Doctorate Dissertation
博士論文
Search for Neutrinos associated with Gamma-ray Bursts
in Super-Kamiokande(スーパーカミオカンデにおけるガンマ線バーストに伴うニュートリノ探索)
A Dissertation Submitted for Degree of Doctor of Philosophy

December 2018
平成 30 年 12 月博士(理学)申請

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

Orii Asato
織井 安里

Search for Neutrinos associated with Gamma-ray Bursts inSuper-Kamiokande
A. Orii
February 21, 20191

Abstract
Gamma-Ray Bursts (GRBs) are one of the most luminous astronomical objects. Thoughsatellites and ground telescopes have observed some features, much of their mechanism is still
not confirmed. We searched for neutrinos associated with GRBs in the Super-Kamiokande(SK) detector.
From Dec. 2008 to Mar. 2017, 2208 GRbs occurred during SK normal data-taking periods.
In a search window of ±500 sec around each GRB trigger time, 250 events remained after reduction with an expected background rate of 0.114 events/1000 seconds. The time distributionof the number of events and energy distribution of combined data does not show significant
excess over the background.
For individual GRBs, 3 or less SK events were detected in the search window. The only
GRB with 3 SK events is GRB140616A. The 3 SK events may be events caused by cosmic raymuons.
The number of SK events between GRB start/stop time (Nev ) observed by satellites andtelescopes are also studied. From toy Monte Carlo simulation, the distribution of Nev wasevaluated as consistent with background.
Assuming a flat spectrum, the fluence limit was calculated. The fluence limit from 8 MeV to
100 MeV for all 2208 GRBs is 1.03 × 108 cm−2 . The limit as a function of energy was calculated
and is 3.4 × 109 cm−2 at 12 MeV.

2

Contents
1 Introduction
1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Gamma-Ray Burst . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 MeV Neutrinos from GRBs . . . . . . . . . . . . . . . . . . .
1.3 Previous Experimental Searches . . . . . . . . . . . . . . . . . . . . .

6
6
6
7
7
12
13

2 The Super-Kamiokande Detector
15
2.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Water Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Radon Free Air Systems . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Front-end Electronics and Data Acquisition System . . . . . . . . . . 20
2.7 Monitoring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Detector Calibration
24
3.1 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Relative Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Water Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Decay Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2 DT generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.3 Decay Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Event Reconstruction
30
4.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 Muon Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.1 Muboy Fitter . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.2 Brute Force Fitter . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.3 Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3

4.5

Cherenkov Angle Reconstruction . . . . . . . . . . . . . . . . . . . .

34

5 Event Simulation
37
5.1 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.1 Particle Tracking . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.2 Cherenkov Photon Tracking . . . . . . . . . . . . . . . . . . . 37
5.1.3 Photon Detection by PMT and Electronics . . . . . . . . . . . 38
5.1.4 Water Transparency . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Neutrino Interaction Simulation . . . . . . . . . . . . . . . . . . . . . 40
6 Data Reduction for GRB Neutrino Search
41
6.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2.1 Calibration Event Cut . . . . . . . . . . . . . . . . . . . . . . 41
6.2.2 Noise Event Cut . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2.3 OD cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.2.4 50 µs Time Difference Cut . . . . . . . . . . . . . . . . . . . . 42
6.2.5 Fiducial Volume Cut . . . . . . . . . . . . . . . . . . . . . . . 42
6.2.6 Goodness Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.3 Spallation Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.4 Gamma cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.5 Pion Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.6 OD Correlated Event Cut . . . . . . . . . . . . . . . . . . . . . . . . 51
6.7 Multi-Ring Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.8 Solar Events Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.9 Pre/Post Activity Cut . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.10 µ/π Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.11 N16 cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.12 Cherenkov Angle Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.13 Summary of Reduction Efficiency . . . . . . . . . . . . . . . . . . . . 56
7 Results of GRB neutrino searches
59
7.1 Neutrino Search for Individual GRB . . . . . . . . . . . . . . . . . . 59
7.1.1 ±500 sec Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.1.2 t1-t2 analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.2 Stack Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.2.1 Fluence Limit Calculation . . . . . . . . . . . . . . . . . . . . 66

4

8 Summary and Outlook
71
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5

1

Introduction

Gamma-Ray Bursts (GRB) are luminous explosions in Universe. Enormous energy
is released in gamma-rays in a short time. After their 1967 discovery, much research
revealed their features, though still their mechanism is not clear.
Neutrinos interact less than photons. If a GRB is observed through neutrinos,
the information would be helpful.
The 2017/10/7 observation of GW170917 was reported in [3]. This event was also
observed as a short GRB. Follow-up observations by ground telescope determined
its progenitor to be a neutron star-neutron star merger event.
1.1

Neutrinos

The neutrino was predicted by Pauli in 1930 to conserve momentum in beta decays.
It was experimentally observed in 1956 by Reines and Cowan. Originally, neutrinos
were thought to be massless. Now, it is known that they have mass due to theobservation of neutrino oscillation. They have 3 flavors corresponding to the leptons.
Because their mass eigenstate and flavor eigenstate is different, the flavor oscillates
or changes during travel.
In the Standard Model, the neutrino is a fundamental particle. The interaction
by gravity is negligible due to its small mass. It is electrically neutral and does notinteract with the strong force. The weak nuclear force is the main interaction channel.
Neutrinos pass through massive objects with little interaction. Its experimental study
needs a large detector and sophisticated techniques.
Neutrinos are generated via nuclear reactions like fusion in the sun, fission in
the Earth’s crust and mantle, and in reactors. Neutrinos are also generated whena cosmic ray interacts with a nucleus in the atmosphere, creating unstable particles
that decay. There are also artificial neutrino beams. Neutrino properties have beenstudied from these various sources.
Neutrinos can also be used for studying astronomical events. Many astronomical
events make or are predicted to make large amounts of neutrinos. Because of its smallinteraction rate, neutrinos can bring different information to the Earth without theeffect of scattering or shielding. The only currently observed astronomical neutrinos
are from the sun and from supernova 1987A. This thesis is the result of the search
for neutrinos from gamma-ray bursts.
1.2

Gamma-Ray Burst

Gamma-ray bursts (GRB) are one of the most luminous astronomical object everobserved. The observed energy of GRBs distribute from high energy gamma-rays6

to radio. GRBs comes from random directions without notice. During the prompt
phase, typical GRBs are more luminous than the rest of the gamma-rays in the sky.
Assuming isotropic emission, the released energy is 1054 erg. However, In fact,gamma-ray emission is a directional beam. Therefore, the total gamma-ray energyof a GRB is much less and comparable to a supernova. GRBs are categorized as long
GRBs or short GRBs depending on the duration of the gamma-ray. Long GRBs
have durations longer than 2 sec and short GRBs less than 2 sec.
1.2.1

Observation

GRBs are observed about once a day in the entire sky on average. After an observation of gamma-rays by the satellites, the afterglow of X-ray, optical ray, or radio
is observed by follow-up ground telescopes. The redshift of the afterglow enables
determination of the distance and host galaxy. The progenitor is at a cosmologicaldistance.
Their gamma radiation is non-thermal and can be usually characterized by a Band
function[18] . The function is made of two smoothly joined power-laws (Fig. 1). For
some GRBs, a small thermal component is observed.
The duration of GRBs (Fig. 2) have 2 peaks, one at 30 sec and the other at 0.3 sec.
Most of the GRBs have durations between 0.1 sec to 1000 sec.
The light curves of GRBs have various time development (Fig. 3. The bursts havefeatures like a single peak with a fast rise exponential decay (FRED), erratic multipeaks, and long quiet periods between peaks.
After the prompt gamma-ray signal, a longer signal called afterglow is observed.
The observed afterglows have a power-law energy spectrum from x-ray to radio.
They decay as a power-law function of time. Fig. 4 shows the time development of
30 afterglows before the launch of Swift. Most of the x-ray afterglows disappear as
a power-law with exponent ∼1.2.
More features were observed by the rapid follow-up of the ground telescope with
Swift. The schematic features are shown in Fig. 5. The rapid decay of many bursts
is consistent with the low energy tail of the prompt gamma-ray. The continuous
injection of the fireball energy into the interstellar medium (ISM) is thought tocause the shallow decay after this rapid decay. The exponent of the shallow decay is∼0.5. The continued activity of the fireball makes x-ray flares.
1.2.2

Model

Gamma rays are emitted from the relativistic fireball. The fireball model is confirmedby the observation of the afterglow[33, 51, 45] . In the fireball model, the GRB is7

Figure 1: The spectra of GRB990123 from the Compton Gamma-ray Observatory. The top panel
shows photon flux and the bottom shows the energy flux. Figure from [24].

generated when relativistic ejecta slow down by interactions with the external massor another layer of the ejecta. Neutrinos are also generated by this process.
As the central engine, different models are widely accepted for long GRBs andshort GRBs. The model for long GRBs is the rotating core of the massive star thatdecays into a neutron star (NS) or a black hole (BH)[38] . The model for short GRBs
is the merger of a NS or BH[38] .
The neutrino energy and flux depend on the model of the central engine and thatof neutrino generation. The primary neutrino production interactions of the fireballmodel are p − γ interactions (Eν ∼ 1014 1019 eV or higher)[52, 20, 29, 53, 51] or p − ncollisions (Eν ∼10 MeV-10 GeV)[52, 20, 8, 42, 37] .

8

Figure 2: The duration of GRBs in the 4th BATSE catalog. Figure from [26].

9Figure 3: The light curves of 8 bursts observed by BATSE. Figure from [27].

10Figure 4: The observed near infrared afterglow from [32]. The two black line correspond to decay
slopes of α = 0.5.

11Figure 5: The schematic features observed in early x-ray afterglows with Swift[17].

1.2.3

MeV Neutrinos from GRBs

In the fireball scenario, the neutrino fluence is estimated as [31],



2
Eν,tot65 MeV
4000 Mpc
Φν =cm−2 ,
2 × 1053 erg
Eν
D

(1)

where Eν,tot is the total energy in the fireball, Eν is average neutrino energy, andD is the distance to a GRB. For a GRB of typical energy at redshift z = 2, Φν ∼1 cm−2 for several tens of MeV neutrinos. This estimated fluence is much smaller
than the fluence limit of MeV neutrinos given by the previous study with SuperKamiokande[28] is 105 − 108 cm−2 .
However, a larger fluence of low energy neutrinos is predicted with a cosmic string
scenario than with a fireball scenario. Cosmic strings are linear defects predicted
in most grand unified models. At a symmetry breaking phase transition in theearly universe, cosmic strings could be formed as thin superconducting wires that
respond to external electromagnetic fields[10] . Cosmic strings models can give a
better explanation to the following:• The high-redshift GRBs, GRB 080913, and GRB 090423 have short durations
but have high energy release, typical for long GRBs.
• The rate of high-redshift GRBs is larger than the predicted rate by the collapsar
model with an ordinary star formation rate[11] .
12

The estimated neutrino fluence is[31] ,−1  η −1  E
Fγ
νobs
ν
8
cm−2 ,
Φν = 1010−10100MeV
10−6 ergcm−2(2)where ην is the ratio of gamma-gay energy release to that of the neutrino, Eνobs isthe average neutrino energy and Fν is fluency in photons. Φν ∼ 107 − 108 cm−2 isestimated with same condition GRB to that of fireball model.
The prediction of neutrino fluence limit differs much depending on models. The
neutrino search with SK will help to constrain the model.
1.3

Previous Experimental Searches

Until now, no clear neutrino signal is observed in GRBs. The following is a summaryof the previous experimental searches. Fig. 6 shows the fluence limit.

Figure 6: Fluence upper limits for electron antineutrinos from GRBs at low energy. Figure from[22].

• SK-IThe correlation with 1454 GRBs from April, 1996 to May, 2000 was searched[28] .
The solar neutrino, atmospheric neutrino and up-going muon sample was used.
Their energy is 7 MeV to 100 TeV.
After this, the search for the bright GRB, GRB080319B is done[19] .
13

• Kamland
Kamland is a liquid scintillator detector[21] . The data period from Aug. 2002
to Jun. 2013 is divided into Period I and II by the condition of the reactors.
In Period I, 7.5 MeV to 100 MeV neutrinos were searched for in 192 GRBs. In
Period II, 0.9 MeV to 100 MeV neutrino were searched for in 39 GRBs.
• Borexino[22]Borexino is also a liquid scintillator detector. It searches ν¯e via inverse beta
decay and all flavors via the scattering on electrons.
The neutrinos correlated with 2,350 GRB from Dec. 2007 to Nov. 2015 wassearched. The target energy range is from 1.8 MeV to 15 MeV.
• IceCube
IceCube, a Cherenkov detector, searched the TeV and PeV range of neutrino
for 1172 GRBs from May 2010 to May 2015.
• ANITA[13]
ANITA is a balloon experiment which searches for radio emission from electromagnetic showers by the interaction of ultra-high energy neutrino with theantarctic ice sheet. During 31 days of the second flight of ANITA, 26 GRBs areobserved by Swift or Fermi. The fluence limit of 108 − 1012 GeV is calculated.
• ANTARESANTARES is a water Cherenkov detector in the Mediterranean sea. It searchedneutrinos with energies of TeV to PeV for 40 GRBs in 2007[5] and 296 GRBs
in 2007 to 2011[6] .
• SNO[16]The SNO detector is a Cherenkov detector of heavy water in Sudbury’s Creighton
mine. The neutrino is typically below 20 MeV around 190 GRBs are searched.
• BUST[36]
BUST, Bakusan Underground Scintillation Telescope searched for 20-100 MeV
neutrinos during 97 GRBs in 2012.

14

2

The Super-Kamiokande Detector

2.1

Detector Overview

Super-Kamiokande (SK) is a 50 kton water Cherenkov detector located in the Kamioka
mine. Cosmic ray muons are reduced by 1,000 m rock (2700 m.w.e.) shield. The
detector has a cylindrical shape with a diameter of 39.3 m and height of 41.4 m.

Figure 7: Schematic view of the SK detector.

A stainless steel frame structure divides the detector into two volumes, an innerdetector (ID) and outer detector (OD). The structure forms an optical barrier andsupport for photo-multiplier tubes (PMTs). In the OD, 1,885 8inch PMTs monitor
particles entering from outside and 2.5 m of water shields gamma-rays from the rocksurrounding the detector. Tyvek sheet which surround the outer side of the frame
structure increase the veto sensitivity.
The inner side of the frame structure is surrounded by polyethylene terephthalate
black sheet to reduce optical reflections. The ID is monitored by 11,129 20 inch
PMTs providing a photo-coverage of ∼40%.
The volume within 2 m from the ID wall is not used for low energy analysis due totoo many background events. The remaining 22.5 kton volume is called the fiducial
volume (FV). The space above the detector is a research dome with 4 electronics
huts and a central control room.
SK has five observation phases:
1. SK-I started observation on April, 1996. This period ended on July, 2001.

15

2. After regular maintenance in July, 2001, a shock wave from the implosion ofa PMT caused the chain implosion of almost half of the PMTs. Then, theremaining PMTs were re-distributed and SK-II started on October, 2002. From
SK-II, PMTs are protected from shock waves by acrylic covers and fiberglass
reinforced plastic (FRP). SK-II was stopped to mount new PMTs on October,2005.
3. After the PMT mounting work, SK-III started on June, 2006.
4. In August, 2008, new electronics and data acquisition system was installed,
ending SK-III and beginning SK-IV. SK-IV was stopped for tank refurbishment
work from May, 2018.
5. The work finished in January, 2019, beginning SK-V. Gadolinium sulfate will
be added to the water later during this phase.
2.2

Detection Principle

SK detects Cherenkov light, which is emitted when a charged particle travels fasterthan the speed of light in the medium. Cherenkov light is radiated with a cone
pattern along the path of the charged particle.
The angle between the direction of the charged particle and that of the Cherenkov
light is called the Cherenkov angle θc and is calculated bycos θc =

1
,
βn(λ)

(3)

where β is the speed of the charged particle relative to light speed in vacuum andn(λ) is the refractive index at the wavelength λ. In pure water, the refractive index
at 589 nm is 1.33. For the ultra relativistic particles like electrons and positrons, θc
is 42◦ . In the energy range of interest, heavier particles like muons and pions have asmaller Cherenkov angle.
The energy threshold for emitting Cherenkov light is determined bymEthr = p,(4)(1 − (1/n)2 )where m is the rest mass of the charged particle.
The number of Cherenkov photons along the trajectory per wavelength is calculated byd2 N
2πz 2 α12πz 2 α 2
=
(1
−
)
=
sin θc ,
(5)
dλdx
λ2
β 2 n2 (λ)λ
where z is the particle charge in units of e and α is the fine structure constant.
16

2.3

Photomultiplier Tubes

The 20-inch PMT (R3600) [15] for the ID was developed by Hamamatsu Photonics.
The schematic is shown in Fig. 8.

Figure 8: A schematic of the Hamamatsu R3500 PMT.

Its photo-cathode is made from bailkali (Sb-K-Cs) and is sensitive to photons ofwavelength 300∼600 nm. Its quantum efficiency is about 20% at maximum (Fig. 9).
A photo-electron (p.e.) generated through the photoelectric effect is amplified by
107 through the chain of dynodes. The PMT dark noise is 4 kHz. The earth magnetic field, which affects the PMT response, is reduced from 450 mG to 50 mG by
Helmholtz coils surrounding the detector.

Figure 9: The quantum efficiency of the Hamamatsu R3600 as a function of wavelength.

17

2.4

Water Systems

The water purification system (Fig. 10) was developed to maintain the quality ofwater transparency and radioactivity. The higher transparency gives less attenuationof the Cherenkov light. Radioactivity can produce backgrounds in the low energy
analysis.

Figure 10: The SK water purification system.

The water system consists of the following components:• 1 µm filter:
Removes large particles.
• Heat exchanger:
Maintains the water temperature at 13◦ . Water temperature variations cause
convection, while higher temperatures increase PMT dark noise and the growthof bacteria.
• Cartridge polisher:
Removes heavy ions.
• UV sterilizer:
Kills bacteria.
• Vacuum de-gasifier:Removes oxygen and radon in water.
18• Ultra filter:
Removes particles larger than 10 nm.
• Membrane de-gasifier:Removes dissolved gas.
• Reverse osmosis:
Removes large particles with molecular weight > 100.
The water circulates at 60 tons per hour. Due to heat from the PMTs, the water
becomes hot as it remains in the tank. It is filled from the bottom of the detector
and drained from the top (Fig. 11).
The water temperature is monitored in the ID and OD. It is uniform from thebottom to 11 m below the center and slightly increases with height (Fig. 12). The
difference between top and bottom is 0.2 ◦ C.

Figure 11: The SK water flow.

2.5

Radon Free Air Systems

The air in the mine includes radon from the surrounding rocks. Radon affects thelow energy background rate and workers’ health. SK has a system that takes air
from outside the mine and reduces radon in the air. A schematic view of the radon
free air system is shown in Fig. 13 and consists of the following components:• Compressor:
Provides air pressure up to 7-8.5 atm.
19

Figure 12: The z-dependence of the water temperature.

• Air filter:
Removes dust in the air. The air goes through 3 types of filters, 0.3 µm, 0.1 µm,
and 0.01 µm, from large to small.
• Air drier:Removes water and CO2 in the air.
• Carbon column:
Absorbs the radon in the air. 8 m3 of charcoal is used in total.
• Cooled charcoal:Has better random removal efficiency. The volume is 50 L.
The radon level increases to ∼2000 Bq/m3 in the summer and decreases to∼260 Bq/m3 in the winter. The radon free air system maintains ∼40 Bq/m3 in theexperimental area. The radon free air in the tank keeps higher pressure (0.3 kPa)
than the outside of the tank. This prevents the air with radon in the mine fromgetting into the tank.
2.6

Front-end Electronics and Data Acquisition System

The front-end electronics and data acquisition system (DAQ) was upgraded in August, 2008. This upgrade enables more stable data taking and larger data throughput.
20

Figure 13: The radon free air system

Each PMT hit is recorded without loss and selected by a software trigger. Since
SK has various physics purposes, several types of software triggers were installed. The
low energy (LE) trigger, the high energy (HE) trigger, and the super high energy(SHE) trigger have a 40-µs timing window. 5 µs before the trigger is stored forpre-activity gamma studies and the following 35 µs is for post-activity studies. The
trigger threshold is 47, 50, and 70 hits in 200 nsec for LE, HE, and SHE, respectively,
at the beginning of the new DAQ period. The SHE threshold was changed to 58 hits
in the summer of 2011.
Fig. 14 shows the schematic of the new DAQ system. The signals from PMTs
go to the new front-end electronics, QTC (charge-to-time converter) Based Electronics with Ethernet (QBEE, Fig. 15). The QBEE has a 24 analog input channel
with a dynamic range of 0.2 to 2500 pC. It works 5-times faster than the previous
electronics [1]. 8 QTC chips mounted in the QBEE integrate the input charge andoutput a pulse of proportional width. The pulse width and timing is digitized bya time-to-digital converter (TDC). The digital information is processed by a Field
Programmable Gate Array (FPGA) [30].
The TCP packets of data from 500 QBEEs are sent to the 20 front-end PCs.
The front-end PCs sort the data in time and send the data to 10 merger PCs. The
merger PCs also sort the data in time and then, apply the event building process
to the data in the same time region. In the event building process, the data from
20 front-end PCs is scanned by the software trigger. The triggered events are sent
to the organizer PC and recorded on disk. The Gigabit Ethernet is used for datatransfer between PCs.
Since the new DAQ can handle large throughput, it can record events at a hightrigger rate. The high trigger rate is caused by the lower trigger threshold or highrate burst such as a supernova at the distance of the galactic center (∼8.5 kpc).
21

Figure 14: The schematic of the DAQ system.

For a much higher trigger rate target like a nearby supernova (Betelgeuse, ∼200 pc),
a DAQ system that records the number of hit PMTs was installed[44] . The QTC on
QBEE outputs the digital hitsum, the number of hit PMTs within ∼17 nsec. This
DAQ makes 2 types of hitsums, a 60 MHz sum and 60 kHz sum. The 60 MHz sumis the sum of the digital hitsum for all QBEEs and recorded only when a high rate
event occurs. The 60 kHz sum is the sum of the 60 MHz sum in 17 µs and used tomonitor the hit rate. This DAQ system enables to record the time development of
the total energy deposit.
2.7

Monitoring system

The condition of data taking is monitored by various tools. The “slow control”
monitor checks the status of the high voltage and the temperature of the electronics.
The data stream, the PMT conditions, and the trigger rate are monitored by theprocess making their distributions. The data transfer and the offline process is also
monitored. The online display program shows the visual image of an event in realtime. The display helps to monitor the DAQ system and the PMTs.

22

Figure 15: QBEE.

23

3

Detector Calibration

3.1

PMT Calibration

PMT calibration is necessary for interpreting the recorded charge and timing. First,
the high voltage on each PMT is tuned to make the response of all PMTs almost
uniform. Then, the PMT gain is measured to convert ADC counts to number ofphoto-electrons (p.e.). The relative hit timing between PMTs is also corrected.
3.1.1

Absolute Gain

The global absolute gain, a conversion factor from pC to p.e., is measured with a NiCf source. As the γ-rays from this source are about 9 MeV, almost all of the PMT
hits are caused by single photons. The absolute gain is derived from the averagecharge distribution of single photons.
3.1.2

Relative Gain

The relative gain of PMTs is determined by a laser system. The system has a laserof high intensity and low intensity. The charge of the i-th PMT for the high intensity
laser is given by:
Qobs (i) ∝ Ihigh (i) × QE(i) × G(i)(6)
and for low intensity:
Mhit (i) ∝ Ilow (i) × QE(i),(7)

where Ihigh/low is the light intensity expected at the i-th PMT for high and low
intensities, respectively. QE(i) is the quantum efficiency and G(i) is the relative
gain. The ratio of two equation is:
G(i) =

Ilow (i)Qobs (i)×.
Mhit (i) Ihigh (i)(8)

The effect of attenuation in water and geometry is canceled out in the ratio. Namely,
the Ilow (i)/Ihigh (i) is common for all PMTs, such that
G(i) ∝

Qobs (i).
Nobs (i)(9)

Fig. 16 shows the obtained relative gain. From absolute and relative gain, the ADC
count is converted to p.e.

24Figure 16: The distribution of relative PMT gains.

3.1.3

Timing

The relative timing is important for vertex reconstruction. The variation of timing
is caused by differences in PMT transit time and cable length. Furthermore, when
the observed charge is different, the timing also changes due to the slewing effect ofthe discriminator.
The timing calibration is performed with a N2 laser. wavelength of N2 laser isshifted to 398 nm by a dye. Via a optical fiber, the N2 laser goes into a diffuser ballin the center of the SK tank. The light intensity is changed by optical filters andthe response for several pulse height is measured. Fig. 17 is the typical ”TQ-map”,
a 2-D plot of PMT timing versus pulse height. The TQ-map is made for each PMT
individually.
The global timing resolution is calculated from the residual timing difference of
PMT hits with the TQ-map. For single photo-electrons, the global timing resolution
is 3 ns. The global timing resolution is input for the vertex reconstruction and Monte
Carlo simulation.
3.2

Water Transparency

The number of Cherenkov photons observed by a PMT is affected by absorption andscattering in the water. For accurate energy reconstruction, SK has two methods to25

Figure 17: TQ-map, a scatter plot of the PMT timing (vertical axis) and charge (horizontal axis).

measure water transparency, by N2 laser and decay electrons. The N2 laser allows theindependent measurement of absorption and scattering coefficients. Decay electrons
from cosmic ray muons allow the measurement of the effective attenuation length.
3.2.1

Lasers

The wavelength of the lasers are 337, 375, 405, 445, and 473 nm. During normal
data taking, the laser is pulsed every 6 sec and injected into the tank vertically fromthe top by a light injector.
Hits in the bottom PMTs are caused mostly by direct photons, while hits in thebarrel and the top PMTs are caused by photons scattered by the water or reflected
off the bottom PMTs or the black sheet.
From the total number of scattered photons and the distribution of the arrivaltime of PMT hits, the attenuation length parameters are obtained by comparing
with the expectations from Monte Carlo simulation. The attenuation length isLatten =1
αabs + αscat,sym + αscat,asym

,

(10)

where αscat,sym is the coefficient of symmetric (i.e. same intensity for forward andbackward) scattering, which is mainly due to Rayleigh scattering and Mie scattering,and αscat,asym is the coefficient of asymmetric scattering due to Mie scattering.
These parameters are used for the model of water in the event simulation. The
event simulation is consistent with the data of the following decay electron study.

26

3.2.2

Decay Electrons

There are thousands of muons per day that stop in the tank and decay into electrons.
These events can be used as a calibration sample. The following criteria are applied
to obtain a pure sample:• The time difference ∆t between the stopping muon and the electron event is
3.0 µsec < ∆t < 8.0 µsec.
• The vertex of the electron event is in the fiducial volume.
• The distance between the muon stopping point and the vertex of the electron
is less than 250 cm.
• The number of PMT hits in the residual time within 50 ns is larger than 50.

Water transparency[m]About 700 events/day are selected.
The water transparency is calculated from the distribution of the number of PMT
hits versus the distance from the reconstructed vertex to each PMT hit. The PMT
hits with opening angle 32◦ to 52◦ and the residual time ≤ 50 ns are used for removing
noise and indirect hits. The same correction as for the energy reconstruction isapplied to the contribution from each PMT. The water transparency for a given day
is estimated from the average of the 2 weeks before and after to reduce the statisticalfluctuation. Fig. 18 shows the time variation of this water transparency. This value
is used as a parameter for the energy reconstruction.
160
150
140
130
120
110
100

2009 2010 2011 2012 2013 2014 2015 2016
Year

Figure 18: Water transparency of SK-IV measured from decay electron

27

3.3

Energy Calibration

3.3.1

LINAC

The absolute energy scale is mainly determined from the electron linear accelerator (LINAC) calibration. The LINAC ejects a mono-energetic down-going electron.
The beam energy is less than 19 MeV and measured with ±20 keV accuracy by agermanium detector. The details of the LINAC is found in Ref. [23].
The LINAC data was taken in August 2010, July 2012, August 2016, and August
2017. Data were taken at the several ejection heights and electron energies. Various
MC parameters are tuned from LINAC data.
The conversion function from the effective hits to the total energy is tuned by
LINAC. The function is not directly determined from LINAC data because the events
have a fixed vertex and direction. First, fixed energy and uniformly distributed eventsare generated by the LINAC-tuned MC. Second, the average effective hit (Nef f ) for
each energy is calculated by fitting the Nef f distribution with a Gaussian. The
relation between energy and Nef f is fit with a 4th order polynomial function. Thisis the function for the absolute energy. The accuracy is better than 1%.
The LINAC data is also used to study the energy resolution, vertex resolution,
and angular resolution.
3.3.2

DT generator

The deuterium-tritium (DT) neutron generator is used to cross-check the absolute energy scale. The neutron produces 16 N from 16 O via (n,p) interactions. 16 N has a beta
decay Q-value of 10.4 MeV and emits an electron (<4.3 MeV) and γ-ray (6.1 MeV)
dominantly. The DT data is measured every few months. The reconstructed energy
from DT data matches with the LINAC-tuned MC within ≤1% accuracy. Since DT
events are isotropic, the position dependence can be checked. The dependency isless than ± 0.5%. The DT calibration can be done at more radial positions than the
LINAC. The radial and height dependency is less than ±0.5% and ±1%, respectively.
3.3.3

Decay Electrons

The spectrum of decay electron events is the well-known Michel spectrum. It can beused to check the energy scale under 60 MeV. Considering the effect of muon captureby oxygen nuclei, the decay electron data is reproduce by MC within ≤2% accuracy.
The time variation of the energy scale is also checked with decay electron data.
The 30-days average of Nef f is calculated from the same sample as the water transparency measurement. The averaged Nef f in SK-IV is shown in Fig. 19. The variation is less than ±1%.

28

Figure 19: The time variation of the effective hits from decay electrons. It is corrected by watertransparency. Red shows the average and the blue shows the ±0.5% line.

29

4

Event Reconstruction

When an event meets a software trigger condition, that event is reconstructed bya vertex reconstruction tool for low energy events, called ”low energy reconstruction tool”. After that, event direction and energy are reconstructed. Using thereconstructed vertex, direction, and energy, further reductions are applied to reduce
backgrounds.
The muon track fitter is applied to events that have more than 1000 p.e. andmeet the HE trigger condition and OD trigger condition. The criterion of more than
1000 p.e. corresponds to muons whose track length is more than about 1 m. The
spallation events along a track length of less than 1 m is outside of the fiducial volume
and can be removed by the fiducial volume cut. Muon information such as time tolow energy event, energy deposit in the detector, and distance from the low energy
event and the muon track are used for identify spallation events.
After some reduction process, the Cherenkov angle, the angle between the direction of the charged particle and that of the Cherenkov light, is calculated to identify
electron-like events.
4.1

Vertex Reconstruction

The vertices of low energy events are reconstructed only from the PMT hit timing,
because most of the PMT hits are caused by a single photon. Due to the short travel
distance of low energy electrons and positron (∼20 cm at 50 MeV), Cherenkov light isconsidered as emitted from a point source. The fitter BONSAI (Branch Optimization
Navigating Successive Annealing Iterations) works as follows [48].
BONSAI fits the maximum likelihood function of the timing residual of the hit
PMTs. For a test vertex (~v ) and a test event start time (t0 ), the timing residual isdefined as:∆ti = ti − tof(~v ) − t0 ,(11)
where ti is timing of a PMT hit and tof(~v ) is the time-of-flight from the test vertex
to the hit PMT. The likelihood is calculated from the probability density functionof ∆ti as
Nhit
X
Likelihood =log(P (∆ti )).
(12)
i=1

The P (∆ti ) is obtained from the LINAC calibration. For a LINAC event, the vertex
and the event start time is known. We can get true ∆t distribution. Fig. 20 isthis distribution normalized as the peak height = 1 and it is used as P (∆ti ). The
two peaks after the main peak are caused by re-incidence of electrons reflected by
the dynodes. Since ∆ti for the true vertex and start timing distributes like Fig. 20,30

the point with maximum likelihood is selected as the vertex. The goodness of thefitting is also calculated. The vertex resolution of BONSAI fit is 70 cm for 10 MeV
electrons.

Figure 20: Probability distribution of TOF normalized as the peak height = 1.

4.2

Direction Reconstruction

The direction of the charged particle is reconstructed from the Cherenkov ring pattern. The d~ which maximize the following likelihood function L is the event direction,
~ =
L(d)

N20
X

log(f (cosθdir,E )i ) ×

i

cosθi
,
a(θi )(13)

where N20 is the number of hit PMTs in a 20 nsec window, f (cosθdir,E ) is the expecteddistribution of the opening angle, and θdir,E is the angle between d~ and the vector
from the vertex to a PMT(d~0 ). cosθi /a(θi ) corrects the PMT acceptance, where θi isthe opening angle between d~0 and the vector normal to the PMT surface.
The resolution of the direction reconstruction is 25◦ for 10 MeV electrons.
4.3

Energy Reconstruction

The number of Cherenkov photons is approximately proportional to the energy deposit by a charged particle. For low energy events, the number of hit PMTs is also
proportional to the energy deposit, because most of the PMT hits are caused by a31

single photon. The energy reconstruction method is based on this idea with somecorrections added. The hits of its residual time in 50 ns window is the target. Thisnarrow window removes most of the dark noise. From N50 PMT hits, the effective
hits (Nef f ) is calculated as:
Nef f =

N50
X
i

Nall
Rcover(Xi − tail − dark ) ××× exp
Nnorm S(θi , φi )ri
λ(run)

× Gi (t), (14)where:• Occupancy Xi
The occupancy Xi is the correction for multiple photo-electrons from a relatively
high energy event. When a PMT has multiple p.e., the other PMTs around that
PMT tend to have a hit. The occupancy Xi is defined as a function of the ratio(xi ) of hit PMTs to all PMTs around the PMT:(1
log 1−xixi < 1
xi
Xi =
(15)
3.0
xi = 1• Late hits tailSome photons are outside the 50 ns window due to scattering or reflection. tailcorrects this effect.
• Dark Noise dark
dark is the correction to remove hits by dark noise. The value is calculated fromthe number of operating PMTs and the dark noise rate.
• Bad PMTs Nall /Nnorm
This term corrects the number of PMTs. Nall is the number of all PMTs. In
SK-IV, Nall is 11,129. Nnorm is the number of operating PMTs.
• Photo-cathode coverage Rcover /S(θi , φi )The PMT coverage Rcover is corrected by S(θi , φi ), the coverage depending on
the incident angle. The incident angle is calculated from the reconstructedvertex.
• Water transparency λThe attenuation in the water is corrected by the observed water transparency
λ and the distance ri between the vertex and the PMT.
• PMT gain Gi (t)Gi (t) is the gain for a single photon depending on time.
32

The total energy is reconstructed as a function of Nef f . The function is calibrated
with LINAC data (Sec. 3.3.1). The uncertainty in the absolute energy scale is better
than 1%. The energy resolution is 14% for 10 MeV electrons.
This energy reconstruction is for an electron or positron.
4.4

Muon Reconstruction

Most of the events that remain after the fiducial volume cut in the energy range
between 6 MeV and 20 MeV are spallation products by cosmic ray muons. The
spallation events can be removed by searching for spatial and timing correlation withpreceding muons. Therefore, the precise reconstruction of muon events is important.
4.4.1

Muboy Fitter

Events with more than 1000 p.e. are fitted by a fitter, Muboy [55, 46]. Muboyfits a single track muon and multiple (≤10) track muons. The fitted muon event isclassified as a single through-going muon, a stopping muon, multiple muons, or acorner clipper. When an event is fitted as multiple muons and its second track has a
few hits after removing the hits of the first track, the event is classified as one track
multiple muons. Muboy also returns a goodness value of the fit quality.
Due to the wide time window at SK-IV, a muon can be accidentally includedin the window of another event and not tagged as a muon event. There are a few
hundreds of untagged muons per day. To search for untagged muons and remove
spallation events from them, the software trigger is applied to each event. Muboy isapplied to these extracted untagged muons.
4.4.2

Brute Force Fitter

The Brute Force Fitter (BFF) is another fitter for the single through-going muons
poorly fitted by Muboy. If the Muboy goodness is less than 0.4, the BFF is applied.
BFF searches for the muon entry and exit point in a grid on the inner surface of thedetector [34]. It takes more time than Muboy. BFF correctly fits 75% of badly fit
muons by Muboy and improves spallation cuts.
4.4.3

Energy Loss

The muon energy loss along the track tends to be maximum at the point where themuon causes spallation. After fitting the muon track, the energy loss per unit length
along the track, dE/dx, is calculated. From timing information, the light each PMT
catches and the point on the track is matched.

33

4.5

Cherenkov Angle Reconstruction

In the low energy analysis, particles can be identified mainly by Cherenkov opening
angle. The electron and positron are ultra-relativistic and exhibit a Cherenkov angleof about 42◦ . Heavier particles such as muons or pions are not ultra-relativistic andhave smaller Cherenkov angle. PMT hits by multiple γ-rays are isotropic and not
shaped as a clear ring.
The Cherenkov angle is reconstructed from a 3-hit combination. Every combination of 3 PMTs gives an opening angle. The distribution of opening angles for
all combinations of hit PMTs have a peak at the Cherenkov angle of the event. To
reduce the effect of PMT dark noise, only the PMT hits whose residual time is in
the 15 ns window are used. Here, those 3 PMTs are viewed from the reconstructedvertex position. A typical electron event is shown in Fig. 4.5. In the left panel, theCherenkov angle is fitted at 43.2◦ . Since the shape of the distribution is difficult toparameterize, a sliding window in which the contents of neighboring 7 bins are added
to the middle bin is used for searching for the peak instead of fitting.
A typical muon event is shown in Fig. 4.5. It has a different opening angle
distribution. The Cherenkov angle is fitted at 31.5◦ .
A typical γ-ray event is shown in Fig. 4.5. The distribution is isotropic and fitted
at 87.3◦ .
NUM
1
RUN
62865
EVENT
111953134
DATE
9-Jan- 8
TIME
1:10: 0TOT PE:
208.8
MAX PE:
15.5
NMHIT :
135
ANT-PE:
6.6
ANT-MX:
1.4
NMHITA:
6

Opening Cherenkov Angle from 3-PMT combinations

600

h1

7-bin angle : 43.2 °

500

400

nrun : 62865
nevt : 111953134
nhits : 137
energy: 9.1 MeV
pi-like: 0.40
pi-like2: 0.89
pi-like3: 0.99

300

200

RunMODE:NORMALTRG ID :00000111
T diff.:0.145E+04us: 1.45ms
FSCC:
TDC0: 14910.0
Q thr. :0.0
BAD ch.: masked
SUB EV : 2/-1

100

0
0

10

20

30

40

50

60

70

80 90
DegreeFigure 21: Typical electron event. Left: opening angle distribution, right: event display.

A typical relatively high energy pion event is shown in Fig. 4.5. The reconstructed
Cherenkov angle is 44.1◦ . This kind of event cannot be distinguished be from electron
34

NUM
2
RUN
63568
EVENT
48046007
DATE
9-Mar- 6
TIME
22:53:40
TOT PE:
250.4
MAX PE:
33.8
NMHIT :
138
ANT-PE:
4.6
ANT-MX:
1.6
NMHITA:
6

Opening Cherenkov Angle from 3-PMT combinations

1200
1000
800

h2

7-bin angle : 31.5 °nrun : 63568
nevt : 48046007
nhits : 139
energy: 10.2 MeV
pi-like: 0.46
pi-like2: 0.97
pi-like3: 1.13

600
400
200
0
0

10

20

30

40

50

60

70

RunMODE:NORMALTRG ID :00000111
T diff.:0.286E+05us: 28.6ms
FSCC:
TDC0: 14910.0
Q thr. :0.0
BAD ch.: masked
SUB EV : 2/-1

80 90
DegreeFigure 22: Typical muon event. Left: opening angle distribution, Right: event display.

NUM
1
RUN
63288
EVENT
46200028
DATE
9-Feb-19
TIME
10:49:26
TOT PE:
152.2
MAX PE:
6.3
NMHIT :
124
ANT-PE:
14.1
ANT-MX:
2.5
NMHITA:
15

Opening Cherenkov Angle from 3-PMT combinations

450
400
350
300

h1

7-bin angle : 87.3 °nrun : 63288
nevt : 46200028
nhits : 125
energy: 8.8 MeV
pi-like: 0.75
pi-like2: 1.65
pi-like3: 1.81

250
200
150
100

RunMODE:NORMALTRG ID :00000111
T diff.:0.329E+05us: 32.9ms
FSCC:
TDC0: 14910.0
Q thr. :0.0
BAD ch.: masked
SUB EV : 2/-1

50
0
0

10

20

30

40

50

60

70

80 90
DegreeFigure 23: Typical γ-ray event. Left: opening angle distribution, Right: event display.

35

NUM
1
RUN
64313
EVENT
65670502
DATE
9-May-22
TIME
17: 5:40
TOT PE: 1340.1
MAX PE:
14.4
NMHIT :
798
ANT-PE:
5.0
ANT-MX:
1.3
NMHITA:
7

Opening Cherenkov Angle from 3-PMT combinations

h1

7-bin angle : 44.1 °35000
nrun : 64313
nevt : 65670502
nhits : 799
energy: 131.6 MeV

30000

pi-like: 0.62
pi-like2: 1.38
pi-like3: 1.66

25000
20000
15000
10000

RunMODE:NORMALTRG ID :00000111
T diff.:0.108E+05us: 10.8ms
FSCC:
TDC0: 14910.0
Q thr. :0.0
BAD ch.: masked
SUB EV : 2/-1

5000
0
0

10

20

30

40

50

60

70

80 90
DegreeFigure 24: Typical pion event. Left: opening angle distribution, Right: event display.

events by Cherenkov angle. Therefore, the peak width is used. The ring of a pion
event is sharp while the ring of an electron event is fuzzy. The ring sharpness isrelated to the peak width of the opening angle distribution. The peak width isevaluated with a pion likelihood:
πlike =

number of PMT sets in ± 3◦ around peak.
(number of PMT sets in ± 10◦ around peak) − (number of PMT sets in ± 3◦ around peak)

36

(16)

5

Event Simulation

To evaluate the reduction efficiency, a Monte Carlo simulation sample is used.
5.1

Detector Simulation

The Super-Kamiokande detector simulation package, SKDETSIM, is based on GEANT 3.21.
SKDETSIM include three steps in the simulation as follows,• Tracking of particles in the water.
• Propagation of emitted Cherenkov photons in the water.
• Detection of Cherenkov photons by PMTs and electronics.
The generated photons are attenuated in water and reflected by the detector structure and impurities in water. The photo-electron generated at a PMT surface isrecorded according to the timing resolution of PMTs. These parameters are tuned
to reproduce the calibration data[40, 39] .
5.1.1

Particle Tracking

For particle tracking, GEANT 3.21[2] is used. It is a system developed at CERN
to simulate electromagnetic processes. In addition to Cherenkov radiation, multiple
scattering, ionization, δ-ray production, Bremsstrahlung, and e+ annihilation are
considered for electrons. For gamma-rays, e+ e− pair creation, Compton scattering,and the photo-electric effect are taken into account.
The direction of Cherenkov photon emission is calculated as cos θ = 1/nβ. The
refractive index n depends on the wavelength, the water temperature and pressure.
The number of emitted photons along the trajectory of a charged particle per wavelength is calculated as Eq. 5.
5.1.2

Cherenkov Photon Tracking

The emitted photons propagate and are scattered and absorbed by water molecules.
The group velocity vg of light in water is defined as
c
,
(17)
vg =
n(λ) − λ dn(λ)
dλwhere c is the speed of light in vacuum, λ is the wavelength of the photon, and n(λ)
is the effective refractive index.
The considered photon interactions are Rayleigh scattering, Mie scattering, andabsorption. Due to the shorter wavelength of Cherenkov photons compared to theradius of water molecules, Rayleigh scattering is dominant. Rayleigh scattering has
37

a 1/λ4 dependence in the short wavelength region. The effect of absorption becomeslarger for the longer wavelength. The dependence is studied in [14].
The coefficients of water quality are tuned with the LINAC calibration at somewavelength (See Sec. 3.3.1). The time dependence of the water quality is monitoredby the N2 laser calibration and decay electrons.
5.1.3

Photon Detection by PMT and Electronics

After a photon reaches a PMT surface, the responses of the PMT and electronics arecalculated.
• Whether a photo-electron can be emitted or not
is determined from the quantum efficiency of the PMT (Fig. 9).
• The output charge
is simulated from the charge distribution of a single photo-electron (Fig. 25).
• The PMT hit timing
is calculated considering the timing resolution of the PMTs as a Gaussian random variable with a 1σ width (Fig. 26).
• The dark noiseare determined as randomly distributing throughout the detector with the measured dark noise rate.

Figure 25: Single photo-electron pulse height distribution. The peak close to 0 ADC count is due
to PMT dark current. From [25].

38Figure 26: Relative transit time distribution for a typical test with 410 nm wavelength light at thesingle photo-electron intensity level. From [25].

5.1.4

Water Transparency

The attenuation in water is related to the propagation of Cherenkov photons. The
intensity reduces exponentially:I(x) = I0 (λ)exp(−x/L(λ)),(18)

where I0 is the initial intensity, x is the traveling length and L is the total attenuation length (water transparency). The water transparency consists of 3 coefficients,
absorption αabs , Rayleigh scattering αRay , and Mie scattering αM ie . The angular
distribution of Rayleigh scattering is symmetric. Mie scattering favors the forward
direction. The empirical equations for the water transparency are:1
LM C (λ) =αabs + αsym + αasym
P1
αabs = P0 × 4 + C
λ
(19)
P4
P5
αsym = 4 × (1.0 + 2 )λλP7αasym = P6 × (1.0 + 4 × (λ − P8 )2 ,λwhere P1 8 are fitting parameters. The parameters are tuned with calibration data.
39

The water transparency has position dependency due to the convection under z =-11 m. It is monitored by two calibration sources, auto Xenon light and Ni-Cf. The
hit rate of the top PMTs and the bottom PMTs is used. The difference, top-bottom
asymmetry (T BA), is defined as:< top > − < bottom >,(20)< barrel >where < top > is the mean hit rate for the top PMTs and so on. The absorption
coefficient is corrected with T BA:
αabs (λ, z) = αabs (λ) × (1.0 + βz), z ≥ −11 m(21)= αabs (λ) × (1.0 − 1100β)z < −11 m.
T BA =

5.2

Neutrino Interaction Simulation

Inverse beta decay has been studied theoretically. In this thesis, Strumia and Vissani’s calculation[49] is used for the cross-section of ν¯e p → e+ n. The energy of thepositron is approximated as:
Ee = Eν − ∆∆ = Mn − Mp ≈ 1.293 M eV.

(22)

To get the reduction efficiency, the electron event is generated as follows:• Set electron energy, mono energetic (above 24 MeV) or randomly in the target
range (below 24 MeV).
• Set electron vertex in the SK full volume and direction randomly.
• Attach time information to consider water transparency.
• Simulate the detector reaction for the generated events by SKDETSIM.

40

6Data Reduction for GRB Neutrino Search

6.1

Data Set

The neutrino search was done for SK-IV data. At the beginning of SK-IV, GPSinformation was not available. Therefore, the target period is from December 7,2008 to May 31, 2017.
The GRB database is based on the Gamma-Ray Candidate Network (GCN). The
GCN distributes two types of information, the notices and circulars. A notice gives
the GRB location detected by the satellites. Most of the notices distribute during the
burst to the follow-up observations. A circular contains the various data of follow-up
observations by optical, radio, X-ray, TeV photons, or other particles.
Because circulars are unformatted e-mail messages, the system extracting information from the GCN circulars was developed. The database by the system, grbweb
online catalog1 , parses all GRBs archived at GCN circulars once a day. In the grbweb, parameters like GRB time, direction, start time, stop time, and redshift areincluded. When different values are reported from different satellites, one value isselected by a fixed order. The lists of that order and of parameters each satellites
gives are shown in Ref. [7].
2208 GRB were observed during SK normal data taking.
6.2

First Reduction

By first reduction, non-physical events and background events that are obviously
decay electron events or events near the wall are removed. This reduction is basedon that of the solar neutrino analysis and supernova relic neutrino search.
6.2.1

Calibration Event Cut

During normal data taking, calibration by laser and Xe light is done periodically.
The calibration events are marked by a specific event flag and ID trigger. We use
the events without these flags.
6.2.2

Noise Event Cut

One PMT flashes a thousand times per second. This sometimes causes noise events.
The p.e. by dark noise tend to be little, therefore the ratio of charge which is lessthan 0.5 p.e. to total charge is used for the noise event cut. Fig. 27 shows the
distribution of this ratio. Events with more than 0.55 ratio are removed.
1 http://grbweb.icecube.wisc.edu

41events/0.01

6000

5000

4000

3000

2000

1000

0
0

0.1

0.2

0.3

0.4

0.5

0.6
0.7
0.8
0.9
1
charge<0.5 p.e./total charge

Figure 27: ratio of charge < 0.5 p.e. to total charge

6.2.3

OD cutOD triggered events are the ones where charged particles come from outside of thedetector. We remove these events.
6.2.4

50 µs Time Difference Cut

Events after the 50µs LE trigger events or after un-tagged muon events are removed.
Un-tagged muon events are events included in the preceding HE trigger. A software
trigger requiring HE and OD trigger pair is applied to the events in a 35 µs window
after HE trigger. The events removed by this cut may be decay electron events or
ringing noise events from cosmic ray muons. The cosmic ray muons come into thedetector at 2 Hz. Fig. 28 shows the distribution of the time difference from the last
LE trigger to the events after Sec. 6.2.1-Sec. 6.2.3 reductions. It has a peak at 0 nsec
caused by decay electron events and ringing noise and tail after ∼50 nsec caused byindependent muons.
6.2.5

Fiducial Volume Cut

The SK detector is surrounded by rock. The radioactive events from the rock aredetected near the SK wall. The events with vertex within 2 m from wall are removed.
The fiducial volume cut is applied in two stages. At first, the events within 1 m

42number of events

103

102

10

1
2

4

6

8
10
log (tdiff(nsec))
10

Figure 28: Time difference from the last LE trigger to an event.

z axis(cm)# of event/10cm

from the wall are removed. The vertex distribution before the cut is shown in Fig. 29.
After this rough fiducial volume cut, the candidate events of the spallation parent
muon are selected. The parent muon for the spallation events in the fiducial volume
is less likely to be missed at muon selection.

7

10

15
10

6

10

5
5

10

0
4

10

-5
3

10

102

-10

0

500

1000

-15
0

1500
distance from wall(cm)

50

100

150
200
distance from center^2(cm^2)

Figure 29: Vertex distribution at first reduction. Left: histogram of distance from the wall. Right:
scatter plot of z versus x2 + y2 .

43

6.2.6

Goodness Cut# of events/0.01

We select well reconstructed events by a goodness cut. The combination of two
goodnesses Gv and DirKS is used. Gv shows the quality of vertex reconstruction
and DirKS the uniformity of azimuthal angle. The combined variable ovaQ (Onedimensional variable of Vertex and Angular reconstruction Quality) is defined as
G2v − DirKS2 . As shown in Fig. 30, the ovaQ distribution has two peaks, one at∼0 from badly reconstructed events and the other at ∼0.4 with well reconstructed
events. When ovaQ is less than 0.2, the event is removed.

2500

2000

1500

1000

500

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
G2v-DirKS2

Figure 30: Distribution of ovaQ, G2v − DirKS2 .

6.3

Spallation Cuts

Cosmic ray muons induce radioactive nuclei when muons produce hadronic cascadeshowers in the detector. To remove the event from the decay of this radioactive
isotope, following reduction was applied.
The spallation cuts are tuned for the supernova relic neutrino study [54]. The
possible radioactive isotopes induced by cosmic ray muons are listed in Table 1.
The spallation cuts are based on four variables, Dt, lt, ln, and Qpeak , where• Dt, time difference to a muon event.
• lt, transverse distance from muon track.

44

Table 1: The possible radioactive isotopes induced by cosmic ray muons.
Isotope Mean-life(s) Decay mode
Ekin. (MeV)
Primary process
11
−
19.9
β
11.51
(n, α+2p)
4 Be
β−γ9.41+2.1(γ)
16
10.3
β−
10.44
(n,p)
7 N
β−γ
4.27+6.13(γ)
15
3.53
β−
9.77
(n,2p)
6 C
β−γ
4.51+5.30(γ)
9
1.21
β−
∼13.0
(π − , α +2 H + p + n)
3 Li
8
+
B
1.11
β
∼13.9
(π + , α + 2p + 2n)
5
16
−
C
1.08
β
+
n
∼4
(pi− , n + p)
6
9
−
−
Li
0.26
β
13.6
(pi
, α + 2p + n)3
β− + nsim10
90.18
β+ + p3∼15(n, α + 4n)
6C
8
−
− 3
He
0.17
β
γ
9.67+0.98(γ)(π, H + 4p + n)2
β− + n
12
0.034
β−
11.71
(π − , α + p + n)
4 Be
12
−
0.029
β
13.37
(n, α + p)
5 B
13
−
−
B
0.025
β
13.44
(π
, 2p + n)
5
14
−
B
0.02
β
γ
14.55+6.09(γ)(n,3p)
5
12
0.016
β+
16.38
(π + , 2p + 2n)
7 N
13
+
−
0.013
β +p
8∼14
(µ , µ− + p + 2n + π − )
8 O
11
−
0.012
β
20.62
(pi+ , 5p + π 0 + π + )
3 Li
−
β +n
∼16

45

• Qpeak , the maximum value of energy deposit of the muon, dE/dx for 50 cm bin
along muon track.
• ln, longitudinal distance from the spallation point where dE/dx is maximum.
These variables are calculated for the muons within 30 sec before the low energy
event (Fig. 31-Fig. 34). Cosmic ray muons are categorized into four types, single
through-going muon, multiple muons, stopping muons, and corner-clipping muons.
The cut for stopping muons was applied at a later stage (N16 cut). To get the cut
efficiency, a random sample is prepared. In the random sample, muons 30 sec or lessafter low energy event are selected. The efficiency is shown in Table 2.

# of events

Table 2: Efficiency for the spallation cut.
Energy (MeV) Efficiency
9.0
83.2%
10.5
85.6%
11.5
85.5%
13.0
85.2%
15.0
83.5%
21.0
92.5%
27.0
100%

Entries 106025
Mean
15.07
RMS
8.675

640
620
600
580
560
540
520
500
480
460
0

5

10

15
20
25
30
time difference from muon (sec)Figure 31: Time difference from a muon.

46

# of events

Entries 106025
Mean
1700
RMS
808

2500

2000

1500

1000

500

0
0

500

1000 1500 2000 2500 3000 3500 4000 4500 5000
transverse distance from muon track(cm)# of events

Figure 32: Transverse distance from the muon track.

Entries 106025
Mean
198.1
RMS
158.2

240
220
200
180
160
140
120
100
80
60
40
20
0
0

50

100

150

200 250 300 350 400 450 500
maximum energy deposit of muon(/50cm)

Figure 33: Maximum energy deposit of the muon along its track.

47

# of events

Entries 106025
Mean
941.6
RMS
694.1

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

500

1000 1500 2000 2500 3000 3500 4000 4500 5000
longtitude distance from spallation point(cm)Figure 34: Longtitudinal distance from the spallation point to the maximum energy deposit point.

6.4

Gamma cut

The events incoming from outside the detector, such as environmental gamma-rays
from the surrounding rock are removed. For this cut, the variable effwall is used.
As shown in Fig. 35, effwall is the expected travel distance from the ID wall. It is
calculated from the vertex position and the event direction. The threshold is effwall
300 cm above 22 MeV and 450 cm under 22 MeV (Fig. 36).
6.5

Pion Cut

Atmospheric neutrinos sometimes make pions in the detector. The pion events withhigher momentum have a similar Cherenkov angle compared to neutrino events.
The pions soon interact in the water, lose energy, and stop emitting Cherenkov light.
Their rings are sharper than the neutrino ones. πlike defined as:
number of entry in ± 3◦ from peak
πlike =,
number of entry in ± 10◦ from peak − number of entry in ± 3◦ from peak
(23)
which shows the sharpness of the ring. The distribution of πlike (Fig. 37) has apeak from electron evens at ∼0.4 and a tail depending on the length of a π emitting
Cherenkov light. The events with πlike >= 0.58 are removed. Fig. 38 shows an event
display of a e-like and π-like event. The e-like event has ambiguous ring pattern andits πlike is 0.34. The π-like event has sharp ring patter and its πlike is 1.47.
48

200

# of events/50cm# of events/50cm

Figure 35: Definition of effwall.

180
160
140

20
18
16
14

120

12

100

10

80

8

60

6

40

4

20

2

0
0

1000

2000

3000

0
0

4000
effwall(cm)

1000

2000

3000

4000
effwall(cm)Figure 36: Distribution of effwall. Left: under 22 MeV, right: above 22 MeV.

49

Entries
3467
Mean
0.4445RMS
0.09335

1200
1000
800
600
400
200
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 37: The distribution of πlike .

Figure 38: Event display of an e-like event (left) and π-like event (right).

50

6.6

OD Correlated Event Cut

Because the OD coverage is lower than the ID, some incoming events are not triggered
as an OD event. To remove these events, the correlation of ID and OD is searched.
First, the peak of ID hits in a 50 ns sliding time window is searched considering
the time of flight from the candidate vertex. Then, OD hits within 5 m from thecandidate vertex and 150 ns from the ID peak is counted. The events with 2 or more
OD hits are removed. A schematic view of such an event is shown in Fig. 39.
In addition, the peak of OD hits in a 100 ns sliding time window is searched within
5 m from the candidate vertex. The events with 3 or more OD hits are removed.

Figure 39: Schematic view of the OD correlated event cut.

6.7

Multi-Ring Cut

The events that have two rings and an angle between rings more than 60◦ are removed. This cut removes atmospheric neutrino events that have a charged lepton
and a charged pion in the same event. They can produce multiple charged particles.
Since the ring pattern of a single electron event is fuzzy, it sometimes looks like
multiple rings.
A ring pattern fit is performed with a tool from Ref. [41]. After reconstructionof the vertex position and dominant ring by the vertex fitter, the ring fitter looks fora second ring by a pattern recognition technique using a Hough transformation [12].
The ring fitter repeats this four times (5th ring) while a probable ring can be found.
The fitter returns the number of rings and the direction of each ring.
To save these single electron events, only the multiple ring events with an angle
between rings more than 60◦ are removed. The distribution of angles between tworings is Fig. 6.7. The threshold, 60◦ is between peaks at ∼ 40◦ and ∼ 90◦ .
51

event/10°

Fig. 6.7 shows a typical multi ring event. The PMT hit timing after time-of-flight
subtraction looks like one event, but two rings are clearly seen in the event display.
The fitted angle for this event is 104◦ .
30

25

20

15

10

5

0
0

50

100

150
angle(°)

Figure 40: Angle between 2 rings.

6.8

Solar Events Cut

Events like solar neutrinos are removed. Since they interact via ν + e− → ν + e− ,the direction of the scattered electrons are oriented in the direction from the sun tothe earth to some extent.
Total energy, multiple scattering goodness (MSG), and angle to the sun are used.
MSG shows the goodness of anisotropy of the PMT hit pattern[4] . During Cherenkov
light emission, electrons scatter multiple times. The multiple scattering makes thering pattern broader and the angular resolution worse. MSG is calculated as follows:• Select pairs of hit PMTs within 20 ns from the initial event time after TOF
subtraction. The vectors from the vertex to each PMT are defined as ”hitdirection’”s.
• From the vertex, cones with 42◦ opening angle to the hit directions are projected.
For each pair of hit PMTs, 2 cones intersect at 0, and 1 or 2 points on thedetector surface.
• When pairs of PMT have 2 intersection points, the unit vector from the vertex
to the 2 intersections are taken. All the possible pairs of hit PMTs, this ”unit
vector” are found.
• For each candidate of ”unit vector”, the ”sum vector” is defined as a vector sumof the ”unit vectors” in 50◦ of that ”unit vector”. The longest ”sum vector” isselected as the ”best direction vector” and its direction as the ”best direction”.
52

Figure 41: Typical multi-ring event. The left is the event display. The top-right is the PMT hit
timing distribution after time-of-flight subtraction. The bottom right is the charge distribution.

• The MSG value is
MSG =Length of the best direction vector
number of unit vector for the best direction vector(24)

The electrons with many scattering has less MSG value (Fig. 42).
As reconstruction goodness and energy dependence of the direction distribution,
the cut criteria was decided as in Table 3

Figure 42: The schematic view of MSG calculation.

53

Table 3: Solar cut criteria. Cossun is the cosine of the angle to the sun.
Energy(MeV)
MSG
Cossun
19-20
0.93
18-19
< 0.4
0.45
0.4-0.5
0.77
0.5-0.6
0.81
> 0.6
0.91
17-18
< 0.4
0.35
0.4-0.5
0.61
0.5-0.6
0.73
> 0.6
0.73
< 16
< 0.4
-0.11
0.4-0.5
0.29
0.5-0.6
0.37
> 0.6
0.65

6.9

Pre/Post Activity Cut

We select events with a single charge peak in the gate window to remove events fromlow energy muons.
The electron events decayed from the muon with some energy are removed by
50 µs time difference cut. However, 50-µs cut, which uses the time difference to the
LE triggered event, can not remove events from the parent muons with lower energy
than the threshold of the LE trigger. These events can be detected by the promptγ, a few µs before the candidate. The prompt γ is produced with the muon at theinteraction of cosmic ray and the atmosphere.
Sometimes, the low energy muons themselves seem like the neutrinos because they
have similar Cherenkov angle. These muons decay in the detector and the electron
is observed after the main peak.
The width of the event gate window is 40 µs, 5 µs before the trigger and 35 µs
after. Because the lifetime of the muon is 2.2 µs, 35 µs is enough. In the gatewindow, the peak of the number of PMT hits within a 15 nsec(N15 ) sliding window
are searched. When an event has more than 12 hits peak before the trigger or 15 hits
peak after trigger, the event is removed. If a candidate event has SLE only triggered
event within the 40 µs gate and the distance between candidate event and SLE eventis less than 500 cm, that candidate event is removed.

54

6.10

µ/π Cut

Though most of the muon and pion events are removed by the pion cut or Cherenkov
angle cut, a few events/year survive. Because these events deposit large energy along
a short track, they have more charge in one PMT. From the number of hit PMTs in a
50 ns time window (N50) and the sum of the charge of those PMTs (Q50), the averagecharge per PMT (Q50/N50) is calculated. If Q50/N 50 > 2.0 + 0.0025 × energy, thenthat event is removed.
Q50/N50(p.e./hit)

Graph

70
60
50
40
30
20
10
0
0

2000

4000
energy(MeV)

Figure 43: The distribution of Q50/N50 as a function of the reconstructed energy.

6.11

N16 cut

When the low energy muon is captured by 16 O, 16 N is produced. 16 N decays with ahalf-life 7.13 sec and emits γ and/or electron. To remove this γ or electron events,
the correlation with the stopping muons are searched. If there is a stopping muon
between 100 µs to 30 s before the candidate and that muon vertex is within 250 cm
from the candidate vertex, that candidate event is removed.
6.12

Cherenkov Angle Cut

The Cherenkov angle cut removes low energy muons produced by atmospheric νµ andmultiple gamma-ray events which are often caused by neutral current interactions ofatmospheric neutrinos. The electron at SK energy range is relativistic. Its Cherenkov
55

Events/degree

angle is 42◦ . The interaction of atmospheric neutrinos and oxygen produces multiple
γ. A multiple γ event looks to have large Cherenkov angle. As muons are nonrelativistic, they have smaller Cherenkov angle. The cut criteria is the Cherenkov
angle be less than 38◦ (µ-like) or larger than 50◦ (γ-like).

350
300
250
200
150
100
50
0
0

10

20

30

40

50

60
70
80
90
Cherenkov angle (degrees)

Figure 44: Cherenkov angle distribution.

6.13

Summary of Reduction Efficiency

To estimate the reduction efficiency, mono-energetic events were generated by MC
simulation. The generated events distribute uniformly in the 32 kton FV.
The random sample (Sec. 6.3) is used for the spallation cuts and N16 cut, because
they need the correlation to proceeding muons.
The efficiency summary of each reduction steps is shown in Table 4. The total
efficiency was calculated as
number of survived events through all cuts
total efficiency =.
(25)
number of generated events in 22.5 kton
Thus, the efficiency is normalized by the size of the fiducial volume. The total
efficiency for the events in the 22.5 kton fiducial volume is shown in Fig. 45.

56

efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

50

100
energy(MeV)

Figure 45: Total reduction efficiency.

57

Table 4: Reduction efficiency.
Reduction
First reduction
Spallation cut
Gamma cut
Pion cut
OD correlated event cut
Multi ring cut
Solar event cut
Pre/post activity cutµ/π cut
N16 cut
Cherenkov angle cut

Data
1.7 × 10−4
0.11
0.84
0.84
0.91
0.95
0.96
0.94
0.55

12MeV
0.62
0.85
0.93
0.98
1.0
1.0
0.64
1.0
1.0
1.0
0.9

17MeV
0.67
0.87
9.94
0.99
1.0
0.99
0.80
1.0
1.0
1.0
0.94

19MeV
0.67
0.90
0.94
0.99
1.0
0.99
0.91
1.0
1.0
1.0
0.95

Efficiency
22MeV
0.67
0.95
0.97
0.99
1.0
0.99
0.99
1.0
1.0
1.0
0.95

38MeV
0.67
1.0
0.98
0.98
1.0
0.99
1.0
1.0
0.96
1.0
0.97

65MeV
0.67
1.0
0.98
0.96
1.0
0.98
1.0
1.0
0.91
1.0
0.98

80MeV
0.67
1.0
0.98
0.96
1.0
0.98
1.0
1.0
0.88
1.0
0.98

Efficiency methodMCrandom
MC
MC
MC
MC
MC
randomMC
randomMC

58

7Results of GRB neutrino searches

In this section, we analyze the data after the reduction in Sec. 6 and show the result.
In Sec. 7.1, neutrinos correlated with a GRB were searched for in the time windows
for each GRB. The time window is fixed to ±500 sec in Sec. 7.1.1. In Sec. 7.1.2,
the start and end time for each GRB is read from the GRB database and used as
the start/end time for the analysis time window. The significance of the number of
events in the time window to the expected background is discussed.
In Sec. 7.2, the excess from the background was searched for by stacking the dataof 2208 GRBs. The fluence limit for 1 GRB average was calculated.
7.1

Neutrino Search for Individual GRB

7.1.1±500 sec Analysis

GRBs with more neutrino events than expected background are searched for. Among±1000 sec reduction data, the inner 1000 sec (±500sec) is used as a search window
and outer 1000 sec (-1000∼-500 sec, +500∼+1000 sec) are used for backgroundestimation (Fig. 46).

Figure 46: The signal window and background window around a GRB event. The GRB trigger
time is the time from the GRB database (Sec. 6.1).

The search window was decided from the time scale of models and from theeffect of neutrino mass. For a core collapse supernovae, the neutrino luminosity is
expected to decrease in ∼10 sec and to be within 1 sec from explosion[43, 50] . For
neutron star mergers, neutrino emission is expected to continue a few tens of msec
after merging[35] . In Ref. [10], a cosmic string model is thought to be better suited
to describe the short GRB population. The neutrino emission time from gamma
emission is less than ∼10 sec for these three models.
Assuming neutrinos and gamma-rays are emitted at same time, neutrino detection59

is delayed by# of SK events

 2
1 mν
× (gamma-ray time-of-flight).
(26)
2 Eν
The combination of observations of the cosmic microwave background (CMB), baryon
acoustic oscillations, and CMB lensing limits the sum of neutrino masses to ≤0.23 eV. From the mass differences measured by neutrino oscillation experiments,
the maximum mass is less than 0.087 eV. The delay of 8 MeV neutrino from z=8.2
is ∼24 sec. Conservatively, a ±500 sec search window is selected.
No previous GRB neutrino search was done in SK-IV and the background ratein the detector may change during the 10 years of SK-IV running. The numberof events in the time window around a search window (Fig. 46) was checked. The
number of events after the first reduction and spallation cut for each GRB and its
distribution is shown in Fig. 47 and Fig. 48. Most of the events after the spallation
cut are events from cosmic rays, solar neutrinos, and surrounding rocks. The rateof these events is stable and the histogram becomes a Poisson distribution. Because
Fig. 48 is consistent with a Poisson distribution, the time variation of backgrounds
in the detector is negligible. The sum of the background window is used as the
background sample.

10

8

6

4

2

0
2008

2010

2012

2014

2016
2018
GRB time(year)

Figure 47: Number of events in the background window for each GRB after the spallation cut.

Fig. 49 shows a distribution of the number of events in each GRB after all reduction cuts are applied. For 2208 GRBs, 251 events remain in the background window
after reduction. The background rate for 1 GRB is 251/2208=0.114 events/GRB. In
Fig. 49, the red line shows number of GRBs that have a specific number of SK eventsin the search window. The black line shows expected number of Poisson distribution
with an average of 0.114 and 2208 samples.
60

1000

800

600

400

200

0
0

1

2

3

4

5

6

7

8

9

10

# of GRBs

Figure 48: Distribution of the number of events in the background window after spallation cut.

103

102

10

1

0

1

2

3

4
# of SK events

Figure 49: Number of SK events within ±500 sec around a GRB trigger. The black line shows the
expected number with the estimated background rate. Red points are the observed numbers.

61total energy(MeV)

The distribution of the observed number of events is consistent with background.
However, as shown in Fig. 49, 3 events remain in search window for a GRB. The GRB
with 3 SK events, 140616A is listed in Table 50. The energy and time difference fromthe remaining 3 SK event is shown in Fig. 50. These events can be spallation events.
The energy is in the spallation region (Sec. 6.3). The time, traversal distance, andlongitudinal distance from the most likely parent muon is small (Table 5).
12

10

8

6

4

2

0

-1000

-500

0

500
1000
time from GRB trigger(sec)Figure 50: The SK events around GRB140616A.

Energy (MeV)
11.0
10.7
11.2

Time difference (sec)
0.41
0.66
0.44

Traversal distance (m)
2.5
2.9
1.9

Longitudinal distance (m)
-6.6
-3.3
-7.5

Table 5: The status of the SK events around GRB140616A.

7.1.2

t1-t2 analysis

A GRB duration is distributed from 0.01 sec to 1000 sec (Fig. 51). If the neutrino
emission period is related to this duration, it would be better for reducing backgrounds to limit the time window to the GRB duration time rather than opening afixed time window like the analysis in the previous sub-section. The number of SK
events (Nev ) observed from the GRB start time (t1) to end time (t2) were counted(Fig. 52). There are 2194 GRBs with t1 and t2 available in the database.
The estimated number of background events in a t1-t2 window is 0.114events/2000 sec.×(t2 − t1). The probability of Nev in t1-t2 is calculated from a Poisson distribution of
62

# of GRBs

this expected background (<0.114). The probability distribution is shown in Fig. 53.
The most “rare” event is GRB130315A. This GRB has 2 SK events in a time widthof 271 sec and the probability is 0.00046.
30

25

20

15

10

5

0

-2

0

2
log10(t2-t1(sec))

2.5# of GRB

Nev

Figure 51: The distribution of t2-t1.

2

103

1.5
102
1

0.5

10

0
1
-0.5 -2
10

-1

10

1

10

2

10

3

10-4

10
t2-t1(sec)Figure 52: Nev versus t1-t2 width.

-3

10

10-2

10-1

1
probablity

Figure 53: The probability of Nev in t1-t2.

The consistency of Fig. 53 was estimated by toy Monte-Carlo (MC) simulation.
One MC set is calculated as follows.
• For a GRB, the number of SK events in ±1000 sec, N2000 , is determined from a
Poisson distribution of the background rate, 0.114 event/2000 sec.
• N2000 time differences from the GRB trigger time are randomly allocated (∆t1 , ∆t2 , ..., ∆tN2000 ).
• ∆ti in the t1-t2 window is counted. This is Nev for a GRB.
63

• The probability of Nev is calculated as in the data analysis.
• Repeat the above process for 2194 GRBs (where t1 and t2 data is available)
and make the probability distribution.

number of MC sets

From 10,000 sets of MC, the importance of “rare” events is evaluated. In the data,
1 GRB has Nev of probability less than 0.001 and 5 GRBs less than 0.01. 25.7% of
MC sets have 1 or more GRBs of probability less than 0.001 (Fig. 54). 60.5% of
MC sets have 5 or more GRBs of probability less than 0.01 (Fig. 55). The data is
consistent with the background.

104

103

102

0

2

4

6
8
10
number of rare GRB event

Figure 54: Number of MC sets with GRBs of toy MC probability less than 0.001.

7.2

Stack Analysis

As described in the previous sections, no obvious excess of events was observed foreach individual GRB. It can be understood that the expected number of events at
SK is much smaller than a single event and cannot be detected in the individual
GRB search. However, an excess could be seen by accumulating SK data for many
GRBs. We call this method the “stack analysis”. Fig. 56 shows the time variation of
SK events based on the GPS trigger time. In Fig. 56, no obvious excess around GRB
triggers is seen. The background sample is -1000 to -500 sec and 500 to 1000 sec fromthe GRB trigger times (total 25.6 days). The energy distribution shown in Fig. 57
is consistent with the background.

64

number of MC sets

1800
1600
1400
1200
1000
800
600
400
200
0
0

5

10

15
20
number of rare GRB event# of SK events/10sec

Figure 55: Number of MC sets with GRBs of toy MC probability less than 0.01.

10
9
8
7
6
5
4
3
2
1
0
-1000

-500

0

500
1000
time from GPS trigger(sec)Figure 56: Number of stacked SK events per 10 sec from GRB trigger times.

65

number of events/MeV

140
120
100
80
60
40
20
0
0

5

10

15

20
total energy(MeV)

Figure 57: Energy distribution of observed data (red) and background (black). The 21 MeV bin
includes events above 20 MeV.

7.2.1

Fluence Limit Calculation

Since no excess was seen, the fluence limit was calculated from the stacked data in
the following way[19] . Using a Poisson distribution with the background rate, N90 ,the 90% C.L. limit on the number of neutrino events in the search window can becalculated as
Z N90
Z ∞
dx Poisson(Nobs , x) = 0.9
dx Poisson(Nobs , x),
Nbg
Nbg
(27)
exp(−x)xNobs
Poisson(Nobs , x) =Nobs !
where Nbg is the expected number of background events, Nobs is the number ofobserved events and Pisson(Nobs , x) is the poisson probability for Nobs events withmean of x. When Nbg is expected and Nobs is observed, the probability that the
number of neutrino events is less than N90 , is 90%. For limit calculation, the eventsof 8-100 MeV are counted. Without the events above 100 MeV, Nbg is 221 and Nobs
is 218. From Nobs = 218, Nbg = 221, N90 is 23.9.
Then, the fluence limit Φ can be calculated by the equation,
N90
R
Φ=
,
(28)
NT dEν λ(Eν )σ(Eν )(Ee )where NT is the number of target nuclei in the SK 22.5 kton fiducial volume, λis the neutrino spectrum normalized to unity, σ is the total neutrino cross section
as a function of neutrino energy, and  is the detector efficiency. The neutrino
spectrum λ is assumed to be flat in this thesis. The cross-section σ by Strumia and66

Vissani [49] was used. The neutrino energy and the positron energy has a relationof Ee = Eν − 1.293 M eV (Sec. 5.2). The efficiency is calculated by applying the
reduction (Sec. 6) to the MC sample (Sec. 5) or random sample. Since the MC
sample was generated in the 32 kton inner detector volume, the efficiency for the
calculation is the one normalized to the 22.5 kton fiducial volume from the 32 kton
efficiency in Fig. 45.

Figure 58: The total cross-sections of quasi-elastic scattering. Figure from [49].

The fluence limit from 8 MeV to 100 MeV for all 2208 GRB is 1.03 × 108 cm−2 .
The fluence limit as a function of energy is also calculated. The energies selected
are 8, 15, 28, 38, 53, 65, and 80 MeV to divide the whole energy range in a log scale.
To see the effect of the energy threshold, a 10 and 12 MeV sample are added.
As observed events or background events, the events in the limited energy aroundthe target energy are counted. The energy range for each target energy is determined
as following.
First, the MC sample of that energy is made. The event vertex in the detector
and direction is decided randomly. Cherenkov light generation, propagation and thedetector response is simulated.
Then, the data reduction is applied to the sample and the energy distribution isfitted with a Gaussian to get the peak (Epeak ) and the RMS of the energy distribution(σ). 3 σ around Epeak is the energy range. For example, Fig. 59 is the energy
distribution after reduction of the 28 MeV sample. The energy peak is 28.02 MeV.
2.89 MeV is the deviation and 19.35-36.69 MeV is the energy range. Table 6 showsthe energy peak and the RMS for the each MC energy and Table 7 shows the N90
67and the fluence limit.

Figure 59: The energy distribution of the 28 MeV MC sample after reduction.

The background events in the 25.6 days sample is too small for the samples above
38 MeV. The background sample was enlarged to the normal data taking period from
December 2008 to March 2017 without ±1000 sec around GRBs. The livetime is 2826
days. The numbers of expected events around each energy is shown in Table 7.
The 4 events of 38 MeV and 53 MeV are the same events. Their energies are
41.7 MeV (GRB100911A), 44.8 MeV (GRB110801A), 47.4 MeV (GRB150127C),
and 41.5 MeV (GRB150301A). The 1 event in the 65 MeV and 80 MeV samples is75.4 MeV around GRB130509A.
The limit for all GRBs is listed in Table 7. The limits for 1813 long GRBs / 323
short GRBs are also calculated from the number of observed events around long/short
GRBs and the background ratio is the same for all GRBs. Table 8 and Table 9 show
number of observed events, number of expected background events, N90 , and theneutrino fluence limit for long and short GRBs. From Fig. 6 in Sec. 1.3, we compare
this limit to the limit of the previous SK study and limit from Borexino. Fig. 60 shows
the neutrino fluence upper limit per GRB. This study gives the best limit at 28 MeV
to 80 MeV. In the previous SK study, the fluence limit as a function of energy is
the limit on monoenergetic neutrinos at specific energies (Eν0 ). Therefore the energy
range and N90 is same for all energy point. The efficiency at those energies ((Eν0 ))were calculated by MC simulation of the monoenergetic neutrino events. With thisefficiency, the fluence limit was obtained by replacing λ(Eν0 ) in eq. 28 by a delta
function δ(Eν − Eν0 ). The limit of the previous SK study is still better under 20 MeV
due to its wide energy range (7-80 MeV).
68

Figure 60: The fluence limt per GRB per MeV. Width of the marker is the energy range of thelimit calculation. Red is this study. Green is the previous SK study [28]. In the previous SK study,energy range of events were same for all the data points and are indicated with the horizontal bar.
The detector efficiency was estimated by simulations assuming a monochromatic neutrino energy
indicated by the filled circle. Black is Borexino study [22].

Positron energy (MeV)
8
10
12
15
28
38
53
65
80

Energy peak after reduction (MeV)
7.94
10.07
12.10
15.25
28.02
37.97
52.71
64.50
79.38

RMS (MeV)
1.31
1.45
1.60
1.91
2.89
3.68
4.78
5.47
6.07

Table 6: The relation of MC energy and reconstructed energy.

69

Neutrino energy (MeV)
9.23±3.93
11.36±4.35
13.39±4.80
16.54±5.73
29.31±8.67
39.26±11.04
54.0±14.34
65.79±16.41
80.67±18.21# of observed event
198
212
213
80
0
4
4
1
1

# of expected event
210
219
220
67
0
1.78
1.59
1.06
0.90

N90
18.6
21.5
21.6
26.9
2.30
6.28
6.44
3.25
3.31

Fluence limit (cm−2 )1.62 × 1010
5.75 × 109
3.40 × 109
2.27 × 109
3.14 × 107
4.98 × 107
2.99 × 107
1.12 × 107
1.73 × 107

Table 7: The 90% C.L. of number of event and the fluence limit for 2208 GRBs.

Positron energy (MeV)
9.23±3.93
11.36±4.35
13.39±4.80
16.54±5.73
29.31±8.67
39.26±11.04
54.0±14.34
65.79±16.41
80.67±18.21# of observed event
152
161
162
59
0
3
3
1
1

# of expected event
172
180
181
55.0
0
1.47
1.31
0.87
0.74

N90
13.2
14.2
14.3
16.6
2.30
5.32
5.44
3.32
3.38

Fluence limit (cm−2 )1.15 × 1010
3.78 × 1010
2.25 × 109
1.15 × 109
3.14 × 109
4.22 × 107
2.53 × 107
1.15 × 107
1.77 × 108

Table 8: The 90% C.L. of number of event and the fluence limit for 1813 long GRBs.

Positron energy (MeV)
9.23±3.93
11.36±4.35
13.39±4.80
16.54±5.73
29.31±8.67
39.26±11.94
54.0±14.34
65.79±16.41
80.67±18.21# of observed event
41
45
45
18
0
1
1
0
0

# of expected event
30.7
32.0
32.2
9.80
0
0.26
0.23
0.16
0.13

N90
19.9
22.9
22.8
15.0
2.30
3.67
3.69
2.30
2.30

Fluence limit(cm−2 )1.73 × 1010
6.11 × 109
3.58 × 109
1.31 × 109
3.14 × 107
2.91 × 107
1.71 × 107
7.93 × 106
1.20 × 107

Table 9: The 90% C.L. of number of event and the fluence limit for 323 short GRBs.

70

8

Summary and Outlook

8.1

Summary

Neutrinos associated with GRBs were searched for in the SK detector. GRBs are
one of the most luminous astronomical objects ever observed. By the improvementof satellites and ground telescopes, some features of GRBs are observed. However,no models are confirmed as the mechanism for GRBs. Neutrino observation will help
to study the mechanism.
Until now, no clear neutrino signal is observed with GRBs. In the previous stackstudy of SK, neutrinos for 1454 GRBs in the SK-I period were searched for. In thisstudy, 2208 GRBs from Dec. 2008 to Mar. 2017 is the target. After reduction, 250
events remain in the search window, ±500 sec around each GRB trigger time, while
the background rate is 0.114 events/1000 sec. No obvious excess was seen in the timedevelopment of the number of events and energy distribution of the combined data.
Three or less SK events are detected in the ±500 sec window for individual GRBs.
Three SK events around GRB140616A may be spallation events because their vertex
and timing is near the most likely parent muons.
Considering the neutrino emission period that is related to the gamma duration,
we tried a new analysis method as follows. The number of SK events between GRB
start/stop time (Nev ) was also studied. The probability that a GRB has Nev or more
SK events was calculated for each GRB. The distribution of this probability wasevaluated by toy MC simulation. The timing of SK events were randomly allocatedand a distribution of the probability was generated. In this study, the data is consistent with the background. Though no obvious signal is observed, the fluence limit
was calculated from stacked data. The limit from 8 MeV to 100 MeV for all 2208
GRB is 1.03 × 108 cm−2 . The flat spectrum was assumed. The limit per GRB is
5.07 × 105 cm−2 . The redshift of 189 GRBs were observed and the average is z = 1.8.
The expected fluence from a cosmic string model at this distance is ∼ 107 −108 cm−2 .
The mechanism for most GRBs is not the cosmic string model.
The limit as a function of energy is calculated. MC events are generated andreductions are applied for typical energies. In the energy distribution after reduction,
the energy peak ±3σ was set as the energy range for each energy. The events in theenergy range are counted as signal or background. Then, the limit is calculated to be
1.5 × 105 cm−2 /MeV/GRB at 12 MeV. In this study, the limits for long GRBs andshort GRBs are calculated. The better efficiency of SK-IV and the large statistics
gives a better fluence limit between 28 MeV to 80 MeV.

71

8.2

OutlookA new phase of SK, SK-Gd[9] will start soon. In SK-Gd, 0.2% gadolinium sulfate
Gds(SO4 )3 will be added to the SK water in order to identify ν¯e events. The identification of ν¯e is useful for the detection of supernova relic neutrinos and the directionof supernova bursts. Gadolinium captures a neutron from inverse beta decay andemits gamma rays of ∼8 MeV total energy (Fig. 8.2).

Figure 61: Neutron tagging with gadolinium. Figure from Ref. [47].

Supernova relic neutrinos are the accumulated neutrinos of the supernovae thathave been occurring since the beginning of the universe. The background rate for the
relic neutrino search can decreased by detecting the coincidence of positron signals
and delayed gammas from protons that capture neutrons. The detection of this
2.2 MeV gamma-ray with Cherenkov light has a low efficiency to clearly distinguishfrom the background. On the other hand, 8 MeV gamma-rays from gadoliniumthat captures neutrons can be detected with Cherenkov light. The cross-section ofneutron capture by gadolinium is about 5 orders of magnitude larger than that ofproton.
The effect of dissolving gadolinium in the SK water was studied by an R&D
project called EGADS. Gd2 (SO4 )3 is dissolved into a 200 m3 tank like a small SK
tank. A selective water filtering system which removes impurities except for gadolinium has been developed. The neutron capture efficiency and impact to the watertransparency was studied. The EGADS experiment determined a target concentration of Gd2 (SO4 )3 to be 0.2%.
72

In the current study, the dominant backgrounds are spallation events below ∼20 MeV
and decay electron events from invisible muons by atmospheric neutrino above that.
Most of the spallation processes emit neutrons and will be removed by neutron tagging. 93 Li is a possible radioactive isotope produced by the cosmic ray muons thatemits neutrons and electrons above the energy threshold. The backgrounds by spallation will become small and neutral current events will be the dominant background.
The expected background rate is ∼2 events/year. The decay electron events do notemit neutrons and the background will become sim1/4. The fluence limit of 10 years
SK-Gd observation can be estimated by substituting expected background rate anddetector efficiency of 80% to Eq. 28. The limit is expected to become ∼1/6 below
15 MeV and ∼1/2 above 28 MeV.

73

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