally, 11,129 20-inch
photomultiplier tubes (PMTs) are mounted on the ID wall, top, and bottom structures
directed inwards. The photo-cathode coverage for the entire ID surface is ∼ 40%.
The gap between each PMT is concealed by a black sheet that exhibits minimal lightreflectance and restricts the reflection of light on the ID surface. Consequently, ID
and the stainless-steel structure remain optically isolated.
The thickness of the OD is ∼ 2 m, encompassing a total water mass of ∼ 17.5 kilotons. In total, 1,885 8-inch PMTs are affixed to the ID-OD separation structure,oriented outwards. The inner surface of the OD is covered by a white Tyvek sheet,
exhibiting high photon reflectivity, on the OD side, and a black sheet on the opposing
side. Similar to the gaps between PMT, those between the OD and the stainless-steel
structure are also optically separated by the white Tyvek and black sheets. Additionally, the photon collection efficiency is enhanced by the elevated reflectivity of2.2. Super-Kamiokande Detector

23

the Tyvek sheet. A structure comprising 12 ID PMTs, 2 OD PMTs, an OD Tyvek
sheet, and an ID black sheet is termed a Super-Module. The schematic cross-sectionalviews of the ID, OD, and separation structure for the top, side, and bottom of theSuper-Module, are displayed in Figure 2.2.

Figure 2.2: Overall schematic of SK (Left) and magnified to eachface of the support structure (Right)[22].

2.2.2

History of SK phase

The SK experiment commenced in April 1996, with the observational phase segmented
into seven periods: SK-I through SK-VII. Each period is distinguished by alterationsin the geometry, electronics, and post-dissolution of gadolinium. The state of thedetector for each phase is summarized in Table. 2.1
SK-I
SK-I commenced in April 1996 and was terminated in July 2001, employing the initial
electronics system called ATM. During this period, certain preliminary observational
results were published regarding solar and atmospheric neutrinos and the search for
proton decay search within the SK. Most notably, the evidence demonstrating neutrino
oscillation for the atmospheric neutrinos was revealed, which is deemed as one of theworld’s most significant results.
In July 2001, the replacement work for damaged PMTs was conducted. However,on November 12, 2001, a PMT at the bottom imploded, triggering a chain reactionthat destroyed more than half of the PMTs–approximately 7,900 in total.

24

Chapter 2. Super-Kamiokande

SK-II
Following the accident, the experiment was temporarily halted. The remaining ID
PMTs were relocated during this pause, and new OD PMTs were installed. Additionally, each ID PMT was encased in an acrylic and Fiberglass Reinforced Plastic (FRP)
case, enhancing the water pressure resistance of PMT and mitigating the risk of chain
destruction if damage occurred. The part covering the photo-cathode is constructedfrom high-transparency acrylic, whereas its other components are fabricated from
FRP. An image of the case is displayed in Figure 2.3. The experiment resumed in October 2002 with 5,182 ID PMTs in place, amounting to 19% photo-cathode coverage.
This period is known as SK-II.

Figure 2.3: Image of the shockwave prevention case for 20-inch PMT

SK-III
Between SK-II and SK-III, new ID PMTs were manufactured and installed. SK-III
commenced in July 2006, at which point 40% of photo-cathode coverage was recovered.
During this period, 17 ID PMTs installed at the top and bottom edges of the tankduring SK-I were removed due to the conflict with the acrylic cover. Consequently,
the SK has operated with 11,129 ID PMTs and 1,885 OD PMTs from this period
onward.
SK-IV
In September 2008, a new data acquisition(DAQ) system known as QBEE was installed instead of the ATM, enabling the recording of extended PMT signal time
windows for neutron search. The specifications of the QBEE are described in Section 2.4.
SK-V
In May 2018, a tank refurbishment was initiated in preparation for loading gadolinium
into the SK tank. The process was completed by the end of January of the following
year, initiating the new SK-V phase. Various preparations for the forthcoming SK-Gd25

2.2. Super-Kamiokande Detector

experiment were carried out during this period, such as changes to the water flow,
water leakage repairs, and PMT replacements.
SK-VI
In July 2020, the SK experiment was reincarnated as the ‘SK-Gd’ experiment byloading 13 tons of Gd2 (SO4 )3 · 8H2 O, equivalent to about 0.011 ppm of Gd, into theultrapure water of SK. Loading Gd enhances the neutron signal, achieving higher
neutron identification efficiency than in the previous period. This phase continued
until the end of May 2022 and is referred to as SK-VI.
SK-VII
From June 2022, three times the amount of Gd was loaded into the SK detector,
concluding the loading process in July. The additional loading increased the neutron
capture fraction on Gd to approximately 1.5 times higher than that in SK-VI. This
period is designated as SK-VII.
Table 2.1: The detector situation for each observation period of SK.

Phase
Start
End
Live days
Num. of ID PMT (Coverage)
Electronics
Analysis threshold
Phase
Start
End
Live days
Num. of ID PMT (Coverage)
Electronics
Analysis threshold

2.2.3

SK-I
Apr. 1996
Jul. 2001
1496 days
11146 (40%)
5 MeV

SK-IV
Sep. 2008
May. 20183235 days

SK-II
Oct. 2002
Oct. 2005
791 days
5182 (19%)
ATM
7 MeV

SK-III
Jul. 2006
Aug. 2008
548 days11129 (40%)
4.5 MeV

SK-V
SK-VI
Feb. 2019 Jul. 2020
Jul. 2020 May. 2022
530 days
623 days11129 (40%)
QBEE
3.5 MeV

SK-VII
Jun. 2022––

ID PMT

The PMT used on the ID is the Hamamatsu R3600, produced by Hamamatsu Photonics K.K. This PMT has a diameter of 20-inches (about 50 cm). Figure 2.4 provides
an overview of the Hamamatsu R3600 PMT. The photocathode of the PMT consistsof bialkali(Sb-K-Cs), which offers excellent quantum efficiency for the wavelength of
Cherenkov light. The sensitivity range of this PMT extends from 280 to 660 nm,
and the quantum efficiency (QE) peaks at about 22% at the peak of ∼ 390 nm, as
illustrated at the top of Figure 2.5.
The average collection efficiency at the first dynode is around 70%, and the PMT
gain is approximately 107 at around 2000 V of HV. The transit time is roughly 10
ns, with a relative spread of about 2.2 ns at one sigma. The nominal distribution of
the transit time can be observed in the bottom left panel of Figure 2.5. The single
photo-electron (p.e.) peak is visible in the ADC charge distribution, depicted in the

26

Chapter 2. Super-Kamiokande

Figure 2.4:

Overview of Hamamatsu R3600 used for SK ID
PMT [22].

bottom right panel of Figure 2.5. The distributions illustrated in Figure 2.5 wereobtained from tests conducted with the 410 nm wavelength light.

Counts / binCounts / bin

1σ = 2.16 ns

Relative transit time(ns)ADC count

Figure 2.5: Wavelength dependence of QE (top), distribution ofrelative transit time (bottom left), and ADC charge count distribution(bottom right) for Hamamatsu R3600 PMT [22].

2.2.4

OD PMT

The PMT installed on the OD surface has a diameter of 8 inches (about 22 cm).
These were repurposed from the IMB experiment [96] during the SK-I period. Afterthe 2001 accident, most of OD PMTs were replaced with new ones, the Hamamatsu
R5912. These PMTs are of similar size and possess comparable photon sensitivity

2.2. Super-Kamiokande Detector

27

characteristics to the IMB PMTs. To compensate for the smaller coverage of OD
PMT, each PMT is affixed to a wavelength shifter (WS) plate measuring 60 cm ×60 cm × 1.3 cm. The WS is an acrylic plate impregnated with 50 mg/L of bisMSB(C24 H22 ), which absorbs light in the wavelength of ultraviolet range and emits
light in the blue to the green range, which is close to the peak of QE for the OD PMT.
Thanks to the WS, the collection efficiency of the OD increases to 60%. However, thetiming resolution has decreased from 13 ns to 15 ns. Presently, 1,275 OD PMTs areevenly distributed on the OD walls, with 308 on the bottom and 302 on the top. An
overview of the OD PMT setting and the relationship between ID and OD PMT is
illustrated in Figure 2.6.

Figure 2.6: Relationship between ID PMT and OD PMT [23].

2.2.5

Compensation Coils

The photo-electron emitted on the surface of the photocathode is collected by theelectric field of the PMT. During this process, the geomagnetic field can affect thecollection efficiency. To mitigate this effect, 26 sets of coils are wound around thetank to compensate for the geomagnetic field within the tank. Thanks to these coils,
the magnetic field within the tank is kept below 100 mG. The schematic view of thecompensation coils is illustrated in Figure 2.7.

28

Chapter 2. Super-Kamiokande

Figure 2.7: Schematic view of compensation coils wounding the SK
tank [24].

2.3

Water and Air purification system

2.3.1

Water purification

Water system at SK-IV
Until the end of the SK-V phase, the SK tank was filled with ultrapure water transported from the Kamioka mine. Dust, radioactive contaminants, and bacteria cancause low-energy background events and degrade water transparency. As a result,a water purification system is implemented, circulating water at a rate of roughly
60 tons/hour to eliminate these impurities. Since the water flow and PMT noise rates
are highly sensitive to the water temperature, the system maintains the water at approximately 13◦ C. The schematic of the water purification of SK-IV is illustrated in
Figure 2.8.
The flow of water purification is detailed as follows:• 1 µm mesh filter: Removes dust and larger impurities• Heat exchanger (HE): Exchange heat from the water circulation pump and maintain the water temperature at approximately 13 ◦ C. This aids in preventing increased PMT dark noise, stabilizing water flow, and hindering bacteria growththat occurs at high water temperatures.
• Ion exchanger: Eliminates heavy ions that can decrease water transparency,
including radioactive contaminants.
• UV sterilizer: Kills bacteria present in the water by irradiating ultraviolet light.
• Radon-free Air Dissolving system: Dissolves radon-free air into the water toenhance the radon removal efficiency in the subsequent vacuum degasification
step.

2.3. Water and Air purification system

29

Figure 2.8: Schematic diagram of the water purification system in
SK-IV. This figure is taken from [25].

• Reverse Osmosis filter(RO): Further removes organic contaminations with molecular weights of about 1000.
• Vacuum degasifier: Removes gases dissolved in the water with an efficiency of
96% for radon and 99% for oxygen gas.
• Ultra filter(UF): Removes small particles that are larger than the size of 10 nm.
• Membrane Degasifier: Reduces the radon gas dissolved in the water with anefficiency of approximately 83%.
After these steps, the radon concentration in the supply water entering the SK
tank is estimated to be 1.74 ± 0.14 mBq/m3 , whereas that of the return water is
9.06±0.58 mBq/m3 . The water resistivity entering the purification system is typically
11 MΩ · cm. However, because of these meticulous purification steps, the resistivityof water entering the SK tank increases to about 18.2 MΩ · cm.
Water system from SK-V
In the SK-V phase, the water purification system was entirely revised in preparation
for the subsequent SK-Gd experiment. Figure 2.9 illustrates the new water circulation
system for SK-Gd. In this experiment, it is crucial to eliminate contaminants at thesame level as in the SK-IV phase, while preserving the gadolinium and sulfate ionsdissolved in the water.
During the Gd-dissolving process, a high-concentration Gd solution first passes
through the pretreatment system. This system comprises three filters, UV light, andIon-exchange resins (yellow dotted box in Figure 2.9). The ion exchanger (Anion andCation resins) used in SK-Gd is specifically designed to prevent the loss of dissolved
gadolinium and sulfur ions. The main recirculation system is branched into two identical parts, each with a water flow capacity of ∼ 60 m3 /h. The water flow rate canbe controlled up to 120 m3 /h using both branches. The design also allows continuous
circulation with one line while the other is under maintenance.

30

Chapter 2. Super-Kamiokande

Figure 2.9: Schematic of SK-Gd water system. This figure is takenfrom [26].

2.3.2

Air purification system

As the rock is Rn-rich, the air in the mine is abundant in Rn gas, substantially morethan the Rn gas concentration in the air outside of the mine. Radon gas concentrationsin the mine air fluctuate between 1000 and 2000 Bq/m3 during summer and between
100 and 300 Bq/m3 during winter because of the variation in airflow inside the mine
induced by the outside temperature. Accordingly, the air purification system is utilized
to reduce Rn in the air inside the mine and produce Rn-free air. This system comprises
three compressors, a buffer tank, dryers, filters, and activated charcoal filters, and it
reduces the Rn concentration in the Rn-free air to < 3 mBq/m3 . Post-purification,
Rn-free air is introduced into the space between the water surface and the top of theinside of the SK tank.

2.4

Electronics and Data Acquisition

The electronics for data acquisition were uploaded from SK-IV to a new system named
QBEE [28]. The data used in this study were acquired during the period of these newer
electronics. Thus, the detailed explanations of the older ATM system are omitted.

2.4.1

Electronics and DAQ from SK-IV

From SK-IV, the DAQ system was switched to QTC-based Electronics with Ethernet (QBEE), replacing the older Analog-Timing-Module (ATM). Figures 2.10 and 2.11
provide schematic diagrams of the QBEE electronics and the entire DAQ system of SK.

31

2.4. Electronics and Data Acquisition

Each QBEE module is fitted with eight QTCs designed for Application-Specific Integrated Circuits (ASIC) [27]. Each QBEE processes 24 PMT signals because each QTC
has three channels. When a charge, exceeding the threshold equivalent to 1/4 p.e.,
is sent to a QBEE module, the QTC integrates the charge and emits a rectangularpulse proportional to the integrated charge. The leading edge of the pulse signifies
the timing of the signal. Each QTC has three different gain ranges, labeled ‘Small,’‘Medium,’ and ‘Large,’ to enhance charge resolution and expand the charge range
from ATM. The gain ratio for each gain range is set at 1, 1/7, and 1/49. The total
charge range is 0.2–2500 pC, roughly five times larger than the ATM module. The
detectable dynamic ranges, including the charge resolution for each range, are listed
in Table 2.2.
The pulse generated in QTC is transmitted to the TDC and digitized. The digitized charge and timing information is then processed by an FPGA before beingtransmitted to the front-end PC via Ethernet, as depicted in Figure 2.11. These
front-end PCs are connected to Merger PCs via a 10-Gigabit Ethernet cable. Thisconnection initiates the event-building process, during which a software trigger is applied to signals, and selected candidates are used for analysis. Ultimately, the event
information is gathered by the Organizer PC and stored on the Disk.

Figure 2.10: Schematic of the DAQ system with QBEE[27].

Table 2.2: Detectable dynamic range and charge resolution for eachrange.

Gain channel
Small
Medium
Large

2.4.2

Dynamic range [pC]
0.2-51
1-357
5-2500Charge resolution [pC/Count]
0.1
0.7
4.9

Software Trigger

With the high-speed signal digitization capabilities of the QBEE system, all PMT hits
can tentatively be collected on the merger PC. As a result, the signals gathered in the
Merger PC can be processed by the software trigger and formed into an event. The
software trigger initiates a trigger when the number of hits within a 200 ns window,
corresponding to the time for light to travel from one edge of the tank to the other,exceeds a specific threshold. There are four types of triggers for ID: SHE(Super High

32

Chapter 2. Super-Kamiokande

Figure 2.11: Schematic of the DAQ system with QBEE[28].

Energy), HE(High Energy), LE(Low Energy), SLE(Super Low Energy), and one OD
trigger. Table 2.3 displays the standard trigger conditions in SK-VI. When a trigger
is issued, all hits from −5 µsec to +35 µsec are recorded for SHE, HE, and LE, as alarger time window makes it easier to efficiently tag subsequent signals such as Michelelectrons from muon decays. Due to their high rate, only PMT hits around 1.5 µsec
are saved for SLE events.
A special trigger, AFT, was implemented from SK-IV onward to save delayed
neutron capture signals. Following the issuance of the SHE trigger, a 500 µsec window
opens, during which all hits are recorded. To conserve data capacity and transfer rate,
the AFT trigger is issued only after an event with the SHE trigger and without the OD
trigger, i.e., the trigger is not issued by muon until SK-IV. The AFT rate limit is set to50 Hz, as this trigger was originally designated for the Inverse-Beta decay of electron
anti-neutrinos. However, owing to increased interest in neutron events caused by muon
events, including muon spallation, the condition of no OD trigger was removed fromthe AFT trigger conditions from the commencement of SK-V. Moreover, the limit of
the AFT rate was further broadened by upgrading the online system from the middleof SK-VI onwards.
Table 2.3: Threshold for each type of trigger in SK-VI

Trigger type
SLE
LE
HE
SHE
OD

N200 Threshold [/µsec]
34
49
52
60
22(Only OD)

Event window [µsec]
1.5 [-0.5,+1.0]
40 [-5,+35]
40 [-5,+35]
40 [-5,+35]
40 [-5,+35]

Trigger rate [Hz]3.0-4.0
80
30
3
2

33

Chapter 3

Simulation
This chapter describes the Monte Carlo (MC) simulation and the tools used in the SK
analysis. The events studied in the SK are divided into low-energy and high-energy
events, with the boundary set at an energy level of approximately 100 MeV. The
simulation stage of a neutrino event is divided into three primary parts: neutrino flux
calculation, neutrino interaction, and detector simulation. Notably, the neutrino flux
calculation and neutrino interaction components are characteristic of each event type.

3.1

Simulation for High-Energy Neutrino Event

High-energy neutrino events are predominantly composed of Atmospheric neutrinos,
making their simulation complex due to various types of neutrinos and secondary
products that span a wide energy range. The main visible energy range for the
DSNB search is around a few tens of MeV. However, some events resulting from theatmospheric neutrino interaction and subsequent secondary interaction extend into
the search region. Hence, precisely simulating of the atmospheric neutrino events is
crucial for the DSNB search.

3.1.1

Atmospheric neutrino flux

Atmospheric neutrinos are produced in the Earth’s atmosphere via the decay of mesons
and muons from cosmic rays, as illustrated in Figure 3.1. Despite various atmospheric
neutrino flux models, the flux calculation for the SK is based on the Honda-KajitaKasahara-Midorikawa(HKKM) model [97, 98, 99, 33, 29]. This model primarily comprises three parts: primary cosmic-ray flux, hadronic interaction models, and a virtual
detector.
Primary cosmic-ray
The primary cosmic-ray flux has been measured by several experiments to date. The
flux below 100 GeV is accurately estimated by the BESS experiment [100, 101] and the
AMS experiment [102]. For flux above 100 GeV, the flux curve is effectively calibrated
by data obtained from the emulsion chamber [103, 104]. The primary cosmic-ray flux
at the Earth’s surface is influenced by solar activity. Given the periodicity of solar
activity, the cosmic-ray flux is classified by high and low activity periods. Depending
on solar activity intensity, cosmic rays at around 1 GeV can fluctuate by a factor of 2
or more, while at 10 GeV and above, the difference is about 10%.
Additionally, the incoming cosmic-ray particles are influenced by the geomagnetic
field. This effect is calculated based on the position and direction of the incoming
particle, and the calculation employs the IGRF2005 model https://www.ngdc.noaa.
gov/IAGA/vmod/igrf.html. The cosmic rays penetrating the atmosphere interact

34

Chapter 3. Simulation

primary cosmic-ray
Earth's atmosphere

π ±,

±

μ±
±

𝖾
𝖾

𝖾

νμ(ν̄μ)ν (ν̄ )

𝖪

Figure 3.1: Illustration of atmospheric neutrino production.

with air molecules, primarily generating mesons. The calculation adopts the U.S.
standard’76 model for the atmospheric environment. This model provides atmospheric
data such as pressure, temperature, density, and viscosity, encompassing a vast rangeof altitudes and elevations globally.
Hadronic interaction
Two models for cosmic-ray interaction with molecules are implemented, with 32 GeV
as the dividing line. Below 32 GeV, the JAM model [105] is utilized, whereas above
32 GeV, the DPMJET-III [106] is applied for calculation. The JAM model is a
hadronic cascade model employed for Particle and Heavy-Ion Transport code Systems (PHITS) [107]. DPMJET-III is a code system based on the Dual Parton Model(DPM) [108] capable of calculating interactions such as those involving hadrons above
a few GeV, nuclei, and high-energy photons. The JAM, DPMJET-III, and the resultsof the Hadron Production (HARP) experiment are comparatively presented in Figure 3.2 [109, 110]. The HARP experiment examined the hadronic interactions ofprotons on N2 and O2 targets at a few GeV/c momentum regions.
The mesons resulting from the hadronic interaction of cosmic rays further decay into secondary muons referred to as cosmic-ray muons. The flux of cosmic-ray
muons from the simulation is compared with some experimental results. The flux ofcosmic-ray muon was measured by BESS [101][111] and L3+C experiment [112]. The
DPMJET-III was refined based on these results. Figure 3.3 displays the comparisonof the flux of cosmic-ray muon between various experimental data and simulation,
displaying an agreement within 10% for the 1–100 GeV range.
Neutrino Flux at the SK
Figure 3.4 illustrates the zenith angle dependence of the atmospheric neutrino flux
at the Kamioka site, computed using the Honda flux model. The peaks depicted
in Figure 3.4 are due to the greater travel distance for muons and pions from thehorizontal than the vertical direction. The up-down asymmetry in the lowest energy
region is induced by the geomagnetic field for the charged cosmic-ray particles.

3.1. Simulation for High-Energy Neutrino Event

35

Figure 3.2: Comparison between HARP data and the theoretical
calculations of JAM and DPMJET-III for the cross-section of pion
production. The figures are taken in [29].

The spectra of the atmospheric neutrinos coming to Kamioka using various models
are displayed in Figure 3.5. Since the cosmic-ray muon, which is the source of electron
neutrinos, reaches the Earth’s surface before decaying into electron neutrinos, a faster
drop in electron neutrinos appears in the higher energy region as depicted in Figure 3.5.
The atmospheric neutrino events are simulated based on the expected flux at
Kamioka. It should be noted that the neutrino oscillation effect is not considered at
this stage. It is assumed that the neutrino created in the atmosphere reaches theSK while maintaining its original flavor. Then, the neutrino oscillation effect is taken
into account by calculating weight based on the latest neutrino oscillation analysis
result [72] for each MC event at the analysis stage.
The oscillation parameters used in this study are listed as follows:∆m221 = 7.53 × 10−5 eV2 (fixed in fit)

(3.1)

∆m232 = 2.50 × 10−3 eV2 (fixed in fit)sin2 θ12 = 0.304 (fixed in fit)sin2 θ13 = 0.0219 (fixed in fit)sin2 θ23 = 0.588 (fitted)(3.2)

δCP = 4.18 (fitted)

(3.3)
(3.4)
(3.5)
(3.6)

36

Chapter 3. Simulation

Figure 3.3: Comparison of muon flux between the theoretical calculations and experimental data. Dashed line represents the sum of
the error in the calculation and observation at Mt. Tsukuba (bluesquares), at Mt. Norikura(red triangles) using the BESS detector,
and at CERN using the L3 detector(black circles). Results from the
DEIS experiment [30] and MUTRON experiment [31] are presented aswell. The figure is taken from [32].

Figure 3.4: Zenith angle dependence of atmospheric neutrino flux,
averaged over all azimuthal angles, for Kamioka. Here the θ is thezenith direction of coming neutrinos. The figure is taken from [29].

3.1.2

Neutrino Interaction

The neutrino interaction at the SK is calculated based on NEUT [36] [113]. NEUT
manages the neutrino interaction with the water (H2 O) and the rocks around thedetector (SiO2 ) as the target material for the energy range of a few tens MeV to a

3.1. Simulation for High-Energy Neutrino Event

37

Figure 3.5: Comparison of the atmospheric neutrino flux for some
calculations: Honda prediction(solid red), previous Honda model(bluedotted-dashed line) [33], Bartol model[34], and the Fluka model[35].
The figure is taken from [29].

hundred TeV. The interaction with the electron is disregarded in the calculation since
the cross-section is 10−3 smaller than the interaction with the nucleus.
The neutrino interaction is primarily categorized into two types: charged-current(CC) and neutral-current (NC) interactions. Although the flavor of neutrinos can be
identified based on the types of charged lepton produced for the CC interaction, no
information regarding the neutrino flavor will be retained on NC interaction as no
charged leptons are produced. In the NEUT, five reactions are evaluated based on
CC and NC interaction.
• CC/NC (Quasi-)inelastic scattering: νℓ + N → ℓ + N ′ ,• CC meson exchange interaction: νℓ + N N ′ → ℓ + N ′′ N ′′′ ,• CC/NC single meson production: νℓ + N → ℓ + N ′ + M eson,• CC/NC deep inelastic scattering: νℓ + N → ℓ + N ′ + Hadrons,• CC/NC coherent pion production νℓ + N → ℓ + N ′ + pion,
where N, N ′ (N ′′ , N ′′′ ) represent the nucleon states before and after an interaction,and ℓ denotes a lepton and neutrino.
The flavor of the original neutrino flux produced in the atmosphere is composedof only muon and electron types. Nonetheless, the tau neutrino also arrives at the SK
because of neutrino oscillation. The CC interaction of tau neutrino occurs beyond a
few GeV of energy owing to its large mass (1.78 GeV/c2 ). Consequently, the numberof tau neutrino interactions is significantly smaller than that of electron neutrinos
and muon neutrinos. The production and decay of tau particles are calculated using
TAUOLA [114].

38

Chapter 3. Simulation

Elastic and Quasi-elastic Scattering
NC elastic scattering is a process wherein a neutrino scatters and transfers momentum
to the target nucleon, without generating any new particles. Conversely, CC quasielastic scattering process (CCQE) results in a charged lepton and modifies the target
nucleon, conserving charge and momentum but not leading to fragmentation. NC
elastic and CCQE interactions can be represented as follows:
NC elastic scattering : νℓ (ν̄ℓ ) + N → νℓ (ν̄ℓ ) + N ′ ,′CCQE : νℓ (ν̄ℓ ) + N → ℓ(ℓ̄) + N .

(3.7)
(3.8)

The CCQE interaction in NEUT is calculated by [115], and the differential crosssection can be expressed as"#
2dσ CCQE M 2 G2F cos θC2
2 s−u
2 (s − u)=A(q ) ∓ B(q )+ C(q )
,
(3.9)
dq 2
8πEν2
M2
M4
where the Eν denotes the energy of the incoming neutrino, M represents the massof the target nucleon (∼ 0.938 GeV), GF represents the Fermi coupling constant(=
1.1663787 × 10−5 GeV−2 ), θC indicates Cabibo-angle, q = qℓ − qν accounts for the
momentum transfer, m denotes the lepton mass, and s, u denote the Mandelstam
variables. Definitions of A, B, and C are referred from [115]. Furthermore, therelativistic Fermi gas model [116] is used for the neutrino-nucleon interaction at theboundary of the oxygen nucleus. Figure 3.6 presents a comparison of the cross-section
for CCQE scattering interaction among NEUT computation and certain experimental
results.

Figure 3.6: Cross-section of CCQE scattering of muon neutrino (leftpanel) and anti-muon neutrino (right panel). Lines denote the NEUT
calculation for the free target (solid) and the bound target(dashed).
Data points are taken from ANL (crosses), BNL (triangles), SKAT
(stars), Serpukhov (asterisks), and GGMs (circles). The figures aretaken from [36].

CC Meson Exchange Interaction
The calculation of the CCQE scattering interaction outlined above is based on an
approximation that there are no relations among individual nucleons in a nucleus.
However, it is necessary to account for the interaction between a neutrino and multiple nucleons simultaneously. The Mini-BooNE results suggests the existence of this3.1. Simulation for High-Energy Neutrino Event

39

process [117]. Thus, the meson exchange current (MEC) model deviseed by Nieves etal. [118] is integrated into NEUT. This is a prominent model that expands the existing
CCQE model. The incident neutrino interacts with a pair of nucleons as follows:νℓ + N N ′ → ℓ + N ′′ + N ′′′ ,(3.10)

where N , N ′ , N ′′ , and N ′′′ denote the nuclei before and after interaction. Althoughother multi-nucleon correlations may exist for any neutrino interaction on a bound of
the nucleon, only the CC MEC interaction is considered in the NEUT calculation.
Single Meson Production
A nucleus can exist in the baryon resonance state, resulting in the production of asingle meson for the final state, as follows:ν + N → ℓ(ν) + N ∗ ,∗′N → N + meson,(3.11)(3.12)

where N ∗ represents the baryon resonance state, and a meson emerges as the final
state of N ∗ . When the invariant mass in the hadron system W is less than approximately 2 GeV/c2 , this process becomes the primary mechanism for hadron production. Above 2 GeV/c2 , the interactions are simulated as deep inelastic scattering,which will be described in the following section. The process in NEUT is grounded in
the Rein-Sehgal [119] model, and an enhanced model that includes the lepton mass
correction [120] has also been incorporated. New form factors have since been developed [121] and employed in NEUT. The angular calculation for the interaction leading
to an intermediate state ∆(1232), the primary channel of single pion production, isbased on Rein’s prescription [122]. For other channels, the angular distribution ispresumed to be uniform.
Deep Inelastic Scattering
The interaction of the neutrinos with the quarks composing nucleons results in multiple hadrons via CC deep inelastic scattering (DIS). This process is dominant for
W > 1.3 GeV/c2 in NEUT calculation. When W > 2 GeV/c2 , all interactions producing at least one meson are simulated by PYTHIA/JETSET [123]. For interactions
with W < 2.0 GeV/c2 , only pions are produced as the hadrons in the final state. To
prevent double counting with single meson production, only multiple pion production
is considered in this mass region. The nucleon structure is modeled based on the
Parton Distribution Function. The default function is derived from the GRV98 [124]and corrected by the Bodel and Yang model [125].
Coherent pion production
The process of pion production interaction with the whole oxygen nucleus, preserving
charge, is referred to as coherent pion production interaction. This interaction can be
defined as follows:ν + 16 O → ℓ + 16 O + π,

(3.13)

Until the previous NEUT version 5.3.6, this process had been simulated based on
the Rein-Sehgal model [126]. However, the interaction model was updated to theBerger-Sehgal model [127], incorporating improved elastic pion-carbon cross-section

40

Chapter 3. Simulation

data and considering the lepton-mass effect. This improvement allows NEUT to apply
this interaction to neutrinos with energies below 10 GeV. Due to the low momentum
transfer to the oxygen in this interaction, both the produced lepton and pion tend tomove in forward directions.

3.2

Simulation for the IBD-like Event

3.2.1

DSNB Signals MC creation

Although all three flavors of neutrinos and their anti-neutrinos are emitted from supernovae, as described in Section 1.2, the most detectable signal in SK is the inverse-beta
decay (IBD) of the electron anti-neutrinos (ν̄e + p → e+ + n) owing to its largest
cross-section below 30 MeV, as depicted in Figure 1.8. As described in Section 1.2.3,
various SRN flux shapes are proposed, and it is challenging to create DSNB signal
MC simulations for each flux model. Therefore, the DSNB signal MC simulation is
produced uniformly in the positron energy and isotropically for the positron and neutron directions across the entire ID. The energy will later be normalized by the actual
fluxes derived from model predictions. This normalization considers the differential
cross-section of IBD, referred to as the Strumia-Vissani model [128].
In addition to the DSNB signals, backgrounds with the energy of O(1–10) MeV andthe same event structure, such as an e+ (e− ) + n-like signal, cannot be distinguishedfrom IBD by the SK, and are normalized by their spectrum shape. These details will
be further explained in Chapter 7.

3.3

Detector Simulation

Currently, the transport of the secondary particles from neutrino interactions is currently computed by a Monte-Carlo simulation toolkit. Traditionally, SK DETector
SIMulation (SKDETSIM) based on GEANT3 [129, 130] toolkit is used in the SK analysis. SKDETSIM, developed in the FORTRAN programming language, is grounded
in a suite of simulation tools, such as GEometry ANd Tracking(GEANT), originallydeveloped by CERN, the final version was released in 1994. Given that the last updateof GEANT3 occurred in 1994, implementing the latest physics model in a GEANT3based simulation is problematic. Consequently, a new simulation based on Geant4(SKG4) was developed to utilize the most current physics model and interpolate newfunctionality into the SK simulation. In 1998, the successor to GEANT3 was launchedas Geant4 [131, 132, 133], and it is regularly updated and programmed in C++.
SK detector simulation accounts for particle tracking and interactions throughout
the detector, the generation and propagation of photons emitted through scintillationand the Cherenkov radiation effect, PMT responses to photons, and electronic digitization. Calibration of parameters for detector conditions, such as water and PMT
conditions, are performed using known light sources. The detector calibration will be
described in Chapter 5, whereas this section will focus on physics and how to track
the particles in the detector simulation.

3.3.1

Particle tracking

The Geant4 package offers various interaction models for hadrons, charged leptons,
and photons. FTFP_BERT_HP physics list[133] is the package of hadronic physics,

3.3. Detector Simulation

41

except for the gamma-ray emission of thermal neutron capture on Gd and pion interactions below 500 MeV/c. For the pion interaction below 500 MeV/c, a custom program [134] based on an experiment of π-16 O scattering [135] and π-p scattering [136] isemployed. As the gamma-ray emission from thermal neutron capture on Gd in SK-Gd
is crucial, a model based on experimental results of ANNRI(ANNRI-Gd) [137, 37] isapplied for gamma-ray emission from neutron capture on Gd. Figure 3.7 provides acomparison between data and MC in the ANNRI experiment, wherein the proposedmodel reproduced the measured data within 17% tolerance.

Figure 3.7: Comparison between measured data from ANNRI experiment and MC with ANNRI-Gd model. This figure was taken from
[37].

3.3.2

Optical Photon Emission and Tracking

SK measures the physical phenomena by detecting the optical photons generated by
the Cherenkov effect and scintillation. In particular, the emission of Cherenkov photons is a crucial aspect of the SK simulation. The process of Cherenkov emission in
the simulation is described in Chapter 2. In the simulation, only the photons withwavelengths of 300–700 nm are generated, which correspond to the sensitive regionof SK PMT, considering the optical photon propagation, scattering, absorption, andboundary effects. The probability of these processes depends on parameters reproducing the properties of water. For the scattering process, the simulation considers two
types of scattering: Rayleigh and Mie scattering. As described in Chapter 5, theseparameters are calibrated using laser measurement [43].

3.3.3

PMT response

When a photon reaches the PMT, the behaviors occurring on the PMT surface, including the photoelectric effect, are simulated. The probability of photoelectric effect,reflection, and absorption on the PMT surface is based on measurements. If photons
are converted into a signal, the process of signal integration and digitization of charge
and timing are also simulated as well. Finally, the simulated data are reformatted
and stored in the output file, enabling them to be analyzed in the same manner as
the observed data.

43

Chapter 4

Event Reconstruction
In the SK analysis, an event reconstruction is performed according to the target
physics events, including electrons, muons, and other hadronic particles. This chapter
outlines the event reconstruction algorithms used to estimate event energy, vertex, anddirection for each physics target, with a particular emphasis on electron-like particles
and muons.

4.1

Low Energy Event Reconstruction

In the SK analysis, the total energy of low-energy electron-like events (e.g., the electrons, positrons, and gamma rays) is reconstructed using the number of PMT hits.
This section describes the algorithm used for reconstructing the vertex, direction, andenergy of events.

4.1.1

Vertex reconstruction

The event vertex for low-energy events is reconstructed using the timings of the PMT
hits. Considering an electron-like event with the energy of O(10) MeV moves only
∼ 10 cm in water, which is shorter than the timing resolution of SK PMT, the track
can be considered as the vertex. It is determined by the likelihood method. The
likelihood L is defined as
L(x, t0 ) ≡

N
hit
X

log P (tres , i),

(4.1)

i=1

tres,i = ti − ttof,i − t0 .

(4.2)

Here, x denotes the candidate of the reconstructed vertex, Nhit denotes the numberof PMT hits, t0 indicates the candidate of the event time, ti represents the PMT hit
timing, and ttof,i denotes the time of flight from vertex to PMT for i-th hit. P (tres,i )denotes the Probability Density Function (PDF) for tres,i . The PDF distributionof timing residuals is illustrated in Figure 4.1. The event’s vertex and timing aredetermined as these with a maximum likelihood by scanning the entire tank.
The reconstructed vertex resolution is presented in Figure 4.2 as a function of
the true electron energy evaluated by MC [38]. The resolution can be improved byenhancing the reconstruction and timing resolution.
The goodness of the event vertex and timing gvtx is evaluated as follows
"
#
N
hits
X
t2res,i1
1gvtx = N×
exp − 2
.
(4.3)
hits
w2 (tres,i )2σ (tres,i )X
i1/w2 (tres,i )44

Chapter 4. Event Reconstruction

Figure 4.1: PDF distribution for the PMT hit timing residuals. Additional peaks surrounding 30 and 100 ns are caused by late pulse,which is caused by the photoelectrons reflected at the dynode and further incidence.

Figure 4.2: Vertex resolution as a function of true electron energy
for SK-I, II, III, IV by dotted, dot-dashed, dashed, and solid lines,
respectively. This figure is taken from [38].

√ Here, the w(tres,i ) = exp −tres,i / 2ω denotes the resolution function of the tres,idistribution with ω set of 60 s, and σ(tres,i ) denotes the same form with the w withreplacing ω to the PMT timing resolution of 5 ns.

45

4.1. Low Energy Event Reconstruction

4.1.2

Direction Reconstruction

The event direction is determined by the Cherenkov light pattern to maximize likelihood as follows
L(d) ≡

N20X
i=1

log{f (cos θi , E)} ×

cos θi,a(θi )(4.4)

where the N20 denotes the number of hits that tres,i are within 20 ns from the t0 ,f (cos θi , E) indicates the expected distribution of the opening angle for the event energy E, and the cosine of the angle between PMT direction and the reconstructed
event direction cos θi , and a(θi ) is a factor correcting the PMT acceptance. In particular, a(θi ) depends on the geometry of the PMT and acrylic case, and it is extracted
by the MC as follows:a(θi ) = 0.205 + 0.524 cos θi + 0.390 cos2 θi − 0.132 cos3 θi .

(4.5)

Consequently, the resolution at 10 MeV is evaluated to be 25◦ . Figure 4.3 represents
the energy dependence of the 1σ directional resolution estimated by SK-I MC.

Figure 4.3: Energy dependence of the directional resolution. This
plot was taken from [39].

A parameter, gdir , which is the KS test result for the azimuthal angle uniformity,with the z-axis representing the reconstructed direction, can be calculated asmax ∠iuniform − ∠idata − min ∠iuniform − ∠idata,(4.6)
gdir =
2π
where the ∠iuniform denotes the expected azimuthal angle of the i-th hit along theCherenkov angle of electrons, and ∠idata indicates the azimuthal angle of the i-th hitfrom a certain start point. The ∠iuniform is calculated by i × ∠iuniform = 2π/Nhits .
Figure 4.4 represents the calculation of the ∠iuniform and ∠idata . The azimuthal angle
is distributed equally if the PMT hits are more likely to be the Cherenkov ring.
In contrast, if these are accidental clusters like PMT flasher, then the equality isinadequate. Thus, the parameter gdir exhibits a smaller value when the hits are akinto electrons, whereas it displays a larger value if the event contains a clustered hit
pattern.

46

Chapter 4. Event Reconstruction∠idata∠iuniform

Reconstructed
Direction

Figure 4.4: Illustration of the definition of ∠iuniform and ∠idata . Bluecircles exhibit the PMT hits, and gray circles indicate the expected
point if the hits are equally distributed at an azimuthal angle.

4.1.3

Effective hit calculation

The number of PMT hits can vary depending on factors like water transparency,
PMT noise rate, and PMT signal efficiency, including QE and the gain, for a given
reconstructed vertex and direction. All these factors must be taken into accountduring energy reconstruction. Consequently, an effective number of hits, Neff , that
does not depend on these parameters is computed. Neff is defined as follows:
"
N50
X
1
Nall
×
(4.7)
Neff ≡(Xi + ϵtail − ϵdark ) ×Nalive S(θi , ϕi )
i
#


1
ri
×
.
× exp
QEi (1 + C · Gi (t))
LieffHere, N50 indicates the number of hits in which the timing residual is within 50 ns fromthe t0 , and Nall /Nalive denotes the inverse proportion of the number of functioning
PMTs to the number of all PMTs (=11,129). QEi indicates the relative QE describedin Section 5.1.4. Other parameters are listed below, wherein the notation i represents
the i-th hit PMT.
• Multiple hit correction Xi :If multiple photons hit one PMT within the same PMT gate (multiple photoelectrons), the number of photons is counted as a single hit, whereas the charges
are integrated. If the event occurs proximate to the wall and the direction is toward the wall, this effect becomes crucial for energy reconstruction. Therefore,

47

4.1. Low Energy Event Reconstruction
the occupancy correction of neighboring PMT hits is expressed as log{1/(1 − xi )} (x < 1)
i
Xi =
xi

3.0
(xi = 1)

(4.8)

(4.9)

xi = Nneighbor /Ntotal

where xi denotes the occupancy of these hits, Nneighbor indicates the number ofhits for the surrounding 3 × 3 PMTs patch surrounding the target PMT, andNtotal denotes the total number of hits.
• Delayed hit correction ϵtail :A number of Cherenkov photons fall out from the signal window because of thedelay induced by the reflection on the PMT and the black sheet. To include
these leaked hits in the Neff , the factor ϵtail is defined as
ϵtail =

ave × 50 nsec
N100 − N50 − Nalive × Rdark,
N50(4.10)

where the N100 denotes the number of hits that the timing residual is within
100 ns from the t0 , and Rdark is the averaged dark noise rate of all PMT. This
correction estimates the number of hits originating from sources other than thedark noise during 50 ns after the N50 window.
• Dark noise correction ϵidark :The dark noise stemming from the Cherenkov light owing to the thermionicemission of PMT and the radio activities should be considered when evaluating
Neff . As the dark noise rate for each PMT varies over time, the correction is
calculated using the dark rate at the time of observation as follows:
ϵidark =ave × 50 ns × N
i
Rdark
rdark
alive
.
×
i
N50
PN50 rdarki(4.11)

N50

i
Here, the rdark
denotes the dark rate for each PMT, depending on the time. The
first term represents the averaged fraction of dark noise hits in 50 ns, and thesecond term represents the variation from the averaged dark noise rate.

• Correction for the actual photo coverage S(θ, ϕ) :As ID PMTs are mounted on the inner surface of the ID, the actual photo
coverage is varied depending on the photon incident angle θ and ϕ as displayedin Figure 4.5.
The actual photo coverage S(θ, ϕ) is evaluated by injecting optical photons froma uniform vertex and isotropic direction into SKG4. The S(θ, ϕ) is defined asS(θ, ϕ) = Nobs (θ, ϕ)/Ninc (θ, ϕ),(4.12)

where Nobs (θ, ϕ) denotes the number of total photoelectrons incident from (θ, ϕ),and the Nph (θ, ϕ) represents the total number of photons reaching the PMT with
the incident angle (θ, ϕ). The evaluation using SKG4 enables the consideration

48

Chapter 4. Event Reconstruction

Figure 4.5: Definition of the incident angle θ and ϕ. This plot isreferred from [40].

of the QE dependence on the incident angle. As the angle range varies between the barrel PMT, and top and bottom PMT, two types of the S(θ, ϕ) arecalculated as displayed in Figure 4.6.

Figure 4.6: S(θ, ϕ) distribution for barrel PMTs (left) and top andbottom PMTs (right). The plots are taken from [40].

ri:• Water transparency correction exp
Lieff
The correction is performed to consider the light attenuation in the water. ri
denotes the distance between the event vertex and the PMT. λieff indicates theeffective transmission length considering the variation of water quality from theevent vertex to the PMT. As described in Section 5.2.2, the water transparency
exhibits an asymmetry along with the z-position. The photon transmission
length L is modeled asL(λ, z) ≡1
αabs (λ) × (1 + βz) + αsym (λ) + αasym (λ)(4.13)

49

4.1. Low Energy Event Reconstruction

where λ denotes the wavelength of photons, β represents the slope parameter
describing non-uniformity of water transparency, and αabs , αsym , and αasym
represent the attenuation coefficient of the absorption, symmetric scattering, andasymmetric scattering, respectively, as described in Section 5.2.1, respectively.
Furthermore, the cross-section with the water in the case of the photon travels
a distance ri , σi (λ) is denoted as"!#
1σi (λ) = αabs (λ) 1 + β z + ri · dzi+ Csca · (αsym (λ) + αasym (λ)) (4.14)
2where the dzi indicates the z component of photon direction, and Csca represents
the correction of the scattering effect. Csca is estimated to minimize the position
variation of Neff using 10 MeV SKG4 MC simulation as Csca ∼ 0.44. According
to these equations, the probability that the photon generated by the event vertex
reaches the PMT, pi (λ), is calculated as
Z λmaxw0 (λ) exp(−σi (λ) · ri )dλpi (λ) =(4.15)

λmin

where w0 (λ) denotes the PDF of the wavelength for the Cherenkov photons,
λmax = 650 nm, and λmin = 300 nm. Therefore, pi (λ) can be rewritten as!
ri(4.16)pi (λ) = exp − i ,Leffand the effective transmission length Lieff can finally be expressed asri
Lieff = − Z λmax
.
w0 (λ) exp(−σi (λ) · ri )dλln(4.17)

λmin• Relative QE and gain correction 1/[QEi × (1 + C · Gi (t))]:
The PMT QE varies for each PMT, as does the gain, described later in Section
5.1.4. The parameter C is introduced to reproduce the gain increase over time,
assuming a proportional relationship. In the SK-V, the tank refurbishment was
conducted, and the PMT high voltage (HV) and gain were tuned during that
period. As no increase in gain has been observed to date, we assigned C = 0 for
SK-V and SK-VI.

4.1.4

Energy reconstruction

After calculating Neff , the total energy of the event can be estimated by a combinationof the 5th-order polynomial function and linear function. The energy reconstruction
Etot function can be described as

5

X


pi (Neff )i(Neff ≦ Nthr )
i=0
Etot =.
(4.18)5Xpi (Nthr )i + a × (Neff − Nthr ) (Neff > Nthr )


i=0

50

Chapter 4. Event Reconstruction

Here, pi denotes the coefficient of the polynomial function as a fitting parameter, Nthr
indicates the connection point of two functions, and a denotes the first derivativeof the upper function in order to ensure the continuity of functions. To determine
parameters, the electron MC simulations were conducted across an energy range of 3–
100 MeV, and accordingly, the Neff was calculated. The parameters were determinedby fitting the correlation between Neff and true total energy. The parameters for theenergy reconstruction are summarized in Table 4.1. After evaluating p0 –p5 , Nthr wasdetermined to be 2.202 × 102 for SK-VI.
Table 4.1: Parameter settings for the reconstructed energy calculation in SK-VI.

p0
0.702

4.1.5

p1
0.131

p2
−2.35 × 10−4p32.640 × 10−6p4
−1.188 × 10−8p51.930 × 10−11

Cherenkov angle reconstruction

In the DSNB search, the Cherenkov angle of the event is used to filter out nonelectron-like events, such as muon, pion, those involving muons, pions, and multiple
gamma rays. The Cherenkov angle is determined using the pattern of PMT hits toachieve this separation. Only PMT hits with timing residuals from the reconstructedvertex within 15 ns are considered for this process. All three-hit combinations of three
PMT hits are explored because, theoretically, a circle can be drawn given any threepoints on its circumference. According to the theorems of sine and cosine, if a, b, andc in Figure 4.7 are given, the opening angle θ for each three-hit combination can becalculated in the following:
a
= 2R,
sin A
a
∴R= √
= v
u
2 1 − cos2 Au
2t1 −(4.19)
ab2 + c2 − a2

!2 ,

2bc

abc
sin θ = R = p2(a2 b2 + b2 c2 + c2 a2 ) − (a4 + b4 + c4 ),()
abc∴ θ = sin−1 p2(a2 b2 + b2 c2 + c2 a2 ) − (a4 + b4 + c4 )(4.20)

The angle θ for each combination is stored for each 0.9◦ bin. The central value ofthe maximum continuous 7 bins is identified as the reconstructed Cherenkov angles.
Figure 4.8 presents an θ distribution created from three-hit combinations for electronlike and muon-like events. Peaks are observed around these typical Cherenkov angles.

4.2

Muon Event Reconstruction

A muon event generally has more energy than an electron-like event, resulting in much
more PMT hits and charges in SK. The trajectory of a muon event is also more tracklike than electron events. This section details the algorithm for identifying muons and51

4.2. Muon Event Reconstruction

Hit PMTs

a

b

S

θ

A
c

R

1

VertexFigure 4.7: Illustration defining the calculation of θ. Circles comprise unit vectors from the reconstructed vertex to the three PMT hits.

Figure 4.8: Example of θ distribution of three-hits combinations forelectron-, and muon-like events. Plots are taken from [41].

reconstructing their direction and trajectory.
Cosmic-ray muon events observed at SK are usually identified by ID triggers pairedwith OD-triggered events. These events are classified into five categories: singlethrough going, stopping, multiple, corner-clipping, and misfit muons. Figure 4.9 provides illustrations of each muon type. Multiple muons are further divided into two
types: those where only one track can be fitted or those where multiple tracks can be
fitted.
A muon reconstruction algorithm, called ‘Muboy’ fitter, works depending on the

52

Chapter 4. Event Reconstruction

Single-through going

Stopping

Multiple

Corner-clipping

Figure 4.9: Illustration of muon categories for single-through (top,left), stopping (top, right), multiple (bottom, left), and corner-clipping(bottom, right) muons.

category of each muon. At first, Muboy looks at the muon type, whether the event hasa single track or multiple tracks in the ID, then identifies whether the muon stopped
in the ID. This section describes the overview of the Muboy fitter, and more detailcan be found in [23, 138]

4.2.1

PMT hit selection

Typically, a cosmic-ray muon deposits more charge per PMT than electrons due to its
high energy and distinct Cherenkov ring pattern. Therefore, the ID PMT hits usedin reconstruction are pruned by applying a certain charge threshold for each PMT,
depending on the number of PMT hits (first cleaning cut), as summarized in Table 4.2.
Table 4.2: Charge thresholds for ID PMT corresponding to the number of ID PMT hits.

Number of PMT hits
< 80008000 – 10000> 10000

Threshold charge to select ID PMT
2.0 p.e.
2.5 p.e.
3.0 p.e.

Following the first cleaning cut, Muboy calculates the nearest neighbor hits Nnn ,which consists of PMT hits from eight surrounding PMTs and own, within 15 ns for53

4.2. Muon Event Reconstruction
each PMT. Figure 4.10 displays the example of the counting of Nnn .

: PMT hit
: No PMT hit

Figure 4.10: Illustration of the concept for the counting of Nnn withthe case of Nnn = 5 in the central PMT.

For further PMT hit reduction, the PMT is selected by a certain threshold relating
to Nnn , as listed in Table 4.3.
Table 4.3: Nnn thresholds for ID PMT corresponding to the numberof ID PMT hits.

Number of PMT hits after first cleaning≤ 500
500–2500
2500–5000
5000–7500> 75004.2.2

Nnn threshold to select ID PMT
1
7
8
9
10

Initial Entry Point

The entry point and timing — the location and instant the muon enters the ID tank —is estimated by the earliest hit PMT with Nnn > 3. If no PMT hit has three neighbor
hits, the threshold is decreased by one neighbor. The entry point is determined as thecoordinate of the earliest hit PMT, and entry time is the timing of the earliest PMT
hit. Moreover, the tentative exit point was determined as the position of the PMTwith maximal Qnn , representing the total charge among the surrounding PMTs.

4.2.3

Direction Reconstruction

For the direction reconstruction, further constraints regarding hit timing are applied
to the PMT hits. In the case of a single-through going muon, the PMT hit timing
cannot be advanced in comparison to the muon travel distance of the muon in the

54

Chapter 4. Event Reconstruction

water. Furthermore, the photon directly produced from the muon should arrive at
the PMT prior to the period in which the light travels from the muon entry point.
Therefore, the hit timing constraint to the earlier side Tearly and later side Tlater canbe described as,D,
v1
D
Tlater = Tentry + ,v2

Tearly = Tentry +(4.21)(4.22)

where Tentry denotes the PMT hit timing of the enter point, D indicates the distancefor each hit PMT, and v1 and v2 denote the speed of muon and light in the water,
expected to be 34 cm/ns and 18 cm/ns, respectively. Muboy performs the direction
fit based on the PMT hits between Tearly and Tlater . Accordingly, the number of PMT
hits before the Tearly (Nearly ) is counted. If Nearly > 45, the event is classified as
the multiple muons because the constraint by Tearly cannot be applied to the multiple
muons (called MultiMu-1). The reconstruction of multiple muons is treated separately
for estimating the entry point and direction reconstruction, which will be describedlater. To assert that the direction from the entry point towards the PMT hit is within
the Cherenkov angle, either or both of the following conditions should be satisfied:
1. d⃗ · ⃗r > 0.74, where the d⃗ denotes the unit vector from the entry point to hit
PMT, and ⃗r indicates the muon track direction.
2. D < 2 m.
Using the selected hits, Muboy estimates the direction to maximize the goodnessof fit (GOF). The GOF is defined as follows,N

Ccone X
GOF(fcone ) =g(δti ),
N

(4.23)

i=1

where fcone denotes the number fraction of hit PMTs in the Cherenkov cone, δti
indicates the time difference between the measured time ti of the i-th PMT hits andthe expected timing at which the PMT hit should be hit from a given muon track anddirection. Furthermore, Ccone presumes the following form:

0.9


(fcone < 0.75)
fcone
Ccut
Ccone =,
(4.24)
0.1fcone + 0.9 − Ccut
(fcone > 0.75)
1 − Ccutwhere Ccut = 0.74. The function g(δti ) is defined as follows,
"
#

δt

i
 exp −
(δti < 0),λ(qi )"#
g(δti ) =
2

(δt
−
t
(q
))

i
mean
i
 exp −
(δti > 0 or qi > 30 p.e.),
2σ(qi )2

(4.25)

55

4.2. Muon Event Reconstruction

where qi denotes the charge for i-th hit PMT, tmean (qi ), σ(qi ), and λ(qi ) can be defined
as follows:(4.26)

tmean (q) = 2.563 − 0.029 · q"
σ(q) = 1.691 + 2.514 exp −

q
2.453

#

#
q
λ(q) = 1.254 + 14.863 exp −.
2.316(4.27)"(4.28)(4.29)

Direction estimation is conducted by iterating around the first tentative direction
while keeping the entry point and timing constant. After identifying the maximized
direction, a second iteration is performed. At this stage, the entry time is permitted
to change with the direction changes. The entry time can be smeared within a rangeof 26.7 nsec around the track. Subsequently, the GOF( fcone ) is again optimized with
Ccut = 0.74 replaced by Ccut = 0.65. After the second iteration, Muboy counts thenumber of early PMT hits with the condition of δti − tmean (qi ) > 250 ns under the
optimized direction and entry time. If the count exceeds 35, the muon is categorized
as a multiple muon (MultiMu-2). If the number of PMT hits is less than 10, under any
timing of hit reduction, the muon is considered a misfit muon. All other remaining
events are categorized as the through-going muons. The track length of these muons
is calculated geometrically using the direction and entry point. Figure 4.11 illustrates
the flowchart of hit reduction for the direction reconstruction.

4.2.4

Event classification

As discussed in the previous section, the muons are separated into misfit muons,
two types of multiple muons, and single-through going muons. Muboy subsequently
investigates single-through-going muons to further divide them into two other types:
corner-clipping and stopping muons. A different reconstruction approach is used forthe multiple muons.
Corner-clipping muonsCorner-clipping muons, which merely scrape the edge of the ID, typically exhibit short
track lengths and minimal PMT hits. As such, any muon with a track length under
7 m and fewer than 2,000 ID PMT hits is investigated to determine if it qualifies asa corner-clipping muon. As the entry point of the corner-clipping muon is typicallynear the top or bottom corner, a muon is tested using the following conditions:
Xentry cos θx + Yentry cos θyq> 0.05

2
2
Xentry+ Yentry(Zentry > 1750 cm), (4.30)

q


 X2
2
entry + Yentry > 1500 cm
(Distance between entry and exit point) < 4 mq(Zentry < −1600 cm), (4.31)
2
2

Xentry+ Yentry> 1600 cm

56

Chapter 4. Event Reconstruction

Apply Muboy

1st cleaning

Categorize Misfit with certain thresholdabout the small number of hits

NN search

2nd cleaning

Timingconstraint

Nearly>45

Yes

Multiple- Mu1
ANo
PMT removing
1st iteration

13.3 ns cut

Yes

MultiMu- 1

1st iteration

No

10 ns cut

1st iteration(last)

2nd iteration

2nd iteration

Nearly>35

Multiple(tentative)

Yes

Multiple- Mu2

A

No

Single- through(tentative)

Figure 4.11: Flowchart of Muboy about the direction reconstruction
with a part of event classification.

where the Xentry (Yentry , Zentry ) denotes the x (y, z) coordinates of the muon entry
point, and θx (θy ) indicates the x (y) direction of the muon. The muons satisfying
the conditions mentioned earlier are categorized as corner-clipping.
Stopping muonsFinally, Muboy determines whether the muons qualify as Stopping muons. To analyze
the muon events, the number of p.e.s generated within 2 m from the exit point in the
ID (QID ) and within 4 m from the exit point in the OD (QrmOD ), are counted. If amuon meets any of the following conditions, it is classified as a Stopping muon.
• QID < 200 p.e.
• QID < 400 p.e. and QOD < 30 p.e.

4.2. Muon Event Reconstruction

57• QID < 150 p.e. and QOD > 30 p.e.
• QID > 300 p.e. and No OD PMT hit data.
For Stopping muons, The track length and stopping point are estimated. The track
length is determined by the energy deposit per unit track length dE/dx, correlating to
the quantity of detected Cherenkov light per geometrically estimated unit track length
dQ/dE. A typical dE/dx distribution for a muon event is depicted in Figure 4.12.
The track length is determined up to the point where the dQ/dx reduces to less than
40% of the average value of the first 1.5 m. For the case presented in Figure 4.12, thestopping point is defined as 25 m.

Figure 4.12: Histogram of typical dQ/dx distribution for considering
the length along the muon track as the horizontal axis. This figure istaken from [42].

Multiple muons
There are two times when Muboy classifies muon into Multiple muons, such as forMultipleMu-1 and -2. After the MultipleMu-1 branch, these muons are subject to astricter hit timing cut, identical in approach to Tearly and Tlater , whereas v1 and v2
are altered to 32 and 19.5, respectively. Furthermore, before the final maximizationof the first iteration, with a fixed entry time, all hits are further pruned to remove any
hit time residuals outside 13.3 ns. This hit reduction is also applied to MultipleMu-2.
After this, two types of multiple muons are merged. The first iteration, with afixed entry time, is repeated using a new set of PMT hits, and the second iteration is
also repeated, but only using hits with a timing residual inside 10 ns. At this instant,the direction fitting is completed for one track of the multiple muons.
After that, for Multiple muons, additional entry points and directions for othermuons are sought. Initially, the PMT hits, removed by the cut after cleaning describedin Section 4.2.1, are recovered. This search assumes that these muons are moving in a

58

Chapter 4. Event Reconstruction

track parallel with the first determined track. To sample the PMT hits, these PMTs
require the following direction from the first track:⃗nPMT,i · d⃗track > 0,(4.32)

where ⃗nPMT,i denotes the normal vector of i-th hit PMT, and d⃗track indicates the
direction of the first track. The remaining PMTs are further selected to gather thehits close to the muon tracks using the ‘plane wave time’ tplane . tplane , indicating thetime at which the PMT would have been hit if the light was a plane wave travelingat c, denoted as
tplane = Tentry +|⃗rPMT,i − ⃗rentry · d⃗track |c(4.33)

where ⃗rPMT,i indicates the PMT position, and ⃗rentry denotes the entry point. If thetime difference Tplane − ti is beyond the range of −33.3 ns and 16.6 ns, the hits are
eliminated.
To locate the additional tracks, Muboy iterates the procedure stated below until
the number of remaining tubes is less than t or 9 tracks are detected by eliminating
the PMT hits with 0 < Texpected − ti < 10 ns, and they are within 12 m from thetrack.
1. Locate the earliest PMT hit. It becomes an entry point for an additional track.
2. Remove PMT hits that are located closer than 12 m and with 0 < Texpected −ti <10 ns.
3. Count the number of clustered hits. If the count is greater than 5, the track isvalid.
4. Subtract the number of clustered hits. If ≥ 6 PMT hits remain, revert to search
further (to (1)).
Classification summary
Figure 4.13 portrays the muon types and reconstruction goodness gµ defined as the
maximized GOF. The majority of the muons are classified as the single-through going
muons. The misfit muons tend to exhibit a lower value of goodness than other types.

59

4.2. Muon Event Reconstruction

×10
7000

goodness

3

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

6000
5000
4000
3000
2000
1000
mis

fit

sing

le

stop

ping

mul

tiple

mul

tiple

(one

)

clip
(mu

lti)

ping

0

Figure 4.13: Muon types and reconstruction goodness. The term‘single’ represents the single-through muons.

61

Chapter 5

Detector Calibration Measurement
In SK, periodic detector calibrations are essential to investigate the functionality ofthe detector behavior and ensure accurate signal measurement. Results from thesecalibration measurements feed into the analysis software, detector tuning, and thedetector simulation, as described in Section 3.3.
The data procured at SK primarily comprises timing and the charge information
captured by PMTs and consolidated through electronics. The integrity of the signal isinfluenced by the QE and the gain characteristics of each PMT. Additionally, photon
behaviors such as absorption and scattering by the water and other materials in thetank must be well-understood and integrated into the detector simulation and analysis
software. Evaluating attributes such as PMT response and water properties fromcalibration measurements is critical for event reconstruction and physics analysis.
This is especially true for low-energy analyses, such as O(1–10) MeV range, where
calibration data is vital for the event energy reconstruction given the low photon
yield, as outlined in Section 4.1.3. This chapter describes calibration measurements
performed in SK and the utilization of parameters obtained from calibration.

5.1

ID Detector Calibration

As physics analyses in SK are based on signals detected by the ID, a detailed understanding of the PMT in ID is essential for evaluating the functionality of SK.
This section explains the measurement process and the parameters obtained for eachcalibration.

5.1.1

High-Voltage determination

The amplitude of photoelectrons on the dynode, stemming from the photoelectriceffect on the PMT, is influenced by the High-Voltage (HV) applied to the PMT. For
consistent gains across all PMTs, individual HV adjustments ensure uniform outputs.
To facilitate this, an isotropic light source, created by injecting light from a Xe lamp
into a 5 cm diameter acrylic diffuser ball via a UV filter, is employed. Positioned at
the center of the tank, measurements from this diffused light are susceptible to factors
like PMT position, water properties, and PMT glass surface reflectivity. To ensure
accuracy, 420 pre-calibrated PMTs, termed Standard PMTs, are evenly placed within
the ID. Prior to their SK introduction, the HV of these standard PMTs is calibratedusing an identical light source and DAQ system. Figure 5.1 illustrates the placementof Standard PMTs and their associated PMT grouping.
For all PMTs, except the Standard ones, HV is adjusted to align the charge fromthe light source with the average charge of a corresponding group’s Standard PMT.
The consistency of the HV is verified to be within a 1.3% range, which is also aligned

62

Chapter 5. Detector Calibration Measurement

Figure 5.1: Positions of the Standard PMTs (left) and schematic of
the grouping of the PMTs (right). Red points indicate the location.
The figures are taken from [43].

with the measurement outcomes of the Standard PMTs. Given the permanent placement of the light source in the tank, routine HV measurements are feasible.

5.1.2

Relative Gain Measurement

The gain for each PMT is determined by the output charge relative to the amountof input light intensity. This gain can be ascertained from the average gain acrossall PMTs (Absolute gain) and individual PMT deviations from this average (Relativegain). A two-step measurement process using the aforementioned isotropic light sourceis employed for relative gain calculation.
Initially, light is introduced in abundance to ensure adequate illumination for all
PMTs. Following this, a minuscule light quantity is introduced allowing PMTs tocapture a single photon, registering a 1 p.e. signal. From this, the average charge
under intense light (Qobs ) and the instances the PMT charge exceeds a set threshold(Nobs ) are determined for each PMT. Upon conducting the two measurements at thesame location, Qobs and Nobs can be described as
Qobs (i) ∝ IH × a(i) × ϵ(i) × G(i),(5.1)

Nobs (i) ∝ IL × a(i) × ϵ(i).

(5.2)

Here, IH (IL ) denotes the averaged light intensity of the larger (smaller) light, a denotes
the acceptance of each PMT, ϵ indicates a relative QE described below, and G denotes
gain. The notation i represents i th PMT. Thus, the gain for each PMT can becalculated as
G(i) ∝

Qobs (i).
Nobs (i)(5.3)

5.1. ID Detector Calibration

63

The relative gain indicates the deviation from the average of G. In this case, thestandard deviation is ∼ 5.9%. This deviation arises from the QE variability of each
PMT, given the HV adjustments for uniform PMT charge. Relative gain serves as acoefficient for the charge to the p.e. conversion.

5.1.3

Absolute Gain Measurement

Absolute gain is determined from the charge distribution of 1 p.e. signal. The measurement is performed using apparatus consisting of a Cf source and a surrounding
NiO2 sphere, called a Ni-Cf source. The appearance is shown in Figure 5.2. The
Ni-Cf source emits multiple gamma rays totaling 9 MeV by the thermal neutron capture on the 58 Ni. Neutrons are emitted from the spontaneous decay of the 252 Cf, andtheir half-life is 2.56 years, resulting in an average of 3.76 neutrons producing with anaverage energy of 2.1 MeV. The spontaneous decay of 252 Cf is only 3% of the decay
fraction, and the remaining 97% is alpha decay. By placing the Ni-Cf source into thecenter of the tank, each PMT detected an average of 0.004 p.e./event so that over
99% of PMT signals are 1 p.e..

Figure 5.2: Appearance of the Ni-Cf source geometry. The figures
are taken from [43].

After the correction of relative gain, described above, the charge distribution ismade like Figure 5.3. The highest peak, around 0 pC, is formed by the photoelectrons
not amplified at the first dynode. The second peak at 3 pC represents the averaged
1 p.e. peak. This measurement results in the conversion factor between pC andp.e. being 2.055, 2.297, 2,243, 2.645, 2.46 [pC/p.e.] for SK-I to SK-V, respectively.
The factor in SK-VI is the same as SK-V since HV tuning for SK-VI is not changed
from SK-V. The charge distribution shown in Figure 5.3 is also used in the detector
simulation as the PMT response for the photoelectrons.

5.1.4

Relative QE measurement

For the low energy hit, such as the charge for each PMT being 1 p.e., the variationof QE for each PMT affects the physics measurement. Thus, we define the relative
QE for each PMT. That is used for the energy reconstruction of particles (whichappeared as QE in Equation 4.8) and reproduction of PMT response in the detector

64

Chapter 5. Detector Calibration Measurement

Figure 5.3: Charge distribution taken using Ni-Cf source used in
SK-III. The figures are taken from [43].

simulation. The measurement also uses the Ni-Cf source described above. As shown inEquation 5.2, the averaged number of hits in the low luminosity is proportional to therelative QE. Consequently, the relative QE is discerned by comparing deviations in the
average hit counts between actual data and an MC model, which does not account forindividual PMT relative QE. Comparing with the MC model neutralizes effects likegeometry, water interactions, individual PMT acceptances, and other PMT responses.
Concurrently, hit counts must be adjusted for relative gain, PMT acceptance, andsource proximity. The discrepancy from the amended hit average, termed the ‘hit
rate’ (Rhit ), can be defined as follows:
Rhit (i) = Ncorr (i) × N
PMTX
Ncorr (i) = Nhit ×

1

,

(5.4)

Ncorr (i)/NPMT

r2
1
×
,
a(θ) G(i)(5.5)

where NPMT denotes the number of appropriately functioning PMT, Nhit indicatesthe number of hits obtained surrounding the event timing, G(i) denotes the relativegain, r indicates the distance between PMT and the source, and a(θ) represents theacceptance function, similar to that in Equation 4.5. The position dependence of thehit probability is exemplified in Figure 5.4.

5.1.5

Timing Response Calibration

The timing response of a PMT varies due to factors like cable length, intrinsic PMT
response, and the processing time of the electronic circuit. Additionally, the timing
response is influenced by the amplitude of the PMT signal waveform, a phenomenon
referred to as ‘Time walk.’ The purpose of timing response calibration is to establish
a correction function that considers the comprehensive processing time of the detector

65

Average
hit rate
Average of hit
rate of[/bin]

5.1. ID Detector Calibration

1.15

Barrel
1.1
1.05
1
0.95
0.9
0.85

Data (#085609)
SKG4 (β = 0.00956463)

−1500

−1000

−500

0

1.05
1
0.95
0.9
0.85
0

1000

1500
z [cm]

1.15

Top
1.1

3

×10
500 1000 1500 2000 2500 3000
r2 [cm2]

Average of hit rate [/bin]Average of hit rate [/bin]

1.15

500

Bottom
1.1
1.05
1
0.95
0.9
0.85
0

3

×10
500 1000 1500 2000 2500 3000
r2 [cm2]

Figure 5.4: Hit rate distribution as a function of PMT positions
measured in SK-VI. Top: barrel PMTs, with the z-position of PMTs
plotted in the horizontal axis. Bottom: two plots indicate top (left)
and bottom (right) PMTs, where the horizontal axis denotes the squareof the radial distance on the x-y plane. Black points indicate the data,
and red points display MC.

for each PMT. Correcting for the time walk is vital for the accurate reconstruction ofparticle tracks and vertices.
Figure 5.5 illustrates the design of the light source apparatus employed for thiscalibration. Monochromatic pulsed light, emanating from Nitrogen lasers, exhibits
a 337 nm wavelength and a full-width at half maximum (FWHM) of 0.4 ns. This
light is monitored and triggered by a fast-response 2-inch PMT. The wavelength ofthe laser light is shifted to 398 nm by a dye, which is within the combined response
range of the PMT to Cherenkov emission, photon absorption, and PMT QE peaks.
After that, the modified light attains a diffuser ball situated at the center of thetank. Any directional discrepancies in photon emission time from the diffuser ball are
negligible, staying under 0.2 ns. Adjusting the intensity of light with a filter facilitates
measurement of the timing response across various PMT signal amplitudes. As the
PMT pulse height corresponds to the charge, this calibration is referred to as the TQ
calibration.
Two-dimensional histograms plotting the timing against the charge for every PMT
are exemplified in Figure 5.6, wherein the timing T denoted in the vertical axis is calculated as T = Tobs − T OF − T2-inch , where the Tobs denotes the hit time of PMT,T OF indicates the time-of-flight (TOF) between each PMT and the light source, andT2-inch is the trigger timing of the monitoring 2-inch PMT. Calibration constants,
termed ‘TQmap’ are extracted by fitting the TQ distributions to polynomial functions. The charge displayed on the horizontal axis in Figure 5.6 is segmented into
180 bins (Qbins). EachQbin is defined on a linear scale below 10 pC with a width of
0.2 pC/Qbin and on a logarithmic scale ≥ 10 pC with a width of 50 log(pC)/Qbin.
After determining the timing peak for each Qbin, the time peaks for respective charges

66

Chapter 5. Detector Calibration Measurement

Figure 5.5: Schematic view of the timing calibration system. The
figures are taken from [43].

are fitted by polynomial functions depending on Qbin as follows:
polN (x) ≡ p0 + p1 x + p2 x2 + · · · + pN xN ,(5.6)

Qbin ≤ 10 : F1 (x) ≡ pol3(x),(5.7)

Qbin ≤ 50 : F2 (x) ≡ F1 (10) + (x − 10)[F1′ (10) + (x − 10)pol3(x − 10)],(5.8)

Qbin > 50 : F3 (x) ≡ F2 (50) + (x − 50)pol6(x − 50),

(5.9)

where F1′ denotes a derivation of F1 that is introduced to ensure continuity between
F1 (x) and F2 (x). In total, 15 fitting parameters are determined for each PMT.
The timing resolution of each PMT, contingent upon the charge, can also be investigated using the same TQ calibration dataset. To gauge this resolution, timing
distributions for all PMTs — corrected via the TQmaps — are compiled for every
Qbin. These timing distributions are then modeled by an asymmetric Gaussian, characterized as follows:f (t; t > Tpeak ) ≡ A1 · exp(−(t − Tpeak )2 /σt2 ) + B1 ,(5.10)

f (t; t ≤ Tpeak ) ≡ A2 · exp(−(t − Tpeak )2 /σt′2 ) + B2 ,(5.11)

where the Ai , Bi , σt , and σt′ represent the fit parameters that should satisfy a boundary
condition of A1 + B1 = A2 + B2 to connect two Gaussians at t = Tpeak . An example

5.2. Photon tracking

67

Figure 5.6: Typical scatter plot of the timing and the charge. For
the vertical axis, larger (smaller) T corresponds to the earlier (later)
hits. The figures are taken from [43].

of the timing distribution and the function resulting from the fitting for the Qbin=14
is presented in Figure 5.7, and the distribution of timing resolution is displayed in
Figure 5.8 as a function of the charge. For lower charges, the two resolutions areobserved to be more distributed. Thus, the timing resolution is implemented in thedetector simulation.

Figure 5.7: Timing distribution and the function resulting from thefitting for the Qbin = 14. The figures are taken from [43].

5.2

Photon tracking

A comprehensive understanding of photon tracking is pivotal for accurate data replication in detecter simulation. Moreover, refining the correction for photon absorption

68

Chapter 5. Detector Calibration Measurement

Figure 5.8: Distribution of timing resolution as a function of thecharge, measured during in SK-IV. The figures are taken from [43].

enhances energy reconstruction. Thus, multiple parameters are evaluated to refineboth the detector simulation and energy reconstruction in the SK.

5.2.1

Water Transparency Measurement

For photon tracking in the detector simulation, accounting for material properties likescattering and absorption within the tank is crucial. Light attenuation is represented
using an attenuation length L(λ) of a photon at wavelength λ and light path lengthl as the exp(−l/L(λ)). In the SK analysis, the L(λ) is defined as
L(λ) =

1.
αabs (λ) + αsym (λ) + αasym (λ)(5.12)

Here, the αabs (λ), αsym (λ), and αasym (λ) denote the attenuation coefficient for theabsorption, symmetric scattering, and asymmetric scattering, respectively. αasym (λ)
is introduced to consider the forward Mie scattering easily. αsym (λ) is used to consider
the symmetric Rayleigh scattering and the remaining symmetric components of Mie
scattering. To measure three attenuation length variables, we injected the monochromatic laser with some wavelength from the top of the tank downward. The schematic
illustration of the measurement is depicted in Figure 5.9.
To understand wavelength dependence, the measurement uses lasers of five distinct
wavelengths (337, 375, 405, 445, and 473 nm). The PMT hit timings are subtracted
by the TOF from the light-blue area displayed in Figure 5.9. After that, the optimal
attenuation coefficient is identified by comparing TOF subtracted time across various
PMT regions between measured data and simulations while tweaking the coefficients.
Figure 5.10 presents the TOF subtracted timing distribution for each PMT zone alongwith the best-fit outcome in the SK-IV. The region pinched in the two blue lines on
the right-hand side is considered the hits after reflection on the PMT, acrylic surface,
and the black sheet at the bottom of the ID tank.
After the three best coefficients with minimum χ2 , representing the discrepancy
between data and MC, are determined for each wavelength, the attenuation coefficientsare evaluated as functions of the wavelength by fitting to discrete coefficients for five

5.2. Photon tracking

69

Figure 5.9: Schematic of the laser measurement system. The analysis
uses PMTs pertaining to five segmented barrel regions B1-B5 and thetop. The figures are taken from [43].

wavelengths. The attenuation coefficients are calculated using 9 parameters P0 -P8 asfollows:
P1+C
λ4
C ≡ P0 × P2 × (λ/500)P3 (for λ < λthr )!
P4
P5
αsym (λ) ≡ 4 × 1 + 2λλ!
P7αasym (λ) ≡ P6 × 1 + 4 × (λ − P8 )2λαabs (λ) ≡ P0 ×

(5.13)(5.14)(5.15)(5.16)The parameters P0 –P8 are called ‘water parameters.’ C can be calculated using Equation 5.14 until λ < λthr . In contrast, for wavelength exceeding λthr , the experimental
result of Pope and Fry’s model [139] is invoked. λthr is determined as the wavelength
at the intersection between our numerical calculation and the Pope-Fry model.
The best-fitting results of the water parameters recorded by the laser measurementin SK-VI are summarized in Figure 5.11.
We compared two types of simulation to review whether any deviation is detectedin the asymmetric scattering. It can be concluded based on the modeling variations of
the angular dependence of asymmetric scattering. SKG4 refers to the angular dependence of Mie scattering as a ‘Henyey-Greenstein’(HG) approximation [140], whereas
SKDETSIM assumes that the probability increases linearly increased along with cos θ.

70

Chapter 5. Detector Calibration Measurement

Figure 5.10: Best-fitted timing distribution of data and MC for each
PMT region in SK-IV measurement. The circle with the black line
represents the data, and the red line indicates the MC. Both are normalized by total observed photoelectrons. The top panel represents
the PMTs at the top of the ID wall, whereas the second-to-bottom
panels correspond to the five segmented barrel regions B1–B5, as displayed in Figure 5.9. The region between the two blue-solid lines on
the left-hand side was used to fit the attenuation coefficients. The
region between the two blue-solid lines on the right-hand was utilized
in the PMT reflection measurement. The figures are taken from [43].

According to the HG approximation, the differential cross-section of the Mie scattering
can be approximated asdσ
1 − g2∼,dΩ (1 + g 2 − 2g cos θ)3/2(5.17)

where dΩ = d cos θϕ, σ denotes the cross-section, θ represents the scattering angle, andg indicates the cosine of the mean angle. Therefore, the normalized density function
P (cos θ0 ) can be expressed as follows:
R cos θ0 dσ
d cos θ−1dΩ
P (cos θ0 ) =R 1 dσ−1 dΩd cos θ!
1 − g21
1=−2g
1 + g 2 − 2g cos θ0 1 + g(5.18)

71

5.2. Photon tracking
Water amplitude

Inverse Water transparency [1/m]

10−1

10−2

−3

10

10−4
300

320

340

360

380

400

420

440

460 480 500
Wavelength [nm]Figure 5.11: Distributions of the coefficient as functions of the wavelength. Each point represents the Best-fitted coefficients for each laser
wavelength and interaction. Red, blue, and magenta points and thelines represent the αabs , αsym , and αasym , respectively. Circles (triangles) and solid (dot-dashed) lines of the Geant4-based (GEANT3based) simulation result are described in Section 3.3.

It yields the angular distribution of HG approximation, computed using the random
number p between 0 and 1, as follows:
!
2
1
1
−
g
cos θ =
)2
1 + g2 −2g
1 − g + 2gp(5.19)(1 + g)2 (1 − g + gp)= 2p−1(1 − g + 2gp)2

5.2.2

Top-Bottom Asymmetry Measurement

The water under z = −11 m in the SK tank is continuously circulated to maintainwater transparency. However, above this depth, the water temperature with height,
with a maximum variation in temperature at 0.2 ◦ C. This increase in temperature also
affects water quality, causing up to a 5% discrepancy in transparency. Due to thesefactors, the water in the tank is not uniform. Understanding the nonuniformity along
the z-axis becomes critical. To estimate this, we examine the top-bottom asymmetryof water transparency (TBA) using both the Ni-Cf and Xe isotropic light sources.
TBA αtba is calculated asαtba ≡⟨Ntop ⟩ − ⟨Nbottom ⟩,⟨Nbarrel ⟩(5.20)

where the ⟨Ntop ⟩, ⟨Nbottom ⟩, and ⟨Nbarrel ⟩ denote the average of hit rate Rhit for the
PMT on the top, bottom, and wall of the tank, respectively. The variation of the TBA
during the SK-V and the SK-VI is represented in Figure 5.12, in which variation ranges

72

Chapter 5. Detector Calibration Measurement

up to ∼ 5%. A notable decrease in TBA was observed post the water convection period
when relative QE measurements were operated in March 2020. With the introductionof Gd, the pattern of TBA remained consistent. Almost daily measurements of TBA
are performed using the Xe light source, whereas the Ni-Cf source is utilized monthly.

Figure 5.12: Variation of the TBA during the SK-V and SK-VI,
taken by the Ni-Cf source and Xe light source (top), and differences of
TBA between both measurements and between data and MC for Ni-Cf
source measurement (bottom). Thick dotted-dashed line indicates the
0.5% difference region.

Given that TBA variation is assumed to emerge as the absorption effect, thecoefficient αabs is adjusted by multiplying the factor A(z, t), which is denoted as(
1 + z · β for z ≥ −11 m,
A(z, t) ≡(5.21)
1 − 11 · β for z < −11 m,
where the β(t) denotes the time-dependent slope of the water transparency alongwith the z-axis. To estimate the correlation between β and TBA, the optimizationof the parameter β for all Ni-Cf source data in the SK-VI period by scanning various
β to determine the β that most accurately reproduces the TBA of the actual data.
Consequently, the correlation between Ni-Cf data and MC is estimated asβ(t) [cm−1 ] = 0.01 × (−0.006322 × 100 × TBA − 0.004130).

(5.22)

Here, the time dependence of β(t) is derived from the daily measured TBA by the Xe
light source. The correlation is introduced into the MC and the energy reconstruction.

5.2.3

Photon Reflection on the Material Surface

For an accurate photon transportation simulation, it is crucial to incorporate photon
reflection on the material surfaces into the MC. In particular, the reflectivity of PMTs
and the black sheet is evaluated using two types of laser systems.
Reflection on PMT Surface
The simulation considers four refractive index layers from the surface inwards towards
the PMT: water, glass, bi-alkali, and vacuum. Their refractive indices are 1.33, 1.472+
3670/λ2 , nreal + i · nimg , and 1.0, respectively. Here, λ denotes the wavelength of thephoton, nreal , and nimg denote the real and imaginary parts of the complex refractive

5.3. Energy Scale Calibration using LINAC

73

index. The light reflection of the PMT surface in the MC is adjusted using thesame laser data from Section 5.2.1. The best pair of parameters for nreal and nimg aresearched by comparing the timing distribution of the region between the two blue lines
on right-hand side in Figure 5.10. For the wavelengths 337, 375, 405, and 445 nm,
the optimized pairs are (2.8, 1.4), (3.2, 1.5), (3.4, 1.6), and (3.6, 1.7), respectively, inboth SK-V and SK-VI.
Reflection on Black Sheet
Although the majority of the photons are absorbed by the black sheet, a minority
gets reflected. This reflectivity is gauged using a light injector. Figure 5.13 depicts
the schematic representation of the measurement setup.

Figure 5.13: Schematic of a laser light injector to measure black
sheet reflectivity. The figure is taken from [43].

The apparatus is inserted into the central region of the tank. The laser is injected
into the black sheet at the incident angle θ of θ = 30, 45, and 60 degrees such that
the ID PMTs detect the reflected light. The reflected charge Qscattered is measured forwavelengths of 337, 400, and 420 nm. In addition, a direct charge in the absence ofthe black sheet (Qdirect ) is measured for reference purposes. Reflectivity (R) is tuned
using the equation R = Qscattered /Qdirect . The comparison of R between the laser
data and laser MC with the best-tuned reflectivity is depicted in Figure 5.14. Boththe actual data and MC results align within a 1% margin across all wavelengths andangles.

5.3

Energy Scale Calibration using LINAC

To calculate the energy scaling factor for low-energy MC simulations, the electronlinear accelerator (LINAC) is employed. The LINAC is capable of producing monoenergetic electron beams. As depicted in Figure 5.15a, these electrons are bent by
the D1–D3 magnet, directing them above the tank and then downward. The LINAC
is positioned above the tank, and its beam pipe extends into the tank through acalibration hole approximately 18 cm in diameter. As indicated in Figure 5.15a, the74

Chapter 5. Detector Calibration Measurement

Figure 5.14: Comparison between laser data and MC in the black
sheet measurement. The three left panels show the ratio of the charge
between reflected and direct incident light, and the right panels show
the ratio between data and MC for the left plots, for the wavelength
at 337 nm (top), 400 nm (middle), and 420 nm (bottom). The figure
is taken from [43].

x-position of the beam can be shifted by moving the tower on top of the tank, whereas
its z-position can be modified by extending or retracting the beam pipe. The energy isdiscretely selected from kinematic energies of 5–18 MeV. Thus, the LINAC is utilized
to estimate the scaling factor, review the uniformity of energy reconstruction, andevaluate systematic uncertainty on the energy reconstruction up to several tens of
MeV.
After optimizing the parameters for evaluating Neff and the detector simulation,
Neff for the LINAC data should be ideally comparable to the LINAC MC at eachenergy point and beam position. Any remaining discrepancies can be attributed tointricate PMT property reproductions, like PMT collection efficiency, which poseschallenges for individual estimations. By comparing the Neff of the LINAC datawith MC across beam positions and energies, an overarching scaling factor for MC
application is deduced. Typically, this scaling factor is multiplied by the QE of the
ID PMT. In SK-VI, this factor is estimated to be ∼ 0.88.

5.3. Energy Scale Calibration using LINAC

I(a) Schematic of the LINAC calibration geometry.
The marker A-I is the injection position.

(b) Schematic of the part of the electron acceleration for LINAC calibration.

75

77

Chapter 6

Development of Neutron Tagging
in SK-Gd
Detecting a neutron signal, i.e., the gamma rays resulting from thermal neutron capture, is the key aim of the SK-Gd experiment. The event identification using a prompt
signal and delayed-neutron signal is called a ‘delayed coincidence method.’ This chapter begins by outlining the method of neutron tagging during the pure water period,
progressing to a description of a newly constructed tagging algorithm, and concluding
with its application to actual neutron source data.

6.1

Neutron Tagging Algorithm

6.1.1

Neutron Tagging in Pure Water

As introduced in Section 2, the SK detector was upgraded from SK-IV onward torecord all PMT hits post-SHE triggers. Within SK, the event triggering SHE has been
designated as the prompt signal. Until SK-VI, the neutron signal was represented bya single 2.2 MeV gamma ray, a product of thermal neutron capture on the proton.
Initially, neutron tagging was implemented through a series of rectangular cuts [48].
Given the challenge of detecting the low 2.2 MeV signal in SK, a machine learning(ML) based algorithm was developed to maximize the efficiency of neutron signal
identification. Notably, in the SRN search during SK-IV [20], the Boosted Decision
Tree (BDT) discriminator [141] with 22 characteristic variables was applied, which
delivered ∼ 20% efficiency with approximately 12.5% relative uncertainty.

6.1.2

Neutron Tagging in SK-Gd

In SK-Gd, the neutron signal is augmented by the thermal neutron capture on Gd, resulting in multiple gamma-ray emissions totaling ∼ 8 MeV. Moreover, the Gd isotope
possesses one of the highest cross-sections for thermal neutron capture among natural
isotopes. Consequently, even at minute concentrations, the capture fraction is considerable. Additionally, the capture time constant is reduced compared to pure water.
The cross-sections of thermal neutron capture for 155 Gd and 157 Gd are summarizedin Table 6.1, which predominantly contain large cross-sections.
In SK-VI, where the Gd mass concentration is around 0.011%, the capture time
constant is ∼ 115 µs, leading to ∼ 50% of the neutrons being captured on Gd [26].
This short lifetime ensures that over 99% of neutrons are captured by the end of
the AFT window. Given the augmented neutron capture signal on Gd (Gd-capture),
there should be a marked improvement in neutron tagging efficiency. Measurements
by weight and Atomic Absorption Spectrometer (AAS) have estimated the Gd massconcentration at 109.7 ± 0.7 ppm and 114 ± 2 ppm, respectively [26]. The capture

78

Chapter 6. Development of Neutron Tagging in SK-Gd
Table 6.1: Summary of thermal neutron capture on 155 Gd and157
Gd [37]155 Gd157 Gdnat GdAbundance [%]
14.80
15.65
–

Cross-section σNC [barn]
60,900254,000∼ 49, 000

Total γ energy [MeV]
8.45
7.86
–

time constant, reported as 115 ± 1(syst.+stat.) µs in Ref [26], is correlated with thecross-section of neutron capture and the Gd concentration. Nevertheless, the variations in neutron transportation computation in Geant4.10.5 indicate that the capture
probability of Gd surpasses the actual calculation based on cross-section values. Thus,in detector MC simulations, the Gd mass concentration is adjusted to align the capture time constant with the data acquired from the measured radioactive source, asdetailed in [26].

6.1.3

Delayed Neutron SearchThis section delves into the process of neutron selection and the corresponding efficiency. The efficiency is estimated from neutron MC simulations, which produce a
million neutrons with a kinetic energy of 0.1 MeV within the entire ID tank. In thisstudy, the neutron signals are searched between 4 µs to 535 µs post the prompt eventto mitigate the thermalization effect and any prompt event influences in SK. Thissearch window captures over 95% of the neutron capture.
Injection of Realistic Noise into MC
Assessing the potential inaccuracies of the algorithm, especially when it misconstrues
noise hits as neutrons, is essential for evaluating the neutron tagging algorithm. Nevertheless, simulating random noise, particularly from radioactive decay, poses challenges. As a result, SKG4 does not produce these hits. Instead, the real noise hits
are introduced into the MC after a delay of 2.7 µs. This real noise hit data is sourced
from the ‘T2K dummy spill data’ and the ‘SK wide random trigger data.’ The former
is collected using the T2K trigger when the T2K beam is inactive within a 1024 µstime frame. The latter is gathered during regular SK normal runs every ∼ 30 seconds
over a time span of 1000 µs. From these datasets, a 532 µs noise segment is trimmed
and appended to the MC. Figure 6.1 illustrates the schematic diagram of noise hit
generation for each event.
Pre-selection
The search window primarily contains a number of PMT hits attributable to the darknoise. To address this, the initial criteria require a N200 (number of hits within 200 ns)
between 25 and 200 hits in the SHE and AFT time window (535 µs). Hit clusters thatmeet this requirement are retained. The primary selection is visually represented in
Figure 6.2.
Cut-based neutron selection
For the subsequent step, low-energy reconstruction (Section 4.1) is applied to all candidates passing the pre-selection, because the Gd-capture signal can be reconstructed79

6.1. Neutron Tagging Algorithm
0 μs

535 μsSimulate particle transportation & Software trigger

Simulateddark noise

Noise data
(T2K dummy spill or SK random-wide)

2.7 μsFigure 6.1: Schematic diagram of the procedure of noise production.
The contents with the blue characters and lines are simulated in thedetector MC, while those with red characters and lines are appended
later.

25 hits/200 ns trigger
Gd capture γ
25 Hits/200 ns

p capture γ

backgroundT = 4 μs

T

Figure 6.2: Illustration of the primary selection. Dashed line indicates the N200 threshold.

using a nominal low-energy reconstruction algorithm owing to its high-energy gammaray emission. Mis-reconstructed events and low-energy events resulting from radioactive decay products are typically situated closer to the perimeter of the tank wall. To
filter out these events, a fiducial volume cut is implemented using the dwall , representing the distance between the event vertex and the ID wall. Only the events withdwall > 200 cm are considered after this.
The remaining events are further reduced through two threshold values related toevent quality, i.e., gvtx and gdir ; these variables are defined in Section 4.1. Distributionsof both event quality variables are presented in Figure 6.3. To ensure optimal event
quality, only events that satisfy the criteria gvtx > 0.4 and gdir < 0.4 are advanced tothe subsequent stage.
In the final step of distinguishing noise events, the Gd(n, γ) event is chosen basedon energy and vertex criteria. Given the spallation correlation between the promptand delayed events, the distance from the reconstructed vertex to the prompt event
vertex, termed dprompt , can serve as an effective classifier. As such, a dprompt criteriaof less than 300 cm is implemented. In this MC study, the prompt event vertex
is presumed to be the accurate neutron-generated vertex. The dpropmt distribution
is illustrated in Figure 6.4. Here, the Gd-captured event appears to be accurately
reconstructed in proximity to the prompt event vertex.
Finally, the reconstructed energy is considered the basis for selecting Gd-capture.
Figure 6.5 illustrates the reconstructed energy distribution of gamma rays captured
from Gd, protons, and noise candidates. While the Gd signal comprises the combination of multiple gamma rays, whose individual energies are not discernible in SK, thevisible energy in SK is typically less than that of a single gamma ray with an energy
equivalent to the sum of the multiple gamma rays. Nonetheless, it remains a reliable

80

Chapter 6. Development of Neutron Tagging in SK-Gd

0.08

0.06

BG

0.05

BG

0.07

H-capture
Gd-capture

H-capture

0.06

0.04

0.05

0.03

0.04

Gd-capture

0.03

0.02

0.02
0.01
0

0.01
0

0.2

0.4

0.6

0.8

1
bsgood

0

0

0.2

0.4

0.6

0.8

1
bsdirks

Figure 6.3: Distribution of the gvtx (left) and gdir (right) for signals from neutron capture on Gd (magenta) and proton (cyan), andnoise (gray) candidates. The red arrows show the cut criteria. These
distributions are normalized by area.

indicator for distinguishing the Gd signal from the background noise. Thus, an energy
threshold of E > 3 MeV is set for the reconstructed energy in this analysis.
The cut variables and criteria of the Gd-capture signal are summarized in Table 6.2.
Table 6.2: Summary of neutron selection variables.

Cut variables
Capture time t
N200
Fiducial volume cut
Vertex reconstruction goodness gvtx
Direction reconstruction goodness gdirDistance from prompt vertex dprompt
Reconstructed energy E

6.1.4

Criteriat > 4 µs
N200 ≥ 25
dwall > 2 m
gvtx > 0.4
gdir < 0.4
dprompt < 300 cm
E > 3 MeV

Neutron Tagging Efficiency

Table 6.3 summarizes the selection efficiency for p-capture, Gd-capture, and the reduction power of background for each cut. Events with a prompt vertex locatedoutside the fiducial volume are omitted from the initial event count. The cut criteria
aim to maximize Gd-capture selection and minimize background. Consequently, theefficiency of p-capture is compromised. In the end, the implemented criteria successfully diminish the background signal to 10−5 while retaining a Gd-capture efficiencyof 78.6%.
Therefore, the neutron tagging efficiency for true neutrons ϵtrue
n , which was calculated as
ϵtrue
=
n

Number of remaining neutron capture events,
Number of initial capture events

and which was calculated as 39.5 ± 0.1%.

(6.1)

81

6.1. Neutron Tagging Algorithm

0.18
BG

0.16

H-capture

0.14

Gd-capture

0.12
0.1
0.08
0.06
0.04
0.02
0
0 200 400 600 800100012001400160018002000
distance [cm]Figure 6.4: Distributions of the dprompt for the signal from neutron
capture on Gd (magenta) and proton (cyan), and noise (gray) candidates. Red arrow indicates the threshold. These distributions arearea-normalized.

Table 6.3: Summary of selection and reduction efficiency for theneutron event and background.

Cut criteria
Initialt > 4 µs and N200 ≧ 25
dwall > 200 cm
bsgood > 0.4
bsdirks < 0.4
dprompt < 300 cm
E > 3 MeV
Final

p-capture355360
41.2%
29.8%
18.8%
16.8%
8.0%
2.4%
8521

Gd-capture
336046
95.0%
88.8%
85.4%
84.6%
81.9%
78.6%
264276

Background
–
100%
47.0%
11.6%
10.3%
0.06%
0.002%–

The capture time distribution is illustrated in Figure 6.6. The time constant is
ascertained by fitting the range from 20 µs to 500 µs using an exponential function.
f (t) = A · exp(−x/τ ) + B(6.2)

where A denotes the scale for fitting, B indicates the constant component, and τ
signifies the capture time constant. The obtained value of 115.3 ± 0.5 µs is strongly
consistent with the measured data [26].

6.1.5

Misidentification rate

The misidentification refers to the rate of the algorithm falsely recognizing non-neutron
events as neutrons. Accurate event search analysis hinges on this, given the necessity
for a minimal background rate when searching low-intensity events. To gauge themisidentification rate per event, termed εmis , the neutron search algorithm is utilized

82

Chapter 6. Development of Neutron Tagging in SK-Gd

0.16
0.14

BG

0.12

H-capture
Gd-capture

0.1
0.08
0.06
0.04
0.02
0
0

2

4

6

8

10

12
14
energy [MeV]

Figure 6.5: Distributions of the reconstructed energy for the signal
from neutron capture on Gd (magenta) and proton (cyan), and noise(gray) candidates. Red arrow indicates the cut criteria. These distributions are normalized by area.

22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0

χ 2 / ndf

37.11 / 42

Prob0.6853Scale

2.677e+04 ± 1.052e+02

Time Constant
Constant

115.3 ± 0.5
33.51 ± 12.47

BG
H-capture
Gd-capture

100

200

300
400
500
Capture Time [µs]Figure 6.6: Capture time distribution of the neutron MC and thefitting result.

on the random trigger data detailed in Section 6.1.3. The vertex of the prompt event
is assumed to be (x, y, z) = (35.3, −70.7, 0) cm, which is the center calibration hole83

6.2. Americium-Beryllium Calibration
for x, y and the center for z position. The value for εmis was calculated as follows:
εmis [/event] =Ndelayed · Tdelayed,
Nrandom · Trandom(6.3)

Mis-ID rate [/event]where Ndelayed denotes the number of selected events as neutrons, Nrandom indicatesthe number of random trigger data, Tdelayed denotes the time width of delayed neutron search (531 µs), and Trandom indicates the time duration of the random trigger
data. The consistency of εmis is assessed across all random trigger data from SK-VI.
Figure 6.7 portrays the εmis distribution based on the observation period. When considering the entirety of the live time of SK-VI, it is classified into 20 uniform segments.
Throughout the SK-Vi period, the mean εmis value stands at (1.83 ± 0.03) × 10−3 per
event.

0.00260.00240.00220.002
0.00180.00160.0014
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

run period

Figure 6.7: Time variation of ϵmis . Black-dotted line denotes theweighted mean value for the entire period, and the gray-shaded region
indicates the standard deviation.

6.2

Americium-Beryllium Calibration

An accompanying prompt event for the neutron is required to evaluate the neutron
tagging within actual SK data. Consequently, neutron detection was undertaken
utilizing the Americium-241/Beryllium-9 (AmBe) radioactive source, renowned foremitting neutrons along with gamma rays. The main reaction chain can be describedas follows:
241
9

Am → 237 Np + α

(6.4)

12

(6.5)

Be + α →C + n + γ(4.4 MeV),

where the gamma-ray emission is sourced from the de-excitation of the first excitedstate of 12 C. Figure 6.8 exhibits the major final state of the AmBe source. In thismeasurement, the pair of a neutron and a prompt 4.4 MeV gamma ray are used as
the target of the delayed coincidence.

6.2.1

Measurement

The AmBe source employed in this study is near-cylindrical, with dimensions of ∼1.2 cm diameter and height, as depicted in Figure 6.9a. Due to the low energy of theCherenkov light from the 4.4 MeV gamma ray, which is not sufficient to trigger SHE,

84

Chapter 6. Development of Neutron Tagging in SK-Gd

C

13

・
・
・

α +9 Be(α, n2 +12 C*)( ∼ 7.6 MeV)(α, n1 +12 C*)(α, n0 +12 C)∼ 4.4 MeV

n+ C
12

3α

Figure 6.8: Major final state of 13 C. A de-excitation from the second
excited state was not observed in the Kamioka AmBe source.

a unique setup was adopted. In this arrangement, the source was combined witha BGO scintillator crystal to boost the gamma-ray light yield. The BGO crystals
utilized in this measurement are cubic-shaped, though one corner is missing. Figure
6.9b displays the appearance of BGO crystal.

(a) Appearance of the AmBe source.

(b) Appearance of the four pieces of
BGO scintillator crystals.

Figure 6.9: Appearance of the Am/Be source (left) and the fourpieces of BGO scintillator crystals (right).

Source structure
The data was collected from two distinct source geometries to examine the influenceof BGO on tagging efficiency: ‘1BGO’ and ‘8BGO.’ The 8BGO configuration entirely
envelopes the source with eight BGO crystals, creating a cube with the missing cornerat its center. On the other hand, the 1BGO setup positions the source atop a single
BGO crystal, resulting in the source being only partially enveloped by BGO. All
source components are housed within the acrylic casing. The visual and schematic ofsource geometries can be observed in Figure 6.10.

85

6.2. Americium-Beryllium Calibration

Acrylic case

Am/Be source
Acrylic case
Am/Be

Am/Be

BGO

BGO

BGO scintillator(a) Appearance and Schematic of the 1BGO (b) Appearance and Schematic of the 8BGO
geometry.
geometry.

Figure 6.10: Appearance and schematic of 1BGO geometry (left)
and 8BGO geometry (right).

Data taking
In January 2021, data from nine distinct AmBe points were taken. Figure 6.11 visualizes the measurement points. At the central point, 8BGO data was gathered over
1 hour, while 1BGO data spanned 2 hours. Measurements at other off-center points
were conducted over a 30-minute interval, primarily to evaluate position dependenceof efficiency. Note that 1BGO data was exclusively taken at the center point.

z
−12 m

0m

+12 m

x

+12 m
0m
−12 m

Figure 6.11: Illustration of measurement points. Orange squares
exhibit measurement points, and the darker blue circle denotes calibration holes, where x = −1237, 35.3, 1080 cm ∼ −12, 0, +12 m.

6.2.2

AmBe MC simulation

To compare the neutron tagging efficiency between the measured data and MC, theAmBe source geometry was reproduced by Geant4 and introduced to the SKG4 detector simulation.

86

Chapter 6. Development of Neutron Tagging in SK-Gd

Primary Particles
As introduced at the beginning of this chapter and depicted in Figure 6.8, the AmBe
source decay typically culminates in one of three states: the emission of n0 , theemission of n1 , accompanied by 4.4 MeV gamma-ray, and the emission of n2 . As thedominant channel of the second excited state of 12 C is 12 C∗ → 3α reaction, whichcannot be observed in the SK, only a neutron is simulated from the n2 state. In
the MC simulation, the proportional representation of these three states is given as(n0 : n1 : n2 ) = (0.498, 1.0, 0.26), as cited in Ref. [45]. The kinetic energy of neutrons
across each spectrum examined in this analysis is portrayed in Figure 6.12.

0.09
n0

0.08

n1

0.07

n2

0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6
8
10
12
neutron kinetic energy [MeV]

Figure 6.12: Kinetic energy spectrum of the emitted neutron fromeach state, calculated as the combination referring measurements ofGuarrini and Malaroda [44], and ISO8529-1 [45].

Parameter tuning for BGO scintillator
To ensure a realistic simulation, certain scintillation, — parameters such as the lightyield and the decay time constant of the scintillation light, should be tuned. The
parameters were evaluated using the AmBe data at the center point. As such, the
BGO scintillator exhibits two types of decay constant: slow (τs ) and fast (τf ). , which
are estimated by fitting the PMT hit timings with the following function:f (t) =√H(t − T0 )(erf((t − T0 − µ)/( 2 × σ)) + 1)
2
h

(6.6)

i
× Af (e−(t−T0 )/τf − e−(t−T0 )/rf ) + As (e−(t−T0 )/τs − e−(t−T0 )/rs ) + C,
where the Af and As denote the amplitudes, T0 indicates the time offset, rf and rs
represent the rise time for fast and slow components, respectively, and C denotes aconstant component. erf(t) represents the error function, and µ and σ indicate theparameters of the error function. By assuming Af : As = 10% : 90% as described inRef. [142], the decay constants were estimated as τs = 440 ns and τf = 100 ns. As

87

6.2. Americium-Beryllium Calibration

indicated in Figure 6.13, these results are consistent with the measurements recorded
at 13.5 ◦ C (SK water temperature) [46].

Figure 6.13: Correlation between scintillation time constant for eachcomponent with BGO temperature. This figure is taken from [46].

After calibrating the decay time constant, the scintillation light yield is tuned bycomparing the total PMT charge within 1.3 µs around the SHE trigger (QISMSK).
The QISMSK distribution of events triggered with the SHE and without the OD
trigger is displayed in Figure 6.14. The prominent peak nearing 1000 highlights the
4.4 MeV scintillation photo-peak, while the trough near QISMSK ∼ 300 reveals thetapering section of the low-energy background event.

12000

10000

8000

6000

4000

2000

0
0

200

400

600

800

1000

1200

1400

1600

1800 2000
QISMSK

Figure 6.14: QISMSK distribution of the AmBe MC with 8BGO atthe center point for various scintillation yield parameters.

Given that the total charge of the photo-peak of 4.4 MeV gamma-ray should be
relatively proportional to the scintillation photon yield, optimization ensures that the
QISMSK mirrors the data. Figure 6.15 illustrates the QISMSK distribution acrossvarious yield settings, with the higher side of the peak varying in line with the yield.
After fitting these peaks using a Gaussian distribution, the interrelation between the

88

Chapter 6. Development of Neutron Tagging in SK-Gd

yield and QISMSK is gauged through a linear function, as observed in Figure 6.16.
Consequently, the yield parameter is determined to be 5900 MeV−1 .

Yield = 4000 [/MeV]
Yield = 4300 [/MeV]
Yield = 4600 [/MeV]
Yield = 4900 [/MeV]
Yield = 5200 [/MeV]
Yield = 5500 [/MeV]
Yield = 5800 [/MeV]
Yield = 6100 [/MeV]
Yield = 6400 [/MeV]
Yield = 6700 [/MeV]
Yield = 7000 [/MeV]

4500
4000
3500
3000
2500
2000
1500
1000
500
0
0

500

1000

1500

2000

2500

3000

Figure 6.15: QISMSK distribution of the 8BGO at center point datawith some light yield setting.

1300
1200
1100
1000
900
MC

800

DATA

700
600

Linear fitting to MC

4000 4500 5000 5500 6000 6500 7000

Figure 6.16: Correlation between yield and QISMSK in MC. Blackcircles denote the MC peak and its deviation for each yield settingin Figure 6.15. Red line indicates the QISMSK peak for the data in
Figure 6.14.

QISMSK distribution data at the center point and the best-fitted MC data arecomparatively presented in Figure 6.17.
Table 6.4 summarizes the parameters determined from the measurements.
MC production procedure
The procedure for noise data injection, detailed in Section 6.1.3, is employed to gauge
noise contamination precisely. The creation process of the data structure for the
AmBe MC comprises the following steps:

6.3. Neutron Tagging Efficiency Evaluation
with AmBe Source

89

Data
n0 MC
n1 MC
n2 MC

0.25

0.2

0.15

0.1

0.05

0
0

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 6.17: QISMSK distribution for the data and best-fitted MC;
n0 , n1 , and n2 MC indicates the MC simulation for each excited stateof 12 C.

Table 6.4: Parameters determined from the measurements, including
the rise time parameters and resolution scale parameter.

Parameter
Fast time constant τfSlow time constant τsRise time of fast component
Rise time of slow component
Photon yield
Resolution scaling factor
Fraction of fast component

Name in Geant4
FASTTIMECONSTANTSLOWTIMECONSTANTFASTSCINTILLATIONRISETIMESLOWSCINTILLATIONRISETIMESCINTILLATIONYIELDRESOLUTIONSCALEYIELDRATIO

Value
100 ns
440 ns
1.0 ns
1.0 ns5900 MeV−1
1.0
0.1• Simulate primary particles within the Am/Be geometry and record PMT hits
up to 535 µs.
• Calculate noise hits sporadically between 0–2.7 µs, considering the primary trigger due to scintillation ends at 1µs.
• Produce software triggers up to 300 ns from generating time to prevent erroneous
triggers due to Gd-capture gamma-ray activating the SHE.
• Append noise data (T2K or SK random-wide) into simulated PMT hits from
2.7 µs to 535 µs.

6.3

Neutron Tagging Efficiency Evaluation
with AmBe Source

Evaluating the neutron tagging efficiency is essential to estimate the physics sensitivity
in the SK-Gd experiment. To assess the performance of the neutron tagging algorithm
and estimate the reproducibility of the actual neutron tagging by the MC, the neutron
tagging efficiency calculated from AmBe measurements was compared between themeasured data and MC results.

90

Chapter 6. Development of Neutron Tagging in SK-Gd

6.3.1

Prompt event selection

To accurately extract the neutron tagging efficiency, rigorous prompt event selection
is essential. The obtained data undergoes processing to select the 4.4 MeV gamma-ray
using these criteria meticulously:• Events triggered by SHE and that do not trigger the OD, followed by an AFT
event.
• Time differences exceed 1 ms from the previous SHE.
• Number of OD hits is less than 11.
• QISMSK values are contained within an acceptable region.
The first cut criterion ensures that the neutron signal is recorded over an extended time window and sidesteps significant charge events caused by muons. The
second cut criterion helps to prevent interference from lingering signals of the previous prompt event and scintillation light. The third one ensures that the prompt event
does not originate from the cosmic muons. The final criterion is tailored to single out
scintillation prompt events compatible with the 4.4 MeV gamma-ray. The QISMSK
distribution for specific measurement points is presented in Figure 6.18.
Given that QISMSK varies based on the distance between the source position
and the ID wall, the selection criteria are segmented into three categories based on
measurement locations: central data (both x and z coordinates at 0 m), edge data(either x or z at ± 12 m while the other remains at 0 m), and corner data(both x
and z coordinates ± 12 m). Suitable criteria for each dataset are implemented, as
depicted in Figure 6.18.

6.3.2

Neutron Signal Search

The neutron detection algorithm, as detailed in Section 6.1.3, is applied to both AmBe
data and MC. The distribution of the number of delayed candidates surpassing theN200 ≧ 25 threshold for the central source position is illustrated in Figure 6.19. For
MC, the peak value is 92.0, whereas for the data, it was 94.5. This difference arises
from the drift of neutrons from a different event originating from the AmBe source,
termed ‘random neutrons,’ and the capacity of the MC to reproduce noise hits.
All conditions for neutron selection, elaborated in Section 6.1.3, are applied to
all candidates filtered by the N200 selection threshold. Figure 6.20 illustrates the
distributions of variables used for selection. Each distribution has already applied
thresholds other than the variable itself.
The data shapes largely align with the outcomes from the MC. Owing to themore expansive photon emission time scale of scintillation light emission, scintillation
events generally exhibit a lower gvtx compared to Chernekov events. This indicatesa potential flaw in replicating scintillation, as the observed data contain more eventswith reduced gvtx than the MC does for the gvtx distribution. The majority of thisvariation is rectified by the imposed cut.
The timing distribution of the final neutron candidates, after passing all the requirements, is presented in Figure 6.21. These distributions are fitted with a range of
5 to 500 µs by the exponential function f (t) as
f (t) = A exp(−t/τ ) · (1 − exp(−x/µ)) + B,

(6.7)

6.3. Neutron Tagging Efficiency Evaluation
with AmBe Source

Center data

91

(X=-12m, Z=-12m)

850 < QISMSK < 1100

950 < QISMSK < 1200

(X=+12m, Z=0m)
900 < QISMSK < 1150

Figure 6.18: QISMSK distributions for center data (top left), (X=−12 m, Z= −12 m) data (top right), and (X= +12 m, Z= 0 m) data(bottom) obtained by 8BGO AmBe measurement; arrows indicate thethreshold criteria for each source position.

where A denotes an amplitude parameter, τ indicates the decay time constant, µ refers
to the thermalization time constant, and B indicates the constant component. In thisanalysis, µ is set to 4.3 µs. The time constant for the data (τdata ) and MC (τMC ) wereτdata = 115.1 ± 2.3 µs, and τdata = 118.1 ± 0.9 µs, respectively. The constant offset
B observed only in data, primarily containing the random neutron, was evaluated as
B = 26.2 events/bin.

6.3.3

Tagging Efficiency Estimation

The neutron tagging efficiency ϵdata
for AmBe data can be calculated as
n
ϵdata
=
n

Ntagged − Nuncorr,
Nprompt(6.8)

where Ntagged denotes the total remaining neutron candidates after neutron selection,
Nuncorr indicates the number of events without time correlation with the prompt
events, and Nprompt represents the number of prompt events. Nuncorr is estimated by
the constant component B that appeared in Equation 6.7 as follows:
Nuncorr = Twidth · B/Tbin ,(6.9)

where Twidth denotes the neutron search window as [4, 535] µs, B is a constant component presented in Figure 6.21a, and Tbin refers to the bin width of the capture
timing distribution used for fitting. Nuncorr can be estimated to reduce the effect of
the random neutron event from tagging efficiency.

92

Chapter 6. Development of Neutron Tagging in SK-Gd

0.1

DATA
n0 MC

0.08

n1 MC
n2 MC

0.06

0.04

0.02

0
0

20

40

60

80

100

120
140
No. of Candidates

Figure 6.19: Distribution of the number of delayed candidates passing N200 ≥ 25.

In contrast, for the MC, as all neutron events are correlated with the prompt eventand the potential misidentification is negligible, Nuncorr should be zero. Therefore, theϵMC
can be estimated as
n
ϵMC
=
n

Ntagged.
Nprompt(6.10)

Considering each excited state, ϵMC
can be modified tonPstate i
Ntagged × WiiMCϵn = Pstate i,
Nprompt × Wii

(6.11)ii
where the Ntagged
denotes the number of tagged candidates for the i-th state, Nprompt
indicates the number of prompt events for the i-th state, and Wi refers to the fractionof each state, respectively. The estimated capture time constant and the tagging
efficiency obtained from the 1BGO and 8BGO source data and MC are listed inTable 6.5, wherein the neutron tagging efficiency of the data was relatively 12% lower
than that derived by the MC for 8BGO and 9% for 1BGO.

Table 6.5: Summary of capture time constant and neutron tagging
efficiency for the DATA and MC for each BGO geometry. Errors only
include only statistical uncertainty.

Data
MC(Data-MC)/Data

Capture time constant [µs]
1BGO
8BGO
118.9 ± 3.1
115.1 ± 2.3
115.9 ± 1.2
118.1 ± 0.9––

Tagging efficiency[%]
1BGO
8BGO
36.4 ± 0.7 34.0 ± 0.5
39.7 ± 0.3 38.3 ± 0.2−0.088−0.123

93

6.4. Discussion on Tagging Efficiency Measurement

0.045

0.06

data
BG
H-capture
Gd-capture

0.04
0.035
0.03

data
BG
H-capture
Gd-capture

0.05

0.04

0.025
0.03
0.02
0.015

0.02

0.01
0.01
0.005
0

0

0.2

0.4

0.6

0.8

1
goodness0(a) Distribution of the gvtx .

0

0.2

0.4

0.6

0.8

1
dirks

(b) Distribution of the gdir .
0.03

0.16

data
BG
H-capture
Gd-capture

0.14
0.12

data
BG
H-capture
Gd-capture

0.025

0.02

0.1
0.015

0.08
0.06

0.01

0.04
0.005
0.02
0
0

200

400

600

800 1000 1200 1400 1600 1800 2000
Distance [cm](c) Distribution of the distance from prompt
event vertex.

0
0

1

2

3

4

5

6

7

8
9
10
BSenergy [MeV](d) Distribution of the reconstructed energy.

Figure 6.20: Distributions of neutron selection variables. Each colorfilled histogram exhibits the MC, and solid point represents the data,
which is aligned with the statistical error. Red arrow indicates the cut
criteria for neutron selection. These distributions are normalized by
the number of prompt events.

6.4

Discussion on Tagging Efficiency Measurement

The results listed in Table 6.5 indicate about 10% discrepancy between the data and
MC. Compared to the 1 BGO, this difference is more pronounced in the 8 BGO case,suggesting that the BGO might be a contributor to the variance.
A potential explanation for this discrepancy can be attributed to the effect of
creating a ‘dummy prompt event.’ In the measured data, neutron capture tends tooccur in the vicinity of the BGO scintillator. Therefore, the gamma rays from neutron
capture on the nucleus might sometimes trigger a SHE due to scintillation. This can
reduce the neutron tagging efficiency as there is no subsequent neutron. This effecthas not been incorporated in the MC, necessitating an assessment of the impact of
this dummy prompt event on efficiency. At this time, the effect is estimated using(Dummy prompt event) = (Measurement time [s])(6.12)× (Random neutron intensity [Hz])(6.13)× (Probability of prompt event from neutron)(6.14)× (SHE trigger efficiency)(6.15)× (AFT trigger efficiency),(6.16)

94

Chapter 6. Development of Neutron Tagging in SK-Gd

700

DATA
fitting600

n0 state
n1 state
n2 statefitting

1000
800

500

τ = 115.1 ± 2.3 µs
B = 26.2 /bin

400

600

300

τ = 118.1 ± 0.9 µs

400

200

200

100
0
0

100

200

300

400
500
Capture time [µs]

0
0

100

200

300

400
500
Capture time [µs](a) Capture timing distribution for measured (b) Capture timing distribution for MC simuladata.
tion.

Figure 6.21: Capture timing distributions for measured data (left)
and MC simulation (right). Dotted line only displayed in the data plot
represents the flat component evaluated by exponential fitting.

The measurement times of the center data for 1BGO and 8BGO configurations were7329 s and 4002 s, respectively.

6.4.1

Random neutron intensity

Random neutrons lack a timing correlation with any prompt event, as depicted in
Figure 6.22. They might produce the dummy prompt event if the 4.4 MeV gamma
ray from the AmBe source does not trigger a SHE event. This random neutron intensity manifests as a portion of the constant component in the neutron capture time
distribution. The timing fit is detailed in Section 6.3.2. However, several of the 4.4

γ(4.4 MeV)AmBe

not trigger SHE

BGOnCaptured outside of AFT

Figure 6.22: Illustration of emission of the random neutron.

MeV gamma-ray events were also accidentally tagged by a delayed neutron selection,
as described in Section 6.1.3. Thus, this constant component encompasses these unintentional events. Consequently, when considering the random neutron intensity,
the count of tagged 4.4 MeV gamma rays must be factored in. The intensity can be6.4. Discussion on Tagging Efficiency Measurement95

determined as:(Random neutron intensity [Hz]) =Nconst − N4.4MeV.
Nprompt × Tbin [s] × ϵMC
n(6.17)

Here, Nconst [/bin] (B in Equation 6.7) denotes the constant component in the timing
distribution, and N4.4MeV [/bin] represents the number of tagged 4.4 MeV gammaray events per bin. The constant component obtained by the timing distribution oftagged-neutron candidates is 26.2 [events/bin] for 8BGO and 17.4 events[/bin] for
1BGO. The bin width for all data is 5.35 × 10−6 [s].
After that, the number of tagged 4.4 MeV gamma-ray events per bin N4.4MeV isexpressed as follows:
N4.4MeV = Rn1 × Tbin × Nprompt × ϵMC
4.4MeV ,(6.18)

where Rn1 [Hz] denotes the emission rate of the 4.4 MeV gamma ray from the firstexcited state of the AmBe source, and ϵMC
4.4MeV signifies the survival probability of
the 4.4 MeV gamma ray. This is estimated by applying the same neutron event
selection cut to its MC simulation. Survival probabilities for each cut are summarizedin Table 6.6. The probability of tagging 4.4 MeV gamma-ray as a neutron signal is
33.8% for 8BGO, and 59.7% for 1BGO, respectively. Rn1 is assumed to be 110.1 Hz
from the result of the external experiment [143]. Consequently, the random neutron
intensity for 8BGO is estimated to be 187.2 Hz, and for 1BGO, is estimated to be
149.2 Hz, as summarized in Table 6.7.
Table 6.6: Summary of contents in the calculation for the tagging
efficiency of 4.4 MeV gamma-ray.

Content
N200 > 25
FV cutgoodness cut
dirks cutenergy cut
distance cut
Total probability

Efficiency
8BGO 1BGO
97.2% 90.8%
61.4% 92.0%
68.1% 87.5%
99.3% 99.3%
92.2% 90.7%
90.9% 90.7%
33.8% 59.7%

Table 6.7: Break down the contents in the calculation of random
neutron intensity.

Content
Nconst [/bin]
N4.4MeV [/bin]
Nprompt
Tbin [µs]ϵMCnRandom neutron intensity [Hz]Survival probability
8BGO
1BGO
26.6
17.3
11.4
11.6
44960
25873
5.35
5.35
38.3%
39.7%
187.2
149.2

96

Chapter 6. Development of Neutron Tagging in SK-Gd

6.4.2

Probability of prompt event from neutron

The probability of the gamma-ray from neutron capture on Gd(n, γs)Gd evolving into
a prompt event is calculated. The 2.2 MeV gamma ray from hydrogen capture should
not influence the prompt event selection, given that the QISMSK is likely half thatof the 4.4 MeV gamma ray. Instead, we examined the captures from other isotopes,with Ge(n, γs)Ge being the primary candidate, as illustrated in Figure 6.23.

10−1
10−2
10−3
10−4
10−5

e-

S33

S34

O19

S33

deuteron

O18

O19

e-

O17

O18

deuteron

Ni65

S35

Ni63

Ni59
Ni59

O17

Mo99
Mo99

Ni65

Mo98
Mo98

Ni63

Mo97
Mo97

Ni61

Mo96
Mo96

Ni62

Mo95
Mo95

Ni62

Mo93
Mo93

Ni61

Ge77

Mo101

Ge75

Mo101

Ge74

Ge77

Gd161
Gd161

Ge75

Gd159
Gd159

Ge74

Gd158
Gd158

Ge71

Gd157
Gd157

Ge73

Gd156
Gd156

Ge73

Gd155

Ge71

Fe59

Gd153

Gd155

Fe58
Fe58

Gd153

Fe57

Fe59

Cr55

Fe55

Fe57

Cr54
Cr54

Fe55

Cr53
Cr53

Cr55

C14

C13

Cr51
Cr51

Bi210

C13

C14

Bi210

10−6

10−1
10−2
10−3
10−4
10−5
10−6

Figure 6.23: The probability of thermal neutron capture in the SK
with AmBe source geometry for 8BGO (top) and 1BGO (bottom).
These probabilities were calculated based on the result of the five million neutron MC, which uses ENDF.VII.1 as a nuclear data library[47].

To ascertain the probability, these steps are followed:
1. Generate 5 million neutron MC.
2. Store neutron capture data, like vertex, capture nucleus, and energy of each
capture gamma-ray.
3. Based on this data, generate millions of gamma-ray MC for Gd(n, γs)Gd and
30,000 MC events for Ge(n, γs)Ge.
4. Determine the likelihood by applying identical cuts as the prompt event selection.
The outcomes indicate that the Gd(n, γs)Gd probability is 0.285%, and for Ge(n, γs)Ge,
it was 10.2%. MC calculations yield neutron capture fractions of 48.1% for Gd and0.7% for Ge. Thus, the final estimated probability stands at 0.2% (Table 6.8). Using
the same calculations for the 1BGO setup, neutron capture fractions are 48.4% on
Gd and 0.1% on Ge. The associated probabilities for a neutron emerging as a prompt
event on Gd and Ge capture are 0.026% and 1.4%, respectively, resulting in an overall
probability of 0.014% for 1BGO.

97

6.4. Discussion on Tagging Efficiency Measurement
Table 6.8: Summary of the contents of the dummy prompt event.

Content

8BGO

Trigger SHE
pass QISMSK cut
Total remaining
Capture fraction
Final prob.

6.4.3

Probability

GdGe
10.65% 88.61%
2.68% 11.17%
0.285% 9.90%
48.15% 0.65%
0.137% 0.045%
0.182%

1BGO

Gd
Ge
5.81%
79.08%
0.54%
7.23%
0.0311% 5.72%
48.43%
0.11%
0.015% 0.006%
0.021%

Trigger efficiency

To determine the number of dummy prompt events, the SHE and AFT trigger efficiencies must be accounted for and derived from the SHE and AFT trigger rates. For
the central data measurements, the rates of SHE and AFT are 81.7 Hz and 37.7 Hzfor 8BGO, and 25.8 Hz and 19.8 Hz for 1BGO, respectively. Occasionally, a SHE
event might be overlooked due to overlap with another SHE or AFT event window.
The inefficiency arising from this overlap can be assessed by the combined SHE andAFT window duration per second. Consequently, the dead time of the SHE trigger,
induced by the AFT event, was recorded at 22 ms/sec for 8BGO and 11 ms/sec for
1BGO, translating to SHE trigger efficiencies of 97.8% for 8BGO and 98.9% 1BGO.
From the DAQ setup in January 2021, the AFT rate is limited to once every
20 ms. This constraint may lead to overlooked AFT events, essentially SHE events
not followed by an AFT event. The proportion of such instances is deduced from theratio of SHE to AFT events, resulting in values of 46.1% for 8BGO and 76.7% for
1BGO.

6.4.4

ResultAs discussed in this section, the potential components of the dummy prompt eventsby the captured gamma-ray from neutron capture are estimated as defined by Equation 6.12. The terms in Equation 6.12 are summarized in Table 6.9.
Table 6.9: Summary of contents in dummy prompt event.

Content
Measurement time [s]Random neutron intensity [Hz]Probability that neutron will be the prompt event
SHE trigger efficiency
AFT trigger efficiency
Estimated number of events
Dummy event probability

Values8BGO 1BGO
4002
7329
187.2
149.2
0.182% 0.021%
97.8%
98.9%
46.1%
76.7%
614.8
174.2
1.368% 0.673%

Consequently, we can express the expected neutron tagging efficiency for MC ϵ′n
as follows:ϵ′n = ϵn ×1.
1 + (Dummy event probability)(6.19)

98

Chapter 6. Development of Neutron Tagging in SK-Gd

Based on the findings presented in Table 6.5, only about 1.5% and 0.7% in 8BGO and1BGO of relative discrepancy in absolute value can be attributed to dummy prompt
events caused by source neutrons. This discrepancy will be factored into the MC
efficiency correction.

6.5

Systematic Uncertainty Extraction

The systematic uncertainty contingent on the MC simulation is also gauged. It is
broadly categorized into four areas: prompt event selection, delayed event selection,
MC simulation settings, and position dependence. All these uncertainties are derived
from the 8BGO central data and its MC counterpart.

6.5.1

Prompt event selection

0.95
0.94

lower side = 850
lower side = 800

0.93lower side = 750
lower side = 700

DATA/MCDATA/MCAs described in Section 6.3.1, the prompt event selection encompasses four conditions. Among these, only the QISMSK cut significantly impacts the tagging efficiency.
Therefore, uncertainty arising from the QISMSK cut criteria needs assessment. This
uncertainty is gauged by varying the QISMSK cut parameters at the central point,
as depicted in Figure 6.18. For the lower threshold, the range is scanned from 700 to
850 [p.e.], whereas the upper limit varies from 1100 to 1250 [p.e.]. The most extensive
criteria span is double the nominal range. The uncertainty is assigned as the maximum deviation in the neutron tagging ratio between data and MC when comparedto the nominal cut criteria. Figures 6.24 and 6.25 display these comparative results.
From this analysis, the largest discrepancy from nominal criteria is found within the[700, 1150] range, leading to an assigned uncertainty of 0.47%.

0.95
0.94

higher side = 1150

0.92

0.91

0.91

0.9

0.9

0.89

0.89

0.88

0.88

0.87

0.87

0.86

0.86
1100

1150 1200 1250 1300
QISMSK cut at higher sidehigher side = 1200
higher side = 1250

0.92

0.85
1050

higher side = 1100

0.93

0.85
650

700

750
800
850
900
QISMSK cut at lower side

Figure 6.24: QISMSK cut criteria and the data-MC difference in theneutron tagging efficiency as a function of the higher side (left) andlower side (right).

6.5.2

Delayed event selection

The delayed event selection is associated with four distinct variables. Thus, the uncertainty for each variable is combined to determine the overall uncertainty of thedelayed event selection. In this evaluation, the variation in tagging efficiency is considered equivalent to efficiency shifts when altering neutron selection criteria.

99

Higher thr. [p.e.]

6.5. Systematic Uncertainty Extraction

0.4
1250

0.3
0.2

1200
0.1
0

1150

−0.1
−0.2

1100
700

750

800

850
Lower thr. [p.e.]−0.3

Figure 6.25: QISMSK cut criteria and the data-MC difference inneutron tagging efficiency. Color depicts the difference between data
and MC from the nominal criteria.

Vertex reconstruction goodness
The uncertainty surrounding the vertex reconstruction goodness gvtx is determinedby contrasting the distribution between data and MC after imposing all cuts, except
for the gvtx cut. Figure 6.26 indicates a noticeable shift in the gvtx distribution ofMC, corresponding to about 2.1% towards a lower gvtx side compared to the data.
Thus, survival efficiency was calculated by applying a gvtx threshold adjusted basedon the difference between data and MC peak. The subsequent uncertainty was ascertained by comparing the survival efficiencies of MC for the nominal and shifted cut.
Consequently, the gvtx dependent uncertainty was evaluated to be 0.94%.
Direction reconstruction goodness
Similarly, the uncertainty from the gdir cut is estimated. This evaluation follows themethod used for gvtx . Figure 6.27 depicts the gdir distributions and cut criteria. The
MC peak deviating from the data is 0.7%, and the resultant uncertainty was estimatedat 0.03%.
Reconstructed energy
The variations in the energy scale between data and simulation should be considered
for systematic uncertainty. This deviation is gauged by examining the distribution ofreconstructed energy after applying all cuts, bar the energy cut, across data and MC.
As displayed in Figure 6.28, the average discrepancy between the data and MC was
0.32%. By smearing the cut threshold to examine the impact of this difference, theuncertainty was determined as 0.23%.

100

Chapter 6. Development of Neutron Tagging in SK-Gd

0.07
0.06

DATA
MC
Cut thr. (nom.)

0.05

Cut thr. (shift)

0.04
0.03
0.02
0.01
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Figure 6.26: Distribution of gvtx for data and MC. Solid green line
indicates the smeared cut threshold. Both plots are normalized by
area.

0.09
0.08

DATA
MC

0.07
0.06

Cut thr. (nom.)Cut thr. (shift)

0.05
0.04
0.03
0.02
0.01
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Figure 6.27: Distribution of gdir for data and MC. Solid green line
indicates the smeared cut threshold. Both plots are normalized byarea.

Vertex resolution
Vertex reconstruction manifests as the distance from the source cut in neutron selection. Any discrepancy in vertex resolution between data and MC inherently introduces a systematic uncertainty in tagging efficiency. Accordingly, vertex resolution
is analyzed. For this study, vertex resolution is defined as r satisfying the following
equation:
R rcm ′ ′0cm dr h(r )= 1σ ∼ 68.27%,(6.20)
R 500cm′ h(r ′ )dr0cm
where h(r′ ) denotes the distance distribution between the reconstructed vertex andsource position. These distributions for data and MC are illustrated in Figure 6.29.

101

6.5. Systematic Uncertainty Extraction

0.07
DATA

0.06

MC
Cut thr. (nom.)

0.05

Cut thr. (shift)

0.04
0.03
0.02
0.01
0

1

2

3

4

5

6

7

8

9

10

Figure 6.28: Distribution of reconstructed energy for data and MC.
Solid green line denotes the smeared cut threshold. Both plots arenormalized by area.

The resolution was 97.85 and 103.15 cm for data and MC, respectively.
The systematic uncertainty associated with vertex resolution can be calculated
based on the efficiency differential between data and MC when altering the source
distance cut criteria based on the vertex resolution discrepancies. This yields anuncertainty estimate of 0.44%.

DATA

0.05
MC
Cut thr. (nom.)

0.04

Cut thr. (shifted)

0.03

0.02

0.01

0
0

50

100

150

200

250

300

350

400
450
500
Distance [cm]Figure 6.29: Distribution of the distance between reconstructed delayed event vertex and the source position for data and MC. Solidgreen line denotes the smeared cut threshold. Both plots are normalized by area.

6.5.3

MC simulation settings

MC simulation operates on various parameters. While the majority have a limited
effect on tagging efficiency, certain settings related to the neutrons and their capture

102

Chapter 6. Development of Neutron Tagging in SK-Gd

play a significant role. Therefore, their influence requires further assessment.
Gd concentration

220
200
180
160
140
120
100
80
60
40
20
0

Capture on Gd nuclei

Capture Time Constant [µs]The uncertainty of Gd concentration is anticipated to impact neutron tagging efficiency, which can be ascertained by examining the tagging efficiency of Gd capture
and the Gd capture fraction in SK-VI. Figure 6.30 displays the time constant (left)
and the Gd capture efficiency (right) as a function of Gd mass concentration. Theseplots stem from fitting data points measured by the AmBe MC simulation based on
the Geant4.10.5 using an inverse polynomial function. Recent studies posit the average time constant at SK-VI to be 116.5 ± 0.2 µs. Consequently, the corresponding
Gd mass concentration stands at 105.0±0.4 ppm, derived from the function in the left
panel of Figure 6.30. After that, the capture fraction on Gd nuclei is estimated to be
47.8 ± 0.1%, obtained from the right panel of Figure 6.30.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
10−5
10−4
10−3
Concentration of Gd nuclei [fraction of weight]

0

10−5
10−4
10−3
Concentration of Gd nuclei [fraction of weight]

Figure 6.30: Correlation between the time constant and Gd massconcentration (left), and the Gd capture fraction and Gd mass concentration (right).

The relative error concerning the Gd nuclei capture fraction is deduced to be
0.21%. Referring to Table 6.3, 78.6% of Gd are tagged by the selection. Thus, therelative uncertainty of Gd mass concentration on the neutron tagging uncertainty is
0.17%. Generally, the effect of hydrogen capture is negligible owing to low tagging
efficiency.
Gamma-ray emission model of neutron capture on Gd
As described in Section 3.3, the gamma-ray emission following neutron capture on
Gd employs the ANNRI-Gd model. Variabilities in this model necessitate carefulconsideration. Consequently, the gamma-ray emission model for Gd capture is transitioned from ANNRI-Gd to the Photon-Evaporation model — a pre-installed modelin Geant4. Subsequent MC simulations reveal that the energy distribution under the
Photo-Evaporation model deviates significantly from that of the original ANNRI-Gd
model, making a discrepancy of 1.7%.
Neutron excited state fraction
As expressed in Section 6.2.2 and Equation 6.11, the neutron tagging efficiency for
MC was calculated considering the excited state branches of 12 C (0.498, 1.0, 0.26)
determined according to ISO [45]. By examining potential extreme fractions, the103

6.5. Systematic Uncertainty Extraction

influence of state fraction on neutron tagging efficiency becomes apparent. Table 6.10
collates the state fraction patterns assumed for this analysis alongside neutron tagging
efficiency. The external measurement conducted by Ito et al. [143] aligns with theseassumptions. The most significant deviation from the nominal branch ratio of thestate is identified as 0.39%, and this value is designated as the associated uncertainty.
Table 6.10: Summary of excited state fraction and neutron tagging
efficiency

State fraction (n0 :n1 :n2 )(0.498, 1.000, 0.260) (Default)(0.760, 1.000, 0.000)(0.500, 1.000, 0.000)(0.650, 1.000, 0.000)

Neutron tagging efficiency
38.31 ± 0.37%
38.30 ± 0.36%
38.46 ± 0.34%
38.36 ± 0.36%

Relative difference
–
0.03%
0.39%
0.13%

Neutron energy spectrum of the first excited state
As the prompt event selection focuses on selecting the gamma-ray event from the firstexcited state of 12 C, the primary impact of the neutron energy spectrum on tagging
efficiency stems from the spectrum of the first excited state. As such, the influence of
only the first excited state is deemed relevant for uncertainty regarding the uncertainty
on the neutron energy spectrum. Analysis of the spectrum variation uses data fromexperiments conducted in Kamioka [143]. Figure 6.31 displays the differential neutron
spectrum for the first excited state between the default MC and the measured version.
When substituting the default first excited state MC with the measured spectrum,

14000
Nominal Spectra (ISO)12000
Measured Spectra (Wada et al.)

10000
8000
6000
4000
2000
0
0

1

2

3

4

5
6
7
8
9 10
Neutron kinetic energy [MeV]

Figure 6.31: Neutron kinetic energy spectra from the first state of
12
C based on ISO (black) and measured (red).

efficiency shifts to 38.10%. This yields a relative discrepancy of 0.53%, incorporated
as a systematic uncertainty.

104

6.5.4

Chapter 6. Development of Neutron Tagging in SK-Gd

Position Dependence

Tagging efficiency[%]

The potential variability in tagging efficiency based on position mandates inclusion in
the systematic uncertainty assessment. Efficiencies across nine measured points areevaluated and illustrated in Figure 6.32.

41
DATA
MC
Average(DATA)
Average(MC)

40
39
38
37
36
35
34
33
x=0 z=-12

x=0 z=0x=0 z=12 x=-12 z=-12 x=-12 z=0 x=-12 z=12 x=12 z=-12 x=12 z=0 x=12 z=12

Source position [m]Figure 6.32: Neutron tagging efficiency for each measured point.

On average, the efficiency levels were 34.4% for data and 37.4% for MC. The
considerable statistical uncertainty associated with the data points complicated theposition dependence estimation. As such, the variability is gauged via MC deviations,
resulting in a 0.47% value attributed to position dependence.

6.5.5

Total Systematic Uncertainty

The section culminates with an amalgamation of all systematic uncertainties concerning tagging efficiency — these are combined using a quadrature method. For thisanalysis, systematic uncertainties tied to the dummy prompt event estimation are
deemed negligible. The systematic uncertainty of this measurement is presented inTable 6.11. In total, 2.22% of systematic uncertainty is considered for the tagging
efficiency of MC.

6.6

Result6.6.1

Neutron Tagging Efficiency

The representative value of neutron tagging efficiency is evaluated using both thecenter point data and MC at this time. For the center point, the efficiency without
any surrounding apparatus (0BGO) is solely assessed for MC. The efficiencies, alongwith their respective errors, are summarized in Table 6.12. Figure 6.33 visualizes thetagging efficiency in relation to the quantity of surrounding BGOs. The efficiencyof MC consistently surpasses the data, evident in both the 1BGO and 8BGO scenarios. Efficiency reveals a negative correlation with the BGO count. Moreover, thediscrepancy between data and MC is more pronounced in the 8BGO scenario compared to the 1BGO setup. This suggests potential inaccuracies in understanding theinfluence of BGO and acrylic cases on efficiency, with the implications becoming less

105

6.6. Result
Table 6.11: Summary of systematic uncertainty on AmBe measurement.

Tag. efficiency[%]

Content
Prompt event selection
Timing goodness gvtx
Direction goodness gdir
Reconstructed energy
Vertex resolution
Gd concentration
Gd(n, γ)Gd model
Neutron excited state
Neutron energy spectrum
Position dependence
Total

Systematic uncertainty
0.47%
0.47%
0.94%
0.03%
1.06%
0.23%
0.44%
0.17%
1.70%
1.83%
0.39%
0.53%
0.47%
0.47%
2.22%

42

DATA (w/ stat. error)

41

MC (w/ stat.+sys. error)

40
39
38
37
36
35
34
33

0

1

2

3

4

5
6
7
8
Number of BGOs

Figure 6.33: Neutron tagging efficiency as a function of the surrounding BGOs. Efficiency without BGO (0BGO) is only estimatedby MC because it cannot be estimated for actual data.

pronounced as the number of BGOs decreases. Consequently, the divergence observedin the 1BGO scenario when comparing data and MC is recognized as an added systematic uncertainty for the MC in the 0BGO context. The final assessment pegs theneutron tagging efficiency for 0BGO at 40.2 ± 0.1 (stat.) +0.1
−3.4 (syst.) %.

6.6.2

Time variation

Monthly inspections, each spanning 30 minutes, are conducted at the center point tomonitor potential fluctuations in tagging efficiency. This rigorous monitoring, which
covered the entirety of the SK-VI period — from January 2021 through January 2022
— relies on the monthly AmBe source measurement at the center point. Figure 6.34
depicts variation in tagging efficiency with the data-taking date. On average, the106

Chapter 6. Development of Neutron Tagging in SK-Gd
Table 6.12: Summary of neutron tagging efficiencies for the DATA
and MC for each BGO geometry.

Data
MC(Data-MC)/Data

1BGO
36.4 ± 0.7(stat.)%39.5 ± 1.2(stat. + syst)%−0.08 ± 0.03

8BGO
34.0 ± 0.5(stat.)%37.8 ± 1.0(stat. + syst.)%−0.10 ± 0.03

Tagging efficiency[%]

efficiency values are 33.7 ± 0.7% for the 8BGO configuration and 36.8 ± 0.3% for
the 1BGO setup. This data underscores the stability of neutron tagging efficiency
throughout the SK-VI period.
40
39

8BGO
1BGO
Average(8BGO)
Average(1BGO)

38
37
36
35
34
33
32
31
30
2021/01/01

2021/03/07

2021/05/12

2021/07/17

2021/09/21

2021/11/26
2022/01/31
Measured date

Figure 6.34: Neutron tagging efficiency as a function of the surrounding BGOs.

6.6.3

Conclusion

The neutron tagging algorithm to detect neutron capture on Gd is newly developed for
the SK-Gd experiment. Using this method, the study of AmBe neutron measurement
is carried out for the first time in SK-Gd. Alongside the measurement using the
8BGO geometry, an additional study using the 1BGO geometry was conducted tocomprehend the effect of the BGO and acrylic apparatus. Also, this marks the firsttime to evaluate neutron tagging efficiency in MC with BGO geometry. Notably,
the data and MC reveal a relative discrepancy of about 10%. The magnitude of thedivergence varies based on the specific BGO configuration. In light of these findings, anadditional uncertainty, mirroring the efficiency disparity for 1BGO between data andMC, is factored into the neutron tagging efficiency. The newly acquired understandingof the relationship between the apparatus configurations and neutron tagging efficiency
has contributed to refining the margin of the uncertainty, shrinking it from the SK-IV
pure-water study. The relative error derived for the 0BGO efficiency is applicable to
the SRN analysis, as described in Chapter 7.

107

Chapter 7

Search for Diffuse Supernova
Neutrino Background in SK-Gd
Using the data observed during July 2020 and May 2022, the first SRN search in the
SK-Gd experiment is operated. This chapter provides an overview of the analysis, interms of the data set, search energy window, and background sources.

7.1

Data Set

In this analysis, all SHE-triggered data linked to AFT-triggered events in the normal physics runs during SK-VI are utilized. From the middle of SK-V, tracking the
AFT events after the OD-triggered event (primarily muons) became feasible, making
post-muon neutron searches a potent method for spallation identification as described
below. The trigger conditions are detailed in Chapter 2.
With the upgraded trigger system during SK-VI, AFT trigger event downtimes
saw a significant decline. Until the mid-SK-VI, only one AFT event could be triggered
once every 21 ms. However, post-March 3rd, 2022, the rate tripled, allowing three
AFT triggers within the same timeframe. Consequently, the AFT trigger efficiency
soared from around 97% to over 99.9%. The trigger conditions and live time during
SK-VI are summarized in Table 7.1. Although SK-VI commenced on July 14th, 2020,
the water and trigger conditions were stable on August 26th, 2020. Accordingly, thelive time was accounted for from that date, and in total, operated for 552.2 days,
which was 18.6% of the previous SK-IV SRN search (2970 days) [20]. As observed inTable 7.1, the SHE threshold decreased for about 11 days, but given the optimizationof the energy window to 60 hits, this alteration does not affect the analysis.
Table 7.1: Trigger conditions and live-time during SK-VI.

Start dateAug. 26, 2020
Aug. 26, 2021
Sep. 12, 2022
Mar. 3, 2022

7.2

End dateAug. 26, 2021
Sep. 12, 2021
Mar. 3, 2022
Jun. 1, 2022

SHE threshold
60
52
60
60

Live time [day]305.6
10.97 day
157.49 day
78.15 dayAFT rate limit
1/21 ms
1/21 ms
1/21 ms
3/21 ms

Signal Energy Window

This study targets the SRN signal within the 7.49–29.49 MeV energy region for the
positron kinetic energy. The lower threshold stems from the energy level where SHE
efficiency is sufficiently high, while the upper limit aligns with traditional analysis

108

Chapter 7. Search for Diffuse Supernova Neutrino Background in SK-Gd

windows. The side-band region exceeding 29.49 MeV aids in calibrating the atmospheric neutrino MC flux. For background evaluation, the energy spectrum is parsed
into 2 MeV segments.

7.3

Overview of Background Events

Chapter 6 elucidates the achievement of a low misidentification rate for neutrons.
Consequently, several low-energy events without neutron emission — solar neutrinos, most isotopes decay from muon spallation, radioactivity, etc. — are discounted.
This chapter centers on events featuring neutron accompaniments, with primary background sources delineated in subsequent sections. The major background sources arecharacterized as follows:
1. Radioisotope decays originating from cosmic-ray spallation.
2. Atmospheric neutrinos.
3. Reactor neutrinos.
4. Accidental coincidence of low-energy event and neutron-like signal.
Other low-energy events, such as solar neutrinos and radioactivity, are adequately
eliminated by neutron tagging. The modeling for each background source is describedlater in this chapter.

7.3.1

Radioisotope Decays from Muon Spallation and Lithium-9

Despite a 2700 m.w.e. overburden, the SK detector is exposed to the cosmic-ray muonsat ∼ 2 Hz. Certain of the muons break the oxygen nuclei of water, resulting in ‘muon
spallation.’ The case of breaking the gadolinium and sulfur nuclei is ignored becauseof the small amount relative to the water. The muon spallation produces daughter
isotopes and hadrons, such as neutrons and pions, as well as photons. The hadrons
produced by this reaction cause subsequent spallation reactions, and eventually, theradioactive isotopes remain. Their radioactive decay emits γ and β rays, occasionallyeven neutrons. Since these visible electromagnetic (electron-like) particles have anenergy below 20 MeV, they could pose as major backgrounds in the SRN analysis.
Their counts in this energy region are 106 times the expected flux of SRN.
For each isotope in water, Li et al. [144, 145, 146] studied the half-life, decay mode,yield, and primary process with FLUKA [35], summarized in Table 7.2. Furthermore,
the end-point energies of the electron-like particles, the half-lives, and the yield above
3.5 MeV for the electron-like particles, are presented in Figure 7.1. Although theseare significantly reduced by neutron tagging because most spallation isotope decays
do not produce neutrons, the decays with neutron production are not reduced. Moreover, spallation isotope decay acts as a major source of the accidental coincidence
background, as described later in this section. Thus, a detailed understanding andefficient reduction of spallation isotope events are essential to be considered in thisanalysis. The reduction is dedicated to tuning below 24 MeV since the highest energy
from 14 B and 11 Li amounts to 20.4 MeV.
Isotopes accompanied by neutron
The decays resulting β + n emission are indistinguishable from the ν̄e signals, evenwith neutron tagging, because SK cannot discern between electrons and positrons.

109

7.3. Overview of Background Events
Table 7.2: Summary of the muon spallation products in the water.
This table is taken from Ref. [35].
Isotope
n
N
17
N
16
N
16
C
15
C
14
B
13
O
13
B
12
N
12
B
12
Be
11
Be
11
Li
9
C
9
Li
8
B
8
Li
8
He
15
O
15
N
14
O
14
N
14
C
13
N
13
C
12
C
11
C
11
B
10
C
10
B
9
Be
9
Be
sum
18

Half-life[s]

Decay mode

0.624
4.173
7.13
0.747
2.449
0.01380.00860.01740.01100.02020.023613.8
0.0085
0.127
0.178
0.77
0.838
0.119

β−
β +n
β − + γ(66%), β − (28%)β− + nβ − + γ(63%), β − (37%)β− + γ
β+
β−
β−
β+
β−
β − (55%), β − (31%)β− + nβ+−β + n(51%), β − (49%)β+β−−β + γ(84%), β − + n(16%)−

Yield[×10−7 µ−1 g −1 cm2 ]
2030
0.02
0.59
18
0.02
0.82
0.02
0.26
1.9
1.3
0.02
12
0.10
0.01
0.89
1.9
5.8
13
0.23
351
773
13
295
64
19
225
792
105
174
7.6
77
24
38
3015

Primary process

18

O(n, p)O(n, n + p)
(n, p)(π − , n + p)(n, 2p)(n, 3p)(µ− , p + 2n + µ− + π − )(π − , 2p + n)(π + , 2p + 2n)(n, α + p)(n, α + p + n)(n, α + 2p)(π + , 5p + π + + π 0 )(n, α + 4n)(π − , α + 2p + n)
(π − , α + 2p + 2n)(π − , α + 2 H + p + n)
(π − , 3 H + 4p + n)
(γ + n)(γ + p)(n, 3n)(γ, n + p)(n, n + 2p)(γ, 3 H)2(n, H + p + n)(γ, α)(n, α + 2n)(n, α + p + n)(n, α + 3n)(n, α + p + 2n)(n, α + 2p + n)(n, 2α)18Although the energy of neutrons is not identical to the IBD signal, SK is not sosensitive to such a minor variation in the order of MeV. Therefore, these decays should
be inspected. From Table 7.2, the major isotopes accompanying the neutrons include
8 He, 9 Li, 11 Li, and 16 C. However, 8 He, 11 Li, and 16 C do not form the dominantbackgrounds owing to their low yield and the low branching ratio of β +n. As reported
earlier, 11 Li has a short lifetime, and thus, its signal should be strongly correlated withthe parent muon track and easy to eliminate.
Compared to other isotopes, 9 Li has a relatively long lifetime (∼ 0.26 s) andprovides a large yield. As 9 Li decays into β + n channel with a branching ratio of
50.8% (Figure 7.2), the total yield is 1.9 × 50.8% × 10−7 µ−1 g−1 cm2 . In addition, theenergy of β is contained in the signal energy window. Therefore, in this analysis, only
9 Li will form a nonnegligible background.
The previous measurement result of the 9 Li rate at SK [48]: 0.86 ± 0.12(stat.) ±0.15(syst.) kton−1 day−1 is utilized to estimate the amount of 9 Li in this analysis.
The spectrum of β from 9 Li decay is modeled by the BESTIOLE code [147] asdepicted in Figure 7.3 with the reconstructed electron energy.

110

Yield (E>3.5 MeV) [×10-7µ-1g-1cm2]

Half-life [s]Chapter 7. Search for Diffuse Supernova Neutrino Background in SK-Gd

11

Be

10

16

N

15

C

16

C

8

1

Li 8B

Li

He

10−1

12

Be

10

12

B

B

1

B
B

9

12

N

Li

12

Be
8

14

B

He

11

Li

16

16

B
11
Li

N

18

20

Be

C

14

12

11
15

10

12

14

8

13

−2

13

10−2

10

N

Li

B

10−1

9
8

16
8

12

C

10−3

10−2

10−1

1

End-point energy [MeV]10
Half-life [s]Figure 7.1: Correlation between end-point energies and half-lives(left) and that between half-lives and yield (right) for spallation isotopes detected in the DSNB search window and generated by cosmicray muons in water. Red circles in both figures represent undergoingbeta decay with neutrons. For the isotopes undergoing decay withneutrons, the yield includes the fraction of decay with neutrons. The
fraction of these plots referred from [48].

Figure 7.2: Decay scheme of 9 Li based on PDG [49].

7.3.2

Atmospheric Neutrinos

In this analysis, signals of a few tens of MeV from the atmospheric neutrinos significantly contribute to the background. Specifically, the events described below can be
identified as a source of background:• Decay electron from muons:
Muons with energy below the Cherenkov threshold, known as ‘invisible muons.’
decay into electrons or positrons with a lifetime of 2.2 µs(decay-e). This kindof event cannot be identified by the parent muon event. Therefore, when atmospheric neutrino interactions yield invisible muons accompanied by neutrons,
these interactions become indistinguishable from IBD interactions. Figure 7.4

111

7.3. Overview of Background Events

0.08
True kinetic energy

0.07

Reconstructed kinetic energy

0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10

12 14 16 18 20
Kinetic energy [MeV]

Figure 7.3: True and reconstructed electron kinetic energy for the
β-decay of 9 Li.

provides a visual representation of this electron decay background. The decay-e
event might also arise from the decay of pions into muons when both the muonand pion remain invisible. Since the decay-e event exhibits the familiar Michel
spectrum, one can estimate the occurrence of such events by examining theside-band region data.

νμ

16

O

De-excitation γ

decay-eμ (invisible)

n or pFigure 7.4: Illustration of decay electron background. In the figure,the decay electron from an invisible muon produced via CCQE interaction of atmospheric neutrino is displayed.

• Visible pions and muons:
For pions and muons with energy surpassing their Cherenkov threshold, theirlight pattern observed by SK aids in their identification. If these particles decay
within the ID, the double coincidence of their signals can be harnessed. Figure 7.5 displays a graphical representation of a visible muon background followed
by a decay-e event.
• Electrons from CC νe interactions:Electrons emitted from νe interaction with neutrons cannot be separated fromsignals. The cross-section increases with energy, and these electrons mirror
the energy of the original neutrino. The frequency of such events is similarly

112

Chapter 7. Search for Diffuse Supernova Neutrino Background in SK-Gdνμdecay-eO

16μ, πn or pDe-excitation γ

Figure 7.5: Illustration of the visible muon and pion background. In
the figure, the visible muon and the decay electron produced via the
CCQE interaction of atmospheric neutrino are displayed.

estimated using side-band data. Figure 7.6 depicts an electron event stemmingfrom the CC interaction.

νe

O

16

De-excitation γen or pFigure 7.6: Illustration of the electron background event via CCQE
interaction of the atmospheric electron neutrinos.

• NCQE interaction events:
During NC interaction with a high-energy neutrino, if one or more nucleons
are knocked out, and the remaining nuclei nucleus transitions to an excitation
state, it emits a de-excitation gamma-ray. The final state particles of this interaction are the knocked-out nuclei and the de-excitation gamma-ray. Often,these knocked-out nucleons cause another hadronic interaction in the water.
This results in the generation of multiple gamma rays. Although these canbe minimized by the procedures mentioned in Chapter 8, the behavior of such
events at low energies is poorly understood, leading to substantial uncertainties. Figure 7.7 exhibits an example of the de-excitation gamma-ray event fromNCQE interaction.

7.3.3

Reactor Neutrinos

During the reactor activity, ν̄e are abundantly created via β − decay as follows:AA′−
Z X → Z+1 X + e + ν̄e ,

(7.1)

113

7.3. Overview of Background Events

ν

O

16

n or pDe-excitation γ
Figure 7.7: Illustration of the NCQE background event.

Fractionwhere X(X ′ ) represents a specific nuclei. The neutrino flux from reactors fluctuates
based on the reactor operations near the SK location. To determine the reactor
neutrino flux at the SK, data on the activity of each reactor and neutrino emissions
information is essential. The anticipated flux is calculated using SKReact [148], which
is a tool for calculating the ν̄e flux from reactors. The situation for each reactor inJapan is referenced for the input reactor activity. The activities of the Japanesereactor are presented in Figure 7.8. Considering the neutrino oscillation, the neutrino

1

SK-V

SK-VI

Ohi-3

SK-V

SK-VI

Ohi-4

SK-V

SK-VI

Mihama-3

SK-V

SK-VI

Takahama-3

SK-V

SK-VI

Takahama-4

SK-V

SK-VI

Ikata-3

SK-V

SK-VI

Genkai-3

SK-V

SK-VI

Genkai-4

SK-V

SK-VI

Sendai-1

SK-V

SK-VI

Sendai-2

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1

Fraction

0.5

1
0.5
0

10

20

30

40

50

Time [Month from Apr. 2018]

Figure 7.8: Activities of Japanese reactor from Apr. 2018 to Sep.
2022; dashed line indicates 100% operation time.

flux at the SK site per year is computed as depicted in Figure 7.9.

114

Chapter 7. Search for Diffuse Supernova Neutrino Background in SK-Gd

×10

-1

Flux [MeV cm-2 yr-1]

9

2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0

2

4

6

8

10

12 14 16 18
Neutrino energy [MeV]

Figure 7.9: Expected neutrino energy flux from Japanese reactors
at the SK site, considering the neutrino oscillation effect.

7.3.4

Accidental Coincidence backgroundIn this analysis, ‘accidental coincidence background’ refers to events accidentallyformed by pairing electron-like events with true or fake neutrons. If the pairing involves a true neutron, primarily a byproduct of muon spallation, differentiating thesebackgrounds from true signals becomes challenging.
Fake neutron signals can arise from low-energy radioactive backgrounds, clustered
PMT dark noise, and other low-energy signals. The noise cluster of PMT hits canbe substantially reduced by leveraging Gd-capture as an indicator for neutron signals
since a typical Gd-capture signal results in a considerably higher count of PMT hits
than one from the noise clusters. Other sources of fake neutron signals are meticulously
investigated using neutron tagging, as detailed in Chapter 6.

7.4

MC Creation

To evaluate reduction efficiency and determine the final samples for both backgroundand signal, Signal and Background MC are employed. The foundational principles ofatmospheric neutrino MC production, covering aspects like flux and interactions in
the tank, are outlined in Section 3.1. In this study, atmospheric neutrino MC events
are simulated equivalent to the 497 years using the SKG4.
As explained in Section 3.2, the signal MC is designed with a uniform positron
spectrum. This is used to estimate not only the various SRN spectra but also thebackgrounds from 9 Li and the reactor. Appropriate flux weights are applied to thesignal MC, and the methodology for this application is elucidated in Section 9. Signal
MC events are created on the assumption of one event taking place every minuteduring the whole live time, amounting to ∼ 800, 000 events in total. The event vertex
is uniformly distributed throughout the ID with an isotropic direction. Additionally,energies are presumed to be consistently distributed between 1–90 MeV.
To emulate a realistic noise environment for the neutron tagging, genuine noise
hits are injected into the MC 1.7 µs post the initial generated time. The procedure
for this data integration mirrors the one detailed in Section 6.1.3.

115

Chapter 8

Event reduction
The data undergoes the four reduction stages to reduce the background events. The
first reduction removes non-physical and poor-quality events. The second reduction
targets the minimization of muon spallation events. The third reduction selects the
IBD prompt events while removing atmospheric neutrino and radioactivity events,
and the fourth reduction implements neutron tagging. This chapter delves into thespecifics of each reduction method, detailing the criteria and associated efficiencies.

8.1

First Reduction: Pre-cut

8.1.1

Nonphysical Event and Invalid Triggered Event Cut

In this analysis, the events should at least trigger the SHE. Moreover, the events
triggered by OD are disregarded, as they are typically associated with muon activities.
Initially, nonphysical events as listed below, are eliminated:• Calibration trigger event• Pedestal event• Badly processed and incomplete event• Runs that something unsolvable issue occurs• Periodic trigger event• T2K beam trigger event
In addition to the above cut, additional criteria were applied to remove the events
triggered by PMT noise hit. The number of hits caused by PMT noise is smaller
than those caused by the light from the actual physical signal in the physical event.
Additionally, the PMT charge stemming from noise hits tends to be smaller. Thus,
the condition N (Q < 0.5 p.e.)/Nall < 0.55 is applied to eliminate events influenced
by PMT noise. Here, N (Q < 0.5 p.e.) represents the number of hits where the PMT
charge is below 0.5 p.e., and Nall denotes the number of total hits.

8.1.2

Cosmic-ray muon-induced event cut

Cosmic-ray muons arrive at SK at a rate of ∼ 2 Hz. These muons typically issue the
OD trigger. Some muons result in decay-e events with a lifetime of 2.2 µs. However,
if a considerable time difference exists between the muon and decay-e, leading them
to be identified as separate events, then decay-e is not triggered by OD. Any eventsoccurring within 50 µs post muon event are discarded as a precaution. This reduction
additionally filters out short-lived isotopes resulting from muon spallation, as outlined
in Section 7.3.1.

116

Chapter 8. Event reduction

8.1.3

Fiducial volume cut

Numerous low-energy events emanate from the radioactivity surrounding the wall of
the tank. To eliminate these events, standard fiducial volume (FV) cuts that remove
events within 200 cm from the tank wall are applied.

8.1.4

Fit-quality cut

1

gvtx

gvtx

At times, low-energy events exhibit subpar reconstruction quality. To counteract this,events are filtered using the fit goodness parameter, gvtx . Events that have a gvtx lessthan 0.5 are removed. Figure 8.1 illustrates the relationship between reconstructedkinetic energy (Erec ) and fit goodness (gvtx ) after applying the above-mentioned noise
reduction cut for both data and signal MC. For energies above 8 MeV, the gvtx >0.5 criterion does not adversely affect the signal, as depicted in the right panel of
Figure 8.1. The pronounced event peak at gvtx ∼ 0.4 below 8 MeV region appears
to stem from radioactive backgrounds near the tank wall, lingering despite the FV
cut. These should be further removed using subsequent cuts. The gvtx criterion
effectively removes events with poor fit quality related to radioactivity while retaining
over > 99.9% of signal MC.

DATA(85220 - 87220)

0.9

1

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

5

10

15

20

MC

0.9

25
Erec [MeV]

0

5

10

15

20

25

Erec [MeV]

Figure 8.1: Reconstruction goodness and reconstructed energy distribution for data (left) and signal MC (right). Vertical magenta line
exhibits the energy threshold of 7.49 MeV, and the horizontal magenta
line presents the gvtx threshold.

8.1.5

Trigger Requirement

As described in Chapter 2, the SHE and AFT triggers are required to search for thedelayed neutron signals in this analysis. Furthermore, events must not trigger the OD
in the quest for neutrino signals. Events meeting this criterion, i.e., SHE-triggered
but OD-untriggered, are henceforth labeled as ‘SHE event.’ However, owing to the
AFT trigger rate being limited to once every 21 ms until the middle of SK-VI, SHE
triggers can occur without a subsequent AFT. This discrepancy needs to be assessedusing real data and factored into the normalization of MC. The AFT efficiency εAFT
is evaluated for each reconstructed energy bin of 2 MeV, as follows:
εAFT =

NAFT
,
NSHE

(8.1)

8.2. Second Reduction: Spallation Cut

117

where NAFT denotes the number of AFT-triggered events and the NSHE indicates thenumber of SHE-triggered events for each 2 MeV bin. The values of εAFT for each bin
are summarized in Table 8.1.
Table 8.1: AFT trigger efficiency calculated using 2 MeV energy
bins. These values are calculated by considering the average of theentire SK-VI period.

Energy bin [MeV]
8–10
10–12
12–14
14–16
16–18
18–20
20–22
22–24
24–26
26-28
28–30
>30

8.2

After-trigger efficiency [%]
85.3%
80.4%
74.3%
70.0%
67.9%
63.4%
89.7%
90.0%
90.0%
100.0%
90.5%
93.7%

Second Reduction: Spallation Cut

Following the first reduction, the isotope decay events stemming from the cosmic
muon spallation become the dominant background within the signal energy region.
Currently, no reliable simulation can reproduce muon spallation. Thus, a data-driven
muon spallation is developed, for the present analysis, called the spallation cut. The
core idea behind the spallation cut is to explore the relationship between the SHE
events and muons observed close in time to the SHE events to potential events produced by earlier muons.
Muon spallation also prominently contributes to the prompt event of the accidental
coincidence background. Events resulting from muon spallation are anticipated tooutnumber those from SRN by a factor of O(106 ). The efficacy of the spallation cut
should sufficiently reduce the muon spallation by a O(10−6 ), when combined with theneutron misidentification to offer a meaningful constraint on the SRN flux.
To prove the correlation between SHE events and the muons, nearby muon eventsto the SHE occurrences in time are identified, specifically those that trigger both HE
and OD. For every SHE event, muons within a ±60-second window of the SHE eventare compiled. Since the muon rate is ∼ 2 Hz at SK, ∼ 240 muons for each SHE event
are found. For this analysis, the muon information included the time difference fromSHE events, track information including the number of tracks estimated by Muboy
fitter (Section 4.2), and the deposited energy dE/dx along with the track.
Muons surrounding the SHE event are categorized into ‘pre-’ and ‘post-’ regions. If
we consider the timing of the SHE event, any time prior to it is designated as the ‘pre-’region, while the time posterior is labeled the ‘post-’ region. Figure 8.2 illustrates thisdefinition and the conceptual distinction between ‘pre-’ and ‘post-’ regions. A vitalfeature of this categorization is that while a muon from the pre-region might give rise
to a SHE event, a muon from the post-region cannot, especially if the SHE event is

118

Chapter 8. Event reduction

due to spallation. All muon events from these two regions are compiled for all SHE
occurrences and labeled as ‘pre-’ and ‘post-’ samples.

"pre-region"−60 sec"post-region"± 0 sec+60 sec( ∼ msec)

ΔT

muons
SHE eventFigure 8.2: Illustration of muon concept for the spallation.

The spallation cut consists of five reduction contents.
• 1-ms cut: Filters out hadronic interaction events resulting from the particles
induced by muon spallation.
• Neutron cloud cut: Assess muon spallation events that occurred with neutrons along with the muon track.
• Multiple Spallation cut: Detects the presence of clustered low-energy eventsin both space and time.
• Spallation likelihood cut: Compute the likelihood of a SHE event originating from muon spallation.
• Spallation Box cut: A more stringent cut than others, utilizing muon goodness, time variance, and spatial difference to eliminate sufficiently high-energy
spallation events.

8.2.1

1-ms cutMuon spallation yields a cascade of particles, sometimes numbering in the thousands.
These particles, being highly energetic, can instigate subsequent hadronic nuclear
reactions, emitting gamma rays, neutrons, and more. Occasionally, these particles
might activate the SHE triggers, with neutrons potentially causing a delayed signal
due to neutron capture.
To filter out evident SHE events induced by the muon spallation, any SHE events
within 1 ms muon occurrences are excluded. Factoring in the 2 Hz muon rate, theimpact of this cut on signal efficiency is calculated as 1 ms/0.5 s = 0.2%.

119

8.2. Second Reduction: Spallation Cut

8.2.2

Multiple Spallation Cut

Energetic muons occasionally produce multiple radioactive isotopes. If one such instance is a SHE event, another low-energy event should be observed close to the SHE
event both in time and space. To identify correlated low-energy events with the SHE
event, the selection criteria from the solar neutrino analysis [38] are employed on all
low-energy events with a reconstructed energy range of 6–25 MeV. Spatial correlations between a specific SHE event and any selected low-energy events within a ±60 s
window are subsequently investigated. Figure 8.3 visualizes the shortest distance between a given SHE event and its neighboring low-energy events. The contribution of
spatially correlated events is clearly apparent when contrasted against a randomized
distance distribution. Consequently, SHE events with a minimum distance of lessthan 4.0 m from the low-energy event are excluded. The efficiency of random eventsis gauged using a randomized vertex and stands at 98%.
60000

60000

50000

Spallation sample

50000

40000

Random vertex

40000

30000

30000

20000

20000

10000

10000

0

500 1000 1500 2000 2500 3000 3500 4000
Min. distance to low energy event [cm]0500 1000 1500 2000 2500 3000 3500 4000
Min. distance to low energy event [cm]Figure 8.3: Minimum distance between the SHE event and the lowenergy event within ±60 s, obtained from the SHE event and randomized vertex (left) and the subtracted distribution (right).

8.2.3

Neutron Cloud Cut

Muon spallation produces thousands of hadronic particles, including neutrons. These
neutrons get captured by the nuclei, notably Gd in SK-Gd, within a timescale ofO(100) µs. Such events generate neutron event clusters near the spallation origin
point. This characteristic helps discerning muon spallation events, a phenomenon
termed ‘Neutron cloud.’ The neutron events accompanying each identified muon are
subsequently sought. The selection parameters for these neutrons mirror the methodsof the cosmogenic neutron yield analysis [149] as follows:• triggered with 25 hits/200 ns• timing within [35, 535] µs from the muon
• gvtx > 0.4 and gdir < 0.4• Distance from the muon is within 5 m.
If two or more neutrons are detected, the muon is considered to possess a neutron
cloud. Figure 8.4 displays the count of accompanying neutrons for pre and post-muonsamples, emphasizing the prominence of neutron clouds in the pre-sample.

120

Chapter 8. Event reduction

105

pre-sample
post-sample

4

10

103
102
10
1

10

102
Number of neutrons

Figure 8.4: Number of neutrons after muons for pre (black) and post(red) samples.

Figure 8.5 plots the muon timing using the SHE event time as a reference. Muons
with an increased neutron count show a timing correlation with SHE events. Expectedly, a spatial relationship exists between the neutron cloud and the SHE event. The
vertex of the neutron cloud ⃗rc denotes the weighted averaged vertex of the selected
neutrons for each muon. Figure 8.6 demonstrates the distance separating the SHE
event and the neutron cloud vertex, underscoring a spatial correlation only in the
pre-sample. This relationship assists in pinpointing muon spallation.
×103
180

Nncloud = 2

160

Nncloud = 3

140

Nncloud = 4,5

120
100

Nncloud = 6-980

Nncloud = 10+

60
40
20
0

−60

−40 −200204060Time diff. from relic candidate [s]Figure 8.5: Time difference between muons and the SHE event. Eachcolor exhibits the number of neutrons after muons.

To refine the cut criteria targeting muon spallation, a new coordinate system is
introduced where the z-axis aligns with the muon track. Vertex difference along withthis new coordinate system, labeled ∆x , ∆y , ∆z , and the vertex difference ∆l as∆l = ∆2x + ∆2y + ∆2z is calculated. The characterization of muon spallation with
the neutron cloud incorporates these variables alongside the time difference between
the muon and SHE event (∆T ). Figure 8.7 illustrates the definition of the newly

121

8.2. Second Reduction: Spallation Cut

×103
12000

100

pre-sample
post-sample

80

pre-sample
10000

post-sample

8000
60
6000
40

4000
Total

20
0

500 100015002000250030003500400045005000
Distance from relic candidate [cm]5000

pre-sample
post-sample

4000

0

500 100015002000250030003500400045005000
Distance from relic candidate [cm]8000

pre-sample

7000

post-sample

6000
5000

3000

4000

2000

3000
Nncloud = 31000
0Nncloud = 2
2000

Nncloud = 4,5

2000
1000

500 100015002000250030003500400045005000
Distance from relic candidate [cm]12000

pre-sample
10000

post-sample

0

500 100015002000250030003500400045005000
Distance from relic candidate [cm]70000

pre-sample

60000

post-sample

50000

8000

40000

6000

30000
4000
Nncloud = 6-9
2000
0

20000

Nncloud = 10+

10000
500 100015002000250030003500400045005000
Distance from relic candidate [cm]0500 100015002000250030003500400045005000
Distance from relic candidate [cm]Figure 8.6: Distance between neutron cloud position and the SHE
event. Each panel exhibits the difference in Nncloud .

defined axis and variables. Given the varying dependence of the cloud on the muon,

cloud-muon coordinate system

μ

z

lt

barycenter of cloud

relic candidate
rotationprojection tomuon track

Δl

ll
O

μ

Figure 8.7: Illustration of definition for the variables used in theneutron cloud cut.

as illustrated in Figures 8.5 and 8.6, the cut criteria for the neutron cloud can be
distinguished by Nncloud .

122Chapter 8. Event reduction

Figure 8.8 displays the 2D distribution for each spatial variable ∆x , ∆y , ∆z ,including the cut criteria in this plane. The event cluster observed around log(∆t) = 1
will be later removed based on the elliptical shape cut. Moreover, the correlation withthe ∆l and ∆T is depicted in Figure 8.9. Considering these distributions and taking
into account the elliptical shape of cloud distribution, the cut criteria are determined.
The criteria are consolidated in Table 8.2 with reference to the previous analysis [20]. The neutron cloud cut reduces about 68% of the spallation events following
Equation 8.8 while maintaining 98% of random efficiency defined by Equation 8.5.
Table 8.2: Cut criteria of neutron cloud cut. The signature (+) inthe multiplicity column signifies equal or more than the value.

Nncloud
2+
2+
2
3
4, 5
6–9
10+

8.2.4

Time [sec]∆T < 0.1∆T < 1∆T < 30∆T < 60∆T < 60∆T < 60∆T < 60

Spatial [cm]∆l < 1200∆l < 8002222(∆x + ∆y )/200 + ∆z /4002 > 1.2
2(∆x + ∆2y )/(6 × 104 ) + ∆2z /5002 > 1.2(∆2x + ∆2y )/(1.2 × 105 ) + ∆2z /5502 > 1.2(∆2x + ∆2y )/(2 × 105 ) + ∆2z /6502 > 1.2(∆2x + ∆2y )/5002 + ∆2z /7002 > 1.2

Spallation Likelihood Cut

The 1-ms cut, combined with the multiple spallation cut and neutron cloud cuts,eliminates roughly 70% of muon spallation events. To further minimize these events,
a statistical method employing log-likelihood is explored. This approach aims toderive a single cut variable termed ‘spallation likelihood,’ which includes information
concerning the correlation between the muon and SHE event. The spallation likelihood
Lspall is defined as follows:!
Y
PDFispall (x)Lspall = log
,
(8.2)
i
PDF
(x)
randomiwhere the PDFispall denotes the Probability Density Function (PDF) of the spallation
sample, and PDFirandom represents the PDF of the random sample, comprising thepost-muon samples. i indicates the i-th variable used in the calculation, and x denotes
the value of the i-th variable. The procedure for creating the PDF will be detailed
subsequently.
Spallation variables
Key variables integral to the spallation likelihood (termed spallation variables) include:• dt: Time difference between the SHE event and muon (same as the definition
described in Section 8.2.3).
• ℓt : Transverse distance separating the SHE event from the muon track. For
spallation occurrences, this typically does not exceed a few meters.
• ℓl : Longitudinal distance between the SHE event and sites of peak energy deposition (dE/dx) on the muon track. When a muon instigates spallation, this

123

50

∆y [m]∆y [m]

8.2. Second Reduction: Spallation Cut

40

12000

50
40

90

30

80

10000

20

70

8000

10

60

0

50

−10

6000

−10

40

−20

4000

−20

30

−30

20

−40

10

30
20
10
0

−30

2000

−40

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50
0−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

40

102

∆z [m]∆z [m]

104

40

30

103

20
10

30
20

10

10
102

0
−10

0
−10

−20

10

−30

−20

1

−30
−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50∆z [m]

10440∆z [m]

−40

40

30

103

20
10

30
20

10

10

0

102

−10

0
−10

−20

10

−30

1

−20
−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50

−50
10−1
−50−40−30−20−10 0 10 20 30 40 50∆y [m]∆y [m]

Figure 8.8: Two-dimensional distribution of ∆x , ∆y , and ∆z . Leftcolumn represents the pre-samples, and right column indicates thepost-samples. Magenta lines indicate the cut criteria. These are clouds
with Nncloud ≥ 10.

124

50
45

700

40

600

35

∆t [m]∆t [m]

Chapter 8. Event reduction

50
45
40
35

30

500

30

25

400

25

20

300

20

15

200

10

15
10

5

100

5

0
−5

0

0
−5

−4

−3

−2

−1

0

1
2
log(dt)

−4

−3

−2

−1

0

1
2
log(dt)

200
180
160
140
120
100
80
60
40
20
0

Figure 8.9: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud ≥ 10.

peak energy point tends to be proximate to the spallation side. Consequently,
for such events, ℓl should remain within a few meters.
• Qµ : Cumulative charge deposition of the muon within the ID of the tank. In
instances where a muon triggers spallation, the energy deposition typically surpasses that of the Minimum Ionization Particle (MIP).
• Qres : Residual charge deposition relative to the expected MIP value, expressedas:Qres = Qµ − QMIP × L(8.3)

where QMIP denotes the number of photoelectrons per centimeter expected from
the MIP, and L indicates the track length of the muon. For multiple muons,the L represents the sum of the tracks since the Qµ denotes the sum of charge
deposition of all muons. Qres is independent of the SHE event; however, it
indicates the probability of muon to induce spallation.
The spallation variables are defined in Figure 8.10.
PDF and Likelihood
For likelihood computations, two area-normalized histograms are generated as PDFs;
one for spallation (PDFispall ), and another for random (PDFirandom ). To derive thespallation component from the pre-muon sample for constructing PDFispall , distributions of post-muon samples are subtracted from those of the pre-muon sample foreach respective variable. Subsequently, all resulting distributions undergo area normalization. Separate PDFs are established for each likelihood variable, tailored to themuon type. Additionally, the PDFs for ℓl , Qres , and Qµ are segmented by dt (0–0.05
s, 0.05–0.5 s, 0.5–60 s) and ℓt (0–300 cm, 300-1000 cm, 1000–5000 cm) to optimize
the removal of spallation events.
Given that the post-sample distribution is subtracted from the pre-sample to form
PDFispall , it is more susceptible to statistical variations compared to PDFirandom . To
mitigate these potential discrepancies, a Kernel Density Estimation (KDE) method is
employed.

125

8.2. Second Reduction: Spallation Cut

muon track

max. dE/dx pointℓlℓt

SHE eventFigure 8.10: Illustration for variables related to spatial correlation

Estimated PDF fˆ(x) is described as:n
1 X
ˆf (x) =knh
i=1

x − Xih!
(8.4)

where the k(x) denotes Kernel function, n indcates the number of total entries, idenotes the entry number, Xi represents the center value of the bin at i-th entry, andh indicates the bin width of PDF histograms. A Gaussian function, characterized bya mean of 0 and a variance of 1, utilized the Kernel function. The KDE methodology
is implemented, resulting in new PDFs for all variables. Figure 8.11 shows PDFs ofthese variables for the single-through muon with dt < 0.05 s and ℓt < 300 cm forℓl , Qres , and Qµ , as an example. The clear contributions are seen as the difference
between spallation and random samples.
Lspall value for all muons are calculated for each SHE event. Lspall distributions
are organized into bins based on the energy of the SRN candidate (reconstructedenergy = 8–10, 10–12, 12–14, 14–16, 16–18, 18–20, 20–24 MeV) because the spallation
event rate from each isotope is highly correlated with its energy. Furthermore, as
the single-through and multiple muons are major types and it is required to review
more carefully, the cut criteria of Lspall are determined for each dt and ℓt binning;
dt binning is common for two muon types: 0–0.05, 0.05–0.5, 0.5–60 s, whereas ℓtbinning is divided for two types: 0–200, 200–300, 300–500, 500–1000, 1000–5000 cm
for single-through muon and 0–100, 100–200, 200–300, 300–500, 500–700, 700–1000,
1000–5000 cm for multiple muons, respectively. For the misfitted muon, only dt isused to calculate Lspall , as the other variables are unreliable. Figure 8.12 presents thelikelihood distributions for different muon types, showcasing the dt = 0–0.05 s andℓt = 0–200 cm region for single-through muons, and dt = 0–0.05 s and ℓt = 0–100 cm
region for multiple muons are shown as examples.

8.2.5

Spallation Box Cut

The muon spallation sample is drastically decreased at the high-energy region beyond 16 MeV. Therefore, the accurate optimization of spallation likelihood criteria isdifficult. Thus, a series of strict cuts is applied primarily above 16 MeV.

126

Chapter 8. Event reduction

0.04
0.035

10−1

0.03
10−2

0.025
0.02

10

0.015
0.01

−3

10−4

0.005
0
10−2

10

10−1

1

10

−5

0

1000

2000

3000

4000

|dt| [sec]5000
l t [cm]

0.2

10

−1

0.15
10

−2

0.1
10

−3

0.05
10

0
−4000

−2000

0

2000

10

4000
l l [cm]

−4

×10

−5

0

1000

2000

3000

3

4000
Qres [p.e.]

10−1

10−2

10

−3

10−4

−5

10 0

500

1000

1500

×10
2000
2500
Qµ [p.e.]3

Figure 8.11: Random (red) and spallation (blue) PDFs for dt (top,left), ℓt (top, right), ℓl (middle, right), Qres (middle, right), and Qµ(bottom). These muons belong to the single through-going muons withthe dt region of 0–0.05 s and the ℓt region of 0–300 cm.

Isotopes with relatively higher end-point energy, such as 12 N, 14 B, and 11 Li,typicallyhave a very short lifetime as shown in Figure 7.1. Therefore, these events can be removed with more simple and robust cuts. Thus, a series of rectangular cuts for events
mainly above 16 MeV and events with shorter ℓt and dt for each muon type. Table 8.3
summarizes the criteria for cuts.

127

8.2. Second Reduction: Spallation Cut105

pre region105

post region

pre region
post region

104

104

103
103

102
10

102
−20

0

20

1
Lspall

−20

0

20

0

20

0

20

Lspall104
pre region

103

105

post region

pre region
post region

104
103

102

102
10
10
1

−20

0

20

1
Lspall−20

Lspall105
104

pre region

pre region

104

post region

103

103

102

102

10

10

1

post region

−20

0

20

1
Lspall−20

LspallFigure 8.12: Spallation likelihood distributions of pre (blue) and post(red) samples, for misfit (top, left), stop (top, right), single throughgoing with dt = 0–0.05 sec (middle, left), and ℓt = 0–200 cm (middle,
right), and multiple muons with dt = 0–0.05 sec (bottom left), andℓt = 0–100 cm (bottom, right). These findings correspond to thereconstructed energy in the 8–10 MeV region.

8.2.6

Spallation Cut Efficiency Estimation

Survival probabilities after whole spallation cuts are estimated for the remaining background and signal events. In this study, four types of efficiencies that the events remaining rate after spallation cut are evaluated: spallation event (εspall ), random event(εrandom ), solar event (εsolar ), and 9 Li event (εli9 ).

128Chapter 8. Event reduction
Table 8.3: Summary of cut criteria of spallation box cuts for eachreconstructed energy E region.

Energy region
E < 24 MeV
16 < E < 20 MeV
16 < E < 18 MeV
16 < E < 18 MeV
16 < E < 20 MeV
16 < E < 20 MeV

Muon type–misfitsinglestopping
stopping
multipleCut criteria
dt < 0.1 s and ℓt < 400 cm
dt < 1.5 s
gµ ≥ 0.4 and dt < 7 s and ℓt < 150 cm
gµ < 0.3 and dt < 6 s
dt < 0.05 s
dt < 0.1 s and ℓt < 400 cm

Efficiency for random event
As earlier outlined, efficiencies of the multiple spallation and neutron cloud cuts for
random events stand at approximately 98%. The impact of a 1-ms cut on these eventsis negligible. Subsequent references to these three cuts collectively label them as thespallation pre-cut.
The spallation cut efficiency for a random event εrandom , which is equivalent tothe signal efficiency after the spallation cut, can be calculated as follows:
εrandom =Npost,after,Nbefore(8.5)

where Nbefore denotes the number of SHE events before cuts. Npost,after indicates thenumber of remaining SHE events after applying likelihood cut and box cut, considering
the spallation pre-cut efficiency. Here, the likelihood and box cut use the correlation
only with post-sample muons.
Efficiency for solar neutrino event
Given that solar neutrino events should not correlate to any muons, they offer avaluable benchmark to verify the randomness of the post-sample. By examining thecorrelation between the solar neutrino event direction and the sun’s direction, thenumber of solar SHE events Nsol is calculated as follows:
Nsol = Ncos θ⊙ >0.5 − Ncos θ⊙ <−0.5 ,(8.6)

where the Ncos θ⊙ >0.5 denotes the number of SHE events from the solar direction, andNcos θ⊙ <−0.5 (Nnonsol ) indicates the number of SHE events from the opposite directionof the sun. Figure 8.13 illustrates the schematic of the definition of solar neutrino
events. To cross-check independently from the post-muon sample, the spallation cut
is applied to the solar neutrino events using only pre-muon samples. After that,spallation cut efficiency for the solar neutrino event εsolar is evaluated.
The definition of εsolar is stated as follows:εsolar =Nsol,pre,after,Nsol,before(8.7)

where Nsol,pre,after denotes the number of solar SHE events after the spallation cut
using only the pre-muon sample, and Nsol,before refers to the number of solar SHE
events before the spallation cut.

129

8.2. Second Reduction: Spallation Cut

Sun

SK
θsun

Nsol

NnonsolNnonsol
-0.5

-1

0

0.5

1

cosθsunFigure 8.13: Schematic of definition of θsun and cos θsun .

Figure 8.14 portrays the correlation between the random and solar event efficiency
for events in the 8–10 MeV range as likelihood cut threshold shift. A linear correlation between the two efficiencies is clearly seen, confirming that εrandom can be used in
our analysis. The post-sample is used to evaluate εrandom rather than the solar SHE
sample because the statistic of the post-sample is much larger than the solar sample. Moreover, εrandom is unreliable at the higher energy region owing to drasticallydecreased statistics of the solar neutrino event in the higher energy region.

Solar efficiency

8-10 MeV

0.8

0.6

0.4

0.2
0.2

0.4

0.6
0.8
Signal efficiency

Figure 8.14: Correlation between εrandom and εsolar .

Spallation remaining rate
To evaluate spallation cut performance, the spallation remaining rate must be calculated. Below 16 MeV, solar neutrino events primarily predominate before neutron

130

Chapter 8. Event reduction

tagging, except for the spallation event. To circumvent the solar neutrino event contamination, the spallation remaining rate employs non-solar events:
εspall =Ncos θ⊙ <0,pre,after − Natm,after,
Ncos θ⊙ <0,before − Natm,before(8.8)

where the Ncos θ⊙ <0,pre,after and Ncos θ⊙ <0,before denote the number of events before andafter all likelihood cuts using only pre-sample muons with cos θ⊙ < 0, and Natm,before
and Natm,after indicate the number of atmospheric neutrino events before and after
likelihood cut. Because a second major event above 14 MeV is an atmospheric neutrino event, εspall is estimated by subtracting atmospheric neutrino events. Natm,before
denotes estimated by the atmospheric neutrino MC, and the Natm,after can be calculated by Natm,before × εrandom .
Efficiency for the Lithium-9
9 Li survival probability εli9 should be estimated as the spallation events from

9 Li decay

remain dominantly after even all cuts are applied. As estimating the e the number of
9 Li events is challenging, εli9 is evaluated by combining certain survival probabilities.
In principle, muon events in the pre and post-samples for a given SHE are classified
into three types: (a) a muon that produces the given SHE event, (b) muons that
produce other SHE events, and (c) muons that do not produce any SHE events. The
survival probabilities after spallation cut by these muons (a), (b), and (c) are definedas εa , εb , and εc , respectively. The survival probabilities after spallation cut using preand post-muon samples εpre and εpost can be described as follows:
εpre = εa × εb × εc(8.9)

εpost = εb × εc ,(8.10)

because εa , εb , and εc are independent of each other. Therefore, εa can be computedby εa = εpre /εpost . As the εli9 is equivalent to the εpre for the 9 Li event, it can beevaluated in the same manner as follows:
εli9 = εa,li9 × εrandom × εmulti+ncloud ,εmulti+ncloud = εspall /ε1-ms+likeli+box ,(8.11)(8.12)

where εa,li9 denotes the same definition as εa for the 9 Li event, εmulti+ncloud indicatesthe efficiency after the multiple spallation and neutron cloud cuts, and ε1-ms+likeli+box
denotes the efficiency after the 1-ms, likelihood, and box cuts.
In order to estimate εa,li9 , 9 Li likelihood should be computed considering the 9 Li
property. In this analysis, we assumed that only dt is unique to the isotope among
the spallation variables. Therefore, the 9 Li likelihood can be calculated by replacing
only dt with the random number based on the 9 Li lifetime (τ = 0.26 s).
ROC curve
The Receiver Operating Characteristic(ROC) curve serves as a good indicator to evaluate reduction performance and optimize spallation cuts. For energy levels exceeding 16 MeV, the estimation of εli9 becomes unnecessary, given its end-point energy.
Additionally, any spallation remaining rate above 16 MeV is unreliable because theatmospheric event becomes the dominant factor, and the statistical uncertainty tied
to the spallation event becomes substantially pronounced.

131

8.2. Second Reduction: Spallation Cut

The ROC curve for the 8–10 MeV events is plotted in Figure 8.15. In the 8–
10 MeV region which is the most affected by the spallation event, the spallation
remaining rate can be reduced to be O(1)%. Other distributions are discussed in
Chapter B. Furthermore, the correlation with the spallation remaining rates εspall andεli9 is illustrated in Figure 8.16. As a portion of 9 Li can be reduced by spallation, theremaining rate of 9 Li should have a positive correlation with the remaining rate ofspallation. Other distributions are discussed in Chapter B.

Signal efficiency

8-10 MeV

0.8

0.6

0.4

0.2
0

0.05

0.1
0.15
0.2
Spallation remaining rate

Figure 8.15: ROC curve representing the correlation between spallation remaining rate and random event efficiency for 8–10 MeV region.

Li9 remaining rate

8-10 MeV

0.15

0.1

0.05

0
0

0.05

0.1
0.15
0.2
Spallation remaining rate

Figure 8.16: Correlation between spallation remaining rate andlithium-9 event efficiency for 8–10 MeV region.

132

Chapter 8. Event reduction

Optimization of the spallation cut criteria below 16 MeV energy region focuses on
maximizing significance. This is achieved by evaluating the composite of all potential
backgrounds and expected signals. The specifics of this optimization process areelaborated upon in the concluding segment of this chapter (Section 8.5.1).
Efficiencies above 16 MeV
Constructing a ROC curve to optimize the likelihood cut for the events above 16 MeV
presents a challenge because the limited statistics at this energy region compromise
the precision of the PDF. As a result, the threshold for the likelihood cut is set atthe point where random efficiency maximizes after the box cut. The random event
efficiencies and spallation remaining rates for the cut point with separated energy
binning are summarized in Table 8.4.
Table 8.4: Summary of the cut efficiency of spallation cut above
16 MeV.

Energy region
16 − 18 MeV
18 − 20 MeV
20 − 24 MeV

Spallation remaining rate
0.010
< 0.001< 0.001

Random event efficiency
73.4%
81.8%
86.1%

8.3. Third Reduction: Positron Event Selection

8.3

133

Third Reduction: Positron Event Selection

For energy regions above 16 MeV, most all spallation byproducts have minimal impact
on the results. In this energy range, the dominant background stems from atmospheric
neutrino events. An electron-like event triggered by an atmospheric neutrino is virtually indistinguishable from an IBD signal in the absence of neutron tagging. However,
events involving muons, pions, and gamma rays — resulting from the interaction of
atmospheric neutrinos with Oxygen nuclei — can be differentiated and eliminatedbased on certain characteristic variables. These events include the Cherenkov angle,
the ratio of charge to the number of hits, pion likeness, and additional PMT activities.
Additionally, to further reduce residual radioactivity following the fiducial volume cut,a distance-from-the-wall cut, aligned with the reconstructed event direction deff is applied. Except for deff cut, the cut criteria and selection efficiencies are derived fromsignal and atmospheric neutrino MC simulations.

8.3.1

Cherenkov angle

The Cherenkov angle θC is primarily determined by its mass and velocity. As describedin Section 2.1, the Cherenkov angle of electrons is about 42◦ , whereas heavier particles
such as muons and pion exhibit smaller Cherenkov angles. As each of the multiple
gamma rays cannot be distinguished in SK, these events should have large Cherenkov
angles by mis-reconstruction of the angle, as depicted in Figure 8.17.

Recon. ring
PMT hits

True rings of multi-γ

Figure 8.17: Mis-reconstruction of the Cherenkov ring owing to themultiple Cherenkov ring.

Consequently, the Cherenkov angle cut emerges as an effective variable for filteringout heavier particles and multiple photon events. Figure 8.18 reveals the distributionsof the reconstructed Cherenkov angles. Notably, events resulting from the NC interaction tend to exhibit larger angles. On the other hand, low-energy muons and pionsfrom the CC interaction, peak at an angle lower than the angle of electron signals.
For this analysis, the reconstructed angle θC is restricted within θC ∈ [38◦ , 53◦ ].

134

Chapter 8. Event reduction

0.5

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

0.4
0.3
0.2
0.1
0
0

10

20

30

40

50

60

70 80 90
Angle [deg]Figure 8.18: Distribution of the Cherenkov angle. Color plot describe the type of atmospheric neutrino interaction, and black line denotes the DSNB signal MC assuming the Horiuchi+09 flux model [10].
These are obtained from the events after only passing the first reductions.

8.3.2

Ratio of charge over the number of hits

Energetic muons deposit more charge on a single PMT compared to electrons in the
MeV scale. This characteristic can be harnessed to filter out muons by calculating theratio of charge to the number of hits in a 50 ns time-of-flight subtracted window centered on the primary activity peak. Figure 8.19 displays the q50/n50 distribution for
the atmospheric and signal MC. Typically, low-energy events are assumed to produce

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

0.25
0.2

10−2

0.15

10−3

0.1

10−4

0.05

10−5

0
0

2

4

6

8

10

12

14
q50/n50

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

10−1

0

1

2

3

4

5

6

7

8

9 10
q50/n50

Figure 8.19: Distribution of the q50/n50 with the linear (left) andlogarithmic (right) for the vertical axis. Color plot exhibits the typeof atmospheric neutrino interaction, and black line denotes the DSNB
signal MC assuming the Horiuchi+09 flux model [10]. These are madefrom the events after passing only the first reductions.

one photo-electron per PMT. Therefore, a selection criteria of q50/n50 < 2 effectively
identifies the low-energy positron events.

8.3.3

Pion likenessElectron rings appear diffused due to their multiple scattering in the tank, whereas
pions produce a distinct ring pattern. This difference is exploited by computing

135

8.3. Third Reduction: Positron Event Selection

the ‘fuzziness’ of the ring pattern. To compute this fuzziness, PMT hits in a 15
ns time-of-flight subtracted window centered on the main activity peak are used. The
opening angles for all possible three-hit combinations are then calculated using thesame method described in Section 4.1.5. Based on the peak of these opening angle
distributions θ0 , the fuzziness of the ring pattern is evaluated as follows:
Lpion =

Ntriplets (θ0 ± 3◦ ),Ntriplets (θ0 ± 10◦ )(8.13)

where Ntriplets (θ0 ± θ) denotes the number of three-hits combinations within θ0 ± θ.
Lpion tends to be proximate to one for pions. Figure 8.20 displays the Lpion distribution
for the atmospheric MC and signal MC. The contribution from the pion-producing
interaction events is seen at the larger Lpion . Therefore, the events require Lpion <
0.37.

10−1
10−2

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

10−3
10−4

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lpion

Figure 8.20: Distribution of Lpion . Color plot denotes the type of
atmospheric neutrino interaction, and black line exhibits the DSNB
signal MC assuming the Horiuchi+09 flux model [10]. These are madefrom the events after passing only the first reductions.

8.3.4

Pre-PMT activities and post-PMT activities

Events arising from visible muon decays to electrons result in two signal activities
within the same event trigger window of [−5, 35] µs. Depending on which signal isdesignated as the primary trigger, in other words, which signal most deposits charge,
another activity is seen before or after the triggered time.
To search additional activity before the main peak (pre-activity), the time-of-flight
subtracted timing window is scanned to search the hit clusters using a 15 ns window
from the start of the event window until 12 ns before the main peak. Figure 8.21
max ). Compared with the IBD
displays the number of maximum hits within 15 ns (Npremax should be less than 12 hits.
MC, the Npre
The primary cause of the additional PMT activities after the main event peak
(post-activity) is the decay-e from the muons or pions. To quantify this, the numberof additional events from the decay electron Ndecay-e is searched utilizing an algorithm used in previous SK analyses to search and reconstruct decay-e from muon orpion [150]. Figure 8.22 presents the count of decay electron-like hit clusters within

136

Chapter 8. Event reduction

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

−1

10

10−2
10−3
10−4
10−5
0

50

100

150

200

250

300
max
Npre

max
Figure 8.21: Distribution of Npre
. Color plot exhibits the type of
atmospheric neutrino interaction. These are made from the events
after passing only the first reductions.

the 35 µs of the event window (Ndecay-e ). As there should be no decay electron-likeevent after IBD, the events are required to be Ndecay-e = 0.

1
IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

0.8
0.6

IBD
Total
CCQE+2p2h
CC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

10−1
10−2

0.4

10−3

0.2
0
0

1

10−4
1

2

3

4

5

6
Ndecay-e

0

1

2

3

4

5

6
Ndecay-eFigure 8.22: Distribution of Ndecay-e with the linear (left) and logarithmic (right) for the vertical axis. Color plot exhibits the type of
atmospheric neutrino interaction. These are made from the events
after passing only the first reductions.

8.3.5

Remaining Radioactivity cut using Effective wall distanceThe cut using deff enables the removal of the remaining radioactive events around thewall while maximizing effective volume. Figure 8.23 illustrates the definition of thedeff .
The deff distribution after the first reduction for the data and signal MC is plottedin Figure 8.24. In the bottom panel of Figure 8.24, a clear excess at a small deff region
in the data over MC can be observed.
The cut criteria are considered by the data and signal MC (Fig. 8.24). The criteria
are optimized between 300–500 cm following the same approach as the previous SK-IV
search:deff > max[300 cm, 500 cm − 50(Erec − 16 MeV)](8.14)

137

8.3. Third Reduction: Positron Event Selection

de

z

de

y
vertexxr

vertexdirection
direction

ff

Figure 8.23: Illustration of definition of deff .

6000
5500
5000
4500
4000
Data

3500

IBD MC

3000

Data/MC

2500
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]

400

600

800

1000

1200

1400
1600
deff [cm]Figure 8.24: Comparison of deff after 1st reduction between data
and MC.

Other distributions are exhibited in Chapter C.

8.3.6

Systematic Uncertainty Estimation with LINAC data

The event produced by LINAC is the mono-energetic electron, as detailed in Section 5.3. Consequently, this data can mirror the likeness of the positron signature in
the IBD signal at each beam energy. Some of the systematic uncertainties related tothe selection of positron-like events can be estimated using LINAC data and MC. The
target energy and position of the beam edge of the LINAC data operated in SK-VI
are listed in Table 8.5. There are 10 data samples, and the energy is between 6–15
MeV and z-position −12, 0, 12 m. Major systematic uncertainties on the reduction

138

Chapter 8. Event reduction
Table 8.5: LINAC positions and target energies used in the evaluation

Target energy [MeV]
8.0
12.0
15.0
6.0
8.0
12.0
15.0
8.0
12.0
15.0

x-position [m]
−12
−12
−12
−12
−12
−12
−12
−12
−12
−12

z-position [m]
12
12
12
0
0
0
0
−12
−12
−12

originate from the variables associated with the Cherenkov light signature, such as
the Cherenkov angle, Lpion , and q50/n50 cuts.
Cherenkov angle

Events [/N/1.0 deg]

Figure 8.25 demonstrates the angle distribution for LINAC data and MC. The distribution for data slightly skews toward larger angles. Nevertheless, this skewness only
marginally impacts the cut efficiency since the skewed region falls within the selection criteria. A comparison of cut efficiency between data and MC indicates that thelargest discrepancy is 1.1% for energies above 12 MeV, with 0.5% for other values.
The 1.1% is conservatively assigned as a systematic error. Additional distributions
are available in Chapter C.

0.18
LINAC Data

0.16

LINAC MC

0.14

LINAC run #86138
Energy = 12.0 MeV

0.12

x,y,z = -12 ,0 ,0 m

0.1
0.08
0.06
0.04

Data/MC

0.02

Cherenkov angle [deg]

1.5
1
0.5
0

10

20

30

40

50

60
70
80
90
Cherenkov angle [deg]Figure 8.25: Comparison of Cherenkov angle distribution between data and MC (top) and the data/MC ratio (bottom) for theE =12 MeV LINAC run.

139

8.4. Forth Reduction: Neutron Tagging
Pion likeness

Events [/N/Bin]

Figure 8.26 displays the angle distribution of LINAC data and MC, highlighting discrepancies around the cut criteria. However, these cut criteria are robust enough toselect a positron signal, given the low statistics in the vicinity of the cut criteria. The
efficiency is therefore not significantly affected by these criteria. Upon comparing thecut efficiency between data and MC, the largest discrepancy noted is 1.1% for thoseabove 12 MeV in Figure 8.26 and 0.6% for others. The 1.1% discrepancy is conservatively assigned as the systematic error. Details on other distributions can be found in
Chapter C.

0.2

LINAC Data

0.18

LINAC MC

0.16

LINAC run #86138
Energy = 12.0 MeV

0.14

x,y,z = -12 ,0 ,0 m

0.12
0.1
0.08
0.06
0.04

Events [/N/Bin]0.02#mathcal{L}

pion

1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8
0.9
#mathcal{L}

1

pion

Figure 8.26: Comparison of Lpion distribution between data and MC(top) and the data/MC ratio (bottom) for the E =12 MeV LINAC run.

q50/n50
Figure 8.27 depicts the angle distribution of LINAC data and MC. As portrayed in
Figure 8.27, this cut criterion adequately selects the positron signal. By comparing
the cut efficiency between data and MC, the largest discrepancy is 0.5%. Thus, 0.5%
is assigned as a systematic error. Other distributions are detailed in Chapter C.

8.3.7

Reduction summary

The cut criteria and signal efficiency are summarized in Table 8.6. The total uncertainty on the third cut is estimated by summing the quadrature of these uncertainties
to be 1.6%.

8.4

Forth Reduction: Neutron Tagging

The final reduction step involves neutron tagging, utilizing a method nearly identicalto that detailed in Section 6 for neutron signal identification. For the IBD interaction,
only one neutron is consistently generated. Given their low energy, these neutrons

140

Events [/N/0.05]

Chapter 8. Event reduction

0.16

LINAC Data
LINAC MC

0.14
LINAC run #86138

0.12

Energy = 12.0 MeV
x,y,z = -12 ,0 ,0 m

0.1
0.08
0.06
0.04

Data/MC

0.02

Q50/N50 [p.e.]

1.5
1
0.5
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

Figure 8.27: Comparison of q50/n50 distribution between data andMC (top) and the ratio of data/MC (bottom) for the E =12 MeV
LINAC run.

Table 8.6: Summary of the cut criteria and efficiencies.

Variable
Cherenkov angle θc
Charge/Hit ratio q50/n50
Pion likeness Lpion
max
Pre-PMT activities Npre
Post-PMT activities Ndecay-e
Effective distance from wall deff

Cut criteriaθc ∈ [38◦ , 53◦ ]q50/n50 < 2.0
Lpion < 0.37
max < 12
Npre
Ndecay-e < 1(Equation 8.14)

Efficiency (Syst. unc.)
94.4 (1.1)%
98.6 (0.5)%
98.6 (1.1)%
99.8 (< 0.1)%
99.8(< 0.1)%
95.0 (< 0.1)%

seldom yield secondary neutrons through nuclear interactions. Consequently, thisanalysis requires a single tagged neutron after the SHE events. This cut powerfully
reduces events lacking neutron emissions, including most decay events induced bymuon spallation decay and electron scattering events of solar neutrinos. Additionally,
it can eliminate some events involving multiple neutron emissions, such as those fromatmospheric neutrinos.

8.4.1

Neutron misidentification rate

As described in Section 7.3.1, muon spallation events at SK occur at a rate 106 greaterthan that of SRN. Despite a significant reduction to O(1)% level due to the spallation
cut is achieved as discussed in Section 8.2, the remaining ∼ 104 higher rate is problematic for the SRN search. The neutron tagging cut can further diminish spallation
events since most spallation isotopes do not produce any neutrons. Thus, in order tomake neutron tagging effective, a sufficiently low misidentification rate is needed forneutron selection. This ensures the effective identification of events devoid of neutron

141

8.4. Forth Reduction: Neutron Tagging

1.5 MeV
1.8 MeV10<1

2.1 MeV
2.4 MeV
2.7 MeV10<210

mis-ID rate [/event]mis-ID rate [/event]emission, thereby reducing accidental coincidence background events. To reduce accidental coincidence background events from muon spallation to the same level as theSRN, a misidentification rate εmis is required to achieve O(10−4 ).
To achieve this low rate, parameters such as the distance from the prompt event
dprompt and reconstructed energy Edelayed , which are the most effective for neutron
selection, are investigated. Figure 8.28 depicts the εmis per prompt-event as a functionof cut criteria for dprompt and Edelayed obtained by the data taken on Jan. 21, 2021,
which was the closest day to the AmBe data measurement. The nominal criteria for
the AmBe measurement were (1.8 ± 0.6) × 10−3 per prompt event. Based on thisinspection, although changing the dprompt criteria does not alter εmis , the effect ofvarying Edelayed can pose a relatively large impact. Consequently, Edelayed > 3.5 MeV
is required to achieve O(10−4 ) of εmis . Based on the new criteria, εmis is re-evaluatedthroughout the entire SK-VI period, following the same approach as Section 6.7.
Figure 8.29 depicts the time variation of ϵmis to be (2.75 ± 0.15) × 10−4 per event.

3.0 MeV
3.3 MeV<3

3.6 MeV
3.9 MeV
4.2 MeV10<4150 cm10<1

240 cm10<4

360 cm420 cm10<6
1

300 cm390 cm10<60.8

270 cm330 cm

10

<3

10<5

0.6

210 cm

10<2

10<5

10<7
0.4

180 cm

10<7
0.4

1.2
1.4
1.6
1.8
Cut Point [ × 300 cm]

0.6

0.8

1

1.2
1.4
1.6
Cut Point [ × 3 MeV]

Mis-ID rate [/event]Figure 8.28: Distribution of ϵmis as a function of the cut criteria forthe dprompt (left) and the Edelayed (right). Color for the left (right)
plot exhibits the cut criteria of Edelayed (dprompt ).

× 10

−3

0.35
0.3
0.25
0.2
0.15
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

run period

Figure 8.29: Time variation of ϵmis . Black-dotted line depicts theweighted mean value for the entire period, and the gray-shaded region
indicates the standard deviation. Horizontal axis represents the same
factor as that in Figure 6.7.

142

8.4.2

Chapter 8. Event reduction

Neutron tagging efficiency

Neutron tagging efficiency is re-evaluated by altering the energy threshold for thedelayed signal search. Consequently, the efficiency for the Am/Be MC with 0BGO is35.6 ± 2.5%. The relative systematic uncertainty can be assumed to be the same asthat described in Section 6.5.

8.4.3

Tagged neutron multiplicity

Tagged neutron multiplicity is reviewed from the signal MC and atmospheric neutrino
MC. Figure 8.30 depicts the number of tagged neutrons Ntagged , which is definitely
0 or 1 for the signal MC owing to the absence of a secondary neutron because of its
low energy. In contrast, the atmospheric neutrinos, especially the NCQE events, tend
to contain multiple Ntagged due to the subsequent interaction of emitted nucleons.
Thus, the neutron tagging reduction requiring Ntagged = 1 can power to reduce these
atmospheric neutrino background events.

1
IBD
CCQE2p2hCC1pi
CC(other)nuNCQE
nubNCQE
NC1pi
NCother

10−1

10−2

10−3
0

1

2

3

4

5
6
7
8
9 10
Number of tagged neutron

Figure 8.30: Distribution of number of tagged neutrons for the IBD
MC and atmospheric neutrino MC, after first to third reductions, inthe signal energy region. Histograms of atmospheric neutrino MC are
stacked with each other.

8.5

Reduction Summary

8.5.1

Optimization of Spallation Cut Criteria

The most dominant background in the absence of neutron tagging stems from spallation. Therefore, the number of accidental coincidence background events largely
hinges on the residual spallation events after neutron tagging. The spallation likelihood cut criteria for energies below 16 MeV are refined after the neutron tagging, withthe defining criteria being the point where signal significance is maximized. This significance is computed using the approach outlined in [151]. To determine significance,
the expected background for all sources is required. Thus, the number of 9 Li, reactor

143

8.5. Reduction Summary

neutrino, and atmospheric neutrino background events are estimated by MC and its
flux. In particular, εli9 is also put into the computation. The accidental coincidence
background is derived by the spallation remaining rate and εmis . Thus, the signal
efficiency, spallation remaining rate, and εli9 of the spallation cut are optimized assummarized in Table 8.7
Table 8.7: Summary of the signal efficiencies at each cut stage forenergy E = 8–16 MeV.

Energy region
8 < E < 10 MeV
10 < E < 12 MeV
12 < E < 14 MeV
14 < E < 16 MeV

8.5.2

Signal efficiency
51.8%
78.2%
86.0%
93.1%

Spallation remaining rate
5.1%
6.8%
6.8%
5.3%

εli9
3.4%
5.0%
5.9%
5.5%

Signal Efficiency

Signal Efficiency [%]The signal efficiency is estimated by applying all the above cuts to the signal MC.
Figure 8.31 displays the signal efficiency after each cut stage at each 2 MeV bin forreconstructed kinetic energy Erec . The cut was initiated after recording 100% of theevents in the first reduction. The efficiency plot displayed in Figure 8.31 refers to theefficiency from the black line.

100

80
SHE+AFT, precut
spallation cut
effwall,pre-/post-activity cuts

60

ring clearness cut
charge/hit cut
Cherenkov angle cut

40

neutron tagging

20

0

8

10

12

14

16

18

20

22

24

26

28

Erec [MeV]
Figure 8.31: Signal efficiency as a function of kinetic energy Erec .

Efficiencies for signals at each cut stage are summarized in Tables 8.8, 8.9, and 8.10.
After the spallation cut, the signal efficiency dwindles in the lower energy spectrum
due to an abundance of spallation events in that range. Nevertheless, since the muon
spallation event frequently diminishes at elevated energies, the spallation cut efficiency

144

Chapter 8. Event reduction

rebounds, attributed to reduced owing to the low εmis and accidental coincidence background rates when Erec <15.49 MeV. However, for Erec > 15.49 MeV, the reliabilityof the spallation likelihood cut wanes due to limited data statistics. Therefore, astringent box cut is implemented to entirely purge the spallation event, circumventing potential systematic errors from misjudging the spallation background in that
region. This rigorous cut criterion results in diminished signal efficiency within the
Erec =15.49–23.49 MeV.

145

8.5. Reduction Summary
Table 8.8: Summary of the signal efficiencies at each cut stage for
the Erec = 7.49–15.49 MeV.

Energy region [MeV]Spallation cut
deff cutmax cut
Npre
Ndecay-e cut
Lpion cut
q50/n50 cut
Cherenkov angle cut
Neutron tagging

7.49–9.49
0.518
0.912
> 0.999> 0.999
0.966
0.994
0.844
0.362

9.49–11.49
0.782
0.916
> 0.999> 0.999
0.97
0.993
0.896
0.346

11.49–13.49
0.86
0.915
> 0.999> 0.999
0.974
0.99
0.919
0.359

13.49–15.49
0.931
0.915
> 0.999> 0.999
0.975
0.987
0.939
0.363

Table 8.9: Summary of the signal efficiencies at each cut stage for
Erec =15.49–23.49 MeV.

Energy region [MeV]Spallation cut
deff cutmax cut
Npre
Ndecay-e cut
Lpion cut
q50/n50 cut
Cherenkov angle cut
Neutron tagging

15.49–17.49
0.734
0.936
> 0.999> 0.999
0.973
0.982
0.953
0.357

17.49–19.49
0.818
0.967
> 0.999> 0.999
0.977
0.978
0.962
0.351

19.49–21.49
0.861
0.985
> 0.999> 0.999
0.973
0.975
0.972
0.348

21.49–23.49
0.861
0.982
> 0.999> 0.999
0.97
0.974
0.974
0.357

Table 8.10: Summary of the signal efficiencies at each cut stage for
Erec = 23.49–29.49 MeV.

Energy region [MeV]Spallation cut
deff cutmax cut
Npre
Ndecay-e cut
Lpion cut
q50/n50 cut
Cherenkov angle cut
Neutron tagging

23.49–25.49
0.961
0.983
> 0.999> 0.999
0.969
0.975
0.979
0.362

25.49–27.49
0.961
0.985
> 0.999> 0.999
0.968
0.975
0.984
0.353

27.49–29.49
0.961
0.985
> 0.999> 0.999
0.966
0.982
0.985
0.347

147

Chapter 9

Background Estimation
In this chapter, we evaluate the remaining background events after the reduction foreach category. As detailed in Chapter 7, Lithium-9 and reactor neutrino background
events are modeled using IBD MC and later weighted by each expected flux. The
atmospheric neutrino background is already weighted, being derived directly from theneutrino flux. Conversely, the accidental coincidence background must be derived
from the real data.

9.1

Atmospheric neutrinos

The atmospheric neutrino background is deduced using MC as outlined in Section 7.3.2.
From now on, events are bifurcated into two categories: NCQE events and other nonNCQE events.

9.1.1

NCQE event

The prevailing atmospheric neutrino background for energies below 16 MeV is primarily due to NCQE interactions. This encompasses the NC-2p2h interaction, where twonucleons are dislodged from the nucleus. The cross-section of the NCQE interactionin SK, as measured by the T2K beam [51], enables the evaluation of the scaling factor
for each ν and ν̄ cross-section is evaluated as:fν-NCQE = 0.80 ± 0.08(stat)+0.24−0.18 (syst),(9.1)

fν̄-NCQE = 1.11 ± 0.18(stat)+0.29−0.22 (syst).

(9.2)

Thus, the number of NCQE events from ν-NCQE and ν̄-NCQE are renormalized by
0.80 for ν and 1.11 for ν̄, respectively.
Systematic uncertainties related to the NCQE-like events can be split into preand post-neutrino interactions in SK. The pre-interaction uncertainties are sourcedfrom:• Atmospheric neutrino flux and spectrum shape.
• NCQE-like interaction cross-section.
In contrast, post-interaction uncertainties arise from:• Neutron-related aspects.
• Observed event spectrum shape.

148

Chapter 9. Background Estimation

Neutrino flux and flux shape
Flux uncertainty originates from the absolute uncertainty and the flux shape variance
between atmospheric neutrinos and the T2K neutrino beam (since the cross-sectionuses the scale of the T2K neutrino beam). The former is approximated at 15%, as perreferences [33, 29]. The latter is deduced by determining the ratio of flux-averaged
events between the T2K beam and atmospheric neutrino fluxes, denoted as Rνi andRν̄i , for various cross-section models i:
R T2K iϕν σν-NCQE dEν
Rνi = R ATM i,(9.3)
ϕν σν-NCQE dEν
R T2K iϕν̄ σν̄-NCQE dEν
,(9.4)
Rν̄i = R ATM iϕν̄ σν̄-NCQE dEν

σNCQE [× 10-38 cm2]

σNCQE [× 10-38 cm2]

where the ϕT2K
(ϕT2K
) denotes the ν (ν̄) neutrino flux of the T2K beam, ϕATM
(ϕATM
)
ν
ν̄
ν
ν̄
i
i
indicates the ν (ν̄) neutrino flux of the atmospheric neutrinos, σν-NCQE (σν̄-NCQE ) represents the ν (ν̄) cross-sections on oxygen from model i, respectively. In this analysis,
seven cross-section models such as Spectral Function (SF) [152, 153], Relativistic
Mean Field (RMF) [154], SuperScaling (SUSA) [155], Relativistic Green Function(RGF) with two types of the functional forms (EDAI, Democratic) [154, 156], andRelativistic Wave Impulse Approximation (RPWIA) [154], as depicted in Figure 9.1,
are investigated to extract uncertainty. The maximum difference of all models foreach Rνi and Rν̄i are assigned as systematic errors, which is set to 7%.

3
2.5
2
1.5

NEUT
SF
RMF
SUSA
RGF_EDAIRGF_Democratic

1
0.5
0
0

RPWIA

0.5

1

1.5

2
2.5
Eν [GeV]

2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

NEUT
SF
RMF
SUSA
RGF_EDAIRGF_Democratic
RPWIA

0.5

1

1.5

2

2.5
3
Eν [GeV]Figure 9.1: Total cross-section for neutrino (left) and antineutrino(right) for 16 O(ν, ν ′ N) interaction.

Cross-section
The systematic uncertainty before interaction comes from the neutrino interaction
cross-section and flux. The cross-section uncertainty is extracted from the scaling
factor of the T2K measurement, which is set to 44%.

9.1. Atmospheric neutrinos

149

Neutron tagging efficiency and neutron multiplicity
After neutrino interaction, some uncertainties remain at the detector. Neutrons originating from the NCQE interaction and following secondary interaction are important
for the SRN search as neutron tagging is utilized. Thus, the uncertainty related to
the neutron, such as the neutron tagging efficiency and the neutron multiplicity at
the final state, should be considered. Figure 9.2 displays the averaged tagged neutron
multiplicity as a function of reconstructed four-dimension momentum Q2 , measured
by the T2K experiment with the CC-dominant samples [50]. These are separately obtained for ν-mode (FHC) and ν̄-mode (RHC). The ratio of the predicted and observed
tagged neutrons multiplicity is summarized in Table 9.1. The values in Table 9.1 exT2K = N FHC +N RHC
hibit combined multiplicity for ν and ν̄, which is calculated by Nobs
obs
obs
T2K = N FHC + N RHC . Moreover, Figure 9.3 illustrates the number of tagged
and Npred
pred
pred
neutrons of atmospheric neutrino MC for each Q2 region. Assuming the multiplicity
for the atmospheric neutrino MC is also higher than the actual data, which is analogous with the fact of T2K, the corrected multiplicity that should reproduce the data
can be evaluated as
atm
atm
T2K
T2K
Ndata
= NMC
× Nobs/Npred,(9.5)

atm denotes the expected mean tagged neutron multiplicity of the atmowhere Ndata
atm denotes that of the atmospheric neutrino MC. The
spheric neutrino data, and NMC
uncertainty is estimated by moving the number of tagged neutrons for a given eventin Figure 9.3 to a lower multiplicity bin. The probability of shifting one lower multiplicity bin is defined as ϵtrans . The best ϵtrans is determined to correspond to theatm by varying ϵmean multiplicity to Ndata
trans . Subsequently, after smearing the neutron
multiplicity, the variation of Ntagged = 1 bin is calculated. The maximum variance inall Q2 regions is assigned to the systematic errors, set to 30% for both the ν and ν̄.

Figure 9.2: Average of the number of tagged neutrons in the T2K
CC-dominant samples, as a function of reconstructed Q2 , for FHC(left) and RHC (right). Plots are taken from [41], and the original
work was done by [50].

Spectrum shape of the observed event
Knocked-out nucleon from NCQE interaction causes subsequent secondary interactionin the water, as depicted in Figure 9.4. NCQE spectrum shapes highly rely on thesecondary interaction because the gamma rays from both primary and secondary

150

Chapter 9. Background Estimation
T2K
Table 9.1: Ratio of the number of observed neutrons Nobs
over theT2K
2predicted by MC Npred in each Q region.

Q2 region
0.00–0.25 GeV2
0.25–0.50 GeV2
0.50–0.75 GeV2
0.75–3.00 GeV2

Nobs /Npred
0.65
0.72
0.51
0.82

102
ν
ν
Combined10ννCombined1

1
Mean: 0.270

Mean: 0.654

10−1

10−1

10−2

10−2

0

1

2

3 4 5 6 7 8 9
Number of tagged neutronsννCombined

1

0

1

2

1

3 4 5 6 7 8 9
Number of tagged neutronsννCombined

10−1

10−1
Mean: 0.745
10−2

Mean: 0.894

10−2

10−3
0

1

2

3 4 5 6 7 8 9
Number of tagged neutrons

0

1

2

3 4 5 6 7 8 9
Number of tagged neutrons

Figure 9.3: Neutron multiplicity distribution for Q2 < 0.25 GeV2
(upper left), Q2 = 0.25–0.5 GeV2 (upper right), Q2 = 0.5–0.0.75 GeV2(bottom left), and Q2 = 0.75–3.0 GeV2 .

interactions, caused within the nano sec-scale, are considered one event in SK. Thesede-excited gamma rays have a typical energy range within 6–8 MeV [157].
The recent T2K NCQE cross-section measurement highlighted a distortion in thereconstructed Cherenkov angle distribution of the measured data relative to the MC
for the reconstructed kinetic energy range of ∈ [7.49, 29.49] MeV, as depicted in
Figure 9.5. Notably, within the signal θC region for this study, specifically θC ∈[38◦ , 53◦ ], the FHC sample data exceeded the MC predictions. However, the actual

151

9.1. Atmospheric neutrinos
Secondary interactions

ν

Nuclearinteractions

O

16

NCQE interaction(Primary interaction)n or pn or pPrimary γ
Secondary γ's

Figure 9.4: Illustration of the NCQE interaction and subsequent
nuclear interactions.

data falls short of the MC for larger angle regions, which are likely dominated bymultiple gamma-ray events from NCQE interactions. This discrepancy underscorespotential modeling inaccuracies for secondary interactions and gamma-ray emissions.
Therefore, the uncertainty stemming from the spectrum shape inaccuracies should beconsidered.

Figure 9.5: Reconstructed Cherenkov angle distribution in the T2K
FHC (left) and RHC (right) measurements. These plots are recitedfrom [51].

Because the energy spectrum in multiple gamma-ray regions for Cherenkov angle
distribution is profoundly model-dependent, straightforward scaling for this domain
is challenging when estimating systematic uncertainty. To address this, an energy
spectrum is smeared using a pseudo-Gaussian distribution with an energy-dependent
standard deviation σ(Erec ). By employing this method, a new effective spectrum
S ′ (Erec ) is obtained from the simulated atmospheric NC event spectrum S(Erec ) as
follows:
"
#
Z
2
(E
−
E
)
rec
S ′ (Erec ) = N S(E) × exp −
dE,
(9.6)
2σ(E)2

152

Chapter 9. Background Estimation

where N denotes the overall normalization of the pseudo-Gaussian. In this analysis,
the deviation σ(E) was determined to 3 MeV with reference to [20], sufficient to cover
the discrepancy about θC of the T2K result. Systematic uncertainty is gauged byreweighting the NCQE atmospheric MC after the third cut, using reweighting factors
εν and εν̄ , defined as follows:εν(ν̄) =′Sν(ν̄)(Erec )

(9.7)

Sν(ν̄) (Erec )ενενAs the efficiency of the third cut depends on the energy, the εν(ν̄) is calculated immediately after the first reduction. Figure 9.6 depicts the calculated εν(ν̄) distribution foreach 2 MeV bin. εν(ν̄) is larger beyond 16 MeV, where the NCQE event with multiple
gamma-rays becomes dominant. Moreover, the difference increases with every 2 MeV,
which may indicate the effect of NCQE multiple gamma-ray events.

1.35
1.3

1.5
1.4

1.25
1.3

1.2
1.15

1.2

1.1

1.1

1.05
1

1
0.95

0.9
10

15

20

25

30

10

Recon. energy [MeV]

15

20

25

30

Reconstructed energy [MeV]

Figure 9.6: Weighting factor εν(ν̄) of neutrino (left) and antineutrino(right), each 2 MeV bin.

The energy-dependent systematic uncertainty εsys (Erec ) is deduced from the relative mean difference between the reweighted and original spectrum after post the cuts
as follows:εsys (Erec ) =′(Erec )
Sν+ν̄ (Erec ) − Sν+ν̄.
Sν+ν̄ (Erec )(9.8)

Figure 9.7 displays the ν + ν̄ combined weighting factor depending on the reconstructed energy, and Figure 9.8 depicts the reconstructed energy spectrum before andafter reweighting, after the third reduction. The resultant systematic uncertainty,
determined by comparing these two energy distributions, is conservatively set at 37%.
Total systematic uncertainty
The breakdown of systematic uncertainty for the NCQE interaction event is consolidated in Table 9.2. Being mutually exclusive, the total systematic error is calculated
by quadratically summing individual uncertainties, amounting to 68%.

153

ε ν +ν

9.1. Atmospheric neutrinos

1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
10

15

20

25
30
Reconstructed energy [MeV]Events/2-MeV

Figure 9.7: Weighting factor εν+ν̄ each 2 MeV bin.

18
nominal16

reweighted

14
12
10
8
6
4
2
0

10

15

20

25
30
bsenergy [MeV]

Figure 9.8: Energy distribution before and after reweighting by εν+ν̄ ,after the third reduction.

Table 9.2: Break down the systematic uncertainty on the NCQE
interaction events.

T2K cross-section
Atmospheric neutrino flux
Flux difference
Reductions
Neutron tagging efficiency
Neutron multiplicity
Spectral shape
Total

9.1.2

44%
15%
7%
2%
9%
30%
37%
68%

Non-NCQE like interactions

After the third reduction, the dominant background source from non-NCQE interactions in the 8–30 MeV region is the decay electrons/positrons from the decay ofinvisible muon, which is produced by the νµ CC interaction and decay from pions
originating from atmospheric neutrino interactions. The shape of the spectrum aligns

154

Chapter 9. Background Estimation

Events/2-MeV

with the well-known Michel spectrum from muon decay, reliably gauged using cosmicray muon data over many years. While significant systematic uncertainty exists forheavy particle production rates, such as muon, pion, and neutrons, these only impact
the scaling of the Michel spectrum. Thus, the number of non-NCQE-like events is
estimated by comparing the spectrum in the side-band region of 30–80 MeV between
observed data and MC before neutron tagging. The scaling factor is determined to theminimum χ2 value, estimated to be 0.846. Figure 9.9 illustrates the energy spectrum
for the data and MC before and after scaling.

7

Data

6

MC (nominal)
MC (scaled)

5
4
3
2
1
0

35

40

45

50

55

60

65

70

75
Erec [MeV]

Figure 9.9: Energy spectrum in the side-band region of 31.49–
79.49 MeV for the reconstructed kinetic energy.

χ2Figure 9.10 displays χ2 distribution as a function of the scaling factor. All uncertainties associated with the non-NCQE events, except for the neutron tagging andneutron multiplicity, are contained in the statistical uncertainty for the scaling factor tuning, which is 17% by the 1σ regions of χ2 distribution. Upon considering the22mean scale factor (0.85)

20

1σ region of scale factor

18
16
14
12
10
8
6
0.2

0.4

0.6

0.8

1
1.2
Scale factor

Figure 9.10: χ2 distribution as a function of the scaling factor.

neutron-related uncertainty, such as the neutron multiplicity and tagging efficiency,

155

9.2. Lithium-9

the total uncertainty associated with the non-NCQE interaction is estimated to be
36%.

9.2

Lithium-9

The number of remaining 9 Li events (B9 Li ) can be estimated as follows:
B9 Li =R9 Li × Tlive × 22.5

(9.9)

9

× Br[ Li → β + n] × fwindow × ϵreduc ,where the R9 Li denotes the production rate of 9 Li by spallation, Tlive denotes thelive time of this measurement (552.2 days), Br[9 Li → β + n] indicates the branching
fraction for the β+n decay of 9 Li, fwindow indicates the fraction of the energy spectrum
for 9 Li event above the search energy threshold, and ϵreduc represents the reduction
efficiency.
The two types of uncertainty on the 9 Li are assumed in this analysis; one is basedon the production rate, and the other is from the reduction efficiency. The production
rate of 9 Li is estimated to be 0.86 ± 0.12 (stat.) ± 0.15 (sys.) kton−1 · day−1 , by [158],
and this value is used in this analysis. This estimation results in 22% uncertainty intotal.
The 9 Li efficiency is evaluated by assuming that only the dt is isotope dependent,
as discussed in Section 8.2.6. This is caused by the absence of the accurate spallation
MC for the SK. However, the assumption is approximate and probably incorrect.
Thus, the uncertainty depending on that assumption is conservatively assigned to be
50%, similar to the previous SK-IV analysis. Therefore, the other uncertainty basedon the reduction efficiency primarily emerges from neutron tagging, which is 10% in
total. The total uncertainty on the B9 Li is assigned to be 55%.

9.3

Reactor Neutrinos

The reactor neutrino event is estimated by scaling the IBD signal MC to the reactor neutrino spectrum. This background forms the lowest energy in all consideredbackgrounds, and these populate only the lowest energy bin. Conservatively, the systematic uncertainty for the reactor neutrino backgrounds is assigned to 100%. Owing
to the low rate of this background in the signal energy region, the effect is quite small
for the result.

9.4

Accidental Fake background

The remaining accidental fake coincidence background Bacc can be calculated as:data
Bacc = εmis × Npre-ntag,(9.10)

data
where the εmis denotes the misidentification rate at the neutron selection, and Npre-ntag
indicates the remaining data event after the first to the third reduction, described in
Section 8. The contribution from the multiple misidentifications can be ignored at
this instant because the effect can obviously be ignored. The uncertainty, dependingon the estimation from the εmis , is estimated as 5%.

156

9.5

Chapter 9. Background Estimation

Expected Background Spectrum

Number of events [bin-1]

Figure 9.11 displays the estimated background across the entire SK-VI period with
552.2 days of live time. To compensate for the small statistic of SK-VI, the energy bin
is merged based on the type of background, such as 7.49–9.49 MeV, 9.49–11.49 MeV,
11.49–15.49 MeV, 15.49–23.49 MeV, and 23.49–29.49 MeV. Figure 9.12 exhibits thebin-merged background energy spectrum, wherein the first and second bins are notmerged because of their relatively large statistic. The third bin is the highest energy
bin among including 9 Li background. The almost NCQE background is contained
below the fourth bin. The final bin is dominated by an atmospheric non-NCQE
background. The breakdown of each background and these systematic errors for eachmerged bin is depicted in Table 9.3.
102
Atmospheric-ν (non-NCQE)
Atmospheric-ν (NCQE)
9

Spallation Li
Reactor-ν

10

Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)

1

10−1
8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Figure 9.11: Expected background spectrum with these total systematic uncertainties (hatched) for each 2 MeV bin. Dotted-dashed
red line denotes the expected SRN signal based on [10].

Table 9.3: Breakdown of the expected background events and thesesystematic errors at each merged bin.

Erec bin [MeV]
non-NCQE background
NCQE background
9 Li background
Reactor background
Accidental backgroundTotal

7.49–9.49
0.32 ± 0.12
1.81 ± 0.90
3.92 ± 2.16
0.25 ± 0.25
1.43 ± 0.07
7.73 ± 2.35

9.49–11.49
0.27 ± 0.10
1.30 ± 0.64
1.73 ± 0.95
0.01 ± 0.01
0.83 ± 0.04
4.14 ± 1.15

11.49–15.49
0.41 ± 0.15
1.06 ± 0.53
0.28 ± 0.15
0.00 ± 0.00
0.38 ± 0.02
2.13 ± 0.57

15.49–23.49
0.71 ± 0.26
0.26 ± 0.13
0.00 ± 0.00
0.00 ± 0.00
0.01 ± 0.00
0.98 ± 0.29

23.49–29.49
0.94 ± 0.34
0.03 ± 0.02
0.00 ± 0.00
0.00 ± 0.00
0.00 ± 0.00
0.98 ± 0.34

157

Number of events [bin-1]

9.5. Expected Background Spectrum

102
Atmospheric-ν (non-NCQE)
Atmospheric-ν (NCQE)
9

Spallation Li
Reactor-ν

10

Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)

1

10−1
8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Figure 9.12: Expected background spectrum with these total systematic uncertainty (hatched) for each merged bin (hatched). Dotteddashed red line portrays the expected SRN signal based on [10].

159

Chapter 10

Results
10.1

Search Result

All reduction criteria were applied to the data from 552.2 days of the SK-VI operation.
The reduction efficiency for each energy bin is summarized in Table 10.1.
Table 10.1: Breakdown the event reduction and signal efficiency ateach merged bin.

Erec binFirst reduction
Spallation cut
deff cutmax
Npre
Ndacay-eLq50/n50 cut
θc cutNeutron tagging

7.49–9.49
204328
13352
9581
9521
9492
8740
8713
5003
5

9.49–11.49
58993
5778
4606
4582
4563
4293
4280
2924
5

11.49–15.49
18292
1982
1628
1613
1593
1541
1538
1334
3

15.49–23.49
630
115
101
96
56
41
35
21
2

23.49–29.49
54
47
47
43
14
8
8
5
1

After all reductions, 16 events remain in the signal energy region. The energy
spectrum for these observed events, alongside the expected background, is presented
in Figure 10.1. The error for these observed events is assigned as the square root of
the number of events.
To investigate the significance of the observed events (Nobs ) relative to the expected background events (Nbkg ) for each bin, a p-value, indicating the probabilityof obtaining the number of observed events under the assumption that all events
are background, is utilized. The p-value across each energy bin is calculated via the
toy-MC as follows:
1. Estimate the expected background using a Gaussian probability, adopting the
expected mean value and the mean and systematic error as the deviation.
2. Generate the number of events based on a Poisson probability with the earlier
deduced background as the mean. This set is one toy MC.
3. Interactively perform the prior step a million times, curating a Poisson-like toyMC.
4. Count the number of toy MC instances exceeding the number of observed events.

160

Number of events [bin-1]

Chapter 10. Results

14

SK-VI Data (552.2 days)
Atmospheric-ν (non-NCQE)
Atmospheric-ν (NCQE)

12

9Spallation Li
Reactor-ν

10

Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)

8
6
4
2

Number of events [bin-1]

0

8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]102
SK-VI Data (552.2 days)
Atmospheric-ν (non-NCQE)
Atmospheric-ν (NCQE)
9

Spallation Li
Reactor-ν

10

Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)

1

10−1
8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Figure 10.1: Observed and expected background spectrum withthese total systematic uncertainties (hatched) with linear scale (top)and logarithmic (bottom). The dot-dashed red line shows the expected
SRN signal based on [10].

5. The p-value is defined as
p-value =The number of counts
The number of generated toy MC(10.1)

Figure 10.2 visualizes the derived toy MC distribution and the consequent p-value
for each bin. The result of the p-value test were: 80.7% (7.49–9.49 MeV), 39.8%(9.49–11.49 MeV), 35.8% (11.49–15.49 MeV), 25.6% (15.49–23.49 MeV), 60.2% (23.49–
29.49 MeV). Specifically, the p-value for the energies above 15.49 MeV, almost released
from the NCQE and 9 Li background, is 32.6%. For all cases, the p-value surpassed
5%, concluding that no significant excess can exist over the expected background.

161

7.49-9.49 MeV

9.49-11.49 MeV

×103

250

160

100

140

80

200

120

150

100

60

11.49-15.49 MeV

×103

Number of toy MC

×103

Number of toy MC

Number of toy MC

10.2. Upper Limit Extraction

80
40

100

60
40

20

50

20
0
0

15.49-23.49 MeV

×103
400

23.49-29.49 MeV

×103

400

350

250

200

200

150

150

100

100

50

50

0
0

0
0

2

4

6 8 10 12 14 16 18 20
Pseudo number of event4

6 8 10 12 14 16 18 20
Pseudo number of event

Total

×103

100

300

250

2

120

350

300

0
0

5 10 15 20 25 30 35 40 45 50
Pseudo number of event

Number of toy MC

5 10 15 20 25 30 35 40 45 50
Pseudo number of event

Number of toy MC

Number of toy MC

0
0

80
60
40
20

2

4

6 8 10 12 14 16 18 20
Pseudo number of event

0
0

2

4

6 8 10 12 14 16 18 20
Pseudo number of event

Figure 10.2: Toy MC result for calculating the p-value for each energy bin above 11.49 MeV (bottom, right). Red line exhibits the actual
observed event in this analysis.

10.2

Upper Limit Extraction

10.2.1

Upper limit on the number of signal events

No significant excess is observed in data over the expected background prediction
for all energy bins. Therefore, the upper limit of ν̄e flux is extracted in the signal
energy region. First, the 90%-confidence level (C.L.) upper limit on the number oflimit is calculated by operating a pseudo experiment as the following
signal events N90
procedure.
toy
toy
in a toy data
and the expected events Nbkg
1. Number of observed events Nobs
set are calculated by the Gaussian probability, with random variations of thestatistical error on Nobs and the systematic error on Nbkg .
toy
toy
toy
2. The number of signal events Nsig
is calculated by subtracting Nobs
from Nbkg.
toy
3. Make Nsig
distribution by 106 times iteration of the prior pseudo test.
limit as the number through integration between zero and N , con4. Calculate N90
sigtaining 90% of the integration above zero.

Figure 10.3 exhibits the Nsig distribution as the pseudo-experiment results for the
9.49–11.49 MeV bin.

162

Chapter 10. Results

3500
toy

3000

Nsig = 0

2500

N90

limit

2000
1500
1000
500
0
−10

−5

0

5

10

15
toy
Nsig

Figure 10.3: Nsig distribution for Erec = 9.49–11.49 MeV bin as an
limit
limit
example of N90. The region between Nsig = 0 and Nsig = N90
contains 90% of the total of Nsig > 0 events.

10.2.2Flux Upper Limit Calculation

The flux upper limit ϕlimit[cm−2 sec−1 MeV−1 ] is calculated based on the following
90
formula:ϕlimit
=
90

limit
N90
,
σ̄IBD · Np · T · εsig

(10.2)

where σ̄IBD [cm2 ] illustrates the averaged cross-section of IBD interaction for the mean
neutrino energy (Eν ) for the corresponding energy region, Np denotes the number oftarget protons in SK, T [sec] indicates the live-time for SK-VI (552.2 days), and εsig
denotes the averaged signal efficiency, as indicated in Figure 8.31. Eν is obtained by
the Erec + 1.8 MeV for IBD interaction.
−2 sec−1 MeV−1 ], NTo calculate the expected sensitivity ϕexp
obs in the calcu90 [cmlimit
lation of N90 is replaced by Nbkg .
Figure 10.4 exhibits the observed and expected flux upper limit on the ν̄e flux,
including certain flux limits estimated by other searches and some theoretical flux
predictions (caption of Figure 10.4). These values are also summarized in Table 10.2.
Table 10.2: Summary table of upper limits, sensitivity.

Neutrino energy [MeV]Live time T
Number of Target Np
limit
N90
exp
N90
ϕlimit[/cm2 /sec /MeV]90
exp
ϕ90 [/cm2 /sec /MeV]

9.29–11.29

11.29–13.29

13.29–17.29 17.29–25.29
552.2 days
1.5 × 1033 protons
3.59
3.09
2.58
1.69
3.75
0.89
2.70
0.49

25.29–31.29

3.94
5.99
32.32
49.16

4.70
3.85
18.21
14.89

1.75
1.72
0.32
0.32

163

νe Flux Upper Limit [cm-2 sec-1 MeV-1]

10.2. Upper Limit Extraction

SK-VI 552.2 days, Observed 90% C.L. (This work)
SK-VI 552.2 days, Expected 90% C.L. (This work)
SK-IV 2970 days, Observed 90% C.L. (PRD. 2021)

102

SK-IV 2970 days, Expected 90% C.L. (PRD. 2021)
KamLAND 4529 days (ApJ. 2021)
Modern DSNB Theoretical Predictions

10

1

10−1

10−2

10

15

20

25
30
νe Energy [MeV]

Figure 10.4: Upper limits on the ν̄e flux. Solid lines denote theobserved upper limit for SK-IV (blue), SK-VI (red), and KamLAND(green), respectively. Dot-dashed lines represent the expected sensitivity based on the expected background for SK-IV (black) and SK-VI(yellow). Gray-shaded region represents the range of the modern theoretical expectation. The expectation drawn in the figure includes
DSNB flux models [15, 16, 14, 12, 11, 10, 9, 3, 8, 6, 5, 4, 52]. Ando+03
model was updated in [13].

165

Chapter 11

Discussion and Conclusion
11.1

Future Prospects on the SRN Search

The additional Gd is loaded into the SK tank to achieve the Gd concentration of approximately 0.03% for SK-VII. This process started at the beginning of June 2022 andwas completed at the beginning of July 2022. The Gd capture fraction is about 75%
for the SK-VII, leading to an anticipated 1.5 times higher neutron tagging efficiency
and keeping εmis consistent with SK-VI. Additionally, a machine-learning approachto neutron identification, inspired by previous SK-IV searches, is under development.
Current projections suggest that this will enhance neutron tagging efficiency by a factor of 1.2. Moreover, with the complete implementation of AFT trigger improvement
discussed in Section 2.4.2, an AFT efficiency εAFT exceeding 99% is expected. Basedon considerations of advancements and certain analysis improvements, the expected
sensitivity for running SK-VII can be estimated.
The first improvement concerns the NCQE interaction background, predominantly
evident below the Erec = 15.49 MeV region. Efforts are underway to reduce this
NCQE interaction further. For instance, leveraging machine-learning-based characterization to differentiate the PMT hit patterns of NCQE from IBD interactions could
potentially diminish NCQE interaction events [159]. Thus, an assumption is assignedthat 30% of NCQE events are removed by additional reduction. Because it is difficult
to estimate the effect of neutron tagging with multiple neutron events on the amountof NCQE background, the effect is ignored at this time.
Moreover, the systematic uncertainty on the NCQE event, currently assigned toabout 70%, is expected to be reduced by refining the physics model of the detector
simulations, validated by external measurement with neutron-oxygen interaction. The
dominant uncertainty arises from the spectrum shape originating from the gamma-ray
multiplicity. External measurements promise a deeper insight into proton interaction
around O(10) GeV, offering a clearer understanding of the systematic uncertainty
associated with atmospheric neutrino flux. These efforts may halve the current uncertainty.
In addition to the NCQE events, 9 Li events resulting from the muon spallation
are key contributions to the major background in the lowest two energy bins. Most
systematic uncertainties associated with the 9 Li event stem from the belief that thetiming from muon is only an isotope-dependent variable in the spallation cut. In the
future, accurate muon spallation MC models will validate the accuracy of this assumption, aiming to reduce uncertainty by half. As estimating the potential reduction in
9 Li is challenging, its projected event rate remains unchanged.
As a further improvement, the atmospheric non-NCQE event should be reduced.
In this analysis, the non-NCQE event is scaled using the side-band data before neutron tagging. It causes additional systematic uncertainty on the neutron multiplicity.

166

Chapter 11. Discussion and Conclusion

In addition, given that the current MC displays an augmented neutron signal (Section 9.1.1), more events with one neutron signal are expected. It makes an overestimation of non-NCQE events. In the future, these effects should be reduced by ∼ 60%
by scaling from the comparison after neutron tagging. The systematic uncertainty on
non-NCQE events, estimated from side-band region fitting uncertainties, is assumed
to be reduced by the increasing statistic by ∼ 60%.

11.2

Future Sensitivity Calculation

Factoring these conditions, the prospective model-independent sensitivity for the ν̄eis derived, following the methodology outlined in Section 10.2. Considering various
assumptions, Figure 11.1 visualizes the expected 90% C.L. sensitivity for future SK-Gd
operations in the two lowest energy bins. These assumptions, pivotal for sensitivity
estimations, are cataloged in Table 11.1. Due to significant contamination from thereactor, 9 Li, and accidental background in these bins, which are challenging to mitigate
effectively, the sensitivity in these areas is restricted.

Nominal Bkg. rate (with SK-VII ntag eff.)(Black) + × 1.2 ntag eff.
(Red) + NC × 0.7(Green) + ε NC × 0.5(Blue) + ε Li9 × 0.5(Orange) + CC and ε CC × 0.6
Model expectation (Kaplinghat+20)

SK-Gd 0.03% (11.3-13.3 MeV)
90% sensitivity [/cm2/sec/MeV]

90% sensitivity [/cm2/sec/MeV]

SK-Gd 0.03% (9.3-11.3 MeV)
102

Nominal Bkg. rate (with SK-VII ntag eff.)(Black) + × 1.2 ntag eff.
(Red) + NC × 0.7

102(Green) + ε NC × 0.5(Blue) + ε Li9 × 0.5(Orange) + CC and ε CC × 0.6
Model expectation (Kaplinghat+20)

10

1
0

2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year]

Figure 11.1: Expected future sensitivity for 9.3–11.3 MeV (left) and
11.3–13.3 MeV energy bins with various background conditions, suchas nominal case (black), and further higher neutron tagging efficiency(red), 70% of NCQE background (green), 50% of the error on the
NCQE background (blue), 50% of the error on the 9 Li (Orange), 50%of the CCQE background and their error (Magenta). Thick-dottedline denotes the most optimistic theoretical expected flux. In the 9.3–
11.3 MeV region, the theoretical expectation is excluded from thisfigure as it is smaller than the sensitivity.

Conversely, future sensitivities for higher energy bins — 13.3–17.3 MeV, 17.3–
25.3 MeV, and 25.3–31.3 MeV — are depicted in Figure 11.2, the optimistic flux
models, such as Kaplinghat+00 [14], stand to be validated with 3σ precision throughintensified background reductions efforts discussed above section. As events above
17.3 MeV are largely devoid of NCQE and 9 Li contamination, the sensitivity fluctuates chiefly based on assumptions regarding neutron tagging efficiency and CCQE
backgrounds.

167

11.2. Future Sensitivity Calculation
Table 11.1: Assumptions for calculating future sensitivity. Titles
about color indicate the line color for each panel shown in Figure 11.1.

(1) Black(2) Red(3) Green(4) Blue(5) Orange(6) Magenta

Neutron tag. eff.
×1.5
×1.8
×1.8
×1.8
×1.8
×1.8

NC bkg.
100%
100%
70%
70%
70%
70%

2

0.4

0.5

0.2

0.15

0.2

0.15

1

0

0.3

0.25

1.5

SK-Gd 0.03% (25.3-31.3 MeV)
0.25

0.35

2.5

CC bkg. and unc.
100%
100%
100%
100%
100%
60%

100%
100%
100%
100%
50%
50%

90% sensitivity [/cm2/sec/MeV]

3

9 Li unc.

SK-Gd 0.03% (17.3-25.3 MeV)
0.45

90% sensitivity [/cm2/sec/MeV]

90% sensitivity [/cm2/sec/MeV]

SK-Gd 0.03% (13.3-17.3 MeV)
3.5

NC unc.
100%
100%
100%
50%
50%
50%

0.1

0.1

0.05

0.05
2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year](a) 90% C.L. sensitivity with the same assumption as Figure 11.1.
SK-Gd 0.03% (17.3-25.3 MeV)

3

0.4

0.35

2.5
2

0.5

0.2

0.15

0.2

0.15

1

0

0.3

0.25

1.5

SK-Gd 0.03% (25.3-31.3 MeV)
0.25

2σ sensitivity [/cm2/sec/MeV]

0.45

2σ sensitivity [/cm2/sec/MeV]

2σ sensitivity [/cm2/sec/MeV]

SK-Gd 0.03% (13.3-17.3 MeV)
3.5

0.1

0.1

0.05

0.05
2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year](b) 2σ C.L. sensitivity with the same assumption as Figure 11.1.
SK-Gd 0.03% (17.3-25.3 MeV)

3

0.4

0.35

2.5
2

0.5

0.2

0.15

0.2

0.15

1

0

0.3

0.25

1.5

SK-Gd 0.03% (25.3-31.3 MeV)
0.25

3σ sensitivity [/cm2/sec/MeV]

0.45

3σ sensitivity [/cm2/sec/MeV]

3σ sensitivity [/cm2/sec/MeV]

SK-Gd 0.03% (13.3-17.3 MeV)
3.5

0.1

0.1

0.05

0.05
2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year]

0

2

4
6
8
10
Observation period [Year](c) 3σ C.L. sensitivity with the same assumption as Figure 11.1.

Figure 11.2: Expected future sensitivity for 13.3–17.3 MeV (left)
17.3–25.3 MeV (middle), and 25.3–31.3 MeV (right) energy bins withthe same assumption as Figure 11.1; colors represent the assumptions
listed in Table 11.1. Two thick-dotted lines exhibit the range of model
expectations.

168

11.3

Chapter 11. Discussion and Conclusion

Limitation to the Failed Supernova Rate

The failed supernova rate, a fraction that the supernova forms the black hole (BH)
before successfully exploding and forming a neutron star (NS), can be estimated using
the flux upper limit on the SRN. According to [53], the supernova neutrino spectrum
and total neutrino emission energy from a supernova depend on its fate, i.e., its
remnant, low-mass NS (Canonical-mass NS; CNS), high-mass NS (High-mass NS;
HNS), and failed supernova. The distinction between low- and high-mass NS is basedon a baryon mass of MNS,b = 1.6M⊙ . Furthermore, it is assumed that the explosion
does not occur, and in the case of the failed supernovae, only continuous mass accretionoccurs which results in a BH. Introducing the failed supernova fraction fBH and thehigh-mass NS forming supernova fraction fHNS to the SNe with NS, the neutrino
number density term dN/dEν in Equation 1.35 can be rewritten as*+dN (Eν′ )dNBH (Eν′ )=f+ (1 − fBH )(11.1)
BH
dEν′
dEν′
"
#
dNHNS (Eν′ )dNCNS (Eν′ )× fHNS+ (1 − fHNS )
,
dEν′
dEν′
where the dNBH (Eν′ )/dEν′ , dNCNS (Eν′ )/dEν′ denote the number spectrum for the failed
SN, SN with creating HNS, and SN with creating CNS, respectively. The event rate
spectrum is shifted to higher energy depending on the remnant mass, as depicted in
Figure 11.3. The total energy of neutrino emission depends on the condition of NS
formed after the explosion, and the nuclear Equation Of State (EOS) is responsible
for the final state of the remnant. At this time, the three EOS models, such as
Togashi [160], LS220 [161], and Shen [162], as following [53] are considered.

Figure 11.3: Event rate spectra of DSNB ν̄e for SK 22.5 kton water
per year. The EOS model is assumed to be (a) Togashi EOS, (b) LS220
EOS, (c) Shen EOS, respectively. Colors correspond to the remnant
types and mass hierarchy of the neutrino oscillation. These plots are
sourced from [53].

The HNS contributes more to the flux than the CNS, although their spectrum
shapes are similar. However, the neutrino spectrum from BH-forming supernovae
varies based on the EOS model. Differences in the event rate spectrum become significant above ∼ 15 MeV, especially between Togashi EOS and Shen EOS. On the other
hand, for the LS220 EOS, the spectrum contributions from BH-forming supernovae
are similar to those from NS-forming ones. Thus, the parameters fBH and fHNS can11.3. Limitation to the Failed Supernova Rate169

be investigated based on the flux upper limit, considering such differences in the contribution of BH-forming SN to the DSNB flux. In this thesis, the expected fluxes forvarious fBH and fHNS are compared with the future sensitivity under assumption (6)in Table 11.1. The strategy for the evaluation is the same as [53]. The two energy
regions, namely, 13.3 < Eν < 31.3 MeV and 17.3 < Eν < 31.3 MeV, are investigatedas the integrated flux.
The formulation of the expected neutrino flux is stated in Equation 1.34. Moreover,the flux of ν̄e at SK is described by Equation 1.40, and the CCSN rate adopts thedefinition of Equation 1.42. The minimum progenitor mass that causes the corecollapse is set to 8M⊙ , with other settings and assumptions detailed in [53]. The
expected integrated flux limit in 10 years of SK-Gd observations is 2.12 cm−2 sec−1
for the 13.3 < E < 31.3 MeV range and 0.78 cm−2 sec−1 for the 17.3 < E < 31.3 MeV
range with 3σ, respectively. Using this information, the limit is assigned for the fBH
and fHNS parameter-space. Figures 11.4 and 11.5 display comparisons between futuresensitivities and expected fluxes for nominal (NH) and inverted (IH) mass hierarchies,
respectively. Flux values exceeding the dot-dashed line are expected to be inspected in
the upcoming decade. Exclusion areas vary depending on EOS models, mass hierarchy,and search energy region. Notably, for the NH case (Figure 11.4), the higher energy
threshold sets stricter limits on fHNS and fBH , deviating from the finding in [53].
This change is mainly attributed to the improved estimation of CCQE events, which
dominate above the 17.3 MeV bins. Specifically, the limit for fBH is harsher thanfor fHNS in the Shen model, as this model has the characteristic BH flux shape. In
contrast, the sensitivity for fBH is limited for all fHNS regions in the LS220 model
since the BH spectrum is similar to the HNS and CNS spectrum. The tendency issimilar in the IH case (Figure 11.5).
The overlaid exclusion areas of three EOS models for each energy range are depicted in Figures 11.6 and 11.7. Since more neutrinos are emitted from HNS than
CNS, detecting neutrinos at larger fHNS for all models is easier. However, specificallyin LS220 models, the tendency for BH is dissimilar to that for HNS flux since the flux
from the BH is less than that of HNS and CNS with even higher energy thresholdregions. Thanks to the CCQE improvement, fHNS > 0.8 region with any fBH can beinvestigated for both NH and IH cases. Specifically, the Shen model can be verified
for almost all parameters in the IH case. Although the result is model-dependent,
10 years of SK-Gd operation can explore the higher fHNS and lower fBH regions for
all three models based on these tendencies.

170

Chapter 11. Discussion and Conclusion

1.0

0.00.0(1a) Togashi EOS
13.3 < Eν < 31.3 MeV

0.8

0.2
0.00.00.2 0.3
fBH

fHNS

1.0

0.4

0.8

0.2
0.00.00.4(2a) Togashi EOS
17.3 < Eν < 31.3 MeV

0.2 0.3
fBH

0.1

0.2 0.3
fBH[cm 2 sec 1]

1.0

0.4

1.4

0.8

1.2

0.6

1.0

0.4

0.8

0.2

0.6
0.1

e

fHNS

0.00.0(1c) Shen EOS
13.3 < Eν < 31.3 MeV

1.2

0.6

0.6
0.1

1.0

1.4

0.8
[cm 2 sec 1]

fHNS

1.0

0.4

0.4

e

1.2

0.6

0.2 0.3
fBH(1b) LS220 EOS
13.3 < Eν < 31.3 MeV
1.4

0.8

0.1

1.5

0.6

0.00.00.4(2b) LS220 EOS
17.3 < Eν < 31.3 MeV[cm 2 sec 1]

0.4

fHNS

0.2 0.3
fBH

2.0

0.4
0.2

[cm 2 sec 1]

0.1

2.5

0.6

e

0.00.0

1.5

0.2

0.8

e

1.5

0.2

2.0

0.4

3.0
[cm 2 sec 1]

2.0

0.4

2.5

0.6
fHNS

fHNS

0.6

0.8
[cm 2 sec 1]

2.5

e

0.8

3.0

e

3.0

0.1

0.2 0.3fBH

0.4(2c) Shen EOS
17.3 < Eν < 31.3 MeV

Figure 11.4: Two-dimensional map of the DSNB ν̄e flux as a functionof fBH and fHNS in normal mass hierarchy. Dotted-dashed line reports
the 3σ expected sensitivity derived from the 10 years of future SK-Gd
operation. These are estimated as the integrated flux for the neutrinoenergy 13.3 < Eν < 31.3 MeV (top) and 17.3 < Eν < 31.3 MeV(bottom) with distinct EOS models such as Togashi EOS (left), LS220
EOS (middle), and Shen EOS (right), respectively.

0.00.0(1a) Togashi EOS
13.3 < Eν < 31.3 MeV

0.8

0.2
0.00.00.6
0.1

0.2 0.3fBH

0.4(2a) Togashi EOS
17.3 < Eν < 31.3 MeV

0.00.0

fHNS

1.0

0.4

0.8

0.2
0.00.00.6
0.1

0.2 0.3fBH

0.4(2b) LS220 EOS
17.3 < Eν < 31.3 MeV

0.2 0.3
fBH[cm 2 sec 1]

1.0

0.4

(1c) Shen EOS
13.3 < Eν < 31.3 MeV

1.2

0.6

0.1

1.4

0.8

1.2

0.6

1.0

0.4

0.8

0.2
0.00.00.6
0.1

0.2 0.3fBH

0.4(2c) Shen EOS
17.3 < Eν < 31.3 MeV

Figure 11.5: Distributions with the same manners as Figure 11.4, incase of inverted mass hierarchy.

e

fHNS

1.0

1.4

0.8
[cm 2 sec 1]

fHNS

1.0

0.4

0.4

e

1.2

0.6

0.2 0.3
fBH(1b) LS220 EOS
13.3 < Eν < 31.3 MeV
1.4

0.8

0.1

[cm 2 sec 1]

fHNS

1.0

1.5

[cm 2 sec 1]

0.4

fHNS

0.2 0.3
fBH

2.0

0.4
0.2

[cm 2 sec 1]

0.1

1.5

0.2

2.5

0.6

e

0.00.0

2.0

0.4

3.0
0.8

e

1.5

0.2

[cm 2 sec 1]

fHNS

2.0

0.4

2.5

0.6

e

2.5

0.6

3.0
0.8

e

3.0
0.8

171

11.3. Limitation to the Failed Supernova Rate

NH

NH

0.8

0.8

fHNS

0.4
0.2
0.00.0Togashi
LS220
Shen

0.6
fHNS

Togashi
LS220
Shen

0.6

0.4
0.2

0.1

0.2

fBH

0.3

0.00.0

0.4

0.1

0.2

fBH

0.3

0.4

Figure 11.6: 3σ detectable areas on the fBH -fHNS plane assuming
NH for three distinct EOS models in the energy range of 13.3–31.3 MeV(left) and 17.3–31.3 MeV (right) according to the future flux limit at
10 year of the SK-Gd observation.

IH

IH

0.8

0.8

fHNS

0.4
0.2
0.00.0Togashi
LS220
Shen

0.6
fHNS

Togashi
LS220
Shen

0.6

0.4
0.2

0.1

0.2

fBH

0.3

0.4

0.00.0

0.1

0.2

fBH

0.3

0.4

Figure 11.7: Distributions with the same manners as Figure 11.6
but assuming IH.

172

11.4

Chapter 11. Discussion and Conclusion

Conclusion

In this thesis, the data from the recent SK-Gd phase was analyzed to search forsupernova relic neutrinos. Initially, a novel algorithm was formulated to detect neutron
capture on Gd. This involved evaluating fit quality, analyzing reconstructed energy,
and gauging the distance from a given prompt event to the delayed candidates. The
performance of this neutron identification was evaluated using the newly taken AmBe
data. For this, the AmBe calibration geometry was established in detector simulation
for the first time to compare it with the measurement. The subsequent neutron tagging
efficiency in the SK-Gd is estimated at 40.2+1.0−3.5 %. When evaluating the efficiency ofneutron tagging with two distinct BGO shapes, the outcomes aligned with the MC
simulation within 10% of the actual data. Given that disparities between actual data
and MC simulations depend on the BGO geometry, it was deduced that an unidentified
BGO effect might impact neutron interaction. Thus, the uncertainty on the neutron
tagging in SK-Gd is estimated to be 8.8%, including position dependence.
After evaluating neutron tagging efficiency, the first search for SRN using 552 daysof SK-Gd data is performed. All simulations used in this analysis were based on a
newly constructed MC, termed SKG4. Cut criteria for removing spallation events,
atmospheric neutrinos, and radioactive background are optimized. Consequently, thesignal efficiency was estimated to range between 13.9–31.6% in the signal energy region. Notably, this efficiency is significantly improved from the previous SRN searches
in SK below the 16 MeV energy regions, attributable to high neutron tagging efficiency
while keeping sufficiently low misidentification probability in the neutron tagging.
Background events estimation for individual components, along with their systematic uncertainties were newly determined using SKG4. Not that this is the firsttime to evaluate the atmospheric neutrinos event MC via SKG4. The observed data
was also passed through a reduction, and finally, 16 events remained within the signal
energy region. However, following a p-value test, it was discerned that there was no
significant excess over the background. In the absence of a marked event surplus overthe expected background across energy bins, a 90% confidence level upper limit wasset. The observed and expected upper limits of SRN flux are 0.32–32.32 and 0.32–
49.16 cm−2 sec−1 MeV−1 , depending on energy bins. A pivotal observation was that
owing to the enhanced signal efficiency stemming from Gd-induced neutron capture,
the flux upper limit based on 552.2 days in the SK-VI period is comparable to theoutcomes from a 2970 days exploration in a previous pure-water phase, which is theworld’s stringent upper limit in the energy regions above 15.3 MeV. This proves the
SK-Gd experiment is the most sensitive to the SRN search, considering 20% of thelive time as the previous search.
Peering into future prospects, the estimations were made for the expected performance for future SK-Gd observations, grounded on the meticulous actual data
analysis and validation with the expected backgrounds. Pragmatic assumptions concerning background reductions and related systematic uncertainties were incorporated.
Additionally, a Gd concentration of 0.03% was assumed, mirroring current levels in
the SK-VII operation. The expected sensitivity with a decade of SK-Gd operation
indicates that several DSNB models are validated.
Lastly, by applying these findings to pertinent physics parameters, proportions offailed supernovae and those associated with high-mass neutron stars over 10 years
of SK-Gd operations were explored. These insights accentuate how future DSNB
observations of SK-Gd illuminate our understanding of the fate of Supernova.

173

Appendix A

Theoretical prediction of SRN flux
with integrated bins
Table A.1: Summary of model projections of average flux and obtained sensitivity in each bin. The future sensitivity in SK-VII represents the magenta line in Figure 11.1. The unit of each value iscm−2 sec−1 MeV−1 .

Neutrino energy [MeV]
Present results in SK-VI
Future sensitivity in SK-VII
Horiuchi+21 [4]Galais+10 [9]Tabrizi+20 [5]Kresse+20 [6]Nakazato+15 (IH, Max) [3]Nakazato+15 (NH, Min) [3]Horiuchi+18 (ξ2.5,crit = 0.1) [8]Horiuchi+18 (ξ2.5,crit = 0.5) [8]Horiuchi+09 (6 MeV, Max) [10]Ando+03 [12, 13]
Lunardini09 [11]Malaney97 [15]Hartmann+97 [16]Kaplinghat+00 [14]9.29–11.29
49.16
17.46
1.71
1.03
0.69
1.31
0.47
0.20
0.77
0.75
1.11
0.57
0.55
0.26
0.47
2.40

11.29–13.29
14.89
4.20
1.01
0.72
0.46
0.87
0.30
0.13
0.53
0.46
0.81
0.38
0.37
0.17
0.33
1.66

13.29–17.29
2.70
0.51
0.51
0.42
0.29
0.48
0.16
0.07
0.32
0.24
0.49
0.20
0.20
0.09
0.19
0.94

17.29–25.29
0.49
0.07
0.14
0.15
0.09
0.15
0.05
0.02
0.12
0.06
0.18
0.06
0.07
0.03
0.06
0.30

25.29–31.29
0.32
0.04
0.04
0.04
0.02
0.04
0.01
< 0.01
0.03
0.01
0.05
0.02
0.02
0.01
0.02
0.07

175

Appendix B

Spallation Distributions

50
45

500

∆l [m]∆l [m]

Neutron cloud distributions

40
400

45

500
400

35

30

30
300

25
20
10

300

25
20

200

15

200

15
10

100

5
0
−5

50
40

35

100

5
−4

−3

−2

−1

0

1
2
log|∆T|

0

0
−5

−4

−3

−2

−1

0

1
2
log|∆T|

0

50
45
40
35
30
25
20
15
10
5
0
−5

−4

−3

−2

−1

0

1
2
log|∆T|

240
220
200
180
160
140
120
100
80
60
40
20
0

∆l [m]

Figure B.1: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud = 2.

∆l [m]

B.1

50

250

45
40

200

35
30

150

25
20

100

15
10

50

5
0
−5

−4

−3

−2

−1

0

1
2
log|∆T|

0

Figure B.2: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud = 3.

176

50
200

45

180
160
140
120

40
35
30
25
15
10
5
−4

−3

−2

−1

0

1
2
log|∆T|

50

200

45

180

40

100
80
60
40

20

0
−5

∆l [m]∆l [m]

Appendix B. Spallation Distributions

20
0

160

35

140

30

120

25

100

20

80

15

60

10

40

5

20

0
−5

−4

−3

−2

−1

0

1
2
log|∆T|

0

50
160

45

∆l [m]∆l [m]

Figure B.3: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud = 4-5.

50
45

140

40

140

35

120

35

30

100

30

25

80

25

80

20

60

20

60

15
5
−4

−3

−2

−1

0

1
2
log|∆T|

120
100

15

40

10
0
−5

40

40

10

20

5

0

0
−5

20
−4

−3

−2

−1

0

1
2
log|∆T|

0

50

1200

45
40

1000

35

50

1200

45
1000

40
35

800

30
25

600

20

800

30
25

600

20
400

15
10

200

5
0
−5

∆l [m]∆l [m]

Figure B.4: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud = 6-9.

400

15
10

200

5
−4

−3

−2

−1

0

1
2
log|∆T|

0

0
−5

−4

−3

−2

−1

0

1
2
log|∆T|

0

Figure B.5: Two-dimensional distribution of log |dt| and ∆l for the
pre-sample (left) and the post-sample (right). Magenta lines are cut
criteria in this plane. These are for clouds with Nncloud ≥ 2.

177

50
2500

40
30

2000

20
10

1500

0
−10

1000

−20
−30

500

∆y [m]∆y [m]

B.1. Neutron cloud distributions

50
40

250

30
200

20
10

150

0
−10

100

−20
−30

50

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50
0−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

103

40
30

∆z [m]−40∆z [m]

−40

40

102

30

20

20
102

10

10

0

10

0

−10

−10

−20

10

−20
−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

103

40
30

1

∆z [m]∆z [m]

−30

40

102

30

20

20
102

10

10

0

0

−10

−10

−20

10

10

−20

−30

−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50−50−50−40−30−20−10 0 10 20 30 40 50∆y [m]

1∆y [m]

Figure B.6: Two-dimensional distribution of ∆x , ∆y , and ∆z . The
left column shows the pre-samples and the right column shows thepost-samples. Magenta lines are cut criteria. These are clouds with
Nncloud = 2.

178

50

∆y [m]∆y [m]

Appendix B. Spallation Distributions

50

40

1600

30

1400

30

20

1200

20

10

1000

0

40

100
80

10
60

0

−10

800

−10

−20

600

−20

−30

400

−30

−40

200

−40

40
20

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

103

40
30

102

∆z [m]∆z [m]−50
0−50−40−30−20−10 0 10 20 30 40 50∆x [m]

40
30

20

2

10

10

20

0

0

−10

−10

−20

10

10

10

−20

1

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

103

40
30

∆z [m]−30∆z [m]

−30

102

40
30

20

102

10
0

20
10

10
0

−10

−10

−20

10

−20

1

−30

−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50−50−50−40−30−20−10 0 10 20 30 40 50∆y [m]∆y [m]

Figure B.7: Two-dimensional distribution of ∆x , ∆y , and ∆z . The
left column shows the pre-samples and the right column shows thepost-samples. Magenta lines are cut criteria. These are clouds with
Nncloud = 3.

179

50

2500

40
30

2000

20

∆y [m]∆y [m]

B.1. Neutron cloud distributions

50

90

40

80

30

70

20
1500

10

60

0

0

50

−10

1000

−10

40

−20

30

−30

20

−40

−40

10

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50
0−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

−20
−30

∆z [m]

500

103

40
30

102

∆z [m]

10

40
30

20

20
102

10
0

0

−10

−10

−20

10

10

10

1

−20
−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

103

40
30

102

∆z [m]∆z [m]

−30

40
30

20

20
102

10
0

0

−10

−10

−20

10

10

10

−20

1

−30

−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50−50−50−40−30−20−10 0 10 20 30 40 50∆y [m]∆y [m]

Figure B.8: Two-dimensional distribution of ∆x , ∆y , and ∆z . The
left column shows the pre-samples and the right column shows thepost-samples. Magenta lines are cut criteria. These are clouds with
Nncloud = 4-5.

180

3000

40
30

2500

20
10

2000

0

1500

−10
−20

1000

−30

500

−40

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]∆y [m]

50

50

80

40

70

30
60

20
10

50

0

40

−10

30

−20
−30

20

−40

10

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50∆z [m]

50
40

3

10

30

∆z [m]∆y [m]

Appendix B. Spallation Distributions

40
30

20

10

20

10

2

10

10

0

0

−10

−10

−20

10

1

−20

−30

−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50∆x [m]−50−50−40−30−20−10 0 10 20 30 40 50∆x [m]

40

3

10

30

∆z [m]

50∆z [m]

50

10−1

40
30

20

20

10

102

0

0

−10

−10

−20

10

−30

−40

−40
∆y [m]

1

−20

−30
−50
1
−50−40−30−20−10 0 10 20 30 40 50

10

10

10−1
−50
−50−40−30−20−10 0 10 20 30 40 50∆y [m]

Figure B.9: Two-dimensional distribution of ∆x , ∆y , and ∆z . The
left column shows the pre-samples and the right column shows thepost-samples. Magenta lines are cut criteria. These are clouds with
Nncloud = 6-9.

181

24000
22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0

∆y [m]

50
40
30
20
10
0

−10
−20
−30
−40
−50
−50−40−30−20−10 0 10 20 30 40 50∆x [m]∆z [m]

50

104

40
30

50

600

40
500

30
20

400

10
0

300

−10
200

−20
−30

100

−40

−50
0
−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50∆z [m]∆y [m]

B.1. Neutron cloud distributions

40
30

103

20
10

102

20
10

0

0

2

10

−10
−20

−10

10

−20
10

−30

−30
−50
−50−40−30−20−10 0 10 20 30 40 50∆x [m]

50

50

104

40
30

40
30

103

20
10

1

∆z [m]−40−50
1−50−40−30−20−10 0 10 20 30 40 50∆x [m]∆z [m]

−40

102

20
10

0

2

10

−10
−20

0
−10

10

−20
10

−30

−30

−40

−40

−50
1
−50−40−30−20−10 0 10 20 30 40 50−50−50−40−30−20−10 0 10 20 30 40 50∆y [m]

1∆y [m]

Figure B.10: Two-dimensional distribution of ∆x , ∆y , and ∆z . The
left column shows the pre-samples and the right column shows thepost-samples. Magenta lines are cut criteria. These are clouds with
Nncloud ≥ 2.

182

Appendix B. Spallation Distributions

B.2

PDF distributions

0.04

0.04

0.035

0.035

0.03

0.03

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0
10 − 2

10 −1

1

10

0
10 − 2|dt| [sec]10 − 110 − 110 − 210 − 210−3

10

10 − 4

10

−5

0

1000

2000

3000

4000

5000
l t [cm]

1010 − 1−3

1010 − 4

0

1000

2000

3000

4000

5000
l t [cm]

0

1000

2000

3000

4000

5000
l t [cm]

0

1000

2000

3000

4000

5000
l t [cm]−3

10 − 4

−5

0

1000

2000

3000

4000

5000
l t [cm]

10−5

10 − 110 − 110 − 210 − 2−3

1010 − 410|dt| [sec]−5

10 − 21010−3

10 − 110

110 − 410 − 2

10

10 −1

−3

10 − 4

−5

0

1000

2000

3000

4000

5000
l t [cm]

10−5

Figure B.11: Random (blue) and spallation (red) PDFs for dt (top),
and ℓt (second from the top to bottom). ℓt PDF distributions are
separated for the muon with dt region of 0–0.05 sec (second from top),
0.05–0.5 sec (third from top), and 0.5-60 sec (bottom). These muons
belong to the stopping (left) and multiple (right) muons.

183

B.2. PDF distributions

−1

−1

10

−2

−3

−3

−4

−3

10

−4

−4

10

−4000

−2000

−5

0

2000

4000
l l [cm]

−1

10

10

−4000

−2000

−5

0

2000

4000
l l [cm]

−1

10

−2

−2

−3

0

2000

4000
l l [cm]

−1

10

−2000

0

2000

4000
l l [cm]

−2

−2

−4

−4

−2000

0

2000

4000
l l [cm]

10

−2000

0

2000

4000
l l [cm]

−4

10

−5

−4000

−4000

−3

10

10

−5

4000
l l [cm]

−2

10

10

2000

10

−3

10

0

10

10

−3

10

−1

10

10

−2000

−5

−4000

−1

10

−4000

−4

10

−5

−2000

4000
l l [cm]

−3

−4

−4000

2000

10

10

−5

0

−2

−3

−4

−2000

10

10

10

−4000

10

10

10

10

−1

10

10

10

10

10

10

10

−2

10

10

−5

10

−2

10

10

−1

10

−5

−4000

−2000

0

2000

4000
l l [cm]

10

Figure B.12: Random (blue) and spallation (red) PDFs for ℓl with dt
region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec (bottom),and ℓt region of 0–300 cm (left), 300–1000 cm (middle), and morethan 1000 cm (right). These muons belong to the single throughgoing muons.

184

Appendix B. Spallation Distributions

−1

−1

10

−2

−3

10

−3

−3

10

−4

10

−4

10

−4

10

3

−5

0

1000

2000

3000

4000
Qres [p.e.]

×10

−1

10

3

−5

10

0

1000

2000

3000

4000
Qres [p.e.]

×10

−1

10

−2

−2

−3

×10
0

1000

2000

3000

4000
Qres [p.e.]

−1

×10
0

1000

2000

3000

4000
Qres [p.e.]

−2

−2

−4

−4

×10
0

1000

2000

3000

4000
Qres [p.e.]

1000

2000

3000

4000
Qres [p.e.]

−4

10

3

×10

−5

10

0

−3

10

10

3

−5

3

×10

−2

10

10

4000
Qres [p.e.]

10

−3

10

3000

10

10

−3

2000

−5

10

−1

10

10

1000

−4

−1

10

0

×10

10

3

−5

10

4000
Qres [p.e.]

−3

−4

−5

3000

10

10

3

2000

−2

−3

−4

1000

10

10

10

0

10

10

10

3

−5

10

−1

10

10

10

−2

10

10

10

10

−2

10

10

−1

10

0

1000

2000

3000

4000
Qres [p.e.]

3

×10

−5

10

Figure B.13: Random (blue) and spallation (red) PDFs for Qreswith dt region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec(bottom), and ℓt region of 0–300 cm (left), 300–1000 cm (middle), andmore than 1000 cm (right). These muons belong to the single throughgoing muons.

185

B.2. PDF distributions

−1

−1

10

−2

−3

−3

−4

−4

500

1000

1500

×10
2000
2500
Qµ [p.e.]

−1

−4

10

3

−5

10 0

500

1000

1500

2000

×10
2500
Qµ [p.e.]

−1

10

−2

−2

−3

−4

−5

500

1000

1500

×10
2000
2500
Qµ [p.e.]

−1

0

500

1000

1500

2000

×10
2500
Qµ [p.e.]

−1

10

−2

−2

−4

−4

500

1000

1500

×10
2000
2500
Qµ [p.e.]

0

×10
2000
2500
Qµ [p.e.]

−4

10

3

−5

10

1500

10

10

3

−5

1000

−3

10

10

500

−2

10

−3

10

×10
2000
2500
Qµ [p.e.]

3

0

10

10

−3

1500

−5

10

−1

10

10

1000

−4

10

3

−5

10

500

−3

10

10

3

×10
2000
2500
Qµ [p.e.]

−2

−3

−4

1500

10

10

10

1000

10

10

10

3

500

−5

10 0

−1

10

10

0

−3

10

10

3

−5

10

10

10

10

0

−2

10

10

10

10

−2

10

10 0

−1

10

500

1000

1500

2000

×10
2500
Qµ [p.e.]

3

−5

10

0

Figure B.14: Random (blue) and spallation (red) PDFs for Qmu
with dt region of 0–0.05 sec (top), 0.05–0.5 sec (middle), 0.5-60 sec(bottom), and ℓt region of 0–300 cm (left), 300–1000 cm (middle), andmore than 1000 cm (right). These muons belong to the single throughgoing muons.

186

Appendix B. Spallation Distributions

B.3

ROC Curves for each energy bin
10-12 MeV

Signal efficiency

Signal efficiency

8-10 MeV

0.8

0.6

0.8

0.6
0.4
0.4
0.2
0

0.05
0.1
0.15
0.2
Spallation remaining rate

0

14-16 MeV

Signal efficiency

Signal efficiency

12-14 MeV

0.9
0.8
0.7
0.6

0.05
0.1
0.15
Spallation remaining rate

0.8

0.6

0.5
0.02

0.04 0.06 0.08
Spallation remaining rate

0.02
0.04
0.06
Spallation remaining rate

Figure B.15: ROC curve for each 2 MeV bin below 16 MeV.

187

B.4. Correlation between Spallation and Li9 efficiency

B.4

Correlation between Spallation and Li9 efficiency
10-12 MeV

Li9 remaining rate

Li9 remaining rate

8-10 MeV

0.15

0.1

0.1

0.05
0.05

0
0

0.05
0.1
0.15
0.2
Spallation remaining rate

0

14-16 MeV

Li9 remaining rate

Li9 remaining rate

12-14 MeV

0.08

0.06

0.05
0.1
0.15
Spallation remaining rate

0.06

0.05

0.04

0.04

0.03

0.02
0.02

0.04 0.06 0.08
Spallation remaining rate

0.02
0.04
0.06
Spallation remaining rate

Figure B.16: Correlation between spallation remaining rate and 9 Li
efficiency for each 2 MeV energy bin below 16 MeV.

189

Appendix C

Third Reduction Cut Variables
Effective wall distance distribution
6000

1800

5500

1600

5000

1400

4500

1200

4000
1000

Data

3500

IBD MCData
IBD MC

800

3000
600
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]Data/MC

Data/MC

2500

400

600

800

1000

1200

1400
1600
deff [cm]

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]

400

600

800

1000

1200

1400
1600
deff [cm]

140

500
450

120

400
100

350
300

80

250

Data

200

IBD MC

Data

60

150

IBD MC

40

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]Data/MC

Data/MC

100

400

600

800

1000

1200

1400
1600
deff [cm]

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

400

600

800

1000

1200

1400
1600
deff [cm]

18

35

16

30

14

25

12
10

20
15

Data

8

Data

IBD MC

6

IBD MC

10

4

5

2
deff [cm]Data/MC

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]20

40

Data/MC

C.1

400

600

800

1000

1200

1400
1600
deff [cm]

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
200

deff [cm]

400

600

800

1000

1200

1400
1600
deff [cm]Figure C.1: deff wall distribution for the data (black) and MC (blue).
Each panel show the reconstructed energy E for E > 8 MeV (left-top),
E > 10 MeV (right-top), E > 12 MeV (left-middle), E > 14 MeV(right-middle), E > 16 MeV (left-bottom), and E > 20 MeV (rightbottom).

190

Appendix C. Third Reduction Cut Variables

Cherenkov Angle

0.12

LINAC Data
LINAC MC

0.1

LINAC run #86154
Energy = 8.0 MeV
x,y,z = -12 ,0 ,-12 m

0.08

0.18
0.16

LINAC Data
LINAC MC

0.14

LINAC run #86157
Energy = 12.0 MeV
x,y,z = -12 ,0 ,-12 m

0.12
0.1

Events [/N/1.0 deg]

C.2.1

Events [/N/1.0 deg]

Third reduction variables in LINAC data

Events [/N/1.0 deg]

C.2

0.2
0.18

LINAC Data

0.16

LINAC MCLINAC run #86160
Energy = 15.0 MeV
x,y,z = -12 ,0 ,-12 m

0.14
0.12
0.1

0.08

0.06

0.08

0.06

0.04

0.06

0.04

1

0.5
10

20

30

40

50

60
70
80
90
Cherenkov angle [deg]0.14
LINAC Data

0.12

LINAC MCLINAC run #86135
Energy = 8.0 MeV
x,y,z = -12 ,0 ,0 m

0.1

0Events [/N/1.0 deg]

Events [/N/1.0 deg]

1

20

30

40

50

60
70
80
90
Cherenkov angle [deg]

0.18
0.16

LINAC Data
LINAC MC

0.14

LINAC run #86138
Energy = 12.0 MeV
x,y,z = -12 ,0 ,0 m

0.12
0.1

0.08

0.04

40

50

60
70
80
90
Cherenkov angle [deg]

0.2
0.18

LINAC Data
LINAC MC

0.16

LINAC run #86142
Energy = 15.0 MeV
x,y,z = -12 ,0 ,0 m

0.14
0.12

0.04

1

0.02
Cherenkov angle [deg]1.5

Data/MC

Cherenkov angle [deg]1.5

Data/MC

1
0.5

20

30

40

50

60
70
80
90
Cherenkov angle [deg]

0.16
0.14

LINAC Data

0.12

LINAC run #86119
Energy = 8.0 MeV
x,y,z = -12 ,0 ,12 m

LINAC MC

0.1

0Events [/N/1.0 deg]

10

20

30

40

50

60
70
80
90
Cherenkov angle [deg]0.18
LINAC Data

0.16

LINAC MC

0.14

LINAC run #86126
Energy = 12.0 MeV
x,y,z = -12 ,0 ,12 m

0.12
0.1

0.08

0.5
20

30

40

50

60
70
80
90
Cherenkov angle [deg]

50

60
70
80
90
Cherenkov angle [deg]0.2
LINAC Data
LINAC MCLINAC run #86129
Energy = 15.0 MeV
x,y,z = -12 ,0 ,12 m

0.14
0.12

0.02

1.5
1

0

40

0.16

Cherenkov angle [deg]

0.5
10

30

0.18

Data/MC

Data/MC

1

20

0.04

0.02

1.5

10

0.06

0.04

Cherenkov angle [deg]

0

0.08

0.06

0.02

1

0.1

0.08
0.06
0.04

Cherenkov angle [deg]

1.5

0.5
10

Events [/N/1.0 deg]

Data/MC

Events [/N/1.0 deg]

30

0.1

0.02

0.5

Data/MC

20

0.06

0.04

0.02

0

10

0.08
0.06

0

1

0

0.08

0.06

Cherenkov angle [deg]

1.5

0.5
10

Events [/N/1.0 deg]

0.5

0.02
Cherenkov angle [deg]1.5

Data/MC

Cherenkov angle [deg]

1.5

0

0.04

0.02

Data/MC

Data/MC

0.02

Cherenkov angle [deg]

1.5
1
0.5

10

20

30

40

50

60
70
80
90
Cherenkov angle [deg]

0

10

20

30

40

50

60
70
80
90
Cherenkov angle [deg]Figure C.2: Reconstructed Cherenkov angle distribution for LINAC
data (black) and MC (blue). For each plot, the lower panel shows
the ratio of data over MC. For the LINAC position, figures show thez = −12 m (top), z = 0 m (middle), and z = 12 m (bottom). For
the LINAC energy, figures show the E = 8 MeV (left), E = 12 MeV(middle), and E = 15 MeV (right).

191

C.2. Third reduction variables in LINAC data

0.14
LINAC Data

0.12

LINAC MCLINAC run #86154
Energy = 8.0 MeV
x,y,z = -12 ,0 ,-12 m

0.1
0.08

0.14

LINAC MC

0.1

LINAC MC

0.12

0.06

0.04

0.04

0.04

0.02

0.02

1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

LINAC Data
LINAC MC

0.12
LINAC run #86135
Energy = 8.0 MeV
x,y,z = -12 ,0 ,0 m

0.1

0

0.06
0.04

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

LINAC Data
LINAC MCLINAC run #86138
Energy = 12.0 MeV
x,y,z = -12 ,0 ,0 m

0.12

0

2

2.5

3

0.14

3.5

0.1

0.06

0.04

0.04

LINAC Data
LINAC MC

0.12

LINAC run #86119
Energy = 8.0 MeV
x,y,z = -12 ,0 ,12 m

0.1

Data/MC

1

0.06
0.04
0.02

1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

LINAC Data
LINAC MC

0.14

LINAC run #86126
Energy = 12.0 MeV
x,y,z = -12 ,0 ,12 m

0.12
0.1

0.5
1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

LINAC MC

Q50/N50 [p.e.]

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

LINAC Data

0.16

LINAC MC

0.14

LINAC run #86129
Energy = 15.0 MeV
x,y,z = -12 ,0 ,12 m

0.12
0.1

0.04

0.04
0.02

Q50/N50 [p.e.]
Data/MC

1.5
10

LINAC Data

LINAC run #86142
Energy = 15.0 MeV
x,y,z = -12 ,0 ,0 m

0.18

0.06

0.5
0.5

0

0.08

Data/MC1

44.5
5
Q50/N50 [p.e.]

1

0.06

Q50/N50 [p.e.]

3.5

1.5

0.08

0.02

1.5

3

0.5
0.5

0.16

0.08

2.5

0.02

Q50/N50 [p.e.]

1.5

0

2

0.12

0.08

4
4.5
5
Q50/N50 [p.e.]

1.5

0.14

0.06

Events [/N/0.05]

1.5

Events [/N/0.05]

1

1

0.16

0.5
0.5

0.5

0.18

0.08

Q50/N50 [p.e.]

1

1

0.1

0.5

Data/MC

2

0.02

1.5

0

1.5

0.14

Data/MC

Data/MC

0.02

1

0.16

0.08

Q50/N50 [p.e.]

1.5

0.5
0.5

Events [/N/0.05]

1

0.14

0

1
0.5

0.5

Events [/N/0.05]

0

0.02

Q50/N50 [p.e.]

1.5

Data/MC

Data/MC

Data/MC

Q50/N50 [p.e.]

LINAC run #86160
Energy = 15.0 MeV
x,y,z = -12 ,0 ,-12 m

0.1
0.08

1.5

LINAC Data

0.14

0.06

0.5

Events [/N/0.05]

LINAC run #86157
Energy = 12.0 MeV
x,y,z = -12 ,0 ,-12 m

0.08

0.06

Events [/N/0.05]

LINAC Data

0.12

Events [/N/0.05]

Cherenkov Angle
Events [/N/0.05]

Events [/N/0.05]

C.2.2

Q50/N50 [p.e.]

1.5
1
0.5

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Q50/N50 [p.e.]

0

0.5

1

1.5

2

2.5

3

3.5

Figure C.3: Ratio of charge over number of hits in 50 ns distribution
for LINAC data (black) and MC (blue). For each plot, the lower panel
shows the ratio of data over MC. For the LINAC position, figures show
the z = −12 m (top), z = 0 m (middle), and z = 12 m (bottom). For
the LINAC energy, figures show the E = 8 MeV (left), E = 12 MeV(middle), and E = 15 MeV (right).

44.5
5Q50/N50 [p.e.]

192

Appendix C. Third Reduction Cut Variables

0.2

LINAC Data

0.18

LINAC MC

0.16

LINAC run #86154
Energy = 8.0 MeV
x,y,z = -12 ,0 ,-12 m

0.14

0.22

LINAC MCLINAC run #86157
Energy = 12.0 MeV
x,y,z = -12 ,0 ,-12 m

0.16
0.14

0.12
0.1
0.08
0.06

0.04

0.04

0.04

0.02

1
0.5
0.2

0.3

0.4

0.5

0.6

0.7

0.8
0.9
#mathcal{L}

1

pion

1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

LINAC Data
LINAC MC

0.16

LINAC run #86135
Energy = 8.0 MeV
x,y,z = -12 ,0 ,0 m

0.14
0.12

1

#mathcal{L}
1
0.5
0

0.2

LINAC Data

0.18

LINAC MC

0.16

LINAC run #86138
Energy = 12.0 MeV
x,y,z = -12 ,0 ,0 m

0.14

0.1
0.08
0.06

0.04

0.04

0.04

0.02

0.02

pion

1
0.5
0.7

0.8
0.9
#mathcal{L}

1

pion

1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.2
LINAC Data

0.18

LINAC MC

0.16
LINAC run #86119
Energy = 8.0 MeV
x,y,z = -12 ,0 ,12 m

0.14
0.12

1

#mathcal{L}

0.2

LINAC Data

0.18

LINAC MC

0.16

LINAC run #86126
Energy = 12.0 MeV
x,y,z = -12 ,0 ,12 m

0.14

0.04

0.04

0.04

0.02

0.02

0.5

0.6

0.7

0.8
0.9
#mathcal{L}

1

pion

0.7

pion

1
0.5
0

0.8
0.9
#mathcal{L}1

LINAC Data
LINAC MCLINAC run #86129
Energy = 15.0 MeV
x,y,z = -12 ,0 ,12 m

0.02#mathcal{L}

1.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8
0.9
#mathcal{L}1

Events [/N/Bin]

Events [/N/Bin]

0.1

0.4

0.6

0.12

0.06

0.3

0.5

0.14

0.08

0.2

0.4

0.2

0.06

0.1

0.3

0.16

0.06

0

0.2

0.18

0.1

0.5

0.1

pion

0.08

1

pion

0.5
0

0.12

pion

LINAC MC1

0.1

#mathcal{L}1

LINAC Data

1.5

0.08

1.5

0.8
0.9
#mathcal{L}

LINAC run #86142
Energy = 15.0 MeV
x,y,z = -12 ,0 ,0 m

pion

Events [/N/Bin]

pion

0.8
0.9
#mathcal{L}Events [/N/Bin]

0.6

0.7

0.02
#mathcal{L}Events [/N/Bin]

Events [/N/Bin]#mathcal{L}

0.5

0.6

0.12

0.06

0.4

0.5

0.14

0.06

0.3

0.4

0.2

0.1

0.2

0.3

0.16

0.08

0.1

0.2

0.18

0.12

0.1

0

0.1

pion

0.08

1.5

pion

1.5

pion

Events [/N/Bin]

Events [/N/Bin]

0.2
0.18

0.8
0.9
#mathcal{L}Events [/N/Bin]

0.1

0.02
Events [/N/Bin]

Events [/N/Bin]

1.5#mathcal{L}pion

Events [/N/Bin]

0.14

0.06

pion

LINAC MCLINAC run #86160
Energy = 15.0 MeV
x,y,z = -12 ,0 ,-12 m

0.16

0.06

#mathcal{L}

LINAC Data

0.2
0.18

0.1

0

Events [/N/Bin]

0.22

0.08

0.02

Events [/N/Bin]

0.24

0.12

0.1
0.08

Events [/N/Bin]

LINAC Data

0.2
0.18

0.12

Events [/N/Bin]

Pion likeness
Events [/N/Bin]

Events [/N/Bin]

C.2.3#mathcal{L}

pion

1.5
1
0.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

pion

Figure C.4: Pion likeness distribution for LINAC data (black) andMC (blue). For each plot, the lower panel shows the ratio of data over
MC. For the LINAC position, figures show the z = −12 m (top), z =0 m (middle), and z = 12 m (bottom). For the LINAC energy, figures
show the E = 8 MeV (left), E = 12 MeV (middle), and E = 15 MeV(right).

0.8
0.9#mathcal{L}

1

pion

193

Bibliography[1] K. Nakazato et al., “SUPERNOVA NEUTRINO LIGHT CURVES AND SPECTRA FOR VARIOUS PROGENITOR STARS: FROM CORE COLLAPSE TO
PROTO-NEUTRON STAR COOLING,” The Astrophysical Journal Supplement
Series, 205(1):2, feb 2013.
[2] K. S. Hirata et al., “Observation in the kamiokande-ii detector of the neutrino
burst from supernova sn1987a,” Phys. Rev. D, 38:448–458, Jul 1988.
[3] K. Nakazato et al., “Spectrum of the supernova relic neutrino background andmetallicity evolution of galaxies,” The Astrophysical Journal, 804(1):75, May
2015.
[4] S. Horiuchi et al., “Impact of binary interactions on the diffuse supernova neutrino background,” Phys. Rev. D, 103:043003, Feb 2021.
[5] Zahra Tabrizi and Shunsaku Horiuchi, “Flavor triangle of the diffuse supernova neutrino background,” Journal of Cosmology and Astroparticle Physics,
2021(05):011, may 2021.
[6] Daniel Kresse, Thomas Ertl, and Hans-Thomas Janka, “Stellar collapse diversity
and the diffuse supernova neutrino background,” The Astrophysical Journal,909(2):169, mar 2021.
[7] H. de Kerret et al., “Double chooz θ13 measurement via total neutron capture
detection,” Nature Physics, 16(5):558–564, 2020.
[8] S. Horiuchi et al., “Diffuse supernova neutrino background from extensive corecollapse simulations of 8–100 M⊙ progenitors,” Monthly Notices of the Royal
Astronomical Society, 475(1):1363–1374, 12 2017.
[9] S. Galais et al., “Shock waves in supernovae: New implications on the diffuse
supernova neutrino background,” Phys. Rev. D, 81:053002, Mar 2010.
[10] Shunsaku Horiuchi, John F. Beacom, and Eli Dwek, “Diffuse supernova neutrino
background is detectable in super-kamiokande,” Phys. Rev. D, 79:083013, Apr
2009.
[11] Cecilia Lunardini, “Diffuse neutrino flux from failed supernovae,” Phys. Rev.
Lett., 102:231101, Jun 2009.
[12] S. Ando, K. Sato, and T. Totani, “Detectability of the supernova relic neutrinos
and neutrino oscillation,” Astroparticle Physics, 18(4):307–318, 2003.
[13] S. I. Ando Relic supernova neutrino background: Current status and prospectsof future detectors In Jacques Dumarchez, editor, Proceedings of the Next Generation of Nucleon Decay and Neutrino Detectors, Aussois, Savoie, France, number C0504071 in SLAC eConf, April 2005.

194

BIBLIOGRAPHY[14] M. Kaplinghat, G. Steigman, and T. P. Walker, “Supernova relic neutrino background,” Phys. Rev. D, 62:043001, Jul 2000.
[15] R.A. Malaney, “Evolution of the cosmic gas and the relic supernova neutrino
background,” Astroparticle Physics, 7(1):125–136, 1997.
[16] D.H. Hartmann and S.E. Woosley, “The cosmic supernova neutrino background,” Astroparticle Physics, 7(1):137–146, 1997.
[17] G. L. Fogli et al., “Probing supernova shock waves and neutrino flavour transitions in next-generation water cherenkov detectors,” Journal of Cosmology andAstroparticle Physics, 2005(04):002, apr 2005.
[18] S. Appel M. Agostini, K. Altenmüller et al., “Search for low-energy neutrinos
from astrophysical sources with borexino,” Astroparticle Physics, 125:102509,
2021.
[19] S. Abe et al., “Limits on astrophysical antineutrinos with the kamland experiment,” The Astrophysical Journal, 925(1):14, jan 2022.
[20] K. Abe et al., “Diffuse supernova neutrino background search at superkamiokande,” Phys. Rev. D, 104:122002, Dec 2021.
[21] K. Abe et al., “The T2K experiment,” Nucl. Instruments Methods Phys. Res.
Sect. A Accel. Spectrometers, Detect. Assoc. Equip., 659(1):106–135, dec 2011.
[22] S. Fukuda et al., “The super-kamiokande detector,” Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors
and Associated Equipment, 501(2):418 – 462, Apr 2003.
[23] Z.Conner A Study of Solar Neutrinos Using the Super-Kamiokande Detector
PhD thesis, University of Maryland, http://www-sk.icrr.u-tokyo.ac.jp/sk/_pdf/articles/zoa-thesis.pdf, 1997.
[24] T.Yamaguchi Observation of 8B solar neutrinos from 300-day data at superkamiokande PhD thesis, The University of Osaka, 1998.
[25] Y. Nakano et al., “Measurement of the radon concentration in purified water in the super-kamiokande iv detector,” Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 977:164297, 2020.
[26] K. Abe et al., “First gadolinium loading to super-kamiokande,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 1027:166248, 2022.
[27] H. Ishino et al., “High-speed charge-to-time converter ASIC for the SuperKamiokande detector,” Nuclear Instruments and Methods in Physics ResearchA, 610(3):710–717, Nov 2009.
[28] S. Yamada et al., “Commissioning of the new electronics and online system
for the super-kamiokande experiment,” IEEE Transactions on Nuclear Science,57(2):428–432, 2010.
[29] M. Honda et al., “Improvement of low energy atmospheric neutrino flux calculation using the jam nuclear interaction model,” Phys. Rev. D, 83:123001, Jun
2011.

BIBLIOGRAPHY

195[30] O. Allkofer et al., “Cosmic ray muon spectra at sea-level up to 10 tev,” Nuclear
Physics B, 259(1):1–18, 1985.
[31] S. Matsuno et al., “Cosmic-ray muon spectrum up to 20 tev at 89° zenith angle,”
Phys. Rev. D, 29:1–23, Jan 1984.
[32] T. Sanuki et al., “Study of cosmic ray interaction model based on atmosphericmuons for the neutrino flux calculation,” Phys. Rev. D, 75:043005, Feb 2007.
[33] M. Honda et al., “Calculation of atmospheric neutrino flux using the interaction
model calibrated with atmospheric muon data,” Phys. Rev. D, 75:043006, Feb
2007.
[34] G. D. Barr et al., “Three-dimensional calculation of atmospheric neutrinos,”
Phys. Rev. D, 70:023006, Jul 2004.
[35] G. Battistoni et al., “The FLUKA code: description and benchmarking,” AIP
Conference Proceedings, 896(1):31–49, 03 2007.
[36] Y. Hayato, “A Neutrino Interaction Simulation Program Library NEUT,” Acta
Physica Polonica B, 40(9):2477, Sep 2009.
[37] T. Tanaka et al., “Gamma-ray spectra from thermal neutron capture on
gadolinium-155 and natural gadolinium,” Progress of Theoretical and Experimental Physics, 2020(4), 04 2020 043D02.
[38] K. Abe et al., “Solar neutrino measurements in super-kamiokande-iv,” Phys.
Rev. D, 94:052010, Sep 2016.
[39] J. Hosaka et al., “Solar neutrino measurements in super-kamiokande-i,” Phys.
Rev. D, 73:112001, Jun 2006.
[40] M. Shinoki Master thesis PhD thesis, Tokyo University of Science, March 2020.
[41] Y. Ashida
Measurement of Neutrino and Antineutrino Neutral-Current
Quasielastic-like Interactions and Applications to Supernova Relic Neutrino
Searches PhD thesis, Kyoto University, Feb 2020.
[42] H.Kitagawa
Measurement of the charge ratio of cosmic-ray muons inSuper-Kamiokande PhD thesis, Okayama University, https://www-sk.icrr.utokyo.ac.jp/sk/_pdf/articles/2022/Master_Thesis_Kitagawa.ver8_.pdf,
March 2022.
[43] K. Abe et al., “Calibration of the super-kamiokande detector,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 737:253 – 272, 2014.
[44] F De Guarrini and R Malaroda, “Two different technique measurements of
the neutron spectrum of an am–be source.,” Nucl. Instrum. Methods 92: 27784(1971)., 1 1971.
[45] ISO ISO 8529-1:2021 Neutron reference radiations fields — Part 1: Characteristics and methods of production pub-ISO, 2021.
[46] W. Wolszczak et al. Temperature properties of scintillators for pet detectors:
A comparative study In 2014 IEEE Nuclear Science Symposium and Medical
Imaging Conference (NSS/MIC), pages 1–4, 2014.

196

BIBLIOGRAPHY[47] M. Chadwick et al., “Endf/b-vii.1 nuclear data for science and technology:
Cross sections, covariances, fission product yields and decay data,” Nuclear
Data Sheets, 112(12):2887–2996, 2011 Special Issue on ENDF/B-VII.1 Library.
[48] Y. Hayato H. Zhang, K. Abe et al., “Supernova relic neutrino search with neutron
tagging at super-kamiokande-iv,” Astroparticle Physics, 60:41–46, 2015.
[49] D. Tilley et al., “Energy levels of light nuclei a=8,9,10,” Nuclear Physics A,
745(3):155–362, 2004.
[50] R. Akutsu A Study of Neutrons Associated with Neutrino and Antineutrino
Interactions on the Water Target at the T2K Far Detector PhD thesis, Universityof Tokyo, December 2019.
[51] K. Abe et al., “Measurement of neutrino and antineutrino neutral-current
quasielasticlike interactions on oxygen by detecting nuclear deexcitation γ rays,”
Phys. Rev. D, 100:112009, Dec 2019.
[52] N. Ekanger et al., “Impact of late-time neutrino emission on the diffuse supernova
neutrino background,” Phys. Rev. D, 106:043026, Aug 2022.
[53] Yosuke Ashida and Ken’ichiro Nakazato, “Exploring the fate of stellar corecollapse with supernova relic neutrinos,” The Astrophysical Journal, 937(1):30,
sep 2022.
[54] I. Esteban et al., “The fate of hints: updated global analysis of three-flavor
neutrino oscillations,” Journal of High Energy Physics, 2020(9):178, 2020.
[55] G. A. Tammann, W. Loeffler, and A. Schroeder, “The Galactic Supernova Rate,”
The Astrophysical Journal Supplement Series, 92:487, June 1994.
[56] H. A. Bethe and J. R. Wilson, “Revival of a stalled supernova shock by neutrino
heating,” The Astrophysical Journal, 295:14–23, August 1985.
[57] K. Sumiyoshi et al., “Postbounce evolution of core-collapse supernovae: Longterm effects of the equation of state,” The Astrophysical Journal, 629(2):922,
aug 2005.
[58] Tomoya Takiwaki, Kei Kotake, and Yudai Suwa, “THREE-DIMENSIONAL
HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR
AN 11.2M⊙ STAR WITH SPECTRAL NEUTRINO TRANSPORT,” The Astrophysical Journal, 749(2):98, mar 2012.
[59] T. Foglizzo et al., “Instability of a stalled accretion shock: Evidence for theadvective-acoustic cycle,” The Astrophysical Journal, 654(2):1006, jan 2007.
[60] Y. Fukuda et al., “Evidence for oscillation of atmospheric neutrinos,” Phys. Rev.
Lett., 81:1562–1567, Aug 1998.
[61] Q. R. Ahmad et al., “Measurement of the rate of νe +d → p +p +e − interactions
produced by 8 b solar neutrinos at the sudbury neutrino observatory,” Phys. Rev.
Lett., 87:071301, Jul 2001.
[62] B. Pontecorvo, “Mesonium and Antimesonium,” Sov. Phys. JETP, 33(2):549, 2
1957 [Zh. Eksp. Teor. Fiz.53,1717(1967)].

197

BIBLIOGRAPHY[63] B. Pontecorvo, “Inverse beta processes and nonconservation of lepton charge,”
Zh. Eksp. Teor. Fiz., 34:247, 1957.
[64] Ziro Maki, Masami Nakagawa, and Shoichi Sakata, “Remarks on the Unified
Model of Elementary Particles,” Prog. Theor. Phys., 28(5):870–880, nov 1962.
[65] B. Pontecorvo, “Neutrino Experiments and the Problem of Conservation of
Leptonic Charge,” Sov. Phys. JETP, 26:984–988, 1968 [Zh. Eksp. Teor.
Fiz.53,1717(1967)].
[66] L. Wolfenstein, “Neutrino oscillations in matter,” Phys. Rev. D, 17:2369–2374,
May 1978.
[67] L. Wolfenstein, “Neutrino oscillations and stellar collapse,”
20:2634–2635, Nov 1979.

Phys. Rev. D,[68] S. P. Mikheyev and A. Yu. Smirnov, “Resonance Amplification of Oscillations in
Matter and Spectroscopy of Solar Neutrinos,” Sov. J. Nucl. Phys., 42:913–917,
1985 [Yad. Fiz.42,1441(1985); ,305(1986)].
[69] Yasuhiro Nakajima Recent results and future prospects from super-kamiokande,Jun 2020.
[70] B. Aharmim et al., “Combined analysis of all three phases of solar neutrino datafrom the sudbury neutrino observatory,” Phys. Rev. C, 88:025501, Aug 2013.
[71] A. Gando et al., “Reactor on-off antineutrino measurement with kamland,” Phys.
Rev. D, 88:033001, Aug 2013.
[72] K. Abe et al., “Atmospheric neutrino oscillation analysis with external constraints in super-kamiokande i-iv,” Phys. Rev. D, 97:072001, Apr 2018.
[73] M. Jiang et al., “Atmospheric neutrino oscillation analysis with improved event
reconstruction in Super-Kamiokande IV,” Progress of Theoretical and Experimental Physics, 2019(5), 05 2019 053F01.
[74] K. Abe et al., “Constraint on the matter–antimatter symmetry-violating phasein neutrino oscillations,” Nature, 580(7803):339–344, 2020.
[75] Patrick Dunne Latest neutrino oscillation results from t2k, July 2020.
[76] M. A. Acero et al., “First measurement of neutrino oscillation parameters using
neutrinos and antineutrinos by nova,” Phys. Rev. Lett., 123:151803, Oct 2019.
[77] Alex Himmel New oscillation results from the nova experiment, July 2020.
[78] D. Adey et al., “Measurement of the electron antineutrino oscillation with 1958
days of operation at daya bay,” Phys. Rev. Lett., 121:241805, Dec 2018.
[79] Y. Suwa et al., “Observing supernova neutrino light curves with superkamiokande: Expected event number over 10 s,” The Astrophysical Journal,881(2):139, aug 2019.
[80] K. Nakazato et al., “Observing supernova neutrino light curves with superkamiokande. ii. impact of the nuclear equation of state,” The AstrophysicalJournal, 925(1):98, jan 2022.

198

BIBLIOGRAPHY[81] Y. Suwa et al., “Observing supernova neutrino light curves with superkamiokande. iii. extraction of mass and radius of neutron stars from synthetic
data,” The Astrophysical Journal, 934(1):15, jul 2022.
[82] K. Hirata et al., “Observation of a neutrino burst from the supernova sn1987a,”Phys. Rev. Lett., 58:1490–1493, Apr 1987.
[83] R. M. Bionta et al., “Observation of a neutrino burst in coincidence with supernova 1987a in the large magellanic cloud,” Phys. Rev. Lett., 58:1494–1496, Apr
1987.
[84] E. N. Alekseev et al., “Possible Detection of a Neutrino Signal on 23 February 1987 at the Baksan Underground Scintillation Telescope of the Institute of
Nuclear Research,” JETP Lett., 45:589–592, 1987 [,739(1987)].
[85] H. A. Bethe, “Supernova mechanisms,” Rev. Mod. Phys., 62:801–866, Oct 1990.
[86] Amol S. Dighe and Alexei Yu. Smirnov, “Identifying the neutrino mass spectrum
from a supernova neutrino burst,” Phys. Rev. D, 62:033007, Jul 2000.
[87] H. Sana et al., “Binary interaction dominates the evolution of massive stars,”
Science, 337(6093):444–446, 2012.
[88] Zapartas, E. et al., “Effect of binary evolution on the inferred initial and final
core masses of hydrogen-rich, type ii supernova progenitors,” A&A, 645:A6,
2021.
[89] P. Madau et al., “High-redshift galaxies in the Hubble Deep Field: colour
selection and star formation history to z ∼ 4,” Monthly Notices of the Royal
Astronomical Society, 283(4):1388–1404, 12 1996.
[90] J. R. WILSON et al., “Stellar core collapse and supernovaa,b,” Annals of the
New York Academy of Sciences, 470(1):267–293, 1986.
[91] Andrew M. Hopkins and John F. Beacom, “Erratum: “on the normalization of
the cosmic star formation history” (apj, 651, 142 [20067]),” The AstrophysicalJournal, 682(2):1486, aug 2008.
[92] A. de Gouvêa et al., “Fundamental physics with the diffuse supernova background neutrinos,” Phys. Rev. D, 102:123012, Dec 2020.
[93] M. Malek et al., “Search for supernova relic neutrinos at super-kamiokande,”Phys. Rev. Lett., 90:061101, Feb 2003.
[94] K. Bays et al., “Supernova relic neutrino search at super-kamiokande,” Phys.
Rev. D, 85:052007, Mar 2012.
[95] Tomonori Totani and Katsuhiko Sato, “Spectrum of the relic neutrino background from past supernovae and cosmological models,” Astroparticle Physics,
3(4):367–376, 1995.
[96] R. Becker-Szendy et al., “Imb-3: a large water cherenkov detector for nucleon decay and neutrino interactions,” Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 324(1):363 – 382, 1993.

BIBLIOGRAPHY

199[97] M. Honda et al., “Calculation of the flux of atmospheric neutrinos,” Phys. Rev.
D, 52(9):4985–5005, Nov 1995.
[98] M. Honda et al., “Comparison of 3-dimensional and 1-dimensional schemes in
the calculation of atmospheric neutrinos,” Phys. Rev. D, 64:053011, Aug 2001.
[99] M. Honda et al., “New calculation of the atmospheric neutrino flux in a threedimensional scheme,” Phys. Rev. D, 70:043008, Aug 2004.
[100] T. Sanuki et al., “Precise measurement of cosmic-ray proton and helium spectrawith the BESS spectrometer,” The Astrophysical Journal, 545(2):1135–1142,
dec 2000.
[101] S. Haino et al., “Measurements of primary and atmospheric cosmic-ray spectrawith the bess-tev spectrometer,” Physics Letters B, 594(1):35 – 46, 2004.
[102] J. Alcaraz et al., “Cosmic protons,” Physics Letters B, pages 27–35, 01 2020.
[103] T. Gaisser et al., “Primary spectrum to 1 tev and beyond,” Proceedings of the27th International Cosmic Ray Conference., page 1643, 08 2001.
[104] T. K. Gaisser and M. Honda, “Flux of atmospheric neutrinos,” Annual Review
of Nuclear and Particle Science, 52(1):153–199, 2002.
[105] Y. Nara et al., “Relativistic nuclear collisions at 10a gev energies from p + Be to
au+au with the hadronic cascade model,” Phys. Rev. C, 61:024901, Dec 1999.
[106] S. Roesler, R. Engel, and J. Ranft The monte carlo event generator dpmjet-iii In
A. Kling et al., editors, Advanced Monte Carlo for Radiation Physics, Particle
Transport Simulation and Applications, pages 1033–1038, Berlin, Heidelberg,
2001. Springer Berlin Heidelberg.
[107] K. Niita et al., “Phits—a particle and heavy ion transport code system,” Radiation Measurements, 41(9):1080 – 1090, 2006 Space Radiation Transport,
Shielding, and Risk Assessment Models.
[108] A. Capella et al., “Dual parton model,” Physics Reports, 236(4):225 – 329, 1994.
[109] M. Catanesi et al., “Measurement of the production cross-sections of π± in p–c
and π±–c interactions at 12gev/c,” Astroparticle Physics, 29:257–281, 05 2008.
[110] M. Catanesi et al., “Forward π± production in p–o2 and p–n2 interactions at
12gev/c,” Astroparticle Physics, 30:124–132, 10 2008.
[111] T. Sanuki et al., “Measurements of atmospheric muon spectra at mountain
altitude,” Physics Letters B, 541(3):234 – 242, 2002.
[112] P. Achard et al., “Measurement of the atmospheric muon spectrum from 20 to3000 gev,” Physics Letters B, 598(1):15 – 32, 2004.
[113] Yoshinari Hayato and Luke Pickering, “The neut neutrino interaction simulation
program library,” The European Physical Journal Special Topics, 230(24):4469–
4481, 2021.
[114] S. Jadach et al., “The τ decay library tauola, version 2.4,” Computer Physics
Communications, 76(3):361 – 380, 1993.

200

BIBLIOGRAPHY[115] C.H. Llewellyn Smith, “Neutrino reactions at accelerator energies,” Physics
Reports, 3(5):261 – 379, 1972.
[116] R.A. Smith and E.J. Moniz, “Neutrino reactions on nuclear targets,” Nuclear
Physics B, 43:605 – 622, 1972.
[117] A. A. Aguilar-Arevalo et al., “First measurement of the muon neutrino charged
current quasielastic double differential cross section,” Phys. Rev. D, 81:092005,
May 2010.
[118] J. Nieves, I. Ruiz Simo, and M. J. Vicente Vacas, “Inclusive charged-current
neutrino-nucleus reactions,” Phys. Rev. C, 83:045501, Apr 2011.
[119] Dieter Rein and Lalit M Sehgal, “Neutrino-excitation of baryon resonances andsingle pion production,” Annals of Physics, 133(1):79 – 153, 1981.
[120] Ch. Berger and L. M. Sehgal, “Lepton mass effects in single pion production by
neutrinos,” Phys. Rev. D, 76:113004, Dec 2007.
[121] K. M. Graczyk et al., “C5A axial form factor from bubble chamber experiments,”
Phys. Rev. D, 80:093001, Nov 2009.
[122] D. Rein, “Angular distribution in neutrino-induced single pion production processes,” Zeitschrift für Physik C Particles and Fields, 35(1):43–64, Mar 1987.
[123] Torbjorn Sjostrand Pythia 5.7 and jetset 7.4 physics and manual, 1995.
[124] M. Glück, E. Reya, and A. Vogt, “Dynamical parton distributions of the protonand small-x physics,” Zeitschrift für Physik C Particles and Fields, 67(3):433–
447, Sep 1995.
[125] A. Bodek and U. K. Yang Modeling neutrino and electron scattering inelastic
cross sections, 2003.
[126] Dieter Rein and Lalit M. Sehgal, “Coherent π0 production in neutrino reactions,”
Nuclear Physics B, 223(1):29 – 44, 1983.
[127] Ch. Berger and L. M. Sehgal, “Partially conserved axial vector current andcoherent pion production by low energy neutrinos,” Phys. Rev. D, 79:053003,
Mar 2009.
[128] Alessandro Strumia and Francesco Vissani, “Precise quasielastic neutrino /nucleon cross-section,” Physics Letters B, 564:42–54, 2003.
[129] R. Brun et al. GEANT 3: user’s guide Geant 3.10, Geant 3.11; rev. version
CERN, Geneva, 1987.
[130] R. Brun et al. GEANT: Detector Description and Simulation Tool; Oct 1994
CERN Program Library. CERN, Geneva, 1993 Long Writeup W5013.
[131] S. Agostinelli et al., “Geant4—a simulation toolkit,” Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors
and Associated Equipment, 506(3):250–303, 2003.
[132] J. Allison et al., “Geant4 developments and applications,” IEEE Transactions
on Nuclear Science, 53(1):270–278, 2006.

BIBLIOGRAPHY

201[133] J. Allison et al., “Recent developments in geant4,” Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors
and Associated Equipment, 835:186–225, 2016.
[134] M. Nakahata et al., “Atmospheric neutrino background and pion nuclear effectfor kamioka nucleon decay experiment,” Journal of the Physical Society of Japan,
55(11):3786–3805, 1986.
[135] E. Bracci Compilation of cross sections, 1972.
[136] A. S. Carroll et al., “Pion-nucleus total cross sections in the (3,3) resonanceregion,” Phys. Rev. C, 14:635–638, Aug 1976.
[137] K. Hagiwara et al., “Gamma-ray spectrum from thermal neutron capture on
gadolinium-157,” Progress of Theoretical and Experimental Physics, 2019(2), 02
2019 023D01.
[138] S. Desai High Energy Neutrino Astrophysics With Super-Kamiokande PhD
thesis, Boston University, 2004.
[139] Robin M. Pope and Edward S. Fry, “Absorption spectrum (380–700 nm) of purewater. ii. integrating cavity measurements,” Appl. Opt., 36(33):8710–8723, Nov
1997.
[140] Guangyuan Zhao and Xianming Sun Error analysis of using henyey-greensterin
in monte carlo radiative transfer simulations In In Progress In Electromagnetics
Research Symposium Proceedings, 2010.
[141] M. Stockhoff et al., “Advanced optical simulation of scintillation detectors ingate v8.0: first implementation of a reflectance model based on measured data.,”Phys Med Biol, 62(12):L1–L8, Jun 2017.
[142] Glenn F. Knoll Radiation detection and measurement / Glenn F. Knoll Wiley
New York, 2nd ed. edition, 1989.
[143] H. Ito et al. Analyzing the neutron and γ-ray emission properties of anamericium-beryllium tagged neutron source, 2023.
[144] Shirley Weishi Li and John F. Beacom, “First calculation of cosmic-ray
muon spallation backgrounds for mev astrophysical neutrino signals in superkamiokande,” Phys. Rev. C, 89:045801, Apr 2014.
[145] Shirley Weishi Li and John F. Beacom, “Spallation backgrounds in superkamiokande are made in muon-induced showers,” Phys. Rev. D, 91:105005,
May 2015.
[146] Shirley Weishi Li and John F. Beacom, “Tagging spallation backgrounds withshowers in water cherenkov detectors,” Phys. Rev. D, 92:105033, Nov 2015.
[147] Thomas Mueller Expérience double Chooz : simulation des spectres antineutrinos issus de réacteurs PhD thesis, IRFU, SPhN, Saclay, 2010 2010PA112124.
[148] SKReact Skreact-git hub.
[149] M. Shinoki et al., “Measurement of the cosmogenic neutron yield in superkamiokande with gadolinium loaded water,” Phys. Rev. D, 107:092009, May
2023.

202

BIBLIOGRAPHY[150] K. Abe et al., “Measurement of neutrino and antineutrino oscillations by theT2K experiment including a new additional sample of veinteractions at the far
detector,” Phys. Rev. D, 96(9):1–50, 2017.
[151] J. Lundberg et al., “Limits, discovery and cut optimization for a poisson processwith uncertainty in background and signal efficiency: Trolke 2.0,” Computer
Physics Communications, 181(3):683–686, 2010.
[152] O. Benhar et al., “Spectral function of finite nuclei and scattering of gev electrons,” Nuclear Physics A, 579(3):493–517, 1994.
[153] O. Benhar et al., “Electron- and neutrino-nucleus scattering in the impulse
approximation regime,” Phys. Rev. D, 72:053005, Sep 2005.
[154] R. González-Jiménez et al., “Relativistic description of final-state interactions
in neutral-current neutrino and antineutrino cross sections,” Phys. Rev. C,
88:025502, Aug 2013.
[155] J. E. Amaro et al., “Superscaling and neutral current quasielastic neutrinonucleus scattering,” Phys. Rev. C, 73:035503, Mar 2006.
[156] Andrea Meucci and Carlotta Giusti, “Final-state interaction effects in neutralcurrent neutrino and antineutrino cross sections at miniboone kinematics,” Phys.
Rev. D, 89:057302, Mar 2014.
[157] A. M. Ankowski et al., “Analysis of γ-ray production in neutral-current neutrinooxygen interactions at energies above 200 mev,” Phys. Rev. Lett., 108:052505,
Feb 2012.
[158] Y. Zhang et al., “First measurement of radioactive isotope production throughcosmic-ray muon spallation in super-kamiokande iv,” Phys. Rev. D, 93:012004,
Jan 2016.
[159] D. Maksimović, M. Nieslony, and M. Wurm, “Cnns for enhanced backgrounddiscrimination in dsnb searches in large-scale water-gd detectors,” Journal of
Cosmology and Astroparticle Physics, 2021(11):051, nov 2021.
[160] H. Togashi et al., “Nuclear equation of state for core-collapse supernova simulations with realistic nuclear forces,” Nucl. Phys. A, 961:78–105, May 2017.
[161] James M. Lattimer and Douglas F. Swesty, “A generalized equation of state for
hot, dense matter,” Nucl. Phys. A, 535(2):331–376, December 1991.
[162] H. Shen et al., “Relativistic equation of state for core-collapse supernova simulations,” The Astrophysical Journal Supplement Series, 197(2):20, nov 2011.