Master Thesis

Study of Super-Kamiokande detector calibration
using cosmogenic neutron capture on Gadolinium( ガドリニウムによる核破砕中性子捕獲を用いたスーパーカミ
オカンデ検出器較正の研究 )March 19, 2023

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

Shizuka Shima
志摩靜香Abstract
The Super-Kamiokande experiment is an experiment observing neutrinos andsearching for proton decay using the world’s largest water Cherenkov detector. In
the summer of 2020, the gadolinium was added to pure water in Super-Kamiokande.
This resulted in a gadolinium concentration of about 0.01%, and significantly improved the efficiency of neutron detection. Furthermore, in the summer of 2022,
additional Gd was introduced, increasing the Gd concentration from 0.01% to
0.03%.
In this study, spallation neutrons are used for calibrating and monitoring theSuper-Kamiokande detector. Spallation neutron is the neutron produced by thespallation reaction of cosmic ray muons with oxygen nuclei in water. There are
two advantages of using spallation neutrons. First, they can be detected acrossthe entire detector, which allows us to investigate detailed position dependence.
Second, sufficient statistics can be obtained in a short time. They have also thedisadvantages that the detected energy is low and background is difficult to remove,and they are affected by pile-up. The event selection for spallation neutrons has
been developed to take these into account.
The stability of the detector response at ordinarily times and the Gd concentration during Gd-loading are monitored using these properties. In the former,
the stability of the detector was checked by evaluating the energy and Gd concentration. As a result, the energy detected by the detector was stable at about±1%, and the Gd concentration was also stable at about ±2%. In the latter, thetransition of Gd concentration during Gd-loading was checked by evaluating thenumber of spallation neutron signals and the time constant. We checked that Gd
was loaded as expected.
An energy calibration method is studied using the spallation neutron. Firstly,
to check if the neutron capture signal by Gd can be used to evaluate the energy
scale of electron events, the position dependence of the energy scale of neutron andelectron is compared using MC simulation. The result is that the energy scale forelectron and neutron events are consistent within about ±2% of the entire detector.
This is however a larger deviation compared to the goal of correcting positional
dependence to within 0.5%. It will be important to understand the causes of this in
the future. Next, to check if the MC simulation reproduces the data, the position
dependence of the energy scale for neutrons is compared between the data andMC simulation. As a result, it is found that the closer to the barrel wall of thetank, the larger the energy of the MC simulation compared to the data, and at
the bottom of the tank, the MC simulation differ from the data by about ±1%.
Since energy reconstruction is carried out using MC simulations, it is important
to investigate these in more detail in the future and to improve the MC simulation
to better reproduce the data.

Contents
1 Physics Motivation
1.1 Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . .
1.2 Solar neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Solar neutrino production . . . . . . . . . . . . . . . . . . .
1.2.2 MSW effect of solar neutrino . . . . . . . . . . . . . . . . . .
1.3 Diffuse Supernova Neutrino Background (DSNB) . . . . . . . . . .
1.3.1 Supernova explosion . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Supernova neutrino . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Diffuse Supernova Neutrino Background . . . . . . . . . . .

5
5
5
8
8
9
12
12
13
14

2 Super-Kamiokande experiment
2.1 The Super-Kamiokande detector . . . . . . . . . . . . . . . . . . . .
2.1.1 Cherenkov light . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Inner detector and Outer detector . . . . . . . . . . . . . . .
2.1.3 Photo Multiplayer Tube (PMT) . . . . . . . . . . . . . . . .
2.2 Data acquisition systems . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Detector performance per data acquisition period . . . . . . . . . .
2.4 Super-Kamiokande with Gd . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Recirculation system for Gd-loaded water . . . . . . . . . . .
2.4.3 Gadolinium loading . . . . . . . . . . . . . . . . . . . . . . .
2.5 Search for DSNB in SK-Gd . . . . . . . . . . . . . . . . . . . . . .
2.5.1 DSNB signal . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Backgrounds for DSNB . . . . . . . . . . . . . . . . . . . . .

18
18
18
20
22
22
25
26
26
27
30
33
33
35

3 Overview of calibrations in a few to tens of MeV region
3.1 Basic calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Energy calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Motivation for energy calibration using spallation neutrons . . . . .

40
40
42
44

2

4 Calibration of SK detector response
4.1 PMT related calibration . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Relative QE . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Relative timing . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Water related calibration . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Water parameter tuning with laser . . . . . . . . . . . . . .
4.2.2 Water transparency measurement with decay electron . . . .
4.2.3 Top Bottom Asymmetry . . . . . . . . . . . . . . . . . . . .

46
46
46
49
51
51
52
54

5 Energy reconstruction and calibration in a few to tens of MeV
region58
5.1 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.1 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . 58
5.1.2 Direction reconstruction . . . . . . . . . . . . . . . . . . . . 60
5.1.3 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . 61
5.2 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Deuterium-Tritium (DT) calibration . . . . . . . . . . . . . 65
5.2.3 16 N energy scale calibration . . . . . . . . . . . . . . . . . . 67
5.2.4 Decay electron . . . . . . . . . . . . . . . . . . . . . . . . . 69
6 Evaluation of spallation neutron signal
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Spallation neutron . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Feature of spallation neutrons . . . . . . . . . . . . . . . . .
6.2.2 Advantages and disadvantages of spallation neutrons . . . .
6.2.3 Study using spallation neutron . . . . . . . . . . . . . . . . .
6.3 Event selection of Spallation neutron . . . . . . . . . . . . . . . . .
6.3.1 Triggers for spallation neutron event search . . . . . . . . . .
6.3.2 Muon selection . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Neutron selection . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Study of pile-up effect . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Evaluation of mean N50 . . . . . . . . . . . . . . . . . . . .
6.4.2 Neutron multiplicity . . . . . . . . . . . . . . . . . . . . . .
6.4.3 Comparison with Am/Be data . . . . . . . . . . . . . . . . .

73
73
73
73
74
75
77
77
77
78
82
82
84
86

7 Detector performance monitoring using spallation neutrons
7.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Evaluation of stability using energy with mean Neff . . . . .
7.1.2 Evaluation of stability using Gd concentration with the time
constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92
92
92

3

94

7.2

Monitor of additional Gd-loading in 2022 . . . . . . . . . . . . . . .
7.2.1 Event selection of Spallation neutron for Gd-loading monitor
7.2.2 Monitor by number of spallation neutron signal . . . . . . .
7.2.3 Monitor by neutron capture time constant . . . . . . . . . .

95
95
96
99

8 Energy scale calibration with spallation neutrons101
8.1 Comparison of position dependence of neutron and electron signals
by MC simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.1.1 Evaluation of the electron and neutron signal with MC simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8.1.2 Results of the event reconstruction . . . . . . . . . . . . . . 104
8.1.3 Comparison of the position dependence of the energy scaleof electron and neutron . . . . . . . . . . . . . . . . . . . . . 104
8.2 Comparison of MC simulation and data for spallation neutron . . . 106
8.2.1 Results of the event reconstruction for data . . . . . . . . . 106
8.2.2 Comparison of the deviation of the energy scale of MC simulation and data for Gd(n, γ) signal . . . . . . . . . . . . . . 106
9 Conclusion

109

A Water circulating system

112

B Calibration of Gadolinium concentration
114
B.1 Am/Be neutron source . . . . . . . . . . . . . . . . . . . . . . . . . 114
C Fitting results
119
C.1 Position dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 119
C.1.1 Electron with MC simulation . . . . . . . . . . . . . . . . . 119
C.1.2 Neutron with MC simulation . . . . . . . . . . . . . . . . . . 119
C.1.3 Neutron with data . . . . . . . . . . . . . . . . . . . . . . . 119

4

Chapter 1
Physics Motivation
In this thesis, the energy calibration of Super-Kamiokande for the observationof solar neutrino and Diffuse Supernova Neutrino Background (DSNB), which
are physical targets in a few to tens of MeV (the low energy region in SuperKamiokande), is discussed. Firstly, in this chapter, explanation of neutrino andintroduction of solar neutrino and DSNB are given.

1.1

Neutrino

Neutrinos are elementary particles with no electric charge. They interact withother particles via the weak force and gravity only. Neutrinos interact with othermatter only rarely. They were predicted to exist by Pauli in 1930 to explain
the missing energy in beta decays, and were first observed by C. Cowan and F.
Reines in 1956 [1]. If we can observe neutrinos produced in the Universe, we
can investigate the phenomena occurring at their source. So far, astrophysicalneutrinos have been observed from fusion reactions in the center of the Sun [2],supernova explosions [3], and blazars [4].

1.1.1

Neutrino oscillation

Neutrino oscillation is one of the important properties of neutrinos. Neutrino
oscillation is a phenomenon in which one flavor of neutrino stochastically changes
to another flavor with time evolution. Neutrino was thought to have no mass in thestandard model of particle physics. However, neutrino oscillation was discovered
with observations of atmospheric and solar neutrinos, revealing that neutrinos havemasses [[5],[6]]. The neutrino flavor eigenstates |να ⟩ (α = e, µ, τ ) can be expressed5using their mass eigenstates |νi ⟩ (i = 1, 2, 3):X|να ⟩ =
Uαi |νi ⟩

(1.1)

i=0

where U is a 3 × 3 unitary matrix which is called Pontecorvo-Maki-NakagawaSakata (PMNS) matrix [7]. This PMNS matrix can be written as,




1
0
0
c13
0 s13 e−iδCPc12 s12 0 −s12 c12 0
010
U = 0 c23 s23  iδCP
0 −s23 c23−s13 e
0
c13
0
0 1


(1.2)
c12 s13s12 c13s13 e−iδCPc13 s23  ,= −s12 c23 − c12 s13 s23 e−iδCP c12 c23 − s12 s13 s23 eiδCPs12 s23 − c12 s13 s23 eiδCP
c12 c23 − s12 s13 s23 e−iδCPc13 c23
where cij = cosθij and sij = sinθij which are the parameters representing thedegree of mixing of mass eigenstates, and are called neutrino mixing angles. δCP
represents the CP phase in the lepton sector, indicating that the CP symmetryof neutrino is broken when sinδCP ̸= 0, but this has not yet been observed. In
vacuum, the time evolution of the neutrino mass eigenstate |νi (t)⟩ satisfies thefollowing Schrödinger equation,−id|νi ⟩ = H |νi (t)⟩ = Ei |νi (t)⟩
dt

(1.3)

|νi ⟩ = exp(−iEi t) |νi (0)⟩ ,(1.4)

where Ei is the energy of mass eigenstate, H represents Hamiltonian and t isa travering time of the neutrino. From Eq 1.1, the time evolution of a flavor
eigenstate |να (t)⟩ can be written asX|να (t)⟩ =Uαi exp(−iEi t) |νi (0)⟩(1.5)
i

The amplitude when νβ is detected at time t starting from να isXX†
A(να → νβ ) = ⟨νβ |να (t)⟩ =exp(−iEi t)Uαi Uβi⟨νi |νj ⟩
i

=

X

j
†
e−iEi t Uαi Uβi
,

(1.6)

i

The neutrino oscillation probability (να → νβ ) in vacuum is given as follows.
P (να → νβ ) = |A(να → νβ )|2XX††=
Uαi UβiUαjUβj exp(−i(Ei − Ej )t)
i

j

6

(1.7)

When the squared mass of a neutrinos m2i are small compared to their momentap, an approximation is as follow,
Ei =q

p2i + m2i ≈ pi +

m2i
m2i
≈p+
,
2pi
2Ei

(1.8)

where pi and mi represent the momentum eigenvalue and mass eigenvalue, respectively. Then, Eq 1.7 becomes
!
2
2
X
(m
−
m
)
i
j
†
†
P (να → νβ ) =Uαi UβiUαjUβj exp −i
t
2E
i,j
!
2
X
∆m
ij
†
†
t
=
Uαi UβiUαjUβj exp −i
2E
i,j
!
2
X
∆m
ij
†
†
=
Uαi UβiUαjUβj exp −i
L
(1.9)
2E
i,j
!
X
∆m2ij
†
†
2
L
= δαβ − 4Re[Uαi Uβi Uαj Uβj ]sin
4E
i<j
!
2
X
∆m
ij
†
†
Uβj ]sin+2
Im[Uαi Uβi
Uαj
L ,
2E
i<j
where ∆m2ij = m2i − m2j is a mass-squared difference, E is the average neutrinoenergy E ≃ γ(mi + mj )/2, t is replaced with a travel distance L = ct and δαβ is
the Kronecker’s delta.
Considering two generations of neutrino oscillation at νe ↔ νµ for simplicity,
since the unitary matrix is written ascosθ sinθU2×2 =(1.10)−sinθ cosθthe neutrino oscillation probability P (νe ↔ νµ ) is written as,!
2∆m
P (νe ↔ νµ ) = sin2 2θsin2
L
4E= sin2 2θsin2!
1.27∆m2 [eV2 ]L[m]E[MeV](1.11)

From Eq 1.11, it can be seen that neutrino oscillation occurs when there is adifference in the neutrino mass eigenvalues.
7

Neutrino oscillation parameters
Neutrino oscillation in a vacuum can be described by six parameters:
θ12 , θ23 , θ13 , ∆m221 , ∆m232 , δCP(1.12)

These parameters have been measured by using various neutrino sources:
solar, reactor, atmospheric and accelerator neutrinos. The best fit values ofglobal analysis of neutrino data are summarized in Table 1.1. There are two
possibilities of mass ordering, which depend on the ordering of the neutrinomass eigenstates. This is because neutrino oscillation experiments can mainly
measure the absolute value of δm2 , but they are not very sensitive to its sign.
The order m1 < m2 < m3 is called Normal Ordering (NO), and the orderm3 < m1 < m2 is called Inverted Ordering (IO).
Table 1.1: Neutrino oscillation parameters [8]. NO is normal mass ordering and IO is
inverted mass ordering.

Oscillation parameter Best fit valuesin2 θ12
0.307 ± 0.013
sin2 θ23 (IO)
0.539 ± 0.022
2
sin θ23 (NO)
0.546 ± 0.021
sin2 θ13(2.20 ± 0.07) × 10−2∆m221
(7.53 ± 0.18) × 10−5 eV2(−2.536 ± 0.034) × 10−3 eV2∆m232 (IO)
∆m232 (NO)
(2.453 ± 0.033) × 10−3 eV2

1.2

Solar neutrino

Solar neutrino is neutrino produced from solar fusion reaction. 2×1038 electron
neutrinos per second are produced mainly through the two processes called ppchain and CNO cycle. Solar neutrino observations have been carried out at SuperKamiokande [9], Kamiokande [10], Homestake[11], KamLAND [12], SAGE [13],GALLEX/GNO [14], Borexino [15], and Sudbury Neutrino Observatory (SNO) [6].

1.2.1

Solar neutrino production

pp-chainIn the pp-chain, solar (electron) neutrinos are produced by the following
reactions:8• pp neutrino• pep neutrino• hep neutrino

3• 7 Be neutrino• 8 B neutrinop + p → 2 H + e+ + νe

(1.13)

p + e − + p → 2 H + νe

(1.14)He + p → 4 He + e+ + νe

(1.15)Be + e− → 7 Li + νe

(1.16)

7

8∗

B + e− → 8 Be + e+ + νe

(1.17)

CNO cycle
In the CNO cycle, solar neutrinos are produced by the following reactions:• 13 N neutrino• 15 O neutrino• 17 F neutrino

13

N → 13 C + e+ + νe

(1.18)

15

O → 15 N + e+ + νe

(1.19)

17

F → 17 O + e+ + νe

(1.20)

Since the central temperature of the Sun is about 107 K, the pp chain is dominant (about 99%). Figure 1.1 shows the solar neutrino energy spectrum predictedfrom the standard solar model. The pep neutrinos and 7 Be neutrinos are produced with two-body final state, so they have a single energy spectrum, while all
the others are produced with three-body final state, so they have a broad energy
spectrum. At Super-Kamiokande, the energy threshold is 3.5 MeV, so 8 B neutrinos
with a relatively large flux above 3.5 MeV can be observed.

1.2.2

MSW effect of solar neutrino

MSW effect
As neutrinos pass through matter, they cause elastic scattering with theelectrons, protons and neutrons in that matter, and the matter field acts on
the neutrinos. The neutral-current interactions occur in all neutrino flavor
states via a neutral current Z boson exchange, whereas the charged-current
reactions occur only in electron neutrinos via a charged current W ± boson
9

Figure 1.1: Energy spectrum of the solar neutrino [16]exchange. The charged current interaction affects the oscillation transition
due to the additional contribution to the Hamiltonian. The effective potentials of the different neutrino flavors are written as,
Ve = VCC + VNC
Vµ = Vτ = VNC(1.21)(1.22)

where NC represents the neutral current and CC represents the charged
current interactions. They are expressed as√(1.23)VCC = 2GF ne√
2
VNC = − GF nn(1.24)
2
where ne is the effective potential of the number density of electrons in thematerial, nn is the effective potential of the number density of neutrons in
the material, and GF is the Fermi coupling constant.
Considering two generations of neutrino oscillation at νe ↔ νµ for simplicity,
the neutrino equation of state in vacuum is expressed as," #  d νe∆m2 −cos2θ sin2θνe= −i(1.25)
sin2θ cos2θ
νµ
dt νµ
4E
10

Considering the additional contribution from the charged current interaction,
it is expressed as,
"
 

 
#  
∆m2 −cos2θ sin2θ
d νe
VCC 0
νe
= −i
+
sin2θ cos2θ
0 0
νµ
dt νµ
4E


√
∆m2
∆m2
  (1.26)
− 4E cos2θ + 2GF ne 4E sin2θ  νe= −i 

∆m2
∆m2
νµ
sin2θ
cos2θ
4E
4E
In order to diagonalize the matrix, the mixing matrix in matter UM is definedas,
cosθM sinθM
UM =(1.27)
sinθM cosθM
where the effective mixing angel θM is given bytan2θM = ∆m2
2E

∆m2
sin2θ
2E

cos2θ −√

2GF neTherefore, the oscillatory term in Eq 1.26 can be written as," #  
d νe∆m2M −cos2θM sin2θM
νe
= −i
ν
sin2θ
cos2θ
ν
dt µ
4E
M
M
µ
where ∆m2M is the effective mixing mass difference,q22∆mM = ∆m (cos2θ − A)2 + sin2 2θ

(1.28)(1.29)(1.30)

where√
2 2GF ne EA=,
(1.31)∆m2
The neutrino oscillation probability PM (νe ↔ νµ ) in matter is expressed asfollows.
!
2∆m
M
PM (νe ↔ νµ ) = sin2 2θM sin2
L
(1.32)
4E
It can be seen that the oscillation probability is determined by the density ofmatter passing through in addition to the neutrino energy and flight distance.
If A = cos2θ, that is,
∆m2
√
cos2θ
(1.33)nR=e
2 2GF Ethe neutrino mixing is maximum. This effect is called the MSW(MikheyevSmirnov-Wolfenstein) effect [17].
11Figure 1.2: Electron density dependence of neutrino masses in the sun [6]. The vertical axis represents neutrino mass squared, the horizontal axis represents
electron density.

MSW effect of solar neutrino
Solar neutrinos are produced near the high-density solar center and are therefore affected by the MSW effect in the process of reaching the surface of thesun.
Figure 1.2 shows the dependence of neutrino mass on electron density in theSun. The flavors of neutrinos are mixed, so they transition along the solidline in the figure, keeping ∆m2M ̸= 0. Thus, νe produced near the dense solar
center changes to νµ when it comes to the solar surface (ne = 0) due to the
MSW effect.

1.3

Diffuse Supernova Neutrino Background (DSNB)

1.3.1

Supernova explosion

A supernova explosion is an explosion that occurs when a massive star or
white dwarf reaches the end of its life or exceeds a certain amount of mass due tointeraction with another dwarf star. After the explosion, the energy (∼ 1051 erg)
spreads throughout the universe and is the basis for the evolution of galaxies,
planets, and other stars. Therefore, supernova events are of great interest to
astrophysics.

12

Figure 1.3: The supernova classification [18].

Supernova explosions are classified according to the emission lines in the spectrum as shown in Figure 1.3. Type Ia supernova explosion is caused by the reactionof thermonuclear fusion. Neutrinos emitted by Type Ia supernova explosions haveenergies of 1049 erg or less. On the other hand, type Ib, Ic and II supernova explosions are caused by core collapse. Neutrinos emitted by them have energies of∼ 1053 erg.

1.3.2

Supernova neutrino

Supernova neutrinos refer mainly to neutrinos produced by supernova explosions caused by core collapse (Type Ib, Ic and II). How neutrinos are emitted fromthese supernova explosions is described below.
1. Start of gravitational collapse
The iron core in the star starts to collapse and the density and temperature increase. Accompanying this, electron capture of elements occurs andneutrinos are produced.
e− + A(N, Z) → νe + A(N + 1, Z − 1)

(1.34)

2. Production of neutrino sphere
When the core becomes ultra-dense around 1011 − 1012 g/cm3 , a region (neutrino sphere) is created in the center of the star where neutrinos are trappedand can only gradually escape.
13

3. Shock wave
When the core density reaches the nucleon density, neutron degeneracy pressure stops contraction. However, since material falls from the outer core atsupersonic speed, a shock wave is generated at the interface between the
inner core and the outer core.
4. Neutronization burst
Electron neutrinos are produced by the capture of surrounding electrons byprotons produced during shock wave propagation. While the shock wave is
propagating inside the neutrino sphere, the electron neutrinos cannot escape,but when the shock wave reaches the outside of the neutrino sphere, theelectron neutrinos can fly out. This is called νe neutronization burst. Also,a Proto Neutron Star (PNS) is formed inside the star.
5. Cooling of the PNS
After the shock wave has passed through, the nuclei, electrons and positrons
produced fall into the PNS. The various flavor neutrinos are produced at thistime. The neutrinos heat the material behind the shock wave, reviving thestalled shock wave. The PNS is also cooled because of the heat brought out
by the neutrinos.
6. Supernova explosion
When the shock wave reaches the surface of the star, a supernova explosion
occurs, blowing away all the outer layers.
Neutrinos of different flavors evolve differently, giving the following energy hierarchy.
⟨Eνe ⟩ < ⟨Eνē ⟩ < ⟨Eνx ⟩(1.35)
where x = µ, τ . Figure1.4 shows the time distribution of neutrino energy andluminosity obtained by simulation. νx in the figure represents νx = (νµ + ν¯µ + ντ +ν¯τ )/4. These energies range from 10 MeV to around 20 MeV.

1.3.3

Diffuse Supernova Neutrino Background

The Diffuse Supernova Neutrino Background (DSNB) is the overall neutrino
flux of all core-collapse Supernovae that happened in the history of universe. There
are DSNB in the universe from ∼ 1017 supernova explosions from the Big Bang to
the present.
The differential DSNB flux on Earth, taking into account also redshift effects,
is given by,
Z ∞dΦdNν [Eν (1 + z)] dt=c
RSN (z)(1 + Z)dz
(1.36)
dEν
dEν
dz
0
14

Figure 1.4: Time distribution of supernova neutrino energy and luminosity [19]15

where RSN (z) is the Supernova rate at redshift z, Eν is the neutrino energy received,dNν /dEν is the number spectrum emitted by the explosion where the neutrino wasemitted at a higher energy Eν (1 + z). dz/dt is the relation between cosmic time t
and redshift z given by,pdz= −H0 (1 + z) ΩΛ + Ωm (1 + z)3dt(1.37)

where H0 is the Hubble constant and Ω is the cosmological parameters.
Many theoretical models have been proposed to predict the DSNB flux. Figure 1.5 shows the predicted energy distribution of the ν¯e flux. Various searches
for supernova background neutrinos have been conducted so far, but they have
not yet been discovered. In Super-Kamiokande, gadolinium has been loaded to
improve the detection capability of DSNB and DSNB event rate is expected to be
several times per year [20]. The details are explained in Section 2.5. If we can observe the supernova background neutrinos and compare their energy spectra withtheoretical predictions, we will be able to understand the mechanism and rate ofsupernova explosions, as well as the initial mass distribution of stars.

16

Figure 1.5: DSNB ν¯e flux predictions from various theoretical models [20] The color ofeach line represents the difference in theoretical models.(red dotted line andbrown dotted line: Horiuchi +18 model [21], blue line and pink dotted line:
Nakazato +15 model [22], light blue dotted line: Lunardini +09 model [23],green line: Ando +03 model [24], Gray line: Kaplinghat +00 model [25],ocher line: Malaney +97 model [26], purple dotted line: Hartmann +97
model [27], dark green dotted line: Totani +96 model [28])17Chapter 2
Super-Kamiokande experiment
2.1

The Super-Kamiokande detector

Super-Kamiokande detector (SK detector) [29] is a 50 kton water Cherenkov
detector. It is placed 1,000 m underground of Mt. Ikenoyama, in the Kamioka
mine, Hida City, Gifu Prefecture, Japan. SK detector is a cylindrical tank with
39.3 m in diameter and 41.4 m in height as shown in Figure 2.1. Previously, purewater was used as the detector medium. In 2020, gadolinium with a concentrationof 0.01% was introduced. The concentration was increased to about 0.03% in 2022.

2.1.1

Cherenkov light

Cherenkov light is emitted when a charged particle moves faster than the speedof light in a medium. It is emitted in a conical shape at an opening angle θcwith respect to to the direction of movement of the charged particle as shown in
Figure 2.2. The opening angle θc between the charged particle and Cherenkov
light is given by
1
,
(2.1)
cosθc =
nβ
where n is the refractive index of the medium and β = v/c is the speed of thecharged particle. When the medium is water, the refractive index is n ∼ 1.34.
Similarly for gadolinium water, n ∼ 1.34. The opening angle is around 42◦ forparticles travelling at β ∼ 1 in water. The momentum threshold for the Cherenkov
radiation ismc
pthresh = √.
(2.2)
n2 − 1
The threshold for electron and muon are summarized in Table 2.1

18

Figure 2.1: SK detector [30]

The number of Cherenkov photons dN emitted by a particle with charge 1e
per flight distance dx is given by
2πα
1
d2 N
= 2 (1 − 2 2 ),
dλdx
λ
nβ

(2.3)

where λ is the wavelength of emitted light and α is the fine structure constant
1
(=
).
137
When an electron travels 1 cm, in the PMT’s sensitivity range of light wavelengths of 300-600 nm, the number of Cherenkov photons N is given by
Z 1cm Z 1600nm
1
2πα
(2.4)
N=
dx
dλ 2 (1 − 2 2 ) ≃ 340.
λ
nβ
0
300nm
Gamma rays can also be detected by Compton-scattered electrons and by pairproduced electrons and positrons.
Table 2.1: The summary of Cherenkov momentum thresholds in water.

particle mass [MeV/c2 ] pthresh [MeV/c]electron
0.511
0.572
muon
105.66158.7319

Figure 2.2: Outline drawing of Cherenkov light

2.1.2

Inner detector and Outer detector

The Super-Kamiokande detector is divided into two regions: the Inner Detector(ID) and the Outer Detector (OD). (Figure 2.3)
ID is a cylindrical detector with diameter of 33.8 m and height of 36.3 m. 20inch PMTs are installed on the inner wall facing inside. They detect the Cherenkov
light emitted by charged particles within the volume of 32.6 kton and is responsible
for reconstructing the position and energy of the event. There are currently a totalof 11,129 PMTs, covering approximately 40% of the surface area of the ID. The
surfaces without the PMTs are covered with the black sheets to prevent lightreflection on the wall surfaces.
OD is the region outside the ID, covering with the thickness of 2.05 m on the
top and bottom surfaces and 2.2 m on the sides. 1,885 8-inch PMTs are installedfacing outwards on the walls. The OD is responsible for identifying cosmic raymuons and shielding rock-derived neutrons and gamma rays. The surfaces except
the PMTs are covered with the white reflective sheet called a Tyvek sheet in orderto improve the light collection efficiency of the PMTs of the OD and to prevent
light generated in the OD from entering the ID.
The coordinate of the SK detector is taken as shown in Figure 2.4. The x andy axes are taken in the horizontal direction and the z axis in the vertical direction.
The zero point of each axis is the black dot in the figure.
20

Figure 2.3: The cross-section of SK detector [29]Figure 2.4: Coordinate setting of SK detector.

21

Figure 2.5: Schematic view of a 20-inch ID PMT [29]2.1.3

Photo Multiplayer Tube (PMT)

20-inch PMTs developed by Hamamatsu Photonics and University of Tokyo areused for Inner Detector [29]. (Figure 2.5) The performance of the 20-inch ID PMTs
is shown in Table 2.2. The photocathodes of the PMTs are made by the bialkali(Sb-K-Bs) and the sensitive wavelength range is 280 ∼ 600 nm. This wavelength
range is suitable for detecting of Cherenkov light. The quantum efficiency is ∼22% at wavelengths 360 ∼ 400 nm, as shown in Figure 2.6.
There is an average geomagnetic field of 450 mG around the SK detector. In
order to prevent the influence of this magnetic field, Helmholtz coils are installedin the horizontal and vertical directions around the detector. Thanks to this, themagnitude of the magnetic field inside the detector is suppressed to an average of
32 mG, and the effect of geomagnetism on the collection efficiency of the PMTs isestimated to be 1 ∼ 2%.
In the wake of the November 2001 explosion, the PMTs are covered with theacrylic and the fiber reinforced plastic (FRP) covers to prevent the chain failure.

2.2

Data acquisition systems

QBEE
All PMT signals are read out by a front-end electronics called QBEE (QTC22

Table 2.2: Typical performance of the 20-inch ID PMTs. [29]Model number
Photocathode material
Photoelectron collection efficiency
Quantum efficiency
Dynode structure
Gain
Dark current
Dark rate
Transit time
Transit time spread
WeightPressure resistance

R3600
Bialkali (Sb-K-Bs)
70%∼ 22% (λ : 360 − 400nm)
11-stage Venetian blind type107 at 2000V
200 nA at 107 gain
3 kHz at 107 gain
90 ns at 107 gain
2.2 ns (1σ)
13 kg
6 kg/cm2

Figure 2.6: Quantum efficiency of PMT as a function of wavelength [29]23Figure 2.7: QBEE system [31]Based Electronics with Ethernet). The diagram of QBEE is shown in Figure 2.7. When the amplitude of the PMT signal exceeds a value corresponding to 0.25 photoelectron(p.e.), QTC (charge to time converter) calculates
the integrated charge over 400ns and a square wave with a time width proportional to the amount of charge is generated. The rising edge of the squarewave corresponds to the PMT hit time. By digitizing this square wave withTDC (time-to-digital converter), the PMT hit time and integrated charge
information can be read out. The signal information stored in TDC is readout by FPGA (Field Programmable Gate Array), processed, and recorded.
Software trigger
The above recorded data are software-triggered to extract events. Whenthe number of PMT hits in 200ns (N200 ) exceeds a certain threshold, eachsoftware trigger is issued and the surrounding hit information is stored.
Those triggers are classified as SLE (Super Low Energy), LE (Low Energy),
HE (High Energy), SHE (Super High Energy), OD (Outer Detector). The
thresholds and the time window of these triggers are summarized in table 2.3.
In addition, when SHE trigger is issued, AFT trigger which is the 500µs trigger from [+5, +535]µs is issued following SHE trigger. The AFT trigger isthe trigger designed for searching for DSNB. Previously, it was issued when
SHE trigger was issued but OD was not issued, but from June 2020, for
SK-Gd, AFT trigger is also issued when OD trigger is issued at the sametime as SHE trigger to capture the signal of neutron capture by gadolinium
generated by the spallation reaction of cosmic muon.

24

Table 2.3: The summary of the software triggers

Trigger
SLE
LE
HE
SHE
OD

2.3

N200 threshold
34
49
52
60
22

time window [µs][-0.5, +1.0][-5, +35][-5, +35][-5, +35][-5, +35]

Detector performance per data acquisition
periodThere have been seven phases for data taking at Super-Kamiokande. Each
phase is explained below, and the detector condition of each phase is summerizedin Table 2.4.
SK-I
The first data taking period from the start of observations in April 1996 to
July 2001.
In July 2001, work was carried out to replace the faulty PMT. However, inNovember 2001, after the replacement work was completed, the PMT implosion accident occurred while filling water into the detector. The accident
resulted in the loss of 6,777 PMTs in the inner tank and 1,100 PMTs in theouter detector.
SK-II
After the PMT implosion accident, the experiment was resumed from October 2002 with 5,128 PMTs in the ID. Data taking was continued until
October 2005. From SK-II, the PMT is equipped with an anti-shock case toprevent cascading implosion to the PMT.
SK-IIIIn June 2006, the new PMTs were installed to replace those lost in the crash.
As a result of this installation work, the number of the PMTs in the innertank increased to 11,129. Data taking was carried out from July 2006 to
August 2008.
SK-IV
Data acquisition period from September 2008 to May 2018.In August 2008
the data acquisition electronics were upgraded from ATM to QBEE.

25

SK-V
For the SK-Gd experiment, waterproofing reinforcement work, improvementof piping inside the tank and replacement of faulty photomultiplier tubes,
etc. was carried out from July 2018 to January 2019. Data taking period
from the end of January 2019 after the completion of the repair work to June
2020 when the gadolinium addition work started.
SK-VI
From July 2020, 13 ton of Gd2 (SO4 )3 · 8H2 O was introduced into the detector. This loading was completed in August 2020 and SK-VI started. As aresult, the mass concentration of Gd is approximately 0.01% and the neutron
capture efficiency is approximately 50%.
SK-VII
From June 2022, the additional 27 ton of Gd2 (SO4 )3 · 8H2 O was introduced
into the detector. This loading was completed in July 2022 and SK-VII
started. As a result, the mass concentration of Gd is approximately 0.03%
and the neutron capture efficiency is approximately 75 %.
Gd-loading of SK-VI and SK-VII is explained in detail in section 2.4.
Table 2.4: Detector performance per data acquisition period

Phase
SK-I
SK-II
SK-III
SK-IV
SK-V
SK-VI
SK-VII

PeriodID PMT
1996/04 – 2001/07 11,146
2002/10 – 2005/10
5,182
2006/07 – 2008/08 11,129
2008/08 – 2018/05 11,129
2019/01 – 2020/06 11,129
2020/08 – 2022/06 11,1292022/06 –11,129Gd concentration
0%
0%
0%
0%
0%
0.01%
0.03%

2.4

Super-Kamiokande with Gd

2.4.1

Gadolinium

coverage
40%
19%
40%
40%
40%
40%
40%

electronics
ATM
ATM
ATM
QBEE
QBEE
QBEE
QBEE

In ultrapure water without Gd, neutrons are captured by hydrogen and a single 2.2 MeV gamma ray is emitted. This signal is difficult to distinguish frombackground events due to its low energy, and the neutron detection efficiency was
20%.
26

Gadolinium (Gd) is a rare earth element with atomic number 64. 157 Gd has thelargest thermal neutron capture cross-section among natural elements. The thermal neutron capture cross-sections for different isotopes of gadolinium are shownin Table 2.5. When 157 Gd (155 Gd) captures a neutron, it becomes the excitedstate of 158 Gd(156 Gd). Then 158 Gd(156 Gd) emits gamma rays which energies are
7.9 MeV for 157 Gd and 8.4 MeV for 155 Gd in total as it transitions to the groundstate of 158 Gd(156 Gd). The proportion of thermal neutrons that are captured bygadolinium as a function of the mass concentration of gadolinium dissolved in purewater is as shown in Figure 2.8. In the 2020 Gd-loading, at the mass concentrationof 0.011%, the proportion was 50%, and in the additional Gd-loading in 2022, at
the mass concentration of 0.03%, the proportion was about 75%. SK collaboration
has set a goal of 0.1% mass concentration in the end, and the proportion at thattime will be about 90%.
Table 2.5: Thermal neutron capture cross section for each gadolinium isotope

Isotope
152
Gd
154
Gd
155
Gd
156
Gd
157
Gd
158
Gd
160
Gd

2.4.2

Natural abundance ratio [%] Cross section [b]
0.20
740
2.18
85.8
14.80
611000
20.47
1.81
15.65
254000
24.84
2.22
21.86
1.42

Recirculation system for Gd-loaded water

The loading of gadolinium into the SK tank is done by dissolving the Gd2 (SO4 )3 · 8H2 O
powder through the SK water purification system. The conventional water purifiers have ion-exchange resins, where ions are removed, but in SK-Gd, it is necessary to circulate water while retaining gadolinium ions (Gd3+ ) and sulfate ions
(SO2−4 ). Therefore, a new circulation system was developed to remove ions otherthan gadolinium ions and sulfate ions. The main purification steps are shown
below and the SK-Gd water system is shown in Figure 2.9.
Purification system
1. UV total organic carbon reduction lamp (TOC lamp)
Irradiate ultraviolet rays with a wavelength of 184.9 nm to oxidize anddecompose organic matter. It also sterilizes bacteria by irradiating ultraviolet rays with a wavelength of 253.7 nm.
27

Figure 2.8: The proportion of thermal neutrons that are captured by gadolinium

2. Heat exchanger (HE)The temperature of the water in the detector rises due to the heat generated by the circulation pump and high-voltage PMT. This temperature
increase causes dark noise, bacterial growth, and water convection. In
order to prevent them, three heat exchangers are used for one cycleof water circulation, and water temperature is adjusted to about 13
degrees.
3. Strongly acidic cation exchange resin (2400L) (“C-Ex Resin” in Fig 2.9)
The acidic cation resin is inert to gadolinium ions. Ions other thangadolinium ions are removed.
4. Strongly basic anion exchange resin (4600L) (“A-Ex Resin” in Fig 2.9)
The basic cation resin is inert to gadolinium sulfate ions. Negatively
charged impurities are removed.
5. 1 µm mesh filter
Remove dust of 1µm or more and radioactive materials attached to it.
6. UV sterilizer
Ultraviolet radiation is irradiated to kill bacteria.
7. UF modules
28Remove particles smaller than 1 µm using filtration.
8. Membrane degasifier (MD)Remove Rn dissolved in the water.
The two sets of HE, C-EX, A-EX, middle filter (1 µm), and UV sterilizer areconnected in parallel. Each has a supply of 60 ton/hour, making it possible
to supply a total of 120 ton/hour Gadolinium sulfate.
The water supplied to SK detector is purified groundwater in the Kamioka
Mine (Appendix A). It is important to remove Radon 222 Rn, which is aradioactive substance dissolved in water. Radon becomes a background foranalysis near the threshold (3.5 MeV) in solar neutrino observations becauseradon’s daughter nucleus, 214 Bi, emits 3.26 MeV electron through beta decay.
Through the above purification process, the purified ultrapure water has aradon concentration of ∼ 1.7mBq/m3 .
In addition, by the water circulating system in which purified water is put
in from the bottom and withdrawn from the top, there is a problem of top
bottom asymmetry in water quality with higher water transmission at thebottom of the detector than at the top.
Dissolving system
1. The weighing hopper
The Gd2 (SO4 )3 · 8H2 O powder is weighed.
2. The circle feeder
The Gd2 (SO4 )3 · 8H2 O powder is delivered in regulated quantities via
the circle feeder.
3. The solvent tank a fraction of the SK water being continuously recirculated is fed.
4. The shear blender and the dissolving tank
Gd2 (SO4 )3 · 8H2 O powder is dissolved in water from the solvent tank.
5. The solution tank
The resulting solution is sent.
Pre-treatment system
1. Ultra-filters (3 µm, 1 µm, 0.2 µm)
It remove very small dust.
2. UV total organic carbon reduction lamp (TOC lamp)
3. C-EX resin and A-EX resin These are cation exchange resin inert to
Gd+3 , anion exchange resin inert to SO2−
4 .
29

Figure 2.9: Schematic diagram of SK-Gd water system [32]

4. UV sterilizer
Bacteria are removed.

2.4.3

Gadolinium loading

The first Gd-loading [32] was carried out between July 14 and August 17 2020,
with 13.2 ton of Gd2 (SO4 )3 · 8H2 O powder dissolved via the system describedabove. At this loading, the mass concentration of Gd2 (SO4 )3 · 8H2 O was 0.026%,
which corresponds to the mass concentration of Gd of 0.011%. The time evolutionof the mass of the dissolved Gd2 (SO4 )3 · 8H2 O powder is shown in Figure 2.10. It
shows that Gd2 (SO4 )3 · 8H2 O was stably loaded up to the target of 13.2 ton. Water
with dissolved Gd2 (SO4 )3 · 8H2 O is introduced from the bottom of the detector. At
that time, by making the temperature 0.35 degrees lower than the water in the detector, the water in the tank was replaced with gadolinium water from the bottom
as shown in Figure 2.11. The state of Gd-loading can be confirmed by observing
30

Figure 2.10: The time transition of the mass of the dissolved Gd2 (SO4 )3 · 8H2 O powderin 2020

neutrons generated by the spallation reaction of cosmic muons. Figure 2.12 showsthe event distribution for each week from July 9, 2020 to August 23, 2020. We
confirmed that the gadolinium sulphate solution was gradually introduced fromthe bottom of the tank and the concentration was constant throughout the tank.
Additional Gd-loading was carried out between 1 June 2022 and 4 July 2020.
In this loading, 27.3 tons of Gd2 (SO4 )3 · 8H2 O powder was dissolved, resulting in
the Gd2 (SO4 )3 · 8H2 O mass concentration of 0.078% and the Gd concentration of
0.033%. The time evolution of the mass of the dissolved gadolinium powder isshown in Figure 2.13. It can be seen that this Gd-loading was also performed
stably. In this study, we observed Gd-loading by using the number of events inwhich spallation neutrons from cosmic muon are captured by gadolinium and thetime constant until spallation neutrons are captured by gadolinium. The results
are explained in Section 7.2.

31

Figure 2.11: Gadolinium loading scheme

Figure 2.12: Event distribution of cosmic muon derived neutrons captured by gadolinium. The horizontal axis represents the square of the radius of the reconstructed vertex position, and the vertical axis represents the height.

32

Added Gd2(SO4)3⋅8H2O amount [kg]

30000

25000

20000

15000

10000

5000

0

achievements
fit
goal
06/02

06/09

06/16

06/23

06/30

07/07

Figure 2.13: The time transition of the mass of the dissolved Gd2 (SO4 )3 · 8H2 O powderin 2022

2.5

Search for DSNB in SK-Gd

2.5.1

DSNB signal

The search for DSNB by the Super-Kamiokande has provided the world’s moststringent upper limit for the flux of DSNB, but it has yet to be discovered. Thisis because the flux of DSNB is O(1)cm−1 s−1 , which is very small, and even withthe effective volume of Super-Kamiokande (22.5 tons), only 0.8 to 5 events occur
per year.
In Super-Kamiokande, the search for supernova background neutrinos is carriedout using inverse beta decay reactions (Eq. (2.5)) between electron antineutrino
and proton in the water.
ν¯e + p → e+ + n(2.5)
The search is carried out in the energy range of 10-30 MeV, where the influenceof reactor neutrinos and atmospheric neutrinos is relatively small (Figure 2.14).
When the inverse beta reaction occurs in pure water, positron and neutron
are produced. Firstly positron emits Cherenkov light and it is detected by PMTs.
Then neutron is captured by hydrogen with a time constant of about 200µs. At
that time, gamma ray with an energy of 2.2 MeV are emitted. Electrons are
generated by electromagnetic interaction in water and emit Cherenkov light, which
is detected by PMTs. In the search for DSNB, delayed coincidence measurement
is used with two such signals, the prompt signal from the positron and the delayed
signal from the gamma rays emitted when the neutron is captured by hydrogen.
33

Figure 2.14: Fluxes of DSNB (blue diagonal line) and background event neutrinos
expected at Super-Kamiokande [33]. The flux of DSNB depends on themodel and has a range.

34

Figure 2.15: The signals from DSNB (electron antineutrino) observed in pure water

The schematic diagram of this reaction is shown in Figure 2.15. However, it
is difficult to detect neutron capture events by hydrogen. This is because that,firstly the neutron capture cross-section of hydrogen atom is as small as 0.3 barn,
secondly the time taken to capture a neutron is as long as 200 µs, thirdly the
gamma ray energy emitted is as low as 2.2 MeV, making it difficult to distinguishfrom low energy background events. Gadolinium was introduced to overcome theseweaknesses.
SK-Gd, by introducing gadolinium, improves the neutron detection efficiency
and has the purpose of searching for DSNB with high statistics and low background. In SK-Gd, the search for DSNB is performed by delayed coincidence
measurement using the prompt signal from positron and the delayed signal fromseveral gamma rays with a total energy of about 8 MeV emitted by the neutron
captured by Gd. The schematic diagram of this reaction is shown in Figure 2.16.
The 8 MeV energy can be separated from low energy background events and thesignal is easy to tag. As described in the previous chapter, the neutron capture
cross-section of Gd is 60,900 barn for 155 Gd and 254,000 barn for 157 Gd, approximately 200,000 and 1,000,000 times that of hydrogen atoms, and the neutron
detection efficiency is estimated to reach about 90% at a Gd concentration of
0.1% (Figure 2.8).

2.5.2

Backgrounds for DSNB

The observed SK-IV data and expected background spectra are shown in Figure 2.17. As the figure shows, there are three main backgrounds in DSNB search
below 20 MeV: Atmospheric neutrinos (NCQE), Atmospheric neutrinos (nonNCQE), and spallation 9 Li.
Atmospheric neutrinos (NCQE)
35

Figure 2.16: The signals from DSNB (electron antineutrino) observed if Gd exist

In the energy region below 16 MeV, Neutral Current Quasi-Elastic scattering(NCQE) of atmospheric neutrinos and oxygen atoms 16 O in water dominate
as background events. In this event, the gamma rays emitted when excitedoxygen nuclei are de-excited are the prompt signal, and neutrons with energies of tens to hundreds of MeV, which are kicked out by atmospheric
neutrino, are detected as the delayed signal. Nucleons ejected from oxygen
atom have high energy and collide with surrounding oxygen atom to emit
secondary gamma rays and neutrons. Figure 2.18 shows the flow of this interaction. In the event where multiple neutrons are emitted, multiple neutron
capture signals are detected after the prompt signal by gamma ray. On theother hand, since only one neutron is generated from inverse beta decay by
DSNB, it can be distinguished from NCQE in which multiple neutron signals
are detected. Therefore, it is estimated that the background of atmospheric
neutrinos by NCQE is reduced to 1/3 with neutron tagging with Gd.
Atmospheric neutrinos (non-NCQE)
Charged-current quasielastic (CCQE) interaction and pion production dominate at high energy region above 20 MeV. Cherenkov light from electrons
produced by the decay of muons and pions is detected in this reaction. So,
the reconstructed energy follows the Michel energy spectrum from about 15
to 50 MeV. Atmospheric neutrino events are simulated using the HKKM
2011 flux [35].
Cosimc ray muon spallation
SK is exposed to cosmic ray muons at a rate of ∼2 Hz. Muons produce
electromagnetic and hadron showers in water. Spallation of oxygen nuclei
induced by the muons or by secondary particles produce radioactive isotopes.
Those decays could be misidentified as IBD events in the DSNB search and36

Figure 2.17: The energy spectra of DSNB background [20]37Figure 2.18: Schematic of NCQE interaction [34]become background events. In the energy region below about 20 MeV, theassociated background is about 106 times higher than the DSNB flux prediction and the spallation reduction is essential.
Most spallation isotope produce only β and γ and these backgroud events
can be reduced using neutron tagging, but a few isotopes undergo a β + ndecay that mimics the IBD signal and these backgroud events cannot be
removed using only neutron tagging. These spallation reductions require
both dedicated reduction techniques and neutron tagging, with the modelling matched to each isotope. The isotope lifetimes and the end-point
energies of their decays are summarized in Figure 2.19. Isotopes that undergo β + n decays include 8 He, 11 Li, 16 C and 9 Li. In particular, 9 Li has
a non-negligible yield (1.9 × 10−7 µ−1 .g−1 .cm2 ), a half-life of about 0.18
sec, decays into β + n pair with a branching ratio of 50.8%, and the decay of 9 Li is similar to the IBD event in DSNB. The differences are thatthe β of 9 Li is an electron and the neutron energy is higher in 9 Li thanin DSNB. However, since SK does not distinguish between positrons andelectrons and neutron energies cannot be measured, 9 Li decay is modelledusing IBD Monte-Carlo simulations. 9 Li production rate is estimated to be
0.86 ± 0.12(stat.) ± 0.15(syst.) kton−1 .day−1 [36].

38Figure 2.19: End-point energies and half-lives [20]39Chapter 3
Overview of calibrations in a few
to tens of MeV region
In this section, an overview of calibration for the SK low energy region is
described. To evaluate the energy of the particles which are interacted in the SK
detector precisely, calibration is very important. The schematic diagram of theflow of conversion of energy and the kind of calibration used in this flow is shownin Figure 3.1.

3.1

Basic calibrations

In the low energy region, the number of PMT hits is used for energy. Thisis because the number of photoelectrons detected at each PMT is mostly 1 or 0,
as the expected value of the number of incoming photons per PMT is sufficiently
smaller than 1. Therefore, the number of PMTs that detect photoelectrons is agood approximation of the total number of photoelectrons. N50 is the number of
PMT hits within 50 ns. Since the N50 has the event vertex position dependence
due to water conditions and effects of dark noise and quantum efficiency of PMT,
the N50 is corrected for these effects. Basic calibrations can be divided into two
main categories: PMT related and water related, and these calibrations are used
for these correction factors described in the below ”Summary of calibration parameters”. The relation between each correction factor (calibration parameter)and calibration is shown as follows.
Summary of calibration parameters• PMT related– Gain, Cgain
40

Figure 3.1: The schematic diagram of the flow of conversion of energy and the kindof calibration. In the low energy region, energy is detected using the N50(the number of PMT hits within 50 ns) parameter. Neff (the effective
number of hits) is calculated by the correction factors derived from thebasic calibration. Energy calibrations allow MC simulation to accurately
reproduce the data and the total energy is reconstructed.

Scaling factor of the size of PMT signal. It does not affect thereconstructed energy directly, because the number of PMT hits isused for the energy reconstruction. However, it affects the efficiency
to detect a hit above the threshold of the electronics. This effect isreproduced in the simulation.
– QE (Quantum Efficiency to detect photon)
QE affects the probability of a photon detected by a PMT. The
evaluation of QE is described in Section 4.1.1.
– Dark noise
Random PMT hit rate mostly caused by spontaneous thermal electron emission. Dark noise for energy reconstruction is randomly
produced at a defined rate in MC simulation.
• water related– αabs , αsym , αasym
coefficients for absorption and scattering (symmetric or asymmetric). The details of these parameters are described in Section 4.2.1.
– Cabs
Scaling factor of absorption coefficient to implement time variationof water transparency. It is evaluated by fitting the correlation
plot between Cabs and water transparency with 50 MeV electrons
produced for each different value of Cabs in MC simulation.
41

– Csca
Scaling factor of scattering coefficient to minimize position dependence of Neff . 10 MeV electrons are generated in MC simulation
and Neff is calculated at different values of Csca . The best Csca
is selected from the value which minimizes the position dependent
variation of Neff .
– β
Coefficient for z position dependence of water transparency. The
detail of the parameter β is described in Section 4.2.3.
Summary of basic calibration• calibration using NiCf source
NiCf source is inserted into the tank and γ rays are detected to measure
QE and z position dependence of the water transparency. The detail of
NiCf calibration is described in Section 4.1.1.
• laser calibration
N2 laser with short pulse widths (< 0.4ns) is used and inserted into
the tank to measure PMT hit timing and water parameters. The laser
calibration for PMT hit timing is described in Section 4.1.2 and thatfor water parameters is described in Section 4.2.1.
• Decay electron calibration
Decay electron is generated from cosmic ray muon stopped in the detector and is used to grasp the temporal variation of the water quality. The
detail of decay electron calibration for the water quality measurement
is described in Section 4.2.2.
The effective number of hits Neff is calculated by correcting N50 using these
correction factors. Basic calibrations are explained in Chapter 4.

3.2

Energy calibrations

Energy calibrations are explained in Chapter 5. These calibrations measure
the energy scale and help MC simulation reproduces the data more accurately.
The following kinds of energy calibration are used in SK.
Calibration with instruments• LINACAn electron linear accelerator called a LINAC is used to launch electrons42Table 3.1: The relation between calibration parameter and calibration

PMT related parameters
Gain
Cgain
QE
Dark noise
Water related parameters
αabs , αsym , αasym
Water transparency
Cabs
Csca
β

Evaluation method
the hits in the off-timing window of cosmic muons
Decay electron
NiCf calibration
the hits in the off-timing window of the LE trigger data
Evaluation method
laser calibration
Decay electron
MC simulation
MC simulation
NiCf calibrationof certain energy into each position in the SK tank. The absolute valueof the energy scale is calibrated. LINAC is described in Section 5.2.1.
• DT calibration
Electrons generated isotropically by β decay of 16 N are used. The validity of the energy scale determined by LINAC is checked. In addition,
DT calibration is used to evaluate the directional dependence of theenergy scale. DT calibration is described in Section 5.2.2.
Cosmic ray induced• 16 N
This calibration is performed using 16 N generated by cosmic muon captured by 16 O in the tank to evaluate the energy scale for solar neutrino
detection. 16 N calibration is described in Section 5.2.3.
• Decay electron
Electrons generated by muon decay are used to evaluate the energy
scale. The decay electron for energy scale calibration is described in
Section 5.2.4.
LINAC and DT calibration are also used to evaluate the systematic uncertaintyof the energy scale. The systematic uncertainty for position dependence of energy
reconstruction is estimated by comparing the data from LINAC and MC simulation. The systematic uncertainty for directional dependence is estimated by thedata from DT calibration. The systematic uncertainty of the energy scale of thecurrent solar neutrino observation is summarized in Table 3.2.

43

Table 3.2: Systematic uncertainty of energy scale of the current solar neutrino observation [37]Position Dependence
Direction Dependence
Water Transparency
LINAC Energy
Total

0.44%
0.10%
0.20%
0.21%
0.54%

The systematic uncertainty for the position dependence of the energy scale in
the SK-IV result was 0.44%. This uncertainty is due to the difference between
the data and MC simulation. It is necessary to improve MC simulation to reduce
this uncertainty with a more accurate evaluation of the position dependence andthe time dependence of the water transparency. However, the number of datataking points for LINAC and DT calibration is limited and these calibrations don’t
provide sufficient information to improve MC simulation. We need to evaluate
more detailed position dependence.

3.3

Motivation for energy calibration using spallation neutrons

This study aims to develop a new energy calibration using spallation neutron.
In SK, the addition of gadolinium in 2020 made it possible to detect spallation
neutrons via Gd(n,γ) reactions. Spallation neutrons have the following features.
• Produced throughout the entire detector.
• Produced all time.
• High rate of production and detection.
LINAC and DT calibration have limited data taking points and data taking periods. Thanks to the above features of the spallation neutrons, we can do thecalibration of the energy scale that evaluates the position dependence and timedependence in more detail than LINAC and DT calibration.
More details on spallation neutrons and the event selection method developedin this study are described in Chapter 5, the evaluation of time variation of energy
using spallation neutrons is in Chapter 7, and the discussion of energy calibration
methods using spallation neutrons is in Chapter 8. In the study of energy calibration using spallation neutron, our aim is to develop a calibration in which theposition dependence is suppressed to about the level of systematic uncertainty in44

the current solar neutrino observation (∼0.5%). In this thesis, we evaluated theposition dependence using current MC simulation and spallation neutron data.

45

Chapter 4
Calibration of SK detector
response
In this chapter, calibration methods in the Super-Kamiokande detector aredescribed. The main components of the detector are the PMT and water. It isextremely important to understand them in order to obtain reliable data and to
make accurate measurements.

4.1

PMT related calibration

4.1.1

Relative QE

The number of PMT hits is used for energy reconstruction of low-energy events
where only one photon enters one PMT. Each PMT has individual differences andwe need to take that into account. In order to understand the properties of each
PMT, we calculate the relative quantum efficiency from a detector calibration using NiCf source, and make the QE table that summarizes the PMT identification
numbers and relative quantum efficiencies. The structure of the NiCf source isshown in Figure 4.1. A green 16 cm diameter ball made from 35% nickel oxide(NiO) and 65% polyethylene have a hole in the center. A neutron source, californium 252 (252 Cf), is placed in the center of the hole, and the top and bottom
are covered with brass rods.
The principle of Cherenkov light generation from the NiCf source is as follows.
1. 252 Cf has a half-life of 2.65 years, 96.9% undergo α decay and the remaining
3.1% undergo spontaneous fission.
2. The average of 3.76 neutrons with 2.1 MeV and the average of 10 gamma
rays with 10 MeV are produced in a single fission.
46

Figure 4.1: Structure of NiCf source

3. The generated neutrons are elastically scattered about 20 times with theprotons in the polyethylene in a few µsec.
4. Every time elastic scattering occurs, the neutrons lose energy and are eventually thermalized.
5. Thermalized neutrons are captured by Ni nuclei and gamma rays (6-9 MeV)
are emitted.
6. Gamma rays in water cause electron-positron pair production and compton
scattering, resulting in the emission of Cherenkov light. Cherenkov light isdetected by PMTs.
This Cherenkov light is so weak that only one photon can enter one PMT, andis emitted isotropically from the NiCf source. The NiCf source is therefore suitable
for measuring relative quantum efficiency.
Figure 4.2 shows the flow chart of the analysis to obtain the relative QE. NiCf
events are selected from the acquired data and the number of hits for each PMT
is calculated and corrected to determine the relative hit rate. Equivalent analysis
is also performed for MC simulation. Relative QE can be obtained by comparing
data and MC hit rates.
QE =HRDataHRMC(4.1)

where HR represents hit rate.
Figure 4.2 shows the latest (updated on 16/09/2022) relative QE for z-directionof the SK tank.
47

Figure 4.2: the flow chart of the analysis of QE

Figure 4.3: The relative QE updated on 16/09/2022 [38]. The vertical axis represents
QE (ratio of data hit rate to MC hit rate) and the horizontal axis represents
z direction of the SK tank. Black dots represent the QE at each z position.
One plot point is the average of 150 PMTs for one round of the barrel.
The red area is the area within ±0.5%, and the data at any position iswithin 0.5%.

48

Figure 4.4: Schematic diagram of the time walk [39]. High charge signal (red line)
have higher pulses and faster the rise time than low charge signal (blueline).

4.1.2

Relative timing

The PMT timing information is the important item for the reconstruction of
the vertex position. Timing responses are not the same between PMTs due tocable length differences and electronics response variations. Timing calibration
corrects for these variations. Due to the property of the signal of the PMT, thetime-walk occurs when the different amount of charge is observed (Figure 4.4).
Time and charge correlation is evaluated using N2 laser with short pulse widths(< 0.4ns) to correct for time walk and to time calibrate the PMT (Figure 4.5.).
The relation between time and charge is called “TQ-map”, which is the timing
as a function of the pulse height. This map is then fitted by various polynomial
functions depending on the charge range. The fitted parameters are then used
to correct the time response of each PMT as a function of the observed charge.
Figure 4.6 shows the TQ-map for SK-IV. The vertical axis of the TQ-map corresponds to the signal detection time t − ttof , and the larger the value, the earlier thedetection time. QBin on the horizontal axis represents the value corresponding to
the detected charge Q [pC]. The obtained correlation between t − ttof and QBinis fitted with a polynomial function, and the obtained fitting function is added tothe signal detection time to correct the time shift due to the time walk.

49

Figure 4.5: Schematic diagram of time calibration using laser

Figure 4.6: TQ-map for SK-IV PMT. The horizontal axis is charge of each hit (QBin),and the vertical axis is time [ns] after subtracting the time of flight.

50

4.2

Water related calibration

Since the amount of detected Cherenkov light changes depending on the watertransparency, the parameters related to water are important correction terms inreconstructing the energy with high accuracy. There are two methods for measuring the water transparency, one using a laser and the other using decay electrons
from cosmic ray muon.

4.2.1

Water parameter tuning with laser

The attenuation of light is expressed by the exponential function,I(λ) = I0 (λ)exp(−r/L(λ))(4.2)

where λ is the wavelength of light, I0 (λ) is the initial light intensity, r is the
distance traveled by light, and L(λ) is the water transparency.
Light is subject to absorption or scattering effects while traveling through water. Scattering is divided into symmetric scattering and asymmetric scattering.
When the scattering angle is θ, the angular distribution of scattered light in symmetric scattering is expressed as 1+cos 2θ. In asymmetric scattering, the scattering
probability increases linearly when 0 < cos θ < 1, and when cos θ < 0, the scattering probability is zero (Figure 4.7). The water transparency in MC is expressedby the following equation,
L(λ) =

1αabs (λ) + αsym (λ) + αasy (λ)(4.3)

where αabs (λ), αsym (λ), αasy (λ) represent parameters for absorption, symmetricscattering, and asymmetric scattering, respectively. Also, these parameters are
expressed as follows using the coefficients P0 to P8 .
P1
λ P3
+ P0 × P2 × 0.0279 × (
)
4
λ
500
P4
P5
αsym (λ) = 4 × (1.0 + 2 )λλP7αasy (λ) = P6 × (1.0 + 4 × (λ − P8 )2 )λαabs (λ) = P0 ×

(4.4)
(4.5)
(4.6)

The coefficients P0 to P8 are derived by fitting the laser data.
Laser light of five different wavelengths (337, 375, 405, 445, 473 nm) is injected
into the tank. Laser injectors are parmanently installed at seven places (Top×1,
Barrel×5, Bottom×1) as shown in Figure 4.8 and. For data analysis, we select hitsof scattered light from the timing of the hits, compare the hit ratio versus timing
51

Figure 4.7: photon scattering [40]plots between the data and MC, and extract the best values for P0 to P8 . The
values of P0 to P8 obtained from the data obtained from 01/01/2021 to 01/02/2021
are summarized in the table 4.1.
Table 4.1: The summary of the coefficients P0 to P8 .

P0
P1
P2
P3
P4
P5
P6
P7
P8
−4
0.615067 44854600 1.14829 14.4675 103455000 77171.9 2.42803e
14.9426 41475.0

4.2.2

Water transparency measurement with decay electron

Decay electron (decay-e) from cosmic ray muons stopped in the detector areused to measure the average water transparency throughout the detector. The
main purpose of this measurement is to constantly monitor the water in the detector, and to grasp the temporal fluctuations of the water quality. After a decay
electron event from a cosmic-ray muon is selected, the average charge Ni givenby the Cherenkov photon and the average distance di between the PMTs that detected the Cherenkov photon signal and the point where the decay electron event
occurred is calculated. The relation between the number of Cherenkov photon andthe distance is shown in Figure 4.10. Some segments are created by dividing the
Cerenkov ring into the polar angle and the azimuthal angle with respect to thedirection of decay electron. Then, Ni is calculated in each segment as,
Ni = (Xi + ϵtail − ϵdark ) ×NaliveS(0, 0)
1
×
×
.
Nall
S(θi , ϕi ) QEi

52

(4.7)

Figure 4.8: The location of laser injector [38]Figure 4.9: Schematic of water parameter measurement using laser [38]53Figure 4.10: The schematic diagram of the Cherenkov ring [41].

Each element used in this formula is explained in 4.1.3.
The derived distribution of charge vs. distance is fitted with an exponentialfunction to derive the attenuation coefficient (= water transparency). Figure 4.11
shows the time variation of water transparency. The data is used from the middleof SK-IV to SK-VI.

4.2.3

Top Bottom Asymmetry

As described in Section 2.4.2, in the SK water circulating system, purified
water is put in from the bottom and withdrawn from the top, so the bottom hasa higher water transparency than the top. This asymmetry is called Top Bottom
Asymmetry (TBA). TBA is monitored by using the laser and the NiCf source.
The measurement of the hit rate by the NiCf source also provides an estimate
of TBA of the water transparency. As discussed in Chapter 2, it has been observedthat there is a top-bottom asymmetry in water transparency due to the effect ofwater circulation. The TBA is expressed as the following equation,
T BA =⟨top⟩ − ⟨bottom⟩⟨barrel⟩(4.8)

where ⟨top⟩ is the average PMT hit rate on the top surface, ⟨bottom⟩ is the average
PMT hit rate on the bottom surface and ⟨barrel⟩ is the average PMT hit rate on
the sides.
The position dependence of the water transmission length is a source of systematic uncertainty in the energy reconstruction. To suppress this, the positional
dependence of the water transparency is also introduced in the MC simulation

54

Figure 4.11: Time variation of water transparency [41]. The data of the middle of
SK-IV to SK-VI is used.

in the form of dependence linearly in the height z direction, as in the following
equation. For SK-IV and SK-VI,1
z > −11m,
αabs (λ) · (1 + z × β) + αsym (λ) + αasy (λ)L(λ) =
(4.9)
1



z < −11m
αabs (λ) · (1 − 11 × β) + αsym (λ) + αasy (λ)
For SK-V,
L(λ) =

1αabs (λ) · (1 + z × β) + αsym (λ) + αasy (λ)(4.10)

where β is a parameter that expresses the level of TBA of water quality. In SK-IV
and SK-VI, the water at z < −11m was convecting and it can be assumed thatthe water quality is uniform. In SK-V, since convection does not occur, αabs (λ)
depends on z for all range in the z direction. The z dependence is applied to only
the absorption coefficient αabs (λ).
β is a variable introduced to incorporate TBA and its time variation into MC
simulations, expressed as a function of TBA,
β = a × T BA + b(4.11)The parameters a and b are determined in the analysis of NiCf data. The distribution of hit rates for the NiCf data is calculated from runs of different periods.
The value of β that best reproduces the hit rate distribution is then derived for55

Figure 4.12: Hit rate and its ratio with the best β value [38].

each run. The best β in SK-VI was obtained as 0.00731014 [1/m] uisng the Ni
data of Jan, 21st 2021. Hit rate and its ratio with the best β value are shown in
Figure 4.12.
In addition, using the obtained a and b, the time variation of β is derived fromthe time variation of TBA. Time variation of TBA is evaluated using the lamp of
the auto-Xe. Figure 4.13 shows the time variation of TBA.

56

Figure 4.13: Time variation of TBA measured with auto-Xe data [41].

57Chapter 5
Energy reconstruction andcalibration in a few to tens of
MeV region
5.1

Event reconstruction

In the SK, there are many analysis tools to reconstruct events because the
SK detector has many physics targets. In this chapter, the event reconstruction
method for low energy region is described.

5.1.1

Vertex reconstruction

In the low energy region, the trajectory of the charged particle is assumed to
be a point at the vertex. For example, an electron with an energy of 20 MeV cantravel a distance of about 10 cm in pure water, which is much smaller than thevertex resolution of 50 cm [37].
In order to reconstruct the vertex position, a maximum likelihood fit to thetiming of Cherenkov signal is used. This maximum likelihood fitting program iscalled BONSAI (Branch Optimization Navigating Successive Annealing Interactions). The time information in the PMT hit information is used to reconstruct
the event occurrence point. For each hit PMT, a residual time t − ttof − t0 is
defined, where t is the PMT hit time, ttof is the time it took for the photon toreach the hit PMT from the event point, t0 is the time of the interaction. Using
the timing residual information, the likelihood function is defined asL(⃗x, t0 ) =Nhit
XlnP (ti − ttof,i − t0 )

i=0

58

(5.1)

Figure 5.1: The probability density function of the residual time used for the vertex
reconstruction maximum likelihood fit [40]. The second and third peaks
around 30 nsec and 100 nsec are caused by the PMT’s after pulses.

where ⃗x is the position of the event point candidate and P (ti − ttof,i − t0 ) is theprobability density function of the timing residual for a single photoelectron signal
as shown in Figure 5.1. The likelihood function L(⃗x, t0 ) is calculated at each point
while changing ⃗x in the detector, and the position with the maximum value isdetermined as the vertex point. The accuracy of event reconstruction depends onthe energy, as the number of PMT hits varies with the energy of the generated
charged particles. P (ti −ttof,i −t0 ) is derived together with the vertex resolution by
LINAC. The vertex resolution is defined as the distance that contains 68% of thereconstructed events of LINAC and its energy dependence is shown in Figure 5.2.
gvtx is defined as parameters that represents the goodness of the vertex reconstruction. The goodness of vertex reconstruction gvtx is evaluated by the PMT hit
time information.


!2 
!2 
t −t
− t0
ti − ttof,i − t0P
 exp − i √tof,i√
i exp −
2ω
2σ

(5.2)
gvtx =!2 ti − ttof,i − t0P√
i exp −
2ω
where ω is the resolution of the ti − ttof,i distribution and σ is the time resolutionof the PMT. gvtx is the variable that takes values in the range 0 to 1, the closer to
1, the better the reconstruction is.

59

Figure 5.2: The energy dependence of position resolution in vertex reconstruction [42].
Each line represents the SK phase (Blue: SK-I, Red: SK-III, Black: SK-IV).

5.1.2

Direction reconstruction

The Cherenkov light ring pattern is used for direction reconstruction. The
direction reconstruction uses the maximum likelihood method. The likelihood
function is defined as
!
N20
X
cosθ
i
⃗ =
L(d)
(5.3)
lnf (cosΘi , E) ×
F
(θ
)
i
i=1
where d⃗ is the direction of the charged particle and N20 is the number of PMT
hits within 20 ns around the event occurrence time. f (cosΘi , E) is the distribution function of the angle Θi between the direction of the charged particle and theobserved photon direction. Since electrons pass through water undergoing mulcosθitiple Coulomb scattering, f (cosΘi , E) also depends on the energy E.
is a
F (θi )
correction term for solid angle. θi represents the angle of incidence of photons on
the PMT as shown in Figure 5.3. F (θi ) is a function of the sensitive area of the
PMT depending on the incident angle θi and is given as,
F (θ) = 0.205 + 0.524cosθ + 0.390cos2 θ − 0.132cos3 θ.

(5.4)

The goodness of the direction reconstruction gdir is evaluated by the uniformity
60Figure 5.3: The definition of the incident angle of the photon on the PMT [40].

of hit PMTs based on the Kolmogorov-Smirnov test.
gdir =

max{∠uniform (i) − ∠data (i)} − min{∠uniform (i) − ∠data (i)}
2π

(5.5)

where, ∠uniform (i) represents the direction angle of the i-th hit PMT when PMT
hits are assumed to be uniformly distributed around the ideal Cherenkov ring, and∠data (i) represents the direction angle of the actual PMT hit. gdir is the variable
that takes values in the range 0 to 1, the closer to 0, the better the reconstruction
is.

5.1.3

Energy reconstruction

For the energy reconstruction in the low energy (a few to tens of MeV) region,
the effective number of hits Neff is used. Neff is calculated from the number of the
PMT hits within 50 nsec time window N50 with corrections. Neff is represented asfollows,
N50
X
Neff =(Xi + ϵtail − ϵdark )/(1 + Gi × Cgain )i

S(0, 0)1
Nalive
×
×
exp
×
Nall
S(θi , ϕi ) QEi

ri
Leff

!

(5.6)

The each parameter of the correction is as follows.
• Xi : The occupancy correction factor which corrects for the effect of having
multiple photons in a single PMT.
61

• ϵtail : The correction factor to add late hits which are scattered or reflectedduring the travel in the water.
• ϵdark : The correction to remove dark rate hits in the 50 ns time window.
• 1 + Gi × Cgain : The effect of gain. This factor is introduced in SK-IV, but
we do not use it in SK-V and SK-VI because the effect was found to be
negligible in those periods.
•

Nalive: The correction for the bad PMTs.
Nall•

S(0, 0): The correction for the coverage of the PMTs as a function ofS(θi , ϕi )photon incident angles.

•

1: The correction for the quantum efficiency (QE).
QEiri) : The correction for the attenuation of Cherenkov light in theLeffwater.

• exp(

After all parameters are corrected and the number of effective PMT hits Neffis determined, the total (kinetic and mass) electron energy is reconstructed as afunction of Neff . The relation between Neff and reconstructed energy is given by
the following equation obtained from MC simulation.

2
3
4
5

(Neff < p6 )
p 0 + p 1 x + p 2 x + p 3 x + p 4 x + p 5 x
E(Neff ) = p0 + p1 p6 + p2 p26 + p3 p36 + p4 p46 + p5 p56
+(p1 + p2 p6 + p3 p26 + p4 p36 + p5 p46 )(x − p6 ) (Neff > p6 )(5.7)

The values of p0 to p6 are obtained by fitting. E(Neff ) is a 5th polynomial function
below p6 and a linear function above p6 . Parameters for the linear function are derived from the derivative of the 5th polynomial function, so that two functions areconnected smoothly. Figure 5.4 shows the relation between the total reconstructedenergy and Neff and the values from p0 to p6 of SK-VI data.

5.2

Energy calibration

As mentioned above, in the low energy region, the energy is reconstructedusing the effective PMT hit number Neff corrected for the N50 number of PMT
62

Figure 5.4: The the relation between the total reconstructed energy and Neff and thevalues p0 to p6 . Black dots show MC simulation results, blue line represents
function derived by fitting. The SK-VI data is used. The values of p0 to
p6 are obtained by fitting. ”G4” written in the figure is the name of thesimulation package.

hits that detected the light. In order for MC simulations to accurately reproduce
the real data, the difference between the data and the MC simulated detector
response must be kept small. For this purpose, energy calibration is carried out
in the Super-Kamiokande using the electron linear accelerator LINAC (Linear
accelerator) and the DT (Deuterium-Tritium neutron generator). Also, since thecondition of the water in the detector is continuously changing, it is importantto check the energy scale. Cosmic-ray-induced calibration sources are used forthe energy scale evaluation. Since cosmic ray muons enter the entire detector atabout 2Hz, the calibration source generated from the muons is constantly detected
throughout the entire detector. In this chapter, the energy scale evaluation by 16 N
and decay electron are also explained.

5.2.1

LINAC

Overview
The LINAC is placed above the tank of the SK detector. The LINAC beam
pipe is inserted into the detector through a hole, called calibration hole, atthe top of the detector, and electrons with the single energy (5, 6, 8, 10, 12
and 18 MeV) are ejected downwards. By the LINAC, the absolute value ofthe energy scale is calibrated and the systematic uncertainty on the position
dependence of the energy reconstruction is estimated. The position of thecalibration holes and the length of the beam pipe are fixed and data taking
63

Figure 5.5: Schematic diagram of the LINAC measurement in Super-Kamiokande [43].
Points A to I represent data taking points.

is done typically at the nine points as shown in Figure 5.5.
Motivation
In the LINAC analysis, the value called COREPMT is determined which is
introduced to correct for the average quantum efficiency of the PMTs installed in the detector. The Neff between data and MC are compared andthe value of COREPMT is tuned so that the value of Neff becomes thesame between data and MC. Then, the equation for the conversion from
Neff to energy is obtained on the basis of the correlation between Neff andthe energy of the generated charged particles. Furthermore, the data andthe corresponding MC simulation are compared and the systematic uncertainty on the position dependence of the energy reconstruction is estimated(Figure 5.6).
Advantage• Single energy electrons such as 5, 8, 10, 12 and 18 MeV can be injected.
Disadvantage• The calibration holes are fixed, so detailed positional dependence cannot
be checked.
• A lot of people is needed. At least 10 people are required to move thetower and manually extend each 4m beam pipe.
• The calibration can only be carried out once or twice a year.
64Figure 5.6: Ratio of Neff obtained from data and MC simulation [41]. Data from
August 6, 2019 to August 23, 2019 is used.

5.2.2

Deuterium-Tritium (DT) calibration

Overview
DT (Deuterium-Tritium neutron generator) calibration is a calibration that
detects gamma rays and electrons using 16 N generated from the following
reactions. First, helium and deuterium react to emit neutrons.
3

He + 2 H → 4 He + n(5.8)

Neutrons have an energy of 14.2 MeV and they are captured by 16 O. Then
16
N and protons are produced.
16

O + n → 16 N + p(5.9)

The generated 16 N decay has the half life time of 7.13 s according to theBranching Ration (BR). Those with the BR greater than 1% are described
below:
N → 16 O + β − (Q : 4.3 MeV) + γ(6.1 MeV)
16
N → 16 O + β − (Q : 10.4 MeV)
16
N → 16 O + β − (Q : 3.3 MeV) + γ(7.11 MeV)
16

(BR : 66.2%)(BR : 28%)
(BR : 4.8%)(5.10)(5.11)(5.12)

Reactions 5.8 and 5.9 are occurred in the SK detector using a Deuterium
Tritium Generator (DTG) as shown in Figure 5.7. The flow of DT calibration
is as follows.(Figure 5.8)
1. Submerge the DTG in water. DT calibration is carried out in the same
position as LINAC.
65

Figure 5.7: Schematic of the DTG setup [44]2. Activate the DTG and emit neutrons. The pulse are irradiated at maximum 100Hz, ∼ 3 × 106 neutrons are emitted three times.
3. Raise the DTG by 2m so that it does not cast shadows. During this period, the data is not taken in order to eliminate the background caused
by electrical noise generated by the crane.
4. Data taking is done for 40 seconds.
5. Repeat No.1 ∼ 4 20 ∼ 25 times per position.
Motivation
The DT calibration is performed to validate the energy scale and to evaluate the systematic uncertainty of the energy reconstruction determined by
LINAC. In addition, electrons are produced isotropically in DT, whereas in
LINAC electrons were only emitted in a downward direction. Therefore,systematic uncertainties on the directional dependence of the energy reconstruction, which could not be checked in LINAC, can be estimated.
Advantage• Position dependence can be investigated at position where LINAC cannot be used.
66

Figure 5.8: An overview of DTG data taking• DT calibration can be worked with 2-3 people, less than LINAC.
Disadvantage• The DTG itself interferes with the propagation of Cherenkov light, making it impossible to accurately analyze the energy response in somezenith angles.
• Because of beta decay, the electron energy is in a continuous spectrum.
• There are some branch events.
ResultFigure 5.9 shows the results of comparing Neff obtained from the data and
Neff obtained from the MC simulation for each direction of the reconstructed
electrons. A similar comparison was carried out for different generating
positions and the systematic uncertainty for the directional dependence inthe energy reconstruction was calculated to be 0.10 %.

5.2.3

16

N energy scale calibration

Overview

67

Figure 5.9: Directional (θz ) dependence of the difference in Neff obtained from data andMC simulations [44]. The horizontal axis represents the value obtained bytaking the cos of θz , and the vertical axis represents the deviation between
the data and the MC simulation. The rise seen around cosθz = 1 is due tothe MC simulation not reproducing the effect of shadows created by the
DT device itself.

When a cosmic ray muon is captured by 16 O, 16 O becomes 16 N and a muon
neutrino is emitted,

16

O + µ− → 16 N + νµ(5.13)The produced 16 N undergoes the processes in Eqs. 5.10-5.12, which is thesame as 16 N produced by the DT generator. These can be also used forenergy calibration.
Motivation
16

N decay events are background events for solar neutrino observations. 16 N
calibration is used to evaluate the energy scale for solar neutrino detection,
since the observed decay events have the same energy range as solar neutrino.
Advantage• Energy scale evaluation can be performed throughout the entire SK
detector.
• The directional dependence of the energy scale can be investigated.
• The analysis can be performed using the entire SK period.
68Figure 5.10: Energy scale evaluation of 16 N analysis and DT calibraiton analysis [43].
Black dots represent 16 N data, red dots represent DT calibration data.

Disadvantage• 16 N are produced at a low rate and takes a long time to get enoughstatistics.
ResultFigure 5.10 shows the results of the time variation of the energy scale evaluated from the 16 N calibration. Using the selected 16 N events, the energy
scale was evaluated every 2 years for SK-IV and every 6 months for SK-V
and SK-VI [43]. It was found that the energy scale in the detector did notchange significantly before and after the introduction of gadolinium, withagreement from SK-IV to SK-VI within the statistical error range.
The positional and directional dependence of the energy scale were analyzed
using SK-IV data and compared with the DT calibration data. The results
are shown in Figure 5.11 and Figure 5.12 respectively. It was shown thatthe energy scale has no position or direction dependence within a statisticalerror of 16 N.

5.2.4

Decay electron

Overview
Decay-e are used to evaluate the energy scale as well as time variations in thewater transparency. Figure 5.13 shows the reconstructed energy spectrum of69

Figure 5.11: Pocation dependence of energy scale evaluated from 16 N analysis and DT
calibraiton analysis [43] as a function of z(left) and r2 (right) with respect
to reconstructed vertex.

Figure 5.12: Directional dependence of energy scale evaluated from 16 N analysis andDT calibraiton analysis [43]. left: zenith angle cosθ. right: azimuth ϕ70

Figure 5.13: The reconstructed energy spectrum of decay-e [45].

decay electrons. Decay-e take energy from about 10 MeV to about 60 MeV.
Therefore, in the low energy region, it is possible to evaluate the energy scalelarger than 10MeV.
Advantages• Energy scale evaluation can be performed throughout the entire SK
detector.
• The analysis can be performed using the entire SK period.
Disadvantage• Decay-e are produced at a low rate and takes a long time to get enoughstatistics.
ResultFigure 5.14 shows the results of the energy scale evaluation using decaye. The gray area represents Gd-loading period. Soon after Gd-loading, theenergy scale change at most ∼2.7% level. For periods other than Gd-loading,the energy scale is consistent within ∼1% level.

71

Figure 5.14: Energy scale evaluation of decay-e. The gray area represents Gd-loading
period [45]. Soon after Gd-loading, the energy scale change at most
∼2.7% level. For periods other than Gd-loading, the energy scale is consistent within ∼1% level.

72

Chapter 6
Evaluation of spallation neutron
signal
6.1

Motivation

The physics targeted by the low energy region of SK is the observation of solar
neutrinos and the search for DSNB. For solar neutrino observations, the systematic uncertainty of the energy scale is 0.54%, of which 0.44% is due to position
dependence [37]. To reduce this systematic uncertainty, it is necessary to calibrate
the energy scale with a more detailed position dependence. As will be discussed
later, spallation neutrons can be used to calibrate the position dependence of theenergy scale in more detail. Also, for DSNB searches using the IBD reaction, it
is important to check the uniformity and stability of the Gd concentration. Thesecan be checked by using spallation neutrons.
In this chapter, firstly spallation neutrons and their characteristics are explained, then the method developed by us in this study to select and evaluate
spallation neutrons is described.

6.2

Spallation neutron

6.2.1

Feature of spallation neutrons

When cosmic ray muons enter the SK detector, they can fragment nuclei inthe water. This reaction is called spallation. Cosmic-ray muons mainly undergo
spallation reactions with oxygen nuclei and produce neutrons and various typesof radioisotopes. The neutrons produced in this reaction are called spallation
neutrons. Spallation neutrons are thermalized in water within about 5 µs andcaptured by hydrogen or gadolinium. When captured by hydrogen, one γ ray of73

Figure 6.1: The neutron capture signal by gadolinium in the SK tank. Cosmic raymuons undergo a spallation reaction with oxygen atoms in the SK detector, and spallation neutrons are emitted. Spallation neutrons are thenthermalized and captured by gadolinium, and finally a total of 8 MeV
gamma rays are emitted.

2.2 MeV is emitted, and when captured by gadolinium, several γ rays of about 8
MeV in total are emitted. Figure 6.1 shows the schematic of spallation neutron
signal in the SK tank.
Figure 6.2 shows the dt distribution of the spallation neutron signal. The dt
is the time difference between the arrival of the cosmic ray muon and the neutron
capture by gadolinium. The spallation neutron signal decreases exponentially withdt while the background is constant (Figure 6.2a). In this study, we utilize thisfeature to remove the background and extract only the signal. For this, the time
window is divided into signal part time window ([35, 235]µs) and backgroundpart time window ([335, 535]µs) (Figure 6.12a). Then, the background part issubtracted from the signal part.

6.2.2

Advantages and disadvantages of spallation neutrons

There are two major advantages to conducting these studies using spallation
neutrons. These events occur at a high rate and also throughout the entire detector
volume. As described in Chapter 2, cosmic ray muons arrive at the SK detector
at the rate of about 2Hz. It is expected that about 100,000 spallation neutrons
are produced each day in the SK detector. Thanks to this high rate, we can obtain sufficient statistics in a short time. In addition, since cosmic ray muons enter
the detector almost uniformly, spallation neutrons can also be detected almost
uniformly in the detector. On the other hand, there are disadvantages, such as
the low detected energy and close to the trigger threshold, which requires special
74

Events / 5µs

200
180
160
140
120
100
80
60
40
20
0

0

100

(a)

200

300

400

500

dt (µs)(b)

Figure 6.2: (a) The schematic of dt distribution. The spallation neutron signal decreases exponentially, but the background, mostly radioactive impurities,
remains constant. (b) The dt distribution seen from data.

treatment to remove background and the need to consider the effects of pile-up.
From these, it requires special treatment to evaluate energy correctly. Also, since
gamma-rays are initially produced, reconstruction is more difficult than calibrations with electrons. The comparison of advantages and disadvantages with otherenergy calibrations are summarised in Figure 6.3.
In addition, spallation neutrons can check the stability of the gadolinium concentration in a short time and the uniformity of the gadolinium concentration
throughout the entire detector.

6.2.3

Study using spallation neutron

In this study, using the spallation neutron signal, we develop the energy calibration method, monitor the stability of the detector response, and monitor the
additional Gd-loading in 2022.
For the development of energy calibration method, it is possible to investigate
the position dependence in the detector in more detail than with the other energy
calibration methods. The aim is to develop a calibration with an accuracy of 0.5%,
which is the same level of position dependence as the systematic uncertainty ofsolar neutrino measurement [37]. For the monitoring, it is possible to monitor theentire detector in a short time.

75

Figure 6.3: Comparison of spallation neutrons with other energy calibration methods.

76

Figure 6.4: SHE trigger and AFT trigger opened when cosmic-ray muon enter the SK
tank, and sub-events following muon. Signals that exceed the sub-trigger
threshold (N200 = 20) every 1.3 µs time window are stored as sub-events.

6.3

Event selection of Spallation neutron

6.3.1

Triggers for spallation neutron event search

When a cosmic ray muon passes through the SK detector, SHE trigger ([-5,35]µs) is issued, and then AFT trigger ([35, 535]µs) is issued. Sub-events aresearched by applying sub-trigger (off-line screening triggers for low-energy events)
to data stored by SHE trigger and AFT trigger (Figure 6.4). The sub-trigger isapplied to SHE and AFT triggers and sub-events are searched by this sub-trigger.
If there are 20 hits within 200 ns, the sub-trigger is applied and 1.3µs before andafter that is saved as the sub-event. Sub-event is the candidate for neutron capture
signals by gadolinium.

6.3.2

Muon selection

The conditions for the event selection of cosmic ray muon are the following two
points.
• Both OD and SHE triggers are issued.
• The total integrated charge of the signal observed in the ID Qµ > 10, 000
p.e.
Cosmic ray muons emit Cherenkov light immediately after entering the detector.
After PMTs in the outer detector (OD) detect the light and the OD trigger isissued, the cosmic ray muon loses several GeV of energy in the inner detector (ID)and emits Cherenkov light, which is detected by PMTs in the ID and the SHE
trigger is issued.
Also, it is required that the total integral charge observed in the ID, Qµ , to be
Qµ > 10, 000 p.e. The distribution of Qµ is shown in Figure 6.5.
77

Figure 6.5: The distribution of Qµ . Qµ is the total amount of Cherenkov light detectedby ID PMTs. The red line indicates the position of Qµ = 10, 000 p.e., theevents to the right of the red line are selected.

6.3.3

Neutron selection

In this section, the event selection of neutron captures by Gadolinium is described.
Fiducial volume
PMTs are installed on the wall of the SK tank and the noise related to PMTs
increases near the wall. Therefore, the area more than 2 m away from the walls of
the ID is taken as the fiducial volume.
Time window
The neutron capture signal by gadolinium is searched for in the AFT trigger. This
is to remove the signal of muon decay electrons and PMT afterpulse. It has beenfound that the PMTs attached to the SK tank generate the afterpulse about 10–20µs after receiving the main pulse [46].
Reconstruction quality

78The main background in the spallation neutron signal is radioactive impurities in
the SK tank. These backgrounds are constantly occurring near the wall of thetank. These reconstruction quality cuts remove the events near the wall accidentally reconstructed in the fiducial volume. The parameters gvtx and gdir are used toassure the good accuracy of the reconstruction (Refer to chapter 3). The distributions of gvtx and gdir are shown in Figure 6.6b and Figure 6.7b, respectively. These
two distributions are obtained by subtracting the background part ([335, 535]µs)
from the signal part ([35, 235]µs) (Figure 6.6a and Figure 6.7a). Only the cut that
selects the fiducial volume is applied to the signal part and the background part.
Looking at Figure 6.6b, peaks can be seen even in the range where the value of gvtx
is low. These are events in which background events are mistaken for spallation
neutron signals. The range of gvtx < 0.40 is excluded. gdir is also set to condition
gdir > 0.40 to select events with high reconstruction accuracy.
Therefore the conditions for the parameter gvtx and gdir are set,
(gvtx > 0.40) ∩ (gdir < 0.40).

(a)

(6.1)

(b)

Figure 6.6: (a) The gvtx distribution divided by the time window. The blue line represents the signal part window ([35, 235]µs), and the red line represents the
background part window([335, 535]µs). Only the cut that selects the fiducial volume is applied to the signal part and the background part. (b) The
extracted signal of the goodness of event point reconstruction gvtx . The
value of gvtx closer to 1 indicates better reconstruction. The events of the
low gvtx value are that spallation neutrons and background events occur
simultaneously or background events are mistaken for spallation neutron
signals. The right side of the red dotted line (greater than 0.4) is selected.

Distance between muon track and neutron capture vertex Lt
79

(a)

(b)

Figure 6.7: (a) The gdir distribution divided by the time window. The blue line represents the signal part window ([35, 235]µs), and the red line represents
the background part window([335, 535]µs). Only the cut that selects thefiducial volume is applied to the signal part and the background part. (b)The extracted signal of the goodness of direction reconstruction gdir . The
value of gdir closer to 0 indicates better reconstruction. The left side of the
red dotted line (less than 0.4) is selected.

To select the signal of neutron captured by gadolinium, we consider the distance
between muon track and point of neutron capture event Lt as shown in Figure 6.8.
The spallation neutron signal occurs close to the muon track and applying thiscut eliminates background not related to muon. The Lt distribution of eventsfrom neutron captured by gadolinium is shown in Figure 6.9b. The distribution is
obtained by subtracting the background part ([335, 535]µs) from the signal part([35, 235]µs) (Figure 6.9a). The cuts of the fiducial volume and the reconstruction
quality are applied to the signal part and the background part. Most of the eventsfrom neutron captured by gadolinium exist within Lt of 300 cm. We set thecondition Lt ,Lt < 300 cm(6.2)
Reconstructed event time
We set a condition for the reconstructed time t0 ,t0 = [0.7, 1.0] µs(6.3)

If there are multiple events in a trigger, the events cannot be reconstructed well,and the reconstructed time is also shifted. This condition is to reduce this effect.
80Figure 6.8: Distance between reconstructed point of neutron capture event and muontrack.

(a)(b)

Figure 6.9: (a) The Lt distribution divided by the time window. The blue line represents the signal part window ([35, 235]µs), and the red line represents the
background part window([335, 535]µs). The cuts of the fiducial volume
and the reconstruction quality are applied to the signal part and the background part.(b) The Lt distribution of the extracted signal from neutron
capture of gadolinium. The left side of the red dotted line (Lt < 300cm)
is selected.

81Events

3

×10
3000

2500

2000

1500

1000

500

0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

Reconstructed time

Figure 6.10: The distribution of reconstructed time t0 . The histogram contains thefiducial volume cut, reconstruction quality cut and distance cut describedabove. Events in the range 0.7 < t0 < 1.0 µs are selected. The few events
that exist outside this range are events that occur at the same time as
the neutron signal and shift the reconstruction time. It is eliminated toreduce the effect of multiplicity.

When the time is reconstructed successfully, the reconstruction time value of theevent is expected to be around 0.9 µs. The reconstructed time distribution is shownin Figure 6.10. The histogram contains the fiducial volume cut, reconstruction
quality cut and distance cut described above.

6.4

Study of pile-up effectPile-up occurs due to the multiple spallation neutrons generated from one cosmic muon. Pile-up has a large effect on the evaluation of energy and must be
considered when evaluating the energy of spallation neutrons. In this section,
first, the method to evaluate the mean N50 , which is used to evaluate the energy,
is described. The effect of pile-up due to multiplicity is then investigated. Finally, the signal of the Am/Be neutron source, which is less affected by pile-up, iscompared with spallation neutron signal to check the consistency.

6.4.1

Evaluation of mean N50

N50 is the number of PMT hits within a 50ns interval. In the low energy range,
where in most cases one photoelectron is detected by one PMT, N50 is used as aparameter to describe the energy. The N50 distribution of the spallation neutrons
derived from the selection conditions in Section 6.3.3 is shown in Figure 6.11. This82

Events

105

104

103

102

10

1
0

10

20

30

40

50

60

70

80

90

100

N50

Figure 6.11: The N50 distribution.

is the distribution of events that remain after applying the event selection cuts.
The sharp peak at the lower N50 on the left represents background events, and thebroader peak at N50 between 30 and 40 represents the spallation neutron events.
The spallation neutron signal events are extracted by subtracting the backgroundpart ([335, 535]µs) from the signal part ([35, 235]µs) (Figure 6.12a). The N50
distribution of the extracted spallation neutron signal is fitted to derive the mean
N50 . The fitting function is Gaussian,(x − µ)2(6.4)
f (x) = aexp −2σ 2where µ is the mean and σ is the standard deviation. We repeat the fit three times
with different ranges to increase the accuracy. The fit range is shown in Table 6.1.
The obtained µ is regarded as the mean N50 . (Figure 6.12b).
Table 6.1: Number of fits and fit range

Number of times
1st
2nd
3rd

Range of fit
20 < N50 < 70[µ − 0.4 × σ, µ + 1.5 × σ][µ − 0.7 × σ, µ + 1.5 × σ]

83

(a)

(b)

Figure 6.12: (a) The N50 distribution divided by window. The blue line represents thesignal part window ([35, 235]µs), and the red line represents the background part window([335, 535]µs). (b) The extracted spallation neutron
signal and fit function.

6.4.2

Neutron multiplicity

For one cosmic ray muon pass through the SK tank, between one and about
100 spallation neutrons are produced (Figure 6.13). The number of spallation
neutrons produced is called neutron multiplicity, and it is found that the larger
the neutron multiplicity, the larger the mean N50 value (Figure 6.14). This is dueto the pile-up. When multiple events occurred in a single trigger time window,
the one with the greater number of hits is more likely to be selected as the signal(Figure 6.15). Therefore, the greater the neutron multiplicity, the more likely it isthat signals with greater energy will be selected, and the mean N50 value will also
increase.
In addition, it is known that the shape of the dt distribution changes due to theeffect of neutron multiplicity, and the time constant changes. If an event is foundin which more than 20 PMT hits are clustered in 200 ns time width, the PMT hit
information for the surrounding 1.3 µs is stored by the sub-trigger. Therefore, if
one sub-event is stored, 1.3 µs around it becomes a dead time, and if the events
overlap within 1.3 µs, the event will not be detected. Due to this dead time, somesignals are not detected and the number of events decreases in regions with smallvalue of dt, so the shape of the dt distribution becomes smoother than it shouldbe.

84Figure 6.13: The number of spallation neutrons detected by one cosmic ray muon

Figure 6.14: Relation between mean N50 and neutron multiplicity.

85

Figure 6.15: The illustration of the selection of the largest signal by sub-trigger. The
light blue arrow represents the time width of the sub-trigger (1.3 µs) andthe yellow line represents the number of PMT hits. If multiple eventsoccur within one sub-trigger, the signal with the highest number of hits
is selected and reconstructed.

6.4.3

Comparison with Am/Be data

In this section, we test the consistency of the spallation neutron signal and
Am/Be neutron source signal. Multiple neutrons can be produced by a spallation
process and it can affect reconstruction. Therefore it is important to confirm theconsistency with the Am/Be source which only one neutron is produced at a time.
We will first explain the event selection of Am/Be neutron signal and spalltion
neutron signal, and then compare Am/Be neutron signal and spallation neutron
signal.
As mentioned above, spallation neutron signals have the effect of neutron multiplicity. For a more accurate evaluation of spallation neutron signal, it is necessary
to select a signal with the small multiplicity effect. The effect of the multiplicityof spallation neutrons on the mean N50 is shown in Figure 6.16. The top figure
shows the variation of the mean N50 with neutron multiplicity, and the bottom
figure shows the deviation of the mean N50 from one detected neutron number
where we expect no pile-up effect. It is found that when the number of detected
spallation neutrons is up to three, the deviation is within 0.5% compared to when
the number of spallation neutrons detected is one. The effect of the pile-up issmall up to three neutrons, so the data of 1-3 detected neutrons put together iscompared with the Am/Be data in order to increase the number of statistics. Four
samples are made with the detected number of spallation neutrons as shown in
Table 6.2 and compare with the Am/Be source.
Neutron signal selection
86Figure 6.16: The effect of the multiplicity of spallation neutrons on the mean N50 . Up
to 3 productions, the deviation from 1 is suppressed to 0.5%

Table 6.2: Spallation neutron detection number compared to Am/Be

Display name
All
n:1
n:1-3
n:2-10

Number of detected neutrons
Any
1
1-3
2-10

87

The Am/Be neutron source emits only one neutron at a time, so confirming thatthe pile-up effect of the spallation neutrons is negligible after the selection. In
order to compare the Am/Be neutron signal and the spallation neutron signal, theevent selection conditions are matched as much as possible. Each condition item
is described below.
• Sub-trigger threshold
The sub-trigger thresholds for Am/Be and spallation neutron is adjusted to20.
• Reconstruction quality
As mentioned above, both the Am/Be neutron signal and the spallation
neutron signal are analyzed under the condition of(gvtx > 0.40) ∩ (gdir < 0.40).

(6.5)• Reconstructed time
The reconstructed time condition to the selection condition of the spallation
neutron signal is analyzed under the condition of,
t0 = [0.7, 1.0] µs.

(6.6)• Time window
Selected from within the AFT trigger [35, 535] µs• Position and Region
Am/Be neutrons are produced at the limited source positions, whereas spallation neutrons can be detected throughout the entire SK detector. Considering the position dependence in the detector, the detection region for
spallation neutrons was adjusted to that for Am/Be neutrons. The regionis d < 400cm centred on three points (x,y,z) = (-389, -70.7, -1200)cm, (389, -70.7, 0)cm and (-389, -70.7, 1200)cm, where d is the distance between
the position where the Am/Be source is placed and the reconstructed event
point.
• DateThe spallation neutron data was summed over runs of about 5 months sothat the statistical error of the spallation neutron signal was at least thesame as that of the Am/Be neutron signal. Also, taking into account thetime dependence within the detector, two periods were used for comparison
88Table 6.3: Data used to compare Am/Be and spallation neutrons

Spallation neutron

2021/01/22 - 2021/07/19( First period )2021/08/17 - 2022/02/11( Second period )

89

Am/Be
2021/05/14#85828(-12m)#85830(0m)#85832(12m)
2021/05/11#85877(-12m)#85879(0m)#85881(12m)
2021/06/30#86004(-12m)#86006(0m)#86008(12m)
2021/09/22#86291(-12m)#86293(0m)#86295(12m)
2021/11/26#86439(-12m)#86441(0m)#86443(12m)
2021/12/23#86504(-12m)#86506(0m)#86508(12m)with Am/Be. For Am/Be, three runs within one period of spallation neutron
were selected for every three points at z = -12 m, 0 m and 12 m per one
period. The used data is summarized in Table 6.3.
In order to evaluate the same signal in Am/Be as spallation neutrons, the time
window of AFT trigger is divided into signal part time window ([35, 235]µs) andbackground part time window ([335, 535]µs), and the background is subtracted
from the signal. In addition, fitting is applied to the N50 distribution of Am/Be
in the same way as spallation neutron, and the value of mean N50 is derived.
Comparison of Am/Be neutron signal and spallation neutron signal
The result of comparing the mean N50 derived as above is shown in Figure 6.17.
Figure 6.17a shows the N50 comparison between Am/Be source and spallation
neutrons in the first period, and Figure 6.17b shows the mean N50 comparison
between Am/Be source and spallation neutrons in the second period. Figure 6.17cshows the deviation of N50 between Am/Be source and spallation neutrons in thefirst period, and Figure 6.17d shows the deviation of N50 between Am/Be sourceand spallation neutrons in the second period. From Figure 6.17c and Figure 6.17d,
it can be seen that the spallation neutron signal for n:1-3 agrees with the Am/Be
neutron signal within ±2%. Also, a χ2 test was performed at six positions to checkhow much the n:1-3 signal and Am/Be deviated from each other. The χ2 value
with a NDF of 6 is 3.29 and ap-value is 0.78. Therefore, there is no significant
deviation between the spallation neutron signal for n:1-3 and AmBe source data.
It is found that the signal for n: 1-3 is less affected by pile-up.
Table 6.4: The summary of the conditions for the event selection of neutron to use theanalysis.

Type of condition
Condition
Time window
AFT trigger : [+35, +535]µs
Reconstruction quality(gvtx > 0.40) ∩ (gdir < 0.40)
Length of muon track andpoint of neutron capture event
Lt < 300cm
Reconstructed event time
[0.7, 1.0]µs
The number of neutron detected
n:1-3

90

(a)

(b)

(c)

(d)

Figure 6.17: Results of comparison between Am/Be neutron and spallation neutron.
The upper figures show the comparison of mean N50 , and the lower figures
show the deviation from the AmBe source. The left side is the first period
and the right side is the second period. Red star represents Am/Be, andround dots represent the number of spallation neutrons detected in each(Blue: All, Red: n:1, Gray: n:1∼3, Yellow: n: 2∼10).

91Chapter 7
Detector performance monitoring
using spallation neutrons
Spallation neutrons can be used to monitor the stability of the detector response
and the uniformity of the Gd concentration. In this chapter, first, the stability
and uniformity of the detector response and Gd concentration are evaluated, andthen the results of the monitoring of additional Gd-loading in 2022 are described.

7.1

Stability

The stability of the detector response of SK-VI data is monitored in two ways:
evaluating the energy using the mean Neff and evaluating the gadolinium concentration using the neutron capture time constant.

7.1.1

Evaluation of stability using energy with mean Neff

In this section, the stability of the detector response is confirmed using themean Neff . The method to evaluate mean Neff is the same as that of mean Neffdescribed in section 6.4.1.
The data from September 10, 2020, when SK-VI started, to March 12, 2022,
before the additional Gd-loading starts, is used for this study. This period is
divided into 30-day intervals. Also, the sample is divided into nine parts using thereconstructed vertex positions for each period as shown in Figure 7.1a. Then thefitting is performed to evaluate mean Neff in each area (Figure 7.1b).
The mean Neff value for each area and for each 30-day period result is shownin Figure 7.2a. Also, the stability of the whole area of the detector is shown in
Figure 7.2b. This is derived from the difference between the average of the mean
Neff of the nine areas for one period and the average for the whole period divided
92

(a)

(b)

Figure 7.1: (a)Schematic diagram of 9-division detector. (b)The derivation of mean
Neff by performing fittings in each area.

93

by the average for the whole period, written in the equation as follows.
deviation =ave(mean Neff ) ave
one period − (mean Neff ) all period(mean Neff ) ave
all period(7.1)

It is found to be stable at ±0.5% in most areas.

(a) Stability in each area(b) Stability of the entire detector

Figure 7.2: Stability of the detector response monitored using mean Neff .

7.1.2

Evaluation of stability using Gd concentration withthe time constant

The stability and the uniformity of the Gd concentration is also evaluated using
the time constant with the same period and detector division as using mean Neff .
The time constant is derived by fitting the dt distribution with a function,


dt
+b
(7.2)
f (dt) = aexp −τcapwhere a, b, and τcap are values determined by this fitting, a is the normalization
constant for the number of signal events. b is the constant that determines thenumber of background events, and τcap is the time constant for neutron capture bygadolinium. The values of a, b, and τcap are obtained by fitting at dt ∈ [35, 535] µs.
Figure 7.3 shows the results of fitting the neutron capture timing distributions for
one period (about 30 days).
The stability of the time constant from September 10, 2020, to March 12, 2022,
is shown in Figure 7.4a. Time constants are between 125 µs to 140 µs in any area.
94

Figure 7.3: The derivation of the time constant τcap by performing fittings in each are.

This shows that the Gd concentration in the detector is uniform. For the entire
detector area, the time constant is stable within ±2% (Figure 7.4b). This showsthat the Gd concentration in the detector is also stable within ±2%.

7.2

Monitor of additional Gd-loading in 2022

Additional Gd-loading was conducted before the summer of 2022 and the SK
phase shifted from SK-VI to SK-VII. This loading took place from 1st June to
5th July 2022 and a total of 27.265 tonnes of Gd2 (SO4 )3 · 8H2 O was dissolved. In
this section, we reporte the state of the Gd concentration in the detector during
Gd-loading using the number of spallation neutron signal and the neutron capture
time constant with gadolinium.

7.2.1

Event selection of Spallation neutron for Gd-loading
monitorFor the Gd-loading monitor, it is more important to monitor the number ofneutron captures on Gd than for to evaluate energy scale precisely. So the selection
conditions for the event of spallation neutrons used in the Gd-loading monitor differ
a little from the event selection described in Section 6.3.3.
• Time window
The dt distribution of the spallation neutron signal decreases exponentially.
95

(a) Stability in each area(b) Stability of the entire detector

Figure 7.4: Stability of the detector response monitored using the time constant.

As will be described later, the higher the Gd concentration, the smaller thetime constant. When the concentration increases from about 0.01% to 0.03%,
the spallation neutron signal is more prominent within 35 µs before the AFT
trigger is issued (Figure 7.5). As such, the events within the SHE trigger [-5,35]µs were also used. However, as shown in Figure 7.6, there was a problem
that the event before 20 µs in the SHE trigger was not properly detected.
It is known that afterpulses occur at a certain rate with dt in the range of
10-20 µs [46]. It is possible that after-pulse affected the event reconstruction.
Considering that, the time window used in Gd-loading is [20, 35]µs.
• Reconstructed time and the number of neutron detected
To obtain more spallation neutron signals, the conditions of reconstructed
time and the number of neutrons detected are not used.

7.2.2

Monitor by number of spallation neutron signal

Figure 7.7 shows the distibution of spallation neutron vertex. Each figure shows
the state inside the detector up to the date indicated on the top of the figure.
As mentioned in Chapter 2, water containing additional Gd is inserted from thebottom of the detector. The intensity of the Gd concentration appears in thecontrast of the figure, and as the days pass, the concentration increases from thebottom of the detector, and on July 4th, it was evaluated that the concentrationin the detector became constant at 0.03%.
96

Figure 7.5: Schematic diagram of the difference in dt distribution for Gd concentrationsof approximately 0.01% and 0.03%. The blue line represents 0.01% Gd
concentration, and the orange line represents 0.03%. The yellow-green
area represents the AFT trigger, and it can be seen that the increase in
the number of spallation neutron signals is greater in the time before the
AFT trigger.

Figure 7.6: The dt distribution including SHE trigger. The number of events should
increase exponentially as the capture time decreases, but the number of
events decreases before 20 µs. From this, it can be seen that for somereason events are not selected well before 20 µs.

97Figure 7.7: The distibution of spallation neutron vertex. The horizontal axis represents
the square of the radius of the detector, the vertical axis represents theheight, and the plot represents the inside of the detector. The differenceof the contrast represents the difference in the number of events, and thefigure shows that the Gd concentration is becoming more concentrated
from the bottom of the tank by day. The Gd concentration in the tank
became almost constant on July 2, 2022.

987.2.3

Monitor by neutron capture time constant

Next, the Gd-loading state is monitored using the neutron capture time constant. It is expected that the time constant is approximately 120 µs at a concentration of 0.01% and 63 µs at a concentration of 0.03%. The time constants
were derived as follows. First the sample was divided into 10 parts using the reconstructed z vertex position, and then the time constant of each area was obtained byfitting the dt distribution of each area. Figure 7.8 shows the result of evaluating it
about every 3 days. On 4 June (purple line), the time constant was approximately
120 µs across the detector, but the time constant gradually decreased from thebottom of the tank and on 5 July (light blue) the concentration became constantthroughout the detector at around 63 µs.
The monitoring of the Gd-loading was carried out successfully. By using thenumber of spallation neutron signal and the neutron capture time constant withgadolinium, it could be evaluated that Gd concentration gradually increased fromthe bottom of the tank and finally the Gd concentration remained constant at thetime constant expected value of about 63 µs.

99

Figure 7.8: The state of Gd-loading using the neutron capture time constant of gadolinium.The horizontal axis represents the z direction of the detector, and thevertical axis represents the time constant. On June 4th (purple line), thetime constant was about 130µs throughout the detector, but on July 5th(light blue), the concentration became constant around 65µs.

100Chapter 8
Energy scale calibration withspallation neutrons
In this chapter, the energy calibration using spallation neutrons is discussed.
It is important for the energy calibration to evaluate the position dependence.
Firstly, the position dependence of Gd(n, γ) signal is evaluated by comparing withthat of electrons with MC simulation. Then, the Gd(n, γ) signals of data and MC
simulation are compared.

8.1

Comparison of position dependence of neutron and electron signals by MC simulation

The primary signals for solar neutrinos and DSNB are electrons and positrons.
Therefore, it is important to accurately reconstruct electron energy. In SK, there
are calibrations such as LINAC and DT calibration that inject electrons, but theposition of the injections is fixed, making a more detailed evaluation of position
dependence difficult (Chapter 5). We consider the correction for position dependence using spallation neutrons instead of electrons. Spallation neutron signals
have the advantage that they can be observed throughout the entire detector athigh rates, but they also have the disadvantage that gamma cascades are detected
and the detected energy is low and close to the trigger threshold (Chapter 6). In
this section, using the MC simulation, comparison of the deviations in the position
dependence of Neff of the electron and Gd(n, γ) signals is described in order to see
if neutrons can be used to evaluate the energy scale of electrons.

1018.1.1

Evaluation of the electron and neutron signal with
MC simulation

The Geant4-based MC simulation package called SKG4 [47] is used in thissimulation. It can simulate particle interactions and responses of the SK detector.
The output of SKG4 contains the same format as real data, so it can be analyzed
in the same way as real data.
Procedure
1. Generate particles uniformly throughout the detector.
2. Add realistic noise to the resulting output.
3. Apply the sub-trigger to the noise added output and save the sub-events.
4. Perform the event reconstruction (Sec. 5.1).
Simuated initial particles• neutron– The energy is set to 200keV. After neutron thermalization, neutronis captured by Gd and gamma rays are emitted. The ANNRI-Gd
model is adopted as the model for Gd(n, γ) [48].
• electron– The energy is set to 10MeV. This is a typical energy of electrons
generated from solar neutrino reactions observed by SK.
Evaluation of position dependence
1. The fiducial volume cut and the event quality cut are adapted (Sec. 6.3.3)
The distribution of N50 of neutron signal after these cuts is shown in
Figure 8.1.
2. The position dependence is evaluated in five regions for each of r2 andz like Figure 8.2. The mean N50 and mean Neff are estimated in eacharea by fitting (Sec. 6.4.1). The fitting results of electron and neutron
are shown in Appendix C.
3. By comparing the mean N50 and mean Neff in each area, The position
dependence of N50 and Neff is evaluated. N50 has the tendency thatthe closer the distance from the wall where the PMT is installed, thegreater the detected energy. This is because the position dependence
in the detector is largely related to the attenuation of water.
102

The mean Neff is used to evaluate the position dependence of the energy afterreconstruction. The deviation is calculated by the following equation,
deviationi =(mean Neff )i − (mean Neff )ave(mean Neff )ave

(8.1)

where i represents the index for each area.

(a) electron(b) neutron

Figure 8.1: The N50 distribution obtained by MC simulation. The histogram contains
the fiducial volume cut, the reconstruction quality cut. (a) electron. (b)neutron.

(a)(b)

Figure 8.2: (a)The detector divided into five in r2 direction. (b)The detector divided
into five in z direction.

1038.1.2

Results of the event reconstruction

For electron, the position dependence of N50 and Neff in r2 and z are shown in
Figure 8.3a and 8.3b, respectively. For neutron, the position dependence in r2 andz are shown in Figure 8.4a and 8.4b, respectively. It can be seen that the position
dependence of the mean N50 values are mostly corrected for the mean Neff values.

(a) r2(b) z

Figure 8.3: The position dependence of mean N50 and meanNeff for electron. Red dots
represent N50 and blue dots represent Neff .

8.1.3

Comparison of the position dependence of the energy
scale of electron and neutron

The deviations of Neff for r2 and z are shown in Figure 8.5a and Figure 8.6a,
respectively. Green dots represent electrons and blue dots represent neutrons.
Also, the differences in deviation between electron and neutron for r2 and z are
shown in Figure 8.5b and Figure 8.6b, respectively. For the position dependence ofthe energy scale, it is consistent within about ±2% between electron and neutron.
This is however currently larger than the systematic uncertainty of about 0.5%
in SK solar neutrino measurement. This difference is still yet to be understood.
It is important to understand the causes of this in the future in order to use thespallation neutron source for electron energy scale more reliably.

104

(a) r2(b) zFigure 8.4: The position dependence of mean N50 and meanNeff for neutron. Red dots
represent N50 and blue dots represent Neff .

(a)

(b)

Figure 8.5: (a) The deviation of Neff of electrons and neutrons by MC simulation forr2 . Green dots represent electrons and blue dots represent neutrons. (b)The difference of (a). In the range 88.8 < r2 < 177.61 [m2 ], they are
consistent within ±1%. The deviations of electron and neutron are about
2% around the center of the detector (0 < r2 < 88.8 [m2 ]) and about 3%
in the outer region (177.61 < r2 < 222.01 [m2 ]).

105

(a)

(b)

Figure 8.6: (a) The deviation of Neff of electrons and neutrons by MC simulation for z.
Green dots represent electrons and blue dots represent neutrons. (b) The
difference of (a). In the range −9.66 < z < 16.1 [m], they are consistent
within ±1%, while in the range −16.1 < z < −9.66 [m] the deviations ofelectron and neutron are about 2%.

8.2

Comparison of MC simulation and data forspallation neutron

In order to check the reproducibility of the MC simulation, a comparison withthe data is performed.

8.2.1

Results of the event reconstruction for data

The mean N50 and mean Neff of the spallation neutron signal are evaluatedusing the methods described in Section 6.4.1 and the position dependence is investigated. The fitting results of electron and neutron are shown in Appendix C.
The data from January 13, 2022 to March 12, 2022 is used for this study.
The position dependence of mean N50 and mean Neff in r2 and z are shownin Figure 8.7a and 8.7b, respectively. It can be seen that Neff almost properly
corrects for the effect of light attenuation in the water seen in N50 .

8.2.2

Comparison of the deviation of the energy scale of
MC simulation and data for Gd(n, γ) signal

The deviations of Neff of r2 and z are as shown in Figure 8.8a and Figure 8.9a,
respectively. Black dots represent the data and red dots represent the MC simula106

(a) r2(b) zFigure 8.7: The position dependence of mean N50 and meanNeff . Red dots represent
N50 and blue dots represent Neff . It can be seen that the position dependence seen in N50 (energy dropped by Cherenkov light due to attenuationof water) has been corrected.

tion. Also, the differences in deviation between electron and neutron for r2 and z
are shown in Figure 8.8b and Figure 8.9b, respectively. In the comparison of thedata and the MC simulation, they are consistent within about ±0.5% in the rangeof 44.4 < r2 < 177.61 [m2 ] and −3.22 < z < 16.1 [m]. In other regions, they are
consistent in the range of ±1%. From Figure 8.8b, it can be seen that the deviation value of the MC simulation is larger than the data at the outer side of thedetector. One possible reason for this is that the water transparency introducedin the current simulation is shorter than the actual data. Also, from Figure 8.9b,
the difference between the data and MC simulation in the bottom region of thetank (−16.1 < z < −3.22 [m]) is larger than in other areas, taking into accountthe error size of about 0.5%. One of possible reasons of this discrepancy is thatthe model of the top bottom asymmetry (TBA) introduced in the current simulation has shifted in the bottom region of the tank. It is important for energy
reconstruction performed using simulation to investigate these and improve theMC simulation to be more in correspondence with the data.

107

(a)

(b)

Figure 8.8: (a) The deviation of Neff of the data and the MC simulation for r2 . Black
dots represent the data and red dots represent MC simulation. (b) The
difference of (a). The data and the MC simulation are consistent within
1% in all areas.

(a)

(b)

Figure 8.9: (a) The deviation of Neff of the data and the MC simulation for z. Black
dots represent the data and red dots represent MC simulation. (b) The
difference of (a). The data and the MC simulation are consistent within
1% in all areas. The top of the tank in both data and MC shows about
2% deviation.

108

Chapter 9
Conclusion
In 2020, gadolinium was introduced to the Super-Kamiokande detector, and it
became possible to detect neutron capture signals by Gd. We are developing a new
method of calibrating energy reconstruction using spallation neutrons, producedby cosmic ray muons undergoing spallation reaction. The systematic uncertainty
on the energy scale of the current solar neutrino observations is 0.54%, and thegoal is to reduce this uncertainty with improved calibrations. For this purpose,the spallation neutron signal selection method was developed and the position
dependence of the energy reconstruction was evaluated in detail by data and MC
simulation.
Spallation neutron signals have the advantages that they can be detected
throughout the entire detector at high rates, but they have also the disadvantages that the detected energy is low and background is difficult to remove, andthey are affected by pile-up. In this study, the conditions of event selection wasdeveloped to reduce these effects as much as possible.
The stability and uniformity of detector response in SK-VI and the Gd concentration of Gd-loading in 2022 are evaluated using spallation neutrons. For thestability in SK-VI, the energy scale and the Gd concentration were found to bestable for the energy scale and Gd concentration at about ±1% and about ±2%
respectively throughout the detector. For Gd-loading in 2022, the Gd concentration was evaluated by the number of spallation neutron signal and the neutron
capture time constant with gadolinium. Both results showed a gradual increasein Gd concentration from the bottom of the tank as the days passed. After theend of Gd-loading, it was checked that the concentration became constant at the
expected level.
The position dependence of the energy scale is evaluated. In SK solar neutrino
observation, electrons are detected. Therefore, it is necessary to accurately evaluate the position dependence of the electron energy reconstruction. The responseto neutrons and electrons are compared using MC simulation to see if spallation109

neutrons can be used to evaluate the position dependence of energy of electron
signal. The result is that electrons and neutrons are consistent within about ±2%of the entire detector. This is however a larger deviation compared to the goal of
the correction within 0.5% of the position dependence. It is important to understand the causes of this in the future. Also, using the data and the MC simulationof spallation neutron, it was found that the energy value after reconstruction of
the MC simulation is larger than the data at the outer side of the detector andthe difference of the data and MC simulation in the bottom region of the tank(−16.1 < z < −3.22 [m]) are further apart than in other areas. Some possible
reasons for these are that the water transparency currently introduced in the MC
simulation are shorter than the actual data and that the TBA model does notmatch the data in the bottom of the tank. Since energy reconstruction is carriedout using MC simulations, it is important to investigate these in more detail in
the future and to improve the MC simulation to better reproduce the data.

110

Acknowledgment
This thesis was completed owing to many people contribution.
First of all, I would like to express my sincere gratitude to my adviser, Prof. Y.
Nakajima giving me the opportunity of carrying out this study and so much of histime to help me with all aspects. I started in the field of elementary particle experiment from a master student and didn’t know anything about Super-Kamiokande,
but he always supported me throughout this work. I learn many things under hiskind and excellent guidance. I would not have been able to complete this workwithout his support.
I would like to thank Shinoki-san. He taught me the bases of how spallation
neutrons are analyzed and how to use the codes about that. Also, he gave me
advice at the weekly meeting.
I would like to thank Dr. T. Yano for teaching me the analysis method of
Am/Be neutron source.
I would like to thank Dr. K. Ieki for teaching me the analysis method of Neffkindly. His advice was always kind and easy to understand.
I would like to thank Prof. Y. Koshio for teaching me the analysis method of
SKG4. He took the time to create the analysis code for me.
I thank to students of SK and HK Collaborators, especially, Miki-san, Kanemurasan, Kashiwagi-san, Nakanishi-san, Tomiya-san, Kaneshima-san, Yoshida-san, Shimizusan. It was fun to go out to eat and drink.
I would like to thank to all Super-Kamiokande collaborators for their support.
I am grateful to Prof. M. Yokoyama and Prof. K. Nakagiri for giving me lots ofadvice for the study. Their talks were always fun and kind. I appreciate everything
you’ve done for me.
I am grateful to Kodama-kun. He kept me company from everyday chats andconsultations to small questions. I think it was thanks to Kodama-kun that I wasable to graduate!
I thank Yokoyama-Nakajima Laboratory members, Eguchi-san, Yoshimi, LiCheng, Okinaga-kun, Kobayashi-kun, Watanabe-kun. It was fun to talk and goout to eat and drink.
I am grateful to my friends who support and understand me well, especially,
Sato-san, Ishida-kun! Wish our friendship would last forever.
Finally, I would like to express my sincere gratitude to my family for theirsupport!

111

Appendix A
Water circulating system
The water supplied to SK detector is purified groundwater in the Kamioka
Mine. Groundwater contains impurities. Small dust and metal ions scatter orabsorb Cherenkov light, reducing the transmittance of the light. Radioactive materials dissolved in water cause background events for neutrino observations. In
particular, radon 222 Rn becomes a background for analysis near the threshold (3.5
MeV) in solar neutrino observations because radon’s daughter nucleus, bismuth214
Bi, emits 3.26 MeV electron through beta decay. Therefore, radon removal isessential.
In SK, water in the tank is circulated at 60 m3 /h to remove impurities and maintain purity. Water is withdrawn from the top of the detector, purified through thepurifier, and then entered from the bottom of the detector. The process is below.
1. 1 µm mesh filter
Remove dust of 1µm or more and radioactive materials attached to it.
2. Heat exchanger
The temperature of the water in the detector rises due to the heat generated
by the circulation pump and high-voltage PMT. This temperature increasecauses dark noise, bacterial growth, and water convection. In order to prevent them, three heat exchangers are used for one cycle of water circulation,
and water temperature is adjusted to about 13 degrees.
3. Ion exchanger
Remove ions in water (Fe2+ , Ni2+ , Co2+ , CO2−
3 , etc.).
4. UV sterilizer
Ultraviolet radiation is irradiated to kill bacteria.
5. Rn-less-air dissolving system112

Figure A.1: Water circulating system of SK [49]Dissolve radon-free air in pure water in order to improve the removal efficiency of radon gas in purification in a vacuum deaerator.
6. Reverse osmosis filter
Removes organic matter with a molecular weight of about 100 by osmoticpressure and filtration.
7. Cartridge polisher
Removes 222 Rn gas and oxygen dissolved in ultrapure water.
8. Ultra filter
Removes particles larger than 10nm.
9. Membrane degasifier
Removes 222 Rn left in water.
Through the above process, the purified ultrapure water has a radon concentrationof ∼ 1.7mBq/m3 and the transmission length of light is about 100m. However, bywater circulating system in which purified water is put in from the bottom andwithdrawn from the top, there is a problem of top bottom asymmetry in water
quality with higher water transmission at the bottom of the detector than at the
top.

113

Appendix B
Calibration of Gadolinium
concentration
B.1

Am/Be neutron source

Overview
Am/Be (Americium/Berylium) neutron source is used for measuring Gd concentration through the neutron capture time. Am/Be source emits neutrons
and gamma rays simultaneously from americium and beryllium (B.1∼B.3).
241
9Am → 237 Np + α

Be + α →
13

∗

C →

13

12

∗

(B.1)

C + n (2 − 6 MeV)

(B.2)

C + γ (4.43 MeV)

(B.3)

The Am/Be source is surrounded by BGO crystal as shown in B.1. 4.43
MeV gamma ray in a BGO crystal causes photoelectric absorption, Compton
scattering, or electron pair production, and scintillation light is emitted.
Neutrons are identified as the delayed signal produced by subsequent neutron
captures by Gadolinium.
Data acquisition and reduction
In Am/Be data acquisition, the SHE trigger threshold is set to 60 hits or 100
hits due to data transfer volume issues. When 4.43 MeV gamma ray drops
its total energy in the BGO crystal, about 1000 p.e. of scintillation lightis detected. This exceeds the SHE trigger threshold, so an SHE trigger [-5,35]µs is issued, followed by an AFT trigger [35, 535]µs. Events exceeding
the sub-trigger threshold within the AFT trigger become neutron capture
candidates by Gd.
114

Figure B.1: Am/Be neutron source and BGO crystal. The black cylinder in the centeron the left is the Am/Be source, and it is assembled by surrounding itwith 8 BGO scintillators on the right.

• Prompt signal– SHE trigger is issued when there is a PMT hit above the SHE
trigger threshold.
– In order to distinguish between the BGO scintillation light signal
and the cosmic ray muon signal, we select SHE events withtout OD
trigger.
• Delayed signal
We remove scintillation light signal of the prompt event and scintillation
light from the BGO crystals due to gamma rays emitted by gadolinium.
The procedure is below.
– For the parameter gvtx representing the probability of reconstruction of the event occurrence point and the parameter gdir representing the probability of direction reconstruction,(gvtx > 0.40) ∩ (gdir < 0.40)(B.4)– For the number of PMT hits that detected light within 30 ns aroundthe delayed event time N30 and the number of PMT hits that de-115

Figure B.2: Distribution of the number N30 of PMTs that detected light within 30 ns
and the number N200 of PMTs that detected light within 200 ns from thedelayed event occurrence time. The red line represents the straight line
N200 = 1.3 × N30 + 23, and the region below the straight line satisfies thecondition (N200 − 23)/(1.3 × N30 ) < 1.

tected light within 200 ns N200 (Figure B.2),
N200 − 23<1
1.3 × N30

(B.5)

– For the distance d between the position where the Am/Be source
is installed and the reconstructed event point (Figure B.3),
d < 400cm(B.6)

Evaluation of neutron capture time constant
The neutron capture time constant is evaluated by fitting the distributionof the dime difference between the prompt and delayed events (dt) with thefollowing function (Figure B.4):





dt
dt
exp −
+b
(B.7)
f (dt) = a 1 − exp −4.3
τ
a, b, τ are derived by this fit, where a and b are the constants corresponding
to the number of signal and background events respectively,and 
τ is thedttime constant for neutron capture by gadolinium. 1 − exp − 4.3
is theterm that takes into account the neutron thermalization time. The fit isperformed by tentatively fixing the time constant for neutron thermalizationin water to 4.3 µs .
116

Figure B.3: Schematic diagram of the distance d between the position where theAm/Be source is installed and the reconstructed event point. Events in
the region within the yellow sphere with d < 400cm are selected.

Figure B.4: The dt distribution of neutron signal from Am/Be source. Each point
represents the data and the red line represents the fit function to the
data.

117

Figure B.5: History of neutron capture time constant τ by gadolinium obtained fromdetector calibration using Am/Be source

Monitoring of the neutron capture time constant using Am/Be source
From detector calibration using an Am/Be source, the capture time constantτ of neutrons was obtained as shown in Figure B.5. The time constant
was stable at around 120 µs at SK-VI when the Gd concentration is 0.01%.
After the start of SK7 with a Gd concentration of 0.03%, the time constantdecreased to around 60 µs and was stable.

118

Appendix C
Fitting results
C.1

Position dependence

C.1.1

Electron with MC simulation

The fitting results of electron signal with MC simulation for N50 and Neffare shown in Figure C.1 and Figure C.2, respectively. The result of position
dependence of N50 and Neff for r2 as shown in Figure 8.3a is obtained from themean value from the fitting as Figure C.1a and Figure C.2a, respectively. Thatfor z as shown in Figure 8.3b is obtained from the mean value from the fitting as
Figure C.1b and Figure C.2b.

C.1.2

Neutron with MC simulation

The fitting results of neutron signal with MC simulation for N50 and Neff are
shown in Figure C.3 and Figure C.4, respectively. The result of position dependence of N50 and Neff for r2 as shown in Figure 8.4a is obtained from the meanvalue from the fitting as Figure C.3a and Figure C.4a, respectively. That forz as shown in Figure 8.4b is obtained from the mean value from the fitting as
Figure C.3b and Figure C.4b.

C.1.3

Neutron with data

The fitting results of neutron signal with data for N50 and Neff are shown in
Figure C.5 and Figure C.6, respectively. The result of position dependence of N50
and Neff for r2 as shown in Figure 8.7a is obtained from the mean value fromthe fitting as Figure C.5a and Figure C.6a, respectively. That for z as shown in
Figure 8.7b is obtained from the mean value from the fitting as Figure C.5b andFigure C.6b.
119

(a) r2(b) zFigure C.1: The distribution of N50 of electron with MC simulation for r2 and z, andthe results of fitting for each area.

120

(a) r2(b) zFigure C.2: The distribution of Neff of electron with MC simulation for r2 and z, andthe results of fitting for each area.

121

(a) r2(b) zFigure C.3: The distribution of N50 of Gd(n, γ) with MC simulation for r2 and z, andthe results of fitting for each area.

122

(a) r2(b) zFigure C.4: The distribution of Neff of Gd(n, γ) with MC simulation for r2 and z, andthe results of fitting for each area.

123

(a) r2(b) zFigure C.5: The distribution of N50 of spallation neutron with the data for r2 and z,
and the results of fitting for each area.

124

(a) r2(b) zFigure C.6: The distribution of Neff of spallation neutron with the data for r2 and z,
and the results of fitting for each area.

125

List of Figures
1.1
1.2

1.3
1.4
1.5

Energy spectrum of the solar neutrino [16] . . . . . . . . . . . . . .
Electron density dependence of neutrino masses in the sun [6]. The
vertical axis represents neutrino mass squared, the horizontal axis
represents electron density. . . . . . . . . . . . . . . . . . . . . . . .
The supernova classification [18]. . . . . . . . . . . . . . . . . . . .
Time distribution of supernova neutrino energy and luminosity [19]DSNB ν¯e flux predictions from various theoretical models [20] Thecolor of each line represents the difference in theoretical models.(reddotted line and brown dotted line: Horiuchi +18 model [21], blueline and pink dotted line: Nakazato +15 model [22], light blue dotted line: Lunardini +09 model [23], green line: Ando +03 model [24],Gray line: Kaplinghat +00 model [25], ocher line: Malaney +97
model [26], purple dotted line: Hartmann +97 model [27], darkgreen dotted line: Totani +96 model [28]) . . . . . . . . . . . . . .

10

12
13
15

17

2.1 SK detector [30] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Outline drawing of Cherenkov light . . . . . . . . . . . . . . . . . . 20
2.3 The cross-section of SK detector [29] . . . . . . . . . . . . . . . . . 21
2.4 Coordinate setting of SK detector. . . . . . . . . . . . . . . . . . . . 21
2.5 Schematic view of a 20-inch ID PMT [29] . . . . . . . . . . . . . . . 22
2.6 Quantum efficiency of PMT as a function of wavelength [29] . . . . 23
2.7 QBEE system [31] . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8 The proportion of thermal neutrons that are captured by gadolinium 28
2.9 Schematic diagram of SK-Gd water system [32] . . . . . . . . . . . 30
2.10 The time transition of the mass of the dissolved Gd2 (SO4 )3 · 8H2 O
powder in 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.11 Gadolinium loading scheme . . . . . . . . . . . . . . . . . . . . . . 32
2.12 Event distribution of cosmic muon derived neutrons captured bygadolinium. The horizontal axis represents the square of the radiusof the reconstructed vertex position, and the vertical axis represents
the height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

126

2.13 The time transition of the mass of the dissolved Gd2 (SO4 )3 · 8H2 O
powder in 2022 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.14 Fluxes of DSNB (blue diagonal line) and background event neutrinos expected at Super-Kamiokande [33]. The flux of DSNB depends
on the model and has a range. . . . . . . . . . . . . . . . . . . . . . 34
2.15 The signals from DSNB (electron antineutrino) observed in pure water 35
2.16 The signals from DSNB (electron antineutrino) observed if Gd exist 36
2.17 The energy spectra of DSNB background [20] . . . . . . . . . . . . 37
2.18 Schematic of NCQE interaction [34] . . . . . . . . . . . . . . . . . . 38
2.19 End-point energies and half-lives [20] . . . . . . . . . . . . . . . . . 39
3.1

The schematic diagram of the flow of conversion of energy and thekind of calibration. In the low energy region, energy is detected using the N50 (the number of PMT hits within 50 ns) parameter. Neff(the effective number of hits) is calculated by the correction factors
derived from the basic calibration. Energy calibrations allow MC
simulation to accurately reproduce the data and the total energy isreconstructed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1
4.2
4.3

47
48

Structure of NiCf source . . . . . . . . . . . . . . . . . . . . . . . .
the flow chart of the analysis of QE . . . . . . . . . . . . . . . . . .
The relative QE updated on 16/09/2022 [38]. The vertical axis represents QE (ratio of data hit rate to MC hit rate) and the horizontal
axis represents z direction of the SK tank. Black dots represent theQE at each z position. One plot point is the average of 150 PMTs
for one round of the barrel. The red area is the area within ±0.5%,
and the data at any position is within 0.5%. . . . . . . . . . . . . .
4.4 Schematic diagram of the time walk [39]. High charge signal (redline) have higher pulses and faster the rise time than low charge
signal (blue line). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Schematic diagram of time calibration using laser . . . . . . . . . .
4.6 TQ-map for SK-IV PMT. The horizontal axis is charge of each hit(QBin), and the vertical axis is time [ns] after subtracting the timeof flight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 photon scattering [40] . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 The location of laser injector [38] . . . . . . . . . . . . . . . . . . .
4.9 Schematic of water parameter measurement using laser [38] . . . . .
4.10 The schematic diagram of the Cherenkov ring [41]. . . . . . . . . .
4.11 Time variation of water transparency [41]. The data of the middleof SK-IV to SK-VI is used. . . . . . . . . . . . . . . . . . . . . . . .
4.12 Hit rate and its ratio with the best β value [38]. . . . . . . . . . . .
127

48

49
50

50
52
53
53
54
55
56

4.13 Time variation of TBA measured with auto-Xe data [41]. . . . . . . 57
5.1

The probability density function of the residual time used for thevertex reconstruction maximum likelihood fit [40]. The second andthird peaks around 30 nsec and 100 nsec are caused by the PMT’safter pulses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 The energy dependence of position resolution in vertex reconstruction [42]. Each line represents the SK phase (Blue: SK-I, Red:
SK-III, Black: SK-IV). . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 The definition of the incident angle of the photon on the PMT [40]. 61
5.4 The the relation between the total reconstructed energy and Neffand the values p0 to p6 . Black dots show MC simulation results,
blue line represents function derived by fitting. The SK-VI data isused. The values of p0 to p6 are obtained by fitting. ”G4” written
in the figure is the name of the simulation package. . . . . . . . . . 63
5.5 Schematic diagram of the LINAC measurement in Super-Kamiokande [43].
Points A to I represent data taking points. . . . . . . . . . . . . . . 64
5.6 Ratio of Neff obtained from data and MC simulation [41]. Data
from August 6, 2019 to August 23, 2019 is used. . . . . . . . . . . . 65
5.7 Schematic of the DTG setup [44] . . . . . . . . . . . . . . . . . . . 66
5.8 An overview of DTG data taking . . . . . . . . . . . . . . . . . . . 67
5.9 Directional (θz ) dependence of the difference in Neff obtained fromdata and MC simulations [44]. The horizontal axis represents thevalue obtained by taking the cos of θz , and the vertical axis represents the deviation between the data and the MC simulation. The
rise seen around cosθz = 1 is due to the MC simulation not reproducing the effect of shadows created by the DT device itself. . . . . 68
5.10 Energy scale evaluation of 16 N analysis and DT calibraiton analysis [43]. Black dots represent 16 N data, red dots represent DT
calibration data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.11 Pocation dependence of energy scale evaluated from 16 N analysis
and DT calibraiton analysis [43] as a function of z(left) and r2 (right)
with respect to reconstructed vertex. . . . . . . . . . . . . . . . . . 70
5.12 Directional dependence of energy scale evaluated from 16 N analysis
and DT calibraiton analysis [43]. left: zenith angle cosθ. right:
azimuth ϕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.13 The reconstructed energy spectrum of decay-e [45]. . . . . . . . . . 71
5.14 Energy scale evaluation of decay-e. The gray area represents Gdloading period [45]. Soon after Gd-loading, the energy scale change
at most ∼2.7% level. For periods other than Gd-loading, the energy
scale is consistent within ∼1% level. . . . . . . . . . . . . . . . . . 72
128

6.1

6.2

6.3
6.4

6.5

6.6

6.7

6.8

The neutron capture signal by gadolinium in the SK tank. Cosmic
ray muons undergo a spallation reaction with oxygen atoms in the
SK detector, and spallation neutrons are emitted. Spallation neutrons are then thermalized and captured by gadolinium, and finallya total of 8 MeV gamma rays are emitted. . . . . . . . . . . . . . .
(a) The schematic of dt distribution. The spallation neutron signal
decreases exponentially, but the background, mostly radioactive impurities, remains constant. (b) The dt distribution seen from data. .
Comparison of spallation neutrons with other energy calibration
methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SHE trigger and AFT trigger opened when cosmic-ray muon enter
the SK tank, and sub-events following muon. Signals that exceed
the sub-trigger threshold (N200 = 20) every 1.3 µs time window arestored as sub-events. . . . . . . . . . . . . . . . . . . . . . . . . . .
The distribution of Qµ . Qµ is the total amount of Cherenkov lightdetected by ID PMTs. The red line indicates the position of Qµ =10, 000 p.e., the events to the right of the red line are selected. . . .
(a) The gvtx distribution divided by the time window. The blue line
represents the signal part window ([35, 235]µs), and the red line
represents the background part window([335, 535]µs). Only the cutthat selects the fiducial volume is applied to the signal part and thebackground part. (b) The extracted signal of the goodness of event
point reconstruction gvtx . The value of gvtx closer to 1 indicates
better reconstruction. The events of the low gvtx value are thatspallation neutrons and background events occur simultaneously orbackground events are mistaken for spallation neutron signals. The
right side of the red dotted line (greater than 0.4) is selected. . . . .
(a) The gdir distribution divided by the time window. The blue line
represents the signal part window ([35, 235]µs), and the red line
represents the background part window([335, 535]µs). Only the cutthat selects the fiducial volume is applied to the signal part andthe background part. (b) The extracted signal of the goodness of
direction reconstruction gdir . The value of gdir closer to 0 indicates
better reconstruction. The left side of the red dotted line (less than0.4) is selected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distance between reconstructed point of neutron capture event andmuon track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

74

75
76

77

78

79

80
81

6.9

(a) The Lt distribution divided by the time window. The blue line
represents the signal part window ([35, 235]µs), and the red line
represents the background part window([335, 535]µs). The cuts ofthe fiducial volume and the reconstruction quality are applied tothe signal part and the background part.(b) The Lt distribution of
the extracted signal from neutron capture of gadolinium. The left
side of the red dotted line (Lt < 300cm) is selected. . . . . . . . . . 81
6.10 The distribution of reconstructed time t0 . The histogram contains
the fiducial volume cut, reconstruction quality cut and distance cut
described above. Events in the range 0.7 < t0 < 1.0 µs are selected.
The few events that exist outside this range are events that occur
at the same time as the neutron signal and shift the reconstruction
time. It is eliminated to reduce the effect of multiplicity. . . . . . . 82
6.11 The N50 distribution. . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.12 (a) The N50 distribution divided by window. The blue line represents the signal part window ([35, 235]µs), and the red line represents the background part window([335, 535]µs). (b) The extracted
spallation neutron signal and fit function. . . . . . . . . . . . . . . . 84
6.13 The number of spallation neutrons detected by one cosmic ray muon 85
6.14 Relation between mean N50 and neutron multiplicity. . . . . . . . . 85
6.15 The illustration of the selection of the largest signal by sub-trigger.
The light blue arrow represents the time width of the sub-trigger(1.3 µs) and the yellow line represents the number of PMT hits.
If multiple events occur within one sub-trigger, the signal with thehighest number of hits is selected and reconstructed. . . . . . . . . 86
6.16 The effect of the multiplicity of spallation neutrons on the mean
N50 . Up to 3 productions, the deviation from 1 is suppressed to 0.5% 87
6.17 Results of comparison between Am/Be neutron and spallation neutron. The upper figures show the comparison of mean N50 , andthe lower figures show the deviation from the AmBe source. The
left side is the first period and the right side is the second period.
Red star represents Am/Be, and round dots represent the numberof spallation neutrons detected in each (Blue: All, Red: n:1, Gray:n:1∼3, Yellow: n: 2∼10). . . . . . . . . . . . . . . . . . . . . . . . . 91
7.1
7.2
7.3
7.4

(a)Schematic diagram of 9-division detector. (b)The derivation ofmean Neff by performing fittings in each area. . . . . . . . . . . . . 93
Stability of the detector response monitored using mean Neff . . . . . 94
The derivation of the time constant τcap by performing fittings ineach are. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Stability of the detector response monitored using the time constant. 96
130

7.5

7.6

7.7

7.8

8.1

8.2
8.3
8.4
8.5

Schematic diagram of the difference in dt distribution for Gd concentrations of approximately 0.01% and 0.03%. The blue line represents 0.01% Gd concentration, and the orange line represents 0.03%.
The yellow-green area represents the AFT trigger, and it can beseen that the increase in the number of spallation neutron signals
is greater in the time before the AFT trigger. . . . . . . . . . . . . 97
The dt distribution including SHE trigger. The number of eventsshould increase exponentially as the capture time decreases, but the
number of events decreases before 20 µs. From this, it can be seenthat for some reason events are not selected well before 20 µs. . . . 97
The distibution of spallation neutron vertex. The horizontal axis
represents the square of the radius of the detector, the vertical axis
represents the height, and the plot represents the inside of the detector. The difference of the contrast represents the difference in thenumber of events, and the figure shows that the Gd concentration
is becoming more concentrated from the bottom of the tank by day.
The Gd concentration in the tank became almost constant on July2, 2022. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
The state of Gd-loading using the neutron capture time constantof gadolinium.The horizontal axis represents the z direction of thedetector, and the vertical axis represents the time constant. On
June 4th (purple line), the time constant was about 130µs throughout the detector, but on July 5th (light blue), the concentration
became constant around 65µs. . . . . . . . . . . . . . . . . . . . . . 100
The N50 distribution obtained by MC simulation. The histogram
contains the fiducial volume cut, the reconstruction quality cut. (a)electron. (b) neutron. . . . . . . . . . . . . . . . . . . . . . . . . . . 103(a)The detector divided into five in r2 direction. (b)The detector
divided into five in z direction. . . . . . . . . . . . . . . . . . . . . . 103
The position dependence of mean N50 and meanNeff for electron.
Red dots represent N50 and blue dots represent Neff . . . . . . . . . . 104
The position dependence of mean N50 and meanNeff for neutron.
Red dots represent N50 and blue dots represent Neff . . . . . . . . . . 105(a) The deviation of Neff of electrons and neutrons by MC simulation for r2 . Green dots represent electrons and blue dots represent neutrons. (b) The difference of (a). In the range 88.8 <r2 < 177.61 [m2 ], they are consistent within ±1%. The deviationsof electron and neutron are about 2% around the center of thedetector (0 < r2 < 88.8 [m2 ]) and about 3% in the outer region(177.61 < r2 < 222.01 [m2 ]). . . . . . . . . . . . . . . . . . . . . . . 105
131

8.6

8.7

8.8

8.9

(a) The deviation of Neff of electrons and neutrons by MC simulation
for z. Green dots represent electrons and blue dots represent neutrons. (b) The difference of (a). In the range −9.66 < z < 16.1 [m],they are consistent within ±1%, while in the range −16.1 < z <−9.66 [m] the deviations of electron and neutron are about 2%. . . . 106
The position dependence of mean N50 and meanNeff . Red dots
represent N50 and blue dots represent Neff . It can be seen thatthe position dependence seen in N50 (energy dropped by Cherenkov
light due to attenuation of water) has been corrected. . . . . . . . . 107(a) The deviation of Neff of the data and the MC simulation for r2 .
Black dots represent the data and red dots represent MC simulation.
(b) The difference of (a). The data and the MC simulation are
consistent within 1% in all areas. . . . . . . . . . . . . . . . . . . . 108(a) The deviation of Neff of the data and the MC simulation for z.
Black dots represent the data and red dots represent MC simulation.
(b) The difference of (a). The data and the MC simulation are
consistent within 1% in all areas. The top of the tank in both data
and MC shows about 2% deviation. . . . . . . . . . . . . . . . . . . 108

A.1 Water circulating system of SK [49] . . . . . . . . . . . . . . . . . . 113
B.1 Am/Be neutron source and BGO crystal. The black cylinder inthe center on the left is the Am/Be source, and it is assembled bysurrounding it with 8 BGO scintillators on the right. . . . . . . . . 115
B.2 Distribution of the number N30 of PMTs that detected light within
30 ns and the number N200 of PMTs that detected light within 200
ns from the delayed event occurrence time. The red line represents
the straight line N200 = 1.3 × N30 + 23, and the region below thestraight line satisfies the condition (N200 − 23)/(1.3 × N30 ) < 1. . . . 116
B.3 Schematic diagram of the distance d between the position where
the Am/Be source is installed and the reconstructed event point.
Events in the region within the yellow sphere with d < 400cm are
selected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.4 The dt distribution of neutron signal from Am/Be source. Eachpoint represents the data and the red line represents the fit function
to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.5 History of neutron capture time constant τ by gadolinium obtained
from detector calibration using Am/Be source . . . . . . . . . . . . 118
C.1 The distribution of N50 of electron with MC simulation for r2 andz, and the results of fitting for each area. . . . . . . . . . . . . . . . 120

132

C.2 The distribution of Neff of electron with MC simulation for r2 andz, and the results of fitting for each area. . . . . . . . . . . . . . . . 121
C.3 The distribution of N50 of Gd(n, γ) with MC simulation for r2 andz, and the results of fitting for each area. . . . . . . . . . . . . . . . 122
C.4 The distribution of Neff of Gd(n, γ) with MC simulation for r2 andz, and the results of fitting for each area. . . . . . . . . . . . . . . . 123
C.5 The distribution of N50 of spallation neutron with the data for r2
and z, and the results of fitting for each area. . . . . . . . . . . . . 124
C.6 The distribution of Neff of spallation neutron with the data for r2
and z, and the results of fitting for each area. . . . . . . . . . . . . 125

133

List of Tables
1.1

Neutrino oscillation parameters [8]. NO is normal mass ordering
and IO is inverted mass ordering. . . . . . . . . . . . . . . . . . . .

8

2.1
2.2
2.3
2.4
2.5

The summary of Cherenkov momentum thresholds in water. . . . .
Typical performance of the 20-inch ID PMTs. [29] . . . . . . . . . .
The summary of the software triggers . . . . . . . . . . . . . . . . .
Detector performance per data acquisition period . . . . . . . . . .
Thermal neutron capture cross section for each gadolinium isotope .

19
23
25
26
27

3.1
3.2

The relation between calibration parameter and calibration . . . . . 43
Systematic uncertainty of energy scale of the current solar neutrino
observation [37] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1

The summary of the coefficients P0 to P8 . . . . . . . . . . . . . . . . 52

6.1
6.2
6.3
6.4

Number of fits and fit range . . . . . . . . . . . . . . . . . . . . . .
Spallation neutron detection number compared to Am/Be . . . . .
Data used to compare Am/Be and spallation neutrons . . . . . . .
The summary of the conditions for the event selection of neutron
to use the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .

134

83
87
89
90

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