Search for Supernova Relic Neutrino
at Super-Kamiokande
Takashi Iida
Department of Physics, School of Science,
The University of Tokyo
December 18, 2009

Abstract
Supernova relic neutrinos (SRN) are the diffuse supernova neutrino background from all the past supernovae. No experiments have succeeded in detecting SRN yet. This thesis describes a search for SRN using Super-Kamiokande(SK), which is a large water cherenkov detecter in Kamioka, Japan.
In 2003, SK published its first result of SRN search using SK-I data withan energy threshold of 18 MeV. This analysis includes 1496 days of SK-I data,
791 days of SK-II data and 548 days of SK-III data. This is the first result of
SRN search using SK-II and SK-III data.
We improved the analysis with a detailed investigation of background eventsand improvement to the event reduction. These improvements enable us tolower the analysis energy threshold to 16 MeV. The combined analysis of thethree phase of data taking gives a flux upper limit between < 2.0 - 2.2 /cm2
/sec (Eν > 17.3 MeV) for nine SRN models.

Acknowledgments

I am deeply grateful to my adviser, Prof. Masayuki Nakahata giving me theopportunity of studying supernova relic neutrino. I have learned a lot of things
under his excellent guidance. This thesis would never exist without his close
support and encouragement.
I would like to express my gratitude to Prof. Y. Suzuki, the spokespersonof the Super-Kamiokande experiment. He gave me useful advise related to theexperiment and the analysis. I never forget those who worked with me on theanalysis, K. Bays and Dr. M. Smy. This thesis would never be completed
without their help. I would like to express my great appreciation to Dr. Y.
Koshio. I received generous support from him related to the calibration and theanalysis.
I am grateful to those who worked for Super-Kamiokande experiment, especially Prof. Y. Takeuchi, Prof. M. Vagins and Prof. S. Moriyama. They gave
me a great advise and encouraged me in many cases. I want to thank all the
LOWE members, Dr. A. Takeda, Dr. H. Sekiya, Dr. S. Yamada and Dr. B.
Yang. I have greatly benefited from them.
I would like to thank to all other ICRR staffs who worked with me, Prof.
T. Kajita, Prof. K. Kaneyuki, Prof. M. Shiozawa, Prof. Y. Hayato, Prof. M.
Yamashita, Dr. M. Miura, Dr. Y. Obayashi, Dr. J. Kameda, Dr. K. Abe, Dr.
H. Ogawa, Dr. K. Kobayashi, Dr. K. Okumura, Dr. S. Nakayama, Dr. C.
Saji, Dr. I. Higuchi, Dr. N. Tanimoto, Dr. Y. Shimizu, Dr. H. Kaji, Dr. A.
Minamino, Dr. Y. Takenaga, Dr. G. Mitsuka, and Dr. H. Nishino.
I’m also deeply appreciative of my friends who supported me all the time,M. Ikeda, K. Ueshima, C. Isihara, D. Ikeda, N. Okazaki, T. Tanaka, Y. Idehara,
Y. Furuse, K. Ueno, Y. Nakajima, S. Hazama, D. Motoki, Y. Yokosawa T.
Yokozawa, Y. Kozuma, H. Nishiie, A. Shinozaki, K. Iyogi, T.F. McLachlan andMaggie.
Special thanks to Dr. J. Raaf, A. Renshaw and Dr. R. Wendell for their useful advices in writing this thesis. I gratefully acknowledge the financial support
by the Japan Society for the Promotion of Science.
I would like to extend my gratitude to all the people who supported andencouraged me during my time in graduate school.
Finally, I wish to express my deep gratitude to my friends and family.

Contents
1 Physics of Supernova explosion and Supernova Relic Neutrinos 1
1.1 Supernova explosion . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1 Stellar evolution . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.2 Type I Supernova . . . . . . . . . . . . . . . . . . . . . .
4
1.1.3 Type II Supernova . . . . . . . . . . . . . . . . . . . . . .
5
1.2 Supernova Relic Neutrino . . . . . . . . . . . . . . . . . . . . . .
91.2.1 Supernova relic neutrino flux and prediction models . . . 10
1.2.2 Detection of Supernova relic neutrinos . . . . . . . . . . . 13
1.2.3 SRN search in SK-I and other experiments . . . . . . . . 16
2 Super-Kamiokande Detector
20
2.1 Detection of neutrinos . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.1 Cherenkov light radiation . . . . . . . . . . . . . . . . . . 20
2.1.2 Detection method . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Super-Kamiokande detector . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Inner detector and outer detector . . . . . . . . . . . . . . 23
2.2.2 20 inch photomultiplier tube . . . . . . . . . . . . . . . . 25
2.2.3 PMT case . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.4 Comparison of SK-I, SK-II and SK-III . . . . . . . . . . . 29
2.3 Water purification system . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Data Acquisition system . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 Inner detector data acquisition system . . . . . . . . . . . 32
2.4.2 Outer detector data acquisition system . . . . . . . . . . . 35
2.4.3 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Detector Calibration
39
3.1 PMT HV determination . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Precise gain adjustment . . . . . . . . . . . . . . . . . . . 40
3.1.2 HV determination in SK tank . . . . . . . . . . . . . . . . 41
3.2 QE measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Absolute gain measurement . . . . . . . . . . . . . . . . . . . . . 47
3.4 Relative gain measurement . . . . . . . . . . . . . . . . . . . . . 48
3.4.1 Method and setup for relative gain measurement . . . . . 48
3.5 Timing calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 48

i

3.6

3.7

Water transparency measurement . . . . . . . . . . . . . . . . . .
3.6.1 Light scattering measurement by a laser . . . . . . . . . .
3.6.2 The water transparency by decay electron from stoppingmuons . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy scale calibration . . . . . . . . . . . . . . . . . . . . . . .
3.7.1 LINAC calibration . . . . . . . . . . . . . . . . . . . . . .
3.7.2 DT generator calibration . . . . . . . . . . . . . . . . . .
3.7.3 Summary of energy scale calibration . . . . . . . . . . . .

51
51
54
54
55
60
66

4 Event reconstruction
68
4.1 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2 Direction reconstruction . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Data reduction75
5.1 1st reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Spallation event cut . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 Spallation cut in SK-I and SK-III . . . . . . . . . . . . . . 78
5.2.2 Spallation cut in SK-II . . . . . . . . . . . . . . . . . . . . 81
5.3 Double timing peak cut . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Cherenkov angle cut . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5 Pion like event cut . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.6 Solar direction cut . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.7 Effwall cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.8 OD correlated event cut . . . . . . . . . . . . . . . . . . . . . . . 99
5.9 Multi ring event cut . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.10 Sub-event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.11 Summary of data reduction . . . . . . . . . . . . . . . . . . . . . 105
6 Event simulation
110
6.1 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.2 SRN event simulation . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3 Atmospheric neutrino event simulation . . . . . . . . . . . . . . . 115
7 Remaining background119
7.1 Decay electron from invisible muon . . . . . . . . . . . . . . . . . 120
7.2 Atmospheric νe , ν¯e . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3 Spallation background . . . . . . . . . . . . . . . . . . . . . . . . 124
8 Systematic error estimation
130
8.1 The uncertainty for signal efficiency . . . . . . . . . . . . . . . . 130
8.2 Energy scale uncertainty . . . . . . . . . . . . . . . . . . . . . . . 131
8.3 Background shape error . . . . . . . . . . . . . . . . . . . . . . . 131

9 Results
140
9.1 Spectrum fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.1.1 The spectrum fitting by Gaussian method . . . . . . . . . 140
9.1.2 Spectrum fitting by Poissonian method . . . . . . . . . . 141
9.2 flux upper limit extraction . . . . . . . . . . . . . . . . . . . . . . 144
10 Discussion
151
10.1 Comparison with theoretical models . . . . . . . . . . . . . . . . 151
10.2 Comparison with other experiments . . . . . . . . . . . . . . . . 157
11 Conclusion

160

A Comparison with previous result in SK

161

Chapter 1

Physics of Supernova
explosion and Supernova
Relic Neutrinos
On 23 February 1987, a supernova SN1987A appeared in the Large Magellanic
Cloud at a distance of ∼ 50 kpc was observed. This was the first observation by
naked eye after Kepler’s supernova (SN1604). At that time, neutrinos originating from the supernova were also observed at Kamiokande [1, 3], which is thepredecessor of Super-Kamiokande, and at IMB[2, 4]. This was the first observation of a stellar object outside the solar system without optical observation
method; it was an epoch-making event. Thereby this observation is said to be
the birth of the neutrino astronomy.
But supernovae are very rare events which are expected to happen once per
several tens of years per galaxy. In this thesis, we focus on the supernova relicneutrinos which originated from all of the past supernovae since the beginningof the universe.
In this chapter, stellar evolution and general physics description of supernovae are presented. Then physics and old experimental results of supernova
relic neutrinos will be described.

1.1Supernova explosion

Supernova explosions are the last stage of stellar evolution of large stars.
Heavy elements (above helium) up to iron are generated in the middle stage ofstellar evolution and emitted by supernova at the end of the evolution. There
are several processes of stellar evolution which depend on the stellar mass asfollows.

1

Figure 1.1: Supernova 1987A happen in Feb. 1987.

1.1.1

Stellar evolution

1. Protostar formation
The origin of a star starts with the formation of the core by gravitational
contraction of interstellar gases. This core becomes larger as more surrounding interstellar matter is absorbed. The kinetic energy of absorbed
matter is transformed into thermal energy and therefore the inner pressure of the star starts to rise. If the surface temperature exceeds 2000
degrees, light emission spectrum is in the visible light region and the protostar starts shining. Hydrogen burning starts when the core temperature
is over 107 [K], but a star whose mass is less than 0.08M⊙ cannot reachthis stage and such a star becomes a planet like Jupiter.
2. Main sequence stars
In stars larger than 0.08M⊙, energy is supplied from hydrogen burningwhich keeps the inner pressure in a state of thermodynamic equilibriumwith gravitation. Although there are several hydrogen burning process,basically it is expressed by equation 1.1.
4p →4 He + 2e+ + 2ν

(1.1)

The Q value for this reaction is 26.73MeV, with the neutrinos carrying
2× 263keV away from the stars, therefore leaving 26.20keV in real thermalenergy1 . Figure 1.2 shows the solar neutrino flux for each reaction mode.
Temperature and pressure are balanced in the state of hydrogen burning
if there is no degeneracy pressure. For example, if the temperature is
1 This is the case of PP chain I. The energy carried away is different for each reaction mode.

2

Figure 1.2: Flux of solar neutrino. X-axis is neutrino energy and Y-axis is
expected flux in Bahcall-Serenelli 2005 SSM.

changed, the radius of the star is also changed in order to keep dynamical
equilibrium, this is called the self stabilization effect. Most stars, including
the sun, are in this step, which we call the main sequence. Although PP
chain interactions dominate other nuclear fusion process in the sun whose
core temperature is 1.5×107[K], other more massive, hotter stars can have
the CNO cycle as a dominant reaction mode. Light stars, whose mass isless than M < 0.46M⊙, end their life by becoming white dwarves withhelium core because they cannot move onto the next step of nuclear fusion.
3. He burning
Stars with mass greater than 0.46M⊙ start to gravitationally contract
again once the hydrogen burning has ceased and core temperature thenbegins to increase. If the core temperature exceeds ≃ 108 degrees, helium
burning is started. There are no stable nuclei in the case of atomic number
5 and 8, so the next step in the nuclear reaction is the process of making
12
C from 4 He (α particle) through 8 B nuclear. This process is called thetriple alpha process.
34 He →12 C + γ(1.2)

Q = 7.27MeV(1.3)

Once helium burning has started, the pressure in the center of core
becomes very high. The whole star then expands and the temperature of
the stellar penumbra decreases until finally the star becomes a red giant3

star. Stars as massive as the solar mass stop their growth, blasting off
their penumbra and leaving the core behind to become a white dwarf.
In the case that this helium burning occurs under degenerate pressure,the nuclear reaction burns up. Degenerate pressure does not depend on
temperature, so contraction cannot start even after the ignition of helium
burning. However, the core temperature will increase even in that case,thus causing the helium burning to proceed explosively. This temperature
increase continues until the star is no longer under degenerate pressure.
This peculiar process is called helium flash.
4. Heavy ion burning
Helium burning in stars with masses between 4M⊙ and 8M⊙ proceedsin the absence of degenerate pressure until the generated C-O core starts
burning. Carbon deflagration is caused due to the same principle as helium
flash. This is the mechanism of type Ia supernovae.
More massive stars, 12M⊙ > M > 8M⊙ , make Ne-Mg cores by carbon
burning under the degenerate pressure.
Stars with mass greater than 12M⊙ do not reach degenerate pressure, so
finally Mg burning produces an iron core. Iron, 56 F e, is the most stableelement; further burning is impossible.
5. End of the massive starCore temperature and pressure increase only by gravitational contraction
because iron core does not supply energy. At the final stage, the ironcore photodisintegration begins and this endoergic reaction accelerates thegravitational contraction. The stars finally end their life with a supernova
explosion. Details of the supernova explosion are described in the next
subsection.

1.1.2

Type I Supernova

Type I supernovae are distinguished by the lack of hydrogen absorption lines
in their spectrum. Type I supernovae can be classified into three different types
based on their spectrum. Type Ia include a large Si absorption line. Type Ib
can be distinguished by the lack of both hydrogen and Si absorption lines. TypeIc spectra don’t have any hydrogen, helium and silicon lines.
Type Ia is caused by carbon deflagration occurring in the condition of degenerate pressure. In the case that the white dwarf of a binary system receives
some mass from the other star of the binary system, core collapse starts aslong as the white dwarf mass exceeds the Chandrasekhar mass (1.4M⊙ ). It also
causes carbon deflagration and eventually a big explosion. It is by this process which everything gets blown to pieces so that nothing can exist after the
explosion. Although type Ia supernovae appear in every type of galaxy (e.g.,
elliptic galaxies, spiral galaxies, etc.), their rate of occurrence is lower than typeII supernovae, which are described in the next subsection.
4

Because the absolute light intensity of type I supernovae are almost constant,they are called ”standard candle” and are used for measurement of the distanceto the galaxy including the type I supernova. They also enable us to measure
the cosmological constant.
Type Ib and Ic are formed through a different process. They are basicallythe same as a type II supernova which is caused by core collapse of massive
stars. But type I supernovae don’t include the hydrogen absorption lines, so the
explosion should happen with the outer layer absent of hydrogen. The detailsof type Ib and Ic are not understood yet.

1.1.3

Type II Supernova

General description of type II Supernova
Type II supernovae are caused by iron core collapse of massive stars whose
masses are larger than 8M⊙ . This kind of star can form an iron core as well asburning the silicon at T ≃ 3.4×109 K. If the mass of the iron core is greater thanthe Chandrasekhar mass (Mch ≃ 1.4M⊙ with Y e ≃ 0.4 ;where Ye is the fractionof the electrons per nucleon), gravitational core collapse and photodisintegration
will happen within ∼ 10 sec, thus liberating a large amount of energy. Neutronstars or black holes are left after this process.
In the case when a neutron star is left, the released energy from this typeII supernova is calculated to be as follows:

∆E

=
=





M2
M2
− −G
−G
R GScore
R NS

−1
2 
M
R
2.7 × 1053
[erg]
M⊙
10km

(1.4)
(1.5)

Where GS and NS express giant star and neutron star and the first term isalmost negligible.
Meanwhile, the energy expended by photodisintegration is estimated tobe less than 1.4M⊙ × 6 × 1023 × 3.2 MeV ≃ 1 ×1051 erg. The kinetic energy
for the ejecta mass of Mej=10M⊙ is on the order of Ekin =1/2Mej ×v 2 ≃ 1
×1051 erg, assuming v ≃ 2000km/s. Optical energy and gravitational waves
also carry away energy smaller than this order. Most of the energy, more than
99%, released by core collapse is carried away by neutrino emission.
To calculate neutrino flux from type II supernova, one may carry out
a hydrodynamic calculation with neutrino transport. The core density is >1013 g/cm3 , so the core is opaque to neutrino transport. The effective temperature of the core surface is estimated by the radiation law as follows.
"

1
∆E/τ
Tef f =
2
4πσRef f (7/8)gν

5

#1/4

(1.6)

where σ is Stefan-Boltzmann constant, gν is the number of neutrino species
and R ≃ several times 10 km. τ is the cooling time of the core whose order is 5-10
sec. Then the effective temperature is calculated ≃ 4MeV and average neutrinoenergy ǫν = 3.15Tef f ≃ 10MeV. The total neutrino flux can be estimated asfollows.

Φν =∆E≃ 2 × 1058
ǫν

(1.7)

Therefore, the neutrino flux of a supernova at the center of galaxy is

φν =

Φν
≃ 1.6 × 1012 cm−2 /burst
4πd2

(1.8)

From this flux, we expect the event rate in a 1kt water detector for a galactic
supernova:
ν¯e → e+ n : 170events
νe → νe e− : 8events(1.9)

Time evolution of type II Supernova
If the contraction proceeds, the core density will become larger until the Fermi
pressure of the electron increases. Large Fermi pressure accelerates the electron
capture by iron with a Q value of 3.695MeV. The density threshold of electron
capture is ρ/µe ≃ 0.53 × 109 g/cm3 . The state just before core collapse isρcore ≃ 109 −1010g/cm3 , Tcore ≃ 0.7MeV and the radius of the sphere encircling
the Chandrasekhar mass is ∼ 3000 km.
Once core collapse starts, free protons are generated by photodisintegrationof iron as follows:
56

F e + γ → 134 He + 4n − 124.4MeV
4He + γ → 2p + 2n − 28.3MeV(1.10)(1.11)

Because this process is an endoergic reaction, contraction of the massive coreand electron capture proceed furthermore with free protons (electron capture on
free protons has a larger cross section than iron). The number of electrons per
nucleon (Ye) decrease by electron capture and it also reduces the Chandrasekhar
mass (Mch ). The consumed proton is supplied through the photodisintegration
process. This process produce a large number of neutrinos whose luminosity is≃ 1052 erg/sec for about ∼ 10 msec.
If R > 10λ, where R is the radius of the core and λ is the mean free path ofneutrinos, the core becomes opaque to neutrinos.
A region whose density is larger than 1011 g/cm3 forms a neutrino sphere
whose radius is ≃ 70km. This neutrino trapping increases the neutrino Fermi
6

gas pressure, thus electron capture is suppressed. The time scale of this process
is about 25 ms.
These process described above cause the decrease of the inner supportingpressure so that core collapse is promoted further and core density becomeslarger. Once the core density exceed the nuclear density of 3 × 1014 g/cm3 , thecontraction is halted by the degenerated pressure of neutron. The outer core
free-falls onto inner core and bound on the surface of inner core and the shock
wave propagating outward is generated[6]. The time evolution of stellar shell isshown in Fig1.3.

Figure 1.3: Time evolution of stellar shell. 0.0sec is the beginning of freefalling. [13]Electron neutrinos remain trapped in the neutrino sphere until the shock
wave reaches the sphere. Once it reaches, the matter temperature is heated
up to T ∼ 10 MeV thereby protons and neutrons are liberated. This process
promotes the electron capture drastically, generating large amount of electron
neutrinos. This is called the deleptonisation burst (or electron neutrino burst)
generally. The time scale of the burst is order of 10 ms and its liberating energy
is a few times 1051 erg [7].
After this degenerate pressure, a shock wave heats the neutrino sphere andthen an equal number of all species of neutrinos and anti-neutrinos are generated mainly from neutrino pair creation. Then a protoneutron star is formed,
consisting of dense core and mantle, and it cools by emitting neutrino black
body radiation in the neutrino diffusion time scale of ∼ 10 sec.
7

After the deleptonisation burst, neutrino luminosity is almost same for all
the species of neutrino. The average energy of each neutrino species is:hEνe i < hEν¯e i < hEνµ,τ i(1.12)

where νµ,τ include their anti particles. νe (n, p) e− has a lager opacity thanν¯e (p, n) e+ because neutrons are more abundant than protons. Therefore neutrino sphere of anti-electron is deeper and hotter than that of electron neutrino.
Neutrino sphere of muons and tau neutrinos and their anti neutrinos is locatedstill deeper because their interaction is only by a neutral current interaction.
Generally the average energy for each species is given as follows:hEνe i ≃ 10 − 15MeV(1.13)

hEνµ,τ i ≃ 20 − 25MeV(1.15)hEν¯e i ≃ 12 − 18MeV(1.14)

These calculations depend on the authors[9, 10, 11]. Time evolution of neutrino luminosity and their average energies are shown in Fig1.4. The sharp peakaround 0.05sec is due to electron neutrino from deleptonisation burst. Timeintegrated energy spectrum for each species are also shown in Fig1.5

8

Figure 1.4: Time evolution of neutrino luminosities(upper) and their averageenergies (lower) [13]1.2Supernova Relic Neutrino

Kamiokande detected neutrinos from supernova SN1987A. This enabled us toinvestigate the mechanism of supernova explosion and also showed that neutrinos can be an effective tool for the space observation, especially for deep inside
the stars. But supernovae are quite rare events, said to happen once per several
tens of years per galaxy. In this thesis I focused Supernova Relic Neutrinos(SRN), which are the diffuse neutrino background originating from all the pastsupernova since the the beginning of universe. Measurement of supernova relicneutrinos enable us to know the history of supernova in the whole universe.
For example, flux and spectrum of supernova relic neutrinos are related to thehistory of galaxy evolution and mass distribution in the universe. So the measurement of supernova relic neutrinos is very important for the astrophysics.
In this section, I discuss the supernova relic neutrino itself, followed by adiscussion of the detection of SRN in Super-Kamiokande, and finally old experimental results for SRN will be described.

9

2.5e+10
nu_e
anti_nu_e
nu_x

Flux (counts / cm^2 / MeV)

2e+10

1.5e+10

1e+10

5e+09

0
0

10

20

30

40

50

60

70

Energy (MeV)

Figure 1.5: Time-integrated energy spectrum for each species

1.2.1

Supernova relic neutrino flux and prediction models

Supernova relic neutrinos are the diffuse supernova neutrino background andtheir origin is all the supernovae occurring between big bang and present day.
Thus their neutrino spectrum is a superposition of the neutrino emission of eachsupernova explosion. Considering red shift caused by the overall expansion of
the universe, we can calculate the SRN spectrum as follows:

c
dFν
=
dEν
H0

Z zmax0

RSN (z) ′
dNν Eν
dEν′dz(1 + z)q3Ωm (1 + z) + ΩΛ

(1.16)

where c is the speed of light, H0 is the Hubble constant, z is the red shiftparameter. Ωm and ΩΛ are the fraction of the cosmic energy density in matterand dark energy, respectively. RSN is the supernova rate depending on the red
shift parameters; at present it is RSN (0) ∼ O(10−4 )M pc−3 yr−1 . Observations
indicate this rate increases with the red shift, it meaning that supernovae occurred more frequently in the earlier universe. The supernova rate dependingon the red shift is expressed using RSN (0) and the red shift parameter z.
β

RSN (z) ≃ RSN (0) (1 + z)

(1.17)The best fit value for β is 3.28 up to red shift z ∼ 1 [31] and the rate
becomes flat at large z. Fig 1.6 is the evolution of star formation rate densitywith redshift.
There are several models predicting supernova relic neutrino flux in thisway. Even before SN1987A happened, SRN were predicted theoretically [17] and10

Figure 1.6: Evolution of star formation rate density with red shift. Solid line s
are best fitting parametric forms. See [31] for the detail discussion.

the flux was also calculated [18, 19]. The models of an early date are calculated
without any experimental data assuming the constant supernova rate. The
models after SN1987A calculate the flux and spectrum precisely using advanced
theoretical assumptions [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. The SRN
fluxes predicted in these theories range from ∼ 0.3 − 4.6ν¯e cm−2 s−1 above 17.3
MeV. The predicted spectra are shown in Fig 1.7.
• Constant SN rate [20] (Totani et al. 1995)
An early paper on SRN was published in 1995 by Totani et al. in which
the Supernova rate is hypothesized to be constant across all space andtime. This model used supernova simulation and considered a cosmologicalconstant for the first time. The absolute flux value was estimated using
the abundance of oxygen, because oxygen should be generated in the star
which can make the supernova explosion.
• Population synthesis [21] (Totani et al. 1996)
The same author published another paper in 1996 using a population
synthesis in the galaxy evolution. In this paper, the difference of supernova rate between elliptic galaxies and spiral galaxies are discussed andthen supernova rate was estimated for each kind of galaxy. Although several cosmological parameters are used in this paper, we take the case of(h,Ω,λ)=(0.8,0.2,0.8) in this thesis. Here h is the Hubble constant, Ω isthe density parameter2 and λ is the cosmological constant.
2 Ratio of density and critical density11• Cosmic gas infall [22] (Malaney et al. 1997)
This paper, published in 1997 by Malaney et al., considers the density
distribution of interstellar gas for the red shift parameter. Absorption
lines of a quasi-stellar objects, QSO, were used. Generally the interstellar
gas gets together to make the star and is then returned to the gas throughan explosion. But according to this paper, it is only possible for thisprocess to happen in the region z ≤ 2 so the flux becomes smaller thanother models.
• Cosmic Chemical evolution [23] (Hertmann et al. 1997)
This model is calculated using chemical evolution of the universe. Galactic halo and chemical evolution information are obtained from the observation of Damped Ly α system (DLA). They are used for the predictionof the global star-formation history. In this paper, they compare several
models; for example, one considering time evolution of neutrino energy
in the supernova explosion, one changing cosmological parameters, onechanging the star formation rate and so on. In this thesis, we adopt theone with Ω = 1 and without time evolution of neutrino energy, called”standard model”.
• Heavy metal abundance [24, 25] (Strigari et al. 2004)
In 2000, Kaplinghat et al. present the paper that predict the theoretical
SRN flux upper limit using abundance of heavy elements. The flux prediction is updated in 2004 including the new star formation history fromthe Sloan digital sky survey. Supernova neutrino spectrum is typicallymodeled by a Fermi-Dirac spectrum with an effective chemical potential(≡ µν /Tν ). Zero chemical potential and Tν¯e are assumed in their paper. Neutrino oscillation effect inside a supernova is also considered withnormal hierarchy.
• LMA neutrino oscillation [26] (Ando et al. 2002)
This model considered the neutrino oscillation inside the stars in orderto calculate the flux and spectrum of the SRN. Oscillation parameter used
are those obtained from solar and atmospheric neutrino observation. BothSMA and LMA solutions are discussed in this paper but solar neutrino
observation has revealed that the LMA solution is correct.
If oscillation is considered, ν̄µ,τ whose energy is higher than that of ν¯e ,is mixed so the spectrum shifts to a higher region. The cross section of
inverse beta decay interaction, discussed later, increase with the square of
the energy. Therefore event rate in SK increase if the effect of neutrino
oscillation is taken into account. The star formation rate used in thispaper was increased by factor 2.56 in 2005 [27].
• Cosmic star formation history [28] (Horiuchi et al. 2008)

12

In this paper, SRN prediction is started with the cosmic star formation
history of Hopkins and Beacom[31] and it’s crosschecked by the measurement of core-collapse supernovae[32, 33, 34], the extragalactic backgroundlight (which records the total stellar emission overall time [35]), and thestellar mass density [36]. By crosschecking other measurements, the uncertainty of SRN spectrum originating from astrophysical input is foundas ∼ ±40%. As an uncertainty of neutrino emission per supernova, effective temperature of 4, 6, and 8 MeV are adopted. In our analysis, the caseof 6 MeV is used.
• Star formation rate constraint [29] (Fukugita, Kawasaki 2003)
Star formation rate (SFR) is discussed with the old Super-Kamiokande
SRN search result[16] in the paper published by Fukugita and Kawasaki.
Obtained SFR constraint (< 0.040 M⊙ yr−1 Mpc−3 ) is about twice the
SFR estimated from radio observations, and five times that estimatedfrom Hα. In this paper, reducing uncertainty in neutrino spectrum wastried using the observation of 1987A neutrinos as a constraint for neutrino energy spectrum[4]. Although the minimum and maximum case areconsidered from the 90% CL for the IMB events, we took the average ofminimum and maximum case.
• Failed supernova [30] (Lunardini 2009)This model considers supernova from core collapse with direct blackhole formation (failed supernova). According to this paper, the average
neutrino energy of a failed supernova is hotter than that of a normal supernova which makes neutron star. Although the fraction of failed supernova
is considered as the uncertainty, our analysis adopted 22% case which islargest assumption.
These seven models were used in this thesis when we simulated the spectrumof SRN in SK as discussed later. The predicted SRN fluxes are listed in table
1.1.

1.2.2

Detection of Supernova relic neutrinos

Because Super-Kamiokande is a water Cherenkov detector, neutrinos are detected by their interaction with water molecules. Considering the cross section,
the following three interactions are possible. Fig1.9 shows the expected event
rate for each interaction mode.
1. Inverse beta decay
Inverse beta decay is the charged current quasi elastic interaction ofanti-electron neutrino on proton:ν¯e + p → n + e+
13

(1.18)

ModelPredicted flux

LMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Heavy metal abundanceCosmic Chemical evolution
Population synthesis
Cosmic SF history
SFR constraint
Failed supernova

1.7 ν¯e /cm2 /sec
4.6 ν¯e /cm2 /sec
0.3 ν¯e /cm2 /sec
0.4 − 1.8 ν¯e /cm2 /sec
0.5 ν¯e /cm2 /sec
0.54 ν¯e /cm2 /sec
1.1-1.9 ν¯e /cm2 /sec
0.4-1.1 ν¯e /cm2 /sec
0.9-1.2 ν¯e /cm2 /sec

Table 1.1: Predicted flux in each models (our analysis energy threshold of Eν >17.3MeV).

One water molecule has two free protons. An anti electron neutrino caninteract with these protons by inverse beta decay and the cross section
is largest of the interaction between neutrino and water [20]. In SuperKamiokande, almost all the detectable events are originating inverse beta
decay. In this interaction, emitted positron does not keep the direction
information of original neutrino although cross section is very large.
The cross section of inverse beta decay can be simply calculated in firstorder approximation for Eν <∼ 30M eV as follows.

σ≃ 9.52 × 10−44

Ee= Eν − ∆pe Ee[cm2 ]
MeV2(1.19)

Here pe is the momentum of positron and Ee is the total energy of positron,
both in unit of MeV. ∆ is the mass difference between neutron and proton and it’s about ∼ 1.3MeV. So the measurable e+ energy is strongly
correlated with the ν¯e energy.
Recently, a more precise calculation was also performed covering the higher
energy region[57, 15]. We adopted the one which includes the dominant
low energy effects in the calculation, as discussed in [15].
2. Neutral current interaction with oxygen / protonνx +16 O → νx + γ + X(1.20)

This is a neutral current interaction for all types of neutrinos with oxygen
nucleus or proton. In this interaction, the neutrino kicks out a nucleon
from the oxygen in water and generate 15 O and 15 N . Nucleus in an
excited state is generated and a gamma-ray of 5 - 10 MeV is emitted
14

Figure 1.7: Colored line shows the predicted SRN spectrum in each model.
Black lines are representing other background neutrinos.

simultaneously. These gamma rays are below our analysis threshold sothat they cannot be used for SRN analysis.
3. Electron elastic scattering
ν + e− → ν + e−

(1.21)

This is the neutrino-electron elastic scattering interaction. Recoiledelectrons keep the direction information of the original neutrino, but it is
not effective for the SRN search because SRN have no specific direction. In
addition, the cross section of this interaction is negligibly small comparing
with inverse beta decay.
According to the discussion above, the interaction modes other than inverse
beta decay of ν¯e are negligible for SRN search. The predicted ν¯e spectra fortheoretical SRN models are shown in Fig1.7. The energy region below ∼ 15MeV
is not appropriate for SRN search because Solar neutrinos are dominant in thisregion. Also atmospheric neutrinos are much higher than SRN above several
tens of MeV. Thus the search window for SRN is ∼ 15 - several tens MeV.
15

Cross section (10-40 cm2)

3

2.5
2

1.5
1

0.5
0

10 15 20 25 30 35 40 45 50

Neutrino Energy (MeV)

Figure 1.8: The calculated cross section of inverse beta decay as a function ofneutrino energy. Red line is approximated cross section in equation 1.20. Greenline shows the precise calculation by Strumia and Vissani[15].

1.2.3

SRN search in SK-I and other experiments

Kamiokande
The Kamiokande collaboration published the result of SRN search in 1988 [42].
Kamiokande was a water Cherenkov detector for nucleon decay and neutrino
detection. This detector was located at the Kamioka mine at ∼ 1000m depth.
It consists of a large steel water tank with 3000 tons of pure water and 1000
20-inch PMTs. Its fiducial volume was ∼ 680 tons.
Using 357 days of data, the upper limit on the SRN flux in the energy range
between 19 - 35 MeV is obtained as 226 /cm2 /sec at 90% confidence level.
Additional SRN flux upper limit obtained from 1040 days of Kamiokande-II data
was set on the total SRN flux (< 780 ν¯e /cm2 /sec) [43]. This is corresponding
to 50 ν¯e /cm2 /sec in the energy region above 19 MeV.
SNO
Sudbury Neutrino Observatory (SNO) is a neutrino detector using heavy water;
its first motivation is solar neutrino measurement. The SNO detector consistof an acrylic vessel filled with 1 kton heavy water surrounding 10,000 PMTs.
Using heavy water, the SNO detector is sensitive to electron neutrinos throughthe charged current interaction as follows.

16

Figure 1.9: Expected event rate for each neutrino interaction modes inside theSK fiducial volume. A constant SN rate model is used for the SRN flux. The
event rate of inverse beta decay is higher than that of other modes by two ordersof magnitude. [20]17νe + D → P + P + e−

(1.22)The SNO collaboration published its result for SRN search in 2006 using
their first phase data with an exposure of 0.65 kton − years [44]. In theiranalysis, no events are observed in the neutrino energy range of 22.9 - 36.9
MeV, and consequently, the flux upper limit on the νe component of SRN was
set to < 70/cm2 /sec at the 90% confidence level.
Mont Blanc
The LSD liquid scintillation detector has been operating since 1985 in the Mont
Blanc Laboratory. The detector consists of 90 tons of liquid scintillator, contained in 72 stainless-steel tanks and each counter is watched by three PMTs
with 15 cm diameter. Since the amount of luminescence of liquid scintillator islarge, LSD can detect the gamma-rays emitted by neutron capture so that ν¯eevent can be separated from other background such as solar νe .
Anti neutrino limit flux of < 8.2 × 103 /cm2 /sec are obtained. with 90%
confidence level[45].
KamLAND
KamLAND is a 1 kton liquid scintillation detector located 1000m depth underground in Kamioka, Japan where is the same site as Super-Kamiokande.
Because this detector consists of liquid scintillator, the gamma-rays from a neutron capture can be tagged and it enable us lower background rate and lower
energy threshold.
The KamLAND result was obtained by searching inverse beta decay event
originating from the sun and other sources. This flux limit can be applied for
the SRN. From the KamLAND result, SRN flux limit of ∼ 102 /cm2 /sec are
obtained in the energy region of 8 - 14 MeV[46].
SRN search in SK-I
1496 days of SK-I data were analyzed in the first SK analysis and no clear
SRN signal was discovered [16]. Fig1.10 shows the energy spectrum for the real
data and expected backgrounds and they are consistent. In the result of thatanalysis, most strict flux upper limit was obtained. In the energy region, Eν >19.3MeV, SK-I SRN flux upper limit of < 1.2/cm2 /sec was obtained for allmodels and it’s close to predicted SRN flux.
Note that this flux limit was obtained using the first order approximation
expressed by equation 1.20. This cross section is ∼20% larger than latest
calculation[15].

18Observed events / 1496 days / 22.5 kton / 4 MeV

50
45
40
35
30
25
20
15
10
5
0

20

30

40

50

60

70

80

Energy (MeV)
Figure 1.10: Spectrum of SK-I data and background of atmospheric neutrinos.
Black points with error bars are data and the red solid histogram is best fit
of atmospheric neutrino MC. Red dotted histogram which has a peak around
40MeV is the νµ component of atmospheric neutrinos and the other one is theνe component. Blue dotted line shows the sum of the total background and the
90% C.L. upper limit on the SRN flux signal.Black dotted line at 34 MeV is aboundary line where the efficiency changes.

19Chapter 2

Super-Kamiokande
Detector
Super-Kamiokande detector [51] is a 50,000 ton water cherenkov detector forneutrino observation (Kamioka Neutrino Detection Experiment) and nucleon
decay (Kamioka Nucleon Decay Experiment) which is located 1000m depth
underground of Ikenoyama, Japan as shown in Figure-2.1 in order to reduce
cosmic ray muon background. It reduce the cosmic ray muons by 5 orders ofmagnitude. 50kton of water is filled in 39m diameter and 42m height cylindricalstainless steel water tank surrounded by more than 10,000 20-inch diameter
PMTs. In this chapter, the principle of detection, photomultiplier, water tank,pure water system and data acquisition system are described.

2.1

Detection of neutrinos

2.1.1

Cherenkov light radiation

Super-Kamiokande detects relativistic charged particles by Cherenkov lightwhich is emitted when the speed of a charged particle exceeds the speed oflight.
When charged particle travels through a medium, charge polarization occurs.
The charged particle exchanges photons with surrounding electric field but if the
speed of the particle is faster than the speed of light in medium, photons cannot
catch up with former particle. Those photons are emitted with the opening
angle θ with the following equation. The basic concept of Cherenkov radiationis shown in Figure-2.2.
cos θ =

20

1
nβ

(2.1)

LINAC roomelectronics hut

control room

20" PMTs

water system
Mt. IKENOYAMA

1000m

Figure 2.1: The overview of Super-Kamiokande detector.

21Here β is v/c. The condition for Cherenkov light emission, v ≥ nc , is obtained
from Equation-2.1 and −1 ≤ cos θ ≤ 1. The energy threshold of Cherenkov
light radiation (Ethr ) corresponds to a lower limit of the speed β = n1 and it isexpressed using the mass of charged particle m as follows:nm
Ethr = pn2 − 1(2.2)

In the case of water, Cherenkov photons are emitted with an opening angleof 42 degrees because the refractive index is about 1.33. Then the Cherenkov
radiation threshold, Ethr , for electron, muon and charged pion are 0.767, 157.4
and 207.9 [MeV], respectively as shown in Table-2.1.
particleThreshold [MeV]

±

0.767
157.4
207.9

e
µ±
π±

Table 2.1: Cherenkov radiation threshold
The Cherenkov radiation spectrum per unit path length dL can be obtainedby following formula:
12παZ 2d2 Nphoton
1− 2 2
(2.3)
=
dλdL
λ2
n β

where N is the number of emitted photons, λ is wavelength of Cherenkov
1light and α is the fine structure constant (≃ 1/137). Substituting cos θ = nβ
for this formula, following equation is given:dNphoton
dL

Z λ2

dλ
λ2

=

2παZ 2 sin2 θ

=


1
1
1
2
2
−
2παZ sin θ
λ1
λ2

λ

(2.4)

Figure-2.3 shows the spectrum of Cherenkov radiation with the quantum
efficiency of 20-inch PMTs used in SK. It indicates that the most sensitivedNphotonregion is between 300 ∼ 600nm.
≃ 340 [photon/cm] are emitted withindL
this region with θ = 42◦ 、Z = 1.

2.1.2

Detection method

In this section, how the Super-Kamiokande detector detects Cherenkov lightand gets the neutrino information is described.
Super-Kamiokande detects the particles which is emitted from the interaction between neutrinos and protons/16O nuclei in water. We get the Cherenkov
ring information with photo multiplier tubes (PMTs) placed uniformly surrounding the water tank like Figure-2.4. The event vertex is reconstructed from22

direction of
Cherenkov photons

θdirection of
charged particle

Figure 2.2: Emitted direction of Cherenkov photons.

PMT hit timing information and the energy is reconstructed from the number of hit PMTs. The direction of charged particle is also reconstructed fromCherenkov ring pattern. Details of the detector are described in next section.

2.2

Super-Kamiokande detector

The Super-Kamiokande detector is a large water Cherenkov detector consistingof a cylindrical stainless water tank, 39m radius and 41.4m height, filled with
50ktons of pure water, a purification system for water and air, photomultipliertubes, electronics and data acquisition system, etc. The detector is located atcoordinates of 36◦ 25’N in latitude, 137◦ 18’E in longitude and 1000m underground, 2700 meters water equivalence. In order to reduce cosmic ray muons,the detector is located deep underground; the muon rate in Super-Kamiokande
is about 2 Hz which is reduced five orders of magnitude compared with that ofon surface. Detector construction started from 1991 and completed in 1995. After filling with pure water and test operation, neutrino observation was started
from April, 1996.

2.2.1

Inner detector and outer detector

The Super-Kamiokande detector consists of an inner detector (ID) and an outerdetector (OD). The ID and OD are separated by an array of steel frames calledsuper module (SM) like figure 2.5. In each SM, twelve 20-inch PMTs are set
inward on SM and two 8-inch PMTs are outward on SM. The purpose of the
OD is to reduce the γ-ray background from surrounding rocks and to distinguishthe cosmic ray muons from neutrino signal.

23

Figure 2.3: The spectrum of Cherenkov radiation and the quantum efficiencyof 20 inch PMT

24

Figure 2.4: Detection method of Cherenkov radiation

8-inch PMTs, Hamamatsu R1408, are used in the outer detector. A 60cm ×60cm wavelength shifter plate is placed around the photocathode of each PMT
in order to extend and increase the light collection efficiency. In addition, theOD wall is covered with white tyvek sheet whose reflectance is ∼ 80%.
On the other hand, the ID wall is covered with black sheet to prevent a
mis reconstruction. 20-inch PMTs are mounted on the ID wall with about 40%
photo coverage. This is described in the next section.

2.2.2

20 inch photomultiplier tube

The 20-inch PMT (Figure-2.6) was originally developed by Hamamatsu photonics in cooperation with the Kamiokande collaboration[50]. For the SuperKamiokande experiment, this PMT was improved in order to achieve bettertiming resolution and single photo-electron detection. The specifications of the
20-inch PMT are summarized in Table 2.1. The photocathode of the PMT iscoated with Bialkali (Sb-K-Cs) so that the sensitive region is 300nm∼600nm
and quantum efficiency is maximum (∼22%) at 390nm as shown in Figure-2.3.
The dynode structure was optimized to achieve high collection efficiency
which results in a good 1 p.e. distribution and timing resolution. Figure-2.8
shows the charge distribution for the single photo-electron (1p.e.) signal. 1p.e.
peak is clearly separated from dark current peak. The average dark rate is25

$NCEMUJGGVFigure 2.5: PMT frame used in Super-Kamiokande (super module)

26

about 3.5 kHz at the threshold of 0.3p.e. Timing resolution is about 2.2 nsec asshown in Figure-2.9.
Product name
Photocathode shape
Photocathode area
Photocathode material
DynodeQuantum efficiency
Gain
Dark rate
Timing resolution
WeightPressure tolerance

R3600
Hemispherical
50cm diameter
Bialkali (Sb-K-Cs)
11 stage Venetian bind type
22% @390nm
107 at ∼ 2000 V
3.5kHz2.2ns RMS @1p.e.
13kg
6kg/cm2 water proof

Table 2.2: The specifications of the 20 inch PMT

Figure 2.6: 20 inch PMT used in Super-Kamiokande

2.2.3

PMT case

The inside of the PMT is vacuum for preventing discharge and accelerating
photo-electrons effectively. Therefore, if the glass tube is broken, it causes astrong shock wave. The accident which occurred in 2001 was caused by chain
reaction started from one PMT breakage. In oder to avoid such a cascade of
implosions of PMTs, all of the ID PMT are covered by acrylic covers and fiber27

Figure 2.7: The structure of 20 inch PMT

Figure 2.8: The single photo-electron charge distribution of 20 inch PMT

28

Figure 2.9: The single photo-electron timing distribution of 20 inch PMT

reinforced plastic cases (Figure-2.10) since the beginning of SK-II. Figure-2.11
shows the transparency of the acrylic case as a function of wavelength. It is
more than 96% at 350 nm of wavelength. The optical effect of the acrylic cover
is confirmed to be small.

2.2.4

Comparison of SK-I, SK-II and SK-III

The main differences of SK-I, SK-II and SK-III are the number of PMTs andPMT cases. In this section, differences in detector configuration are described.
SK-I was started from April, 1996 with 11146 20-inch PMTs (∼ 40% photo
coverage). After 5 year of observation, bad PMTs (high dark rate, dischargeetc.) were replaced in 2001. After the replacement the accident happened when
the tank was being filled with pure water in Novenber, 2001. One of the bottom
PMT was broken at that time and 6777 PMTs in the ID and 1100 PMTs in the
OD were broken by the chain reaction.
After the accident, all of the PMTs were covered with PMT cases and replaced in the tank. The SK-II period was started from October, 2002 with 5182
ID PMTs which corresponds to photo coverage of ∼ 19%.
Full reconstruction took place from July, 2005 to June, 2006 in order torecover the initial photo coverage of PMTs. 11129 PMTs were equipped in the
ID tank during the SK-III period. Photo coverage was recovered back to ∼ 40%
and detector performance, especially energy resolution, was also recovered to29

Figure 2.10: PMT case used in SK-II and SK-III

1
0.98
0.96
0.94
0.92
0.9
0.88
0.86

300

350

400

450

500

550

600

Figure 2.11: The transparency of the acrylic case30

the level of the SK-I period. Table-2.2.4 shows the comparison of SK-I, SK-II
and SK-III.

Start of data taking
livetime1
PMT case
Number of ID PMT
Number of OD PMT
Photo coverage
Energy resolution @10MeV
Position resolution @10MeV
Angular resolution @10MeV
Energy threshold (solar ν analysis)

SK-I

SK-II

SK-III

April, 1996
1496 days
No
11146
1885
40%
14%
87cm
26◦
5MeV

October, 2002
791 days
Yes
5182
1885
19%
21%
110cm
28◦
7MeV

July, 2005
548 days
Yes
11129
1885
40%
14%
87cm
26◦
4.5MeV

Table 2.3: The features for each phase in Super-Kamiokande

2.3

Water purification system

The 50 ktons of pure water, used in Super-Kamiokande are taken from underground water in Kamioka mine. Small dust, ions, and bacteria are includedin the original underground water. These impurities not only shorten the lightattenuation length, but also can be a background source for low energy neutrino observation. Therefore, it is crucial to remove impurities from the water
as much as possible before filling the detector.
Figure-2.12 is an overview of the water purification system in Super-Kamiokande.
The tank water is constantly circulated through the water purification systemwith a flow rate of about 30 ∼ 60 tons per hour. The water circulation process
is as follows:
1. Water Filter
Removes large contaminants (∼ 1 µm) such as dust. 222 Rn attached tothe dust is also removed.
2. Heat Exchanger
The water heated by the pumps of the water purification system cause
an increase of bacteria. Also, any temperature gradient in the tank may
cause strong convection which result in poor water transparency. Water
temperature is kept constant after the heat exchanger.
3. Ion Exchanger
Removes metallic ions (Fe2+ ,Ni2+ etc.) using a resin which has ionexchange group with a 3 dimensional retiform structure.
31

4. UV sterilizer
Kills bacteria by irradiating ultraviolet light.
5. Rn-free-air dissolving system
Dissolves radon free air into the water to improve the radon removal capabilities of the vacuum degasifier.
6. Reverse Osmosis filter
Filter out dissolved gases and contaminants heavier than mass of 100
molecular weight using a high performance membrane.
7. Vacuum Degasifier system
Removes dissolved gases (96% removal efficiency for radon and 99% foroxygen) from the water.
8. Cartridge Ion Exchanger
Further high performance ion-exchange resins selectively remove ions with
99% elimination efficiency.
9. Ultra Filter
Removes contaminants down to several nanometers using the filter which
has a few nanometers hole.
10. Membrane Degasifier
Further removes dissolved radon and oxygen gases by membrane degasifier.
This water purification system reduces the radon concentration from 104 Bq/m3
to 10−3 Bq/m3 . The light attenuation length in this pure water is 80 ∼ 90m.
It’s longer than our detector size of 40m.

2.4

Data Acquisition system

There are central hut and 4 peripheral huts on the Super-Kamiokande tank. The
trigger system and control electronics are placed in the central hut, and frontend electronics and high voltage systems are placed in peripheral huts. PMT
output signals come to the peripheral hut through a 70m long cable. The analog
PMT signal is converted to digital signal by electronics. Two workstations areplaced in each hut, which collect data from electronics and send to the hostcomputer in the control room.

2.4.1

Inner detector data acquisition system

Figure-2.14 shows the schematic view of the ID data acquisition system. Output
signals from the ID PMTs come into the front-end electronics, called ATM(Analog Timing Module), which were developed based on the TKO (Tristan
KEK Online) standard for Super-Kamiokande experiment [47, 48]. Integrated
32

Figure 2.12: Overview of the water purification system in Super-Kamiokande

33

charge and the arrival time informations are recorded and digitized by the ATM
module with a 12-bit ADC (Analog to Digital Converter). One ATM board cantreat 12 PMT signals, thus 934 ATM boards are used in total.
The block diagram of the analog input part of the ATM is shown in Figure2.13. The input signal to ATM is amplified 100 times and divided in the hybrid
IC (integrated circuit) as follows.

to PMTSUMHITOUTDISCRI.
CURRENT SPLITTER&AMPLIFIER

PMT INPUT

W:200ns

to HITSUM

ONE-SHOT HIT
W:300ns

SELF GATESTART/STOP

TAC-A

TAC-A

CLEAR
GATE

QAC-A

QAC-A

to ADCSTART/STOP

TAC-B

TAC-B

CLEAR
GATE

THRESHOLD

QAC-B

QAC-B

DELAY

GATE
TRIGGERPED_START

Figure 2.13: The block diagram of the analog input part of the ATM

1. HITSUM
In the case that the signal from PMT is over the threshold of 0.3 photoelectron, a HITSUM signal, 200 nsec width and -15 mV height, and HIT
signal, 900 nsec width and -15 mV height, are output from the front panelof the ATM board. A HITSUM signals are integrated to be used for the
global trigger which is the definition of an ’event’ in Super-Kamiokande.
HIT signals are sent to QAC and TAC through the self gate in order to
get charge and timing information of each PMT.
2. PMTSUM
PMTSUM signal is the sum of input signals for one ATM board. This
output signal goes into a Flash ADC that records the waveform information.
3. TAC/QAC
When the pulse height of the input signal exceeds the threshold, QAC(Charge to Analog Converter) starts integrating the charge for 400 nsec
34

and TAC (Time to Analog Converter) also starts integrating the charge
proportional to hit timing. If the global trigger signal is generated, theTAC stops the charge integration and the integrated charge in QAC and
TAC are digitized by the ADC. If a global trigger is not generated within
1.3 µsec, the information in QAC and TAC are cleared. Because it takes
5.5 µsec for ADC to process one channel, each channel of the ATM has
two switching pairs of QAC and TAC so that two close events, such as themuon and its decay electron, can be processed.
The digitized signal through the above process is read out by SCH (Super
Control Head) and sent to VME memory modules called SMP (Super Memory
Partner). The data on SMPs are transferred to online host computer via highspeed network.

2.4.2

Outer detector data acquisition system

Figure-2.15 shows a schematic view of the OD data acquisition system [49].
The paddle cards distribute high voltage from the mainframe to the OD PMTs.
A coaxial cable is used to supply the high voltage from the mainframe to the
OD PMTs. These paddle cards also can receive the PMT signal through a highvoltage capacitor.
The signals from the OD PMTs are sent to QTC (Charge to Time Converter)
modules which is consist of LeCroy MQT200 chips and comparators. The QTC
module converts the PMT signal to a rectangular pulse whose width is proportional to the input charge. At the same time, a HITSUM signal is also generated
by the QTC module and sent to the global trigger module. The threshold of
the QTC module is same as that of the ATM module. Once the global trigger isgenerated and received by OD electronics, the leading edge and the width of therectangular pulse are converted to timing and charge information respectively
by the LeCroy 1877 multi-hit TDC module. The TDC module can record 8
QTC signals and its resolution is 0.5 nsec. The digitized data stored in the
TDC module are read by a slave computer through a VME memory module,
called DPM (Dual Port Memory), and sent to the online host computer.

2.4.3

Trigger system

The HITSUM, 200 nsec width and -15mV height, signal from each PMT iscollected at the central hut through a TKO crate, from each electronics hut. If
sum of HITSUMs exceeds the threshold, a global trigger is generated. The widthof the HITSUM signal is 200 nsec because the event duration time in SuperKamiokande is up to 200 nsec (in the case of an event which goes through thetank diagonally). A deadtime is produced between 400 nsec and 900 nsec fromthe HIT signal in order to remove the signal reflection noise (which comes 700
nsec later).
There are three types of global triggers depending on energy: the high energy
trigger (HE), the low energy trigger (LE) and the super low energy trigger (SLE).
35

20-inch PMT
SCH
ATM
x 20
x 240

ATM
GONG

20-inch PMTSCHATMinterface
Ultra Sparc

x 20
x 240

SMP

ATM

online CPU(slave)

SMP

GONG

SMP
SMP
SMP
SMP

x6

Super Memory Partner

VME
20-inch PMT
SCHUltra Sparc

ATM

online CPU(slave)

x 20
x 240

Ultra Sparc

ATM
GONG

online CPU(host)

Analog Timing Module

online CPU(slave)
TKO

FDDI

Ultra Sparc

Ultra sparc

online CPU(slave)
Ultra Sparc

online CPU(slave)
Ultra Sparc

FDDI

online CPU(slave)
Ultra Sparc

online CPU(slave)

online CPU(slave)interface
Ultra Sparc
SMP

Ultra Sparc

online CPU(slave)

SMP
SMP
SMP
SMP
SMP

Super Memory Partnerinterface

VME
VME

interrupt reg.
TRG

20-inch PMT
SCH
TRIGGERATM

TRIGGERx 20

PROCESSORHIT INFORMATION

x 240

ATM
GONG

Analog Timing ModuleTKO

PMT x 11200

ATM x ~1000

SMP x 48

online CPU(slave) x 9

Figure 2.14: Schematic view of ID data acquisition system

36

Local Hitsum

QTC
Modulex40/quadx10/quad

TDC
x5
4 LSBsHigh Voltage

16 bit event #TDC

FASTBUSPMT

Paddle Card

StruckSupply~470/quadrant

FSCC

AUX

84 pin data ribbon cables

Ethernet FSCC Control

Figure 2.15: The schematic view of OD data acquisition system

At the end of SK-I period, HE, LE and SLE trigger required 34 mV (after 1/10
attenuation), 320 mV and 186 mV respectively. The SLE trigger threshold of
186 mV is equivalent to 4.6 MeV threshold in total electron energy. Each trigger
condition in each period are summarized in Table-2.4.
Because of very low threshold, the SLE trigger rate is quite high due to the
gamma-ray background from surrounding rocks and PMTs. Therefore, in orderto reduce the huge number of SLE triggered events, a software trigger whichremoves events outside of the fiducial volume, is also applied.

SLE
LE
HE

SK-I
186mV
320mV
34mV

SK-II
110mV
152mV
18mV

SK-III
186mV
302mV
32mV

Table 2.4: Trigger threshold in each data taking period.

37

Figure 2.16: The overview of the global trigger generation

38

Chapter 3

Detector Calibration
Super-Kamiokande consists of 11000 PMTs and 50ktons of pure water for
detecting Cherenkov light from charged particle. The particle informations arereconstructed from PMT output, so calibration is very important. Gain andquantum efficiency calibration affects the energy determination and timing calibration affects the vertex reconstruction. We performed a precise calibrationon the gain, quantum efficiency (QE), and timing for each PMT individually.
Also water transparency measurement is done. In this chapter, details of SuperKamiokande detector calibration are described. Since calibration methods usedin SK-I, SK-II, SK-III are almost similar, in this chapter calibration for SK-III
is mainly described.

3.1

PMT HV determination

The gain of PMTs must be uniform in order to achieve a uniform response over
the whole SK tank and small systematic error of energy reconstruction. We
determine the high voltage value (HV) to be supplied to each PMT using Xelamp and scintillator ball located in the SK tank.
First of all, we define QE and gain. QE (quantum efficiency) is a probabilityof photo-electron emission when photon hit the PMT photo cathode. In our definition, CE (collection efficiency), a probability that an emitted photo-electron
reaches the PMT dynode, is also included in QE. “Gain” is defined to be an
amplification factor in PMT dynodes simply.
We use the output charge of PMT (Qobs ) to determine the high voltage(HV). Qobs is defined as follows:

Qobs (i) ∝ Nphoton (i) × QE(i) × Gaini = 1, ....,P M T sequentialnumber

where Nphoton is the number of photons which hit the photo cathode.
The gain of each PMT is given using HV as follows:

39

(3.1)

Gain(i) = αi × HV (i)βi(3.2)

where α and β is the parameter for each PMT. In our calibration in SuperKamiokande, we adjusted the HV to give same Qobs for the same Nphoton .
The SK tank is 40m diameter cylindrical shape and light intensity has∼20% non-uniformity for Z direction even if we make a perfectly uniform lightsource. The number of photons that reach each PMT depends on the position of
the PMT in the tank. This is a problem when we determine HV value because
Equation-3.1 include the number of photons.
To solve this problem we provided “standard PMTs” whose gain is adjusted
within a few %. These standard PMTs are located as in Figure-3.4 and the
PMTs which have the same geometrical relation to the light source, are grouped.
Each PMT gain are determined to the standard PMT gain in its group. In thisway, the effect of the asymmetry described above and water scattering can becanceled.

3.1.1

Precise gain adjustment

A schematic view of our setup for the standard PMT calibration is shown in
Figure-3.1.

Figure 3.1: The schematic view of our setup for the precise PMT gain measurement. Xe flash lamp are placed inside a box and emitted light input opticalfibers through a fiber bundle. Fiber go into the box in which 20 inch PMT isset.
We made 420 standard PMTs using a Xe lamp as the light source. The Xelamp (L4634-01) made by Hamamatsu photonics is an optimum light source
whose instability of output intensity is 5% at maximum and lifetime is 5 ×108
flash. Its time constant is 200nsec and light emitting rate is up to 100Hz. Light
output from Xe lamp goes through a UV filter which passes only UV light andis then divided into three optical fibers. One goes to the scintillator ball placedin the dark box. The other two fiber go into APD modules, which monitor the40

light intensity of the Xe lamp. The scintillator ball include 15ppm of POPOP
and 2000ppm of MgO to make the light emission uniform. The dark box which
the PMT and scintillator ball are put in is made of µ metal to reduce the effectof geomagnetism to less than 20mG.
Using this setup we adjusted the gain to 107 for 420 PMTs. To do this wemeasured the output charge at four different HV values and determined theparameter αi and βi given in Equation-3.2. The output charge is corrected bymonitor APD counts and the HV supplied to each PMT is set so that it returns
the same output charge within 1%.
As a result, the supplied HV for 420 PMTs are determined with 0.4% RMS.
Figure-3.2 shows the ratio between the mean of output charge and target chargeof 107 gain. To check the reproducibility of our measurement, we selected 50
PMTs randomly from the 420 PMTs and performed the same measurement
again. Figure-3.3 shows the result of second measurement. We confirmed good
reproducibility with an accuracy of 1.3% RMS.

100

ID
Entries
Mean
RMS

80

Constant
Mean
Sigma

12
412
-0.8252E-02
0.39109.300 / 1083.60
-0.1613E-01
0.3846

ID
Entries
Mean
RMS

20
17.5

Constant
Mean
Sigma

13
50
0.22001.327
6.341 / 419.26
0.24020.9083

15
12.5

60

10
40

7.5
5

20
2.5
0
0

-3

-2

-1

0

1

2

-6

3

correct by APD1

-4

-2

0

2

4

correct by APD2

Figure 3.3: Result of the reproducibility
Figure 3.2: Gain dispersion after themeasurement in the gain determination.
HV determination. Applied HV for 420
Reproducibility are checked for 50PMTs
PMTs are determined within 1%.
and confirmed with 1.3% level.

3.1.2

HV determination in SK tank

Here HV determination in SK tank using standard PMTs whose gain are adjusted within 1% is described.
Setup for HV determination in SK
The standard PMTs are mounted in SK tank as shown in Figure-3.4. The
scintillator ball, which is the light source of our calibration, is placed at the41

6tank center. PMTs are grouped depending on their geometrical groups withthe scintillator ball. All the 11129 PMTs are divided into 17 groups for barrel
PMTs and 8 groups for top and bottom PMTs, as shown in the Figure-3.5.
Each group includes 9 - 12 standard PMTs.

Figure 3.4: The standard PMT setup inside SK tank. The standard PMT setup
inside SK tank are shown. Red points are representing standard PMTs.

Figure-3.7 shows a schematic view of the HV determination calibration system. Light emitted from the Xe lamp goes into the scintillator ball at the SK
tank center through the UV pass filter. The scintillator ball diffuses input light
uniformly and the observed photo-electrons in each PMT are around 50p.e inthis system. Another optical fiber goes to a monitor PMT and generates acalibration trigger.
Result of HV determination
The measurement is performed several times, rotating the scintillator ball tocancel the ball non-uniformity. Observed charge is corrected by the distancefrom the ball to PMT and acceptance as follows:
Qcorr =

Qobs × r2
faccept (θ)(3.3)

Mean of Qcorr is calculated for all of the PMT and supplied HV is determined42Figure 3.5: Definition of PMT grouping method (Barrel). Barrel PMTs aregrouped for three layer; there are 17
groups.

Figure 3.6: Definition of PMT grouping method (Top, Bottom). Top (Bottom) PMTs are grouped by distancefrom tank center; there are 8 groups for
each.

Figure 3.7: A schematic view of the setup for gain calibration using Xe lamp.
Same tools as standard PMT calibration are used in this setup.

43to make Qcorr equal to the Qcorr mean of the standard PMTs in each group(target charge). After HV determination, output charge relative to the meanof the standard PMT is measured for all PMTs. Figures-3.8 and 3.9 shows theratio between Qcorr and its target charge.

10

3

10

2

10
10972
0.99980.1272E-01

ID
Entries
Mean
RMS

10

1
0.8

Figure 3.8: The difference from target charge output before HV determination. The distribution has a width of
9% RMS.

0.85

0.9

0.95

1

1.05

1.1

1.15

Figure 3.9: The difference from target
charge output before HV determination.
The distribution has a width of 1.3%
RMS.

As a result, the relative output charge can be adjusted to within 2% in SKII and SK-III, though it was ∼9% before HV determination. Since we don’t
have precalibrated PMTs in SK-I, data were taken by changing the light source
position to reduce the effect of a difference of acceptance for each PMTs. Using
this method, the gain spread in SK-I was 7%.

3.2

QE measurement

The quantum efficiency (QE) is different for each PMTs. Especially the PMTs
used in SK-II have an asymmetry between top and bottom due to manufacturingterm. Especially for low energy analysis, since we use the number of hit PMTs
for energy determination, this effect is quite important. We need to measure theQE value for individual PMTs and its difference must be corrected to reduce
the systematic error due to top-bottom asymmetry.
Ni-Cf light source
For the light source of QE measurement, we used a radio isotope make fromNi and 252 Cf as a gamma-ray source. As shown in Figure-3.10, the 252 Cf
source is put in the center of the vessel. This vessel has a cylindrical shape44

1.2

with 20cm height and diameter and it is filled with Ni wire and water. 252 Cf
causes α decay (97% branching ratio) or spontaneous fission with a lifetime of
2.645 years. When a spontaneous fission occurs, 3.8 neutrons are emitted on
the average. Emitted neutrons are captured by surrounding Ni wire after it isthermalized by water in ∼ 200µsec and gamma-rays with 6 - 9MeV are emitted.
These gamma-rays give their energy to electrons in water by Compton scatteringwith a typical scattering length of ∼ 50 cm. The electron emits Cherenkov light
if its energy is above Cherenkov threshold. The light intensity at each PMT
is 0.004 p.e/PMT so that more than 99% of observed light is due to a single
photo-electron origin. We used this light source for the QE measurement andabsolute gain calibration.

Figure 3.10: A schematic view of Ni-Cf gamma ray source.

Result of QE measurement
The number of hits in each PMT is given by the following like Qobs given in
Equation-3.1:
N hit(i) ∝ Nphoton (i) × QE(i)(3.4)

We can measure the relative QE value by measuring the number of hit foreach PMT and correcting for the geometrical effect on number of photons. The
one dimensional distribution of measured QE is shown in Figure-3.11. Figure3.12 shows the position dependence of QE measurement. The QE value has a∼ 7% dispersion throughout the SK tank and there is a top-bottom asymmetry
due to their manufacturing term as described before.

45

Figure 3.11: The distribution of measured QE for each PMTs

Figure 3.12: Position dependence of QE. Red is for the PMT used in SK-II,
Green is the PMT newly added in SK-III and Black is for all

46

3.3

Absolute gain measurement

PMT gain can be expressed as the product of global gain of the SK detector(conversion factor from photo-electron to pC) and a relative gain of each PMTs
like in Equation-3.6. They were measured individually in Super-Kamiokande.

Gain = global gain × relative gain(i)(3.5)

i = 1, ...., # of P M T

Using the same Ni-Cf light source as for QE measurement, we measured theabsolute gain in Super-Kamiokande. The mean of the 1p.e. charge distribution
was used to obtain an absolute gain. Figure-3.13 shows the charge distribution
for SK-II and SK-III PMTs. As shown in this figure, SK-III PMT which were
newly mounted at the beginning of SK-III (SK-III PMT) have lower gain than
PMTs that were used during SK-II period (SK-II PMT). This is caused by theeffect of QE difference between SK-II and SK-III PMT. It clearly appears also
in the relative gain measurement as described later.

Figure 3.13: Measured charge distribution from Ni calibration. Horizontal axis
is number of photo-electrons. Black is SK-II PMT and Blue is SK-III PMT.

From the mean of 1p.e. charge distribution, we obtained charge to photoelectron transformation factor for all three phase of SK and they are shown in
Table-3.1.

47

SK phase

Absolute gain [pC/p.e.]

SK-I
SK-II
SK-III

2.055
2.297
2.243

Table 3.1: Charge to count transformation factor obtained from absolute gain
measurement using Ni source in each SK data taking phase.

3.4

Relative gain measurement

From the 1p.e. measurement by Ni-Cf source, absolute gain was obtained but
it’s not for individual PMT. So we measured the relative gain for all ID PMTs
and made the correction table. This value should have inverse correlation with
QE according to Equation-3.1.

3.4.1

Method and setup for relative gain measurement

According to Equation-3.1 and Equation-3.4, we can get the relative gain bytaking a ratio between Qobs and Nhit as follows.
Qobs (i)∝ gain(i)Nhit (i)(3.6)

We took the data for this measurement using laser with two different lightintensity (Figure-3.19). Using exactly same setup except light intensity andtaking ratio, all the effect, e.g. water transparency and magnetic field, can becanceled.
The result of relative gain measurement is shown in Figure-3.16. As seen inthis figure, RMS of relative gain is 5.9%. Position dependence of relative gainis shown in Figure-3.15. Top SK-II PMT have higher gain than bottom SK-II
PMT because of QE difference.

3.5

Timing calibration

The relative timing calibration is essential for the vertex reconstruction of SRN
candidates. Ideally timing response of each PMT are same after subtracting
time-of-flight from the vertex position to each PMT. However there are difference of PMT response due to the length of the PMT signal cable and the
response time of electronics. The effect of the electronics depend on a detectedcharge because of the time-walk effect of discriminators 1 as shown in Figure3.18.
A laser calibration system, shown in Figure-3.17, is used for the timing
calibration in Super-Kamiokande. N2 laser generate the high intensity light
1 The PMT that are exposed to larger light intensity exceed their discriminator thresholdsooner. This is called “TQ-map”

48

Figure 3.14: A schematic view of the laser calibration setup for relative gain
measurement.

pc2pe
1.2
1.15
1.1

10

3

10

2

ID
Entries
Mean
RMS

10
11111
1.000
0.5904E-01

1.05
1
0.95
0.9

10

0.85
0.8

0

5

10

15

20

25

30

35

1

Group

0.6

0.8

1

1.2

1.4

1.6

pc2pe in SK3

Figure 3.15: An average of measured
relative pc2pe value in each group + :SK-II PMT、○ : SK-III PMT Red：
Barrel, Green：Top, Blue：Bottom

49

Figure 3.16: relative gain distribution.
Mean value of this distribution is one.

Figure 3.17: A schematic view of the timing calibration system using laser. The
diffuser ball is placed at the center of the tank.

50

980
970

Linear Scale

Log Scale960

T (nsec)

950
940
930
920
910
900
890
880
1

5

10

100

Q (p.e.)Figure 3.18: A typical TQ-map distribution are plotted as a two dimensional
plot of timing vs. charge distribution. Larger value in the vertical axis iscorresponding to earlier hits. Data is taken by a laser setup shown in Figure3.17.

within ∼ 3 nsec whose wavelength is 337 nm. Emitted light go into a dye laser
module which convert the wavelength of 384 nm, similar to the Cherenkov light.
The light intensity can be controlled using the variable attenuation filter from
1 photo-electron level to several hundred of photo-electrons. The light passthrough the filter is injected into a diffuser ball, set at the center of the tank,
via an optical fiber. In order to provide the uniform light emission, injected
light is first diffused by a TiO2 and then further diffused by the LUDOX, which
is a silica gel composed of 20 nm glass fragments in SK-I calibration system.The
acrylic diffuser ball containing MgO powder is used in SK-II and SK-III system
for the purpose of better uniformity of the light.

3.6

Water transparency measurement

Water transparency in the SK tank affect the number of photons arrive at the
PMT so that it can be an important parameter to characterize detector response especially for energy determination. There are two method of watertransparency measurement. The scattering and absorption parameter is measured by N2 laser changing the dye of the laser. Furthermore the transparency
is independently measured using decay electron from the stopping muons.

3.6.1

Light scattering measurement by a laser

The light attenuation length in water can be described as follows.

L=1(αabs + αRayliegh + αMie )
51

(3.7)

Where αabs , αRayliegh and αMie are the absorption , Rayliegh scattering and
Mie scattering coefficients, respectively. Rayliegh scattering occur if the lightwavelength is longer than scattering particle. This scattering effect dominate inshorter wavelength region as shown in . Mie scattering is the case that particle
is equivalent to the wavelength.
Each coefficient is separately measured by a N2 laser. Figure-3.19 shows the
setup of the water parameter measurement in Super-Kamiokande. The laser
light is injected into this detector from top of the tank toward the bottom
direction. Each laser whose wavelength is 337, 371, 400 and 420 fires every six
seconds during usual data taking period for the measurement.
LASER
Optical Fiber

Top

337nm
371nm
400nm
420nm
NUM
2
RUN
8399
EVENT
3919
DATE **-Mar- 1
TIME
5:34:38
TOT PE:
820.0
MAX PE:
19.6
NMHIT :
331
ANT-PE:
13.6
ANT-MX:
2.7
NMHITA:
17

Scattering

RunMODE:NORMALTRG ID :00010111
T diff.: 2.08
us
:0.208E-02ms
FSCC:
2FF90
TDC0: 8899.2
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 0

BottomFigure 3.19: A schematic view of the scattering and absorption parameter measurement using the laser.

The barrel part of the detector is separated into 5 groups as shown in Figure3.19. the PMT hit timing distribution in each region for the calibration data
are shown in Figure-3.20. There are PMT his in top and barrel due to thescattering by water molecule or due to the reflection by the bottom PMTs or
black sheets. The absorption and scattering coefficients are tuned to make thehit timing distribution of MC simulation agree with the calibration data.
The attenuation coefficients obtained by this method are shown in Figure3.21. The lines are showing the tuned parameter for each attenuation coefficient
determined by fitting to the data.

52

2

Top

1
0
1

Barrel 1

PMTs / BottomQ

0

Barrel 2
1
02

Barrel 3

1
02

Barrel 4

1
0
2

Barrel 5

1
0

700

800

900

1000

1100

1200

PMT Hit Time (nsec)

Figure 3.20: PMT hit timing distributions in each groups defined as shown in
Figure-3.19. The points shows data and lines shows the MC simulated events.
The first peak and second peak are corresponding to the photons scattered inwater and reflected on the surface of the bottom PMTs.

attenuation coefficient(1/m)

Light scattering measurement

-1

10

-2

10

absorption

Rayliegh scattering-3

10
Mie scattering

300

400

500

600

700

wavelength(nm)Figure 3.21: Attenuation coefficients as a function of wavelength. Star markers show the result obtained by the water scattering measurements. Lines are
representing the expected one tuned by this measurement.

53

3.6.2The water transparency by decay electron from stopping muons

The water transparency in SK is monitored continuously by using the decay
electrons (positrons) from cosmic ray muon events stopping inside the SK tank.
As mentioned in section 7.1, decay electron from muons has a spectrum following
a Equation-7.3. Since this physics process is well known, decay electron events
can be used for monitoring the water transparency.
At the depth of 1000m underground of SK site, approximately 6000 muons
per day stop inside the SK tank and produce a decay electron. In order to selectthe decay electron events, following selection criteria are applied.
1. The time difference between decay electron candidate and preceding stopping muon is in the range of 2.0 µsec - 8.0 µsec
2. The reconstructed vertex of the candidate event is within 22.5 kton fiducial
volume3. Number of hit PMT greater than 50
By applying these criteria, ∼1500 events are selected in one day and it’senough statistics to measure the time variation of water transparency.
To remove the effect of scattered and reflected photons, hit PMTs are selected by following criteria.
1. Hit timing must be within 50 nsec time window after time-of-flight subtraction
2. PMTs must be within a come of opening angle 32 - 52 degrees with respect
to the reconstructed direction
A plot of the number of hit PMT is made using the selected PMTs and isfitted with linear function. The inverse of the slope gives the water transparency.
Figure-3.22 (top) shows the time variation of water transparency during SK-I
period.
The selected decay electron sample are also used for monitoring the energy
scale stability. The average number of hit PMT in one week is plotted as afunction of time in Figure-3.22. The energy scale variation was within 0.5%
during SK-I period.

3.7

Energy scale calibration

For the supernova relic neutrino analysis, energy scale calibration is one of themost important calibration because energy spectrum fitting will be done at the
final stage of our analysis. The effective number of hit PMT (Nef f ) is used
to determine the energy of positron in our analysis. We measured conversion
factor from Nef f to energy within ∼ 1% level using two calibration sources. In
this section these energy calibration systems are described.
54

Figure 3.22: Time variation of the measured water transparency (top) andstability of the energy scale as a function of time(bottom). Both of them aremeasured using decay electron events.

3.7.1

LINAC calibration

To better determine the energy, electron linear accelerator (LINAC) is used togenerate energetic electron for the energy scale calibration in Super-Kamiokande[52].
Setup of LINAC system
The LINAC used in SK is a Mitsubishi ML-15MIIII LINAC which was originally made for medical purposes. The specifications of our LINAC system aresummarized in Table-3.2.
Accelerator tube
Frequency of micro wave
Electron intensity
Max beam intensity
Beam momentum
Pulse width
Pulse rate
Spread of the beam momentum

1.69m length and 26mm diameter
2.856 [GHz]MAX 200 µA∼ 106 /pulse @end of accelerator tube
5 -18 [MeV/c]
1-2 [µsec]
10-66 [/sec]< ±0.3%

Table 3.2: The specifications of LINAC

The LINAC accelerate electrons using microwave of 2.8656GHz generated by
the klystron. The length of one pulse is about 2µsec and its rate is 10 - 66 Hz.
55

The required electron beam intensity is one electron per one pulse. To achievethis, 106 electron in one pulse is required at the exit point of the acceleration
tube.

Figure 3.23: Setup of LINAC calibration system at Super-Kamiokande.

The LINAC system produce some background noise such as X-ray andgamma-ray. The mainframe of LINAC is located far from the SK tank in order to prevent those background from affecting data. Electrons, accelerated
by LINAC, go into SK tank through the stainless beam pipe whose maximum
length is 60m. Inside of the beam pipe is surrounded by µmetal2 for the purposeof reducing the effect from external magnetic field. Also inside of the beam pipe
is vacuated down to 10−4 Torr so that electron beam can reach end of pipe
without any effect from scattering by air.
The beam pipe is installed to the SK tank from calibration hole on the topof the SK tank. The end of pipe is capped by the titanium cap with 100µm
thickness as shown in Figure-3.24. Set of scintillator and PMT is placed at theend of beam pipe for making the LINAC trigger as well as scintillator and PMT
for making VETO.
There are 8 dipole and quadratic magnets along the beam line to bend thebeam direction and to narrow the beam width. The quadratic magnets control
the beam width within ∼6mm and 3mrad spread. See Figure-3.25 through 3.27
for a schematic view of magnet setting.

2 µmetal is a nickel-iron alloy that has very magnetic permeability.

56

Figure 3.24: The end-cap of the LINAC beam line. A scintillation counter islocated above titanium window, used for the trigger.

KLYSTRON
C1 COLLIMATOR
D1 MAGNET

ELECTRON GUNACCELERATING TUBES1 STEERING
C2 COLLIMATOR

1000 mm

VACUUM PUMP

BEAM PIPEIN ROCK

Figure 3.25: The first bending magnet (D1). This magnet determines the beam
momentum.

57

M1 BEAM MONITOR
C3 COLLIMATOR
D2 MAGNETS2 STEERINGROCK

HORIZONTAL BEAM PIPE

1350 mmLEAD SHIELD

LEAD SHIELD

SUPER-KAMIOKANDE TANK

Figure 3.26: The second bending magnet (D2).

M2 BEAM MONITOR
C4 COLLIMATOR

Q1 QUADRUPOLE
D3 BENDING MAGNETHORIZONTAL BEAM PIPE

1350 mm

TURBO-MOLECULAR
PUMP
Q2 QUADRUPOLE

SUPER-KAMIOKANDE TANKROTARY PUMPXY STEERINGWATER LEVEL

Figure 3.27: The quadratic magnets (Q1, Q2) and 90◦ bending magnet (D3).

58Germanium detector
It is very important to know the electron momentum accurately. The germanium detector, negative type semiconductor detector, is used for the electron
momentum measurement. Germanium in the detector is the cylindrical purecrystal with a 57.5mm diameter and a 66.4mm length.
Because the ionization energy of germanium is very small (2.96ev), a lotof carriers are generated so that germanium detector can provide a very goodenergy resolution. Germanium detector not only has a good resolution but also
has a good output linearity for input particle energy. This is also very importantbecause the calibration gamma sources for germanium detector are up to 9MeV.
Figure-3.28 shows the output charge of the germanium detector as a functionof gamma-ray energy from calibration source with a fitting result by a linear
function. The deviation from fitting result at each point is shown in Figure-3.29.
Although deviation is larger in very low energy region, it is still less than 1% in
all points.
Deviation(%) VS Obs.energy(keV)

Obs. energy(keV) VS Bin

1

9000

0.8
0.6

8000
1.711

7000

P1
P2

/ 16
31.08
5.225

0.4
0.2

6000

0

5000

-0.2
4000
-0.4
3000
-0.6
2000
-0.8
1000
-1
200

400

600

0

1000 2000 3000 4000 5000 6000 7000 8000 900010000

800 1000 1200 1400 1600

Figure 3.29: Deviation of the outputof Germanium detector from the fitted
line. X-axis is energy of gamma ray
source [MeV]. Y-axis is the deviationof the data point from the fitted line[%].

Figure 3.28: The linearity of the Germanium detector. X-axis is the output
from the Germanium detector [count]
and Y-axis is the energy of the calibration gamma ray source [MeV].

Result of LINAC calibration
LINAC data are taken at six position changing X (-12m, -4m) and Z (-12m,
0m, +12m); X and Z is the defined axis in SK. For every position data wastaken with four momenta (5.1MeV, 8.8MeV, 13.6MeV, 18.9MeV). In SK-I and
SK-II, LINAC beam momentum is limited at ∼16MeV due to the power of the59bending magnet. We replaced D3 magnet which bend the beam by 90degrees
in order to obtain higher energy beam. By this improvement we succeeded tomake the upper limit of LINAC beam up to 18.9MeV in SK-III.
Nef f distribution of 8.8MeV and 18.9MeV electron at each six positions areshown in Figure-3.30 and Figure-3.31. Black is LINAC real data and red issimulated Nef f using Monte Carlo method (MC). Their consistency seems very
good.
The relation between total energy of electron accelerated by LINAC and
Nef f is shown in Figure-3.32. Total energy is measured by germanium detector
with accuracy of +/-20keV. Conversion function from Nef f to energy is obtained
from this result. The difference between data and MC are shown in bottom two
figures. As shown in this figure, position dependence of the energy scale in SK
fiducial volume is less than 0.5%. Resolution of Nef f is also compared with
MC and the result is shown in Figure-3.33. Difference of resolution of 2.5% is
obtained.

Figure 3.30: Nef f distribution of 8.8MeV and 18.9MeV electron at each six
positions. Black is data and red is MC.

3.7.2

DT generator calibration

The Deuteron-Tritium Generator (DTG) [53] which is a device to generate neutrons, is used for the cross check of energy scale calibration by LINAC. LINAC
beam always move in a downward direction because beam pipe can be installed
only from top of the tank. DT generator provide uniform direction source using
the decay of 16 N so that it can be used to check the directional dependence ofthe energy scale.
60

Neff of MC

120
100

140
120
100

80

80

60

60

40

40

20

(MC-DATA)/DATA

X = -1237cm, Z = 1197cm
X = -1237cm, Z = -6cm
X = -1237cm, Z = -1209cm
X = -388.9cm, Z = 1197cm
X = -388.9cm, Z = -6cm
X = -388.9cm, Z = -1209cm

140

4

6

8

10

12

14

16

18

20

20

0.05

(MC-DATA)/DATA

Neff of DATA

Figure 3.31: Nef f distribution of 18.9MeV electron at each six positions. Blackis data and red is MC.

0.04
0.03
0.02
0.01
0
-0.01

8

10

12

14

16

18

20

4

6

8

10

12

14

16

18

20

0.03
0.02
0.01
0
-0.01
-0.02

-0.03

-0.03

-0.05

6

0.04

-0.02
-0.04

4

0.05

-0.04
4

6

8

10

12

14

16

18

-0.05

20

expected energy in tank

Figure 3.32: The relation between total energy of electron accelerated by LINAC
and Nef f . Top two figures are Nef f .VS. total energy and left top figure shows
data and right top figure shows MC. Bottom two figures are MC - data divided
by data. Left figure shows each point and right figure shows average of all
points.

61

20
18
16

Resolution of MC(%)

22

26
24
22
20
18
16

14

14

12

12

10

(MC-DATA)/DATA

X = -1237cm, Z = 1197cm
X = -1237cm, Z = -6cm
X = -1237cm, Z = -1209cm
X = -388.9cm, Z = 1197cm
X = -388.9cm, Z = -6cm
X = -388.9cm, Z = -1209cm

24

4

6

8

10

12

14

16

18

10

20

0.2

(MC-DATA)/DATA

Resolution of DATA(%)

26

0.15
0.1
0.05
0
-0.05

10

12

14

16

18

14

16

18

20

4

6

8

10

12

14

16

18

20

0

-0.2

20

12

-0.05
-0.1

8

10

0.1

-0.15
6

8

0.05

-0.1

4

6

0.15

-0.15
-0.2

4

0.2

expected energy in tank

Figure 3.33: Resolution of Nef f compared the LINAC data with MC. Top two
figures are Resolution .VS. energy and left top figure shows data and right top
figure shows MC. Bottom two figures are MC - data divided by data. Left figure
shows each point and right figure shows average of all points.

62

Setup of DTG system
At first DTG starts with a collision of deuterium and tritium inside the generator
to create 4 He and neutron. 106 neutrons with the 14.2MeV are created at one
pulse of collisions. The neutrons interact with 16 O and generate 16 N and proton,
16
o(n,p)16 N. 16 N decays with the half-life of 7.13 seconds with a Q value of
10.4MeV. The decay products are mainly 6.13 MeV gamma rays and 4.29 MeV
beta particles (66.2% fraction) as well as 10.4 MeV beta (28.0%fraction).

Figure 3.34: A schematic view of the setup of DT generator
Overview of DTG data taking is shown in Figure-3.34. When we take data
at SK, the DTG is lowered to the position where data is to be taken. Next the
DTG is fired creating neutrons and these neutrons generate 16 N surrounding
the DTG. Once DTG is fired, it is withdrawn 2 meters to remove the generator
from the area of 16 N. After the fire of DTG, it takes ∼10 seconds to withdraw
apparatus completely, and ∼60% of 16 N has decayed.
While the crane is moving, we don’t take the data to prevent electrical noisefrom containing the data. Once the crane stop moving, data are collected for
40 seconds.

63

Result of DTG calibration
Data from the DTG calibration are reconstructed using the same analysis tools
as SRN analysis and then they are compared with MC simulation. Figure-3.35
is the direction dependence of reconstructed energy of DTG event. From thisfigure, direction dependence of energy scale is almost less than 0.5%.

Figure 3.35: The direction dependence of reconstructed energy from DT calibration data from a position-weighted average over all positions in fiducial volume.
Horizontal axis is azimuthal angle [degrees] (top figure) and cos(zenithangle)(bottom figure).

Next, position dependence of energy scale is checked using DTG calibration
data. Since DTG is relatively smaller than LINAC, data can be taken in many
positions and then it’s better calibration tool for checking the position dependence of energy scale. Figure-3.36 shows Z (R) dependence of energy scale.
Difference between data and MC is very small in small X region (near tankcenter). Although it’s become larger in outer region as shown in Figure-3.36,
difference is less than 2% at a maximum in the fiducial volume. Even outsideof fiducial volume (X=15m), energy scale difference is 3% level.
At last the DT generator data and the LINAC data are compared as shownin Figure-3.37 and very good consistency can be seen. If we select downward
DTG events, energy scale differences LINAC and DTG are less than 0.5% andit’s within statistical error. Even if we use all direction of DTG events, energy
64

Figure 3.36: Position dependence of the energy scale from DT calibration datafrom a position-weighted average over all positions in fiducial volume. Horizontal axis of the top figure is Z position of SK tank and that of bottom figure ishorizontal distance from tank center.

65

scale in DTG and LINAC are consistent within 1%. This result demonstratereliability of the LINAC energy scale calibration.

Figure 3.37: Comparison between DTG data and LINAC data. Energy scale in
DTG and LINAC are consistent within 1%.

3.7.3

Summary of energy scale calibration

Since the energy scale calibration is quite important for the SRN search analysis, we carefully performed the energy scale calibration. For example, LINAC
calibration can determine the conversion factor from the number of hit PMTs
to particle energy and also position dependence of energy scale is measured bytaking the LINAC data at the several positions. DTG is uniform source incontrast to LINAC so that it can be a good calibration source to measure thedirectional dependence of energy scale.
The summary of these energy scale calibration is described in this section.
Considering the effect of66

• Position dependence of energy scale• Time variation of energy scale• MC tuning accuracy• Electron beam determination in LINAC calibration• Directional dependence of energy scale
we estimate the energy scale uncertainty for SK-I, SK-II and SK-III. They
are listed in Table-3.7.3.
Data taking phaseenergy scale uncertainty

SK-I
SK-II
SK-III

0.64%
1.4%
0.53%

Table 3.3: Energy scale uncertainty in SK-I, SK-II and SK-III.

67

Chapter 4

Event reconstruction
The event reconstruction is performed to obtain information such as the vertex,
direction and energy from the taken data. In Super-Kamiokande, the vertex of
the SRN candidate events are reconstructed using PMT hit timing information.
The reconstruction of the event direction is done using the PMT hit pattern. After that, Nef f , the effective number of hit PMTs, is calculated and is converted
into the corresponding energy using the conversion function obtained from the
LINAC calibration. In this chapter, the methods of event reconstruction for
SRN candidate events are described.

4.1

Vertex reconstruction

For the reconstruction of the vertex position the hit timing of each ID PMT isused. SRN candidate events are categorized as low energy events whose total
charge is less than 2000 photo-electrons (corresponding ∼ 250MeV) in SK-I and
SK-III, and less than 1000 photo-electrons in SK-II. Our vertex fitter is applied
for these low energy events. Figure-4.1 shows an example of typical low energy
events. In this section, the method of vertex Reconstruction for SRN candidates
is described.
Particles emitting Cherenkov light are moving, but low energy events such
as SRN candidates can move only ∼ 10 cm in water due to scattering. This issmaller than the vertex resolution of Super-Kamiokande, so we are able to treat
the vertex as a point. For the event vertex reconstruction for this SRN analysis
we performed a maximum likelihood fit to a timing residual of the Cherenkov
signals, as well as a dark noise background, for each vertex hypothesis. The
hypothesis which gives a maximum likelihood is chosen as the reconstructedvertex. The likelihood of the vertex fitting is defined as:
Likelihood =

N
hit
X
i=1

log(P (ti (x~i ) − tof − t0 ))(4.1)

Where ti (x~i ) is the timing of each hit PMT and tof is the time-of-flight

68

NUM
4
RUN
23177
EVENT
64072003
DATE
3-Oct-10
TIME
18:51: 5
TOT PE:
285.9
MAX PE:
10.6
NMHIT :
175
ANT-PE:
86.9
ANT-MX:
55.4
NMHITA:
36

RunMODE:NORMALTRG ID :00000111
T diff.:0.337E+04us: 3.37ms
FSCC:
88027F90
TDC0: 8902.8
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 4.1: An example of a typical low energy event. An example of a typical
low energy event as a development view of the SK tank. Each circle shows hit
PMTs and its diameter is corresponding to an output charge.

69

from the vertex position to each hit PMT. t0 is the timing for which that event
occurred, thus ti (x~i ) − tof − t0 is ideally zero for all PMTs. P is the probability
density function of ti (x~i )−tof −t0 which is obtained from the LINAC calibration
data.

Figure 4.2: Timing distribution of LINAC calibration data after time-of-flight
subtraction. The two peaks after the main peak are caused by re-incidence ofreflected electrons by the dynodes.

However, sometimes dark noise hits after the time-of-flight subtraction can
produce local maxima of the likelihood, at several positions far from the global
maximum. Because of the large size of SK, it is tricky and time consuming
to search for the global maximum. To reduce mis-reconstruction, as well as
improvement of the fitting speed, the likelihood is maximized from a vertex
search by the combination of all four PMTs. Each of the four PMT combinations
can give a unique vertex so that any event whose number of hit PMTs is fouror more can be reconstructed. Then grid vertex search is done for each vertex
candidate to avoid selecting a local maximum point. It’s iterated, tightening thesearch range, until it finds a larger and more stable likelihood value, comparedto the surrounding grid points. Position resolution using this method for each
SK data taking term is obtained from LINAC calibration data and shown in
Table-2.2.4.

4.2

Direction reconstruction

Once the vertex position has been determined, the direction of the particle isreconstructed at the next step. Emitted Cherenkov light produces a cone, so
the PMT hit pattern should be a ring with an opening angle of 42 degrees.
Direction reconstruction uses the likelihood method following the Equation-4.2.

70

likelihood =

NX
hits
i=1

log[f (φi (d))] ×

cos θifaccept (θi )(4.2)

Where φi (d) is the angle between d and the vector from vertex to the PMT
position. f (φ) is the probability of photon emission as a function of φ directionand estimated using MC simulation. d=(dx , dy , dz ) is the set of test directions.
When we determine the direction, this test direction is changed and the value
which maximizes the likelihood of Equation-4.2 is chosen. Figure-4.3 shows thisfunction. The Photon emission distribution shows a peak at 42 degrees and a taildue to scattering. θi is the acceptance of a PMT photo cathode and faccept (θi )is its acceptance function. The right side of Figure-4.3 is the distribution of thisfunction.

Figure 4.3: The probability density function of photon emission for Cherenkov
light from an electron (left figure). PMT acceptance function (right figure).

The accuracy of direction determination is limited by multiple scattering.
From LINAC calibration data, the angular resolution of this method is ∼ 26
degrees in SK-I.

4.3

Energy reconstruction

The energy of a charged particle is proportional to number of emitted photons.
The number of photons can be estimated from number of hit PMTs, (Nhit ), forlow energy events. The reasons why we don’t use the number of photo-electrons,
but instead Nhit , are listed following.
• PMT charge resolution is not good enough at the 1 photo-electron level(∼
50%)• Most of the hits in low energy events are 1 photo-electron.

71• Number of photo-electrons is easily effected by electric noise.
At first, PMTs to be used are selected to maximize the number of hit PMTs
within a 50 nsec time window (N50 ), in order to reduce the effect of dark noise
hit. Next various corrections are applied to this N50 , obtaining a Nef f , which
is not dependent on the position in the SK tank as follows:
N50 
X


Nall
ri
(Xi − ǫdark + ǫtail ) ×
Nef f ≡× S(θi , φi ) × exp( )/QE(i) (4.3)
Naliveλi=1
The meaning of each term is:• Xi : Correction about multi photo-electron hit
If the event occurs near the tank wall, though it’s still inside of fiducial
volume, it can cause a hit whose number of photo-electrons is more thanone. We correct for this effect using the following correction:

Xi =

(

log[(1−xi )−1 ]xi

2.5(xi 6= 0)(xi = 0)(4.4)

xi = ni /Ni(4.5)

Where Ni is a number of PMTs surrounding hit PMT and ni is a numberof hit PMT in Ni . The multi photo-electron hit effect is corrected using aratio of these two numbers, xi = ni /Ni .
• ǫdark : Correction for PMT dark hit
The dark noise hit rate is about 3kHz for each PMT, and there were about
10,000 PMTs mounted in the SK detector during SK-I and SK-III, so ∼ 1
hit or less is expected within 50 nsec. This should be subtracted because
these hits are not originating from Cherenkov light. The following ǫdark
is used for the correction of this effect.

ǫdark ≡

Nalive × Rnoise × 50nsec
N50

(4.6)

In this equation, Nalive is number of normal PMTs and Rnoise is the darknoise rate [hits/nsec] in each run.
• ǫtail : Effect of the reflection
Cherenkov light reflected by a PMT or the black sheet has a possibility offalling on a PMT photo cathode and emitting a photo-electron. But thesereflected photons are delayed and do not usually come within the 50 nanosec timing window. To recover such delayed hits for the energy calculation,
tail hits within 100 nano sec are used as the following correction factor.
72ǫtail ≡N100 − N50− ǫdark
N50(4.7)

Here N100 is the number of hits within the 100 µsec timing window. Ifǫtail is negative, the effect of reflection is not considered.
• Nall /Nalive : Dead PMT correction
There are more than 10,000 PMTs in SK, however, ∼ 100 PMTs weredead during the SK-I period. Although the fraction of dead PMTs wasless than 1%, this fraction varied with time. In order to compensate for theeffect of dead PMTs, the ratio of all PMTs and living PMTs is multiplied.
• exp( rλi ) : Correction of water transparency
The attenuation length of pure water in SK is about 100m, meaning theemitted Cherenkov photons are attenuated by exp( rλi ) before reaching the
PMT from the vertex position. Here ri is the distance between a hit PMT
and the vertex position of a SRN candidate, λ is the attenuation length of
SK pure water. Attenuation length changes during data taking terms andit’s measured using decay electrons from stopping muons as described in
the previous chapter.
• S(θ, φ) : Correction of PMT-photon acceptance
Figure-4.4 shows the PMT-photon acceptance as a function of photonincident angle. The correction function, S(θ, φ), distributes like Figure4.5. The reason for the φ asymmetry is an effect of shadowing of surrounding PMTs.

Figure 4.4: Definition of photon incident angle to PMT

73

Figure 4.5: Correction function of photon incident angle obtained from MC
simulation : S(θ, φ)• QE(i) : Correction of quantum efficiency
As described in Chapter 3, each PMT has a different QE value which iscorrected using each measured QE individually.
Reconstructed energy is determined from Nef f , with all the corrections
above. This conversion factor is obtained from LINAC calibration as describedin section 3.7. Energy resolution for 10 MeV electrons in SK-I and SK-III was
14% using this method. In SK-II, it was 20% due to the smaller number of
PMTs.

74

Chapter 5

Data reduction
The data taking term for the first SK phase was from April 1996 to November 2001. Additionally data was collected from October 2002 to October 2005
in a second phase and from July 2006 to September 2008 in the third phase.
The livetimes for each period were 1496days, 791days and 548days respectively.
These data sets included many kinds of events, for example, cosmic-ray muons,solar neutrinos, gamma-rays from the tank structure and so on. Such events canbe background for our SRN analysis. We applied several reductions in order toremove these background events and select our SRN candidate events. In thischapter, we focus on the reductions we applied to the SK data to select the SRN
candidate events.

5.1

1st reduction

The 1st reduction which is applied removes cosmic ray muons and bad quality
events which should not be SRN candidate events. The cuts applied in the 1st
reduction are explained in this section.
Total charge cut
Most of the events originating from cosmic ray muons or atmospheric neutrinos deposit energy usually higher than 1GeV, while the positrons from SRN
interactions deposit only up to several tens MeV. To remove very high energy
events such as cosmic ray muons, a total charge and total number of hits cuts
are applied. The cut criteria is 2,000 photo-electrons and 800 hits in SK-I and
SK-III, corresponding to ∼ 200MeV. The criteria in SK-II is half of that in SK-I
and III due to the half PMT coverage. The total charge distribution in typicalruns in SK-III is shown in Figure-3.1.
Time difference cut
The events, whose timing difference from preceding LE/HE trigger event isless than 50 µsec, are removed from data in order to remove decay electron75

Number of Events

Number of Events

SRN
Candidates

10

8

10

7

10

6

10

5

10

4

10

3

10

2

50µsec

10

Muons

1
-1

10

log(total charge)

10 p.e.

Figure 5.1: Total charge distribution in SK-I. The second peak ismainly caused by muons.

2

3

4

5

6

7

8

9

10

log(time since previous event (nsec))x

Figure 5.2: Time difference fromprevious LE/HE event (dt). The
events whose dt is shorter than
50µsec are rejected to remove Decay electron and electronics noise
events.

of stopping muon. This cut also can remove an electric noise event, so called’ringing’, that occur after an event deposited large amount of light. Figure-5.2
shows a distribution of time difference from preceding eve nt.
Fiducial volume cut
The gamma-rays from the material of the ID wall and the surrounding rock can
be a background of SRNs. Since these background events occur near the wall,
we can remove these events using a cut for distance from the ID wall. The events
whose reconstructed vertex are less than 200cm from the ID wall are removed.
By this cut, the fiducial volume of the SRN analysis is 22.5 ktons.
Pedestal event cut
ATM pedestal data is taken every 30 minutes in our DAQ system. Duringpedestal data taking, the ATM channels cannot record signals from their connecting PMTs. Pedestal data is taken for 1/8th of the SK ID area, all at once,
so this data is lacking parts. Therefore, the events taken during the pedestal
data taking period are rejected.
Calibration event cut
In order to check the detector stability(PMT Gain, Timing and Water transparency etc.), calibration sources are set in the SK tank and are fired automatically. These events cannot be used for SRN analysis, so they are removed from76

data by being tagged with a calibration trigger flag.
Outer Detector event cut
Cosmic rays originate outside of the detector and must deposit energy in the
OD, so they can be tagged by an OD trigger. As described in section 2.4.2, theOD trigger is activated when the number of OD PMT hits exceeds 19 within a
200 nsec time window. OD triggered events are removed from our data sample
to remove cosmic ray muon backgrounds.
First electric noise event cut

10

8

10

7

10

6

Number of Events

Number of Events

PMT hits from electric noise generally tend to be small charge hits, so events
induced by electric noise are cut using a fraction of small charge hit PMTs. If
the fraction of PMTs having less than 0.5 photo-electrons(called “noise ratio”)
is more than 0.4, such events are removed. The noise ratio distribution in typicalruns is shown in Figure-5.3.

(a)

5

10
4
10
10

3

10

2

10
1
10

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10
1

-1

0

0.2

0.4

0.6

0.8

1

(b)

10

Noise ratio

-1

0

0.25

0.5

0.75

1

ATM ratio

Figure 5.3: Noise ratio distribution (left) and ATM ratio distribution (right).

Second electric noise event cut
If some of the ATM board have some electric noise, most of the channels of
this board should have hits. In the case that the fraction of hit channels in one
board(ATM ratio) is more than 95%, such events are removed.

5.2

Spallation event cut

Approximately two cosmic ray muons are coming into the SK tank every one
second, even under 1000m of rock. These muons can cause spallation in the oxy77

gen nucleus of the water molecule and other radioactive nuclei will be generated
as follows.
µ +16 O → µ + X(5.1)

We call these nuclei spallation products and these are one of the most serious
backgrounds in this analysis. Possible spallation products and their characteristics are listed in Table-5.1. Some of the spallation products, for example
11
Li,12 N , can be a background around 20 MeV due to the detector energy
resolution.
Isotope82 He

τ 21 (sec)
0.119

8
3 Li
8
3B
9
3 Li

0.838
0.77
0.178

9
6C
11
3 Li

0.127
0.0085

11
4 Be

13.8

decay mode
β−
β− n
β−
β+
β−
β− n
β+ n
β−
β− n
β−

11
4 Be
12
5 B
12
7 N
13
5 B
13
8 O
14
5 B
15
6 C

0.02360.02020.01100.01740.00860.0138
2.449

β−
β−
β+
β−
β+
β−
β−

16
6 C
16
7 N

0.747
7.13

β− n
β−

Kinetic Energy (MeV)
9.67 + 0.98(γ)
16%
∼ 13
13.9
13.6 (50.5 % )(∼ 50 % )3∼15
16∼20 (∼ 50 % )∼ 16 (∼ 50 % )11.51 ( 54.7 % )9.41 + 2.1 (γ) ( 31.4 % )
11.71
13.37
16.32
13.44
13.2 16.7
14.55+6.09 (γ)
9.77 ( 36.8 % )4.47+5.30 (γ)∼410.42 ( 28.0% )
4.29+6.13 (γ) (66.2% )Table 5.1: A list of spallation products and their decay modes.

We developed a new spallation cut with a likelihood based on four variables
in order to increase the efficiency and lower the energy threshold.

5.2.1

Spallation cut in SK-I and SK-III

A spallation cut for SRN analysis uses a likelihood method based on four variables. The four variables include the time difference between the preceding
muons and SRN candidate event (dt), and the transverse distance from muon78

track to reconstructed relic candidate position (dltrans ). For the cut we also use
two other variables by making a histogram like Figure-5.4 for every muon.

Figure 5.4: Charge distribution along a muon track. Each bin corresponding to
50 cm of muon track length. Number of photo-electrons on the vertical axis iscorrected by considering the effect from water transparency and PMT coverage.
The horizontal axis of Figure-5.4 corresponds to the length of the muontrack(0 is muon entering point into the inner detector). The vertical axis is
the charge produced from each segment along the muon track(extracted fromthe observed charge in every PMT and their geometrical relations to the muontrack). The effect of PMT coverage and water transparency are also consideredwhen making this charge distribution. If we find a strong peak, this indicateswhere spallation occurs along the muon track. The third variable for our likelihood method is the longitudinal distance from the reconstructed position of
the relic candidate to the position where we expect the spallation event along
the muon track(dllong ). The fourth variable is the total charge which is emitted
within +/-5 m of the peak position on the muon track(Qpeak ). Figure-5.5 shows
the relation between the muon track and these parameters as a conceptual view.
Each parameter is calculated for every muon beginning 100 seconds before
the SRN candidate. In addition muons are categorized into four muon types asfollows.
• Single through going muon (∼ 84%)

Most muons originating from cosmic rays, and coming from outside thedetector, are categorized as a single through going muon. It has only one
track and goes through the entire ID.

• Multiple muon (∼ 6%)

Multiple muon events have two or more muon tracks. The SK event
timing window is 1.3 µsec and the muon rate is 2 Hz, so the probabilityof chance coincidence is very small. However, sometimes multiple muons
79

Figure 5.5: An explanation of the variables used in the new spallation cut. The
cylinder in this figure represent SK inner detector.

80

originating from the same cosmic ray come to the detector within the same
event timing window.
• Stopping muon (∼ 7%)

Stopping muons stop in the detector and decay into electrons and neutrinos. There is no exit point, but the vertex of its decay electron can tellus the muon stopping position.

• Corner clipping muon (∼ 3%)

These events just clip the ID tank corner. Their muon track lengths areless than five meters.

The distributions of the four variables for a single through going muon are
shown in Figure-5.6 and Figure-5.7.

Figure 5.6: dLtrans (right) and dLlong (left) distribution with single through going muons. Black histogram is for spallation like sample that is made by real
data minus the random sample. Red histogram is for the random sample. Clear
separation can be seen.
The likelihood distribution is made for each type of muon and a cut point istuned individually. In the case of multiple muon events, muon reconstruction
is more difficult and the cut criteria is more strict to remove all the spallation
background. For an example, the spallation likelihood distribution for a single
through going muon in SK-I is shown in Figure-5.8.
The inefficiency of the spallation cut was estimated using random sample
and, it was 18.5% in the 18 - 24 MeV and 23% in 16-18 MeV.

5.2.2

Spallation cut in SK-II

Energy resolution in SK-II is worse than that of SK-I and SK-III so that more
spallation events are expected to contaminate SRN search energy region. We
81

Figure 5.7: dt(right) and Qpeak (left) distribution with single through going
muons. Black and red histograms are the same sample as Figure-5.6.

Figure 5.8: Spallation likelihood distribution for SK-I data(black) and the random sample(red) using single through going muons.

82adopted the spallation cut developed for solar neutrino analysis in SK-II [39]because it is a tighter than spallation cut described in previous section although
its inefficiency is larger. In SK-II analysis, the spallation cut is applied in
two steps. First is a cut based on a three variable likelihood method which
was developed and optimized for SK’s solar ν analysis. Three variables are;time difference from the candidate event to preceding muon (dt), the transverse
distance from the reconstructed position of candidate event to preceding muontrack (dltrans ) and residual charge which is observed total charge minus expectedcharge from muon track length (Qres )1 . Thus likelihood is calculated as follows.
likelihood = £(∆T ) × £(∆L) × £(Qres )(5.2)

The likelihood distribution for real data and random sample are shown in
Figure-5.9. We tuned the cut criteria to save 80% of random sample.

Figure 5.9: Likelihood distribution
for real data (Solid line) and random sample (dotted line). Top figure is for the reconstructed muon
event and bottom figure is for thefailed reconstructed muon events.
In failed case, it is impossible to obtain dltrans so that only dt can beused for likelihood calculation.

Figure 5.10: Time difference from
SRN candidate event to preceding
muons (dt). Even after likelihood
cut, the is an excess in short dt region. We removed all the events
whose dt is shorter than 0.15 sec.

Since this cut is not tight enough, we need to apply additional cut. A second
cut was applied using a time difference from last muon (dtlast ). We know higher
energy spallation product has basically shorter half-life (see Table-5.1). Figure5.10 show dtlast distribution in SK-I and this cut rejects events whose timedifference from the last muon is shorter than 0.15 sec.
1 Expected charge from muon is 1000 photo-electron / meter83

By applying these two cuts, all the spallation events can be removed above
20 MeV but several spallation like events exist in SK-II data even after thistighter spallation cut. The combined inefficiency of these cuts is 36% below
34MeV.

5.3

Double timing peak cut

Event timing window in SK is 1.3 µsec. Since the muon livetime is 2.2 µsec, someof the decay electrons and their parent muons can be in the same event. Thiscan happen if a low energy muon, but still higher than Cherenkov threshold,stops in the detector and decays quickly, within same event timing window. In
such cases, the ID hit PMT timing distribution has two peaks, as shown in
Figure-5.11.
NUM
11
RUN
21934
EVENT
3858817
DATE 3-Mar-18
TIME
11: 0:41
TOT PE: 306.0
MAX PE:
8.2
NMHIT : 226
ANT-PE:
33.3
ANT-MX:
17.6
NMHITA:
35

20
17.5
15
12.5
10
7.5
5
2.5
0

600

800

1000

1200

1400

3

4

5

1600

1800

5
4

DIR: 0.44, 0.88,-0.17
X: -130.7cm
Y: 422.2cm
Z: 324.1cm
R: 442.0cm
NHIT: 121
good: 0.81

3
RunMODE:NORMALTRG ID :0000001 1
T diff.:0.597E+04us 2: 5.97
ms
FSCC:
D0027F90
1
TDC0: 8896.8
Q thr. : 0.0
BAD ch.: no mask 0
SUB EV : 00/
0

1

2

6

7

8

Figure 5.11: An example of timing, two peak events. Left figure is a development
view of the SK tank and the right top figure is the PMT hit timing distribution.
The first peak of the timing distribution is low energy muons and the second
peak is the decay electrons.

We removed the events whose timing histogram has multi peaks. To search
for timing peaks, we open a 15 nsec timing window, after time-of-flight subtraction, and count the number of hit ID PMTs within that 15 nsec window. If thenumber of hits in the first and second peak are both more than 5, such an eventis removed from our data sample. The inefficiency of this cut is estimated usinga SRN MC simulation sample, and is less than 0.5%.

5.4

Cherenkov angle cut

The opening angle of the Cherenkov light(θ), is determined by the equation of1
cos θ = nβ
. In the case of water, the refractive index is 1.33, so that Cherenkov
84

Cherenkov Angle (degrees)

light is emitted with an opening angle θ of 42 degrees, if β=1. Since the electronmass is 0.511 MeV, electrons above the SK trigger threshold(∼ 5 MeV) always
have β=1, that is to say an opening angle θ which is 42 degrees.
On the other hand, in the case of heavier particles, such as muons, cannot be
relativistic enough to approximate β = 1 and so the Cherenkov opening angle
becomes less than 42 degrees. The expected Cherenkov opening angle for muons
as a function of energy is shown in Figure-5.12.

45
40
35
30
25
20
15
10
5
0

150

200

250

300

350

400

450

500

Muon Momentum (MeV/c)
Figure 5.12: Cherenkov opening angle of muons is plotted as a function of themuon momentum. Muons contaminating the SRN search have muon momentum< 300 MeV which correspond to Cherenkov angle < 38 degrees.

Figures-5.13 and 5.14 show an example of an electron-like event and a muonlike event, respectively. The solid line is the expected ring assuming 42 degrees
by the reconstructed vertex position and direction. The muon-like ring clearlyshows a smaller ring than the expected ring of 42 degrees, as for the electron-likeevent. We have separated muon-like background using the difference of opening
angle θ.
Also neutral interactions of atmospheric neutrinos on oxygen nuclei occasionally occur and the excited nuclei’s decays emit several gamma rays. These
gamma rays have uniform direction and so this event generates an isotropic hit
pattern. This event clearly gives a larger opening angle than 42 degrees, so we
can separate this from electron-like events. The example of such a gamma ray
event is shown in Figure-5.15. There is no clear Cherenkov ring pattern unlike
for the electron-like and muon-like events.
Calculation method of the Cherenkov angle follows the steps below.
1. Search the hit timing peak, which includes the maximum hit PMTs(N15 )within a 15 nsec timing window after TOF subtraction.
2. Choose any combination of three hit PMTs in N15 and get the unit vector
from the vertex position of the SRN candidate event to each PMT(see
85

NUM
6
RUN
21586
EVENT
83203
DATE
3-Jan18
TIME
20:39:43
TOT PE:
365.8
MAX PE:
11.3
NMHIT :
262
ANT-PE:
49.9
ANT-MX:
12.0
NMHITA:46

DIR:-0.17,-0.99,-0.03
X: -932.8cm
Y:
720.5cm
Z: -955.8cm
R: 1178.6cm
NHIT: 191
good:
0.84

RunMODE:NORMALTRG ID :000000
11
T diff.:0.269E+04us: 2.69ms
FSCC:
88027F90
TDC0: 8896.8
Q thr. :0.0
BAD ch.: no mask
SUB EV : 00/

Figure 5.13: The event display of typical electron like event. Lines represent
the expected Cherenkov opening angle, assuming 42 degrees.

NUM
65
RUN
22013
EVENT
3
559579DATE
3-Apr19
TIME
14:33:21
TOT PE:
248.2
MAX PE:
8.3
NMHIT :
190
ANT-PE:
0.0
ANT-MX:
0.0
NMHITA:0

DIR:-0.54,-0.84, 0.05
X:
13.4cmY: -126.4cm
Z:
306.4cmR:
127.1cm
NHIT: 190
good:
0.83

RunMODE:NORMALTRG ID :00000011
T diff.:0.812E+08us:0.812E+05ms
FSCC:
0
TDC0: 14910.0
Q thr. :0.0
BAD ch.: no mask
SUB EV : 00/

Figure 5.14: The event display of typical low energy muon like event. The
Cherenkov ring is smaller than 42 degrees.

86

NUM
14
RUN
21661
EVENT
599
4 1
DATE
3-Jan29
TIME
9:55:32
TOT PE:
294.5
MAX PE:
11.3
NMHIT :
231
ANT-PE:
0.0
ANT-MX:
0.0
NMHITA:0

DIR:-0.05,-0.99, 0.12
X:
518.5cm
Y:
806.7cmZ:-81.9cmR:
959.0cm
NHIT: 231
good:
0.77

RunMODE:NORMALTRG ID :000000
11
T diff.:-.698E+10us:-.698E+07ms
FSCC:
0
TDC0: 14910.0
Q thr. :0.0
BAD ch.: no mask
SUB EV : 00/

Figure 5.15: The event display of typical gamma like event. Hit PMTs are
uniformly distributed and no clear Cherenkov ring can be seen.

Figure-5.16).
3. The vertex position and unit vectors obtained above can form a unique
circular cone. The opening angle of this cone is calculated. Each combination of three hit PMTs gives the opening angle from the vertex position.
4. Repeat step 2 and 3 for all the combination of three hit PMTs(repeat
N15 C3 times). The results of this opening angle calculation for electronlike, muon-like and gamma-like events are shown in Figure-5.17.
5. Find the peak of the opening angle distribution from this histogram with
6 degree windows.
6. Remove the events whose obtained Cherenkov angle is smaller than 38◦ (µlike) or larger than 50◦ (γ-like).
Figure-5.18 shows the Cherenkov angle distribution of real data for SK-I.
The three peaks caused by muon, electron and gamma-ray events are clearly
separated. We cut the events whose Cherenkov angle less than 38 degrees andthose whose angle is greater than 50 degrees, in order to select only electron
like events. The inefficiency of this cut is ∼ 90%, estimated from the SRN MC
simulation events.

87

B
^
B

C

A
^
C

^
A

VertexFigure 5.16: Three unit vectors are obtained from each three hit PMTs. The
vertex and those three vectors give a unique solution of Cherenkov opening
angle.

Figure 5.17: The opening angle distribution for e-like(left), µ-like(middle) and
γ-like(right).

88

140
120
100
80
60
40
20
0

0

10

20

30

40

50

60

70

80

90

Cherenkov angle distribution (degree)
Figure 5.18: An average of the Cherenkov opening angle distribution. The
shaded black histogram with error bars is SK-I data and the green histogram is
the SRN MC simulation events. Clearly three peaks are shown in the real data
histogram. Only the e-like peak around 42 degrees is selected.

89

5.5

Pion like event cut

Sometimes atmospheric neutrinos create pions in the detector. If a created pion
has a high enough energy to emit Cherenkov light, it can be recognized as a
SRN candidate. We cut these pions using a difference of the Cherenkov ringpattern between a pion and an electron.
Generally a pion created from an atmospheric neutrino interaction emits
Cherenkov light and is soon captured by a nucleus in a water molecule. In thiscase, the Cherenkov ring tends to be very clear, as shown in Figure-5.19. Mostof the hit PMTs are near the 42 degree line as expected from the reconstructedvertex and direction. While an electron undergoes multiple scattering in water,
and thus the ring pattern looks more broad as shown in Figure-5.19.

2009/11/16 21.49

25000

20000

15000

10000

5000

0

0

10

20

30

40

50

60

70

80

90

Opening Cherenkov Angle from 3-PMT combinations

Figure 5.19: Event display of simulated
pion event. Ring edge is very clear andmost of the hit PMTs are around the 42
degree line.

Figure 5.20: Cherenkov opening angle distribution of the pion event
shown in Figure-5.19. The distribution is very sharp.

In order to evaluate the pion likelihood, we used the distribution of theCherenkov opening angle which is explained in the Cherenkov angle cut. A distribution width of the pion event is expected to be narrower than that of the electron event. The opening angle distribution of the pion-like event and electronlike event(the event of Figure-5.19 and Figure-5.21) are shown in Figures-5.20
and 5.22, respectively. The pion-like event indicates a much narrower distribution width.
Evaluating a pion-likelihood, we took the ratio of the number of entries
between +/-3 degrees and +/-10 degrees from the peak bin.

pilike =number of entry in ± 3degrees f rom peak
number of entry in ± 10 degrees f rom peak

(5.3)

The distribution of the pilike variable for the pion and electron are shown90

30000

25000

20000

15000

10000

5000

0

0

10

20

30

40

50

60

70

80

90

Opening Cherenkov Angle from 3-PMT combinations

Figure 5.21: Event display of simulated
electron event. Due to multiple scattering, the ring pattern becomes broader.

Figure 5.22: Cherenkov opening angle distribution of the electron event
shown in Figure-5.21. A wider distribution than the pion event can be
seen.

Figure 5.23: The distribution of the pilike value for pion and electron MC
simulations. The green one is for electron MC and the red one is for pion MC.
They are separated and the cut criteria is determined as pilike < 0.58.

91

in Figure-5.23. The cut point was determined to be 0.58 and the inefficiency ofthis cut was ∼ 1%.

5.6

Solar direction cut

Figure-1.2 shows the solar neutrino spectrum as predicted by the Standard Solar
Model(SSM). These neutrinos, mainly from 8 B, exist up to ∼ 20 MeV andcan be a background of our SRN search, even though it’s a small flux. Since
solar neutrinos are only electron neutrinos, the following electron scatteringinteraction is dominant. Therefore recoil electrons should keep the original
direction of the neutrinos from the sun.
ν + e− → ν + e−

(5.4)

We use the angle between solar direction and the reconstructed event direction(θsun )to separate solar neutrino background events and SRN candidate events. Figure5.27 shows a θsun distribution for solar neutrino MC simulation events2 .
In the old SRN analysis, only θsun was used for the solar neutrino cut. In
order to improve the cut efficiency, we developed a new method using a goodnessof the direction.
Electrons in the SRN search energy region experience multiple scattering
during Cherenkov light emission. Due to the multiple scattering, the ring pattern becomes broader and so the angular resolution of the scattered electron
becomes worse. So the θsun distribution of scattered events is also expected to
be broader. We measured multiple scattering using a hough transformation(seeFigure-5.24 for the conceptual overview).
We can draw a circle around each hit PMT with the radius expected fromthe 42 degree opening angle. Such a circle is ideally passed through the true
direction, as shown in Figure-5.24(left). Two circles give two solutions, trueand fake, as shown in Figure-5.24(right). However wrong solutions are excluded
because they don’t fit together well with all the other solutions.
Next, a unit vector is provided from each solution and these unit vectors
are connected like in Figure-5.25(top). The connected vector length becomesshorter if this event is scattered a lot. This length is compared with the lengthof the case in which all the vectors are on the straight path. The ratio of these
two lengths is defined as a goodness of direction. This goodness distribution andthe relation between the average of θsun and the direction goodness, for solar
neutrino MC events, are shown in Figure-5.26. Events with worse goodness
clearly give worse direction reconstruction.
We tuned the cut criteria using the following significance function.
ǫ(5.5)
κS + ǫαWhere ǫ is the efficiency of the cut for the SRN signal and background
events other than solar neutrinos and κ is the effectiveness of the cut for thesig = √

2 Bahcall 1998 spectrum is used92

Figure 5.24: The basic idea of a hough transformation. The true direction isthe cross point of each circle, which is centered at the hit PMTs, although twocircle gives two solutions.

Figure 5.25: The Unit vector is obtained from each solution of two circles in
Figure-5.24 and are connected. The length of this connected vector is comparedwith the length in the case that all unit vectors are lined straight. The ratio ofthese two lengths is defined as a goodness of direction.

93

Figure 5.26: The goodness distribution of the solar neutrino MC(top) and average cos θsun as a function of goodness(bottom). Events with worse goodness(that means more scattering) have worse angular resolution.

94

solar neutrino background events. S is the solar neutrino background event,estimated from the solar neutrino MC simulation. α is a background frominvisible decay electron background events. To estimate this background we
obtained a spectrum shape from decay electrons of stopping muons which isnormalized by the number of SRN candidate events.
Figure-5.27(left) plots the θsun distribution of the solar MC events, for eventswith different goodness values. The right figure shows the significance as a function of θsun , for each events of a certain goodness(energy is 17-18MeV region).

Figure 5.27: The cos θsun distribution for the solar neutrino MC events areplotted for different goodness events(left). The significances are also plotted asa function of cos θsun (right). The Cut point was determined to maximize thesignificance.
The cut criteria is determined for every 1 MeV, at the peak of the significance. The cut criteria is listed in Table-5.2.
Figure-5.28 shows the cos θsun distribution before and after the solar neutrino cut. A clear excess exists in the solar direction distribution before thesolar cut. After the cut, this excess disappears, and the distribution becomes
flat, similar to the distribution of the simulated SRN events(should be random
direction distribution). By this reduction 24 events were rejected and the remaining solar neutrino background events were estimated to be less than 0.35
event / 1496days.
The number of PMTs in the SK-II detector were half of that of SK-I and SKIII. Therefore the energy resolution was worse and also the goodness calculation
is more difficult to do. Thus we applied a more strict cut, without a goodness
method for SK-II data, in order to remove all the solar neutrino background.
In SK-II, the events whose energy is less than 25 MeV and cos θsun less than
0.75, are removed. This cut criteria is strict enough and the expected number
95

Table 5.2: The list of solar direction cut criteria in SK-I and SK-III . Cut criteria
is determined for each 1MeV up to 20 MeV. For the tuning, we used a solar
neutrino MC simulation.

96

Figure 5.28: The cos θsun distribution before the cut(top) and after thecut(bottom) in SK-I. In both figures the black markers show the distribution ofreal data and the green line shows the distribution of simulated SRN events.

97

of solar neutrino backgrounds after this cut is less than 0.2 event / 791 days,
although the inefficiency of the cut is worse than that of SK-I and SK-III.

5.7

Effwall cut

The event rate near the ID wall is higher than that of inside fiducial volume
due to gamma rays from the PMTs and ID structure. Also decay electrons fromlow energy muons come from out of the detector and can remain in our sample.
Such decay electrons have a vertex near the wall.
In order to remove such backgrounds, we apply the cut using an expectedtravel distance from the ID wall(effwall). The schematic view of the effwall
definition is shown in Figure-5.29.

Figure 5.29: The definition of effwall. The schematic view of the definition of
the effective wall distance(effwall). Effwall is defined as the distance from thereconstructed vertex of the SRN candidate event to the ID wall reversely along
the reconstructed direction.
Figure-5.30 is the effwall versus the energy distribution of relic candidate
events. We determined the cut criteria to remove the excess of the effwall
distribution of the data. In SK-I we adopted an energy dependent cut criteria
as shown in Figure-5.30. Meanwhile in SK-II, since the vertex resolution waspoorer, we applied a more strict cut(effwall > 450 cm in all energy region). The
right figure in Figure-5.30 shows the SK-III case and an effwall > 450 cm cut
is needed for the energy < 22 MeV region as well as effwall > 300 cm above 22
MeV.

98

Figure 5.30: The effwall versus energy distribution for the relic candidate events
in SK-I(right) and SK-III(left). The lines represent the cut criteria in each phaseand the red dot is removed by this cut. In the SK-III figure, there are no events
below effwall < 300 cm because we removed such events at a very Early stageof reduction in order to reduce the process time of the spallation cut.

After this cut, the effwall distribution of the data becomes consistent withthat of the MC simulated SRN events(see Figure-5.31).

5.8

OD correlated event cut

The OD triggered events are removed from the data sample at the 1st stageof reduction. However the OD PMT coverage is much less than the ID andsometimes low energy cosmic ray muons can enter the detector without any
OD trigger and can generate decay electrons. Those decay electrons can be abackground for our analysis. However even in these cases, the OD PMTs still
have been hit, although the number of hit PMTs is small. For an example ofthis event, see Figure-5.32.
We removed the events which have OD PMT hits having timing correlation
with ID PMT hit timings and position correlations with the reconstructed vertex. To select correlated PMTs efficiently, we also used the distance from thevertex position to each PMT position(dL).
The number of OD PMT hits is obtained using PMT hit timing informationand dL as follows.
• Search for a peak in the ID PMT hit timing histogram after TOF subtraction and within a 50 nsec sliding timing window.
• Count the number of PMTs in the OD timing histogram within +/- 150
nsec from the ID peak and dL < 500 cm. This number is defined as N1.
• Search for a peak in the OD PMT hit timing histogram within a 100 nsec
sliding timing window.
99

Figure 5.31: Effwall distribution in SK-I(after 2m fiducial volume cut). The
marker histogram is the data and the green histogram is the MC simulated
SRN events, which should be randomly distributed.

Figure 5.32: An example of a typical OD correlated event. The left top figureis the OD development view. There is a cluster hits on the top of OD.

100• Count the number of PMTs within this 100 nsec timing window and dL< 500 cm (defined as N2).
For a conceptual view of the peak search see Figure-5.33. If N1 > 1 hit or
N2 > 2 hits, the event is removed as an OD correlated event. This cut criteria
is tuned using the control sample of two years of SK-I real data. The N1 andN2 distributions of SK-I data are shown in Figure-5.34.

Figure 5.33: OD peak search method. Top figure shows ID hit timing after TOF
subtraction. Bottom figure shows OD PMT hit timing. The ID peak search isdone using a 50 nsec timing window. +/- 150 nsec from this ID peak is the firstOD timing window for the OD hit PMT counting (N1). The Second OD peak issearched using 100 nsec timing window in the OD PMT hit timing distribution.
The counted number of PMTs in the 2nd window is defined as N2.
The inefficiency of this cut is estimated using a random OD PMT hit sample.
The cosmic-ray-muons randomly come to the detector with a rate of about 2
Hz. Using hit PMTs in these events(before muon peak), we made a random
OD timing distribution of random events, and estimated the inefficiency of thecuts. Figure-5.35 shows the N1 and N2 distributions of the random events, theinefficiency is less than 1%.

5.9

Multi ring event cut

If an atmospheric neutrino creates a pion and muon simultaneously, and theenergy of both resultant particles is higher than the Cherenkov threshold, two
Cherenkov rings can occur with the same timing, causing double timing peaks,
events which cuts cannot remove. Figure-5.36 shows a typical multi ring eventwith one timing peak.
To count the number of rings in each event we used “the ring counting
method”, based on the Hough transformation [55] which was developed foratmospheric neutrino analysis. Details of this method are described in [54].
101Figure 5.34: N1 and N2 distributions for SK-I data. The blue line shows the
OD correlated event cut criteria. The events of N1 > 1 and N2 > 2 are rejected.

Figure 5.35: N1 and N2 distributions for the random event sample made bymuon events. The inefficiency of this cut is estimated from this sample and is
< 1%.

102

Figure 5.36: Example of a multi ring event. The left figure is the event display,
two rings can clearly be seen. The right top figure is the PMT hit timing
distribution of this event after time-of-flight subtraction. There is only one
peak.

This ring counting method gives us the number of rings and the directionof each ring. However, for low energy electrons the ring patterns become broad
due to multiple scattering causing such rings to be recognized as multi rings. In
such cases, the reconstructed two ring direction is very close to the same. To
save these fake two ring events, the angle between the first and second rings isrequired to be larger than 60 degrees. The distribution of this angle is shownin Figure-5.37.
If the reconstructed number of rings is more than two, and the angle between
two of the ring’s directions is more than 60 degrees, the event is removed fromour data sample.

5.10

Sub-event cut

Sometimes an atmospheric neutrino interacts with an oxygen nuclei and activates it. In such cases, there will be a gamma ray event several micro seconds
before the decay electron event. Tagging this pre activity allows us to remove
this invisible mu-e decay background.
Also if a SRN candidate is a low energy muon, the decay electron event must
exist just after the candidate event. So we also tag the post activity to remove
such background events. See Figure-5.38 for an example of this event.
Additionally this cut removes the decay electron events whose parent muon
only registers an SLE trigger. If other muons come to the detector within thetiming window of some low energy event, which triggers only an SLE trigger,
the decay electron cannot be rejected by the 50 micro second cut in the 1st
reduction because this cut uses the timing difference from the previous LE/HE
trigger event. Typical events of this background are shown in Figure-5.39.

103

Figure 5.37: The distribution of the angle between the first and second rings.
The upper figure is for SK-I real data and the lower figure is for a SRN MC
simulation. If this value is larger than 60 degrees, the event is removed.

Figure 5.38: An example of an event which has a sub-event after itself. The left
figure shows a SRN candidate event. The right figure is its sub-event, which
occur after 1.44 µsec from the SRN candidate event.

104

Figure 5.39: An example of a SLE triggered muon case. The left figure shows amuon which triggers only the SLE. Its decay electron is shown in right figure.

We apply a sub-event cut mainly to remove these three types of background
events described above. The cut criteria is determined as follows.
1. Remove events which have pre/post activity within +/- 50µsec from a
SRN candidate if the vertex of the SRN candidate event and sub-eventare closer than 500cm.
2. Remove events which have SLE events within 50 µsec before the candidate
event and the total charge of sub-event is larger than 1000 photo-electron.
Figure-5.40 is the vertex difference between SRN candidate events and subevents within 50 µsec.

5.11

Summary of data reduction

In this section we summarize the data reduction process for SK-I, SK-II and SKIII. We applied various cuts to remove background events which are not true
SRN signal events. The number of events at each reduction step in SK-I, SK-II
and SK-III are listed in Table-5.11, 5.11 and 5.11 respectively. These numbers
are counted within the fiducial volume(2m from ID wall) which an energy region
between 16-90 MeV in SK-I and SK-III, and 18-82 MeV in SK-II. The energy
spectrum of the data in each reduction steps is also shown in Figure-5.41, 5.42,
and 5.43.

105

Figure 5.40: The distribution of the distance between SRN candidates and subevents. The red histogram is within the 500 cm cut criteria.

The applied reduction process was the same for SK-I and SK-III but not
for SK-II. Although we improved the data reduction method to increase theefficiency for the SRN signal, it does not work for SK-II due to poor detector performance. Because the number of PMTs in SK-II was only half that of
SK-I and SK-III, vertex, energy and direction resolution was worse and morebackgrounds contaminated the data sample in SK-II. Therefore we applied inefficient, but strict cuts for the SK-II data. Even after these strict cuts, the SK-II
data has an excess in the low energy region. This remaining background is due
to spallation products and will be described in the next chapter.
The number of events after all reductions is 236 events(SK-I), 115 events(SKII) and 102 events(SK-III). These correspond to event rates of 0.16 ± 0.01 events/ day(SK-I), 0.15 ± 0.01 events / day(SK-II) and 0.18 ± 0.02 events / day(SKIII). These are consistent, within statistical error.

106

Reduction step

Number of event

cut efficiency

1st reduction
Double peak cut
Spallation cut
Cherenkov angle cut
effwal cut
Solar cut
OD correlated cut
Pion like event cut
2ring cutSub-event cut cut

3970
3580
1032
341
336
314
312
290
283
236

99%
99%
85% @20MeV
94%
97.5%
95%
99%
99%
99%
99%

Number of events /22.5kt /1496days /4MeV

Table 5.3: Number of events after each reduction step in SK-I. (16-90MeV)

140

1st reduc + Spallation + 2peak cut+ Cherenkov angle cut

120+ effwall + OD + pion + solar cut+ 2ring + suvevent cut

100
80
60
40
20
0

20

30

40

50

60

70

80

Reconstructed energy (MeV)

Figure 5.41: Energy spectrum for SK-I data in each reduction step. (16-80MeV)

107

Reduction step

Number of event

cut efficiency

1st + spallation cut
Cherenkov angle cut
Solar direction cut
Timing spallation cut
Sub-event cut
Effwall cut

569
241
228
213
123
115

80% below 34 MeV
83%
90%
64% including normal spacut
99%
93%

Number of events /22.5kt /791ays /4MeV

Table 5.4: Number of events after each reduction step in SK-II. (18-82MeV)100

1st reduc + likelihood spallation cut+ Cherenkov angle cut
solar + timing spallation cut

80+ effwall + suvevent cut

60

40

20

0

20

30

40

50

60

70

80

Reconstructed energy (MeV)
Figure 5.42: Energy spectrum for SK-II data in each reduction step. (1882MeV)

108

Reduction step

Number of event

cut efficiency

1st reduction
Double peak cut
Spallation cut
Solar cut
Cherenkov angle cut
effwal cut
OD correlated cut
2ring cutSub-event cut

1840
1592
393
348
153
146
145
127
102

99%
99%
80% @20MeV
95%
93%
93%
99%
99%
99%

Number of events /22.5kt /548days /4MeV

Table 5.5: Number of events after each reduction step in SK-III. (16-90MeV)

50
45

1st + Spallation + 2peak + solar cut+ Cherenkov angle cut+ effwall + OD + pion cut+ 2ring + suvevent cut

40
35
30
25
20
15
10
5
0

20

30

40

50

60

70

80

Reconstructed energy (MeV)

Figure 5.43: Energy spectrum for SK-III data in each reduction step. (1680MeV)

109

Chapter 6

Event simulation
In order to obtain the shape of the energy spectrum of SRN events and evaluate
the efficiency of the reduction process, we simulated inverse beta decay, caused
by SRN’s anti-electrons, using the Monte Carlo method. Similarly, background
events, mainly coming from atmospheric neutrinos, were also simulated using
the Monte Carlo simulation. Both simulated SRN and background events werepassed through the detector simulation followed, by the same analysis chain as
the real data.

6.1

Detector simulation

We simulated the propagation of the particles produced in the detector by the
SRN and the atmospheric neutrino events. This simulation is described later.
Our detector simulation program consists of the following three steps.
• Particle tracking through the water• Propagation of emitted Cherenkov photons through water• Detection of Cherenkov photons by PMTs and electronics
Particle tracking
GEANT 3.21 [59] was used for the particle tracking. It was developed at CERN
and is able to simulate the electro-magnetic processes in the energy range from
10keV to 10TeV.
Figure-6.1 shows tracks of 10MeV electrons in water, as simulated by GEANT.
The interactions we considered in our simulation were not only Cherenkov radiation but also Multiple scattering, Ionization, δ-ray production, bremsstrahlung
and e+ annihilation for electrons. For γ-ray, e+ e− pair creation, Compton
scattering and the photo-electron effect were considered.
The direction of photon emission is calculated using equation 2.1. The refractive index is dependent on the photon wavelength as shown in Figure-6.2(left).

110Figure 6.1: The tracks of 20 electron events with 10 MeV/c as simulated by
GEANT. The generated vertex is (0,0,0) and the direction is (1,0,0).

Figure 6.2: The solid line of the left figure shows the refractive index as a function of wavelength. The dashed line shows “effective index”. The right figure
shows the number of generated Cherenkov photons as a function of generated
electron energy in the MC simulation. The solid line shows a linear fit to thepoints.

111

The wavelength of the emitted photon is calculated from equation 2.3. Figure6.2 (right) shows the total number of Cherenkov photons emitted from an electron in water as a function of electron kinetic energy. The number of Cherenkov
photons is approximately proportional to the electron energy.
Cherenkov photon tracking
The speed of light in water is dependent on the wavelength of the photons. The
group velocity, vg , is defined asvg =cn(λ) − λ dn(λ)
dλ

(6.1)

Where c is the speed of light in vacuum, λ is the wavelength of the photon andn(λ) is the so called effective refractive index, which depends on wavelength(seefigure 6.2(left)).
The emitted photons propagate with this group velocity and are scatteredand absorbed by water molecules. We considered Rayleigh scattering, Mie scattering and absorption. Since the wavelengths of the Cherenkov photons areshorter than the radius of the water molecules, Rayleigh scattering is dominant, with a 1/λ4 dependence in the shorter wavelength region. However, we
also considered Mie scattering. While the effect of absorption becomes larger
for longer wavelengths, its wavelength dependence is studied in [63] separately.
The wavelength dependences of the water parameter coefficients are tuned by
the LINAC calibration and plotted in Figure-6.3.
In addition, the water quality has changed as a function of time as shownin Figure-3.22. This change of water attenuation length is mainly coming fromthe absorption parameter, so we take into account the change of the absorption
coefficient.
The reflection of the PMT glass and black sheet depend on photon incident
angle and are also included in our simulation.
Photon detection by PMT and electronics
Once a photon comes to a PMT surface, the responses of the PMT and the electronics are simulated. First, the quantum efficiencies of the PMTs(see Figure2.3) are considered and whether a photon-electron can be emitted or not isdetermined. Next, the output charge is simulated, the charge distribution of asingle photo-electron is shown in Figure-2.8. The PMT hit timing is determinedconsidering the timing resolution of the PMTs by a Gaussian random variablewith a 1σ width, as shown in Figure-2.9. The dark noise is simulated by randomly distributing hits throughout the detector according to the measured ofthe dark noise rate.

112

Figure 6.3: Wavelength dependence of the water parameter coefficients in SKI. Absorption(solid line), Rayleigh scattering(dashed line) and Mie scattering(dotted line) are shown. The absorption coefficient is also a function ofwater transparency. The filled region shows the range of the parameters as
water transparency is changed.

6.2

SRN event simulation

To perform the SRN event extraction, we need to know the energy spectrum
shape of SRN events. For this purpose, SRN events are simulated by Monte
Carlo simulation using nine different theoretical SRN models which predict spectrum shape and absolute flux. There is a strong model dependence in the flux
prediction, but a weak dependence in the spectrum shape. The predicted SRN
flux of anti-electron neutrinos by [27] and cross section of this interaction are
shown in Figure-6.4(Top).
As discussed in chapter 1, most of the events we can detect in SuperKamiokande are anti-electron neutrinos which undergo inverse beta decay.
ν¯e + p → e+ + n(6.2)

The inverse beta decay cross section we used is the result of the latest calculation by A.Strumia and F.Vissani [15]. Figure-6.4(Bottom) shows the expected
event rate in Super-Kamiokande for 1496 days.
The positron total energy is approximated by:
Ee = Eν − ∆(6.3)

Where ∆ is the mass difference between the neutron and the proton(1.3
MeV). This approximation is correct, as long as the neutrino energy is smaller(<1/10)
than the neutron mass. Because most of the input quantities, including the form

113

2/sec/MeV

Flux /cm

10
1
-1

10
-2

10
-3

10
-4

10
-5

10

0

10

20

30

40

50

60

70

80

Cross section *10

40 /cm2

Neutrino energy (MeV)

1

-1

10

-2

10

0

10

20

30

40

50

60

70

80

Event rate *10

40 /sec/MeV

Neutrino energy (MeV)
1
-1

10
-2

10
-3

10
-4

10

0

10

20

30

40

50

60

70

80

Neutrino energy (MeV)

Figure 6.4: Anti-electron neutrino flux from SRN theoretical models(Top).
Cross section as calculated by A.Strumia and F.Vissani [15](Middle). Event rateof SRN events in Super-Kamiokande(Bottom). Red is the LMA model[27], green
is the constant SN rate model[20] and blue is the cosmic gas infall model[22].

114factors, have been measured precisely, the cross section in this calculation has
only 0.4% uncertainty in the low energy region.
Since supernovae have happened all over the universe, SRN events do nothave a specific direction. So direction of the simulated SRN events are randomly distributed. Similarly, the vertex position of the SRN events are also
given randomly inside the 32 kton full volume of the Super-Kamiokande innerdetector.
Although an energy range of 16-80MeV is used for this SRN analysis, we
generated positrons with energy above 5MeV. This is because the energy resolution of the detector can cause some of the SRN events with low energy to
be reconstructed above our threshold. Events below 5MeV cannot contaminate
above 16MeV, even considering energy resolution. Time information is given
to the simulated events for considering the time variation of the water transparency. The generated number of events are; 96965 events, 69783 events and68495 events in SK-I, SK-II and SK-III respectively.
Response of the detector was simulated using the method described in theprevious section. Then output of the detector simulation was treated like real
data by applying the same reconstruction and reduction tools. The spectrum
shape was obtained as above, but using the assumption that a SRN was detected
every 10 minutes. So normalization is needed for each model based on the
expected number of events as follows.
Z ∞Nexp = (τ × NP ) ×σ(Eν )φ(Eν )dEν
(6.4)
5MeV

Where τ is the livetime of each data taking term, 1496 days in SK-I, 791
days in SK-II and 548 days in SK-III. NP is the number of protons in the
Super-Kamiokande inner detector(= 2.17 × 1033 protons / 32kton), which are
the target for the inverse beta decay interaction. σ is the cross section of inverse
beta decay [cm2 ] and φ is the predicted SRN flux [/cm2 /sec].
Performing this calculation, we obtained Nexp = 49.4 events /1496days/32kt (Eν > 5M eV ) for the LMA model. The normalized energy spectrum
expected in Super-Kamiokande for the LMA model, the Constant SN modeland the Cosmic gas infall model are shown in Figure-6.5.
Eventually the number of expected events above 16MeV after all reductions
is Nexp = 10.4 events /1496days /22.5kt (Ee >16MeV) for the LMA model.
The numbers of expected events for other models are listed in Table-6.1.

6.3

Atmospheric neutrino event simulation

As described later, atmospheric neutrino events are one of the irreducible backgrounds for SRN searches in Super-Kamiokande. To understand these background we used atmospheric MC simulation events which are generated by theSuper-Kamiokande group(see [64] for the detail discussion).
There are several detailed calculations of the atmospheric neutrino flux at theSuper-Kamiokande site, however, we adopted the flux calculation by M.Honda
115

Number of events /22.5kt/1496d

1

-1

10

-2

10

-3

10
20

30

40

50

60

70

80

Reconstructed energy (MeV)
Figure 6.5: Reconstructed energy spectrum of simulated SRN events after all
reductions. Red is the LMA model, green is the constant SN rate model andblue is the cosmic gas infall model.

116

SRN model

SK-I

SK-II

SK-IIILMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Cosmic Chemical evolution
Heavy metal abundance
Population synthesis
Cosmic SF history
SFR constraint
Failed supernovae

9.9 events
26.6 events
1.4 events
3.5 events
9.6 events
3.0 events
11.4 events
3.9 events
4.3 events

3.4 events
9.1 events
0.5 events
1.2 events
3.2 events
1.0 events
3.9 events
1.3 events
1.5 events

3.5 events
9.4 events
0.5 events
1.2 events
3.4 events
1.1 events
4.0 events
1.4 events
1.6 events

Table 6.1: Expected number of SRN events for each SRN model after all reductions. The energy region is 16-80MeV in SK-I and SK-III, and 18-82MeV
in SK-II. The fiducial volume is 22.5 ktons for all phases and the livetimes are
1496 days, 791 days and 548 days in SK-I, SK-II and SK-III.
et al.(Honda flux [60]) for our simulation. Figure-6.6 shows the predicted atmospheric neutrino flux. The solid line is the Honda flux we used and the othertwo lines are the neutrino fluxes from G.Battistoni et al.(Fluka flux [61]) and
G.Barr et al.(Bartol flux [62]).
There are two large uncertainties for the atmospheric neutrino flux. The
First is the uncertainty of the primary cosmic ray flux and is about 30% in the
low energy region. The Second is the uncertainty of the cross section of hadronicinteractions, which produce atmospheric neutrinos. This effect is about 20% andis discussed in [70].
The effect of solar activity and the geomagnetic field is about 10%, and istaken into account in the calculation. The geomagnetic field works as a shield sothat cosmic rays which have relatively lower momentum cannot continue down
to earth’s surface. This effect is especially important for low energy region
and the difference between solar maximum and solar minimum about 10% forneutrino flux.
The systematic uncertainty for the atmospheric neutrino flux described above
effects the absolute flux, but does not effect the spectrum shape much. So only
the spectrum shape was obtained from this MC simulation.
Atmospheric neutrinos interact with nucleons and electrons in the water, in
the Super-Kamiokande detector. The neutrino interactions are simulated by
NEUT [65], in our Monte Carlo simulation. NEUT was developed to study atmospheric neutrinos as a background for the nucleon decay analysis first donein the Kamiokande experiment, and was inherited to the Super-Kamiokande experiment with various modifications. In the NEUT code, the following charged
current(CC) and neutral current(NC) interactions are considered.
CC/NC (quasi-)elastic scatteringν + N → l + N′

CC/NC single meson production

ν + N → l + N ′ + meson117

CC/NC deep inelastic interaction

ν + N → l + N ′ + hadrons

CC/NC coherent pion production

ν + 16 O → l + 16 O + π

Where N and N ′ are nucleons(proton or neutron) and l is a lepton.
Since the cross-section of neutrino-electron elastic scattering is about 103
times smaller than that of the neutrino-nucleon interactions at a neutrino energyof ∼1 GeV, it is neglected in our simulation.

Figure 6.6: Predicted atmospheric neutrino flux(left) and the νµ + ν¯µ and νeν¯e ratio(right). The solid line shows the Honda flux which was used in our
simulation. The dashed line is the calculation by G.Battistoni et al. [61] andthe dotted line is G.Barr et al. [62].

118Chapter 7

Remaining background
Even after applying all reduction steps, more events than expected remain as
SRN candidates in the data. Figure-7.1 shows the energy spectrum of the final
data sample in SK-I and SK-II. It is important to understand these irreducible
backgrounds for our analysis. In this chapter, we discuss these remaining background events.

Figure 7.1: The reconstructed energy spectrum of final data sample after all of
the reduction. The left figure is SK-I and the right figure is SK-II. The SK-III
spectrum is similar to SK-I.
Possible backgrounds in the the analysis energy region 16-80MeV are:• Cosmic ray muons• Solar neutrinos• νe components of atmospheric neutrinos
119• Decay electrons from muons (cosmic ray muon or atmospheric νµ origin)• Spallation products
Cosmic ray muons which are not rejected by the OD trigger event cut during
the 1st reduction are rejected by the sub-event cut, making the cosmic ray muon
background negligibly small. Solar neutrino events are rejected by the solar
neutrino event cut based on the events’s directional correlation with the solar
direction. As described in Chapter 5, the remaining solar neutrino background is
expected to be less than 0.3 events in SK-I. Spallation backgrounds are basicallyall removed in SK-I and SK-III, however due to the poor energy resolution in
SK-II, some of spallation products remain in the final data sample. The numberof remaining spallation backgrounds are estimated in this chapter.
The irreducible backgrounds in this energy region both come from atmospheric neutrinos. The origin of atmospheric neutrinos is the decay of secondary
cosmic rays(e.g. pion), which are produced by the interactions of primary cosmic rays(e.g. proton) with atmospheric nuclei such as nitrogen and oxygen. For
example, a π ± decays through the following steps.
π+ →

µ+

−

−

π →

+νµ

ց e+ + νe + ν µ(7.1)

ց e− + ν e + νµ

(7.2)

µ

+ν µ

That is to say, one π ± can produces two νµ and one νe by this process.
Atmospheric νµ , ν¯µ induce a muon via charged current (CC) interaction and
it decays into an electron (decay-e). This is one of the irreducible backgrounds
and most dominant background for SRN search in this energy region. Electrons
originating from atmospheric νe , ν¯e are also an irreducible background source.
In this chapter, we will discuss these backgrounds and estimate their energy
spectra.

7.1

Decay electron from invisible muon

As described above, one of the irreducible backgrounds comes from decay electrons produced by invisible muons from atmospheric neutrino interactions. We
evaluated the decay electron spectrum by collecting a decay electron sample using real cosmic ray stopping muons. Since these events are also decay electrons,
they follow the Michel spectrum, which is expressed by the following equation:


4Ee
G2F
dN
2 2
3
−
=
m
E
dEe
12π 3 µ e
mµ


mµ 
Ee <
2

(7.3)

The positron from the µ+ decay follows this function, however, in the caseof µ− , the energy spectrum is distorted because almost all of the muons are120

number of events

trapped by oxygen atoms in K-shell orbits. The decay electron is influenced
both by the orbital motion of the parent muon and by the electric potential of
the oxygen nucleus. Figure-7.2 shows the calculated energy spectra of the decay
electrons and positrons.

40000

µ+

35000

µ-

30000

25000

20000

15000

10000

5000

0

0

10

20

30

40

50

60

70

total energy (MeV)

Figure 7.2: The calculated energy spectra for decay electron events in water.
The solid line represents the positron spectrum and the dashed line represents
the electron spectrum.
The µ+ /µ− ratios from atmospheric neutrinos and cosmic rays are different.
The primary particles of cosmic rays are mainly free protons which have positive
charge. Therefore the fraction of µ+ is larger than that of µ− in the cosmic ray
stopping muon case. While in the atmospheric neutrino’s case, the νµ interaction
is larger than ν¯µ , due to the almost twice as large cross section[69]. Figure-7.3
shows the calculated cross section of the charged current quasi-elastic interactionfor νµ and ν¯µ . µ− from the νµ interaction is greater than µ+ in the atmosphericorigin case.
Although the µ+ /µ− ratio for the atmospheric neutrino origin and the cosmic
ray origin are different its effect is not significant when determining the flux
limit. Because the electric potential of the oxygen nucleus is ∼ 0.2 MeV, thedifference in mean value of the energy spectrum for µ+ and µ− decays is small.
The difference in energy spectrum shape mainly come from Lorentz boost ofµ− .
Considering the difference of the µ+ /µ+ ratio, the decay electron energy
spectra for both cases are obtained by MC simulation and they are plotted in
Figure-7.4.
The red line shows the energy spectrum using the µ+ /µ− ratio of atmo121

Figure 7.3: The calculated charged current interaction cross section for νµ (ν¯µ )on a nucleon.

Figure 7.4: Red line shows the energy spectrum using µ+ /µ− ratio of atmospheric neutrino case (µ+ /µ− = 0.3/0.7) and green is that of the stopping
muon case(µ+ /µ− = 0.7/0.3)

122spheric neutrino case (µ+ /µ− = 0.3/0.7) and green is that of the stopping
muon case(µ+ /µ− = 0.7/0.3). The difference of mean value is less than 0.5%
and they are consitent in the low energy signal region. So the decay electron
spectrum obtained from the stopping muon sample can be used as a background
spectrum.
We collected the decay electron sample from stopping muons with the following selection criteria:• Time difference from stopping muon is between 3-8 µsec
• Distance from muon stopping point to vertex is closer than 500cm.
The energy spectrum after this reduction is shown in Figure-7.5 comparing
with decay electron MC. The consistency was checked by calculating χ2 using statistical error of data and MC. Calculated χ2 is 20.1 / 13 d.o.f (∼10%
probability).

1000

800

600

400

200

0

20

30

40

50

60

Reconstructed energy (MeV)

Figure 7.5: The energy spectrum for the decay electron sample obtained fromstopping muon real data and decay electron MC. Calculated χ2 is 20.1 / 13 d.o.f(∼10% probability).

Since this sample is real data, systematic error due to energy scale calibrationis negligible. It does not include any gamma rays produced by NC interactionsof atmospheric neutrinos. These low energy gamma rays have large uncertainty
so they are considered as a systematic error and are described in section 8.3.

123

7.2

Atmospheric νe, ν¯eAtmospheric electron-neutrinos and anti-electron-neutrinos are an irreducible
background in this energy region. Atmospheric anti-electron-neutrinos interact
with a proton in the water via inverse beta decay as do SRN anti-electron
neutrinos. However atmospheric electron-neutrinos interact with a neutron in
the 16 O nucleus via the following interaction:
νe + n → e− + p, ν¯e + p → e+ + n(7.4)

Neither can be separated from the SRN events and are dominant backgroundsources.
Using the Honda flux and NEUT, described in section 6.3, 50 years of atmospheric neutrino MC were generated and passed through the detector simulation
described in section 6.1.
The reconstructed energy spectrum of the atmospheric neutrino MC, after
reductions is shown in Figure-7.6(right) for νe , ν¯e . The original neutrino energy
for those events are also shown in Figure-7.6(left).

Figure 7.6: Charged current interactions are selected. The original neutrinoenergy for the events is shown in left figure. The reconstructed energy spectrumof atmospheric νe and ν¯e events after the reductions(right).

7.3

Spallation backgroundThe backgrounds in SK-I and SK-III are understood to be due to an atmospheric
neutrino origin as described in the previous section. But there is still a remaining
unknown background in the low energy bin in the SK-II data as shown in Figure7.1. There is a possibility that this excess is due to spallation backgrounds which124are reconstructed above the 18 MeV energy threshold due to the worse SK-II
energy resolution, even though we adopted a tighter spallation cut in SK-II as
used for the solar neutrino analysis, as described in section 5.2.2. We estimatedhow many spallation background events are still remaining in our final data
sample after all reductions.
The spallation cut was applied in two steps for SK-II as follows.
• The cut based on the likelihood method using three variables• The cut using time difference from the last muon (∆Tlast > 0.15sec)
The first step of this spallation cut uses the spallation likelihood expressedby the following equation.
likelihood = £(∆T ) × £(∆L) × £(Qres )(7.5)

As described in section 5.2.1, the three variables are; ∆T which is the timedifference between the preceding muon and the SRN candidate event, ∆L whichis the transverse distance from the muon track to the reconstructed relic candidate position, and Qres which is the residual charge that is defined as theobserved total charge minus the expected charge from the muon track length.
If the likelihood value is greater than 3.9, the event is rejected by this cut.
Figure-7.7 shows the energy spectrum before and after the likelihood spallation
cut. 616 events(corresponding to 85%) are rejected by this cut in the 18-22MeV
region. This means a lot of spallation events are included before the cut, in thisbin, but are now rejected. Most of the rejected 616 events are “spallation like”
events.
Using these “spallation-like” events, the time difference from preceding muons(dt)distribution is made and is shown in Figure-7.8. The red line shows the distribution for “spallation-like” events and the green line shows “random” events,
which has random timing and vertex information. For the “random” event sample, we selected very low energy events near the ID wall, and generated theirvertex randomly instead of the reconstructed vertex. Most of these events are
gamma ray events originating at the PMTs or tank structures so that they
have no correlation with the muon. The black line shows the distribution of“spallation-like-random”, which is called the “true spallation”.
The obtained ∆T distribution for the “true spallation” has events above 0.15
seconds. These events pass the second spallation cut using ∆T , and remain in
the final sample if the likelihood spallation cut cannot reject them. We estimatedhow many “true spallation” events were remaining after both spallation cuts.
To do this, we need to know the likelihood distribution for “true spallation”
events. We estimated this likelihood distribution by generating a spallation MC
based on the ∆T , ∆L and Qres distribution of “true spallation”.
We started from making the ∆L and Qres distribution using a “Spallationlike” sample with all the preceding muons occurring within 100 seconds. The
125

Figure 7.7: The energy spectrum of the SK-II data, before and after spallation
cut.

Figure 7.8: The distribution of time difference from the last muon (dtlast ).

126

distribution is made in two categories, one is “on-time”(0.1sec > ∆T > 0.0sec)
and the other is “off-time“(100.0sec > ∆T > 90.0sec). Figure-7.9 shows the∆L and Qres distribution, the green line is “on-time”, the red line is “off-time”,
and the black line is the “true spallation” which was made by the “on-time off-time” after normalization by time as follows.
0.1[sec](7.6)
10.0[sec]
0.1[sec]
Qres (truespallation) = Qres (on − time) − Qres (of f − time) ×(7.7)
10.0[sec]∆L(truespallation) = ∆L(on − time) − ∆L(of f − time) ×

Figure 7.9: ∆L, Qres distribution. Green is “on-time”, red is “off-time” andblack is “true spallation” defined by “on-time - off-time”.

By the method described above, we obtained all of the distributions needed
for the simulation of the spallation likelihood distribution. The random variables of ∆T , ∆L and Qres were generated following the distribution of “truespallation”. This calculation was done for every 0.6 second bin of the ∆T distribution. The center value of each bin is used as ∆T for the spallation likelihood
calculation. The results of the likelihood simulation, in the case of ∆T = 0.375
seconds and 0.9 seconds, are shown in Figure-7.10. The cut point in both islikelihood < 3.9, so that 9.7% and 10.2% of the simulated events can pass thelikelohood spallation cut, respectively. The results in other ∆T bins are listed
in Table-7.3. Integrating the number of events passing through the spallation
cut, for ∆T > 0.15 second, gives a total of 9.2 events which can remain in thedata sample after the spallation cut in the 18-22MeV region.
Because this number of events is just after the spallation cut, we multiplied
the efficiency(≈67%) of the other cuts to evaluate the number of spallation
127

background events in the final data sample. This analysis was also done using
622 days of SK-II data, although the SK-II data was collected for 791 days
overall. Considering the cut efficiency and livetime normalization, the expected
number of spallation background events in the final data sample in each energy
bin was calculated and is listed in Table-7.3. In the 18-22MeV region, 7.8
spallation events are expected to exist in our final data sample for SK-II.

Figure 7.10: The simulated likelihood distribution for “true spallation” events.
The left figure is the case of ∆T = 0.37 seconds and the right figure is ∆T =0.9 seconds. The shaded region is rejected by the spallation cut.

Remaining spallation in SK-I and SK-III
Most of the spallation backgrounds must be rejected by the spallation cut in
SK-I and SK-III. Looking at the dt and dLtrans distributions, there is no strong
evidence for any remaining spallation events. If spallation is long lived and thefit is poor, it can be missed. Even considering that case, remaining spallation
events are less than one or two both in SK-I and SK-II. In our analysis, theremaining backgrounds are assumed as signals. So even if there are remaining
spallation events, the obtained flux upper limit should be a conservative result.

128

∆T

# of “true spallation”

pass rate [%]remaining events

0.0 - 0.15
0.15 - 0.6
0.6 - 1.2
1.2 - 1.8
1.8 - 2.4
2.4 - 3.0
..
.

517.3
26.1
12.3
8.09
6.65
5.76
..
.

0.0
9.7
10.2
11.9
12.7
13.4
..
.

0.0
2.5
1.3
1.0
0.8
0.8
..
.

Total

593.5

1.6%

9.2

Table 7.1: Expected number of remaining events in the final data sample foreach time bin. The energy range is between 18MeV and 22MeV. The events in
0.0 - 0.15 second bin are rejected by the second spallation cut using the timing
difference from the muon.

Energy [MeV]

Number of remaining events

18-22
22-26
26-30
> 30

7.8
0.5
0.2
≈0

Table 7.2: Number of expected events in the final data sample for each energy
bin. These values are estimated by integrating the number of remaining eventsin each timing bin and multiplying the efficiency of the other cuts. The expected
livetime is 791 days of all SK-II period.

129Chapter 8

Systematic error estimation
Since the data statistics are not large, the effect of most systematic errors is
not significant. But in order to extract SRN signal more correctly, we considered three non-negligible source of uncertainty in this analysis. The first is
the uncertainty on the signal efficiency estimation originating from the difference between data and MC. The second is the energy scale uncertainty. Thisis important because the SRN spectrum is “soft” meaning that the number of
expected events can be strongly affected by the energy scale. Finally the third
is the background shape error on the decay electron spectrum. Since this spectrum is made from a pure decay electron sample, we need to consider events
originating from atmospheric neutrino interactions (e.g. gamma rays from NC
interaction).

8.1

The uncertainty for signal efficiency

The uncertainty on the SRN signal efficiency is evaluated as described below.
The cross section of inverse beta decay is important because it affects thedetection efficiency directly. As described in [15], most input quantities havebeen measured precisely. The cross section uncertainty is approximated by 1%×(Eν /40M eV )2 . The SRN spectrum decreases with increasing energy and mostpart of the SRN flux is bellow 40 MeV so the systematic error originating fromcross section uncertainty is less than 1%.
The uncertainty from each reduction step are estimated by applying the same
reduction to LINAC data and LINAC MC and comparing the difference of theirefficiency. The uncertainty of solar neutrino event cut are negligible, becauseθsun distribution must be flat for SRN signal even if the angular resolution
is different for data and MC. The spallation cut uncertainty is estimated by
calculating the efficiency in the several different period. Other cuts, for example
OD correlated event cut, double T peak cut, sub-event cut and so on, have small
inefficiencies for SRN signal (∼1% or less). Therefore, we took the quadratic
sum of these errors as a single error source on the inefficiency. The estimateduncertainties for each reduction step are listed in Table-8.1.
130reduction

SK-I

SK-II

SK-III

Cherenkov angle cut
Effwall cut
Spallation cut
Pion-like event cut
Other cuts

±0.4%
±0.5%
±3.0%
±0.2%
±2.0%

±3.0%
±1.0%
±0.4%
±1.3%

±0.3%
±0.3%
±1.0%
±0.5%
±1.7%

Table 8.1: The systematic uncertainty from each reduction step in this analysis.

The uncertainties on the fiducial volume and detector livetime calculation
are quoted from the solar neutrino analysis in Super-Kamiokande[38, 39, 40],
because the data set and vertex reconstruction program are same as that ofsolar neutrino analysis although applied cut is different.
In total, the uncertainty on the SRN signal efficiencies are ±3.9% in SKI, ±4.6% in SK-II and ±2.5% in SK-III. The uncertainty described above aresummarized in Table-8.1.

Cross section of inverse β decay
Reduction efficiency
Fiducial volume
Livetime calculation
Total

SK-I

SK-II

SK-III

±1.0%
±3.6%
±1.3%
±0.1%

±1.0%
±4.3%
±1.1%
±0.1%

±1.0%
±2.1%
±1.0%
±0.1%

±3.9%

±4.6%

±2.5%

Table 8.2: The summary table of systematic uncertainty in our analysis.

8.2

Energy scale uncertainty

The energy scale uncertainty is obtained from energy scale calibration as described in section 3.7. The systematic uncertainty for energy scale is calculated
considering the effect of position dependence of energy scale, time variation ofenergy scale, MC tuning accuracy, electron beam determination in LINAC calibration and directional dependence of energy scale. As shown in table 3.3,
obtained uncertainty is 0.64% in SK-I, 1.4% in SK-II and 0.53% in SK-III respectively. To be conservative, we applied a larger uncertainty, 1% in SK-I and
SK-III and 1.5% in SK-II.

8.3

Background shape error

As described in section 7.1, the decay electron spectrum is obtained from decay
electron real data from cosmic ray stopping muon data. This sample does not131include other atmospheric neutrino interactions. These low energy neutral current interactions have large uncertainties so we considered them as a systematic
error on the background shape.
In order to investigate the influence of atmospheric neutrino interactions,
atmospheric neutrino MC events were classified into four groups, based on theoriginal neutrino flavor. Each group is further classified into six groups based on
the interaction mode. The energy spectrum obtained for each group is shown in
Figure-8.1, 8.2(νe , ν¯e ), Figure-8.3, 8.4(νµ , ν¯µ ). The interaction mode is definedin Table-8.3(for νe and ν¯e ) and 8.4(for νµ and ν¯µ ).
idelectron neutrino interactionid

anti-electron neutrino interaction

10
11

νe + n → e− + p
νe + p → e− + p + π +νe + n → e− + p + π 0
νe + n → e− + n + π +νe +16 O → e− +16 O + π +νe + p(n) → e− + p(n) + multi π
νe + n → e− + p + η 0
νe + n → e− + Λ + K +νe + p(n) → e− + p(n) + mesons
νe + n → νe + n + π 0
νe + p → νe + p + π 0
νe + n → νe + p + π −νe + p → νe + n + π +νe +16 O → νe +16 O + π 0
νe + n(p) → νe + n(p) + multi π
νe + n → νe + n + η 0
νe + p → νe + p + η 0
νe + n → νe + Λ + K 0
νe + p → νe + Λ + K +νe + n(p) → νe + n(p) + mesons
νe + p → νe + p
νe + n → νe + n

2021

ν¯e + p → e+ + nν¯e + p → e+ + n + π 0ν¯e + p → e+ + p + π −ν¯e + n → e+ + n + π −ν¯e +16 O → e+ +16 O + π −ν¯e + p(n) → e+ + p(n) + multi πν¯e + p → e+ + n + η 0ν¯e + n → e+ + Λ + K −ν¯e + p(n) → e+ + p(n) + mesons
ν¯e + n → ν¯e + n + π 0ν¯e + p → ν¯e + p + π 0ν¯e + n → ν¯e + p + π −ν¯e + p → ν¯e + n + π +ν¯e +16 O → ν¯e +16 O + π 0
νe + n(p) → νe + n(p) + multi πν¯e + n → ν¯e + n + η 0ν¯e + p → ν¯e + p + η 0ν¯e + n → ν¯e + Λ + K 0ν¯e + p → ν¯e + Λ + K +ν¯e + n(p) → ν¯e + n(p) + mesons
ν¯e + p → ν¯e + p
ν¯e + n → ν¯e + n

12

13

14

15

22

23

24

25

Table 8.3: The definition of the id number in each interaction mode for electron
and anti-electron neutrinos.

132

Figure 8.1: The energy spectrum of atmospheric electron neutrinos for eachinteraction mode using 50years of MC. The horizontal axis is the reconstructedenergy. The definition of the id number of interaction modes are described inTable-8.3.

133

Figure 8.2: The energy spectrum of atmospheric anti-electron neutrinos for eachinteraction mode using 50years of MC. The horizontal axis is the reconstructedenergy. The definition of the id number of interaction modes are described inTable-8.3.

134

Figure 8.3: The energy spectrum of atmospheric muon neutrinos for each interaction mode using 50years of MC. The horizontal axis is the reconstructedenergy. The definition of the id number of interaction modes are described inTable-8.4.

135

Figure 8.4: The energy spectrum of atmospheric anti-muon neutrinos for eachinteraction mode using 50years of MC. The horizontal axis is the reconstructedenergy. The definition of the id number of interaction modes are described inTable-8.4.

136

id
30
31

32

33

34

35

muon neutrino interaction−

νµ + n → µ + p
νµ + p → µ− + p + π +νµ + n → µ− + p + π 0
νµ + n → µ− + n + π +νµ +16 O → µ− +16 O + π +νµ + p(n) → µ− + p(n) + multi π
νµ + n → µ− + p + η 0νµ + n → µ− + Λ + K +νµ + p(n) → µ− + p(n) + mesons
νµ + n → νµ + n + π 0
νµ + p → νµ + p + π 0
νµ + n → νµ + p + π −νµ + p → νµ + n + π +νµ +16 O → νµ +16 O + π 0
νµ + n(p) → νµ + n(p) + multi π
νµ + n → νµ + n + η 0νµ + p → νµ + p + η 0νµ + n → νµ + Λ + K 0
νµ + p → νµ + Λ + K +νµ + n(p) → νµ + n(p) + mesons
νµ + p → νµ + p
νµ + n → νµ + n

id

anti-muon neutrino interaction4041ν¯µ + p → µ+ + nν¯µ + p → µ+ + n + π 0ν¯µ + p → µ+ + p + π −ν¯µ + n → µ+ + n + π −ν¯µ +16 O → µ+ +16 O + π −ν¯µ + p(n) → µ+ + p(n) + multi πν¯µ + p → µ+ + n + η 0ν¯µ + n → µ+ + Λ + K −ν¯µ + p(n) → µ+ + p(n) + mesonsν¯µ + n → ν¯µ + n + π 0ν¯µ + p → ν¯µ + p + π 0ν¯µ + n → ν¯µ + p + π −ν¯µ + p → ν¯µ + n + π +ν¯µ +16 O → ν¯µ +16 O + π 0
νµ + n(p) → νµ + n(p) + multi πν¯µ + n → ν¯µ + n + η 0ν¯µ + p → ν¯µ + p + η 0ν¯µ + n → ν¯µ + Λ + K 0ν¯µ + p → ν¯µ + Λ + K +ν¯µ + n(p) → ν¯µ + n(p) + mesonsν¯µ + p → ν¯µ + pν¯µ + n → ν¯µ + n

42

43

44

45

Table 8.4: The definition of id number in each interaction mode for muon andanti-muon neutrinos.

137

Charged current interactions (CC) create leptons that can be source of background. In the case of νµ and ν¯µ , decay electron from invisible muon is main
background source. Pion is produced in the CC pion production interaction as
well as lepton, but some fraction of pion cannot go out of oxygen nuclei due to apion absorption. Neutral current interactions (NC) emit gamma rays and they
can be a background in the SRN search (nuclear γ).
Additionally, deexcitation gamma rays from the interactions of final state
nucleons in surrounding medium are another source of background(secondaryinteraction γ). If charged particle is not produced at prompt interaction, those γ
can be detected as prompt signal. Though CC interaction also can emit gamma
rays, such event should have two timing peaks or sub-event (i.e. gamma ray
and decay electron). So most CC events, including gamma rays originating fromneutrino interaction, are already removed by the data reduction.
To evaluate the effects of atmospheric neutrino interactions other than decay electrons from invisible muons, we compared decay electron MC and atmospheric neutrino MC including all interaction in Figure-8.5.

Figure 8.5: Energy spectra are compared between atmospheric neutrino MC
and decay electron MC. The red histogram is the atmospheric neutrino MC
including all interactions and the blue histogram includes only CC interaction
events. Decay electron MC spectrum is normalized by number of entries in theblue histogram.
The decay electron MC (black) is generated as an electron (positron) whoseenergy follows the Michel spectrum. The red histogram is atmospheric neutrino138

MC including all interactions and the blue includes only CC interactions. The
difference between red and blue is due to gamma rays mainly caused by nuclear
γ. The small difference between blue and black comes from secondary γ althoughmost CC secondary γ events are rejected by data reduction. The decay electron
MC spectrum is normalized by the number of entries in the blue histogram. The
systematic error of background shape is estimated from the difference between
all interaction modes of atmospheric MC (red) and decay electron MC (black).
This difference is assumed to be 1σ level systematic uncertainty.

139

Chapter 9

Results
After all reductions, the final data sample was obtained, and still remaining
backgrounds were understood as atmospheric neutrino origin as stated in theprevious chapter. Because the individual SRN events cannot be identified, astatistical method was used to extract the SRN signal. In this chapter, a fitting
method using the energy spectra and its results are described.

9.1

Spectrum fitting

Although nine SRN models predict slightly different spectral shape, those shapes
all basically decrease exponentially with increasing energy, as shown in Figure6.4. In contrast, the spectral shape of the expected background, i.e. invisibleµ-e decay, atmospheric νe , ν¯e , rise with energy increase. See Figure-7.5 and 7.6.
Since their spectra are different from the SRN spectrum, spectrum fitting canbe used to discriminate those components.

9.1.1

The spectrum fitting by Gaussian method

The expected signal and background spectra obtained in the previous chapter
were normalized by the livetime and used to fit the final data spectrum. Theenergy spectra of our final data samples for SK-I and SK-II are shown in Figure7.1. The lower threshold of this analysis is 16 MeV (SK-I, SK-III) and 18 MeV(SK-II), which is limited by the spallation backgrounds. Although the decay
electron spectrum is up to ∼65 MeV, even considering detector resolution, theupper threshold of this analysis was extended to 80 MeV, in order to evaluate
the contribution from the atmospheric νe , ν¯e .
For the fitting, the data was divided into sixteen bins, with 4 MeV width,
and the following χ2 function was used.
2

χ =

16
X
(NData (i) − NSpec (i))

σ2

i=1

NSpec (i) = α × NSRN (i) + β × Natmνe (i) + γ × Natmνµ (i) + NSpal (i)
140

(9.1)
(9.2)

Where:• NData : The spectrum of the final data sample• NSRN : The spectrum of the SRN MC• Natmνe : The spectrum of the atmospheric νe , ν¯e MC• Natmνµ : The spectrum of the decay electron from stopping muon realdata
• Nspal : The expected number of remaining spallation events (only for
SK-II)α, β and γ are the normalizing factors for SRN, atmospheric νe , ν¯e andinvisible µ-e decay respectively.
σ is the statistical error of the Gaussian standard deviation and systematic
error, added quadrature, represented as follows.
222
σ 2 = σdata+ σMC+ σsys(9.3)

2
Since the MC statistics are much larger than the data statistics, σMC
isnegligible in all energy regions. The systematic error, described in section 7.3, isalways <5% and is also much smaller than the data statistical error. Minimizing
the χ2 function(Equation-9.1), the α, β and γ parameters were determined. To
avoid the best fit SRN flux being in the unphysical region, the α parameter was
required to be non-negative.
By the spectrum fitting method described above, we obtained the α parameter, which indicates the expected number of SRN events in our data sample.
We obtained the best α value and its 1 σ error, which were 0.2 ± 0.9 in SK-I, <1.5(1σ) in SK-II and 0.8 ± 1.8 in SK-III1 . All of them are consistent with zero,
within a 1σ error. This means there is no clear evidence of SRN events in SK-I,
SK-II and SK-III. The minimum χ2 value is 11.9, for 13 degree of freedom, in
SK-I which corresponds to 54% probability. For SK-II and SK-III, the χ2 values are 10.6 and 8.8, both for 13 degree of freedom, and correspond to 64% and
79% probabilities. These χ2 values demonstrate the validity of our backgroundhypothesis.
As we discuss later, the Gaussian method was used in the old SK-I analysis[16], which gave the current flux upper limit of < 1.2 /cm2 /sec(>18 MeV).

9.1.2

Spectrum fitting by Poissonian method

In the previous section, the fitting method by the Gaussian method was described. But even in the SK-I data, which has the largest statistics in the threephases, the number of entries in each bin is not large enough to approximate
the statistical errors by a Gaussian standard deviation. In the case of SK-II
1 since the best fit α is in the unphysical region in SK-II, only the upper 1σ side is shown141

and SK-III, statistics are even poorer than SK-I. So we developed a new flux
extraction method, based on the Poissonian distribution.
The χ2 is defined in equation 9.6, and can be transformed as follows.
(Nobs − Nspec )2
G(Nobs , Nspec )= −2Σ log
2
σG(Nobs , Nobs )exp(−(Nobs − Nspec )2 /2σ 2 )√G(Nobs , Nspec ) =2πσ

χ2 = Σ

NSpec (i) = α × NSRN (i) + β × Natmνe (i) + γ × Natmνµ (i) + NSpal (i)

(9.4)

(9.5)

Where G(Nobs , Nspec ) is a Gaussian distribution and Nspec is signal + BG
spectrum expected from α, β and γ. Then by replacing the Gaussian distribution
by a Poisson distribution, we obtained the χ2 of the Poissonian method:

χ2

=
=
=

P (Nobs , Nspec )P (Nobs , Nobs )
Nobs

Nspec
exp (Nobs − Nspec )−2Σ log
Nobs



Nspec
−2Σ log Nobs − Nspec + Nobs log
Nobs−2 log

(9.6)

where
P (Nobs , Nspec ) =(Nspec )Nobs exp(−Nspec )Nobs !

(9.7)

In the Poissonian fitting method, this χ2 was used instead of the Gaussian χ2 ,defined by Equation-9.1. Since this χ2 definition does not include σ, systematic
errors were considered as follows.

2

χ =

Z

χ2 (η, ξ, δ)

exp(−η 2 /2ση2 ) exp(−ξ 2 /2σξ2 ) exp(−δ 2 /2)√√√dηdξdδ
2πση
2πσξ
2π

(9.8)

where η is the energy scale error and its uncertainty (ση ) was obtained fromthe LINAC and DTG calibration (section 3.7). ξ is the systematic error of the
expected number of SRN events(e.g. due to reduction efficiency, fiducial volume,
livetime etc). The estimated error was summarized in Table-8.1. By changing
η and ξ manually, SRN spectrum is regenerated (see Equation-9.9) and χ2 iscalculated for each η and ξ. η and ξ is changed from -3σ to +3σ and χ2 issummed up with the weight of Gaussian distribution.

(1 + ξ) × NSRN (E × (1 + η))(9.9)

δ is the background shape uncertainty for decay electron spectrum. Realbackground shape include not only decay electron but also some gamma rays142

originating from atmospheric neutrino interaction. This error changes the decay
electron spectrum as follows:Natmνµ (i) + δ × ∆Natmνµ (i)(9.10)

We estimated this error (∆Natmνµ (i)) using atmospheric MC as describedin section 8.3.
δ is changed only for positive side from 0 to +3σ, because additional nuclear
and secondary γ rays distort the spectrum only to positive direction.
Fitting result
The fitting was performed using the Poissonian χ2 , defined by Equation-9.6, forall of the SRN models and the best fit parameters were obtained by minimizing
the χ2 value.
The Poissonian distribution is asymmetric and the error bar is larger for
the upper direction. So the best fit parameters are likely to be larger values
than those for the Gaussian case. Between the 30 and 60 MeV region, where
the decay electron background is dominant, the number of entries is more thanten, so the error bar can be approximated by the Gaussian distribution. So theγ parameter, which is the normalizing factor of the decay electron spectrum,
does not changed. Since the signal energy region, below 30 MeV, also has small
statistics, this increases the limit of α. Thus the limit on the number of events,
and the flux, should be worse in the Poissonian method.
The best fit parameters are listed in Table-9.1. The best fit spectra areshown in Figure-9.1(SK-I), 9.2(SK-II) and 9.3(SK-III), respectively. The data
points with error bars represent the data spectrum, the red line is the spectrumof atmospheric νe , ν¯e MC, the green line is the spectrum of decay electrons fromstopping muon real data. The black line shows the sum of the red and green
spectra.

parameter

best fit value
SK-I

best fit value
SK-II

best fit value
SK-IIIαβγ
χ20.12 ± 0.8
1.26
1.39
14.1 / 13 d.o.f

0.0
0.94
0.47
8.5 / 13 d.o.f

0.66 ±1.81.51
1.169.1 / 13 d.o.f

Table 9.1: The best fit parameters from the χ2 spectrum fitting in SK-I, SK-II
and SK-III, by the Poissonian method, are listed. The LMA model was used forgetting this result. α, β and γ are the normalizing factors for SRN, atmosphericνe , ν¯e and invisible µ-e decay, respectively.

143

Number of event /1496days /4MeV

SK1 spectrum fitting
30
25

DATA

20

Best fit
15
10

Atm. neumu
5Atm. neue
0

20

30

40

50

60

70

80

Energy (MeV)
Figure 9.1: The result of the χ2 fitting for the distribution of the SK-I final
data sample, by Poissonian method, are shown. The LMA model was used forgetting this result. The data points are SK-I data and the red and green dashedhistograms represent the fitted backgrounds from atmospheric νe (and ν¯e ) andinvisible µ-e decay. The black solid line shows the sum of both backgrounds.

9.2

flux upper limit extraction

In the previous section, we discussed the spectrum fitting results. From theseresults we could not find a significant SRN signal in any of the three data taking
phases, so we extracted the flux upper limit from the fitting result, as described
below.
1. Get the χ2 distribution as a function of α, by changing α, with minimizing
χ2 with two free parameters(β and γ). The χ2 values thus obtained ateach α are defined as χ2α . the χ2α distribution in SK-I for the LMA modelis shown in Figure-9.4(top).
2. The probability is calculated for each χ2α , defined by Equation-9.11. Figure9.4(middle) shows the probability distribution as a function of χ2α .
χ2
P robability = K · exp − α2(9.11)

Where K is the normalizing factor, determined to make the integrated
value equal to 1 as follows.
144

Number of event /791days /4MeV

SK2 spectrum fitting
16
14

DATA

12
10

Best fit

8
6

Atm. neumu

420

Atm. neue
Spallation
20

30

40

50

60

70

80

Energy (MeV)
Figure 9.2: The result of the χ2 fitting for the distribution of the SK-II final
data sample, by Poissonian, method are shown. The LMA model was used forgetting this result. The data points are SK-II data and the red and green dashedhistograms represent the fitted backgrounds from atmospheric νe (and ν¯e ) andinvisible µ-e decay. The black solid line shows the sum of both backgrounds.

Z ∞



χ2
K · exp − α dα = 12
α=0(9.12)

3. The probability is integrated up to α = 40. The α value whose sum of theprobability exceeds 0.9 corresponds to the 90% confidence level α upper
limit and is defined as α90 . The sum of the probability as a functionof α is shown in Figure-9.4(bottom) and the dotted line shows the 90%
confidence level limit.
4. Multiplying the expected number of events shown in Table-6.1 by theobtained α90 , the 90% confidence level limit of the SRN events(Nlimit ) is
obtained. Similarly, multiplying the expected flux value by α90 gives us
the 90% confidence level flux upper limit(Flimit ).
Nlimit (> 16M eV ) = N (16 − ∞M eV ) × α90(9.13)

Flimit (> 16M eV ) = F (16 − ∞M eV ) × α90(9.14)

145

Number of event /550days /4MeV

SK3 spectrum fitting
12

DATA

10
8
6

Atm. neumu
Best fit

4

Atm. neue

2
0

20

30

40

50

60

70

80

Energy (MeV)
Figure 9.3: The result of the χ2 fitting for the distribution of the SK-III final
data sample, by Poissonian method, are shown. The LMA model was used
for getting this result. The data points are SK-III real data and the red andgreen dashed histograms represent the fitted backgrounds from atmospheric νe(and ν¯e ) and invisible µ-e decay. The black solid line shows the sum of bothbackgrounds.

However, N(F) is the predicted number of events(flux) for each model andis integrated for the region in parenthesis. Table-9.2 shows the numberof events and the flux upper limits at the 90% confidence level for nine
SRN theoretical models, for the analysis energy region (16MeV electronenergy corresdonds to 17.3MeV neutrino energy). The flux upper limits
were obtained for SK-I, SK-II and SK-III and for each SRN model. For
LMA model, 90% confidence level flux upper limits were < 2.6/cm2 /sec
(SK-I), < 5.0/cm2 /sec (SK-II) and < 5.9/cm2 /sec (SK-III), respectively.
The flux upper limits are summarized in Table-9.3.

Combined flux upper limit
The flux upper limit was obtained for SK-I, SK-II and SK-III individually. In
this section, a combined analysis using these three phase results is described.
The χ2 distributions for all three phases are summed up to obtain the combinedχ2 (=χ2comb ) distribution as follows.

146

Figure 9.4: The chi-squared, probability and sum of the probability distributions
are plotted as a function of alpha. The red dotted line shows the 90% confidence
lebel.

147

χ2comb = χ2SK−I + χ2SK−II + χ2SK−III(9.15)The χ2comb (and χ2 in each phase) distribution, as a function of α is shown in
Figure-9.5. α90 was obtained from the χ2comb distribution and is converted to the
90% confidence level flux upper limit. The 90% flux upper limits, corresponding
to Eν >17.3 MeV, obtained by this combined method are listed in Table-9.4.

50
45
40
35
30
25
20
15
10
5
0

-1

0

1

2

3

4

5

-1

0

1

2

3

4

5

1
0.8
0.6
0.4
0.2
0

Figure 9.5: The chi-squared(top) and sum of the probability(bottom) distributions, for the LMA model, are plotted as a function of alpha. Red is SK-I, green
is SK-II, and blue is SK-III respectively. The black line shows the combined χ2
distribution.

148

Theoretical model

SK-I(16-80 MeV)

SK-II
(18-82 MeV)

SK-III(16-80 MeV)LMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Cosmic Chemical evolution
Heavy metal abundance
Population synthesis
Cosmic SF history
SFR constraint
Failed supernova< 15.6< 15.2< 13.0< 14.4< 13.4< 14.7< 16.1< 17.4< 12.7< 14.2< 13.3< 11.2< 12.8< 12.8< 13.1< 14.2< 14.0< 11.1< 12.1< 12.0< 10.1< 11.3< 10.8< 11.6< 12.7< 12.3< 10.0

Table 9.2: The limit on the number of events for each model, by Poissonian
method, are listed for all three data taking phase. The fiducial volume was 22.5
kton for all three phases. The livetimes are 1496 days in SK-I, 791 days in SK-II
and 548 days in SK-III.

Theoretical model

SK-I
Eν >17.3MeV

SK-II
Eν > 19.3MeV

SK-IIIEν > 17.3MeV

LMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Cosmic Chemical evolution
Heavy metal abundance
Population synthesis
Cosmic SF history
SFR constraint
Failed supernova

< 2.6
< 2.7
< 2.5
< 2.6
< 2.5
< 2.6
< 2.7
< 2.6
< 2.8

< 5.0
< 4.9
< 4.2
< 4.8
< 4.8
< 4.8
< 4.9
< 4.9
< 5.3

< 5.9
< 5.9
< 5.5
< 5.9
< 5.7
< 5.9
< 6.0
< 5.9
< 6.1

Table 9.3: The upper limit on the anti-electron neutrino flux for each model,
by Poissonian method, are listed. All three data taking phases are listed. The
flux units are [/cm2 /sec].

149

Theoretical model

Flux limit (Eν >17.3 MeV)LMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Heavy metal abundanceCosmic Chemical evolution
Population synthesis
Cosmic SF history
SFR constraint
Failed supernova< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.0 ν¯e /cm2 /sec
< 2.0 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.2 ν¯e /cm2 /sec

Table 9.4: The combined 90% C.L. upper limit on the SRN flux, for each model,
by poissonian method. The second column is the flux limit for Eν >17.3MeV.

150

Chapter 10

Discussion
The SRN flux upper limit of < 2.0 - 2.2 /cm2 /sec (Eν > 17.3M eV ) was obtainedin the previous chapter. This obtained upper limit is compared with the SRN
theoretical models and other experimental results in this chapter.

10.1

Comparison with theoretical models

In this thesis, nine theoretical models were used to evaluate the SRN spectrum
shape. The flux upper limit was obtained for each model, all within the rangeof ∼ 2.0 - 2.2 /cm2 /sec. They are compared with the predicted flux from eachmodel and are discussed in this section.
The “LMA oscillation model” includes neutrino oscillation effects inside stars
and was calculated by Ando et al[26, 27]. Due to the oscillation effects, the ν¯espectrum becomes relatively harder and the predicted flux is higher among themodels we used in this analysis. The predicted flux for the neutrino region withenergy above 17.3 MeV(corresponding to 16 MeV of electron energy) is ∼ 1.7/cm2 /sec. The 90% flux upper limit obtained from the combined analysis was< 2.1 /cm2 /sec(Eν > 17.3 MeV). Our flux limit is higher than the prediction by∼ 20%. Figure-10.2(top) shows the predicted flux and the obtained flux limit
for this model. The black line shows the SRN spectrum. The upper region of
the red line is excluded by our 90% confidence level flux limit. Since we used
the spectrum fitting method, the flux limit curve is parallel with the model
spectrum. The main search region in our analysis is effectively up to ∼ 30
MeV. This is because the invisible muon background dominates above 30 MeV,
although spectrum fitting has been done up to 80 MeV.
The “Constant SN rate model” [21] predicts the largest flux by assuming a
constant rate of core collapse supernovae, since the beginning of the universe
till now. The predicted flux in this model is ∼ 4.6 /cm2 /sec for neutrino energy
above 19.3 MeV. The obtained flux limit was 2.1 /cm2 /sec and is already strict
enough to exclude this model prediction. Figure-10.2(middle) is the comparison
between the model prediction and our limit. The “Constant SN rate model” was151

excluded in our analysis, in the energy region of Eν > 17.3MeV(corresponding
to 16 MeV electron energy).
The “Cosmic gas infall model” [22] is predicts the smallest neutrino flux
among the nine models used in this analysis. The spectrum shape of this model
most sharply decreases with increasing energy. The spectrum shape is mostdifferent from the other background spectrum, so the lowest flux upper limit(<
2.0 /cm2 /sec for above 17.3 MeV) was obtained. However, this upper limit is stilllarger than the predicted flux(0.3 /cm2 /sec) by almost one order of magnitude.
The predicted spectrum and our limit is plotted in Figure-10.3(bottom).
According to the calculation of the “Cosmic chemical evolution model” [23],the flux should be about 0.6 /cm2 /sec. Our limit of < 2.1 /cm2 /sec is still
higher than the predicted flux by more than a factor of three. A comparison
between our limit and the predicted spectrum is shown in Figure-10.3.
The predicted flux of the “Heavy metal abundance model” [24] is between
0.4 and 1.8 /cm2 /sec. Comparing with our flux limit(< 2.0 /cm2 /sec), the prediction is ∼ 10% smaller in the maximum case of flux prediction. This indicates
our sensitivity is now close to the SRN detectable region for this model. Figure10.3(top) shows the predicted flux both in the maximum and the minimum case,as well as our flux limit.
The “Population synthesis model” [21] predicts a large flux when integrated
over all energy regions. However, the predicted flux above 17.3 MeV is thesecond smallest in all the models. This is because this model uses a supernova
rate which drops sharply as a function of the red shift parameter, and theneutrino energy is strongly redshifted below our energy threshold before reaching
the earth. The predicted flux is 0.5 /cm2 /sec, and the limit from this analysis
is 2.1 /cm2 /sec. Our limit is larger than that prediction by a factor of ∼ 4.
To dramatically increase the sensitivity for this model, we need to lower the
analysis energy threshold down to at least ∼ 10 MeV.
The “Cosmic SF history model” [28] predicts the second highest SRN flux
for above 17.3 MeV neutrino energy. This model predicts the SRN spectrum
using three different effective temperature of neutrinos(4, 6 and 8 MeV). In thecase of 6 MeV, which was used in our analysis, the predicted neutrino flux is
1.1 - 1.9 /cm2 /sec, above 17.3 MeV. This is not so far from our flux limit of< 2.1 /cm2 /sec. As shown in Figure-10.4(top), the case of 8 MeV effective
temperature is excluded by our 90% confidence level flux upper limit.
The “SFR constraint model” [29] gives a flux prediction of 0.7 /cm2 /sec,
above 17.3 MeV. This is the average of the maximum case and the minimumcase. Both cases are plotted in Figure-10.4(middle). Our limit of < 2.1 /cm2 /secis almost a factor of two larger than the maximum case of ∼ 1.1 /cm2 /sec.
Comparing with the minimum case of ∼0.4 /cm2 /sec, the difference from ourlimit is a factor five.
The predicted flux from the calculation of the “Failed SN model” [30] predicts
a hard spectrum due to higher energy neutrino emission from failed supernova
explosions. This flux is between 0.9 and 1.2 /cm2 /sec (> 17.3 MeV), depending
on a fraction of failed supernovae(9-22%) and other parameters. The spectra152in the maximum and minimum cases are shown in Figure-10.4(bottom). In thecase of the largest fraction of failed supernovae, the spectrum becomes hardest
and then the predicted flux above our energy threshold becomes higher. Since
we used the case of maximum failed supernovae fraction, the spectrum shape ishard, so that our flux limit for this model(< 2.2 /cm2 /sec) is larger than theother models. Comparing with the limit, the model prediction is smaller thanour limit by a factor of ∼ 2.

Figure 10.1: The flux upper limit and the predicted flux for each model above
19.3 MeV are shown. The uncertainty of the model prediction is represented byyellow arrows.

153

Figure 10.2: The flux limit vs the predicted SRN spectra are shown in thisfigure. The red line shows our 90% flux limit, obtained in the previous chapter.
Since we used the spectrum shape of each model, the obtained flux limit has thesame shape as each model. The black dashed line is the predicted SRN flux.

154Figure 10.3: The flux limit vs the predicted SRN spectra are shown in thisfigure. The red line shows our 90% flux limit, obtained in the previous chapter.
In the top figure, the dashed line is the minimum case of the prediction and thedotted line is the maximum case.

155

Figure 10.4: The flux limit vs the predicted SRN spectra are shown in thisfigure. The red line shows our 90% flux limit, obtained in the previous chapter.
In the middle and bottom figures, the dashed line is the minimum case of theprediction and the dotted line is the maximum case. In the top figure, thedifferent colors show the prediction with different effective temperatures.

156

Theoretical model

Predicted flux
(Eν >17.3MeV)

Flux limit(Eν >17.3MeV)

LMA neutrino oscillation
Constant SN rate
Cosmic gas infall
Heavy metal abundanceCosmic Chemical evolution
Population synthesis
Cosmic SF history
SFR constraint
Failed supernova

1.7 ν¯e /cm2 /sec
4.6 ν¯e /cm2 /sec
0.3 ν¯e /cm2 /sec
0.4-1.8 ν¯e /cm2 /sec
0.5 ν¯e /cm2 /sec
0.4 ν¯e /cm2 /sec
1.1-1.9 ν¯e /cm2 /sec
0.4-1.1 ν¯e /cm2 /sec
0.9-1.2 ν¯e /cm2 /sec

< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.0 ν¯e /cm2 /sec
< 2.0 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.1 ν¯e /cm2 /sec
< 2.2 ν¯e /cm2 /sec

Table 10.1: The combined 90% C.L. upper limit on the SRN flux for each model,
by Poissonian method. The second column is the flux limit for the energy region
above 16 MeV and the third column is for that above 18 MeV.

10.2

Comparison with other experiments

Our experimental result was compared with other experiments, e.g. Kamiokande,
SNO, KamLAND etc, in this section. The 90% confidence level flux upper limits
in this thesis were < 2.0 - 2.2 /cm2 /sec, depending on the spectrum shape ofthe used SRN model. Using the LMA model, the flux limit was < 2.1 /cm2 /sec,
which is better than other experimental result by an order of magnitude. Figure10.5 shows our flux limit(red line) and other experimental result in the unit ofneutrino flux(/cm2 /sec/M eV ), as a function of neutrino energy.
22
The green line shows the “KamLAND” result of <∼ 10 /cm /sec/, in theenergy range of 8 - 14 MeV. Although the search region is different from ouranalysis, their limit is larger than the prediction from the LMA model by anorder of magnitude or more.
The “Mont Blanc” result is shown as a light blue line. This limit is given forthe same energy region as our analysis, however, our limit is better than theirresult by more than three orders of magnitude.
The “SNO” experiment searched for electron neutrinos in the energy regionof 22.9 - 36.9 MeV. Their result showed the electron neutrino flux, for 22.9 - 36.9
MeV, is smaller than 70 /cm2 /sec. The flux of electron neutrinos, emitted fromcore collapse supernovae, is smaller than that of anti-electron neutrinos, above
the 20 MeV region as shown in Figure-1.5. So our flux limit is much closer tothe predicted SRN flux than the SNO result.
Previously, the “Kamiokande” result was the most strict limit, which was
obtained using the “Constant SN rate model”. The result from Kamiokande isshown as a pink line, which has a slope that is the same as the “Constant SN
rate model” spectrum. Even when comparing with this result, our flux limit isbetter by at least an order of magnitude.

157

Figure 10.5: The flux upper limit of our result and other experimental results areplotted. The horizontal axis is neutrino energy and the vertical axis is neutrino
flux in units of /cm2 /sec/M eV . For the SRN spectrum, the LMA model was
used.

158

Experiment
KamLAND
Mont Blanc
SNO
Kamiokande
Super-Kamiokande

Channel
ν¯e
ν¯e
νe
ν¯e
ν¯e

Energy window
8 - 1420 - 50
22.9 - 36.9
> 19
> 17.3Flux upper limit∼102
8.2 × 1037050
2.0 - 2.2

Table 10.2: The flux upper limit for each experiment. The third column isthe search window of neutrino energy. The units of the flux upper limit are/cm2 /sec.
As we discussed in this chapter, the flux upper limits obtained in thisanalysis(< 2.0 - 2.2 /cm2 /sec) are already close to the model predicting SRN
flux(0.3 - 4.6 /cm2 /sec). The difference between our limit and the prediction isless than one order of magnitude, even in the model which predict the smallest
SRN flux. Furthermore, some of the optimistic cases of SRN predictions were
excluded by this result. Comparing with other experimental results, our result
is much better by orders of magnitude.

159

Chapter 11

Conclusion
The diffuse supernova neutrino background from all the past supernova, known
to be Supernova relic neutrino (SRN), were searched for in Super-Kamiokande,
which is a large water Cherenkov detector located at 1000m underground in
the Kamioka mine. Three data taking phases were used in this analysis andeach phase has a livetime of 1496 days (SK-I), 791 days (SK-II) and 548 days
(SK-III). This is the first search for supernova relic neutrinos using SK-II and
SK-III data.
From the old SK-I analysis, we developed a new statistical method based on
the Poisson distribution which is more suitable for small statistics. We improved
the reduction method from SK-I old analysis in order to increase the efficiency
and to lower the energy threshold. This enabled us to lower the analysis energy
threshold down to 16 MeV from 18 MeV with better signal efficiency.
No evidence for supernova relic neutrino signals were found in this search.
The 90% confidence level upper limit on the SRN flux was obtained by the
Poissonian method and improved reduction method. The flux upper limits on
SRN ν¯e were obtained for nine theoretical models which predict the spectrum
and absolute flux of supernova relic neutrinos. The obtained flux limits bycombined analysis of SK-I, SK-II and SK-III range from 2.0 /cm2 /sec to 2.2/cm2 /sec (Eν > 17.3 MeV) depending on the spectrum shape of the SRN model
considered. Our results are now close to the predicted SRN flux ranging from
0.4 - 4.6 /cm2 /sec (Eν > 17.3 MeV).
The new result presented in this thesis supersedes the previous Super-Kamiokande
limit [16] based on the improved analysis method and the increased statistics.
The updated limit is an order of magnitude better than the values obtainedby other experiments.
Some of the optimistic predictions for the SRN are
excluded by this result.

160

Appendix A

Comparison with previous
result in SK
In this appendix, we compare the results with the previous SK-I result of < 1.2/cm2 /sec (>18 MeV). This previous result was obtained using almost the same
reduction process as for our SK-II analysis, except for the sub-event cut. In
addition, the inverse beta decay cross section used in the previous analysis wasoverestimated, especially in the higher energy region(see section 1.2.2). Thischanged the result by ∼ 20% overall. After applying the sub-event cut andusing the most recent cross section calculation, the flux upper limit becomes< 1.4/cm2 /sec using the Gaussian method and < 1.7 /cm2 /sec using the Poissonian method, both using the LMA model[27]. Since the data statistics is nothigh enough, the Poissonian method should be used to extract the flux upper
limit, even in SK-I. So the result of < 1.7 /cm2 /sec should be compared with
our new result.
Considering only the SK-I result of the new analysis, the flux upper limit is
1.9 /cm2/sec, for the LMA model. The new result is worse, meaning it is higher,
than the previous analysis. In order to understand this difference, the old andnew results are compared step by step. In this analysis, we improved the data
reduction to increase the efficiency of the SRN signal. By this improvement, theanalysis energy threshold was lowered from 18 MeV down to 16 MeV. Due tothe lower energy threshold, the binning used in the energy spectrum fitting was
also changed from 18 - 82 MeV, to 16 - 80 MeV, although bin width is exactly
the same(4 MeV/bin).
Table-A.1 shows the change of the flux upper limit, step by step.
We started from the SK-I old result of < 1.7 /cm2 /sec, by the Poissonian
method. After changing the cut criteria, but still using the same binning andenergy threshold of 18 MeV, the 90% confidence level flux limit becomes < 2.3/cm2 /sec.
Although our new reduction method achieved a better efficiency, the data
161

Table A.1: The change of the flux upper limit in SK-I from the previous result
is summarized. Starting from the old SK-I result, a new cut criteria is appliedat the second line. The binning is changed from 16-80MeV to 18-82MeV(energy
threshold is still 18MeV) at the third line. At last, the energy threshold is
lowered to 16MeV. The best fit α value is also listed in the right column. The
number shown in parentheses is the unphysical best fit value.

increased more than expected due to the efficiency increase. The expected SRN
spectrum for the LMA model in SK-I, by old reduction method(Green line),and new reduction method(Red line), are compared. Figure-A.2 shows theincreasing rate of data and MC as a function of energy. The data points show
the ratio of the number of events between the old and new reduction processesof the SK-I data. The green line shows the new/old ratio of MC events, whichmeans the increase of reduction efficiency. Above 34 MeV, the signal efficiency
become slightly worse due to the pion-like event cut and the multi-ring event
cut, which were newly added. However, these cuts can also remove background
events, making the S/N ratio better than in the old reduction method. As
shown in this figure, the efficiency was increased, mainly in the region below 34
MeV. Unfortunately, the increase of data is larger than the efficiency increase,even though the change is within statistical uncertainty. The best fit α value islisted in the right column of Table-A.1. In the old result, the best fit α value
was shifted to negative region by the statistical fluctuation. That is the reason
why old flux upper limit was smaller than our new limit.
Next, the binning of the fitting spectrum was changed from 18-82 MeV to
16-80 MeV, both with 4 MeV bin widths. The third line shows this binningchange, although the energy threshold remained at 18 MeV. By this change,
the flux upper limit for energies above 18 MeV becomes > 1.8 /cm2 /sec.
At last, the energy threshold was lowered from 18 MeV to 16 MeV(see bottom line in Table-A.1). After lowering the energy threshold, a flux limit of 1.9/cm2 /sec was obtained. This effect can be understood by noticing that there
is an excess of data below 18 MeV. In our method, the flux upper limit was
obtained assuming that all the events, other than invisible µ-e decay and atmospheric νe (and ν¯e ), were SRN signals. This method gives a conservative upper

162

3

2.5

2

1.5

1

0.5

0

20

30

40

50

60

70

80

Figure A.1: The expected energy spectrum of SRN events in SK-I with the
new/old reduction are compared using
the LMA model. The red is the new
reduction and the green is the old reduction. Events are increased mainly
below 34 MeV, due to the spallation
cut difference.

163

Figure A.2: The increase in number of
events from the old analysis method
are plotted. The efficiency increase expected from the MC is shown as thegreen line. The data increase is larger
than expected, although it’s within
statistical error.

limit.

164

Bibliography[1] K.S. Hirata et al. [The Kamiokande Collaboration], Phys. Rev. Lett. 58,
1490 (1987).
[2] R.M. Bionta et al. [The IMB Collaboration], Phys. Rev. Lett. 58, 1494
(1987).
[3] K.S. Hirata et al. [The Kamiokande Collaboration], Phys. Rev. D 38, 448(1988).
[4] C.B. Bratton et al. [The IMB Collaboration], Phys. Rev. D 37, 3361 (1988).
[5] A.M. Hopkins and J.F. Beacom Astrophys. J. 651, 142 (2006).
[6] H.A. Bethe, G.E. Brown, J.H. Applegate, J.M. Lattimer, Nucl. Phys. A324,
487 (1979)[7] A. Burrows, T.J. Mazurek, Astrophys. J. 259, 330 (1982)[8] M. Fukugita, T. Yanagida, Physics of Neutrinos, (Springer), ISSN 01725998[9] S. Yamada, J.-T. Janka, H. Suzuki, Astron. Astrophys. 344, 533 (1999)[10] T. Totani, K. Sato, H.E. Dalhed, J.R. Wilson, Astrophys. J. 496, 216(1998)[11] A. Burrows et al., Astrophys. J. 539, 865 (2000)[12] H. Suzuki, from Physics and Astrophysics of Neutrinos p. 763 (1994).
[13] T. Totani et al., Astrophys.J. 496, 216 (1998).
[14] K. Takahashi, M. Watanabe, and K. Sato, Phys. Lett. B 510, 189 (2001).
[15] A. Strumia and F. Vissani Phys.Lett. B564 42-54 (2003).
[16] M. Malek [The Super-Kamiokande collaboration] Phys. Rev. Lett 90,
061101 (2003)[17] G. S. Bisnovatyi-Kogan, S. F. Seidov, Ann. N.Y. Acad. Sci. 422, 319 (1984).
[18] L. M. Krauss, S. L. Glashow, and D. N. Schramm, Nature 310, 191 (1984).
165

[19] S. E. Woosley, J. R. Wilson, and R. Mayle, Astrophys. J. 302, 19 (1986).
[20] T. Totani and K. Sato, Astropart. Phys. 3, 367 (1995).
[21] T. Totani, K. Sato, and Y. Yoshii, Astrophys. J. 460, 303 (1996).
[22] R. A. Malaney, Astropart. Phys. 7, 125 (1997).
[23] D. H. Hartmann and S. E. Woosley, Astropart. Phys. 7, 137 (1997).
[24] M. Kaplinghat, G. Steigman, and T. P. Walker, Phys. Rev. D 62, 043001(2000).
[25] L. E.Strigari, M. Kaplinghat, G. Steigman, and T. P. Walker, J. Cosm. D
62, 043001 (2000).
[26] S. Ando, K. Sato, and T. Totani, Astropart. Phys. 18, 307 (2003).
[27] S. Ando, NNN05 conference in Aussois, France (2005).
[28] S. Horiuchi, J.F. Beacom and E. Dwek, Phys. Rev. D 79, 083013 (2009).
[29] M. Fukugita and M. Kawasaki Mon. Not Astron. Soc. 340, L7-L11 (2003).
[30] C. Lunardini, Phys. Rev. Lett. 102, 231101 (2009).
[31] A.M. Hopkins and J.F. Beacom, Astrophys. J. 651, 142 (2006).
[32] E. Cappellaro et al., Astron. Astrophys. 430, 83 (2005).
[33] T.Dahlen et al., Astrophys. J. 613, 189 (2004)[34] M.T. Botticella et al., Astron. Astrophys. 479, 49 (2008)[35] M.G. Hauser and E.Dwek, Annu. Rev. Astron. Astrophys. 39, 249 (2001)[36] S.M. Wilkins, N. Trentham, and A.M. Hopkins, Mon. Not. R. Astron. Soc.
385, 687 (2008)[37] Y. Fukuda et al. [The Super-Kamiokande Collaboration], Phys. Rev. Lett.
81, 1562 (1998).
[38] Y. Koshio et al. [The Super-Kamiokande Collaboration], Phys.Rev. D73
112001 (2006)[39] J.P. Cravens et al. [The Super-Kamiokande Collaboration], Phys.Rev. D78
032002 (2008)[40] M. Ikeda, Super-Kamiokande Collaboration meeting (2009)[41] S. Fukuda et al. [The Super-Kamiokande Collaboration], Phys. Rev. Lett.
86, 5656 (2001).
[42] W. Zhang et al. [The Kamiokande Collaboration], Phys. Rev. Lett. 61, 385(1988)
166

[43] K. S. Hirata, Search for Supernova Neutrinos at Kamiokande-II PhD thesis,
University of Tokyo (1991).
[44] B. Aharmim, et al., Astrophys. J. 653, 1545 (2006)[45] M. Aglietta et al., Astropart. Phys. 1, 1 (1992)[46] K. Eguchi et al., Phys. Rev. Lett. 92, 7 (2004)[47] H. Ikeda et al., Nucl. Inst. and Meth. A 261, 540 (1987)[48] T.K. Ohsuka et al., KEK Report 85-10 (1985)[49] J. George, Ph.D Thesis, University of Washington (1998)[50] A. Suzuki et al., Nucl. Instr. and Meth. A 329 299 (1993)[51] S. Fukuda et al. [The Super-Kamiokande Collaboration], Nucl. Instrum.
Methods Phys. Res. Sect. A 501, 418 (2003).
[52] M. Nakahata et al. [The Super-Kamiokande Collaboration], Nucl. Instrum.
Methods Phys. Res. Sect. A 421, 113 (1999).
[53] E. Blaufuss et al. Nucl. Instrum. Methods Phys. Res. Sect. A 458, 636(2001).
[54] M. Shiozawa Ph.D. thesis, University of Tokyo (1999).
[55] E. R. Davies, Machine Vision: Theory, Algorithms, Practicalities, Academic Press, San Diego (1997).
[56] C. Michael Lederer and Virginia S. Shirly, Table of Isotopes. John Wiley &Sons.
[57] P. Vogel and J. F. Beacom, Phys. Rev. D 60, 053003 (1999).
[58] S. Michael, Proceedings of 30th International Cosmic Ray Conference, 0213
(2007)[59] GEANT, CERN Program Library Long Writeup W5013 (1994).
[60] M. Honda et al., Phys. Rev. D 52, 4985 (1995).
[61] G. Battistoni et al., Astropart.Phys. 19 269 (2003) [Erratum-ibid. 19 291(2003)]. (http://www.mi.infn.it/˜battist/neutrino.html)[62] G. Barr et al., Phys. Rev. D 70, 0423006 (2004).
[63] A. Morel et al., Limnology and Oceanography 22, 709 (1977)[64] G. Mitsuka , Ph.D Thesis, University of Tokyo (2008)[65] Y. Hayato, Nucl. Phys. Proc. Suppl. 112, 171 (2002)[66] H. Ejiri, Phys. Rev. C 48, 1443 (1993)167

[67] K. Kobayashi et al., Nucl-ex / 0604006 (2006)[68] J.O. Johnson and T.A.—Gabriel, ORNL/TM 10340, (1988)[69] M. Gluck, E.Reya and A.Vogt, Z. Phys. C67, 433 (1995)[70] J. Kameda, Ph.D Thesis, University of Tokyo (2002).

168