学位論文

Measurement of Cosmic-Ray Muon Spallation Products
in Super-Kamiokande with Gadolinium Loaded Water（スーパーカミオカンデにおけるガドリニウム含有水を用いた宇宙線ミューオンの核破砕反応による生成物の測定）

2024 年 3 月

篠木 正隆

ABSTRACT
High-energy muons produced by the interactions of cosmic-rays with nuclei in the atmosphere arecalled cosmic-ray muons. Cosmic-ray muons reaching the surface of the Earth interact with nuclei inmaterials, producing multiple neutrons and radioactive isotopes. These are the major backgrounds
in the rare event searches, including neutrino observations by underground experiments. This thesis
describes the results of the measurement of cosmogenic neutrons and 9 Li isotopes by analyzing thedata from the Super-Kamiokande (SK) detector.
The SK detector is a water Cherenkov detector located 1,000 m underground, with 50,000 tons ofultra-pure water filled in a cylindrical tank. As the upgrade of the detector, gadolinium is loaded inwater and the SK-Gd experiment has been started. In the SK-Gd experiment, neutrons are tagged
by detecting rays emitted after neutron capture reaction on gadolinium. One of the motivationsof the SK-Gd experiment is the first observation of neutrinos from past supernovae since the earlystage of the universe (supernova relic neutrinos, SRNs). In the SK detector, positrons and neutrons
generated by the interactions of electron antineutrinos with protons in water (¯⌫e + p ! e+ + n) aredetected. Comparison of the energy spectrum of SRNs, if it is observed, with theoretical predictions
will provide further insight into the frequency and explosion mechanism of supernovae.
In order to detect SRNs in the SK-Gd experiment, it is important to continue stable observations
over a long period of time. In this study, the uniformity and stability of gadolinium concentration
were confirmed through the detection of neutrons produced by cosmic-ray muons overall the detector. This method established in this study enables monitoring the stability of the detector in parallelwith the observations and will lead to the first observation of SRNs in the future. In addition, theproduction yield of neutrons induced by cosmic-ray muon (cosmogenic neutrons) was measured inthis study. Cosmogenic neutrons and recoil nuclei from the neutron scattering are the backgroundfor the measurements below the MeV scale. While, it is difficult to accurately reproduce the processes in simulations due to large uncertainty in the hadron production and scattering process.
Currently, empirical approaches are ongoing to evaluate the neutron production by the models derived from the measurements, and additional data are required to advance the studies. In this study,
neutron yield measurement was measured to be (2.76±0.02 (stat.)±0.19 (syst.))⇥10 4 µ 1 g 1 cm2 .
This is the second measurement of neutron yield in water following the SNO experiment. In addition, this measurement was made near the KamLAND detector which measured the neutron
yield in carbon. As the muon energy spectrum depends on the depth, this result allows a directcomparison of neutron yields in di↵erent targets for the first time. The measurement described inthis thesis provides important insights that contribute to advancing a systematic understanding of
neutron production by cosmic-ray muons.
This thesis also describes the measurement of the energy spectrum of electrons emitted fromdecay of the 9 Li. 9 Li produced via muon spallation decays with a lifetime of 0.26 s, emitting
an electron and a neutron. As electrons and positrons can not be distinguished by the SuperKamiokande detector, the decay of 9 Li is indistinguishable from the interactions of electron antineutrinos (¯⌫e + p ! e+ + n). Therefore, 9 Li is one of the major background sources in the SRN
search in low energy region. In this study, decay of 9 Li produced by cosmic-ray muon was selectedby requiring the detection of associated neutrons and correlations with the muons. In SK with purewater, the -spectrum of 9 Li was measured above 8 MeV, while, the range of the measurement was
extended down to 4.5 MeV using the data acquired with gadolinium-loaded water. Due to theredshift by the expansion of the universe, SRN flux is predicted to be larger in the low energy side.
The result of the 9 Li spectrum measurement and the analysis method established in this study
contribute to improving the sensitivity of the SRN search.

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ACKNOWLEDGEMENT
I would like to express my great appreciation to my supervisor Prof. Masaki Ishitsuka. He has
guided me with great care daily, and I have been impressed many times by his deep insight into
physics. Furthermore, I learned a lot from him, not only about the attitude toward research but
also about how to communicate things to others. I would not have been able to complete thisresearch without his support.
The Super-Kamiokande collaborators have taught me much about the low-energy neutrino
analysis in Super-Kamiokande, and have given me sound advice on many occasions. In particular,
I would like to extend my special thanks to Prof. Yusuke Koshio of Okayama University andProf. Yasuhiro Nakajima of the University of Tokyo for their extraordinary support since I started
this research. I am deeply grateful to them for taking time out of their busy schedules. I am also
grateful to Prof. Masayuki Nakahata, Prof. Hiroyuki Sekiya, Dr. Yuuki Nakano, and Dr. Takatomi
Yano of the Institute for Cosmic Ray Research at the University of Tokyo, Prof. Yasuo Takeuchiof Kobe University, and Prof. Blair Jamieson of the University of Winnipeg for discussions andimportant remarks on my research.
I have been got along very well with the members of Okayama University and Tokyo Instituteof Technology. Dr. Yota Hino, Dr. Masayuki Harada, Seiya Sakai, Fumi Nakanishi, Tomoaki Tada,
Tomohiro Tano, Yuki Shiraishi, Dr. Ryo Matsumoto, and Shota Izumiyama. We not only discussed
physics but also went out to eat together many times on business trips. Thanks to them, I wasable to enjoy my research life.
I would like to thank all Ishitsuka Lab members including alumni. Without their support, myresearch life would not have been successful and enjoyable. I hope they will continue to be my goodfriends.
This work supported by JST SPRING Grant Number JPMJSP2151 and Grant-in-Aid for JSPS
Fellows Grant Number 22KJ2809. I thank the financial support.
In closing, I would like to express my sincere gratitude to my family for their support throughout
my life.

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Contents
1 Physics Background
1.1 Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Hadrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Neutrinos from Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Overview of Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Core-Collapse Supernovae and Neutrino Emission . . . . . . . . . . . . . . . .
1.4.3 Observation of Neutrinos from SN1987A . . . . . . . . . . . . . . . . . . . . .
1.5 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Flux Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2 Status of SRN Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Cosmogenic Productions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1 Cosmic-Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Cosmogenic Neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.3 Cosmogenic Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Motivation29

3 Super-Kamiokande
3.1 Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Overview of Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Detector Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Water Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Photomultiplier Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Observation Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Front-End Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Water Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Air Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 The SK-Gd Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1 Gadolinium Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.2 SK-Gd Water System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Detector Calibration
4.1 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Quantum Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 PMT Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Measurement of Water Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Laser Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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50

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Contents
4.2.2 Top-Bottom Asymmetry of Water Quality . . . . . . . . . . . . . . . . . . . .
Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 DT Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measurement of Gadolinium Concentration . . . . . . . . . . . . . . . . . . . . . . .

53
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55

5 Event Reconstruction
5.1 Vertex and Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Muon Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59
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6 Evaluation of Stability and Uniformity of Neutron Detection
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Analysis Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Cosmic-Ray Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Neutron Capture Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Overview of Neutron Search . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3 Event Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4 Number of Hit-PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.5 Transverse Distance from Muon Track . . . . . . . . . . . . . . . . . . . . . .
6.5 Measurement of Neutron Capture Time Constant . . . . . . . . . . . . . . . . . . . .
6.6 Evaluation of the Stability and Uniformity . . . . . . . . . . . . . . . . . . . . . . . .

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4.3

4.4

7 Measurement of Cosmogenic Neutron Production
87
7.1 Overview of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2 Detector Configuration and Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.3 Cosmic-Ray Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.4 Neutron Capture Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.4.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.4.2 Event Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.4.3 Number of Hit-PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.4.4 Transverse Distance from Muon Track . . . . . . . . . . . . . . . . . . . . . . 93
7.5 Number of Neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.6 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6.1 Muon Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6.2 Neutron Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.6.3 Transverse Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.6.4 Number of Hit-PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.6.5 Leak-In and Leak-Out of Neutrons . . . . . . . . . . . . . . . . . . . . . . . . 100
7.6.6 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8 Measurement of Cosmogenic Lithium-9 Production
103
8.1 Overview of 9 Li + n Decay Event Search . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Selection of Prompt and Delayed Event Pair . . . . . . . . . . . . . . . . . . . . . . . 104
8.2.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.2.2 Event Quality Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.2.3 Energy Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.2.4 Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.2.5 1 ms Veto After Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.3 Selection of Muon Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Contents
8.4
8.5

vii

Extraction of 9 Li Production Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Prospects for SRN Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

9 Conclusion

121

Bibliography

123

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Contents

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7

Diagram for beta decay of neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of the process of a core-collapse supernova . . . . . . . . . . . . .
Time evolution of neutrino energy and luminosity . . . . . . . . . . . . . . . . . . . .
Distribution of time and energy of neutrinos from SN1987A . . . . . . . . . . . . . .
SRN ⌫¯e flux predictions from various theoretical models . . . . . . . . . . . . . . . .
Correlation between redshift z and the frequency of supernova explosions (SNR) . .
Cross sections of neutrino interactions in Super-Kamiokande as a function of neutrinoenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8 Upper limits of the ⌫¯e flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9 Energy spectrum of the primary cosmic-rays . . . . . . . . . . . . . . . . . . . . . . .
1.10 Schematic illustration of cosmic-ray muon productions . . . . . . . . . . . . . . . . .
1.11 Spectrum of muons at zenith angle ✓ = 0 and ✓ = 75 at sea level . . . . . . . . . .
1.12 The rate of energy loss for positive muons in copper as a function of momentum . .
1.13 b(E) as a function of the muon energy E and each contribution for bremsstrahlung,e+ e pair production, and photonuclear reaction in some materials. . . . . . . . . .
1.14 Correlation between intensity of cosmic ray muons and depth for di↵erent underground sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.15 Energy spectra of cosmic-ray muons reach various underground sites . . . . . . . . .
1.16 Diagram of muon spallation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.17 Diagram of photonuclear reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.18 Diagram of photonuclear reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.19 Simulated energy spectrum neutrons induced in Cn H2n by 280 GeV muons . . . . . .
1.20 Comparison between the previous measurement results and predictions with FLUKAbased simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.21 Half-lives and predicted yield above 3.5 MeV . . . . . . . . . . . . . . . . . . . . . .
1.22 Schematic illustration of the IBD event of SRN (¯⌫e ) and the 9 Li + n decay event .
9
1.23 Decay scheme of Li based on Particle Data Group . . . . . . . . . . . . . . . . . . .
1.24 Reconstructed kinetic energy spectrum of the observed data and the expected background for the SRN searches in SK with 0.01% Gd-loaded water . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5

Schematic illustration of Cherenkov detection . . . . . . . . . . . . . . . . . . . . . .
Example of an event display for an electron . . . . . . . . . . . . . . . . . . . . . . .
The Super-Kamiokande detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cross section of the SK detector and the support structure for PMTs . . . . . . . . .
Schematic illustration of an electron neutrino and a cosmic-ray muon arriving at the
SK detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Schematic illustration of the detection principle of PMT . . . . . . . . . . . . . . . .
3.7 Schematic illustration of 20-inch PMT installed the SK detector . . . . . . . . . . . .
3.8 Wavelength dependence of quantum efficiency of the 20-inch PMT . . . . . . . . . .
3.9 Schematic illustration of water purification system . . . . . . . . . . . . . . . . . . .
3.10 Schematic illustration of air purification system . . . . . . . . . . . . . . . . . . . . .
ix

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List of Figures
3.11 Correlation between the time constant and Gd mass concentration, and between
neutron capture fraction on Gd and Gd mass concentration . . . . . . . . . . . . . .
3.12 Schematic illustration of Gd loading . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 The time variations of the amount of Gd sulfate octahydrate added to the water andthe event rate of neutron capture events on Gd . . . . . . . . . . . . . . . . . . . . .
3.14 Distributions of event vertex where cosmic-ray muon-induced neutrons were captured
on Gd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Schematic illustration of SK-Gd water system . . . . . . . . . . . . . . . . . . . . . .

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46

4.1 Schematic illustration of the NiCf source . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Positional dependence of PMT hit rate . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Schematic illustration of time-walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Example of TQ-map for a PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5 Schematic illustration of the laser calibration for measuring water quality parameters 52
4.6 Time distribution of the ratio of the number of hit PMTs Nhit to the total charge Qtot 52
4.7 Wavelength dependence of water quality parameters . . . . . . . . . . . . . . . . . . 53
4.8 Time variation of top-bottom asymmetry . . . . . . . . . . . . . . . . . . . . . . . . 54
4.9 Schematic illustration of LINAC calibration . . . . . . . . . . . . . . . . . . . . . . . 55
4.10 Schematic illustration of DT calibration . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.11 Schematic illustration of DT calibration . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.12 The distribution of the time di↵erence t between the prompt and delayed events . 57
4.13 The neutron capture time constants obtained from the Am/Be source calibrations
performed in the latter half of 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.1
6.2
6.3
6.4
6.5
6.6
6.7

Event displays of the Super-Kamiokande detector for electrons with energies of
15.6 MeV and 310 MeV for the data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probability density function of the residual time determined from the LINAC calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertex resolution as a function of total energy of an electron . . . . . . . . . . . . . .
Vertex resolution as a function of total energy of an electron . . . . . . . . . . . . . .
Definition of incident angle (✓, ) of photon to PMT . . . . . . . . . . . . . . . . . .
Correction function for photocathode coverage S(✓, ) . . . . . . . . . . . . . . . . .
Probability density distribution of Cherenkov photon wavelengths . . . . . . . . . . .
Comparison of eventdisplays for an electron and a cosmic-ray muon . . . . . . . . .
Schematic illustration of the case of Nnn = 4 . . . . . . . . . . . . . . . . . . . . . . .

Overview of muon-induced neutron observation in SK . . . . . . . . . . . . . . . . .
Event display of a cosmic-ray muon which penetrates the SK detector . . . . . . . .
Schematic illustration of cosmogenic neutron searches . . . . . . . . . . . . . . . . .
Distributions of the radial and central axial positions (r and z) for the data . . . . .
Distributions of gvtx and gdir for the data . . . . . . . . . . . . . . . . . . . . . . . .
Distributions of N50 for the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definition of transverse distance (Lt ) between the muon track and the reconstructedvertex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Distributions of Lt for the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 Distributions of t for the data applied event reductions in sequence . . . . . . . . .
6.10 Distribution of the time di↵erence between the muon and the followiing neutron
capture candidates, t, for the data . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 Distribution of the number of neutron candidates following a muon after the event
selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Schematic illustration of the dead time e↵ect in the short t region . . . . . . . . .

60
60
61
62
62
65
66
67
68
73
73
74
75
75
76
77
77
78
79
79
80

List of Figuresxi

6.13 Distribution of the time di↵erence between the muon and the followiing neutron
capture candidates, t, for the data . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.14 Stability of the neutron capture time constant for events in the fiducial volume ofthe detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.15 Distribution of capture time constant in each 15 days period . . . . . . . . . . . . . 82
6.16 The vertex positions of neutron capture events for M = 1 and the nine divided regions 82
6.17 The t distributions in each region at the period 0 . . . . . . . . . . . . . . . . . . . 83
6.18 Stability of the neutron capture time constant in each region . . . . . . . . . . . . . 84
6.19 Gaussian fit for evaluating the time variation of the time constant including theuniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7.1
7.2
7.3
7.4
7.5
7.6
7.7

Distributions of muon path length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Zenith (✓) and azimuthal ( ) dependence of the muon rate at the SK site . . . . . . 90
Distribution of gvtx and gdir for neutron capture on Gd in the MC . . . . . . . . . . 92
Distributions of N50 for the data in on-time window and o↵-time window. . . . . . . 92
Schematic illustration of t distribution . . . . . . . . . . . . . . . . . . . . . . . . . 93
Distribution of N50 for data and MC . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Distribution of transverse distance between the muon track and the reconstructedvertex for data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.8 Distribution of the time di↵erence between the muon and the following neutron
capture candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.9 Shapes of the normal exponential function and the exponential function considered
neutron thermalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.10 The example of event displays for a well-reconstructed event and a mis-reconstructed
event for multiple muons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.11 Comparison of N50 distributions for MC with data for M = 1 and M 10 . . . . . . 99
7.12 Schematic illustrations of leak-in/-out of neutrons around the detector center andnear the detector wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.13 Correlations between neutron yields and muon energies in various experiments . . . 102
Overview of cosmogenic 9 Li analysis in SK . . . . . . . . . . . . . . . . . . . . . . . . 104
The definition of the e↵ective distance from the ID wall de↵ . . . . . . . . . . . . . . 105
Reconstructed total energy of the prompt events for the data after the fiducial volume
cut is applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.4
energy spectrum of the 9 Li + n decay generated from MC simulation . . . . . . 107
8.5 Distribution of g 2 for neutron capture on Gd. . . . . . . . . . . . . . . . . . . . . . 108
8.6 Distribution of reconstructed total energy Erec for neutron capture on Gd. . . . . . . 108
8.7 Distribution of g 2 for neutron capture on Gd. . . . . . . . . . . . . . . . . . . . . . 109
8.8 Schematic illustration of transverse distance Lt and longitudinal distance Llong . . . 110
8.9 Definition of pre-sample and post-sample for the spallation variables . . . . . . . . . 111
8.10 The PDFs of the spallation sample and random sample . . . . . . . . . . . . . . . . 112
8.11 Lt distribution for pre-/post-sample and spallation sample . . . . . . . . . . . . . . . 112
8.12 Distribution of time di↵erence between muon and prompt event tµp for each reconstructed total energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.13 Distribution of time di↵erence between prompt and delayed event tpd . . . . . . . 115
8.14 The spectrum from the 9 Li + n decay . . . . . . . . . . . . . . . . . . . . . . . . 115
8.15 SRN flux from various redshift ranges . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.16 The spectrum from the 9 Li + n decay . . . . . . . . . . . . . . . . . . . . . . . . 117
8.17 Schematic diagram of the correspondence between the SRN and 9 Li analysis . . . . . 117
8.18 Expected energy spectrum for ten years of observations with Gd concentration of
0.03% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.1
8.2
8.3

xii

List of Figures

List of Tables
1.1
1.2
1.3
1.4
1.5
1.6

Elementary particles in the Standard Model of particle physics . . . . . . . . . . . . 2
Summary of properties of pion, kaon, proton, and neutron . . . . . . . . . . . . . . . 2
Neutrino processes in supernovae and proto-neutron star matter . . . . . . . . . . . 6
Summary of variables used in the Bethe formula . . . . . . . . . . . . . . . . . . . . 17
Measurements of the neutron yield Yn in di↵erent experiments . . . . . . . . . . . . 23
Radioactive isotopes induced by cosmic-ray muon spallation . . . . . . . . . . . . . . 25

3.1
3.2
3.3
3.4
3.5

Energy thresholds to emit Cherenkov light in water . . . . . . . . . . . . . . . . . . .
Characteristics of the 20-inch PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observation phases of SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigger condition for SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermal neutron capture cross sections for each Gd isotope. . . . . . . . . . . . . . .

5.1
5.2

Selection criteria of the ID hit-PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Requirements for Nnn corresponding to the number of ID hit-PMTs after the firstcleaning cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.1

The features of the neutrons from Am/Be source and cosmic-ray muons . . . . . . . 72

7.1
7.2
7.3
7.4
7.5

Detector configurations and the number of events during the analysis period . . . . . 88
Number of observed events after each selection . . . . . . . . . . . . . . . . . . . . . 95
Summary of the signal efficiencies for each event selection . . . . . . . . . . . . . . . 97
Summary of the systematic uncertainties on the measurement of neutron yield . . . 97
Average muon energy and neutron yield for each azimuthal angle of muon travel . . 101

8.1
8.2

Reduction summary for 9 Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Summary of the fit results and N9 Li for each Erec region . . . . . . . . . . . . . . . . 113

xiii

32
36
38
39
42

xiv

List of Tables

Chapter 1

Physics Background
High-energy muons are produced from the interactions of cosmic-rays in the atmosphere and penetrate deep underground. Muons induce electromagnetic showers and hadronic showers, and theyinteract with nuclei in material to produce secondary particles consisting of nucleons and mesons in
chain. Furthermore, the secondary particles induce the neutrons and unstable radioactive isotopes,
which are called cosmogenic products. Produced neutrons are captured on nuclei after thermalization, and the rays with the energy of several MeV are emitted. While, isotopes emit electrons
with MeV-scale via decay. Therefore, these are background in rare event search in the MeV scale
such as neutrino observations. This thesis measured the production of neutrons and 9 Li isotopes
induced by cosmic-ray muons. This is especially the first measurement of muon-induced neutron
yield in SK realized by the upgrade of the detector with Gd loading in ultra-pure water.
This chapter will provide the physics background for this study. The Standard Model of particle
physics will be first described, followed by a brief explanation of hadrons and neutrinos. There
are various neutrino sources in the universe, and Super-Kamiokande has been observing them.
This thesis focuses on neutrinos emitted from past supernovae, supernova relic neutrinos (SRNs).
However, SRNs have not been discovered so far, and only the upper limit of flux has been given.
This chapter will explain the predictions for the flux and the current status of the searches. Finally,
cosmogenic production, which is the subject of this study, will be described and the contributions
as the background for SRN searches will be discussed.

1.1Standard Model of Particle Physics

The Standard Model is the most fundamental theoretical framework describing modern particle
physics. In the Standard Model, quarks and leptons make up matter. These fermions interact via
gauge bosons such as photons, gluons, and weak bosons. Table 1.1 summarizes the elementary
particles included in the Standard Model. There are four basic interactions in nature: strong
interaction, electromagnetic interaction, weak interaction, and gravitational interaction. Threeof these, other than the gravitational interaction, are treated in the Standard Model. Strong
interaction, electromagnetic interaction, and weak interaction are mediated by gluons, photons,
and weak bosons, respectively. In addition to the above particles, there are also scalar bosons
called Higgs bosons. In the Standard Model, quarks and leptons acquire mass through interaction
with the Higgs field.
Quarks and leptons are associated with weak bosons that di↵er in charge by only one, making
each a pair (e.g. up quark and down quark, electron and electron neutrino). There are three typesof quarks and leptons that have the same charge but di↵erent mass scales, and each of the two
types of quarks and two types of leptons constitutes one “generation”. For every quark and lepton,
there is an antiparticle with the same mass and spin but opposite sign of charges.
The Standard Model has succeeded in describing almost all of the experimental results in theparticle physics so far. On the other hand, there are several problems that have not been explained1

2

Chapter 1. Physics Background
Table 1.1: Elementary particles in the Standard Model of particle physics
Generations
Quarks
Leptons

FermionsI
II
Up (u)
Charm (c)Down (d)Strange (s)Electron (e)Muon (µ)
Electron neutrino (⌫e ) Muon neutrino (⌫µ )III
Top (t)Bottom (b)Tau (⌧ )Tau neutrino (⌫⌧ )Bosons
Gauge
ScalarPhoton ( )Gluon (g)Higgs (H 0 )Z0W±

Table 1.2: Summary of properties of pion, kaon, proton, and neutron.
HadronPion
Kaon

ProtonNeutronSymbol⇡ + (⇡ )⇡0
K + (K )
KS0
KL0
p
n

Componentud¯ (ūd)p¯(uū dd)/2
us̄ (ūs)p¯(ds̄ sd)/p2¯(ds̄ + sd)/
2
uud
udd

Mass (MeV)
139.57134.98493.68497.61497.61938.27939.57

Lifetime (s)2.6 ⇥ 10 8
8.4 ⇥ 10 17
1.2 ⇥ 10 8
9.0 ⇥ 10 11
5.2 ⇥ 10 8—880

by the Standard Model, such as the origin of neutrino mass, generation structure, and dark matter.

1.2

Hadrons

Quarks (antiquarks) and gluons exist in nature as composite particles called hadrons. Multiple
quarks (antiquarks) are bound together via a strong force mediated by gluons and form hadrons.
Hadrons are classified into two types according to the number of quarks (antiquarks): mesons andbaryons. Mesons consist of quark and antiquark pairs, while baryons contain three quarks. Among
various mesons, pion and kaon are the major mesons in nature which are produced by cosmic-ray
interacting with nuclei in the Earth’s atmosphere. On the other hand, examples of typical baryons
are protons and neutrons, which are components of the nucleus. Table 1.2 summarizes propertiesof pion, kaon, proton, and neutron.

1.3

Neutrinos

Neutrinos are neutral leptons with spin 1/2 that interact only via the weak interaction except for
the gravitational interaction. There are three generations (flavors) of neutrinos: electron neutrino⌫e , muon neutrino ⌫µ , and tau neutrino ⌫⌧ , corresponding to the charged leptons of electron,
muon, and tauon, respectively. There are corresponding antiparticles: electron antineutrino ⌫¯e ,muon antineutrino, ⌫¯µ , and tau antineutrino ⌫¯⌧ , corresponding to the charged leptons of positron,
positive muon, and positive tauon, respectively.
Neutrinos were predicted by W. E. Pauli in 1930 to explain the conservation of energy in beta
decay. The diagram for beta decay of neutron is shown in Figure 1.1. In 1956, the existenceof neutrinos was proved by F. Reines and C. Cowan by the observation of electron antineutrinos⌫¯e produced from a nuclear reactor [1]. In 1962, L. Lederman, M. Schwartz, and J. Steinberger
confirmed that ⌫e and ⌫µ are di↵erent elementary particles and that neutrinos have flavors [2].
Subsequently, ⌫⌧ was observed by the DONUT experiment in 2000, and the existence of all three
generations of neutrinos were confirmed [3].
Although the Standard Model assumes that neutrinos have no mass, observations of atmospheric
neutrinos in Super-Kamiokande experiment led to the discovery of neutrino oscillation phenomena
in 1998, which revealed that neutrinos have non-zero mass [4].

1.4. Neutrinos from Supernovae

3

u

u

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Figure 1.1: Diagram for beta decay of neutron.

1.4

Neutrinos from Supernovae

Massive stars with more than ⇠8 times the solar mass reach their end with the explosion. The explosion is called supernova. Supernovae release a large amount of energy, ⇠1051 erg (corresponding
to 1044 J), and more than 99% of the energy is carried out by the emission of neutrinos. Since theseneutrinos have information on the explosion mechanism and the supernova rate, neutrino observations are expected to advance our understanding of supernovae. This section describes supernova
explosions and neutrino emissions.

1.4.1

Overview of Supernovae

Supernovae are classified into the following categories according to the spectral lines.
• Type I: Supernova without hydrogen spectral line.
– Type Ia: Supernova with silicon line.
– Type Ib: Supernova without silicon line but with helium line.
– Type Ic: Supernova without helium and silicon line.
• Type II: Supernova with hydrogen spectral line.
Type Ia supernovae are called thermonuclear supernovae. In type Ia, the weight of a white dwarf ina binary is increased by the gas absorbed from the other star, and the white dwarf cannot support
its own weight at a certain point. Then, a runaway nuclear fusion of the carbon that makes up thecore of the white dwarf causes an explosion. The neutrinos emitted from a type Ia supernova havethe total energy of ⇠1049 erg or less. On the other hand, type Ib, Ic, and II supernovae are called
core-collapse supernovae, and the neutrinos emitted by these supernovae have the total energy of⇠1053 erg.

1.4.2

Core-Collapse Supernovae and Neutrino Emission

When supernovae occur, a large amount of neutrinos are emitted. The amount of neutrinos emitted
from core-collapse supernovae is greater than thermonuclear supernovae. The mechanism of corecollapse supernovae and neutrino emissions is explained in this section. Figure 1.2 shows a schematic
diagram of the process of a core-collapse supernova as explained below.
(1) The core of a star is formed when interstellar gas (mainly hydrogen) in space is collected bygravity.

4

Chapter 1. Physics Background

(1)

(2)
)

(5)

(3)

)
)F

(6)

(4)
'F

・・・

(7)

'FDPSF(8)
TIPDLTUBMM/FVUSJOPTQIFSF(9)CPVODF(10)(11)

TIPDLSFWJWBM(12)4/FYQMPTJPO

1/4DPPMJOHЗIFBUJOH

1/4/FVUSPOTUBSPS
#MBDLIPMF

Figure 1.2: Schematic diagram of the process of a core-collapse supernova assuming a neutrino
heating mechanism.

1.4. Neutrinos from Supernovae

5(2) As the gas falls toward the center, potential energy is converted into thermal energy, and thecenter becomes hot and pressurized. When the temperature near the center exceeds 107 K,
helium is produced through nuclear fusions:
4p ! 4 He + 2e+ + 2⌫e + 26.73 MeV.

(1.1)

On the other hand, as a nuclear fusion is not occurred by the hydrogen near the surface, alayered structure is formed in the star.
(3) Stars maintain their shape by the balance between self-gravitational contraction and theinternal pressure caused by the nuclear fusion. Therefore, when the hydrogen near the centeris burned out, gravitational contraction occurs again. This contraction raises the temperaturenear the center, and when the temperature exceeds 1.5 ⇥ 108 K, the nuclear fusion by helium
begins. This process is repeated to form multiple layers in the star. The main elementsthat make up each layer are, in order from the outside: hydrogen, helium, carbon/oxygen,oxygen/neon/magnesium, silicon, and iron. Since iron has the highest binding energy, thenuclear fusions cannot proceed any further.
(4) The internal pressure of the iron core is supported by electron degeneracy pressure andthermal pressure, but when these pressures begin to decrease, the balance between self-gravity
and internal pressure is disrupted and core-collapse occurs. When the density of the iron coreexceeds 109 g/cm2 , electrons are captured by the protons in the iron nucleus and electron
neutrinos are emitted:
e + p ! ⌫e + n.
(1.2)
Photodisintegration of iron also occurs when the temperature at the core exceeds ⇠5 ⇥ 109 K
as56
Fe + ! 13↵ + 4n 124.4 MeV,
(1.3)
then the core-collapse occurs because the pressure in the core decreases.
(5) In the early stages of the core-collapse, electron neutrinos can escape outward without interacting with surrounding matter. However, when core-collapse proceeds and the core density
exceeds 1011 g/cm3 , electron neutrinos cannot escape from the core. The boundary surface
where electron neutrinos cannot escape the core is called the neutrino sphere.
(6) When the density of the core near the center reaches 1014 g/cm3 , the repulsive force between
approaching nucleons stops core-collapse. However, because material is falling from the outer
core at supersonic speeds, shock waves are generated at the boundary between the inner andouter cores. The shock waves propagate outward while breaking up the surrounding nuclei
into free nucleons.
(7) Electron neutrinos are produced when the produced free protons capture the surrounding electrons as Eq. (1.2). Electron neutrinos cannot escape while the shock wave propagates inside
the neutrino sphere. Then, once the shock wave reaches the outside of the neutrino sphere,
electron neutrinos are emitted to the outside. This neutrino emission is called neutronization
burst, which occurs within 10 ms from the beginning of core-collapse. The proto-neutron star(PNS) is formed in the innermost part of the star.
(8) During propagation, the shock wave loses energy due to interactions with matter (photodisintegration of nuclei and electron capture by free protons). In this process, neutrinos andantineutrinos of all flavors are produced by the interactions shown in Table 1.3. Due tothe electron (positron) capture interactions, the number of ⌫e (¯⌫e ) is greater than ⌫µ and⌫⌧ (¯⌫µ and ⌫¯⌧ ).

6Chapter 1. Physics Background

Table 1.3: Neutrino process in supernovae and proto-neutron star matter. N means nucleons(neutrons or protons). ⌫ represents neutrinos and antineutrinos of all flavors and ⌫x represents ⌫µand ⌫⌧ [5].
Process
Electron and ⌫e absorption by nuclei
Electron and ⌫e capture by nucleons
Positron and ⌫¯e capture by nucleons
Nucleon-nucleon bremsstrahlung
Electron-position pair process
Plasmon pair-neutrino process
Neutrino-pair annihilation
Neutrino scattering
Neutrino scattering with nuclei
Neutrino scattering with nucleons
Neutrino scattering with electrons and positrons

Interactione + (A, Z) $ ⌫e + (A, Z 1)
e + p $ ⌫e + n
e+ + n $ ⌫¯e + p
N + N $ N + N + ⌫ + ⌫¯e + e+ $ ⌫ + ⌫¯⇤ $⌫+⌫¯⌫e + ⌫¯e $ ⌫x + ⌫¯x⌫x + {⌫e , ⌫¯e } $ ⌫x + {⌫e , ⌫¯e }⌫ + (A, Z) $ ⌫ + (A, Z)⌫+N $⌫+N⌫ + e± $ ⌫ + e±

(9) The produced neutrinos heat the material behind the shock wave, and the stalled shock wave
is revived. This phenomenon is called neutrino heating mechanism.
(10) The proto-neutron star is cooled because heat is taken out by the neutrinos.
(11) When the revived shock wave reaches the surface of the star, a supernova explosion occurs,
blowing away all the outer layers.
(12) After the explosion, the cooled central proto-neutron star becomes a neutron star or blackhole.
The neutrino energy emitted depends on the flavor of the neutrino. Muon neutrino and tau
neutrino interact only via neutral current interaction, whereas electron neutrino interacts throughboth charged and neutral current interactions. As the interaction cross-sections of muon and tau
neutrinos are lower than that of electron neutrinos. Muon neutrinos and tau neutrinos can escapefrom the center where the temperature is higher and therefore they tend to have higher energy
than electron neutrinos. Figure 1.3 shows the time evolution of the mean neutrino energy andluminosity obtained from numerical simulations. The results of this numerical simulation predictthat the average neutrino energy is about 10–20 MeV.

1.4.3

Observation of Neutrinos from SN1987A

The supernova SN1987A is a type II supernova appeared within the Large Magellanic Cloud.
On February 23, 1987, neutrinos from SN1987A were observed in the Kamiokande [7], IMB [8],and Baksan experiments [9]. Figure 1.4 shows the distribution of time and energy of neutrinos
from SN1987A in the Kamiokande-II and IMB detectors. These are the first observed neutrinos
from outside the solar system, and are the only supernova burst neutrinos observed by humans
so far. These observations marked the beginning of neutrino astronomy. Because supernova burst
neutrinos hold information to understand the supernovae explosion mechanism, Super-Kamiokande
and other detectors around the world are eagerly awaiting the next supernova.

1.5

Supernova Relic Neutrinos

Although supernovae are rare in a galaxy (it is estimated to be about once to a few times every
100 years with some assumptions), the neutrinos emitted by the supernova that have occurred1.5. Supernova Relic Neutrinos

7

The Astrophysical Journal Supplement Series, 205:2 (17pp), 2013 March

Figure
14. Time
evolutionof neutrino
luminosity
average energy (left) and number spectrum of
Figure 1.3:
Timing
distributionsof averageenergy hEand⌫ i and luminosity L⌫ of neutrinos, whereinterpolation
the
model
(Minit ,peakZ, trevive(13respectM⊙ , 0.02,
100 ms). In⌫x = (⌫µ + ⌫¯µ(13)+ ⌫for¯⌧ )/4[6]. with
The sharpfor ⌫) e =with
to luminosity
is thedue leftto panel, sol⌧ + ⌫CHAPTER1.
INTRODUCTION
12 0(dot-dashedlines),
respectively.
In
the
right
panel,
thelines
correspond,
from
top
to
bottom,to0.1, 0.25,
neutronization bursts.
(A color version of this figure is available in the online journal.)

and shock revival
 time trevive are compared in Figure 13. The 
luminosity
andaverageenergyarehigherforthemodelswith 
larger neutron star mass Mg,NS (see also Figure 11), though the so large.
difference is not With inequalities(9) and (10), we construct the light curvemodels ofneutrinos. For this, we introduce a fraction factor of 
the accretion
term to its maximum, f (t), as a function of time:
 
¾Ĥ
 acc
acc,max(E, t).
(11)
Fνi (E, t) = f (t) Fνi 





         and energy ofWhile f (t) may also depend on 
the species




 

neutrino,
we ignoreoftheirdependences
for from
simplicity.
is are observed in
Figure 1.4: Distributions
time andenergy of neutrinos
SN1987A, It
which
for f(12(t)ofevents)
tosatisfy(t)(8of∼
1 forthe early
the Kamiokande-II
and the f
IMB
events)experiments[10]. phase
Figure required
1.5:
Distribution
timeand energy
theneutrinos
from
SN1987A, observed in the
(t
∼
100
ms)
and
f
(t)
=
0
for
the
phase
after
the
explosion.
Kamiokande-II (12 events) and IMB (8 events) experiments. The figure is taken from Ref. [30].
Using f (t), the neutrino flux is expressed as
Fνi (E, t) = f (t) Fνacc,max(E, t) + Fνcool(E, t)ii
νRHD= f (t) F(E, t) + (1 − f (t)) F PNSC0 (E, t).

8Chapter 1. Physics Backgroundsince the beginning of the universe to the present should be uniformly distributed in space. Those
neutrinos are called supernova relic neutrinos (SRNs) or di↵use supernova neutrino backgrounds(DSNBs). Although there have been many searches for SRNs, including the Super-Kamiokande
experiment, no observations have yet been made. If SRNs are observed and their energy spectra
can be compared with the theoretical predictions, it will lead to a better understanding of thesupernova explosion mechanism and star formation.

1.5.1

Flux Predictions

The predictions of the current energy spectrum of SRNs are determined by the rate of core-collapse
supernovae, the flux of neutrinos emitted in individual supernovae, and the redshift of neutrinoenergy with the expansion of the universe. Since the amount of neutrinos emitted by a supernova
explosion (N⌫ ) depends on the stellar mass (M ) and the metallicity (Z), the neutrino spectrum iswritten as follows:dN⌫ (E⌫0 , M, Z)
,
(1.4)
dE⌫0
where E⌫0 is the energy of neutrino observed on Earch. The relationship between E⌫0 and the energyof neutrino at the time of emission E⌫ is expressed as E⌫ = (1 + z)E⌫0 using the redshift z. The
number density of SRNs at present dn⌫ (E⌫ ) is expressed as:
dt dN (E⌫0 ) 0
dz
dE⌫
dz
dE⌫0
dt dN (E⌫0 )= RCC (z) dz(1 + z)dE⌫ ,dz
dE⌫0dn⌫ (E⌫ ) = RCC (z)(1.5)

where RCC (z) is the rate of core-collapse supernovae.
SRN is the integral of the neutrinos from supernova emitted so far. The SRN flux at present isexpressed as follows:Z 1d ⌫ (E⌫ )dt dN (E⌫0 )=c
RCC (z)(1 + z)dz,
(1.6)
dE⌫
dz dE⌫00
where d ⌫ (E⌫ ) represents the flux, d ⌫ (E⌫ )/dE⌫ is the energy spectrum, and c is the speed oflight. The relationship between time t and redshift z is also given by the Friedmann equation as
follows:
dt
1
p
=
,
(1.7)
dz
H0 (1 + z) ⌦m (1 + z)3 + ⌦⇤where H0 is the Hubble constant, ⌦m is the matter density parameter, and ⌦⇤ is the cosmologicalconstant. Therefore, Eq. (1.6) can be transformed as follows:Z 1d ⌫ (E⌫ )1dN⌫ (E⌫0 )=c
RCC (z) p
dz
(1.8)
dE⌫
H0 ⌦m (1 + z)3 + ⌦⇤ dE⌫00
As shown in Eq. (1.4), the neutrino number spectrum is a function of the stellar mass M and themetallicity Z. Using the initial mass function IMF (M ) and the metallicity distribution function
ZF (z, Z), Eq. (1.8) is also expressed as:
Z 1
d ⌫ (E⌫ )
dz
p
= c
dE⌫
H0 ⌦m (1 + z)3 + ⌦⇤0⇢Z Mmax
Z ZmaxdN⌫ (E⌫0 , M, Z)⇥ RCC (z)
(z,
Z)
(M
)
dM dZ , (1.9)
ZF
IMF
dE⌫0
0
Mmin

where Mmax and Mmin are the upper and lower limits of the mass of the stars that end with corecollapse. Many theoretical models have been proposed to predict the SRN flux [11–23]. Figure 1.5
shows the predicted energy distribution of the ⌫¯e flux.

1.5. Supernova Relic Neutrinos

9

DSNB νe Flux [/cm2/sec/MeV]

4

10
Horiuchi+21 (Extrapolated, α λ =0.1, NO)
Tabrizi+21 (NS+BH, NO)
Kresse+21 (W20-BH2.7- α 2.0, NO)
Horiuchi+18 (ξ12.5,crit= 0.1)

Nakazato+15 (Max, IO)
Nakazato+15 (Min, NO)
Galais+10 (NO)
Horiuchi+09 (6 MeV, Max)
Lunardini09
Ando+03 (updated at NNN05)

10−1

Kaplinghat+00
Malaney97
Hartmann+97
Totani+95

10−2

10−3

10−4

10

20

30

40

50

60
70
80
νe Energy [MeV]

Figure 1.5: SRN ⌫¯e flux predictions from various theoretical models [11–23]. This figure is taken

FIG. 1. DSNB ⌫¯e flux predictions from various theoretical models (Horiuchi+21 [13], Tabrizi+21 [14], Kresse+21 [12],from Ref.
[24].
Horiuchi+18[11],
Nakazato+15 [6], Galais+10 [15], Horiuchi+09 [16], Lunardini09 [10], Ando+09 [17], Kaplinghat+00 [9],Malaney97 [7], Hartmann+97 [18], and Totani+95 [8]). Refer to each publication for the detailed descriptions of model. In
the legend, “NO” and “IO” represent neutrino normal and inverted mass orderings assumed in the calculation, respectively.
For the Horiuchi+09 model with a 6 MeV temperature, only the maximal flux prediction is shown. The prediction for the
Galais+10 model here is extrapolated up to 50 MeV as the original publication was served up to 40 MeV. The prediction by
Nakazato+15 is only available up to 50 MeV. The values of the flux used in this analysis for the Ando+03 model are the ones
released at the NNN05 conference [19]. The corresponding flux is larger by a factor of 2.56 than in the original publication [17].

only allowed for an exposure of 6.72 kton·year. In 2015,a new SK analysis including neutron identification led
to stronger constraints down to 13.3 MeV neutrino energies [23]. Since the SK triggers did not allow to record
the neutron capture signal until 2008, this analysis could
only be performed on a small part of the SK data set,with a total livetime of 22.5 ⇥ 960 kton·days. Due tothis low exposure and the low neutron tagging efficiency
in water, this search however yielded weaker limits thanto present two DSNB searches for antineutrino energies
ranging from 9.3 to 81.3 MeV, with significantly improved background modeling and reduction techniques.
In the 9.3 to 31.3 MeV range, we derive di↵erential upper limits on the ⌫¯e flux independently from the DSNB
model, following the strategy outlined in Ref. [23] using
a 22.5 ⇥ 2970-kton·day data set. In the 17.3 to 81.3 MeV
range we constrain a wide variety of DSNB models using
spectral fits analogous to the ones described in Ref. [22].

10

Chapter 1. Physics Background
The Astrophysical Journal, 738:154 (16pp), 2011 September 10

-4

-1

-3

SNR [10 yr Mpc ]CC SNe, so the tw
Figure 1 are fits to
FR
cS
i
m
discrepancy persists
10
cos
m
o
r
are available.9fnoi
The nominal unc
dictPre
smaller than the normstof the discrepancy is
n
me
e
r
u
s
uncertainties of the Smea
RNsignificance is wea
S
mic
s
o
the cosmic SNR meCtrend—much better
1
Indeed, the measure
supported by recen
uncertainties (Dahle
Li et al. (2011a)
fits to be a good repr
Cappellaro et al. (1999)
Botticella et al. (2008)
persists over a wide
Cappellaro et al. (2005)
resolutions to the smean local SFR
Bazin et al. (2009)(see Figure 2)
Dahlen et al. (2004)
the cosmic SNR prewhether the measure
0.1
or a combination of
0
0.2
0.4
0.8
1.0
0.6
In Section 2, we dRedshift z
SNRs in detail and s
Figure 1. Comoving SNR (all types of luminous core collapses including Type II
Figure 1.6: Correlation
betweenredshiftzandthesupernova
rate
(SNR)
[25].
The
light
blue
band possible cau
discussand Type Ibc) as a function of redshift. The SNR predicted from the cosmic SFR
represents thefitSNR
expected
from
the
star
formation
rate(SFR).
The
yellowband
represents
thecautions.
We summa
and its supporting data (Hopkins & Beacom 2006), as well as that predicted
SNR obtainedfrom
fromtheopticalmean ofobservations.
the local SFR measurements, are plotted and labeled. The fit toThroughout, we ad
the measured cosmic SNR, with a fixed slope of (1 + z)3.4 taken from the cosmicΩm = 0.3, ΩΛ = 0.

SFR, is shown with the uncertainty band from the LOSS measurement. The
Figure 1.6predicted
shows thebetweenredshiftz and thesupernova
Althoughand correlation
measured cosmic
SNRs
are consistently
discrepant
by a rate
factor(SNR).
ofthe observed ∼2:
SNRs
only about
half ofHowever,the predictions,the aresupernova
rate problem.
rates fromthe
SNexistence
catalogs inofthefaintverysupernovae or 2. NORMAL
light-blockinglocal
matteris suggested
as sucha possible
Since
neutrinos
interact only throughvolumedo not showa largeexplanation.
discrepancy (seeFigure3).
The cosmic SNR
the weak interaction
besidesoftheobservationsof SRNs
can be realized, the frequency(A color version
thisgravity,
figure is if
availablein the online
journal.)knowledgeof the eof supernova explosions can be confirmed without interference by the absorption or scattering inrecent SFR is traceinterstellar medium if observations of SRNs are realized.

SNRs (Cappellaro et al. 1999; Dahlen et al. 2004; Cappellaro
shortest lifetimes. Th
et al.
were somewhat lower than those predicted from
UV, FIR, and radio—
1.5.2 Statusof 2005)
SRN Searches
the SFR. Similar conclusions were reached by Mannucci et al.
where necessary, toAs mentioned in the previous section, SRNs contain important information for understanding(2007) and Botticella et al. (2008).
However, since thethe formation rate of massive stars and the mechanism of a supernova explosion. TheoreticalIn
recentyears,
measurementsofthecosmicSFR
andpredictions of the energy spectrum of SRNs have been made based on various cosmological smaller
models masses, thecosmic
SNR haverapidly
improved.
The ofcosmic
SFR
has
scaled upward accorand mechanismsof explosion.
Until now,experimental
searches
SRNs havebeen
made to confirm
beenmeasuredusing
multiple
indicatorsbymanycompetingexample, for a givethese predictions but no observation has yet been realized.
groups.
The
accuracy
andprecisionofthecosmicSFR
has
All flavors of neutrinos and antineutrinos are emitted from supernovae. In almost all detectors,
is more steeply falli
been fordocumented(e.g.,
Hopkins& Beacom
2006)
andantineutrinos:
areSRNs are searchedthrough inverse
beta
decay (IBD)
reactions ofelectroncompared to a shallo
supported by recent data (e.g., Pascale
et
al.
2009;
Rujopakarn
of calibration factor⌫¯e + pBothwell! e+ + n, et al. 2011). The Lick
(1.10)
et al. 2010; Ly et al. 2011;
codes that calculate
Observatory
Supernova
Search(LOSS)
hasasrecently
stars following an as
because its crosssection is by
far the largest
below⇠20 MeVshown inpublished
Figure 1.7.
thebestmeasurementofthecosmicSNR
atlowredshifts,using
We adopt the dus
Figure 1.8 shows the results of recently reported SRN searches in Super-Kamiokande and KamCC
collected over many
years
of systematicallysurveying of the prompt
LAND [24, 26,27].SNeIn Super-Kamiokande,SRNs
are searched
for by the coincidence
Beacom (2006). Th
galaxies∼200(Leaman2011;signal
Li etal. rays emitted
signal from thepositronwithin
producedby theMpc
IBD reaction
andettheal.delayed
frompower law of the fordue to the neutron
captureon
nucleiinwater.
Cherenkov
lightisemittedwhen
chargedparticles
2011a, 2011b; Maoz et al. 2011). The Supernova Legacy Survey!
(SNLS) has published the most precise SNR measurement at
higher redshifts, using a large sample of CC SNe collected inρ̇∗ (z) = ρ̇0 (1their extensive rolling search of four deep fields (Bazin et al.
2009).

1.5. Supernova Relic Neutrinos

11

Chapter 2 Supernova Neutrino Detection with Super-Kamiokande Detector

44

Figure 1.7: Cross sections of neutrino interactions in Super-Kamiokande as a function of neutrino

Fig. 2.14:
CrossThe
sectionsof lineneutrino
interactions
in betaSK as
a functionof neutrino[52].
The solid redenergy.
solid red
represents
the inverse
decay(IBD) reaction.
Theenergy
blue lines
represent
theIBD,
neutrino
interactions
withrepresent
oxygen nuclei,
andthe greenflavor:lines represent
elastic
represents
and thegreen lines
ES witha neutrino¯e scattering(solid), of(dotted),e (dashed),
neutrinos.
and ¯ (dot-dashed). The dashed blue and solid blue lines stand for oxygen CC reactions of e and e ,respectively. The dot-dashed cyan line indicates oxygen NC reactions.

interactions) represented with
e+

16

O

16
e+ O

Their cross section exceeds that of ES at

e +16 Fe+ +16 N.

(2.8)
(2.9)

20 MeV (Fig. 2.14). The electron/positron emission has

a backward anisotropy. Oxygen CC interactions sometimes are accompanied by neutron capture

12

Chapter 1. Physics Background

The Astrophysical Journal Letters, 951:L27 (8pp), 2023 July 10

Harada et al.

Figure 3. Upper limits on the n̄e ﬂux, calculated by Equation (2). The red lines show the observed (solid) and expected (dotted–dashed) 90% C.L. upper limit for SKVI. The bluelines show
the observed
and ofexpected
C.L.
upper
limit show
for SK-IV
et al. (2021).(solid)
The greenline represents
the 90% C.L.
Figure1.8:
Upper(solid)
limitsthe ⌫¯(dotted–dashed)
The
red
lines
theAbeobserved
andexpectede flux [26]. 90%
observed upper limit placed by KamLAND Abe et al. (2022c). The gray-shaded region represents the range of the modern theoretical expectation. The expectation(dotted-dashed) 90% confidence level (C.L.) upper limit for the period of August 2020 to Junedrawn in the ﬁgure includes DSNB ﬂux models (Hartmann & Woosley 1997; Malaney 1997; Kaplinghat et al. 2000; Ando et al. 2003; Horiuchi et al. 2009;
Lunardini 2009;
al. 2010;inNakazato
et al. 2015; Horiuchi(SK)et al. 2018,
KresseGd-loaded
et al. 2021; Tabrizi& Horiuchi
2021; Ekanger
et al. 2022).
2022Galais(552etdays)
Super-Kamiokande
with2021;
0.01%
water.
The bluelines show
the Ando+03
model was updated in Ando (2005).

observed (solid) and expected (dotted-dashed) 90% C.L. upper limit for the period of September
2008 to May 2018 (2970 days) in SK with ultra-purewater [24]. The green line shows observed
Table 2
90%
C.L.
upper
limit
placedKamLAND[27].DSNB
TheExpectation
gray-shaded
region etshowstheandrangeof ettheSummary
Tableof UpperLimits,Sensitivity,and byOptimistic
and Pessimisticfrom Kaplinghatal. (2000)
Nakazatoal. (2015),
Respectively
modern theoretical expectation, corresponding
to Figure 1.5.

Neutrino Energy

Observed upper limit

(MeV)

(cm

9.29–11.29
11.29–13.29
13.29–17.29
17.29–25.29
25.29–31.29

−2 −1

s

Expected sensitivity−1(cm−2 s−1 MeV−1)

MeV )

SK-IV

SK-VI

SK-IV

SK-VI

37.30
20.43
4.77
0.17
0.04

34.07
18.43
3.76
0.90
0.33

44.35
11.35
2.05
0.21
0.11

50.78
15.12
2.71
0.50
0.33

et al. 2000), and the most pessimistic one is Nakazato+15(Nakazato et al. 2015) with the assumption of normal massordering in whole energy ranges, respectively. The upper limitof the ﬂux for each bin is summarized in Table 2.
6. Future Prospects
In 2022 June, the SK-Gd experiment was upgraded to the

Averaged theoretical expectation of DSNB
(cm−2 s−1 MeV−1)
0.20–2.40
0.13–1.66
0.67–0.94
0.02–0.30<0.01–0.07

threshold. Hence we can search in a lower-energy region,
which will increase signal acceptance for DSNB, solar
antineutrinos, and light-dark-matter searches.
7. Conclusions
We searched for astrophysical n̄e , using the SK-VI data
below 29.5 MeV for Erec between 2020 August and 2022 May,

1.6. Cosmogenic Productions

13

move through water at speeds faster than the speed of light in water. The light is detected byphotomultiplier tubes (PMTs) installed on the inner wall of the detector (Chapter 3). The results
for two observation periods of SK (SK-IV and SK-VI) are shown in Figure 1.8. Ref. [24] is the resultof observations in SK with ultra-pure water for 2,970 days from September 2008 to May 2018 andRef. [26] is in SK with 0.01% gadolinium (Gd)-loaded water for 552 days from August 2020 to June
2022. In the ultra-pure water period, a neutron is captured by a hydrogen nucleus (proton) after⇠200 µs on average, and a single ray is emitted with an energy of 2.2 MeV in this process. The
neutron detection efficiency was ⇠20% in SK with ultra-pure water. In 0.01% Gd-loaded water period, neutrons are captured on Gd at a fraction of ⇠50% within ⇠110 µs on average. Several rays
totaling about 8 MeV are emitted after neutron capture on Gd. This can be clearly distinguishedfrom the background consisting of environmental radiation and dark noise of PMTs. Therefore,
the neutron-tagging efficiency is significantly improved by loading Gd in water. Ref. [26] is thefirst result of the SRN search in SK with Gd-loaded water. Despite the fact that the observation
period is only about one-fifth of the ultra-pure water period, the sensitivity is comparable to theprevious results thanks to high neutron detection efficiency. As the result of the observation in
SK with ultra-pure water [24] and Gd-loaded water [26], no significant excess above the expectedbackgrounds was found, and the limit was set to the SRN ⌫¯e flux above 13.3 MeV.
In KamLAND, SRNs are searched for via the IBD reaction, as was done by SK. The KamLAND
detector is filled with liquid scintillator with the volume of about one-twentieth of the SK detector.
The scintillation light emitted from charged particles is detected by the PMTs mounted on thewall. The neutron from the IBD reaction is captured on hydrogen in the liquid scintillator and aray is emitted with the energy of 2.2 MeV. Since the light intensity of scintillation emission (inKamLAND) is ⇠103 times larger than that of Cherenkov emission (in SK), the ray from neutron
capture on a proton is identified with the efficiency of ⇠100%. Ref. [27] is the result of observationsin KamLAND for 4,528 days from May 2002 to July 2020. No significant excess over backgroundmodel predictions was found, and a flux upper limit was set for the energy region below ⇠10 MeV.

1.6

Cosmogenic Productions

The earth is exposed to cosmic-rays, mainly protons with energies widely distributed up to the
TeV scale and above. Cosmic-rays interact with nuclei in the atmosphere to produce high-energymuons (cosmic-ray muons). The fraction of those muons reaches the Earth’s surface before they
decay due to relativistic e↵ects. In experiments that require low background, such as neutrino
observations and proton decay searches, the cosmic-ray muons are unavoidable backgrounds. In
order to suppress the e↵ects of cosmic-ray muons, those experimental detectors are often constructed
deep underground. While, although the thick bedrock reduces the muon flux, cosmic-ray muons
with energies above several hundred GeV can reach the detector. These muons interact with themedium in the detector and induce neutrons and unstable radioactive isotopes called cosmogenic
products. The rays and electrons emitted due to neutrons and isotopes are backgrounds in MeVscale neutrino observations or dark matter searches. The interaction between muons and nuclei
above the several hundred GeV scale is a complex physical process including the hadron scatteringwith QCD, and reliable simulations have not yet been developed. Therefore, measurements ofcosmogenic neutrons and isotopes give an important contribution to understanding the backgroundin neutrino observations and to nuclear physics.
In this section, cosmic-ray muons, their interactions, and the productions of neutrons andradioactive isotopes are explained.

1.6.1

Cosmic-Ray

The Earth’s atmosphere is constantly exposed to high-energy particles called “cosmic-rays”. Cosmic
rays contain ⇠90% protons, ⇠9% alpha particles (helium nuclei), and ⇠1% other particles. The

14

Chapter 1. Physics BackgroundFigure 1.9: Energy spectrum of the primary cosmic-rays [29].

Figure 1.2: Energy spectrum of cosmic-rays. The equivalent lab energies of particle accelerator
energyare
spectrumof primarycosmic-rays
is shown
experiments
indicatedon theenergy axis[5]. in Figure 1.9. It shows above 1 GeV, whichis relevant to the measurement described in this thesis. The intensity of primary cosmic-ray isapproximated as follows:dN/ E ( +1) ,(1.11)
0
dE
E
d
(E,
E
)
N
N
0
)=
(1.5)
where N is the number ofFnucleonsand
E is inel
total energyof nucleons. , is the integral spectral
N N (E, E
0)dE(E
N the energy regions as follows [28]:index determined by observations and dependsNon8
inel0
where N
6 GeV)section, d N N (E, E ) is the cross section
N is the total inelastic nucleon-nucleon>
1.7 (E < 10cross<
9 GeV) E in nucleon-nucleon
for a nucleon of energy E 0 to produce
nucleoninteraction.
' a2.0(1.12)(106  with
E < 10energy>:
The solution of Eq. (1.4) is obtained by
Eq. (1.3) as the boundary condition. For
1.6 applying(E 109 GeV).

nucleons, the solution is given as:

Cosmic-ray Muon Production

N (E, X) = C exp ( X/ ) E

+1

,

(1.6)

Primary comic-rays interact with nuclei in the atmosphere and produce hadrons. The hadrons

2
where Cproduced
is a constant,andattenuation
length(g/cm
of nucleon.
are mainly
pions isandthekaons.
Those pions
and kaonshave)short
lifetime and decay tomuons and muon neutrinos at ⇠15 km above the ground.

1.2.2⇡ ± ! µ± +particles⌫µ (¯⌫µ ) (⇠ 100%)
Production of secondary±(1.13)±µ + ⌫µ (¯⌫µ )as(⇠the64%)set of coupled diffusions(1.14)
The cascade of various hadrons canKbe!expressedin principle.
muons areFigure1.10 shows
the detailschematic
illustration
AnalyticThese
solutionsforcalledthe “cosmic-ray
diffusion muons”.
equationsprovidetheandspecificof cosmicinformation of
ray muon productions. Muons are the most numerous charged particle at sea level. Muons have aparticle lifetime
flux andenergies of secondary particles.
of 2.2 µs at the rest frame and decay through weak interactions into electrons and neutrinos
Considering
only pions and kaons as the secondary particles, the diffusion equation of pions
as follows.
+⌫µ± ! e± + ⌫e (¯⌫e ) +¯and(1.15)
can be expressed as the sum of two components,
as follows:µ (⌫µ )

dN (E, X)
=
dX

✓

1

1
+
d

◆

N (E, X) +Z 1
0

N (E/xL , X)F (E , E /xL ) dxL(E/xL )
x2L

1.6. Cosmogenic Productions

15

Primary cosmic-ray<latexit sha1_base64="uFeniXw6mxf8hUF2m+5lpSKLQCI=">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</latexit>

Nucleus<latexit sha1_base64="WgqMnQyCw/rgjwQ2IgN3HSRHHas=">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</latexit><latexit 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Figure 1.10: Schematic illustration of cosmic-ray muon productions.
Since the muons travel at nearly the speed of light, relativistic e↵ects slow the progress of intrinsic
time, allowing them to reach the ground surface if they have sufficiently high energy, typicallyabove GeV scale.
The approximate extrapolation formula of the cosmic-ray muon flux at sea level is introduced
by T. Gaisser [30] based on calculations from primary cosmic-ray flux as follows:
dNµ= 0.14
dEµ

✓

Eµ
GeV

◆ 2.7

0
B
@

1

1
0.054
C
+
,
1.1Eµ cos ✓1.1Eµ cos ✓ A
1+
1+
115 GeV
850 GeV(1.16)

where Nµ is the number of muons, Eµ is the muon energy in GeV, and ✓ is the zenith angle. Here,this formula is valid under the two conditions: (1) muon decay is negligible (Eµ > 100/ cos ✓ GeV)
and (2) the curvature of the Earth can be neglected (✓ < 70 ). In the formula, the contributions
from charged pions and kaons are considered, while the contributions from charm and heavier
particles are negligible below ⇠10 TeV. Figure 1.11 shows muon spectra at ✓ = 0 and 75 , inwhich compared of the results from Eq. (1.16) and measurements are compared. For the large
zenith angle (✓ > 70 ), the standard Gaisser formula does not reproduce the measurement results.
Therefore, the modified Gaisser parametrizations are also proposed in Ref. [31].
Muon Energy Loss
Because the Earth’s surface is exposed to cosmic-ray muons, detectors used in experiments forparticle physics are often constructed deep underground to avoid the e↵ect of cosmic-ray muons.
Magnitude of the suppression will be explained later in this section. Charged particles, including
muons, loses the energy in materials through ionization and radiative processes. Figure 1.12 shows
the rate of energy loss for positive muons in copper as a function of the momentum.

16

Chapter 1. Physics Backgroundpµ2.7dN/dpµ [m−2 s−1 sr−1(GeV/c)1.7]

24. Cosmic rays 7

27. Passage of particles through matter

1000

the’s theory extends only to some energy above which
ic e↵ects were not important. The free-electron crosson (Eq. (27.1)) can be used to extend the cross section to. At high energies B is further modified by polarization of
medium, and this “density e↵ect,” discussed in Sec. 27.2.4,
also be included. Less important corrections are discussedw.
100
he mean number of collisions with energy loss between E
E + dE occuring in a distance x is Ne x (d /dE)dE, where; )/dE contains all contributions. It is convenient to define
momentsZd (E; )Mj ( ) = Ne x E j
dE ,dEcollision, and the other variables are defined in Table 27.1. A
minor dependence on M at the highest energies is introduced
through Tmax , but for all practical purposes hdE/dxi in a given
material is a function of alone. With the symbol definitionsand values given in Table 27.1, the units are MeV g 1 cm2 .
Few concepts in high-energy physics are as misused as
hdE/dxi. The main problem is that the mean is weighted byvery rare events with large single-collision energy deposits. Even
with samples of hundreds of events a dependable value for themean energy loss cannot be obtained. Far better and moreeasily measured is the most probable energy loss, discussed
in Sec. 27.2.7. The most probable energy loss in a detector isconsiderably below the mean given by the Bethe equation.
In a TPC (Sec. 28.6.5), the mean of 50%–70% of the samples
at M0 is the mean number of collisions in x, M1 is thewiththe smallest
used as an estimator.
1 the variance, etc. 10
100 signals is often 1000
The
energy loss in x, M2 M12 is
Although
it
must
be
used
with
cautions and caveats, hdE/dxi
ber of collisions is Poisson-distributed with mean M0 . Ne pisµ [GeV/c]
as described in Eq. (27.3) still forms the basis of much of our un3
r measured
in electrons/gelectrons/cm
e = NA Z/A)
Figure24.4: (NSpectrumoformuonsat ✓ = derstanding
0 ( [38],[44], particles.
[45],Extensive⇥,of energy[43],loss by charged
tables= NA ⇢Z/A).Figure
The former
used throughout
this1.11: isSpectrumof muons
at chapter,zenith angle ✓ = 0 (points other than white rhombuses) andare
available[5,4,pdg.lbl.gov/AtomicNuclearProperties/].
[46])
.
The
line
plots
the
result
from
+
[40],
[41],
and
•
[42]
and
✓
=
75
quantities of✓interest(dE/dx,X0 , etc.) varysmoothly
withsolid line is the result from Eq. (1.16) at ✓ = 0 [32].
= 75 (whiterhombuses)
at sealevel. The
ositionEq.
when(24.4)
there is forno density
dependence.
verticalshowers.

2.

Stopping power [MeV cm2/g]

1.6µ+ on Cu

100

Scharff

10Fµ+ /F
Lindhardµ−

1.5

µ−

BESS
L3C
Radiative
MINOS

Bethe

AndersonZiegler

Eµc

1.4
Minimum
ionization

Nuclear
1.3
lossesRadiative
lossesRadiative
effects
reach 1%

Without δ

1
0.001
0.1

1.2

0.01

0.1

1

10

1

10

100

1

βγ

100

1000

10 4

10 5

10 6

10

100

1

10

100

[GeV/c][TeV/c]Muon momentum
10
103
104
102
Fig. 27.1: Stopping power (= h dE/dxi) for positive muons in copper as a function of= p/M c overpµ ofmuons[GeV/c]Figure
1.12:
The rate inof momentum
energy loss (12for positivein copper
as a energy).
function Solidof momentum
[32].
nine
ordersof magnitude
ordersmagnitude
in kinetic
curves indicate
solidline Muon
is power.
the totalenergylosses.
theThetotal
stopping
Data
below
the break0.1 ofare thetaken muonfrom ICRU
49 [4], andfrom
data
Figure24.5:
chargeratio
as a atfunction
momentumat higher energies are from Ref. 5. Vertical bands indicate boundaries between di↵erent approximations
Refs.
[41,42,48].
discussed in the text. The short dotted lines labeled “µ ” illustrate the “Barkas e↵ect,” the dependenceof stopping power on projectile charge at very low energies [6].

1.1
1.0

[MeV/c]Stopping power at intermediate energies :he mean rate of energy loss by moderately relativistic

The function as computed for muons on copper is shownas the “Bethe” region of Fig. 27.1. Mean energy loss behavior

1.6. Cosmogenic Productions

17

Table 1.4: Summary of variables used in the Bethe formula.
Variable
E
x
v
c

me
re
NA
ze
Z
A
K/A

Definition
Incident particle energy
Travel length
Speed of particle from a stationary system
Speed of lightv/cp2
Lorentz factor 1/ 1
Electron massClassical electron radius
Avogadro’s number
Charge of incident particle
Atomic number
Atomic mass
4⇡NA re2 me c2 /A

Tmax
I
( )

Maximum energy transfer possible in a single collision
Mean excitation energy
Density e↵ect correction to ionization energy loss

Units or Value
MeV
cm
2.998 ⇥ 108 m s 1
0.511 MeV/c2
2.82 fm
6.02 ⇥1023 mol 1g mol 10.307 MeV g 1 cm2for A = 1 g mol 1
MeVeV

Ionization process The ionization processes are dominant below ⇠100 GeV, corresponding to
the “Bethe” region of Figure 1.12. When charged particles pass through materials, the electric fieldof the charged particles causes to ionize or excite the atoms in the materials. If an electron in theatom or molecule receives energy from charged particles and the energy received is greater thanthe binding energy of electrons, the electron is ejected from the atom or molecule. On the other
hand, if the energy received is less than the binding energy of the electron, the atom or molecule
are excited. The mean rate of energy loss for charged particles is described by the Bethe formula,dE
1 2me c2 2 2 Tmax
( )
2Z 1
2
= Kz
ln
.
(1.17)
2
2
dx
A
2
I
2
The variables used in the Bethe formula are summarized in Table 1.4. When charged particles travel
through matter at speeds greater than ⇠96% of the speed of light (corresponding to “Minimum
ionization” threshold of Figure 1.12), the energy loss of the particles becomes a nearly constantvalue, ⇠2 MeV g 1 cm2 . Charged particles with the energy loss in matter close to the possible
minimum value are called minimum ionization particles (MIPs). Cosmic-ray muons in GeV scale
are known as typical particle in this category.
Radiative process The radiative processes are more important than ionization above ⇠100 GeV,
corresponding to the “Radiative” region of Figure 1.12. In this process, muons induces photons,
electromagnetic showers, and hadronic showers via the electromagnetic and strong interactions inmaterials. The average rate of energy loss is written asdE= a(E) + b(E)E,dx(1.18)

where a(E) is the energy loss by the ionization processes given by Eq. (1.17) and b(E)E is the radiative contributions. The radiative process consists of the three contributions; bremsstrahlung, directe+ e pair production, and photonuclear reaction. When a muon is suddenly slowed or its path isbent in electric fields in materials, photons are radiated. This radiation is called bremsstrahlung.
In the e+ e pair production, a muon emit a virtual photon, which produces a pair of electrons

18

Chapter 1. Physics Backgroundand positrons in the Coulomb field of the nucleus. In the photonuclear reaction (photodisintegration), a muon interacts with a nucleus via a virtual photon, and then hadrons are emitted.
Figure 1.13 shows b(E) as a function of the muon energy E and the contributions for each radiative process in the b(E). In the region of E & 100 GeV, the term b(E)E is dominant because ofa(E) ' 2 MeV g 1 cm2 .
Muon Flux UndergroundIf the detector is located deep underground, cosmic-ray muons lose energy in rock before they reachthe detector due to the above interactions. Therefore, the flux underground is suppressed comparedto the surface. The muon intensity is described as a function of a slant depth asI(h) = I1 e h/ 1 + I2 e h/ 2 ,(1.19)

where I(h) is the muon intensity at the slant depth, h [34]. The parameters in Eq. (1.19) aredetermined using the experimental data in Figure 1.14, I1 = (8.60 ± 0.53) ⇥ 10 6 cm 2 s 1 sr 1 ,I2 = (0.44 ± 0.06) ⇥ 10 6 cm 2 s 1 sr 1 , 1 = 0.45 ± 0.01 km.w.e., and 2 = 0.87 ± 0.02 km.w.e.
Here, the unit km.w.e. (kilo-meter water equivalent) is the conversion of general depth to water
depth. As a well-known guide, cosmic-ray muons fall at a frequency of ⇠1 s 1 on a palm-sizedarea (⇠100 cm2 ) at the Earth’s surface. The flux of cosmic-ray muons is suppressed to 10 5 of
the ground surface at 1,000 m underground (2,700 m.w.e.) where the Super-Kamiokande detector
is located. As a result, about two muons per second enter the SK detector although the surface
area on the top of the detector is ⇠107 cm2 . Not only the muon flux but also the average muonenergy correlates with the depth from the surface. The deeper underground, the higher the energy
required to reach that depth. Figure 1.15 shows the muon energy spectra in various undergroundsites with several km.w.e. overburden. For each site, The spectrum extends to above 103 GeV andthe average muon energy is several hundred GeV.

1.6.2

Cosmogenic Neutrons

Neutron Production Process
Cosmogenic neutrons (muon-induced neutrons), the target of this study, refer to neutrons producedby cosmic-ray muons and the secondary particles caused by them. The production processes aredescribed as follows.
(a) Muon spallation:
Muons directly interact with nuclei via the exchanging of a virtual photon or Z-boson. Nucleons and mesons (e.g. neutrons and pions) are emitted subsequently. The diagram of muon
spallation is shown in Figure 1.16.
(b) Photonuclear reaction:
As described in Section 1.6.1, the radiation loss is dominant in the energy region above⇠100 GeV. When a muon passes through materials, the muon direction is bent due to the
Coulomb field created by the nucleus. Then muons lose the energy and photons are emitted bybremsstrahlung. These photons interact with electrons in matter via the photoelectric e↵ect,Compton scattering, and e+ e pair production. These processes produce electromagnetic
showers, which are composed of electrons, positrons, and photons. Among those, high-energy
photons are often absorbed by nuclei via the photonuclear reactions, and then nucleons andmesons are produced. The diagram of photonuclear reaction is shown in Figure 1.17.
(c) Hadron spallation:
High-energy pions produced in the process (a) and (b) interact with the nucleus via pion
absorption and pion-nuclear scattering, emitting a large number of high-energy nucleons and1.6. Cosmogenic Productions

19

D. E. GROOM, N. V. MOKHOV, and S. STRIGANOV

2.5

3.5

106 b(E) (g−1 cm2)

3.0

btot

106 b(E) (g−1 cm2)

Hydrogen
Z=1

2.0
1.5
1.0

bpair
bbrems

0.5

bnuc

btot

106 b(E) (g−1 cm2)

Iron
Z = 266bpair
4bbrems

2

2.0
bpair

1.5
1.0

bbremsbnuc

020
Uranium
Z = 92

15

btot

5
bnuc

100
1000
Muon energy (GeV)

10

104

2

bpair
bbrems1Standard rock4

bbrems

2

btot

0

bpair
10

Water

3

bnuc

bnuc

106 b(E) (g−1 cm2)

106 b(E) (g−1 cm2)

btot

0.0

8

106 b(E) (g−1 cm2)

2.5

Carbon
Z=6

0.5

0.0

0

Muon Stopping Power and Range

105

btot

3
bpair
2

bbrems

1
0

bnuc

2

10

100
1000
Muon energy (GeV)

104

Figure 5: b-values for a sampling of materials. Solid lines represent our results,

105

Figure 1.13: b(E)asthe
a functionof themuonenergyE andwhiledashed/dottedlines
are from
Lohmann
et eachal. [4].contribution
The circles forfor bremsstrahlung+(bbrems ), e e pair
production(bpairGaisser), andand
photonuclear
standardrock are from
Stanev [55]. reaction (bnuc ) in some materials [33].

LBNL-44742

20

Atomic Data and Nuclear Data Tables, Vol. 76, No. 2, July 2001

n flux andund labo20

GroomTheet al.
proposeda model[3] to fitinthe
experimental
cavern.
energyspectrumis discussed
Refs.
[14,17]:00data to a depth-intensity-relation (DIR), appropriate for the#bh ##
range dN
(1–10
" km.w.e.):
Ae#bh$#! #1% & $E! ' "! $1 # eChapter%% 1.! ;Physics(8)Background

dE!

0.1

0

FIG. 7 (color).

Normalized Local Spectrum (GeV -1)-2

Differential Muon intensity (cm s-1sr -1)

ailable for
I%h& # %I1 e%"h=!1 & ' I2 e%"h=!2 & &;(1) various undergro
where
A
is
a
normalization
constantwithrespecttothen of depth
been normalized-6
differential
muon
intensity
at
a
given
depth
and
E
is
the
10
!
ome conLVD - Gran Sasso Rockpurposes.
LVD - Standard Rock
muon
energyafter
crossing
the
rock
slant
depth
h
MACRO - Standard Rockderground
Frejus(km.w.e.).
Figure 6 shows the local muon
WIPP energy spectrum-7
flat over10
Soudanfor the various underground laboratories
under consideraKamioka
TABLE II. Singutions are
Boulbytion using the parameters b " 0:4=km:w:e:,#! " 3:77
underground site
Sudburyerate, via
Barrett et al.
-8
Miyakethe
et al. local angularand10 "! " 693 GeV [18]. Figure 7 shows
Castagnoli et al.
fast neuSite
Lip
distribution for the same sites where we assume a sec$$%utions are
WIPP
16
distribution,
valid for depths in excess of 1:5 km:w:e: [19].
-910a and we
Soudan19Note that the overall angular distribution of muons at thet can beKamioka19
surface is proportional to cos2 $$% with an average muon
at a given-10
Boulby23energyof about 4 GeV [17].
10Gran Sasso
25
betweenFrom Eq. (8), the average muon energy at depth h is
Sudbury32
rovide an
given
by
-11
10
n flux and
1
2
3
4
5
6
7
8
#bh
"
$1
#
e
%
Slant
Depth
(km.w.e.)!
e detector
hE! i ":
(9)
Z " 11, % " 2:#! # 2 muons and the slant depth for di↵erent
y is dis-Figure 1.14: Correlation between intensity of cosmic-ray
FIG. sites
1 (color).
Measurementsof theflux(1.19).
as a ters are due to u[34]. The points
are experimental
datadifferential
and the solidmuonline is Eq.
energy inunderground
The parameters#! Castagnoli
in Eq. (9) havestudied! , b andfunctionof slant "depth
from[67],been
Barrett[68], in the atmosphc study of
by several[15,18,20]
standard
rock[12],(A "22,
Miyake[69], authors
WIPP [4],Soudan for[23],
Kamioka
Boulbymedia, and th
utrinoless[6], Gran Sasso [8,70], Fréjus [11] and Sudbury [7]. Note that the Table II summ
monstratemeasurements for Kamioka [12] and Sudbury [7] are reported as various sites w
ivity and10-2
the numberof muons per day. We calculate the effective detector parameters prov
concludeacceptance for these two measurements in order to obtain the #! " 3:7 and "ew studies
muon flux. The solid curve is our global fit function described by 0:4=km:w:e: [2
Eq. (1).-3

053004-1

10

WIPP (1.6 km.w.e.)
Soudan (2.0 km.w.e.)
Kamioka (2.1 km.w.e.)
2006 The American Physical Society
Boulby©(2.8
km.w.e.)10-4Gran Sasso (3.1 km.w.e.)
Sudbury (6.0 km.w.e.)

The measured a[21] is 270 ( 3tainty of 6.8%.
parameters agre
sured uncertain

III. M

We distingui
neutrons producand neutrons cre
Figure 1.15: Energy spectra of cosmic-ray muons reach various underground sites [34]. The
the veto detecto
6 (color).
Theto muonenergy spectrum
local
the asvariousequivalentFIG.
vertical
depth relative
a flat overburden
for each site
are toadded
Ref. [34].
an external vet
underground sites calculated using Eq. (8). The areas under thecentral detector
curves are normalized to the vertical muon intensity for comtag in coincideparison purposes.
10-5

1

10

102

3

10
Muon Energy (GeV)1.6. Cosmogenic Productions

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NN<latexit sha1_base64="eNwYHCkkOF/e0GlW0d45V7Mqr5M=">AAADR3ichVLLTttAFD0xpdAUyqObSN2kjYJYRRPUAuoqajesqjwIiRQQss0ErDi2ZU8i0YgfaLetumDVSl1U/Qw29ANY5BMQiy6o2i5YcOxYIB6BsTz3zLnnzNx5GJ5tBUqIfkIbeTD6cGz8UfLxxOSTqemZ2bXA7fimrJqu7fp1Qw+kbTmyqixly7rnS71t2LJmtN6G+VpX+oHlOqtq15MbbX3bsZqWqStSpXeb0xmRE1FL3wT5GGQQt6I7k0hhHVtwYaKDNiQcKGIbOgJ+DeQh4JHbQI+cT2RFeYk9JOntUCWp0Mm22G9z1IhZh+NwziBym1zF5u/TmUZWHIkf4lQcip/iWJwNnasXzRHWsstoDLzS25z6kKr8u9fVZlTYuXTdWbNCE8tRrRZr9yIm3IU58HfffzmtvC5ne3Pimzhh/V9FXxxwB073j/m9JMv7d9RjsJbhJxbmfeIWsYp1W8RNxiC+jR1keBs9Mg5PUTE+j5hhauMW/e2eMNqx87reu7h1nXn6+Mby11/UTbC2kMsv5l6VXmYKb+LXNo5neIF5rr6EAlZQRJUnIPERn/BZ+6X91v5q/wdSLRF7nuJKG0mcA/wDtU4=</latexit>

Figure 1.16: Diagram of muon spallation [35].

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N

Figure 1.17: Diagram of photonuclear reaction [35].
pions. These secondary particles interact with other nuclei, repeating the same process, andthe number of nucleons and mesons increase accordingly. These cross sections are not wellunderstood and this process makes it difficult to evaluate neutron production by simulation.
(d) Muon capture:
When a negative muon is slowed down in materials, the muon is captured by a proton in a
nucleus via a W -boson. The proton is transferred into the neutron and a muon neutrino is
produced asµ + p ! ⌫µ + n.
(1.20)The diagram of muon capture is shown in Figure 1.18. In case nucleus is excited, a deexcitation ray is emitted.
Figure 1.19 shows the simulated energy spectrum of neutrons induced in Cn H2n by 280 GeV
muons. The spectrum extends to ⇠1 GeV. The photonuclear reaction of
ray and nucleon isdominant below the neutron energy of ⇠40 MeV, while the pion spallation is dominant above thatenergy.
Neutrons induced by cosmic-ray muons lose the energy in material via the interaction with
nuclei, and finally they are captured by nuclei. Various types of nuclear interaction occur inmaterial, depending on the type of nucleus and the energy of the neutrons. Above several tensof MeV, the initial energy of muon-induced neutrons, neutrons knock out nucleons and nuclei via
the inelastic scattering. In particular, when a neutron imparts significant energy to a nucleus,
multiple neutrons, protons, and alpha particles are released. Neutrons further lose the energy
through multiple scatterings and reach thermal equilibrium with the thermal motion of the atom.

22

Chapter 1. Physics Backgrounduu<latexit sha1_base64="y6/Yh0ymDM7FSlT1E/gcIkd0C2c=">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</latexit><latexit sha1_base64="tL+SbzcEBEfIDei/Xw3wb6gYFfk=">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</latexit><latexit sha1_base64="y6/Yh0ymDM7FSlT1E/gcIkd0C2c=">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</latexit>

p d
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d n
d

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Figure 1.18: Diagram of muon capture.

10

-6

Total
γ→N
n→N
π→N
π abs
p→N
µ→N

10

10

10

-7

-8

-9

10

10
1

-2

2

-5

total neutron yield, n/µ/(g/cm )2 cm2 MeV−1)
Neutrons(μ−1 g−1n/µ/(g/cm
)/MeV

10

10

10

10

2

10

-3

-4

3

, MeV
EE
n n(MeV)Figure 1.19: Simulated energy spectrum neutrons induced in Cn H2n by 280 GeV muons [36], whichis shown as the black line. The contributions of the neutron production processes are also shown:
Figure 2: Differential energy spectrum of neutrons produced in Cn H2n by
Figure 3: Neu
photonuclear reaction ( ! N ), neutron scattering (n ! N ), pion spallation (⇡ ! N ), pion
280 GeV muons (in thick black). Also shown are the contributions of the mostdent muons ofabsorption (⇡ abs), proton spallation (p ! N ), and muon spallation (µ ! N ).

important individual processes: photonuclear interaction of -rays (N),
neutron inelastic scattering (nN), pion spallation (N) and absorption( abs), and proton (pN) and muon (µN) spallation.

FLUKA-1999
eterisations) an

NaCl, agree

1.6. Cosmogenic Productions

23

Table 1.5: Measurements of the neutron yield Yn in di↵erent experiments. hEµ i is average of muonenergy at the detector. LS represents organic liquid scintillator.
Experiment
Hertenberger [37]Bezrukov [38]Boehm [39]Bezrukov [38]Aberdeen [40]
Enikeev [41]Daya Bay [42]KamLAND [43]
LVD [44]
Borexino [45]
SNO [46]

Target
LS
LS
LS
LS
LS
LS
LS
LS
LS
LS
D2 O

Depth (m.w.e.)
20
25
32
316
611
750
860
2700
3100
3800
5890

hEµ i (GeV)
13
14.7
16.5
55
90
120
143
260
270
283
363

Yn (µ 1 g 1 cm2 )(2 ± 0.7) ⇥ 10 5
(4.7 ± 0.5) ⇥ 10 5
(3.6 ± 0.3) ⇥ 10 5
(1.21 ± 0.12) ⇥ 10 4
(1.19 ± 0.22) ⇥ 10 4
(2.15 ± 0.15) ⇥ 10 4(1.70 ± 0.12) ⇥ 10 4
(2.8 ± 0.3) ⇥ 10 4
(4.5 ± 1.2) ⇥ 10 4
(3.1 ± 0.1) ⇥ 10 44
(7.28+1.59
1.12 ) ⇥ 10

These neutrons are called thermal neutrons. The thermal energy of the nucleus is kB T , where kB
represents the Boltzmann constant, 8.6 ⇥ 10 5 eV/K, and T is the thermodynamic temperature.
The typical kinetic energy of thermal neutrons is about 25 meV at room temperature (T ⇠ 300 K).
When thermalized neutrons are captured by nuclei in the materials, the nuclei are excited, and thenrays are emitted when the excited nuclei transition to the ground state. In this study, neutron
capture interactions on gadolinium are observed as described in Section 3.7.
Cosmogenic Neutron Yield
Neutrons produced via the muon spallation and following inelastic scattering have been measured
in several experiments. In practice, rays emitted from neutron capture are detected by liquid
scintillator and water Cherenkov detectors constructed underground. The amount of cosmogenic
neutrons is evaluated using the neutron yield. Neutron yield Yn is defined as the number of neutrons
produced per muon, per unit muon path length, and per density of the target material:
Yn =

Nn
,
Nµ Lµ ⇢

(1.21)

where Nn is the amount of neutrons captured by nuclei in the detector. Nµ is the number of muons
entering the detector, Lµ is the average track length of the muons, and ⇢ is the density of themedium. The unit of the neutron yield is expressed as follows:
neutrons= µ 1 g 1 cm2 ,muons ⇥ cm ⇥ g/cm3(1.22)

where µ 1 represents “per muon”. The measurements of the neutron yield are listed in Table 1.5.
Several experiments have measured cosmogenic neutron production yields at various depths withdi↵erent muon energies. Most of these measurements were made with organic liquid scintillator,
which contains mostly carbon and hydrogen. Among those, the majority of neutrons are produced
via cosmic-ray muon spallation interactions with carbon nuclei. While, the measurement in water
is limited and SNO is the only experiment that measured the neutron yield using heavy water(D2 O) [46]. In a water-based detector, the neutrons are produced via the muon spallation interactions with oxygen nuclei. Figure 1.20 shows the measurement results from various experiments
shown in Table 1.5. The overlaid dashed lines are the models assumed in the FLUKA-based simulations for cosmogenic neutron productions and propagation [47, 48], in which the neutron yield is
calculated as Yn = aEµb with the parameter to reproduce experiment results. The FLUKA-based
simulations are developed for the precise estimation of the cosmogenic neutron background in rare

Chapter 1. Physics Background

Neutron yield (µ −1 g−1 cm2)

24

10−3
SNO
LVD-corrected
Borexino
KamLAND
Enikeev
Daya Bay

10−4

BezrukovAberdeen

Bezrukov
Boehm

Water-based measurements
LS-based measurements
Wang et al
Kudryavtsey et al

Hertenberger

10−5
0

50

100

150

200

250

300

350

400

Average muon energy (GeV)
Figure 1.20: Comparison between the previous measurement results [37–46] and predictions forliquid scintillator with FLUKA-based simulations calculated by Wang et al [47] (blue dotted line)
and Kudryavtsey et al [48] (red dashed line). The open circles represent the liquid scintillator-based(LS-based) results and the filled circles represent the water-based results.
event searches such as neutrino observation and dark matter search. Therefore, additional experimental data will lead to improving the FLUKA-based simulation and more reliable estimation of
the cosmogenic neutron background.
In this study, neutron yield in water is measured using the Super-Kamiokande detector. Thismeasurement can be compared with that from the SNO experiment which measured the neutron
yield in heavy water at the di↵erent depth with di↵erent muon energy. In addition, this measurement can be also compared with that from the KamLAND detector which measured the neutron
yield in liquid scintillator at the same depth as the SK detector.

1.6.3

Cosmogenic Isotopes

Isotopes Produced in Water
Cosmic-ray muons induce not only neutrons but also various radioactive isotopes through theinteractions with oxygen nuclei. The isotopes produced in water are predicted using FLUKAsimulation by Ref. [49] and summarized in Table 1.6. Figure 1.21 shows the half-lives and predicted
yield above 3.5 MeV (corresponding to the energy threshold of SK). Isotopes that emit electrons
with neutrons via decay are especially indicated in Figure 1.21 (red circles); 8 He, 9 Li, 11 Li, and
16 C. The+ n decay of those isotopes cannot be distinguished from inverse beta decay (IBD)
reaction by ⌫¯e (¯⌫e + p ! e+ + n). Therefore, those isotopes are major background sources for SRN

1.6. Cosmogenic Productions

25

Table 1.6: Radioactive isotopes induced by cosmic-ray muon spallation; the fourth column is theend point kinetic energy of the emitted electrons (or positrons) [49, 50].
Isotope
11 Be

Life time (s)
19.9

16 N

10.3

15 C

3.53

8 Li

1.21
1.11
1.08
0.26

8B
16 C
9 Li
9C
8 He
12 Be
12 B
13 B
14 B
12 N
13 O
11 Li

0.18
0.17
0.034
0.029
0.025
0.020
0.016
0.013
0.012

Decay mode
(55%)
(31%)
(66%)
(28%)
(63%)
(37%)
+

+n
(49%)
+ n (51%)+p(84%)+ n (16%)

+
++p

(6%)
+ n (86%)

Q-value (MeV)
11.51
9.41 + 2.10( )10.44
4.27 + 6.13( )9.77
4.51 + 5.30( )
⇠13.0
⇠13.9
⇠4
13.6
⇠10
3–15
9.67 + 0.98( )
11.71
13.37
13.44
14.55 + 6.09( )
16.38
8–14
20.62
⇠16

Production process
16 O(n, ↵ + 2p)11 Be
16 O(n, p)16 N
16 O(n, 2p)15 C
16 O(⇡, ↵ + 2 H + p + n)8 Li

16 O(⇡ + , ↵ + 2p + 2n)8 B
18 O(⇡, n + p)16 C
16 O(⇡ , ↵ + 2p + n)9 Li
16 O(n, ↵ + 4n)9 C
16 O(⇡, 3 H + 4p + n)8 He

18 O(⇡, ↵ + p + n)12 Be
16 O(n, ↵ + p)12 B

16 O(⇡, 2p + n)13 B
16 O(n, 3p)14 B
16 O(⇡ + , 2p + 2n)12 N
16 O(µ , µ + p + 2n + ⇡ )13 O
16 O(⇡ + , 5p + ⇡ 0 + ⇡ + )11 Li

rch for Diﬀuse Supernova Neutrino Background in SK-Gd
Chapter 1. Physics Background

Yield (E>3.5 MeV) [×10-7µ-1g-1cm2]

26

16

Li

12

B

10

8

B

13

B

1

10−2

9

12

N

Li

Be

C

12

Be
8

14

B

He

11

Li

14

16

B
Li

C

11

20

11
15

10−1

18

N

8

10−3

10−2

10−1

nt energy [MeV]1

10
Half-life [s]Figure 1.21: Half-lives and predicted yield above 3.5 MeV [51]. The yields for each isotope are
predicted by Ref. [49]. The red circles represent isotopes which emit electron with neutron. The
black triangles represent isotopes which emit only electron.

rrelation between end-point energies and half-lives
tween half-lives and yield (right) for spallation iso9 Li has a
the DSNB
searchwindow
andgenerated
search.
Among those,relatively
large yield, aby
highcosmicbranching ratio of + n decay, and along lifetime which makes it difficult to reject using the time correlation with muon. On the otherer. Red hand,circles
in isboth
figures represent undergoing
8 He yieldless than one-tenth of 9 Li yield, and 8 He has a lower branching ratio of + n
11 Li has a short lifetime and strong timing correlation with the cosmic-ray muons.
decayFor(⇠16%).
neutrons.
theisotopes undergoing decay with
16
The yield of C is much less than those of other isotopes. Therefore, 9 Li is the major backgroundd includes
the fraction of decay with neutrons. The
source among those isotopes.
tion of these plots referred from [48].
Lithium-9 Background for SRN Searches

Figure 1.22 shows the comparison of SRN signal and 9 Li decay. The SK-Gd experiment observes
SRNs through the coincidence of the IBD reaction of ⌫¯e and the neutron capture reaction on Gd.
Several rays with a total energy of about 8 MeV are emitted after neutron capture on Gd. On theother hand, the 9 Li emits an electron and a neutron via decay at a branching ratio of 50.8% (9 Li+ n decay event) as shown in Figure 1.23. These 9 Li + n decay event cannot be distinguishedfrom the IBD signal. For the SRN search in SK, the muon-induced isotopes are eliminated using
the distance between the muon track and decay positions of isotopes. However, a certain rate of
isotopes remain and become the major background in SRN search below ⇠15 MeV as shown in
Figure 1.24.

10

16

N

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8

1

Li 8B

p

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He

10−1

<latexit sha1_base64="PiNJ36+KfglrPhLenhx1rD2B6sI=">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</latexit>

e
12

Be

10−2
12

+

B
13
B

14

8

B

13

B

1

9

12

N

Li

Gd

11

Be

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15

C

12

Be
8
<latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit>

14

B

10−2

12

He

11

Li
<latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit>

14

N

µ
18

(b)
16

16

B
11
Li

12

<latexit sha1_base64="OdXPW79udRAdOxphg5QmMcIU1CM=">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</latexit>

10

B

10−1

9
8

Li

12

10

N
27

8

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C

16

n

(a) ⌫ e<latexit sha1_base64="7xIFj3OQASvx0sI91VXlBKEZor0=">AAADUnichVLLTttAFD2JoVBKy6MbpG6gEVXYRJOqPNQVajdd8spDShCynQlY8Uv2JAIsfqAf0C666EPqoupndNMPgAWfgFgGqVLVRY8dCwQhMJbnnjn3nJk7D8O3rVAJcZrJakPDD0ZGH449Gn/8ZGJyaroceu3AlCXTs72gauihtC1XlpSlbFn1A6k7hi0rRuttnK90ZBBanrulDny57ei7rtW0TF2RqteV3FeBE+X1haOdyZwoiKTN9oNiCnJI25o3lZlBHQ14MNGGAwkXitiGjpBfDUUI+OS2EZELiKwkL3GEMXrbVEkqdLIt9rsc1VLW5TieM0zcJlex+Qd0zmJenIgfoit+i5/iTPwbOFeUzBHXcsBo9LzS35l4P7P5516Xw6iwd+W6s2aFJlaSWi3W7idMvAuz5+8cfuxuvt6Yj16Ib+Kc9X8Vp+IXd+B2Lszv63Lj0x31GKxl8InF+YC4RaxSXYO4yRimt7GHHG8jIuPyFBXjXMIMUhu36G/3xNFOnTf1/uWt68zTxzdWvPmi+kH5ZaG4VFhcf5VbfZO+tlE8w3PkufoyVvEOayjxBHx8wGd8yR5n/2oZTetJs5nU8xTXmjb+Hw8euBo=</latexit>

15

Yield (E>3.5 MeV) [×10-7µ-1g-1cm2]

Half-life [s]111.6. Cosmogenic
Productions
Be

C

10−3

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20n<latexit sha1_base64="oeptCw94cxZ6ZzVnsVkF5gZhoH0=">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</latexit>

9
End-point energy [MeV]
Li<latexit sha1_base64="8eX+rvuSVrvUq9lPkZ96DieYO3o=">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</latexit>

10−2

10−1

1

Gd

10
Half-life [s]<latexit sha1_base64="3JeD/iPW2ZV5I//b8m2SBhLuUT4=">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</latexit><latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit>

16
Figure 7.1: Correlation
between end-point energies and half-lives
O(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 circlese in both figures represent undergoingbeta decay with neutrons. For the isotopes undergoing decay withneutrons, the yield includes the fraction of decay with neutrons. The
fractionof theseplots
from[48].(b) the 9 Li + n decay
Figure 1.22: Schematic
illustrationof (a) the
IBD referred
event of SRN(¯⌫e ) and<latexit sha1_base64="JjbXfsXnHXXtwK5Z2gE45fc2jok=">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</latexit><latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit><latexit sha1_base64="sKi0+qT7Z8rBwtjjWse6neZAyAU=">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</latexit><latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit>

event.

9

Figure 1.23: Decay scheme of Li based9 on Particle Data Group [52].
Figure7.2: Decay scheme of Li based on PDG [49].

7.3.2

Atmospheric Neutrinos

28

Chapter 1. Physics Background

Chapter 10. Results

Number of events [bin-1]

160

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
0

8

10

12

14

16

18

20

22

24

26

28
Erec [MeV]

Number of events [bin-1]

Figure 1.24: Reconstructed kinetic energy spectrum of the observed data and the expected back2
ground for the10SRN searches in SK with 0.01% Gd-loaded water [51]. The green component in the
SK-VI Data (552.2
histogram shows muon-induced 9 Li background expected fromthe 9 Lidays)
yield measured in SK with
Atmospheric-ν (non-NCQE)
ultra-pure water.
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)Chapter 2

Motivation
Since July 2020, gadolinium (Gd) has been loaded in ultra-pure water of the Super-Kamiokande(SK) detector aiming for the first observation of neutrinos from past supernovae (supernova relicneutrinos, SRNs). The new phase of the experiment with Gd-loaded water is named SK-Gd. The
detection efficiency of neutrons and the background rejection are significantly improved by the
introduction of Gd. The SK-Gd experiment was operated with a Gd mass concentration of 0.01%
from August 2020 to May 2022, and this study was performed with the data acquired during theperiod. This thesis describes the following three studies in Chapter 6, 7, and 8.
1. The stability and uniformity of the Gd concentration in the detector were verified by measuring neutrons induced by cosmic-ray muon spallation (Chapter 6).
2. Extending the above study, the yield of the neutron from the muon spallation in water wasmeasured (Chapter 7).
3. The energy spectrum of decay with neutrons of 9 Li, the major background in the low energy
region in the SRN search, was measured (Chapter 8).
1. Evaluation of stability and uniformity of Gd concentration
The expected number of SRN interactions in SK depends on the models but it is typically a few
events per year in the energy region of 10–30 MeV. Therefore, rare signals must be searched forin a large amount of the background for more than 10 years to observe the signals with morethan 3 significance. Thus, in order to detect SRN in the SK-Gd experiment, it is necessary tomonitor the stability of the detector including the uniformity of the Gd concentration and continue
stable observations over a long period. Indeed, the introduction of Gd into a large detector ischallenging as the unexpected chemical reaction of Gd solute with the detector material may cause
degradation of the Gd-loaded water such as precipitation although soak tests have been performed
carefully before the installation. In this study, the stability and uniformity of the Gd concentrationin the detector were evaluated with neutrons induced by cosmic-ray muons. The result for the firstsix months of data is reported in Ref. [53], which is extended to the entire observation period with
0.01% concentration in this thesis.
2. Measurement of cosmogenic neutron production
The production yield of neutrons induced by cosmic-ray muons was measured in this study. Neutrons and the recoil nuclei produced by their scattering cause the background in the search for rare
events at the MeV scale, such as the recoil nuclei by dark matter, by the underground experiments.
While, it is difficult to precisely calculate the processes with simulation due to the large uncertainties in the calculations of hadron production and scattering processes. Previous experimental
results suggest that there is a relationship of Yn / (Eµ )a between the average energy of cosmic-ray
muons arriving at the detector Eµ and the neutron production yield Yn . The FLUKA simulation29

30

Chapter 2. Motivation

reproduces the measurement of Yn / (Eµ )a in the organic liquid scintillator but it still underestimates the neutron yield by about 10–30% [34, 47, 48]. GEANT4-based simulation reported
even lower estimation of neutron yield by ⇠30% than that from FLUKA above 100 GeV of muonenergy [54]. Therefore, it is important to experimentally measure the neutron production yield atdi↵erent conditions in order to better understand and model the physics processes. Most previous
experiments have used organic liquid scintillator (carbon target) to measure neutron yield, while
the neutron yield in water was measured in this study using the SK detector. This is the secondcase after the SNO experiment [46] which measured at much deeper underground than SK, corresponding to higher muon energy. The comparison of the two measurements provides informationon the energy dependence for the water target. Furthermore, as the SK detector is located near
the KamLAND detector which is a liquid scintillator detector, this study enables a comparison ofneutron yield measurements with di↵erent targets at the same depth (same muon energy) for the
first time. For these reasons, this study provides a further understanding of neutron production
and secondary interactions and helps establish a reliable simulation of muon spallation. The resultof this study is reported in Ref. [55].
3. Measurement of cosmogenic 9 Li production
The energy spectrum of electrons from decay of 9 Li was measured in this study. 9 Li is one of
the cosmogenic isotopes produced in water by cosmic-ray muon. 9 Li is an unstable nucleus with alifetime of 0.26 s and emits an electron and a neutron, which are indistinguishable from the SRN
signals, ⌫¯e + p ! e+ + n. In previous analysis in SK, SRNs have been searched in the energy region
above 8 MeV. Correspondingly, 9 Li has been measured in the region above 8 MeV with ultra-purewater [50]. In this study, data from SK with 0.01% Gd-loaded water were analyzed by a newly
developed method to measure the spectrum of 9 Li down to 4.5 MeV. Theoretical prediction of
the SRN flux depends on the number of supernovae in the history of the universe, and this depends
on the number of stars formed in the universe and the fraction of stars massive enough to cause
core-collapse supernovae. The uncertainty regarding the history of star formation increases as itis older. As neutrinos produced from supernovae in the earlier stage of the universe have lower
energy due to the e↵ect of redshift, it is important for experiments to measure the SRN flux atlower energy. This study measured the energy spectrum of electrons from 9 Li decay, which is the
major background at low energy below 10 MeV. In addition, the analysis method developed in thisstudy can be applied in the future SRN search by the SK-Gd experiment to extend the energy
range at the lower side and improve the sensitivity of the observation.

Chapter 3

Super-KamiokandeThis study was performed using the data observed by the Super-Kamiokande detector. This chapter
describes the details of the configurations of the Super-Kamiokande detector and then describes
the upgrade with gadolinium loading, the SK-Gd experiment, which has been started since August
2020.

3.1

Detection Principle

Charged particles generated in the Super-Kamiokande (SK) detector are observed by the detectionof the Cherenkov light in water as shown in Figure 3.1. Cherenkov light is emitted when charged
particles travel faster than the speed of propagation of light in a medium. The light is emitted ina conical shape at an angle ✓c with respect to the direction of travel of the charged particle, which
satisfies the following equation1
cos ✓c =,(3.1)
nwhere n represents the refractive index of the medium and (= v/c) is the ratio of the velocity vof a charged particle in vacuum to the speed of light c. Since the refractive index of pure water is
1.34, ✓c is about 42 for a charged particle traveling at nearly the speed of light ( ' 1).
Since Cherenkov light is not emitted unless the velocity of the charged particle exceeds the speedof propagation of light in the medium, there is a threshold for the energy of a charged particle that<latexit sha1_base64="4RE2RXPNVbu6d5y4oDUV2l+jqv8=">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</latexit>

Photosensor (PMT)

Cherenkov light<latexit sha1_base64="URqwi1ipj+K1TBuBAwclMW5zg5Q=">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</latexit>

Charged particle<latexit sha1_base64="cRya+f/64JJnkrNqeB1nYt/TjLM=">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</latexit>✓c<latexit sha1_base64="UQgao95zWiRSUNYIAe9UKAePLEk=">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</latexit>

Figure 3.1: Schematic illustration of Cherenkov detection.
31

32

Chapter 3. Super-Kamiokande
Table 3.1: Energy thresholds to emit Cherenkov light in water.
Charged particle
Electron
Muon
Pion
Kaon
ProtonMass m (MeV/c2 )
0.511
106
140
494
938

Energy threshold Eth (MeV)
0.768
159
210
742
1,410

Super-Kamiokande IV
Run 61941 Sub 520 Ev 101555720
08-10-25:08:35:00
Inner: 3658 hits, 7729 pe
Outer: 1 hits, 1 pe
Trigger: 0x10000007
D_wall: 731.0 cm
Evis: 902.1 MeV
e-like, p = 902.1 MeV/c

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7< 0.2
1200
0 mu-e0 decays

960
720
480
240
0
0

500

1000

1500

2000

Times (ns)Figure 3.2: Example of an event display for an electron. Points correspond to PMTs on the innerwall and the color scale represents the observed electric charge of each PMT.
can emit Cherenkov light, given by the following equation:
E

p
1

mc2
1/n2

⌘ Eth .

(3.2)

The threshold Eth for each charged particle is summarized in Table 3.1.
The number of photons dN emitted as Cherenkov light while an electron travels a small distancedx at a velocity in a medium with refractive index n is given by
d2 N
2⇡↵
= 2
dxd

✓

1

1
n2 2

◆

,

(3.3)

where is the wavelength of the photon and ↵ is the fine-structure constant.
Cherenkov photons are detected by photosensors (photomultiplier tubes, PMTs) mounted on
the inner wall of the detector. Figure 3.2 shows an example of an event display for an electron.
Electron generated or scattered in water emits Cherenkov photons until the momentum is decreased
below the Cherenkov threshold due to the energy loss in water. Vertex (position where the charged
particle is generated), direction, and kinetic energy are measured by the amount of the detected
photons, timing of the detection, and the location of the hit-PMTs (ring pattern).

4.3

3.2. Overview of Super-Kamiokande

33

Control room

Inner Detector
41m

Outer Detector

Photo multipliers

1,000m39m

Detector hall

Access tunnel

Figure 7: AFigure
schematicof the Super-Kamiokande
Detector.
3.3: Theview
Super-Kamiokande
detector [56].
3.2

Overview of Super-Kamiokande

Far detector: Super-Kamiokande

The SK detector is a large water Cherenkov detector located 1,000 m underground, corresponding
2,700 m-water-equivalent
overburden, at themine
HidaKamioka
City, Gifu Prefecture,Japan
The fartodetector,
Super-Kamiokande,
isKamioka
locatedinintheObservatory,
Institu(Figure 3.3). The detector is a cylindrical tank, 39.3 m in diameter and 41.4 m high, filled withfor Cosmic 50Ray
of itsTokyo,
which
beenenter
successfullytakkton Researchof ultra-pure (ICRR),
water. PMTsUniversity
are equipped on
inner wall.
Whenhasneutrinos
the SK
interact with electrons or nuclei in the water or rays scattered in the water, charged
data since detector
1996. andThe
detector is also used as a far detector for K2K experiment. It i
particles are generated. The neutrinos can be observed by detecting the Cherenkov light emitted
the charged
particles detector
as they travel
through the
Althoughcosmic-ray
muons water
are the equivale
50,000 ton bywaterČerenkov
locatedat water.
a depthof 2,700
metersmajor background for the observation, the flux of cosmic-ray muons is suppressed to ⇠10 5 of thatn the Kamioka
minesurface
in Japan.
Itsperformancein atmospheric neutrin
at the ground
thanks to thedetector
being located and1,000 mresults
underground.

or solar neutrinos have been well documented elsewhere[1, 5, 6]. A schematic view
Detector
Structuredetector is 3.3
shown
as Fig 7.
The detector cavity is 42 m in height and 39 m in diamet
3.3.1 Water
Tank
filled with 50,000
tons ofpure water. There is an inner detector (ID), 33.8 m diameter a
Thesurrounded
SK detector is bydividedinto twodetector
concentric regions:theinner detector (ID) andthethick.
outer The inn
36.2 m high,
an
outer
(OD)
of
approximately
2mdetector (OD) as shown in the left of Figure 3.4. The ID and OD are optionally separated.
The ID is a50
cylindrical
33.8 m in diameterand 36.2
m high, filledwith 32.5 kton of ultradetector has 11,146
cm volume,
photomultipliertubes(PMTs),
instrumented
on all surfa
pure water. 20-inch PMTs facing inward are mounted on the walls. The number of PMTs installedof the innervaries
detector
ononathe70.7
cm grid
spacing.
Theafterouterdetector ofisgadolinium,
instrumented w
dependingobservation
period.
In the period
the introduction
11,129 PMTs
PMTs wereattached
to the⇠40% of thearea ofentering/exiting
the inner wall with
1,885 20 cm
andused
as wall,an coveringanti-counterto surface
identify
particthe photocathode. The 3 ⇥ 4 PMTs are laid out on the wall as one set (super module) as shown in
to/from ID.theThefiducial
is definedas 2 m isaway
and the toright ofFigure 3.4.volume
The area outside
the photocathodecoveredfrom
with a theblack ID
sheetwall,
to prevent
light from reflecting o↵ the wall.
fiducial massis 22,500 ton. Čerenkov rings produced by relativistic charged particles
The OD is the volume surrounds the ID with a thickness of 2.05 m on the top and bottom andm onPMT’s.
the sides. Theof the OD
are equipped
1,885 outward-facing
detected by2.2ID
Thewalls
triggerthresholdis withrecentlyachieved 8-inch
to bePMTs.
4.3 MeV. T
The main purpose of the OD is to identify cosmic-ray muons and to attenuate -rays and neutrons
pulse hightgenerated
and timing
informationof thePMT’s
arefittedto interact
reconstructin the surroundingrock. Whenneutrinos
incidenton thedetectorin the ID the vert
and Cherenkov
is emittedidentificationby the charged particles
produced,the light rings.
is detectedAonly
by
direction, energy,
andlight
particleof theČerenkov
typicalvert
angular and energy resolution for a 1 GeV µ is 30 cm, 3 and 3% for vertex, respective
The Čerenkov ring shapes, clear ring for muons and fuzzy ring for electrons, provid
good e/µ identification. A typical rejection factor to separate µ’s from e’s (or vice ver

34

Chapter 3. Super-Kamiokande

S. Fukuda et al. / Nuclear Instruments and Methods in Physics Research A 501 (2003) 418–462

427

Fig. 6. A cross-section of the Super-Kamiokande detector.

Figure 3.4: Cross section of the SK detector (left) and the support structure for PMTs (right) [56].
bottom of the tank and to the top structure.
high voltage ranging from 1700 to 2000 V. The
In addition to serving as rigid structural elements,
neck of each PMT was coated with a silver
supermodules
simplified
initial inassemblyof On the other hand, as thereflector to block
external
light,
althoughasnoted,
the 20-inch PMTs in the ID andnot by the
8-inch the
PMTs
the OD.
the ID. Each supermodule was assembled on thelight can enter through the back of the hemicosmic-ray
muons are charged particles,
Cherenkov
is final
detectedtank floor andthen hoistedlightinto its
position.by both the PMT in the OD
spherical portionof the PMT.
the ID
is in theeffectdetector.
tiled with supermodules.
Fig. 11 showsdetailPMTof the insupportstructure
anda thethe ID
when theThus
muons
enter
Thus, neutrinos and cosmic-ray muons
installation,
PMTsinwere
for the ID PMTs.
All support structurecompo- theDuring
are distinguishedby checking
reactionof the ID
PMTs
thepreassembled
OD. The schematic diagram is shownin units of three for easy installation. Eachnents are stainless steel.
inFigure3.5.
supermodule has two OD PMTs attached on its
The basic unit for the ID PMTs is a ‘‘superback side.
Thephotocathodesupport structureoffor
the bottom
module’’, a frameIn
which
3 ! 4surfacesarray
the supports
ID, the awall
other
than
PMTs
are covered with black sheets as
PMTs is attached to the bottom of the stainlessof PMTs. Supermodule frames are 2.1 m inwritten
before,whereas
the
wall
of
the
OD
are
coveredwithwhitereflective sheets called Tyvek
steel tank by one vertical beam per supermodule
height, 2.8 m in width and 0.55 m in thickness.
to improvetheotherlightincollection
PMTs. for the top offrame. efficiency
The supportof structure
These framessheets
are connectedto eachthe tank is also used as the support structure forboth the vertical and horizontal directions. Thenthe top PMTs.
the whole support structure is connected to the

3.3.2

Photomultiplier Tube

PMTs are sensitive photosensors which consists of photocathode to convert photons into electrons(photoelectrons, p.e.) by the photoelectric e↵ect and dynodes to multiply the electrons and extract
them as electrical signals. PMTs detect photons by the following process as illustrated in Figure 3.6.
1. A photon incidents the photocathode of the PMT and excites an electron in the photocathode(external photoelectric e↵ect), causing the photoelectron to strike out.
2. Photoelectron is accelerated and led to the first dynode by the focusing electrode. Multiple
secondary electrons are emitted when it strikes the first dynode.
3. The secondary electrons are accelerated by the electric field created by the potential di↵erence
between adjacent dynodes and collide with the second dynode. Multiple electrons are emitted
for each incident electron.
4. Electrons multiplied by repeated collisions at the dynode reach the anode and are extracted
as electric current.

3.3. Detector Structure

35

ID
OD

Figure 3.5: Schematic illustration of an electron neutrino and a cosmic-ray muon arriving at the
SK detector.

Figure 3.6: Schematic illustration of the detection principle of PMT [57].

36 S. Fukuda et al. / Nuclear Instruments and Methods in Physics Research
Chapter
3. (2003)
Super-Kamiokande
A 501
418–46228~ 70000

cable length
φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure( 610 20 )

~ 720

(mm)

Fig. 7. Schematic view of a 50 cm PMT.
Figure 3.7: Schematic illustration of 20-inch PMT installed the SK detector [56].

Quantum efficiency

Table 3.2: Characteristics of the 20-inch PMT.
0.2

0.1

0

300

Model number
Photocathode area
WeightPressure tolerance
Photocathode material
Quantum efficiency
DynodeGain
Dark current
Dark noise rate
700
400
500
600
Transit time
Wave length(nm) time spread
TransitHamamatsu R3600
50 cm in diameter
13 kg
6 kg/cm2
Bialkali (Sb-K-Cs)
22% at wavelength of 390 nm
Venetian blind type (11 stages)
107 at ⇠2 kV
200 nA at 107 gain
3 kHz at 107 gain
90 ns at 107 gain
2.2 ns (1 )ig. 8. Quantum efficiency of the photocathode as a function
Fig. 10. Relative transit time distribution for a typical PMT
f wavelength.
The 20-inch PMTs (Hamamatsu R3600) are equipped
the410innerof light
SK (Figure3.7). photoelectron
tested inwith
nm detector
wavelength
at the single
The photocathode of PMT is made of bialkali (Sb-K-Cs)
and level.
a sensitive to the wavelength of 280–
intensity
660 nm, which matches the typical wavelength of Cherenkov light in SK, ⇠390 nm. The probability
that a photon is converted to a photoelectron at the photocathode is called the quantum efficiency.
Opaque black polyethylene telephthalate sheets
The quantum efficiency reaches a maximum at a wavelength of 390 nm with a value of 22% (FigcoverHigh-voltage
the gaps between
PMTs
in the ID surface
ure 3.8). The dynote has 11-stage Venetian blind type.
(HV) of the⇠2 kV
are applied(see represents
Fig. 11). theThesesheets ratio
improveto the PMTs to give the gains of ⇠107 where the gain
amplificationof thethe opticalnumber of electrons in the output signal to the numberof photoelectrons.
TableID
3.2andsummarizes
separation
between the
OD and suppress
the characteristics of the 20-inch PMT.
unwanted low-energy events due to residual radioSince the interior of the PMT is in a vacuum to improvecollection
efficiency
activityphotoelectron
occurring behindthePMTs.andThe reflectivprevent internal discharges, an implosion occurs if the glass of the PMT is broken. SK experienced
ity of the photocathode surface of PMTs and thea serious accident in 2001 in which about half of the PMTs were damaged by an implosion of one
sheetprotection
were measured,with results
PMT. Since then, all PMTs have been equipped withblack
shock-wave
cases to prevent
chain shown in
Fig. with
12, alongwiththecalculated
valuesimplosion. The photosensitive area of the PMT is covereda 12 mmthickacrylic
cover, andthe which areMontesimulations.
back side is covered with fiberglass-reinforced plastic.used
Holesinare
drilled Carloin the caseto allow outside
water to flow in, and the gap between the case and the Cables
PMT is filledwithwater.
The
coverare bundledfrom each group ofacrylic
3 PMTsig. 9. Single photoelectron pulse height distribution. The peakose to zero ADC count is due to PMT dark current.

together. All cables run up the outer surface of
the PMT support structure, i.e., on the OD PMT
plane, pass through cable ports at the top of

~ 720Fig. 7. Schematic view of a 50 cm PMT.

Quantum efficiency

3.3. Detector Structure

37

0.2

0.1

0

300

400

500

600

700

Wave length (nm)Fig. Wavelength
8. Quantum
efficiencyofofquantum
the photocathodeas a20-inchfunction
Figure 3.8:
dependence
efficiency of thePMT [56].

Fig. 10. Relative
tested with 410 nmof the photosensitive area has a transmittance of more than 96% for a photon of 350 nm wavelength
intensity level.
of wavelength.

and has only a small impact on the detection of Cherenkov photons.
Photoelectrons generated inside the PMT may not reach the dynode if there is a geomagnetic
field; a 100 mG magnetic field parallel to the dynode reduces the light collection efficiency by about
Opaque bla
10% [58]. There is a geomagnetic field of about 450 mG around the SK detector site. Therefore,
cover the gaps
26 Helmholtz coils are wound around the detector to reduce the influence of the geomagnetic field.
(see toFig. 11).
These coils reduce the influence of the geomagnetic field on the detection efficiency of the PMT
2% [58].
separation bet

unwanted lowactivity occurr
The SK experiment started the observation in April 1996. The observation period of SK has been
ity of the pho
divided into seven phases. Table 3.3 summarizes the detector configuration in each phase.
black sheet we
Fig. 12, along
SK-I
The period from the start of the observations in April 1996 to July 2001 is referred to asused
SK-I.in MonteIn July 2001, the water inside the detector was drained and the defective PMTs were replaced.
Cables from
However, in November 2001, while pouring water into the detector after the replacement work wastogether. All
completed, the PMT breakage accident described above occurred. As a result of this accident,
the PMT supp
Singlepulse height distribution. The peak
6,779 ID PMTsFig.
and9.1,017
ODphotoelectron
PMTs were lost.
plane, pass thclose to zero ADC count is due to PMT dark current.
3.3.3

Observation Phases

SK-II
After the accident, 5,182 ID PMTs were reloceted to cover the inner wall uniformly and the observation was resumed in October 2002, and the data acquisition continued until October 2005. This
period is called SK-II. The PMTs are equipped with shock-wave protection cases from the SK-II
period to prevent chain breakage of the PMTs.
SK-IIIIn June 2006, the water tank was opened again and new PMTs were installed to fill the missing
locations due to the accident. This installation brought the total number of ID PMTs to 11,129,
and observation was conducted from July 2006 to August 2008. This period is referred to as SK-III.

38

Chapter 3. Super-Kamiokande
Table 3.3: Observation phases of SK. This analysis used the data acquired during SK-VI.
Phase
SK-I
SK-II
SK-III
SK-IV
SK-V
SK-VI
SK-VII

Start
Apr. 1996
Oct. 2002
Jul. 2006
Sep. 2008
Feb. 2019
Jul. 2020
Jul. 2022

End
Jul. 2001
Oct. 2005
Aug. 2008
May 2018
Jul. 2020
May 2022—

ID PMTs (coverage)
11,146 (40%)
5,182 (19%)
11,129 (40%)
11,129 (40%)
11,129 (40%)
11,129 (40%)
11,129 (40%)

OD PMTs
1,885
1,885
1,885
1,885
1,885
1,885
1,885

Gd concentration (%)
—
—
—
—
—
0.01
0.03

SK-IV
A new electronics module, QBEE, was introduced in August 2008 to record the low energy signals a specific condition for neutron search (Section 3.4.1). The data acquisition took place from
September 2008 through May 2018. This period is referred to as SK-IV. At present, SK-IV has thelongest observation period.
SK-V
In preparation for the installation of gadolinium (Gd) in ultra-pure water, modifications of thedetector were made from July 2018 to January 2019. The modification includes water seals toprevent a leak of Gd-loaded water, improvement of piping in the tank, and replacement of defective
PMTs. The data acquisition period from the end of January 2019, after the completion of therefurbishment work, to June 2020, when the Gd-loading work begins, is referred to as SK-V. SK-V
is the last phase for the observation using ultra-pure water.
SK-VI
In July 2020, 13 tons of gadolinium sulfate octahydrate Gd2 (SO4 )3 · 8H2 O were introduced to ultrapure water in the detector, corresponding to 0.01% of Gd mass concentration. The experiment using
the Gd-loaded water in the SK detector is specially named the SK-Gd experiment. The Gd-loading
work was completed in August 2020 and the SK-VI period has been started. In this study, thedata acquired during this period was used to evaluate the performance of neutron detection andthe stability and measure the cosmogenic productions.
SK-VIIIn July 2022, 26 tons of Gd2 (SO4 )3 · 8H2 O were added to Gd-loaded water in the detector. The
Gd mass concentration has reached to 0.03% and the SK-VII data-taking period has been started.

3.4

Data Acquisition System

3.4.1

Front-End Electronics

The analog signal from each PMT is sent via a 70 m cable to the electronics hat on top of the tank.
The analog signal is then digitized by a front-end electronics module, and the timing of photodetection and the integrated charge of the signal, which is nearly proportional to the number ofobserved photons, are sent to a computer for data storage. The data from all hit PMTs are sorted
in time order, collected as an event, and stored on disk if one of the trigger conditions described in
the next sections is satisfied.

3.4. Data Acquisition System

39
Table 3.4: Trigger condition for SK.

Trigger type
SLE
LE
HE
SHE
AFT
OD

Trigger condition
N200 34
N200 47
N200 52
N200 60
SHE trigger is issued.
N200 22

Time window (µs)
[ 0.5, +1.0][ 5, +35][ 5, +35][ 5, +35][+35, +535][ 5, +35]

Since the beginning of the SK-IV data-taking period, data acquisition has been upgraded witha new front-end electronics module, QTC-Based Electronics with Ethernet (QBEE). In the SuperKamiokande detector, the event rate is higher at lower energy due to environmental radiation
and random coincidence of PMT dark noise. Therefore, the energy threshold (corresponds to thenumber of hit-PMTs) is determined by the upper limit of the rate handled by the electronics anddata acquisition system. The high-speed data process with QBEE enabled the observation of lowenergy events that could not be recorded with simple hardware triggers. One of the major analyses
that benefited from this update is the SRN search with neutron tagging. A positron and a neutron
are generated through the IBD reaction of an electron antineutrino, in which the background islargely suppressed by detecting a delayed coincidence: the signals of the positron and rays fromthe neutron capture on the nucleus. During the SK-IV phase with ultra-pure water, the neutron is
captured on a proton (hydrogen nucleus) in the water after ⇠200 µs on average and a 2.2 MeV
ray is emitted. It was not possible to observe 2.2 MeV rays with only ⇠6 hit-PMTs because thetrigger threshold could not be lowered. With the introduction of QBEE, all PMT signals, including
PMT dark noise, can be sent from the electronics to the merger PC for event selection later bysoftware.

3.4.2

Trigger System

The data of events are stored if they satisfy one of the conditions set by the trigger. When the
total number of coincidence ID PMT hits within 200 ns, N200 , exceeds a certain threshold, a trigger
is issued, and hit information surrounding the trigger timing is recorded. There are four levels of
primary triggers in SK with di↵erent thresholds: trigger types are super low energy (SLE), lowenergy (LE), high energy (HE), and super high energy (SHE) as summarized in Table 3.4. In
addition to these, the AFT trigger is issued after the SHE trigger without OD since SK-IV after
the upgrade of the electrons as explained in the previous section. Since SK-VI, the AFT trigger isissued after the SHE trigger regardless of whether the OD trigger is issued or not. All PMT signals
are stored for 500 µs after the AFT trigger is issued. These data are used mainly for the detectionof neutron captures as described in this thesis. The time window is the range for taking the dataaround the timing when N200 exceeds the threshold.
For example, the SHE trigger has been used for SRN search. If N200 exceeds 60, the SHE
trigger is issued and opens a 40 µs time window (from 5 µs before to 35 µs after the trigger timing).
Furthermore, the AFT trigger is also issued and data of all PMT signals in a 500 µs time window(from 35 µs to 535 µs after the SHE trigger timing) is stored. For the IBD event (¯⌫e + p ! e+ + n)
by an electron antineutrino, the prompt positron event is searched from SHE-triggered events, andthe delayed neutron capture event is searched from PMT signals in SHE+AFT time window.
For the measurement of the cosmogenic neutron production discussed in Chapter 6 and 7,
neutron capture events are searched for in the time window after a cosmic-ray muon event. The
SHE and OD triggers are issued simultaneously for a cosmic-ray muon event and the AFT trigger
window is opened after the muon event. The neutron capture events are searched in the AFT
window.

40

Chapter 3. Super-Kamiokande
S. Fukuda et al. / Nuclear Instruments and Methods in Physics Research A 501 (2003) 418–462

443

Fig.
22.Schematic
A schematic
view of thewater purification
purification systemsystem. [56].
Figure3.9:
illustrationof water

Waterradon
Purification
Systemremoval efficiency in the vacuum degasifier (VD
d provide 3.5
a possible
source insidethestage which follows.
per-Kamiokande
detector.
The ultra-pure water for the SK detector is produced by purifying groundwater in the Kamioka
A VD
removesdissolved
gases in the water. I
The heat exchanger
is usedcontains
to coolimpurities
the water
toas particulates,
mine. Groundwater
such
metal
ions, bacteria,
and radioactive
consistsof a Cherenkov
cylindricalstainlessduce PMTmaterials.
dark noiselevels,andParticulates,
metal
ions,suppress
and bacteria scatteror absorb
light,
reducingsteel
the vessel and a
3 "1
water
transmittance,andradioactive
materials
dissolved
in
water
can
cause
background
eventsvacuum pump (16 Torr, 410 m h forowth of bacteria, which also reduce water, 11 kW). The
214
222 Rn),neutrino
observations.
In
particular,
bismuth-214(
Bi),
adaughter
nuclideofradon-222(
nsparency. Surviving bacteria are killed by thevessel is 1.4 m in diameter and 4.5 m in height
emits an electron with energies below 3.26 MeV through decay. This is the major backgroundV sterilizersourcestage.
Typical water temperatures
Radon gas dissolved in water is a serious backaround the energy threshold (⇠3.5 MeV) for the SK analysis at MeV scale such as anfore the firstheat exchanger
and afterTherefore,
the second
ground isevent
sourcefor measurement
solar neutrinos in theobservationof solar neutrinos.
water purification
essential
to improve!
!
at exchanger
are 14.2 C and 12.9 C, respectively.
MeV energy range, while dissolved oxygen en
accuracy.
To maintainhighpurity, water
is constantly
throughthe detector
and purified
a water. The
courages
growthof bacteria
in attheA cartridge polisher(CP)eliminates
heavy
ions circulated
flow
rate
of
60
tons/h.
Water
collected
from
the
top
of
the
detectorispurifiedthroughapurifier
typical concentration of the dissolved oxygen after
hich also reduce water transparency and include
and then flows into the detector from the bottom. This purification system suppresses
the radon
the VD is 0.06 mg L "1. The removal efficiency fordioactive species.
The amount of CP resin usedconcentration from 9.1 mBq/m3 to 1.7 mBq/m3 [59] and keep the water attenuation length to be1500 L. ⇠100
Originally,an asion-exchanger(IE) in fromradongas isofestimatedbeisabout96%.
m. However,the purified water flows
the bottom
the detectortoandcollected
lumn wasfrom
includedin written
the water
purification
The causes
ultra afilter
consistsof hollow fiber
the top asabove, thewater circulation system
vertical(UF)asymmetryin waterquality. The
clearer atthat
the bottom
top. This is avoidable
makingconvection particle size
stem. However
it water
was isfoundthe than
IE at themembranefilters. byThe
minimuminthedetector
but
it
mixes
the
Rn
contaminated
water
close
to
the
wall
with
the
water
in thein was a significant radon source and it waswhich the UF can remove corresponds
to molecentral region with lower Rn contamination and eventually increase the background in the fiducial
moved. volume for the analysis. Therefore, water convection cularweight approximately 10,000 (or abouin the detector is intentionally suppressed by
The typicalcontrolling
resistivity
the recirculating
nm diameter).
The typicalnumber of particles
the oftemperature,
flow rate, input
and location 10
of water
supply and drainage.
The temperater (i.e., water
Super-Kamiogreaterthan 0.2
mm in thebefore theture offlowing
the waterfrom
in thethetankis maintained at aboutof14size
C andis constantly
monitored
withwateranaccuracy
of
0.01
C.
This
prevents
water
convection,
suppressthebacteria
growth,
and
keeps
the
nde tank to the water purification system) is
purification system is 1000 particles/cc; this istemperature-dependent
PMT
performancestable.
The
schematicof waterpurification
MO cm. After the CP module the resistivity of
reducedto illustration
6 particles/cc
after
purification.
system is shown in Figure 3.9. The water is purified by the following steps [56].
e water is 18.24 MO cm, approaching the chemiA membrane degasifier (MD) also removes
limit.
radon dissolved in water. It is made of 30 hollow
1. 1 µm mesh filter:
A RO system, and a tank to dissolve Rnfiber membrane modules and a vacuum pump. A
duced air (see following Section) into the water,
flow rate of 30 L min"1 of Rn-reduced air from there installed in March 1999. The RO step
air purification system is supplied to the MD
moves additional particulates. The introduction
system as purge gas. The typical pressure in theinto the cavity dome, as described below. Typicalradon concentration in the dome air is measured
to be 40 Bq m!3.
3.6. Air Purification System

located at the Rn Hut) is fed into the air pump,and is then pumped through a dehumidifier, acarbon filter tank, and finally through a 1.8 km air
41

Fig. 23. A schematic view of the air purification system.

Figure 3.10: Schematic illustration of air purification system [56].
To remove particulates larger than 1 µm.
2. Heat exchanger:
To keep the water temperature at 14 C. The pumps used for water circulation and the PMTs
are the major heat sources in the water.
3. Ion exchanger:
To remove ions (Fe2+ , Ni2+ , Co2+ , CO3 2 , etc.) from water.
4. Ultraviolet sterilizer:
To kill bacteria.
5. Rn-less-air dissolving system:
To improve the efficiency of radon gas removal during purification in a vacuum deaerator,
radon-removed air is dissolved in pure water.
6. Reverse osmosis filter:
To perform filtration using osmosis and remove organic compounds with molecular weights
greater than 1,000.
7. Cartridge ion exchanger:
To removes 99% of ions dissolved in water.
8. Ultra filter:
To remove particulates of a few nm in size.
9. Membrane degasifier:To remove radon and oxygen dissolved in the water.

3.6

Air Purification System

Radon concentrations are higher in the Kamioka mine than outdoors because radon is produced
by uranium in the rock. There is a gap of about 60 cm between the water surface in the detector
and the top cap of the detector. To prevent radon in that air from dissolving into the water, theRn free air is fed into the gap. The schematic illustration of air purification system is shown in
Figure 3.10. The air is purified by the following steps [56].
1. Compressor:
To compress air to 7.0–8.5 bar.
2. Air filter:
To remove dust from compressed air.

42

Chapter 3. Super-Kamiokande

Table 3.5: Thermal neutron capture cross sections for each gadolinium isotope, hydrogen, oxigen,and sulfur [60]. The unit of cross section b corresponds to 10 24 cm2 .
Isotope152 Gd154 Gd155 Gd156 Gd157 Gd158 Gd160 Gd
1H
16 O
32 S

Natural abundance (%)
0.20
2.18
14.80
20.47
15.65
24.84
21.86
99.99
99.76
94.85

Cross section (b)740
85.8
61,1001.81
254,000
2.22
1.42
0.33
0.00020.53

3. Air drier:
To remove water and CO2 in the air to improve the efficiency of radon removal.
4. Carbon column:
To absorb radon using activated carbon.
5. Cooled charcoal:
To absorb radon using activated carbon cooled to

3.7

The SK-Gd Experiment

3.7.1

Gadolinium Loading

60 C.

Gadolinium (Gd) is a rare earth element with atomic number 64. It has the largest thermal neutron
capture cross-section of any natural elements. Table 3.5 shows the thermal neutron capture crosssections for each Gd isotope.
The 157 Gd (155 Gd) captures a neutron and is excited to a resonance state of 158 Gd (156 Gd).
It then transitions to the ground state of 158 Gd (156 Gd) through multiple energy levels, emitting
several rays. Several rays with a total energy of 7.9 MeV are emitted from 157 Gd,⇤

n + 157 Gd ! 158 Gd ! 158 Gd + ’s (7.9 MeV in total),and several(3.4)

rays with a total energy of 8.5 MeV are emitted for 155 Gd,⇤

n + 155 Gd ! 156 Gd ! 156 Gd + ’s (8.5 MeV in total).

(3.5)

When Gd is introduced to water at a mass concentration of 0.01%, ⇠50% of neutrons are captured
on Gd (the right of Figure 3.11) and the remaining 50% is captured on protons (hydrogen nuclei).
Furthermore, the Gd concentration correlates with the time it takes for neutrons to be captured
on Gd, t.
t follows an exponential function exp(t/⌧ ), where ⌧ is called the capture time
constant. Dense Gd concentrations shorten the time it takes for neutrons to be captured on Gd.
The left-hand plot of Figure 3.11 shows the correlation between the capture time constant and theGd mass concentration.
The first Gd loading began on July 14, 2020, and was completed on August 17, 2020. In
this period, 13.2 tons of Gd sulfate octahydrate Gd2 (SO4 )3 · 8H2 O was dissolved in 50 ktons ofwater, resulting in a Gd sulfate mass concentration of 0.026% which corresponds to 0.01% massconcentration of Gd. In order to make the Gd concentration uniform, Gd-loaded water was injectedfrom the bottom of the tank and pure water was drained from the top of the tank, as shown in

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

Capture on Gd nuclei

Capture Time Constant [µs]ciency, 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 Thethe SK-Gd
Gd capture
eﬃciency (right) as a function of Gd mass concentration. These
3.7.
Experiment43
plots 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
0

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

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

Figure 3.11: Correlation between the time constant and Gd mass concentration (left), and between
Figure 6.30: Correlation between the time constant and Gd mass
neutron capture fraction on Gd and Gd mass concentration (right) [51].

concentration (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

2

Day 1

4 3

Day 9

2

4 3

2

4 3

Day 18

2

41.4m

2

2

20.7m

10.4m 0.02 %0.026 %

0.0 %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 tranpure water
sitioned from ANNRI-Gd topure
the water
Photon-Evaporation
model — a pre-installed
model
0.026%
pure water
Gd
(SO
)
∙8H
O
in Geant4. Subsequent MC simulations reveal thatthe energy distribution under the0.026%Gd (SO ) ∙8H O
Photo-Evaporation model deviates
0.026% significantly from that of the original ANNRI-Gd
Gd (SO ) ∙8H O
model, making a discrepancy of 1.7%.
Day 35

Neutron excitedFigurestate3.12:
fraction
Schematic illustration of Gd loading [60].
Figure 3: Gadolinium loading scheme.

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)
before water is returned to the tank [8]. Prior to Gd loading, the water temdetermined according to ISO [45]. By examining potential extreme fractions, theperature in the tank was raised by setting the supply water temperature to13.90 C at Temperature Control Unit B in Fig. 1. Water was recirculated
under these conditions for about 45 days. Afterwards the supply temperature was lowered to 13.55 C to begin the the Gd loading. This createdan additional density difference between the Gd-loaded water and the purewater in the tank beyond that caused by the compound itself. In this way
the spatial profile of the Gd-loaded water could be monitored by measuring

7000

14000

12000

Spallation neutron Gd(n, γ ) candidates
Observed event
Start of Gadolinium injection

6000

10000

(July 14th, 2020 10:54 AM)
End of Gadolinium injection

5000(August 17th, 2020 14:54 PM)
Gd2(SO ) 8H2O

8000

4 3

Target of Gd (SO ) 8H2O
2

4000

4 3

6000

3000
4000

4 3

8000

Added Gd2(SO ) 8H2O [kg]Chapter 3. Super-Kamiokande

Event rate [event/day]

44

2000
2000

1000

0

0

07/05
2020

07/12
2020

07/19
2020

07/26
2020

08/02
2020

08/09
2020

08/16
2020

08/23
2020

Figure 3.13: The time variations of the amount of Gd sulfate octahydrate added to the waterand the event rate of neutron capture events on Gd. The red points represent the event rate ofmuon-induced neutrons captured on Gd, and the blue line represents the amount of Gd sulfate
octahydrate doped in the water.
Figure 3.12. Gd-loaded water supplied at lower temperature than that in the tank so that the purewater was efficiently drained from the top. Figure 3.13 shows the time variations of the amountof Gd sulfate octahydrate added to the water and the event rate of neutron capture events on Gdfor the neutrons induced by the cosmic-ray muon spallation and captured on Gd in the fiducial
volume (the region more than 2 m from the ID wall). The reason for the gap between the start of
Gd loading and the rise of the event rate is that it took time for the Gd sulfate solution to reachthe fiducial volume. Similarly, the reason for the gap between the time when the event rate became
constant and the end of Gd loading is that the Gd sulfate solution filled the fiducial volume at
2 m below the top. Figure 3.14 shows the time variation of the vertex distribution for events thatmuon-induced neutrons are captured on Gd. It was confirmed by the vertex distributions that the
Gd is loaded gradually upward from the bottom.

3.7.2

SK-Gd Water System

In the water circulation system of SK-Gd, the bacteria and particulates removal system used is stillin operation. On the other hand, since it is necessary to circulate water while retaining gadolinium(Gd3+ ) and sulfate (SO24 ) ions, an ion exchange resin was newly developed to remove only ionsother than Gd3+ and SO24 . A schematic illustration of the SK-Gd water system is shown in
Figure 3.15, and the main purification process is described below [60].
1. Gd-dissolving system:
The Gd2 (SO4 )3 · 8H2 O powder delivered by the hopper is weighed and dissolved into waterin a bu↵er tank via a circle feeder. The solution is sent to the solution tank and pretreatment
system.

20

Jul.26, 2020 (Run #085075)

15

z (m)

Jul.19, 2020 (Run #085015)

15

z (m)

20

45
20

10

10

5

5

5

0

0

0

-5

-5

-5

-10

-10

-10

-15

-15

-15

-20
0

-20
0

100

20

150

200

250
R2 (m2)Aug.09, 2020 (Run #085142)

15

50

100

20

150

200

-20
0

250
R2 (m2)

Aug.16, 2020 (Run #085171)

15

z (m)

50

10

10

5

5

0

0

0

-5

-5

-5

-10

-10

-10

-15

-15

-15

-20
0

-20
0

150

200

250
R2 (m2)

50

100

150

200

250
R2 (m2)

100

150

200

250
R2 (m2)

Aug.23, 2020 (Run #085197)

15

5

100

50

20

10

50

Aug.02, 2020 (Run #085110)

15

10

z (m)

z (m)

z (m)

3.7. The SK-Gd Experiment

-20
0

50

100

150

200

250
R2 (m2)

Figure 3.14: Distributions of event vertex where cosmic-ray muon-induced neutrons were captured
on Gd. The horizontal axis represents the square of the detector radius, and the vertical axis
represents the height. From July 19 to August 23, 2020, changes in the event vertex distribution
were checked on a weekly basis.
2. Pretreatment system:
Ions other than Gd3+ and SO24 are removed by a cation exchange resin inert to Gd3+ and ananion exchange resin inert to SO24 , and an ultraviolet total organic carbon reduction lamp
(TOC lamp) decomposes organic impurities. As in the purification system for pure water,
ultraviolet radiation and ultrafilters are also used in the pretreatment section to kill bacteria
and remove microscopic dust particles.
3. Purification system:
After merging with pure water, the gadolinium sulfate solution is purified by the TOC lamps,
heat-exchange units (HE), ion exchange resins, ultraviolet sterilizer, and ultrafiltration modules (UF). These units are arranged in two parallel systems, circulating at 60 m3 /h each fora total flow rate of 120 m3 /h.
In the Gd loading process, pure water was drained from the top of the detector to the dissolution
device to dissolve Gd3+ and SO24 , which was then introduced into the detector from the bottom. In
this process, the water temperature inside the detector was raised by about 0.3 C higher than thatof the Gd-loaded water introduced from the bottom so that the Gd-loaded water was introducedby piling up from the bottom of the detector as explained Section 3.7.1. That situation is shownin Figure 3.12, 3.13, and 3.14.

46

Chapter 3. Super-Kamiokande

Gd2 (SO4)3 8H2O

Dissolving system
Weighing hopper
Circle feeder

Solution tank Dissolving Solvent tank
tank

2400L

0.2 m

2400L

Shear blender

1 m
1 m Dissolving system bypass line
C-Ex
A-Ex
TOC
UV
Resin Resin

Pretreatment system

Returnwater ﬁlter

Main return line

1st buﬀer tank

2400L

4600L

C-Ex A-ExUVResinResin
1 m

Pump

2nd buﬀer tank Temp. control

unit A

UF

Supply HE
pump

4600L

2400L

TOC HETOC HE C-Ex A-Ex 1 m UVResin Resin

Temp. control
unit BMD
SK tankUFHEbottomRe-circulation system

Returnpumps

Figure 3.15: Schematic illustration of SK-Gd water system [60].
Figure 1: Schematic diagram of SK-Gd water system.

To remove positively charged impurities, and radium ions in particular, astrongly acidic cation exchange resin, AMBERJET™1020 [6] (“C-Ex Resin”
in Fig. 1) is used. For the SK-Gd water system, this resin has been modified
to contain gadolinium as the ion exchange group such that the resin’s cationexchange action never results in a loss of dissolved Gd content; Gd2 (SO4 )3 ·7

Chapter 4

Detector Calibration
This chapter describes the calibration method for the Super-Kamiokande (SK) detector. The SK
detector is filled with 50 kton of gadolinium-loaded water and 11,129 20-inch PMTs are mounted on
the inner wall. In order to realize the precise measurement with stable conditions, it is important tounderstand the detector response and monitor it from time to time by the detector calibration. The
target of the calibration includes the fundamental properties such as the characteristics of PMTs
and the individual di↵erence, absorption, and scattering of photons in water, as well as the physics
measurement such as the energy scale and neutron detection. Monte Carlo (MC) simulation isdeveloped based on the measurement by the calibration with some corrections to reproduce thetime variations of the observed data.

4.1

PMT Calibration

In the SK detector, Cherenkov photons emitted by charged particles are observed by PMTs mounted
on the wall, and the number of photons and the detected time are used for the data analysis. Threecalibration methods are described in this section: the calibration of the quantum efficiency, which isthe probability that an incident photon is converted into a photoelectron at the PMT photocathode,the gain, which is the amplification rate of photoelectrons at the PMT, and the time to acquire thesignal.

4.1.1

Quantum Efficiency

As explained in Section 3.3.2, a photon incident on the photocathode of a PMT excites electrons andemits photoelectrons due to the photoelectric e↵ect. The probability that a photon is converted
into a photoelectron is called the quantum efficiency (QE) which is typically ⇠20%. There areindividual di↵erences in the QE of PMTs attached to the inner detector (ID), which can be a sourceof systematic uncertainty in the energy reconstruction. Therefore, it is necessary to accurately
measure the QE of individual PMTs.
The NiCf source (Figure 4.1) is used to measure the QE. The NiCf source is a ray source that
contains californium-252 (252 Cf), a neutron source, in a spherical polyethylene resin mixed withnickel oxide (NiO) powder. Californium is an actinide element with atomic number 98, and 252 Cf
is one of its isotopes. The 252 Cf has the half-life of 2.65 years, and it decays with emission of an ↵particle at a branching ratio of 96.9% or by spontaneous fission with a probability of 3.1%. During
spontaneous fission, an average of 3.76 neutrons with the energies of ⇠2 MeV and an average of
10.8 rays with a total energy of 8.2 MeV are emitted. The intensity of the Cf source currently
used in SK is 0.3 MBq.
The neutrons emitted by spontaneous fission lose energy through elastic scattering with protons
in the polyethylene and be thermalized. The thermalized neutrons are captured by the Ni nucleus
and a ray with 6–9 MeV is emitted. Because the source is spherical, rays are emitted isotropi47

48

Chapter 4. Detector Calibration

16 cm

NiO
Neutron
252Cf

Figure 4.1: Schematic illustration of the NiCf source.
cally. The emitted rays produce or scatter electrons in water and the photons are emitted fromCherenkov radiation. Since the amount of light is not large and only zero or one photon incident
on each PMT in most cases, the NiCf source is suitable for measuring QE.
The hit rate for each PMT is calculated for both the data and the MC simulation, and the ratio
is taken to obtain the value of the relative QE for each PMT. Figure 4.2 summarizes the PMT
hit rates for each PMT location (barrel, top, and bottom of the detector). In order to suppress
the positional dependence of water quality, the water condition is made uniform in the detector
by convecting the water in the detector, and the data is acquired by measurement using a NiCf
source placed near the center of the detector. MC simulations are generated assuming that QE of
all PMTs are equal. The obtained relative QE of each PMT are stored as a “QE table” and used
for energy reconstruction.

4.1.2

PMT Gain

When a photon is incident on the photocathode of a PMT, photoelectrons are emitted by thephotoelectric e↵ect. The photoelectrons are accelerated by the electric field applied inside the
PMT, and several secondary electrons are emitted when they hit the dynode. After photoelectrons
are amplified by multiple dynodes, they are extracted as electrical signals. The amplification factor
for a single photoelectron is called gain. The expected value of the output charge is expressed as:
Qi = Ni ⇥ QEi ⇥ Gi ,(4.1)

where Qi represents the output charge and the unit is pC. Ni represents the number of incident
photons to the i-th PMT, QEi represents the quantum efficiency, and Gi is the gain of the i-th
PMT. Therefore, the unit of the gain Gi is pC/p.e. Gi is defined in SK by two components of theabsolute gain Gabs and the relative gain Grel,i :Gi ⌘ Gabs ⇥ Grel,i .

(4.2)

The absolute gain Gabs was determined from average of output charge distribution for single photoelectron to be 2.46 pC/p.e. using the NiCf calibration. Grel,i is a relative gain of each PMT
measured using an N2 laser. The ratio of the amount of charge Qi to the number of photoelectrons
Ni observed at the i-th PMT is proportional to Grel,i because Qi / QEi ⇥ Grel,i and Ni / QEi :Grel,i /

Qi
Ni

(4.3)

4.1. PMT Calibration49

Hit rate

1.3
1.2

Data
MC

1.1
1
0.9
0.8
0.7

-1500

-1000

-500

0

500

1500

z (cm)

1.3

Hit rate

Hit rate

1.3

1.2

1.2
1.1

1.1

1

1

0.9

0.9

0.8

0.8

0.7
0

1000

×103
500 1000 1500 2000 2500 3000

R2 (cm2)

0.7
0

×103
500 1000 1500 2000 2500 3000

R2 (cm2)

Figure 4.2: Positional dependence of PMT hit rate for the barrel (top), the top (bottom left),
and the bottom (bottom right). For the top figure, the horizontal axis shows height (z). For thebottom two figures, the horizontal axes show the radius squared (R2 = x2 + y 2 ). The black and red
point shows the data and MC, respectively. The plots are normalized so that the hit rate averages
one overall the detector. The larger PMT hit rate at the edge of the detector, where |z| and R2
are large, is due to the e↵ect of reflection.

50

Chapter 4. Detector Calibration

Time

ThresholdLow charge signal
High charge signal

Figure 4.3: Schematic illustration of time-walk.
Since Grel,i is a relative value, it is normalized so that the average is one. The observed charge
in each PMT is converted into the number of photoelectrons (equivalent to number of detected
photons) from Grel,i and Gabs obtained above.

4.1.3

Timing Calibration

For low-energy events below several tens of MeV, it is assumed that at most one photon is detectedby each PMT, and the reconstruction for the event vertex is performed using the information of
the signal detection time by hit-PMTs. Assuming that all photons are emitted from a single vertex
at the same time, the time di↵erence of the time t at which the signal from each PMT is detected
and the time of flight ttof of the photon to reach the PMT, t ttof are ideally identical for all
hit-PMTs. The purpose of timing calibration is to correct for the variations of each PMT due todi↵erences in cable lengths and the response of the electronic device.. In addition, a signal witha large amount of charge has a higher pulse, resulting in a faster signal rise compared to a signal
with a smaller amount of charge. This is called “time-walk” and shown in Figure 4.3. Therefore,
the time to read out the signal depends on the amount of the charge. To correct for this e↵ects,
the correlations between time and charge for all PMTs are measured beforehand using an N2 laser
with a short pulse width and stored in the database (called “TQ-map”). The correction is applied
from the TQ-map to the detection time for the time shift. Figure 4.4 shows an example of TQ-map
for a PMT. The TQ-map are prepared for all 11,129 PMTs.

4.2

Measurement of Water Transparency

4.2.1

Laser Calibration

The intensity of the light attenuates exponentially with the distance traveled in the water as:✓◆rI( ) = I0 ( ) exp
,
(4.4)
L( )
where is wavelength of light, I0 ( ) is initial value of light intensity, r is light travel distance,and L( ) is an attenuation length in water. As light travels through water, it is either absorbed
or scattered. Scattering e↵ects can be divided into symmetric scattering (Rayleigh scatteringand symmetric Mie scattering) and asymmetric scattering (forward Mie scattering). The water
attenuation length L( ) in the MC simulation is introduced with those contributions as:
L( ) =

1↵abs ( ) + ↵sca,sym ( ) + ↵sca,asy ( )

,

(4.5)

where ↵abs ( ), ↵sca,sym ( ), and ↵sca,asy ( ) are water quality parameters representing absorption,
symmetric scattering, and asymmetric scattering, respectively. These parameters are determinedby laser calibration.

timing versus pulse height (charge), correlation tables that are called “TQ distributions”. Figure 22 shows a typical scatter plot of the TQ distribution for one readout channel. The calibration
constants, called the “TQ-map”, are derived by fitting the TQ distribution to polynomial functions.
A TQ-map includes
process time and the time-walk effect; each readout channel
4.2. Measurementof Wateroverall
Transparency
51
has its own TQ-map.

T (ns)

tqmap of cable # 00010
3102

0 1 2 3 4 5 6 7 8 9 10
1230

10

Q (p.C.)
1.0
0.9

1220

0.8
0.7

1210

0.6
1200

0.5
0.4

1190

0.3

Entries 561679
1180

0.2
0.1

1170
0

20

40

60

80

100

120

140

160

180

0.0

QBin

Figure22:4.4:
Typical
TQ distribution
for a readout
channel.The
Theverticalhorizontalaxis
axiscorresponds
is charge (Qbin)
eachhit, and theverticalFigureExampleof TQ-map
for a PMT.
toofthedetection
time
of
axis
is
time-of-flight-corrected
timing
(T)
of
the
hits.
Larger(smaller)Tcorresponds
toearlier(later)
hits
in
this
figure.
the signal, with a larger value indicating a faster detection time. The horizontal axis corresponds

to the detected charge.

In the laser event selection, we require that the monitor PMT is fired. The fired timing defines
The PMTtiming
hit ratesin various
wavelength
using
laser dinodewith wavethe referenceof arethe monitored
laser flashed.
For laser
events, regions
we applya timing
correction,
calledlengths
of
337,
375,
405,
445,
and
473
nm.
The
measurement
flow
is
as
follows.
time-of-flight (TOF) correction, that subtracts time of flight from the diffuser ball to the respective PMT position using group velocity of light with the measured wavelength, 398 nm. Using
1. To measure the e↵ect of scattering at di↵erent angles, the inner wall of the detector is divided
26 regions (Figure 4.5).
into six regions: one top and five side (B1–B5)
2. For each PMT in each region, the number of hit PMTs (Nhit ) and the total observed photoelectrons (Qtot ) are measured, and the ratio (Nhit /Qtot ) is obtained.
3. MC simulations corresponding to this measurement are generated while varying water quality
parameters and the Nhit /Qtot values are compared to the data.
4. Water quality parameters are determined to reproduce the data by minimum
minimizing the di↵erence between the data and MC.

2 method, i.e.

From the above measurements, the water quality parameters ↵abs ( ), ↵sca,sym ( ), and ↵sca,asy ( )were obtained as a function of light wavelength as follows:↵abs ( ) =

8
✓
P
>
>
<P0 ⇥ 41 + P0 ⇥ P2 ⇥

500

>
>
:P0 ⇥ P1 + Popefry( )

◆P 3

4

↵sca,sym ( ) =

P4
4

✓

⇥ 1.0 +✓

↵sca,asy ( ) = P6 ⇥ 1.0 +

P5
2

P7
4

◆

⇥(

P8 )

( 

thr )

( >

thr )

(4.6)

(4.7)
2

◆

.

(4.8)

The additional function Popefry( ) of ↵abs ( ) for > thr is defined by the absorption coefficient
calculated theoretically by R. M. Pope and E. S. Fry [61].

52

Chapter 4. Detector Calibration

LASER

337, 375,
405, 445,
473 nmB1
B2
B3

Scattering

B4
B5

Figure 4.5: Schematic illustration of the laser calibration for measuring water quality parameters.
The blue arrows indicate the position of the laser incidence.
0.004
0.003
0.002
0.001

Top cap

1500
0.004
0.003
0.002
0.001

1600

1500
0.004
0.003
0.002
0.001

1600

1500
0.004
0.003
0.002
0.001

1600

1500
0.004
0.003
0.002
0.001

1600

1500
0.004
0.003
0.002
0.001

1600

1500

1600

1700

1800

1900

B1
1700

1800

1900

B2
1700

1800

1900

B3
1700

1800

1900

B4
1700

1800

1900

B5
1700

1800

1900

Time (ns)Figure 27: Typical TOF-subtracted (see text) timing distributions for the vertical down-going laser beam with the
Figureat4.6:
Time
distribution
theandratio
numbertheofbest
hittune)
PMTs
Nhit tototaltotal
chargewavelength
405 nmbetweendata (black of
circle)MC of(redthehistogram,normalized
by theobserved
Q[58].
Distributions
are
shown
in
order
from
top
to
bottom.
Thehorizontal
axis
is
the
time
tot
photoelectrons.
The top plot is for the PMTs at the SK tank top wall. The second to bottom plots correspond to the five that
thePMT
detects
thetolight
after
subtractionof the timeof26.
flightthelight,
in ns.theThebarrelwall
regionsfrom topbottomof theSK tank as indicatedin Fig.
The oftime
regionbetweenleftvertical
two blue axis
solidisverticallines N
ishit
usedabsorption
and scattering
described
in thisSection
3.2.1 and
theMC
rightsimulations.
region is
the ratio/Qtototmeasure. Blackthecircles
represent
the data
and redlines
represent
theusedThefor themeasurement
reflection
describedsidein Section
3.2.2.
gradualpeaksofon
the left-handare due
to hits from light scattered in water. The peak on

the right-hand side is derived from light reflected at the bottom of the detector.

where l is the travel length of the light, I0 ( ) is the initial intensity, I( ) is the intensity at l,and L( ) is the total attenuation length caused by scattering and absorption, which we call watertransparency. L( ) is defined in the SK-MC as follows:14.3. Energy Calibration

53

Inverse water transparency (1/m)

10-1
Total

Absorption

Symmetric

Asymmetric

10-2

10-3

10-4
300

325

350

375

400

425

450

475

500

Wavelength (nm)FigureTypicalfitted water dependencecoefficient functions
usedquality
in the SK-MC.
The points
the data
obtained
April 2009.
Figure28:4.7:
Wavelengthof waterparameters[58]. areRed
dashedline inshows
Thethroughthelinepointsfor absorption,
scattering andasymmetric scatteringshow↵thefittedfunctions↵abseach( ),lines
blue
dottedshows↵sca,sym (symmetric), and magenta
dashed-dottedline shows
sca,asy ( ),
while
the
top
line
shows
the
total
of
all
fittedfunctions
addedtogether.
respectively.

4.2.2

Top-Bottom Asymmetry of Water Quality

The top-bottom asymmetry of the water transmission in the SK detector is also measured by the
hit rates with the NiCf source. As described in Section 3.5, it has been confirmed that there is avertical asymmetry in the transmittance of the water in the SK detector due to the water circulation
system. Top-bottom asymmetry is defined using the average PMT hit rate Rtop on the top cap, theaverage PMT hit rate Rbot on the bottom cap, and the average PMT hit rate Rbar on the barrel.
↵TBA =

Rtop Rbot⇥ 100 (%)
Rbar

(4.9)

32

Figure 4.8 shows the time variation of ↵TBA measured using the NiCf source from December 2008
to September 2022.

4.3

Energy Calibration

In the SK experiment, the energy is calibrated using the linear accelerator (LINAC) and DeuteriumTritium neutron (DT) generator. Below O(10) MeV, the total energy of the charged particle isreconstructed using the e↵ective number of hit PMTs, Ne↵ , corrected for the light attenuation,
acceptance anf the other e↵ects (see Chapter 5).

4.3.1

LINAC

The LINAC is located around the top of the SK tank as shown in Figure 4.9 and used to injecta mono-energetic electron with 5–18 MeV downward into the detector from various positions. Theenergy of the injected electrons is measured beforehand with an accuracy within ±20 keV by agermanium detector. The absolute value of the energy scale is calibrated by a comparison of
the reconstructed Ne↵ value and the energy of the injected electron. The resulting function is545.4Pure-water00.01wt% Gd

Data

Gd loading

Simulation

Refurbishment

Difference (Data - Simulation)
Refurbishment

Gd loading−1−2
TBA [%]

51
Chapter 4. Detector Calibration্ԼඇରশੑΛද͢ύϥϝʔλͷ࣌ؒมಈ

0.03wt% Gd

−3
−4
−5
−6
−7

Difference [%]

3
2
1
0
−1
12/31
2008

12/31
2010

12/31
2012

12/31
2014

12/31
2016

12/31
2018

12/31
2020

12/31
2022

ਤ 5.7: ্ஈ͸ 2008 ೥ 12 ݄͔Β 2022 ೥ 9 ݄·Ͱʹ Ni-Cf ઢ‫ݯ‬Λ༻͍ͯଌఆ͞Εͨ T BA ͷ࣌ؒมಈɻ੺఺͕࣮

Figure 4.8: Time variation of top-bottom asymmetry measured using the NiCf source from Deࡍʹଌఆ͞Εͨ T BAɺ੨఺͕γϛϡϨʔγϣϯ͔Β‫ٻ‬ΊΒΕͨ T BA Λද͢ɻԼஈ͸σʔλͱγϛϡϨʔγϣϯ
cember2008 to September 2022. The red and blue triangle show the TBA value of the data andͷ
TBA
the MC, ͷࠩΛࣔ͢ɻೱ͍փ৭ͷઢ͸‫ݕ‬ग़‫ث‬ͷվम‫ؒظ‬ɺബ͍փ৭ͷઢ͸‫ݕ‬ग़‫ث‬தʹΨυϦχ΢ϜΛಋೖ͍ͯͨ͠
respectively. The blue open circle shows the di↵erence between the data and the MC.
࣌‫ظ‬ɺ఺ઢ͸‫ݕ‬ग़‫ث‬શମͰରྲྀΛ‫ͯ͜͠ى‬ਫͷಁա཰ͷ্ԼඇରশੑΛখͨ࣌͘͞͠‫ظ‬Λද͢ɻThe
vertical dashed line shows the convection period to suppress TBA. This figure is taken from
Ref. [62].
described in Section 5.2. The data obtained from the LINAC calibrations at several positionsin the SK detector are compared with the corresponding MC simulations to check the position
純水
Gd濃度 0.01%
Gd濃度 0.03%
dependence of the energy scale and evaluate the systematic uncertainties.
0-1

4.3.2-2 DT Generator

Data

Gd loading

Simulation

Refurbishment

Difference [%]TBA [%]-3
The energy
scale determined by LINAC is verified using the DT generator which produces electrons-4
isotropicallyemitted from decay of 16 N. Since electrons are produced isotropically by the DT-5generator,
unlike the LINAC which injected electrons only downward, it is possible to check the-6
directional
dependence of the energy reconstruction.
DT- 7 generator is a neutron source that emits neutrons from helium and deuterium in the following3 reaction:
Difference (Data - Simulation)
Gd loading
3
4
2
He + 2 H ! Refurbishment
He + n(4.10)
1

The neutron
has an energy of 14.2 MeV, which are captured by 16 O in the water, in addition to0-1hydrogenand Gd, and subsequently 16 N and a proton are produced.
12/31
2018

07/02
2019

01/01
2020

07/01

16 2020

12/31
2020

O + n ! 16 N + p

07/01
2021

12/31
2021

07/02
2022

12/31
2022

(4.11)

ਤ 5.8: ্ஈ͸‫ݕ‬ग़‫ث‬վम‫ޙ‬ͷ 2019 ೥ 1 ݄͔Β 2022 ೥ 9 ݄·Ͱʹ Ni-Cf ઢ‫ݯ‬Λ༻͍ͯଌఆ͞Εͨ T BA ͷ࣌ؒม

16 N has the lifetime of 10.3 s and it emits an electron (< 4.3 MeV) andThe(6.1 MeV) at theಈʢਤ 5.7 ͷ 2019 ೥Ҏ߱Λ֦େͨ͠΋ͷʣɻ੺఺͕࣮ࡍʹଌఆ͞Εͨ T BAɺ੨఺͕γϛϡϨʔγϣϯ͔Β‫ٻ‬ΊΒbranching ratio of 66% or only an electron (< 10.4 MeV) at 28%:

Εͨ T BA Λද͢ɻԼஈ͸σʔλͱγϛϡϨʔγϣϯͷ T BA ͷࠩΛࣔ͢ɻೱ͍փ৭ͷઢ͸‫ݕ‬ग़‫ث‬ͷվम‫ؒظ‬ɺബ

16͍փ৭ͷઢ͸‫ݕ‬ग़‫ث‬தʹΨυϦχ΢ϜΛಋೖ͍ͯͨ࣌͠‫ظ‬ɺ఺ઢ͸‫ݕ‬ग़‫ث‬શମͰରྲྀΛ‫ͯ͜͠ى‬ਫͷಁա཰ͷ্Լ
N ! 16 O + e + ⌫e
(4.12)

ඇରশੑΛখͨ࣌͘͞͠‫ظ‬Λද͢ɻ

The DT generator is not suitable for calibration of the absolute energy scales, but the systematic
uncertainty on the directional dependence of the energy reconstruction can be estimated using theisotropic emission of decay electrons and rays. The procedure of DT calibration is shown below
and also illustrated in Figure 4.10:
1. The DT generator attached is submerged in the water in the detector using a crane. When the
DT generator reaches a predetermined position, it stops and the DT generator is activated.
2. The DT generator produces ⇠ 3 ⇥ 106 neutrons. About 1% of these neutrons are captured
by 16 O, which undergoes the reaction described above to produce 16 N.

4.4. Measurement of Gadolinium Concentration

55

MagnetMagnetMagnetSK

LINAC
Beam pipez = +12 m

①

④

⑦

z=0m

②

⑤

⑧

③

⑥

⑨

z = -12 mzx

Fiducial volume: 22.5 kton

x = -12 m, -8 m, -4 m
Figure 4.9: Schematic illustration of LINAC calibration.
3. To avoid shadowing of the DT generator itself, the DT generator was pulled up by 2 m. The
data of electrons and rays generated by the decay of 16 N are then acquired.

4.4

Measurement of Gadolinium Concentration

In August 2020, the dissolution of gadolinium sulfate octahydrate Gd2 (SO4 )3 · 8H2 O into the ultrapure water in the SK detector was completed and the SK-Gd experiment has been started. The
Gd mass concentration in the water was 0.01% from August 2020 to May 2022 (SK-VI) and wasincreased to 0.03% from July 2022 (SK-VII). In order to ensure Gd is dissolved in water without
unexpected chemical reactions, it is necessary to periodically measure the Gd concentration in thedetector. For this purpose, measurement of Gd concentration is conducted about once every a few
weeks using the Americium/Beryllium (Am/Be) source.
A neutron and a ray are emitted from an Am/Be source through the following reactions:
241
9

Am !

237

Np + ↵(4.13)

12

⇤

C +n

(4.14)⇤

12C+(4.15)Be + ↵ !
12

C!

(4.4 MeV).

As shown in Figure 4.11, the Am/Be source is surrounded by eight BGO scintillators. The calibration source is submerged in water in the detector for 30 minutes and the data is acquired. Oncea 4.4 MeV ray is generated by the AmBe source, it produces electrons in the BGO scintillator
through interactions such as photoelectric absorption, Compton scattering, and electron pair production. Then, scintillation light is emitted as the electrons pass through the BGO scintillator. This
process occurs on a time scale of ns. Since it takes ⇠100 µs for neutrons to be thermalized in waterand captured on Gd or hydrogen, the neutron capture event occurs after the scintillation emission.

56

Chapter 4. Detector Calibration

(a)

(b)

(c)

E n=14.2 MeV
16

O(n,p)16 N

2m
n
n
n

n
n

16

N

n

Figure4.10: data
Schematic
illustration
DT DTG
calibration.
Fig. 2. An overview
of DTGtaking.
In (a),ofthe
is lowered to the position where data is to be taken, The DTG is fired in (b) at that location, and (c)withdrawn 2 meters and data collected.
16

O + µ ! 16 N +µ.

A fraction of 16 N created will be in the ground state, and beta decays witha 7.13 sec half life. These events are found by collecting events that occur inthe area surrounding the stopping point of a captured muon and subtracting
random background events.
The expected rate of 16 N events from muon capture per day in the inner 11.5
kton fiducial volume is given by
Nev = Nstopmu ( µ+µ+µ )fcapture fgs ,where:
4.11: isAm/Be
sourceofand
BGO scintillators.
The cylindricalin the volume
center on per
the•FigureNstopmuthe rate
stopping
muons foundin the source
11.5 kton
left is the AmBe source. The source is surrounded by BGO scintillators. One of the eight pieces isday. This rate is measured using the same stopping muon fitter that is usedshown on the right.
in the search for 16 N events and is found to be 2530 ± 60(stat. + sys.) perday.
• ( µ+µ+µ ) is the fraction of events that are µ , taken to be 0.44 ± 0.01[19].
• fcapture is the fraction of µ that are captured on 16 O before decaying, andis determined by the known capture and decay rates[20,21] to be 18.39% ±0.01%.
• fgs is the fraction of captures that results in the formation of 16 N in the

Events

4.4. Measurement of Gadolinium Concentration

57

900
800

Data

700

Fit result

600
500
400
300
200
100
0
0

100

200

300

400

500

∆t (µs)Figure 4.12: The distribution of the time di↵erence t between the prompt and delayed events.
The points are the data and the solid line is the fit result with Eq. 4.16.
The scintillation signal is called the prompt signal and the following neutron capture signal is called
the delayed signal. The neutrons are identified by delayed coincidence measurement.
When the 4.4 MeV
rays lose all their energy inside the BGO, a scintillation emission of⇠1,000 p.e. is detected (amount of scintillation light emission is larger than Cherenkov light emission
for the same energy deposition by approximately one order of magnitude). This is sufficient tosatisfy the SHE trigger (>60 ID hit-PMTs within 200 ns time window) to be issued. Once an SHE
trigger is issued, all PMT hit information is stored up to the following 535 µs, and the delayed
signal is searched in the time window. The time constant of neutron capture on Gd is determinedby the time di↵erence between the prompt and delayed signals, and the Gd concentration in thewater is indirectly measured using the correlation between the capture time constant and the Gdconcentration (Figure 3.11).
Figure 4.12 shows the distribution of the time di↵erence t between the prompt and delayed
events. The t distribution is fitted by the following function:
✓
✓
◆◆
✓
◆
t
t
f ( t) = a 1 exp
exp+ b.
(4.16)⌧th⌧
The fit determines a, b, and ⌧ , where a and b are normalization constants corresponding to thenumber of signal and background events, respectively, and ⌧ is the capture time constant on Gd.
⌧th represents the thermalization time constant, which is set to 4.3 µs [60]. Figure 4.13 shows
the neutron capture time constants obtained from the Am/Be source calibrations performed in thelatter half of 2020, as an example. The average of ⌧ measured by the Am/Be source is 116.5±0.2 µs
overall the observation period with the Gd mass concentration of 0.01% (SK-VI).

Chapter 4. Detector Calibration

Capture Time Constant [µs]

58

200

Z: 0m
180

Z: +12m160

Z: −12m

140

Neutron capture time constant in pure water
202.6±3.7µs

120
100 26/Jul/20 09/Aug/20 23/Aug/20 06/Sep/20 20/Sep/20 04/Oct/20 18/Oct/20 01/Nov/20 15/Nov/20
Measurement Date

Figure4.13:14:The
time constantsfrom in
theSK
Am/Be
FigureTheneutron
history captureof the neutron
capture obtained
time constantin thesource
latter calibrations
half of2020, obtained
fromhalf
theofanalysisof Am/Be source data. All data were taken using aperformed
in the latter2020 [60].
calibration port near the detector’s center in the X-Y plane (X= 3.9 m, Y= 0.7 m).
Three positions along the Z-coordinate were selected for periodic measurement: Z=0 m(red circles), Z=+12 m (blue squares) and Z= 12 m (magenta triangles). The shaded
area at the top of the plot indicates the neutron capture time constant in pure water[20]. Though the July 29 and August 5 data points at Z=+12 m are out of range (toohigh), they are nevertheless consistent with the pure water shaded region within about
one sigma.

versities and Innovation (grant PGC2018-099388-B-I00), the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Scinet andWestgrid consortia of Compute Canada, the National Science Centre, Poland(2015/18/E/ST2/00758), the Science and Technology Facilities Council (STFC)
and GridPPP, UK, the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement
no.754496, H2020-MSCA-RISE-2018 JENNIFER2 grant agreement no.822070,
and H2020-MSCA-RISE-2019 SK2HK grant agreement no. 872549.

Chapter 5

Event Reconstruction
As shown in Chapter 6, 7, and 8, the signal and background are identified by the distance between
the muon track and the vertex of neutron capture and electron events. This chapter will describe theoverview of the algorithm to reconstruct the MeV scale events and muon events. Vertex positions
and muon track are reconstructed from the signal (integral charge proportional to light intensity
and timing information) of each PMT detected by Super-Kamiokande.

5.1

Vertex and Direction Reconstruction

Figure 5.1 shows the event displays of the Super-Kamiokande (SK) detector for electrons with thereconstructed energies of 16 MeV and 310 MeV for example. No clear rings can be seen at the
MeV scale energies. As a guide, at 10 MeV electrons, the signal is detected in ⇠60 PMTs. In mostPMTs, a single photon (actually a single electron produced by the photoelectric e↵ect of a single
photon) is detected. Hereafter, the signal generated when a single photon is detected at a PMT isreferred to as 1 p.e.
The reconstruction is performed by an algorithm called BONSAI (Branch Optimization Navigating Successive Annealing Iterations) [63]. In the vertex reconstruction of the low-energy region(typically between a few MeV to a few tens of MeV in SK), the trajectory of a charged particle isassumed to be a point, i.e. all Cherenkov photons are emitted from a point source. An electron withenergy of 20 MeV can travel a distance of about 10 cm in pure water, which is small enough for thesize of the detector (about 40 m), so this assumption is valid for the MeV scale. Among the many
PMTs placed in the detector, the PMT that detects photons is called the “hit-PMT”. The time
information of the hit-PMTs is used to reconstruct the event vertex position. For each hit-PMT,
the residual time t ttof t0 is defined. where t is the time when the photon was detected at the
PMT (hit time), ttof is the time it took for the photon to reach the hit-PMT from the event vertex
position (the subscript “tof” represents “time of flight”.), and t0 is the time when the Cherenkov
light is emitted from the charged particle in the detector. Using this residual time, the likelihood
function L(x, t0 ) is defined for each position x of the event candidate as
L(x, t0 ) =

N
hit
X

ln P (tittof,i

t0 ),

(5.1)

i=1

where P (ti ttof,i t0 ) is the probability density function of the residual time determined fromthe LINAC calibration (see Chapter 4), as shown in Figure 5.2. The likelihood function L(x, t0 )is calculated at each point in the detector as x is changed, and the location with the largest value
is determined as the reconstructed vertex position. The number of emitted Cherenkov photons
depends on the energy of the generated charged particles, and the total number of hit-PMTs
changes. Therefore the accuracy of the event reconstruction depends on the energy. Figure 5.3
shows the energy dependence of the vertex resolution in event reconstruction. The vertex resolution
59

60

Chapter 5. Event Reconstruction

Super-Kamiokande VI

Super-Kamiokande IV

Run 86138 Sub 1 Ev 138

Run 77902 Sub 538 Ev 548735717

21-08-05:15:17:18

18-05-04:21:46:41

Inner: 184 hits, 265 pe

Inner: 1335 hits, 3016 pe

Outer: 0 hits, 0 pe

Outer: 5 hits, 6 pe
Trigger: 0x10000007

Trigger: 0x03

D_wall: 488.8 cm

D_wall: 485.0 cm
Evis:

Evis: 310.2 MeV

0.0 MeV

Solar: E= 15.59 MeV

e-like, p = 310.2 MeV/ccos(sun)= 0.807

Solar: gdn= 0.68 dirks= 0.16

Charge(pe)Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
25

360

20

288

15

216

10

144

5

0 mu-e0 decays

72

0

0
0

500

1000

1500

2000

0

Times (ns)

500

1000

1500

2000

Times (ns)ln P(t − ttof − t0)

Figure 5.1: Event displays of the Super-Kamiokande detector for electrons with reconstructedenergies of 15.6 MeV (left) and 310 MeV (right) for the data. The center developed view shows theinner detector and the upper right shows the outer detetor. The color points shows PMTs and thecolor scale represents the total number of detected photoelectrons by each PMT. The light green
rings in the event displays are the reconstructed rings.

0

50

100

150

200
250
t − ttof − t0 (ns)Figure 5.2: Probability density function of the residual time used to reconstruct the event vertex
position. The second and third peaks are those seen due to the PMT afterpulses.

CHAPTER 4. SUPER-KAMIOKANDE

51

Vertex Resolution (cm)5.1. Vertex and Direction Reconstruction

61

250
SK-IV

200
150
100
50
0

5

7.5
10
12.5
15
True Electron Energy (MeV)

Figure 5.3: Vertex resolution as a function of total energy of an electron. This figure is taken from

FigureRef.
4.13:[64].Vertex resolution as a function of electron energy in SK-IV. The figure is takenfrom Ref. [81].
(1 ) is defined as the range of distances between the true and reconstructed vertex that includes
68.3% of the true event vertex position (Figure 5.4). The resolution decreases with the energy ofelectron from ⇠130 cm at 4 MeV to less than 60 cm above 10 MeV.
N20
X

cos i
As the next step, direction
particleis reconstructed.
The Cherenkov light ringL(d)of=the charged
log f (cos,i , E) ⇥pattern is used for direction reconstruction as the center of theringcorresponds
to the direction
a(
)
i
i=1
of the charged particle. The maximum likelihood method is used to determine the direction. The
likelihood function is defined as(4.3)

where N20 is the number of hit PMTs within a 20 ns timing window around t ttof t0 = 0,
✓ expected distribution◆
N20
d is the event direction, f (cos i , E) isX
theof the opening angle betweencos ✓i
L(d) observed=
ln fdirection(cos ⇥i , E) ⇥,(5.2)
the true event direction and thewhere
F (✓i ) E is the event energy, i is thei=1
reconstructed event direction, and a( i ) is the correction for the PMT acceptance. The angularresolution is 25 for the 10 MeV electrons.
where d is the direction of the charged particle and N20 is the number of hit-PMTs that detectedWithreconstructed event vertex and direction, two parameters which are used in the analysis
the photon within 20 ns around the time of the event. f (cos ⇥i , E) is the distribution function of
are defined,
and effwall:
dwall
represents
the distancefrom thevertex to
the angledwall⇥i between
the directionof thecharged particle
and the direction
fromreconstructed
the vertex position
the closest
wall andeffwallis the distancefromof thethei-threconstructedvertexthe
tophoton.
the ID wall(where ID
Cherenkov
photonsare emitted)
to the location
PMT which observesItalsodepends
ontheenergyEduetomultiplescattering
in
water
by
the
electromagnetic
as measured backward along the reconstructed direction. Schematic illustration for fieldthese two
(Coulomb
scattering).
cos
✓
/F
(✓
)
is
the
correction
term
for
the
solid
angle
of
each
PMT
viewediiparameters is given in Figure 4.14.
from the vertex position. The definition of the angle is shown in Figure 5.5. F (✓) represents theThe
fit quality parameters, gvtx and gdir , are obtained and used in the analysis. The vertex
PMT acceptance given byquality parameter, gvtx , is defined as:F (✓) = 0.205 + 0.524 cos ✓ + 0.390 cos2 ✓gvtx =

i wi e

1
2

(

i wi

ti

)

0.132 cos3 ✓.

2with wi =

1
2

✓

ti

◆2

(5.3)

,

The parameters gvtx and gdir are defined to indicate the certainty of event point and direction reconstruction. The parameter gvtx , which represents the degree of certainty of the vertex(4.4)

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

Chapter 5. Event Reconstruction

Number of events

62

9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0

50

100
150
200
250
300
350
Distance between true and reconstructed vertex (cm)Figure 5.4: Distribution of the distance between the true and reconstructed vertex for a Monte
Carlo (MC) simulation with 10 MeV electrons generated uniformly in the detector. Since the range
from 0 cm to the dotted line (58 cm) contains 68.3% of the total, 58 cm is the resolution of thevertex reconstruction.

$IFSFOLPWQIPUPO

1.5

Figure 5.5: Definition of incident angle (✓, ) of photon to PMT surface.

5.2. Energy Reconstruction

63

reconstruction, is defined as

gvtx =

X

exp

i

"

1
2

✓

X
i

⌧i
!
"

◆2 #

✓
◆ #
1
⌧i 2
exp
2
,
✓
◆2 #
1
⌧i
2
!

exp

"

(5.4)

where ⌧i ⌘ ti ttof,i t0 . ! gives the weight to suppress the dark noise and is the time resolutionof the PMT for a single photoelectron signal, which are set to 60 ns and 5 ns, respectively. gvtx
takes values in the range from zero to one. The closer to one, the more certain the reconstructionis.
The certainty of direction reconstruction, gdir , is evaluated by the uniformity of the hit-PMTs
based on the Kolmogorov-Smirnov test as follows
gdir =

max{

uni,i

data,i }min{data,i }

uni,i

2⇡

,

(5.5)

where uni,i is the direction angle of the i-th hit-PMT when PMT hits are assumed to be uniformly
distributed around the ideal Cherenkov ring, and data,i is the angle formed by the direction of thereconstructed charged particle and the direction from the vertex position to the location of the i-th
hit-PMT. gdir takes values in the range from zero to one, with the value closer to zero for morecertain reconstruction.
Using the two parameters gvtx and gdir , the parameter g 2 is defined to represent the certaintyof the event reconstruction1 .
2
2
g 2 ⌘ gvtx
gdir
(5.6)
The g 2 takes values in the range fromreconstruction.

5.2

1 to +1, with larger value for more accurate event

Energy Reconstruction

In the energy region below a few tens of MeV, the number of hit-PMTs is used for the energy
reconstruction. For the energy scale with small number of emitted photons, most hit-PMTs detect
only one photoelectron although same PMTs close to the vertex position may detect multiple photoelectrons. The number of hit-PMTs is used instead of using the total number of photoelectrons
because the resolution of PMTs is not sufficiently high to accurately count the number of photoelectrons in the signal. Firstly, the number of PMTs that detected light within 50 ns around theevent time, N50 , is counted for energy reconstruction. It is known that if N50 is used as is, thereconstructed energy will di↵er depending on the event vertex positions. Therefore, the e↵ective
number of hit-PMTs with some corrections, Ne↵ , is usedfor the energy reconstruction. The Ne↵ iscalculated from N50 with some corrections as
Ne↵ =

N50 
X

(Xi

✏tail
i

i=1

✏dark
)⇥
i

Nall
S(0, 0)⇥⇥ exp
Nalive S(✓i , i )

✓

ri
Le↵
i

◆

⇥

1
.
QEi (1 + C · Gi (t))(5.7)

Below is an explanation of each correction term in Eq. (5.7).
• Occupancy Xi :If an event occurs at the edge of the fiducial volume and Cherenkov photons are emitted
toward the detector wall, multiple photons may be detected in one PMT. In this case, it islikely that photons are also detected by the surrounding PMTs. Thus, the expected number
1The

g 2 is internally called as “ovaQ” (One dimensional variable of Vertex and Angular reconstruction Quality).

64

Chapter 5. Event Reconstructionof photons detected by a PMT is estimated by the number of hit-PMTs surrounding the
PMT. Using the ratio xi (= ni /Ni ) of the number of PMTs Ni surrounding the i-th hit-PMT
and the number of hit-PMTs ni among them, Xi is expressed as8
log(1 xi )><(xi < 1)
xi
Xi =
>
: 3.0
(xi = 1)

• Correction for delayed hits ✏taili :Fraction of hits leaks out of the 50 ns time window due to scattering in water or reflection
on the detector wall or surface of the PMT before the photons are detected. The ✏tailisi
introduced to compensates the leak of the delayed hits. The definition is
✏tail
=
i

N100 N50
N50

ave
Rdark
⇥ 50 ns ⇥Nalive
,
N50

(5.8)

ave is the average dark
where Nalive is the total number of properly working PMTs and Rdark
rate of all PMTs.

• Correction for PMT dark hit ✏dark:i
Even in the absence of light irradiation, single photoelectron is often detected by PMT due
to thermionic emission and Cherenkov light emitted by radioactive isotopes contained in theglass of PMT. This signal is called dark noise, and the rate is called dark rate. Averaged darknoise rate of all PMTs in the inner detector of SK is 3 kHz depending on the obsevation priod.
As 11,129 PMTs are equipped in the SK detector, ⇠2 PMT output the dark noise in 50 ns
in average. For the event below 10 MeV, the e↵ect of dark noise cannot be ignored because
the amount of light observed is small, typically ⇠60 photons at 10 MeV. The expected valueof dark noise is subtracted in the measurement of the energy. Since the dark rate varies withtime, it must be corrected according to the observation period.
The correction for hit-PMTs due to dark noise is defined as
ave
✏dark
= Rdark⇥ 50 ns ⇥irjdarkNalive
⇥N
,
50
N50
X
rdark

(5.9)

j

j

N50

i
where rdarkis the measured dark rate for the i-th hit-PMT. The expected number of dark
hits in a time width of 50 ns is calculated from the average dark rate of the hit-PMTs.

• Correction for fraction of properly working PMTs Nall /Nalive :Nall is the total number of PMTs installed in the inner detector, which was 11,129 during thedata taking period from August 2020 to May 2022 (SK-VI). About 1% of the installed PMTs
were not in operation due to malfunction in that period. N50 is normalized by Nall /Nalive tocorrect the time variation, where The number of PMTs in normal operation, Nalive , varies
depending on the observation period.
• Correction for photon incident angle S(✓, ):The PMTs protrude from the inner wall of the detector. Therefore, the e↵ective photocathodecoverage depends on the angle of incidence of photons. To correct for this, a function S(✓, )is introduced. The definitions of the photon incident angles ✓ and are shown in Figure 5.5.
S(✓, ) was obtained by a simulation with the cylindrical structure using a Geant4 and generating photons at random positions and directions in the detector. The definition of S(✓, )isNobs (✓, )S(✓, ) =,(5.10)
Ninc (✓, )65

S(θ, φ)S(θ, φ)5.2. Energy Reconstruction

0.2
0.18

0.16
0.14

0.16

0.12

0.14
0.12

0.1

0.1
0.08

0.08
0.06
90
θ ( 80de 70
gre 60
e) 50
40
30
20
10

0 0 1090
70 80 e)50 60 φ (degre
40
20 30

(a) Correction function S(✓, ) for barrel PMTs.

0.06
90θ ( 80de 70
gre 60
e) 50
40
30
20
10

0 0

5 10

25
15 20

40 45
30 35φ (degree)(b) Correction function S(✓, ) for cap PMTs.

Figure 5.6: Correction function for photocathode coverage S(✓, )where Ngen (✓, ) is the total number of photons incident on the PMT at angle (✓, ), andNinc (✓, ) is the total number of photoelectrons produced by the photoelectric e↵ect fromphotons incident on the PMT at angle (✓, ). Figure 5.6 shows the shape of the functionS(✓, ). Note that the PMTs attached to the side wall of the detector (barrel PMTs) andthose attached to the top and bottom of the detector (cap PMTs) have di↵erent ranges ofangles at which photons can incident the PMT surface, so they are defined separately.
• Correction for water attenuation e↵ects exp(ri /Le↵i ):Cherenkov light is attenuated from the emission point to the PMT due to scattering andabsorption in water. The attenuation rate is expressed as exp( ri /Le↵i ), where ri is the
distance from the event vertex position to the i-th PMT and Le↵isthe e↵ective wateritransmission length from the event vertex position to the i-th PMT, taking into account theposition dependence and time variation of water quality. As described in Section 4.2.2, it has
been confirmed that there is a position dependence of the transmission length L of water inthe detector along the vertical axis due to the e↵ect of water circulation system. The position
dependence is modeled as follows with the first-order dependence in the height (z-axis):
8
1>>(z > 12 m)>< ↵abs ( ) ⇥ (1 + z) + ↵sca ( )L( , z) =(5.11)>
1>>(z  12 m):↵abs ( ) ⇥ (1
· 12 m) + ↵sca ( )where is the wavelength of the photon. When the photon travels a distance ri in water, thereaction cross section i ( ) is expressed as
✓◆1
z + ri · dzi+ Csca · ↵sca ( ),(5.12)i ( ) = ↵abs ( ) 1 +2

where dzi is the z component of the unit direction of the photon. The Csca is a constantintroduced to account for the e↵ect of photon scattering. Since it is difficult to accurately
estimate the contribution of scattering of photons in water, the position dependence of Ne↵
is compared by changing the value of Csca , and the value with the smallest magnitude is used
for event reconstruction. In this case, the probability pi of a photon arriving at the i-th PMTfrom the event point is expressed as
Z max
pi =
w0 ( ) exp( i ( ) · ri )d ,(5.13)
min

66

Chapter 5. Event Reconstruction

0.007
0.006
0.005
0.004
0.003
0.002
0.001
0

250 300 350 400 450 500 550 600 650 700

Wavelength (nm)Figure 5.7: Probability density distribution of Cherenkov photon wavelengths w0 ( ).
where w0 ( ) is the probability density distribution of Cherenkov photon wavelengths, as
shown in Figure 5.7. It is integrated with the weight for attenuation e↵ects from min =300 nm to max = 650 nm. The probability pi can also be expressed using the e↵ective watertransmission length Le↵
i as
✓
◆
ri
pi = exp.
(5.14)
Le↵i
From the comparison of Eq. (5.13) and (5.14), the e↵ective water transmission length Le↵ican be expressed as follows:
Le↵
i =
ln

✓Z

ri
max

w0 ( ) exp(mini(

) · ri )d◆(5.15)

Le↵i is uniquely determined from the distance between the event vertex and the i-th hit-PMT.
• Correction for PMT quantum efficiency and PMT gain variation [QEi (1 + C · Gi (t))] 1 :Since the quantum efficiency is di↵erent for each PMT, the non-uniformity is corrected. QEi
is the relative quantum efficiency of the i-th PMT, which is evaluated using the data takenwith a NiCf source (see Section 4.1.1). Gi (t) is relative gain of i-th hit-PMT. C is a constantcalculated based on the assumption that the correlation between the time variation of PMT
gain and the time variation of hit rate is linear.
From the above corrections, the e↵ective number of hit-PMTs, Ne↵ , is determined. The energyof the charged particles is reconstructed from Ne↵ using the following relationship between Ne↵

5.3. Muon Event Reconstruction

67

Super-Kamiokande VI

Super-Kamiokande VI

Run 86146 Sub 1 Ev 124

Run 85806 Sub 1 Ev 12500

21-08-05:23:03:43

21-04-01:15:11:49

Inner: 114 hits, 216 pe

Inner: 8637 hits, 99205 pe

Outer: 0 hits, 0 pe

Outer: 234 hits, 2062 pe

Trigger: 0x01

Trigger: 0x1000000f
D_wall: 1690.0 cm

D_wall: 151.9 cm
Evis:

Evis:

0.0 MeV

Solar: E=

5.64 MeV

0.0 MeV

Solar: E=cos(sun)= 0.131

0.00 MeVcos(sun)= 0.000

Solar: gdn= 0.00 dirks= 0.00

Solar: gdn= 0.47 dirks= 0.14

Charge(pe)Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
8

1500

7

1200

5

900

3

600
300

2
0

0
0

500

1000

1500

2000

0

Times (ns)

500

1000

1500

2000

Times (ns)Figure 5.8: Comparison of eventdisplays for an electron with a few MeV (left) and a cosmic-ray
muon (right).
and the reconstructed total energy Erec .
8 6
X
>
>
>
Pi (Ne↵ )i 1
>
>
<
i=1
Erec =
6
6
>
X
X
>
>
i 1
>
Pi (Nthr )+ (Ne↵ Nthr )
(i
>
:
i=1

(Ne↵ < Nthr )(5.16)
1)Pi (Nthr )

i 2

(Ne↵

Nthr )

i=2

where Nthr = 331.7. The parameters Pi are determined by a fit to the calibration data using
LINAC by which electrons with known energies are generated inside the detector (Section 4.3.1).
P1 = 0.74, P2 = 0.13, P3 = 1.07⇥10 4 , P4 = 9.68⇥10 7 , P5 = 3.04⇥10 9 , P6 = 3.31⇥10 12 .

5.3

Muon Event Reconstruction

Cosmic-ray muon events are by far more energetic than the MeV-scale electron-like events discussed
in the previous sections, resulting in much higher PMT hits and charges observed in SK as shownin Figure 5.8. In addition, the trajectories of cosmic-ray muon events are track-like unlike MeVscale electron-like events which can be treated as a point source in the SK detector. This section
provides an overview of the algorithm that identifies muons and reconstructs their directions andtrajectories. Further details are described in Ref. [65, 66].
Before the muon reconstruction, the ID hit-PMTs used in the reconstruction are selected withthe observed charged in each ID hit-PMT (first cleaning cut). The criteria of the ID hit-PMT
selection are classified by the total number of ID hit-PMTs, as shown in Table 5.1.
Table 5.1: Selection criteria of the ID hit-PMT.
Number of ID hit-PMTs< 8,000
8,000–10,000> 10,000

Observed charge of ID hit-PMT
2.0 p.e.
2.5 p.e.
3.0 p.e.

After the first cleaning cut, the number of hit-PMTs contained in the eight PMTs surrounding
a hit-PMT within 10 ns window, Nnn , is calculated. Nnn is called the nearest neighbor hits andFigure 5.9 shows an example for Nnn = 4. Only the ID hit-PMTs which have more than certain

68

Chapter 5. Event Reconstruction

Figure 5.9: Schematic illustration of the case of Nnn = 4. The central red circle shows the standard
hit-PMT. In the surrounding eight PMTs, the orange circles show hit-PMTs and the gray circles
show the unhit-PMTs.
number of Nnn are used for the muon reconstruction. The conditions for Nnn are shown in Table 5.2.
Table 5.2: Requirements for Nnn corresponding to the number of ID hit-PMTs after the firstcleaning cut.
Number of ID hit-PMTs after the first cleaning< 500
500–2,500
2,500–5,000
5,000–7,500> 7,500

Nnn threshold
1
2
3
4
5

After the PMT hit cleaning above, the entrance position of the cosmic-ray muons to the ID andthe timing are estimated as the location and hit timing of the earliest hit-PMT with Nnn 3. If
there is no hit-PMT with Nnn 3, the threshold is reduced until an entrance position candidate isfound.
Next, the direction is reconstructed. Hit-PMTs used for the direction reconstruction are restricted by the hit timing. Considering a fact that velocity of muons at GeV-scale is faster than the
speed of light propagation in water, Cherenkov light from the muon can not reach a PMT earlier
than the travel time of the muon:D
Tearly = Tentry + ,(5.17)
v1
where Tentry represents the PMT hit timing at the entrance position, D represents the distance
between the entrance position and the location of each hit-PMT, and v1 is set to be 3.4 ⇥ 108 m/s
which is slightly faster than the speed of light to accommodate fluctuations of PMT hit timing. In
addition, Cherenkov light from the muon also can not reach a PMT later than the travel time ofthe photons in the water:D
Tlater = Tentry + ,(5.18)
v2
where v2 is set to be 1.8 ⇥ 108 m/s which is slightly slower than the speed of propagation of light in
the water by the same reason as written above. The direction reconstruction is performed using thehit-PMTs with the hit timing from Tearly to Tlater . Then, the direction is estimated to maximize

5.3. Muon Event Reconstruction

69

goodness G, defined as follows:
G = F (fcone )NXg( ti ),

(5.19)

i=1

where fcone represents the ratio of the number of PMTs in the Cherenkov cone to the total numberof the selected hit-PMTs. The direction from the entry point to the PMT hit should be within the
Cherenkov cone. Therefore, the relationship between muons and hit-PMTs should satisfy at least
one of the following two conditions:• d · r > 0.74, where d represents a unit vector from the muon entrance position to hit-PMT
and r represents the muon direction.
• D < 2 m.
The latter condition is used to collect hit-PMTs close to the entrance position. After fcone isevaluated, F (fcone ) is calculated based on the following form:
8
0.9
>
>
(fcone < 0.75)>< Ccut fcone
F (fcone ) =,(5.20)>
0.1fcone + 0.9 Ccut>>:
(fcone > 0.75)
1 Ccutwhere Ccut = 0.74. ti represents the time di↵erence between the measured hit timing of the i-th
hit-PMT and the expected timing given by the muon track assumed in the iteration. g( ti ) isdefined as follows:
✓
◆
8
ti
>
>exp
( ti < 0)><(qi )g( ti ) =,(5.21)
✓
◆
2
>
>
(
t
t
(q
))
i
mean i>:exp( ti > 0 or qi > 30 p.e.)2( (qi ))2
where qi represents the observed charge of i-th hit-PMT. tmean (q), (q), and (q) were determinedby timing distributions from the data as follows:tmean (q) = 2.563

0.029 ⇥ q⇣q ⌘(q) = 1.690 + 2.514 exp⇣ 2.453q ⌘(q) = 1.254 + 14.863 exp.
2.316(5.22)(5.23)(5.24)

70

Chapter 5. Event Reconstruction

Chapter 6

Evaluation of Stability andUniformity of Neutron Detection
In order to observe supernova relic neutrinos (SRNs) in Super-Kamiokande (SK) with Gd-loaded
water (SK-Gd), it is important to continue stable observations for a long period of time. It takes
more than 10 years to achieve the observation with modern theoretical expectations. The key of the
SK-Gd experiment is the detection of neutron capture on Gd in the water. Electron antineutrinos
in SRN interact with free protons (hydrogen nuclei) in the entire volume of the detector to produce
positrons and neutrons (¯⌫e +p ! e+ +n). Therefore, it is important to confirm the Gd concentrationis uniform in the detector and monitor the stability during the observation period. In this study,
a method was established to evaluate the stability and uniformity of the neutron detection by the
SK-Gd detector using neutrons induced by cosmic-ray muons. This chapter describes the evaluation
method and the stability in the period from September 2020 to June 2022 after gadolinium loading.

6.1

Overview

As described in Chapter 1, cosmic-ray muons and muon-induced showers interact with oxygen nuclei
in water to produce neutrons, which are called muon-induced neutrons or cosmogenic neutrons.
These neutrons are thermalized in water within ⇠5 µs and then captured on hydrogen or Gd. If aneutron is captured on hydrogen, a 2.2 MeV ray is emitted. On the other hand, if a neutron is
captured on Gd, multiple rays totaling ⇠8 MeV are emitted. Among those, the selection criteriaof the data analysis were set to collect neutron captures on Gd to suppress background at low energy
region. The time from neutron production to capture by hydrogen or Gd and the fraction of Gd
capture depend on the concentration of Gd dissolved in water. 13 tons of Gd sulfate octahydrate(Gd2 (SO4 )3 · 8H2 O) were dissolved in 50 kton of ultra-pure water during the first SK-Gd phase(SK-VI), which has been started since August 2020. This corresponds to a Gd mass concentrationof 0.01%, at which concentration neutrons are captured on hydrogen or Gd in ⇠116 µs on average.
⇠50% of neutrons are captured on Gd with this Gd concentration.
The calibration with the Am/Be neutron source (Section 4.4) is performed about once every
a few weeks to confirm the stability of Gd concentrations in the water. The Am/Be source issubmerged in the detector along the center axis using a wire and data are acquired at three positions:bottom ( 12 m), center, and top (+12 m) for 30 minutes each. The calibration source allows
precise measurement of the neutron detection efficiency, while there are a few limitations: (1)neutron detection efficiency o↵ the counter axis of the cylindrical detector can not be measured;(2) variations between the calibrations can not be monitored. In order to compensate for thelimitations and to measure the uniformity and stability of Gd concentration in the detector, a new
method using cosmogenic neutrons was proposed and established in this study. As the cosmic-ray
muons are reaching SK at a frequency of ⇠2 s 1 , the muon-induced neutrons allow monitoring of
Gd concentration in parallel to the neutrino observation. Furthermore, as the spallation interaction71

72

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection
Table 6.1: The features of the neutrons from Am/Be source and cosmic-ray muons.
Neutron source
Frequency
Position
Multiplicity

Am/Be
Every a few weeks
Specific (3 positions)1

Cosmic-ray muonContinuous (⇠2 s 1 )Uniform
0 to O(102 )occurs overall the detector, it is possible to confirm the uniformity of Gd concentration with muoninduced neutrons. Table 6.1 shows the features of the neutrons from the Am/Be source andcosmic-ray muon spallation.

6.2

Analysis Flow

After cosmic-ray muons enter the SK detector and produce neutrons via the spallation interaction,
those neutrons are thermalized and captured on hydrogen or Gd. Among those, neutrons captured
on Gd are selected in the analysis as written above. Neutrons are identified by detecting rays
emitted immediately after the neutrons are captured on Gd. Figure 6.1 shows the schematic
illustration of the muon-induced neutron observation in SK. The analysis flow is shown as follows.
1. A cosmic-ray muon enters the SK detector. The muon is selected by the signals in the outerdetector and the total number of observed photons in the inner detector.
2. Neutrons are often produced by the muon or the secondary shower interacting with 16 O as
explained in Section 1.6.2. Those neutrons are thermalized in water and then captured onhydrogen or Gd after ⇠116 µs on average in Gd-loaded water with 0.01% Gd mass concentration. Once a neutron is captured on Gd, several rays of ⇠8 MeV in total are emitted.
Signals from neutron capture on Gd are searched in the time after the time of cosmic-ray
muon arrival.
3. In order to distinguish the neutron capture signals from the background mainly due to radioactivity, the event selections are applied. Neutron capture candidates are selected using theevent quality (based on the PMT hit pattern and hit timing), the total number of hit-PMTs,
and the distance between the muon track and the vertex of neutron capture events.
4. Distributions of the time di↵erences between the muon arrivals and neutron capture eventsare fitted by exponential functions to evaluate the neutron capture time constant for eachregion in the detector. The Gd concentration in water can be checked from the neutron
capture time constant referring to their correlations.

6.3

Cosmic-Ray Muons

Figure 6.2 shows the event display when a cosmic-ray muon entered the SK detector from the
top and passed through it while losing energy in the water. Signals of cosmic-ray muons arerecorded in both inner detector (ID) and outer detector (OD) (Section 3.4.2 for trigger system).
In this analysis, muon candidates are selected by requiring the total number of observed photons(equivalent to the number of observed photoelectrons) of the ID PMTs to be greater than 1,000 p.e.,which corresponds to ⇠140 MeV, and the tracks are reconstructed with the muon fitter.

6.3. Cosmic-Ray Muons

73

Cosmic-ray

O

16

Gd

ShowernSK

Figure 6.1: Overview of cosmogenic neutron obsevation in SK.

Super-Kamiokande VI
Run 85806 Sub 1 Ev 246388
21-04-01:15:12:05
Inner: 8657 hits, 100336 pe
Outer: 111 hits, 716 pe
Trigger: 0x1000000f
D_wall: 1690.0 cm
Evis:

0.0 MeV

Solar: E=

0.00 MeVcos(sun)= 0.000

Solar: gdn= 0.00 dirks= 0.00

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2
1400
1120
840
560
280
0
0

500

1000

1500

2000

Times (ns)Figure 6.2: Distribution of PMTs that detected photons when a cosmic-ray muon penetrates the
SK detector (event display). The center developed view shows the ID PMTs and the upper rightshows the OD PMTs. The color of each point indicates the total charge of PMT signal whichcorresponds to the number of photons detected by the PMT.

74

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection

0 µs

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Search<latexit sha1_base64="oZt6UsNJrnuOTHrfXHGIBxw86wg=">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</latexit><latexit sha1_base64="jWv9GKswX0psUTa6AfCQ+9PPVlg=">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</latexit>µ<latexit sha1_base64="U+YSSQPLQT6nOnjGiWjje0N41AM=">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</latexit>t

Low energy events<latexit sha1_base64="e+lP3gHHnJORPV/VMhTiS1+E2ck=">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</latexit>

Figure 6.3: Schematic illustration of cosmogenic neutron searches.

6.4

Neutron Capture Event Selection

6.4.1

Overview of Neutron Search

As explained in Section 3.4.2, not all PMT hit information is stored due to the limitation of thedata transfer and the storage size, while the hit information is stored for specific conditions with thetriggers. Once the ID and OD triggers are issued due to cosmic-ray muon, all PMT hit information
for up to 535 µs following the muon event is stored. Event candidates are searched for in the stored
data, and event reconstruction (Section 5) is applied to the event candidates. These delayed eventsat the MeV scale following the muon are called “low-energy events” in this analysis. In order toselect neutron captures on Gd against the background events, several cuts are applied to the lowenergy events following the muon. In this section, the data acquired in the 24-hour of September
11–12, 2020, will be presented as an example. The rest of the data were available in the same way
to check the stability of the neutron detection. The schematic illustration of cosmogenic neutron
searches is shown in Figure 6.3.

6.4.2

Preselection

Neutron capture candidates are searched within the time window 40 µs  t  530 µs, wheret represents the time interval from the muon arrival. The events with t < 40 µs are notused to avoid the contamination of the electron from a muon decay and fake signals from PMT
called after-pulses. After the large signals of PMTs by cosmic-ray muons, fake signals are often
generated by the same PMTs. This is due to the ionization of the residual gas in the PMT by
the photoelectrons. The ionized gas is led to the photocathode by the electric field and further
photoelectrons are emitted when it hits the photocathode. It is known that PMTs installed in SK
generate after-pulses approximately 10–20 µs after the first signal (main pulse).
In order to exclude the background due to radioactivity near the ID wall [59], a fiducial volume
cut is applied based on the reconstructed vertex position. Typical SK analysis uses the data in thefiducial volume defined with the boundary 2 m away from the ID wall, corresponding to 22.5 kton
(full volume of the ID is 32.5 kton). Therefore, in this study, the Gd concentration was evaluatedin the fiducial volume.

6.4.3

Event Quality

Unlike signal events, which have a peaked timing distribution and a ring pattern, the time andlocation of hit-PMTs for the background due to PMT dark noise are randomly distributed. Such
distributions are deviated from the expectation by the Cherenkov light emitted from a point-likesource. These backgrounds can be reduced by evaluating the goodness of event reconstruction,
which is described in Section 5.1. Figure 6.5 shows the distributions of gvtx and gdir of the data
after all cuts except for the quality cut are applied. In this analysis, events with gvtx > 0.4 andgdir < 0.4 are retained as signal candidates.

75

6

10

EventsEvents

6.4. Neutron Capture Event Selection

5

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Before selections
10

Before selections
10

After all selections

1
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250
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After all selections

−15

−10

−5

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15

z (m)

r (m )

2000

EventsEventsFigure 6.4: Distributions of the radial (left) and central axial (right) positions (r and z) for thedata (September 11, 2020) before (black) and after (red) the event selections. Events are rejected if
the distance from the ID wall is less than 2 m. The dashed lines correspond to the boundary of thefiducial volume. A large number of events are found around the center of the detector before theevent selections, which are caused by the background events due to random coincidence of PMT
dark hits.

1800
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gvtx

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gdir

Figure 6.5: Distributions of gvtx (left) and gdir (right) for the data (September 11, 2020) after all
cuts except for the quality cut are applied. The points show the data and the dotted lines show
the cut conditions to select the signals from neutron captures on Gd.

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection
Events

76

104

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40

50

60

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N50

Figure 6.6: Distributions of N50 for the data (September 11, 2020) after all cuts except for the
N50 cut are applied. The points show the data and the dotted lines show the range to select thesignals from neutron captures on Gd.

6.4.4

Number of Hit-PMTs

The energy is determined from the number of hit-PMTs with some corrections as explained in
Section 5.2, which is nearly equivalent to the number of observed photons as most of the hit-PMTs
detect only one photon. Since radioactive isotopes are primarily present up to ⇠4 MeV which is
below the signal from neutron capture on Gd, event selection is applied by the number of hitPMTs. In order to suppress the contamination of the background, the number of hit-PMTs within
a 50-ns time window (N50 ) is counted after the time of flight of photon from the reconstructedvertex to the hit-PMTs is subtracted from the PMT hit time. Figure 7.4 shows the distribution of
N50 of the data after all cuts except for the N50 cut are applied. The selection criterion is set as
24  N50  70.

6.4.5

Transverse Distance from Muon Track

As the neutrons produced from muons are thermalized typically within a few meters and captured
on Gd, it is e↵ective to use the transverse distance between the muon track and the reconstructedvertex to identify muon-induced neutrons. The definition of the transverse distance Lt is outlinedin Figure 6.7. Lt exhibits a correlation with the distance traversed by secondary particles produced
within the muon-induced hadronic shower in water. In cases of multiple muons entering the detector
at the same timing, Lt is defined as the distance from the reconstructed vertex to the nearest muontrack. Figure 6.8 shows the distribution of Lt of the data after all cuts except for the Lt cut are
applied. For this analysis, the selection criterion is set as Lt < 500 cm.

6.5

Measurement of Neutron Capture Time Constant

The time di↵erence from the preceding muon, t, is calculated for every low-energy event. The
reduction of low-energy events after each selection is shown in Figure 6.9 for the t distribution.
The time constant for neutron capture on Gd is evaluated with the t distribution after the event
selections (the red line in Figure 6.9). Since the time di↵erence between neutron production and6.5. Measurement of Neutron Capture Time Constant77

Muon track<latexit sha1_base64="tsIYK12ciJ8muwlYUyydbHCj/i8=">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</latexit>

Lt<latexit sha1_base64="U5NzZ1W0NIMF8yoHtfjmrs3SxT0=">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</latexit><latexit sha1_base64="WatzYuCS3itesKuZzoBI1u+RNdg=">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</latexit>

VertexEventsFigure 6.7: Definition of transverse distance (Lt ) between the muon track and the reconstructedvertex.

4500
4000
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500
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1000

1500

2000

2500

3000

3500

Lt (cm)Figure 6.8: Distributions of Lt for the data (September 11, 2020) after all cuts except for the Lt
cut are applied. The points show the data and the dotted lines show the criterion to select thesignals from neutron captures on Gd.

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection

Events78

104
Fiducial volume cut
Event quality cut
N50 cut
Lt cut

3

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500

∆t (µs)Figure 6.9:
sequence.

Distributions oft for the data (September 11, 2020) applied event reductions in

capture on Gd follows an exponential distribution, the t distribution is fitted by the following
function:✓◆tf ( t) = A exp
+ B,
(6.1)
⌧
where A represents the normalization of neutron events and B represents background events. ⌧represents the time constant of the neutron capture. ⌧ is correlated with the Gd concentration in
the water, and the stability of ⌧ corresponds to the stability of the Gd-loaded water and detector
response. The average of ⌧ measured with the Am/Be source (Section 4.4) is 116.5 ± 0.2 µs during
the entire observation period in SK with 0.01% Gd-loaded water (SK-VI phase). Figure 6.10 shows
the fit result of the t distribution for the data after the event selections (corresponding to the redline in Figure 6.9). As a result of the fit, ⌧ is evaluated to be 126.1 ± 2.3 µs, which is significantlydi↵erent from the result from Am/Be calibration.
One of the di↵erences between the measurements with the Am/Be sources and cosmic-ray muons
is the number of simultaneously produced neutrons (neutron multiplicity). In the measurementswith Am/Be source, only one neutron is produced at a time. Therefore, at most one neutron capture
event on Gd is detected following the prompt signal. While, in the measurements with cosmic-ray
muon, multiple neutrons may be produced through the spallation interaction. In such cases, there
may be multiple neutron capture events on Gd following a prompt signal due to a cosmic-ray
muon. Figure 6.11 shows the number of neutron capture candidates following a muon after the
event selections, M . The distribution expands to M ⇠ 100. The true neutron multiplicity is evenlarger because some of the neutrons, such as the neutrons captured on hydrogen, are missed dueto the event selection. As the probability of neutron capture follows exponential function, neutron
capture occurs more frequently in shorter time intervals in case multiple neutrons are producedby the muon spallation. Neutron capture candidates are searched with sliding time windows andthe PMT hits within the 1.3 µs time window are collected as a single event. If there are multiple
neutron captures within 1.3 µs, only one of them is selected as a signal candidate as illustrated in
Figure 6.12 and the missing neutrons in the dead time cause inefficiency depending on the neutron
multiplicity and t. Thus, a large neutron multiplicity makes the efficiency in the short t region

Events / 5µs

6.5. Measurement of Neutron Capture Time Constant

79

700
600

Data
Fit result

500
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500

∆t (µs)Number of muons

Figure 6.10: Distribution of the time di↵erence between the muon and the followiing neutron
capture candidates, t, for the data (September 11, 2020). The points are the data and the solidline is the fit result.

5

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Neutron capture event candidates following a muon
Figure 6.11: Distribution of the number of neutron candidates following a muon that remain after
the event selections.

80

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection

0 µs

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40 µs

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Figure 6.12: Schematic illustration of the dead time e↵ect in the short
represent neutron capture events.

t region. The gray circles

lower. As a result, the capture time constant is biased to a larger value.
Based on the above considerations, only muons with M = 1 are selected, and the capture time
constant ⌧ is obtained from the t distribution. The t distribution and the fit result for the data
are shown in Figure 6.13, where ⌧ is fitted to be 116.1 ± 3.6 µs. This value is consistent with thetime constant 116.5 ± 0.2 µs measured with the Am/Be source.

6.6

Evaluation of the Stability and Uniformity

This section describes the evaluation of the stability and uniformity of the neutron detection using
neutrons induced by cosmic-ray muons. As the time constant for the neutron capture depends on
the Gd concentration (shown in Figure 3.11 of Section 3.7), the stability and uniformity of Gdloaded water can be checked by this measurement. Here, the stability and uniformity of the neutron
capture time constant are evaluated during the observation period in SK with 0.01% Gd-loaded
water. The period from September 10, 2020, to June 1, 2022, is divided into 42 periods with 15
days for each period, and the neutron capture time constant is evaluated for each period.
Figure 6.14 shows the time variation of the neutron capture time constant as a function of time.
Neutron capture conditions (M = 1) in the entire fiducial volume were used for this plot. The
variation of the time constant was obtained by fitting the values obtained at each time period witha Gaussian function as shown in Figure 6.15. The mean and standard deviation are found to be116.3 ± 0.2 µs and 1.1 ± 0.1 µs, respectively. As a result, the neutron capture time is found to bestable within 0.9%. This corresponds to the stability of Gd concentration to be 2.3% and fractionof Gd capture to be 1.1% referring to Figure 3.11.
In addition, the fiducial volume is divided into nine regions to confirm the uniformity of Gdloaded water in the fiducial volume and the stability. Figure 6.16 shows the vertex positions ofneutron capture events for M = 1 on the period 0 (shown in Figure 6.14). Dashed lines in the plotshow the boundary of nine regions. The position dependence of the time constant for the neutron
capture on Gd is confirmed from the t distributions for events in each region. As an example,
Figure 6.17 shows the t distributions in each region at the period 0 and the values of the time
constants obtained by fitting the distributions. This analysis is performed for the entire period, andFigure 6.18 shows the stability of the capture time constant in each region. The variation of thetime constant for each period and each region is obtained by Gaussian fit as shown in Figure 6.19.
The mean and standard deviation are found to be 116.4 ± 0.2 µs and 3.0 ± 0.1 µs, respectively. As

Events / 5µs

6.6. Evaluation of the Stability and Uniformity

81

220
200

Data

180

Fit result

160
140
120
100
80
60
40
20
0

50

100

150

200

250

300

350

400

450

500

∆t (µs)Capture time constant (µs)

Figure 6.13: Distribution of the time di↵erence between the muon and the followiing neutron
capture candidates, t, for the data (September 11, 2020). Only the events with one neutron(M = 1) are plotted. The points are the data and the solid line is the fit result.

135
130
125
120
115
110
105
100
95

0

5

10

15

20

25

30

35

40

PeriodFigure 6.14: Stability of the neutron capture time constant for events in the fiducial volume of thedetector. The period from September 10, 2020 to June 1, 2022 is divided into 42 periods each with15 days.

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection

Count

82

12
10
8
6
4
2
0
112

113

114

115

116

117

118

119

120

Capture time constant (µs)

55

15
10

Region 6

Region 7

Region 8

50

Events / binz (m)Figure 6.15: Distribution of capture time constant in each 15 days period. Solid line shows theGaussian fit with mean value of 116.3 ± 0.2 µs and sigma of 1.1 ± 0.1 µs.

45
5
0

40
Region 3

Region 4

Region 5

35
30

−5
−10

25
20
Region 0

Region 1

Region 2

15
−15
0

20

40

60

80 100 120 140 160 180 200 220

10

r2 (m2)
Figure 6.16: The vertex positions of neutron capture events for M = 1 on the period 0. The
horizontal axis represents the square of the detector radius, the vertical axis represents the height,
and the color scale shows the number of events per bin. Dashed lines show the boundaries of nine
regions.

350

Region 6
300

200

Data

400
350
300
250

Fit result
τ = 112.9 ± 2.7 µ s

50

50

300

Data

250

Fit result0

50 100 150 200 250 300 350 400 450 500

Region 3

τ = 118.6 ± 2.9 µ s

100
50
0

50 100 150 200 250 300 350 400 450 500

50 100 150 200 250 300 350 400 450 500∆t (µ s)Events / 5µ s

Events / 5µ s

350

150

200
150

∆t (µ s)200

Region 8

Fit result
τ = 116.4 ± 2.7 µ s

100

250

350

Data

150

100

300

400

200

150

0

Region 7

Data
Fit result

350

300
250
200

τ = 117.9 ± 3.0 µ s

150∆t (µ s)Events / 5µ s

250

83

Events / 5µ s

Events / 5µ s

Events / 5µ s

6.6. Evaluation of the Stability and Uniformity

Region 4
Data

400
350

250

Fit result200

τ = 113.1 ± 2.8 µ s

Region 5

300

Data
Fit result
τ = 113.3 ± 2.9 µ s

150
100

100

50

50

0

50 100 150 200 250 300 350 400 450 500

50

300

Region 0

250

Data
200

150

Fit result

350
300
250
200

τ = 117.9 ± 3.1 µ s

50 100 150 200 250 300 350 400 450 500∆t (µ s)Events / 5µ s

Events / 5µ s

350

050 100 150 200 250 300 350 400 450 500∆t (µ s)150

∆t (µ s)Events / 5µ s

0100Region 1
Data

400
350

250

Fit result
τ = 116.5 ± 2.9 µ s

Region 2

300

200

Data
Fit result
τ = 113.0 ± 2.8 µ s

150
100

100

50

50

0

50 100 150 200 250 300 350 400 450 500∆t (µ s)

0

100
50

50 100 150 200 250 300 350 400 450 500∆t (µ s)0

50 100 150 200 250 300 350 400 450 500∆t (µ s)Figure 6.17: The t distributions in each region at the period 0. The points are the data and thesolid lines are fit results. Time constants obtained by the fits are also shown in each plot.

Capture time constant (µs)

84

Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection
Region 0

Region 3

Region 6

Region 1

Region 4

Region 7

Region 2

Region 5

Region 8

135
130
125
120
115
110
105
100
95

0

5

10

15

20

25

30

35

40

PeriodFigure 6.18: Stability of the neutron capture time constant in each region. The period from
September 10, 2020 to June 1, 2022 is divided into 15 days. The color of each point represents theregion in the detector defined in Figure 6.16.
a result, stability and uniformity of the neutron time constant were confirmed within 2.6%. This
corresponds to the stability and uniformity of Gd concentration to be 6.3% and the fraction of Gd
capture to be 3.1% referring to Figure 3.11.
SRN search is performed by the comparison of the reconstructed energy spectra for the observed
data and the expected background as shown in Figure 1.24. Therefore, in order to conclude theexistence of the SRN signals from the data, it is important to estimate the expected backgroundand suppress the uncertainties. As the major background events, atmospheric neutrinos, 9 Li, andreactor neutrinos consist of the prompt signal and the neutron capture events, any systematic
biases in the neutron detection efficiency, such as due to time variation or position dependenceof Gd capture fraction, result in the underestimation or overestimation of the background rate.
According to the study described in this thesis, the stability and uniformity of the Gd capture
fraction were confirmed within ±3.1% for the data taken from September 2020 to June 2022 (SK-IV
period). This value is negligible compared to the current estimation of the systematic uncertainties
from the other sources (⇠30%). This method using the neutrons induced by comic-ray muons canbe also applied to the observed data in the future to monitor the stability and uniformity of Gd
concentration or detect the unexpected problems in the water quality at the early stage, which areessential to collect reliable data for long time period realize the first observation of SRN signal.

85

Count

6.6. Evaluation of the Stability and Uniformity

50

40

30

20

10

0

105

110

115

120

125

Capture time constant (µs)
Figure 6.19: Distribution of capture time constant in each 15 days period and each region. Solidline shows the Gaussian fit with mean value of 116.4 ± 0.2 µs and sigma of 3.0 ± 0.1 µs.

86Chapter 6. Evaluation of Stability and Uniformity of Neutron Detection

Chapter 7

Measurement of Cosmogenic Neutron
Production
Neutrons produced by the cosmic-ray muon spallation are a major background source for underground neutrino experiments. Cosmogenic neutron production yields have already been measured
in underground neutrino experiments using liquid scintillators, such as KamLAND [43] and Daya
Bay [42], while neutron production yield in the water Cherenkov detector has so far been measured
only by SNO [46] with D2 O. Since the accuracy of theoretical prediction to cosmogenic neutron
production is limited due to the complicated process in the nucleus and secondary hadron scattering, estimation of the neutron yield heavily relies on the experimental data. Therefore, it isimportant to accumulate the measurements at di↵erential depths (corresponding to di↵erent muonenergy) and detector medium. As explained in Section 3.7, gadolinium (Gd) was introduced to theSuper-Kamiokande detector in 2020 to improve the detection efficiency of neutrons and started theoperation of SK-Gd. This enabled us to measure the cosmogenic neutron production in water withhigh precision. In this study, the neutron production yield was measured using 283.2 days of datataken by the Super-Kamiokande detector with Gd-loaded water from September 2020 to September
2021 (called SK-VI data-taking period to distinguish from the other configurations). This study
is the first physics measurement by the Super-Kamiokande detector with Gd-loaded water andtherefore it is important as a confirmation of the detector performance in detecting neutrons. The
results of this study are reported in Ref. [55].

7.1

Overview of the Analysis

In this study, the amount of neutrons produced by cosmic-ray muons was measured. The searchmethod for neutron capture events on Gd is almost the same as that described in the previous
chapter.
1. The method of the neutron capture event selection following the cosmic-ray muon is the sameas described in Section 6.2. In addition, this chapter will discuss selection efficiencies because
it is necessary to correct the number of neutron capture events missed due to event selections(Section 7.4).
2. The number of neutron capture events is estimated from the distribution of the time di↵erence
between the cosmic-ray muon and the remaining neutron candidates after the selections areapplied (Section 7.5).
3. The neutron yield is obtained from the sum of muon track lengths and the number of neutron
capture events with the corrections for the selection efficiencies. Systematic uncertainties on
the measurements are estimated for each source of the uncertainty (Section 7.6). Finally, theresults are presented in Section 7.7.
87

88

Chapter 7. Measurement of Cosmogenic Neutron Production
Table 7.1: Detector configurations and the number of events during the analysis period.
Detector
PeriodTriggers

Muons
Low-energy events

7.2

Phase
Gd concentration
Start dateEnd date
Livetime
ID (SHE)OD
AFT sub
EventsEvents (corrected)
Events

SK-VI
0.01%
Sep. 10, 2020
Sep. 26, 2021
283.2 days
60 PMTs/200 ns
22 PMTs/200 ns
20 PMTs/200 ns
49,495,584 (174,773 /day)
47,677,780 (168,354 /day)
1,825,281,155 (6,445,202 /day)

Detector Configuration and Data Set

Table 7.1 summarizes the detector configurations during the period. This analysis used 283.2 daysof data taken in the SK detector with Gd-loaded water from September 10th, 2020 to September
26th, 2021. As described in Section 7.1, a muon is first observed, and then neutron capture events
are searched for in the time window following the muon. Since Cherenkov light is detected in the
inner detector (ID) and outer detector (OD) for muons entering the SK detector. Events takenwith both ID (SHE trigger, Section 3.4.2) and OD triggers are stored as cosmic-ray muon events.
Once a SHE trigger is issued, all PMT hits for 500 µs following the SHE-triggered event are stored(AFT trigger, Section 3.4.2). Low-energy events are searched from the PMT hits recorded by the
AFT trigger in the analysis as the candidates for neutron capture events (AFT sub-trigger search).
The following description is about the trigger problem found in the data set and its correction.
It was found that the AFT trigger rate was limited to once every 21 ms during the data acquisition
period of this analysis, and therefore the AFT trigger was not always issued following the SHE
trigger. This causes an underestimation of the number of muon-induced neutrons after muons due
to missing low-energy events. The discrepancy between SHE and AFT trigger rate was evaluatedto be 3.7% and the number of muons was scaled by 0.963 (= 1 0.037) to correct for this.

7.3

Cosmic-Ray Muons

As explained in the previous chapter, cosmic-ray muons are recorded by both the ID and OD
triggers. Muon candidates are selected by requiring the total number of observed photons of the ID
PMTs to be greater than 1,000, which corresponds to ⇠140 MeV, and the tracks are reconstructedwith the muon fitter. The cosmic-ray muons are classified into following four types:• Single through-going muon: A single muon penetrates the ID.
• Stopping muon: A single muon loses energy and stops inside the ID.
• Multiple muons: Multiple muons (muon bundles) pass through the ID. These muons areproduced by the same cosmic-ray within the atmosphere. Therefore, the directions of allmuons are assumed to be the same (muon tracks are in parallel) in the track reconstruction
algorithm.
• Corner-clipping muon: A single muon gazes the edge of the ID.
The total number of muons used in this analysis, Nµ , is counted as Nµ = 47,677,780 ' 4.77 ⇥ 107
for 283.2 days of exposure.

Events / 100 cm

7.3. Cosmic-Ray Muons

89

×103
1800
1600
1400
1200

Single through-going
Multiple (all tracks)
Stopping
Corner-clipping (×1000)

1000
800
600
400
200
0
0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Muon path length (cm)Figure 7.1: Distributions of path length Lµ for single through-going (solid), multiple (dashed),
stopping (dotted), and corner-clipping (dot-dashed) muons. The distribution of corner-clippingmuons is scaled by a factor of 1,000.

Figure 7.1 shows the distributions of the measured track lengths of muons in the detector. The
peak of the track length distribution at around 3,700 cm corresponds to muons that penetrate thedetector from the top to the bottom. The average path length Lµ was obtained to be Lµ = 2,427 cm.
The average number of neutrons produced in muon spallation depends on the energy of themuon. The energy of cosmic-ray muons at the SK site is estimated using the simulation. The
muon flux at sea level is modeled by modifying Gaisser’s parametrization [30] according to Ref. [31].
The MUSIC code [67] is used to simulate muon propagation in the rock. The simulations accountfor the topography of Mount Ikenoyama surrounding the SK area [43, 68] and the rock modelsof standard [33, 69] and Ikenoyama [31]. The density of the rock is assumed to be in the rangeof 2.65–2.75 g/cm3 . The average muon energy incident on the SK detector E µ is estimated to
be E µ = 259 ± 9 GeV with the calculation method from Ref. [43], where the uncertainty wasestimated by varying the rock model and density. Figure 7.2 shows the cosine of the zenith angle
and azimuthal angle of muons at the SK site. The muon flux from the MUSIC code is overlaid withthe reconstructed directions of the data. The MUSIC simulation reproduces the dependence ofthe muon flux as the topography of Mount Ikenoyama is implemented in the simulation. Muon
flux is higher for ⇠ 170 and ⇠ 280 where the overburden of the rock is thinner than theother directions. Small discrepancy tells the mismodeling of the topography due to the limitationof the modeling for the detailed structure of the topography and rock density. The discrepancyof the cos ✓ distribution around cos ✓ ⇠ 1, which corresponds to vertically entering muons, is not
yet understood. Possible causes are the mismodeling of the primary cosmic-ray flux, atmosphere,
and geomagnetic field around the experimental site. The cut o↵ energy of primary cosmic-ray
and the trajectory of muons depend on the magnetic field. In order to evaluate the impact of thediscrepancy in cos ✓ distribution, the averaged energy of muons entering the detector was calculatedwith the weight as a function of cos ✓ to reproduce the data. The variation of the averaged energy
was found to be ±0.17 GeV which is negligible compared to the other uncertainties.

90

Chapter 7. Measurement of Cosmogenic Neutron Production

Number of muons / 283.2 days

31800 ×10
1600

Data
Muon flux (MUSIC)

1400
1200
1000
800
600
400
200
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of muons / 283.2 days

cosθ
×103
1400

Data
Muon flux (MUSIC)

1200
1000
800
600
400
200
0
0

50

100

150

200

250

300

350

φ (degrees)

Figure 7.2: Zenith (✓) and azimuthal ( ) dependence of the muon rate at the SK site. Reconstructed directions of the muons from the data (black points) are overlaid with the muon flux at
the SK site calculated by the MUSIC code (red lines). Muon flux distributions are normalized tothe data. = 0 corresponds to the direction from east to west.

7.4. Neutron Capture Event Selection

7.4

91

Neutron Capture Event Selection

The method of the neutron capture event selection is almost the same as the method described in
the previous chapter. Once the ID and OD triggers are issued due to a muon arrival, the data forthe 535 µs following the muon event are also stored. Event candidates of neutron capture on Gd aresearched for in that time window. The objective here, however, is to count the number of neutrons
produced by cosmic-ray muons. Therefore, a more detailed analysis is also performed to estimate
the selection efficiency for the events of neutron capture on Gd and systematic uncertainties.

7.4.1

Preselection

The time di↵erence between the muon and the following low-energy events is defined as t. Neutron
capture candidates are searched within the time window 40  t  530 µs. The events witht < 40 µs are not used to avoid the contamination of the electron from a muon decay and fakesignals from PMT after-pulses (Section 6.4.2).
In order to exclude the background due to radioactivity near the ID wall [59] and neutrons
entering from the surrounding rock, a fiducial volume cut is applied based on the reconstructedvertex position. The fiducial volume of this analysis is defined with the boundary 4 m away fromthe ID wall corresponding to 14.7 kton. As shown in the latter section, neutron yield is measured
for the total volume of the inner detector with the correction for the signal efficiency of the volume
cut given by the ratio of the fiducial volume to the total volume of the ID. In order to accurately
calculate the number of neutrons produced in the fiducial volume (neutron yield), the propagationof neutrons, i.e. number of neutrons entering the fiducial volume and those exiting the fiducial
volume, should be taken into account. If neutrons produced by muons in the fiducial volume leakout of the fiducial volume, the number of neutrons is underestimated. On the other hand, if neutrons
produced in the bedrock surrounding the detector or outside the fiducial volume leak in the fiducial
volume, the number of neutrons is overestimated. They are not perfectly cancelled each otherdue to entering neutrons generated by the muons outside of the detector. The fiducial volume issmaller than the other analysis in SK [24] in order to suppress the systematic uncertainty associatedwith the leak-in/-out of neutrons as shown in Section 7.6.5, while the statistical uncertainty is still
smaller than the systematic uncertainty1 .

7.4.2

Event Quality

In order to reduce the background due to PMT dark noise, the goodness of event reconstruction isevaluated as described in Section 5.1. The distribution of gvtx and gdir for neutron capture on Gd
in the Monte Carlo simulation (MC) is shown in Figure 7.3. In this analysis, events with gvtx > 0.4
and gdir < 0.4 are retained as signal candidates. The signal efficiency for the event quality cut isevaluated with the MC as (92.62 ± 0.29)% with the MC statistical uncertainty.

7.4.3

Number of Hit-PMTs

In order to reject the background due to the radioactivity, the event selection is applied by setting
a criterion for the number of hit-PMTs in a 50-ns time window, N50 . The distributions of N50 forthe data are shown in Figure 7.4, where the data is divided into the sample of 40 µs  t  240 µs(on-time) and the sample of 430 µs  t  530 µs (o↵-time). Since neutrons of ⇠98% are captured
within 430 µs, the background component is dominant in the o↵-time window. The schematic
illustration of t distribution and on-/o↵-time is shown in Figure 7.5. Background events from
accidental coincidences are assessed using the o↵-time sample and subsequently subtracted fromthe on-time sample. The resulting distributions of N50 for the data are compared with the MC
as shown in Figure 7.6, in which the discrepancy between the data and MC is due to the overlap
1

The standard fiducial volume is defined with boundary 2 m away from the ID wall, corresponding to 22.5 kton.

Chapter 7. Measurement of Cosmogenic Neutron Production

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ggpp
gdir

92

0.9

0.0035

0.8

0.003

0.7
0.0025

0.6
0.5

0.002

0.4

0.0015

0.3

0.001

0.2
0.0005

0.1
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

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EventsFigure 7.3: Distribution of gvtx and gdir for neutron capture on Gd in the MC. The color scale isthe number of events normalized by area. The gray dashed lines are the cut thresholds.

106

SK-VI (283.2 days)
Data (on-time)

105

Data (off-time × 2)

104
103
102
10
1

0

10

20

30

40

50

60

70

80

90

N 50
Figure 7.4: Distributions of N50 for the data in on-time (40 µs and o↵-time (430 µs  t  530 µs) window (dotted line).

t  240 µs) window (solid line)

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Events

7.5. Number of Neutrons

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240

430

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530<latexit sha1_base64="7+lV7DYuRADGzYpyvPvS6VlLulc=">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</latexit>O↵-time<latexit sha1_base64="7XvVR85VSz7dD9G9p05PnmTOV0I=">AAADWXichVLLThRBFD0zzWMceczIhsQNOIGwYVJDQI0roht38nCABMiku6mGyvQr3TWj2OEH/AEXxoUmagyf4cYfYEH8AuMSEzcuPN3T0fAYqE7XPXXuOVW3HlboqlgLcVooGgODQ8OlW+XbI6Nj45XqnY046ES2bNqBG0RblhlLV/myqZV25VYYSdOzXLlptZ+k+c2ujGIV+M/1YSh3PXPfV46yTU2qVanuaPlSR17yzHHmtfLkUatSE3WRtanLoJGDGvK2ElQLk9jBHgLY6MCDhA9N7MJEzG8bDQiE5HaRkIuIVJaXOEKZ3g5VkgqTbJv9PkfbOetznM4ZZ26bq7j8IzqnMCNOxBdxJr6JY/FD/Ok7V5LNkdZyyGj1vDJsjb+eXP99o8tj1Dj477q2Zg0HD7NaFWsPMybdhd3zd1+9OVt/tDaTzIoP4ifrfy9OxVfuwO/+sj+uyrW319RjsZb+J5bmI+I2sc51e8QOY5zfxgFqvI2EjM9T1IzTGdNPbV2hv9qTRjd3XtSH/27dZJ4+vrHGxRd1GWws1Bv360uri7Xlx/lrK+Eu7mGOqz/AMp5iBU2ewAu8wyd8Ln43CkbJKPekxULumcC5Zkz8Bfb2ucM=</latexit><latexit sha1_base64="oT3ZncchpN7M/82EOUcdvKp1S4s=">AAADYnichVK7bhNBFD328gjmETtpIqAwWEGJhKwxIoCoIqCgzAMnkbKRNbsZxyvPPrQ7thRWkaj5AQoqkEBCFPAPNPwARXoaRBkkGgrOrlcgkjjMaueeOfecmTsPJ9JeYoTYL5WtU6fPnJ04Vzl/4eKlyWptai0JB7Gr2m6ow3jDkYnSXqDaxjNabUSxkr6j1brTf5jl14cqTrwweGJ2I7Xly53A63quNKQ61cv2I6WNrBv75pztS9OL/dT2B/Vkb75TbYimyFv9KGgVoIGiLYW10gxsbCOEiwF8KAQwxBoSCb9NtCAQkdtCSi4m8vK8wh4q9A6oUlRIsn32OxxtFmzAcTZnkrtdrqL5x3TWMSu+iHfiQHwW78U38WvsXGk+R1bLLqMz8qqoM/l8ZvXnf10+o0Hvr+vEmg26uJfX6rH2KGeyXbgj//Dpi4PV+yuz6Q3xWnxn/a/EvvjEHQTDH+6bZbXy8oR6HNYy/sSyfEzcJzaFbpu4y5gUt9FDg7eRkgl4iobxWs6MUzvH6I/3ZFEXzsP66M+tS+bp4xtrHX5RR8HarWbrTnNh+XZj8UHx2iZwBdcxx9XvYhGPsYQ2T+AZ3uIDPpa/WhWrZk2PpOVS4ZnGP826+huc4ryP</latexit>

Figure 7.5: Schematic illustration oft (µs)

t distribution and on-/o↵-time windows.

of multiple neutrons as explained in Section 7.6. To suppress the contamination of the events ofa single ray with 2.2 MeV from neutron capture on hydrogen, the threshold criterion is set as
24  N50  70. The signal efficiency resulting from the N50 cut is estimated as (80.22 ± 0.27)%,
utilizing the distribution of neutron captures in the MC. The uncertainty is attributed to MC
statistics. Details of systematic uncertainties are explained in Section 7.6.4.

7.4.4

Transverse Distance from Muon Track

In order to select events that are correlated with muons, it is e↵ective to use the transverse distance
between the muon track and the reconstructed vertex. The definition of the transverse distance
Lt is shown in Figure 6.7 in Section 6.4.5. Figure 7.7 shows the distribution of Lt of the data
after all cuts except for the Lt cut are applied. For this analysis, the selection criterion is set as
Lt < 500 cm. The signal efficiency is calculated as (97.25 ± 0.10)% from the data after backgroundsubtraction.

7.5

Number of Neutrons

Number of events after each selection criterion is summarized in Table 7.2. Because the background
events remain after all event selections, the number of signals for neutron capture on Gd is estimatedfrom the distribution of the time di↵erence between the muon and the following neutron candidates,
t. Figure 7.8 shows t for the data after all selection criteria are applied. The t distribution
follows an exponential function with a small flat component due to the background events. The
total number of neutron capture signals is extracted by a fit to the t distribution. The capture
time of neutrons in SK is measured using the Am/Be source as 116.4 ± 0.3 µs for a single neutron
emitted from the Am/Be source. While, the multiple neutron production by the cosmic-ray muonscauses the missing of neutrons due to the data acquisition described in Section 6.5. Therefore,Chapter 7. Measurement of Cosmogenic Neutron Production

Events

94

×103
140
SK-VI (283.2 days)
Data
MC (total)
MC (Gd capture)
MC (H capture)

120
100
80
60
40
20
0

0

10

20

30

40

50

60

70

80

90

N 50

Events / 100 cm

Figure 7.6: Distribution of N50 for data (black points, background subtracted) and MC (red lines).
Contributions of the Gd capture (dashed line) and hydrogen capture (dotted line) are also plotted.
All cuts except for the N50 cut are applied for the data and the remaining background is evaluatedfrom o↵-time (430 µs  t  530 µs) and subtracted from on-time (40 µs  t  240 µs). Only
the event quality cut is applied for MC and the entries of the total MC distribution are normalized
to the data by the height of the peak. The gray dashed lines are N50 cut thresholds.

106
105

SK-VI (283.2 days)
Data (on-time)
Data (off-time × 2)
Data ((on-time)−(off-time)×2)

104
103
102
10
1
0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Distance from muon track (cm)Figure 7.7: Distribution of transverse distance (Lt ) between the muon track and the reconstructedvertex for data (black points). The background is evaluated from o↵-time (430 µs  t  530 µs,
dotted line) and subtracted from on-time (40 µs  t  240 µs, solid line). Since neutrons arecaptured on Gd after ⇠100 µs on average, events also occur in the o↵-time range and a peak is seen
within 500 cm. The dashed line is the Lt cut threshold.

7.5. Number of Neutrons

95

Table 7.2: Number of observed events after each selection

Events / 1 µs

Event selection
Analysis volume
Event quality
Number of hit-PMTs N50
Transverse distance Lt

Number of events
1,825,281,155
478,986,895
3,363,430
3,084,524

30000
SK-VI (283.2 days)
Data
Fit result
Neutron capture component

25000
20000
15000
10000
5000
0

50

100 150 200 250 300 350 400 450 500∆t (µs)Figure 7.8: Distribution of the time di↵erence between the muon and the following neutron
capture candidates. The data are shown by filled circles. The solid red line is the fit result with
Eq. (7.1). The dashed blue line is the neutron capture component. The reduced 2 is found to be
2 /d.o.f. = 500.6/487 as the fitting result, corresponding to a p-value of 32.5%.
variation of the e↵ective capture time should be taken into account for several neutrons emitted
from muon spallation. Since the t dependence of the inefficiency follows an exponential function,
the t distribution is fitted with the function:
✓
✓
◆
◆✓
✓
◆◆
t
t
f ( t) = A exp+B
1 C exp
,
(7.1)
⌧n
⌧d
in which A, C, and ⌧d are parameters determined by a fit. The first part of Eq. (7.1) corresponds tothe neutron capture components and the second part represents the inefficiency due to the dead timee↵ect. ⌧n is the neutron capture time constant obtained from measurements of Am/Be calibrationas ⌧n = 116.4 ± 0.3 µs and A represents the normalization of neutron events. B represents the
background rate which was estimated to be 27.80 ± 1.57 using the data obtained with random
triggers. B is fixed in the fit at the central value and the uncertainty on the background estimationis accounted as the systematic uncertainty. The second term absorbs the e↵ect of dead time withthe time constant ⌧d and the normalization parameter C. The dead time e↵ect is more significant
at small t where the neutron captures are more frequent and it is gradually moderated with t.
The best-fit parameters are A = (4.39 ± 0.02) ⇥ 104 , C = 0.256 ± 0.003, and ⌧d = 216.6 ± 10.0 µs.
It is confirmed with a toy MC for di↵erent neutron multiplicities that the time dependence andmagnitude of the dead time e↵ect are reasonable. The total number of detected neutron captureChapter 7. Measurement of Cosmogenic Neutron Production

Entry

96

1
0.9

<latexit sha1_base64="IPzcnulqQInl2/AmpUcCmDjc+9c=">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</latexit>

exp

0.8

✓
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0.7

✓

1

t

◆

⌧n
✓
exp

t
⌧th

◆◆

exp

✓

t
⌧n

◆

0.6
0.5
0.4
0.3
0.2
0.1
0
0

100

200

300

400

500

600

∆t (µs)Figure 7.9: Shapes of the normal exponential function and the exponential function considered
neutron thermalization. ⌧n and ⌧th represent the time constants for neutron capture on Gd andthermalization of neutron in water, ⌧n = 116.4 µs and ⌧th = 4.3 µs, respectively.
signals, Sn is obtained as Sn = (3.57 ± 0.02) ⇥ 106 using the integral:✓◆Z 530 µs
t
Sn =
A exp
d( t).
⌧n
40 µs

(7.2)

The signal efficiency for the time window ✏t is obtained by dividing Sn by the integral fromzero to infinity for the function f ( t). Here, it should be taken into account that neutrons arethermalized before being absorbed by Gd and that thermalization takes several µs. Therefore, inthe short t region, the functional form deviates from the exponential function. The time for theneutrons to thermalize in water is taken into account in the following function:
✓
✓
◆◆
✓
◆
t
t
fth ( t) = A 1 exp
exp
,
(7.3)
⌧th
⌧n
where ⌧th is the time constant for thermalization of neutrons in water, ⌧th = 4.3 µs [60]. The shapeof the function is shown in Figure 7.9. ✏t is evaluated from the ratio of integrals from 40 to 530 µs
to integrals from zero to infinity for the function fth ( t) as follows:✏t = Z 1

Sn

(7.4)

fth ( t) d( t)0As the result, the signal efficiency for the time window ✏t is evaluated to be (72.45 ± 0.39)%.
The total number of neutrons produced by the muons can be obtained by correcting Sn for thesignal efficiency:
Sn
Nn =
,
(7.5)
✏
where Nn is the total number of neutrons and ✏ is the signal efficiency given by a product of theefficiencies for each event selection summarized in Table 7.3. The neutron capture fraction on Gd

7.6. Systematic Uncertainties

97

Table 7.3: Summary of the signal efficiencies for each event selection. The efficiency for the volume
cut is calculated by the ratio of the analysis volume to the full volume. The Gd capture fraction
and the uncertainty are estimated from the neutron capture time constant by the Am/Be calibration (Section 4.4) based on the correlation given by the GEANT4-based simulation. The otheruncertainties are statistical.
Event selection
Analysis volume
Gd capture fraction
Event quality
Number of hits N50
Transverse distance Lt
Time window
Total

Efficiency (%)
45.39
47 ± 192.62 ± 0.29
80.22 ± 0.27
97.25 ± 0.10
72.45 ± 0.39
11.17 ± 0.08

Table 7.4: Summary of the systematic uncertainties on the measurement of neutron yield.
SourceNumber of muons
Muon path length
Gd capture fraction
Gd capture time
Neutron thermalization
Signal efficiency for Lt cut
Signal efficiency for N50 cut
Contamination of hydrogen capture
Leak-in/-out of neutrons
Background estimation
Total

Uncertainty (%)
2.0
1.3
2.2
1.2
2.2
0.6
4.7
0.4
2.2
0.3
6.7

depends on the Gd concentration in water and the neutron capture time constant. The Gd capture
fraction is estimated to be 47% from the correlation with the neutron capture time constant givenby the GEANT4-based simulation with the uncertainty estimated to be 1%, which corresponds toa systematic uncertainty of 2.2% for Nn . Total signal efficiency was obtained as (11.17 ± 0.08)%.

7.6

Systematic Uncertainties

The systematic uncertainties on the measurement of neutron yield are described in this section.
The systematic uncertainties are summarized in Table 7.4. The total systematic uncertainty is
estimated to be 6.7% by adding all in quadrature.

7.6.1

Muon Tracks

The uncertainties associated with the count of muons and the path length originate from theperformance of the muon fitter. In the case of multiple muons, simultaneously incident muons
are counted up to ten muons, and the reconstruction assumes their parallel traversal throughthe detector. To validate the accuracy of the counting by the muon fitter, the number of muontracks is counted by eyes from the event display by identifying the entry and exit points of muons.
The examples of event displays for well-/mis-reconstructed events are shown in Figure 7.10. A
discrepancy of 2.0% is found in the comparison of the results for 2,000 events by eye-scan and the

98

Chapter 7. Measurement of Cosmogenic Neutron Production
Super-Kamiokande VI

Super-Kamiokande VI

Run 85806 Sub 1 Ev 129046

Run 85806 Sub 177 Ev 162454961

21-04-01:15:11:57

21-04-01:18:12:06

Inner: 9328 hits, 162826 pe

Inner: 10908 hits, 1153481 pe

Outer: 345 hits, 1580 pe

Outer: 480 hits, 2342 pe

Trigger: 0x1000000f

Trigger: 0x1000000f

D_wall: 1690.0 cm
Evis:

D_wall: 1690.0 cm
Evis:

0.0 MeV

Solar: E=

0.00 MeV

0.0 MeV

Solar: E=cos(sun)= 0.000

0.00 MeVcos(sun)= 0.000

Solar: gdn= 0.00 dirks= 0.00

Solar: gdn= 0.00 dirks= 0.00

Charge(pe)Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

1500

2400

1200

1920

900

1440

600

960
480

300

0

0
0

500

1000

Times (ns)

1500

2000

0

500

1000

1500

2000

Times (ns)Figure 7.10: The example of event displays for a well-reconstructed event (left) and a misreconstructed event (right) for multiple muons. For the well-reconstructed event, two tracks arerecognized by both the eye-scann and reconstruction by muon fitter. For the mis-reconstructed
event, four tracks are recognized by the eye-scan from the entering and exit points while the reconstructed number of tracks is six.

muon fitter. This value is factored in as the systematic uncertainty associated with Nµ , stemmingfrom the accuracy of the muon fitter.
The accuracy of the path length reconstruction has been estimated to be 30 cm for each track.
This is caused by the granularity of the PMTs on the wall which are arranged with ⇠50 cm intervals.
The systematic uncertainty on the neutron yield due to the measurement of Lµ is estimated to be
1.3%.

7.6.2

Neutron Capture

The systematic uncertainty associated with the Gd capture time is assessed at 1.2%, taking into
account the uncertainty on ⌧n . Although the cut on N50 , 24  N50  70, is designed to selectneutron captures on Gd, a small fraction of neutron captures on hydrogen is contaminated in the
final neutron capture candidates (as shown in Figure 7.6). According to the MC, the proportionof neutron capture on hydrogen nuclei is 0.4%. This value is accounted for as the systematic
uncertainty.
Uncertainty on the Gd capture fraction is mainly due to the modeling of the neutron thermalization process. As the ratio of neutron capture cross sections for hydrogen to Gd is higher
at higher energy, a fraction of Gd capture becomes smaller for a slower thermalization process.
A Geant3-based [70] detector simulation is used in Super-Kamiokande (SKDetSim) including thisstudy. However, a high precision transport model for neutrons is not implemented in Geant3. Since
the physics processes of neutrons become more important in SK-Gd, Geant4-based [71] detector
simulation (SKG4) is being developed. SKG4 can describe the physics process of neutrons moreaccurately. In order to estimate the uncertainty on the neutron thermalization, Gd capture fractions are compared with SKDetSim and SKG4 while changing the neutron kinetic energy from
1 MeV to 100 MeV. The maximum deviation between SKDetSim and SKG4 is found to be 1%. The
systematic uncertainty on the neutron yield measurement stemming from the 1% uncertainty on
the Gd capture fraction from the neutron thermalization model is estimated to be 2.2% from thedi↵erence.

Events

7.6. Systematic Uncertainties

99

45000
SK-VI (283.2 days)
Data (M = 1)
Data (M ≥ 10)
MC

40000
35000
30000
25000
20000
15000
10000
5000
0

25

30

35

40

45

50

55

60

65

70

N 50
Figure 7.11: Comparison of N50 distributions for MC (solid red line) with data for M = 1 (filled
circles) and M 10 (open circles), where M is the number of neutron capture candidates following
a muon that remain after the event selections.

7.6.3

Transverse Distance

The systematic uncertainty of the Lt cut is evaluated by applying di↵erent Lt cuts with thresholds
ranging from 400 to 600 cm. The resolution on the muon entrance position is ⇠50 cm. The vertex
resolution for neutron capture on Gd was measured by the calibration with AmBe source to be⇠100 cm. Therefore, the threshold 500 cm for Lt cut is sufficiently larger than the resolutions ofevent reconstructions. The variation of neutron yield was checked by changing the cut thresholdby ±100 cm, which is a comparable size to the resolutions of event reconstructions. The relative
variation is below 0.6%, which is assigned as the systematic uncertainty.

7.6.4

Number of Hit-PMTs

The primary source of systematic uncertainty lies in the signal efficiency related to the N50 cut.
As explained in Section 7.5, N50 represents the number of hit-PMTs within a 50 ns time window,
which is strongly correlated with the total energy of rays generated in the detector. In the N50
distribution shown in Figure 7.6, a 4.1% disparity in the N50 scale is observed between the data
and the MC. This value is estimated by scaling the MC distribution to fit the data in the range
24  N50  70. While neutrons are generated uniformly in the ID one at a time in the MC, several
neutrons are produced at once from muon spallation and multiple neutron captures can occur
simultaneously within the same time window. Inefficiency is caused by this feature as explained in
Section 7.5, and in addition, N50 from the data tends to be larger due to overlaps of hit-PMTs inthe same time window. The correlation between the number of neutron capture events following
a muon and the N50 distributions is shown in Figure 7.11 in which MC is generated with single
neutrons. For candidates with single neutron capture, the discrepancy is 1.6%, while it is 7.9% forevents with greater than or equal to ten neutron captures. As the number of neutron candidates
increases, the discrepancy increases due to the pile-up e↵ect. This pile-up e↵ect is also confirmedin the MC with multiple neutrons generated simultaneously as shown in Figure 7.11. As there is
no reliable model to predict the number of neutrons produced by the cosmic-ray muon spallation

100

Chapter 7. Measurement of Cosmogenic Neutron Productionµ<latexit sha1_base64="U+YSSQPLQT6nOnjGiWjje0N41AM=">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</latexit>µµ<latexit 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SK<latexit sha1_base64="yOvB8ZXUOJzFBJMdjcXwlyoJVPU=">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</latexit>

SK<latexit sha1_base64="yOvB8ZXUOJzFBJMdjcXwlyoJVPU=">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</latexit>

Figure 7.12: Schematic illustrations of leak-in/-out of neutrons around the detector center (left)
and near the detector wall (right). As shown in the left hand figure, the event rate around thecenter of the neutron capture is expected to be uniform as the numbers of neutrons that leak-in
and leak-out are likely balanced. While, in the right hand figure, the event rate near the wall is
expected to be lower than that around the center because the muon correlation is not taken.

at the underground detector, the systematic uncertainty of 4.7% is assigned to account for thevariation in the N50 scale. The uncertainty on the signal efficiency for the N50 cut is estimated to
be 4.7% from the variation when the N50 distribution is scaled by 4.1%.

7.6.5

Leak-In and Leak-Out of Neutrons

Leak-in/-out of neutrons is one of the main sources of systematic uncertainty in other experiments,
such as KamLAND [43] and Daya Bay [42]. The fraction of leak-in and leak-out neutrons to thetotal neutron captures depends on the ratio of surface area to volume of the detector (⇠ 1/r). Since
SK has a larger volume than the other detectors listed above, a fraction of leak-in/-out neutrons
should be smaller. The event rate of neutron capture around the center of the ID is expected to
be uniform as the numbers of neutrons that leak in and out are likely balanced. On the other
hand, the event rate near the ID wall is expected to be lower than that around the center. Thisis because when muons penetrate the surrounding rock or the OD, neutrons from their spallation
are not counted even if they are reconstructed in the ID because the parent muons are not taggedin this analysis. The schematic illustrations described in the above are shown in Figure 7.12. A
systematic uncertainty of 2.2% is assigned to account for the leak-in/-out by changing the boundaryof the fiducial volume from 5 to 7 m from the ID wall.

7.6.6

Background Estimation

The uncertainty on the background estimation was evaluated to be 5.7% from the statistical uncertainty of the random trigger sample. Systematic uncertainty on the neutron yield measurement
is evaluated from this value to be 0.3% by fitting the t distribution shown in Figure 7.8 varying
the parameter B in Eq. (7.1).

7.7. Results

101

Table 7.5: Average muon energy and neutron yield for each azimuthal angle of incident muons.
The units of the neutron yield are 10 4 µ 1 g 1 cm2 . The error is statistical only.
Azimuthal angle
315 –45
45 –135
135 –225
225 –315

7.7

Fraction (%)
19.4
11.5
27.1
42.0

E µ (GeV)
265
272
257
253

Yn
2.81 ± 0.05
2.88 ± 0.06
2.77 ± 0.04
2.67 ± 0.03

Results

The neutron yield Yn is defined as the neutron production rate per unit muon track length and perunit density, which can be calculated as
Yn =

Nn
Sn
=
,
Nµ Lµ ⇢
✏Nµ Lµ ⇢(7.6)

where ⇢ is the density of the Gd-loaded water, ⇢ = 1.000 g/cm3 with 0.026% concentration of
Gd2 (SO4 )3 · 8H2 O. The uncertainty of the density is less than 0.1% and negligible compared to beother uncertainties. The other parameters are as previously described: Sn = (3.57 ± 0.02) ⇥ 106 ,✏ = 11.17 ± 0.08%, Nµ = 4.77 ⇥ 107 , and Lµ = 2,427 cm. Definitions of these parameters are
explained in the previous sections. It should be noted that the neutron yield includes both primary
neutrons from muon spallation and secondary neutrons from hadronic interactions. The neutron
yield is measured to be (2.76 ± 0.02 (stat.) ± 0.19 (syst.)) ⇥ 10 4 µ 1 g 1 cm2 .
Figure 7.13 shows the comparisons with other experiments. Most of those yields were measured
using liquid scintillators except for the SNO experiment which measured the yield in heavy water.
Super-Kamiokande is the first experiment to measure the yield in light water. The KamLAND
detector is located in the same mountain as the SK detector at almost the same depth. Although
the target material in the SK detector is water and di↵erent from the KamLAND detector, themeasured neutron yields are consistent within the uncertainties.
In addition, neutron yields are calculated for each muon direction. Due to the shape of themountains surrounding SK, the flux and average energy of muons from each azimuthal angle at thedetector site are di↵erent. The azimuthal dependence of the muon flux is shown in Figure 7.2. The
azimuthal distribution is divided into four parts of 90 each, and the muon energy and neutron
yield are estimated for each region. The results shown in Table 7.5 show that the higher the muonenergy, the greater the neutron yield, as expected.

Chapter 7. Measurement of Cosmogenic Neutron Production

Neutron yield (µ −1 g−1 cm2)

102

10−3
SNO
LVD-corrected
Borexino
Super-K

KamLAND

Daya Bay−4

Aberdeen

10

Boehm
Prediction for liquid scintillator (LS)
Water-based measurements
LS-based measurements

Hertenberger

10−5
0

50

100

150

200

250

300

350

400

Average muon energy (GeV)
Figure 7.13: Correlations between neutron yields and muon energies in various experiments. The
muon energy corresponds to the depth at which the detector is located. The filled circles represent
the water-based results [46]; in particular, the red one shows the result of this analysis. The open
circles represent the measurements with liquid scintillator (LS) detector [37, 39, 40, 42–45]. The
gray solid line shows predictions for LS using FLUKA [47].

Chapter 8

Measurement of Cosmogenic
Lithium-9 Production
Cosmic-ray muons induce the secondary showers in water, which interact with 16 O and produce
neutrons and various radioactive isotopes. Of those isotopes, 9 Li is one of the major backgroundsources in the search for SRNs below ⇠14 MeV. 9 Li emits an electron and a neutron via decay at
a branching ratio of 50.8% (9 Li + n decay, 9 Li ! 8 Be + e + ⌫¯e + n). The 9 Li + n decay can fakethe inverse beta decay of SRNs (¯⌫e + p ! e+ + n) as e+ and e can not be distinguished by the SK
detector. The 9 Li decays with a lifetime of 0.257 s and a Q-value of 13.6 MeV. This lifetime is larger
than the veto time after muons which is set to 1 ms with 2 s 1 muon rate. The SRN analysis in SK
uses correlations between the muon and electron events such as the time di↵erence from the muonto the electron event and the distance from the muon track to the vertex position of the electron
event to reduce the background. While, a fraction of the 9 Li + n decay events remains after event
reduction and becomes the background for the SRN search. Therefore, it is important to measure
the energy spectrum of 9 Li in advance in order to estimate the amount of the 9 Li background in
the SRN search. The previous 9 Li analysis was performed above 8 MeV, the same energy range
as the SRN search with the data in SK with ultra-pure water [50], while the energy range of the
SRN search will be expanded to the low-energy side below 8 MeV in SK with Gd-loaded water toincrease the statistics of the data and improve the sensitivity. In this study, the analysis method
was newly developed for the data taken with Gd-loaded water, and the 9 Li energy spectrum wasmeasured down to 4.5 MeV for the first time in the SK detector.

8.1

Overview of 9 Li

+ n Decay Event Search

The 9 Li events were selected by searching for pairs of electron events and neutron capture on Gd(n-Gd capture) events following cosmic-ray muon events. Figure 8.1 is the schematic illustrationof the time correlations of these three events. In this analysis, the pair of the electron and nGd capture event was searched first, and then the parent muon of the 9 Li isotope was searchedwithin the previous one second. Hereafter, an electron event and a neutron capture event are called“prompt event” and “delayed event”, respectively. The analysis flow is as follows.
1. An electron and a neutron are emitted from 9 Li decay. The signal from the electron should
be observed first (prompt event), and then the neutron is thermalized in water, and rays
are emitted after the thermalized neutron is captured on the surrounding hydrogen or Gd(delayed event). The selection criteria are set to collect n-Gd capture events in this analysis
in the time window from 35 µs to 535 µs after the prompt events. The pairs are selectedusing the information of the reconstructed energy and the distance between the prompt anddelayed events.
2. The presence of a 9 Li

+ n decay event means that there should be a cosmic-ray muon that
103

104

Chapter 8. Measurement of Cosmogenic Lithium-9 Productionµ<latexit sha1_base64="U+YSSQPLQT6nOnjGiWjje0N41AM=">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</latexit>

9n<latexit sha1_base64="EhetYRq8JAUdhhDe84asDnB+9k4=">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</latexit>

16<latexit sha1_base64="oeptCw94cxZ6ZzVnsVkF5gZhoH0=">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</latexit>

Li<latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit><latexit sha1_base64="BGVqV4zPsetai59b6kYRfwPdMRk=">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</latexit>

O
Gd<latexit sha1_base64="sNb5RJY5JC8ACNrbtMq5MxBpLlE=">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</latexit><latexit sha1_base64="YqfZajT+AlOGaP82ZKn5u1sqPcs=">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</latexit>e<latexit sha1_base64="sKi0+qT7Z8rBwtjjWse6neZAyAU=">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</latexit>

535 µs1s<latexit sha1_base64="SSHM+4XrkW+CCGWhEMmMJWneWqk=">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</latexit><latexit sha1_base64="8XvfsMHC5kZ1rnwFJvGBJJpFfhU=">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</latexit>t<latexit sha1_base64="V0ntX0MQixK0O85ifmWQE/v5P3E=">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</latexit>

Muon<latexit sha1_base64="eYHymf2LT5MtKyaMUs4tZ/dfl+E=">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</latexit>

Prompt<latexit sha1_base64="nKCou5Q+vzztsUKqH617q42ZC0U=">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</latexit>

Delayed(n-Gd capture)<latexit sha1_base64="lDEnlBBae/zf3rv5BIMPusBOMIU=">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</latexit><latexit sha1_base64="gVMZobHT4bJ2Of3LRG/tgBuhR2I=">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</latexit><latexit sha1_base64="j7d4+yEktDQtAEwxQ3g3D4DdfEI=">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</latexit>(e )Figure 8.1: Overview of cosmogenic 9 Li analysis in SK.
induced the 9 Li at the time preceding the 9 Li + n decay event. In this analysis, if thepair of prompt and delayed events is found in Step 1, the muon is searched within 1 s before
the prompt event. As there are more than one muons within 1 s in general with the muon
rate of 2 s 1 in the SK detector, the candidate muon is selected using the likelihood which isdefined by the variables for the features of muons with large energy deposit in the detector
due to the spallation interaction and the spacial relationship between the muon track and theprompt event vertex. If there are muons within 1 ms immediately before the prompt event,the prompt and delayed events are not selected as 9 Li candidate because these events arelikely caused by muon-induced neutrons.
3. If the triple coincidence of muon, prompt, and delayed event is found, the time di↵erence
between the muon and prompt events ( tpd ) is calculated.
tpd is used to evaluate thenumber of the 9 Li + n decay events by fitting the distribution. The fit is applied for eachenergy region of prompt events to extract the number of 9 Li + n decay in each energy, andthe spectrum of the 9 Li + n decay is obtained.

8.2

Selection of Prompt and Delayed Event Pair

8.2.1

Preselection

Cherenkov photons are emitted due to the environmental radiations from the rock surrounding thedetector or PMTs mounted on the wall. To eliminate such backgrounds, the events are selectedwith the distance between the vertex position and the inner detector (ID) wall, dwall . Eventswith dwall > 2 m are used in the analysis. The region corresponds to the volume of 22.5 kton.
Furthermore, the directions of the background events occurring near the ID wall are mostly inward.
Therefore, in addition to the selection criteria for the distance between the event vertex position
and the ID wall, the distance to the wall along the direction of the particle (Cherenkov ring) isused as a selection criterion. Such distance is called e↵ective distance de↵ , which is defined by thereconstructed vertex and direction as the distance from the reconstructed vertex to the ID wallback along the reconstructed direction. A schematic illustration is shown in Figure 8.2. Because

8.2. Selection of Prompt and Delayed Event Pair

105

SK outer detector
SK inner detector

deff
ReconstructedvertexReconstructed
direction

Figure 8.2: The definition of the e↵ective distance from the ID wall de↵ .
the energy of environmental radiation is distributed mostly below a few MeV, the selection criteria
are set separately for the region of reconstructed energy Erec : de↵ > 650 cm for Erec < 5 MeV
and de↵ > 400 cm for Erec
5 MeV. A tighter cut is applied for lower energy events to suppress
the contamination of the background due to environmental radiation. Note that this cut alreadyhas been applied as part of data acquisition (real-time process) to reduce the data storage. In
the real-time process, the cuts for event quality and reconstructed energy have been also applied:g 2 0.10 and Erec 3.0 MeV.
Since prompt and delayed event pairs will be searched, prompt event candidates are removed
if there are no other events within the following 535 µs.

8.2.2

Event Quality Cut

In order to reject the background event due to PMT dark noise, the event quality cut is applied.
The goodness of vertex reconstruction gvtx and the goodness of direction reconstruction gdir wereused for the event quality cuts. The explanations of gvtx and gdir are described in Section 5.1.
Both gvtx and gdir take values from zero to one. The larger gvtx and the smaller gdir are given for
more reliable reconstruction results (i.e. hit pettern and timing distribution consistent with the2
2 takes a value from 1 to +1,
Cherenkov light from charged particles). Therefore, g 2 ⌘ gvtx
gdirwith a larger value for higher event quality. In this analysis, an event satisfying g 2
0.25 wasobtained as the prompt event candidate.

8.2.3

Energy Cut

Figure 8.3 shows the reconstructed total energy Erec of the prompt events for the data after thefiducial volume cut is applied. The event rate increases at lower energy due to environmental
radiations remaining in the fiducial volume. The prompt event candidates that satisfy 4.5 MeV 
Erec < 14.5 MeV are selected in this analysis. In SK, triggers are issued for events with morethan 34 hit-PMTs, and the data is recorded. This trigger threshold corresponds to the energy of⇠3.5 MeV, but because the number of hit-PMTs depends on the event vertex positions and has
statistical fluctuation, the detection efficiency at 3.5 MeV is ⇠50%. The lower energy threshold

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Events

106

9

10

8

10

107
6

10

5

10

104
3

10

102
10
5

10

15

20

25

30

Reconstructed total energy (MeV)
Figure 8.3: Reconstructed total energy of the prompt events for the data after the fiducial volume
cut is applied. The events with the energy of 4.5–14.5 MeV are selected as the prompt event
candidates in this analysis.
for this analysis is set to 4.5 MeV to ensure a detection efficiency of ⇠100%. The upper limit isdetermined to be 14.5 MeV to cover the reconstructed energy spectrum of the 9 Li + n decay
generated from the MC simulation shown in Figure 8.4.

8.2.4

Neutron Tagging

A delayed event (n-Gd capture) was searched within 535 µs after the prompt event (electron). The
selection criteria for delayed events are listed as follows.
(1) Event selections are applied using the distance between the vertex positions and the ID wall
as follows (same as the prompt events):• dwall > 200 cm• de↵ > 650 cm for Erec < 5 MeV• de↵ > 400 cm for Erec

5 MeV.

(2) 35 µs  tpd  535 µs, where
delayed events.
(3)

tpd represents the time di↵erence between the prompt andg 2 0.10, where g 2 represents the event quality (Section 5.1). g 2 for MC and data areshown in Figure 8.5. This cut eliminates the background events due to PMT dark noise andmis-reconstructed events.

(4) 3.5 MeV  Erec < 10 MeV, where Erec represents reconstructed total energy. The range ofthe cut is defined to select a total 8 MeV rays emitted from neutron capture on Gd. Erec
distributions for the data and MC are shown in Figure 8.6. The peaks of the distributions
are shifted from 8 MeV for the reasons explained below.
(5)

r < 350 cm, where r is the distance between the prompt and delayed vertex (Figure 8.7).
The upper limit was set to suppress the accidental coincidence of two background events while
keeping the efficiency to 9 Li + n decays.

107

Events

8.2. Selection of Prompt and Delayed Event Pair

5000
True

4000

Reconstructed

3000

2000

1000

0
0

2

4

6

8

10

12

14

16

18

20

Total energy (MeV)
Figure 8.4: energy spectrum of the 9 Li + n decay generated from the MC simulation. The solidline shows the true total energy and the dashed line shows the reconstructed total energy Erec . The
distribution of the reconstructed total energy drops o↵ around ⇠4 MeV because of the efficiency of
SLE trigger which is ⇠50% at 3.5 MeV and reaches ⇠100% at round 4 MeV.
The range of the energy cut is extended with respect to the cut applied to the prompt event selection.
In the prompt event selection, the lower limit is set to 4.5 MeV to measure the spectrum with
⇠100% trigger efficiency independent of the energy. While, the range is extended to the delayed
events to increase the efficiency and avoid the cut around the peak of neutron capture on Gd. As
the energy of the prompt and delayed events are not correlated, the inefficiency of the delayed
events should not cause distortion of the energy spectrum of the prompt events.
The peak of the reconstructed energy of rays is lower than ⇠8 MeV as shown in Figure 8.6 forthe following reasons. When a neutron is captured on Gd, several rays totaling ⇠8 MeV are emitted. These rays interact with electrons through the electromagnetic interactions; photoelectronice↵ect and Compton scattering, then the electrons travel in water and the Cherenkov photons are
emitted. However, the amount of the Cherenkov photons is not proportional to the energy of theelectron below a few MeV due to the Cherenkov threshold. The number of emitted photons perunit energy deposition (photons/MeV) is fewer for electrons with lower energy. In this analysis,
since the energy is reconstructed from the number of detected photons (hit-PMTs) assuming all
photons are emitted from an electron, reconstructed energy is underestimated for the total energyof multiple electrons as in the case of neutron capture on Gd.
If a delayed event that satisfied the criteria was found, the pair was selected as the 9 Li
decay event candidate.

8.2.5

+n

1 ms Veto After Muon

If there are muons within 1 ms before the prompt events, these prompt events are excluded fromthe analysis as these events are likely to be the muon-induced neutrons.

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

EventsEvents (area-normalized)

108

0.14
Signal0.12

Background

5

10

104

0.1

3

0.08

10

0.06

102

0.04
10
0.02
0
−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8

1
0.1

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

∆g2

0.9

1

∆g2

EventsEvents (area-normalized)

Figure 8.5: Distribution of g 2 for neutron capture on Gd for MC and data obtained with random
triggers (left), and the delayed event candidates of the data before the selection criteria are applied(right). The selection g 2 0.10 (dashed line) has been applied for the SLE trigger events in thereal-time process.

0.4
0.35

Signal0.3

Background

5

10

104

0.25

3

10
0.2

102

0.15
0.1

10

0.05
0
0

1
2

4

6

8

10

12

14

Reconstructed total energy (MeV)

5

10

15

20

25

Reconstructed total energy (MeV)

Figure 8.6: Distribution of reconstructed total energy Erec for neutron capture on Gd for the MC
and data taken with random triggers (left), and the delayed event candidates of data before theselection criteria are applied (right). The dashed lines represent the selection criterion 3.5 MeV 
Erec < 10 MeV. The selection Erec 3 MeV has been applied in the real-time process.

109
EventsEvents (area-normalized)

8.3. Selection of Muon Events

0.3
Signal
0.25

20000
18000
16000

Background

14000

0.2

12000
10000

0.15

8000

0.1

6000
4000

0.05

2000

0
0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

∆r (cm)00500 1000 1500 2000 2500 3000 3500 4000 4500 5000

∆r (cm)Figure 8.7: Distribution of the distance between the prompt and delayed vertex, r, for neutron
capture on Gd for the MC and data taken with random triggers (left), and the delayed event
candidates of data before the selection criteria are applied (right). The dashed lines represent the
selection criterion r < 350 cm.

8.3

Selection of Muon Events

Once the pair of prompt and delayed events (prompt-delayed pair) is found, the parent muon
event candidate is searched within the last 1 s. As the muon rate is ⇠2 s 1 at SK, there are often
more than one muon within 1 s. Among those, the parent muon of the 9 Li isotope is selected withthe following five variables which represent the characteristics of energetic muons and spallationinteractions.
• Lt : transverse distance from the the prompt event vertex position to the muon track (Figure 8.8). The positions of muon-induced isotopes decay should be near the muon track.
• Llong : longitudinal distance between the vertex position of the prompt event and the pointin the muon track associated with the maximum dE/dx (Figure 8.8). The point with the
maximum dE/dx is likely to be the point where the muons or induced showers interact withoxygen. Therefore, the muons which produce isotopes should have short Llong .
• Qµ : total number of photons (photoelectrons) observed by the ID PMTs for the muon track.
Muons that produce isotopes should deposit significantly large energy in the detector via thespallation interaction with oxygen.
• Qres : di↵erence between the observed number of photons (photoelectrons) and the expectationfrom the muon track length assuming a minimum ionization particle (MIP). The Qres definedas
Qres ⌘ Qµ q · Lµ ,(8.1)
where q and Lµ are the expected number of photoelectrons per unit length from the minimum
ionization and the muon track length, respectively. The muon that produces isotopes not only
loses energy continuously via ionization but also causes spallation interaction which breaks
oxygen nuclei at a point along the track. Therefore, the energy loss of the muon-induced
spallation interaction should be larger than the energy loss assuming the MIP throughout the
trajectory in the detector.
• Nn : number of spallation neutron candidates following the muon. The muons which produce
isotopes tend to induce electromagnetic and hadronic showers. Those showers interact withoxygen nuclei in a chain, producing many neutrons.

110

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Muon track<latexit sha1_base64="G6YpC/6gIku5zbzRge4zH8VE7qk=">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</latexit><latexit sha1_base64="wAlFTfYEv3C5cYXpleXnmvoG/1Q=">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</latexit>

Max dE/dx

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VertexFigure 8.8: Schematic illustration of transverse distance Lt and longitudinal distance Llong . Max
dE/dx is the point in the muon track associated with the maximum dE/dx.
First, the parent muon candidate is selected with the likelihood method using probability density
functions (PDFs) for four variables Llong , Qµ , Qres , and Nn . Second, the triple coincidence of theprompt-delayed pair and the parent muon is selected as a 9 Li candidate if the Lt for the muoncandidate is less than 500 cm.
As only ⇠104 9 Li isotopes are expected to be produced in the SK detector within the datataking period described in this study due to the small production rate, it is difficult to generate the
PDF for each variable with high precision. Instead, PDFs are generated using another isotope 12 B.
The production yield of 12 B is the largest among cosmogenic isotopes with lifetimes within 1 s [50].
12 B has a lifetime of 0.029 s and emits an electron via
decay with a Q-value of 13.37 MeV. To
generate PDFs for spallation variables, two di↵erent samples were prepared from the data. One isa “pre-sample” composed of prompt-delayed pairs and associated muons within 0.05 s before theprompt event candidate, and the other is a “post-sample” composed of prompt-delayed pairs andassociated muons within 0.05 s after the prompt event candidate. The pre-sample and post-sample
is schematically shown in Figure 8.9. The time width of 0.05 s is selected because 12 B isotopes
are dominant within 0.05 s from muons. If an event with energy of several MeV is due to anelectron emitted from an isotope (mostly 12 B) decays, the pre-sample should contain the muonthat induced the event in addition to uncorrelated muons, while the post-sample should consistof only uncorrelated muons. Hence, the information (distribution of the variables described in
the previous section) for decay events of muon-induced isotopes is extracted by subtracting thepost-sample from the pre-sample.
The PDFs were generated for spallation samples and random samples, separately. The spallation
sample was generated by subtracting the post-sample from the pre-sample, while the random sample
was taken directly from the post-sample. The PDFs of the spallation sample (PDFspall) and randomirandsample (PDFi ) are shown in Figure 8.10, where i represents the variable i = Llong , Qµ , Qres ,and Nn . Using these PDFs for four variables, the spallation likelihood L is defined as!
Y PDFspalli
L = log
.
(8.2)
rand
PDF
i
i
The likelihood L was calculated for each muon within 1 s before the prompt event candidate, and8.4. Extraction of 9 Li Production Rates

111

Pre -region

Post-region<latexit sha1_base64="r/38CLVNjmDAvyFCYpvi8P1DcN4=">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</latexit><latexit sha1_base64="UfwDO6mUDljp/V7Oyp2CNDAFB3Q=">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</latexit>

Time<latexit sha1_base64="CmLt6rW1fCko4TACz/w7spJcANk=">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</latexit>µ<latexit sha1_base64="U+YSSQPLQT6nOnjGiWjje0N41AM=">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</latexit>

LowE event<latexit sha1_base64="NLu9RiiLs1QJ3TspLzph9xj6j7Y=">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</latexit>

Figure 8.9: Definition of pre-sample and post-sample for the spallation variables. The “LowE
event” (star) represents the event with several MeV from the decay of cosmogenic isotope. Muons
around the LowE event are shown by circles. The parent muon induced the isotope (LowE event)should be in pre-region, and not in post-region.
Table 8.1: Reduction summary for 9 Li
Erec (MeV)
Pre-selection
Event quality
Neutron tagging
1 ms cut
Muons
Transverse distance

4.5–5.5
2,606,347
154,737
14,671
1,281
1,114
188

5.5–6.5
206,088
35,63814,445
1,077
954
223

6.5–7.5
39,901
25,923
5,726
689
619
210

7.5–8.5
30,01026,847
720
360
336
147

8.5–9.5
19,156
18,235
219
175
169
101

9.5–14.5
21,974
21,512
304
281
274
186

the muon with the largest L was selected as the parent muon candidate. If the muon candidate
satisfies Lt < 500 cm, the prompt-delayed pair is selected as the 9 Li + n decay event. Otherwise,
the prompt-delayed pair is rejected as there is no parent muon candidate. Figure 8.11 shows the
distributions of Lt for pre-/post-sample and spallation sample.

8.4

Extraction of 9 Li Production Rates

Events that satisfy the triple coincidence of muon, prompt, and delayed event were obtained as 9 Li
candidates. Table 8.1 summarized the number of observed events for each Erec region. For the 9 Li
candidates, following two types of time di↵erence are obtained.
•tµp : time di↵erence between the muon and prompt event•

tpd : time di↵erence between the prompt and delayed eventtµp is used to count the number of 9 Li while tpd is used to confirm neutron capture events are
selected.
The tµp distributions are shown in Figure 8.12 for each Erec region; Erec = 4.5–5.5 MeV, 5.5–
6.5 MeV, 6.5–7.5 MeV, 7.5–8.5 MeV, 8.5–9.5 MeV, and 9.5–14.5 MeV. The excesses in the short timedi↵erence regions are the contributions of 12 B. High-energy muons occasionally produce multiple
12 B’s and other isotopes (X). Some of the isotopes have lifetimes of tens to hundreds of ms, which
is much larger than the time scale of neutron capture but a small fraction still decays within the
535 µs time window. If those decays of the 12 B or the other isotopes occur twice in the same time
window, they are recognized as a pair and become a fake signal of 9 Li + n decay events. Sucha pair is denoted 12 B-12 B/X as at least one of them is decay of 12 B which is dominated in thetime scale of this analysis. The pairs of 12 B-12 B/X remain even after the event reductions to fake9 Li
+ n decay, therefore the tµp distribution was fitted with a combination of two exponentialfunctions including 9 Li and 12 B components:
✓
◆
✓
◆
tµp
tµp
f ( tµp ) = A exp+ B exp
+ C,
(8.3)
⌧9 Li
⌧12 B

112

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Qμ (p.e.)

Llong (cm)

Qres (p.e.)

Nn

EventsEventsFigure 8.10: The PDFs of the spallation sample and random sample. PDFs for Lt (top left), Qµ(top right), Qres (bottom left), Nn (bottom right). The black and red line shows the spallation andrandom sample, respectively.

Distance from muon track (cm)(Pre-sample) − (Post-sample)

Distance from muon track (cm)Figure 8.11: Lt distributions for pre-/post-sample (left) and spallation sample (right). The spallation sample is obtained by subtracting the post-sample from the pre-sample. The dotted line in
the right figure represents the cut threshold.

8.5. Prospects for SRN Search

113

Table 8.2: Summary of the fit results and N9 Li for each Erec region. A, B, and C correspond to
the parameters in Eq. (8.4). The errors are statistical only.
Erec (MeV)
4.5–5.5
5.5–6.5
6.5–7.5
7.5–8.5
8.5–9.5
9.5–14.5A
8.4 ± 3.3
14.5 ± 3.5
17.0 ± 3.6
10.1 ± 3.1
5.4 ± 2.1
12.7 ± 2.6

B
181 ± 22230 ± 25
183 ± 23128 ± 20115 ± 18
220 ± 24C
2.6 ± 0.7
1.6 ± 0.6
1.5 ± 0.6
1.5 ± 0.6
0.7 ± 0.4
0.4 ± 0.4

2 /d.o.f

29.13/17
11.81/17
30.09/17
18.70/17
25.13/17
23.05/17

N9 Li
42 ± 1773 ± 1786 ± 1851 ± 1627 ± 1164 ± 13

where ⌧9 Li and ⌧12 B are the lifetime of 9 Li and 12 B isotopes, which are 0.257 s and 0.029 s, respectively. These parameters are fixed to fit tµp . The parameters A and B represent the normalizations of 9 Li and 12 B events, and C is the background rate. The background is mainly due toradioactivities, such as the decay products of Rn from PMTs which have no correlation with muon.
Therefore, the background component is set to a constant. The number of 9 Li candidates N9 Li is
calculated by integrating the fitting results for each Erec as
✓
◆
Z 1s
tµp
N9 Li =A exp
d( tµp ).
(8.4)
⌧9 Li
1 ms
The fit results and N9 Li for each Erec region are summarized in Table 8.2.
The tpd distribution is shown in Figure 8.13. The tpd distribution was fitted by the single
exponential function✓◆
tpd
f ( tpd ) = An exp+ Bn ,(8.5)⌧nwhere ⌧n represents the time constant for neutron capture on Gd. An is the normalization ofneutron capture events and Bn is the background rate. The parameter ⌧n is determined from thefit as ⌧n = 102.3 ± 14.7 µs, which is consistent with the measurement result from the Am/Be,
116.5 ± 0.2 µs (Section 4.4). The constant component in the distribution of tpd is due to thebackground and 12 B-12 B/X pair. Although the time di↵erence of the 12 B-12 B/X pairs should
follow an exponential function with a time constant of more than a few ten ms, it is long enoughfor the time width of 535 µs to be considered a constant component here.
The spectrum from the 9 Li + n decay was extracted using N9 Li for each Erec region. The
result is shown in Figure 8.14 and compared with the MC. The result is normalized by the fiducial
volume 22.5 kton and the livetime 454.2 days, while the correction for the efficiency is not applied.

8.5

Prospects for SRN Search

The energy spectrum of 9 Li produced by cosmic-ray muons was measured in SK with 0.01% Gdloaded water in this study. The previous study [50] was performed using the data of 1,890 daysin SK with ultra-pure water, where 9 Li events were searched above 8 MeV. In this study, taking
advantage of the neutron detection efficiency and background rejection improved by the Gd loading
to lower energy side, from 8 MeV to 4.5 MeV, using the data of 454.2 days with Gd-loaded water.
Prospects for the SRN search and the relation to this study are described in this section.
The SRN flux depends mainly on the cosmic star formation rate (SFR) which is proportional
to the core-collapse supernova rate. Since neutrinos emitted by old supernovae are a↵ected by theredshift z due to the expansion of the universe, their energy is reduced by a factor of (1 + z) 1 .
Therefore, SRNs with lower energy of a few MeV provide information about the supernovae in theearly stage of the universe as shown in Figure 8.15. Because the uncertainty on the SFR is large
in the old universe, the prediction of the neutrino flux varies larger by the di↵erent models as the

114

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

4.5 MeV

Erec < 5.5 MeV

5.5 MeVData

6.5 MeV

Erec < 7.5 MeV

Data

7.5 MeVData

8.5 MeV

Erec < 9.5 MeV
Data

Erec < 6.5 MeV

Erec < 8.5 MeV
Data

9.5 MeV

Erec < 14.5 MeV
Data

Figure 8.12: Distribution of time di↵erence between muon and prompt event tµp for each reconstructed total energy Erec . The black circles represents the data and the solid blue line is the fit
result. The dotted red, green, and gray lines are 9 Li, 12 B, and constant component in the fitting
function Eq. (8.3), respectively.

8.5. Prospects for SRN Search

115

Data
Fit result

Δt between prompt and delayed event (μs)

Li→β+n candidates / kton / day / MeV

Figure 8.13: Distribution of time di↵erence between prompt and delayed event
circles represents the data and the solid blue line is the fit result with Eq. (8.5).

tpd . The black

0.014

Data

0.012

MC

0.01

0.008

9

0.006
0.004
0.002
0

5

6

7

Figure 8.14: The

8

9
10
11
12
13
14
Reconstructed totalbsenergy
energy (MeV)(MeV)

spectrum from the 9 Li

+ n decay.

R FORMATION RATE AND SUPERNOVA NEUTRINOS
116

5

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Figurefromvariousredshiftthe supernova
modele reference modelsof 8.15:
originalSRN fluxF IG. 3.—
SRN fluxfrom ranges
various assuming
redshift ranges.
LL is adopted
as theof Ref. [72]. This
TBP, and KRJ.figure
The fluxof at- fromsupernova
is takenRef. [73].model.
rr et al. 1989) is also shown forredshift increases. Figure 8.16 shows the SRN event rates observed in SK for various SFR models.
The di↵erences between
are particularly
pronounced
in the low-energy
whilethethemodels
high-redshift(z > 2) supernova
contribution
is very region. Current
SRN search in SK issmall.
performed above 8 MeV while it is beneficial for the test of SFR models if theenergyger at E = 60
MeV.range
Thisof the search is extended to low energy region.
9
3.2. Event
Rate at Water
Since
the cosmic-ray
muonCerenkov
spallation,Detectors
events with a short distance frommainly contributedby Li
theis produced through9
the muonas Li
events. While,thedetectors
opposite event
selectionsuccriteria are applied
eutrino spectrum;in track
the were selected
The water
Cerenkovneutrino
have greatly
in
the
SRN
search,i.e.
eventswithalong
distance
from
the
muon
track
are
selected.
Therefore,
age energy of the harderceeded in probing the properties of neutrinos as elementarytheSRN
analysisinthelow-energy
regionisfeasibleiftheanalysis
methoddeveloped
inthis study
than that ofother two
particles, such as neutrino oscillation. The SK detector is one
reversed(Figure 8.17).
We show the isvaluesof theof these detectors, and its large fiducial volume (22.5 kton)energy ranges in
Table
Here, the2.sensitivity
future SRN
candiffuse
be estimated.
Figureof8.18
shows the expected
mightofenable
us tosearches
detect thebackgroundSRNs.
o the upper energy
part of spectrum
Table forFurthermore,
10 years of observations
GdCerenkov
concentrationof 0.03%.
much largerwith
water
detectors
such Inas the actual SRN
discussed inanalysis,§ 5.3.) The
HKis and
UNOissueare being
SRN detection
mostbackgrounda majorin the planned.
search at lower
energy. Inisparticular,
the major
9
m−2 s−1 for ourreference
withatmospheric
the inverseneutrinos,-decay reaction
with antineutrinos
protons in wa-from the reactor
background sourceslikely
are Li,and electron+
sensitive tocore
the (reactor
shape ofneutrinos)
ter, ⌫¯although
and its crossis precisely
it depends
on thesection
conditionof nuclearunderstood
power plant operation. In
e p ! e n,
9h-z. The energy
rangein(Vogel&Beacom1999;
Strumia&
Vissani2003).
In
our cal- The component
this study, Li and atmospheric neutrinos are assumed as the background sources.
9h-energy regions
suchas
the oftriggerthresholdof SK-I(before neutrino
the ac- background isof Li background isculation,
based onwe
theuseresultthis study
and theatmosphericeV, because referred
as discussed
cident).
from Ref. [51].
So far, the 9 Li background for SRN search has been estimated by weighting
9 Li productions critical andthe
thetotal
reaction
The rate
expected
event above
rates at8such
shown inFig- obtained bymeasured
MeVdetectors
by the 9are
Li energy
spectrum−1−1
uch a range, MC
the SRN
flux
ures
4
and
5
in
units
of
(22.5
kton
yr)
MeV
;
with
SK,
it the daughterwith GEANT4. GEANT4 does not accurately model the deexcitation of 9 Be,
takessomea yearto obtain the
spectrum,
whilewith ratios of 9 Be
> 11.3 MeV)
and 0.14–
nucleusof 9 Li, leaving
uncertainties
dueshown
to theSRN
energylevels andbranching
9
HK
and
UNO,
much
less
time
[1
yr
⇥
(22.5
kton/V),
where
us, the uncertainty
about
fid
decay. Therefore, a more accurate estimation of the Li background abundance
can be obtained
Vfid spectrum
is the fiducial
volumeof HK orUNO]
necessary
be- the backgroundnd its luminosity
gives
by using
theatmeasured
insteadof estimationfrom
MC. isBelow
9.5 MeV,cause butof theirlarger isfiducial
Figurecompares normalization.
expected SRN
flux in thecomponent
is dominant,the region
useful volume.
for constraining
the 4background
the
three
modelsoftheoriginal
supernova
neutrino
spectrum,
The advantage obtained by the results of this study is significant in the region 9.5–14.5 MeV. The
and onFigure5 shows the neutrino
contribution
to the total
event rateby supernova
neutrinos
systematic
uncertainty
the atmosphericbackgroundin assumed
based on Ref. [51]
from
each
redshift
range.
In
Table
2
we
summarizetheevent
s. At high-energy
regionalthough the reduction of the rate and systematic uncertainty is investigated in the collaboration.
rate integrated over various energy ranges for three supernova
mes from theThe
local
supersystematic uncertainty of 9 Li in that region is constrained by background normalization
below
−1

nergy side is mainly con(z > 1). This is because
mitted from a supernovaof (1 + z)−1 reflecting theefore high-redshift super-models. The expected event rate is 0.97–2.3 (22.5 kton yr)
for Ee > 10 MeV and 0.25–1.0 (22.5 kton yr)−1 for Ee > 18
MeV. This clearly indicates that if the background events thathinder the detection are negligible, the SK has already reached
the required sensitivity for detecting SRNs; with the future8.5. Prospects for SRN Search

117

Figure 9. Same as Figure 7 but for the models with metallicity evolution of DA08+M08, shock revival time of t rev

Lt < 500 cm

Previous 9 Li
analysis<latexit sha1_base64="G8T5iPpjSP3c5QpvxlzhrKHizrM=">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</latexit>

This study<latexit sha1_base64="TOUMhnCrBTV65r4j17QkKklYNqY=">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</latexit><latexit sha1_base64="iX05B/l9IioHI4xwezbYjX4RktY=">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</latexit>

Analysis method<latexit sha1_base64="U/6bHuZnZ+xAF9lLwJTq7zUR+wE=">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</latexit><latexit sha1_base64="GbNNi8wGvu9WhynirMUZbjk6AGQ=">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</latexit>

Distance from muon

Figure 8.16: Event
the SRNtoobservedin SKvarious
CSFRD
modelsassuming
the normal
dottedrates
linesofcorrespondmodels withthe forCSFRD
of HB06,
DA08
and K13,respectively.
mass ordering. This figure is taken from Ref. [11]. The legends HB06, DA08, and K13 represent
Ref. [74], [75], and [76], respectively. The vertical dotted and dashed lines are overwritten at
4.5 MeV and 8 MeV.

Lt > 500 cm

Figure 10. Total ﬂuxes of SRNs (solid) and contributions from various redshift ranges for the reference model. The l
to bottom, to the redshift ranges 0 < z < 1, 1 < z < 2 , 2 < z < 3, 3 < z < 4 , and 4 < z < 5, for En > 10 MeV. T
prospect
Previous DSNB
and inverted massFuture
hierarchies,
respectively.
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analysisstage (see Figure 14 of Nakazato et al. 2013) because a mean
mass accretion. Note thblack hole formation,
free path of nx is longer than those of ne and n̄e . On the othermass accretion, than Sh
hand, high-energy ne and n̄e are more efﬁciently emitted than nx
4.5 MeV  Erec < 8 MeV
Erec 8 MeVlater on the accretion phase (200 ms after the bounce) and the
6. CONCLU
Energydifference in the total emission
number of n̄e and nx getssmaller. Thus the difference in the SRN spectra for the normal
In this paper, we hav
Figure 8.17:
Schematicof the correspondence
betweenwith
the SRN
and 9 Li analysis.
andinverted diagram
mass hierarchies
is clear for models
a shortrate involving black-h
for DSNB analysis<latexit sha1_base64="BbbsBTP1xlmRPMkIoysQ33ZpDNg=">AAADf3ichVLLThRBFL1DiwI+GHRD4qZ1grognTsGBI0LojFhY8LDGUgYMuluapjOVD+srpkEO/MD/AAL4kITF4bPYONCly74BOMSEzcsON3TaHgMVKfrnjr3nKpbDyeSXqyZDwoDxrXB6zeGhkdu3rp9Z7Q4drcah23lioobylCtOnYspBeIiva0FKuRErbvSLHitF6n+ZWOULEXBu/0ViTWfXsz8Bqea2tQ9eLMlDVdm6z5tm4qP3krql2zJsV78039hFPC7ZovzdnTqnqxxBZnzTwPyjkoUd4WwrHCONVog0JyqU0+CQpIA0uyKca3RmViisCtUwJOAXlZXlCXRuBtQyWgsMG20G9itJazAcbpnHHmdrGKxK/gNGmCf/JXPuRvvMe/+KjvXEk2R1rLFqLT84qoPro9vvz3SpePqKn533VpzZoaNJvV6qH2KGPSXbg9f+fDzuHyi6WJ5BF/5t+o/xMf8D52EHT+uF8WxdLuJfU4qKX/iaV5BdwC1rluA7iBGOe30aQSbiMBE+AUNeKDjOmndi7QX+xJo8ydZ/XRv1u3kYcPb6x89kWdB9WnVvmZNb04VZp7lb+2IbpPD+kJVp+hOZqnBargBD7SPn2nH0bBeGxYBvekA4Xcc49ONeP5MVdVxw8=</latexit><latexit sha1_base64="ai4zPHX6EK5hf4U48cDAROBSXFY=">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</latexit><latexit sha1_base64="FeBO1H8mMexewz/4DQ3xF9tiOQc=">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</latexit>

11Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Events / MeV

118

102

10

1

Background (BG)
BG + Kaplinghat+00
BG + Horiuchi+09
BG + Nakazato+15

−1

10

6

8

10

12

14

16
18
20
22
24
Reconstructed energy (MeV)

Figure 8.18: Expected energy spectrum for 4.5–24.5 MeV assuming ten years observation with
0.03% Gd concentration. The black points represent the expected background assuming 9 Li andatmospheric neutrinos. 9 Li component is based on the result of this study and the atmospheric
neutrino background is referred from Ref. [51]. The dotted lines represent the expected numberof SRN candidates, i.e. background plus expected SRN signals. The color represents the SRN
flux model: blue is Kaplinghat+00 [18], green is Horiuchi+09 [13], and red is Nakazato+15 [11]assuming normal mass ordering.

8.5. Prospects for SRN Search

119

9.5 MeV and -spectrum shape measured by the data as shown in Figure 8.14. The systematic
uncertainty of the 9 Li background rate is estimated to be 50% in the latest analysis [26], while
the uncertainty could be suppressed to ⇠20% in the next ten years by the additional constraints
from the lower energy. This will lead to improve the sensitivity of SRN search especially in the
9.5–14.5 MeV region.

120

Chapter 8. Measurement of Cosmogenic Lithium-9 Production

Chapter 9

Conclusion
The gadolinium (Gd) has been loaded into ultra-pure water in Super-Kamiokande (SK) in order toimprove the neutron detection efficiency and the new observation phase (SK-Gd) has been started
since August 2020. The major motivations for the upgrade are the first observation of neutrinos
from past supernovae (supernova relic neutrinos, SRNs) and the suppression of the atmospheric
neutrino background in the proton decay search. Neutrons are also produced via spallation interactions by cosmic-ray muons together with the other isotopes. These cosmogenic products are
known as the background source in underground experiments, such as neutrino observations anddark matter searches. This thesis described the measurement of the cosmogenic products using thedata from the SK-Gd experiment.
In order to realize the first observation of SRNs, it is necessary to continue the operation
for a long time period, more than 10 years, with stable detector and water conditions. This
thesis described a new method to monitor the stability and uniformity of neutron detection using
neutrons produced in the detector by cosmic-ray muons. This method enables monitoring theneutron detection in the entire volume of the detector in parallel to the observation, and therefore
is complementary to the calibration using the neutron source deployed in the detector. As a result,the measured Gd concentration was consistent with the expectation, and it was confirmed that thevariation in time and positions are within ±6.3% (corresponds to ±3.1% of Gd capture fraction)
during the data-taking period from September 2020 to May 2022. This variation is negligible
compared to the other systematic uncertainties on the expected background rate in the SRN search.
This method can be applied to secure stable operation, which leads to the first observation of SRNs
in the future.
Extending the above study, the cosmogenic neutron production yield was measured using 283.2
days of data from September 2020 to September 2021 with 0.01% Gd-loaded water. The yield wasmeasured to be (2.76 ± 0.02 (stat.) ± 0.19 (syst.)) ⇥ 10 4 µ 1 g 1 cm2 at an average muon energyof 259 GeV. This is the second case in which the neutron yield is measured with a water target,
and the result provides information on the muon energy dependence. In addition, this study was
performed at the same depth as the KamLAND detector with organic liquid scintillator, which isthe first case that the neutron yields have been measured in di↵erent targets for the same muonenergies. The result of this study is consistent with that of KamLAND, which shows no significant
di↵erence in neutron yield from oxygen and carbon spallation at this depth. These measurements
provide the knowledge to systematically understand the neutron production and the secondaryinteractions, which leads to realizing the reliable simulations for the background estimations in theunderground experiments.
In addition, the energy spectrum of electrons fromdecay of 9 Li was also measured using454.2 days of data from September 2020 to April 2022. Various radioactive isotopes are produced
from the cosmic-ray muon spallation interactions. Among those, the decay of 9 Li with an emissionof neutron is one of the major background sources in SRN search at low energy region below 10 MeV,
where the predicted SRN flux largely depends on the star formation models. 9 Li has been measured
121

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Chapter 9. Conclusion

above 8 MeV in the previous study with ultra-pure water, whereas the energy range was expanded
down to 4.5 MeV in this study. Low energy bind together with the measured 9 Li spectrum will help
to constrain contamination in the signal region and lead to improve the sensitivity of SRN search.

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