Search for Astronomical Neutrinos
from Blazar TXS0506+056
in Super-Kamiokande

2020, March
Hagiwara Kaito

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

OKAYAMA UNIVERSITY

1

Abstract
The IceCube Neutrino Observatory detected a high-energy neutrino event withan estimated energy 290 TeV on 22 September 2017 at 20:54:30:43 Coordinated
Universal Time. The arrival direction of the neutrino coincides with the location of
the blazar named TXS0506+056, which is located at right ascension= 77.3582◦ anddeclination= +5.6931◦ (redshift z = 0.3364 ± 0.0010). Within a minute of detection,
the information of this event shared via the Gamma-ray Coordinate Network andfollow-up observations over a wide range of energies were carried out by several
observatories. According to the Fermi All-sky Variability Analysis, TXS0506+056
brightened in the GeV band starting in April 2017. Subsequently, the IceCube
collaboration additionally reported a possible neutrino event excess from this blazar
in older data between September 2014 and March 2015. However, about the average
from 2014 to 2015, neither excessive gamma-rays nor significant changes in the
gamma ray spectrum are observed. The coincidence between the neutrino arrival
direction and the blazar location as well as timing correlated with the associatedgamma-ray flare suggest that the observed neutrinos originated from the blazarand strongly motivate searches for neutrinos in the other energy regions by SuperKamiokande.
Super-Kamiokande is a large water Cherenkov detector located 1,000 m underground in the Kamioka-mine, Gifu Prefecture, Japan. It is a cylindrical detector,
39.3 m in diameter and 41.4 m in height and contains 50 kilotons of ultra-pure water
as neutrino target.blazar The experiment has been operated since April 1996 andhas made observations in four distinct phases known as SK-I, SK-II, SK-III, and
SK-IV. In this study neutrino data from SK-I to SK-IV through February 2018 corresponding to 5,924.4 live days are used for analysis. To estimate the atmospheric
neutrino background for this study, a 500-year-equivalent Monte Carlo simulationof each phase has been used.
The present analysis utilizes the Super-Kamiokande neutrino data with morethan 100 MeV of visible energy, divided into three classes depending upon the event
topology. In the fully-contained and partially-contained event samples, the neutrino
interaction is reconstructed within the inner-detector using Cherenkov rings produced by its daughter particles. An event where all daughter particles stop insidethe detector is classified as fully-contained and those where at least one particle
exits the detector is classified partially-contained. Upward-going muon events areobserved when energetic muons produced by muon-neutrino interactions with therock surrounding the detector penetrate the detector from below its horizon.
To use events with suﬃcient angular resolution for association with the blazar
direction, cut on the observed energy is applied. For these criteria, fully-contained
and partially-contained samples are ensured that the angular deviation of the reconstructed direction from the truth is within 10 degrees for more than 68% of
these events. Since upward-going muon events originate from neutrinos with higher
energy than other categories, their arrival direction is estimated with higher accuracy. Therefore, no additional restriction on the upward-going muon energy is used2

as more than 77% of events are reconstructed within 5 degrees of the true arrival
direction.
By comparing to the expected backgrounds, no significance excess was observed
at greater than the 1.2σ level in the blazar direction. The average and variance ofthe number of observed events in these oﬀ-source are compared with those in the
on-source region around the blazar and showed consistency within 1.6σ. And theevent rate in the on-source and the oﬀ-source are also consistent, indicating no excess
of neutrino events in the direction of the blazar. No significant temporal increaseof neutrino flux was found in the blazar direction by examining the change of theevent rate using the Kolmogorov-Smirnov-test.
Based on no signal assumption, upper limits of the neutrino fluence, the energydependent neutrino flux, and the neutrino luminosity are given for both electronneutrinos and muon-neutrinos. We prepared four types of the neutrino energy spectrum for the calculation, which are three power-law types and one log-parabolatype. The averaged fluence upper limits are placed on the electron-neutrino fluence of 1.9 × 104 cm−2 below 10 GeV and the muon-neutrino fluence of 8.0 × 104
to 3.1 × 10−1 cm−2 in the range 1 GeV to 10 TeV. The averaged upper limits ofthe energy-flux are 6.1 × 10−7 erg cm−2 sec−1 for electron-neutrinos and 4.8 × 10−7
to 1.1 × 10−9 erg cm−2 sec−1 for muon-neutrinos. The luminosity is 1.9 × 1050 to
4.3 × 1047 erg sec−1 in the range 1 GeV to 10 TeV.
The upper limit obtained in this study was compared with the numerical calculation by simulation. As a result, it was shown that neutrinos from the blazar ispossible to be detected by SK. By using neutrinos in the GeV to TeV region thatcan be observed by SK, it is possible to limit the model parameters of blazar’s jetmechanism. From limiting the parameters, the origin of high-energy CRs and themechanism of acceleration of CRs will be elucidated.

3

Acknowledgement
I want to show the expression of my deep gratitude to my supervisor Prof. Yusuke
Koshio for his enormous support. The discussion of physics with him has greatly
helped my research. He taught me many important and useful things not only
physics but also career, private life and so on. This thesis would never exist without
his kind comments and detailed suggestions. He also gave me the opportunity to
study in Italy and I had a wonderful experience. I am very happy that I decided tojoin his group.
I would like to appreciate all SK collaborators and all the staﬀs at Kamioka
Observatory. This study could not be done without their studies and various advice.
Especially, Prof. Kimihiro Okumura and Prof. Roger Wendell in the ATMPD groupgave me a lot of advice on the analytical method, from basic to detailed things.
Without their great guidance, my research could not be accomplished.
I am grateful to Prof. Makoto Sakuda and Prof. Hirokazu Ishino for theirkind guidance in the physics lecture in Okayama University. I also would like tothank to laboratory members and secretary in Okayama University; Dr. Shintaro
Ito, Atsushi Nakamura, Nishtha Piplani, Masayuki Harada, Toshiaki Horai, Seiya
Sakai, Ryo Okada, Wenjie Ma, Hussain Kitagawa, Shoya Tanaka, Nahoko Koeda,
and Kayoko Nagatsuna. Discussing and drinking with them was an integral part of
my research life. I wish them a greater success in every situations.
Finally, I want to hank to my family and all friends. They have been supported
me for everything. I was able to enjoy student life thanks to them.
Thank you everyone for everything !

CONTENTS

4

Contents
1 Introduction
1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Oscillation Parameters . . . . . . . . . . . . . . . . . . . . . .
1.2 Multi-messenger Astronomy . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 CR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Active Galactic Nucleus (AGN) . . . . . . . . . . . . . . . . . . . . .
1.3.1 Blazar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Neutrinos from Blazars . . . . . . . . . . . . . . . . . . . . .

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2 Super-Kamiokande (SK)
2.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 SK Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 History of SK . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 ID PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 OD PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Water and Air System . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Water Purification System . . . . . . . . . . . . . . . . . . . .
2.3.2 Air Purification System . . . . . . . . . . . . . . . . . . . . .
2.4 Electronics and Data Acquisition (DAQ) System . . . . . . . . . . .
2.4.1 ID Electronics and DAQ: SK-I to SK-III . . . . . . . . . . . .
2.4.2 OD Electronics and DAQ: SK-I to SK-III . . . . . . . . . . .
2.4.3 Hardware Trigger: SK-I to SK-III . . . . . . . . . . . . . . .
2.4.4 Electronics and DAQ for ID & OD: SK-IV and SK-V . . . .
2.4.5 Online System for ID & OD: SK-IV and SK-V . . . . . . . .
2.4.6 Software Trigger: SK-IV and SK-V . . . . . . . . . . . . . . .

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3 Simulation
3.1 Atmospheric Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Primary Cosmic Ray . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Hadronic Interaction . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 3D Flux Calculation . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Neutrino Flux at SK . . . . . . . . . . . . . . . . . . . . . . .
3.2 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Elastic and Quasi-Elastic Scattering . . . . . . . . . . . . . .
3.2.2 Meson Exchange Current . . . . . . . . . . . . . . . . . . . .
3.2.3 Single Meson Production . . . . . . . . . . . . . . . . . . . .
3.2.4 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . .
3.2.5 Coherent Pion Production . . . . . . . . . . . . . . . . . . . .

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CONTENTS

5

3.2.6 Nuclear Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . .
Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 SK Detector Simulation . . . . . . . . . . . . . . . . . . . . .
3.3.2 SK Geant4 based Simulation . . . . . . . . . . . . . . . . . .

63
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65
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4 Calibration
4.1 ID PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 High-Voltage (HV) . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Relative Gain . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 QE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.5 Timing Response . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Water Transparency in the ID . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Light Absorption and Scattering . . . . . . . . . . . . . . . .
4.2.2 Light Reflection at the PMT and Black Sheet . . . . . . . . .
4.3 OD PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Charge Response . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Timing Response . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Optical Properties of the OD . . . . . . . . . . . . . . . . . . . . . .
4.5 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 High Energy Stopping Muons . . . . . . . . . . . . . . . . . .
4.5.2 Low Energy Stopping Muons . . . . . . . . . . . . . . . . . .
4.5.3 Neutrino Induced π0 Events . . . . . . . . . . . . . . . . . . .
4.5.4 Decay Electrons . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.5 Summary of Energy Calibration . . . . . . . . . . . . . . . .

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5 Event Reduction
5.1 FC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.6 Final FC Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.1.7 Summary of FC Reduction . . . . . . . . . . . . . . . . . . .
5.2 Partially Contained . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.5 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.6 Final PC Reduction . . . . . . . . . . . . . . . . . . . . . . .
5.2.7 Summary of PC Reduction . . . . . . . . . . . . . . . . . . .
5.3 UPMU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.3

CONTENTS

5.3.2
5.3.3
5.3.4
5.3.5

6

Second Reduction . . . . . . . . . . . . . . . . . . . . . . . .
Third Reduction . . . . . . . . . . . . . . . . . . . . . . . . .
Final UPMU Reduction . . . . . . . . . . . . . . . . . . . . .
Summary of UPMU Reduction . . . . . . . . . . . . . . . . .

113
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114

6 Event Reconstruction
116
6.1 Vertex Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.4 Momentum Determination . . . . . . . . . . . . . . . . . . . . . . . . 123
6.5 Improvements in Reconstruction . . . . . . . . . . . . . . . . . . . . 123
6.5.1 Ring number Correction . . . . . . . . . . . . . . . . . . . . . 123
6.5.2 Decay electron Finding . . . . . . . . . . . . . . . . . . . . . 123
6.5.3 π0 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 124
6.6 Event Reconstruction for UPMU Sample . . . . . . . . . . . . . . . . 124
7 Search for Astronomical Neutrino from Blazar
125
7.1 Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 Expected Background . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 On-source vs. Oﬀ-source . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.4 Kolmogorov–Smirnov (KS) Test . . . . . . . . . . . . . . . . . . . . . 130
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8 Limit Calculation
134
8.1 90% Confidence Level (C.L.) . . . . . . . . . . . . . . . . . . . . . . 134
8.2 FC and PC Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.3 UPMU Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.3.1 Eﬀective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.3.2 Probability of a Neutrino Creating a Muon . . . . . . . . . . 138
8.3.3 Shadow Eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.4.1 Fluence Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.4.2 Energy-flux Limit . . . . . . . . . . . . . . . . . . . . . . . . 144
8.4.3 Luminosity Limit . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A Table of the Upper Limit

150

B Gamma-ray Spectrum from Gadolinium

153

LIST OF FIGURES

7

List of Figures
1.1 Energy flux spectra of CRs for all particles. . . . . . . . . . . . . . . 22
1.2 Schematic of AGN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Spectral-energy distribution of Markarian 421. . . . . . . . . . . . . 25
1.4 Time-dependent multi-wavelength observations of TXS0506+056. . . 27
1.5 Broadband spectral-energy distribution of the blazar TXS0506+056.
27
2.1 Schematic of the SK detector (cutaway view). . . . . . . . . . . . . 28
2.2 The image of the Cherenkov radiation. . . . . . . . . . . . . . . . . . 29
2.3 Schematic of the module structure of the PMT support frame. . . . 32
2.4 20-inch ID PMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 FRP case and acrylic cover of the ID PMT. . . . . . . . . . . . . . . 34
2.6 Quantum eﬃciency of the 20-inch ID PMT. . . . . . . . . . . . . . . 35
2.7 Single-p.e. pulse height distribution expressed in light-intensity-dependent
ADC count. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.8 Schematic of a module of ID and OD PMTs. . . . . . . . . . . . . . 36
2.9 Logic diagram of the electronics system for the ID used with SK-I to
SK-III. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.10 Block diagram of the circuit in the ATM. . . . . . . . . . . . . . . . 40
2.11 Timing chart for signal and trigger in an ATM. . . . . . . . . . . . . 40
2.12 Data accusation system for OD. . . . . . . . . . . . . . . . . . . . . . 41
2.13 Block diagram of the QTC and its surroundings. . . . . . . . . . . . 43
2.14 Timing chart for signal and trigger in a QTC. . . . . . . . . . . . . . 44
2.15 Block diagram of the new online system. . . . . . . . . . . . . . . . . 45
3.1 Measured primary CR flux and the model used for the HKKM calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Comparison between HARP data and theoretical models. . . . . . . 49
3.3 Comparison of CR muon flux between experimental data and modified
flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 Interaction areas of primary CRs, and atmosphere for 1D and 3D flux
calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.5 Atmospheric neutrino flux in three energy bins. . . . . . . . . . . . . 52
3.6 Comparison of calculated atmospheric neutrino fluxes averaged overall directions (left panel). Comparison of flavor ratio and neutrino
anti-neutrino ratios (right panel). . . . . . . . . . . . . . . . . . . . . 53
3.7 Cross-section for the CCQE scattering of muon neutrino (left panel)and muon anti-neutrino (right panel). . . . . . . . . . . . . . . . . . 56
3.8 Cross-section for single pion production of the muon neutrino. . . . . 58
3.9 Comparison between experimental and calculated data of the total
cross-section of the CC interaction for ν and ν . . . . . . . . . . . . . 61
3.10 Cross-section of coherent pion production from the carbon nucleus
via CC interaction (left panel) and NC interaction (right panel). . . 62
3.11 Interaction probabilities of a nucleon in 16O as a function of the nucleon momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

LIST OF FIGURES

3.12 Distributions of the wavelength of Cherenkov photon. . . . . . . . .
3.13 Comparison between SKDETSIM and SKG4 to confirm the eﬀect ofabsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Distributions of neutron capture time and distance from emission
location to capture location. . . . . . . . . . . . . . . . . . . . . . . .
3.15 The energy spectra of gamma-rays emitted from the thermal neutron
capture on Gd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 SKG4 Logo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 The location of standard PMTs and the schematic view of grouping
for the PMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Distribution of the observed charge for the single p.e. signal. . . . . .
4.3 Typical TQ distribution for one PMT. . . . . . . . . . . . . . . . . .
4.4 Fitted water coeﬃcient functions. . . . . . . . . . . . . . . . . . . . .
4.5 Global timing oﬀset. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Summary of absolute energy scale measurements for each SK phase.
4.7 Energy scale stability as a function of date since the start of SK
operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Three types of high-energy neutrino events at SK . . . . . . . . . . .
5.2 Expected energy distributions from atmospheric neutrino simulationfor each event classification. . . . . . . . . . . . . . . . . . . . . . . .
5.3 FC first reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 FC second reduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 FC third reduction for through-going muon . . . . . . . . . . . . . .
5.6 FC third reduction for stopping muon . . . . . . . . . . . . . . . . .
5.7 Cable hole and veto counter. . . . . . . . . . . . . . . . . . . . . . .
5.8 FC third reduction for flasher events . . . . . . . . . . . . . . . . . .
5.9 FC fifth reduction for stopping noise event . . . . . . . . . . . . . . .
5.10 FC fifth reduction for invisible muon . . . . . . . . . . . . . . . . . .
5.11 FC fifth reduction for coincidence muon . . . . . . . . . . . . . . . .
5.12 FC fifth reduction for electric nosise . . . . . . . . . . . . . . . . . .
5.13 PC first reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.14 Algorithm for finding hit clusters in OD. . . . . . . . . . . . . . . . .
5.15 PC second reduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.16 PC third reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.17 PC fourth reduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.18 PC fifth reduction for through-going muon cut B . . . . . . . . . . .
5.19 PC fifth reduction for through-going muon cut C . . . . . . . . . . .
5.20 PC fifth reduction for through-going muon cut D . . . . . . . . . . .
5.21 PC fifth reduction for stopping muon cut A . . . . . . . . . . . . . .
5.22 PC fifth reduction for stopping muon cut B . . . . . . . . . . . . . .
5.23 PC fifth reduction for stopping muon cut C . . . . . . . . . . . . . .
5.24 PC fifth reduction for corner clipping muon cut A . . . . . . . . . .
5.25 PC fifth reduction for corner clipping muon cut B . . . . . . . . . .
6.1 Illustration of the basic idea of finding ring candidates. . . . . . . . .
6.2 Ring-counting likelihood distributions. . . . . . . . . . . . . . . . . .

8

67
68
69
70
70
72
74
75
77
78
82
83
84
84
85
86
87
88
88
89
91
92
92
93
97
98
99
99
101
102
103
104
104
105
106
107
108
118
120

LIST OF FIGURES

9

6.3 PID likelihood distributions of single-ring events. . . . . . . . . . . . 121
6.4 PID likelihood distributions of multi-ring events. . . . . . . . . . . . 122
7.1 Resolution of angle between reconstructed direction and true neutrino
direction by MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.2 A sky map of the reconstructed arrival direction if selected neutrino
events around the blazar direction for all samples. . . . . . . . . . . 127
7.3 Area ratio (blue circle/green area and blue circle/yellow area). . . . 128
7.4 Number of detected events in each search region and expected background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.5 The number of event in the on-source and oﬀ-source. . . . . . . . . . 129
7.6 Event rate of the on-source and oﬀ-source. . . . . . . . . . . . . . . . 130
7.7 Kolmogorov-Smirnov test for FC, PC, and UPMU. . . . . . . . . . . 131
7.8 Distribution of maximum distance calculated by the toy-MC with theresult of experimental data. . . . . . . . . . . . . . . . . . . . . . . . 132
8.1 Poisson distribution with expected background and 90% C.L. upper
limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2 Neutrino-nucleon interaction cross-section. . . . . . . . . . . . . . . . 135
8.3 Detection eﬃciency for FC and PC. . . . . . . . . . . . . . . . . . . 136
8.4 Eﬀective area of UPMU. . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.5 Eﬀective area as a function of zenith angle. . . . . . . . . . . . . . . 138
8.6 Probability that a neutrino creates a muon via neutrino interaction
and that the muons reach the detector. . . . . . . . . . . . . . . . . . 139
8.7 Earth’s shadow eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.8 Relationship between the reconstructed momentum and neutrino energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.9 Fluence upper limits at 90% C.L. . . . . . . . . . . . . . . . . . . . . 143
8.10 The energy-flux upper limit at 90% C.L. compared with IceCube event.145
8.11 Energy-flux upper limit at 90% C.L. compared with gamma-ray spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.12 Spectral energy distributions and muon neutrino fluxes. . . . . . . . 147
8.13 Time evolution of the muon neutrino emission from the jet of AGN. 149
B.1 The energy spectrum from 157Gd(n, γ) reaction with diﬀerent multiplicity values and hit values . . . . . . . . . . . . . . . . . . . . . . . 154
B.2 The energy spectrum of single gamma-rays from 157Gd(n, γ) reaction. 155
B.3 The Ratio of data by MC for the single gamma-ray from 155Gd(n, γ),157
Gd(n, γ), and naturalGd(n, γ) reaction. . . . . . . . . . . . . . . . . 155

LIST OF TABLES

10

List of Tables
1.1 Best fit values of the neutrino oscillation parameters. . . . . . . . . . 21
2.1 Cherenkov threshold of various particles. . . . . . . . . . . . . . . . 30
2.2 Summary of characteristics of each SK phase. . . . . . . . . . . . . 34
2.3 Water Purification System. . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Trigger threshold for each SK-I to SK-III phase. . . . . . . . . . . . 42
2.5 Trigger threshold of SK-IV phase. . . . . . . . . . . . . . . . . . . . . 46
3.1 List of resonances and background terms used in the NEUT simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Simulated process for each particle in SKDETSIM. . . . . . . . . . 66
5.1 Reduction eﬃciency after each FC reduction step . . . . . . . . . . . 94
6.1 Vertex resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2 Angular resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1 The number of expected events at each SK phase. . . . . . . . . . . 130
7.2 Summary of analysis of neutrino search from the blazar TXS0506+056.133
8.1 Parameters of the neutrino energy spectrum. . . . . . . . . . . . . . 142
8.2 Summary of upper limits of luminosity . . . . . . . . . . . . . . . . . 146
A.1 Summary of upper limits at 90% C.L. (Parameter1) . . . . . . . . . 150
A.2 Summary of upper limits at 90% C.L. (Parameter2). . . . . . . . . . 151
A.3 Summary of upper limits at 90% C.L. (Parameter3). . . . . . . . . . 151
A.4 Summary of upper limits at 90% C.L. (Parameter4). . . . . . . . . . 152

LIST OF TABLES

11

Acronym
3FGL: The third Fermi-LAT source catalog
ADC: Analog Digital Converter
AFT: After Trigger
AGN: Active Galactic Nuclei
AMS: Alpha Magnetic Spectrometer experiment
ANNRI: Accurate Neutron-Nucleus Reaction measurement Instrument detector
ASAS-SN: All-Sky Automated Survey for Supernovae
ASIC: Application Specific Integrated Circuits
ATM: Analog Timing Module
BEBC: Big European Bubble Chamber experiment
BESS: Balloon-borne Experiment with Superconducting Spectrometer experiment
C.L.: Confidence LevelCAPRICE: Cosmic Antiparticle Ring Imaging Cherenkov Experiment
CC: Charged-Current interaction
CCQE: Charged-Current Quasi-Elastic scattering
CMB: Cosmic Microwave Background
CP: charge-parity
CR: Cosmic Ray
DAQ: Data Acquisition system
DIS: Deep Inelastic Scattering
DONuT: Direct Observation of the Nu Tau experiment
DPM: Dual Parton Model
DSM: Data Sort MappingDec.: Declination

LIST OF TABLES

12

FAVA: Fermi All-Sky Variability Analysis
FC: Fully-Contained event
FIFO: First-in First-out memory
FKM: Feynman-Kislinger-Ravndal baryon model
FPGA: Field Programmable Gate Array
FSCC: Fastbus Smart Crate Controller
FSRQ: Flat-Spectrum Radio Quasar
FV: Fiducial Volume
Fermi-ASP: Fermi’s Automated Science Processing
Fermi-LAT: Fermi Large Area Telescope
GCN: Gamma-ray Coordinate Network
GEANT: Geometry and Tracking
GONG: Go/NoGo module
GRV: Gluck-Reya-Vogt parton distribution
HARP: Hadron Production experiment
HE: High Energy
HKKM: Honda-Kajita-Kasahara-Midorikawa neutrino flux model
HV: High-Voltage
ID: Inner Detector
IMAX: Isotope Matter-Antimatter Experimen
IMB: Irvine-Michigan-Brookhaven experiment
J-PARC: Japan Proton Accelerator Research Complex
JACEE: Japanese-American Cooperative Emulsion Experiment
JSNS: Japan Spallation Neutron Source
K2K: KEK-to-Kamioka experiment
KEK: The High Energy Accelerator Research Organization (in Japanese :Ko Enerugi Kasokuki Kenkyu Kiko)
KNO: Koba-Nielsen-Olsen scaling factor

LIST OF TABLES

13

KS-test: Kolmogorov-Smirnov Test
KamLAND: Kamioka Liquid scintillator Anti-Neutrino Detector experiment
LE: Low Energy
LEAP: Low Energy Antiproton balloon flight experiment
LPF: Low-Pass Filter
LVDS: Low Voltage Diﬀerential Signaling drivers
MC: Monte Carlo
MEC: Meson Exchange Current
MINOS: Main Injector Neutrino Oscillation Search
MLF: Material and Life Science Experimental Facility
MSW: Mikheev-Smirnov-Wolfenstein eﬀect (matter eﬀect of neutrino oscillation)
MiniBooNE: Mini Booster Neutrino Experiment
NC: Neutral-Current interaction
OD: Outer Detector
PC: Partially-Contained event
PDF: Parton Distribution Function
PHITS: Particle and Heavy-Ion Transport code System
PID: Particle Identification
PMT: Photomultiplier Tube
QAC: Charge to Analog Converter
QBEE: QTC based Electronics with Ethernet
QE: Quantum eﬃciency
QTC: Charge to Time Converter
R.A.: Right Ascension
RENO: Reactor Experiment for Neutrino Oscillation
RMS: Root Mean SquareRUNJOB: Russian-Nippon Joint Balloon experiment

LIST OF TABLES

SCH: Super Control Header module
SF: Spontaneous Fission
SHE: Special High Energy
SIC: System Interface Control
SK: Super-Kamiokande experiment
SKAT: Sequential Kernel Association Test experiment
SKDETSIM: Super-Kamiokande Detector Simulation
SKG4: Super-Kamiokande Geant4 based simulation
SLE: Super Low Energy
SMP: Super Memory Partner
SNO: Sudbury Neutrino Observatory
T2K: Tokai-to-Kamioka experiment
TAC: Time to Analog Converter
TDC: Time to Digital Converter
TKO: Tristan KEK Online system
TOF: Time-of-Flight
TRG: Trigger module
UPMU: Upward-going Muon event
UTC: Coordinated Universal Time
V/I: Voltage-to-Current converter
VME: Versa Module Europa
WS: Wavelength Shifting plate
p.e.: photoelectorn

141. INTRODUCTION

115Introduction

Neutrinos emitted from cosmic bodies play an important role in understanding celestial phenomena. Owing to their small cross-sections, neutrino observations arelimited only by detector volume. Currently, neutrino detectors have extremely large
volumes are operating worldwide. This chapter introduces the general properties ofneutrinos, followed by those originated from high energy celestial objects, and thenby the current status of astronomical neutrino observations.

1.1

Neutrinos

Neutrinos are elementary particles possessing a half-integer spin of the lepton sector.
They interact only via the weak subatomic force and gravity1 . There have been, thus
far, many theoretical and experimental achievements of neutrino physics.

1.1.1

History

The existence of neutrinos was first postulated by Pauli [1] in 1930 to explain the continuous energy spectrum of β decay. About 20 years after Pauli’s proposal, (1956),
the electron-anti-neutrino was discovered by Reines and Cowan [2, 3] at a nuclear
reactor. In 1962, the existence of the muon-neutrino was confirmed by Danby et al.
[4] using a neutrino beam produced created by the decay of charged pions shot into abeam of muon neutrinos. The third type neutrino, the tau neutrino, was discoveredin 2001 via the Direct Observation of the Nu Tau (DONuT) Experiment [5] and thedetection of tau leptons in neutrino interactions.
The first measurement of an electron-neutrino flux from the core of the sun wasmade in the 1960s via the Homestake Experiment [6]. The measured value of theflux was between one third and one-half the number predicted by the standard solar model [7]. A similar diﬀerence was observed at the Kamioka Observatory [8]and at the Sudbury Neutrino Observatory (SNO) [9]. Another indication that theneutrino flux diﬀered between simulation and observation was found using the atmospheric neutrino of Kamiokande [10] in 1988 and the Irvine-Michigan-Brookhavenexperiment (IMB) [11] in 1992.
The problem was solved after gaining an improved understanding of the properties of neutrinos. It was first believed that neutrinos did not have mass. However,in practice, the mass was found to be nonzero. Furthermore, the masses of individual states diﬀer. Allowing the interacting flavor state to diﬀer from the massstate appears as an oscillation. Evidence of neutrino oscillations was reported via
the Super-Kamiokande Experiment (SK) in 1998 using the asymmetry of upwardand downward atmospheric neutrinos [12]. Furthermore, by comparing solar neutrinos measured at the SK [13] and at the SNO [14] concerning neutrino oscillations,the problem of solar neutrinos was completely solved. Later, in 2015, the Nobel
1

The eﬀect of gravity is negligible because of the neutrino’s tiny mass.

1. INTRODUCTION

16

Prize was awarded to Takaaki Kajita (SK) and Arthur B. McDonald (SNO) for the
discovery of neutrino oscillations, which proved that neutrinos had mass.
More astronomical neutrinos were observed in 1987. The neutrinos emitted froma supernova explosion (SN1987A), located in the Large Magellanic Cloud, was detected at Kamiokande [15], IMB [16], and Baksan [17] observatories. On 23 February
1987 at 07:35 Coordinated Universal Time (UTC), the Kamiokande detected 11 neutrino events. The IMB detected eight, and Baksan detected five. Although only 24
events were detected, the observations were consistent with theoretical supernova
models, in which 99% of the decay energy was emitted in the form of neutrinos [18].
This was the first time neutrinos were known to have been emitted from a supernova and were directly observed. This further demarked the beginning of neutrino
astronomy. For pioneering contributions to astrophysics for the detection of cosmic
neutrinos, Masatoshi Koshiba and Raymond Davis were awarded the Nobel Prize in
2002.
The IceCube neutrino observatory detected a high-energy neutrino event on 22
September 2017 [19]. The origin of the event was found to have been the blazar
TXS0506+056, and it became the third astronomical neutrino event. This neutrino
event attracted attention for three reasons. First, the event produced high-energy
neutrinos of several-hundred PeV. Second, an automated alert was distributed totelescopes around the world 43 sec later, and follow-up observations were quickly
conducted. Finally, a gamma-ray flare was found in the GeV band in April 2017.
From these discoveries, the blazar TXS0506+056 was the first known source of amulti-messenger between a high-energy astronomical neutrino and gamma rays.

1.1.2

Neutrino Oscillation

Neutrino oscillations reflect transitions between the diﬀerent types of neutrinos,
because neutrino flavor eigenstates are not identical to mass eigenstates. A theory
was proposed by Pontecorvo [20, 21] for neutrino and anti-neutrino oscillations. The
idea for the quantitative theory of neutrino oscillation was first developed by Maki
et al. [22] in 1962 and further expanded on by Pontecorvo [23] in 1968.

In vacuum
The neutrino flavor state, |ν α ⟩ (α =e, µ, τ ), can be described as a linear combinationof diﬀerent mass eigenstates |ν i ⟩ having masses i =1, 2, and 3,|ν α ⟩ =

3
∑

∗
Uαi
|ν i ⟩ ,

(1.1)

i=1

where U is a 3 × 3 matrix between these states, called the Pontecorvo–Maki–
Nakagawa–Sakata (PMNS) matrix,




1
0
0
c13
0 s13 e−iδCPc12 s12 0





−s

U =
(1.2)
0
1
0
0 c23 s23  12 c12 0,−iδCP
0 −s23 c23−s13 e0c13
00 1

1. INTRODUCTION

17

( )
( )
where sij = sin θij and cij = cos θij . The angle θij represents the mixing between
states i and j. The δ is the charge-parity (CP) violating phase for the lepton sector.
The time evolution of the flavor eigenstate is|ν α ⟩ =3∑∗ −iEi t
Uαie|ν i (t = 0)⟩ ,

(1.3)

i=1

where Ei is the energy of the eigenstate ⟩of ν i . The probability amplitude of detecting
a neutrino in the flavor eigenstate, ν β , at time t from one created as |ν α ⟩ at time
t = 0 is⟨⟩Aν α →ν β (t) ≡ ν β ν α⟩∑⟨∗ −iEi t=ν β Uαi
e
νi
i

=
=
=

∑ ∑ ⟨
i

γ=e,µ,τ

i

γ=e,µ,τ

∑ ∑∑∗ −iEi tν β Uαie
Uγi ν γ

⟩

⟩
⟨
∗
Uαi
Uγi e−iEi t ν β ν γ∗UαiUβi e−iEi t .

(1.4)

i

The probability of the flavor transition is then given by2Pν α →ν β (t) =Aν α →ν β (t)
∗
(
)
∑ ∗
∑
∗
=
Uαi Uβi e−iEi t UαjUβj e−iEj t 
i

=

∑∑
i

=

∑

j
∗
∗ −i(Ei −Ej )tUαi
Uβi Uαj Uβj
e

j
∗
∗
Uαi
Uβi Uαi Uβi
+

i

∑

∗
∗ −i(Ei −Ej )tUαi
Uβi Uαj Uβj
e

(1.5)

i̸=j

When the neutrinos are relativistic (p2 ≫ m2 ), the relationship between the energy
and the mass can be approximated as follows, using natural units (c = ℏ = 1):√√22
Ei − Ej =pi + mi − p2j + m2j
(
)
(
)
m2j
m2i
≃ pi 1 + 2 − pj 1 + 2
2pi
2pj
=

∆m2ij
2E

(1.6)

where ∆m2ij = m2i − m2j is the mass-squared diﬀerence between two mass eigenstates
and the relativistic neutrino energy, expressed as E ≃ |pi | = |pj | . Furthermore,1. INTRODUCTION

18

considering the distance traveled by neutrino L = ct, Equation 1.5 can be expressed
as follows:
)
(
∑ ∗
∑ ∗
∆m2ij L∗∗Uαi Uβi Uαi Uβi +Pν α →ν β (t) =Uαi Uβi Uαj Uβj exp −i
2E
i
i̸=j
∑ ∗
∑ ∗
∗
∗
=
Uαi Uβi Uαi Uβi+Uαi Uβi Uαj Uβj
i

i̸=j

)
2
∆m
L
ij
∗
∗
−2
Uαi
Uβi Uαj Uβj
sin2
4E
i̸=j
(
)
2
∑ ∗
∆m
L
ij
∗
+i
Uαi Uβi Uαj Uβj
sin
2E
∑

(

i̸=j

= P1 + P2 − 2P3 + iP4(1.7)

P1 and P2 are evaluated jointly:
P1 + P2 =

∑∑
i

=

∑(

∗
∗
Uαi
Uβi Uαj Uβj

j
∗
Uαi
Uβi

)∑(

i

=

∗
Uαj Uβj

)

j

∑

2
∗
Uαi
Uβi

i

(1.8)

= δαβ ,
where δ is the Kronecker delta function. We proceed similarly for P3 :
)
(
2
∑( ∗
∗
∗
∗)
2 ∆mij L
P3 =Uαi Uβi Uαj Uβj + Uαj Uβj Uαi Uβi sin
4E
i>j
)
(
2
∑( ∗
( ∗
∗
∗ )∗ )
2 ∆mij L=
Uαi Uβi Uαj Uβj + Uαj Uβj Uαi Uβi
sin
4E
i>j
(
)
∑ { ∗
∆m2ij L∗ }= 2
Re Uαi Uβi Uαj Uβj
sin2
.
4E

(1.9)

i>j

Finally, P4 is expressed as follows:
P4

∑(

∗)

(

∆m2ij L∗∗∗=Uαi
Uβi Uαj Uβj− UαjUβj Uαi Uβi sin
2E
i>j
(
)
∑ { ∗
∆m2ij L∗ }= −2i
Im Uαi Uβi Uαj Uβj sin
.
2E
i>j

)

(1.10)

1. INTRODUCTION

19

Net, putting Equation 1.8, 1.9, and 1.10 in Equation 1.7, we get
)
(
2
∑ { ∗
∗ }
2 ∆mij L
Pν α →ν β (t) = δαβ − 4Re Uαi Uβi Uαj Uβj sin
4E
i>j
(
)
∑ { ∗
∆m2ij L∗ }+2
Im Uαi Uβi Uαj Uβj
sin
.
2E

(1.11)

i>j

Matter eﬀect
When neutrinos propagate through matter, the neutrino oscillation changes becauseof the interactions between the neutrino and matter. The eﬀect is known as the
Mikheev–Smirnov–Wolfenstein (MSW) [24–26] eﬀect or the matter eﬀect of neutrino
oscillation.
All three flavors of neutrinos undergo neutral-current coherent scattering with
protons, neutrons, and electrons. For only the electron neutrinos, coherent charged
current scattering also occurs, because ordinary matter contains electrons. The
eﬀective potentials of neutral current, VN C , and charged current, VCC , are expressed
as
√
VCC =
2GF Ne ,(1.12)√
2
VN C = −(1.13)G N ,2 F n
where GF is the weak-coupling constant, and Ne,n are the number densities of electrons or neutrons in the matter. In the case of an anti-neutrino, the potentials
are negative. After subtracting the universal neutral current contribution, the time
evolution of the mass eigenstates for the two-flavor-mixing case is expressed as
( )
( ) 
E1 0
ν
d ν1
 1 .
=
i
(1.14)
dt ν 20 E2
ν2It is then converted into the flavor basis, as

 ( )
( )
0
E1
ν
d νe
U † e
= U
i
dt νµ
0 E2
νµ
)( )
(
νe
∆m2M − cos 2θM sin 2θM=4E
νµsin 2θM
cos 2θM(1.15)

where ∆m2M is the eﬀective mass-squared diﬀerence, and θM is the eﬀective mixing
angle. These eﬀective parameters are defined by√
22∆mM = ∆m sin2 2θ + (cos 2θ − x)2 ,(1.16)
sin2 2θM=

sin2 2θ
sin2 2θ + (cos 2θ − x)2,(1.17)

1. INTRODUCTION

where x quantifies the degree of the eﬀect and is defined as√
2 2GF Ne E
x≡
∆m2

20

(1.18)The survival probabilities of νe propagating and the two neutrino oscillation througha matter of constant electron density, Ne , can be written as
)
(
2
∆m
L
M
Pνe →νe = 1 − sin2 2θM sin2
(1.19),
4E()
2
2
2 ∆mM LPνe →νµ = sin 2θM sin.
(1.20)
4E

1.1.3

Oscillation Parameters

Neutrino oscillations in a vacuum are fully characterized by six parameters: three
mixing angles (θ13 , θ12 , θ23 ), two mass-splittings (∆m221 , ∆m231 ), and one CPviolating phase (δCP ). Most are determined by reactor, atmospheric, solar, andlong-baseline neutrino experiments.
The solar neutrino analysis of SK [27], SNO [28], and the Kamioka Liquid scintillator Anti-Neutrino Detector (KamLAND) experiment [29] measured parametersθ12 and ∆m221 . Parameters θ23 and ∆m232 are measured by the atmospheric neutrino
and log-baseline neutrino experiments: SK [30]; KEK to Kamioka (K2K) [31]; Main
Injector Neutrino Oscillation Search (MINOS) [32]; and Tokai to Kamioka (T2K) [33]experiments. Measurements at reactor experiments (the Daya Bay [34], the Reactor Experiment for Neutrino Oscillation (RENO) [35], and the Double Chooz [36])and T2K [37] established that the mixing angle, θ13 , was small but nonzero. The
precise value of δCP is still unknown, but long-baseline experiments (T2K [38] andNOvA [39]) have begun to constrain it.
The values of these parameters are derived from a global fit of current neutrino
oscillation data [40], as listed in Table 1.1. There are two possibilities of mass
hierarchy, which depend upon the ordering of the neutrino mass eigenstates. The
normal hierarchy (inverted hierarchy) corresponds to the order, m1 < m2 < m3
(m3 < m1 < m2 ).

1.2

Multi-messenger Astronomy

Cosmic rays (CR), electromagnetic radiation, neutrinos, and gravitational waves are
the most important messengers that deliver information from celestial bodies to us.
They are created by diﬀerent processes, and they reveal varying knowledge about
their sources. Therefore, observing these messengers is useful, but more comprehensive information can be obtained by observing their combinations.

1. INTRODUCTION

21

Table 1.1: Best fit values of the neutrino oscillation parameters. The definition of∆m2 is ∆m2 = m23 − (m22 + m21 )/2. The errors stated are at the 3σ level.
Parameter∆m212 [10−5 eV2 ]sin2 θ12 [10−1 ]2−32

Normal Hierarchy

Inverted Hierarchy

7.37+0.60
−0.44
+0.57
2.97−0.47

eV ]2.50 ± 0.13

sin2 θ13 [10−2 ]2.46+0.14−0.13

2.14+0.32−0.29

2.18+0.30−0.32

4.37+1.79−0.58

5.69+0.68−1.86

1.35+0.65−1.35

1.32+0.68−1.32∆m [10sin2 θ23 [10−1 ]δCP [π]1.2.1Best FitCR

CRs are particles produced and accelerated by astrophysical sources. About 90%
are protons; 9% are atoms, such as helium; and electrons comprose less than 1% [41].
The origin of CRs and their processes of acceleration remain a mystery of astroparticle physics.
The magnitude of the kinetic energy of a nucleus is often measured with units of
GeV and EeV. Figure 1.1 shows the flux of high-energy CRs for all particles, providing a good approximation of the power-law: E −γ . The power-law index changes
at two diﬀerent points, creating a ”knee” (around 3 × 1015 eV) and ”ankle” (around1019 eV). Although less certain, the most recent experiments revealed an extra feature around 1017 eV called the ”2nd knee.” The spectral indices are observed as:• γ ≈ 2.7 for about 1010 to 3 × 1015 eV• γ ≈ 3.1 for about 3 × 1015 to 3 × 1018 eV• γ ≈ 2.6 for about 3 × 1018 to 1020 eV
If high-energy CR fluxes are cosmological in origin, there should be a rapid steepening of the spectrum around 5 × 1019 eV. This is called the Greisen–Zatsepin–Kuzmin(GZK) limit [42, 43], which results from inelastic interactions of CRs with the cosmic
microwave background (CMB).
Because CR particles arrive at the Earth at energies much larger than the thermal energies of typical astrophysical objects, specific acceleration mechanisms apartfrom blackbody radiation are needed to explain the spectra observed. It is known
that CRs from the sun arrive at upwards of 108 to 1010 eV [45]. Therefore, the mechanism of acceleration of high-energy CRs probably diﬀers from one energy region toanother.
The acceleration process of CRs could be generated within our galaxies or atpoint-like sources of extreme extragalactic energy densities. In 1949, Fermi proposed a mechanism whereby particles could gain energy from collisions with moving

1. INTRODUCTION

22

Figure 1.1: Energy flux spectra of CRs for all particles as a function of energy per
nucleus obtained from air-shower measurements [44].
interstellar ionized gas clouds [46]. That mechanisms provided an estimate of achievable energies for particles trapped in the magnetic field of our galaxy. However, puregalactic acceleration is insuﬃcient to produce CRs in the high-energy tail of the spectrum. The highest energetic CRs are probably created by extragalactic source (e.g.,
neutron stars, gamma-ray bursts, active galactic nuclei). Hillas reported that the
maximum energy of a CR was a correlation between the magnitude of the magnetic
field and the radius of the object [47]. However, if the magnetic field becomes toolarge, the protons lose more energy because of synchrotron radiation. Neutron stars
and active galactic nuclei may not reach the GZK limit because of this synchrotron
loss.

1.2.2

Gamma Rays

Gamma rays are produced by accelerated electrons and possibly protons; they havebeen measured at very high energies in the CR spectrum. Contrary to charged
particles, photons are not deflected by magnetic fields, and they point straight to theobjects from which they originated. Gamma rays, on the other hand, are producedby radiation or decay by both leptonic and hadronic processes.

1. INTRODUCTION

23

Proton acceleration is always accompanied by photons and neutrinos generated
by charged and neutral meson decays. These mesons are mostly pions and are
generated by proton–proton collisions (pp) or photo–hadronic (pγ) interactions:p + p → π± , π0 , K ± , K 0 , p, n, ...
+

+

+

0

p+γ → ∆ → π +n

or

or

,

,

(1.21)(1.22)

p + γ → ∆ → π + p.

(1.23)

In both scenarios, the decays of the neutral pions, π0 → 2γ, give rise to a flux ofhigh-energy gamma rays. The two gamma rays per meson produced by this decay
are emitted isotropically in the rest frame but are boosted similar to the mesons
from the laboratory frame. As a result, the original proton spectrum is reproduced
after the gamma-ray spectrum rises above the production threshold energy.
The energy window of gamma-rays from radio to soft X-rays is dominated byradiation emitted by accelerated electrons propagating through a strong magnetic
field. The radiation pattern of the relativistic electron in a magnetic field is beamedin the direction of the motion of the electron itself, which turns proportionally tothe magnetic field. The synchrotron flux from its source having a power-law energy
distribution of dN /dE ∝ E −γ is shown to be
F ∝

R3
d2

B 1+α f −α ,(1.24)

where the source having radius R at a distance d emits a population of particles. B
is the magnetic field, f is the synchrotron frequency, and α = (γ − 1)/2. Charged
particles having masses greater than electrons suppress synchrotron radiation in
proportion to their mass.

1.2.3

Neutrinos

It is important to search for neutrinos at CR sources to elucidate acceleration mechanisms. Because neutrinos do not interact with surrounding materials, owing to theirvery small cross-sections, it is possible to study the hadron processes that occur at
CR sources.
The interaction of proton–proton collisions explains not only the production of
gamma rays, but also the production of high-energy neutrinos. Together with π0 ,
π+ , and π− are produced in approximately the same number. Although the neutralpion decays into two photons, the processes connected to charged pion decay are
π+ → µ+ + νµ → e + + νe + νµ + νµ−−−

π → µ + νµ → e + νe + νµ + νµ .

and ,(1.25)(1.26)The injected neutrino flavor ratios for neutrinos and anti-neutrinos depend on
the details of energy loss mechanisms at the source. However, the neutrino oscillations over astrophysical distances will alter the injected flavor ratio, from which
one expects to observe a nearly equal admixture of neutrino flavors in the measured
flux, (νe : νµ : ντ ) = (νe : νµ : ντ ) ≈ (1 : 1 : 1), at the Earth.

1. INTRODUCTION

1.3

24

Active Galactic Nucleus (AGN)

AGNs are extreme extragalactic objects and candidates for CR accelerations at thehighest energies. They are observable across a wide range of wavelengths up to1027 Hz, and the most distant detected AGNs are at a redshift of z = 7.1 [48]. An
AGN consists of a supermassive black hole (about 106 to 1010 solar masses) with anaccretion disk at its gravitational potential.
From the unified view of AGNs [49], the black hole and accretion disk appear
surrounded by a dusty torus and a cloud obscuring the AGN center, and a fractionof the AGN emits jets orthogonal to the rotating disk. For a 108 solar-mass blackhole, the radius is about 3 × 1013 cm; the accretion disk emits between 1 × 1014 to
30 × 1014 cm; the clouds are located within about 2 × 1016 to 20 × 1016 cm; and theinner radius of the dusty torus is perhaps 1017 cm. Jets have been detected on scales
from 1017 to several-times 1024 cm.

Figure 1.2: Schematic of AGN (not to scale) [49]. Surrounding the central blackhole is a luminous accretion disk and a dusty torus. The clouds of gas move rapidly
in the potential of the black hole. Beyond the torus, the clouds of gas move slower.
The jets emanate from the region near the black hole.

1. INTRODUCTION

1.3.1

25

BlazarAGNs having jets aligned with the line of sight of the observer are classified as
the blazars. These emit non-thermal radiation mainly from jets at all observed
wavelengths and have broad absorption characteristics or no absorption at all.
The spectrum of a blazar is Doppler-boosted and blue-shifted because of theemission of light emitted at a small angle from a very relativistic jet [49]. It formsa characteristic shape having two wide humps (10 MeV to 100 GeV and 50 GeV to
10 TeV). Low-energy humps are assumed to originate from synchrotron radiation,
but high-energy bumps are not fully understood.
Blazars comprise two types of objects: BL Lac and flat-spectrum radio quasar(FSRQ). FSRQs show broad absorption lines, and BL Lac type objects display theselines only very weakly or not at all. The spectrum from a BL Lac usually extends
to higher energies. Furthermore, blazars can be subdivided into classes based on
the peak position of their first bump. If the first bump peaks above 1015 Hz (below
1014 Hz), the object is called a high- (low-) synchrotron-peak HSP (LSP) or high(low-) synchrotron-peaked BL Lac HBL (LBL) for BL Lac blazars [50, 51]. Theintermediate objects are called ISP or IBL.
Figure 1.3 shows the spectral-energy distribution of Markarian 421 (MRK421),
resulting from the 4.5-month-long multifrequency campaign. MRK421 is one of
the closest (redshift z = 0.031 [52]) and the most prominent BL Lac blazar. It
clearly distinguishes the two hump characteristic. The first is a tracer of synchrotron
emission, and the second can be attributed to hadronic processes.

Figure 1.3: Spectral-energy distribution of Markarian 421 averaged over all observations taken during the multifrequency from January 19 to June 1, 2019 [53, 54].

1. INTRODUCTION

1.3.2

26

Neutrinos from Blazars

Neutrino detection from blazars help probe hadronic interactions in the jets. Furthermore, it helps clarify the structure of relativistic jets, jet content, and acceleration processes.
The IceCube Neutrino Observatory [55] detected a high-energy neutrino event
having an estimated energy of 290 TeV on 22 September 2017 at 20:54:30:43 UTC [19,56]. The event was called IceCube-170922A. The arrival direction of the neutrino
event coincided with the location of a blazar named TXS0506+056, assuming a BL
Lac type blazar (redshift z = 0.3364 ± 0.0010 [57]) and located at a right ascension(R.A.) of 77.3582◦ and declination (Dec.) of +5.6931◦ (J2000 equinox) [58]. Withina minute of detection, the information of this event was shared via the Gammaray Coordinate Network (GCN)2 and follow-up observations over a wide range ofenergies have been carried out at several observatories. According to the Fermi Allsky Variability Analysis (FAVA) [59], TXS0506+056 brightened in the GeV band
starting in April 2017 [60]. Independently, Fermi’s Automated Science Processing(ASP) [61] found a gamma-ray flare. The coincidence between the neutrino arrival
direction and the blazar location and timing correlated with the associated gammaray flare suggesting that the observed neutrinos originated from the blazar.
Figure 1.4 and 1.5 summarize the multi-wavelength light curves and the changes
in the broadband spectral-energy distribution. To calculate the energy flux, the IceCube collaboration considered two neutrino-emission periods. In the first scenario,
neutrinos were assumed to have been emitted only during the 6-month period corresponding to the duration of the gamma-ray flare. The second scenario presumes
that neutrinos are emitted over the entire IceCube observation (7.5 years).
Furthermore, time-dependent analysis was performed at the coordinates of TXS0506+056 [56]. As a result of the analysis, one data period contained a significant
signal, identified by both time window shapes (gaussian-shaped and box-shaped
windows). The excess consists of 13 ± 5 events above the expectation from theatmospheric background. However, there was no excess gamma-ray flare nor a significant gamma-ray spectral change with respect to the average during the time of2014 to 2015 (Figure 1.4).

2

The GCN/AMON : https://gcn.gsfc.nasa.gov/amon.html

1. INTRODUCTION

27

Figure 1.4: Time-dependent multi-wavelength observations of TXS0506+056 [19].
From top to bottom, the panels show diﬀerences in observed energy. The left panels
show measurements between 22 August 2008 and 6 September 2017. The right panels
show an expanded scale for times ranging from 6 September to 24 October 2017.
The red dashed–line marks the detection time of the neutrino IceCube-170922A.

Figure 1.5: Broadband spectral-energy distribution of the blazar TXS0506+056
with neutrino flux [19]. The distribution based on observations obtained within
14 days of the detection of the IceCube-170922A event. The neutrino flux upper
limits produced on average per detection over a period of 6 months and 7.5 years
are shown. The neutrino energy assumes the most probable energy (311 TeV).

2. SUPER-KAMIOKANDE (SK)2

28Super-Kamiokande (SK)SK is a large water Cherenkov detector build in the Kamioka mine at a depth ofabout 1,000 m underground (2,700 m water equivalent) [62]. It is located at latitude36◦ 25′ N and longitude 137◦ 18′ E in Mt. Ikenoyama, Gifu Prefecture, Japan. Owing
to the overburden of the mountain above the detector, the cosmic muon backgroundis reduced by a factor of ∼ 10−5 , compared to that at the mountain’s surface.
The detector is a cylindrical tank, and it is optically separated into inner andouter detectors. The tank contains a total of 50 kilotons of ultra-pure water as theneutrino target. The layout of the detector is shown in Figure 2.13 .
The primary purpose of this experiment was to search for proton decay and study
neutrinos from atmospheric, solar, and astrophysical sources, including supernovae,
gamma-ray bursts, and active galactic nuclei. SK also serves as the far detector for
the Tokai-to-Kamioka (T2K) long-baseline neutrino experiment [63].

Figure 2.1: Schematic of the SK detector (cutaway view).

3

The figure taken from the web page of Super-Kamiokande http://www-sk.icrr.u-tokyo.ac.
jp/sk/index.html

2. SUPER-KAMIOKANDE (SK)

2.1

29

Cherenkov Radiation

In dielectrics, having a refractive index greater than 1, an electromagnetic shockcalled Cherenkov radiation occurs when the velocity of charged particles is greaterthan the speed of light passing through the medium.
v>

c
,
n

(2.1)

where v is the velocity of the charged particle, c is the speed of light in a vacuum,and n is the refractive index of the medium. This phenomenon was first discoveredby Cherenkov [64], and a theory of this eﬀect was later developed by Frank andTamm [65]. The direction of the emitted light can be calculated using classicalphysics, the Huygens–Fresnel principle. The eﬀect is caused by coherent radiationfrom atoms and molecules excited along the charged- particle trajectory. Figure 2.2
shows a schematic of Cherenkov radiation, comprising the movement of a relativistic
and non-relativistic charged particle.

Figure 2.2: Cherenkov radiation. A particle moves along the projection of the left
to the right during time t in the medium. The case of β < c/n (left) and β > c/n(right) are shown .
The relativistic charged particle can cross a distance of xp = vt. However,
the Cherenkov radiation travels radially at a distance xc = ct/n. Thus, the angle
between the direction of Cherenkov light and the direction of the charged particle
is defined as the Cherenkov angle θC ,cos θC =

xp
1
=
,
xc
nβ

(2.2)

where n is the refractive index of the medium, and β is the ratio of the velocity ofthe particle to the speed of light in a vacuum, β = v/c. The refractive index of
the ultra-pure water of SK is about 1.33 for 580 nm photons. Thus, the maximum

2. SUPER-KAMIOKANDE (SK)30

emission angle of Cherenkov light is about 42◦ at β = 1. Assuming that a particle’s
charge is equal to 1, the energy of emitted photon is given by the Frank–Tammformula [66, Chap. 6]:
(
)
d2 E
ℏα
1
=
ω 1− 2 2 ,
(2.3)
dx dω
c
β n
where α is the fine-structure constant, x is the per-unit path length, and ω is thefrequency. There exists a relationship between frequency and wavelength, ω =2πc/λ, and between the energy and the number of photons, E = N hν = N hc/λ. It
is easy to convert this to an expression regarding the number of Cherenkov photons
generated:
(
)
2πα
1
d2 N
= 2 1− 2 2 .
(2.4)
dx dλ
λ
β n
With SK, Cherenkov radiation is estimated to emit hundreds of photons per centimeter. From this relation, the minimum energy needed to emit at least one photon
can be calculated as the Cherenkov threshold. The threshold is thus reached whenthe expression is exactly equal to zero, or
βthr =

1
.
n

(2.5)

Because there exists relationships, E = γmc2 and γ = (1 − β 2 )−1/2 , the energy
threshold can be written as
mc2,
Ethr = √1 − 12(2.6)

nwhere m is the mass of the charged particle. The Cherenkov threshold of eachcharged particle detected with SK (refractive index n = 1.33) is shown in Table 2.1.
Table 2.1: Cherenkov threshold of various particles.
Particle
e

±
±

µ

π±
K

±

Rest Mass [MeV/c2 ]Cherenkov Threshold [MeV]

0.511

0.775

105.7

160.3

139.6

211.7

493.7

748.8

With SK, neutrinos are indirectly observed when they interact with the waterand produce charged particles above the Cherenkov threshold. The ring-image of
Cherenkov light is detected by the PMTs on the detector wall. For each event,the information of the photon arrival time and the integrated charge at each PMT
is recorded. Thus, it is possible to identify the vertex position of the neutrino
interaction, the number of Cherenkov rings, the momentum of the charged particle,
and the particle type of the daughter particle. The details are described later.

2. SUPER-KAMIOKANDE (SK)

2.2

31

SK Detector

The detector shape is cylindrical: 39.3 m diameter and 41.4 m tall. It contains
50 kilotons of ultra-pure water. The inside of the tank is optically separated into
an inner detector (ID) and an outer detector (OD). Between the ID and OD, there
is a steel support structure having a width of about 60 cm to accommodate the
PMTs (Figure 2.3). The surface of the SK dome cavity above the tank houses fiveelectronic huts, a linear accelerator for detector calibration, and storage for various
equipment. Additionally, to avoid disturbing the photoelectrons (p.e.) in the PMTs
with the Earth’s magnetic field (about 450 mG), 26 Helmholtz coils are lined up
along the wall of the SK tank, reducing it to 50 mG.
The ID wall exists about 2.7 m inward from the wall of the SK tank and about
2.6 m from the top and bottom, comprising a total water mass of about 32 kilotons.
It consists of 20-inch PMTs facing inward, and the space between the ID PMTs iscovered with a black sheet to reduce unnecessary photon reflection. ID PMTs arearranged in modules, each consisting of 3 × 4 PMTs spaced about 70 cm from eachother. A fiducial volume (FV) of the ID is defined as the cylindrical volume 2 minward from the ID wall and has a mass of 22.5 kilotons.
The OD region has a width of about 2.2 m along the wall of the SK tank and isabout 2.1 m thick at the top and bottom with a total water mass of about 18 kilotons.
It tags outgoing charged particles, and can also be used as a veto detector for cosmic
rays and the gamma rays from surrounding rocks. It detects photons with 1,885 8inch PMTs facing outward from the support structure, and the space between the
OD PMTs is covered with a white Tyvek sheet to maximize the light detection
eﬃciency.

2.2.1

History of SK

The Kamioka Nucleon Decay Experiment (KamiokaNDE) detector, the predecessorof SK, has a tank 15.6 m in diameter and 16 m in height. It contains about 3 kilotonsof pure water and 948 PMTs in the ID with 123 PMTs in the OD [67]. Its observation
was carried out from July 1983 to April 1996, during which it observed the neutrinos
from a supernova (SN1987A) [15].
The construction of the SK detector started in 1991 as a successor to the KamiokaNDE experiment. For the SK tank, the cavity in the mine was excavated until the
middle of 1994. Afterwards, water-tank construction started, and PMTs were installed until the end of 1995. Water-filling started in January 1996. Experimental
data were collected starting 1 April 1996 after a 1-month test run. From the startof the operation to the present, SK has five phases (i.e., SK-I, SK-II, SK-III, SKIV, and SK-V). Furthermore, the SK-Gd phase, in which gadolinium is loaded toultra-pure water to improve neutron identification accuracy, is scheduled to start.

SK-I
The SK-I phase started 1 April 1996 continually operated until July 2001. At theID, 11,146 PMTs were placed at intervals of about 70 cm, and the photo coverage

2. SUPER-KAMIOKANDE (SK)32

Figure 2.3: Schematic of the module structure of the PMT support
frame [62]. The inward-facing ID PMTs
and the outward-facing OD PMT canbe seen. The region of ID and OD are
optically separated by a black sheet inside the support structure and a Tyvek
sheet outside the support structure.

was 40%. During this period, in 1998, the SK collaboration released the first highly
significant experimental evidence for neutrino oscillations [68]. Furthermore, theK2K experiment [31, 69, 70] started during that phase. The experiment was thefirst accelerator neutrino long-baseline experiment, which sent a nearly pure νµ beam
250 km from the Japanese accelerator facility KEK to the SK. The main data wastaken from June 1999 to November 2004 and 112 beam-originated neutrino eventswere observed. From this observation, the probability of the expectation for noneutrino oscillation was estimated to be 0.0015% (4.5σ) [31].

SK-II
On 12 November 2001, one of the bottom PMTs imploded during a post-maintenancetank refill. A total of 7,796 PMTs were damaged (6,779 ID PMTs and 1,017 OD
PMTs) because of the subsequent chain reaction.4 Since this accident, each ID PMT
has been covered with an acrylic and fiberglass reinforced plastic (FRP) case toprotect from shock waves. The remaining ID PMTs were relocated, and the new
OD PMTs were prepared to resume observations. The observation period from4

The details of the accident were reported at http://www-sk.icrr.u-tokyo.ac.jp/
cause-committee/index-e.html.

2. SUPER-KAMIOKANDE (SK)33

October 2002 to October 2005, called SK-II, was operated with 5,182 covered ID
PMTs and 1,885 OD PMTs, and the photo coverage of ID was 19%.

SK-IIIIn October 2005, work began to reinstall PMTs. This work was completed in July
2006, and full operation with 11,129 ID PMTs was given. 17 ID PMTs were removed, compared with SK-I, owing to the size of the acrylic cover. However, thephoto coverage of ID was 40%. Moreover, the barrel and end-cap regions of OD
were optically separated by the Tyvek sheet directory upward and downward fromthe barrel region. Via optical partitioning, it was possible to distinguish between
neutrino events with leptons exiting from ID and muon events, both activating the
top/bottom and barrel regions of the OD. This helped improve the reduction of
background. The data period from July 2006 to August 2008 is called SK-III.

SK-IV
Since September 2008, the detector was shut down once because all of the front-end
electronics were upgraded. SK-IV then was continued from September 2008 to June
2018. During this period, the T2K experiment using SK as a far detector started,and on 24 February 2010, the first event of the T2K experiment was successfully
observed at SK.

SK-V
Repair work started in June 2018 for the next SK phase, known as SK-Gd. The
main purpose was to repair a leak in the SK tank, install new plumbing to smoothout the water flow in the tank, replace dead ID and OD PMTs, and clean up thedetector. SK-V has been running since January 2019. It represents the final phaseof using ultra-pure water as a neutrino target at SK. A summary of the diﬀerences
between each of the SK phases can be found in Table 2.2.

SK-Gd
The SK-Gd phase is the next project, which will dissolve gadolinium in ultra-purewater at SK [71]. Gadolinium has the largest cross-section of thermal neutron capture among natural elements, and a total of about 8 MeV gamma rays are emitted.
Therefore, it is possible to distinguish between neutrino reactions with neutrons andthose without. This new phase, SK-Gd, is scheduled to start March 2020.

2. SUPER-KAMIOKANDE (SK)34

Table 2.2: Summary of characteristics of each SK phase.
Phase

SK-I

SK-II

SK-III

SK-IV

SK-V

Start Time1996 Apr.

2002 Oct.

2006 Jul.

2008 Sep.

2019 Jan.

End Time

2001 Jul.

2005 Oct.

2008 Sep.

2018 Jun.

(running)

ID PMT

11,146

5,182

11,12911,12911,129OD PMT

1,885

1,885

1,885

1,885

1,885

PMT Coverage

40%

19%

40%

40%

40%

Electronics

ATM

ATM

ATM

QBEE

QBEE

2.2.2

ID PMT

Figure 2.4 shows an overview of Hamamatsu R3600 PMT, an ID PMT having a
diameter of 20-inch (50 cm). It was developed by Hamamatsu Photonics K.K. in cooperation with SK collaborators [72]. The dynode structure and bleeder circuit were
improved to achieve better timing responses and collection eﬃciencies for SK [73].
All ID PMTs were installed with an acrylic cover and an FRP case, as shown in
Figure 2.5, during the SK-II phase, because of 2001 accident. Prior to the accident,
the ID PMTs were used with 7,650 tubes on the barrel and 1,784 tubes on the top
and bottom. However, after the accident, 17 PMTs, eight from the top and ninefrom the bottom, were removed because of the size of the acrylic covers and theirinstallation position. The transparency of the acrylic cover was higher than 96% at
350 nm wavelength.

Figure 2.4: 20-inch ID PMT [62].

Figure 2.5: FRP case and acrylic
cover of the ID PMT [74]. Units arein mm.

The photocathode of the PMT was coated with a bialkali (Sb – K – Cs) thatmatched the wavelength of the Cherenkov light. Its sensitivity range was 280 to
660 nm. The maximum quantum eﬃciency (QE) was about 21% at a peak of 360
to 400 nm, which can be seen in Figure 2.6. The QE is the ratio of photons striking

2. SUPER-KAMIOKANDE (SK)35

the PMT to the p.e.. The average collection eﬃciency at the first dynode is 70%,
which is uniform within ±7% across the whole PMT surface. The gain of the PMT
is 1 × 107 at a high voltage around 2,000 V. The single-p.e. peak can be clearlyseen in the charge distribution shown in Figure 2.7. The relative transit time spreadfor the single p.e. signal is about 2.2 nsec (1σ), which was got from the test with
410 nm wavelength light using a typical ID PMT. The average dark-noise rate at
the 0.25 p.e. threshold is about 3 kHz.

Figure 2.6: Quantum eﬃciency of the 20-inch ID PMT as a function of the lightwavelength [nm] [62].

Figure 2.7: Single-p.e. pulse height distribution expressed as a light-intensitydependent analog-to-digital-converter (ADC) count. The peak nearest zero ADC
count is caused by the PMT dark current [62].

2. SUPER-KAMIOKANDE (SK)

2.2.3

36

OD PMTThe OD has 1,885 PMTs with a diameter of 8-inch (22 cm). During the SK-I phase,
OD PMTs were reused from the IMB experiment [75] after it was decommissioned
in 1991. However, after the accident in 2001, most OD PMTs were replaced. The
new OD PMT, Hamamatsu R5912 PMT, is the same size and has similar characteristics as the older IMB PMT. Each OD PMT is attached to a 60 cm×60 cm×1.3 cm
wavelength-shifting (WS) plate to compensate for the relatively few numbers of
PMTs, also taken from the IMB detector. The WS plates are acrylic-doped panelswith a 50 mg/L scintillator, bis-MSB (C24 H22 ). It absorbs light in the ultraviolet
region and emits blue green light closer to the sensitivity peak of the OD PMTs. The
light collection eﬃciency thus increased by 60%, but the timing resolution slightly
decreased from 13 to 15 nsec for the single-p.e. signal. Because the OD functions
primarily as a veto, observing the extra photons is of much more importance thanbetter timing resolution.
The OD PMTs are uniformly distributed using 1,275 tubes on the barrel, 302
tubes at the top, and 308 tubes at the bottom. The OD is lined with a layer of
Tyvek between the OD PMTs and is over 80% reflective to enhance the OD lightcollection. The relationship between ID PMT and OD PMT is shown in Figure 2.8.

Figure 2.8: Schematic of a module of ID and OD PMTs [76]. Each OD PMT ishoused in an inner structure that holds 12 ID PMTs facing inward for every 2 OD
PMTs facing outward.

2. SUPER-KAMIOKANDE (SK)

2.3

Water and Air System

2.3.1

Water Purification System

37

The original SK water was produced from the mine, and it was thus very important to keep the water transparency as high as possible. It is also important toremove radioactive materials, especially radon and radium. Gamma rays emitted
from such radioactive nuclides become the background for observation in the MeVenergy range. The water is constantly circulated through a purification system at aflow rate of about 50 tons/h. The system is summarized in Table 2.3.
Table 2.3: Water Purification System: the components and their purpose and result.
Component

Purpose & Results

1 µm Mesh Filter

Removes dust and larger particles

Heat Exchanger

Cools water to suppress the growth of bacteria.
Typical water temperatures before the first heatexchanger and after the second heat exchanger
are 14.2 ◦C and 12.9 ◦C, respectively

Cartridge Polisher

Eliminates heavy ions which also reduce watertransparency. It is able to remove ions such as
Na+ , Cl – , Ca2+ , and others

Ultraviolet Sterilizer

Kills bacteria that could not be killed with aheater exchanger

Radon-reduced Air Dissolving

Dissolves radon-reduction air into the water toincrease radon removal eﬃciency at the vacuum
degasifier stage

Reverse Osmosis Filter

Further removal of contaminations heavier than
1,000 molecular weight. This is newly added
when the SK-III phase

Vacuum Degasifier

Removes dissolved gases in water, such as theoxygen and radon. Radon gas is removed about
96% and oxygen gas is also removed about 99%

Ultra Filter

Removes minute particles of the order of 10 nm

Membrane Degasifier

Removes radon dissolved in water with about
83% eﬃciency. After going through the system,
the radon concentration is reduced to less than
0.4 ± 0.2 mBq/m3

The typical resistivity of water entering the purification system from the detector
is about 11 MΩ · cm. After purification, the water has an average resistivity of
18.20 MΩ · cm, approaching the chemical limit. Thanks to this water system, the2. SUPER-KAMIOKANDE (SK)38transparent of ultra-pure water reaches about 90 m.

2.3.2

Air Purification System

The air in the mine is richer in radon gas than is the outside of the mine, because
the rocks of mine contain radon. The concentration of radon gas inside the mine
is about 1,000 to 2,000 Bq/m3 during summer and about 100 to 300 Bq/m3 during
winter because of the changing air-flow patterns. To reduce the radon level in theair, an air purification system is used. It consists of three compressors, a buﬀer tank,dryers, filters, and activated charcoal filters. The resulting radon concentration isless than 3 mBq/m3 , which is supplied between the water surface and the top of the
SK tank.

2.4

Electronics and Data Acquisition (DAQ)
SystemThe DAQ system for SK-I and SK-III (1996–2008) phases used the analog timing
module (ATM) of the Tristan KEK Online (TKO) standard [77, 78]. During thosephases, the DAQ system did not undergo any major upgrades. During the SK-IV
phase, the ATM was replaced with new electronics, QBEE [79], short for a chargeto-time converter (QTC) based electronics with ethernet. Owing to the QBEE, thedead time associated with the DAQ system was reduced, the dynamic range was
expanded, and the energy threshold was lowered.
The data analyzed in this work spans SK-I through SK-IV phases. The detailed
description of the original DAQ system and the new DAQ system are provided.

2.4.1

ID Electronics and DAQ: SK-I to SK-III

Each ID PMT signal is connected to an ATM, and each ATM accepts 12 input channels. 20 ATMs are included in each TKO crate with a super control header (SCH)
module and go/nogo (GONG) module. The SCH module is a bus-interface module
between TKO and Versa Module Europa (VME). The GONG module distributes
control signals as a master module to its slave module. In the VME crate, there
are six data-buﬀer modules (i.e., super-memory partner (SMP) and an Sbus-VME
interface). There are four separate electronics huts atop of the SK tank, each having
12 TKO system crates and two VME crates. The schematic of the electronics system
is shown in Figure 2.9.
Figure 2.10 shows a schematic of the analog input block of the ATM. The signal
from each PMT has two switching pairs of charge-to-analog converter (QAC) andtime-to-analog converter (TAC) to measure the charge of the input pulse and thetime. The QAC provides 550 pC full range with 0.2 pC resolution, and the TAC
provides 1.2 µsec full range in time with 0.3 nsec resolution. Each PMT signal is
divided by four after amplification at a factor of 100.

2. SUPER-KAMIOKANDE (SK)39

Figure 2.9: Logic diagram of the electronics system for the ID used with SK-I to
SK-III [80].
One PMT signal travels through a discriminator threshold that is set to about
0.25 p.e.. When the pulse height of a signal exceeds the threshold, a 900 nsec gate
signal as a HIT signal, a 400 nsec gate signal for QAC, and a start signal for the
TAC are generated. For the HIT signal, any subsequent PMT signal is rejected.
Simultaneously, a rectangular signal (200 nsec wide and 15 mV pulse height) is generated. The rectangular signal from every 12 PMTs are summed and output as the
ID-HITSUM signal.
The other two PMT signals are fed to the QAC and TAC. If the global trigger
arrives within 1.3 µsec after the HIT signal, the charge/timing information fromthe QAC/TAC are digitized by an ADC. Otherwise, the readouts of QAC/TAC iscleared. The ADC outputs are stored in the 1,024 word first-in first-out (FIFO)
memory with an event number. It takes 5.5 µsec to convert from analog to digitaland store it in memory, during which time the signal is not processed. Therefore,
the QAC/TAC has two channels to minimize the electronics dead time during datacollection for two successive events, such as a muon followed by its decay electron.
The final signal from the PMT is an output signal without a discriminator threshold (i.e., PMTSUM). The timing chart of the signal in the ATM is shown in Fig-

2. SUPER-KAMIOKANDE (SK)

Figure 2.10: Block diagram of the circuit in the ATM [81].

Figure 2.11: Timing chart for signal and trigger in an ATM [80].
ure 2.1140

2. SUPER-KAMIOKANDE (SK)

2.4.2

41

OD Electronics and DAQ: SK-I to SK-III

The schematic of the electronics system for OD is shown in Figure 2.12. The OD
PMT signal is connected to the paddle cards, and each paddle card handles 12 OD
PMTs. The signals from four paddle cards are sent to the QTC module. The QTC
output signals are digitized using a LeCroy 1877 multi-hit time-to-digital converter(TDC), which can record up to two QTC pulses. The fastbus crate holds four modules: five TDCs, an event-number latch, a fastbus smart-crate controller (FSCC),
which reads out the signals recorded by the TDCs, and a custom-built interface
board. The fastbus crate is placed in each electronics hut with ID electronics. The
paddle cards fan-out high voltage from one of the mainframe channels into the OD
PMT output. Thus, it plays a role in picking oﬀ the PMT signals through a highvoltage capacitor, allowing the disconnection of the channel. All 12 outputs have
jumpers.

Figure 2.12: Data accusation system for OD [82].
The purpose of the QTC modules is to measure the hit time and charge of theOD PMT signal. The output of the QTC module is a logic pulse. The leadingedge of the pulse represents the hit-arrival time, and the width is proportional tothe integrated charge of the OD PMT pulse. The QTC modules also provide an
OD-HITSUM signal of 200 nsec width and 20 mV pulse, as does the ID.
Each TDC module behaves as a circular buﬀer that can store pulses with aresolution of 0.5 nsec. The dynamic range was originally set to 32 µsec, centeredaround the trigger time. However, after September 1996, the width is set to 16 µsec

2. SUPER-KAMIOKANDE (SK)42

which starts from 10 µsec prior to trigger timing to reduce the data size. The TDC
signal is then read by the FSCC, and the stored data are sent to the online computer
via the VME bus.

2.4.3

Hardware Trigger: SK-I to SK-III

There are three types of ID triggers: the high energy (HE) trigger, the low energy(LE) trigger, and the super low energy (SLE) trigger. Trigger thresholds are definedby the level of the ID-HITSUM signal. The HE trigger is used to identify CR muon,
atmospheric neutrinos, and proton decay. The LE is used for solar neutrino analysis,and SLE was implemented in May 1997 to perform solar neutrino analysis at lower
energy.
During the SK-I phase, the HE trigger requires the pulse height of the IDHITSUM signal to exceed a threshold of −340 mV within a 200 nsec time window.
The HE trigger rate is about 5 Hz with an energy threshold of 10 MeV. The threshold of LE trigger is set to −320 mV, equivalent to a signal expected from a 5.7 MeV
electron with 50% trigger eﬃciency. The LE trigger rate is about 11 Hz with anenergy threshold of 8 MeV. The threshold level of the SLE gradually decreases as
the trigger central processing unit (CPU) power increases. The threshold as set to−186 mV in July 2000, which is equivalent to signal expected from a 4.6 MeV electron, and the trigger rate is about 1 kHz. In the SK-II and SK-III, the same trigger
scheme having diﬀerent thresholds for each phase is used. The trigger conditions ineach phase are summarized in Table 2.4.
Table 2.4: Trigger threshold for each SK phase. The SLE threshold is sometimes
lowered during SK-I phase, and here is the final value.
Trigger Type

SK-I

SK-II

SK-III

High Energy (HE)−340 mV−180 mV−320 mV

Low Energy (LE)−320 mV−152 mV−302 mVSuper Low Energy (SLE)−186 mV−110 mV−186 mV

Outer Detector (OD)

19 hits

19 hits

19 hits

The OD trigger is generated using a similar procedure as the one for ID. The
threshold for the OD trigger corresponds to 19 hits of the OD PMTs in a 200 nsec
time window. If the ID does not trigger on its own within 100 nsec, the OD alone
will trigger the readout of the full detector.
These four trigger signals (i.e., HE, LE, SLE, and OD) are fed to the hardware
trigger (TRG) module. When any of the trigger types is asserted, the TRG module
generates a global trigger signal and a 16-bit event number. These are sent to allelectronics huts to initiate DAQ for the current event.

2. SUPER-KAMIOKANDE (SK)

2.4.4

43

Electronics and DAQ for ID & OD: SK-IV and
SK-V

To improve detector sensitivity, new front-end electronics were installed in September 2008. The existing ATMs were replaced with QBEE boards, which are housedin the same TKO crates used to house the ATMs. However, the readout scheme wascompletely changed. The output signal from QBEE is now transmitted to the online computers via ethernet cables using TCP/IP. This greatly improves the transfer
time for data and eliminates bottlenecks, which were sometimes caused by the TKO
readouts in the original DAQ. The same QBEE is also used for the OD PMTs.
Each QBEE board is equipped with eight QTCs, which are custom applicationspecific integrated circuits (ASIC) [83, 84]. Because each QTC has three inputs,
one QBEE board processes the signal from 24 PMTs. As shown in Figure 2.13, theoutput signal of the QTC is sent to the multi-hit TDC.
The digitized information of the TDC is sent to a field-programmable gate array(FPGA) for data-sort mapping (DSM). There are four DSM chips in each QBEE
board, and each DSM chip deals with data from six input channels. The DSM
outputs are sent to another FPGA, called the system-interface controler (SIC). SIC
sorts the data from the DSM and stores them into FIFO memory.

Figure 2.13: Block diagram of the QTC and its surroundings. PMT signals are sent
to the QTC using an RG58 coaxial cable and are divided among three gain ranges.
Output signals are generated with low-voltage diﬀerential signaling (LVDS) drivers.
The figure was taken from [84].
Each QTC channel has three gain ranges (i.e., small, medium, and large), which
can be adjusted using an external resistor network. When the relative gain ratio1
is 1: 17 : 49
, the charge dynamic ranges from 0.2 to 2,500 pC. Following the gainstage, the signal from PMTs is amplified using a low-noise amplifier (LNA), delayed
by a low-pass filter (LPF), processed by a voltage-to-current (V/I) converter, andintegrated using a capacitor. One of the output waveforms of the V/I converter issaved as the analog sum (i.e., PMTSUM).
The other output signal is sent to the charge integration stage. When the amplified signal crosses the discriminator threshold, the leading edge of the output
signal represents this timing, and a trigger-flag signal (HIT) is generated. Starting2. SUPER-KAMIOKANDE (SK)44with the HIT-trigger flag, three gates are created: charging, discharging, and veto(see Figure 2.14). The charging gate operates for 400 nsec, the switch between the
V/I converter and charging capacitor closes, and charge accumulates in the capacitor. After operation of the charge gate, the discharging gate operates for 350 nsec.
During this phase, the switch between the discharging current source and capacitor
closes, and arriving signals are ignored. Then, the reset and the veto gate are issued.
The width of the veto gate is 150 nsec, and all input signals are ignored. In total,
the processing time for one input signal is 900 nsec.

Figure 2.14: Timing chart for signal and trigger in a QTC. The gradation of PMT
signal corresponds to that of the integrated charge and output. The figure was takenfrom [84].

2.4.5

Online System for ID & OD: SK-IV and SK-V

Figure 2.15 shows the schematic of the new online system. The signal from about
13,000 PMTs (ID and OD PMTs) are transferred to 20 front-end PCs via about
550 QBEEs. One front-end PC receives the data from 30 QBEE boards. The data
are then sent to 10 merger PCs for event building. The front-end PCs and themerger PCs are linked by 10-Gigabit ethernet. In the merger PCs, the data fromall the front-end PCs are merged. At that time, a software trigger is applied to
select candidates for physics analyses. The data from the merger PCs are sent toan organizer PC via ethernet, where they are merged and written onto a disk for
oﬄine analysis.
The front-end PC system comprises three components: collector (receives datafrom QBEEs), sorter (sorts data in time order), and sender (sends data to merger
PCs). These components run as threads during the same process.

2. SUPER-KAMIOKANDE (SK)45

Figure 2.15: Block diagram of the new online system. Data are transferred from
QBEEs to the organizer PC via 100 Base-T (broken line), gigabit ethernet (solidline), and 10-Gigabit Ethernet (bold solid line). The figure was taken from [79].
The data from the front-end PCs are merged onto the merger PC, and all merged
events are again sorted by time order. At that time, because the data were alreadysorted by each front-end PC, the heap-sort technique is used for sorting to reduce theCPU costs. Another component of a merger PC is its software trigger management
system. One merged block contains hit data within a 22 msec time window and issent to the software trigger.
The final component of the online data system is the organizer, which sorts thedata blocks from the merger PCs in time order. A 22 msec data block has an adjacent
block and a 1 msec overlap area, so that no events are missed at the boundary. The
organizer checks for this duplicate area and removes the double-count event. The
data are then written to disk, and further data reduction and physics analysis are
performed by the oﬄine system. The oﬄine system has 700 TB disk storage and a
1,080 CPU cluster.
The capability of data transfer was greatly improved in QBEE by adopting
ethernet data transfer to online PCs. As a result of measuring the throughput of
the QBEE by feeding analog pulses to the QBEE and receiving output data in a PC,
11.8 MB/sec per QBEE board was achieved, which nearly reaches the 100 Base-T
theoretical limit.
The data flow of the new online system is much larger than that of the previous
system, because the new system receives all hit data from the front-end electronics.
Assuming a hit-rate per 4.5 kHz PMT, the data flow rate can reach 18.5 MB/sec
in the front-end PC and 37 MB/sec in the merger PC. Adding the size of headers,trailers, and other information, the total data rate for all the merger PCs is about
470 MB/sec.

2. SUPER-KAMIOKANDE (SK)

2.4.6

46

Software Trigger: SK-IV and SK-V

The hardware trigger used for SK-I to SK-III was replaced with a software trigger
for SK-IV. With the achievement of high-speed signal digitization, all PMT hits
are now collected on merger PCs. With the previous hardware trigger, the event
width was always set to 1.3 µsec. This event width can now be selected according
to the trigger type per software trigger. There are five main triggers: special highenergy (SHE), high energy (HE), low energy (LE), super low energy (SLE), andouter detector (OD).
The software trigger scans the data block and searches for events that satisfy thetrigger condition. The base trigger is set to replicate the previous hardware trigger
condition. When the number of hits within a 200 nsec time frame (sliding time
window) exceeds the threshold, the data for the time window around the triggered
timing are sent downstream. The SHE, HE, LE, and OD triggers have a wider
event width of 40 µsec, and the SLE trigger is set to 1.5 µsec because of its high rate
and radioactive background. The software trigger threshold and gate window aresummarized in Table 2.5.
The SHE trigger is installed at the SK-IV phase as a new trigger. If a SHE
triggered event is not accompanied by an OD trigger, an additional after-trigger(AFT) is issued. AFT stores an additional 500 µsec of data, which can be used toanalyze neutron capture.
Table 2.5: Trigger threshold of SK-IV phase. SHE, HE, LE, and SLE triggers are
based on ID hits, and the OD trigger is calculated using the hits in the OD PMTs
only. The SHE and SLE triggers were lowed in September 2011 and May 2015
respectively.
Trigger TypeHit Threshold

Gate Window(hits/200 nsec)[µsec]

Special High Energy (SHE)

70 → 58[-5, +35]

High Energy (HE)50[-5, +35]

Low Energy (LE)47[-5, +35]

Super Low Energy (SLE)

34 → 31[-0.5, +1.0]

Outer Detector (OD)

22 (only in OD )[-5, +35]

3. SIMULATION

3

47

Simulation

Physics analysis at SK is performed by comparing the observed data with predictions from Monte Carlo (MC) simulations. MC comprises neutrino flux, neutrino
interaction, and SK detector simulation. In the search for astronomical neutrinos
from a blazar, signals originating from atmospheric neutrinos are the primary background. The atmospheric neutrino flux at the SK is calculated by considering theflux of primary CRs, interactions that produce neutrinos, and the propagation to the
SK. Neutrino interactions simulate diﬀerent modes of interaction between water andneutrinos at various energy ranges. From the relationship between the neutrino fluxand interaction in the detector, the events observed by the detector are calculated.
The detector simulates particles, Cherenkov photon emissions, photon propagation,and detector hardware responses using the information of produced particles, suchas vertex, direction, momentum, etc.

3.1

Atmospheric Neutrino Flux

The atmospheric neutrino flux model was calculated by Honda et al. [85, 86, 87, 88,89]. It is called the Honda–Kajita–Kasahara–Midorikawa (HKKM) flux model, andthere are several versions. The SK uses the flux model announced in February 2011(HKKM2011), and this model has three components: a CR flux, hadron interaction
models, and a virtual detector.

3.1.1

Primary Cosmic Ray

Many experiments have attempted to determine the flux of primary CRs, as summarized with the HKKM flux model in Figure 3.1. As the input of the neutrino
flux calculation, the primary CR flux (up to 100 GeV) can be precisely measured
using balloon-borne experiment with superconducting spectrometer (BESS) [90, 91]
and the alpha magnetic spectrometer (AMS) [92] experiments. Above 100 GeV, thecurve is adjusted slightly to agree with emulsion-chamber data [93, 94].
The flux of primary CRs is aﬀected by solar activity and the geomagnetic field.
The solar wind drives back the low energy CRs that enter into the solar sphere of
influence. Because solar activities change periodically, the CR flux during periodsof intense and mild solar activity is defined as solar maximum and solar minimum,
respectively. The diﬀerence at solar maximum and solar minimum is more than afactor of two for 1 GeV CRs, whereas it decreases to about 10% for 10 GeV CRs.
The geomagnetic field determines the minimum energy (rigidity cutoﬀ) with which
CRs can arrive at the Earth. The rigidity cutoﬀ is expressed as a function of theentering position at the Earth and the arrival direction. This information can beobtained using the IGRF2005 model5 .

5https://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

3. SIMULATION

48

Figure 3.1: Measured primary CR flux and the model used for the HKKM calculation (solid line). The x-axis shows the kinetic energy of the proton, and the y-axis
shows the proton flux multiplied by the energy spectrum having an index of 2.5.
The data were taken from Webber et al. [95] (crosses), MASS [96] (open circles),
LEAP [97] (upward triangles), IMAX [98] (downward triangles), CAPRICE [99](vertical diamonds), AMS [92] (squares), BESS98 [90] (circles), Ryan et al. [100](horizontal diamonds), JACEE [101] (downward open triangles), RUNJOB [102](open diamonds), Ivanenko et al. [103] (upward open triangles), and Kawamura
et al. [104] (open large squares). The figure was taken from Mclachlan Fukuei [105].

The U.S. standard atmosphere 1976 model6 is used to treats atmospheric information, such as the pressure, temperature, density, and viscosity, and it covers awide range of altitudes and elevations worldwide.

3.1.2

Hadronic Interaction

Two theoretical models are used to measure interactions between the air molecules
and the CRs. The JAM [106] model is used below 32 GeV, and The DPMJETIII [107] model is used above it. The JAM is used in the Particle and Heavy-Ion
Transport code System (PHITS) [108]. It is a hadron cascade model that handles
6

https://ntrs.nasa.gov/search.jsp?R=19770009539

3. SIMULATION49

the established hadron states, including resonances with explicit spins and isospins.
The DPMJET-III is a code system based on the dual-parton model (DPM) [109],and it treats interactions between hadrons, nuclei, and photons above a few GeV.
Figure 3.2 shows a comparison of the JAM, DPMJET-III, and the hadron production (HARP) experiment [110, 111]. The HARP experiment investigated detailsof hadronic interactions of protons on thin N2 and O2 targets at low energy. In the
figure, the JAM model shows slightly better agreement with the HARP experimentthan did the DPMJET-III model.

Figure 3.2: Comparison between HARP data (cross-section of forwarding pion
production by low energy hadron interactions) and theoretical models: JAM (solidline) and DPMJET-III (dashed line). The HARP data on N2 and O2 targets werecombined into a ratio of 78.5% and 21.5%, respectively, to simulate an air target.
The red (blue) lines and points indicate the cross-section for producing π+ (π− ).
The figure was taken from Honda et al. [89].

3. SIMULATION50

In the high energy region, to confirm that the hadron interactions are correct andto fine-tune interactions in the simulation, the flux of CR muons from the simulationis compared with external experimental data. CR muons are produced in the decay
chain, and their flux has been measured by BESS [91, 112] and L3+C [113]. The
DPMJET-III model was modified using the results of these experiments. The ratio
between the CR muon spectrum and the modified model is shown in Figure 3.3. Aftermodification, the hadronic interaction model agrees with the data within ≲ 10% in
the 1 to 100 GeV muon energy range.

Figure 3.3: Comparison of cosmic ray muon flux between experimental data andmodified flux [88]. The data were observed at Mt. Tsukuba (squares) and Mt.
Norikura (triangles) using the BESS detector, and at CERN (circles) using the L3
detector. The results of the DEIS [114] and MURTON [115] experiments are alsoplotted, but they are not included in the calculation of error bars. The dashed lineis the sum of the errors in data and calculation. The figure was taken from Sanuki
et al. [116].

3.1.3

3D Flux Calculation

When primary CRs hit the atmosphere, mainly pions and kaons are generated as
secondary particles. The decay of secondary mesons creates mostly muons and neu-

3. SIMULATION

51

trinos. The calculation of neutrino flux treats the interactions and the propagationof particles in a 3D manner. In the 3D calculation, the point of entry into the Earthand the point of emergence from the Earth are calculated. The neutrinos that do notenter the Earth are discarded. In the 1-dimensional (1D) calculation, all particles
are treated using COSMOS simulation [117]. All secondary particles are producedin the direction of primary CRs. The features of 3D calculation compared to the
1D calculation are the enhancement of neutrino flux near the horizontal direction
and the neutrino generation at low altitude near the horizontal. Figure 3.4 shows aschematic of the 1D- and 3D-flux calculation methods.

Figure 3.4: Interaction areas of primary CRs, and atmosphere for 1D and 3D flux
calculation.
The enhancement of neutrino flux coming from near horizontal is explained as thediﬀerence in the eﬀective area of primary CRs interacting with Earth’s atmosphere.
As seen in Figure 3.4, because the eﬀective area is always perpendicular to thehorizontal direction in the case of 1D calculation, the eﬀective area is smaller thanthe case of 3D calculation. This eﬀect does not aﬀect the neutrinos coming fromthe vertical. Furthermore, the increase in neutrino flux is also related to the low
energy charged particles aﬀected by the geomagnetic field [86]. Figure 3.5 provides
a comparison of the neutrino flux of the two calculations (1D and 3D) and two
simulation models (FLUKA [118] and DIPOLE [86]).
The neutrino generation at low altitude near the horizontal can be explainedusing the diﬀerence in the path length of the primary CRs. In the case of the 1D
calculation, the primary CRs from the horizontal direction travel a longer distancethrough the atmosphere than vertical rays to reach the same altitude. In the 3D
calculation, a primary CR that has a more vertical incident angle and then curves

3. SIMULATION

52

to the horizontal direction has a shorter path length than the equivalent horizontal
1D case. Therefore, the neutrinos reach low altitudes in 3D calculations before
interacting. This eﬀect is also prominent at lower energies.

Figure 3.5: Atmospheric neutrino flux in three energy bins (Left: 0.1 to 0.32 GeV,
Center: 0.32 to 1.0 GeV, Right: 1.0 to 3.2 GeV). The x-axis shows the zenith
angle from which the averages are taken. The y-axis shows the neutrino flux withhistograms for each neutrino flavor multiplied by a constant to avoid overlapping.
The red solid lines are for 3D, magenta dotted lines for 1D, blue dashed lines for
FLUKA, and green thin solid lines for DIPOLE. The figure was taken from Honda
et al. [87].

3.1.4

Neutrino Flux at SK

Figure 3.6 shows the energy spectrum of atmospheric neutrinos at the SK site, whichis compared among HKKM06, HKKM11, FLUKA, and Bartol [119] models. The
calculated spectra and ratio of neutrino fluxes are shown averaged over all directions
from 0.1 to 32 GeV.
The flux of the electron neutrinos drops at a faster rate than the muon neutrinos
with increasing energy. This is explained by the higher energy muons reaching thesurface of the Earth before they can decay and produce electron neutrinos. The
ratio between muon neutrino and electron neutrino is around two up until few GeV
with increasing energy.
The MC events are generated using the predicted flux at the SK without considering neutrino oscillations. All neutrinos reach the detector with production flavors
from the atmosphere. The neutrino oscillations are applied at the time of performing
an analysis by re-weighting each MC event according to its oscillation probability
based on the neutrino energy and direction.

3. SIMULATION

53

Figure 3.6: Comparison of calculated atmospheric neutrino fluxes averaged overall directions (left panel). Comparison of flavor ratio and neutrino anti-neutrino
ratios (right panel). The solid line shows the HKKM11 flux model, and the previous
version of the HKKM model is shown with a dot-dashed line. For comparison, the
FLUKA model (dotted line) and Bartol model (dashed line) are also shown. The
figure was taken from Honda et al. [89].

3.2

Neutrino Interaction

The interaction of neutrinos at the SK is handled using an interaction generator
called NEUT [120, 121]. NEUT handles a wide energy range of neutrinos from a
few tens of MeV to hundreds of TeV, and the primary target materials are hydrogenand oxygen inside the water and the rock (SiO2 ) surrounding the detector.
Neutrino interaction can be classified into charged current (CC) and neutral
current (NC) interactions determined by the type of weak bosons exchanged (W ±and Z bosons for CC and NC reactions, respectively). The incoming neutrino in
a CC event can be identified by distinguishing the flavor of the charged lepton.
However, an NC event does not have a signal about the neutrino flavor remaining in
the detector because the outgoing lepton is also a neutrino. In NEUT, the following
CC and NC interactions are simulated:
CC/NC (Quasi-) Elastic Scatteringνℓ + N → ℓ/νℓ + N ′ /N

CC Meson Exchange Current

νℓ + N N ′ → ℓ + N ′′ N ′′′CC/NC Single Meson Production

νℓ + N → ℓ/νℓ + N ′ /N + Meson

CC/NC Deep Inelastic Scatteringνℓ + N → ℓ/νℓ + N ′ /N + Hadorn

CC/NC Coherent Pion Production

νℓ + 16O → ℓ/νℓ + 16O + π

3. SIMULATION

54

where N and N ′ represent nucleon (proton or neutron) states before and after interaction, and ℓ is a lepton.
The cross-section of neutrino–electron elastic scattering is about three ordersof magnitude smaller than the neutrino–nucleon interaction at neutrino energies ofabout 1 GeV. Therefore, the interaction between atmospheric neutrinos and electrons are neglected in the simulation.
Although the original neutrino flux produced in the atmosphere only contains
electron and muon neutrinos, tau neutrinos are also detected at the SK because of
oscillations. Because the tau lepton has a large mass value (1.78 GeV/c2 ), their CCinteraction can only occur at energies above several GeV. For that reason, the number of events caused by tau neutrino interactions is significantly smaller comparedwith electron and muon neutrino interactions. Nevertheless, tau neutrino interactions are simulated in the same manner as electron and muon neutrino interactions
by NEUT, and the produced tau leptons are simulated by TAUOLA [122].

3.2.1

Elastic and Quasi-Elastic Scattering

There is a way to classify neutrino interactions based on the final state of the nucleon.
NC elastic scattering is a process in which a neutrino simply scatters oﬀ of a nucleon
target by transferring some momentum without producing any new particles. This
is CC quasi-elastic scattering (CCQE), in which the nucleon changes but does notbreak up. For example, NC and CCQE interactions are shown as follows:
NC elastic : νℓ (νℓ ) + p → νℓ (νℓ ) + p,

(3.1)

NC elastic : νℓ (νℓ ) + n → νℓ (νℓ ) + n,

(3.2)

CCQE :νℓ (νℓ ) + p → ℓ(ℓ) + n,

(3.3)

CCQE :νℓ (νℓ ) + n → ℓ(ℓ) + p,

(3.4)

where the neutrons are assumed to be present in the oxygen nuclei. It is also assumed
that protons are present in the oxygen nuclei and with a free nucleon (free proton
in water). The cross-section of the CCQE interaction is calculated from two typesof reactions (ν − p and ν − O). The cross-section of the NC elastic is estimated fromthe cross-section of the CCQE interaction.
For the CCQE interaction in NEUT, the interactions on a free nucleon target
were first simulated by Llewellyn Smith [123]. The diﬀerential cross-section is written
as:
[
]
2
dσ CCQE
M 2 G2F cos2 (θC )22 s−u
2 (s − u)=A(q ) ∓ B(q )+ C(q )
(3.5)
dq 2
8πEν2
M2
M4
where Eν is the neutrino energy, M = 0.938 GeV is the nucleon mass, GF =1.1663787 × 10−5 GeV−2 is the Fermi coupling constant, θC is the Cabibbo angle,q = qν − qℓ is the transferred four-momentum, s and u are Mandelstam variables,3. SIMULATION

55

m is the mass of outgoing lepton, and factors A, B, and C are expressed as
[(
)
(
)
2
m2 − q 2
q2
q2
2
2
1
A(q ) =
4
−
|F
|
−
4
+
F
A
V
4M 2
M2
M2
)
(
2
q2
4q 2 FV2 ξFV2
q2
− 2 ξFV2
−
1+
M
4M 2
M2
]
(
)
2
m2
1
2
2
− 2 FV + ξFV + |FA |
M
(
)
q2
1
2
F
F
+
ξF
B(q 2 ) =
A
V
V
M(2
)
2
2
2
q
1
C(q 2 ) =|FA |2 + FV1 −
ξFV2
4
4M 2

(3.6)
(3.7)
(3.8)

where ξ is defined by anomalous magnetic moment, ξ ≡ µp − µn = 3.71, FA (q 2 )is the axial-vector form factor, and FV1 (q 2 ) and FV2 (q 2 ) are the vector form factor.
They are expressed as(
FA (q 2 ) = −gA 1 −(
FV1 (q 2 )

=

1−
(

ξFV2 (q 2 )

=

1−
(

GE (q 2 ) =

1−

q2

q2

2

GE (q ) −
)−1

4M 2
)−2
q2
MV2

(3.9)

MA2
)−1 [

4M 2
q2

)−2

q2
4M 2

]
2

[
]
GM (q 2 ) − GE (q 2 )(3.11)(,(3.10)GM (q )GM (q 2 ) = (1 + ξ) 1 −

q2
MV2

)−2
(3.12)

where gA is the axial-vector coupling constant, MV and MA are the masses of vector and axial-vector, respectively, and GE and GM are the electric and magnetic
form factors, respectively. At NEUT, MV is set to be 0.84 GeV, and MA is set tobe 1.21 GeV. Both values were obtained from the experimental measurement at
K2K [124] and the Mini Booster Neutrino Experiment (MiniBooNE) [125]. ThisMA value is also used for single meson production. The gA is measured by polarized nucleon beta decay [126, 127] and set to be 1.232 in the NEUT simulation.
The world average gA value is 1.2673 ± 0.0035 [128], although the change of crosssection-caused by the diﬀerence gA value is less than 5%. In addition to the dipole
form factor, several types have been proposed [129–131]. The diﬀerence of the crosssection between their models and the dipole form factors is estimated to be less than
10% [132].
The interactions for a nucleon bound in an oxygen nucleus were used for the
relativistic Fermi gas model by Smith and Moniz [133] to account for Fermi motion

3. SIMULATION

56

and Pauli blocking of the nucleon. The outgoing momentum of the nucleons in
the interactions is required to be larger than the Fermi surface momentum to allow
quasi-elastic scattering to occur. The Fermi surface momentum is set to 225 MeV/c,
which is required to reproduce the quasi-elastic peak in electron scattering. The
NEUT model was compared with other models [134, 135] to estimate systematic
uncertainties of neutrino interactions and nuclear eﬀects. Figure 3.7 shows the crosssection of the quasi-elastic scattering from the experimental data and the calculations
from the NEUT library.

Figure 3.7: Cross-section for the CCQE scattering of muon neutrino (left panel)and muon anti-neutrino (right panel). Solid lines show the calculated free targets,and the dashed lines show the calculated bound targets. Data points are takenfrom ANL [136] (crosses), BNL [137] (triangles), Gargamelle [138–140] (circles), Serpukhov [141] (asterisks), and SKAT [142] (stars). The figure was taken from Hayato[121].
The NC elastic scattering cross-sections were estimated from the CC cross-section
by the following relations [143, 144]:

3.2.2

σ NC (νp → νp) = 0.153 × σ CCQE (νn → e − p)

(3.13)σ NC (ν p → ν p) = 0.218 × σ CCQE (ν p → e + n)

(3.14)σ NC (νn → νn) = 1.5 × σ NC (νp → νp)(3.15)σ NC (ν n → ν n) = 1.0 × σ NC (ν p → ν p)

(3.16)

Meson Exchange Current

The CCQE interaction is approximated so that the neutrino interacts with a single
nucleon only if it ignores the direct correlation between the nucleons in the nucleus.
In reality, however, the interaction between nucleons must introduce some direct
correlation, such that the incident neutrino interacts simultaneously with multiple

3. SIMULATION

57

nucleons. The diﬀerence between the existing CCQE and the result of the MiniBooNE experiment [145] suggests the existence of this process.
The meson exchange current (MEC) model by Nieves et al. [146] was introduced
for NEUT. It is a prominent model that attempts to extend the preexisting simplistic
model of CCQE. The incident neutrino interacts with a pair of two nucleons as
opposed to a single nucleon target, as follows:νℓ + N N ′ → ℓ + N ′′ N ′′′(3.17)

where N N ′ and N ′′ N ′′′ represent the nucleon pair before and after the interaction,
respectively. Although multi-nucleon correlations should be present in any neutrino
interaction on a bound nucleon, the CC MEC interaction is the only process that is
considered in NEUT.

3.2.3

Single Meson Production

The interactions that produce a single meson occurs via baryon resonance. Whenthe invariant mass of the hadron system, W , is less than about 2.0 GeV/c2 , theinteractions are dominant hadron production processes. In NEUT simulation, their
method is extended with some modification to simulate single η and K productions.
For W larger than 2.0 GeV/c2 , the interactions are simulated as deep inelastic scatterings. An example of single meson production is shown as follows:νµ + p → µ− + ∆(1232 ) P 33∆(1232 ) P 33 → p + π+

(3.18)The process in NEUT is based on a previous model [147, 148], originally developed for single pion production. The amplitudes of each resonance production
multiplied by the decay probability of resonance into one pion and one nucleon arecalculated to obtain the cross-section. When the diﬀerential cross-section is calculated ignoring the width, it can be expressed as follows:
d2 σ single π2dq dEν

=

1

∑

1
1
Γ
2
T (νN → ℓNj∗ ) ·
(
)2
2 · 2
2π
32πM Eν
W − Mj + Γ2 /4
j,spin(3.19)

where M is the mass of the target nucleon, Eν is the neutrino energy, T (νN → ℓNj∗ )is the amplitude of a baryon excitation, N is the nucleon, N ∗ is a baryon resonance,
W is the invariant mass of the hadronic system, Mj is the mass of the baryon
resonance, and Γ the finite decay width. The matrix elements of the hadron current
are calculated using the Feynman–Kislinger–Ravndal (FKR) baryon model [149].
The resonance width is considered using the Breit–Wigner factor [150]. The lepton
mass eﬀects and the pion-pole term are adopted to the CC interactions [151, 152],
resulting in the suppression of the cross-section at lower q 2 .
The calculated cross-sections of the single pion productions and the experimental results are shown in Figure 3.8. When calculating the cross-section for theseinteractions, 18 resonances and three background terms are considered, as listed inTable 3.1.

3. SIMULATION

58

Figure 3.8: Cross-section for single pion production of the muon neutrino. The solidlines show the calculated cross-section. The experimental data are summarized in
the bottom right panel. The figure is taken from Hayato [121]
To determine the angular distribution of a pion in the final state for ∆(1232 ) P 33
resonance, the model of Rein and Sehgal [147] is used. For the other resonances, theisotropic feature of the resonance rest frame is used as the directional distributionof the generated pion. The Pauli blocking eﬀect in the decay of resonances is also
considered, which suppresses the interaction cross-section by the fewest percent. The
pion-less delta decay is also considered, and 20% of the resonance decay is assumed
to disappear without meson emission.

3. SIMULATION

59

Table 3.1: List of resonances and background terms used in the NEUT simulation.
Resonances

Mass (W )Width (Γ)(Background)[GeV/c][GeV/c]S11 (1540)

1.535

0.150

S31 (1620)

1.620

0.140

S11 (1640)

1.650

0.150

P33 (1232)

1.232

0.115

P11 (1450)

1.440

0.200

P33 (1640)

1.600

0.370

P11 (1710)

1.710

0.110

P13 (1740)

1.720

0.200

P31 (1920)

1.910

0.220

P33 (1960)

1.920

0.250

D13 (1525)

1.520

0.125

D13 (1670)

1.700

0.100

D15 (1680)

1.675

0.155

D33 (1730)

1.700

0.250

F15 (1680)

1.680

0.125

F35 (1920)

1.905

0.300

F37 (1950)

1.950

0.240

F17 (1970)

1.990

0.325

(Proton)

0.940

3.000

(Neutrion)

0.940

3.000

(J = 3/2)

0.940

3.000

3. SIMULATION

3.2.4

60

Deep Inelastic Scattering

The interaction of incident neutrinos with the constituent quarks of the target nucleon often generates multiple hadrons via CC deep inelastic scattering (DIS). Whenthe hadronic invariant mass, W , is greater than 1.3 GeV/c2 , this process is dominant
in NEUT. The diﬀerential cross-section of DIS is calculated as follows.
d2 σ CC DIS
dx dy

=

GF MN Eν
×
π
[(
)
]
(
)
y2
y
2
2
1−y+
+ C1 F2 (x, q ) ± y 1 − + C2 xF3 (x, q )22(3.20)

C1 =

xyMN
m2
m2ℓ
−
− ℓ2 −
4MN Eν x
2Eν
2MN Eν x
4Eν
2mℓ

C2 = −yMℓ2

4MN Eν x(3.21)(3.22)

where the Bjorken parameters, x and y, are defined as x = −q 2 /(2M (Eν − Eℓ ))and y = (Eν − Eℓ )/Eν , MN is the nucleon mass, mℓ is the outgoing lepton mass,Eν and Eℓ represent the energies of the incoming neutrino and the outgoing lepton,
respectively, in the laboratory frame. The nucleon structure functions, F2 and xF3 ,are taken from the Parton distribution function (PDF) GRV98 [153]. The correction
function given by Bodek and Yang [154] is adopted to improve agreement withexperiments in the low q 2 region.
The cross-section of DIS via NC reactions is assumed to have the following
relations, which are estimated from the experimental results [155, 156].

(Eν < 3 GeV)
0.26
σ NC DIS (νN → νX)= 0.26 + 0.04(Eν /3 − 1) (3 GeV ⩽ Eν < 6 GeV) (3.23)
σ CC DIS (νN → µ− X) 

0.30
(Eν ⩽ 6 GeV)(Eν < 3 GeV)
0.39
σ NC DIS (ν N → ν X)
= 0.39 − 0.02(Eν /3 − 1) (3 GeV ⩽ Eν < 6 GeV) (3.24)
σ CC DIS (ν N → µ+ X) 

0.37
(Eν ⩽ 6 GeV)
The kinematics of the hadronic system is treated by two methods according to
the ranges of invariant mass. For the interaction in the range, 1.3 to 2.0 GeV/c,
only pions are considered as outgoing mesons. The mean multiplicity of pions isestimated from the result of an experiment at Fermilab [157].
()⟨nπ ⟩ = 0.09 + 1.83 ln W 2(3.25)The number of pions is determined using the Koba–Nielsen–Olsen (KNO) scaling
factor [158]. NEUT requires nπ > 2 to avoid overlapping with the W region for
single pion production. The forward-backward asymmetry of pion multiplicity in3. SIMULATION

61

the hadronic center of mass system is obtained from the result of the Big European
Bubble Chamber (BEBC) experiment [159].
(
)
2
F
0.35
+
0.41
ln
W
nπ
(
)
(3.26)
=
2
nB
0.50
+
0.09
ln
W
π
For the region of W greater than 2.0 GeV, the kinematics of the hadronic system
are calculated using the PYTHIA/JETSET package [160], which treats K , η, ρ, andπ.
The total CC cross-section, including CCQE, single meson productions, and DIS
for ν and ν , are shown in Figure 3.9.

Figure 3.9: Comparison between experimental and calculated data of the total crosssection of the CC interaction for ν and ν . The upper 4 lines correspond to neutrino
and the lower 4 lines correspond to the anti-neutrino. The experimental data weretaken from CCFR [161], CDHSW [162], GGM-PS [163], CHARM [164], BNL [165],
CRS [166], BEBC-WBB [167], IHEP-JINR [168], IHEP-ITEP [137], CCFRR [169],
and SKAT [170]. The figure was taken from Hayato [121].

3.2.5

Coherent Pion Production

The reaction in which a single pion having the same charge as the incoming weakcurrent can be generated by the interaction between an oxygen nucleus and theneutrino and is called the coherent pion production.
νℓ + 16O → ℓ + 16O + π(3.27)

Because the momentum transmitted to the oxygen nucleus is very small, theangular distribution of the outgoing leptons and pions are peaked in the forward

3. SIMULATION

62

direction. The formalism developed by Rein and Sehgal [171] is adopted to simulatethese interactions, and the diﬀerential cross-section is given byd3 σ coherent
dQ2 dy dt= β

G2F MN
2π 2

fπ2 A2 Eν (1 − y)()× 1 + r2r =(Re{fπN (0)}Im{fπN (0)}MA2MA2 + Q2

1 [ πN ]2σ
16π tot)2|F (t)|(3.28)(3.29)

where Q2 is the square of the 4-momentum transfer of the lepton, y is the lepton
fractional energy loss, t is the momentum transferred to the nucleus, β is the axialvector coupling constant, which is 1 (2) for NC (CC) interactions, M is the nucleon
mass, fπ = 0.93mπ is the pion decay constant, A is the atomic number (=16 forπN
oxygen), σtot
is the averaged pion-nucleon cross-section, and F (t) is the nuclear
form factor. fπN (0) in r is the π − N scattering amplitude.
The cross-section of the CC coherent pion production is measured using theK2K experiment, and the upper limit is set [172] as shown in Figure 3.10. The
experimental upper limit is significantly lower than the calculated cross-section,according to Rein and Sehgal [171]. NEUT modifies the results of Rein and Sehgal[173] to account for the non-vanishing leptonic mass of CC interactions. In thecase of νµ , the cross-section at about 25% is suppressed at 1.3 GeV because of theinterference of the axial vector and the pseudoscalar amplitudes.

Figure 3.10: Cross-section of coherent pion production from the carbon nucleus
via CC interaction (left panel) and NC interaction (right panel). The solid anddashed lines represent the Rein and Sehgal [171] model with and without modification, respectively. The dotted and dash-dotted lines correspond to the model of
Kartavtsev et al. [174] and Alvarez-Ruso et al. [175], respectively. The experimental
data were taken from K2K [172] (filled squares), SciBooNE [176] (filled circle), MiniBooNE [177] (open circle), Aachen-Padova [178] (open square), and Gargamelle [179](open cross).

3. SIMULATION

3.2.6

63

Nuclear Eﬀects

The interaction of mesons produced in neutrino interactions with nucleons inside
the 16O nuclei is also simulated at NEUT. These are secondary interactions of theoutgoing mesons, although they are still inside the nucleus. All the mesons generated
in the 16O nuclei are tracked until they exit or are absorbed by the nucleus. To
propagate the π, K , and η, the cascade model is used at NEUT, which considers
the interactions, the inelastic scattering, the charge exchange, and absorption.
At Eν > 1 GeV, the cross-sections for pion production from neutrino interactions
are large. Moreover, the cross-section of pion-nucleon interaction is also large. Thus,
the secondary interactions of pions are especially important. The initial pion production point in the nucleus where neutrino-nucleon interactions occur is determinedusing the Wood–Saxon density distribution [180].
ρ(r) =

Z1()
ρ0
A 1 + exp r−ca(3.30)

where ρ0 is the average density of the nucleus, a and c are the density parameters,
Z is the atomic number, and A is the mass number. For 16O nucleus : ρ0 = 0.48m3π ,a = 0.41 fm, c = 2.69 fm, Z = 8, and A = 16 [181]. The mean free path of thepion interactions is modeled according to Salcedo et al. [182], who depend on their
momenta and positions in the nucleus. Fermi motion and Pauli blocking are also
considered. The energy of the outgoing nucleon must be greater than the Fermi
surface momentum:
(
)1/3
3 2
pF (r) =(3.31)π ρ(r)
2
Using the results of a phase shift analysis from the π−N scattering experiment [183],the momentum of the pion after the interaction is determined. We use the medium
correction suggested by Seki and Masutani [184]. The pion interaction is tested using
experimental data for the three interactions: π − 12C scattering, π − 16O scattering,and the pion photoproduction, γ + 12C → π− + X [185, 186].
For the kaons at NEUT, elastic scattering and charge exchange interactions are
considered using the results of K ± − N scattering experiments [187–189]. For η
mesons, the absorption (ηN → N ∗ → π(π)N ) is considered [190], where the pions
are tracked as previously described.
Nucleons generated in the nucleus often cause secondary interactions with nucleons bound in the nucleus. The nucleon-nucleon elastic scattering was consideredusing cross-section measurements [191]. The production of delta resonances, which
decay to produce pions, comes from those interactions. This eﬀect was consideredwith the isobar production model proposed by Lindenbaum and Sternheimer [192].
Figure 3.11 shows the probability of the nucleon-nucleon interaction in 16O. The
production of nucleons with nucleon momenta below 225 MeV/c is suppressed by
the Pauli exclusion principle, and half of the nucleons interact mainly via elastic
scattering in the range above 300 MeV/c. Therefore more than one nucleon escapesfrom the oxygen.

3. SIMULATION

64

Figure 3.11: Interaction probabilities of a nucleon in 16O as a function of thenucleon momentum [MeV/c]. The curves correspond to no interaction (solid line),
the elastic scattering (dashed line), single pion production (dotted line), and double
pion production (dash-dotted line), respectively. The figure was taken from Hayato[121].
The distances or times from the interaction points of neutrinos and hadrons are
considered for all hadrons produced in the nucleus. The intermediate types are
assumed to be non-bound quark states, and the formation length of each hadron isexpressed as:
L=

p
µ2

(3.32)

where p is the momentum of the hadron and µ2 = 0.08 GeV2 is a fitted constantfrom the SKAT experiment7 . The nucleon-nucleon interaction in the nucleus has agrate eﬀect and results in significant distortion of the geometry of particles observedin the detector.

3.3

Detector Simulation

Currently, secondary particles produced by NEUT are propagated in the SK detector
simulation (SKDETSIM). SKDETSIM was developed based on the GEANT3 [193,194] toolkit and is implemented in the FORTRAN programming language. GEANT3
toolkit contains a series of simulation programs for geometry and tracking (GEANT),
originally developed by CERN for high energy physics experiments. The first version
was created in 1982, and the final version was released in 1994.
7

V. Ammosov, Talk at NuINT01 workshop at KEK, Tsukuba, Japan (2001). http://neutrino.
kek.jp/nuint01/

3. SIMULATION

3.3.1

65

SK Detector Simulation

SKDETSIM simulates the tracking of outgoing particles through the detector, thegeneration and propagation of Cherenkov photons in water, and PMT responses. It
also produces an electronics readout. The structure and electronics system of the SK
detector is slightly diﬀerent for each phase (SK-I to SK-IV), and the environmentof measurement also slightly changes for each. These diﬀerences are considered in
SKDETSIM. Table 3.2 shows the processes for particles in the SKDETSIM.

Particle tracking
In SK water, multiple processes can occur depending on the type of particles. Eachparticle interaction is calculated using a physics model provided by GEANT3.
Hadronic interactions are simulated using GCALOR [195], expect for pions below
500 MeV/c. For low energy pions, a custom program [196] based on experimental
data from π − 16O scattering [197] and π −p scattering [198] is used. To estimate thesystematic uncertainty in the hadron simulation, results of the GCALOR package
and FULKA model are used. Especially for the νµ -enriched samples, the uncertainty
aﬀects the contamination of NC interactions.
For the propagation of charged particles, the number of Cherenkov photons andtheir wavelengths are calculated using Equation 2.4. The opening angle of theCherenkov ring is calculated using Equation 2.2. Only photons in the 300 to 700 nm
range, the sensitive region of PMTs, are generated.

Cherenkov photon tracking
Cherenkov photons produced by the charged particles can be scattered or absorbed
in water. The probability of either of these processes occurring is characterized byparameters that depend on the transparency of the water. When the Cherenkov
photon is absorbed, tracking of that photon stops. Otherwise, the photon can cause
two types of scattering: Rayleigh and Mie.
When the Cherenkov photons arrive at the wall of the tank (i.e., black sheet,acrylic cover, or PMT), reflections on the surface can occur. The calculated reflection
value, including the polarization, is used for the SKDETSIM.

PMT response
The charge and timing response of the PMT and the electronics are simulated basedon the calibration measurements. Then the detector simulation provides the samedata structure as the observed data so that the two can be analyzed in the samemanner.

3. SIMULATION

66

Table 3.2: Simulated process for each particle in SKDETSIM.
(e − , e + ) pair productionγCompton scattering
Photoelectric eﬀect
Multiple scattering
Ionization and δ-rays productione±Bremsstrahlung
Annihilation of positron
Generation of Cherenkov radiation
Decay in flight
Multiple scattering
Ionization and δ-rays production±µBremsstrahlung
Direct (e − , e + ) pair production
Nuclear interactions
Generations of Cherenkov radiation
Decay in flight
Multiple scattering

Hadrons

Ionization and δ-rays production
Hadronic interactions
Generations of Cherenkov radiation
Rayleigh scattering
Mie scattering
Absorption on the black sheet

PhotonAbsorption on the acrylic case
Absorption on the PMT surface
Reflection on the black sheet
Reflection on the acrylic case
Reflection on the PMT surface

3. SIMULATION

3.3.2

67

SK Geant4 based Simulation

The current detector simulation (i.e., SKDETSIM) was built on the GEANT3
toolkit. The simulation toolkit, GEANT3, had its last update in 1994, and it has
diﬃculty using the latest physics models. Instead, GEANT4 [199–201] was released
as a successor to GEANT3 in 1998 and has been updated to date. It was created via
software engineering and object-oriented technology and implemented in the C++
programming language.
For the upcoming SK-Gd phase, a new simulation is required that can use thelatest physics models and can be easily maintained and expanded. The SK GEANT4
based simulation (SKG4 [202, 203]) is being developed to solve this problem. In
particular, the physics model of the neutron capture reaction is important in the
SK-Gd phase. The gamma-ray emission from thermal neutron capture on Gd wasmodeled by Das et al. [204], Hagiwara et al. [205, 206]: the ANNRI-Gd model. Thismodel was installed in the SKG4 simulation. The details of the ANNRI-Gd modelare described in Appendix B. Various tests were performed for use as a new SK
detector simulation.

Electromagnetic physics
The electromagnetic processes adopted the Livermore physics list [207] and compared it with the SKDETSIM. Figure 3.12 shows the distributions of the wavelength of Cherenkov photons calculated by SKG4 and SKDETSIM using 10 MeV
electrons. SKDETSIM emits 2.6% more photons than SKG4 and has a slightly different distribution. This diﬀerence occurred because SKDETSIM did not consider
the wavelength dependence of the refractive index of water.

Figure 3.12: Top: distributions of the wavelength of Cherenkov photon emitted from
10 MeV electron in SKG4 (red) and SKDETSIM (black). Bottom: ratio between
SKG4 and SKDETSIM.

3. SIMULATION

68

Optical photon physics
The Cherenkov photons scatter and absorb depending on their wavelengths prior
to reaching the PMT. The scattering and absorption factors are defined by thelaser calibration described in Chapter 4. Figure 3.13 shows the number of photons
reaching the PMTs with and without the absorption eﬀect of water. The numberof photons reaching the PMT was reduced 29.8% by SKDETSIM, where SKG4 was
reduced by 29.2%. This diﬀerence was caused by the slightly diﬀerent wavelength
distribution of the Cherenkov photons.

Figure 3.13: Comparison of SKDETSIM and SKG4 to confirm the eﬀect of absorption, as indicated by the number of photons reaching the PMTs. The solid line is asimulation result considering the eﬀect of absorption, and the dashed line is a resultof ignoring the eﬀect of absorption. The black line is the result of SKDETSIM andthe red line is the result of SKG4.
Photons reaching the inner wall are absorbed or are reflected by the black sheet.
Some photons reaching the PMT are absorbed or reflected, but about 20% generatep.e.. The QE of photons to p.e. depends on the wavelength of the photons and is
22% at a wavelength of 390 nm. When the test was performed without the eﬀectof photon wavelength, the behavior of photons on the black sheet and the PMT in
SKG4 completely replicates those of SKDETSIM.
We found a few percent diﬀerence between SKDETSIM and SKG4 in the electromagnetic and optical processes. These diﬀerences can be explained by diﬀerencesin the wavelength distribution of Cherenkov light between SKDETSIM and SKG4
as shown, in FIgure 3.12.

3. SIMULATION

69

Hadronic physics
The testing of a physics model of the hadron process is ongoing. The neutron
capture on Gd is an important process for the SK-Gd phase. To test the behaviorof the neutron capture reaction, neutrons were released in an environment where
Gd2 (SO4 )3 was dissolved in ultra-pure water at a mass concentration of 0.2%. At
this concentration, it is estimated that about 90% of the neutrons emitted frominverse beta decay are captured by Gd, and the remaining about 10% are captured
by hydrogen. This is the target concentration for the SK-Gd experiment.
An electron antineutrino of a few tens of MeV emits a neutron having the momentum of several hundred keV via inverse beta decay. Therefore, the test was
performed using 200 keV neutrons. When the neutrons were emitted downward
from the center of the tank, the capture time by Gd was 27 ± 1 µsec, and that of the
proton was 18 ± 1 µsec (Figure 3.14, left). For ultra-pure water without dissolved
Gd, neutrons were captured by a proton in 196 ± 3 µsec. The distance from thepoint where neutrons were generated to the point where Gd (proton) captured theneutrons is 70 ± 33 mm (68 ± 31 mm) (Figure 3.14, right). In the case of ultra-purewater, neutrons were captured by protons 107 ± 60 mm from the center of the tank.

Figure 3.14: Left: time distribution in which neutrons were captured by Gd (black)and captured by proton (red) are shown. Right: distance from the center of thetank to the point where neutrons are captured by Gd (black) and by proton (red).
Figure 3.15 shows the energy spectra of gamma-rays emitted from the thermal
neutron captured by Gd. For comparison with our model, the spectrum calculated by
the model, FTFP BERT HP of Geant4, is drawn. The FTFP BERT HP model adds
a low energy neutron reaction model to the high energy physics model recommendedby Geant4. The feature of the Geant4 model is that many gamma-rays are de-excited
at once from the excited state to the ground state. Our model, on the other hand,
has a low probability of de-excitation at once and has a characteristic peak at 5
to 8 MeV. Furthermore, the slope of the spectrum in the region below 5 MeV is
diﬀerent.
The neutrons were 86.5 ± 0.9% captured by Gd and 13.5 ± 0.4% captured byprotons. Oxygen nuclei capture the neutrons with a probability of 1% or less. This is3. SIMULATION

70

Figure 3.15: The energy spectra of gamma-rays emitted from the thermal neutron
capture on Gd is shown. The red line is the gamma-ray spectrum calculated by ourmodel and the black line is the spectrum calculated by the model of Geant4.
in good agreement with the expectation provided by Beacom and Vagins [71]. When
protons capture neutrons, they emit 2.2 MeV gamma-rays. Oxygen and neutrons
may emit gamma-rays of various energies owing to capture and inelastic reactions.

Current status of SKG4
SKG4 will be an indispensable tool for the physical analysis of the SK-Gd experiment, and our model has been confirmed to well-reproduce gamma rays from thethermal neutron capture reaction of Gd (Appendix B). The current status of SKG4
development includes reproducing the data acquisition process, comparing resultswith calibration experimental data, and developing a better user interface.

Figure 3.16: SKG4 logo.

4. CALIBRATION

471

Calibration

To understand the detector and keep its performance high, calibrations were performed at the SK. Several parameters were measured or calibrated: ID calibrationfor each PMT and photon tracking; OD calibration for each PMT and photon properties, and the absolute energy scale. Calibration results are used to produce thedetector simulation and to analyze the observed data. Details on the calibration
methods can be found in Abe et al. [208].

4.1

ID PMT Calibration

There are several PMT calibrations, which directly aﬀect SK performance. In thedefinition for the PMT charge calibration, “gain” is a conversion factor from thenumber of p.e. to charge in units of pC. “QE” is the product of the quantum
eﬃciency and collection eﬃciency of p.e. onto the first dynode of the PMT. The
timing behavior of PMTs depends on the charge of the measured pulse.

4.1.1

High-Voltage (HV)All PMTs are set to match the HV charge of the incident light. For the incident
light, the light from a Xe lamp is passed through a UV filter and injected into a
scintillator ball: a 5 cm diameter acrylic ball containing a diﬀuser. The scintillator
ball/Xe lamp light source remains permanently centered in the SK tank for real-timeand long-term monitoring of the PMT gain.
To control the incident light yields to each PMT at diﬀerent locations, 420 precalibrated PMTs were positioned. They are standard PMTs and serve as a reference
for other PMTs that have a similar geometric relationship to the light source at thecenter of the ID. The HV of the standard PMTs was adjusted in advance using
the same light source. The standard PMTs were placed as shown on the left of
Figure 4.1, and examples are shown on the right side of Figure 4.1.
The HV setting of the other PMTs was adjusted so that the observed charge
from the light source flash matched the average charge of the standard PMTs in thegroup. After determining the HV setting for all PMTs, reproducibility was checkedand confirmed to be within 1.3% in RMS.

4.1.2

Relative Gain

The gain for each PMT is determined to interpret the output charge from the PMTs
across several p.e.. To measure the relative gain diﬀerence, a stable light source
emitting a constant intensity flash (high-intensity and low-intensity) is placed at a
specific location in the tank. An average charge, Q(i), for each PMT, i, is createdusing a high-intensity flash, from which every PMT receives a suitable number ofphotons. Single-p.e. hits are measured by using a low-intensity flash that hits only
a few PMTs during each event. The number of times N (i) that PMT i records a

4. CALIBRATION

72

Figure 4.1: Left figure shows the net drawing of the SK tank, and the red points
indicate the location of the standard PMTs. The right figure shows the schematic
view of PMT groupings. These PMTs serve as references for others belonging to
the same group having similar geometrical relationship to the light source. The redpoint corresponds to the location of standard PMTs. The figure was taken fromAbe et al. [208].
charge that is greater than the threshold value are counted. Because the locationof the light source does not change between the two measurements, the factors arealmost identical:
Q(i) ∝ IH × a(i) × ε(i) × G(i),(4.1)

N (i) ∝ IL × a(i) × ε(i),(4.2)

where IH and IL are the average intensities of high- and low-intensity flashes, a(i)is the acceptance of PMT, ε(i) denotes its QE, and G(i) denotes its gain. The gainof each PMT can then be derived by taking the ratio of Q(i) and N (i) as:
G(i) ∝

Q(i)
.
N (i)

(4.3)

The relative gain of each PMT can then be obtained via normalization with theaverage gain over all PMTs. The common factor, IH /IL , is also eliminated by thisnormalization.
The standard deviation of the gain for all PMTs is found to be 5.9%. Because
the HV value of each PMT is determined to cause Q to be the same, this deviation
is presumed to be caused by the diﬀerence in QE among PMTs. Using the relative
gain diﬀerence of each PMT, the output charge is converted to the number of p.e.
observed at each PTM.

4. CALIBRATION

4.1.3

73

Absolute Gain

The absolute gain is used to convert the charge recorded by a PMT in pico Coulombs
into the number of incident p.e.. A uniform plus a stable source of single p.e. levellight is required for measurement. Therefore about 9 MeV gamma rays emitted fromthe reaction of thermal neutrons captured on 58-Nickel, 58Ni (n, γ) 59Ni, were used.
The neutrons were produced by the spontaneous fission (SF) of 252-Californium( 252Cf), whose the half-life is 2.56 years. Approximately 97% of the time, it decays
via an α, whereas the remaining 3% undergoes SF. An average of 3.76 neutrons
are produced per fission, and the average neutrino energy is 2.1 MeV. The spectrum extends to about 14 MeV. The neutrons lose energy via elastic scatteringoﬀ the protons in the water and are thermalized. The gamma rays are delivered
0.004 p.e./event for each PMT, ensuring more than 99% hits are single p.e. hits.
The reaction is shown below.
252

SF: 3%

Cf −−−−→ 251Cf + 3.76 n (about 2.1 MeV)
capturen + 58Ni −−−−−−−−−−→ 59Ni + γ (about 9 MeV)
thermal neutron

The relative gain correction is applied to measure the cumulative single-p.e.
distribution for all PMTs. The result of charge distribution at the SK-III phase isshown in Figure 4.2. A sharp peak near zero is caused by electrons passing throughthe first dynode, and the second round peak corresponds to a single-p.e. signal. The
average pC for the whole distribution is defined as the conversion factor from pC
to a single-p.e.: 2.044 pC/p.e. for SK-I, 2.297 pC/p.e. for SK-II, 2.243 pC/p.e. for
SK-III, and 2.658 pC/p.e. for SK-IV.

4.1.4

QE

The relative diﬀerence in QE is also measured for each PMT. It aﬀects the charge
response for a small number of incident photons as can be seen in Equation 4.2. MC
simulation was used to predict the number of photons reaching each PMT. From
the results, we determine the rate at which photons are converted to p.e..
The Ni – Cf source is used for measurement and for absolute gain calibration.
The hit probability depends on the PMT position because of the photon path. The
PMT position dependence of the hit probability is calculated using the following
correction:
N (i) ×R2 (i)a(θi )(4.4)

where i indexes the PMTs, R(i) is the distance from the source position to the PMT
position, and a(θi ) is the acceptance as a function of incident angle θ [209]. Even after
this correction, some position dependence remains owing to reflection, scattering,
and absorption by the water or surface of the wall. These further corrections are
estimated via MC simulation, which considers the water property and the behaviorof the surfaces of the PMTs and black sheet. The remaining diﬀerence between
calibration data and MC simulation is attributed to the QE of individual PMTs.
This quantity is tabulated for use in the MC simulation.

4. CALIBRATION

74

Figure 4.2: Distribution of the observed charge for the single p.e. signal at the
SK-III phase. The signals were observed from the calibration using Ni – Cf source.
The figure was taken from Abe et al. [208].

4.1.5

Timing Response

The readout response time varies among PMTs because of cable length, the transit
times, and the processing time of electronics. Moreover, the response times of readout channels depend on the pulse height of PMTs, known as the “time-walk” eﬀect.
The purpose of timing calibration is to make a correction table for the time-walkeﬀect of each PMT, accounting for the overall process time.
A nitrogen laser as a light source was used for timing calibration. It is a gas flow
laser that emits fast pulses of light at 0.4 nsec FWHM at a wavelength of 337 nm.
Because the light intensity varies per optical filter, the time responses of readouts aremeasured by various pulse heights. For the selection of laser events, we apply a timeof flight (TOF) timing correction. It subtracts the TOF from the diﬀuser ball toeach PMT position, using the group velocity of light at a measurement wavelengthof 398 nm.
Timing versus pulse height correlation tables create individual TQ distributions
based on the 2D distribution of each PMT. Figure 4.3 shows a typical scatterplotof the TQ distribution. The plot is fitted by the function described below. By
multiplying the reciprocal of the fitted function by the TQ distribution, the timecorrection is found.

4. CALIBRATION

75

Figure 4.3: Typical TQ distribution for one PMT. The horizontal axis is the chargeof each hit, and the vertical axis is the TOF subtracting the timing of the hits. The
lager (smaller) TOF timing corresponds to earlier (later) hits in this figure. The
figure was taken from Abe et al. [208].
The selected laser-hit events for each readout are divided into 180 bins of charge,(i.e., Qbins). Each Qbin is defined as the amount of charge from the PMT in pC,
using a linear scale from 0 to 10 pC and a logarithmic scale from 10 to 3,981 pC. The
peak timing and standard deviations for respective charges are fitted to polynomial
functions depending on the Qbin:
polN (x) ≡ p0 + p1 x + p2 x2 + · · · + pN xN ,Qbin ≤ 10 : F1 (x) ≡ pol3(x),

(4.5)
[ ′
]
Qbin ≤ 50 : F2 (x) ≡ F1 (10) + (x − 10) F1 (10) + (x − 10)pol3(x − 10) , (4.6)
Qbin > 50 : F3 (x) ≡ F2 (50) + (x − 50)pol6(x − 50),

(4.7)

where F1′ is a derivation of F1 introduced for continuity between F1 (x) and F2 (x) at
Qbin = 10. F1 (x) and F2 (x) have four fit parameters each and F3 (x) has seven fit
parameters. Thus, the number of the fit parameter is 15 in total. The parameters
resulting from the fit are saved in a dataset as the TQ-map and are used to correct
the timing response of each PMT.

4.2

Water Transparency in the ID

MC simulations must consider the Cherenkov light eﬀect on photons during propagation. The photons are absorbed or scattered by the water, each of which has

4. CALIBRATION

76

a wavelength dependence. When the photons reach the surface of PMT or black
sheet, they are reflected or absorbed.

4.2.1

Light Absorption and Scattering

The attenuation of light in the water is expressed as()ℓI(λ) = I0 (λ) exp −
,
L(λ)

(4.8)

where I0 (λ) is the initial intensity, ℓ is the distance the light travels, and L(λ) is thetotal attenuation length as a function of wavelength λ. In the SK simulation, L(λ)
is defined as
L(λ) =

1αabs (λ) + αasym (λ) + αsym (λ)(4.9)

where αabs (λ), αasym (λ), and αsym (λ) are coeﬃcients for absorption, asymmetricscattering, and symmetric scattering, respectively. Note that these are tuning parameters used in the SK simulation, and they are SK-based empirical functions.
To calculate these parameters, a collimated laser beam is injected verticallydownward from the top of the SK tank. The laser beams are generated with adjusted
wavelengths of 337, 375, 405, 445, and 473 nm. The scattered and reflected lightis detected by the PMT, and the detected time distribution is compared with the
MC. The inverse transparency depends on the wavelength applied during the MC
simulation. Figure 4.4 shows the result based on the data taken in April 2019.

4.2.2

Light Reflection at the PMT and Black Sheet

The same laser data are used to calibrate the light reflection at the PMT surface.
Four layers of material from the surface to the inside of the PMT are considered.
Each material and refractive index include water (1.33), glass (1.472 + 3670/λ2 ,where λ is the wavelength in nm), bialkali (nreal + i · nimg ) [210], and vacuum (1.0).
Here, nreal and nimg are the real and imaginary parts of the complex refractive index,
respectively. The best fit values from the tuning include the following: nimg is 1.677,
and nreal is 2.31, 2.69, 3.06, and 3.24 at λ = 337, 365, 400, and 420 nm, respectively.
The reflectivity of the black sheet is measured using a light injector set in the SK
tank. The reflected charge is measured at three incident angles (30◦ , 45◦ , and 60◦ )at three-wavelengths (337, 400, and 420 nm). The adjustment results in agreement
between data and MC at better than the ±1% level at each wavelength and position.

4.3

OD PMT Calibration

The primary role of the OD PMTs is identifying incoming CRs and atmospheric
neutrino interactions with particles leaving the ID. Charge reconstruction accuracies
of about 10% to 20% and the timing accuracy of 5 to 10 nsec are suﬃcient for physics
analysis.

4. CALIBRATION

77

Figure 4.4: Typical fitted water coeﬃcient functions used for the SK simulation.
The points represent the average value of data obtained from April 2019. The red,
blue, and magenta lines represent tuned αabs (λ), αasym (λ), and αsym (λ), respectively.
The black line is the sum of the three, which is the inverse of the attenuation length.
The figure was taken from Abe et al. [208].

4.3.1

Charge Response

To determine the charge in pC corresponding to a single-p.e., OD hits leading outside
the trigger time window are used (dark rate method). Hits preceding the trigger
time have a high probability of being single-p.e. hits because of the noise of PMT.
Thus, the mean value is taken as pC per p.e.. To validate the charge response per
p.e. at low light levels, the laser is flashed at a low light level. The results fromthe laser method and the dark rate method are found to be in agreement within
10%. The typical conversion factor is 1 to 6 pC/p.e. for SK-IV. The value of theconversion factor is stable within a maximum of 5% for one tube for 1 year.

4.3.2

Timing Response

The purpose of timing calibration of the OD is to confirm the relative timing oﬀset
of each OD PMT and the global timing oﬀset between ID and OD. For the relative4. CALIBRATION

78

timing oﬀset, cable length diﬀerences are considered. About 87% of the cables are
70 m long, and the remaining are 71 to 78 m. For the global timing oﬀset, a laser
system and CR muon are used. The laser events are taken by flashing the laser at
the ID center and the OD top at the same time. From the results, a global timing
oﬀset is determined to be within several nsec. Using CR muon data, the global time
oﬀset can be independently confirmed. The OD resolution for determining the timethe muon passes through the OD was found to be within about 10 nsec as shown in
Figure 4.5.

Figure 4.5: Timing distribution of CR muons data used to calculate the global
timing oﬀset. Top: distribution of times (nsec) for the nearest hit OD-PMT to thefit tracks of downward CR muons. Center: the same histogram as that of the top
with the nearest hit ID-PMT. Bottom: distribution of the diﬀerence between ID
and OD time after correction for TOF of the muon. The figure was taken from Abe
et al. [208].

4. CALIBRATION

4.4

79

Optical Properties of the OD

The optical properties of OD materials are treated as parameters to be tuned in theMC simulation. The reflectivity of the Tyvek sheet is modeled as a combination ofGaussian specular reflections and Lambert diﬀuse reflections [211]. The contributionof these model varies as a function of the angle. The relative reflectivity of Tyvek
on each OD surface and transmissivity of Tyvek for the segmentation barriers are
tuned. The OD collection eﬃciency is also adjusted as an averaged parameter forthe three optically separated segments (i.e., top, bottom, and barrel) of the OD.
This quantity takes into account both QE and photon collection.

4.5

Energy Calibration

The reconstructed momentum of the neutrino is based on the total charge observedby the PMTs. Determining the systematic uncertainty of the energy scale is alsoessential. Four sources from highest to lowest energies are used to study this.
• Track length of high energy stopping muons (1 to 10 GeV/c)• Cherenkov angle of low energy stopping muons (200 to 500 MeV/c)• The invariant mass of π0 produced by neutrino interactions (about 130 MeV/c)• Momentum distribution of decay electron (about 50 MeV/c)
The accuracy of the absolute energy scale is checked by comparing data from all
calibration sources from the MC simulation. Time variation, detector uniformity,
and uncertainty of energy scale are also estimated.

4.5.1

High Energy Stopping Muons

Because the energy loss ( dE/dx ) is approximately constant in water, the momentumof CR muon can be determined by track length. Muon events that decay and emit
electrons in the detector are used to estimate the track length. This muon events is
a “stopping muon event”. The track length is defined by the distance between theentering position at the detector and the vertex position of the subsequent decay
electron. Selection criteria for stopping muons are listed follows:
1. The entering the position of the cosmic muon is at the top wall of the detector
2. The direction of the stopping muon is downward
3. Only one decay electron is detected
4. Reconstructed range of the muon track is 7 < L < 30 m
The first three criteria are used to select vertical downward going muons that have aclear Cherenkov ring. Therefore, it can be well reconstructed. The fourth criterion
selects high energy events.

4. CALIBRATION

80

Muon momentum loss is thus calculated. The range of the muon is determinedfrom the distance between the entrance point and the vertex point of the decay
electron. The distribution of momentum per range is then compared with the MC
simulation. Data and MC agree at 2.1%, 0.4%, 1.7%, and 0.7% for SK-I, SK-II,
SK-III, and SK-IV, respectively.

4.5.2

Low Energy Stopping Muons

The momentum of stopping muons having low energy (<500 MeV/c) can be estimated using the Cherenkov angle. The relationship between the Cherenkov angle
and momentum can be expressed as follows:√11m2
cos θC =
=
1+ 2
nβ
n
P (θC )m
∴ P (θC ) = √(4.10)
2
2
n cos θC − 1
where θC is the Cherenkov angle, n is the refraction index of water, β = v/c, m
is mass, and P is momentum, respectively. Selection criteria for the low energy
stopping muons are as follows:
1. The entering the position of the cosmic muon is at the top wall of the detector
2. The direction of the stopping muon is downward
3. Only one decay electron is detected
4. Total number of p.e. in the ID is less than 1,500 p.e. (750 p.e. for SK-II)
The first three criteria are the same as those for the high energy muon events.
The fourth criterion selects low energy cosmic muons having momenta less than
380 MeV/c. The momentum estimated from the total charge is then compared withthe estimation from the Cherenkov opening angle, P (p.e.)/P (θC ). The ratio iscompared between data and MC. The agreement is within 3.3%, 2.1%, 1.5%, and2.1% for SK-I, SK-II, SK-III, and SK-IV, respectively.

4.5.3

Neutrino Induced π0 Events

Single π0 events are produced by NC interactions of atmospheric neutrinos in thedetector. The produced π0 decays into two photons almost immediately. Therefore
the invariant mass of π0 can be calculated using the reconstructed momentum of
two photons.
√
M 0 = 2Pγ1 Pγ2 (1 − cos θ)(4.11)
π

where Pγ1 and Pγ2 are the momenta of the two gamma-rays, and θ is the opening
angle between them, NC π0 events are selected from the atmospheric neutrino event
sample by the following criteria.

4. CALIBRATION81

1. Two electron-like rings are detected
2. An electron from muon decay is not detected
3. Vertex position is reconstructed within the FV
The second criterion rejects events in which charged pions are produced with the π0
or CC events.
The actual π0 mass is 135 MeV/c2 , and the mean invariant mass reconstructed
is about 139 MeV/c2 . This shift to a slightly larger mass can be explained two ways.
First, the pion is produced from the interaction with an oxygen nucleus, which isleft in an excited state. That oxygen nucleus emits gamma-rays and transitions into
its the ground state. Owing to the energy of the de-excitation of the gamma-ray,the reconstruction energy is large. Second, the gamma rays from the pion decay
propagate for a short distance before causing an electromagnetic shower. Therefore,
the reconstructed vertex is slightly forward, and the opening angle between two
gamma rays is reconstructed slightly larger. This provides a larger pion invariant
mass. The MC considers the de-excitation of the oxygen nucleus. The peak positionof data and MC agree with 0.3%, 2.8%, 0.9%, and 1.0% for SK-I, SK-II, SK-III, and
SK-IV, respectively.

4.5.4

Decay Electrons

Stopping CR muons produces many decay electron events. Decay electrons haveenergy spectra below about 53 MeV (i.e., the Michel spectrum). This energy range
is compared between the data and the MC. Selection criteria for decay electron arelisted follows:
1. Time interval from a stopping muon is 2.0 to 8.0 µsec
2. The number of PMT hits in a 50 nsec window is > 60 (30 for SK-II)
3. The goodness of vertex fit is greater than 0.5
4. Vertex position is reconstructed within the FV
The first criterion involves the eﬃcient timing of decay electron tagging. The second criterion rejects gamma rays of 6 MeV or more emitted from muon capture on
nucleons.
The observed momentum spectra of the decay electrons have tails extending
upwards to around 70 MeV/c. This is because some muons (µ− ) are captured by
the K-Shell of an oxygen. The decay electrons are aﬀected by the potential of theoxygen nucleus and muon orbital motion [212]. The MC considers this eﬀect and themeasured charge ratio (µ+ /µ− ) of 1.37 [213]. The mean values of the data spectrum
agree with MC within 1.0%, 1.5%, 0.2%, and 1.5% for SK-I, SK-II, SK-III, and
SK-IV, respectively.

4. CALIBRATION

4.5.5

82

Summary of Energy Calibration

The absolute energy scale is calibrated by various methods for diﬀerent momentum
ranges. To estimate the systematic uncertainty of the energy scale, the ratio of values
between data and MC in each calibration method is used as shown in Figure 4.6.

Figure 4.6: Summary of absolute energy scale measurements for each SK phase.
The percentage of diﬀerences between data and MC are shown. Vertical error bars
denote the statistical uncertainty and horizontal error bars denote the momentum
range spanned by each analysis. The figure was taken from Abe et al. [214].
Because the distribution of the decay electron vertex and direction is almost uniform, the detector uniformity of the energy scale detector can be estimated using the
decay electron sample. Electrons perpendicular to the direction of the parent muon
are used for this measurement to take consider muon polarization. This condition is| cos θµe | < 0.25, where θµe is the opening angle between the muon and the electron
directions. The ratio of averaged momenta of decay electrons between data and MC
as a function of the opening angle is checked. The detector gains are uniform within
0.6%, 0.6%, 1.3% and 0.5% for SK-I, SK-II, SK-III, and SK-IV, respectively.
The stability of the energy scale is confirmed by stopping muons and decay electrons. Figure 4.7 shows the time variation of the energy scale, which is the average ofthe reconstructed momentum divided by range. During the SK-III phase, the transparency of water is poor, resulting in an energy scale with severe time fluctuations.
The SK-IV phase is a result of improvements in the water purification system and of
corrections for the time variation of the PMT responses. During the SK-IV phase,the energy scale has small time fluctuation caused by the further improvement to
the water purification system and the correction of the time fluctuation of the PMT
response.
Based on the results thus far, the final energy scale uncertainty in each phase
was estimated at 3.3% in SK-I, 2.8% in SK-II, 2.4% in SK-III, and 2.1% in SK-IV.

4. CALIBRATION

83

Figure 4.7: Energy scale stability as a function of date since the start of SK operations. The stability parameter was taken from the results of stopping muon. The
vertical axis shows the deviation of this parameter from the mean value for each SK
phase separately. The figure was taken from Abe et al. [214].

5. EVENT REDUCTION

584Event Reduction

The atmospheric neutrino events observed at SK are classified into three types:
fully-contained (FC), partially-contained (PC), and upward-going muon (UPMU),
as shown in Figure 5.1. In the FC and PC event samples, neutrino interactions arereconstructed within the ID using Cherenkov rings generated by charged particles.

Figure 5.1: Three types of high-energy neutrino events at SK.
Events where all charged particles stop within the ID are classified as FC, andthe events where at least one particle exits the ID and deposits energy in the OD
is classified as PC. UPMU events are observed when energetic muons, generated
by muon neutrino interactions with the rock surrounding the detector, enter the
ID from below the horizon. Because a large amount of CR muons are detected
as background from the top of the detector, the direction of the UPMU sample isrequired to be upward. There are no such restrictions for FC and PC events.
The mean energies of these event categories are about 1 GeV for FC, 10 GeV
for PC, and 10 to 100 GeV for UPMU. Figure 5.2 shows the atmospheric neutrinoenergy spectra from the simulation without the eﬀect of neutrino oscillations. The
data reduction procedures are diﬀerent for each of these categories and are describedin this chapter.

Figure 5.2: Expected energy distributions from atmospheric neutrino simulationfor each event classification [214].

5. EVENT REDUCTION

5.1

85

FC

FC reduction consists of five steps. During the SK-II period, the ID PMT coverage
was around half that of other SK periods. Thus the values of criteria were individual.
Because SK-IV has a diﬀerent data acquisition system, some values are defined
individually. The histograms in the following sections are criteria for a 5-day dataset
during SK-IV phase.

5.1.1First Reduction

106

Number of Events

Number of Events

The first reduction has two criteria to quickly filter out obvious backgrounds fromCR muons, electrical noises, and low energy background, such as those caused byradiation. This reduction is performed for real time analysis.
To remove most of the low energy background, events are selected based on theamount of light incident on the PMTs. Events whose maximum number of total
p.e. observed by the total ID PMTs in a sliding 300 nsec time window (PE300 ) isless than 200 p.e. (100 p.e. for SK-II) are rejected. This threshold corresponds to
22 MeV/c electron momentum Thus, in the analysis, events having a visible energy
below 30 MeV are not used.
To remove the CR muon event that leaves a signal in the OD, events without
OD triggers are selected. Furthermore, events whose number of hit OD PMTs in a
fixed 800 nsec time window around the trigger timing (NHITA800 ) is greater than
50 (55 for SK-IV) are rejected as shown in Figure 5.3.

105
104

107
106

103

105

102

104

10
0

200 400 600 800 1000
PE300

103
0

20

40

60

80

100

NHITA800

Figure 5.3: FC first reduction; the distribution of the number of p.e. observed by
ID (PE300 ) and OD (NHITA800 ). The arrows mark the selected events. A typical
1-week dataset of the SK-IV phase was used.

5. EVENT REDUCTION

5.1.2

86

Second Reduction

Number of Events

Number of Events

The second reduction comprises two cuts to give additional rejection of CR muonsand electric noise events. From this reduction, the analysis is performed oﬄine.
Events are rejected if the maximum number of p.e. observed by an ID PMT(PEmax ) is greater than half that of PE300 . This criterion rejects low energy electric
noise events, to whose signal a single PMT largely contributes. This cut also discards
events that record very large charges, called “flasher events”. A flasher event iscaused by spontaneous flashing due to a discharge of the dynode structure.
For the reduction of lower energy muons, the criterion is set using a tighter
threshold than that of the first reduction. If the NHITA800 is greater than 25 (30for SK-IV), and the PE300 is less than 100,000 p.e. (50,000 p.e. for SK-II), the events
are rejected as shown in Figure 5.4.

105
104

107
106
105

103

104

102
0

103
0

0.2

0.4

0.6

0.8

1

PE300/PEmax

20

40

60

80

100

NHITA800

Figure 5.4: FC second reduction; PE300 /PEmax and NHITA800 distributions. The
arrows mark the selected events. A typical 1-week dataset of the SK-IV phase was
used.

5.1.3

Third Reduction

After the first and second reductions, a third reduction comprises of several cuts
optimized to reduce various types of muons, flasher events, low energy radioactive,and electric noise events.

Through-going muon cut
A high-energy CR muon that passes through the ID is called a through-going muon.
To eliminate these events, a through-going muon fitter is applied for events whose
PEmax is greater than 231 p.e., and the number of hit ID PMTs (NHIT) is morethan 1,000. The fitter first selects the entrance point by locating the earliest hit
PMT with some neighboring hit PMTs and selects the exit point by searching for5. EVENT REDUCTION87

the center of the hit ID PMTs. The goodness of through-going muon fit is defined
as:
(
)
1 ∑ 1
(ti − Ti )2
goodness = ∑ 1
exp −
,
(5.1)
σi
2(1.5 × σi )2
i σ
i

i

Number of Events

Number of Events

where ti and σi are the observed hit time of i-th PMT and its resolution and Ti
is the expected hit time. Events whose values are greater than 0.75 are rejected.
Furthermore, the number of hit OD PMTs located within 8 m of the entrance andexit points in a fixed time 800 nsec time window (NHITAin and NHITAout ) are used
for reduction. The events having more than 10 hits of NHITAin or NHITAout arealso rejected, as shown in Figure 5.5.

102

102

10

10

1
10

10

20

30

40

50

NHITAin,out

0

0.2

0.4

0.6

0.8

1

Goodness of through-going muon

Figure 5.5: FC third reduction for through-going muon: NHITAin (black line),
NHITAout (red line), and goodness distributions. The arrows mark the selected
events. A typical 1-week dataset of the SK-IV phase was used.

Stopping muon cut
CR muons that stop inside the ID detector are called stopping muons and are removed the same way as through-going muons. A stopping muon fitter is applied
which finds the entrance point in a similar way as the through-going case. The
events whose NHITAin is greater than or equal to 10 are rejected as shown in Figure 5.6. When the goodness of fit is greater than or equal to 0.5 and NHITAin isgreater than or equal to 5, the events are rejected for only SK-I.

Cable hole muon cut
There are cable holes on the top of the detector tank to take the signal and HV
supply cables out. The CR muons that enter through cable holes are removed using
veto counter, as shown in Figure 5.7. When one veto counter hit and the distance88

Number of Events

Number of Events

5. EVENT REDUCTION

102

103
102

10

10

1
0

1
0

10

20

30

40

50

NHITAin

0.2

0.4

0.6

0.8

1

Goodness of stopping muon

Figure 5.6: FC third reduction for stopping muon: NHITAin and goodness distributions. The arrows mark the selected events. A typical 1-week dataset of the SK-IV
phase was used.
from the cable hole to the reconstructed vertex (Lveto ) is less than 4 m, the events
are rejected.

Figure 5.7: Cable hole and veto counter. The veto counter is a 2 × 2.5 m plastic
scintillation counter set as veto for four large cable holes, installed in April 1997.

5. EVENT REDUCTION

89

Flasher event cut

Number of Events

Number of Events

A flasher PMT event is an event caused by an electrical discharge in a PMT. Typical
flasher events have broader hit timing distributions than neutrino events. To reducesuch background, the events are rejected if the minimum number of hit ID PMTs
in a sliding 100 nsec time window from 300 to 800 nsec after the trigger (NMIN100 )is greater than 19 (14 for SK-I). Furthermore, when the NMIN100 is greater than 9,
and the number of hit ID PMTs is less than 800, the events are removed for only
the SK-I phase. Furthermore, when the goodness of the TOF fitter is less than orequal to 0.4, the events are rejected as shown in Figure 5.8.

250
200
150
100
50
0
0

20

40

60

80

100

NMIN100

350
300
250
200
150
100
50
0
0

0.2

0.4

0.6

0.8

1

Goodness of TOF fitter

Figure 5.8: FC third reduction for flasher events: NMIN100 and goodness of TOF
fitter distributions. The arrows mark the selected events. A typical 1-week datasetof the SK-IV phase was used.

Accidental coincidence events cut
Sometimes a CR muon event enters the trigger gate which is activated by a low
energy event. These events are rejected to remove such coincidences when the number of hit OD PMTs in a fixed 500 nsec time window from 400 to 900 nsec after thetrigger timing (NHITAoﬀ ) is greater than 19, and the number of p.e. observed by
ID PMTs in the same time window (PEoﬀ ) is greater than 5,000 p.e. (2,500 p.e. for
SK-II).

Low-energy event cut
The remaining low-energy background events are from electronic noise and radioactive decay. After subtracting the TOF of each observed photon assuming all photons
are generated at a point, the number of hit ID PMTs in a sliding 50 nsec time window (NHIT50 ) is counted. When the NHIT50 is less than 50 (25 for SK-II), theevents are rejected.

5. EVENT REDUCTION

5.1.4

90

Fourth Reduction

To remove the remaining flasher events, an intelligent pattern matching algorithm
is used. The flasher events usually repeat with similar hit patterns in the detector,
because the flasher events occur when light is emitted from flasher PMTs. It usuallytakes time before such bad PMTs are identified and turned oﬀ. The algorithm of
the pattern matching is as follows:
1. Divide the ID wall into 1,450 patches of 2 × 2 m square.
2. Compute the correlation factor r by comparing the total charge in each patchof two events, A and B. The correlation is defined as:(⟨ ⟩) (
⟨ ⟩)
A
A
B
Q
−
Q
×
Q
−
QB
∑
i
i
1
r=
,
(5.2)
N
σA × σBiA,B
where N is the numberof⟨⟩ the patches, Qi are the charge of i-th PMT for the

A and B events, QA,B are the averaged charge, and σ A,B are the standard
deviations of charge distribution.
3. Calculate the distance (DISTmax ) between the PMTs with the maximum pulse
heights in the two compared events.
4. If DISTmax less than 75 cm, an oﬀset value is added to r (r = r + 0.15).
5. If r exceeds the threshold (rthr ), events A and B are recognized as matched
events. The rthr is defined as
(
)
B
PEA
+
PE
300
300
r > rthr = 0.168 × log+ 0.13,(5.3)
2
where PEA,B
300 are the total number of p.e. observed in the ID.
6. Repeat the above calculation over 10,000 events around the target event andcount the number of matched events.
7. Remove the events with large correlation factor, r, or a large number ofmatched events.

5.1.5

Fifth Reduction

The fifth reduction is designed to reject the remaining CR muons and flasher events.
The remaining background events are few and can be removed by criteria specialized
for each background event type.

5. EVENT REDUCTION

91

Stopping muon cut

Number of Events

Number of Events

The remaining stopping muons are rejected more tightly than that of the third
reduction. The entrance point is computed by extrapolating backward from thefitted track of the event instead of using the earliest hit PMT. NHITAin and goodness
are calculated using the reconstructed entry point as the third reduction. Events
whose NHITAin is greater than or equal to 10 are rejected. When the goodness of
fit is greater than or equal to 0.5 and the NHITAin is greater than 5, the events arealso rejected as shown in Figure 5.9.

102

102

10

10

1
1

1
0 2 4 6 8 10 12 14 16 18 20

Goodness of stopping muon fit

NHITAin

0

0.2

0.4

0.6

0.8

Figure 5.9: FC fifth reduction for stopping muon: Goodness and NHITAin distributions. The arrows mark the selected events. A typical 1-week dataset of the SK-IV
phase was used.

Invisible muon cut
If the CR muon has too low a momentum to generate Cherenkov photons, it iscalled an invisible muon. Events caused by invisible muons are characterized by alow energy signal from a decay electron and a signal in the OD prior to trigger timing.
If the PE300 is greater than or equal to 1,000 p.e. (500 p.e. for SK-II), this reduction
is not performed, because the events are not from a decay electron. To count the
hit OD cluster, two methods are used. NHITACearly is the maximum number of
hit PMTs in an OD hit cluster in a sliding 200 nsec time window from −8,000 to
800 nsec. NHITAC500 is the number of OD hits in the cluster in a fixed 500 nsec
time window from −100 to 400 nsec around the trigger. If the distance between the
OD hit clusters used for the calculation of NHITACearly and NHITAC500 is less than
500 cm and NHITAC500 is greater than 1, the sum of NHITACearly and NHITAC500 is
defined as a total number of OD PMT hits in the cluster (NHITACtotal ). Otherwise,
NHITACtotal is defined as equivalent to NHITACearly . The events are rejected when
NHITACearly is greater than 5, and NHITACtotal is greater than 10, as shown in
Figure 5.10.

92

Number of Events

Number of Events

5. EVENT REDUCTION

102

102

10

10

1

1

0 2 4 6 8 10 12 14 16 18 20

05

10 15 20 25 30

NHITACearly

NHITACtotal

Figure 5.10: FC fifth reduction for invisible muon: NHITACearly and NHITACtotal
distributions. The arrows mark the selected events. A typical 1-week dataset of the
SK-IV phase was used.

Accidental coincidence muon cut

Number of Events

Number of Events

The remaining accidental events after the third reduction are further removed. Whenthe total number of p.e. observed in the ID in a fixed 500 nsec time window −100 to
400 nsec (PE500 ) is less than 300 p.e. (150 p.e. for SK-II), and the maximum numberof hit OD PMTs in a 200 nsec sliding window from 400 to 1,600 nsec (PElate ) is
greater than 19 p.e., the events are rejected, as shown in Figure 5.11.

102

10

10

1
0

102

1
200 400 600 800 1000
PE500

0

20

40

60

80

100
PElateFigure 5.11: FC fifth reduction for coincidence muon: PE500 and PElate distributions. The arrows mark the selected events. A typical 1-week dataset of the SK-IV
phase was used.

5. EVENT REDUCTION

93

Long-tail flasher cut
The remaining flasher events after the third reduction are further removed. For cut
criteria, the goodness-of-vertex fit and the variable described in the third reduction
NMIN100 are used. For SK-I, when the goodness-of-vertex fitter is less than 0.4
and NMIN100 is greater than 5, the events are rejected. From SK-II, when the
goodness-of-vertex fit is greater than 0.3, and NMIN100 is less than 6, the events are
rejected.

Electric noise event cut

Number of Events

Number of Events

The electric noise from HV systems or electronic boards create a lot of hits witha small amount of charge. To reject thses as non-physical background events, thenumber of hits for ID PMTs having less or more than a single p.e., N0 and N1
respectively, are counted. When the N0 is greater than or equal to 250 (125 for
SK-II) and N0 − N1 greater than or equal to 100 (50 for SK-II), the events are
rejected.

102

102

10

10

1

1

0

200 400 600 800 1000N0-500-400-300-200-100 0 100 200
N 0-N1Figure 5.12: FC fifth reduction for electric noise event: N0 and N0 −N1 distributions.
The arrows mark the selected events. A typical 1-week dataset of the SK-IV phase
was used.

5.1.6

Final FC Selection

After five reduction steps, the neutrino events that satisfy the following three criteria
are finally selected. First, the number of hit PMTs in the largest OD hit cluster(NHITAC) is less than 16 (10 for SK-I). The OD activity is low enough that it can beclassified as an FC event rather than a PC event. Second, the reconstructed vertex(Dwall ) of neutrino interaction locates more than 200 cm away from the ID wall.
This is the FV cut, which defines a 22.5 kilotons FV of the SK detector. Finally, thevisible energy (Evis ) obtained from the reconstruction algorithm should be greater

5. EVENT REDUCTION

94

than 30 MeV, because the atmospheric neutrino flux falls oﬀ at such a low energy.
The cut is applied to reject any potential low energy events which are not relevant.

5.1.7

Summary of FC Reduction

The overall eﬃciency of the FC sample selections for the true neutrino events is
estimated by the atmospheric neutrino MC as shown in Table 5.1. The eﬃciency isgreater than 98% during the SK-I to SK-IV phase, and the systematic uncertainty
is less than 1%. The average number of events per day in the final sample is about
8 events/day, which is stable through all SK phases.
Table 5.1: Reduction eﬃciency after each FC reduction step calculated by atmospheric neutrino MC. The selection eﬃciencies are for events whose FV are cut using
true vertex information.
Eﬃciency [%]

SK-I

SK-II

SK-III

SK-IV

1st Reduction

100.0099.96

100.00100.00

2nd Reduction

100.00

99.90

99.98

99.99

3rd Reduction

99.91

99.77

99.81

99.83

4th Reduction

99.51

99.51

99.68

99.00

5th Reduction

99.47

99.43

99.62

98.95

The remaining backgrounds after reductions are CR muons, flasher events, andneutrons from the rock around the detector. The background contamination in the
final sample is estimated to be about 0.1% based on the eye-scant of the selected
events.
The summary of FC reduction is posted at the end. The definition of variables
is described above.
First & Second Reduction
For a rough background estimation: an event is rejected if one of these criteria
is satisfied.
1. PE300 < 200 p.e. (100 p.e. for SK-II)
2. NHITA800 > 50 (55 for SK-IV)
3. PEmax /PE300 > 0.5
4. NHITA800 > 25 (30 for SK-IV) and PE300 < 100,000 p.e. (50,000 p.e. for
SK-II)
Third Reduction
For through-going muons, an event that satisfies all of the following criteria isremoved as through-going muon events:
1. PEmax > 231 and NHIT ≥ 1,000

5. EVENT REDUCTION95

2. goodness of through-going muon fitter > 0.75
3. NHITAin > 10 or NHITAout > 10
For stopping muons, an event is rejected if one of these criteria is satisfied:
1. NHITAin ≥ 10
2. goodness of stopping muon fitter ≥ 0.5 and NHITAin ≥ 5 (only for SK-I)
For cable hole muons, an event that satisfies all of the following criteria isremoved:1. One veto counter hit
2. Lveto ≤ 400 cm
For flasher events, an event is rejected if one of these criteria is satisfied:
1. NMIN100 ≥ 20 (15 for SK-I)
2. NMIN100 ≥ 10 and NHIT ≤ 800 (only for SK-I)
3. goodness of TOF fitter ≤ 0.4
For accidental coincidence & low energy events, an event is rejected if one ofthese criteria is satisfied:
1. NHITAoﬀ ≥ 20 and PEoﬀ > 5,000 p.e. (2,500 p.e. for SK-II)
2. NHIT50 < 50
Fourth Reduction
For flasher events, a pattern matching algorithm is used to evaluate the similarity of the past events that passed the third reduction.
Fifth Reduction
For stopping muons, an event is rejected if one of these criteria is satisfied:
1. NHITAin ≥ 10
2. NHITAin ≥ 5 and goodness of fitter ≥ 0.5
For invisible muons, an event that satisfies all of the following criteria is removed:
1. PE300 < 1,000 p.e. (500 p.e. for SK-II)
2. NHITACearly ≥ 5
3. NHITACtotal ≥ 10
For accidental coincidence, an event that satisfies all of the following criteria
is removed:
1. PE500 < 300 p.e. (150 p.e. for SK-II)
2. PElate ≥ 20 p.e.

5. EVENT REDUCTION96

For long-tail flasher, an event is rejected if one of these criteria is satisfied:
1. NMIN100 ≥ 6 and goodness of vertex fitter < 0.4 (for SK-I)
2. NMIN100 < 6 and goodness of vertex fitter < 0.3 (for SK-II to SK-IV)
For electric noise, an event that satisfies all of the following criteria is removed:
1. N0 ≥ 250 (125 for SK-II)
2. N0 − N1 ≥ 100 (50 for SK-II)
Final Reduction
For the FV cut, an event that satisfies all of the following criteria is selected:
1. NHITAC < 16 (10 for SK-I)
2. Dwall < 200 cm
3. Evis > 30 MeV

5.2

Partially Contained

PC events are separated from FC events via OD activities. Because OD segmentation was installed during the SK-III phase, the reduction process is modified toadjust. There are five steps for PC reduction. The histograms in the following
sections are also criteria for a 5-day dataset of the SK-IV phase.

5.2.1

First Reduction

To reject through-going CR muons and low energy events, the first reduction is done
for real time analysis. For all SK phases, the PC sample requires that exiting particles have a track length in the ID of at least 2 m, which corresponds to a momentum
loss of 500 MeV/c for muons. Therefore, PE300 should be greater than or equal to1,000 p.e. (500 p.e. for SK-II) conservatively, which corresponds to 310 MeV/c formuons.
For SK-I and SK-II, to remove through-going CR muons, when the width of thehit timing distribution in the OD PMTs (TWIDA) is greater than 260 nsec (170 nsec
for SK-II), and the number of hit cluster in the OD (NCLSTA) is greater than 1(only for SK-I), the events are rejected. Because through-going muon events havea broad hit timing distribution, two hit clusters are found around the entrance andexit point in the OD.
For SK-III and SK-IV phases, a more eﬃcient cut was used because of thesegmentation of the OD. PE300 should be greater than or equal to 1,000 p.e. as with
the SK-I phase. If either the number of OD hits in the top (bottom) (NHITAtop(NHITAbottom )) is less than 11 (10), the event is rejected. Moreover, the events are
rejected if the total number of OD hits in top and bottom called end-cap region(NHITAendcap ) is less than 29 or the number of OD hits in side (NHITAside ) is lessthan 84, as shown in Figure 5.13. Because through-going muons are expected todeposit energy in two regions of the OD, the average distance between all hit pairs5. EVENT REDUCTION

97(ODRmean ) is expected to be larger than PC events. Thus, when ODRmean is greaterthan or equal to 2,140 cm, the events are rejected, as shown in Figure 5.13. The
definition of ODRmean is as follows:N∑⃗xi − ⃗xj .

107

107

107

106

106

106

105

105
104

105

104

104

103

103

3

10

0

20

40

60

80 100(5.4)

i=i j=i+1

Number of Events

Npair

N
−1
∑

Number of Events

Number of Events

ODRmean =1

0

NHITA top,bottom

50

100

150

200

0

1000 2000 3000 4000 5000

NHITA endcap,side

ODR meanFigure 5.13: PC first reduction: NHITA (for top, bottom, endcap, and side)
and ODRmean distributions. The black (red) line of left panel corresponds to the
NHITAtop (NHITAbottom ). The black (red) line of center panel corresponds to the
NHITAendcap (NHITAside ). The arrows mark the selected events. A typical 1-weekdataset of the SK-IV phase was used.

5.2.2

Second Reduction

A clustering algorithm of OD hits is used to reject the through-going muons and thestopping muons. The ID and OD walls are divided into 21 × 21 and 11 × 11 patches.
The charge observed in each patch is counted as shown in Figure 5.14. The clusters
are formed by looking for the charge gradient to the neighboring patches.
For the SK-I, the following three clusters amounts are used to reject the events:
the number of hits in the largest OD cluster (Nouter), the number of hits in the1outersecond-largest OD cluster (N2 ), and the smaller of the number of wall hits andouterthe number of end-cap hits (Nouteror Noutermin ). If either the N2
min is greater than 6,outerthe events are rejected. Furthermore, when N1
is greater than 6, and the numberof the observed p.e. within 200 cm from the highest charge PMT in the ID hit cluster
closest to the OD hit cluster (PE200 ) is less than 1,000 p.e., the events are rejected.
For the SK-II, when the Nouteris greater than 6, the events are rejected as same2
as SK-I. When the NHITAendcap is greater than or equal to 20 and MAX(NHITAside ),the events are rejected. The definition of MAX(NHITAside ) is as follows:{
MAX(NHITAside ) =exp(5.8 − 0.023 × NHITAside )(NHITAside < 75)

exp(4.675 − 0.008 × NHITAside ) (NHITAside ) ≥ 75)(5.5)

5. EVENT REDUCTION

98

Figure 5.14: Algorithm for finding hit clusters in OD. The circles represent the
charge observed at each patch. The size of the circle is proportional to the numberof p.e.. The arrow represent the vector charge gradient, which points to highest
charge among neighboring patches.
If Nouterand PE200 satisfy: Nouter> 6 and Nouter≥ 12 + 0.085 × PE200 , the events
1
1
1
are rejected.
For SK-III and SK-IV, because the first reduction using the OD segmentation isvery eﬃcient, the second reduction consists of two criteria for SK-II. First, when theNouteris greater than 10, the events are rejected. Secondly, when the NHITAendcap is2
greater than or equal to 20 and MAX(NHITAside ), the events are rejected as shownin Figure 5.15.

5.2.3

Third Reduction

The flasher events are rejected in the same way as that of the FC third reduction,in which the broad timing distribution of the flasher events is used for the cut. For
SK-I to SK-IV, when NMIN100 is less than 15, the events are rejected as flasher
events. Otherwise, when NMIN100 is less than 10 and NHIT is greater than or equal
to 800 (400 for SK-II), the events are also rejected.
For the SK-I and SK-II, the stopping muons are also rejected by using the numberof hit OD PMTs near the entrance point. The entrance position is estimated via
backward extrapolation from the reconstructed vertex, which is fitted by point-fit.
The events are rejected when the NHITAin is greater than 10 as shown in Figure 5.16.
For SK-III and SK-IV, the stopping muon cut is applied at the PC fifth reduction
stage.

99

Number of Events

Number of Events

5. EVENT REDUCTION

104

104
103

103

102
0

20

40

60

80

100

0

20

40

60

80

100

NHITAendcap

N 2outer

Number of Events

Number of Events

Figure 5.15: PC second reduction: N2outer and NHITAendcap distributions. The
arrows mark the selected events. A typical 1-week dataset of the SK-IV phase was
used.

104
3

10

102

102

10

10
1
0

20

40

60

80

100

NMIN1001
05001000 1500 2000
NHIT

Figure 5.16: PC third reduction: NMIN100 and NHITA distributions. The two
black arrows represent conditions having two parameters. The arrows mark theselected events. A typical 1-week dataset of the SK-IV phase was used.

5.2.4

Fourth Reduction

The fourth reduction was completely modified for SK-III and SK-IV because of the
OD segmentation. Here, we describe two versions of the fourth reduction.

5. EVENT REDUCTION

100

For SK-I and SK-II
To reject the CR muons, two types of event reconstruction tools are used: Point-fit
and through-going muon fit. There are four criteria, and the event is rejected as a
CR muon event if any of them is not satisfied.
First, the inner product of the reconstructed direction by the Point-fit (d⃗fit ), andthe direction from the reconstructed vertex to the earliest saturated PMT (d⃗PMT )should be greater than −0.8. Second, the goodness of the through-going muon fit
should be greater than 0.85. Third, the track length of a muon (TLMU) estimatedfrom the entrance and the exit points by the through-going muon fit should begreater than 30 m. Finally, the distance (DCORN) from the reconstructed vertex
by the Point-fit to the nearest fringe of the ID should be greater than 150 cm.
The first criterion aims to reject the CR stopping muons that have an entrance
point in the opposite direction to the reconstructed direction. The through-going
muons which have a long track length are rejected by the second and third criteria.
And the corner clipping muons are rejected by the final cut.

For SK-III and SK-IV
An event reconstruction tool is used to classify each event as a stopping muon, athrough-going muon, or a corner clipping muon. For classification, there are fivepossible selection criteria based on the fitter as shown in Figure 5.17.
1. The angle (θmuon ) between the fitting direction and the vector between thefitted vertex and the center of the highest charge OD cluster is less than 90◦ .
2. The inner production of the fitting direction (d⃗muon ) and the vector (d⃗PMT )between the fitted vertex and the earliest PMT is greater than −0.8.
3. The goodness of the muon fitter (goodnessmuon ) is less than 0.52.
4. The length (Lmuon ) of the fitted muon track is less than 17.5 m.
5. The distance (Cornermuon ) between the fitted entrance point and the cornerof the tank is less than or equal to 3 m.
The number of these criteria required to pass this reduction step depends on theclassification of events from the fitter. If an event is classified as a PC through-going
muon, it must pass four of the five criteria. Similarly, if an event is classified as a PC
stopping muon, it must pass four of the five criteria, including the second criterionwith additional requirements. The event must have the goodnessmuon less than 0.5,
or NHITAin should be less than 10. For the other classifications, two of the fivecriteria must be passed.
Finally, when the PE300 is less than 3,000 p.e., the events are rejected to remove
the low energy background. This threshold corresponds to a muon momentum of
500 MeV/c, which is safe for PC events, because exiting muons must have at leasta momentum of 700 MeV/c to reach the OD.

101

105

Number of Events

Number of Events

Number of Events

5. EVENT REDUCTION

104

104
103

103

102

103

10
102

0

102
50

100

150

-1

1
-0.5

0.5

1

0

0.2

5

10

0.4

0.6

0.8

1

Goodness of Muon fit

Number of Events

Number of Events

Number of Events

103

0dmuon • dPMT

θmuon

105

104

102

104
3

10

10

1

102

0

1000 2000 3000 4000 5000

0

L muon500

1000 1500 2000
Distance R [cm]05001000 1500 2000
Distance Z [cm]Figure 5.17: PC fourth reduction: These are distributions of the angle, the innerproduction, the goodness, the length, and the distance from the wall in order fromthe upper left. The arrows mark the selected events. A typical 1-week dataset of
the SK-IV phase was used.

5.2.5

Fifth Reduction

The fifth reduction elaborate selection criteria, specialized for each backgroundsource, are applied. The selections for the SK-I to SK-II and SK-III to SK-IV
phase are diﬀerent. Here, we describe the criteria for using both versions of the fifth
reduction. Two types of reduction are determined by a combination of these cuts.
Low energy event cut The remaining low energy background events areagain rejected by using the PE300 . The PE300 should be greater than 3,000 p.e..
This will remove much of the low energy background.

5. EVENT REDUCTION

102

Through-going muon cut (A) To remove the remaining through-going muons,
OD hit cluster information obtained by the algorithm in the PC second reduction
is used. There are three criteria: the distance (DISTcluster ) between the highest
charge OD hit cluster and the second highest one is greater than 20 m; the numberof p.e. (PEAC2 ) detected in the second-highest charge OD hit cluster is greater thanor equal to 10 p.e.; and the number of hits in third-largest OD cluster (Nouter) is3
greater than or equal to 2. When all of these criteria are satisfied, the events are
rejected as through-going muon events.

103

103

102

2

2

10

10

10

10

1

1

0

Number of Events

Number of Events

Number of Events

Through-going muon cut (B) Some CR muons enter the detector from theedge atop the detector and exit from the edge at the bottom, and these events pass
the prior reduction steps. The light collection eﬃciency around the edge of the OD
is relatively poor, and the event reconstruction tools do not perform well at thedetector boundaries.
An event that satisfies all of the following three criteria is rejected. First, the
NHITAtop and NHITAbottom are greater than or equal to 7. Second, the numberof p.e. (PEAtop and PEAbottom ) in the OD detected in the same sphere as thatfor NHITAtop and NHITAbottom are greater than or equal to 10. Finally, assumingthat the detector tank height is 1, the distance the particle can pass in the timeinterval (TDIFFA) between the averaged hit timing of the top and bottom spheresare calculated. When the TDIFFA × c/40 m is between 0.75 to 1.5, the event may
be a through-going muon event, as shown in Figure 5.18.

20

40
NHITAtop,bottom

0

10

1
20

40
PEAtop,bottom

0

1

2

3

4

5

TDIFFA*c/40 m

Figure 5.18: PC fifth reduction for through-going muon cut B: the distributions of
the NHITA for top (black) and bottom (red), the PEA for top (black) and bottom(red), and the relative track length. The arrows mark the selected events. A typical
1-week dataset of the SK-IV phase was used.

Through-going muon cut (C) The through-going muons are removed per
the number of hit OD PMTs near the entrance and the exit point. The vertex po-

5. EVENT REDUCTION

103

Number of Events

Number of Events

sition and the direction of a particle are reconstructed with a precise fit using theCherenkov ring pattern. The entrance and exit points are estimated by extrapolation.
An event that satisfies all of the following two criteria is rejected. First, NHITAin
is greater than or equal to 5, and NHITAout is greater than or equal to 7. Second, thesame calculation used in the previous cut is performed, but the length of the truck(TRACK) is used instead of the height of the tank. When the 0.75 < TDIFFA ×
c/TRACK < 1.5 is between 0.75 and 1.5, the event may be through-going muon
event, as shown in Figure 5.19.

102

102

10
10
1
0

20

40

60

80

100

NHITAin,out

0

1

2

3

4

5

TDIFFA*c/TRACK

Figure 5.19: PC fifth reduction for through-going muon cut C: the distributions of
the NHITAin (black), the NHITAout (red), and the relative track length. The arrows
mark the selected events. A typical 1-week dataset of the SK-IV phase was used.

Through-going muon cut (D) The remaining through-going muons are removed per the number of hit OD PMTs. The highest charge cluster (Nouter) and1
the second-highest charge cluster (Nouter
)
are
used.
These
valuesarecalculated
the
2
outer
same way as the PC second reduction. When the Nouterisgreater
than
9,
and
N
1
2
is greater than 16, the events are rejected as a through-going muon event, as shownin Figure 5.20.
Stopping Muon Cut (A) The number of hit OD PMTs near the entrance
position is counted for the stopping muon events. The entrance point of the stoppingmuons is estimated by reconstructing the vertex position and direction. When the
NHITAin is greater than or equal to 10, the event is rejected as a stopping muon, as
shown in Figure 5.21.
Stopping muon cut (B) Although the stopping muon has a larger angle
between the reconstructed direction and the OD hit cluster than a PC event, the104

Number of Events

Number of Events

5. EVENT REDUCTION

102

10

103
102
10

1
0 10 20 30 40 50 60 70 80 90100

1
0 10 20 30 40 50 60 70 80 90100

N outer1

N outer2

Number of Events

Figure 5.20: PC fifth reduction for through-going muon cut D: the distributionsof the highest and the second-highest charge cluster. The arrows mark the selected
events. A typical 1-week dataset of the SK-IV phase was used.

102

10

1
0 10 20 30 40 50 60 70 80 90100
NHITA inFigure 5.21: PC fifth reduction for stopping muon cut A; the NHITAin distribution.
The arrows mark the selected events. A typical 1-week dataset of the SK-IV phase
was used.

5. EVENT REDUCTION

105

Number of Events

Number of Events

angle is calculated using two diﬀerent fitters. When the opening angle (θTDCFit orθMSFit ) is greater than 90◦ , the event is rejected, as shown in Figure 5.22.

102

102

10
10
0 20 40 60 80100120140160180
θTDCFit

0 20 40 60 80100120140160180
θMSFitFigure 5.22: PC fifth reduction for stopping muon cut B; the distributions of opening
angles calculated by TDC fitter and MS fitter. The arrows mark the selected events.
A typical 1-week dataset of the SK-IV phase was used.

Stopping muon cut (C) The entrance position as the earliest hit cluster in
the ID is estimated via stopping muon fitting. If the NHITAin is less than or equal
to 6, then the charge inside a 42◦ cone facing the entrance position is checked. Whenthe ratio of charge inside (PEcone ) and outside (PE300 ) the cone is less than 60%,
the event is rejected as stopping muon event as shown in Figure 5.23.
Stopping Muon Cut (D) To reject stopping muon events, the number of
hit OD PMTs within 8 m of the reconstructed entry point (NHITAin ) is used. This
criterion was applied during the PC third reduction for SK-I and SK-II. For SK-III
and SK-IV, the events with NHITAin above 10 are required. Moreover, the entrance
point is compared with two types of fitters: Point-fit (P⃗PointFit ) and MS-fit (P⃗MSFit ).
The PC events require that the diﬀerence between P⃗PointFit and P⃗MSFit be less than
15 m.
Stopping muon cut (E) The same criterion of θmuon in PC fourth reduction
is applied, because the cut was a loser for events that were classified as stoppingor through-going muon events. When the θmuon is greater than 90◦ , the events are
rejected.
Corner clipping muon cut (A) Corner clipping muon events have a small
hit cluster in the ID, and the vertex is sometimes mis-reconstructed in the ID.
Therefore, we reject the mis-reconstructed edge clipping muon using the relation

Number of Events

5. EVENT REDUCTION

106

103

102

0

0.2 0.4 0.6 0.8

1

PEcone/PE300
Figure 5.23: PC fifth reduction for stopping muon cut C: the distributions of theratio of charge. The arrows mark the selected events. A typical 1-week dataset of
the SK-IV phase was used.
between the energy loss and track length from vertex to OD exit position. Whenthe estimated track length from the visible energy (TRACKvis ), assuming an energy
loss of 2 MeV/cm minus TRACK is less than −15 m, the event is rejected as shownin Figure 5.24.
Corner clipping muon cut (B) This is the same criterion that was appliedin the PC fourth reduction for the SK-I and SK-II. This cut avoids clipping muon
events by requiring the edge to be not too close to the edge of the ID. When the
DCORN is less than 150 cm, the events are rejected as shown in Figure 5.25.
Cable hole muon cut There are four veto scintillation counters placed overthe cable holes atop of the detector. Because a PC event can activate those veto, twoNumber of Events

5. EVENT REDUCTION

107

103

102

10
-2000-1500-1000 -5000500

TRACKvis-TRACK
Figure 5.24: PC fifth reduction for corner clipping muon cut A: the distributionof the diﬀerence of track length. The arrows mark the selected events. A typical
1-week dataset of the SK-IV phase was used.
criteria are required. When one veto counter hits, the ring direction reconstructedby TDC-fit (d⃗ring ) and the direction from the hit veto counter to the reconstructedvertex (d⃗veto−vertex ) is calculated. When the inner production of d⃗ring and d⃗veto−vertex
is greater than −0.8, the event is rejected.
Decay electron cut High energy neutrinos interact with nucleons in water
mainly via DIS interaction to produce hadrons containing charged pions. Thosepions decay into muons, and muons decay into electrons. When the number oftagged decay electrons (Ndecay ) is greater 1 and the visible energy (Evis ) is greaterthan 25 GeV, the events are rejected as the CR muons.

For SK-I and SK-II
The PC fifth reduction for SK-I and SK-II requires the following criteria. When all
criteria are satisfied, the events will be saved as a PC sample.
1. Low energy cut
2. Through-going muon cut (A)
3. Through-going muon cut (B)Number of Events

5. EVENT REDUCTION

108

103

102

0

50 100 150 200 250 300
DCORN

Figure 5.25: PC fifth reduction for corner clipping muon cut B: the DCORN distribution. The arrows mark the selected events. A typical 1-week dataset of the
SK-IV phase was used.
4. Through-going muon cut (C)5. Stopping muon cut (A)6. Stopping muon cut (B)7. Stopping muon cut (C)8. Corner clipping (A)9. Cable hole muon cut

For SK-III and SK-IV
There are two types of cuts: hard and soft for SK-III and SK-IV. PC reduction for
SK-III and SK-IV is modified to keep eﬃciency as SK-I and SK-II. PC sample isrequired to pass all hard cuts and the events may fail soft cut just once. The hardcuts are:
1. Low energy cut
2. Through-going muon cut (A)
3. Through-going muon cut (B)5. EVENT REDUCTION

109

4. Stopping muon cut (B)5. Corner clipping (B)
6. Cable hole muon cut
The soft cuts are:
1. Through-going muon cut (C)
2. Through-going muon cut (D)3. Stopping muon cut (A)4. Stopping muon cut (C)5. Stopping muon cut (D)6. Stopping muon cut (E)7. Corner clipping (A)8. Decay electron cut

5.2.6

Final PC Reduction

After five reduction steps, the neutrino events that satisfy the following three criteria
are finally selected. First, the vertex of neutrino interactions should be inside the
FV. Second, the NHITAC should be larger than 15 (9 for SK-I). Finally, the Evisshould be greater than 350 MeV, corresponding to the total observed charge in the
ID greater than 3,000 p.e. (1,500 p.e. for SK-II).

5.2.7

Summary of PC Reduction

The detection eﬃciency after the PC reduction stage is estimated using the atmospheric neutrino MC at about 81%, 75%, 89%, and 86% for SK-I, SK-II, SK-III,and SK-IV, respectively. The background events in the final PC sample are mainly
caused by CR muons. These background events are checked by eye scanning an event
display. Most background events are removed by the FV cut. However, the presenceof background events outside the FV can lead to some contamination. From the eyescanning and extrapolation of the background distribution outside the FV, the CR
muon background contamination was estimated to be less than 2% during the SK-I
to SK-IV phase.
The summary of PC reduction is posted at the end. The definition of variables
is described above.
First Reduction
For SK-I & SK-II, an event is rejected if one of these criteria is satisfied:
1. PE300 < 1,000 p.e. (500 p.e. for SK-II)5. EVENT REDUCTION

110

2. TWIDA > 260 nsec (170 nsec for SK-II)
3. NCLSTA > 1 (only for SK-I)
For SK-III & SK-IV, an event is rejected if one of these criteria is satisfied:
1. PE300 < 1,000 p.e.
2. NHITAtop < 11 or NHITAbottom < 10
3. NHITAendcap < 29 or NHITAside < 84
4. ODRmean ≥ 2,140 cm
Second Reduction
For SK-I, an event is rejected if one of these criteria is satisfied:
1. Nouter>62
2. Noutermin > 6
3. Nouter> 6 and PE200 < 1,000 p.e.
1
For SK-II, an event is rejected if one of these criteria is satisfied:
1. Nouter>62
2. NHITAendcap ≥ 20 and NHITAendcap ≥ MAX(NHITAside )3. Nouter> 6 and Nouter≥ 12 + 0.085 × PE200
1
1
For SK-III & SK-IV, an event is rejected if one of these criteria is satisfied:
1. Nouter> 10
2
2. NHITAendcap ≥ 20 and NHITAendcap ≥ MAX(NHITAside )Third Reduction
For SK-I & SK-II, an event is rejected if one of these criteria is satisfied:
1. NMIN100 < 15
2. NMIN100 < 10 and NHIT ≥ 800 (400 for SK-II)
3. NHITAin ≤ 10
For SK-III & SK-IV, an event is rejected if one of these criteria is satisfied:
1. NMIN100 < 15
2. NMIN100 < 10 and NHIT ≥ 800
Fourth Reduction
For SK-I & SK-II, an event is rejected if one of these criteria is satisfied:
1. d⃗fit · d⃗PMT ≤ −0.8
2. goodness of through-going muon fit ≥ 0.85
3. TLMU ≥ 30 m

5. EVENT REDUCTION

111

4. DCORN ≤ 150 cm
For SK-III & SK-IV, the classification of PC type is required following criteria
based on the fitter results:
1. θmuon < 90◦
2. d⃗muon · d⃗PMT > −0.8
3. goodnessmuon < 0.52
4. Lmuon < 17.5 m
5. Cornermuon < 3 m
An event that satisfies all of the following criteria is categorized as a PC
through-going muon:
1. it should pass four of the above five criteria
2. PE300 ≥ 3,000 p.e.
An event that satisfies all of the following criteria is categorized as a PC
stopping muon:
1. it should pass four of the above five criteria including the second criterion
2. goodnessmuon < 0.5 or NHITAin < 10
3. PE300 ≥ 3,000 p.e.
An event that satisfies all of the following criteria is categorized as another PC
muon:
1. it should pass two of the above five criteria
2. PE300 ≥ 3,000 p.e.
Fifth Reduction
The combination of these criteria determines the conditions for each SK phase.
The criteria is summarized below:
For low energy cut, PC events should be satisfied:
1. PE300 > 3,000 p.e.
For through-going muon cut (A), all criteria should be satisfied to categorized
as a PC event:
1. DISTcluster ≥ 20 m
2. PEAC2 < 10 p.e.
3. Nouter<2
3
For through-going muon cut (B), an event is rejected when all criteria aresatisfied:
1. NHITAtop ≥ 7

5. EVENT REDUCTION112

2. NHITAbottom ≥ 7
3. PEAtop ≥ 10 p.e.
4. PEAbottom ≥ 10 p.e.
5. 0.75 < TDIFFA × c/40 m < 1.5
For through-going muon cut (C), an event is rejected when all criteria aresatisfied:
1. NHITAin ≥ 5
2. NHITAout ≥ 7 (5 for SK-III and SK-IV)
3. 0.75 < TDIFFA × c/TRACK < 1.5
For through-going muon cut (D), an event is rejected as through-going muon
event when all criteria are satisfied:
1. Nouter>91
2. Nouter> 16
2
For stopping muon cut (A), an event satisfying the following criterion is rejected:
1. NHITAin ≥ 10
For stopping muon cut (B), an event satisfying the following criterion is rejected:
1. θTDCFit > 90◦ or θMSFit > 90◦ (75◦ for SK-III and SK-IV)
For stopping muon cut (C), an event is rejected as stopping muon event when
all criteria are satisfied:
1. goodness of stopping muon fit > 0
2. PEcone /PE300 ≥ 0.6
3. NHITAin > 6
For stopping muon cut (D), The classification of PC type is required following
criteria:
1. NHITAin > 10
2. P⃗PointFit − P⃗MSFit < 15 m
For stopping muon cut (E), The classification of PC type is required:
1. θmuon < 90◦
For corner clipping (A), The classification of PC type is required:
1. TRACKvis − TRACK ≥ −15 m

5. EVENT REDUCTION113

For corner clipping (B), PC events are should be satisfied:
1. DCORN ≥ 150 cm
For cable hole muon cut, an event is rejected when all criteria are satisfied:
1. one veto counter hit
2. d⃗ring · d⃗veto−vertex > −0.8
For decay electron cut, an event is rejected when all criteria are satisfied:
1. Ndecay ≥ 1
2. Evis > 25 GeV
Final Reduction
For the PC cut, an event that satisfies all of the following criteria is selected:
1. NHITAC > 15 (9 for SK-I)
2. Dwall < 200 cm
3. Evis > 350 MeV

5.3

UPMU

The reduction for UPMU events is described in this section. The UPMU sample isdivided into UPMU through-going and UPMU stopping subsamples for events thatcross or stop within the ID, respectively.

5.3.1

First Reduction

Low energy and extremely high energy events are rejected in the reduction. For
the UPMU sample, the PE300 is required between 6,000 to 1,750,000 p.e. (3,000 to
800,000 p.e. for SK-II). 6,000 p.e. corresponds to a muon momentum of 1 GeV/c anda track length of 3.5 m. The requirement for the final sample is a track length longer
than 7 m. Thus, this criterion is a conservative cut. At a very high energy ID charge,
the ID electronics are saturated and the muon fitters cannot work.

5.3.2

Second Reduction

To reject down-going CR muons, seven diﬀerent fitters are used. The fitters are specialized to fit stopping muons, through-going muons, and muon events via Bremsstrahlung.
The algorithms are as follows:
1. Muon fitter is applied to an event.
2. If the event is up-going and the goodness of fit is above the threshold (0.35),
the event is saved.

5. EVENT REDUCTION114

3. If the event is down-going and the goodness of fit is above the threshold (0.35),
the event is rejected.
4. If the event is traveling horizontally and the goodness of fit is above the threshold, or if the goodness of fit is below the threshold, the judgment is postponed.
5. The event is brought to the first step for the next muon fitter.
This sequence continues until the event passes through all fitters or is classified.
The event is rejected if the fitter does not give a goodness above the threshold, but
the event is saved if at least one fitter classifies the event as horizontal. A detailed
description of the seven muon fitters and the definition of the goodness can be foundin [74].

5.3.3

Third Reduction

To eliminate the remaining background, events are eye-scanned using a visual display. All events are checked one-by-one. About half of the events remaining after
all the automated reduction steps are rejected.

5.3.4

Final UPMU Reduction

There are three criteria for UPMU stopping events. First, the fitter classification is a
stopping event. Second, the fitted momentum is greater than or equal to 1.6 GeV/c,
which corresponds to a track length of 7 m. Finally, the NHITAout is less than 10(16 for SK-II).
The selection criteria for UPMU through-going events are similar to the stopping
event. First, the fitter classification is a through-going event. Second, the distancefrom the ID entrance point to the ID exit point is greater than or equal to 7 m.
Finally, the NHITAout is less than 10 (16 for SK-II).
The showering muon selection uses a chi-squared test based on the observed
charge and the expected charge of the non-showering muons. The diﬀerence between
the corrected observed charge and the expected charge of a non-showering muon isset as ∆(Q). The selection of the showering is as follows: When the χ2 is greaterthan or equal to 50, the ∆(Q) should be greater than 0.5. Otherwise, when the χ2is less than 50, the ∆(Q) should be greater than 4.5 − 0.08χ2 .

5.3.5

Summary of UPMU Reduction

After all reductions, the remaining background events are most likely CR muons. Because there are multiple Coulomb scatterings of the muons or slight mis-reconstructionsof near horizontally going muons, some CR muons are reconstructed as upwardgoing. Therefore, the background contamination is estimated by extrapolating the
distribution of downward events. To estimate the uncertainty of the background,zenith angle distributions for nearly-horizontal CRs is compared between the tworegions. The first region is reasonably well-insulated from CRs because of the thick5. EVENT REDUCTION

115

of rock around the SK. The second area is where the rocks are thin. From comparing
the two regions, the uncertainty of contamination of horizontal muon to the UPMU
sample is less than 25% during the SK-I to SK-IV phases.
The detection eﬃciency for the final samples is estimated to be over 97% during
the SK-I to SK-IV phase. The final sample is made by subtracting the expectedbackground events.

6. EVENT RECONSTRUCTION

6116

Event Reconstruction

Various event information can be derived by the reconstruction of the Cherenkov
light cone detected by the PMT. With evidence gathered about the ring shape andthe hit patterns, the Cherenkov angle, the number of rings, the vertex position,and the momentum of particles can be obtained. A detailed explanation of thereconstruction is found in Takenaga [215]. Here, FC samples are divided into two
types. Events having visible energies below 1.33 GeV are classified as Sub-GeV,
while events having visible energies above 1.33 GeV are classified as Multi-GeV.

6.1

Vertex Fitting

The vertex position is reconstructed using the timing information of hit PMTs inthree steps. The initial estimation is the vertex position and ring direction assuming
a point source. The opening angle of the ring and improved direction are thenreconstructed. Further improvements of the position and direction, a line-source forthe photons, and scattering are considered.
The first step, the Point-fit, is applied. A vertex is estimated assuming that allphotons are emitted at the same time from a point source. After subtracting the
TOF from a tested vertex, the PMT hit residual time distribution is constructed.
The goodness of fit is defined as follows:)((ti − t0 )2
1 ∑,
goodnessPoint−fit =
exp −
(6.1)
N
2(1.5 × σ)2i

where N is the number of hit PMTs, ti is the time residual of the i-th PMT, t0 is afree parameter, and σ is the PMT timing resolution taken to be 2.5 nsec. The fittersearches for the vertex that gives the maximum value of goodness.
The direction and the outer edge of the dominant ring are measured in the second
step. A pair consisting of direction the opening angle is tested by a parameter asfollows:
)2
( (
(
)2 )
∫ θedgeθ−θPE(θ)dθdPE(θ)edgeexp) ×× exp −, (6.2)Q(θedge ) = 0 (dθsin θedge
2σθ2θ=θedgewhere θexp and σθ are the Cherenkov opening angle expected from the charge within
the cone and its resolution. PE(θ) is the angular distribution of the observed charge
as a function of the opening angle θ from the particle direction. For the first factor,
the numerator of the first element supports more of the charge in the ring and thedenominator is enhanced against the narrower ring. The middle factor favors sharper
rings and the last factor enhances the estimator if it is close to the expectation. The
direction and the ring edge position are determined to maximize the estimator.
The vertex position is then determined using TDC-fit, wherein track lengthof charged particle and scattering are taken into account. The time residuals for
PMTs inside and outside the Cherenkov ring are calculated, and the goodness of6. EVENT RECONSTRUCTION

117

fit is determined. The vertex is determined to be the position that maximizes the
goodness parameter.
Finding the number of Cherenkov rings is described in the next section. However, if the event has a single-ring, a more precise fitter, called MC-fit, is used todetermine the vertex. This can be improved by re-fitting the vertex position using
the information of the ring pattern. The vertex position is adjusted parallel to theparticle direction using TDC-fit and its timing information. This process is iterated
until the changes in the vertex position and particle direction is less than 5 cm and0.5◦ , respectively. Table 6.1 and Table 6.2 summarizes the vertex resolution andangular resolution. The vertex (angular) resolutions are the diﬀerences between thetrue vertex (lepton direction) and the reconstructed vertex (direction). Note that
MS-fit is also used for UPMU reconstruction, assuming that the vertex locates at
the ID surface.
Table 6.1: Vertex resolution of FC and PC for each SK phase. The resolution isdefined as the width where 68% of the events are included.
Vertex Resolution [cm]

SK-I

SK-II

SK-III

SK-IV

e-like

31.3

35.4

30.9

31.2

µ-like

24.0

30.9

24.0

23.3

µ-like

38.5

41.7

45.0

51.3

e-like

35.9

36.8

35.9

34.0

µ-like

25.0

27.0

25.0

23.8

µ-like

68.4

111.2

74.2

87.8

FC : Sub-GeV
Single-ringMulti-ring

FC : Multi-GeV
Single-ringMulti-ring

PC

6.2

Single-ringµ-like

30.8

34.2

31.8

31.6

Multi-ringµ-like

114.6

116.4

106.0

125.6

Ring Counting

When the vertex and the first Cherenkov ring are found, the ring count algorithm
is applied to search for other such rings in the event. Other rings are searchedusing an algorithm with a Hough transformation [216] and the likelihood technique.
Figure 6.1 shows the illustration of the method. The dashed line circles centered oneach hit PMT are drawn with 42◦ half angles. The direction of the Cherenkov ringis identified as the intersection point of those dashed line circles.
By selecting the ring direction using this method, the second and subsequent
ring candidates are searched. The likelihood method is used to determine whether
a candidate ring is consistent with ring properties. When N rings are found for an6. EVENT RECONSTRUCTION

118

Table 6.2: Angular resolution of FC and PC for each SK phase. The resolution isdefined as the width where 68% of the events are included.
Angular Resolution [◦ ]

SK-I

SK-II

SK-III

SK-IV

e-like

3.2

3.4

3.2

3.2

µ-like

1.9

2.2

1.9

1.9

e-like

1.3

1.4

1.3

1.2

µ-like

0.9

1.0

0.8

0.8

1.0

1.2

1.0

0.9

FC : Sub-GeV
Single-ring

FC : Multi-GeV
Single-ringPC
Single-ringµ-likeFigure 6.1: Basic idea of finding ring candidates is shown. The shaded circle
represents the Cherenkov ring image, and the dashed circles are virtual Cherenkov
rings centered on each PMT hit. The point of overlap is to be the center of the real
Cherenkov ring.
event, we test whether the (N + 1)-th ring candidate is true using the likelihood.

6. EVENT RECONSTRUCTION

119

The likelihood function is defined as
(
(
))
N
+1
∑
∑
obs
exp
LN +1 =
log prob qi ,αn · qi,n
,

(6.3)

n=1

i

(
)
prob q obs , q exp
=

( (
) )

obs
exp 2
q −q

 √1 exp −

2for q exp > 20 p.e.

2σSingle p.e. and Poisson convolution for q exp < 20 p.e.
(6.4)

where hit PMTs inside N + 1 Cherenkov rings are summed. qiobs is the observed p.e.
exp
in the i-th PMT, αn · qi,nis the expected p.e. at the i-th PMT from the n-th ring,exp
σ is the resolution for q , and the probability function determines how well the
expected charge reproduces the charge observed in the i-th PMT. The likelihood is
maximized by varying the αn factors with a lower momentum constraint. If it isdetermined that a second ring exists, we repeat the same procedure until a maximumof five other rings is found.
Figure 6.2 shows the ring-counting likelihood distributions comparing the data
and MC. The diﬀerence between the data and MC is taken as the systematic uncertainty for ring counting. Among the reconstructed rings, rings having low momentum and overlapping with other energetic rings are discarded.

6.3

Particle Identification

The detected Cherenkov rings are identified as electron-like (e-like) or muon-like (µlike) using particle identification (PID) programs. Electrons, positrons, or gammarays produce e-like rings owing to their electromagnetic shower via Bremsstrahlung,photon pair production, and multiple scattering. High-energy gamma-rays also generate electromagnetic showers, that are indistinguishable from electrons. Muons andheavy particles such as pions or kaons do not create showers, and their rings tend
to have a very clear edge. Additionally, although the e-like ring has an opening angle of 42◦ , muons and other heavy particles can produce rings with slightly smaller
opening angles if they are not highly relativistic.
To estimate the particle type, the likelihood is defined assuming a lepton. The
definition of the likelihood for the n-th ring is expressed by


∑
∏
exp
probqiobs , qi,n(ℓ) +q exp′ (ℓ),Ln (ℓ) =(6.5)
θi <1.5θc

′

i,n

n ̸=n

where ℓ is the lepton flavor (electron or muon) and the probability function is thesame as that defined by Equation 6.4. The product of the likelihood is taken overeach PMT that is within 1.5 times the estimated Cherenkov opening angle for then-th ring. The expected charge of the n-th ring is then calculated assuming a lepton
type and by adding the charge from all the other rings.

6. EVENT RECONSTRUCTION

SK-I

120

SK-II

Super Kamiokande I 1489.2 days

SK-III

Super Kamiokande II 798.6 days

single ring

multi ring

single ring220

multi ring

FC(Sub-GeV)

400
CCQE

300

CC Single !

CC DISCC DIS

CC Coherent !

CC Coherent !

NCNCsingle ring

Super Kamiokande IV 3118.4 days : Monitoring

multi ring

200

CCQE

200

CC Single !

350

single ring

multi ring
CCQE

CC Single !

CC Single !

1000

CC DIS

160

150

1200

CCQE

180

CC DIS

CC Coherent !

CC Coherent !

NC

NC

800

140

250

120

200

600

100

100

80

150

400

60

100

50

40

50
0
-15

SK-IV

Super Kamiokande III 518.1 days

250

450

200

20
-10

-5

0

5

10

15

Ring counting likelihood sub-GeV(FC), stack0-15

Super Kamiokande I 1489.2 days

-10

-5

0

5

10

15

Ring counting likelihood sub-GeV(FC), stack0-15

Super Kamiokande II 798.6 days

-10

-5

0

5

10

15

Ring counting likelihood sub-GeV(FC), stack0-15

Super Kamiokande III 518.1 days

-10

-5

0

5

10

15

Ring counting likelihood sub-GeV(FC), stack

Super Kamiokande IV 3118.4 days : Monitoring

140

FC(Multi-GeV)

400

single ring250

multi ring

single ring

multi ring

CCQE

350

200

CC DIS300

single ring

CC Single !
CC DIS

CC Coherent !

NC

NC

100

300
200

50
20

50

160

-10

-5

0

5

10

15

Ring
counting likelihood
multi-GeV(FC),Super
Kamiokande
I 1489.2
days stacksingle ring

0
-15

60

multi ring

600

NC

400

40

0
-15

CC DIS

500

60

100

CCQE

700

CC Coherent !

100

150

multi ring
CC Single !

80

200

single ring800

CC Coherent !
NC

150

250

CCQE

CC Single !
CC DIS

CC Coherent !

900

multi ring

120

CCQE

CC Single !

-10

-5

0

5

10

15

RingKamiokande
counting likelihood
multi-GeV(FC),Super
II 798.6
days stack

0
-15

100
-10

-5

0

5

10

15

Ring
counting likelihood
multi-GeV(FC),Super
Kamiokande
III 518.1
days stack

0
-15

-10

-5

0

5

10

15

countingIVlikelihood
stackSuperRing
Kamiokande
3118.4 daysmulti-GeV(FC),: Monitoring

60
single ring

single ring

multi ring

multi ring

single ring

multi ring

300
CCQE

140

CCQE

50

CC Single !

120

CCQE

CC Single !

CC Single !

250

CC DISCC DIS

CC Coherent !

CC Coherent !

CC Coherent !

CC Coherent !

NC

NC

NC

PC

CCQE

50

CC Single !

CC DIS

40

NC

40

200

100
30

30

80
60

150
20

20

100

40

10

10

20

CC DIS

50
0

0
-15

-10

-5

0

5

10

15

Ring counting likelihood (PC), stack

0
-15

-10

-5

0

5

10

15

Ring counting likelihood (PC), stack

-15

-10

-5

0

5

10

15

Ring counting likelihood (PC), stack

0
-15

-10

-5

0

5

10

15

Ring counting likelihood (PC), stack

Figure 6.2: Ring-counting likelihood distributions (L2 − L1 ) for SK-I to SK-IV
is shown. SK phases are shown in order from left to right. FC-Sub-GeV, FCMulti-GeV, and PC are shown in order from the top. The experimental data (dots)
are compared with MC (shaded) for various interaction modes with the two-flavor
oscillation eﬀect. The green-hatched region corresponds to CCQE, the blue is CC
Single π, the magenta is CC DIS, the light blue is CC Coherent π, and the orange
is NC interaction.
The probability of charge pattern and the opening angle of the ring are considered
for PID. The likelihood is taken in the form of a χ2 for the probability contribution
from the charge distribution of the ring. Then, the pattern probability and opening
angle probability are defined as:

(
)2 
2
2
2
χ
(ℓ)
−
min[χ
(e)
,
χ
(µ)]
n
n

 1 n
Pnpattern (ℓ) = exp−
(6.6)
,
2
2
2σχ2
(
)
2
exp
1
(θ
−
θ
(ℓ))
c
n
Pnangle (ℓ) = exp −
,
(6.7)
2
2(δθ)22where χ2n (ℓ) = −2 log L√n (ℓ) + constant. The resolution of the χ distribution isapproximated by σχ2 = 2N , where N is the number of PMTs used in the calcula-6. EVENT RECONSTRUCTION

121

tion. θnobs is the reconstructed opening angle, δθ is the fitting error, and θnexp is the
expected opening angle of the n-th ring. The probability functions of the PID for
single-ring events and multi-ring events are defined as:
Psingle (ℓ) = P pattern (ℓ) × P angle (ℓ)(6.8)

pattern(6.9)

Pmulti (ℓ) = P(ℓ)√√
PPID ≡ − log P (µ) − − log P (e)(6.10)The distribution of PID likelihood for single-ring events and multi-ring events isshown in Figure 6.3 and Figure 6.4. PPID < 0 is e-like events and PPID > 0 is µ-likeevents.

SK-I

SK-II

Super Kamiokande I 1489.2 days
300

FC(Sub-GeV)

e-like 3421

SK-III

Super Kamiokande II 798.6 days

muon-like 3166e-like 1866

200

250

Super Kamiokande III 518.1 days

muon-like 1683

e-like 1275

180
CCQE

200

CCMEC
CC Single !

160

CC DIS

140

NC

CCQE

CCMEC
CC Single !

80

CCMEC
CC Single !

400

CC DISCC DIS

CC Coherent !

CC Coherent !

NC

NC

80

CC DIS
CC Coherent !
NC

60

300

100

100

muon-like 6819

CCQE

CCMEC
CC Single !

120

150

e-like 6831
500

CCQE

CC Coherent !

SK-IV

Super Kamiokande IV 3118.4 days : Monitoring

600
muon-like 1146

100

40

200

60
40

50

20

100

20
0
-10

-8

-6

-4

-2

0

2

4

6

8

10

PID likelihood sub-GeV 1ring (FC)

0
-10

-8

-6

-4

-2

0

2

4

6

8

10

PID likelihood sub-GeV 1ring (FC)0
-10Super Kamiokande II 798.6 days

-8

-6

-4

-2

0

2

4

6

8

10

PID likelihood sub-GeV 1ring (FC)0
-10Super Kamiokande III 518.1 days

-8

-6

-4

-2

0

2

4

6

8

10

PID likelihood sub-GeV 1ring (FC)Super Kamiokande IV 3118.4 days : Monitoring

350

FC(Multi-GeV)

e-like 398

muon-like 402

120

e-like 274

CCQE

100

e-like 1638

muon-like 1544

CCQE

CCQE

250

CC Single !

CC DISCC DIS

CC Coherent !

CC Coherent !

30

NC

300

muon-like 236

40

CC Single !

CC Single !
CC DIS
CC Coherent !

200

NC

NC

80
150

60

20
100

40
10

50

20
0
-30

Super Kamiokande I 1489.2 days70

e-like 93

40

muon-like 416

-20

-10

0

10

20

30

PID likelihood multi-GeV 1ring (FC)Super Kamiokande
II 798.6 days

0
-30

-20

-10

0

10

20

30

PID likelihood multi-GeV 1ring (FC)Super Kamiokande
III 518.1 days

e-like 33

muon-like 172

e-like 50

muon-like 145

All MC25

CC with muon

150-50 -40 -30 -20 -10

10

20

30

40

50

30

0
-50 -40 -30 -20 -10

e-like 206

muon-like 840

60

All MCCC with muon

50

CC with muon

30
20

5

5

PID likelihood : PC 1ring

20

40

10

0

10

10

15

10

0

PID likelihood multi-GeV 1ring (FC)All MC

20
30
20

-10

70

All MCCC with muon

40

-20

Super Kamiokande IV 3118.4 days : Monitoring

80

20

30

50

0
-30

25

35

60

PC

50

140

10
0

10

20

30

40

50

PID likelihood : PC 1ring

0-50 -40 -30 -20 -10

0

10

20

30

40

50

PID likelihood : PC 1ring

0-50 -40 -30 -20 -10

0

10

20

30

40

50

PID likelihood : PC 1ring

Figure 6.3: PID likelihood distributions of single-ring events for SK-I to SK-IV
is shown. SK phases are shown in order from left to right. FC-Sub-GeV, FCMulti-GeV, and PC are shown in order from the top. The experimental data (dots)
is compared with MC (red line) for various interaction modes with the two-flavor
oscillation eﬀect. The MC lines correspond to CCQE (green dashed line), CCMEC(blue dashed line), CC Single π (blue dotted line), CC DIS (magenta long dasheddotted line), CC Coherent π (light blue long dashed-dotted line), and NC (orange
dashed line). For the PC samples, the blue hatched area represents the event owing
to the muon CC reaction.

6. EVENT RECONSTRUCTION

SK-I

SK-II

Super Kamiokande I 1489.2 days

SK-III

Super Kamiokande II 798.6 days

300
muon-likee-likemuon-likee-like350

250Super Kamiokande IV 3118.4 days : Monitoringmuon-likee-like

100

500

80

400

60

300

40

200

20

100

muon-like

300
200
250
150

200
150

100

100
50
50
0
-300

-200

-100

0

100

200

300

PID
likelihood
for all rings inI 1489.2
sub-GeV days
multi-ring (FC)Super
Kamiokande

0
-300

-200

-100

0

100

200

300

PID
likelihood
for all rings inIIsub-GeV
multi-ring (FC)Super
Kamiokande
798.6 days

0
-300

-200

-100

0

100

200

300

PID
likelihood
for all rings inIIIsub-GeV
multi-ring (FC)Super
Kamiokande
518.1 days

0
-300

-200

-100

0

100

200

300

400

600

PID
likelihood
for allIVringsin days
sub-GeVmulti-ring (FC)Super
Kamiokande
3118.4: Monitoring

60

140

FC(Multi-GeV)

SK-IVSuper Kamiokande III 518.1 days
120

400
e-likeFC(Sub-GeV)

122

e-likemuon-like

200

120

e-likemuon-likee-like180

muon-like100

muon-like

250
40

140
80

e-like

300

50

160

200

120
30

100

60

150

80
40

20

100

60
40

10

20

50

20
0
-600

-400

-200

0

200

400

600

PIDSuperlikelihood
for all rings in Imulti-GeV
multi-ring (FC)Kamiokande
1489.2 days

100

e-likemuon-like

0
-600

-400

-200

0

200

400

600

PIDSuperlikelihood
for all rings in multi-GeV
multi-ring (FC)Kamiokande
II 798.6 days

120

-400

-200

0

200

400

600

PIDSuperlikelihood
for all rings in III
multi-GeV
multi-ring (FC)Kamiokande
518.1 days

45
e-likemuon-like

0
-600

-400

-200

0

200

PIDSuperlikelihood
for all rings
in multi-GeV
multi-ring (FC)Kamiokande
IV 3118.4
days : Monitoring250
e-likemuon-likee-like40
100

muon-like

200

35

80

30

80

PC

0
-600

60

150

25
60

20
100

40

15

40

10

20

50

20
5

0
-1000-800 -600 -400 -200 0

200 400 600 800 1000

PID likelihood : PC multi ring0-1000-800 -600 -400 -200 0

200 400 600 800 1000

PID likelihood : PC multi ring0-1000-800 -600 -400 -200 0

200 400 600 800 1000

PID likelihood : PC multi ring0-1000-800 -600 -400 -200 0

200 400 600 800 1000

PID likelihood : PC multi ring

Figure 6.4: PID likelihood distributions of multi-ring events for SK-I to SK-IV
is shown. SK phases are shown in order from left to right. FC-Sub-GeV, FCMulti-GeV, and PC are shown in order from the top. The experimental data (dots)
is compared with MC (red line) for various interaction modes with the two-flavor
oscillation eﬀect.

6. EVENT RECONSTRUCTION

6.4

123

Momentum Determination

The momentum of each particle is estimated by the observed p.e. inside a cone
having an opening angle of 70◦ . The observed p.e. in the hit PMT is separated into
contributions from each ring to determine the momenta of the individual rings. The
observed charge in the i-th PMT from the n-th ring is estimated as:
exp
qi,n
obs
qi,n
= qiobs × ∑ exp
q ′(6.11)

i.n

obs
where qi,nis the fractional p.e. from the n-th ring in the i-th PMT, qiobs is theexp
observed p.e. in the i-th PMT, and qi,nis the expected p.e..
The charge in each PMT is corrected for the light attenuation in water and theacceptance of the PMT as follows:


(
)
(
)
∑
∑
G
cos Θir
obs
RTOTn = MC α ×qi,n−Si  (6.12)
× exp i ×
GdataLf (Θi )◦◦
θi,n <70θi,n <70

where GMC and Gdata are relative PMT gain parameters for data and MC, α is thenormalization factor, ri is the distance from the vertex position to the i-th PMT, L
is the light attenuation length in water, Θi is the angle of photon arriving direction
relative to the i-th PMT facing direction, f (Θ) is the correction function for the
PMT acceptance, and Si is the expected charge for the i-th PMT from scatteredphotons. The summation is restricted to be within the time window of −50 to
250 nsec around the peak of the TOF subtracted hit timing distribution.
RTOTn is converted to momentum using the MC. As√a result, the reconstructed
momentum resolutions √are estimated to be 0.6 + 2.6/ P GeV/c% for single-ringelectrons and 1.7 + 0.7/ P GeV/c% for single-ring muons [217].

6.5

Improvements in Reconstruction

There are three checks used for better reconstruction: ring number correction, decay
electron finding, and π0 reconstruction. These are briefly described next.

6.5.1

Ring number Correction

Some of the rings are mis-fitted and have low momenta or are overlapped withother reconstructed rings. When comparing two rings, if one momentum is low andoverlaps with a large momentum ring, or if one has a very low momentum, the ringis removed.

6.5.2

Decay electron Finding

Electrons are generated from the decay of the muon stopped in the detector. The
information from decay electrons can help estimate the type of neutrino interaction.
The decay electrons are classified to three types as follow.

6. EVENT RECONSTRUCTION

124

primary-event type
Decay electron observed in primary event (∆t < 900 nsec)
sub-event type
Decay electron observed in separated event (∆t > 900 nsec)
split type
Decay electron observed around the border timing of event window. (∆t ∼900 nsec)
Here, ∆t is the timing diﬀerence between primary event and decay electron event.
The detection eﬃciency of decay electrons is 80% and 63% for µ+ and µ− , respectively. Because about 20% of µ− is captured on 16O nuclei [212], the eﬃciency
is lower than µ+ .

6.5.3

π0 Reconstruction

FC Sub-GeV single-ring e-like events represent 9% of all NC events, and they mostly
originated from an NC single π0 production. A π0 immediately decays into two
gamma-rays and produces two e-like rings. If one of these rings is not detected
because of low energy or overlapping rings, the event can be identified as a singlering e-like event.
The π0 fitter reconstructs the second gamma-ray on the assumption of the existence of two rings. Then the likelihood technique is used to determine their best-fit
configuration.

6.6

Event Reconstruction for UPMU Sample

The UPMU event reconstruction algorithm diﬀers from the FC and PC event algorithms. The reconstruction is based on an MS-fit assuming that the particle is amuon and that the vertex is on the ID surface. However, if the muon generates anelectromagnetic shower, almost all ID PMTs will hit, or the Cherenkov ring cannot
be observed. These events use the OD hit information to determine the direction of
the particle. The same program is used for both observational data and atmospheric
neutrino MC events that go through the data reduction process.

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

7

125

Search for Astronomical Neutrino from Blazar

IceCube detected a high-energy neutrino event from blazar TXS0506+056. The neutrino event, first discovered on 22 September 2017, was correlated with a gamma-ray
flare and attracted a great deal of attention in the astroparticle field. Subsequently,
the IceCube collaboration reported a possible neutrino event from the same blazar
from older data between September 2014 and March 2015. However, no gamma-ray
flare was found during that period.
Compared to the IceCube, the SK can observe neutrinos with lower energy andhas continued to observe for a longer time. Therefore, it is strongly motivating tosearch for neutrinos in other energy ranges. The SK experiment has operated sinceApril 1996, and its sensitive energy region is from several MeV to a few tens of TeV.
In this analysis, neutrino data from SK-I to SK-IV until February 2018 are used foranalysis. The livetime of each SK phase is 1,489.2, 798.6, 518.1, and 3,118.5 livetime
days, and the total livetime is 5,924.4 livetime days.
To examine the neutrino from the point source, it is necessary to estimate theangular resolution for each event category. We search for a possible neutrino excessfrom the blazar by first counting the number of neutrinos in an angular region
around the direction to the assumed source. Then, the number of events comingfrom an alternative direction is studied to check the consistency of the observation
and background predictions. Finally, a simple statistical method is used to test for
local increases in the event rate coming from the blazar direction.
The results of the SK are finally compared with the IceCube result in the formof an energy flux. This is the number of neutrinos per square centimeter per unit
time and unit energy multiplied by the square of energy.

7.1

Angular Resolution

The arrival direction of neutrinos is determined via the reconstruction of Cherenkov
rings in the ID. The reconstruction quality typically depends on the initial neutrinoenergy. It is important to use events having suﬃcient angular resolution for association with the blazar direction in this search. The angle between the true neutrino
direction and the reconstructed direction is calculated by MC simulation. By studying the energy dependence of this angle, it gives the energy threshold for the angularresolution required for the analysis.
The searching area is 10◦ for FC and PC and 5◦ for UPMU, which is the samerange as the point source search performed in SK in the past [218]. Figure 7.1 shows
the angular resolution depending on the threshold of the observed energy at the
SK calculated by MC. By applying an additional cut of 5.1 GeV for FC events and
1.8 GeV for PC events to the observed energy, we ensure that the angular deviation
is within 10◦ for more than 68% of the events. Because UPMU events originate
from neutrinos having higher energies than other categories, their arrival direction

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

126

is estimated with higher accuracy. Therefore, no additional restriction on the UPMU
energy is used, because more than 77% of events are reconstructed within 5◦ of thetrue arrival direction.

Figure 7.1: Percentage of events where the angle between reconstructed direction
and true neutrino direction is within the threshold angle, 5◦ (10◦ ) for FC and PC(UPMU). This percentage varies depending on the threshold of observed energy at
the SK. The black, red, and blue points correspond to FC, PC, and UPMU samples,
respectively.
Figure 7.2 shows a sky map of the reconstructed arrival direction of selected
neutrino events around the blazar direction for all samples. There were 18 FC, 29
PC, and 20 UPMU events observed in these regions during SK-I to SK-IV. Notethat neutrino events observed in the FC sample include both electron neutrino andmuon neutrino interactions.

7.2

Expected BackgroundTo quantitatively study possible event excesses above atmospheric neutrino backgrounds, MC is used to predict the event rate in the search region of each sample.
The atmospheric neutrino event rate depends on the arrival direction, because thethickness of the atmosphere and the neutrino oscillation probability change withthe zenith angle in detector coordinates. The thicker the atmosphere, the higher
the probability that atmospheric neutrinos will be generated. For downward- or
horizontally-produced neutrinos the path length to the detector is relatively short,

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

127

Figure 7.2: Reconstructed arrival directions of FC (black circle), PC (red x),
and UPMU (blue +) events around the location of the blazar TXS0506+056(α, β) = (77.3582◦ , +5.6931◦ ) in equatorial coordinates. The horizontal axis is theright ascension and the vertical axis is the declination. The shaded circle in the left
(right) figure shows the 10 (5) degree search cone used in the analysis of FC and PC(UPMU) events.
and the eﬀect of neutrino oscillations is reduced. Consequently, because the zenith
angle is related to declination, the event rate also varies with declination. To simulate the eﬀect of varying right ascension in the actual data, MC events are randomly
assigned right ascension values under the assumption of flat local sidereal time.
The event rates in the search regions are calculated for each SK phase andcombined with appropriate livetime normalization factors. The number of expectedDec.
backgrounds at each declination, Nbkg
, are calculated as follows:
Dec.
Nbkg
=

in search∑ conei

Wi ×

Tlivetime× Rarea
500 × 365

(7.1)

where Wi is the correction factor for the neutrino oscillation to reflect best-fit valuesof systematic error parameters from the analysis of Abe et al. [214]. Because theMC has the 500-year-equivalent dataset at each SK phase, it was normalized to
livetime days. Rarea is the area ratio of the spherical zone and search circle, and theschematic view of the area ratio is shown in Figure 7.3.
Figure 7.4 shows the observed data events in each fixed search cone superimposedon the MC taken over various declinations. Note that the FC and PC background
events distribute across all declinations and show a slight increase at higher declinations, especially PC events, owing to the decrease of UPMU neutrinos lost to
neutrino oscillations. The double-bump structure around −50◦ and 50◦ is caused

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

128

Figure 7.3: Area ratio (blue circle/green area and blue circle/yellow area). Because
the area ratio of the spherical zone and search cone is depended on the declination,
the ratio was calculated for each declination.
by the increased atmospheric neutrino flux coming from the near − horizon direction, where the eﬀective atmospheric depth is deeper than other directions. Because
UPMU events are required to come from below the horizon, their maximum declination is about 54◦ .

Figure 7.4: Number of detected events in each search region (points with error bar)and expected background (solid line) are shown with corresponding predictions for
FC (black), PC (red), and UPMU (blue) samples. The error bar of the y-axis shows
the statistical error, and the error bar of the x-axis shows the range of search cone.
The expected backgrounds at the direction of the blazar are 15.20, 22.91, and14.57 for FC, PC, and UPMU samples, respectively. Therefore, the observed dataagree with the expected background within 0.7σ for FC, 1.1σ for PC, and 1.2σ for
UPMU events, considering statistical uncertainties alone.

7.3

On-source vs. Oﬀ-source

To further check the consistency of the observed event rates in the search cones,
we further investigate by studying similarly sized angular regions taken at the samedeclination as the blazar TXS0506+056 but with diﬀerent right ascension values.

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

129

These “oﬀ-source” regions are compared with the “on-source” region around theblazar.
Because the expected background does not change for the same declination, thenumber of on-source events is compared with the oﬀ-source. Figure 7.5 shows thenumber of observed events at on-source and oﬀ-source with the expected background.
They are consistent within 0.7σ for FC, 1.5σ for PC, and 1.5σ for UPMU based on
counting statistics only.

Figure 7.5: The upper figure shows the number of events in the search cone in
on-source (red triangle) and oﬀ-source (black circle) with the expected background(blue line) for FC (left), PC (middle), and UPMU (right). The lower figure shows therelative diﬀerence, corresponding to the diﬀerence between the observation and the
expectation. The relative diﬀerence distribution of oﬀ-source (black) is comparedwith the on-source (red) for FC (left), PC (middle), and UPMU (right).
The event rate, which is the ratio of the number of events in the search cone tothe live days, is shown in Figure 7.6. The event rate in the on-source search coneis (3.0 ± 0.7) × 10−3 for FC, (4.9 ± 0.9) × 10−3 for PC, and (3.4 ± 0.8) × 10−3 for
UPMU events per livetime day. Averaging the oﬀ-source rates yields (2.7 ± 0.6) × 10−3
for FC, (3.9 ± 0.6) × 10−3 for PC, and (2.5 ± 0.6) × 10−3 events per livetime day.
The errors are calculated from the root mean square (RMS) of the oﬀ-source datasets.
From the comparison of on-source and oﬀ-source, no excess neutrino events fromthe blazar direction exists. The event rate was also no diﬀerent between on-source
and oﬀ-source. Therefore, on-source and oﬀ-source rates are consistent, indicating
no excess of neutrino events in the direction of the blazar.

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

130

Figure 7.6: Event rate of the on-source (open square) and oﬀ-source (closed circle)of FC (black), PC (red), and UPMU (blue). The search range slid in the rightascension direction with a declination fixed in the direction of the blazar. The error
bar shows the statistical error.

7.4

Kolmogorov–Smirnov (KS) Test

We searched for evidence of a local increase in the neutrino event rate in the period
April 1996 to February 2018 range to test for possible correlation with gamma-ray
flaring of the blazar. Because the atmospheric neutrino rate is known to be stableat each SK phase, the number of observed neutrino events is expected to increaselinearly with increasing livetime if there is no neutrino emission from the blazar. On
the other hand, the event rate would deviate from linearity if there were additional
neutrinos from the gamma-ray flare.
To test for the presence of such a variation, we evaluated the probability (p-value)that the observed rate is consistent using a KS-test. The number of observed eventsin each SK phase is estimated from the atmospheric neutrino, MC, as summarizedin Table 7.1.
Table 7.1: The number of expected events at each SK phase.
SK-I

SK-II

SK-III

SK-IV

FC

3.7

2.1

1.3

8.1

PC

5.4

2.6

2.1

13.0

UPMU

3.8

1.9

1.0

7.9

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

131

Figure 7.7 compares the cumulative observed events with the expected events asa function of a livetime day. The maximum distance between the experimental data
and the expectation is 0.13 for FC, 0.25 for PC, and 0.21 for UPMU.

Figure 7.7: Normalized cumulative events as a function of livetime day for FC, PC,
and UPMU. The solid lines are observed events from the on-source region and thedashed lines are estimated background events assuming a constant event rate foreach SK phase. The ranges of each SK phase are shown as vertical dashed lines.
To calculate the p-value of the KS-test, a set of 10,000 pseudo experiments (toyMC) were generated assuming the expected background from the MC in each SK
phase. One toy-MC is calculated as follows:• The total number of events in each SK phase is determined via Poisson distribution centered on the expected number (Table 7.1).

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

132• The observed time of each event is randomly assigned assuming a constantrate in each SK phase.
• By calculating the maximum diﬀerence between the pseudo dataset and the
expected events, the maximum distance is obtained.
The maximum distance is compared to that from the observed SK data to calculate ap-value (Figure 7.8). This represents the percentage of pseudo experiments having amaximum distance larger than the data. The estimated p-values are 91.74%, 12.26%,
and 48.75% for FC, PC, and UPMU events, respectively, indicating consistency witha constant event rate. Accordingly, we conclude that no significant signal from thedirection of the blazar TXS0506+056 exists in the SK data during the observation
period considered.

Figure 7.8: Distribution of maximum distance calculated by the toy-MC (solidline) with the result of experimental data (dashed line) shown for FC (left), PC(middle), and UPMU (right) samples. The percentage contained on the right sideof the dashed line is calculated as the p-value.

7. SEARCH FOR ASTRONOMICAL NEUTRINO FROM BLAZAR

7.5

133

Summary

In the above analyses, there was no significant signal. The results of these analyses
are summarized in Table 7.2.
Table 7.2: Summary of analysis of neutrino search from the blazar TXS0506+056.
FC

PC

UPMU

5.1

1.8

1.6

10

10

5

Search Criteria
Threshold Energy [GeV]◦

Search Range [ ]Number of Events
Observed Events

18.0 ± 4.2

29.0 ± 5.4

20.0 ± 4.5

Expected Events

15.2

22.9

14.5

Agreement

0.7σ

1.1σ

1.2σ

Relative Diﬀerence of On-source and Oﬀ-source
On-source

0.18

0.27

0.37

Oﬀ-source Mean

0.064

0.0041

0.014

Oﬀ-source RMS

0.24

0.16

0.24

Agreement

0.7σ

1.5σ

1.5σ

Event Rate [/1,000 livetime day]On-source

3.0 ± 0.7

4.9 ± 0.9

3.4 ± 0.8

Oﬀ-source

2.7 ± 0.6

3.9 ± 0.6

2.5 ± 0.6

Agreement

not significant

not significant

not significant

Kolmogorov-Smirnov Test
Maximum Distance

0.13

0.25

0.21

p-value

91.74%

12.26%

48.75%

8. LIMIT CALCULATION

8134

Limit Calculation

Because no significant indications of a signal from the blazar are found in any of thetests of the previous chapter, we estimate fluence limits based on the expected background throughout the entire observation period. Neutrino-fluence is the numberof neutrinos per square centimeter. The fluence is calculated to find out how many
neutrinos arrived based on the number of neutrino observations at SK, according toSwanson et al. [219], Thrane et al. [220, 221].

8.1

90% Confidence Level (C.L.)

For the upper limit, the 90% C.L. limit on the number of neutrino events from theblazar direction is calculated as follows:
∫ N90
∫ ∞
dλ Poisson(Nobs , λ) = 0.9
dλ Poisson(Nobs , λ)
(8.1)
Nbkg

Nbkg
x −λ

λ e
x!

∵ Poisson(x, λ) =(8.2)

where Nbkg is the number of expected background events, Nobs is the number of observed events, N90 is the 90% C.L. upper limit of observed events, and Poisson(λ, x)is the Poisson probability.
The number of observed events and the expected background are estimated in
the previous chapter. Figure 8.1 shows the Poisson distribution centered on thenumber of observations for FC, PC, and UPMU samples. The 90% C.L. upper limitof observed events is 10.2 for FC, 14.5 for PC, and 12.7 for UPMU samples.
FC

0

10

20

PC

30

40

50

0

10

20

30

UPMU

40

50

0

10

20

30

40

50

Figure 8.1: Poisson distribution centered on the number of observed events. The
solid line corresponds to the number of expected background and the dashed line
corresponds to the 90% C.L. upper limit. Of the area displayed in red and blue, thered area accounts for 90%.

8. LIMIT CALCULATION

8.2

135

FC and PC Fluence

The FC samples mix both electron and muon neutrino events. However, the PC
samples are dominant muon neutrino events. This is because the mean free path ofelectrons in water is short and cannot pass through the structure between ID and
OD.
For the FC and PC dataset, the neutrino fluence can be calculated as follows:νx +νx
ΦFC

ν +ν

µ µ
ΦPC

=
NT
=
NT

∫
∫

(

FC
N90

)
,
dEν σ νx (Eν )ενx (Eν ) + σ νx (Eν )ενx (Eν ) λ(Eν−γ )
(

PC
N90

)
,
dEν σ νµ (Eν )ενµ (Eν ) + σ νµ (Eν )ενµ (Eν ) λ(Eν−γ )

(8.3)

(8.4)

where νx is the electron type neutrino or muon type neutrino, σ is the total neutrino
interaction cross-section, ε is the neutrino detection eﬃciency, and λ is the number
density distribution from the blazar direction. Finally, NT is the number of nucleonsin the 22.5 kilotons FV of the detector. It expresses as NT = 2.25 × 1010 ×NA , where
NA is the Avogadro constant.
Figure 8.2 shows the cross-section for all interactions combined in the range of
0.01 to 100 GeV. The cross-sections are calculated by NEUT version 5.3.5 [121].

Figure 8.2: Neutrino-nucleon interaction cross-section. The black line corresponds
to the electron neutrino, blue is the muon neutrino, red is the electron anti-neutrino,
and purple is the muon anti-neutrino. Because it is inferred that the model changes
around 100 MeV, it has a large fluctuation.

8. LIMIT CALCULATION

136

Figure 8.3 shows the detection eﬃciency of FC and PC for each neutrino flavors.
The detection eﬃciency is defined as the ratio of the number of detected neutrino
events to the total number of neutrinos reacting within the FV.

Figure 8.3: Detection eﬃciency for FC (black) and PC (red) as a function of neutrinoenergy. Because the Cherenkov threshold for the muon is 160.3 MeV, there is nosensitivity for νµ and νµ below the threshold. Furthermore, more energetic neutrinos
are usually needed to produce PC events. Thus, the sensitivity is near 0 below
1 GeV.

8.3

UPMU Fluence

Because the neutrinos of the UPMU sample penetrate the Earth and interact with
the nucleus of the rock surrounding the detector, the method of calculation forneutrino fluence is the diﬀerence from the FC and PC samples. For the UPMU
samples, the neutrino fluence can be calculated as follows:νµ +νµ
ΦUPMU

=

UPMU
N90

)
∫
Aeﬀ (z) dEν P νµ (Eν )S νµ (z, Eν ) + P νµ (Eν )S νµ (z, Eν ) λ(Eν−γ )((8.5)
where z is the zenith angle, Aeﬀ is the eﬀective area, P (Eν ) is the probability thata neutrino with energy Eν creates a muon with energy greater than Eµmin , S(z, Eν )

8. LIMIT CALCULATION

137

is the shadowing of the neutrinos caused by interactions in the Earth depending on
zenith angle, and λ is the number density distribution from the blazar direction. In
this calculation, the fluence limit is calculated using the average zenith angle to thesource taken over the detector observation period.

8.3.1

Eﬀective Area

The eﬀective area is the required area to get enough information for UPMU which
has a given direction. The sensitivity depends on azimuth and zenith angles of muon
path. Because a track length longer than 7 m is required for UPMU, the area longer
than the track length in the detector is called the eﬀective area. The schematic of
the eﬀective area is shown in Figure 8.5.

Figure 8.4: Eﬀective area. The figure was taken from Saji [222].
The eﬀective area is calculated as follows.
• A large plane enough to be projected is taken.
• 2D grid points at every 10 cm step are plotted.
• A vertical line on the defined plane is drawn from each grid point to thedetector.
• If the length of the line crossing the detector is longer than 7 m, the corresponding grid point is counted as part of the eﬀective area.
• The calculation is performed for every zenith angle of the area divided into 10
directions.
The result of the eﬀective area is shown in Figure 8.5.

8. LIMIT CALCULATION

Effective Area [cm2]

13

×106

138

Effective Area

12.5
12
11.5
11
0

0.2

0.4

0.6

0.8

1
cos(θzenith)Figure 8.5: Eﬀective area as a function of zenith angle. cos = 0 represents thehorizontal direction, and cos = 1 represents the vertical direction.

8.3.2

Probability of a Neutrino Creating a Muon

The probability, P (Eν , Eµmin ), that a neutrino having energy Eν creates a muon withenergy greater than Eµmin can be expressed as follows:
P (Eν , Eµmin ) =

∫ ∞

∫ Eν
NA dX

0

0

(
)
dσCC
× g X, Eµ , Ethr ,
dEµ

(8.6)

where NA is the Avogadro constant. Because the NC interactions do not produce
muons, σCC is the CC component of the neutrino-nucleon cross-section [223]. Furthermore, the probability that a muon having enough energy, Eµ , to survives withan energy larger than Ethr coming into detector after the traveling the thickness
X [g/cm3 ] in the rock is defined as g(X, Eµ , Ethr ). The function, g, can be writtenas:()
g(X, Eµ , Ethr ) = Θ R(Eµ , Ethr ) − X ,(8.7)
where R(Eµ , Ethr ) is a range that the muon travels while its energy decreases fromEµ to Ethr [224]. Θ is the step function as follows:{
Θ(x) =

1 (x ≥ 0)
0 (x < 0)(8.8)

8. LIMIT CALCULATION

139

Therefore, Equation 8.6 is replaced as follows:
∫ Eν
dσCC
× R(Eµ , Ethr )P (Eν , Eµmin ) = NA
dEµ
0

(8.9)

Figure 8.6 shows the result of the calculation of probability. The UPMU samples
includes only muon neutrino or anti-neutrino events.
Probability

10-4
-5
10
Probability

10-7
10-9
10-11
10-13
10-15

10

102

103

104

Neutrino Energy [GeV]

Figure 8.6: Probability that a neutrino creates a muon via neutrino interaction andthat the muons reach the detector. The black line corresponds to muon neutrino
and the red line corresponds to muon anti-neutrino.

8.3.3

Shadow Eﬀect

Some of the high energy neutrinos are absorbed by the Earth. For energies above
1 TeV, neutrino flux is increasingly suppressed by a shadow factor that is a functionof both energy and zenith angle. The Earth’s shadow eﬀect is defined as follows [225,
226]:
(
)
S(z, Eν ) = exp −ℓcol (z)σ(Eν )NA ,(8.10)
where ℓcol is the Earth’s column depth measured in centimeters water equivalentcalculated using the “Preliminary Earth Model” [225], σ is CC and NC neutrinonucleon cross-section, and NA is the Avogadro number.
Figure 8.7 displays the Earth’s shadow eﬀect. This eﬀect is negligibly small forneutrinos coming from near the horizontal direction or with low energy. However, it8. LIMIT CALCULATION

140

cannot be ignored for high energy neutrinos or neutrinos passing through the centerof the Earth. For cos(z) = 1, the shadow factor is 0.94 (0.97) for muon neutrino(anti-neutrino) at 1 TeV and 0.68 (0.78) for a muon neutrino (anti-neutrino) at
10 TeV.

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Shadow Effect (νµ)

Shadow EffectShadow EffectShadow Effect (νµ)

1.5
Log 2 2.5
(En
erg 3 3.5
y [G
eV ]
)

0

0.2

1
0.8 )
0.6 os(z
c
0.4

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.5
Log 2 2.5
(En
erg 3 3.5
y [G
eV ]
)

0

0.2

1
0.8 )
0.6 os(zc0.4Figure 8.7: Earth’s shadow eﬀect for muon neutrino (left) and muon antineutrino(right) as a function of neutrino energy and zenith angle. The neutrino energy isshown in log form, and the zenith angle is shown as the cosine value. cos(z) = 0
corresponds to the horizontal direction seen from SK.

8.4

Results

Above, the calculation method of the upper limit of each sample is described. To
calculate the fluence upper limit, Equation 8.3, 8.4, and 8.5 are used. It is necessary
to define the energy ranges in the integrals, the treatment of the upper limit of theobserved event at 90% C.L., and the number density of neutrino from the blazar.
Here, the final result is shown using specific numerical values.

Energy range
The energy ranges used in the equations are 5.1 to 10 GeV (FC), 1.8 to 100 GeV(PC), and 1.6 GeV to 10 TeV (UPMU). These ranges represent the MC neutrinoenergies populating each sample (see Figure 5.2). For the calculation of the upper
limit, FC is divided into one bin, PC is divided into two bins, and UPMU is divided
into four bins.

90% C.L.
Upper limits are calculated for both electron and muon neutrinos using FC events,
because this sample is sensitive to both. Only that of muon neutrino fluence limits
are estimated for the other samples. For the FC sample, we conservatively make no8. LIMIT CALCULATION

141

distinction between electron and muon neutrinos when calculating observed eventsat the 90% C.L. upper limit. The FC sample is populated almost entirely by events
having energies less than 10 GeV. Thus, our limit for electron neutrinos spans asingle bin. Note that tau neutrinos are present in the SK data but they represent
negligible contributions to the current dataset.
For the PC and UPMU samples, the same observed event value at 90% C.L. isused to calculate the upper limit in each energy bin. The neutrino energy cannot bereconstructed for UPMU events, because they are produced by neutrinos interacting
in the rock surrounding the detector. The PC sample also cannot reconstruct theneutrino energy, because the charged particles generated by the neutrino interaction
exit the detector.
Figure 8.8 shows the relationship between the reconstructed momentum of thecharged particle produced by neutrino interactions and true neutrino energy calculated by atmospheric MC. It can be seen that there is no correlation between charged
particle momentum and neutrino energy and that the neutrino energy cannot be reconstructed.
PC
106

120

105

100
104
80
103
60
102

40

Reconstructed Momentum [GeV]Reconstructed Momentum [GeV]

FC
140

140
104
120
100

103

80
102

60
40

10
20
0
0

20

40

60

80

100

120

140
160
180
200
Neutrino Energy [GeV]

10

20

1

0
0

20

40

140
104

120
100

103

80
102

60

80

100

120

140
160
180
200
Neutrino Energy [GeV]

40

140
104

120
100

103

80
102

60
40

10
20
0
0

1

UPMU (zoom)
Reconstructed Momentum [GeV]Reconstructed Momentum [GeV]

UPMU

60

10
20

5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
Neutrino Energy [GeV]

1

0
0

2000

4000

6000

8000
10000
Neutrino Energy [GeV]1

Figure 8.8: Relationship between the reconstructed momentum of charged particles
produced by neutrino interactions and neutrino energy. There are FC (upper left),
PC (upper right), UPMU (lower left), and UPMU enlarged views of the x-axis (lower
right). The colors correspond to the number of events.

8. LIMIT CALCULATION

142

Energy spectrum of neutrino
Because the gamma rays associated with neutrino production can cascade down tolower energies, the neutrino flux is likely to be correlated with the gamma-ray energy
flux [227]. Therefore, the following spectral analysis is performed.
The third Fermi Large Area Telescope (Fermi-LAT) source catalog (3FGL) [228]models the gamma-ray spectrum of TXS0506+056 as a power function:dN∝ E −γdE(8.11)The IceCube collaboration assums an energy spectrum of γ = 2 [19] for the highenergy neutrino event, IceCube-170922A. Furthermore, for the analysis of the neutrino flare from 2014 to 2015 (IceCube-14/15), the IceCube collaboration performed
time-dependent analysis. The results of the best-fitting parameter are given byγ = 2.1 ± 0.2 for the Gaussian time window and by γ = 2.2 ± 0.2 for the box-shaped
time window [56].
The Fermi-LAT, the All-Sky Automated Survey for Supernovae (ASAS-SN), and
IceCube collaboration analyzed 9.6 years of Fermi-LAT data in the TXS0506+056
region (10◦ × 10◦ ) using the source-finding algorithm. As a result, an alternative
spectral model (log-parabolic function) was obtained, having additional free parameters compared to a simple power-law:
dN
∝
dE

(

E
E0

)−α−β log(E/E0 ),(8.12)

where E0 = 1.44 GeV is given from Massaro et al. [229]. The parameters of thebest-fit are α = 2.03 ± 0.02 and β = 0.05 ± 0.01, respectively [227].
From Equation 8.12, we prepare four parameter sets of the energy spectrum forthe limit calculation. The parameters are summarized in Table 8.1. These values
are used in the next section.
Table 8.1: Parameters of the neutrino spectrum using Equation 8.12.
Parameter1a Parameter2b Parameter3b Parameter4c
E0

1

1

1

1440

α

2

2.1

2.2

2.03

β

0

0

0

0.05

a

see reference Aartsen et al. [19]see reference Aartsen et al. [56]csee reference Garrappa et al. [227]b8. LIMIT CALCULATION

8.4.1

143

Fluence Limit

The fluence limit is calculated for electron-neutrinos as 1 to 10 GeV in one bin. For
muon-neutrinos, the energy range (1.6 GeV to 10 TeV) is divided into four bins,
and the fluence limit is calculated for each. For the first bin and the second binof the muon-neutrino limit, the limit is calculated using the total observation and
expectation as follows;Φνµ +νµ

=

FC
PC
UPMU
N90
+ N90
+ N90
ν +ν

ν +ν

ν +ν

FC
PC
UPMU
µ µ
µ µ
µ µ
N90
/ΦFC
+ N90
/ΦPC
+ N90
/ΦUPMU.

(8.13)

Fluence [cm-2]

Figure 8.9 shows the upper limits at 90% C.L. on the neutrino fluence forelectron-neutrinos (νe +νe ) and muon-neutrinos (νµ +νµ ) by SK observations. The
limits are calculated using the four parameters described above. Each diﬀerence isexpressed as an error bar, and the specific numbers are summarized in the appendix
of this paper.
Fluence Limit

610

νe + νeνµ + νµ

5

10

104
103
102
10
1
10-1
1

10

102

103

104

Energy [GeV]

Figure 8.9: Fluence upper limits at 90% C.L. for electron-neutrino (blue) andmuon-neutrino (red). The error bars of the x-axis represent the energy range ofthe integral. The error bars of the y-axis represent diﬀerences when calculated withParameter 1 to 4.

8. LIMIT CALCULATION

8.4.2

144

Energy-flux Limit

To compare the results of the IceCube, the energy-flux is calculated. The definitionof the energy-flux is as follows;E2dNΦ= E2 ××C
dE
TL (Emax − Emin )[erg cm−2 sec−1 ],(8.14)

where TL is 5,924.35 days, which is the sum of SK livetimes for all periods, Emax
(Emin ) is maximum (minimum) energy of the integration range, and E is the energy
at the center of the bin. The unit of energy is converted from MeV to erg by theconstant value, C = 1.60218 × 10−6 .
The IceCube collaboration considers two neutrino emission periods to calculate the flux limit. In the first scenario, neutrinos are assumed to be emitted only
during the about 6 month period corresponding to the duration of the gammaray flare. Alternatively, neutrinos emitted over the whole observation of IceCube(7.5 years) are considered. The results of these two benchmark cases correspond to
1.8 × 10−10 erg cm−2 s−1 and 1.2 × 10−11 erg cm−2 s−1 .
We note that the IceCube group observed evidence of the neutrino event excess between 2014 and 2015 from the direction of the blazar whose best fit the−11energy spectrum was E −2.2 and whose flux was 2.6+1.1
erg cm−2 sec−1 at−1.0 × 10
100 TeV [56]. This corresponds to a flux of 1.9 × 10−10 , 1.3 × 10−10 , 8.1 × 10−11 ,and 5.1 × 10−11 erg cm−2 sec−1 at 4.0, 3.2 × 101 , 3.2 × 102 , and 3.2 × 103 GeV, respectively. These represent the values at the center of the bin of the SK results.
The comparison between the results of SK observations and the IceCube events(IceCube-170922A and IceCube-14/15) are shown in Figure 8.10.
Figure 8.11 shows the result of the gamma-ray spectrum analysis for
TXS0506+056 using Fermi-LAT data of the whole 9.6 years time range, comparedwith our result. To reproduce the result of the energy-flux of the gamma-ray, we
calculated using the Equation 8.12;
E

2 dN

dE

(
2

= E × N0E
E0)−α−β log(E/E0 ),(8.15)

where E is the energy of the gamma-ray and N0 = 4.16 × 10−12 cm−2 s−1 MeV−1 isthe intensity of the gamma-ray spectrum [227].
The specific values of fluence and flux calculated for each parameter are summarized in the AppendexA.

8.4.3

Luminosity Limit

We finally calculate the upper limit of the neutrino luminosity using the luminosity
distance. The relationship between the energy-flux and the luminosity is expressed
as follows:[]dN
2
L = E2(8.16)
× 4πDLerg sec−1 .
dE

8. LIMIT CALCULATION

145

E2dN/dE [erg cm-2 s-1]

Energy-Flux

-5

10
10-6
10-7
10-8
10-9
10-10
10-11
10-12
10-13
10-14
1

SK (νe + νe)
SK (νµ +νµ )IceCube (0.5 yr)
IceCube (7.5 yr)
IceCube (2014-2015)

10

102

103

104

105

106

107

Energy [GeV]

Figure 8.10: 90% C.L. energy-flux upper limit in the direction of the blazar
TXS0506+056 by SK electron neutrino (blue) and muon neutrino (red) comparedwith IceCube events (IceCube-170922A and IceCube-14/15). For the IceCube170922A event , the upper limit of typical muon neutrino flux that produces, on
average, one detection similar to IceCube-170922A over a period of 0.5 years (dashedblack line) and 7.5 years (solid black line), are shown. They assum a spectrum ofdN /dE ∝ E −2 at the most probable neutrino energy (311 TeV). The IceCube-14/15
event (purple) is deduced from the optimal result of a box-shaped time window using
the E −2.2 energy spectrum.
where L is the luminosity, and DL is the luminosity distance. DL represents the
distance to an object calculated based on the observed luminosity in the absence of
any unanticipated attenuation.
The luminosity distance is expressed as follows [230];∫ zc1
DL = (1 + z)
dz ′ √(8.17)H0 0ΩM (1 + z ′ )3 + Ωk (1 + z ′ )2 + ΩΛ
where z is the redshift, H0 is the Hubble constant, ΩM is the matter density, Ωk is
the spatial curvature density, and ΩΛ is the vacuum density. Because we assume aflat Universe, Ωk = 0 and ΩM + ΩΛ = 1. The value of the cosmological parameters,
H0 = 67.3 ± 1.2 and ΩM = 0.315 ± 0.017, are obtained from the results of the Planck
Collaboration [231]. Therefore, the luminosity distance of the TXS0506+056 locatedat redshift z = 0.336 is 1,835.0 Mpc. 8
8

http://www.astro.ucla.edu/~wright/CosmoCalc.html.

8. LIMIT CALCULATION

146

E2dN/dE [erg cm-2 s-1]

Energy-Flux

-5

10
10-6
10-7
10-8
10-9
10-10
10-11
10-12
10-13
10-14
1

SK (νe + νe)
SK (νµ+νµ)
Log-Parabola

103

102

10

104

105

Energy [GeV]

Figure 8.11: Energy-flux upper limit at 90% C.L. of the electron neutrino (blue) andthe muon neutrino (red) at SK are compared with the gamma-ray spectrum [227].
The green dashed-dotted line corresponds to the log-parabola model.
As a result of luminosity calculation, the upper limit of the luminosity observedat SK is summarized in Table 8.2. These limits are one to five orders of magnitude
higher than the IceCube result [19]. However, this leads to the first limit calculationof this energy region.
Table 8.2: Summary of upper limits (90% C.L.) of luminosity. The unit of luminosity
is erg sec−1 .

8.5

Energy [GeV]4.0

νe +νe2.5 × 1050

νµ +νµ50

1.9 × 10

3.2 × 101

3.2 × 102

3.2 × 103

–

–

–

49

2.0 × 1048

1.6 × 10

4.3 × 1047

Discussion

AGNs are expected to emit high-energy hadrons, gamma-rays, and neutrinos. Because the high-energy hadrons repeatedly interact with various materials to reachour galaxy, information about the origin of the CR emission is lost. The information
inside the jet of the AGN cannot be obtained from gamma-rays because of absorp-

8. LIMIT CALCULATION

147

tion and scattering by interstellar gas. Neutrinos have a very small cross-section,
but they can provide us with information about when they are generated.
Gamma-rays having various wavelengths from blazars have been observed byseveral researchers. These gamma-rays are presumed to have been produced byprotons and electrons accelerated by the jet. In the high-energy hadron processes,
the neutrinos and gamma-rays are also generated in parallel via pion decay. Various
theoretical models of neutrinos and gamma-rays emissions have been verified using
IceCube results [232–237]. The comparisons of the energy-flux of neutrino events
observed by IceCube using gamma-ray data from telescopes placed restrictions on
various model parameters. However, there is no model that completely describes
both.
For example, the results of the 2014/2015 neutrino flare event and gamma-ray
multi-wavelength observations were tested by Rodrigues et al. [237] using a numericalmodel [238]. They demonstrated that the models compatible with the gamma-ray
spectral energy distribution produce too few neutrinos (Figure 8.12: left). On theother hand, a compatible neutrino flux level implies a gamma-ray spectral energy
distribution in tension with observations (Figure 8.12: right). In both cases, the neutrino flux in the GeV to TeV region is very small, because it is parameterized to havea peak in the several hundred TeV region. The neutrino energy-flux is about 10−11
to 10−13 [erg cm−2 sec−1 ] at about 1 TeV and about 10−12 to 10−14 [erg cm−2 sec−1 ]at about 1 GeV. These energy-fluxes are about three to eight orders of magnitude
lower than our limits.

Figure 8.12: Spectral energy distributions and muon neutrino fluxes are shown. The
black points with the error bar reflect the gamma-ray energy-flux observed between
October 2014 and March 2015. The gray points are archival data taken during theyear prior to 2017. The colors represent the results of changing the parameters of
the numerical calculation. On the left, a set of parameters optimized to describe the
gamma-ray spectral energy distribution consistent with observations by IceCube isshown. They fail to explain neutrino emission. On the right, the parameters are set
to account for neutrino flare of IceCube-14/15. They overshoot the multi-wavelength
emission. The figures are taken from Rodrigues et al. [237].
Some models have high neutrino flux in the GeV energy region, which is basedon inverse Compton scattering of soft target photons by highly relativistic electrons

8. LIMIT CALCULATION

148

in the jets [239–242]. In these models, the electron acceleration process must be very
fast to compete eﬃciently with radiation losses at high energies. It is considered,
therefore, that high energy electrons are generated by the interaction of primary
high-energy hadrons.
The AGN jet was modeled by Pohl and Schlickeiser [243] as a plasma consistingof electrons and protons. A typical primary particle is a proton having a Lorentz
factor γ of the order of 100, which is distributed in the jet isotropically, moving
with a bulk Lorentz factor9 , Γ, of the order of 100. The neutrinos produced fromthe decays of pions and subsequent muon decay was calculated by Schuster C. et al.
[244] using the MC model: DTUNUC [245–248].
Of the two calculated examples of resulting proton distributions, the first considers that the radius of the plasma disk, R = 1014 cm, the thickness of thedisk, d = 3 × 1013 cm, the initial Lorentz factor, Γ0 = 300, the plasma density,
nb = 5 × 108 cm−3 , the interstellar medium density, ni = 0.2 cm−3 , and the viewing angle, θ = 0.1◦ . The parameters of second example are R = 2 × 1015 cm,
d = 1014 cm, Γ0 = 300, nb = 108 cm−3 , ni = 1.5 cm−3 , and θ = 2◦ . Figure 8.13
shows two examples of the spectral evolution of total muon-neutrino emissions andgamma-rays created from neutral pions. The diﬀerence between the initial values in
the first and second examples changes the cooling rate of the particles. In the firstexample, the swept-up particles cool down faster than the jet decelerates, whereas
in the second example, the cooling is slow compared with the deceleration of the jet.
In the first example, the neutrino flux has a peak around 103 to 104 GeV. The
highest energy-flux is about 5 × 10−6 GeV cm−2 sec−1 (=8 × 10−9 erg cm−2 sec−1 ),which appears to be above our calculated limit. Therefore, TXS0506+056 might
be a blazar that does not match the parameters of the first example. On the other
hand, in the second example, the peak position is around 101 to 102 GeV, and thehighest energy-flux is about 2 × 10−8 GeV cm−2 sec−1 (=3 × 10−11 erg cm−2 sec−1 ).
The second example flux is predicted to be lower than our calculated limit.
Depending on the theoretical model and the direction of the jet, the neutrinosignal from blazar can possibly be detected by SK. Because the neutrino energy-fluxchanges sensitively depending on the parameters of the AGN jet model, neutrino observations in the GeV to TeV region are important for determining these parameters.
By limiting these parameters, the origin of high-energy CRs and the mechanism ofacceleration of CRs are elucidated.

9

A bulk Lorentz factor is the Lorentz factor of the plasma. The particles in the plasma havetheir own individual velocities.

8. LIMIT CALCULATION

149

Energy [GeV]

E2dN/dE [GeV cm-2 s-1]

Example1 (100hour)

10-3
10-4
10-5
νµ and νµ
10-6γfrom π0
10-7
SK (νµ and νµ )
-8
10
10-9
10-10
10-11
10-12 -2 -1
10 10 1 10 102 103 104 105 106

E2dN/dE [GeV cm-2 s-1]

Example1 (10hour)

10-3
10-4
10-5
10-6
10-7
10-8
νµ and νµ10-9γ from π0
10-10-11
SK (νµ and νµ)1010-12 -2 -1
10 10 1 10 102 103 104 105 106

E2dN/dE [GeV cm-2 s-1]

Example1 (1hour)

10-3
10-4
10-5
10-6
10-7
10-8
νµ and νµ10-9γ from π0
10-10-11
SK (νµ and νµ)1010-12 -2 -1
10 10 1 10 102 103 104 105 106

Energy [GeV]

Energy [GeV]

Energy [GeV]

Energy [GeV]

E2dN/dE [GeV cm-2 s-1]

Example2 (1000hour)

10-3
10-4
10-5
νµ and νµ10-6γ from π0
SK (νµ and νµ )
10-7
10-8
10-9
10-10
10-11
10-12 -2 -1
10 10 1 10 102 103 104 105 106

E2dN/dE [GeV cm-2 s-1]

Example2 (100hour)

10-3
10-4
10-5
νµ and νµ10-6γ from π0
SK (νµ and νµ )
10-7
10-8
10-9
10-10
10-11
10-12 -2 -1
10 10 1 10 102 103 104 105 106

E2dN/dE [GeV cm-2 s-1]

Example2 (10hour)

10-3
10-4
10-5
νµ and νµ10-6γ from π0
SK (νµ and νµ )
10-7
10-8
10-9
10-10
10-11
10-12 -2 -1
10 10 1 10 102 103 104 105 106

Energy [GeV]

Figure 8.13: Time evolution of the muon neutrino emission from the jet of AGN.
The solid line (dashed line) represents the energy-flux of the muon neutrino (gammaray from pion decay). The top figures show the condition of first example, and thebottom figures represent the second example. Those two examples assume that theredshift of the AGN is z = 0.5. The data are taken from Schuster C. et al. [244].
The red line represents the upper limit of energy-flux at SK, as calculated by ourstudy.

A. TABLE OF THE UPPER LIMIT

A

150

Table of the Upper Limit

For the calculation of the upper limit, the energy spectrum was calculated with four
diﬀerent parameter sets. The upper limit when each energy spectrum is used issummarized in a tables. The parameterized equation is expressed as;
dN
∝
dE

(

E
E0

)−α−β log(E/E0 )
.

(A.1)

Table A.1: Parameter1 ; E0 = 1, α = 2.0, β = 0
Energy Range

PC

UPMU

νe +νeνµ +νµνµ +νµνµ +νµ2

E2dFlux/dE[/cm /sec/MeV][erg/cm2 /sec]

1.9 × 104

7.4 × 10−9

6.0 × 10−7

6.9 × 104

2.7 × 10−8

2.2 × 10−6

1.8–101.1 × 105

2.5 × 10−8

7.1 × 10−7

10–100

5.4 × 103

1.2 × 10−10

1.9 × 10−7

1.6–10

6.1 × 105

1.4 × 10−8

3.6 × 10−7

10–100

6.8 × 102

1.5 × 10−11

2.4 × 10−8

100–103

9.4

2.0 × 10−14

3.3 × 10−9

103 –104

2.7 × 10−1

5.8 × 10−17

9.3 × 10−10

5.1–102

dFlux/dE[/cm ][GeV]

FC

FluenceA. TABLE OF THE UPPER LIMIT

151

Table A.2: Parameter2 ; E0 = 1, α = 2.1, β = 0
Energy Range

PC

UPMU

νe +νeνµ +νµνµ +νµνµ +νµ2

E2dFlux/dE[/cm /sec/MeV][erg/cm2 /sec]

1.9 × 104

7.5 × 10−9

6.1 × 10−7

7.0 × 104

2.8 × 10−8

2.2 × 10−6

1.8–101.1 × 105

2.6 × 10−8

7.5 × 10−7

10–100

5.6 × 103

1.2 × 10−10

1.9 × 10−7

1.6–10

6.5 × 104

1.5 × 10−8

3.9 × 10−7

10–100

7.4 × 102

1.6 × 10−11

2.6 × 10−8

100–103

1.0 × 101

2.2 × 10−14

3.5 × 10−9

103 –104

2.8 × 10−1

6.1 × 10−17

9.8 × 10−10

5.1–102

dFlux/dE[/cm ][GeV]

FC

Fluence

Table A.3: Parameter3 ; E0 = 1, α = 2.2, β = 0

FC

PC

UPMU

νe +νeνµ +νµνµ +νµνµ +νµEnergy Range

FluencedFlux/dE

E2dFlux/dE[GeV][/cm2 ][/cm2 /sec/MeV][erg/cm2 /sec]

1.9 × 104

7.6 × 10−9

6.2 × 10−7

7.1 × 104

2.8 × 10−8

2.3 × 10−6

1.8–10

1.2 × 105

2.8 × 10−8

8.0 × 10−7

10–100

5.9 × 103

1.3 × 10−10

2.0 × 10−7

1.6–10

7.0 × 104

1.6 × 10−8

4.2 × 10−7

10–1008.0 × 102

1.7 × 10−11

2.8 × 10−8

100–103

1.1 × 101

2.4 × 10−14

3.8 × 10−9

103 –104

3.0 × 10−1

6.4 × 10−17

1.0 × 10−9

5.1–10A. TABLE OF THE UPPER LIMIT

152

Table A.4: Parameter4 ; E0 = 1440, α = 2.03, β = 0.05
Energy Range

FC

PC

UPMU

νµ +νµνµ +νµνµ +νµ2

E2dFlux/dE[/cm /sec/MeV][erg/cm2 /sec]

1.9 × 104

7.6 × 10−9

6.2 × 10−7

7.1 × 104

2.8 × 10−8

2.3 × 10−6

1.8–101.1 × 105

2.7 × 10−8

7.7 × 10−7

10–100

6.2 × 103

1.3 × 10−10

2.2 × 10−7

1.6–10

6.7 × 104

1.5 × 10−8

4.0 × 10−7

10–1008.9 × 102

1.9 × 10−11

3.1 × 10−8

100–103

1.4 × 101

3.0 × 10−14

4.9 × 10−9

103 –104

4.0 × 10−1

8.6 × 10−17

1.4 × 10−9

5.1–102

dFlux/dE[/cm ][GeV]
νe +νeFluenceB. GAMMA-RAY SPECTRUM FROM GADOLINIUM

B

153

Gamma-ray Spectrum from
Gadolinium

The SK will start new phase, SK-Gd, that dissolves Gd in ultra-pure water. The
natural composition of Gd includes isotopes with the atomic mass numbers A =152,
154-158, and 160. Gd has the largest capture cross-section for thermal neutrons
among all stable elements due to the contributions of the isotopes 155Gd and 157Gd(60,900 b and 254,000 b respectivity) [249]. Natural Gd plays a role in the identification of the electron anti-neutrino interactions by tagging neutrons emitted frominverse beta decay reaction. Modeling of the behavior of gamma rays from Gd forproper simulation was created.
To create a high accurate gamma-ray emission model (ANNRI-Gd model10 [204–206]), the gamma-rays energy spectrum from the thermal neutron capture on an enriched 157Gd and 155Gd targets were measured using the Accurate Neutron-Nucleus
Reaction measurement Instrument (ANNRI) germanium spectrometer [250–254].
The neutron capture reaction is expected to produce about four gamma-rays, whichhave total energy of about 8 MeV.
n + 155Gd → 156Gd∗ → 156Gd + γ rays (8.536 MeV total)
n+

157

Gd →

158

∗

Gd →

158

Gd + γ rays (7.937 MeV total)

(B.1)
(B.2)

Experimental Data
The incident neutron beam from the Japan Spallation Neutron Source (JSNS) at
the Material and Life Science Experimental Facility (MLF) of the Japan Proton
Accelerator Research Complex (J-PARC) [255]. In order to study the gamma-ray
spectrum from thermal neutron capture, the events from neutrons in the kinetic
energy range 4 to 100 meV were selected. The ANNRI spectrometer has two Ge
cluster detectors, one of which consists of seven Ge crystals with a hexagonal front
from the target’s point of view. Two Ge clusters provide a total solid angle coverageof about 15% with respect to the target.
We assigned a multiplicity value M and a hit value H to each recorded event
using the information of 14 Ge crystals. The multiplicity was defined as the combined
number of isolated sub-clusters of hit Ge crystals at the upper and lower clusters.
The hit value describes the total number of Ge crystals hit in the event. Figure B.1
shows that the energy spectra of the experimental results for each multiplicity andhit value.
About 90% of all events are classified as (M =1, H=1) and (M =1, H=2) events,
and the (M =2, H=2) events are about 7% of the total. At low energy, the spectra
are slightly distorted by the eﬀect of Compton scattering.

10

You can see also the homepage of ANNRI-Gd; http://www.physics.okayama-u.ac.jp/~sakuda/ANNRI-Gd_ver1.html, the date of the last access is 29 December 2019

B. GAMMA-RAY SPECTRUM FROM GADOLINIUM

154

Figure B.1: The energy spectrum from 157Gd(n, γ) reaction with diﬀerent multiplicity values, M , and hit values, H, that were observed by the Ge detector No.6 whichis the center of the upper cluster in ANNRI. The figures are taken from Hagiwara
et al. [206].

Simulation Model
The ANNRI-Gd model is composed of two parts; discrete prompt gamma-rays andcontinuum spectrum. The discrete gamma-ray emission in the range from 5 to 8 MeV
is expected to arise mostly from the first transition. Their photo-peak energies andthe relative intensities were estimated from our data. For modeling the continuum
part, the transition probability was computed from the number of transmission
coeﬃcient and level density. The transition probability P (Ea , Eb ) from the initialenergy level Ea to the final energy level Eb , emitting the gamma-ray energy Eγ (=Ea − Eb ), is expressed as follow.
P (Ea , Eb ) = ∫ Ea0ρ(Eb )T (Eγ )ρ(Eb′ )T (Eγ′ ) dEb′

δE,

(B.3)

Eγ′ = Ea − Eb′ ,T (Eγ ) = 2πEγ3 f SLO (Eγ ),∑σi Eγ Γ2i
1SLOf(Eγ ) =,()
3π(ℏc)2 i E 2 − E 2 2 + E 2 Γ2
γ

i

γ i

where δE is a finite energy step in our computation, T (Eγ ) is transmission coeﬃcient,and ρ is the number of level density. The transmission coeﬃcient refers to thephoton strength function, f (Eγ ), depending on cross section (σi ), the width (Γi ),and the energy (Ei ) of the resonances. There are four resonances for 155Gd and two
resonances for 157Gd [256]. Note that we used the simplest model for the photon
strength function named Standard Lorentzian model [257].
For 155Gd, the fraction of the discrete part in the total number of events tobe 2.78 ± 0.02% and remaining part, 97.22 ± 0.02%, contributes to the continuum
part of the gamma-ray spectrum. On the other hand, for 157Gd, the contribution of
discrete part is 6.94 ± 0.01% and continuum part is 93.0 ± 0.01%.

B. GAMMA-RAY SPECTRUM FROM GADOLINIUM

155

Comparison between Data and Model
Figure B.2 shows a comparison between the ANNRI-Gd model and the GLG4Sim
package11 , which is Geant4-based MC developed by KamLAND group. The shape ofthe energy spectrum in our data is significantly better reproduced by our model, themean deviation from the mean ratio is about 17% for the spectrum with 200 keV
binning. Figure B.3 shows the ratio of experimental data divided by ANNRI-Gd
model in bins of 200 keV for 155Gd, 157Gd, and naturalGd. The mean deviation of
the single ratios from the mean ratio is also about 17% for each of spectra.
A more detailed discussion is described in Hagiwara et al. [206].

Figure B.2: Left: The energy spectrum of single gamma-rays (M =1, H=1) from
157
Gd(n, γ) reaction; our measurement data (black), the simulation with ANNRIGd model (red), and the simulation with GLG4Sim package (blue). Right: The
ratio between data and MC per 200 keV of observed energy. The figures are takenfrom Hagiwara et al. [206].

Figure B.3: The Ratio of data by MC for the single gamma-ray (M =1, H=1 and
M =1, H=2) from 155Gd(n, γ), 157Gd(n, γ), and naturalGd(n, γ) reaction.

11

available at https://www.phys.ksu.edu/personal/gahs/GLG4sim/, the date of the last access
is 29 December 2019.

REFERENCES

156

References[1] W. Pauli, “Dear radioactive ladies and gentlemen”, Physics Today, 31N9,
pp.27, (1978).
[2] F. Reines, & C. L. Cowan, “Detection of the Free Neutrino”, Physical Review,92, pp.830, (1953).
[3] F. Reines, & C. L. Cowan, “The Neutrino”, Nature, 178(4531), pp.446, (1956).
[4] G. Danby, J.-M. Gaillard, K. Goulianos, et al., “Observation of High-Energy
Neutrino Reactions and the Existence of Two Kinds of Neutrinos”, PhysicalReview Letters, 9, pp.36, (1962).
[5] K. Kodama, N. Ushida, C. Andreopoulos, et al., (DONUT Collaboration),“Observation of tau neutrino interactions”, Physics Letters B, 504(3), pp.218, (2001).
[6] R. Davis, D. S. Harmer, & K. C. Hoﬀman, “Search for Neutrinos from theSun”, Physical Review Letters, 20, pp.1205, (1968).
[7] B. T. Cleveland, T. Daily, J. Raymond Davis, et al., “Measurement of the
Solar Electron Neutrino Flux with the Homestake Chlorine Detector”, The
Astrophysical Journal, 496(1), pp.505, (1998).
[8] K. S. Hirata, T. Kajita, T. Kifune, et al., “Observation of 8 B solar neutrinosin the Kamiokande-II detector”, Physical Review Letters, 63, pp.16, (1989).
[9] Q. R. Ahmad, R. C. Allen, T. C. Andersen, et al., (SNO Collaboration),“Measurement of the Rate of νe + d → p + p + e − Interactions Produced by
8
B Solar Neutrinos at the Sudbury Neutrino Observatory”, Physical Review
Letters, 87, pp.071301, (2001).
[10] K. Hirata, T. Kajita, M. Koshiba, et al., “Experimental study of the atmospheric neutrino flux”, Physics Letters B, 205(2), pp.416 , (1988).
[11] R. Becker-Szendy, C. B. Bratton, D. Casper, et al., “Electron- and muonneutrino content of the atmospheric flux”, Physical Review D, 46, pp.3720,(1992).
[12] Y. Fukuda, T. Hayakawa, E. Ichihara, et al., (Super Kamiokande Collaboration), “Evidence for Oscillation of Atmospheric Neutrinos”, Physical Review
Letters, 81, pp.1562, (1998).
[13] S. Fukuda, Y. Fukuda, M. Ishitsuka, et al., (Super Kamiokande Collaboration), “Solar 8 B and hep Neutrino Measurements from 1258 Days of SuperKamiokande Data”, Physical Review Letters, 86, pp.5651, (2001).

REFERENCES

157[14] Q. R. Ahmad, R. C. Allen, T. C. Andersen, et al., (SNO Collaboration),“Direct Evidence for Neutrino Flavor Transformation from Neutral-Current
Interactions in the Sudbury Neutrino Observatory”, Physical Review Letters,
89, pp.011301, (2002).
[15] K. Hirata, et al., “Observation of a Neutrino Burst from the Supernova SN
1987a”, Physical Review Letters, 58, pp.1490, (1987).
[16] R. M. Bionta, G. Blewitt, C. B. Bratton, et al., “Observation of a neutrino
burst in coincidence with supernova 1987A in the Large Magellanic Cloud”,
Physical Review Letters, 58, pp.1494, (1987).
[17] E. N. Alekseev, L. N. Alekseeva, V. I. Volchenko, & I. V. Krivosheina, “Possible Detection of a Neutrino Signal on 23 February 1987 at the Baksan Underground Scintillation Telescope of the Institute of Nuclear Research”, JETP
Letters, 45, pp.589, (1987).
[18] K. Scholberg, “Supernova Neutrino Detection”, Annual Review of Nuclear andParticle Science, 62(1), pp.81, (2012).
[19] M. Aartsen, M. Ackermann, J. Adams, et al., (IceCube Collaboration), “Multimessenger observations of a flaring blazar coincident with high-energy neutrino
IceCube-170922A”, Science, 361(eaat1378), (2018).
[20] B. Pontecorvo, “Mesonium and anti-mesonium”, Soviet Physics JETP, 6,
pp.429, (1957).
[21] B. Pontecorvo, “Inverse beta processes and nonconservation of lepton charge”,
Soviet Physics JETP, 7, pp.172, (1958).
[22] Z. Maki, M. Nakagawa, & S. Sakata, “Remarks on the Unified Model of Elementary Particles”, Progress of Theoretical Physics, 28(5), pp.870, (1962).
[23] B. Pontecorvo, “Neutrino Experiments and the Problem of Conservation of
Leptonic Charge”, Soviet Physics JETP, 26, pp.984, (1968).
[24] L. Wolfenstein, “Neutrino oscillations in matter”, Physical Review D, 17,
pp.2369, (1978).
[25] L. Wolfenstein, “Neutrino oscillations and stellar collapse”, Physical Review
D, 20, pp.2634, (1979).
[26] S. P. Mikheyev, & A. Yu. Smirnov, “Resonance Amplification of Oscillationsin Matter and Spectroscopy of Solar Neutrinos”, Soviet Journal of Nuclear
Physics, 42, pp.913, (1985).
[27] K. Abe, Y. Hayato, T. Iida, et al., (Super Kamiokande Collaboration), “Solar
neutrino results in Super-Kamiokande-III”, Physical Review D, 83, pp.052010,(2011).

REFERENCES

158[28] B. Aharmim, S. N. Ahmed, A. E. Anthony, et al., (SNO Collaboration), “Electron energy spectra, fluxes, and day-night asymmetries of 8 B solar neutrinos
from measurements with NaCl dissolved in the heavy-water detector at theSudbury Neutrino Observatory”, Physical Review C, 72, pp.055502, (2005).
[29] S. Abe, T. Ebihara, S. Enomoto, et al., (KamLAND Collaboration), “Precision
Measurement of Neutrino Oscillation Parameters with KamLAND”, PhysicalReview Letters, 100, pp.221803, (2008).
[30] Y. Ashie, J. Hosaka, K. Ishihara, et al., (Super Kamiokande Collaboration),“Evidence for an Oscillatory Signature in Atmospheric Neutrino Oscillations”,
Physical Review Letters, 93, pp.101801, (2004).
[31] M. H. Ahn, E. Aliu, S. Andringa, et al., (K2K Collaboration), “Measurement of neutrino oscillation by the K2K experiment”, Physical Review D, 74,
pp.072003, (2006).
[32] P. Adamson, C. Andreopoulos, R. Armstrong, et al., (MINOS Collaboration),“Measurement of the Neutrino Mass Splitting and Flavor Mixing by MINOS”,
Physical Review Letters, 106, pp.181801, (2011).
[33] K. Abe, J. Adam, H. Aihara, et al., (T2K Collaboration), “Measurement of
Neutrino Oscillation Parameters from Muon Neutrino Disappearance with an
Oﬀ-Axis Beam”, Physical Review Letters, 111, pp.211803, (2013).
[34] F. P. An, A. B. Balantekin, H. R. Band, et al., (Daya Bay Collaboration),“Spectral Measurement of Electron Antineutrino Oscillation Amplitude andFrequency at Daya Bay”, Physical Review Letters, 112, pp.061801, (2014).
[35] J. K. Ahn, S. Chebotaryov, J. H. Choi, et al., (RENO Collaboration), “Observation of Reactor Electron Antineutrinos Disappearance in the RENO Experiment”, Physical Review Letters, 108, pp.191802, (2012).
[36] Y. Abe, C. Aberle, J. C. d. Anjos, et al., (Double Chooz Collaboration),“Reactor ν e disappearance in the Double Chooz experiment”, Physical Review
D, 86, pp.052008, (2012).
[37] K. Abe, J. Adam, H. Aihara, et al., (T2K Collaboration), “Observation ofElectron Neutrino Appearance in a Muon Neutrino Beam”, Physical Review
Letters, 112, pp.061802, (2014).
[38] K. Abe, J. Amey, C. Andreopoulos, et al., (T2K Collaboration), “Combined
Analysis of Neutrino and Antineutrino Oscillations at T2K”, Physical Review
Letters, 118, pp.151801, (2017).
[39] P. Adamson, L. Aliaga, D. Ambrose, et al., (NOvA Collaboration), “Constraints on Oscillation Parameters from νe Appearance and νµ Disappearancein NOvA”, Physical Review Letters, 118, pp.231801, (2017).

REFERENCES

159[40] F. Capozzi, E. Lisi, A. Marrone, D. Montanino, & A. Palazzo, “Neutrino
masses and mixings: Status of known and unknown 3 ν parameters”, Nuclear
Physics B, 908, pp.218 , (2016).
[41] A. D. Panov, “Electrons and Positrons in Cosmic Rays”, Journal of Physics:
Conference Series, 409, pp.012004, (2013).
[42] K. Greisen, “End to the Cosmic-Ray Spectrum?”, Physical Review Letters,
16, pp.748, (1966).
[43] G. T. Zatsepin, & V. A. Kuz’min, “Upper Limit of the Spectrum of Cosmic
Rays”, Soviet Journal of Experimental and Theoretical Physics Letters, 4,
pp.78, (1966).
[44] C. Patrignani, et al., (Particle Data Group), “Review of Particle Physics”,
Chinese Physics C, 40(10), pp.100001, (2016).
[45] L. I. MIROSHNICHENKO, & J. A. PEREZ-PERAZA, “ASTROPHYSICALASPECTS IN THE STUDIES OF SOLAR COSMIC RAYS”, International
Journal of Modern Physics A, 23(01), pp.1, (2008).
[46] E. Fermi, “On the Origin of the Cosmic Radiation”, Physical Review, 75,
pp.1169, (1949).
[47] A. M. Hillas, “The Origin of Ultra-High-Energy Cosmic Rays”, Annual Reviewof Astronomy and Astrophysics, 22(1), pp.425, (1984).
[48] D. J. Mortlock, S. J. Warren, B. P. Venemans, et al., “A luminous quasar at
a redshift of z = 7.085”, Nature, 474(7353), pp.616, (2011).
[49] C. M. Urry, & P. Padovani, “Unified Schemes for Radio-Loud Active Galactic
Nuclei”, Publications of the Astronomical Society of the Pacific, 107, pp.803,(1995).
[50] P. Padovani, & P. Giommi, “The Connection between X-Ray– and Radioselected BL Lacertae Objects”, The Astrophysical Journal, 444, pp.567,(1995).
[51] A. A. Abdo, M. Ackermann, I. Agudo, et al., “The Spectral Energy Distribution of Fermi Bright Blazars”, The Astrophysical Journal, 716(1), pp.30,(2010).
[52] S.-S. Lee, K. Wajima, J.-C. Algaba, et al., “Interferometric Monitoring ofGamma-Ray Bright AGNs. I. The Results of Single-epoch Multifrequency Observations”, The Astrophysical Journal, 227(1):8, (2016).
[53] A. A. Abdo, M. Ackermann, M. Ajello, et al., “Fermi Large Area Telescope
Observations of Markarian 421: The Missing Piece of its Spectral Energy
Distribution”, The Astrophysical Journal, 736(2):131, (2011).

REFERENCES

160[54] A. Franceschini, G. Rodighiero, & M. Vaccari, “Extragalactic optical-infrared
background radiation, its time evolution and the cosmic photon-photon opacity”, Astronomy & Astrophysics, 487(3), pp.837, (2008).
[55] M. Aartsen, M. Ackermann, J. Adams, et al., (IceCube Collaboration), “The
IceCube Neutrino Observatory: instrumentation and online systems”, Journalof Instrumentation, 12(03), pp.P03012, (2017).
[56] M. Aartsen, M. Ackermann, J. Adams, et al., (IceCube Collaboration), “Neutrino emission from the direction of the blazar TXS 0506+056 prior to the
IceCube-170922A alert”, Science, 361(6398), pp.147, (2018).
[57] S. Paiano, R. Falomo, A. Treves, & R. Scarpa, “The Redshift of the BL Lac
Object TXS 0506+056”, The Astrophysical Journal, 854(2), pp.L32, (2018).
[58] E. Massaro, A. Maselli, C. Leto, et al., “The 5th edition of the Roma-BZCAT.
A short presentation”, Astrophysics and Space Science, 357(1), pp.75, (2015).
[59] S. Abdollahi, M. Ackermann, M. Ajello, et al., “The Second Catalog of Flaring Gamma-Ray Sources from the Fermi All-sky Variability Analysis”, The
Astrophysical Journal, 846(1), pp.34, (2017).
[60] Y. T. Tanaka, S. Buson, & D. Kocevski, “Fermi-LAT detection of increased
gamma-ray activity of TXS 0506+056, located inside the IceCube-170922A
error region.”, The Astronomer’s Telegram, 10791, (2017).
[61] J. Chiang, J. Carson, & W. Focke, “Automated Science Processing for GLASTLAT Data”, Proceedings of the AIP Conference, 921, pp.544, (2007).
[62] S. Fukuda, Y. Fukuda, T. Hayakawa, et al., (Super Kamiokande Collaboration), “The Super-Kamiokande detector”, Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 501(2), pp.418 , (2003).
[63] K. Abe, N. Abgrall, H. Aihara, et al., (T2K Collaboration), “The T2K experiment”, Nuclear Instruments and Methods in Physics Research Section
A: Accelerators, Spectrometers, Detectors and Associated Equipment, 659(1),pp.106 , (2011).
[64] P. A. Cherenkov, “Visible luminescence of pure liquids under the influence ofγ-radiation”, Doklady Akademii Nauk SSSR, 2(8), pp.451, (1934).
[65] I. M. Frank, & I. E. Tamm, “Coherent visible radiation of fast electrons passing
through matter”, Physical Institute of the Academy of Sciences of the USSR
Moscow, 14(3), pp.109, (1937).
[66] J. Jackson, “Classical Electrodynamics”. John Wiley & Sons Inc., ISBN 9780-471-30932-1, (1990).

REFERENCES

161[67] M. Koshiba, “KAMIOKA nucleon decay experiment”, Il Nuovo Cimento C, 9(2), pp.141, (1986).
[68] Y. Fukuda, T. Hayakawa, E. Ichihara, et al., (Super Kamiokande Collaboration), “Evidence for Oscillation of Atmospheric Neutrinos”, Physical Review
Letters, 81(8), pp.1562, (1998).
[69] M. H. Ahn, S. Aoki, H. Bhang, et al., “Indications of Neutrino Oscillation in a
250 km Long-Baseline Experiment”, Physical Review Letters, 90, pp.041801,(2003).
[70] E. Aliu, S. Andringa, S. Aoki, et al., “Evidence for Muon Neutrino Oscillationin an Accelerator-Based Experiment”, Physical Review Letters, 94, pp.081802,(2005).
[71] J. F. Beacom, & M. R. Vagins, “Antineutrino Spectroscopy with Large Water
Čerenkov Detectors”, Physical Review Letters, 93(17), (2004).
[72] H. Kume, S. Sawaki, M. Ito, et al., “20 inch diameter photomultiplier”, Nuclear
Instruments and Methods in Physics Research, 205(3), pp.443 , (1983).
[73] A. Suzuki, M. Mori, K. Kaneyuki, et al., “Improvement of 20 in. diameterphotomultiplier tubes”, Nuclear Instruments and Methods in Physics Research
Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,
329(1), pp.299 , (1993).
[74] S. Desai, “High energy neutrino astrophysics with Super-Kamiokande”, PhD
thesis, Boston University, (2004). URL http://lss.fnal.gov/cgi-bin/find_paper.pl?other/thesis/desai-s.pdf.
[75] R. Becker-Szendy, R. Bionta, C. Bratton, et al., “IMB-3: a large water
Cherenkov detector for nucleon decay and neutrino interactions”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 324(1), pp.363 , (1993).
[76] Z. Conner, “A Study of Solar Neutrinos Using the Super-Kamiokande Detector”, PhD thesis, University of Maryland, (1997). URL http://www-sk.
icrr.u-tokyo.ac.jp/doc/sk/pub/icrc97.pdf.
[77] T. Tanimori, H. Ikeda, M. Mori, et al., “Design and performance of semicustom analog IC including two TACs and two current integrators for “SuperKamiokande””, IEEE Transactions on Nuclear Science, 36(1), pp.497, (1989).
[78] H. Ikeda, M. Mori, T. Tanimori, et al., “Front-end hybrid circuit for superKAMIOKANDE”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 320(1), pp.310 , (1992).

REFERENCES

162[79] S. Yamada, K. Awai, Y. Hayato, et al., “Commissioning of the new electronics
and online system for the Super-Kamiokande experiment”, IEEE Transactions
on Nuclear Science, 57(2 PART 1), pp.428, (2010).
[80] Y. Koshio, “Study of Solar Neutrinos at Super-Kamiokande”, PhD thesis,
University of Tokyo, (1998). URL http://www-sk.icrr.u-tokyo.ac.jp/~koshio/dthesis.html.
[81] K. Nitta, “Neutrino oscillation analysis of upward through-going and stoppingmuons in Super-Kamiokande”, PhD thesis, Osaka University, (2003). URL
http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.html#dthesis.
[82] A. L. Stachyra, “A Search for astrophysical point sources of neutrinos with
Super-Kamiokande”, PhD thesis, University of Washington, (2002). URL
https://search.proquest.com/docview/305496752.
[83] H. Nishino, K. Awai, Y. Hayato, et al., “Development of New Front-End
Electronics for Super-Kamiokande”, Proceedings of the 15th IEEE-NPSS RealTime Conference, (2007).
[84] H. Nishino, K. Awai, Y. Hayato, et al., (Super Kamiokande Collaboration),“High-speed charge-to-time converter ASIC for the Super-Kamiokande detector”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 610(3), pp.710 ,(2009).
[85] M. Honda, T. Kajita, K. Kasahara, & S. Midorikawa, “Calculation of the fluxof atmospheric neutrinos”, Physical Review D, 52, pp.4985, (1995).
[86] M. Honda, T. Kajita, K. Kasahara, & S. Midorikawa, “Comparison of 3dimensional and 1-dimensional schemes in the calculation of atmospheric neutrinos”, Physical Review D, 64, pp.053011, (2001).
[87] M. Honda, T. Kajita, K. Kasahara, & S. Midorikawa, “New calculation of theatmospheric neutrino flux in a three-dimensional scheme”, Physical Review D,
70, pp.043008, (2004).
[88] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, & T. Sanuki, “Calculation of atmospheric neutrino flux using the interaction model calibrated withatmospheric muon data”, Physical Review D, 75, pp.043006, (2007).
[89] M. Honda, T. Kajita, K. Kasahara, & S. Midorikawa, “Improvement of low energy atmospheric neutrino flux calculation using the JAM nuclear interaction
model”, Physical Review D, 83, pp.123001, (2011).
[90] T. Sanuki, M. Motoki, H. Matsumoto, et al., (BESS Collaboration), “Precise
Measurement of Cosmic‐ Ray Proton and Helium Spectra with the BESS
Spectrometer”, The Astrophysical Journal, 545(2), pp.1135, (2000).

REFERENCES

163[91] S. Haino, T. Sanuki, K. Abe, et al., (BESS Collaboration), “Measurements ofprimary and atmospheric cosmic-ray spectra with the BESS-TeV spectrometer”, Physics Letters B, 594(1), pp.35 , (2004).
[92] J. Alcaraz, B. Alpat, G. Ambrosi, et al., (AMS Collaboration), “Cosmic protons”, Physics Letters B, 490(1), pp.27 , (2000).
[93] T. K. Gaisser, M. Honda, P. Lipari, & T. Stanev, “Primary spectrum to 1 TeV
and beyond”, Proceedings of the 27th International Cosmic Ray Conference,
5, pp.1643, (2001).
[94] T. K. Gaisser, & M. Honda, “FLUX OF ATMOSPHERIC NEUTRINOS”,
Annual Review of Nuclear and Particle Science, 52(1), pp.153, (2002).
[95] W. R. Webber, R. L. Golden, & S. A. Stephens, “Cosmic ray proton and helium
spectra from 5 - 200 GV measured with a magnetic spectrometer.”, Proceedingsof the 20th International Cosmic Ray Conference, 1, pp.325, (1987).
[96] P. Papini, C. Grimani, G. Basini, et al., (MASS Collaboration), “Observationsof Proton and Helium Spectra Near Solar Maximum”, Proceedings of the 23rd
International Cosmic Ray Conference, 1, pp.579, (1993).
[97] E. S. Seo, J. F. Ormes, R. E. Streitmatter, et al., (LEAP Collaboration),“Measurement of cosmic-ray proton and helium spectra during the 1987 solar
minimum”, The Astrophysical Journal, 378, pp.763, (1991).
[98] W. Menn, M. Hof, O. Reimer, et al., (IMAX Collaboration), “The Absolute
Flux of Protons and Helium at the Top of the Atmosphere Using IMAX”, The
Astrophysical Journal, 533(1), pp.281, (2000).
[99] M. Boezio, P. Carlson, T. Francke, et al., (CAPRICE Collaboration), “TheCosmic‐ Ray Proton and Helium Spectra between 0.4 and 200 GV”, The
Astrophysical Journal, 518(1), pp.457, (1999).
[100] M. J. Ryan, J. F. Ormes, & V. K. Balasubrahmanyan, “Cosmic-Ray Protonand Helium Spectra above 50 GeV”, Physical Review Letters, 28, pp.985,(1972).
[101] K. Asakimori, T. H. Burnett, M. L. Cherry, et al., (JACEE Collaboration),“Cosmic‐ Ray Proton and Helium Spectra: Results from the JACEE Experiment”, The Astrophysical Journal, 502(1), pp.278, (1998).
[102] A. Apanasenko, V. Sukhadolskaya, V. Derbina, et al., (RUNJOB Collaboration), “Composition and energy spectra of cosmic-ray primaries in the energy
range 1013–1015 eV/particle observed by Japanese–Russian joint balloon experiment”, Astroparticle Physics, 16(1), pp.13 , (2001).
[103] I. P. Ivanenko, L. A. Khein, D. M. Podoroznyi, et al., “Apparatus ’AYAKS’for Study of Cosmic Rays Nuclei at Energies 0.1 - 500 TeV”, Proceedings ofthe 23rd International Cosmic Ray Conference, 2, pp.484, (1993).

REFERENCES

164[104] Y. Kawamura, H. Matsutani, H. Nanjyo, et al., “Quasidirect observations ofcosmic-ray primaries in the energy region 1012 -1014 eV”, Physical Review D,
40, pp.729, (1989).
[105] T. Mclachlan Fukuei, “Study of the Oscillation of Neutrinos and AntiNeutrinos and of Non-Standard Neutrino Interactions with the Atmospheric
Data in Super-Kamiokande”, PhD thesis, University of Tokyo, (201504-01).
URL http://www-sk.icrr.u-tokyo.ac.jp/sk/publications/index-e.html.
[106] Y. Nara, N. Otuka, A. Ohnishi, K. Niita, & S. Chiba, “Relativistic nuclear
collisions at 10A GeV energies from p + Be to Au+Au with the hadronic
cascade model”, Physical Review C, 61, pp.024901, (1999).
[107] S. Roesler, R. Engel, & J. Ranft, “The Monte Carlo Event Generator
DPMJET-III”, Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, pages 1033–1038, (2001).
[108] K. Niita, T. Sato, H. Iwase, et al., “PHITS—a particle and heavy ion transport
code system”, Radiation Measurements, 41(9), pp.1080 , (2006).
[109] A. Capella, U. Sukhatme, C.-I. Tan, & J. T. T. Van, “Dual parton model”,
Physics Reports, 236(4), pp.225 , (1994).
[110] M. Catanesi, E. Radicioni, R. Edgecock, et al., (HARP Collaboration), “Measurement of the production cross-sections of π ± in p–C and π ±–C interactions at 12GeV/c”, Astroparticle Physics, 29(4), pp.257 , (2008).
[111] M. Catanesi, E. Radicioni, R. Edgecock, et al., (HARP Collaboration), “Forward π ± production in p–O2 and p–N2 interactions at 12GeV/c”, Astroparticle Physics, 30(3), pp.124 , (2008).
[112] T. Sanuki, M. Fujikawa, K. Abe, et al., (BESS Collaboration), “Measurements
of atmospheric muon spectra at mountain altitude”, Physics Letters B, 541(3-4), pp.234, (2002).
[113] P. Achard, O. Adriani, M. Aguilar-Benitez, et al., (L3 Collaboration), “Measurement of the atmospheric muon spectrum from 20 to 3000 GeV”, Physics
Letters B, 598(1-2), pp.15, (2004).
[114] O. Allkofer, G. Bella, W. Dau, et al., “Cosmic ray muon spectra at sea-levelup to 10 TeV”, Nuclear Physics B, 259(1), pp.1 , (1985).
[115] S. Matsuno, F. Kajino, Y. Kawashima, et al., “Cosmic-ray muon spectrum up
to 20 TeV at 89◦ zenith angle”, Physical Review D, 29, pp.1, (1984).
[116] T. Sanuki, M. Honda, T. Kajita, K. Kasahara, & S. Midorikawa, “Study ofcosmic ray interaction model based on atmospheric muons for the neutrino
flux calculation”, Physical Review D, 75, pp.043005, (2007).

REFERENCES

165[117] K. Kasahara, “Introduction to Cosmos and some Relevance to Ultra High Energy Cosmic Ray Air Showers”, Proceedings of the 24th International Cosmic
Ray Conference, 1, pp.399, (1995).
[118] G. Battistoni, A. Ferrari, T. Montaruli, & P. Sala, “The FLUKA atmospheric
neutrino flux calculation”, Astroparticle Physics, 19(2), pp.269 , (2003).
[119] G. D. Barr, T. K. Gaisser, P. Lipari, S. Robbins, & T. Stanev, “Threedimensional calculation of atmospheric neutrinos”, Physical Review D, 70,
pp.023006, (2004).
[120] Y. Hayato, “Neut”, Nuclear Physics B Proceedings Supplements, 112, pp.171,(2002).
[121] Y. Hayato, “A neutrino interaction simulation program library NEUT”, Acta
Physica Polonica B, 40, pp.2477, (2009).
[122] S. Jadach, Z. Was, R. Decker, & J. Kuhn, “The τ decay library TAUOLA,
version 2.4”, Computer Physics Communications, 76(3), pp.361 , (1993).
[123] C. H. Llewellyn Smith, “Neutrino reactions at accelerator energies”, Physics
Reports, 3, pp.261, (1972).
[124] R. Gran, E. J. Jeon, E. Aliu, et al., (K2K Collaboration), “Measurement of
the quasielastic axial vector mass in neutrino interactions on oxygen”, PhysicalReview D, 74, pp.052002, (2006).
[125] A. A. Aguilar-Arevalo, A. O. Bazarko, S. J. Brice, et al., (MiniBooNE Collaboration), “Measurement of Muon Neutrino Quasielastic Scattering on Carbon”,
Physical Review Letters, 100, pp.032301, (2008).
[126] J. Reich, H. Abele, M. A. Hoﬀmann, et al., “A measurement of the beta
asymmetry in neutron decay with PERKEO II”, Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors
and Associated Equipment, 440, pp.535, (2000).
[127] H. Abele, “The standard model and the neutron beta-decay”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 440, pp.499, (2000).
[128] D. Groom, M. Aguilar-Benitez, C. Amsler, et al., “Review of particle physics”,
European Physical Journal C, 15(1-4), pp.1, (2000).
[129] P. E. Bosted, “Empirical fit to the nucleon electromagnetic form factors”,
Physical Review C, 51, pp.409, (1995).
[130] E. J. Brash, A. Kozlov, S. Li, & G. M. Huber, “New empirical fits to the proton
electromagnetic form factors”, Physical Review C, 65, pp.051001, (2002).

REFERENCES

166[131] A. Bodek, S. Avvakumov, R. Bradford, & H. S. Budd, “Modeling Atmospheric
Neutrino Interactions: Duality Constrained Parameterization of Vector andAxial Nucleon Form Factors”, Proceedings of the 30th International Cosmic
Ray Conference, (2007).
[132] G. Mitsuka, “Study of Non-Standard Neutrino Interactions with Atmospheric Neutr ino Data in Super-Kamiokande”, PhD thesis, Universityof Tokyo, (2009).
URL http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/dthesis_feb9-mitsuka.pdf.
[133] R. Smith, & E. Moniz, “Neutrino reactions on nuclear targets”, Nuclear
Physics B, 43, pp.605 , (1972).
[134] J. Nieves, J. E. Amaro, & M. Valverde, “Inclusive quasielastic charged-current
neutrino-nucleus reactions”, Physical Review C, 70, pp.055503, (2004).
[135] H. Nakamura, & R. Seki, “Quasi-elastic neutrino-nucleus scattering and spectral function”, Nuclear Physics B Proceedings Supplements, 112(1), pp.197 ,(2002).
[136] S. J. Barish, J. Campbell, G. Charlton, et al., “Study of neutrino interactions
in hydrogen and deuterium: Description of the experiment and study of thereaction ν + d → µ− + p + ps ”, Physical Review D, 16, pp.3103, (1977).
[137] A. I. Mukhin, V. F. Perelygin, K. E. Shestermanov, et al., “Energy Dependenceof Total Cross-sections for Neutrino and Anti-neutrino Interactions at Energies
Below 35-GeV”, Soviet Journal of Nuclear Physics, 30, pp.528, (1979).
[138] S. Bonetti, G. Carnesecchi, D. Cavalli, et al., “Study of Quasielastic Reactions of Neutrino and anti-neutrino in Gargamelle”, Il Nuovo Cimento A, 38,
pp.260, (1977).
[139] M. Pohl, M. Dewit, D. Haidt, et al., “Experimental study of the reaction Ν n→ Μ-p”, Lettere Al Nuovo Cimento Series 2, 26(11), pp.332, (1979).
[140] N. Armenise, et al., “CHARGED CURRENT ELASTIC ANTI-NEUTRINOINTERACTIONS IN PROPANE”, Nuclear Physics B, 152, pp.365, (1979).
[141] S. V. Belikov, A. P. Bygorsky, L. A. Klimenko, et al., “Quasielastic neutrino
and antineutrino scattering total cross-sections, axial-vector form-factor”,
Zeitschrift für Physik A Atoms and Nuclei, 320(4), pp.625, (1985).
[142] J. Brunner, et al., (SKAT Collaboration), “Quasielastic Nucleon and Hyperon
Production by Neutrinos and Anti-neutrinos With Energies Below 30-GeV”,
Zeitschrift für Physik C Particles and Fields, 45, pp.551, (1990).
[143] C. H. Albright, C. Quigg, R. E. Shrock, & J. Smith, “Neutrino - Proton Elastic
Scattering: Implications for Weak Interaction Models”, Physical Review D, 14,
pp.1780, (1976).

REFERENCES

167[144] K. Abe, L. A. Ahrens, K. Amako, et al., “Precise Determination of sin2 θWfrom Measurements of the Diﬀerential Cross Sections for νµ p → νµ p and ν µ p →ν µ p”, Physical Review Letters, 56, pp.1107, (1986).
[145] A. A. Aguilar-Arevalo, C. E. Anderson, A. O. Bazarko, et al., (MiniBooNE Collaboration), “First measurement of the muon neutrino charged
current quasielastic double diﬀerential cross section”, Physical Review D, 81,
pp.092005, (2010).
[146] J. Nieves, I. R. Simo, & M. J. V. Vacas, “Inclusive charged-current neutrinonucleus reactions”, Physical Review C, 83, pp.045501, (2011).
[147] D. Rein, & L. M. Sehgal, “Neutrino Excitation of Baryon Resonances andSingle Pion Production”, Annals of Physics, 133, pp.79, (1981).
[148] D. Rein, “Angular distribution in neutrino-induced single pion production
processes”, Zeitschrift für Physik C Particles and Fields, 35(1), pp.43, (1987).
[149] R. P. Feynman, M. Kislinger, & F. Ravndal, “Current Matrix Elements froma Relativistic Quark Model”, Physical Review D, 3, pp.2706, (1971).
[150] G. Breit, & E. Wigner, “Capture of Slow Neutrons”, Physical Review, 49,
pp.519, (1936).
[151] K. S. Kuzmin, V. V. Lyubushkin, & V. A. Naumov, “Lepton polarization in
neutrino nucleon interactions”, Modern Physics Letters A, 19, pp.2815, (2004).
[152] C. Berger, & L. M. Sehgal, “Lepton mass eﬀects in single pion production by
neutrinos”, Physical Review D, 76, pp.113004, (2007).
[153] M. Glück, E. Reya, & A. Vogt, “Dynamical parton distributions revisited”,
The European Physical Journal C, 5(3), pp.461, (1998).
[154] A. Bodek, & U. K. Yang, “Modeling neutrino and electron scattering inelastic
cross- sections in the few GeV region with eﬀective LO PDFs TV Leading
Order”, Proceedings of the 2nd International Workshop on Neutrino-Nucleus
Interactions in the Few GeV Region, (2003).
[155] P. Musset, & J.-P. Vialle, “Neutrino physics with gargamelle”, Physics Reports, 39(1), pp.1 , (1978).
[156] J. E. Kim, P. Langacker, M. Levine, & H. H. Williams, “A theoretical andexperimental review of the weak neutral current: a determination of its structure and limits on deviations from the minimal SU(2)L × U(1) electroweak
theory”, Reviews of Modern Physics, 53, pp.211, (1981).
[157] M. Derrick, P. Gregory, L. G. Hyman, et al., “Properties of the hadronicsystem resulting from ν µ p interactions”, Physical Review D, 17, pp.1, (1978).
[158] Z. Koba, H. Nielsen, & P. Olesen, “Scaling of multiplicity distributions in highenergy hadron collisions”, Nuclear Physics B, 40, pp.317 , (1972).

REFERENCES

168[159] S. Barlag, P. Dam, E. Wolf, et al., “Charged hadron multiplicities in highenergy ν̄µ n and ν̄µ p interactions”, Zeitschrift für Physik C Particles and Fields,
11(4), pp.283, (1982).
[160] T. Sjostrand, “PYTHIA 5.7 and JETSET 7.4: Physics and manual”, CERN
Program Library Long writeups, (1994).
[161] P. S. Auchincloss, R. Blair, C. Haber, et al., “Measurement of the inclusive charged-current cross section for neutrino and antineutrino scattering
on isoscalar nucleons”, Zeitschrift für Physik C Particles and Fields, 48(3),pp.411, (1990).
[162] P. Berge, A. Blondel, P. Böckmann, et al., “Total neutrino and antineutrino
charged current cross section measurements in 100, 160, and 200 GeV narrow
band beams”, Zeitschrift für Physik C Particles and Fields, 35(4), pp.443,(1987).
[163] S. Ciampolillo, B. Degrange, M. Dewit, et al., “Total cross section for neutrino
charged current interactions at 3 GeV and 9 GeV”, Physics Letters B, 84(2),pp.281 , (1979).
[164] J. V. Allaby, U. Amaldi, G. Barbiellini, et al., “Total cross sections of chargedcurrent neutrino and antineutrino interactions on isoscalar nuclei”, Zeitschriftfür Physik C Particles and Fields, 38(3), pp.403, (1988).
[165] N. J. Baker, P. L. Connolly, S. A. Kahn, et al., “Total cross sections for νµ nand νµ p charged-current interactions in the 7-foot bubble chamber”, PhysicalReview D, 25, pp.617, (1982).
[166] C. Baltay, H. French, M. Hibbs, et al., “Cross Sections and Scaling-Variable
Distributions of Neutral- and Charged- Current Neutrino-Nucleon Interactions
from a Low-Energy Narrow Band Beam”, Physical Review Letters, 44, pp.916,(1980).
[167] D. C. Colley, G. T. Jones, S. O’Neale, et al., “Cross sections for charged current
ν and ν̄ interactions in the energy range 10 to 50 GeV”, Zeitschrift für Physik
C Particles and Fields, 2(3), pp.187, (1979).
[168] V. B. Anikeev, S. V. Belikov, A. A. Borisov, et al., “Total cross section measurements for νm u , ν̄µ charged current interactions in 3–30 GeV energy range
with IHEP-JINR neutrino detectorcharged current interactions in 3–30 GeV
energy range with IHEP-JINR neutrino detector”, Zeitschrift für Physik C:
Particles and Fields, 70(1), pp.39, (1996).
[169] D. B. MacFarlane, M. V. Purohit, R. L. Messner, et al., “Nucleon structure
functions from high energy neutrino interactions with iron and QCD results”,
Zeitschrift für Physik C Particles and Fields, 26(1), pp.1, (1984).

REFERENCES

169[170] D. Baranov, A. Bugorsky, A. Ivanilov, et al., “Measurement of the νμ N total
cross section at 2–30 GeV in a skat neutrino experiment”, Physics Letters B,
81(2), pp.255 , (1979).
[171] D. Rein, & L. M. Sehgal, “Coherent π 0 production in neutrino reactions”,
Nuclear Physics B, 223(1), pp.29 , (1983).
[172] M. Hasegawa, E. Aliu, S. Andringa, et al., (K2K Collaboration), “Search for
Coherent Charged Pion Production in Neutrino-Carbon Interactions”, Physical Review Letters, 95, pp.252301, (2005).
[173] D. Rein, & L. Sehgal, “PCAC and the deficit of forward muons in π+ production by neutrinos”, Physics Letters B, 657(4), pp.207 , (2007).
[174] A. Kartavtsev, E. A. Paschos, & G. J. Gounaris, “Coherent pion production
by neutrino scattering oﬀ nuclei”, Physical Review D, 74, pp.054007, (2006).
[175] L. Alvarez-Ruso, L. S. Geng, S. Hirenzaki, & M. J. V. Vacas, “Charged
current neutrino-induced coherent pion production”, Physical Review C, 75,
pp.055501, (2007).
[176] K. Hiraide, J. L. Alcaraz-Aunion, S. J. Brice, et al., (SciBooNE Collaboration),“Search for charged current coherent pion production on carbon in a few-GeV
neutrino beam”, Physical Review D, 78, pp.112004, (2008).
[177] J. L. Raaf, “A Measurement of the Neutrino Neutral Current Pi0 Cross Section
at MiniBooNE”, PhD thesis, University of Cincinnati, (2005). URL http://lss.fnal.gov/cgi-bin/find_paper.pl?thesis-2005-20.
[178] H. Faissner, E. Frenzel, M. Grimm, et al., “Observation of neutrino and antineutrino induced coherent neutral pion production oﬀ Al27”, Physics Letters
B, 125(2), pp.230 , (1983).
[179] E. Isiksal, D. Rein, & J. G. Morfı́n, “Evidence for Neutrino- and AntineutrinoInduced Coherent π 0 Production”, Physical Review Letters, 52, pp.1096,(1984).
[180] R. D. Woods, & D. S. Saxon, “Diﬀuse Surface Optical Model for NucleonNuclei Scattering”, Physical Review, 95, pp.577, (1954).
[181] C. D. Jager, H. D. Vries, & C. D. Vries, “Nuclear charge- and magnetizationdensity-distribution parameters from elastic electron scattering”, Atomic Data
and Nuclear Data Tables, 14(5), pp.479 , (1974).
[182] L. Salcedo, E. Oset, M. Vicente-Vacas, & C. Garcia-Recio, “Computer simulation of inclusive pion nuclear reactions”, Nuclear Physics A, 484(3), pp.557, (1988).
[183] G. Rowe, M. Salomon, & R. H. Landau, “Energy-dependent phase shift analysis of pion-nucleon scattering below 400 MeV”, Physical Review C, 18, pp.584,(1978).

REFERENCES

170[184] R. Seki, & K. Masutani, “Unified analysis of pionic atoms and low-energy
pion-nucleus scattering: Phenomenological analysis”, Physical Review C, 27,
pp.2799, (1983).
[185] D. Ashery, I. Navon, G. Azuelos, et al., “True absorption and scattering ofpions on nuclei”, Physical Review C, 23, pp.2173, (1981).
[186] C. H. Q. Ingram, P. A. M. Gram, J. Jansen, et al., “Quasielastic scattering ofpions from 16 O at energies around the ∆(1232) resonance”, Physical Review
C, 27, pp.1578, (1983).
[187] B. Martin, & M. Pidcock, “KN interactions in the resonance region: (I). Analysis of data”, Nuclear Physics B, 126(2), pp.266 , (1977).
[188] B. Martin, & M. Pidcock, “KN interactions in the resonance region: (II).
Amplitudes”, Nuclear Physics B, 126(2), pp.285 , (1977).
[189] J. S. Hyslop, R. A. Arndt, L. D. Roper, & R. L. Workman, “Partial-wave
analysis of K + -nucleon scattering”, Physical Review D, 46, pp.961, (1992).
[190] D. A. Sparrow, “Eﬀects of the nuclear medium on the observation of baryon
number violation”, Proceedings of the AIP Conference, (1984).
[191] H. W. Bertini, “Nonelastic Interactions of Nucleons and π Mesons with Complex Nuclei at Energies Below 3 GeV”, Physical Review C, 6, pp.631, (1972).
[192] S. J. Lindenbaum, & R. M. Sternheimer, “Isobaric Nucleon Model for Pion
Production in Nucleon-Nucleon Collisions”, Physical Review, 105, pp.1874,(1957).
[193] R. Brun, F. Bruyant, M. Maire, A. C. McPherson, & P. Zanarini, “GEANT
3: user’s guide Geant 3.10, Geant 3.11; rev. version”. CERN, Geneva, (1987).
[194] R. Brun, F. Bruyant, F. Carminati, et al., “GEANT Detector Description and
Simulation Tool”, CERN Program Library, (1993).
[195] C. Zeitnitz, & T. Gabriel, “The GEANT-CALOR interface and benchmark
calculations of ZEUS test calorimeters”, Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment, 349(1), pp.106 , (1994).
[196] M. Nakahata, K. Arisaka, T. Kajita, et al., “Atmospheric Neutrino Background and Pion Nuclear Eﬀect for KAMIOKA Nucleon Decay Experiment”,
Journal of the Physical Society of Japan, 55(11), pp.3786, (1986).
[197] E. Bracci, J. P. Droulez, V. Flaminio, J. D. Hansen, & D. R. O. Morrison,“Compilation of cross-sections”, CERN-HERA-72-01, (1972).
[198] A. S. Carroll, I. H. Chiang, C. B. Dover, et al., “Pion-nucleus total crosssections in the (3,3) resonance region”, Physical Review C, 14, pp.635, (1976).

REFERENCES

171[199] S. Agostinelli, J. Allison, K. Amako, et al., “Geant4—a simulation toolkit”,
Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 506(3), pp.250 , (2003).
[200] J. Allison, K. Amako, J. Apostolakis, et al., “Geant4 developments and applications”, IEEE Transactions on Nuclear Science, 53(1), pp.270, (2006).
[201] J. Allison, K. Amako, J. Apostolakis, et al., “Recent developments in Geant4”,
Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 835, pp.186 , (2016).
[202] M. Harada, Y. Koshio, & K. Hagiwara, “Development of Geant4 based simulation for Super-Kamiokande”, Proceedings of The 4th KMI International
Symposium, (2019).
[203] M. Harada, “Development of Super-Kamiokande detector simulation based on
Geant4”, Proceedings of the 36th International Cosmic Ray Conference, 1,(2019).
[204] P. K. Das, K. Hagiwara, T. Tanaka, et al., “Measurement of Relative Intensityof the discrete γ rays from the thermal neutron capture reaction 155,157 Gd(n, γ) using ANNRI detector (JPARC)”, Proceedings of The 3rd International
Symposium on Quest for the Origin of Particles and the Universe, (2017).
[205] K. Hagiwara, T. Tanaka, P. K. Das, et al., “Comparison of γ production
from thermal neutron capture of gadolinium with the MonteCarlo simulation”,
Proceedings of the 3rd International Symposium on Quest for the Origin ofParticles and the Universe, (2017).
[206] K. Hagiwara, T. Yano, T. Tanaka, et al., “Gamma-ray spectrum from thermal
neutron capture on gadolinium-157”, Progress of Theoretical and Experimental
Physics, 2019(2), (2019).
[207] J. Apostolakis, S. Giani, M. Maire, et al., “GEANT4 low energy electromagnetic models for electrons and photons”, (CERN-OPEN-99-034), (1999).
[208] K. Abe, Y. Hayato, T. Iida, et al., (Super Kamiokande Collaboration), “Calibration of the Super-Kamiokande detector”, Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 737, pp.253 , (2014).
[209] J. Hosaka, K. Ishihara, J. Kameda, et al., (Super Kamiokande Collaboration),“Solar neutrino measurements in Super-Kamiokande-I”, Physical Review D,
73, pp.112001, (2006).
[210] D. Motta, & S. Schonert, “Optical properties of Bialkali photocathodes”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 539, pp.217, (2005).

REFERENCES

172[211] A. Filevich, P. Bauleo, H. Bianchi, J. R. Martino, & G. Torlasco, “Spectraldirectional reflectivity of Tyvek immersed in water”, Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors
and Associated Equipment, 423(1), pp.108 , (1999).
[212] P. Hänggi, R. Viollier, U. Raﬀ, & K. Alder, “Muon decay in orbit”, Physics
Letters B, 51(2), pp.119 , (1974).
[213] M. Yamada, K. Miyano, H. Miyata, et al., “Measurements of the charge ratio and polarization of 1.2-TeV/c cosmic-ray muons with the Kamiokande II
detector”, Physical Review D, 44, pp.617, (1991).
[214] K. Abe, C. Bronner, Y. Haga, et al., (Super Kamiokande Collaboration), “Atmospheric neutrino oscillation analysis with external constraints in SuperKamiokande I-IV”, Physical Review D, 97, pp.072001, (2018).
[215] Y. Takenaga, “Atmospheric neutrino oscillation analysis with solar terms in
Super-Kamiokande”, PhD thesis, University of Tokyo, (2008). URL http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.html#dthesis.
[216] E. R. Davies, “Machine Vision: Theory, Algorithms, Practicalities”. Morgan
Kaufman Publishers Inc., ISBN 0122060938, (2004).
[217] Y. Ashie, J. Hosaka, K. Ishihara, et al., (Super Kamiokande Collaboration), “Measurement of atmospheric neutrino oscillation parameters by SuperKamiokande I”, Physical Review D, 71(11), pp.112005, (2005).
[218] K. Abe, C. Bronner, G. Pronost, et al., (Super Kamiokande Collaboration),“Search for an Excess of Events in the Super-Kamiokande Detector in the
Directions of the Astrophysical Neutrinos Reported by the IceCube Collaboration”, The Astrophysical Journal, 850(2), pp.166, (2017).
[219] M. E. C. Swanson, K. Abe, J. Hosaka, et al., (Super Kamiokande Collaboration), “Search for Diﬀuse Astrophysical Neutrino Flux Using Ultra–High‐Energy Upward‐ going Muons in Super‐ Kamiokande I”, The AstrophysicalJournal, 652(1), pp.206, (2006).
[220] E. Thrane, K. Abe, Y. Hayato, et al., (Super Kamiokande Collaboration), “SEARCH FOR ASTROPHYSICAL NEUTRINO POINT SOURCES
AT SUPER-KAMIOKANDE”, The Astrophysical Journal, 704(1), pp.503,(2009).
[221] E. Thrane, K. Abe, Y. Hayato, et al., (Super Kamiokande Collaboration),“Search for Neutrinos from GRB 080319B at Super-Kamiokande”, The Astrophysical Journal, 697, pp.730, (2009).
[222] C. Saji, “Study of upward-going muons in Super-Kamiokande”, PhD thesis,
Niigata University, (2002). URL http://www-sk.icrr.u-tokyo.ac.jp/sk/
pub/index.html#dthesis.

REFERENCES

173[223] M. Glück, E. Reya, & A. Vogt, “Dynamical parton distributions of the protonand small-x physics”, Zeitschrift für Physik C Particles and Fields, 67(3),pp.433, (1995).
[224] P. Lipari, & T. Stanev, “Propagation of multi-TeV muons”, Physical Review
D, 44(11), pp.3543, (1991).
[225] R. Gandhi, C. Quigg, M. Hall Reno, & I. Sarcevic, “Ultrahigh-energy neutrino
interactions”, Astroparticle Physics, 5(2), pp.81, (1996).
[226] R. Gandhi, C. Quigg, M. H. Reno, & I. Sarcevic, “Neutrino interactions at
ultrahigh energies”, Physical Review D, 58, pp.093009, (1998).
[227] S. Garrappa, S. Buson, A. Franckowiak, et al., (Fermi-LAT, ASAS-SN and IceCube Collaborations), “Investigation of Two Fermi-LAT Gamma-Ray Blazars
Coincident with High-energy Neutrinos Detected by IceCube”, The Astrophysical Journal, 880(2), pp.103, (2019).
[228] F. Acero, M. Ackermann, M. Ajello, et al., “FERMILARGE AREA TELESCOPE THIRD SOURCE CATALOG”, The Astrophysical Journal Supplement Series, 218(2), pp.23, (2015).
[229] E. Massaro, M. Perri, P. Giommi, & R. Nesci, “Log-parabolic spectra andparticle acceleration in the BL Lac object Mkn 421: Spectral analysis of thecomplete BeppoSAX wide band X-ray data set”, Astronomy & Astrophysics,
413, pp.489, (2004).
[230] S. Weinberg, “Gravitation and Cosmology: Principles and Applications of theGeneral Theory of Relativity”. John Wiley & Sons Inc., (1972).
[231] P. A. R. Ade, N. Aghanim, M. Arnaud, et al., (Planck Collaboration),“Planck2015 results”, Astronomy & Astrophysics, 594, pp.A13, (2016).
[232] S. Ansoldi, L. A. Antonelli, C. Arcaro, et al., “The Blazar TXS 0506+056
Associated with a High-energy Neutrino: Insights into Extragalactic Jets
and Cosmic-Ray Acceleration”, The Astrophysical Journal Letters, 863(1):L10,(2018).
[233] A. Keivani, K. Murase, M. Petropoulou, et al., “A Multimessenger Pictureof the Flaring Blazar TXS 0506+056: Implications for High-energy Neutrino
Emission and Cosmic-Ray Acceleration”, The Astrophysical Journal, 864(1),pp.84, (2018).
[234] M. Cerruti, A. Zech, C. Boisson, et al., “Leptohadronic single-zone models forthe electromagnetic and neutrino emission of TXS0506+056”, Monthly Noticesof the Royal Astronomical Society: Letters, 483(1), pp.L12, (2018).
[235] S. Gao, A. Fedynitch, W. Winter, & M. Pohl, “Modelling the coincident observation of a high-energy neutrino and a bright blazar flare”, Nature Astronomy,
3(1), pp.88, (2018).

REFERENCES

174[236] R. Xue, R.-Y. Liu, M. Petropoulou, et al., “A Two-zone Model for Blazar
Emission: Implications for TXS 0506+056 and the Neutrino Event IceCube170922A”, The Astrophysical Journal, 886(1), pp.23, (2019).
[237] X. Rodrigues, S. Gao, A. Fedynitch, A. Palladino, & W. Winter, “Leptohadronic Blazar Models Applied to the 2014–2015 Flare of TXS 0506+056”,
The Astrophysical Journal, 874(2), pp.L29, (2019).
[238] S. Gao, M. Pohl, & W. Winter, “On the Direct Correlation between GammaRays and PeV Neutrinos from Blazars”, The Astrophysical Journal, 843(2),pp.109, (2017).
[239] C. D. Dermer, R. Schlickeiser, & A. Mastichiadis, “High-energy gamma radiation from extragalactic radio sources.”, Astronomy & Astrophysics, 256,
pp.L27, (1992).
[240] C. D. Dermer, & R. Schlickeiser, “Model for the High-Energy Emission from
Blazars”, The Astrophysical Journal, 416, pp.458, (1993).
[241] M. Sikora, M. C. Begelman, & M. J. Rees, “Comptonization of Diﬀuse Ambient
Radiation by a Relativistic Jet: The Source of Gamma Rays from Blazars?”,
The Astrophysical Journal, 421, pp.153, (1994).
[242] S. D. Bloom, & A. P. Marscher, “An Analysis of the Synchrotron Self-Compton
Model for the Multi–Wave Band Spectra of Blazars”, The Astrophysical Journal, 461, pp.657, (1996).
[243] M. Pohl, & R. Schlickeiser, “On the conversion of blast wave energy into
radiation in active galactic nuclei and gamma-ray bursts”, Astronomy & Astrophysics, 354, pp.395, (2000).
[244] Schuster C., Pohl M., & Schlickeiser R., “Neutrinos from active galactic nuclei
as a diagnostic tool”, Astronomy & Astrophysics, 382(3), pp.829, (2002).
[245] H. J. Möhring, & J. Ranft, “Dual parton model with complete formation
zone intranuclear cascade for the description of particle production in hadronnucleus and nucleus-nucleus interactions”, Zeitschrift für Physik C Particles
and Fields, 52(4), pp.643, (1991).
[246] J. Ranft, & S. Roesler, “Single diﬀractive hadron-nucleus interactions within
the dual parton model”, Zeitschrift für Physik C Particles and Fields, 62(2),pp.329, (1994).
[247] A. Ferrari, J. Ranft, S. Roesler, & P. Sala, “Cascade particles, nuclear
evaporation, and residual nuclei in high energy hadron-nucleus interactions”,
Zeitschrift für Physik C Particles and Fields, 70(3), pp.413, (1996).
[248] R. Engel, J. Ranft, & S. Roesler, “Photoproduction oﬀ nuclei and pointlike
photon interactions. I. Cross sections and nuclear shadowing”, Physical Review
D, 55, pp.6957, (1997).

REFERENCES

175[249] S. Mughabghab, “Atlas of Neutron Resonances, Fifth Edition: ResonanceParameters and ThermalCross Sections, Z=1-100”. Elsevier Science, (2006).
[250] M. Igashira, Y. Kiyanagi, & M. Oshima, “Nuclear data study at J-PARC
BL04”, Nuclear Instruments and Methods in Physics Research Section A:
Accelerators, Spectrometers, Detectors and Associated Equipment, 600(1),pp.332 , (2009).
[251] T. Kin, K. Furutaka, S. Goko, et al., “The 4π Ge Spectrometer for Measurements of Neutron Capture Cross Sections by the TOF Method at the
J-PARC/MLF/ANNRI”, Journal of the Korean Physical Society, 59(2(3)),
pp.1769, (2011).
[252] K. Kino, M. Furusaka, F. Hiraga, et al., “Measurement of energy spectraand spatial distributions of neutron beams provided by the ANNRI beamline for capture cross-section measurements at the J-PARC/MLF”, Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 626-627, pp.58 , (2011).
[253] A. Kimura, T. Fujii, S. Fukutani, et al., “Neutron-capture cross-sections of
244Cm and 246Cm measured with an array of large germanium detectors in
the ANNRI at J-PARC/MLF”, Journal of Nuclear Science and Technology,49(7), pp.708, (2012).
[254] K. Kino, M. Furusaka, F. Hiraga, et al., “Energy resolution of pulsed neutron beam provided by the ANNRI beamline at the J-PARC/MLF”, Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 736, pp.66 , (2014).
[255] S. Nagamiya, “Introduction to J-PARC”, Progress of Theoretical and Experimental Physics, 2012(1), (2012).
[256] K. SHIBATA, O. IWAMOTO, T. NAKAGAWA, et al., “JENDL-4.0: A New
Library for Nuclear Science and Engineering”, Journal of Nuclear Science andTechnology, 48(1), pp.1, (2011).
[257] R. Capote, M. Herman, P. Obložinský, et al., “RIPL – Reference Input Parameter Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations”, Nuclear Data Sheets, 110(12), pp.3107 , (2009).