Study of solar neutrinoenergy spectrum above 4.5 MeV
in Super-Kamiokande-I
Chikaori Mitsuda

Doctoral Programin Fundamental Science and Energy Technology
Graduate School of Science and Technology
Niigata University
February 2004

Acknowledgment
First of all, I would like to express my great appreciation to my adviser Prof. Kazumasa
Miyano. He introduced me to experimental physics and gave me ample encouragement. Unfortunately, he retired in March, 2003. He was unable to see the completion of this thesis.
Nevertheless, his great support and excellent advice are manifested in this thesis.
Next, I must thank Prof. N.Tamura and Prof. H.Miyata. They always encouraged andsupported me. Especially, Prof. N.Tamura guided me to complete this thesis. He always
encouraged me by his words. I got many significant words from him. Prof. H.Miyata gave me
many questions and advises in the private discussions with him. His advises were useful to drive
forward my study.
I acknowledge Prof. Y.Totsuka, previous spokesman of the Super-Kamiokande experiments
and Prof. Y.Suzuki, current spokesman. They gave me the opportunity to participate in suchan enthusiastic time of the study of the neutrino oscillation. Prof. Y.Suzuki, previous leader ofsolar neutrino analysis group, supported me to study solar neutrino analysis.
Special acknowledgement goes to Prof. M.Nakahata. I learned from him all of the experimental physics. He always gave me insightful words to aim at physical results. His serious
attitude showed me the style of a true scientist. He gave me lots of advice on analysis and many
opportunities to study experimental physics.
I am grateful to all members of the solar neutrino analysis group. Without their excellent
works, this thesis would never have been completed. I would like to thank Prof. Y.Fukuda, Dr.
Y.Takeuchi, and Dr. Y.Koshio, and Dr. K.Ishihara for their suggestions and advice about solar
neutrino analysis.
I would like to thank all the Super-Kamiokande collaborators for help with the experiments.
Especially, Prof. T.Kajita, Prof. Y.Itow, Prof. K.Kaneyuki, Prof. S.Moriyama, Dr. M.Miura,
Dr. M.Shiozawa, and Dr. Y.Obayashi, the members in USA: Prof. B.Svoboda, Dr. M.Vagins,
Dr. M.Smy, Dr. G.Guillian, Dr. M.Malek, and Mr. D.Liu, and the member in Korea: Dr.
J.H.Yoo, I often had useful discussions with them about the experiment. Particular thanks goesto Mr. Y.Gando, Mr. M.Ishitsuka and all the SK graduate students. They always encouragedme.
I also would like to deeply thank all graduate students in the High Energy Physics groupat Niigata university. The good conversation with members always refreshed me. I could makemyself at ease in my laboratory. Especially, Mr. Allister & Maricel Sanchez gave me a great
support for the English correction of this thesis. I want to thank him very much. I gratefully
acknowledge my best friends to support me throughout my life.
Finally, I thank my parents and my sisters very much for supporting to continue studying
physics. Without their help and understanding throughout my physicist life, I would neveraccomplish my study. This thesis is dedicated to them.

Abstract
Super-Kamiokande-I (SK-I) was operated for solar neutrino observation from May 31, 1996
to July 15, 2001. The measurement of the solar neutrino energy spectrum above 4.5 MeV ispresented in this thesis.
The deficit of solar neutrino flux compared to the predicted flux by solar standard model(SSM) has been discussed for over 30 years, and is called the “solar neutrino problem”. The
solution of the problem was recently concluded to be neutrino oscillation. For the oscillation
mechanism, there are possible four solutions (SMA, LMA, LOW and VO). To solve the oscillation
mechanism, a number of different fits to solar neutrino mixing and mass square difference as
oscillation parameters were performed using 1496 days of solar neutrino data in SK-I. A global
fit combining SK data with the solar neutrino interaction rates measured by Homestake, SNO,
Gallex/GNO and SAGE prefers a single allowed area, the Large Mixing Angle solution, at the
98.9% confidence level (C.L.) [2].
In order to decide the oscillation parameter, we need more precise measurements and morestatistics. Furthermore, we need to discuss an energy spectrum for the lower energy region so that
we can examine the distortion of solar neutrino energy spectrum due to neutrino oscillation. In
this thesis, the energy spectrum, including 4.5∼5.0 MeV energy range, is discussed. The analysis
threshold in SK-I has been limited to 5.0 MeV be the radon background in SK detector. By the
reduction of radon background and understanding the behavior of radon in SK, we succeededin observing for the first time the solar neutrino flux of the 4.5∼5.0 MeV energy bin using 511
days (from September 17, 1999 to July 15, 2001) of solar neutrino data in SK-I. Using 511 days
data set, the distortion of energy spectrum is discussed. Moreover, a number of different fits tosolar neutrino mixing and mass square difference were performed. The results including 4.5∼5.0
MeV data favored LMA and LOW solution by 95% C.L. and gives strong credit to the various
results gathered up to now from different aspect. Finally, it is suggested to lower the energy
threshold in the future for energy spectrum analysis of the solar neutrino.

Contents
1 Introduction

1

2 The Standard Solar Model and Solar Neutrino Observation
2.1 The Sun and the Standard Solar Model . . . . . . . . . . . . . . . . . . . . . . .
2.2 Nuclear energy generation in the Sun and the solar neutrino fluxes . . . . . . . .
2.3 The 8 B neutrino flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Solar neutrino experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Radiochemical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Kamiokande and Super-Kamiokande experiments . . . . . . . . . . . . . .
2.4.3 SNO experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Solar neutrino problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Neutrino oscillation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Vacuum oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Neutrino oscillation in matter . . . . . . . . . . . . . . . . . . . . . . . .
2.7 The evidence of solar neutrino oscillation . . . . . . . . . . . . . . . . . . . . . .
2.8 Global analysis of the solar neutrino data . . . . . . . . . . . . . . . . . . . . . .

3
3
7
11
11
13
15
17
18
20
20
22
26
27

3 Super Kamiokande
3.1 Detection principle in Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . .
3.2 Detector description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The outer detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 ID photomultiplier tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The water purification system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 The air purification system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 The data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 The inner detector system . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 The outer detector system . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 Real-time data process . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.5 The ID online and offline system . . . . . . . . . . . . . . . . . . . . . . .

32
32
35
38
38
39
40
43
46
46
50
50
50
53

4 Event Reconstruction
4.1 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Direction reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55
55
57
59

5 Calibration
5.1 PMT gain monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Xe calibration for relative gain of the PMTs . . . . . . . . . . . . . . . . .
5.1.2 Ni-Cf calibration for absolute gain of the PMTs . . . . . . . . . . . . . . .
5.2 Timing calibration of the PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63
63
63
64
66

i

5.3

5.4

5.5
5.6
5.7
5.8

Water transparency measurements . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Direct measurement of the water transparency . . . . . . . . . . . . . . .
5.3.2 Monitoring water transparency by penetrating muons . . . . . . . . . . .
Energy calibration by LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 The LINAC system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Energy calibration of SK detector . . . . . . . . . . . . . . . . . . . . . .
Angular resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertex resolution and shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy calibration by DT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigger efficiency measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68
68
69
72
72
74
82
82
84
90

6 General data reduction
92
6.1 The data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 First data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.1 Total photo-electron cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.2 Unfitted events cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.3 Fiducial volume cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.4 Veto event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.5 Time difference cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.6 Pedestal event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.7 Incomplete event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.8 Outer detector event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.9 Mismatch event cut in outer detector . . . . . . . . . . . . . . . . . . . . . 95
6.2.10 Noise event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.11 Clustered ATM hits event cut . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.12 First flasher event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.13 Goodness cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.14 Second flasher event cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.15 Bad energy cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 Spallation cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.4 Second data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4.1 Goodness stability cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4.2 Pattern likelihood cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.4.3 Rejection of noise hit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.5 Gamma cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7 The approaches to radon reduction
116
7.1 Solar neutrinos in Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Radon background in the SK tank water . . . . . . . . . . . . . . . . . . . . . . . 117
7.3 The upgrades of water system in March 2000. . . . . . . . . . . . . . . . . . . . . 117
7.4 Radon source search in the SK water purification system . . . . . . . . . . . . . . 118
7.5 Membrane Degasifier as new radon reduction system . . . . . . . . . . . . . . . . 120
7.6 Improvements of water system in October 2000 and in February 2001 . . . . . . 123
7.7 SK low-energy event rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.9 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8 Tight data reduction for 4.5 MeV
133
8.1 Tight Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.1.1 Tight cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.1.2 New fitting cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Monte Carlo simulation of the solar neutrino events . . . . . . . . . . . . . . . . 145
ii

8.3
8.4

Summary and Data quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Remaining background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

9 Results
151
9.1 Solar neutrino signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.2 Results of the flux measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.2.1 The results of total 8 B neutrino flux . . . . . . . . . . . . . . . . . . . . . 155
9.2.2 The results of 8 B neutrino flux from 4.5 to 5.0 MeV . . . . . . . . . . . . 157
9.3 Results of the energy spectrum measurement . . . . . . . . . . . . . . . . . . . . 159
9.4 systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.4.1 Correlated errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.4.2 Uncorrelated error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
10 Discussions
174
10.1 The distortion of solar neutrino energy spectrum . . . . . . . . . . . . . . . . . . 174
10.2 Constraints on neutrino oscillation from energy spectrum . . . . . . . . . . . . . 175
10.2.1 The allowed solutions from flux measurements . . . . . . . . . . . . . . . 175
10.2.2 Constraints from energy spectrum measurements . . . . . . . . . . . . . . 176
10.3 Combined constraints on neutrino oscillation . . . . . . . . . . . . . . . . . . . . 179
11 Conclusions and future prospect
18511.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
11.2 Future prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
A The 7 Be and hep neutrino flux
188
7
A.1 The Be neutrino flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
A.2 The hep neutrino flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B Detector simulation

191

C Reconstruction of cosmic ray muons

195

D Systematic uncertainties with LINAC calibration
198
D.1 LINAC beam energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
D.2 Systematic uncertainty with the LINAC system . . . . . . . . . . . . . . . . . . . 201
D.2.1 Uncertainty of the beam energy determination . . . . . . . . . . . . . . . 201
D.2.2 Beam correlated background . . . . . . . . . . . . . . . . . . . . . . . . . 201
D.2.3 Reflectivity of the end point of the beam pipe . . . . . . . . . . . . . . . . 201
D.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
D.3 The time and directional uniformity of the energy scale . . . . . . . . . . . . . . 201
D.3.1 The time uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
D.3.2 The directional uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
E Bad run selection to make data set
205
E.1 Real-time bad run selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
E.2 Non-real-time bad run selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
E.2.1 Bad run selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
E.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
F The probability function of solar signal for solar signal extraction
210
F.1 Old way to make the signal probability function . . . . . . . . . . . . . . . . . . . 210
F.2 The effect of smoothing for spectrum analysis . . . . . . . . . . . . . . . . . . . . 211
F.3 New way to make the signal probability function . . . . . . . . . . . . . . . . . . 214iii

G Day and Night flux with 4.5∼5.0 MeV data
217
G.1 Flux measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
G.2 Oscillation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

iv

List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9

The procedure of Solar Standard Model . . . . . . . . . . . . . . . . . . . . . . .
The different solar neutrino fluxes originate in the Sun . . . . . . . . . . . . . . .
The solar neutrino energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . .
The pp-chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The CNO cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electron number density, ne , vs. solar radius . . . . . . . . . . . . . . . . . . . .
Energy levels in the 8 B β + 8 Be(2α) decay chain . . . . . . . . . . . . . . . . . . .
The best-estimate (standard) 8 B neutrino spectrum . . . . . . . . . . . . . . . .
The comparison of the predictions of the standard solar model with the total
observed rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Fluxes of 8 B solar neutrinos, φ(νe ),φ(νµ,τ ) . . . . . . . . . . . . . . . . . . . . . .
2.11 Feynman diagrams of neutrino interaction in matter . . . . . . . . . . . . . . . .
2.12 MSW effect in the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 example of MSW effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14 electron density of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.15 example of MSW effect 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 definition of zenith angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.17 The 95% C.L. allowed regions which satisfy all four flux measurements . . . . . .
2.18 The expected energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.19 SSM flux independent excluded areas using the SK zenith spectrum shape alone
2.20 Allowed areas using only SK data and the SSM 8 B neutrino flux prediction. . . .
2.21 The combined fit to SK data and all rates . . . . . . . . . . . . . . . . . . . . . .

19
20
22
24
25
25
26
27
29
29
30
30
31

3.1 The definition of the Čerenkov angle . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 QCD correction and electroweak correction . . . . . . . . . . . . . . . . . . . . .
3.3 Energy dependences of total cross section . . . . . . . . . . . . . . . . . . . . . .
3.4 Differential cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 The energy spectrum of recoil electrons scattered by neutrino . . . . . . . . . . .
3.6 The integrated live time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Overview of the Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 The local detector coordinate system of SK. . . . . . . . . . . . . . . . . . . . . .
3.9 A super-module supports twelve ID PMTs and two OD PMTs . . . . . . . . . .
3.10 Schematic view of a 50 cm photomultipiler tube . . . . . . . . . . . . . . . . . . .
3.11 The single p.e. distribution from 50 m PMTs . . . . . . . . . . . . . . . . . . . .
3.12 The quantum efficiency of the PMTs and the relative Čerenkov spectrum . . . .
3.13 The time variation of dark rate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 The time variation of the number of dead PMTs . . . . . . . . . . . . . . . . . .
3.15 The time variation of high and low energy trigger rate . . . . . . . . . . . . . . .
3.16 A schematic view of the water purification system . . . . . . . . . . . . . . . . .
3.17 The time variation of the number of particles in the purified water . . . . . . . .
3.18 A schematic view of the air purification system . . . . . . . . . . . . . . . . . . .
3.19 The time variation of the number of particles in the purified air . . . . . . . . . .

33
34
34
34
35
36
37
37
39
40
40
40
41
41
41
43
44
45
45

v

5
9
9
10
10
11
12
12

3.20 Rn decay series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.21 The time variation of the radon concentration in various air of the SK water
system site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.22 The time variation of the radon concentration in various air of the SK dome site
3.23 The overview of DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.24 Trigger generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.25 The summary figure of on and offline system . . . . . . . . . . . . . . . . . . . .

47
47
48
51
54

4.1 Event display of a typical low energy event . . . . . . . . . . . . . . . . . . . . .
4.2 Absolute time distribution of hit PMTs . . . . . . . . . . . . . . . . . . . . . . .
4.3 Projection of the gooodness distribution for LINAC calibration events . . . . . .
4.4 Projection of the reconstructed vertex distribution for LINAC calibration events
4.5 The unnormalized probability density function for Čerenkov photon directions .
4.6 The acceptance function of the PMT . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Projection of the direction cosine distribution for LINAC calibration events . . .
4.8 occupancy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 The arrangement of PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Effective photo-cathode area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55
56
57
58
58
58
59
60
61
61

5.1 The Xe-system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The distribution of the corrected charge for all PMTs . . . . . . . . . . . . . . .
5.3 A schematic view of the Ni-Cf calibration system . . . . . . . . . . . . . . . . . .
5.4 The distribution of occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 The laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 The TQ map of a PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 A system for direct measurement of water transparency . . . . . . . . . . . . . .
5.8 The measurement of the water transparency . . . . . . . . . . . . . . . . . . . . .
5.9 The schematic view of how to calculate water transparency . . . . . . . . . . . .
5.10 correlation between distance and logarithm charge . . . . . . . . . . . . . . . . .
5.11 The time variation of water transparency . . . . . . . . . . . . . . . . . . . . . .
5.12 The time variation of water transparency for each zone . . . . . . . . . . . . . . .
5.13 The overview of the LINAC calibration system . . . . . . . . . . . . . . . . . . .
5.14 The end point of the beam pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.15 The trigger logic for LINAC calibration . . . . . . . . . . . . . . . . . . . . . . .
5.16 Examples of single and multi electron events . . . . . . . . . . . . . . . . . . . .
5.17 The scattered plot of vertex distribution . . . . . . . . . . . . . . . . . . . . . . .
5.18 The effective hit distribution of LINAC . . . . . . . . . . . . . . . . . . . . . . .
5.19 The distribution of the effective hit . . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 The polynomial fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.21 LINAC data and MC simulation energy distribution . . . . . . . . . . . . . . . .
5.22 Comparison LINAC data and MC simulation for energy spectrum . . . . . . . .
5.23 The energy deviation between the LINAC data and the MC simulation . . . . . .
5.24 The systematic energy difference . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.25 Energy resolution as a function of energy . . . . . . . . . . . . . . . . . . . . . .
5.26 The systematic energy resolution difference . . . . . . . . . . . . . . . . . . . . .
5.27 The angular distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.28 The angular resolution as a function of electron total energy . . . . . . . . . . . .
5.29 The distributions of distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.30 The vertex resolution as a function of electron total energy . . . . . . . . . . . .
5.31 Schematic of the DTG setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.32 An overview of DTG data taking . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.33 Energy spectrum for Data and MC . . . . . . . . . . . . . . . . . . . . . . . . . .
5.34 Position dependence of the energy scale from DTG data . . . . . . . . . . . . . .

64
65
65
66
67
67
68
69
70
71
71
72
73
73
75
75
76
76
77
78
78
79
80
80
81
81
82
83
84
85
86
87
88
89

vi

46

5.35 Angular dependence of energy scale from DTG data . . . . . . . . . . . . . . . .
5.36 The SLE trigger efficiency as a function of energy by DT calibration . . . . . . .

90
91

6.1 Distribution of total photo-electron number . . . . . . . . . . . . . . . . . . . . . 93
6.2 Fiducial volume cut applied to a typical data sample . . . . . . . . . . . . . . . . 94
6.3 The distribution of time difference . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.4 The distribution of OD hits after OD trigger cut . . . . . . . . . . . . . . . . . . 96
6.5 The event display of one of noise event . . . . . . . . . . . . . . . . . . . . . . . . 97
6.6 The distribution for noise cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.7 The event display of typical flasher event . . . . . . . . . . . . . . . . . . . . . . 98
6.8 The flasher cut criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.9 The cut of goodness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.10 The example of direction test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.11 The validity check of directional test . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.12 The distributions of Dirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.13 The second flasher events cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.15 The position dependence of dead time . . . . . . . . . . . . . . . . . . . . . . . . 104
6.16 The original reconstructed vertex is situated at the center . . . . . . . . . . . . . 105
6.17 The calculated Rbad distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.18 The vertex distribution before and after the GRINGO cut . . . . . . . . . . . . . 106
6.19 The energy distribution before and after GRINGO cut. The hatched area shows
after GRINGO cut at the typical data sample. . . . . . . . . . . . . . . . . . . . 107
6.20 The definition of the θP M T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.21 The distribution of the pattern likelihood function for the ring image . . . . . . . 107
6.22 The likelihood distribution for the solar neutrino . . . . . . . . . . . . . . . . . . 108
6.23 The likelihood distributions from the typical data sample . . . . . . . . . . . . . 109
6.24 The definition of rejecting noise hits . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.25 The distance distribution from the wall before and after the Clusfit cut . . . . . 109
6.26 The definition of effective distance . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.27 The typical vertex distribution before and after the gamma cut . . . . . . . . . . 111
6.28 The final Z vertex distribution by general reduction . . . . . . . . . . . . . . . . 111
6.29 The final R2 vertex distribution by general reduction . . . . . . . . . . . . . . . . 111
6.30 The final zenith direction distribution by general reduction . . . . . . . . . . . . 112
6.31 The final azimuth direction distribution by general reduction . . . . . . . . . . . 112
6.32 Energy spectrums after each reduction step . . . . . . . . . . . . . . . . . . . . . 113
6.33 The expected energy spectrum of daughter nucleus from radon of Radium andThorium series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.34 The hit pattern distribution of cos θ P M T for MC of possible background source . 115
7.1 The cos θsun distribution for each energy thresholds in low energy region . . . . . 116
7.2 The flow chart of the SK water system . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3 The radon concentration at each water system components . . . . . . . . . . . . 120
7.4 Setup to measure radon reduction efficiency of a MD module . . . . . . . . . . . 121
7.5 A typical variation for the MD test runs . . . . . . . . . . . . . . . . . . . . . . . 123
7.6 A typical variation before and after water system improvement in October 2000 . 124
7.7 History of the expected radon concentration in SK tank . . . . . . . . . . . . . . 125
7.8 SK water supply configuration and convection model in SK tank . . . . . . . . . 127
7.9 Z dependence of the SK water temperature . . . . . . . . . . . . . . . . . . . . . 128
7.10 Z Vertex distribution of the low-energy events . . . . . . . . . . . . . . . . . . . . 128
7.11 Setup to measure Z dependence of radon concentration in SK tank . . . . . . . . 130
7.12 Z dependence of Radon concentration in SK tank . . . . . . . . . . . . . . . . . . 130
7.13 The schematic view the ratio of background contamination . . . . . . . . . . . . 131vii

7.14 The improvement of SK water supply pipe . . . . . . . . . . . . . . . . . . . . . . 132
8.1
8.2
8.3
8.4
8.5
8.6
8.7

The run progress of the trigger threshold . . . . . . . . . . . . . . . . . . . . . . . 134
The run progress of the trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . 135
The progress of the background event rate (events/day) from 4.5 to 6.5 MeV . . 136
The event rates for each energy region . . . . . . . . . . . . . . . . . . . . . . . . 136
The decided event rate threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
The significance results for the gamma cut distance . . . . . . . . . . . . . . . . . 138
The vertex R2 distribution in the energy region from 4.5 to 5.0 MeV for eachgamma cut distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.8 The significance plots for the GRINGO cut value . . . . . . . . . . . . . . . . . . 139
8.9 The vertex distribution before and after the strong GRINGO cut . . . . . . . . . 140
8.10 The vertex distribution of R2 and Z distribution with best cut point for the radius
and the height of tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.11 The vertex distribution in 2 dimensions (x versus y cm) from 4.5 to 5.0 MeV . . 142
8.12 The performance of the BONSAI vertex reconstruction in the energy region from
4.5 to 5.0 MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.13 The difference of the vertex position between current fitter and BONSAI fitter . 144
8.14 The reduction efficiencies for each reduction using BONSAI vertex . . . . . . . . 144
8.15 The R2 and Z vertex distribution before and after the three reductions using
BONSAI vertex information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.16 The direction distribution before and after the three reductions using BONSAI
vertex information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.17 The energy distribution for summarized reduction steps . . . . . . . . . . . . . . 147
8.18 The energy distribution of the S/N ratio for each reduction step. . . . . . . . . . 148
8.19 The vertex distribution in the energy region 4.5 to 5.0 MeV after all reductions . 149
8.20 The direction distribution in the energy region 4.5 to 5.0 MeV after all reductions 149
9.1
9.2
9.3
9.4
9.5
9.6

The definition of cos θsun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
The cosθsun distribution of all events(E = 4.5 ∼ 20.0MeV) . . . . . . . . . . . . . 151
The probability density function for signal . . . . . . . . . . . . . . . . . . . . . . 152
The probability density function for background . . . . . . . . . . . . . . . . . . 153
The SSM prediction of the number of solar neutrino recoil electrons in SK detector156
The cos θsun distribution for 5.5∼6.0, 5.0∼5.5 and 4.5∼5.0 MeV energy regionsof the data set III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9.7 The expanded plot of the cos θsun distribution for 4.5∼5.0 MeV energy region . . 158
9.8 The cos θsun distribution in each energy bin from 4.5 to 9.0 MeV . . . . . . . . . 160
9.9 The cos θsun distribution in each energy bin from 9.0 to 13.5 MeV . . . . . . . . 160
9.10 The cos θsun distribution in each energy bin from 13.5 to 20.0 MeV . . . . . . . . 161
9.11 The measured solar neutrino recoil electron energy spectrum . . . . . . . . . . . 161
9.12 The ratio of the measured recoil electron energy spectrum to the predicted spectrum162
9.13 The ratio of the measured recoil electron energy spectrum to the predicted spectrum163
9.14 The total correlated errors for each energy bin . . . . . . . . . . . . . . . . . . . 165
9.15 The progress of the simulated trigger efficiency by solar neutrino MC and the live
time average of the trigger efficiency by the DT calibration . . . . . . . . . . . . 166
9.16 The summary of the trigger efficiency for the solar neutrino MC and the DT
calibration in each trigger threshold . . . . . . . . . . . . . . . . . . . . . . . . . 167
9.17 The fluctuation of probability function of P bg . . . . . . . . . . . . . . . . . . . . 170
9.18 The total uncertainty with the energy spectrum. . . . . . . . . . . . . . . . . . . 172

10.1 The comparison between the energy spectrum and the expected energy spectrum
for the vacuum oscillation solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 177

viii

10.2 The comparison between the energy spectrum and the expected energy spectrum
for the MSW solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.3 The comparison between the energy spectrum and the expected energy spectrum
for the global minimum χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
10.4 The allowed and excluded region in “ Energy spectrum analysis” . . . . . . . . . 181
10.5 The allowed and excluded region in “ Energy spectrum and global analysis” . . . 181
10.6 The allowed and excluded region in “ Energy spectrum and global analysis with
SNO(CC) constrain” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
10.7 The comparison of the global analysis with the SNO(CC) flux constraint between
the data set II without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
10.8 The comparison of the global analysis with the SNO(CC) flux constraint between
the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
11.1 The KamLAND result is overlaid with the results of global analysis for solar
neutrino experiments (Chlorine, Gallium, SK, SNO). . . . . . . . . . . . . . . . . 187
11.2 The expected spectrum from KamLAND result and the energy spectrum of thisthesis with 4.5∼5.0 MeV data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
11.3 The water temperature with the height of the tank in SK-I and SK-II . . . . . . 187
A.1 Predicted versus measured sound speeds . . . . . . . . . . . . . . . . . . . . . . . 189
A.2 Normalized solar luminosity vs. solar age . . . . . . . . . . . . . . . . . . . . . . 190
B.1 The water attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
B.2 The reflectivity of the PMT and black sheet . . . . . . . . . . . . . . . . . . . . . 193
B.3 The charge distribution of 1 photo-electron response . . . . . . . . . . . . . . . . 194
C.1 The definition of the variables used by second muon reconstruction . . . . . . . . 196
C.2 The track resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
D.1
D.2
D.3
D.4
D.5
D.6

The view of the air-core beta spectrometer . . . . . . . . . . . . . . . . . . . . . . 199
The results of the Ge detector calibration . . . . . . . . . . . . . . . . . . . . . . 199
The energy measurement by Ge detector . . . . . . . . . . . . . . . . . . . . . . . 200
The energy spectrum of the spallation events . . . . . . . . . . . . . . . . . . . . 202
Time variation of energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
The directional dependence of the energy scale . . . . . . . . . . . . . . . . . . . 204

E.1 The rejected time by the log book check . . . . . . . . . . . . . . . . . . . . . . . 207
E.2 The detector live time after bad run selection . . . . . . . . . . . . . . . . . . . . 208
F.1
F.2
F.3
F.4
F.5
F.6
F.7
F.8
F.9

The definition of the zenith angle division . . . . . . . . . . . . . . . . . . . . . . 211
The original XANG cosθsun distribution of all events(E = 8.0 ∼ 9.0MeV) . . . . 212
The smoothing XANG cosθsun distribution of all events(E = 8.0 ∼ 9.0MeV) . . . 212
The bad example of the smoothing XANG for cosθ sun distribution . . . . . . . . 213
The ratio between the energy spectrum result by using smoothing XANG and byusing no smoothing XANG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
The ratio between the zenith energy spectrum result by using smoothing XANG
and by using no smoothing XANG . . . . . . . . . . . . . . . . . . . . . . . . . . 214
The results of oscillation analysis by using zenith energy spectrum . . . . . . . . 215
The outline of the new method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
The agreement between the fitting results and the original XANG in the energy
region from 8.0 to 9.0 MeV and the zenith angle from 0.00 to 0.16. . . . . . . . . 216

ix

G.1 The time variation of the ratio of the measured flux to the SSM prediction . . . 218
G.2 The ratio of the measured day time and night time energy spectrum to the predicted spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
G.3 The ratio of the measured day time and night time energy spectrum to the predicted spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
G.4 The comparison between day-night energy spectrum and the expected day-night
spectrum for each allowed solution . . . . . . . . . . . . . . . . . . . . . . . . . . 222
G.5 The comparison of result for global analysis with SNO(CC) flux constraints between the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0
MeV data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

x

List of Tables
2.1
2.2
2.3
2.4
2.5
2.6

Lists some of the main physical characteristics of the Sun . . . . . . . . . . . . .
Neutrino-producing reactions in the Sun . . . . . . . . . . . . . . . . . . . . . . .
Solar neutrino detection rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recent results from the seven solar neutrino experiments . . . . . . . . . . . . . .
Comparison between Super-Kamiokande-I and Kamiokande-II . . . . . . . . . . .
Expected solution from flux constrains . . . . . . . . . . . . . . . . . . . . . . . .

3
6
7
13
16
28

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9

Measured background radiation rates for γ rays and neutrons . . . . . . . . . . .
Several parameters of Super-Kamiokande detector . . . . . . . . . . . . . . . . .
The summary of the quality of the purified water. . . . . . . . . . . . . . . . . .
The summary of the Rn concentration . . . . . . . . . . . . . . . . . . . . . . . .
The summary of the temperature in the various places . . . . . . . . . . . . . . .
The data structure of ATM for 1 channel . . . . . . . . . . . . . . . . . . . . . .
The trigger ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The summary of the switch of LE and SLE trigger threshold . . . . . . . . . . .
Data format of SMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
38
43
46
49
49
51
52
53

5.1
5.2
5.3
5.4
5.5

The averaged transparency for each zone . . . . . . . . . . . . . . . . . . . . . . .
The list of the positions where LINAC data was taken . . . . . . . . . . . . . . .
The vertex shift measured by the Ni-Cf source . . . . . . . . . . . . . . . . . . .
Summary of information used in modeling the beta decay . . . . . . . . . . . . .
Summary of systematic errors from the DTG calibration . . . . . . . . . . . . . .

70
74
84
88
89

6.1

The table of reduction step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.1
7.2
7.3
7.4
7.5

A summary of Uranium/Thorium concentration . . . . . . . . . . . . . . . . . . . 118
The radon concentration at each water system components . . . . . . . . . . . . 119
The specification of a membrane degasifier module . . . . . . . . . . . . . . . . . 121
A summary of the radon reduction efficiency of the MD module . . . . . . . . . . 122
A comparison of the radon concentration between before and after the October2000 improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Radon detection efficiency in SK detector . . . . . . . . . . . . . . . . . . . . . . 126
SK supply water configuration and temperature of SK supply water . . . . . . . 127
Radon emanation from various materials . . . . . . . . . . . . . . . . . . . . . . . 129
Z dependence of the radon concentration in SK tank. . . . . . . . . . . . . . . . . 130

7.6
7.7
7.8
7.9
8.1
8.2
8.3
8.4
8.5
8.6

The summary of the trigger efficiency from 4.5 to 5.0 MeV . . . . . . . . . . . . . 134
The summary of the best parameters of the fiducial volume cut . . . . . . . . . . 140
The summary of the reduction efficiencies for the solar neutrino events . . . . . . 145
The table of the reduction steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
The summary of the calculation results for the S/N ratio and the significance . . 148
The summary of the expected radon concentration in the bottom region of the
SK tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

xi

8.7

The radon detection efficiency in the SK detector . . . . . . . . . . . . . . . . . . 150

9.1
9.2
9.3
9.4
9.5
9.6
9.7

The live-time summary for each trigger threshold in data set I,II . . . . . . . . . 155
The live-time summary for each trigger threshold in data set III . . . . . . . . . . 156
The expected event rates in the SK detector by SSM prediction . . . . . . . . . . 157
The numerical summary of the recoil electron energy spectrum . . . . . . . . . . 162
The numerical results for the correlated error . . . . . . . . . . . . . . . . . . . . 164
The summary of the LE trigger efficiency . . . . . . . . . . . . . . . . . . . . . . 165
The summary of the live time average of the SLE trigger efficiency by the DT
calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9.8 The numerical results of uncertainties with the trigger efficiency for each energy
region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
9.9 The uncertainty with the IT trigger efficiency . . . . . . . . . . . . . . . . . . . . 168
9.10 The uncertainty with the 1st reduction . . . . . . . . . . . . . . . . . . . . . . . . 168
9.11 The uncertainty with the spallation cut . . . . . . . . . . . . . . . . . . . . . . . 168
9.12 The uncertainty with the 2nd reduction . . . . . . . . . . . . . . . . . . . . . . . 169
9.13 The uncertainty with the gamma cut . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.14 The uncertainty with the tight data reduction . . . . . . . . . . . . . . . . . . . . 169
9.15 The uncertainty with the vertex-shift . . . . . . . . . . . . . . . . . . . . . . . . . 170
9.16 The uncertainty with the non-flat background . . . . . . . . . . . . . . . . . . . . 171
9.17 The uncertainty with the angular resolution . . . . . . . . . . . . . . . . . . . . . 171
9.18 The uncertainty with the likelihood fit . . . . . . . . . . . . . . . . . . . . . . . . 171
9.19 The uncertainty with the cross section . . . . . . . . . . . . . . . . . . . . . . . . 172
9.20 The uncertainty with the live time calculation . . . . . . . . . . . . . . . . . . . . 172
9.21 The numerical results for the total error . . . . . . . . . . . . . . . . . . . . . . . 173
10.1 The minimum value of this χ2 is obtained by numerically varying the free parameters for energy spectrum distortion . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.2 The local minimum of χ2 for global analysis . . . . . . . . . . . . . . . . . . . . . 176
10.3 The summary of the numerical results for χ 2 examination for each oscillation
solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
B.1 parameters of index of refraction of water . . . . . . . . . . . . . . . . . . . . . . 192
C.1 The fitting efficiency of muon events . . . . . . . . . . . . . . . . . . . . . . . . . 197
D.1 The correlation between D1 magnet and measured energy . . . . . . . . . . . . . 200
D.2 LINAC systematic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
E.1 The summary of number of the rejected sub-runs by the real-time bad run selection206
E.2 The manual bad run selection summary . . . . . . . . . . . . . . . . . . . . . . . 209
F.1 The region of the zenith angle division . . . . . . . . . . . . . . . . . . . . . . . . 210
G.1 The mean distance between the sun and the earth in this analysis . . . . . . . . . 217
G.2 Numerical results of the flux of night time divided into 5 . . . . . . . . . . . . . . 219
G.3 The numerical summary of the day time and the night time recoil electron energy
spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

xiiChapter 1

Introduction
Over 4.6 billion years, a huge amount of energy is produced in the Sun through nuclear fusion.
As it shines, it radiates energy at a rate of 3.8×10 26 J per seconds. The generated energy is
primarily released as photons, which slowly diffuse their way to the surface of the Sun over thecourse of ∼ 105 years. We are usually looking at the surface information of the Sun, which
is transmitted by photons, by traditional optical observations. However, all information thesephotons might contain regarding the nuclear reactions that created them is lost in the repeatedinteractions these photons undergo as they percolate out of the Sun. On the other hand, theneutrinos which are created in the core can provide direct information of the center of the Sun.
Because, the neutrinos have very small reaction cross section, even in the highest density regionsof the Sun. Solar neutrinos can pass through very dense matter that we never achieve on theearth and they travel the long distance of 1.5×10 8 km from the Sun to the earth. Thus, the studyof solar neutrinos can serve as important test for theories of stellar evolution and structure.
The study of neutrinos is also interesting from particle physics perspective. The neutrino,
denoted ν, is a particle whose existence was proposed by W.Pauli in 1930 to explain the apparent
energy deficit in β decay. It was discovered in the 1950s by F.Reines and C.L.Cowan who
observed neutrinos radiated from a reactor. The neutrino is a lepton which has a spin of (1/2),
no electric charge, and possibly a very small mass. There are three types of neutrinos. Each
type is associated with charged massive leptons, such as electrons, muons, and tau leptons. A
neutrino interacts with other particles only via the weak interaction, so that the cross sectionof interaction is very small. Owing to this small interaction cross section, one can observe thesolar core by the solar neutrino. Such characteristic conditions provide us an opportunity toinvestigate almost unknown properties of neutrinos such as their mass and magnetic moment.
The first solar neutrino detection experiment was carried out by R.Davis and his collaborators
using neutrino capture by 37 Cl. This experiment operated until 1998 and the latest results
show that the observed flux is 33% of the expected flux. Successive observations have reported
significant solar neutrino deficits, too. This is known as the solar neutrino problem. The most
likely solution for the deficits is neutrino oscillation, which is a phenomenon where a neutrinochanges its flavor while propagating. It has been assumed that neutrinos are massless, but theneutrino oscillation indicates that at least some flavors of neutrinos are massive.
Super-Kamiokande (SK) measures the energy of recoil electrons via elastic scattering of
the solar neutrinos and electrons in real-time. Therefore, it has the ability to observe both adistortion of the energy spectrum and daytime-nighttime variation of the flux. In SK, solar
neutrino data has been accumulated since 1996. The observed solar neutrino energy spectrum
is unique in the world so far. The first detector operation of SK (SK-I) had been done from
April 1, 1996 to July 15, 2001 [1].
Solar neutrino has been observed by four old different experiment and new two experiments:
the Homestake experiment which uses Cl nuclei as a target [8], Kamiokande which used electronsin H2 O molecules, and GALLEX [18]/GNO [13] and SAGE [22] which use Ga as a target, andas new experiments SK which uses same principle as Kamiokande, and SNO which use heavy
1

water, D2 O molecules [27]. All experiments have confirmed ’Solar neutrino problems’ and solar
neutrino oscillations between two active flavors. From most recent results, electron densities in
the Sun and the earth can strongly affect the oscillation probability.
In this thesis, neutrino oscillations between two active neutrinos, ν e and νµ,τ , is examined byusing recoil electron energy spectrum of solar neutrino. Then, the distortion of energy spectrumwith 4.5∼5.0 MeV data for various solutions of neutrino oscillation is discussed using 511 days
SK-I data selected from the full data of SK-I 1496 days. It also treated the technical aspect ofbackground reduction to lower the energy threshold from 5.0 to 4.5 MeV.
A detailed description about the theoretical and experimental background is given in Chapter
2. SK and its current status with other solar neutrino experiments throughout the world isdiscussed in Chapter 3. In Chapter 4, the methods on how to reconstruct the vertex, direction,and energy of an event are presented. Calibrations of the SK detector are described in Chapter
5. The general data reduction in SK solar neutrino analysis is explained in Chapter 6. Up to
Chapter 6, the outline of solar neutrino analysis in SK is being introduced.
From Chapter 7, the approach to observe low energy solar neutrino is described. Especially,
the radon background reduction from the hardware aspect is explained in Chapter 7. As themain topic of this thesis, the tight data reduction to analyze 4.5∼5.0 MeV data is presented in
Chapter 8. Chapter 9 gives the results of 511 days data set and the observed solar neutrino fluxin the 4.5∼5.0 MeV energy region. The distortion of solar neutrino energy spectrum above 4.5
MeV is discussed in Chapter 10. Chapter 11 presents the conclusions of this thesis and future
prospects to lower the energy threshold in the future of SK.

2

Chapter 2

The Standard Solar Model and Solar
Neutrino Observation
In this chapter, the theory and other solar neutrino experiments are explained. As the theory,an account of the Standard Solar Model (SSM), and the Mikheyev, Smirno, Wolfenstein (MSW)
effect are given. The SSM describes stellar evolution and predicts the flux of solar neutrinos.
The MSW effect, which describes the propagations of massive neutrinos through matter, opensa pioneering way to solve the contradiction between the SSM prediction and observed data.
Deficits in the observed solar neutrino flux, which is widely known as the solar neutrino problem,
are also explained. Lastly, as the most likely solution of the solar neutrino problem, the neutrino
oscillation is explained.

2.1

The Sun and the Standard Solar Model

The Sun is an astronomical laboratory. Because of its proximity to the Earth, we are able toobtain information about the Sun that is not accessible for other stars. We can measure with
precision solar parameters that are known to only one or two significant figures for any otherstar. For example, we can determine precise values for the solar mass, radius, geometric shape,
photon spectrum, total luminosity, surface chemical composition, and age. They are listed inTable 2.1
Parameter
Photon luminosity
Neutrino luminosity
Mass(M )Radius(R )Effective surface temperature
Age
Initial helium abundance by mass
Initial heavy element abundance by mass
Depth convictive zone
Central density
Central temperature
Central hydrogen abundance by mass

Value
3.86×1033 erg s−1
0.023L
1.99×1033 g
6.96×1010 cm
5.78×10 3 K
4.57×109 yr
0.27
0.020
0.26R
148 g cm −3
15.6×106 K
0.34

Table 2.1: Lists some of the main physical characteristics of the Sun[Dicke, Kuhn, and Libbrecht(1985) [28]]3In order to understand the solar neutrino problem, one needs to know the main ingredients ofthe theory of stellar evolution that are used in the construction of the solar models. The Sun isassume to be spherical and to have evolved quasi-statically (from one approximately equilibrium
configuration to another approximately equilibrium configuration) for a period of about 5×10 9
yr. Evolution is manifested by the loss of photons from the surface of the star, which in turnis balanced by the burning of protons into α-particles in the core of the Sun. It produces anintense flux of electron neutrinos as a consequence of nuclear fusion reactions whose combined
effect is
4p → 4 He + 2e+ + 2νe .

(2.1)

Positrons annihilate with electrons. Therefore, when considering the solar thermal energy
generation, a relevant expression is
4p + 2e− → 4 He + 2νe + 26.73 MeV − Eν ,(2.2)

where Eν represents the energy taken away by neutrinos, with an average value being E ν ∼0.6
MeV. The thermal energy of 26.73 MeV is released for every four protons burned. Each conversion of four protons to an α-particle is known as a termination of the chain of energy-generating
reactions that accomplishes the nuclear fusion. The thermal energy that is supplied by nuclear
fusion ultimately emerges from the surface of the Sun as sunlight. Energy is transported in the
deep solar interior mainly by photons, which means that the opacity of matter to radiation isimportant. The pressure that supports the Sun is provided largely by the thermal motions of
the electrons and ions.
Some of the principal approximations used in constructing standard solar models deserve
special emphasis because of their fundamental roles in the calculations. These approximations
have been investigated carefully for possible sources of departure from the standard scenario.
1. Hydrostatic equilibrium
The Sun is assumed to be in hydrostatic equilibrium, that is, the radiative and particle
pressures of the model exactly balance gravity.
2. Energy transport by photons or by convective motions
In the deep interior, where neutrinos are produced, the energy transport is primarily byphoton diffusion.
3. Energy generation by nuclear reactions
The primary energy source for the radiated photons and neutrinos is nuclear fusion, although the small effects of gravitational contraction (or expansion) are also included.
4. Abundance changes caused solely by nuclear reactions
The initial solar interior is presumed to have been chemically homogeneous. In regionof the model that are stable to matter convection, changes into the local abundances ofindividual isotopes occur only by nuclear reactions.
A standard solar model is the end product of a sequence of models. A standard solar modelis based on the standard theory of stellar evolution. A variety of input information is needed in
the evolutionary calculations. In this thesis, the adopted SSM is a model developed by Bahcall,Basu, and Pinsonneault. It is called “BP2000”(Φ νe = 5.05 × 106 · cm−2 · s−1 ) from now on.
The most elaborate SSM, BP2000 is constructed with the best available physics and input data.
Though they used no helioseismological constraints in defining the SSM, the calculated soundspeed as a function of the solar radius shows an excellent agreement with helioseismologicallydetermined sound speed to precision of 0.1% rms throughout essentially the entire Sun. This4

greatly strengthens confidence in the solar model. The BP2000 prediction for the flux is shownin Table 2.2. Contributions to the event rates in chlorine and gallium solar neutrino experimentsfrom each neutrino-producing reaction are listed in Table 2.3.
By “the standard solar model,” we mean the solar model that is constructed with the best
available physics and input data. All of the solar models we consider, standard or “deviant”
models, are required to fit the observed luminosity and radius of the Sun at the present epoch, aswell as the observed heavy-element-to-hydrogen ratio at the surface of the Sun. No helioseismological constraints are used in defining the standard model. Naturally, standard models improvewith time, as the input data are made more accurate, the calculation techniques become fasterand more precise, and the physical description is more detailed.
Figure 2.1 shows the procedure of Solar Standard Model which have been changed by precise
physical data. The figure also shows the experimental results using Chlorine as a target of thesolar neutrino. Even if the solar standard model was slightly changed, there is still a deficit ofsolar neutrinos between the predicted flux and the observed flux.

Figure 2.1: The procedure of Solar Standard Model (http://www.sns.ias.edu/ j̃nb/).
The SSM predicted 8 B solar neutrino flux is proportional to the low-energy cross section
factor S17 (0) for the 7 Be(p, γ)8 B reaction. The BP2000 [29] and Turck-Chieze et al. . [30] models
adopted S17 (0) = 19+4
−2 eV·b. Inspired by the recent precise measurement of the low-energy crosssection for the 7 Be(p, γ)8 B reaction by Junghans et al.. [31], Bahcall et all. [32] calculated theSSM predictions using S17 (0) = 22.3±0.9 eV·b. The results are: the 8 B solar neutrino flux of
+1.1
6
−2 −1
5.931.00+0.14−0.15 × 10 cm s , the chlorine capture rate of 8.59 −1.2 SNU, and gallium capture rate+9
of 130−7 SNU.
The standard solar model of BP2000 is constructed with the OPAL equation of state (Rogers
Swenson, & Iglesias 1996 [33]) and OPAL opacities(Iglesias & Rogers 1996), which are supplemented by the low temperature opacities of Alexander & Ferguson (1994). The model was
calculated using the usual mixing length formalism to determine the convective flux.
The principal change in the input data is the use of the Grevesse & Sauval (1998) improved
standard solar composition in the OPAL opacities [33] and in the calculation of the nuclear
reaction rates. The refinements in this composition redetermination come from many different
sources, including the use of more accurate atomic transition probabilities in interpreting solar
spectra. The OPAL equation of state and the Alexander and Ferguson opacities are not yet
available with the composition recommended by Grevesse & Sauval(1998).
A present-epoch solar luminosity is estimated 1369 Wm 2 [4π × AU2 ] for all the models.
5Abbr.
Flux(cm−2 s−1 )pp chain+10
pp → d e νpp5.95(1.00+0.01−0.01 )×10
+0.015−pe p → d ν
pep
1.40(1.00−0.015 )×108
3 He p → 4 He e+ ν
hep
9.3×1037 Be e− → 7 Li ν + (γ)
7 Be
94.77(1.00+0.10−0.10 )×10
+0.20
8 B e− → 8 Be e+ ν
8B
5.05(1.00−0.16 )×106
CNO cycle
13 N → 13 Ce+ ν
13 N
8
5.48(1.00+0.21−0.17 )×10
15 O → 15 Ne+ ν
15 O
8
4.80(1.00+0.25−0.19 )×10
+0.25
13 F → 17 Oe+ ν
17 F
5.63(1.00−0.25 )×106
Reaction

Table 2.2: Neutrino-producing reactions in the Sun (the first column) and their abbreviations(second column) and neutrino fluxes(third column). [Bahcall, Basu, and Pinsonneault(2000) [29]]For the neutrino fluxes, more recent best estimate value used a solar luminosity of 1366.2 W
m2 [4π × AU2 ] = 3.842×1033 erg · s−1 (Frohlich & Lean 1998 [34]; Crommelynck et al. 1995 [35]).
The difference between these two values for the luminosity is 0.2%, For the calculations of
uncertainties in neutrino flux productions, we assume a 1σ uncertainty of 0.4%. The uncertainty
in the predicted solar neutrino fluxes due to the luminosity is an order of magnitude smaller
than the total uncertainty in predicting the neutrino fluxes.
The nuclear reaction rates were evaluated with the subroutine exportenergy.f(Bahcall &Pinsonneault 1992) [36], using the reaction data in Adelberger et al. (1998) [37] and withelectron and ion weak screening as indicated by recent calculations of Gruzinov & Bahcall(1998 [38], Salpeter 1954 [39]). The model incorporates helium and heavy-element diffusion
using the exportable diffusion subroutine of Thoul(Thoul, Bahcall, & Loeb 1994 [40]; Bahcall &Pinsonneault 1995 [41]). An independent and detailed treatment of diffusion by Turcotte et al.
(1998 [42]) yields results for the impact of diffusion on the computed solar quantities that arevery similar to those obtained here.
For the standard model, the evolutionary calculations were started at the main-sequencestage. The model has a radius of 695.98 Mm. The ratio of heavy elements to hydrogen(Z/X)
at the surface of the model is 0.0230, which is chosen to be consistent with the value obtainedby Grevesse & Suaval(1998) [43]. A Krishna-Swamy T − τ relation ship for the atmosphere wasused. The adopted solar luminosity is L = 3.844×1033 erg · s−1 and the solar age is 4.57×109
yr (Bahcall & Pinsonneault 1995 [44]).
The uncertainties in the neutrino fluxes and in the experimental event rates were calculated
by including the published errors in all experimental quantities and by taking account of thecorrelated influence of different input parameters using the results of detailed solar model calculations. The procedure for calculating the uncertainties has been developed over the past
three decades and is described in detail in Bahcall(1989, 1992, 1995, BBp98, Bahcall & Pinsonneault). The uncertainties in the nuclear fusion cross sections (except for hep ν) were takenfrom Adelberger et all.(1998) [37], the neutrino cross sections and their uncertainties are from
Bahcall(1994 [45],1997 [46]) and Bacall et al. (1996) [47], the luminosity and age uncertainties
were adopted from Bahcall & Pinsonneault(1995) [48], the 1σ fractional uncertainty in diffusion
rate was taken to be 1.5%(Thoul et al. 1994 [49]), and the opacity uncertainty was determinedby comparing the results of fluxes computed using the model Livermore opacities(Bahcall &Pinsonneault 1992 [50]). The adopted 1 σ uncertainty in the heavy-element abundance ofσ(Z/X) = ±0.061(Z/X).
6

(2.3)

Source, Abbr.
pp
pep
hep
7 Be
8B
13 N
15 O
17 F

Total

Chlorine(SNU) Gallium(SNU)
pp chain
0.0
69.7
0.2
2.8
0.04
0.1
1.15
34.2
5.76
12.1
CNO cycle
0.09
3.4
0.33
5.5
0.0
0.1
+9
7.6+1.3
128
−1.1
−7

SK
0.0
0.0
0.0
0.001
0.999
0.0
0.0
0.0
1.0

Table 2.3: Solar neutrino detection rates in chlorine and gallium for each flux measurements
experiments. For SK, the ratio to the total flux is also shown. [Bahcall, Basu, and Pinsonneault(BP2000) [29]]This uncertainty spans the range of values recommended by Grevesse(1984), Grevesse & Noels(1993),
and Grevesse & Sauval (1998) [51] [52] [53]. In support of the larger uncertainty used in BP2000,
the difference between the Grevesse & Noels (1993) values of Z/X = 0.0230 is 1 σ according toabove equation. The calculated errors are asymmetric in many cases because these asymmetries
in the uncertainties in neutrino fluxes and experimental event rates result from asymmetries
in the uncertainties of some of the input parameters, for example, the important pp, 7 Be + p,
14 N + p, fusion reactions and the effect of excited states on neutrino absorption cross sections.

2.2

Nuclear energy generation in the Sun and the solar neutrino
fluxesThe Sun shines by converting protons into α-particles. About 600 million tons of hydrogen areburned every second to supply the solar luminosity. The SSM predicts that over 98% of solar
energy is produced from the pp-chain reaction which is the conversion of four protons into 4 He.
4p → 4 He∗ + 2e+ + 2νe(2.4)

The energy produced per pp-chain reaction is 26.731 MeV. Figure 2.4 shows the reaction
tree of the pp-chain.
There is another reaction series called the CNO(carbon-nitrogen-oxygen) cycle. Figure 2.5
shows the schematic overview of the CNO cycle.
The reaction rate (number of reactions per unit volume per unit time) between two nuclear
species is described by the formulaR12 =n(1)n(2)hσυi12 ,(1 + δ12 )(2.5)

where n(1), n(2) are the number densities of particles of type 1 and 2, σ is their interaction
cross section, and υ the magnitude of their relative velocity.
As described above, the temperature in the core is about 1.5×10 7 K. Thus, the protons in
the core do not have enough energy to overcome the Coulomb repulsion. The solar nuclear
fission occurs only via the quantum mechanical tunneling effect.
7

The energy dependence of the fusion cross sections can be represented most simply by aformula, in which the geometrical factor, the De Broglie wavelength squared, and the barrier
penetration factor have both been removed, leaving a function S(E) that varies smoothly in theabsence of resonances. The conventional definition is:

σ(E) ≡S(E)
exp(−2πη),
E

(2.6)

where
η(E) = Z1 Z2

e2
.
~υ

(2.7)

Z1 Z2 e2η(E) =
h

r

(2.8)

µ=

µ
.
2E

A1 A2
.
A1 + A 2(2.9)

where E is the center-of-mass energy, η is the Sommerfeld parameter, and Z 1 , Z2 are thecharge numbers of the nuclei, and µ is the reduced mass of the system, and A 1 , A2 are the massesof the nuclei.
The quantity exp(−2πη) is known appropriately as the Gamow penetration factor. The
value of S(E) at the zero energy is known as the cross section factor, S 0 .
In the condition i which the WKB approximation is valid. S(E) is continuous and varies
slowly. Then S(E) can be expanded as follows:
1
S(E) = S(0) + S 0 (0)E + S 00 (0)E 2 .
2(2.10)The S(0) for the solar nuclear fusion reactions are summarized in reference paper [76].
In CNO cycle, high temperature (Tc > 108 K) is required. So, in the current core temperature(Tc ∼ 107 K), the contribution to total energy generation is suppressed to 2%.
The origins of predicted solar neutrino fluxes are shown in figure 2.2.
Neutrino fluxes from continuum sources (such as pp and 8 B) are given in units of counts
per cm2 per second. The pp chain is responsible for more than 98% of energy generation in
the standard solar model. Neutrino produced in the carbon-nitrogen-oxygen CNO chain are notimportant energetically and are difficult to detect experimentally. The arrows at the top of the
figure indicate the energy thresholds for the ongoing neutrino experiments.
The probability of converting an electron-type neutrino to a muon or tau neutrino in the
Sun depends on the profile of the electron number density as a function of solar radius. For
particular values of the electron density, neutrino energy, and neutrino mass, neutrinos can beresonantly converted from one type of neutrino to another. The Mikheyev-Smirnov resonanceoccurs if the electron density at a radius r satisfies
ne,res (r)| ∆m2 | 10MeV≈ 66 cos 2θv ( −4 )(
),
NA
10 eV
E

(2.11)

where ne is the electron number of density measured in cm −3 , NA is Avogadro’s number,θv is the neutrino mixing angle in vacuum, | ∆m 2 | is the absolute value of the difference inneutrino masses between two species that are mixing by neutrino oscillations, and E is theneutrino energy.
8Figure 2.2: This graph shows where in the Sun the different solar neutrino fluxes originate(http://www.sns.ias.edu/j̃nb/).

Figure 2.3: The solar neutrino energy spectrum(http://www.sns.ias.edu/ j̃nb/).

9-CNO cycle (1.5%)?

pp-chain (98.5%)(1) p + p → D + e+ + νe(2) p + e− + p → D + νe

(99.75%)(Eν :<0.42 MeV)

(0.25%)(Eν :<1.442 MeV)?

D + p → 3 He + γ?

?

3 He + 3 He → α + 2p?

(5) 3 He + p → 4 He + e+ + ν

3 He + 4 He → 7 Be + γ(p-p I : 86%)

(0.00002%)?

?

(3) 7 Be + e− → 7 Li + ν

7 Be + p → 8 B + γe(Eν :0.861 MeV,90%)? (Eν :0.383 MeV,10%)
7 Li + p → 2α(p-p II : 14%)?

(4) 8 B → 8 Be∗ + e+ + νe(Eν :<15 MeV)?
8 Be∗ → 2α(p-p III : 0.015%)
Figure 2.4: The pp-chain.

e+<E >=0.707MeV
N13
C12

C13
p

p

p

p

He4
N15

N14
He4
O15

e

+

O17

<E >=0.997MeV

O16
p

p

F17

<E >=0.999MeV

e+

?

?

(6) 4 He + νO +νN(1.49%)(7) 4 He + νO +νF(0.01%)

Figure 2.5: The CNO cycle.

10eFigure 2.6 give the electron number density as a function of solar radius for the standard
model (BP2000). For the so-called LOW MSW solutions and for all MSW solutions with θ v ∼π/4, the resonance radius falls in the outer part of the Sun.
There are no accurate values for the electron density in the outer parts of the Sun, r ≥ 0.8R .
The straight line in the figure is an approximations to the electron number density in the standard
solar model of Bahcall & Ulrich (1998) [54].

Figure 2.6: Electron number density, n e , vs.
solar radius for the standard solarmodel (BP2000).
The straight-line fit shown is an approximation given by Bahcall(1989).(http://www.sns.ias.edu/ j̃nb/)

2.3

The 8B neutrino flux

As shown in Table 2.2, a 8 B neutrino is produced via the β + decay of 8 B. The energy levels of 8 B
decay are shown in figure 2.7. The energy spectrum of 8 B neutrinos is obtained by measurementsof the 8 B β decay spectrum and the α spectrum from the subsequent 8 Be decay. The 8 B β decay
spectrum with the momentum above 8 MeV/c is measured using a β-spectrometer [55]. The errorof the absolute momentum calibration is estimated using the 12 B β spectrum shape (Qβ − = 13.4
MeV) and is obtained to be ±0.090 MeV. The delayed α spectrum of 8 Be is measured by several
experimental groups [56] [57] [58]. These α decay data are compared and used to fit the βdecay data. The best-fit α spectrum and its uncertainty are obtained from this over constrained
comparison. The 8 B neutrino spectrum is determined using the best-fit α spectrum. This isshown in figure 2.8. The spectra allowed by ±3σ uncertainties are also shown on the same figure.
The uncertainty of the 8 B neutrino energy spectrum is caused by the experimental uncertaintyof the α spectrum measurement. A more detailed explanation is given in Ref. [59]. Details about
7 Be and hep neutrino fluxes are given in appendix A.

2.4

Solar neutrino experiments

A pioneering solar neutrino experiment by Davis and collaborators using 37 Cl started in thelate 1960’s. Since then, chlorine and gallium radiochemical experiments and water Čerenkov
experiments with light and heavy water targets have made successful solar neutrino observations.
Observation of solar neutrinos directly addresses the theory of stellar structure and evolution,
which is the basis of the standard solar model (SSM). The Sun, as a well-defined neutrino source,11  



 





  

     
 



 

 



Figure 2.7: Energy levels in the 8 Bβ + 8 Be(2α) decay chain. The gray zone shows the 2 + statesof 8 Be∗ .

Figure 2.8: The best-estimate (standard) 8 B neutrino spectrum λ, together with thespectra σ ± allowed by the maximum ±3σ theoretical and experimental uncertainties.
(http://www.sns.ias.edu/j̃nb/)12

also provides extremely important opportunities to investigate nontrivial neutrino properties
such as nonzero mass and mixing, because of the wide range of matter density and the very long
distance from the Sun to the Earth.
From the very beginning of the solar-neutrino observation, it was recognized that the observed flux was significantly smaller than the SSM prediction provided nothing happens to theelectron neutrinos after they are created in the solar interior. This deficit has been called “Thesolar neutrino problem”. The initial result from Sudbury Neutrino Observatory (SNO) on thesolar neutrino flux measured via charged-current reaction ν e + d → e− + p + p, combined with
Super-Kmioknade’s high statistics flux measurement via ν e + e elastic scattering, provided direct evidence for flavor conversion of solar neutrinos. The most probable explanation is neutrino
oscillation which can also solve the solar neutrino problem. Figure 2.9 shows the ratio between
the predicted solar neutrino fluxes for each target and the observed solar neutrino fluxes in eachexperiment. The uncertainties for the observed solar neutrino fluxes are given for each experiment. The errors for the predicted solar fluxes for each target is due to the uncertainties of the
SSM (BP2000). In Table 2.4, the detailed results for total solar neutrino fluxes are given foreach experiment of solar neutrino observation.
ExperimentHomestake(CLEVELAND 98 [11])GALLEX(HAMPEL 99 [14])GNO(ALTMANN 00 [12])SAGE(ABDURASHI 99B [21])Kamiokande(FUKUDA 96 [3]) (elastic-scattering)
Super-Kamiokande-I(FUKUDA 01 [6])(elastic-scattering)
SNO(AHMAD 02 [26]) (charged-current)
SNO(AHMAD 02 [26]) (elastic-scattering)
SNO(AHMAD 02 [26]) (neutral-current)
SSM (BP2000 [29])
SSM (TURCK-CHIEZE 01 [30])37 Cl → 37 Ar

71 Ga → 71 Ge

SNU-

106 cm−2 s−1
-

-

+4.3
77.5±6.2−4.7

-

-

+4.3
65.8+10.2−9.6 −4.7

-

-

+3.5
67.2+7.2−7.0 −3.0---

2.80±0.19±0.33--

2.32±0.03+0.08
−0.07

-

-

1.76+0.06−0.05 ±0.09--

2.39+0.24−0.23 ±0.12

-

-

+0.46
5.09+0.44−0.43 −0.43

7.6+1.3−1.1
7.44±0.96

128+9−7
128±8.6

5.05(1.00+0.20−0.16 )
4.95±0.72

SNU
2.56±0.16±0.16

8 Bν flux

Table 2.4: Recent results from the seven solar neutrino experiments and a comparison withstandard solar model predictions. [K. Hagiwara et al. (particle Data Group), Phys. Rev. D 66,
010001 (2002) (URL: http://pdg.lbl.gov)]

2.4.1

Radiochemical Experiments

Radiochemical experiments exploit electron neutrino absorption on nuclei followed by their decay
through orbital electron capture. The produced Auger electrons are counted. The Homestake
chlorine experiment in USA uses the reaction:

13

37

Cl + νe → 37 Ar + e− .

(2.12)

Three gallium experiments (GALLEX and GNO at Gran Sasso in Italy and SAGE at Baksan
in Russia) use the reaction
71

Ga + νe → 71 Ge + e− .

(2.13)The produced 37 Ar and 71 Ge atoms are both radioactive, with half lives (τ 1/2 ) of 34.8 days
and 11.43 days, respectively. After an exposure of the detector for two to three times τ 1/2 , thereaction products are chemically extracted and introduced into a low-background proportionalcounter, and are counted for a sufficiently long period to determine the exponentially decaying
signal and a constant background.
Homestake
The first solar neutrino observation was carried out by R. Davis and his Brookhaven collaboratorsin 1968 [9]. Their detector consisted of a horizontal steel tank, 6.1 m in diameter and 14.6 m
long, containing 615 m3 of C2 Cl4 . It was located in the Homestake Gold Mine in Lead, South
Dakota, United States. The average overburden for the detector was 4200± 100 meter waterequivalent (m.w.e).
In order to detect solar neutrinos, they used the inverse β reaction 37 Cl(νe , e− )37 Ar. At theend of each exposure of about eight months, 37 Ar was collected by purging the C2 Cl4 with Hegas. He, carrying with it Ar, was cleaned by a condenser (-40 ◦ C) and a molecular sieve trap
before a charcoal trap. This charcoal trap was cooled by liquid N 2 (-196◦ C) to freeze and absorb
Ar (freezing point of Ar is -189◦ C). Then the trap was warmed (+200◦ C) an Ar was transferred
to a small system to measure the volume. After that, Ar was transferred to gas chromatographic
system. It separated Ar from the heavier gases, such as Kr, Xe, and Rn. Then the volume of
Ar was measured and transferred to the proportional counter. Ar was mixed with CH 4 whose
volume was 7% of the Ar volume. The number of 37 Ar was determined by observing their decay
electrons. The decay electrons with an energy of 2.8 keV represents 81.5% of all decays. An
additional 8.7% of the decays invokes a K orbital electron capture together with emission ofa γ-ray (2.6∼2.8 keV). 10% of those γ-rays converts and deposits an energy of 2.8 keV. The
reaction threshold of 37 Cl neutrino absorption is 0.814 MeV, so the dominant components ofneutrino sources were 7 Be neutrinos and 8 B neutrinos. The contributions of pep neutrinos andneutrinos from CNO-cycle were small because their fluxes are small. The energy of 7 Be neutrinos
is 0.861 MeV, so it can excite just the Gamow-Teller transition to the 37 Ar ground state. 8 B
neutrinos can excite 37 Cl to numerous states. The interaction cross section is calculated fromthe β decay 37 Ca(β + )37 K, which is an isospin mirror of 37 Cl(νe , e− )37 Ar [10]. The number of
events predicted by the SSM and the measured capture rate are given in Table 2.4. SNU is aunit which is the number of interactions per 10 36 targets per second. The ratio of the measured
rate to the SSM prediction is 0.34±0.06 [11].
GALLEX,GNO and SAGEGALLEX and SAGE were radiochemical experiments using Ga. A solar neutrino was detectedby inverse β interaction 71 Ga(νe , e− )71 Ge. The energy threshold of absorption in 232.69±0.15
keV. So, pp neutrinos could be detected by these detectors. The K and L Auger electrons from71 Ge decay have energies of 10.4 keV and 1.2 keV, respectively. The lifetime for 71 Ge electron
capture has been measured as τ1/2 = 11.43±0.03 day [65].
The GALLEX detector was located at Gran Sasso Underground Laboratory at the depthof 3800 m.w.e [18]. The detector observed solar neutrinos from 1991 to 1997 [17] [16] [15] [14].
14The target consisted of 101 tons (53.5 m 3 ) of GaCl3 , of which 12 tons were 71 Ga. At the endof each 20 day exposure about 1 mg of Ge carriers were added to extract 71 Ge chemically. The
GeCl4 was volatile and purged with N2 gas. Then it converted GeH4 and filled a proportionalcounter with Xe, The proportional counter was enclosed in NaI veto counter surrounded by leadshielding and counted the K and L Auger electrons for period of 90 days. The detector wascalibrated twice with neutrino source 51 Cr of known intensity [66]. 51 Cr emits neutrinos withenergies of 428 keV (9.0%), 747 keV (8163%) and 752 keV (8.5%), which is similar to the energiesof pp and 7 Be Solar neutrinos. The source was introduced inside of the detector. The source
emitted about 6×1013 neutrinos per second just after the installation. This flux was 10 times
larger than that of solar neutrinos. After 3 months calibration, the flux was reduced to 1/10 of
the initial one. The 51 Cr calibration showed that the observed neutrino detection efficiency wasconsistent with the estimated value. The result of 51 Cr calibration is [19]:σ(51 Cr)GALLEX
measured= 0.93 ± 0.08,
σ(51 Cr)BU88(2.14)

71
51
where σ(51 Cr)GALLEX
measured is the absorption cross section of Ga measured by the Cr calibration51
as GALLEX. σ( Cr)BU88 is the calculated cross section by Bahcall and Urlich [67] and it is59.2×10−46 (1 ± 0.1)cm−2 . Another test was performed at the end of the experiment by adding
71 As to the target solution [68]. 71 As decays (β + 32% and electron capture 68%) with thehalf-life of 2.72 days into 71 Ge. By using the 71 Ge from 71 As decay, the efficiency of extraction
was studied and it was found to be consistent with expectation. The ratio of the measured
rate to the SSM prediction in GALLEX [14] (+ GNO [12]) is 0.58±0.07. The number of events
predicted by the SSM and the measured capture rate are given in Table 2.4.
The SAGE detector is situated in a tunnel in the northern Causaus mountains in southern
Russia at the depth of about 4700 m.w.e [22]. Solar neutrino observation began in 1990. The
target is 50 tons of metallic Ga. At the end of an exposure period (typically one month), a small
amount ( a few hundred mg) of Ge carrier is added to each detector. Then 71 Ge is extracted
chemically by a solution of dilute HCl and H 2 O2 . The GeCl4 is then transformed into GeH4
and mixed with Xe to be filled in proportional counters to count the K Auger electrons. Eachsample counted for a period of 2 ∼ 3 months. 51 Cr calibration was performed in SAGE too.
The result is [69] [23] [24]:σ(51 Cr)SAGE
measured= 0.95 ± 0.12,σ(51 Cr)BU88(2.15)The ratio of the measured rate to the SSM prediction is 0.59±0.07 [21]. The number of
events predicted by the SSM and the measured capture rate are given in Table 2.4.

2.4.2

Kamiokande and Super-Kamiokande experiments

Kamiokande and Super-Kamiokande in Japan are real-time experiments utilizing ν e scatteringνx + e − → ν x + e −(2.16)

in a large water-Čerenkov detector. It should be noted that the reaction is sensitive to all
active neutrinos, x = e, µ, andτ . However, the sensitivity to ν µ and ντ is much smaller than thesensitivity to νe , σ(νµ,τ e) ≈ 0.16σ(νe e). The solar neutrino flux measured via ν e scattering isdeduced assuming no neutrino oscillations.
These experiments take advantage of the directional correlation between the incoming neutrino and the recoil electron. This feature greatly helps the clear separation of the solar neutrino
15

signal from background. Due to the high thresholds(7 MeV in Kamiokande-II and 5 MeV in
Super-Kamiokande-I) the experiments could observe pure 8 B solar neutrinos.
Kamiokande was a water Čerenkov detector which was located near SK. Purified water of3000 m3 was contained in a stainless steel tank of 15.6 m diameter and 16.1 m height. The innerdetector had 946 50cm-PMTs viewing 2140 m 3 of purified water. The comparison between
Kamiokande detector and Super-Kamiokande detector is shown Table 2.5. The observation ofsolar neutrinos in the Kamiokande-II collaboration started in 1987 using recoil electrons via
neutrino-electron elastic scattering [4]. The vertex, direction, and energy of each event werereconstructed using Čerenkov photons. Solar neutrino events could be extracted using direction
correlation to the Sun. The energy threshold was ∼ 7.0 MeV. Therefore, 8 B neutrinos and hep
neutrinos could be observed. The Kamiokande-II experiment came to an end at the beginningof 1995. The ratio of the measured rate to the SSM prediction is 0.55±0.13 [3]. The number of
events predicted by the SSM and the measured capture rate are given in Table 2.4.
Super-Kamiokande will be discussed in detail later. In this section, only an overview will
be given. Super-Kamiokade is a 50k ton second-generation solar neutrino detector, which ischaracterized by a significantly larger counting rate than then first generation experiments [1].
This experiment started the observation of solar neutrino in April 1996. The average solar
neutrino flux is smaller than, but consistent with, the Kamiokande-II result. The flux measured
in the nighttime is slightly larger than the flux measured in daytime, but it is only a 1.3σ
effect [2]. Super-Kamiokande also observed the recoil-electron energy spectrum. The SuperKamiokande-I experiment was closed in July 2001. Now, Super-Kamiokande-II experiment
which started from November 2003 is running. The ratio of the measured rate to the SSM
prediction is 0.47±0.02 [2]. The number of events predicted by the SSM and the measured
capture rate are given in Table 2.4. In Table 2.5, the comparison between Kamiokande-II and
Super-Kamiokande-I is presented.
Parameters
Total size
Total volume
Fiducial volume

Thickness of outer detector
Number of PMT
Photosensitive coverage
PMT timing resolution
PMT energy resolution
PMT energy resolution
PMT position resolution
PMT position resolution
PMT angular resolution
PMT angular resolution
Energy threshold (Trigger)
Energy threshold (Analysis)
Selection of electron/muon

SK-I
41mh×39mφ
50000t32000t22500t22500t2.6m∼2.75m
11146
40%
∼2.2nsp2.6%/ E2.5%p21.3%/ E/5MeV
50cm
∼10cm
25◦
1.5◦
4.5 MeV
5.0 MeV99%99%

Selection of electron/muon

Kamiokande-II
16mh×19mφ
4500t
2140t
1040t
680t
1.2m∼1.5m
948
20%
∼4ns
p
3.6%/ E15%p
24.9%/ E/5MeV
100cm
∼50cm
26◦
2.7◦
5.2 MeV
7.0 MeV80%

Remarkssupernova neutrino
proton decay
solar neutrino
inner detector

electrons at E (GeV)
muons (E ≤1 GeV)
electrons (E≤50MeV)
10 MeV electron
p →e + π 0
10 MeV electron
through-going muon
Solar neutrino
0.03<p e <1.33 GeV/c
0.2<pµ <1.5 GeV/cstopping-muon

Table 2.5: Comparison between Super Kamiokande and Kamiokande

162.4.3

SNO experiment

In 1999, a new real-time solar neutrino experiment, SNO (Sudbury Neutrino Observatory) in
Canada started observation. SNO is an imaging water Čerenkov detector located at a depthof 6010 m of water equivalent in the INCO, LTD. Creighton mine near Sudbury, Ontario. Itfeatures 1000 metric tons of ultra-pure D 2 O to intercept about 10 neutrinos per day containedin a 12 m diameter spherical acrylic vessel. This sphere is surrounded by a shield of ultra-pure
H2 O contained in a 34 m high barrel-shaped cavity of maximum diameter 22 m. A stainlesssteel structure 17.8 m in a diameter supports 9456 20-cm photomultiplier tubes with light
concentrators. Approximately 55% of the light produced within 7 m of the center of the detector
will strike a PMT.
Events are defined by a multiplicity trigger of 18 or more PMTs exceeding a threshold of ∼0.25 photo-electrons within a time window of 93 ns. The trigger reaches 100% efficiency at 23
PMTs. For every event trigger, the time and charge response of each participating PMT arerecorded. Solar neutrino are extracted using the angle between the reconstructed direction fromthe Sun to the Earth.
Calibration of the PMT time and charge pedestals, slopes, offsets, charge vs. time dependencies, and second order rate dependencies are performed using electronic pulser and pulsed
light sources. Optical calibration is obtained using a diffuse source of pulsed laser light at 337,
365, 386, 420, 500, and 620 nm wavelengths. The absolute energy scale and uncertainties are
established with triggered 16 N source (predominantly 6.13-MeV γ’s) deployed over two planar
grids within the D2 O and a linear grid in the H2 O. The resulting Monte Carlo predictions ofdetector response are tested using a 252 Cf neutron source, which provides an extended distribution of 6.25 MeV γ rays from neutron capture, and a 3 H(p.γ)4 He source providing 19.8 MeV γ
rays. The volume weighted mean response is approximately nine PMT hits per MeV of electronenergy.
SNO measures 8 B solar neutrino via the reactions
νe + d → e− + p + p Charged-Current CC
νx + d → νx + p + n Neutral-Current NC−−

νx + e → νx + e Elastic-Scattering ES(2.17)(2.18)(2.19)The Q-value of the CC reactions is -1.4 MeV and the electron energy is strongly correlatedwith neutrino energy. Thus the CC reaction provides an accurate measure of the shape of the
8 B solar neutrino spectrum. The contributions from the CC reaction nd ν scattering can beedistinguished by using different cos θ sun distribution where cos θsun is the angle with respect
to the direction from the Sun to the Earth. The forward peak of cos θ sun = 1 arises from thekinematics of the ES reaction, while CC electrons are expected to have a distribution which is(1-0.345cos θsun ) by detector response.
The threshold of the NC reaction is 2.2 MeV. In the pure D 2 O, the signal of the NC reaction
is neutron capture in deuterium, producing a 6.25 MeV γ ray. In this case, capture efficiency is
low and the deposit energy is close to the detection threshold of 5.0 MeV. In order to enhanceboth the capture efficiency and the total γ ray energy (8.6 MeV), 2.5 tons of NaCl has been
added to the heavy water in the second phase of the experiment. The chlorine ( 35 Cl) has ahigh absorption cross-section for thermal neutrons, resulting in a gamma ray cascade peakedat around 8 MeV. The neutron capture efficiency will be about 83%. The background for thisprocess will be neutrons produced by photo disintegration of the deuteron, arising chiefly fromthe 2.45 MeV and 2.63 MeV gamma rays in the 232 Th and 238 U chains. Special care was taken
so that the salt is at the highest level of cleanliness. In addition, installation of discrete 3 He
neutron counter is planned for the NC measurement in the third phase.
The energy threshold in SNO is 6.75 MeV as an effective kinetic energy. The reported data
were recorded between November 2, 1999 and January 15, 2001 and correspond to a live time17

of 240.95 days [27].
The ratio of the measured rate to the SSM prediction is 0.47±0.1 for ES reaction. The
number of events predicted by the SSM and the measured capture rate are given in Table 2.4.
Though the results has poor statistics yet, it is consistent with the high statistics SuperKamiokande-I result. Thus the SNO group compared their CC result with Super Kamiokande
ES result, and obtained evidence of active non-ν e component in the solar neutrino flux.
More recently, in September 7, 2003, the SNO collaboration reported the first result on the
8 B solar neutrino flux measurement via NC reaction in salt phase. The total flux measured via
NC reaction is consistent with the solar model predictions [26].

2.5

Solar neutrino problem

Figure 2.9 compares the predictions of the standard solar model with the total observed rates
in the six solar neutrino experiments: chlorine, Super Kamiokande, Kamiokande, GALLEX,
SAGE, and SNO. The model predictions are color coded with different colors for the different
predicted neutrino components. For both the experimental values and the predictions, the 1
sigma uncertainties are indicated by cross hatching. This figure explains the “four solar neutrino
problems” that suggest that new neutrino physics is required to explain the results of the solar
neutrino experiments. The problems exist because it is assumed, following the minimal standard
model, that essentially nothing happens to the neutrinos after they are created in the center of
the Sun.
In all six cases, the blue experimental values are significantly less than the model predictions.
The difference (by a factor of three or more) between the chlorine measurement of Ray Davisand the standard solar model prediction was the “solar neutrino problem” for two decades. The
discrepancy between measured and predicted absolute rates was strengthened at the beginningof the 1990’s by the measurement by the Kamiokande experiment of the 8 B neutrino flux.
For Kamiokande, which has a threshold of 7.5 MeV (compared to 0.8 MeV for the chlorine
experiment), the discrepancy is approximately a factor of two. The discrepancy in absolute
rates is the first “solar neutrino problem.”A second solar neutrino problem, namely, is that the rate of just the 8 B neutrinos observed in
Kamiokande exceeds the total measured rate in the chlorine experiment if the energy spectrumof the solar neutrinos is not changed by new neutrino physics. This problem is exacerbatedby the fact that significant contributions are also expected in the chlorine experiment from7 Be neutrinos and from CNO neutrinos. The predicted rate from the 7 Be neutrinos is welldetermined, especially since the related 8 B neutrinos are observed to be depleted only by afactor of two.
The GALLEX and SAGE experiments present the third, essentially independent solar neutrino problem. The total observed rate is accounted for by the pp neutrinos, whose flux is an
accuracy of 1 %. Therefore, the gallium experiments do not leave any room for the reliably
calculated 7 Be neutrinos. This is the reason why the third solar neutrino problem is sometimes
referred to as “the problem of the missing 7 Be neutrinos.” Moreover, both the GALLEX andSAGE experiments have been directly calibrated with a radioactive source, 51 Cr, that emits
neutrinos with similar energies to the 7 Be neutrinos.
Most recently and perhaps most dramatically, the SNO experiment has shown that the CC
rate (from electron type neutrinos only) in a deuterium detector is only 0.35 of the standard
model prediction. The Super-Kamiokande experiment, which measures the CC rate plus–with
reduced efficiency–the muon and tau neutrinos, observes 0.46 of the standard model prediction.
The fact that Super-Kamiokande observes 0.46 (with some sensitivity to all three neutrinos)
and SNO observes only 0.35 of the standard rate (from only electron type neutrinos) provesthat some electron type neutrinos become muon and tau neutrinos after they are created in thecenter of the Sun.

18

It is clear from above flux results that the results from all the solar-neutrino experiments,
except the most recent SNO NC result, indicate significantly less flux than expected from BP2000
SSM. There has been a consensus that a consistent explanation of all the results of solar neutrinos
observation is unlikely within the framework of astrophysics using the solar neutrino spectra
given by the standard electroweak model. Many authors made solar model independent analyses
constrained by the observed solar luminosity [26], where they attempted to fit the measured solar
neutrino capture rates and 8 B flux with normalization-free, undistorted energy spectra. All theseattempts only obtained solutions with very low probabilities.

Figure 2.9: This color viewgraph compares the predictions of the standard solar model withthe total observed rates in the six solar neutrino experiments: chlorine, Super Kamiokande,
Kamiokande, GALLEX, SAGE, and SNO. (http://www.sns.ias.edu/ j̃nb/)
Predicted Ratio to SSM
RCl = 0.0 · SSMpp + 0.15 · SSMBe + 0.76 · SSMB8(2.20)

RSK = 0.0 · SSMpp + 0.0 · SSMBe + 0.999 · SSMB8(2.22)

RGa = 0.56 · SSMpp + 0.27 · SSMBe + 0.1 · SSMB8(2.21)

Flux results to SSM from measurements
φ(pp) ∼ 0.9 × φSSM(pp)(2.23)

φ(B8) ∼ 0.5 × φSSM(B8)(2.25)

φ(Be) ∼ 0.0 × φSSM(Be)(2.24)To explain the deficit in the framework of the SSM, some probabilities are discussed such as
the temperature in the core Tc and the cross section of 7 Be proton capture The temperature in
the core influences the rate of nuclear fission. If the T c is much lower than the value used in the
SSM, then all of the neutrino flux is decreased. The temperature dependence of the 8 B neutrino
flux is φ ∼ Tc18 , although that of the 7 Be neutrino flux is φ ∼ Tc8 [87]. Thus, a large reductionin the 7 Be neutrino flux results in a much larger reduction in the 8 B neutrino flux in the SSM.
The ratio of proton capture 7 Be is 0.1 % of that of electron capture by 7 Be. So, if S17 (0) is
larger than expected by 2 orders of magnitude, then the results can be explained. The estimatederror of S17 (0) is 25% at 1 σ. The uncertainty of 7 Be electron capture rate is also studied andfound to be less than 2%.
198
7 SK(ES)SNO(CC)

6
3σ
2σ
1σ

6

2

νµ+ντ flux (10 /cm /sec)

Therefore, the data suggest that the solution to the solar neutrino problem requires nontrivial
neutrino properties. Figure 2.10 shows fluxes of solar neutrino calculated from observed neutrino
fluxes in SK and SNO experiments.

5
4
3

SNO(NC)2

SSM ±1σ

1
0

0

1

2

3
4
5
6
6
2
νe flux (10 /cm /sec)

Figure 2.10: Fluxes of 8 B solar neutrinos, φ(νe ), φ(νµ,τ ), deduced from the SK’s ES result and
SNO’s CC, NC, and ES results. The standard solar model prediction is also shown. The bands
represent the 1σ error. The contours show the 68%, 95%, and 99% joint probability for flux
results.

2.6

Neutrino oscillation mechanism

In this section, the theory of neutrino oscillations is described. It is regarded as the most likely
solution of the solar neutrino problem.

2.6.1

Vacuum oscillation

If neutrinos have mass and different generations mix as quark do, the observed neutrino flavor
will change as they propagate. This phenomenon occurs because the propagation eigenstate,
namely a mass eigenstate, of a neutrino is not a flavor eigenstate. Currently it is believedthat there are three kinds of neutrinos, namely, ν e , νµ , and ντ . For simplicity, only two flavor
oscillations between νe and νµ is taken into account here.
Mixing between two generations can be expressed as follow:

 




| νe icos θ sin θ| ν1 i| ν1 i=≡U(2.26)| νµ i− sin θ cos θ| ν2 i| ν2 iwhere | ν1,2 i are the mass eigenstates, θ is the mixing angle, and U is the mixing matrix. From
now on, i, j denote 1 or 2 and a, b denote e or µ. The propagation of mass eigenstates is expressedas:| νi (t)i = e−iEi t | νi (0)i(2.27)

where t is the time and Ei is the energy of a neutrino for mass eigenstate i. E i is approximatedas follow,qm2
m2(2.28)
Ei = p2 + m2i ' p + i ' E + i
2p
2E
20

where mi is the mass of eigenstate i. Equation (2.26) can be rewritten as:X| νa (t)i =Uai | νi (t)i(2.29)isubstitution of (2.27) in (2.29) yields:| νa (t)i ==Xi

Uai e−iEi t | νi (0)i

XX
i

b

Uai Uib−1 e−iEi t | νb (0)iTherefore, the amplitude that the same flavor is maintained is,XXhνa | νa (t)i =Uai Uib−1 e−iEi t hνa | νb (0)i
i

=

=

X

(2.31)(2.32)bXXi(2.30)

Uai Uib−1 e−iEi t δab(2.33)b−1 −iEi t
Uai Uiae(2.34)i

The probability that the same flavor is kept, P (a → a, t), is:P (a → a, t) = | hνa | νa (t)i |2XX−1−1 −i(Ei −Ej )t=
Uai Uia
Uaj Ujaei(2.35)(2.36)

jFinally substituting equation (2.26) in (2.36) yields:
P (a → a, t) = 1 − sin2 2θ sin2

∆m2
t
4E

(2.37)

where ∆m2 = m22 − m21 . Therefore, the probability that an electron neutrino generated at t = 0
remains an electron neutrino after time t, or distance L (assuming t = L in natural units (c=1))
becomes:
∆m2
L
4E
πL
P (νe → νe , L) = 1 − sin2 2θ sin2
LV

P (νe → νe , L) = 1 − sin2 2θ sin2

(2.38)

where
LV =

4πE
E(MeV)(m)= 2.482∆m∆m2 (eV2 )(2.39)

is the oscillation length in the vacuum.
The vacuum oscillation phenomenon is searched for by several experiments which use accelerators or reactors as neutrino source. However, these experiments did not find the phenomenon.
Recently, observations of atmospheric neutrinos (which are decay products of mesons (π’s, K’s,
or µ’s) created in interactions of primary cosmic rays (protons and nuclei) in the atmosphere),by Super-Kamiokande confirmed that neutrino oscillation does occur between ν µ ↔ ντ channel1 .
The atmospheric neutrinos generated on the opposite side of the Earth travel about 1 × 10 4 km.
Therefore, the observation of 1 GeV atmospheric neutrinos has sensitivity for ∆m 2 down to∼ 2.5 × 10−3 eV2 . Actually, the observations suggest that non-oscillation is rejected at the 6.2σ
1or νµ ↔ νs channel; where νs is sterile neutrino

21

level from the zenith angle distribution of neutrino events and the double ratio of muon neutrino
and electron neutrino flux of measured to expected values, and that the allowed region of ∆m 2
is 10−3 ∼ 10−2 eV2 [70].
Another aspect of vacuum oscillation is expected for solar neutrinos, if ∆m 2 between νe andνµ is suitable. The distance between the Sun and the Earth is about 1.5×10 11 m, and typicalenergy of the 8 B neutrinos is about 10 MeV, therefore, if the ∆m 2 is of order 10−10 eV2 and themixing angle is sufficiently large, a seasonal deviation from the expected value of ν e flux time
variation caused by the elliptical orbit of the Earth may be observed. And the shape of the 8 B
neutrino energy spectrum is distorted due to the energy dependence of the vacuum oscillation
length. Since this oscillation is caused by a just agreement of the vacuum oscillation lengthand the orbital radius, this is called the ’Just-so’ solution. In order to verify this solution, highstatistical solar neutrino events, hence, massive detectors like Super-Kamiokande, are needed.

2.6.2

Neutrino oscillation in matter

Wolfenstein suggested that neutrino oscillations in matter are different from those in vacuum
due to an additional potential the ν e experiences. With analogy to optics, the phase factor of
propagation of the neutrino is changed from ipx to ipn l x, where nl is the index of refraction offlavor l. nl is represented as follow [71],nl = 1 +

2πN
fl (0)
p2(2.40)

where N is the number of density of scatters and f l (0) is the forward scattering amplitude. An
electron, a muon and a tau neutrino interact with an electron, a proton and a neutron via aneutral current interaction. For solar neutrino energy, only electron neutrinos can interact with
an electron via a charged current interaction (figure 2.11). This causes the difference in f l (0)

(a)

(b)
ν

ν

νe

Z

e,p,n

e

W

e,p,n

e

νe

Figure 2.11: The Feynman diagrams of neutrino interaction in matter. Figure (a) shows neutral
current interaction via Z boson exchange between a neutrino and an electron, a proton ora neutron. Figure (b) shows charged current interaction via W boson exchange between an
electron neutrino and an electron.
for an electron neutrino from the other type neutrinos, and this additional phase shift causes
neutrino oscillation in matter to differ from that in vacuum. Since S.P.Mikheyev, A.Yu.Smirnov
22

applied this theory to the solar neutrino problem, this effect is called the ’MSW effect’. The
MSW effect could solve the solar neutrino problems, if ∆m 2 ∼ 10−5 and sin2 2θ ' 10−3 ∼ 1. Inorder to explain the MSW effect mathematically, let us consider the propagation of a neutrino inmatter. Again, only two flavor eigenstates are considered for simplicity. The time development
equation of flavor eigenstates in matter is

  


 

d
| νe (t)i
E1 0
VC + V N 0| νe (t)i
−1
i
= U
U +
(2.41)
0 E2
0VN| νµ (t)i
dt | νµ (t)iwhere VC and VN represent the effective potential for neutral and charged current interactions,R−i VN dt .
respectively. The diagonalcomponent
of
V
can
be
absorbed
intoacommonphase,eN√
VC is calculated to be 2GF Ne , where GF is the Fermi coupling constant and N e is the electron
density. Equation (2.41) is rewritten,d| νe (t)ii
dt | νµ (t)i


 

1 −∆m2 cos 2θ + A
1 2
1∆m2 sin 2θ| νe (t)i2(m + m2 + A)I +Mef f =
(2.42)∆m2 sin 2θ
∆m2 cos 2θ − A| νµ (t)i2E 2 12
where√
A = 2 2GF Ne E

(2.43)and I is the 2 × 2 unit matrix. Eigenvalues of the matrix are regarded as effective masses of two
mass eigenstates in matter. The eigenvalues areq
m2 + m22 + A 1
m2im = 1(∆m2 cos 2θ − A)2 + ∆m4 sin2 2θ
(i = 1, 2)(2.44)±
2
2

and the eigenstate in matter is


 

| νe icos θm − sin θm| ν1m i=| νµ isin θm cos θm| ν2m i(2.45)

where θm is the effective mixing angle in matter and given by,tan 2θ
A
1−
2∆m cos 2θ
tan 2θ
tan 2θm =LV
1−
Le cos 2θ

tan 2θm =(2.46)√
with Le = 2π/GF Ne . Thus, if the following relation is satisfied, the mixing angle in matterbecomes maximal ( θm = π/4 ) even if the vacuum mixing angle is small.
√(2.47)
LV = Le cos 2θ
or∆m2 cos 2θ = 2 2GF Ne E
This condition is called ’resonance condition’. The electron
density at which the resonant con√dition is satisfied is denoted as Ne,res ≡ ∆m2 cos 2θ/2 2GF E.
Let us consider solar neutrinos. As shown in figure 2.6, the electron density varies as afunction of solar radius.
It is largest in the center where nuclear fusion happens and it decreases as the radius increases.
Therefore, a neutrino with energy larger than the critical energy E crit , always passes through aposition where resonance condition is satisfied. The critical energy is given by:∆m2∆m2 cos 2θ
MeV(2.48)= 6.6 cos 2θ
Ecrit = √10−4 eV2
2 2GF Ne,c
23

m

2

ν2

ν2

ν1

ν1
N e,resNe

Figure 2.12: MSW effect in the Sun.

where Ne,c is the electron density in the center of the Sun. Figure 2.12 shows the mass eigenvaluesof two neutrino mass eigenstates in matter as a function of electron density. If the energy ofa neutrino is greater than Ecrit , θm ∼= π/2 from equation (2.46), hence, | ν e i is almost | ν2 i.
While the mass eigenstates propagate from the center of the Sun to the surface of it, the mass ofthe eigenstates changes as shown in figure 2.12. When a neutrino passes the resonance region,
θm becomes π/4 and the mixing becomes maximal. If the variation of the electron density isreasonable (see eq(2.50)), the main component of flavor | ν 2 i state changes from | νe i to | νµ i
adiabatically, if the vacuum mixing angle θ is small enough. Therefore, a neutrino which is
produced as an electron neutrino becomes a muon neutrino when it reaches the surface where
the electron density is almost zero. The condition which allows the transition of neutrino flavor
from νe to νµ adiabatically is called adiabatic condition.
Actually, level jumping from | ν2 i to | ν1 i occurs. The probability of this jump, P jump , isapproximately calculated by L.D.Landau and C.Zener [72], π sin2 2θ
Pjump = exp − 4 E cos 2θ

The adiabatic condition holds if Pjump  1, namely,sin2 2θ∆m2 ≥ E cos 2θ∆m2 1 dNe 
Ne dr

1 dNe
Ne dr

(2.49)(2.50)

Figure 2.13 shows the example of the MSW effect in the Sun, where E/∆m 2 and sin2 2θ are
6.0×105 and 0.001, respectively. As shown in figure 2.13, the resonance occurs at R/R ' 0.3
and it is found that νe is converted to νµ with about 35% probability.
As the MSW effect for certain parameter range in ∆m 2 and sin2 2θ may convert an νe intoa νµ on its way out of the Sun, it is possible for part of this parameter range that the ν µ are
converted back to νe when passing through the Earth. Figure 2.14 shows the electron density
distribution as a function of the radius of the Earth. This effect leads to the prediction that theobserved electron neutrino flux at night when neutrinos go through the Earth may be larger thanthat during the day when the neutrinos come directly from the Sun. This is called the ’day-night24

P(νe → νe)

1

0.8

0.6

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

R/RSUN3

ne/NA (/cm )Figure 2.13: Survival probability P (ν e → νe , L) as a function of the solar radius when E/∆m 2 =6.0 × 105 and sin2 2θ = 0.001.

7
6
5
4
3
2
1
0

0

0.2

0.4

0.6

0.8

1

R / Rearth
Figure 2.14: The electron density distribution as a function of the radius of the Earth[73].

25P(νe→νe)effect’. Again, like the seasonal effect, in order to study this effect, a high statistics observation
E
is necessary. Figure 2.15 shows the probability P (ν e → νe ) distribution as a function of ∆m2
for day-time and night-time (θz = 0, 180◦ , respectively, where θz is the zenith angle defined infigure 2.16). The energy dependence of survival probability of ν e leads to a distortion of energy
spectrum.

1

0.8

sin22θ=0.1

0.6

0.4

day
night
(cosθz=-1)

0.2

0

4

5

6

7

8

9

10

2

2

log(E/∆m ) (MeV/eV )Figure 2.15: The probability P (νe → νe ) at some place on the Earth surface is drawn as aE◦function of ∆m
2 both for day-time (solid line) and night-time (θ z = 180 ) (broken line), where2
sin 2θ = 0.1.

2.7

The evidence of solar neutrino oscillation

Denoting the 8 B solar neutrino flux obtained by the SNO CC measurement as φ CC
SNO (νe ) and that
CC (ν ) = φES (ν ) is expectedobtained by the Super Kamiokande νe scattering as φES
(ν
),
φ
SK x
SNO e
SK x
for the standard neutrino physics. However, SNO’s initial data [27] indicate
CC
6
−2 −1
φES
SK (νx ) − φSNO (νe ) = (0.57 ± 0.17) × 10 cm s .

(2.51)The significance of the difference is > 3σ, implying direct evidence for the existence of a nonνe active neutrino flavor component in the solar neutrino flux. A natural and most probableexplanation of neutrino flavor conversion is neutrino oscillation. Note that both the SNO [26]and Super Kamiokande [2] flux results were obtained by assuming the standard 8 B neutrino
spectrum shape. This assumption is justified by the measured energy spectra in both of theexperiments.
ES
From the measured φCC
SNO (νe ) and φSK (νe ), the flux of non-νe active neutrinos, φ(νµ or τ ),and the total flux of active 8 B solar neutrinos, φ(νx ), can be deduced:φ(νµ or ντ ) = (3.69 ± 1.13) × 106 cm−2 s−1
6φ(νx ) = (5.44 ± 0.99) × 10 cm

−2 −1

s

(2.52)(2.53)The last equation is a solar model independent result and therefore tests solar models. It
shows very good agreement with the 8 B solar neutrino flux predicted by the BP2000 SSM.
26

Z
The earthθz

The sunFigure 2.16: The definition of zenith angle.

The most recently reported SNO’s results including data of salt phase are
+0.08
+0.06
6
−2 −1
φCC
SNO (νe ) = (1.59−0.07 (stat.)−0.08 (syst.)) × 10 cm s

(2.54)

6−2 −1
φNC
SNO (νe ) = (5.21 ± 0.27(stat.) ± 0.38(syst.)) × 10 cm s

(2.56)

+0.31
6
−2 −1
φES
SNO (νe ) = (2.21−0.26 (stat.) ± 0.10(syst.)) × 10 cm s

(2.55)The resultant φ(νµ or ντ ) from SK and SNO flux results is
φ(νµ or ντ ) = (3.62 ± 0.48) × 106 cm−2 s−1(2.57)

where the statistical an systematic errors are added in quadrature. Now φ(ν µ or ντ ) is 7.5σ
above 0, providing stronger evidence for neutrino oscillation.

2.8

Global analysis of the solar neutrino data

A number of solar neutrino flux results in Super Kamiokande and all radio chemical solar neutrino
experiments yielded various solutions in terms of two neutrino oscillations. For example, Bahcall,
Krastev, and Smirnov [74] found at 99.7% confidence level eight allowed descrete regions in
two neutrino oscillation space. From the flux constrained results, these are five solutions for
active neutrinos (LMA, SMA, LOW, VAC, and Just So 2 ) and three separate solutions for sterile
neutrinos (SMA(sterile), VAC(sterile), and Just So 2 (sterile)). LMA, SMA, LOW, VAC, areabbreviations of large mixing angle, small mixing angle, low probability or low mass, and vacuum,
respectively. The summary of solutions is shown in Table 2.6.
The best-fit points for the five solutions for active neutrinos are shown below.
• LMA : ∆m2 = 4.2 × 10−5 eV2 , tan2 θ = 0.26
• SMA : ∆m2 = 5.2 × 10−6 eV2 , tan2 θ = 5.5 × 10−4
• LOW : ∆m2 = 7.6 × 10−8 eV2 , tan2 θ = 0.72
27

Effect
Vacuum Oscillations
MSW effect

Solutionfor Active neutrino
VAC(active)
LMA(active)
SMA(active)
LOW(active)
Just So2 (active)

Solutionfor sterile neutrino
VAC(sterile)
SMA(sterile)
Just So2 (sterile)

Table 2.6: Expected solution from flux constrains of SK and radiochemical experiments.
• Just So2 : ∆m2 = 5.5 × 10−12 eV2 , tan2 θ = 1.0• VAC : ∆m2 = 1.4 × 10−10 eV2 , tan2 θ = 0.38
For the three solutions for sterile neutrinos, the best-fit points are similar to the corresponding solutions for active neutrinos. The oscillation allowed region for each solution from flux
constrains of SK, SNO(CC:Charged current results) and radiochemical experiments is shown infigure 2.17.
The survival probability of expected energy spectrum for each solution is shown in figure 2.18.
The top figure shows the predicted energy spectrum from BP2000 SSM. The solid lines for LAM
and LOW solutions indicates the night-time spectrum. The dashed lines indicates the day-time
spectrum. The horizontal axis is the neutrino energy (MeV).
The survival probability of the expected energy spectrum and day-night energy spectrum(zenith spectrum named in Super Kamiokande) for typical parameter values of oscillation solutions are dependent on recoil electron energy strongly like as the shown figure. So, the information of the spectra shape can be used to distinguish between possible solutions.
In addition to above flux informations, the Super Kamiokande day-night spectrum and SNO
results constrains the probable solution. Especially, Super-Kamioknde-I results of the energy
and zenith spectrum have effect on determination of solar neutrino oscillation parameter remarkably because of the large statistical and precise measurements. Without SK data, thestrongest constraint of the parameters is a χ 2 fit to the charged-current neutrino rates fromGALLEX/GNO, SAGE, Homestake, and SNO experiments.
However, SK data breaks the degeneracy in χ 2 of these regions by analyzing the shape of thezenith-angle spectrum which combines spectrum and daily variation analysis. Here we utilize
the zenith angle spectrum from the entire SK-I data set collected between May 31st, 1996 andJuly 15th, 2001 (1496 live days). There is no indication of spectral distortion, the χ 2 to an
undistorted spectrum is 4.6 for 7 degrees of freedom (71% C.L.). No significant daily variation
is found, the day/night rate asymmetry is

Asym.day,night =φday (νe ) − φnight (νe )= −0.021 ± 0.020(Stat.)+0.013−0.012 (Syst.)
1/2(φday (νe ) + φnight (νe ))(2.58)

If the SMA solution was really a solution of the neutrino oscillation, the survival probabilityof energy spectrum will increase with energy, while it is almost flat for the LMA and LOW
solutions.
Figure 2.19 shows the result of the zenith angle spectrum fit. The SMA and VAC regions
are excluded since they require a distorted 8 B neutrino spectrum. The lower part of the LMA
and the upper part of the LOW solution predict daily variations and are therefore disfavored.
The excluded areas are independent of the SSM neutrino fluxes.
Since there is no indication of a distortion of the SK zenith spectrum, an analysis of thezenith spectrum shape alone can only yield excluded regions. However, if the 8 B flux is known,
28

/cm2 /sec /MeV

10
10
10
10
10
10
10
10

Probability

SK 1496 Days
-4

11

pp

7

Be

10

7

10

3

110

8

B

-1

1
SMA solution

10

1
LMA solution

10

1
LOW solution10

1
VO solution

10

0.5

-5
-6

Probability

10

-3

-7

0 -1
110

0.5

-8
Probability

10-9allowed(Ga+Cl+SNO CC+SK Rates)

-10
-11
-12

10

νe→νµ/τ (95%C.L.)
-4

10

-3

10

-2

0 -1
110

0.5

10

-1

1

10
10
2
tan (Θ)2

Probability

2∆m in eV

2

10

0 -1
110

0.5

0 -1
10

Figure 2.17: The 95% C.L. allowed regions
which satisfy all four flux measurements:
Chlorine, Gallium, SK and SNO(CC).

1

10Energy(MeV)

Figure 2.18: The expected energy spectrum for each oscillation solution and daynight time energy spectrum for LMA and
LOW solutions. The horizontal axis is theneutrino energy (MeV).

29

10
10
10
10
10
10
10
10

2

10

2

-3

10

∆m in eV22

10∆m in eV10

SK 1496 Days
-4
-5

10

-6

10

-7

10

excluded(rate not-8 constrained)

10

-9

10
allowed(Ga+Cl+SNO CC+SK Rates)

-10

10
10

-11
-12

10

Zenith Spectrum νe→νµ/τ (95%C.L.)
-4

10

-3

10

-2

10

-1

1

10
10
2
tan (Θ)

10

-3

-4

-5

-6

-7

-8

-9

-10

-11

-12

10

2

Figure 2.19: SSM flux independent excluded areas using the SK zenith spectrum
shape alone overlaid with the allowed regions.

95%C.L.
Zenith Spectrum+SK Rate νe→νµ/τ
-4

10

-3

10

-2

10

-1

1

10
10
2
tan (Θ)2

Figure 2.20: Allowed areas using only SK
data and the SSM 8 B neutrino flux prediction. Both allowed regions indicate large
neutrino mixing.

the SK rate can be predicted. Then, the zenith spectrum shape can be combined with the SKrate into a single measurement. Figure 2.20 shows the allowed regions using SK rate between
SSM and observed flux and zenith angle spectrum in combination with the 8 B flux prediction
and uncertainty of the SSM. The remained allowed regions is two: the LMA and quasi-VAC
solution.
Finally, a comparison between the SK rate and SNO’s charged-current rate yields another
8 B flux constraint which is independent on the SSM, so a combination of the SK rate and zenith
angle spectrum with the SNO charged-current rate need not rely on any neutrino flux prediction.
Figure 2.21 shows the determination of the oscillation solution from the all solar neutrino data
combination (Homestke, GALLEX/GNO, SAGE, SK, ,and SNO(CC, NC reaction)).
The combined fit to the charged-current interaction rates measured by several experiments
result in many allowed regions of neutrino mixing and mass square difference: LMA, SMA, LOW,
Just-So, VAC. The absence of spectral distortion and daily variations of the SK solar neutrino
interactions rate strongly constrains these regions rejecting SMA, LOW, and VAC solutions at
95% C.L., while leaving only the higher mass square difference LMA and the quasi-VAC region.
When all solar neutrino data are combined with SK data, only the higher mass square difference
LMA solutions remain at 98.9% C.L.. The best fit parameter is like following.
∆m2 = 6.9 × 10−5 eV2 , tan2 θ = 0.38

(2.59)

Thus the combined results of all solar neutrino experiments can be used to determine a uniqueregion of oscillation parameters that explains the famous solar neutrino problem.
The LMA solutions means the following phenomenon. A ν µ converted from νe in the Sun
may oscillate back to νe via the MSW effect in the Earth. So the day-night time results might
be different for a certain parameter region. This is called “neutrino regeneration”. In the Earth,
the resonance condition is represented as follows [72]:∆m2 ≈ 4 × 10−6 eV2 (ρ/5Ye gcm−3 )30(2.60)

2
2

10∆m in eV

10

10
10
10
10
10
10
10
10

-3
-4
-5
-6
-7
-8
-9
-10
-11
-12

10

Ga+Cl+SK+SNO Rates
95%C.L.
8and SK Zen Sp νe→νµ/τ ( B, hep free)
-4

10

-3

10

-2

10

-1

1

10
10
2
tan (Θ)2

Figure 2.21: The combined fit to SK data and all rates favor the LMA solution. The best fit
point is indicated by the asterisk. All fits are independent of the SSM 8 B flux and hep flux.

where the density of the Earth ρ = 3.5 ∼ 13gcm −3 , the neutrino energy Eν ∼ 10M eV
and the electron number per atomic number Y e 1/2. The oscillation length of the resonance inLM,res ∼ 6.8 × 108 cm/ sin 2θ. It is of the order of the diameter of the Earth (1.3×10 3 cm), even
if sin 2θ is large.

31

Chapter 3

Super Kamiokande
In this chapter, the detection principle and the components of the SK detector are described indetail. The cross section for νe − e elastic scattering and Čerenkov radiation is explained. The
water purification system and air purification system to reduce the background of radioactivity
in SK is also presented. The DAQ system is described in detail. About the detector simulation,
the explanation is presented in appendix B.

3.1

Detection principle in Super-Kamiokande

When a charged particle having a velocity of v travels in a medium the index of refraction ofwhich is n, Čerenkov photons are emitted if v > c/n, where c is the light velocity in vacuum.
Čerenkov photons are emitted into a forward cone around the particle track with opening angleof θ measured from the direction of the particle. θ is given by:cos θ =

1
nβ

(β ≡

v
)
c

(3.1)

In the case of pure water, (n = 1.334), θ is about 42 ◦ for β ' 1. The number of Čerenkov
photons (dN ) generated in the wavelength interval dλ per track length dx is,


1
1
dxdλ
(3.2)
dN = 2πα 1 − 2 2n β
λ2α is the fine structure constant. The number of Čerenkov photons in the wavelength range of300∼600nm, which is the sensitive region of the PMTs, is about 340 in water per 1cm track
length for a charged particle having a unit charge and velocity of β ' 1. The energy thresholdfor an electron to emit Čerenkov photons is √nn2 −1 me ' 0.78 MeV, where me = 0.511 MeV isthe rest mass of an electron.
A neutrino interacts with electrons via neutral and charged current interaction:
ν+e→ν+e
The differential cross section dσνe of neutrino-electron elastic scattering is given by:()

G2F me
Te 2
me Te
dσνe
=
A0 + B 0 1 −+ C0 2
dTe
2π
Eν
Eν

(3.3)

(3.4)

where Te is the scattered electron’s kinetic energy, E ν is the incident neutrino energy, GF =1.16636 × 10−11 MeV−2 is the Fermi coupling constant. The order of magnitude for the crossG2 msection is set by the first coefficient F2π e = 4.31×10−45 (cm2 /MeV). The parameters, A0 , B0 , C032

Cherenkov light travel direction

Charged particle travel direction

θC

Cherenkov Ring
Figure 3.1: The definition of the Čerenkov angle.

in equation (3.4), are defined as:
A0 = (gV + gA )2 ,

(3.5)

gV

(3.6)

gV

2
B0 = (gV − gA )2 , C0 = gA
− gV2
1
1
= 2 sin2 θW + , gA = +for νe221
1= 2 sin2 θW − , gA = −for νµ or ντ
2
2

(3.7)

where θW is the Weinberg angle and sin2 θW = 0.2317. The total cross section σνe is calculated
by integrating equation (3.4) for T e from 0 to Tmax ,σνe ==Z Tmax
0
G2F me

2π

dσνe
dTe
dTe
"

B0 Eν
A0 Tmax +
3

(



Tmax
1− 1−
Eν

3 )

2
C0 me Tmax
+
2
Eν2

#

(3.8)

where Tmax is maximum kinetic energy for the recoil electron in (3.3),
Tmax =

Eν
me
1+
2Eν

(3.9)

The differential and total cross sections of ν-e scattering with radiative corrections are calculated by [77]. Some of the Feynman diagrams for the electro-magnetic one loop contributions
are drawn in figure 3.2. These corrections reduce the total cross section by about 2%. For thehighest energy 8 B neutrinos, the cross section is reduced by about 4%. In ν µ -e scattering there
is no contribution from charged current interactions at low energies. Total cross sections forνe -e and νµ -e scattering with radiative corrections as a function of incident neutrino energy are
drawn in figure 3.3. The total cross section for the ν e -e scattering is about 6 times larger thanthat for νµ -e scattering due to the contribution of the charged current interaction. Hence, if
an electron neutrino is converted to another type of neutrino (ν µ or ντ ), the event rate of ν-escattering decreases.
The differential cross section in the case of incident neutrino energy of 10 MeV for ν e +e→
νe +e scattering is shown in figure 3.4 [77].

33



ν





ν




ν

Ζ



ν



   ( )* +  ,   -./  - ' 0 !  #
ν





ν



ν

ν

ν

ν

Ζ

Ζ

γ

γ



γ









! " "#            





$&%

 ' 

150

2

3

-46

10

dσ/dTe ×10 (cm /MeV)

total cross section ×10-46cm2

Figure 3.2: A Feynman diagram for one-loop QCD correction and Feynman diagrams for oneloop electroweak radiative correction.

140
130
120

10

2

110

10

νe+e→νe+e

100

νµ+e→νµ+e

90
80

1

70
60
-1

10

0

2

4

6

8

10

12

14

16

18

50

20

neutrino energy (MeV)

0

2

4

6

8

10

Te(Mev)

Figure 3.3: Total cross sections for ν e -eand νµ -e scattering as a function of energyof an incident neutrino.

Figure 3.4: Differential cross section of
νe +e→ νe +e scattering for an incident
neutrino energy of 10 MeV. The horizontal axis is the kinetic energy of a recoil
electron.

34

The recoil electron energy spectrum F (T e ) is calculated to be:Z Eν,maxdσνe (Eν , Te )F (Te )dTe =φ(Eν )dEν dTe
dTe
0(3.10)

arbitrary unit

where φ(Eν ) is energy spectrum of the neutrinos and E ν,max is the maximum neutrino energy.
In the case of 8 B solar neutrinos, the energy spectrum of the recoil electrons is shown in figure
3.5.

10

4

10

3

10

2

10

1

-1

10

-2

10

-3

10

2

4

6

8

10

12

14

16

18

20

total energy (MeV)

Figure 3.5: The energy spectrum of recoil electrons 8 B solar neutrino scattering. The horizontal
axis is the total energy of the electrons.
The scattering angle θ is determined by the kinematical condition,me
1+Eν
cos θ = r
2me
1+
Te

(3.11)

When the neutrino energy is high enough compared with the electron mass, the scattering angle
can be approximated by:r
2meθ≤(3.12)Te
Therefore, the recoil electron keeps the information about incident neutrino’s direction. However,
because of multiple scattering in the water, the angular resolution is limited to about 27 ◦ for anelectron energy of 10 MeV.
The advantage of using water Čerenkov counters for the observation of solar neutrinos isthat the detector can measure the precise time when an electron is scattered, and the energy
and direction of the recoil electron. Hence, it is possible to measure how much the electron
neutrino flux changes between day and night, or seasonally. Also the energy spectrum of theincident neutrinos can be inferred from the measured energies of the recoil electrons.

3.2

Detector description

SK was commissioned and data taking began April, 1996. It was shut down for maintenanceand upgrade in July 2001, after logging 1,678 live days of running with high efficiency. In this35

elapsed day

paper, this initial 1996∼2001 running period will be treated, referred to as SK-I. Figure 3.6 isthe integrated total live-time as a function of elapsed day from April 1, 1996 to July 15, 2001.

1800

1600

1400

1200

1000

800

600

400

200

0

0

200

400

600

800

1000

1200

1400

1600

1800

elapsed day from 1996.4.1

Figure 3.6: The integrated live time from the beginning of SK. The dashed line is expected total
live time.
SK is a water Čerenkov detector located underground in the Kamioka mine in Gifu Prefecture, Japan. Its latitude and longitude are 36 ◦ 25’ N and 137◦ 18’ E, respectively. The averagerock over burden above SK is 2800 m.w.e. A schematic view of the detector is given in figure 3.7.
The reason why the detector is underground is to shield against cosmic ray muons. Comparedto ground level, the intensity of muons is reduced by about 1/100000 at the depth of the SK
detector. The muon rate in SK is 1.88Hz.
Measured background radiation rates for γ rays and neutrons near the Kamiokande cavity
dome [1] are shown in table 3.1.
Particle
γ raysNeutrons

Energy range
Eγ > 0.5 MeV
Eγ > 5 MeV
En ≤ 0.05 MeV
0.05 < En ≤ 2.5×106 MeV
2.5×106 < En ≤ 2.5×107 MeV

Rate
0.1 cm−2 s−1 sr−1
2.7 ×−6 cm−2 s−1 sr−1
1.4 ×10−5 cm−2 s−1 sr−1
2.5 ×10−5 cm−2 s−1 sr−1
0.33 ×10−5 cm−2 s−1 sr−1

Table 3.1: Measured background radiation rates for γ rays and neutrons near the Kamiokande
cavity.
A cylindrical stainless steel tank forms the SK detector. The tank, whose total height is 41.4
m and diameter is 39.3 m, holds 50,000 m 3 of ultra pure water with a water and air purification
system, photomultiplier tubes (PMTs), electronics and online data acquisition system, andoff-line computer facilities. SK is split into two optically separate detectors: inner and outersummarized in table 3.2. The separation between the inner and outer detectors is provided bya stainless steel structural grid. Tyvek, and polyethylene black sheets. Although the inner andouter detectors are optically separated, water can flow between the two detectors.
The local detector coordinate system of SK is shown in figure 3.8.
The wall of the cave is covered by “Mineguard”, a polyurethane material made by the
Canadian company Urylon, which blocks radon emanating from the rock.
36Central Hut

LINAC

Electronics Huts
Control Room

Water System
Super Rn less air system

Outer
Detector

Inner Detector
Mt. Ikenoyama

MozumiAtotsu tunnel

Entrance of Atotsu tunnel
Radon hutSK

Figure 3.7: Overview of the Super-Kamiokande.

Z
Y

Y

LINAC

0
X

X
Entrance to SK

49.05 degree
North
Figure 3.8: The local detector coordinate system of SK.

37

The tank is sealed tightly to keep the mine’s radon rich air outside. Radon gas is the mostserious background for the solar neutrino analysis. The concentration of radon gas in the dome
is about 1500 Bq/m3 in summer time and 30 Bq/m3 in winter time. This large difference iscaused by the flow of air in the mine. Air blows into the mine in the winter and out of the minein the summer.
Item
Tank dimension
volumeInner part dimension
volumeNumber of PMT
Outer part thickness
volumeNumber of PMT
Fiducial area thickness
Fiducial area volume

Value
39.3m in diameter×41.4m in height
50 ktons
33.8m in diameter×36.2m in height
18 ktons
748 (top and bottom) and 7650 (barrel)
2.6 m on top and bottom
2.75 m on barrel
32 ktons
302 (top), 308 (bottom) and 1275 (barrel)
2m (5.5 R.L. and 3.3 N.L.) from the inner wall
22.5 ktons

Table 3.2: Several parameters of Super-Kamiokande detector. R.L and N.L mean radiation
length and nuclear interaction length, respectively.
We use 11,146 20-inch PMTs in the inner detector and 1885 8-inch PMTs in the outerdetector, as summarized in table 3.2.

3.2.1

The inner detector

The inner detector is a cylinder of 36.2 m in height and 33.8 m in diameter. It encloses 32.481
m3 of water, which is viewed by 11,146 inward-facing 50 cm diameter photomultiplier tubes(PMTs), which will be explained later. All of the PMTs and two of the outer detector PMTs
constitutes one super-module. Figure 3.9 is schematic view of a super module. In the innerdetector, PMTs are placed at intervals of 70 cm, and the ratio of PMT area to all area (photo
coverage) is 40.41%. The wall of the tank is covered with black polyethylene terephthalate sheets(called “black sheet”) behind the inner PMTs to suppress the reflection of Čerenkov light andthe leakage of light from or to the outer detector.
Super-Kamiokande can detect events over a wide range of energy, from 4.5 MeV to over 1
TeV. Each ID PMT has a dynamic range from 1 photoelectron (pe) to 300 pe. For low energy
events used for solar neutrino studies, the energy of event is calculated from the number of PMT
hits, while for high energy is measured terms of net charge detected PMTs.

3.2.2

The outer detector

The outer detector surrounds the inner detector and provides an almost uniformly thick (1.95∼2.20m) 4φ active veto. The purpose of the outer detector is to active veto cosmic ray muons, andto decrease the detection of γ rays from the surrounding rock.
The outer detector is reviewed by 1,885 outward-pointing 20 cm diameter PMTs (HAMAMATSU R1408) with 60 cm square wavelength shifter plates [1] to increase the photo coverage.
All outer surfaces in the outer detector are covered with a reflective material, White Tyvek, toenhance light collection in the OD. Thus, all surfaces of the outer tank are covered with whitetyvek sheets with a reflectivity of above 80%.

38

TyvekTop

8" PMT

Black seat

Barrel20" PMT

BottomFigure 3.9: A super-module supports twelve ID PMTs and two OD PMTs.

3.3

ID photomultiplier tube

We use 50 cm diameter PMTs (HAMAMATSU R3600-05) in the ID. A schematic view of a PMT
is given is figure 3.10. It was originally developed by the HAMAMATSU Photonics Company
and Kamiokande collaborations and improved for use in SK [1]. The improved photons are thefollowing :• The 1 photo electron(p.e.) peak has become clearer by optimizing the structure of thedynode as shown in figure 3.11.
• A lager area for the dynode has reduced the influence of the residual geomagnetic field.
Hence, the timing resolution (i.e. the transit time spread) at the 1 p.e level has become
better (5 nsec → 3 nsec).
The glass body of the PMT is made of Prevex glass of 5 mm thickness which is transparent
to light down to 330 nm in wavelength. The photocathode area is coated with Bialkali material(Sb-K-Cs). The quantum efficiency is a function of light wavelength is shown in figure 3.12. It
is 22% at 390 nm.
The dynode has Venetian blind structure with 11 stages, which provides a large photosensitive area. The dark noise rate caused by thermal electrons from the photocathode is shown
figure 3.13. The average dark rate is stable around 3.14 kHz after 2 months from the start ofSK. The value of supplied voltage which gives a gain of 10 7 is 2000 V. The average transit time
is about 100 nsec for multi p.e. light. For single p.e. light, the variation of the transit time of
PMTs is about 10 nsec in a supplied voltage range 1500 to 2000 V.
The large size of the PMTs makes them susceptible to the geomagnetic field. To obtain auniform response from the PMTs, the geomagnetic field (450 mG in natural conditions) must
be reduced to less the 100 mG [1]. Compensation coils are used accomplish this in SK and theresidual magnetic field in kept at less than 100 mG in every position of the detector.
39

Some of the PMTs are dead by short circuit or some other unknown response. The time
variation in the number of dead PMTs is shown figure 3.14. The fraction of the dead PMTs isabout 1.4%.

~ 70000

φ 116

φ 82 2

φ 254 10

< φ 520

photosensitive area > φ 460

glass multi-sealcable length

cable

water proof structure( 610 20 )

~ 720

(mm)

0.7

0.225
0.2

0.6

quantum efficiency

distribution (arbitrary unit)

Figure 3.10: Schematic view of a 50 cm photomultipiler tube (HAMAMATSU R3600-05).

0.5
0.4
0.3
0.2
0.1
0

0.175
0.15
0.125
0.1
0.075
0.05
0.025

0

1

2
3
photo-electron

4

0

5

Figure 3.11: The single p.e. distribution
from 50 m PMTs. There is a clear peakaround 1 p.e.. A spike near the lowest region is caused by photo-electron that missthe first dynode.

200

300

400
500
wavelength (nm)

600

700

Figure 3.12: The quantum efficiency of
the PMTs and the relative Čerenkov spectrum as a function of light wavelength.

Figure 3.15 shows the time variation of high and low energy trigger rate from the beginningof SK-I in ID detector. The right plot is high energy trigger rate and the left plot is low energy
trigger rate.

3.4

The water purification system

In purities in the SK water can cause strong attenuation and scattering of Čerenkov light.
Moreover, if they are radioactive, like 222 Rn and 220 Rn, they could become a possible source of
background to the solar neutrino events, because the β-decay of their daughter nucleus causes a40

Number of bad PMTs

dark rate (kHz)

6
5.5
5

300

250

200

4.5
4
150

3.5
3
100

2.5
2
50

1.5
1

0

100

200

300

400

500

600

700

800

900

0
1000

2000

3000

4000

elapse day from 96/1/1

Figure 3.13: The time variation of dark
rate from the beginning of SK.

6000

7000

8000

9000

10000

Figure 3.14: The time variation of thenumber of dead PMTs from the beginningof SK.

20

Hz

Hz

5000

Run progress from 1996.4.1 to 2001.7.15

30

18
25
16

14
20
12

10

15

8
10
6

4
5
2

0

0

200

400

600

800

1000

1200

1400

1600

1800

0

2000

elapsed day from 1996.4.1

0

200

400

600

800

1000

1200

1400

1600

1800

2000

elapsed day from 1996.4.1

Figure 3.15: The time variation of high and low energy trigger rate from the beginning of SK.

41

similar event as solar neutrino event which means ν e − e elastic scattering. The decay chain of
222 Rn is shown in figure 3.20. None of the electrons or γ rays from the decay chain have energy
above threshold for this analysis 4.5 MeV. However, because of finite energy resolution of SK,such low energy electrons are sometimes observed as electrons with energy above 4.5 MeV. So,
the purity of the water is essential for solar neutrino observation in SK.
The SK water purification system has been modified and upgraded with Organo Corporation.
In this section, the basic components of the system is explained. The details of the modification
and upgrading of the water system is explained in chapter 7 in detail.
The source of water in SK is an underground aquifer in the Kamiokande mine. The water
purification system makes highly purified water from the mine water. Figure 3.16 is a basic
schematic view of the water purification system. The water passes through the following components:• 1 µm normal filter :Remove relatively large particles. Some of Rn also rejected with dust.
• Heat exchanger(HEX) :Water pumps increase the water temperature. The heat exchanger decrease the temperature down to about 12∼13◦ C to inhibit bacterial growth and to suppress the water
convection in the SK tank.
• Ion exchanger(IEX) :Removes metal ion (Fe2+ , Ni2+ , Co2+ ) impurities in the water. It can also remove 218 Po
which is a daughter nucleus as a result of the decay of 222 Rn and easily ionize. The water
resistance is best indication of the concentration of the ion in the water. If no ion is in
the water, the water resistance will be expected 18.2 MΩ. In the SK water, the water
resistance is 17.9∼18.2 MΩ.
• UV sterizer(UV) :To kill bacteria. The documentation states the number of bacteria can be reduced to lessthan 103 ∼ 104 /100ml.
• Rn-less-air dissolving system :Dissolve Rn less air in water to improve the Rn removal efficiency of the vacuum de-gasifier.
• Reverse Osmosis filters (RO) :Reverse osmosis by a high performance membrane which removes even organisms on theother of 100 modular weight. The output water is put back into the mine stream. The
dissolving oxygen in the out put water is 10.8 µg/L after VD.
• Vacuum De-gasifier (VD) :Removes gases (Rn, Oxygen, etc) dissolved in water; about 96% of the dissolved radon gas
is removed at this stage.
• Cartridge Polisher (CP) :High performance ion exchangers using high quality ion exchanger material.
• Ultra Filter (UF) :Removes sub-µm contamination. After the Ultra filter, the water is returned to the detector. The UF removes 10% of the water passed through. That water is recirculated
through the water purification system again via the following equipment, which is shownby the dashed line in the figure.
• Membrane Degasifier (MD) :A membrane degasifier (MD) also removes radon dissolved in water. It is made of 30
hollow fiber membrane modules and a vacuum pump. A flow rate of 30 L/min of Rn-less42air from the air purification system is supplied to the MD system as purge gas. The typicalpressure in the MD system is 2.6 kPa. The typical concentration of dissolved oxygen after
the MD is 0.3 mg/L. The measured removal efficiency for radon is about 83%.
Usually, the water purification system supplies the purified water from the bottom of thetank and removes it from the top of the tank. The maximum capacity of the flow rate is 70
ton/hour. usually, the flow rate is 35 ton/hour. A summary of the quality of the purified water
is given in table 3.3.
Impurities
222 RnO2
Dust > 0.1µm
Bacteria
Ion

Reduction efficiency
∼99%
∼96%
∼99.7%∼100%∼99%

Table 3.3: The summary of the quality of the purified water.

VACUUM
DEGASIFIERCARTRIDGE
POLISHERPUMPULTRA MEMBRANEFILTER DEGASIFIERUVSTERILIZERFILTER(1µm Nom.)HEAT
EXCHANGER

PUMP
HEAT
EXCHANGER

PUMPREVERSEOSMOSIS FERK

PUMP

RN-LESS-AIR

RN-LESS-AIR
DISSOLVE NK

REVERSEOSMOSISSK TANK

SUPER-KAMIOKANDE WATER PURIFICATION SYSTEM

Figure 3.16: A schematic view of the water purification system.

3.5

The air purification system

SK is situated in mine, and the 222 Rn concentration in the mine air is 50∼2000 mBq/m 3 .
Therefore the detector is literally surrounded by the source of Rn gas. The rock dome above thewater tank and the hallway are covered with Mineguard polyurethane material, which prevents
Rn gas emanation from rocks. Double doors at all entrances also limit the amount of mine airthat entries the detector area.
To keep radon levels in the dome area and water purification system below 100 Bq/m 3 , fresh
air is continuously pumped at approximately 10 m 3 /min from outside the mine through an airduct along 1.8 km Atotsu tunnel to the experimental area. This flow rate generates a slight43

Num. of particles / mL Num. of particles / mL Num. of particles / mL

10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15
10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15
10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15

Figure 3.17: The time variation of the number of particles in the purified water. Each figure
shows the number of particles of 0.1,0.2, and 0.3 µ size respectively from the top figure.

over-pressure in the SK experimental area, minimizing the entry of ambient mine air. A “Radonhut” in figure 3.7 was constructed near the Atotsu tunnel entrance to house equipment for thedome air system : a 40 hp air pump with 10 m 3 /min/15 PSI pump capacity, air dehumidifier,carbon filter tanks, and control electronics. Fresh air from an intake (initially located at theRadon hut) is fed in to the air pump, and is then pumped through a dehumidifier, a carbon
filter tank, and finally through a 1.8 km air duct from the Atotsu entrance to the experimental
area. An extended intake pipe was installed at a location approximately 25 m above Atotsu
tunnel entrance, where radon level concentration was found to remain at 10∼30 Bq/m 3 all year
long. Thus the 10 m3 /min fresh air flow from the Radon hut keeps the radon levels in theexperimental area at approximately 30∼50 Bq/m 3 throughout the year.
A part of the fresh air from the Radon hut is purified to Rn-less air with the air purification
system. Figure 3.18 is a schematic view of the air purification system. It consists of threecompressors, a buffer tank, driers, filters, and activated charcoal filters. The components of the
air purification system as follows:• Compressor : Takes in air from outside the mine and pressurizes it 7∼8.5 atom.
• 0.3,0.1,0.01 µm filter : Removes dust in air.
• Air drier : Absorbs moisture since the radon reduction efficiency of the carbon column
dependents on the humidity air.
• Carbon column (8 m3 ): CO (Activated charcoal) absorbs Rn.
• Active charcoal (50 L) : Active charcoal cooled to -41 ◦ C traps the Rn.
Finally, after the air purification system, Rn reduction efficiency is ∼99.98% [1]. Figure 3.21
and figure 3.22 are the time variations of the radon concentration in various air.
Rn-less air is mainly supplied to ∼60 cm gap between the water surface and the top of theSuper-Kamiokande tank. The Rn-less air is kept at a slight overpressure to help prevent ambientradon-laden air from entering the detector. Typical flow rates, dew point, and residual radon
concentration are 18 m3 /hour, ∼-80(+1 kg/cm2 )◦ C, and a few mBq/m3 , respectively.
44

COMPRESSORAIR FILTER(0.3 m)CARBONCOLUMNCARBONCOLUMNBUFFERTANKHEATEXCHANGER

AIR DRIER

AIR FILTER(0.01 m)AIR FILTER(0.1 m)

COOLEDCHARCOAL(-40 oC)

SUPER-KAMIOKANDE AIR PURIFICATION SYSTEM

Num. of particles / mL Num. of particles / mL Num. of particles / mL

Figure 3.18: A schematic view of the air purification system.

10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15
10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15
10

4

10

3

10

2

10
1
-1

10

0

50

100

150

200

250

300

350

Elapsed day from 1996.8.8 to 1997.9.15

Figure 3.19: The time variation of the number of particles in the purified air. Each figure shows
the number of particle of 0.1,0.2, and 0.3 µ size respectively from the top figure.

45

238

226

U

alpha decay
6.21 MeV

232

Ra

Th

222

220

Rn
alpha decay
5.59 MeV
3.8 dys218

Poalpha decay
6.11 MeV
3 min
214

Pb

214

beta decay
3.26 MeV
20 min214

Bibeta decay
1.02 MeV
27 minRnPoalpha decay
6.40 MeV
alpha decay 56 sec
216
7.83 MeVPo
16 usec alpha decay
210
Pb0.69 MeV
22.3 years 0.15 sec
212

Pb

212

beta decay
2.25 MeV
61 min212

Bibeta decay
0.57 MeV
11 h

Po

208

Tl

alpha decay
8.95 MeV
0.30 usec
208
Pb
stablebeta decay
5.00 MeV
3 min

Figure 3.20: Rn decay series. The left side shows Uranium series of Rn. The right side shows
Thorium series of Rn.

Table 3.4 is the summary of the radon concentration in the various samples. Table 3.5 is thelist of the temperature condition at the various points.
Standard Samples
Fresh air
Air in the underground
Water in the underground
Kamioka Samples
Air in the mine
Dome air on the tankPurified air after the system
Purified air in the tank gap
Purified water after the system
Purified water in the SK tank
Return water from the SK tank

Rn concentration(Bq/m 3 )0.5∼1.0
1.0×103 ∼4.0×106
3.0×103 ∼4.0×107
Rn concentration(Bq/m 3 )winter 8.0×101 ∼1.0×102
summer 6.0×103 ∼1.0×104
5×101 ∼6.0×101
3.0×10 −3 ∼4.0×10−3
1.0×10−2 ∼2.0×10−2−3
6.0×10 ∼10.0×10−3 (before upgrade)<1.0×10−3 (after upgrade)∼5.0×10 −3 (before upgrade)
1.0×10−3 ∼2.0×10−3 (after upgrade)
1.0×10 −2 ∼1.5×10−2 (before upgrade)<2.0×10−3 (after upgrade)

Table 3.4: The summary of the Rn concentration. Before and after mean before water system
upgrading and after water system upgrading respectively.

3.6

The data acquisition system

3.6.1

The inner detector system

An overview of the data acquisition (DAQ) system is shown in figure 3.23. The signal cables
which come from PMTs of ID and OD are extended on the top of the tank, where the electronics
systems are located. The ID PMT signal cables (70m) are fed into ATM (Analog Timing Module)
modules in a TKO (Tristan-KEK-Online) system. A TKO crate contains a GONG module (GOor NoGO, which distributes control signals as a master module to its slave modules), a SCH
module (Super Controller Header, which is a bus-interface module between TKO and VME(Versa Module Europe)), and 20 ATM modules (which digitize analog signals from PMTs for
46

300
200
100
0

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

300

350

1
0.5
0

RnLessAir(Middle)
0.08
0.06
0.04
0.02
0
0

50

100

150

200

250

DAQ stop

RnLessAir
0.006
0.005
0.004
0.003
0.002
0

50

100

150

200

250

300

350

SuperRnLessAir

Figure 3.21: The time variation of the radon concentration in various air of the water purification
system site. The top figure is the radon concentration in mine air. The second figure is theradon concentration in radon less air in middle point of air purification system. The third figureis the radon concentration in radon less air before cooled charcoal in air purification system.
The fourth figure is the radon concentration super radon less air after all air purification system.

10 2

10
0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

10

1
10
10
10

-1
-2
-3

Figure 3.22: The time variation of the radon concentration in various air of the SK dome site.
The top figure is the radon concentration in the dome air on SK tank. The second figure is
the radon concentration in the duct air from outside of mine. The third figure is the radon
concentration of air in the gap between the water surface and top of the SK tank.

47

20-inch PMT
TKO CHATM

x 240
20-inch PMT

x 20
ATM

TKO CHATM
interface
SUN classic
x 20
x 240

MP
ATM

MP
MP

online CPU(slave)

MP
MP
MP

x6

Memory Partner

VME

20-inch PMT
TKO CHSUN classic
ATM

online CPU(slave)
x 20
x 240

SUN classic
ATM

online CPU(host)

Analog Timing Module

online CPU(slave)TKO
SUN classic

FDDI

SUN sparc10

online CPU(slave)
SUN classic

online CPU(slave)
SUN classic

FDDI

online CPU(slave)
SUN classic

online CPU(slave)interface
SUN classic

online CPU(slave)MPMP

SUN classic

online CPU(slave)

MP
MP
MP
MP

Memory Partnerinterface

VME
VME

20-inch PMT

TRG

TKO CHATM

TRIGGER
TRIGGERx 20
HIT INFORMATION

x 240
ATM

PROCESSER

Analog Timing Module

TKO

Figure 3.23: An overview over the DAQ system.

48

SamplePurified water after the system
Purified water in the SK tankPurified air after the system
Dew point of the Purified air
Dome air on the tank

Temperature(◦ C))
12.7
14.1∼14.2
17.0
-78.5
20.6

Table 3.5: The summary of the temperature in various places.

1st word
2nd word
3rd word

15
0
0
1

14
0
1
0

13
0
0

data per 1 channel
11 10 09 08 07 06 05 04
event number (8bit)
AB 0
0
TDC data (12bit)
0
ADC data (12bit)

12

03

02 01
channel00

Table 3.6: The data structure of ATM for 1 channel.

timing and charge information and are controlled as slave modules by GONG). There exist 12
TKO crates in a electronics hut and 4 huts in total. Each electronics hut controls 1/4 of the ID.
A central hut houses the trigger electronics. One ATM module handles 12 PMTs, hence, 934
ATMs are used in SK.
In the first stage of an ATM module [78], the analog signal from a PMT is split into 4. One
copy is used for external monitoring of analog signals, another copy is sent to a discriminatorafter an amplification by a factor 100, and the other copy are sent to the TAC/QAC [79] (Timeto Analog Converter, charge to Analog Converter) circuits. If the amplified signal exceeds thethreshold level of the discriminator, a rectangular signal of 200nsec width and -15mV amplitudeis added to the HITSUM output of the ATM module. From the added output of all ATM
modules ID trigger are derived. The threshold of the discriminator is set to the equivalent of0.2p.e.. The two TAC/QACs for each channel enable the ATM to work dead-time free. This
indicates that SK can handle µ-e decay events (the typical time difference is 2.2µsec) or highrate events (i.e. supernovae bursts; about 1kHz in the case of supernovae explosion at the centerof the Galaxy). The TAC circuit translates time into an integrated charge, which is proportional
to the time difference between the PMT hit and the timing of the global trigger, and the QAC
circuit integrates the charge from the PMT within 400nsec. The integrated charges are held by
capacitors. If the global trigger signal is not issued within about 1.3µsec after a PMT hit, theintegrated charges are discharged automatically. If the global trigger signal is issued, the charges
are digitized by an ADC (Analog to Digital Converter), and the digitized data are stored in a1024 word FIFO (First In/First Out) memory. The ATM provides 1.3µsec full range in timewith 0.3nsec resolution and 600pC full range in charge with 0.2pC ('0.1p.e.) resolution. The
association of a signal to an event is done by an event number. The event number is incremented
by a TRG (TRiGger) module in the central hut which issues the global trigger signal, and theevent number (16bit) is distributed with the trigger to the electronics huts. The GONG in eachTKO crate receives the event number and distributes the lower 8bit of it to the ATMs. The
data structure of one signal recorded in the FIFO of the ATM is shown in table 3.6, where
AB indicates which of the two TAC/QACs was used and ’channel’ is a unique channel number
identifying the PMT and its electronics channel.

493.6.2The outer detector system

The DAQ system for the outer detector is completely different. The OD PMT signals are fed
to QTC (Charge to Time Converter) module after separation from the positive HV by pickoff
cards. The QTC module, which deals with 48 PMT signals and discriminates the signals witha threshold of 0.25p.e., generates rectangular pulses. Each pulse is put out with 200nsec delay
after a signal comes and the width of the pulse is proportional to the charge integrated within a
200nsec gate. These pulses, which have timing and charge information, are sent to a FASTBUS
TDC module. The QTCs also generate HITSUM signals, which are used to generate the outerdetector trigger.
If a global trigger is issued, the QTC signals are digitized in the TDC modules. The TDC
module, which can handle 96 channels, is able to record for time range of 32µsec. The recording
range is tunable relative to the global trigger timing.
The readout of the digitized data is controlled by a FSCC (FASTBUS Smart Crate Controller). The data are sent to a DC2-DM115, which latches the TDC data into its memory, andwritten into a DPM (Dual Ported Memory) modules which plays a role like SMPs (see following
section) in the DAQ of the ID. Finally the data are read out by a workstation.

3.6.3

Trigger system

The all HITSUM signals issued by the ATMs are summed up in each electronics hut withsumming modules, and the summed HITSUM signals from the four electronics huts are again
summed up in the central hut. In this summation, the pulse height contributions from individual
hits drop from -15 to -11 mV. The summed signal is AC-coupled into a discriminator to subtract
the changing offset generated by the dark noise rate of the 1,1146 inner PMTs. A trigger isissued, when the HITSUM signal exceeds a discriminator threshold. The threshold level is set
to -320mV, i.e. if the number of hit PMTs exceeds 29hits in a 200nsec time window, a global
trigger is generated. This trigger level is called Low Energy (LE) trigger. The rate at which LE
triggers are issued is about 10Hz. There are other kinds of similar triggers named Super Low
Energy (SLE) trigger (The data taking with SLE trigger started in May 1997) and High Energy(HE) trigger. The trigger thresholds of SLE and HE are -260mV and -340mV, and the event
rate of these are 100Hz and 3Hz, respectively. Since the rate of SLE trigger was too high tohandle in the off-line system, an intelligent online event reduction system is used to reject theevents near the wall of ID which dominate the SLE trigger (A recent off-line computer upgrade
would allow to take the full SLE rate.). As a result of this trigger, the event rate from the SLE
trigger is reduced to about 16Hz. The OD also generates its own trigger. The threshold of the
OD trigger is 19hits in 200nsec time window and the rate is about 3Hz, which is almost entirely
due to cosmic ray muons.
The global trigger is then fed to the TRG module (VME specification). The TRG increments
the 16 bit event number and distributes the event number signal and the global trigger signal
to all GONGs, records the time at which the global trigger was issued using an internal 50MHz
48bit clock. The TRG also records the trigger ID indicating which trigger was issued by an 8bit
data word. The identification bit of trigger ID is shown in table 3.7. The method to issue theglobal trigger is drawn in figure 3.24.
The threshold of the SLE trigger was changed 7 times in SK-I period to take data with lower
energy. The summary is shown in table 3.8

3.6.4

Real-time data process

For events issuing only the SLE trigger (typically below 6.5 MeV) , a soft ware trigger which iscalled Intelligent Trigger (IT) is applied. This is a real-time fiducial volume cut procedure. Most
very low energy events are due to γ rays from the ID wall materials and the rock surrounding50

Trigger bit
0
1
2
3
4
5
6
7

type of triggerLEHE
SLE and Fission Trigger(for Ni calibration)
OD trigger
Periodical Trigger
Calibration Trigger
Online Veto Start
Online Veto Stop

Table 3.7: The trigger ID. Periodical Trigger is a kind of random trigger issued every 6 seconds.
Online Veto Start and Stop mark the duration of a possible online veto, which is issued if morethan 64 events happen within 120µsec.

Analog signal from PMT
ATM threshold
400nsec width
ADC gate

start

stop

TDC start and stop

200nsec width
HITSUM

global trigger

Sum of HITSUM
Master thresholdglobal trigger

Figure 3.24: Trigger generation.

51

in
ATM
in
centerhut

Trigger threshold
LE (-320 mV)(29 ID hits)
LE (-302 mV)(29 ID hits)
SLE (-260 mV)(24 ID hits)
SLE (-250 mV)(23 ID hits)
SLE (-222 mV)(20 ID hits)
SLE (-212 mV)(19 ID hits)
SLE (-186 mV)(17 ID hits)
SLE (-212 mV)(19 ID hits)
SLE (-186 mV)(17 ID hits)

Period1996.5.31 ∼ 1999.12.22
1999.12.22 ∼ 2001.7.15
1997.5.29 ∼ 1999.5.13
1999.5.13 ∼ 1999.9.17
1999.9.17 ∼ 1999.12.22
1999.12.22 ∼ 2000.7.11
2000.7.11 ∼ 2000.7.31
2000.7.31 ∼ 2000.9.27
2000.9.27 ∼ 2001.7.15

Event rate(Hz)
11
11
106.6
172.2
540.6
561.5
1678.
532.3
1678.

Table 3.8: The summary of the switch of LE and SLE trigger threshold.
the tank, so the vertexes are distributed near the wall. The IT eliminates those events, keeping
only 8% of the incoming events at the SLE threshold = -212 mV.
The data stream of the IT diverges from the online host computer. The online host computer
sends the data which issues only the SLE trigger to 12 CPUs (IT CPUs), which reformat thedata and reconstruct event vertex.
Fast vertex reconstruction by IT is required to keep up with the high data rate. For thispurpose, a fast vertex reconstruction algorithm (Hayai fitter) is applied to the data before theusual one, which is described in chapter 4. First, the fitter makes a list of all hit PMTs thathas a neighboring hit PMT in space (distance within 10 m) and time (hit within 33.3 nsec). A
timing distribution is made from set of PMTs, and the number of PMTs in a sliding window of
16.7 nsec width examined. The set of PMTs that belongs to the window with largest numberof hit PMTs is less than 5.
The initial vertex for the subsequent grid search is obtained as the centroid of the selected hit
PMTs. In order to prevent starting a vertex too close to the wall, the vertex is moved 2 meters
away from the ID wall. Then the Hayai fitter searches the vertex which gives the maximum“goodness“ which is defined as follows :N0(ti − texp
− Tof f set )2
1 X
i
exp(−
)
goodness ≡ f (a)N0
2σ 2(3.13)

i=1

where f (a) is a function which reflects the shape of the expected Čerenkov cone from thetrue vertex. a is the magnitude of the anisotropy defined as follows :−a =| →
a |
→
−
P N0
d
−i
i=1 qi →|d |=| PN0 i |qi=1 i(3.14)→−| di |
c/n(3.15)

N0 is the number of selected hit PMTs. t i is the detection time of i-th hit PMT. T of f set is→−the time offset to make the center of (t i − texp
− Tof f set ) zero. di is the distance vector from theitrial vertex to the i-th hit PMT. The trial vertexes are uniformly distributed with step size of
1.86 m. texp
is the expected detection time of i-th PMT, defined as follows :itexp= T0 +i52

address
1
2
3
4
5
·

data
31· · · · · · · · ·160000
Module address
Module address
Module address
Module address···

15· · · · · · · · ·0
16 bit event number
channel and 8bit event counter
TDC data
ADC datachannel and 8bit event counter
···

GONG
ATM
ATM
ATM
ATM
ATM

Table 3.9: The data format of SMP. The right side line means the origin of data. Module addressis the address of an ATM in a TKO crate. ’address’ is the data address in SMP.

where n is the refractive index of water.
When the vertex which maximizes the goodness is found the location of the vertex is examined. If the distance between the reconstructed vertex and the ID wall is less than 2 m, thevertex is rejected.
After this fast reduction, the normal vertex reconstruction is also applied. The vertex reconstruction method is explained in next section. Events whose reconstructed vertex is locatedwithin 2 m of the ID wall is rejected. The reduction efficiency of the IT dependents on the
SLE trigger rate. For example, when the SLE trigger threshold = -212 mV, 92% of events are
rejected. The event identification number of remaining events are sent to reformatter machine.
Only the data for the these events are reformatted and sent to the off-line host.

3.6.5

The ID online and offline system

The digitized PMTs data stored in the FIFO of the ATMs are read out through the SCH by
a SMP (Super Memory Partner, VME specification), which possesses 2Mbyte internal memory.
One SMP collects the data from one TKO crate in the fixed format shown in table 3.9. The
data size per one channel is 12 bytes. Six SMPs are controlled by one workstation, S4/CL (SunSPARCclassic), which is called ’slave machine’. There are 8 slave machines and each electronics
hut has 2. Therefore, one slave machine controls the data from about 1400 PMTs. The 6 SMPs’
data are read out by block transfer. The data of all slave machines are sent to a workstation,
S4/10 (Sun SPARCstation 10), called ’host machine’ via FDDI (high speed ring network with
optical fiber cable). The TRG is controlled by another workstation, S4/CL, called the ’trigger
machine’, and information related to the trigger are sent to the host machine through it. Yetanother workstation, a S4/20 (Sun SPARCstation 20) collecting OD data, is called an ’anti
slave’, and its data are sent to the host machine via FDDI. The host machine builds the eventfrom the slave machines on the basis of the event counter information. The reconstructed data
are sent on to another workstation (UltraSPARC, ’reformat machine’), which changes the online
format to an off-line format (ZBS, Zebra Bank System), which is easy to handle in the analysis.
The reformatted data are sent to the off-line computer system. The system is composed of a
VPX2105 called ’sukop’ and 10 S4/20 workstations called ’sukeve(1∼10)’ with a MTL (Magnetic
Tape Library) system, which has a capacity of 12Tbyte (until January of 1998). Since February
1998, the system is completely replaced. PetaSite made by SONY can store about 100Tbyte ofdata and the flow rate of data read out is enlarged 14 times as compared to the old MTL system(from 10.8MByte/s to 144Mbyte/s). The sukop machine transforms the ADC and TDC countsof the ATM data to the real charge (pC) and time (nsec), respectively, using the tables provided
by various detector and electronics calibration. This process is called ’TQreal’. The size of datawith real charge and time is 27Gbyte/day. These data are distributed to the 10 sukeve machines,on which the reconstruction of events (vertex, direction, energy, etc) are carried out for solar
neutrino, atmospheric neutrino, and up-going muon events.

53

After reconstruction, these data are recorded on the Data Storage system. A figure summarizing the online and offline system is shown in figure 3.25.
slave machine
#1

SMP*6

triggermachine

#8

anti
slave

........
TRG

DPM

host
machineevent reconstruction

reformatmachinereformat the data
to ZBS format

SuperNovae
real time monitor
insideof the mineoutsideof the mine
TQrealsukop

event reconstruction
Data storage
systemsukeveFigure 3.25: The summary figure of on and offline system.

54

Chapter 4

Event Reconstruction
The event reconstruction algorithms used for the solar neutrino analysis is described in thischapter.
First, vertex reconstruction which uses the time information of hit PMTs is described. The
second step is the reconstruction of the event direction using the pattern of hit PMTs. Afterthese reconstructions, the effective number of hit PMTs, N ef f , is calculated. Nef f is converted
into energy by using a conversion function obtained from LINAC calibration, which is describedin next section. Additionally, muon track reconstruction described in appendix C.

4.1

Vertex reconstruction

The timing information from the hit PMTs is used to reconstruct the vertex position. The path
length of an electron recoiling from the neutrino interaction is less than 10 cm. It is negligible
in comparison with the vertex resolution of approximately 1 m. Therefore, the vertex treatedas a point in vertex reconstruction program.
Prior to the reconstruction, the PMT timing information is evaluated to remove hit causedb random noise and reflected light. A trial timing distribution of hit PMTs is shown figure 4.1
To select the PMTs which are used for vertex reconstruction, the following time window method
is used :
NUM
10
RUN
5957
SUBRUN
3
EVENT115504DATE 98-Jun-26
TIME
22:41:17
TOT PE:
181.2
MAX PE:
14.0
NMHIT :
118
ANT-PE:
27.1
ANT-MX:
9.6
NMHITA:
32

RunMODE:NORMALTRG ID :00000111
T diff.:0.160E+06us: 160.
ms
FSCC:
2FF90
TDC0: 8893.2
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 4.1: Event display of a typical low energy event.

55

200 nsec

number of hits

t1

t2

t3

t4

14
12
10
8
6
4
2
0

500

600

700

800

900

1000 1100 1200 1300 1400 1500

Time (nsec)
Figure 4.2: Absolute time distribution of hit PMTs in the event in figure 4.1.

1. Sort the hit PMTs in chronogical order and locate the 200 nsec time window which contains
the maximum number of hit PMTs (Nsg )2. Estimate the number of dark noise hits, N bg by the relation :Nbg ≡t3 − t 2(Nhit (t1 ∼ t2 ) + Nhit (t3 ∼ t4 ))(t2 − t1 + (t4 − t3 ))(4.1)

t1 ∼ t4 are defined in figure 4.2.
3. Reduce the width of the window in 19 nsec steps to optimize the significance of the signal.
The significance, S, is defined as follows :S≡

Nhit (t2 ∼ t3 ) − Nbg
p
Nbg

(4.2)

Only the hit PMTs within the time within the time window with maximum S are usedfor vertex reconstruction.
The vertex point is found by using a grid search method. The distance between the grid
points used in the initial stage of vertex reconstruction is 397.5 cm. The vertex is placed ona grid point, and for the grid point, the “goodness“ of vertex reconstruction is calculated byfollowing equation. The calculation is repeated for every point on the grid.

goodness(x, y, z) ≡ PN

1
hit

×
1

i=1 σ 2

N
hit
X
i=1

(tres,i (x, y, z) − tcenter (x, y, z))2
1
exp(
)
σ2
2σ 2

(4.3)

where (x,y,z) is the position of the grid point. N hit is the number of hit PMTs selected by
the time window method. σ is the PMT time resolution, which is 5 nsec for all PMTs. t res is
the residual time of i-th hit PMT which is defined as follows :56

np(x − xi )2 + (y − yi )2 + (z − zi )2(4.4)
cwhere ti is the time of the i-th hit PMT. tcenter is the mean time of the distribution of t red,i . n
is the reflective index of water and c is the speed of light in the vacuum. (x i , yi , zi ) is the positionof the i-th hit PMT. In an ideal case, all of the t res are equal, and the goodness will be 1. The
distance between the grid points is reduced to 5 cm as the trials converge upon the final vertex.
Figure 4.3 shows a distribution of the goodness using events from LINAC calibration. Figure 4.4
shows the reconstructed vertex of the same events. The resolution of vertex reconstruction ismeasured by LINAC calibration by LINAC calibration system, and found to be ∼75 cm forelectron energy 10 MeV. A full explanation of the LINAC calibration in chapter 5.
tres,i ≡ ti −Number of events

1400

ID
Entries
Mean
RMS

100
20370
0.73150.6549E−01

1200

1000

800

600

400

200

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

goodness

Figure 4.3: Projection of the gooodness distribution for LINAC calibration events at the position(x=-388.9cm, y=-70.7cm, z=-6cm) with the electron beam energy 6.98 MeV.

4.2

Direction reconstruction

Once the vertex position of an event has been determined, the direction can be reconstructedby examining the pattern of hit PMTs created by the Čerenkov ring. In an ideal case, the event
pattern is expected to be a clear ring with an opening angle of 42 ◦ about the direction of theelectron’s path. However, photons can be scattered in the water, reflected off the PMTs andthe black sheet. Also, the electron may undergo multiple scattering. All of these effects cause
the Čerenkov ring to be smeared. The hit PMTs which are used to reconstruct the direction
are selected using a 50 nsec timing window from the TOF (Time-Of-Fright) subtracted time
distribution. A maximum likelihood method is used to determine the direction. The likelihood
function is defined as :Nhit

X
cos θi→−log(Pi (cos θdir )) ×L( d ) ≡a(θi )

(4.5)

i=1

→
− →
di · −pi)
θi ≡ arccos( →− →| di | · | −
pi |
57

(4.6)

Number of eventsID
Entries
Mean
RMS

6000
4000

100
20370
−383.6
72.30

2000
0
−1500

−1000

−500

0

500

1000

1500

X(cm)

Number of events

6000

ID
Entries
Mean
RMS

4000

100
20370
−67.93
69.35

2000
0
−1500

−1000

−500

0

500

1000

1500

Number of events

Y(cm)
ID
Entries
Mean
RMS

3000

100
20370
−5.806
144.7

2000
1000
0
−1500

−1000

−500

0

500

1000

1500

Z(cm)

Figure 4.4: Projection of the reconstructed vertex distribution for LINAC calibration events at
the position (x=-388.9cm, y=-70.7cm, z=-6cm) with the electron beam energy 6.98 MeV.

acceptanceprobability

Pi (cos θdir ) is probability density function for the angle of Čerenkov photons relative to therecoil electron momentum. Figure 4.5 shows the distribution of P i (cos θdir ). θi is the angle of−incidence of the Čerenkov photon on the i-th PMT. →pi is the vector from the reconstructed→−vertex to the position of the i-th hit PMT. di is the direction vector that the i-th hit PMT isfacing. a(θi ) is acceptance of the PMT photo cathode as function of θ i . The distribution a(θi ) ispresented in figure 4.6. A grid search method is used to find which 9 ◦ ,4◦ ,1.6◦ . The mean valueof the multiple scattering angle is about 27 ◦ for electrons with an energy of 10 MeV. So the step
sizes are small enough to reconstruct the direction of low energy electrons. Figure 4.7 shows
the reconstructed direction of the same events in figure 4.4. The resolution of the direction
reconstruction is measured with LINAC calibration data, and found to be ∼ 27 ◦ for electronenergy of 10 MeV. A full explanation of the LINAC calibration system is given in chapter 5.

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0

20

40

60

80

100

120

140

160

0

180

θ

0

10

20

30

40

50

60

70

80

90

incident angle (degree)

Figure 4.5: The unnormalized probability density function for Čerenkov photon
directions with respect to initial electron
direction for 10 MeV/c electrons.

Figure 4.6: The acceptance function of the
PMT.

58

Number of eventsID
Entries
Mean
RMS

100
20370
−0.8571
0.1664

3500

3000

2500

2000

1500

1000

500

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

direction Z

Figure 4.7: Projection of the direction cosine distribution for LINAC calibration events at theposition (x=-388.9cm, y=-70.7cm, z=-6cm) with the electron beam energy 6.98 MeV.

4.3

Energy reconstruction

As indicated in chapter 2, the measurement of the energy spectrum shape is the most important
key to investigate the neutrino oscillation with solar neutrinos. Hence, the energy determination
has to be done carefully. As discussed earlier, almost all hit PMTs catch only a single photoelectron in a solar neutrino event. The total charge of the event is not a good indicator forthe energy of the recoil electron, because charge resolution at the single photo-electron level ofa 50cm-PMT is not good (∼50%) enough to estimate the total number of emitted Čerenkov
photons. Accordingly, in SK, the energy is calculated from the number of hit PMTs within
a 50nsec timing window (N50 ). However, the number of hit PMTs is still not a good energy
indicator, since it has large position dependence (For example, the measured mean N 50 using
γ-rays from Ni(n,γ)Ni reactions is different by about 10% between the central position (x =(0, 0, 0)) and an edge position of the fiducial volume (x = (0, 0, +16m)).). In order to give
uniform response over the fiducial volume (The fiducial volume is the inner part of the ID,
where the distance from the wall is greater than 2m. It contains 22.5 ktons water.), various
corrections are applied. The corrected number of hits, N ef f , is defined by:
Nef f =

N50
X
Nall
i=1

Nalive(αi + αtail − αdark )S(θi , φi )ex0 ,xi )

R(

λ

pi

(4.7)

The corrections are classified as follows.
Dead PMT correction
In order to reduce the effective difference of the energy scale caused by the variation of thenumber of available PMTs with time, a factor N all /Nalive is used. Here Nall is the total numberof PMTs in the inner detector of SK (i.e. 11146), and N alive is the number of available PMTs
in the detector and the remaining PMTs are dead ones (see figure 3.14).

59

Multi photo-electron hits correction
If an event happens at near the fiducial volume edge toward the nearest ID wall, an observed
number of hit PMTs become effectively small, since a Čerenkov ring of the event become small,which causes multi photo-electron hits on one PMT. The expected number of photo-electrons
received by individual PMTs is estimated from the occupancy of the surrounding tubes. If theaveraged number of photo-electrons is η i per one PMT area in the region surrounding the i-th
PMT, a probability, Ai , that the surrounding PMTs do not hit is calculated from a Poisson
η 0 e−ηidistribution: Ai = i 0! = e−ηi . For a while, when the number of hit PMTs and the numberof alive PMTs surrounding the i-th PMT are n i and Ni (normally Ni = 3 × 3 = 9) respectively,
the probability Ai is equal to (Ni − ni )/Ni = 1 − ni /Ni . Hence, the averaged number of photoelectrons in the area is computed to be:1ηi = log(4.8)
1 − εiwhere εi = ni /Ni . The total number of photo-electrons in the region is N i ηi . Therefore, theexpected number of photo-electrons received by the i-th PMT, α i , is given by:
αi =

Ni ηi
log(1/(1 − εi ))
=
ni
εi

(4.9)

expected number of photon

If εi = 1, we set αi = 3, which is obtained by extrapolating ε i to 1 in equation (4.9) as shownin figure 4.8.

3.5

3

2.5

2

1.5

1

0.5

0

0.2

0.4

0.6

0.8

1

εi

Figure 4.8: The expected number of photo-electrons received by one PMT as a function of ε i .

Recovery for reflected Čerenkov photons
In order to recover the reflected Čerenkov photons which hit PMTs with a considerable timelag (≤ 50nsec), a factor αtail is multiplied, which is defined by:
αtail =

N100 − N50
N50(4.10)

where N100 is same as N50 except that the time window on the TOF subtracted timing is
100nsec.
60

Correction for dark noise hits
In order to drop contribution of dark noise hits from observed N 50 (The dark noise (∼ 3.3kHz)
contribute about 2 hits in a 50nsec window.), a following factor α dark is subtracted:
αdark =

Nalive Rdark × 100 · 10−9N50

(4.11)

where Rdark (Hz) is the mean dark rate evaluated on a run to run basis (see figure 3.13).
Correction for effective photo-cathode coverage
S(θi , φi ) is the effective photo-cathode area from the view of θ i , φi direction, where θi is theincident angle to the i-th PMT and φi is the azimuth angle. A φ dependence is caused by thearrangement of PMTs as shown in figure 4.9. The function S(θ, φ) is shown in figure 4.10.

coveragei-th PMT
1
0.9
0.8
0.7

φ

0.6
0.5

0

θ

photonFigure 4.9: The arrangement of
PMTs and the definition of the azimuth angle φ.

10

20

30

40

50

60

70

80

90
0

10

20

30

40

50

60

70

80

90

φ

Figure 4.10: Effective photo-cathode area as afunction of θi , φi direction.

Water transparency correction
In order to compensates changes in the attenuation of Čerenkov light in water and recovers theR(x0 ,xi )λassociated position dependence of the energy scale, a factor e
is multiplied, where λ is
the water transparency measured from the Čerenkov light output of electrons from the decayof stopping muons. It is a function of time. The details of the calculation of λ are described inchapter 5.
Correction for quantum efficiency
The last term pi is the quantum efficiency correction factor. 375 PMTs were produced in a preseries to the main PMTs. The quantum efficiency of these PMTs is found to be larger(This fact
was established from the occupancy distribution by Ni calibration measurement. See chapter5.). The factor is given by:
0.833(375 PMTs)pi =(4.12)
1.000 the other PMTs
61

The non-uniformity of Nef f in the fiducial volume is measured to be ∼ 1% using γ-rays from
Ni(n,γ)Ni reaction and monochromatic electron beam (LINAC).
A calculation of an MeV value from Nef f is discussed in subsection 5.4.2.

62

Chapter 5

Calibration
In this chapter, details and results of the SK detector calibration are given. First of all, thefundamentals of the detector, namely uniformity of gain and timing adjustment for all PMTs,
have to be investigated, using a Xe light source, a Ni-Cf calibration source and a laser lightsource. To know the water transparency in the SK tank a direct measurement of the watertransparency is carried out using a laser light source and a CCD camera. To monitor thevariation, decay electrons from stopping µ are used.
In order to measure the energy spectrum of solar neutrinos, a liner accelerator for electrons(LINAC) is installed at the detector to calibrate the detector with electrons of energy 4.0∼16
MeV. Uniformity of the energy scale in direction and time is investigated by spallation events,
the Ni-Cf source and the µ decay electron events.
Angular and vertex resolution measured in the LINAC calibration and the trigger efficiency
obtained with the Ni-Cf calibration and DT calibration are also described.

5.1

PMT gain monitoring

Uniformity of gain for all PMTs is monitored by two methods, i.e. a Xe light source for decisionof the relative gain and a Ni-Cf γ-ray source for decision of the absolute gain.

5.1.1

Xe calibration for relative gain of the PMTs

The gain of all PMTs has to be the same to make detector response uniform. As described inchapter 3, the relative gain of all PMTs is adjustable by changing high voltage V (10 7 gain). In
order to check the relative gain of all PMTs and the stability of gain uniformity, a Xe calibration
system is used. Figure 5.1 shows an overview of the Xe light system. An advantage to usinga Xe-lamp is that intensity of the output light is stable within 5%. The light generated by
the Xe-lamp go through a UV-pass (Ultra-Violet) filter and an optical fiber and is sent to a
scintillator ball in the tank. A role of the UV-pass filter is to pass only ultraviolet light which
can be absorbed by the scintillator ball. The scintillator ball is a spherical acrylic ball mixed
with BBOT wavelength shifter and MgO. BBOT absorbs the Xe light passing through the UV
filter and emit 450nm wavelength light, which is similar to Čerenkov light wavelength. MgO isdiffuser to emit the light uniformly. The intensity of the output light is monitored by two silicon
photo-diodes and a 5cm PMT.
Charge observed in each PMT is corrected with PMT acceptance, light attenuation in waterand non-uniformity of the scintillator ball, which are measured independently.
In checking the relative gain of PMTs, the charge of each PMT should be corrected with theacceptance of each PMT, light attenuation in water and the non-uniformity of the scintillatorball. The corrected charge is defined by following equation :63

UV filter ND filter
Xe Flash Lamp

Photo
Diode

SK TANK

Photo
Diode

Optical fiber

ADC

Scintilator Ball
PMT
Scintilator

Monitor20inchPMT

Trigger

Figure 5.1: Overview of the Xe calibration system.

Qcor ≡

Q×r
exp(− λr )facc (θP M T )fball,θ (θ)fball,φ (θ, φ)

(5.1)

where
• Q Charge of a PMT• r Distance from scintillator ball of a PMT• facc Function for acceptance correction• fball,θ Function to correct the zenith angle dependent non-uniformity of the scintillatorball• fball,φ Function to correct the azimuth angle dependent non-uniformity of the scintillator
ball
Figure 5.2 shows distribution of the corrected charge for all PMTs. The gain of all PMTs isconsistent within 7%. The stability of the overall gain for long time period is also studied and
it is found to be stable within 2% for 5 measurements in one year.

5.1.2

Ni-Cf calibration for absolute gain of the PMTs

With the Xe calibration system the gain of all PMTs can be adjusted at large output charge(100∼200p.e.). Hence, it is relevant for high energy events, such as cosmic ray muon events. For
solar neutrino events, the uniformity for single photo-electron PMT response, namely single p.e.
efficiency is essential. For that purpose a Ni-Cf calibration source is used.
A schematic view of the Ni-Cf calibration system is shown figure 5.3.
The source is also used to evaluate the systematic error of vertex reconstruction and obtain
trigger efficiency The Ni-Cf source emits γ-rays with a maximum energy of 9.00 MeV. The γ-rays
cause Compton-electrons, which emit Čerenkov photons. In this case, signal on hit PMTs is at
the 1p.e. level. Hence, the peak value of the output charge of one PMT indicates the absolute
64

2000

1750

1500

11146 PMTs

1250

σ= 7.%

1000

750

500

250

0

0

200

400

600

800

1000

1200

corrected Q

1400

1600

1800

2000
2
x 10

Figure 5.2: The distribution of the corrected charge for all PMTs.

Figure 5.3: A schematic view of the Ni-Cf calibration system. Cf is situated at the center of thecontainer.

65

gain. Figure B.3 shows distribution of the output charge for single photo-electron response of a
triggered PMT. Mean value of the distributions for all PMTs is 2.055 pC/1p.e..
A parameter indicating the uniformity of the 1p.e. efficiency is represented by the occupancy
with a correction for water transparency defined as (number of hits)/(number of total events)for each PMT. Distribution of the averaged occupancy for each layer of barrel part is shown infigure 5.4. Position that the layer number equal one is bottom part and 51 is top part. Figure
5.4 shows a clear increase of the occupancy at the bottom and at the top. This is due to thereflection of light on the PMTs and geometrical condition of the PMT arrangement, and isreproduced in the MC simulation.
The open marks in figure 5.4 are different from the other filled points by about 20%. The
reason is that these layers include the PMTs (375 PMTs) produced in earlier period which havehigher 1p.e. efficiency. The Xe calibration adjusts the gain so that the output charge of all
PMTs become same. Therefore high voltage values of these 375 PMTs are set lower. However,
the occupancy measured by the Ni-Cf source reveals differences in the 1p.e. efficiency, because
1p.e. efficiency is independent of applied high voltage. The difference in the 1p.e. efficiency istaken into account in the calculation of electron energy as described in equation (4.7).

Figure 5.4: Distribution of the averaged occupancy for each layer of the barrel part.

5.2

Timing calibration of the PMTs

In order to get vertex position where an event occurs accurately, relative timing and timing
resolution of all PMTs have to be known. If the relative timing is different PMT by PMT, anadjustment of the timing have to be performed. To do so, a light source of short time width,∼a few nano seconds, is required. Figure 5.5 shows a schematic view of a laser system whichmeasures the timing response of all PMTs. The light source is a N 2 laser which can produce
sufficiently intense light of 337nm wavelength, which width is moderately short (∼3nsec).
The wavelength of the generated light is converted to 384nm by a DYE laser. Light intensity
is controlled using an attenuation filter. The light is divided into two. One light is sent to adiffuser ball in the water tank through an optical fiber, the other is used for monitoring andtriggering. The diffuser ball contains a TiO 2 tip and LUDOX. LUDOX is silica gel with 20nm
glass fragments. The tip is located at the center of the LUDOX. The light is diffused by the tip
and the LUDOX without an additional timing spread.
66

variable
attenuation
filteroptical fiber

optical fiber

N 2 laser
generator
λ =384nm

Super Kamiokande
inner tankmonitor
PMT

sig.
20’PMT

diffuserball

trigger
elec.
sig.

LUDOX

diffuser tip(TiO2 )20’PMT

sig.

sig.

DAQ
elec.

Figure 5.5: The schematic view of the laser system.

By changing the intensity of the light output, the charge dependence of the absolute timing
and timing resolution of the PMTs is established. Figure 5.6 shows a so-called ’TQ map’, whichcharacterizes the timing response of a PMT. The horizontal axis is the number of observed
T (nsec)

Typical TQ map
980
970
960
950
940
930
920
910
900
890
880

Q (p.e.)Figure 5.6: The TQ map of one PMT. The details of this figure are described in the text.
photo-electrons and the vertical axis is the hit timing. The charge dependence of hit timing is
mainly due to slewing in the discriminator on the ATM. The timing resolution also depends onthe detected number of photo-electrons. The typical timing resolution for a 1p.e. signal is 3nsec.

67

5.3

Water transparency measurements

Water transparency in the SK tank is an important parameter to characterize the response of thedetector to the solar neutrino events, since it determines the number of Čerenkov photons which
arrive at the PMTs. There are two aspects of the measurement of the water transparency, i.e.
one is wavelength dependence which is important for MC simulation in the step of the Čerenkov
photon propagation, the other is its long term variation.

5.3.1

Direct measurement of the water transparency

A direct measurement of the water transparency is carried out with the system shown in figure 5.7. Source of light is a N2 dye laser which is able to produce monochromatic light with
Beam Splitter (50:50)
CCD camera
DYE / N2 laser
Lens

Integrating Sphere<< laser box >>Diffuser Ball
2inch PMT
Optical Fiber (70m)<< SK Tank >>Figure 5.7: System for the direct measurement of the water transparency.
wavelengths from 337 to 600nm. The light is split into two, one of which is sent to a diffuserball in the water tank and the other is used to monitor intensity of the light output through an
optical fiber with a 5cm PMT. The diffuser ball is a spherical acrylic ball with MgO. Intensityof the light emerging from the acrylic ball is measured by a CCD camera at the top of the tank.
By varying the distance between the diffuser ball and the CCD camera, the water transparency
can be extracted without knowledge of the absolute light output of the system. The watertransparency λtra is given by:dI(d) = exp −
I0
(5.2)
λtra
where I0 is the intensity of the light source, I(d) is the measured intensity at the distance of d.
Figure 5.8 shows the measured intensity I CCD normalized to the output charge of the monitoring
PMT IP M T as a function of d at a wavelength of 420nm. The fit result for λ tra is 97.9±3.5m.
Figure B.1 shows water attenuation coefficient defined as 1/λ tra as a function of the wavelength.
The open points are the results of measurements. The line is used in the SK detector MC
simulation.

68

ICCD/IPMT
10

4

λtra = 97.9±3.5m(420nm)

0

5

10

15

20

25

30

35

distance from CCD (m)Figure 5.8: The measurement of the water transparency. I CCD /IP M T vs d is shown. The inverseof the slope in the figure is the water transparency; 97.9±3.5m at a wavelength of 420nm. Fourdifferent data sets are overlaid (take1∼4).

5.3.2

Monitoring water transparency by penetrating muons

The water transparency is monitored continuously using µ decay electron events. Though thismethod can only measure the water transparency averaged over the Čerenkov spectrum, thetime variation of the water transparency caused by change of filter performance of the water
purification system can be measured day by day, since about 1500 µ decay events happen everyday. Figure 5.9 shows a schematic view of how the water transparency is calculated. To begin
with, the relevant PMTs, which are within a 50nsec window after TOF subtraction (same as N 50
defined in chapter 4) and seen under an opening angle with respect to the direction of the decay
electron within 32∼52◦ , are selected. These PMTs are projected onto a sphere with radius R,
and the center at the vertex position of the event. On the sphere, these PMTs come to lie ona ring. The ring is divided into 36 equal parts as shown in figure 5.9. The i-th segment on thesphere has effective charge ∆Qi :
∆Qi =

Ni
X

qj expj=1

dj − R
λe



(5.3)

where Ni is the number of PMTs included in the i-th segment, q j is the acceptance correctedcharge of the j-th PMT, dj is the distance from the vertex position to the j-th PMT position,and λe is the water transparency to be calculated. In ideal case, all ∆Q i (i = 1, 36) should beequal:∆Q1 = ∆Q2 = · · · = ∆Q36 = ∆Q
Since each segment can be regarded small, equation (5.3) can be rewritten: r∆Q = expq(r)λewhere r ≡P Ni

j=1 dj /Ni is the mean distance, q(r) ≡

69

P Ni

j=1 qj , and R is set to 0.

(5.4)

(5.5)

10deg52deg

direction of decay electron

32deg
vertexpositionR
Delta Q

i
q
d

j

i

N i hitFigure 5.9: The schematic view of how to calculate the water transparency from a µ decay
electron event.

∆Q is different from event to event since the energies of the µ decay electrons are different,
following the Michel spectrum. q(r) follows this energy distribution, leading to:rq(r) = exp −
∆Q
(5.6)
λe
r
log(q(r)) = − + log(∆Q)(5.7)λewhere the upper bar means an average over the corresponding variable. From log(q(r)) and r, λ e
can be calculated. Figure 5.10 shows log(q(r)) as a function of r. The slope is the inverse of λ e .
Figure 5.11 shows the time variation of the water transparency measured by this method. One
point corresponds to one week. The first significant increase is due to a replacement of Ultra
Filters and another increase is due to an exchange of the 1µm filters. The water transparency
for each day is used in the energy calculation of equation (4.7).
Figure 5.12 shows the tank height dependence of the water transparency by above method.
The height of the tank is divided to three of top, center and bottom. The measured transparencies for each zone are basically same tendency. However, the averaged transparency isslightly different by zone in table 5.1. Because the SK purified water is supplied from bottom
usually, the transparency in bottom zone is better than top zone. The dust from the SK tankmaterial goes up gradually from the bottom to the top by water convection. This tendency of
the transparency for each zone, it is described in chapter 7 that the radon events in the SK tankis accumulated in the bottom zone, indicates that the radon events are independent of the dustin the tank.
Zone
Top
Center
BottomAveraged transparency (cm)8708.8±64.49906.7±64.410200.8±64.4

Table 5.1: The averaged transparency for each zone. The error is statistical error.

70

log(q(r))

1.9

1.8

1.7

1.6

1.5

1.4

λe=8424cm

1.3

1.2

1.1

1
1000

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

r (cm)

Figure 5.10: This figure shows log(q(r)) as a function of r. The slope measures the inverse of
λe .

1996

1997

1998

1999

2000

2001

Figure 5.11: Measured time variation of the water transparency from April 1, 199671

wt(cm)

20000
15000
10000

800

1000

1200

1400

1600

1800

2000

Top zone ’ elapsed day’wt(cm)

20000
15000
10000

800

1000

1200

1400

1600

1800

2000

Center zone’ elapsed day’wt(cm)

20000
15000
10000

800

1000

1200

1400

1600

1800

2000

Bottom zone ’ elapsed day’Figure 5.12: Measured time variation of the water transparency from April 1, 1996 for eachzone. The solid lines are the averaged transparency for each zone.

5.4

Energy calibration by LINAC

The determination of the absolute energy scale is most important for the measurement of theenergy spectrum of the recoil electrons scattered from solar neutrinos. In order to search forpossible distortion of the energy spectrum by neutrino oscillations, for example the small angle
solution of the MSW effect, the absolute energy must be calibrated with an accuracy of ∼1%.
A Ni-Cf calibration source was used for the absolute energy calibration at Kamiokande andbeginning of SK for solar neutrinos. However it has systematic uncertainties by itself which arelarge enough to spoil the measurement of the energy spectrum distortion. The main sources of
uncertainty are the neutron capture cross sections and decay lines of 60 Ni and 62 Ni. A LINAC(LINear ACcelerator [104]) system which can inject electrons, that energy is similar to thatof the recoil electrons, to the detector directly is most suitable for that purpose, since it has
smaller systematic uncertainties. In this section, details of the absolute energy calibration with
the LINAC are described. Uncertainties arising in the LINAC calibration are also discussed.
More details of the LINAC calibration are given in [104].

5.4.1

The LINAC system

Figure 5.13 shows an overview of the LINAC calibration system. An electron LINAC is located
4.2m above and 13m away from the water tank in a mine tunnel. The LINAC was used at thehospital of Miyazaki Medical University as a cure for cancer. Electrons from an electron gun,which is specially improved in order to reduce the current to suitable level, allowing that only
one electron is injected in to the tank, go through an acceleration tube in which the electrons
are accelerated with microwaves of 2µsec width. The frequency of generation of the microwave
is adjustable in a range of 10∼66Hz. The broad momentum of the electrons is determined byan input power to the acceleration tube, which is also adjustable. The electron energy rangethat the LINAC can generate is from 4.5 MeV to 16 MeV. Current of the electron beam can bechanged by adjusting the output current of the electron gun. The accelerated electrons are bent
by a magnet (D1 magnet) at the angle of 15 degrees. The electric current of the D1 magnet
selects the momentum of the electrons fundamentally with two collimators near the magnet.
Reduction factor of the electron current is about 10 −6 . The selected electrons go through a72

TOWER FOR INSERTING BEAM PIPE
D2 MAGNET

D3 MAGNET

D1 MAGNET
LINAC

E C

A

F

B

4200 cm

1300 cm

BEAM PIPE

H

D

G

Z

X
4000 cmY

Figure 5.13: The overview of the LINAC calibration system.

beam pipe surrounded by rock as shown in figure 5.13. The rock plays a role to stop γ-rays
generated by the collisions of the unselected electrons with the collimators or the beam pipe.
By MC simulation, the probability that the γ-rays can penetrate the rock and OD is estimatedto be less than 10−9 . The electron momentum is further selected by a collimator before the D2
magnet. The momentum spread after this collimator is 0.5% at FWHM. Again many γ-rays are
generated by this collimator. Lead blocks located under the collimator stop the radiation. The
electrons passing thought the collimator are bent 15 degrees back to the horizontal direction by
the D2 magnet. The electron beam traveling horizontally on the tank is bent again 90 degrees by
the D3 magnet and injected downward to the tank. Quadrupole magnets (Q-magnets) locatedbefore and after the D3 magnet focus the electron beam on the end point of the beam pipe.
Energy loss by bremsstrahlung at the D3 magnet is negligible small (∼ 1.5 × 10 −8 MeV for totalenergy of 10 MeV).
Figure 5.14 shows the structure of the beam pipe end point. In left side in figure 5.14, upper
TITANIUM WINDOW

102 mmSCINTILLATOR FOR
TRIGGER COUNTER
HV, signal
cables

HV, signal
cables

818 mmScintillation
counters
PMT

PMT FOR TRIGGER
COUNTERPMTSCINTILLATOR FOR
VETO COUNTER

Trigger counter

WAVE-LENGTHSHIFTER

Titanium window

PMT
80 mm

Figure 5.14: The end point of the beam pipe. Left figure shows side view and right figure shows
top view.
scintillation counters are used for optimizing the beam profile at the end point and as a veto73

Position
A
B
C
D
E
F
G
H

x(cm)
−388.9−388.9−813.1−813.1−1237−1237−388.9
−1237

y(cm)
−70.7
−70.7
−70.7
−70.7
−70.7
−70.7
−70.7
−70.7

z(cm)
1228
27
1228
27
1228
27
−1173
−1173

Table 5.2: The list of the positions where LINAC data was taken.

counter. A lower scintillation counter, with radius of 12mm and thickness of 1mm is used as a
trigger counter. Last point of the beam pipe is covered by a 100 µm thick titanium window of
15mm radius which partitions the vacuum (10 −4∼−5 torr) and water.
Electric currents of the D2 and the D3 magnet are set so that the electron beam hit the trigger
counter maximumly. The current of the D1 magnet is set to a fixed value, selecting the electron
momentum. Q-magnet current is calculated by a MC simulation of beam transportation. The
beam intensity is adjusted to 0.1 electron per microwave in order to reduce the injection of morethan 2 electrons in the tank water. The beam intensity can be also monitored on the water tankusing monitoring scintillation counter located before the D3 magnet. By comparing the beam
intensity on the tank and at the end cap, the degree of beam loss can be calculated. The loss
gets worse as the beam momentum becomes small (about 80% at 5 MeV/c electron momentum).
The missing electrons have a possibility to induce a γ-ray background. Discussion related withthe background problem is given later.
The LINAC beam calibration about details is described in appendix D.

5.4.2

Energy calibration of SK detector

The injection of the electron beam to the SK detector was done at 8 positions. List of the 8 positions in terms of the detector coordinates defined in figure 5.13 is shown in table 5.2. A schematic
view of the 8 positions is also shown in figure 5.13. At each position, an electron beam is injectedwith 6∼7 different momenta and about 2×10 4 events hitting the trigger counter are taken. The
trigger logic used for the LINAC calibration is drawn in figure 5.15. In order to get the measured
energy in the SK detector, at first, events issuing LINAC trigger are selected. Further, multiple
electron events, that have more than two electrons injected to the SK detector accidentally in
one event, are rejected. These events can be eliminated easily by counting number of peaksin the TOF subtracted time distribution of the hit PMTs. For example, figure 5.16 shows the
TOF subtracted time distributions for the events selected as having one, two, or three electron
multiplicity. About 5% LINAC triggered events are dropped by this selection. Figure 5.17 shows
scatter plot of reconstructed vertex distribution with histograms of its projections on the x andz axes for finally selected events. The injection point is x=(−388.9cm,−70.7cm,+27cm) and thebeam momentum is 16.31 MeV/c.
The measurement of the Nef f in SK detector is done as follows. At first the measured N ef f
is plotted to one-dimensional histogram as shown in figure 5.18. Next, a Gaussian fit is applied
to the distribution in a range from −1σ to +2σ. A measured N ef f value is defined as a meanvalue of the Gaussian fit and energy resolution is defined as (sigma of the Gaussian fit)/(themean).
In order to get absolute energy scale, namely the relation between N ef f and total electronenergy, a MC simulation is used. A direct correlation between LINAC beam energy and themeasured Nef f value is not useful for that purpose, because there exists ∼1% non-uniformity
74

discriminator

GG(2µ sec width)Amp

discriminatormicrowave
signaltrigger counter
signaldelay
LINAC trigger

GG(50nsec window)
Empty trigger

Clock(100Hz)
Clock trigger

Figure 5.15: The trigger logic for the LINAC calibration. LINAC trigger is used for event
selection. The other trigger is for study of beam correlated background.

20
15
10
5
0
700

800

900 1000 1100 1200 1300 1400 1500
1 electron

20
15
10
5
0
700

800

900 1000 1100 1200 1300 1400 1500
2 electron

20
15
10
5
0
700

800

nsec

nsec

900 1000 1100 1200 1300 1400 1500
3 electron

nsec

Figure 5.16: The TOF subtracted time distribution for the events selected as one, two, or threeelectron multiplicity. Each histogram represents one event that is representative of its class.

751000 1500

1000

500

Z (cm)

1500

500-1500 -1000 -500

0

0
-500
-1000

-1500 -1000
6000
4000
2000
0

-500

0

500

1000

1500

3000
2000
1000
0

-1500

x(cm)
-1500 -1000

-500

0

500

1000

1500

X (cm)

number of events

Figure 5.17: The scattered plot of the reconstructed vertex distribution with histograms of its
projections on the x and z axes. The injection position is x=(−388.9cm,−70.7cm,+27cm) andthe beam momentum is 16.31 MeV/c.

800

700

600

500

400

300

200

100

0

40

60

80

100

120

140

160

measured Neff

Figure 5.18: The measured Nef f distribution in the SK detector at the position of
x=(−388.9cm,−70.7cm,+27cm) and beam momentum of 16.31 MeV/c.

76

number of hitsof Nef f in the fiducial volume and the LINAC calibration is done for only 8 positions with one(downward) direction, and the correlation cannot be easily extrapolated to the total fiducial
volume and all direction. A MC simulation which includes the LINAC system configuration(namely the beam pipe, the trigger counter, and the Ti window) is carried out for various
tuning parameters (collection efficiency and coefficients of scattering and absorption of light inwater: see chapter 3). The input electrons are injected in the beam pipe from before the trigger
counter to a downward direction with the beam spread corresponding to the size of the trigger
counter. MC simulation data are also analyzed as same way as the LINAC data, and measured
Nef f values of both are compared. The tuned parameters for which the MC simulation best
agrees with the LINAC data are selected.
With the best-tuned MC simulation, about 6×10 4 events are generated in the fiducial volume
for electrons of total energy of 4, 5, 6, 7, 10, 15, 30 and 50 MeV. The distribution of the N ef f for
total energy of 10 MeV is shown in figure 5.19. A Gaussian fit is applied to the distribution to
reduce the distribution to a value. An MeV value for the total energy of the electrons is obtainedby fitting a 4-th order polynomial function as shown in figure 5.20. A fitting accuracy is about±0.1%. Thus the energy observed in SK, E SK is defined by in our current MC simulation

2250

2000

1750

1500

1250

1000

750

500

250

0

20

40

60

80

100

120

effective hit

Figure 5.19: The distribution of the N ef f for the electron events of total energy of 10 MeV. A
Gaussian fit is applied to get the peak value of the distribution.

2
ESK = 0.80586 + 0.12982Nef f − 0.17176 · 10−4 Nef
f

3
−9 4
+0.19489 · 10−6 Nef
f − 0.32113 · 10 Nef f(5.8)

If higher order terms are ignored, the conversion from the N ef f to the energy is approximately
represented as 1 MeV'7.71 effective hits.
The measured energy distribution of the LINAC data and the MC simulation for seven beamenergies at the position x=(−1237cm,−70.7cm,+1228cm) is shown in figure 5.21. Agreement
is very good including width of the energy distribution Further, figure 5.22 shows an energy
spectrum of 10.78 MeV/c LINAC data summing the data of 8 positions (cross marks) with thecorresponding MC (boxes, each box height corresponds to square sum of MC statistical error
and energy resolution systematic error(2%), which is described later). As shown in the figure,
the MC simulation reproduces the detector response to electrons even up to a 3σ tail of thespectrum.
77

total energy (MeV)

60

50

40

30

20

10

0

0

50

100

150

200

250

300

350

400

450

Neff

Figure 5.20: A 4-th order polynomial fit to the correlation between the peak values of the N ef f
and the total energies of the electrons.

800
600
400
200
0

16.09 MeV

0

5

10

15

20

25

800
600
400
200
0

6.79 MeV

05energy (MeV)
1000
750
500
250
0

13.44 MeV

0

5

10

15

20

25

1000
750
500
250
0

10.78 MeV

0

5

10

15

20

25

energy (MeV)
1000
750
500
250
0

15

5.84 MeV

05energy (MeV)
1000
750
500
250
0

10

energy (MeV)

1015energy (MeV)
1000
750
500
250
0

4.89 MeV

0

5

10

15

energy (MeV)

8.67 MeV

0

5

10

15

20

25

energy (MeV)

Figure 5.21: LINAC data and MC simulation measured energy distribution for seven beamenergies at a position x=(−1237cm,−70.7cm,+1228cm). The cross marks are the LINAC dataand histograms are the MC simulation.

78

Nubmer of events

10

3

10

2

6

LINAC real data
LINAC MC, box height=((MC statistical error)2+(2% energy resolution error)2)1/2

7

8

9

10

11

12

13

14

15

16

energy (MeV)

Figure 5.22: Summed energy spectrum for real data (cross marks) and MC simulation (boxes)
over the LINAC 8 positions with the beam momentum of 10.78 MeV/c.

The LINAC calibration data are used for tuning of the parameters in the SK detector MC
simulation. However, there still remain systematic discrepancies between data and MC. Anotheruseful aspect of the LINAC calibration data is to evaluate remaining systematic difference between the LINAC data and the MC simulation. Energy deviation between them for each beamenergy and at each position is shown in figure 5.23. Error bars of all marks are statistical ateach point and for each beam energy. From now on, the LINAC data is denoted as ’LINAC’ andthe MC simulation as ’MC’. The energy systematic difference is evaluated for two classifications,i.e. energy dependence and position dependence, and these are shown in figure 5.24. Figure5.24 (a) and (b) shows position averaged and energy averaged deviation between data and MC,
respectively. Outside error bars in figure 5.24(a) are systematic uncertainty of the LINAC calibration. The systematic uncertainties about details is described in appendix D. Inner error bars
are statistically combined error and the rightest mark in figure 5.24(a) is combined difference forall momenta and at all positions. These values are used for an evaluation of the systematic errorof the solar neutrino flux and the measurement of the energy spectrum. The detailed discussionof it is given later. In figure 5.24(a), though the deviation have energy dependence, all points
stay within ±0.5%. These figures are used for evaluating energy correlated systematic errors as
described in next section.
Energy resolution is also investigated. Figure 5.25 shows the energy resolution as a functionof the electron total energy at each position for the LINAC data (a) and the MC simulation(b). Position averaged deviation of the energy resolution as a function of the electron totalenergy is also shown in figure (c). Although the energy resolution is not a tunable parameter,
the deviation between the LINAC data and the MC simulation is consistent within 2%.
The energy systematic energy resolution difference is evaluated for two classifications, i.e.
energy dependence and position dependence, and these are shown in figure 5.26. Figure 5.26(a) and (b) shows position averaged and energy averaged deviation between data and MC,
respectively.
The time and directional uniformity by LINAC calibration about details is described inappendix D.

79

MC total energy in water vs observed energy
observed energy in SK (MeV)

observed energy in SK (MeV)DATA total energy in water vs observed energy
18



16

x =−4 z =12x =−4 z =0 
x =−4 z =−12
x =−8 z =12x =−8 z =0





x =−12 z =12x =−12 z =0
x =−12 z =−12

14

18

16

x =−12 z =12x =−12 z =0
x =−12 z =−12

14

12

12

10

10

8

8

6

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0

6

WT = 83m
4

4

6

8

10

12

14

WT = 83m
16

4

18

4

6

8

10

total energy in water from Ge measurement(MeV)

12

14

16

18

total energy in water from Ge measurement(MeV)(MC − DATA)/DATA

total energy in water vs observed energy deviation
0.05
0.04

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0

 

0.03

x =−12 z =12x =−12 z =0
x =−12 z =−12

0.02
0.01
0
−0.01
−0.02
−0.03
−0.04

WT = 83m
−0.05

4

6

8

10

12

14

16

18

total energy in water from Ge measurement(MeV)

0.05

position dependence of observed energy deviation

45

x= −12 z = −123

x= −12 z = 02

x= −12 z = +121

x= −8 z = +12

0.02



x= −8 z = 0

0.03

0.02



x= −8 z = +12

0.04

x= −4 z = −12

0.03




x= −4 z = 0



0.05

x= −4 z = +12

0.04(MC−DATA)/DATA(MC − DATA)/DATA

Figure 5.23: The energy deviation between the LINAC data and the MC simulation for sevenbeam energies and at 8 positions for LINAC data(a) and MC simulation(b). Figure (c) shows
the deviation of the energy resolution at each position. A∼H mean the positions defined in table
5.2.

0.01
0.01

0

0

−0.01

−0.01

−0.02

−0.02

−0.03

−0.03

combined deviation=
0.00113929
WT = 83m

−0.04
−0.05

4

6

8

10

12

14

16

−0.04

WT = 83m−0.05

18

total energy in water from Ge measurement(MeV)

0

6

7

8

9

10

position tag

Figure 5.24: The systematic energy difference between the LINAC data and the MC simulation, (a) energy dependence (position averaged deviation) and (b) position dependence (energy
averaged deviation). Outside error bars of figure(a) are the LINAC system systematic uncertainty described later. Inside error bars are the statistical error. Error bars of figure(b) are only
statistical error.

80

MC total energy in water vs energy resolutionenergy resolutionenergy resolution

DATA total energy in water vs energy resolution



0.24

x =−4 z =12x =−4 z =0 
x =−4 z =−12
x =−8 z =12x =−8 z =0



0.22



x =−12 z =12x =−12 z =0
x =−12 z =−12

0.2

0.24

0.22

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =00.2

x =−12 z =12x =−12 z =0
x =−12 z =−12



0.18

0.18

0.16

0.16

0.14

0.14

0.12

0.12

WT = 83m
0.1

4

6

8

10

12

14

WT = 83m
16

0.1

18

4

6

8

10

total energy in water from Ge measurement(MeV)

12

14

16

18

total energy in water from Ge measurement(MeV)(MC − DATA)/DATA

total energy in water vs energy resolution deviation
0.2

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0

 

0.15

0.1

x =−12 z =12x =−12 z =0
x =−12 z =−12

0.05

0

−0.05

−0.1

−0.15

WT = 83m
−0.2

4

6

8

10

12

14

16

18

total energy in water from Ge measurement(MeV)

Figure 5.25: The energy resolution as a function of the electron total energy at each position for
LINAC data(a) and MC simulation(b). Figure (c) shows the deviation of the energy resolution
at each position.

position dependence of energy resolution deviation

−0.05

−0.1

−0.1

combined deviation =−0.0111796

2

3

4

5

 

−0.15

WT = 83m
−0.2

4

6

8

10

12

14

x= −12 z = −12−0.05

x= −12 z = 00

x= −12 z = +120x= −8 z = +12

0.05



x= −8 z = 0

0.05



x= −8 z = +12

0.1

x= −4 z = −12

0.1

−0.15



0.15

x= −4 z = 0

  

0.15

0.2

x= −4 z = +12(MC−DATA)/DATA(MC − DATA)/DATA

total energy in water vs energy resolution deviation
0.2

WT = 83m
16

−0.2

18

total energy in water from Ge measurement(MeV)

0

1

6

7

8

9

10

position tag

Figure 5.26: The systematic energy resolution difference between the LINAC data and the MC
simulation, (a) energy dependence (position averaged deviation) and (b) position dependence(energy averaged deviation). Outside error bars of figure(a) are the LINAC system systematic
uncertainty described later. Inside error bars are the statistical error. Error bars of figure(b)are only statistical error.

81

5.5

Angular resolution

Angular resolution at SK detector is measured by the LINAC calibration. Though the LINAC
system can measure the angular resolution for only one direction (downward), it provides a
crucial test of the detector simulation. Figure 5.27 shows distributions of an opening angle
between the direction of the beam injection and the reconstructed direction for LINAC data(cross) and MC simulation (histogram) at a position x=(−1237cm,−70.7cm,+1228cm) for 7
electron momenta. Agreement is excellent. The angular resolution is defined as an angle which

1000

800
600
400
200
0

16.09 MeV

500
0

0

50

100

150

6.79 MeV

050

theta (degree)
800
600
400
200
0

13.44 MeV

1000
500
0

0

50

100

150

0

50

150

4.89 MeV

400
200
0

50

100

0

150

theta (degree)
800
600
400
200
0

100

theta (degree)600

10.78 MeV

150

5.84 MeV

theta (degree)
1000
750
500
250
0

100

theta (degree)

0

50

100

150

theta (degree)

8.67 MeV

0

50

100

150

theta (degree)

Figure 5.27: An opening angular distribution at x=(−1237cm,−70.7cm,+1228cm) for 7 electron
momenta. The cross marks are the LINAC data and histograms are the MC simulation.
includes 68% of the reconstructed directions around the beam direction. Energy dependence of
the angular resolution at 8 positions for LINAC data and MC simulation are shown in figure5.28(a) and (b) respectively. Figure 5.28 (c) shows deviation between LINAC and MC for 7
momenta and at 8 positions. Though the angular resolution of MC simulation is larger thanthat of LINAC data and the deviation has some position dependence, almost all points are
consistent within 5%. Error bars of figure 5.28(a),(b),(c) are only the statistical error. Figure5.28(d) shows the position combined deviation. Error bars of 5.28(d) are variances at eachbeam momentum in figure 5.28(c). This slight disagreement between LINAC and MC causes a
comparatively large systematic error for the measured solar neutrino flux value.

5.6

Vertex resolution and shift

The LINAC system can also calibrate vertex resolution. Figure 5.29 shows distributions of
distance from the end point of the beam pipe to the reconstructed vertex position at a beam
injection position x=(−1237cm,−70.7cm,+1228cm) for 7 beam momenta. Again cross marks
are for LINAC data and histograms are the MC simulation. Vertex resolution is defined as aspherical radius which includes 68% reconstructed vertex position around the end point. Figure5.30 shows (a) the vertex resolution as a function of the electron total energy at 8 positions for
LINAC data, (b) same as (a) but for the MC simulation, (c) deviation between (a) and (b),(d) deviation combined for the 8 positions. Error bars of the figures are the same as those of
figure 5.28. The timing resolution of the ID PMTs for single photo-electron response in the MC
simulation is adjusted so that the vertex resolutions of the LINAC data and the MC simulation82

MC total energy in water vs angular resolution
angular resolution (degree)

angular resolution (degree)

DATA total energy in water vs angular resolution
40



37.5

x =−4 z =12x =−4 z =0 
x =−4 z =−12
x =−8 z =12x =−8 z =0



35



x =−12 z =12x =−12 z =0
x =−12 z =−12

32.5

40

35

x =−12 z =12x =−12 z =0
x =−12 z =−12

32.5

30

30

27.5

27.5

25

25

22.5

22.5

20

20

17.5

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0


37.5

17.5

WT = 83m
15

4

6

8

10

12

14

WT = 83m
16

15

18

4

6

8

total energy in water from Ge measurement(MeV)MC − DATA (degree)

MC − DATA (degree)x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0

2.5

x =−12 z =12x =−12 z =0
x =−12 z =−12

2

16

18

3.5
3




2.5
2

1.5

1.5

1

1

0.5

0.5

0

0

−0.5

−0.5

−1

−1

WT = 83m−1.5

14

total energy in water vs angular resolution deviation

3.5



12

total energy in water from Ge measurement(MeV)

total energy in water vs angular resolution deviation

3

10

4

6

8

10

12

14

WT = 83m
16

−1.5

18

total energy in water from Ge measurement(MeV)

4

6

8

10

12

14

16

18

total energy in water from Ge measurement(MeV)

Figure 5.28: Angular resolution as a function of the electron total energy. (a) is for LINAC
data, (b) is for MC simulation, (c) is the deviation between LINAC and MC at 8 positions and7 momenta and (d) is the position combined deviation. Explanations of error bars of the figures
are given in text.

83

800
600

16.09 MeV

1000
500
0

0

100

200

300

400

500

400
200
0

6.79 MeV

0100

distance (cm)1500

13.44 MeV

1000
500
0

0

100

200

300

400

500

10.78 MeV

300

400

500

distance (cm)
800
600
400
200
0

5.84 MeV

0100

distance (cm)
1000
750
500
250
0

200

200

300

400

500

distance (cm)4.89 MeV

400
200

0

100

200

300

400

500

0

0

distance (cm)

100

200

300

400

500

distance (cm)

1000
750

8.67 MeV

500
250
0

0

100

200

300

400

500

distance (cm)Figure 5.29: Distributions of distance from the end point of the beam pipe to the reconstructedvertex position at a beam injection position x=(−1237cm,−70.7cm,+1228cm) for 7 beam momenta for LINAC data (cross) and MC simulation (histogram).

Source position(35.3,−70.7,−1200.)(35.3,−70.7,0.)(35.3,−70.7,+1200.)(35.3,−70.7,+1600.)(35.3,−1201.,−1200.)(35.3,−1201.,0.)(35.3,−1201.,+1200.)

∆x
−0.3
0.7
−1.0
−0.6
−3.4
−1.1
0.6

∆y
−2.7
−0.5
−0.7
−2.8
7.0
16.0
10.0

∆z
−3.0
−1.9
−1.0
−10.0
−7.0
−1.1
2.0

Table 5.3: The vertex shift measured by the Ni-Cf source. The unit is cm.

are consistent for 8 positions, and the value is determined to be 2.4nsec, which agrees with theindependently measured value [82].
It it important to know a shift of the vertex position in the vertex reconstruction, since
the vertex shift causes a change of the fiducial volume size, i.e. the target number of thesolar neutrinos. In order to estimate the vertex shift, the Ni-Cf calibration source is used. An
advantage to use the Ni-Cf γ-ray source is that the source can emit γ-rays to almost uniform
directions. The vertex shift is defined as a vector from an averaged position of the reconstructedvertex of the data to that of a corresponding MC simulation. Table 5.3 shows the vertex shift atsome source positions. These values are used to obtain systematic error for the measured solar
neutrino flux.

5.7

Energy calibration by DT

The LINAC calibration has limitations. The electrons are only moving in a downward direction
when they exit the beam pipe, possibly introducing systematic errors due to direction dependences of the detector. The presence of the beam pipe in the tank while calibration data aretaken is another limitation. While this is modeled in the simulation, it is still the largest source
84

220

MC total energy in water vs vertex resolution
vertex resolution (cm)vertex resolution (cm)

DATA total energy in water vs vertex resolution

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0


200

  





180

x =−12 z =12x =−12 z =0
x =−12 z =−12


220



200

x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0




180

x =−12 z =12x =−12 z =0
x =−12 z =−12



160

160

140

140

120

120

100

100

80

80

60

60

WT = 83m

40
4

6

8

10

12

14

WT = 83m

40
16

18

4

6

8

total energy in water from Ge measurement(MeV)MC − DATA (cm)MC − DATA (cm)x =−4 z =12x =−4 z =0x =−4 z =−12
x =−8 z =12x =−8 z =0
x =−12 z =12x =−12 z =0
x =−12 z =−12

10





10

−10

−10

−20

−20

WT = 83m
6

8

10

12

14

18

20

0

4

16

30

0

−30

14

total energy in water vs vertex resolution deviation

30

 

12

total energy in water from Ge measurement(MeV)

total energy in water vs vertex resolution deviation

20

10

WT = 83m
16

−30

18

total energy in water from Ge measurement(MeV)

4

6

8

10

12

14

16

18

total energy in water from Ge measurement(MeV)

Figure 5.30: Vertex resolution as a function of the electron total energy. (a) is for LINAC data,(b) is for MC simulation, (c) is deviation between LINAC and MC at 8 positions and 7 momentaand (d) is the position combined deviation. Explanations of error bars of the figures are givenin the text.

85

of systematic error for the calibration, especially at low energies. Additionally, the beam pipeand equipment associated with the LINAC calibration can only be operated at a restricted setof calibration ports, so the calibration must be extrapolated to the entire fiducial volume. Operating the LINAC also requires a great deal of manpower and results in significant detector
down time.
The 16 N used as a calibration source for SK are produced by two different mechanisms [104].
The first source results from the interaction of 14.2 MeV neutrons in the water of the detector.
These neutrons are from a deuterium-tritium neutron generator (DTG), and produce a highstatistics sample of 16 N at a set position in the detector. The second source of 16 N is thecapture of stopped µ− in the water of the detector. These events, like solar neutrinos, areuniformly distributed throughout the detector volume. For both of these data sets, the beta
decay of 16 N is carefully modeled, and the corresponding MC is compared to the data. Since
the energy scale of the MC is set by the LINAC calibration, a comparison of 16 N data to MC
serves as a cross check of the energy scale.
At the center of the DTG setup is a MF Physics Model A-211 pulsed neutron generator.
This neutron generator creates neutrons by the deuterium-tritium reaction,3

H + 2 H → 4 He + n.

(5.9)

This reaction yields isotropically distributed neutrons with an energy of 14.2 MeV.
The schematic view of the DTG generator is shown in figure 5.31.
Epoxy
Feedthru

O-Ring

PVC
Endcap

Spacer

Gas Reservoir
Element
Pulse
Forming
Electronics

VacuumEnvelopeTransformer
Oil Fill

Vsource

150 cmStainless
Housing














Ion Source
Anode
Ion Source
MagnetAccelerator
Anode

Accelerator
Head

VaccelLeakSensor
TargetStainlessEndcapAl
Endcone

O-RingVtarget16.5 cm

Figure 5.31: Schematic of the DTG setup including the stainless steel water-tight housing,accelerator pulse-forming electronics and accelerator head. Details of the accelerator head arealso shown.
The 14.2 MeV neutrons produced by the DTG are energetic enough to produce 16 N by the(n,p) reaction on 16 O [83] in the water of SK, which requires neutron energies greater than ∼11
MeV. [84]. The (n,α) and (n,d) reactions on 16 O result in the creation of stable isotopes, while
the creation of 15 O by the (n,2n) reaction is energetically forbidden. The (n,p) reaction on 17 O
and 18 O are suppressed by the low isotopic abundance and smaller reaction cross sections, which
results in yields < 1 × 10−4 that of 16 N.
When taking data at SK, the DTG is lowered to a position 2 meters above the intended 16 N
production point, and the data taking cycle is started (Figure 5.32). The data taking cycle iscontrolled by computer, directing the crane, the generator and data collection of SK. First, the86crane lowers the DTG 2 meters, to the data collection position. Next, the generator is fired,creating a bubble of 16 N surrounding the end of the DTG. Every time the DTG is fired, thegenerator is pulsed 3 times, at the maximum rate of 100 Hz, producing ∼3 million neutrons.
Third, the DTG is raised 2 meters, removing the generator from the area containing 16 N. Afterthe DTG is fired, ∼10 seconds are required before the apparatus is completely withdrawn, and∼60% of 16 N has decayed. No data are collected while the crane is moving to prevent electricalnoise generated by the crane from contaminating the data. Once the crane has stopped moving
upward, data are collected in SK for 40 seconds. This cycle is repeated ∼25 times at a single
location in the SK tank, yielding a data sample of ∼300,000 16 N events collected by SK.
The creation of 16 N occurs naturally as a background to the solar neutrino measurement. A
stopped µ− can be captured by a 16 O nucleus in the water of the detector,
16

O + µ− → 16 N + νµ .

(5.10)

A fraction of 16 N created will be in the ground state, and beta decays with a 7.13 sec half life.
These events are found by collecting events that occur in the area surrounding the stopping
point of a captured muon and subtracting random background events.

(a)


 
 
     


(b)(c)

                                                                



          
 

E n=14.2 MeV
16

16

O(n,p) N

2m
n

n
n

n
n

16

N

n

Figure 5.32: An overview of DTG data taking. In (a), the DTG is lowered to the position wheredata is to be taken, The DTG is fired in (b) at that location, and (c) withdrawn 2 meters anddata collected.
Careful modeling of the 16 N beta decay is crucial in order to perform accurate MC simulationsof 16 N data. All decay lines with a probability of 10 −8 or greater are included. Table 5.4 contains
information about the included decay lines.
The energy spectrum from a typical data taking run is presented in figure 5.33, along withthe corresponding MC simulation. The peak of the energy distribution is dominated by eventswith a 6.1 MeV gamma ray in coincidence with an electron with a 4.3 MeV endpoint energy.
28% of the events contain an electron with an endpoint energy of 10.4 MeV and are the primarysource of the observed high energy tail. This data was taken at a nominal position of (-388.9
cm, -70.7 cm, 0 cm).
The data from the DTG are also used to study the position and direction dependence ofthe energy scale. DTG data was taken in 6 different calibration port locations, at 7 depths per
87

Fraction
66.2%
28.0%
4.8%
1.06%
0.012%
0.0012%

Jpi →Jpf
2 − → 3−2 − → 0+2 − → 1−2 − → 2−2 − → 0+2 − → 1−

∆I
+1
-2
+1
+0
-2
+1

Gamma Energy (MeV)
6.129
none
7.116
8.872
6.049
9.585

Type
GT allowed
GT 1st forbidden
GT allowed
F+GT allowed
GT 1st forbidden
GT allowed

Table 5.4: Summary of information used in modeling the beta decay of 16 N [85]. Gamma energies
are also included. GT denote Gamow-Teller transitions and F denote Fermi transitions.

8000

7000

6000

5000

4000

3000

2000

1000

0

2

4

6

8

10

12

14
Energy (MeV)

Figure 5.33: Energy spectrum for Data and MC from a typical data taking run at a single pointin the SK tank. The data (points) and MC (line) are fit with a Gaussian function only above
the 5.0 MeV analysis threshold.

88

Contamination from natural background
16 N MC decay modeling
Unmodeled decay lines
Shadowing of Čerenkov photons
DTG data selection systematic
DTG related radioactive backgroundTotal Systematic Error< 0.01%±0.1%< 0.01%±0.1%±0.1%±0.05%±0.2%

Table 5.5: Summary of systematic errors from the DTG calibration.

(MC-DATA)/DATA

port, providing a large sampling of the detector volume. The position dependence of the energy
scale, shown in figure 5.34, is presented as a function of radial distance (r) and height (z) in thedetector, by performing a position-weighted average over z and r, respectively.
The direction dependence is studied as a function of zenith angle, measured with respect tothe vertical (z) axis of the detector, and as a function of azimuthal angle, measured in the x-yplane. The resulting angular dependence of the energy scale is presented in figure 5.35. In bothcases, the variation in the energy scale in direction within the fiducial volume is less than 1%.
0.03
0.02
0.01
0
-0.01
-0.02

(MC-DATA)/DATA

-0.03

-1500

-1000

-500

0

500

1000
1500
z-position (cm)

0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-200

0

200

400

600

800

1000

1200

1400 1600
r-position (cm)Figure 5.34: Position dependence of the energy scale from DTG data. At each r and z vertex
position, a position-weighted average over all z and r positions, respectively, is performed. Only
statistical errors are shown. Dashed lines indicate a deviation of ±1%.
The systematic errors for the DTG calibration for the absolute energy scale measurement
are summarized in table 5.5. A simulation of neutrons in the DTG setup indicates that small
amounts of background isotopes are created, including 24 Na, 62 Co, and 28 Al. Most nuclides havelong half lives and/or insufficient energy to trigger SK, but a MC simulation indicates a small
amount of gamma contamination is possible, and a systematic error of ±0.1% is conservatively
chosen. The DTG data selection systematic error results from a vertex position cut made to
the data to remove background events occurring near the walls of the detector from the data
sample.
A
The total position averaged energy scale deviation, ( M C−DAT), measured during the July
DAT A
1999 survey of the detector is found to be −0.04% ± 0.04%(stat.) ± 0.2%(syst.), indicating
excellent overall agreement of the DTG data with the LINAC-based MC simulation.
89

(MC-DATA)/DATA

0.03
0.02
0.01
0
-0.01
-0.02

(MC-DATA)/DATA

-0.03

0

50

100

150

200

250
300
350
Azimuthal Angle (degrees)

0.03
0.02
0.01
0
-0.01
-0.02
-0.03

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6
0.8
1
cos(Zenith Angle)

Figure 5.35: Angular dependence of energy scale from DTG data obtained from a positionweighted average over all positions in the fiducial volume. An azimuthal angle of 0 degrees
corresponds to the +X axis of SK. Only statistical errors are shown. Dashed lines indicate a
deviation of ±1%.

5.8

Trigger efficiency measurements

For the solar neutrino analysis, we use two difference triggers, as described in chapter 3: theLow Energy trigger (LE) and the Super Low Energy trigger (SLE trigger). Hence, the trigger
efficiency for both has to be measured.
The trigger efficiency is measured using the Ni-Cf system and the DT generator. The low
energy trigger efficiency is defined as follows.

Ef f iciencyLE trigger ≡Ef f iciencySLE trigger ≡NLE trigger
Nspecial trigger
NSLE trigger
Nspecial trigger(5.11)(5.12)

where, Ef f iciencyLE,SLE trigger is the trigger efficiency. NLE,SLE trigger is the numberof events issuing both the LE, SLE trigger and a special low energy trigger with a threshold of-150 mV. Nspecial is the number of events issuing the special low energy trigger. In measuring
the SLE trigger efficiency, the number of event issuing the both the SLE trigger and the special
low energy trigger is used instead of N LE,SLE trigger .
The LE efficiency is 99.8% for events with energy of 6.5∼7.0 MeV, the LE trigger efficiency
is 100%. The trigger efficiency is measured at a various positions in the ID and at various watertransparencies to study the possible dependence on the vertex position, the event direction, andwater transparency. In order to consider these dependences in the MC simulation, a trigger
simulator is used. In the trigger simulator, the trigger threshold is defined by the number ofeffective hits. The threshold level is set to reproduce the energy and position dependence of thetrigger efficiency seen in data.
The SLE trigger was installed in May 1997 and the threshold has been changed 7 times. Thechanges in the SLE trigger threshold are summarized in table of chapter 3
90

Figure 5.36 shows the energy dependence of the SLE trigger efficiency for each trigger threshold. The line shows the analysis threshold for this thesis (4.5 MeV). Above 6.0 MeV, the SLE
trigger efficiency is 100% for all positions.
120

Trigger efficiency’

Trigger efficiency’

120

100

80

  

100

80

    

  

60

60

40

40

20

20

0

2

3

4

5

6

7

8

9

0

10

2

3

4

5

6

     

7

8

Energy(MeV)

Trigger efficiency’’Trigger efficiency’

10

120

100

80

  

100

80

    

  

60

60

40

40

20

20

0

9

Energy (MeV)’

120

2

3

4

5

6

7

8

9

0

10

Energy (MeV)’

2

3

4

5

6

    

7

8

9

10

Energy (MeV)’’Trigger efficiency’

120

100

80

      

60

40

20

0

2

3

4

5

6

7

8

9

10

Energy (MeV)’

Figure 5.36: The SLE trigger efficiency as a function of energy by DT calibration.
As described in chapter 3, when the number of hit PMTs exceeds 29, a global trigger (L.E
trigger) is issued. It is important for the solar neutrino observation to know how much measured
energy is necessary in order to issue the trigger. In order to investigate the trigger efficiency, again
the Ni-Cf source is used. As described in this chapter, the Ni-Cf source can emit sufficiently low
energy γ-rays, by which the trigger efficiency as a function of measured energy can be obtained.
In the Ni-Cf source calibration, an additional trigger, whose threshold is 150mV (corresponds
to about 14 hits) and called a ’Ni trigger’, is provided. The trigger efficiency is obtained by
calculating a ratio of the number of events which issue both the Ni trigger and the L.E. trigger
to the number of events which issue the Ni trigger for several energy regions.

91

Chapter 6

General data reduction
The data set used in this analysis covers the period from May 31, 1996 to July 15, 2001 andrespectively 1496 days of detector live-time (roughly ∼90% for 1678 days detector live time withhigh efficiency).
Background sources to the solar neutrino data sample are :• Electronics noise and flashing PMTs
• Cosmic ray muons.
• Electrons from the decay of stopping muons.
• Muon-induced spallation products.
• Radioactivity in the detector materials and surrounding rock. (For example, external γ
ray and electron from daughter nucleus of 222 Rn.)
To reduce these backgrounds, various general cuts are applied and various additional cuts
are applied for 4.5 MeV bin analysis. The general and additional cuts are applied to the data infour and two stages respectively. The general cuts, we namely, are the first reduction, spallation
cut, the second reduction, and the γ cut. The additional cuts are the tight cut and the new
fitting cut.
The general cut criteria for the data set is described first in this chapter and named “Generaldata reduction” for 1496 days data set. Next, the additional cut criteria applied for 4.5 MeV
energy bin analysis is described in chapter 8 and named “Tight data reduction”.

6.1

The data set

The basic unit of the data set is a run. Each run is at most 24 hours long. Each run is divided
into sub-runs, which are about 2∼10 minutes long. The length of each sub-run depends on thetrigger rate.
To make the basic data set, real-time bad run (sub-runs) selection and non-real-time badrun (sub-runs) selection are applied to the all runs in order. The real-time bad run selection
is automatically applied in real-time process by using some cut criteria. After this selection,
the total lost time is 27.3 days. They might be related to hardware trouble. The non-real-time
bad run selection is applied on all normal runs (sub-runs) after the real-time bad run selection.
The quality of the runs and sub-runs remaining after real-time bad run selection are checked
manually and the bad runs for LE and SLE trigger events were rejected separately. After thisselection, the total lost time is 112 days. The largest rejected time is due to log book checking.
The details of bad run selection is given in appendix E.

92

6.2

First data reduction

6.2.1

Total photo-electron cut

number of eventsFirst of all, high energy events, such as cosmic ray muon events (deposit energy ∼ 8 GeV),
atmospheric neutrino events (deposit energy ∼ 1 GeV), are eliminated. Figure 6.1 shows total
photo-electron number distribution in logarithmic scale. A clear peak on the left side in figure 6.1
corresponds to the high energy events. The cut criterion is the total number of photo-electrons
in the ID ≤ 1000p.e. This photo-electron number (i.e. 1000p.e.) corresponds to about 130 MeV
for an electron event, which is sufficiently high for the solar neutrino events, and therefore theinefficiency of the cut for the solar neutrino events is negligible.

10

4

10

3

10

2

10

1

-1

10

1

2

3

4

5

6

log(total photo electron (p.e.))Figure 6.1: Distribution of total photo-electron number in logarithmic scale. The criterion of
the total photo-electron cut is also shown.

6.2.2

Unfitted events cut

When the number of hit PMTs used for the vertex reconstruction is too small, it is difficult to
get enough accuracy of the vertex position. Events with incomplete fitting results are removed.
An incomplete fitting is defined as :Number of hit PMTs within 200 nsec time window ≤ 10

(6.1)

Number of hit PMTs within 200 nsec time window = 0(6.2)

The event tagged by the above criteria is judged as incomplete fitting event and removed.
This cut corresponds to an energy cut of 2 MeV threshold.

6.2.3

Fiducial volume cut

To reduce events caused by γ rays coming from the surrounding rock and the materials comprising the ID wall, events that have vertex position within 2 m of the ID wall are eliminated.
The fiducial general volume of SK for the solar neutrino analysis is defined by this cut to be 22.5
ktons, or 14.9 m in radius and 16.1 m × 2 in height. Figure 6.2 shows the vertex distribution
from a typical data sample.
93

10

4

10

3

10

2

CUT

CUT

10

5

10

4

10

3

10

2

CUT

10

1

-2000 -1500 -1000 -5000500 1000 1500 2000

0

z(cm)

200 400 600 800 1000 1200 1400 1600 1800 2000

r(cm)Figure 6.2: Fiducial volume cut applied to a typical data sample. The left figure shows thevertex distribution as a function z-position. The right figure shows the vertex distribution as afunction of r-position. The hatched histogram shows the distributions after the fiducial volume
cut.

6.2.4

Veto event cut

An event tagged with veto triggers which correspond to veto start and stop is removed. These
online start and stop vetoes are marked as the duration of a possible online veto, which is issued
if more than 64 events happen within 120 µsec.

6.2.5Time difference cut

In order to eliminate µ decay electron events, after-pulse events, etc., a time difference cut isapplied. Figure 6.3 shows the distribution of the time difference from a previous event. A peakaround 1µsec are due to ringing events and the second peak around 15µsec is due to after-pulse
events described in chapter 3. Interval events between two peaks are stopping µ decay electron
events. When a high energy penetrating muon event happens, almost all PMTs of ID catchlarge photo-electrons. The large output signals from the PMTs are reflected on ATM side due
to impedance mismatch between signal cable and the ATM input side. If the signal is sufficiently
large, the reflected signals are further reflected back on the PMT side due to the same reason
and the reflected signal comes back to the ATM again. The length of the cable between the
PMT and the ATM is about 70m, hence the time that the signal needs to take to travel ATMPMT-ATM is about 700nsec. However, each channel of ATM opens a 900nsec veto window after
it was hit. Therefore, the first reflected signal is discarded. However the second reflected signal
which comes after ∼1.4µsec is recorded by the ATM. These events are called ringing events.The
cut criterion to reject these events is• time difference from previous event > 50µsec
Dead time caused by the cut is 1.8×10 −4 sec, which is negligible for the solar neutrino observation.

6.2.6

Pedestal event cut

Events with a pedestal flag is removed. The pedestal of the ATM is measured by the 1/8 ATMs
out of all ATMs every 30 minutes.

94number of events

10

8

10

7

10

6

10

5

10

4

10

3

10

2

50µsec

10

1
-1

10

2

3

4

5

6

7

8

9

10

log(time difference (nsec))

Figure 6.3: Distribution of time difference from previous event.

6.2.7

Incomplete event cut

Events with the incomplete flag are removed. An incomplete event could be one of the following:• Incomplete ATM data
• Inner detector was OFF• Outer detector was OFF

6.2.8

Outer detector event cut

In order to reject remaining cosmic ray muon events which hit OD PMTs, the following cut is
imposed.
• OD trigger does not issue and number of hits in the OD ≤ 20
Figure 6.4 shows the distribution of OD hits before and after the OD trigger cut on a typical
data sample. The hatched area shows the distribution after the cut.

6.2.9

Mismatch event cut in outer detector

An event with larger than 20 OD hits is removed due to trigger mismatch. This maybe caused
by OD DAQ trouble.

6.2.10Noise event cut

In the electronics system used by the SK experiment, electronic noise sometimes happens.
Sources of the noise are suspected to be PMT flashing, turning on-off of fluorescent lights,
and so on. Figure 6.5 shows an example event display of the noise event. A characteristic pointof this kind of event is that noise hit channels have small charge. Then, a following variable isdefined,95

entry

10

4

10

3

10

2

10

1
0

20

40

60

80

100

120

140

160

180

200

Anti hit

Figure 6.4: The distribution of OD hits after OD trigger cut at a typical data sample, which
the number of OD hits become less 20.

N/S =number of hit channels(|QP M T | < 0.5p.e.)
total number of hit channels(6.3)

where |QP M T | is the absolute charge value of the hit ATM channel. Figure 6.6(a) shows
distribution of the N/S. A higher side peak is due to the noise events. The cut criterion of theN/S cut is• N/S < 0.4

6.2.11Clustered ATM hits event cut

Further, these noise hit channels are often clustered in one ATM board. Then, following cut isalso applied for the noise event cut,
number of hit in one ATM board< 0.95• AT M ratio ≡ max
number of channel in one ATM board

Distribution of the AT M ratio is shown in figure 6.6(b). The inefficiency of this cut for thesolar neutrino events is estimated by the MC simulation as described later.

6.2.12First flasher event cut

The ’flasher events’ are caused by light emission from a PMT resulting from electrical discharge
between dynodes. Figure 6.7 shows an event display of the typical flasher event. Most of the
flashers can be found by an instantaneous increase of trigger rate (strong flasher). In this caseshift crew identify the flashing PMT and high voltage of the PMT is switched off. However, incase of flashers of lower rate and lower light emission, the flasher events remain in the reduced
data. They are rejected by the following criterion. When a PMT is flashing, it often detects alarge pulse height and the PMTs surrounding it have signals. Figure 6.8(a) shows a scatter plotof maximum charge of one PMT (Qmax ) versus number of hit PMTs surrounding that PMT
which gives Qmax (0≤ mx ≤24), for a typical run including flasher events, and figure 6.8(b)shows same as (a) but for a typical normal run. The cut criterion is:
96

NUM
9
RUN
2109
SUBRUN
1
EVENT
4895
DATE 96-Jul- 5
TIME
15:44:10
TOT PE:
95.4
MAX PE:
14.0
NMHIT :
85
ANT-PE:
268.8
ANT-MX:
67.4
NMHITA:
39

RunMODE:NORMALTRG ID :00000001
T diff.:0.342E+06us: 342.
ms
FSCC:
0
TDC0: -1129.5
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

10

8

10

7

10

6

10

5

10

4

10

3

10

2

number of events

number of events

Figure 6.5: An event display of the typical noise event.

(a)

10
1
10

8

10

7

10

6

10

5

10

4

10

3

10

2

1
0.2

0.4

0.6

0.8

1

(b)

10

-1

0

10

10

N/S

-1

0

0.25

0.5

0.75

1

ATMratio

Figure 6.6: (a) shows N/S distribution and (b) shows AT M ratio distribution.

97

Number of hits around maximum charge PMT (mx24) ≥ 2(6.4)

mx24 ≥ 10(6.6)

Maximum charge (Qmax) ≥ −4 × mx24 + 75

(6.5)

An event that satisfied either of the above conditions is removed. Most of Monte Carloevents that are rejected in the first reduction step are caused by this cut. In real data, most of
events have so low energy that they have small charge. Flasher candidates, on the other hands,
have relatively large charge compared with other background. Therefore, the reduction factorof this flasher cut in case of Monte Carlo becomes higher than that of real data. This makes amain source of systematic error in the first reduction step. The events which are in the indicatedregion shown in figure 6.8 are rejected.
NUM
18
RUN
2109
SUBRUN
2
EVENT
7835
DATE 96-Jul- 5
TIME
15:49:26
TOT PE:
136.8
MAX PE:
21.7
NMHIT :
88
ANT-PE:
176.1
ANT-MX:
11.8
NMHITA:
35

RunMODE:NORMALTRG ID :00000011
T diff.:0.556E+05us: 55.6ms
FSCC:
0
TDC0: -1128.5
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 6.7: An event display of the typical flasher event.

6.2.13

Goodness cut

In addition to the above ”very low energy cut”, a goodness cut is also applied. If a goodness g v
value of an event is low, the reconstructed vertex position of the event is suspected to be wrong.
Therefore, a following cut criterion is imposed:• goodness ≥ 0.4 (see figure 6.9)

6.2.14

Second flasher event cut

In addition to the vertex test, there is another re-evaluation using the reconstructed direction.
If the reconstructed vertex position is near the true position, the hit PMTs distribute uniformly
about the reconstructed direction. However, if the reconstructed vertex is far away from thetrue vertex, the PMT hit distribution is non-uniform. In order to test uniformity of the hits,a Kolmogorov-Smirnov (KS) test is applied. Figure 6.10 shows an example of the test. The
left figures in figure 6.10 are for a well-reconstructed event. The lower figure shows correlation
between i-th PMT among the N50 , which is the number of hit PMTs in 50nsec window, and an
98

mx

mx

22.5
20
17.5
15
12.5
10
7.5
5
2.5
0

(a)

reject
0

100

200

22.5
20
17.5
15
12.5
10
7.5
5
2.5
0

300

(b)

reject
0

100

200

Qmax

300

Qmax

number of events

Figure 6.8: Scatter plots of Qmax vs mx. The events which are in the indicated region are
rejected as the flasher events.

x 10 3

10000

8000

6000

4000

2000

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

goodness

Figure 6.9: The goodness distribution. The cut criterion is also drawn.

99

NUM
1
RUN
1742
EVENT
604
DATE 96-May-31
TIME
4:32:18
TOT PE:
155.9
MAX PE:
6.8
NMHIT :
116
ANT-PE:
74.8
ANT-MX:
8.5
NMHITA:
22

DIR:-0.86,-0.14, 0.50
X:
963.1cm
Y: -895.2cm
Z: -375.7cm
R: 1314.9cm
NHIT:
48
good:
0.69

NUM
309
RUN
1743
EVENT
124510DATE 96-Jun- 1
TIME
0:59:57
TOT PE:
124.2
MAX PE:
12.6
NMHIT :
94
ANT-PE:
184.0
ANT-MX:
10.9
NMHITA:
37

RunMODE:NORMALTRG ID :00000011
T diff.:0.251E+06us: 251.
ms
FSCC:
0
TDC0: -1117.8
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

DIR:-0.92, 0.40,-0.07
X: 1205.2cm
Y: -688.2cm
Z: -289.4cm
R: 1387.8cm
NHIT:
32
good:
0.63

RunMODE:NORMALTRG ID :00000011
T diff.:0.390E+06us: 390.
ms
FSCC:
0
TDC0: -1129.2
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 6.10: An example of the directional test. Left figures are for a well-reconstructed eventand right figures are for a bad reconstructed event.

100

azimuth angle of the PMT with respect to the reconstructed direction. In ideal case, all PMTs
should be on the broken line. Now, let us define a variable Dirks which is full width of azimuth
angle deviation from the ideal case, divided by 360. In the bad case as with the right figures,the Dirks becomes large. Figure 6.11 shows correlation between Dirks (horizontal the axis)and ∆r (distance from a generated position in MC simulation to the reconstructed position)
for solar neutrino MC events. Obviously, the events with larger Dirks have large ∆r. Figure

Figure 6.11: The validity check of Dirks. The horizontal axis is Dirks and the vertical axis is∆r. Points are the solar neutrino MC simulation events above measured energy of 6.5 MeV.
6.12 shows Dirks distributions for the real data and the solar neutrino MC simulation in energy
ranges of 6.5∼7.0 MeV and 7∼20 MeV, respectively. The events with Dirks > 0.4 are rejected.
As shown in the figure, the fraction of the rejected events is larger for lower energy.
It is found that certain flasher events, which still remain after the above flasher cut, can berejected using information from the goodness and the Dirks. These flasher events make a tiny
peak in the dz distribution around dz ' −0.7 as shown in figure 6.13(a) (blank histogram). The
following cut can reject the peak:• goodness ≥ 0.6 and Dirks < 0.25
The hatched histograms in figure 6.13 are the d z distribution after applying the cut.

6.2.15

Bad energy cut

Event with the difference between number of hits within 50 nsec time window and effective hitsfor 70m case more 200 is removed due to bad energy reconstruction. However, it was never seenin the present scheme as following reduction tables.

6.3

Spallation cut

Some cosmic ray muons which go through the detector produce radioactive elements by breaking
up an oxygen nucleus.
µ + 16 O → µ + X + ......
101

(6.7)

number of events

number of events

(a)
10

4

Data
6.5 ∼ 7.0 MeV
10

10

10

5

(b)
Data
10

4

10

3

10

2

7 ∼ 20 MeV

3

2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(c)
10

4

MC
6.5 ∼ 7.0 MeV
10

10

1

Dirks

number of events

number of events

Dirks

10

5

(d)
MC
7 ∼ 20 MeV

10

4

10

3

10

2

3

2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Dirks

1

Dirks

number of events

number of events

Figure 6.12: Distributions of Dirks. (a)real data(6.5∼7.0 MeV), (b)real data(7∼20 MeV),(c)MC data(6.5∼7.0 MeV), (d)MC data(7∼20 MeV).

(a)

500
400
300
200
100
0

700

(b)

600
500
400
300
200
100

-1

-0.5

0

0.5

0

1

dz

-1

-0.5

0

0.5

1

dz

Figure 6.13: The dz distribution for runs (a) including and (b) not including the specified flasher
events (blank histograms). There is a tiny peak around d z ' −0.7 in figure (a). The hatchedhistograms are the resultant ones after the second flasher cut.

102

where X represents radioactive nuclei. The nuclei decay by γ and β emission with a lifetimein the range of 0.001 ∼ 14 sec. They are observed in SK and are called “Spallation events”. Theenergies of the spallation events are similar to those of recoil electrons from solar neutrinos, sothey are one of the major backgrounds in the solar neutrino analysis.
To identify spallation events, a likelihood method is used. The parameters for the likelihood
function are:• δL : Distance from the low energy event to the reconstructed track of the preceding muon
event.
• δT : Time difference between the low energy event and the reconstructed track of thepreceding muon event.
• Qres : Residual charge of the preceding muon event.
Qres = Qtotal − Qunit × Ii,µ(6.8)

where Qtotal is the total charge. Qunit is the total charge per cm and Ii,µ is reconstructed
track length of the muon event.
If the muon track reconstruction fails, then only δT and Q total are used. For spallation
events, δL and δT are shorter, and Qres is larger, compared to solar neutrino events.
For the spallation cut, one calculates the likelihood values for muons in the previous 100
seconds and select a muon which gives the maximum likelihood value (L max ) Events with
L > 0.98(for reconstructed muon events) and L > 0.92(for non-reconstructed muon events)
are rejected as the spallation events.
Figure 6.14 shows the Lmax distribution in data and in randomly sampled events.
10

4

CUT

5000

CUT

4000

3000

10

3

10

2

2000
10

1000

0

-4

-2

0

2

4

1

6

Spallation likelihood

-4

-2

0

2

4

6

Spallation likelihood

Figure 6.14: The distribution of spallation likelihood. The left figure shows the likelihood
distribution for muon events with a reconstructed track. The right figure is for the case wheremuon reconstruction failed. The open histogram shows a typical data sample and the hatchedhistogram shows the randomly sampled events.
The dead time of the spallation cut is investigated using a random sample of events. The deadtime is position dependent. It is estimated 21.1%, which was obtained from randomly sampled
events. Figure 6.15 shows the position dependence of dead time as a function of distance fromtop (left figure) and barrel (right figure). Blank marks are obtained dead time at each positionand lines are results of fitted polynomial functions. The position dependence is taken into
account in the solar neutrino MC simulation.

103

Figure 6.15: Position dependence of the dead time induced by the spallation cut. Left figure
shows z dependence and right figure shows r dependence of the dead time (vertical axis of eachfigure).

6.4

Second data reduction

In the second reduction, further cuts were applied in order to analyze the low energy region.
First of all, the vertex reconstruction is re-evaluated by goodness stability cut in order to collectclear events which occurs in the fiducial volume. Next step, the Čerenkov ring image is tested
by pattern likelihood cut comparing with the true ring image in order to reduce the remaining
spallation event and γ like event. True ring image is issued by single electron from solar neutrino
MC Lastly, the vertex position is re-estimated by an other vertex reconstruction fitter which iscalled “Clusfit”. Then, the event issued out of the fiducial volume is rejected.

6.4.1

Goodness stability cut

The goodness stability cut is named GRINGO (Grid Integrated New Goodness) cut from now
on. The principle of the evaluations are summarized as follows :• Evaluate vertex fit quality : compare vertex goodness of fit point to surroundings.
• Define hexagonal grid orthogonal to event direction.
• Require minimum fall-off of goodness with distance.
• From ratio of number of failed point over number of grid point.
Usually, if there are many noise hits in an event, the event is cut because of bad goodness
from vertex reconstruction. However, some events have good goodness by chance by dropping
local minimum chi square in the estimation. To estimate the validity of the goodness, thedifference between the goodness at the original reconstructed vertex and those at test vertices
around the original one are examined. For an event with many noise hits, the timing distributionof PMT hits is broader. As a result, the change in the goodness is small. Figure 6.16 shows
the definition of the GRINGO cut. The left figure shows the definition of the grid point usedin GRINGO cut. The original reconstructed vertex is situated at the center. The right figure
shows the threshold of goodness difference as a function of the distance from the original vertex.
The stability of the goodness of vertex reconstruction is checked as follows.
1. Make a two dimensional grid on the plane which contains the reconstructed vertex point
and normal to the reconstructed direction.
104

∆goodness

Y grid point(cm)

1500

0

-0.05

1000

500

-0.1

0

-0.15

−500

-0.2

−1000

-0.25

-0.3

−1500
−1500

−1000

−500

0

500

1000

-1500 -1000 -500

0

500

1000

1500

Rgrid(cm)1500

X grid point(cm)Figure 6.16: The original reconstructed vertex is situated at the center. The right figure shows
the threshold of goodness difference as a function of the distance from the original vertex.

2. The vertex is assumed to be at each grid point and the goodness defined by chapter 4 iscalculated at each grid point.
3. Calculate the difference between the goodness at the original vertex and at each grid point.
4. Count the number of grid points at which the deviation exceeds the threshold (N bad ).
5. Calculate the ratio of Nbad to the total number of grid points (R bad ). If (Rbad ) is larger
than 0.08 then the event is cut.
The cut criterion of the GRINGO
cut is determined so that the significance, (number of remainp
ing events of solar MC)/ (number of remaining events of DATA), becomes maximal.
Figure 6.17 shows Rbad distribution. The hatched area shows the R bad distribution after
GRINGO cut. Figure 6.18 shows vertex distribution before and after GRINGO cut. The hatchedarea shows the distribution after GRINGO cut. Figure 6.19 shows the energy distribution before
and after GRINGO cut. From this figure, the GRINGO cut is a very powerful tool for SLE
background rejection. This tool gives hope for 4.5 MeV project.

6.4.2

Pattern likelihood cut

When there are additional γ rays in an event, for example, a spallation-like event, then theČerenkov ring image is smeared and the direction reconstruction is not valid. To estimate thevalidity of the reconstructed Čerenkov ring, a likelihood function is made from a MC distributionof the angle between the reconstructed direction and the angle from reconstructed vertex to each
hit PMT. Figure 6.20 shows the definition of the hit pattern of the Čerenkov ring image. θP M T
is defined as an angle between the event direction and the hit PMT as seen in the figure.
The likelihood function is defined as following equation.
PN
log(Pi (cos θP M T,i , E, disf romwall ))L ≡ i=1(6.9)
N
where N is the number of hit PMTs within 50 nsec time window, P i is the probability of
the hit pattern made from a MC distribution of the angle between the reconstructed direction
and the angle from the reconstructed vertex to each hit PMT, cos θ P M T,i is the angle between
the reconstructed direction and the angle from reconstructed vertex to each hit PMT, E is theenergy of the event, and disf romwall is the distance between the wall and the reconstructedvertex point.
105

Number of eventsx 10 2
1200

1000

800

Cut
600

400

200

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R bad

Number of events

Figure 6.17: The calculated Rbad distribution. The hatched area shows after GRINGO cut at
the typical data sample.




 

45000

40000



35000

30000

35000

25000
30000

20000
25000

20000

15000

15000

10000
10000

5000
5000

0

0

250

500

750

1000

1250

1500

1750

R

2

0

2000
3
x 10

−1500

−1000

−500

0

500

1000

 

1500

Figure 6.18: The vertex distribution before and after the GRINGO cut. The left and rightfigures show the radius distribution and the tank height distribution respectively. The hatchedarea shows the distribution after GRINGO cut at the typical data sample.

106

Number of events

10

6

10

5

10

4

10

3

10

2

10

1
6

8

10

12

14

16

18

20

Energy (MeV)

Figure 6.19: The energy distribution before and after GRINGO cut. The hatched area shows
after GRINGO cut at the typical data sample.

direction
PMT

θPMT
Distance from wall
Ring image

Figure 6.20: The definition of the θP M T .

Figure 6.21: The distribution of the pattern likelihood function for the ring imageat the typical energy from 8.0∼10.0 MeV.

107

Figure 6.21 shows the distribution of the pattern likelihood function for the ring image at
the typical energy from 8.0∼10.0 MeV. The solid line is the extracted events as background
events from less than 0.8 of the cos θ sun distribution (See figure 9.1, 9.2). The plots are theextracted events as solar neutrino events distributing in the cos θ sun distribution more than 0.8.
cos θsun means the the reconstructed direction correlated with the solar direction. The remaining
background event is mainly the long lived spallation event with multi γ rays. Thus, the ring
image is smeared compared with the distribution of the solar neutrino like events.
The likelihood distribution for the solar neutrino like event and the background like event
extracted from the typical data sample is shown figure 6.22. The top figures show the distribution using the solar neutrino like events from more than 0.8 of cos θ sun distribution. The
bottom figures show the distribution using background events in less than 0.8 of the cos θ sun
distribution. From the left side figure, the energy of the events are 6.5∼8.0, 8.0∼10.0, 10.0∼20.0
MeV respectively. Searching the maximum significance between the top figure and bottom figure with the change of the cut point for the likelihood function distribution, the cut point of-1.85 is decided. In the figure, the cut point is also shown. This cut is named PATLIK cut(PATtern LIKelihood cut) from now on. The cut criterion of the PATLIK cut is determined sonumber of remaining events of solar neutrino like data
, becomes maximal.
that significance, √number of remaining events of background like data

Cut

Cut

Cut

Figure 6.22: The likelihood distribution for the solar neutrino like event and the backgroundlike event extracted from the typical data sample.
In the SK, this reduction is named “PATLIK cut (PATtern LIKelihood function cut)”. The
likelihood distributions before and after PATLIK cut from the typical data sample is figure 6.23.
The hatched area shows the distribution after the PATLIK cut.

6.4.3

Rejection of noise hit

In order to eliminate the noise contribution to the hit PMTs, the distance and time difference
from other hit PMTs in the event are used. The conditions for noise hit PMTs are given as
follows.
• The minimum distance to any other hit PMT is larger than 1250 cm.
• The minimum time difference to any other hit PMT is larger than 35 nsec.
108



25000

 








20000

15000

10000

5000

0

−2.4

−2.2

−2

−1.8

−1.6

−1.4

−1.2



Figure 6.23: The likelihood distributions from the typical data sample.

For further removal of noise hit PMTs, the selected hit PMTs are paired which each otheragain. If the PMT signals are caused by Čerenkov light emitted from a point, then the timedifference (δt) and the distance (δr) between a pair of hit PMTs satisfy the following relation :δr/c > δt(6.10)

Number of events

A hit PMT pair which satisfies the above relation is called a “Related pair or Cluster”. If
the number of related pairs of a hit PMT is larger than 10, then the hit PMT is selected andused by the vertex fitter. If the distance from the new vertex to the nearest wall is smaller than
200 cm, the event is rejected. This reduction is named “Clusfit cut(Cluster fit cut)” from now
on. Figure 6.25 shows the distributions of the vertex reconstructed before and after rejected
noise hits.
20000

Useful data
17500

15000

12500

true vertex point
10000

7500

direction
PMT

∆r

5000

2500

c∆ t

0

PMT

0

200

400

600

800

1000

1200

1400

Distance from wall (cm)

Related pair PMTs

Figure 6.24: The definition of rejecting
noise hits.

Figure 6.25: The distance distribution
from the wall before and after the Clusfit cut.

109

6.5

Gamma cut

One of the major backgrounds in the solar neutrino analysis is γ ray from the PMT glass and thesurrounding rock. It is called “External γ ray” To remove this background, the reconstructed
direction of each event is projected backward and the distance from the reconstructed vertex tothe detector wall def f . The “External γ ray” from the surrounding rock and ID wall materials
is named gamma ray from now on. Then, the reduction for γ ray is named gamma cut fromnow on.
A characteristic of the γ ray events is that they have small ’effective distance’ to the wall,
def f , which is defined in figure 6.26.

reconstructed
direction

reconstructedvertexdeff
wall of ID
Figure 6.26: The definition of the effective distance d ef f .
The cut
p criterion of the γ cut is determined so that significance, (number of remaining eventsof MC)/ (number of remaining events of DATA), becomes maximal. Therefore the thresholddistance is dependent on energy. It is 8 m when the energy is less than 6.5 MeV and the 4.5 m
when the energy is greater than 6.5 MeV.
Figure 6.27 shows the typical vertex before and after the γ cut for real data for the energy
range of 4.5∼20.0 MeV. As shown in the figure, the application of the γ-cut makes the vertex
distribution uniform.

6.6

Summary

Figure 6.29 and figure 6.28 show the final Z(cm) and R 2 (cm2 )vertex distribution by general
reduction for each energy region respectively. The energy region is presented in figures. From
top figure, the energy ranges are from 4.5 to 5.0 MeV, from 5.0 to 6.5 MeV, and 6.5 to 20.0
MeV respectively. Figure 6.30 and figure 6.30 shows the direction distribution after all general
reduction for each energy region.
Table 6.1 shows the number of remaining events at each reduction step for the real data.
Figure 6.32 shows energy spectrum of the real data after each reduction step. From the figure,the possible sources of the background are remaining spallation events, the radioactive elements
originated from Rn, and remaining γ-ray events.
The origin of the spallation event remnant is attributed to an inefficiency of the muon trackreconstruction. Especially, multiple muons could be mis-reconstructed.
110

Number of events

Number of events

2250

3000

2000

1750

2500

1500
2000
1250

1500

1000

750

1000

500
500
250

0

0

500

1000

1500

2000

2500
3
x 10

vertex rr (cm**2)

0
-2000

2

-1500

-1000

R

-500

0

500

1000

1500

2000

Z

Vertex z-axis (cm)

12000

10000

Number of Events

Number of Events

Number of Events

Figure 6.27: The typical vertex distribution before and after the gamma cut in energy region
from 4.5 to 5.0 MeV. The hatched region is after gamma cut.

5000

4000

2000

1750

1500

8000

1250
3000

6000

1000

2000

750

4000

500
1000

2000

250

0
−2000

−1500

−1000

−500

0

     

500

1000

1500

0
−2000

2000

−1500

−1000

−500

Z(cm)

    
0

500

1000

1500

0
−2000

2000

Z(cm)

−1500

−1000

−500

   0   500 

1000

1500

2000

Z(cm)

18000

Number of Events

Number of Events

Number of Events

Figure 6.28: The final Z vertex distribution by general reductions for each energy region. Theenergy regions are presented in figures.

7000

16000

6000

14000

3000

2500

5000

12000

2000

10000

4000
1500

8000

3000
6000

1000
2000

4000

500
1000

2000

0
−500

0

500

  !  "#%$ &
1000

1500

2000

2

2500

x 10
R (cm)

3

0
−500

0

500

' ( )* 1000
+ ( ', - .

1500

2000

2

2500

R (cm)
x 10

3

0
−500

0

500

/ 0 12 1000
3 4 0 45 6 7 1500

2000

2

2500

R (cm)x 10

3

Figure 6.29: The final R2 vertex distribution by general reductions for each energy region. Theenergy regions are presented in figures.

111

Events

Events

4500

2000

4000

1750

3500

1500

3000

1250

2500

1000

2000

750

1500
1000

500

500

250

0

−1

−0.5

0

0.5

0

1

−1

−0.5

dz

0

0.5

1

dz

5.0 − 6.5 MeV

Events

4.5 − 5.0 MeV
1200
1000
800
600
400
200
0

−1

−0.5

0

0.5

6.5 − 20.0 MeV

1dz

EventsEventsFigure 6.30: The final zenith direction distribution by general reductions for each energy region.
The energy regions are presented in figures.

2000

4500
4000

1750

3500

1500

3000

1250

2500

1000

2000

750

1500

500

1000

250

500
0

−1

−0.5

0

0.5

1

dx

−1

−0.5

0
5.0 − 6.5 MeV

0.5

1

dx

Events

4.5 − 5.0 MeV

0

1200
1000
800
600
400
200
0

−1

−0.5

0

0.5

6.5 − 20.0 MeV

1dx

Figure 6.31: The final azimuth direction distribution by general reductions for each energy
region. The energy regions are presented in figures.

112

Number of events/day/22.5kt/0.5MeV

These events remain as mis-fit events. These mis-fit events are accumulated in center of thetank because of characteristic of fitting tool, one can see that in figure 6.29. Mis-fitting events
increases in lower energy region because the number of hit PMTs becomes small in lower energy
region.
After 1st reduction
10

4

10

3

10

2

After spallation cut
After 2nd reduction
After gamma cut

10

1

SSM(BP2000) * 0.4(efficiencies are considered)
10

-1

5

7.5

10

12.5

15

Energy (MeV)

Figure 6.32: Energy spectrum after each reduction steps. See also table 6.1 for the definition of’first’, ’second’, and ’third’ reduction. Theoretical prediction (BP2000×0.4) is also shown (solidline).
There are two cases of radon background from the different parent nuclei. First case is
Although the spectrum endpoint of the 214 Bi, which is222
decay product of theRn, is 3.26 MeV, due to the finite energy resolution of the detector, theβ-decay events are observed from 4.5 to 6.5 MeV energy threshold. One can see the abnormal
peak in the bottom region of SK tank in figure 6.28 from 4.5 to 6.5 MeV. Another possible caseis due to 208 Tl from the radon in thorium series. The 208 Tl also decays via β-decay with 2.614
MeV gamma rays at total energy of 5.0 MeV. Therefore, in decaying, the event generates theČerenkov light of multi-ring with gamma ray. Figure 6.33 shows the expected energy spectrumof daughter nucleus from radon of Radium and Thorium series for each trigger threshold. The
MC passed only the first data reduction.
Another possible background is γ rays coming from the surrounding rock or material on ID
wall. In the figures 6.29, 6.30, and 6.31, there is abnormal excess around R 2 of 750 cm2 andaround the direction of ±0.5 or +1, respectively. These are remaining external γ rays from thewall in the low energy region.
In order to observe low energy solar neutrino flux from 4.5 to 5.0 MeV, these possible
remaining backgrounds need to be reduced. The still remaining backgrounds in low energy
region are radon and external γ rays from wall materials and surrounding rocks. Figure 6.34
shows the hit pattern distribution of cos θ P M T , which is described earlier in this chapter, foreach MC of electron, γ, 214 Bi and 208 Tl from radon in energy region from 4.5 to 5.0 MeV. For
the electron hit pattern, there is no remarkable difference. Therefore, it is difficult to identify
the background events by analysis tool. It is necessary to reduce the radon as dominant sourceof the background physically.
214 Bi from the radon in radium series.

113

Reduction step
Total
Unfitted event cut
Fiducial volume cut
Veto event cut
DT>50 msec cut
Pedestal event cut
Uncompleted event cut
OD triggered event cut
OD mismatch event cut
OD mismatch event cut
Noise (NS-ratio) cut
Clustered ATM cut
First Flasher cut
Goodness cut
Second flasher cut
Bad energy cut
Spallation cut
GRINGO cut
PATLIK cut
Clusfit cut
GAMMA cut
Reduction step
Total
Bad run cut
Trigger cut
Noise (NS-ratio) cut
Clustered ATM cut
First Flasher cut
Unfitted event cut
Goodness cut
Second flasher cut
Bad energy cut
Fiducial volume cut
GRINGO cut
Clusfit cut
PATLIK cut
Spallation cut
GAMMA cutData
4.5-20.0 MeV
564222879

57729840
44075188

6160188692556MC
4.5-20.0 MeV
24253500
22140060
8176699
8176699817465578334127830026
7829900
775315177531516009388
47886404689600
40418653162060
2757466

Data
5.0-20.0 MeV
176906705
176906705
34301372
34197870
26627697
26413349
26413177
25068589
25068525
25068525
25014073
25004524
2477311924398348
18100641
18100641
12868437
36147812724267
1856647295922Data
6.5-20.0 MeV
23649508
23649508
83738918373638290927928617232861701
2199495
2199452
2199452219120211026452103305
2076264
1956279
1956279397962263761169168151666113058

Table 6.1: The table of the reduction steps. ’MC data’ is the solar neutrino MC simulation in
the energy range of 6.5∼20.0 MeV in the 22.5 kt fiducial volume.

114

Number of events

Number of events  "! # $%!&' $% ()  

1800

1600

@ <ACB"D3;/#3E=;F;D @ 8;34 G/H9 634 6:9
5000*+,.-/10 2 34 556372 836:9 8;< =1400     
4000

1200

    

1000  

800* >?+.>/10 2 34 556372 836:9 8;< =    

3000* >>>/10 2 34 556372 836:9 8;< =    
2000

600

400

1000
200

0

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

0

7

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Energy(MeV)

Energy(MeV)

Probalility

Figure 6.33: The expected energy spectrum of daughter nucleus from radon of Radium andThorium series for each trigger threshold.

1

M NPOHQ

10−1

RTSUVUVS OHQWLXPOHQ
10−2

Y1N[Z\:]_^a`cbdOHQ

10

−3

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Cos θIJLK

Figure 6.34: The hit pattern distribution of cos θ P M T for each MC of electron, γ, 214 Bi and
208 Tl from radon in energy region from 4.5 to 5.0 MeV.

115

Chapter 7

The approaches to radon reduction

Events/day/kton

The radioactivity from radon (Rn) in pure water is a major background for observing solar
neutrinos at SK. After the data reduction, the Rn background is remaining in the data. Since
the Rn events behave as solar events, it is difficult to reduce the Rn events by analysis tool.
Figure 7.1 shows the cos θsun distribution for each energy thresholds in low energy region.
The excess to solar direction indicates observed solar events. The flat contents for the excess
to solar direction indicates Rn dominant background. As a energy threshold is lowered, theobtained peak to solar direction becomes smaller. Then, the Signal(excess)/Noise(flat) ratio
becomes wrong.
0.4

 







 



 

 



−0.8

−0.6

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

−1

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Cos Θ

1

Figure 7.1: The cos θsun distribution for each energy thresholds in low energy region.
Therefore, we have made an effort to reduce the Rn in pure water, physically, in order toobserve low energy solar neutrino flux.
In this chapter, the following Rn reduction approach is described.
• The radon source in the SK water purification system was investigated and improved in
Dec 2000.
• We have also studied the possibility of the Membrane Degasifier as the new radon reduction
system. It was installed in the water system in February 2001.
By water system improvements, the radon concentration in the SK supply water was decreased by a factor of about 5. Basing on this result, the SK low-energy event rate analysis
116concluded that the current main source of the radon background is the emanation from the
PMT glass, and convection is the main driving force for transporting the radon in the detector.
At the last of this chapter, the current status of the radon background reduction and the future
prospects are presented.

7.1

Solar neutrinos in Super-Kamiokande

An important task of the SK detector is to measure the energy spectrum of the recoil electrons
from 8 B and rare HEP solar neutrinos [5].
The energy spectrum of solar neutrino is distributed from 0 MeV up to 20 MeV. However
the current analysis energy threshold is 5.0 MeV in the total recoil electron energy [5]. It is
desirable to discuss the spectrums in the low-energy region in order to determine oscillation
mechanism of the solar neutrinos. One of the important requirements of the solar neutrino
observation in SK is to lower the energy threshold for the solar neutrino analysis as much as
possible. The observation of the solar neutrino spectrums in the low-energy region is precludedby the remaining large background events after the event selection.

7.2

Radon background in the SK tank water

The analysis threshold is determined by the level of the background events and the event trigger
threshold. The trigger threshold at 50% efficiency is 3.7 MeV and at 95% is 4.2 MeV. The
dominant background sources in the low-energy region (E ≤ 6.5 MeV) are 222 Rn in the purewater, which cause a similar event to the solar neutrino events due to the beta decays of theradon daughters and external radioactivity such as gamma-rays from the PMT glass. After all
reduction steps for the solar neutrino analysis, the S/N is approximately 1 above 5.0 MeV in thesolar direction. It is supposed from SK low-energy events that the radon concentration in the
SK tank is 2.0∼3.0 mBq/m3 . In order to study the complete energy spectrum, it is desirable tolower the analysis energy threshold from 5.0 MeV to 4.5 MeV. This subject also means that theradon in pure water must be reduced as far as possible. For example, the radon concentrationin the SK tank should be reduced down to less than 1.0 mBq/m 3 .
For the SK detector, the following steps were done in order to achieve the needed radon
reduction. Sufficient radon reduction for us means that we reduce the radon concentration in
the SK supply water down to 1.0 mBq/m 3 which is not observed as low-energy events in the SK
detector.
First of all, a super high sensitivity radon detector for water was developed to monitor the
low radon concentration in the pure and degasified water before and after the radon reduction.
The sensitivity of the developed radon detector is 0.7 (mBq/m 3 )/day [102]. Secondly, the radonsource was investigated in the SK water system by using the developed radon detector. Thirdly,
we have also studied the utilization of the Membrane Degasifier (MD) as a more efficient radon
reduction system. This new radon reduction system was also estimated by using the developedradon detector. After these steps, SK water system was improved. Finally, we concluded thatthe remaining background events in the low-energy region from 4.5 MeV to 6.5 MeV originatedfrom the radon emanated from the glass of the PMTs in the SK detector.

7.3

The upgrades of water system in March 2000.

The total 50,000 tons of purified water in the SK is circulated through a water purification
system with the flow rate of about 35 ton/hour in a closed system. The flow rate mode has
started since July 1998. The water is circulated by the return pump which returns water from
SK tank, and the supply pump which supplies water to the SK tank.

117

Figure 3.16 in chapter 3 shows a schematic view of the upgrading and improved SK water
purification system in the final state of the SK-I. The SK water purification system has been
improved and upgraded during the experiment basing on various studies.
In March 2000, some upgrading of the water purification system was done for following points
in the figure 3.16.
First, the UF system was reinforced from 17 modules to 23 modules. Secondly, the RO
system was also reinforced just before the VD system in addition to the existing RO system.
These reinforcements make an effect on the removal of of the further dusts. Thirdly, the radonfree-air dissolve tank is installed before the VD system in order to increase radon removableefficiency at the VD system. In the VD system, 3600 L plastic balls like gyros were used toincrease the surface area for vacuum degasification. The plastic balls were pointed out about
the radon emanation from them. We actually measured the radon emanation from 100L ballsof vinyl chloride and a stainless steel with an electro polished. The quality of the material waschanged from a vinyl chloride to a stainless steel with an electro polished in a point of view ofless radon emanation. We analyzed SK low-energy events from 4.5 MeV to 6.5 MeV before andafter these upgrades. However, the effect of these upgrades was not observed.
Table 7.1 shows a summary of uranium and thorium concentration in each water. The
concentration was measured with an ICP-MS device at the detection limit of 4.0 ppq. From thesummary, we conclude that the SK supply water is super-high quality.
Measuring point
Mine water
SK supply water
SK return water

Uranium concentration
3.0×105 ppq
0.2 ppq13.0 ppq

Thorium concentration
32.0 ppq
0.4 ppq59.0 ppq

Table 7.1: A summary of Uranium/Thorium concentration in SK water.

7.4

Radon source search in the SK water purification system

First of all for radon background reduction, the radon source in the SK water purification system
was investigated from Jun. 2000 to Sep. 2000 in order to reduce the radon background in the
SK supply water physically. Figure 7.2 shows the flow chart of the SK water system.
In the figure 7.2, ’Point x’ indicates a measuring point. We have measured the radon concentration between each components using the developed super high sensitivity radon detectors
for water with 700L of collection volume (700L radon detector [102]). The radon is detectedby electrostatic collection of the daughter nuclei of 222 Rn and the energy measurement of thealpha decay with a PIN photodiode. The sample water was taken from these measuring points
using the water pump by the flow rate of 1.0 L/min. The water was forwarded to the radon
detector and measured. The flow rate is set in the same way as the calibration. The detection
efficiency, used as a calibration factor, of the 700L radon detector was measured by a standard
3
radon water source and it is 14.6±1.5(stat.) +1.6
−1.5 (syst.) (counts/day)/(mBq/m ). This value islarger than the previous 70L radon detector [101] by a factor of about five [102]. The detection
limits which means three standard deviation in excess of the signal above the background of
the radon detector for water, is 0.7 (mBq/m 3 )/day in one-day measurement. The details about
the super high sensitivity radon detectors are reported in reference [102]. This value is smaller
than the 70L radon detector by a factor of about six. The radon detectors are connected to aworkstation via a network, and they are monitored in real-time.
Table 7.2 and figure 7.3 (filled circles) shows the radon concentration at each components.
The results show that the radon concentration just after the IE is about a factor of 14 higher
than that of the SK supply water. Even though the radon concentration just after the IE is118   !
d  b FHGIJCK LMONQPSRUTVNQWXJZYONQ[UJQKIGKRU\ RU]QNC[^RUTW`_@a_@[UJQPb   !gcE cb    
    

   ! +-,-,.
h TRUW[i  

h TR^W[^j   !   

& ! h TR^W[^kh TRUW[Ul#*0/-132 13432657"$#&%(') *ef   
&cE c

8:9<;>=@?ACBDEA
h TRUW[Umh TR^W[^nh TRUW[Uoh TRUW[pFigure 7.2: The flow chart of the SK water system and the search points of the radon source.

Measuring point
Point 1
Point 2
Point 3
Point 4
Point 5
Point 6
Point 7
Point 8Component
after return pump
just before IE
just after IE
just after VD
just after supply pump
just after CP
just after UF
just before the SK tankradon concentration(mBq/m 3 )13.6±1.9
16.0±1.3
88.0±0.6
4.2±0.8
3.7±0.7
6.8±1.8
5.8±0.5
6.5±0.2

Table 7.2: The radon concentration at each water system components. Error is statistical only.

119mBq/m3

counts/day

Radon source search in the water system

Point

Figure 7.3: The radon concentration at each water system components. Error is stat. only.
Points of the horizontal axis indicates component number. See table for component number.
so high, it was reduced by the VD system by a factor of about 20. This reduction efficiency(-95.0±1.0%) is almost the same level expected from the specification of the VD system.The CP
produced about 46.0% of the radon concentration of the SK supply water comparing just before
and just after CP system. From these results, we found two radon source points which are theIE system and CP system in the SK water purification system.

7.5

Membrane Degasifier as new radon reduction system

We studied the feasibility of the membrane degasifier (MD) from December 1999 to September
2000. The membrane degasifier is a hollow fiber with an outer diameter of 250 µm. The surfaceof this membrane has a structural feature wherein the inner surface has many small holes witha diameter of about 0.03 µm but no holes on the outer surface. The principle of the membranedegasifier is as follows. In the side separated with the membrane which let gas pass but water
not pass (water phase), the water which contains gas flows. In the other side (gas phase), thepressure is reduced by the vacuum pump. Hence, the gas dissolved in the water pass throughthe membrane and transfered from water phase to gas phase.
In the case of the MD system installation in the SK water purification system, there aresome requirements. The MD must be small, has a high radon reduction efficiency, and has asmall radon emanation from itself. It is most important that radon emanation from membrane
is small.
Before starting the test, we have compared the radon emanation from MD modules made byseveral companies and it was found that the one made by Dai-Nippon-Ink and Chemicals inc.
gave the lowest radon emanation. The product is SEPAREL EF-040P. The radon concentrationemanated from the membrane is 0.020±0.004(stat.) mBq/1module/day. Uranium and Thorium
in the Poly-4Methyl-Penten1 is less than 1 ppb, a value which was estimated by the KAWATESTU TECHNOSEARCH inc. at the level of the detection limit. From these results, we havestudied the radon reduction efficiency only using a Dai-Nippon-Ink module. Table 7.3 shows
the specification of a membrane degasifier module(SEPAREL EF-040-P) which was studied foris the radon reduction efficiency.
This module is able to reduce gas dissolved in water down to less than 25 ppb (25 µg/L)
120

Contents
Material of membrane
Material of housing
Bonding agent
EndcapSize
Capacity of treatment(Max)Active surface of membrane
WeightSpecification
Poly-4Methyl-Penten1
Vinyl chloride resin for super pure water
Urethane and Epoxy resin
Polysulfon
180mmφ×673mmL
2[ton/hour]∼40[m2 ]∼10.0[kg]Table 7.3: The specification of a membrane degasifier module(SEPAREL EF-040-P) whose theradon reduction efficiency was studied.
for a vacuum pressure of 20 torr and a flow rate of 2 ton/hr and water temperature of 25
degrees centigrade and air temperature of 20∼30 degrees centigrade. However, this ability isbasically for oxygen dissolved in the water. In this thesis, it is reported for the first time thatthe radon reduction efficiency of the MD module was estimated using the super high sensitivity
radon detector. Moreover, it is very important that this estimation was done under the special
condition where oxygen in the water is already degasified by -96%.
A small setup was constructed on the SK tank as shown in figure 7.4 in order to estimate
the radon reduction efficiency of the MD module.
From SK water system

Set up to measure Radon reduction efficiency
of a MD module

WATER PUMPWATER FLOW METER

700L
Rn detector

VALVE

bypass1

VACUUM
PRESSURE
RN LESS AIR INLETGAUGE

EXHAUST
VALVE

4An exhaust
covered withRn less air

1L/min2
VACUUM PUMPMD

AIRFLOW METER

WATER PUMPTo SK tank

DISSOLVEDOXYGENMETER

To SK tank3

Rn less air
as carrier gas

Figure 7.4: Setup to measure radon reduction efficiency of a MD module.
The setup consists of a MD module, two water pumps, a vacuum pump, a vacuum pressuregauge, a dissolving oxygen meter, and the 700L radon detector for water. In this setup, there
are two routes of the water flow. In one route, the water passes through the MD module, In theother route, the water bypasses the MD module. When the radon concentration is measured by
the former route, the run is called ’MD run’. The run is called ’SK water run’ when the radon
concentration is measured by the latter route. The water from the SK water purification system
flows to one of the two routes by the manual selection. The flow rate was tuned by the flow rate
meter from 0.2 tons/hour to 1.0 tons/hour. Then, a part of the water is forwarded to the radon
detector to measure the radon concentration with a flow rate of 1.0 L/min and the left water is121forwarded to the SK detector.
In this MD module, the water flows the outside of the hollow fiber membrane and the insideof it is reduced the pressure by the vacuum pump. The water flows from No1 nozzle to No2
nozzle through the MD module in figure 7.4. We need to inject pure air to the vacuum phase inorder to increase the radon reduction efficiency by the combining radon gas with air, because thewater is already degasified. We used the radon-free-air as the carrier gas. The radon-free-air is
produced by the SK air purification system, the details about it are reported in chapter 3. The
carrier gas was injected from the No3 nozzle. The gas separated from the water was exhausted
from the No4 nozzle by the vacuum pump. A noticeable point is that the exhaust of the vacuum
pump was covered with the radon-free-air to prevent the open air from flowing into the MDfrom this exhaust.
In the figure, the data values and the data points were fit by using the following exponentialfunction,N(T ) = N(0) × exp− ln 2.0 · T+ Constant
3.8

(7.1)

where N(T) is the count rate at time T, N(0) is the obtained count rate at the injection time,and T is the elapsed time since the measurement starting in day. Constant indicates the value
in the equilibration state of each of the measurements. We used this value in the case of thecalculation of the radon reduction efficiency.
The efficiency depends on vacuum in the module, the flow rate of water through the module,
and the amount of carrier gas flow into the vacuum phase of the module. We calculated theefficiency of the MD by comparing the radon concentration in ’SK water run’ and it in ’MD
run’. The formulation of the efficiency is given as :Efficiency =MD run[counts/day]-Background run[counts/day]
SK water run[counts/day]-Background run[counts/day](7.2)

where the background run is estimated by stopping the water flow. Figure 7.5 shows a typicalvariation for the each runs, which are SK water run,background run, and MD run. A parenthesis(x/y) in the figure indicates a function of water(x) and carrier gas rates(y). In the figure,
the MD effect was observed clearly for the SK supply water and the radon reduction succeededalmost down to the background level.
Table 7.4 shows a summary of the radon reduction efficiency of the MD module as a functionof water and carrier gas. The error is statistical only.
Vacuumpressure(kPa)
6.13
8.50
0.38
0.35
0.65
0.93

Water flow
(ton/hour)
0.2
0.2
0.4
1.0
1.0
1.0

Carrier gas(L/min)
0.4
1.0
0.0
0.0
1.0
2.0

radon
reduction (%)
-93±4
-90±3
-83±3
-64±12-83±5-90±7Dissolved
oxygen(µg/L)
525
867
5.6
3.7
235
367

Table 7.4: A summary of the radon reduction efficiency of the MD module as a function of waterand carrier gas. Error is statistical only.
It is possible that the MD module reduce radon by about 90% in the optimum condition
although the water was already degasified by the -96% efficiency. In a point of view of theinstallation just before SK tank, the remarkable result is that the MD module is able to reduceradon by a factor of more than about 5 for the water flow rate about 1 ton/hour. A noticeable122counts/day

200

180

160

140

120

100

80

60

40

20

0

120

140

160

180
Data

200

220

elapsed days

Figure 7.5: A typical variation for the each runs, which are SK water run,background run,and MD run. A parenthesis(x/y) in the figure indicates a function of water(x) and carrier gas
rates(y).
point is that in this module test, the radon concentration of the SK supply water was 6.5±0.2
mBq/m3 and the ability of the radon reduction was for the radon concentration in the water.
Considering a treatment of the amount of the SK supply water of 30 tons/hour, and an
ability of the radon-free-air production, we decided to install a system with 30 MD modules
between the water purification system and the SK tank as a final process of the SK supply
water.
In the case of the installation, the optimum conditions are 1 ton/hour/module and the carriergas of 1.0 L/min/module. A deserving special mention is that the exhaust of a vacuum pump
was decided to be covered with radon-free-air because the phenomenon of the open air back-flow
was observed in the experiment.

7.6

Improvements of water system in October 2000 and in February 2001

In the figure 3.16, the CP system and the MD system were the improvements based on thestudies of the radon source search and the feasibility of the MD system.
In October 2000, improvements for the IE and the CP systems were done based on the resultsof the radon source search. First of all, we should explain the difference between IE and CP.
Both have the functionality of removing ions. The main difference between them is that IE isre-generatable, but CP is not. The power to capture ions by IE is weaker than that of CP andthat is why IE is re-generatable. When we get a ”new” IE resin from the water system company,
it is in most cases a re-generated one at the company. The company collected used IE resin
from customers and re-generate them at once using a big plant. Hence, it is quite possible thateven new IE resin has serious amount of Radium for us even though the resin is good enoughfor other customers. On the other hand, CP resin is made from raw materials and used only
once. Therefore, it must have lower Radium concentration. The reason why we have been using
both IE and CP resins in the SK water system was to prolong the life of the rather expensive
CP resin. Since the quality of the SK water is quite high (resistivity is as high as 18.24 MΩ · m),
123

it is possible to remove ions only using CP resin for a reasonable time period without exchange.
In October 2000, we have performed the following changes.
• Empty the IE two vessels and fill CP resin in the vessels.
• Empty the CP vessels.

counts/day

We monitored the radon concentration changes before and after the water system improvement by using the three super high sensitivity radon detectors for water in real time. Figure 7.6
shows a typical variation before and after water system. These data points was monitored realtimely just before SK tank. The other monitoring points were just after IE system and justafter UF system. The radon concentration after the water system improvement is shown by
open circle in figure 7.3 and a numerical summary is shown in table 7.5.
200

180

160

140

120

100

80

60

40

20

0

350

360

370

380

390

Monitor just before SK tank400

elapsed days

Figure 7.6: A typical variation before and after water system improvement in October 2000.
These data was monitored real-timely just before SK tank.
Component
Just after IE
Just after UF
Just before the SK tankradon concentration
before October improvement
88.0±0.6
5.8±0.5
6.5±0.2

radon concentration
after October improvement
6.9±0.90.33±0.60
0.96±0.74

Table 7.5: A comparison of the radon concentration between before and after the October 2000
improvement. Error is statistical only.
The radon concentration just after the IE vessel (now filled with CP resin) is decreased bymore than a factor of 10. The detection of the limit in the radon detector for water is estimated
0.7 mBq/m3 /day in a one-day measurement. We did not observe clear excess of radon counts
over the background level in the radon detectors at ”Just after UF” and ”Just before the SKtank” after the improvement. If the radon concentration in water is close to or lower thanthe equilibrium concentration with the background in a radon detector, no excess or negative
excess should be observed. The radon concentration presented in table 7.5 is based on a simple
124

calculation done by subtracting the background counts. The background counts in the radon
detector for water is measured in the state where the water flow through the detector is stopped.
In February 2001, the MD system was installed just before the SK tank in figure 3.16. We
designed a system of 30 MD modules to process SK supply water of 30 tons/hour and to inlet
the radon-free-air of 1.0 L/min to each module from the module test. Moreover, we covered
the exhaust of a vacuum pump by the radon-free-air. The typical pressure in the MD system is
2.6 kPa. The typical concentration of the dissolved oxygen after the MD is 290 µg/L. In thissetup condition, the removal efficiency for radon is supposed about 90%. However, we could
not confirm the radon reduction efficiency for the low level radon achieved by the October 2000
improvement, because the module test was done in August 2000 and the radon concentration
after the October 2000 improvement was low level which was not sensitive with the radon
detector for water. We monitored the radon concentration of the SK supply water just before
SK tank with the radon detector for water before and after MD system installation. We could
not observe a change in the radon rates, therefore the radon concentration was kept less than
1.0 mBq/m3 after MD system installation. But probably the radon reduction efficiency does
not strongly depend on the initial radon concentration. By these improvements, we succeededin radon reduction in SK supply water down to less than 0.7 mBq/m 3 .

7.7

SK low-energy event rate

mBq/m

3

So far in this section, we have written about success in the radon reduction in the SK watersupply. Hence, the SK detector is separated from radon rich environment. However this radon
reduction does not make an effect on for reducing radon background for the solar neutrino
analysis. Figure 7.7 shows a history the expected radon concentration in the SK tank fromJanuary 2000 to July 2001. One data plot indicates day or night data in a day.
10

9

8

7

6

5

4

3

2

1

0

1

2

3

4

5

6

7

8

9

1
0

1
1

1
1
2
3
4
5
6
7
2elapsed day(day/night)

Figure 7.7: History of the expected radon concentration in SK tank calculated from the lowenergy event rate between Jan. 2000 and Jul. 2001. One plot indicates radon concentration in
day and night time.
The radon concentration is calculated from Super-Low-Energy event rates between 4.5 MeV
and 6.5 MeV using the radon detection efficiency in the SK detector. The used events are within
R<10 m, -16.1 m<Z<16.1 m (R:the radius axis of the SK tank, Z:the cylindrical axis of the SKtank). The event selection of R<10 m means that incoming gamma-ray events from the detector
125

wall are eliminated as far as possible. In order to estimate the radon concentration in the SK
water independent of the radon detector measurements, we used the SK detector to take datawith a known amount of radon in December 1997. The details were reported in reference [100].
From these test run, the radon detection efficiency is defined as a following equation :0.013[events/day/ton] = 1.0[mBq/m 3 ](7.3)

This correlation factor was acquired by the analysis of Super-Low-Energy (SLE) events in thisrun at the hardware trigger threshold of -260 mV [94]. . The SLE events have energies between
4.5 MeV and 6.5 MeV. A fast vertex reconstruction and a fiducial volume cut (32 ktons) wereapplied to all the events in real-time on a workstation. After these cuts, the same event selections
as the SK solar neutrino analysis are applied to SLE events for this analysis. Some additional
noise cuts usually are also applied using the quality of the reconstructed vertex, but for the test
run and the calculation of the radon concentration, the last cuts are not applied in order toleave the raw background events. The used events were within R<10 m, -16.1 m<Z<16.1 m.
Table 7.6 shows the radon detection efficiency in the SK detector for the another hardware
trigger thresholds.
Run
periodMay. 1997∼
Sep. 1999∼
Dec. 1999∼
Sep. 2000∼

hardwaretrigger threshold-260mV,-250mV-222mV-212mV-186mV

Radon detection
efficiency for 1.0mBq/m 3
0.013[events/day/ton]
0.015[events/day/ton]
0.016[events/day/ton]
0.022[events/day/ton]Table 7.6: Radon detection efficiency in SK detector for another hardware trigger thresholds.
In the figure 7.7, the expected radon concentration in the SK tank was quite high inJuly∼August and November 2000. As described in last section, the radon concentration in
the SK supply water is about 0.7 mBq/m 3 after October 2000 and February 20001 by the water
system modification and MD system installation. However the radon concentration in the SK
tank did not changed so much at 2∼3 mBq/m 3 , except for the period of July∼August andNovember 2000. If the supplied water is uniformly diffused in the inner detector and the flowrate is 30 ton/hour, then the radon concentration at equilibrium is :0.7[mBq/m3 ] · 720[m3 /day]= 0.09[mBq/m3 ]0.182[1/day] · 32000[m3 ](7.4)

The expected radon concentration in figure 7.7 is much higher than the contribution fromthe SK supply water. The large variations in the radon concentration of the SK tank in year
2000 is correlated with the changes of the SK supply water configuration. Table 7.7 summarizes
the SK supply water configuration and the temperature of the SK supply water. figure 7.8 also
shows a diagram of the SK supply water configuration.
The rise in the expected radon concentration in the SK tank in July∼August and November
2000 seems to be due to strong convection in the SK tank. Figure 7.9 shows the Z dependenceof the water temperatures in the SK tank measured on August 22, 2000 and January 9,2001.
The temperature measured on August 22, 2000 is uniform within 0.01 degree centigrade in the
inner detector. On the other hand, the temperature profile on January 9 2001 shows that thewater convection is caused only below Z=-10 m.
In this time, the radon concentration was kept at a low level. Figure 7.7 shows vertex position
distribution of the low-energy data sample from 4.5 MeV to 6.5 MeV.
The event selection is the same as the stream of the radon detection efficiency. When thewater temperature is not uniform, the distributions show that the radon background event rate
126

Date
Before Mar.2000
Mar.-Jul.2000
Jul.-Aug.2000
Aug.-Oct.2000
Oct.-Dec.2000
After Dec.2000

Supply tobottomcenterbottombottomcenterbottomReturn fromtop
bottomtop
top
top(1/2)bottom(1/2)
top

Supply water temperature∼12.3 degree centigrade
not measured∼15.2 degree centigrade∼14.3 degree centigrade∼14.3 degree centigrade∼14.3 degree centigrade

Table 7.7: SK supply water configuration and temperature of SK supply water.

SK WATER SUPPLY CONFIGURATIONAND CONVECTION MODEL IN SK TANK

+18.1
+10
OD

OD

ID

ID

+5
Z=0 [m]
-5
Rn

Rn

-10
-18.1

Figure 7.8: SK water supply configuration and convection model in SK tank. The left figure
shows the small convection model when the SK water is supplied to bottom. The right figure
shows the big convection model when the SK water is supplied to top.

127

Temperature(degree centigrade)

15

14.9

Aug.2000

14.8

Jan.2001

14.7

14.6

14.5

14.4

14.3

14.2

14.1

14

−20

−15

−10

−5

0

5

10

15

20

Z(m)

event/sec

Figure 7.9: Z dependence of the SK water temperature measured on August 22 2000 and January
9 2001.

x 10-2

Aug.2000
Sep.2000
Nov.2000
Jan.2001
Mar.2001

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

-20

-15

-10

-5

0

bottom-center-top

5

10

15

20

Z(m)

Figure 7.10: Z Vertex distribution of the low-energy events in Aug. 2000, Sep. 2000, Nov. 2000,
Jan. 2001 and Mar. 2001.

128

is higher just in the bottom region of the SK tank and the radon concentration in figure 7.7 islow. On the other hand, when the water temperature is uniform, the distributions show that theradon background event rate is higher in the region where the water temperature is uniform andthe radon concentration is high. Further, the integration of the distributions in the period when
the water temperature is uniform is larger than another period when the water temperature
is not uniform. Hence, we conclude that the emanation of radon from detector materials isthe dominant source of radon, and the radon is transported by the convection in the SK tank.
Figure 7.8 shows the our assumed convection model. The excess of vertex position distribution
in the bottom region is caused by the model of the left plot in figure 7.8. The expansion ofvertex position distribution in the convective period is caused by the model of the right plot in
figure 7.8.
The radon emanation from various materials, namely PMTs, black plastic sheets and tyvek
sheets, used in the SK tank in large quantities was measured. The measured PMTs are 20 inch
PMTs used in the SK inner detector. The black plastic sheets and tyvek sheets are used in the
inner and outer detector respectively. The measurement was performed by super-high sensitivity
radon detector for air in which various materials were placed. The radon detector is reported
about the details in reference [102]. Assuming that the radon emanated from each material isuniformly distributed over the whole SK detector (50 ktons), the equilibrium radon decay rate isgiven in the following equation. The ’Radon concentration in SK tank’ indicates the results fromthe equation. Concerning the emanation from black sheets, the radon emanation is measured
about the amount used around one PMT.
Radon emanation[mBq/m2 , PMT/day] · 15000, 11146[m2 , PMTs]= [mBq/m3 ]0.182[1/day] · 50000[m3 ](7.5)

The results is consistent with the expected radon concentration in the SK tank during large
Material
Black sheet
Tyvek sheet
PMT

Radon emanation
0.08 mBq/PMT/day
1.5 mBq/m2 /day
∼4.0 mBq/PMT/day

Radon concentration in SK tank0.10 mBq/m 3
0.44 mBq/m3∼ 5.0 mBq/m3

Table 7.8: Radon emanation from various materials.
convection periods (e.g. August and November 2000) within a factor of two.
As a next step, we confirmed whether the radon expected from SK low-energy event ratein the SK tank exists or not. We actually measured the radon concentration in the SK tankwith the super-high sensitivity radon detector for water (700L radon detector) in May. 2001
when the radon concentration was low and it is assumed that the no large convection happened.
Figure 7.11 shows a setup to measure Z dependence of the radon concentration in the SK tank.
The sample water is taken from each Z position, which are Z=+6.5 m (Center) and Z=15.5 m (Bottom), via a rigid nylon tube with a water pump using the bypass route in the
figure 7.11. Then the radon concentration of the sample water was obtained with the radon
detector. The background level in the system was measured with the measurement of theradon less water made with ’Rn less making system’ (See figure 7.11), which make use of themembrane degasifier module explained in the last section. The result in the measurement is theactual background level in this system. The detection limit of the radon detector is 0.7 mBq/m 3 .
Table 7.9 summarizes Z dependence of the radon concentration in the SK tank. Figure 7.12 also
shows the same results.
We calculated the expected radon concentration in the bottom region from Z=-500 m to Z=1610 m and the center region from Z=-500 m to Z=+500 m at R=0 using the SK low-energy
event rate and the radon detection efficiency in May. 2001. The expected radon concentration is
4.1 mBq/m3 and 0.0mBq/m3 in the bottom and center region respectively. From these results,
129

SETUP TO MEASURE Z DEPENDENCE OF
RADON CONCENTRATION IN SK TANK
700L RADON DETECTOR FOR WATERVALVE

BYPASSMD

1L/min
WATER
PUMP

R=0
Z=0

Z

SK TANK

VACUUM
PUMP

Rn less water making system

Figure 7.11: Setup to measure Z dependence of radon concentration in SK tank.

Position(R/Z)
Rn less water(Actual B.G)
Center(0.0/+6.5)
Bottom(0.0/-15.5)

Radon concentration
2.0±0.3mBq/m 3
1.6±0.2mBq/m3
3.2±0.2 mBq/m3

B.G subtraction<0.7 mBq/m3
1.6±0.5 mBq/m3

3

Radon concentration(mBq/m )Table 7.9: Z dependence of the radon concentration in SK tank.

6

5

Absolute value

4

error=statistical error

3

2

1

0

Center(Rnless)Center(0/+6.5)

Bottom(0/-15.5)

Position

Figure 7.12: Z dependence of Radon concentration in SK tank.

130we conclude that the radon concentration in the SK tank is not consistent with the expectedvalue within a factor of 2.6, but we can confirm the radon existence in the bottom region of the
SK tank in the small convection period. Moreover, when the large convection does not happen,
the radon does not exist in the center region.
From the conclusions of the SK event rate analysis, we installed a new chiller system into the
SK water purification system in March, 2000 in order to suppress the convection in the SK tankby lowering the SK supply water temperature to make the temperature gradient in the SK tanklarger. Typical water temperatures before the 1st heat exchanger and after the 2nd heat exchanger are 14.5 degrees centigrade and 13.5 degrees centigrade, respectively in figure 3.16. The
water temperature changed from 14.6 degree centigrades to 12.7 degree centigrades. However,
we could not observe the effect of the installation in figure 7.7 clearly.

7.8

Summary

The radon concentration at various locations in the SK water purification system was measured.
The radon source in the water system was investigated and improved in Dec 2000. The radon
concentration in the SK supply water was decreased by a factor of about 5. We have also studied
the feasibility of the Membrane Degasifier as the new radon reduction system in the water system.
We found a optimum configuration of vacuum, water flow rate and radon-free-air flow rate. A
system consisting of 30 Membrane Degasifier modules was installed in the SK water system in
February 2001. By these improvements, the radon concentration in the SK supply water becameless than 0.7 mBq/m3 and the SK tank was separated from the external radon rich environment
from a point of view of the radon background. After the water system improvements, the SK
low-energy event rate was studied on the details. The SK event rate is much higher than thelevel expected from the supply water. It was concluded that the current main source of theradon background is the emanation from the PMT glass, and convection is the main driving
force for transporting the radon in the detector. Even if radon moves from the surface of PMT
to the inner of fiducial volume by Brownian motion, radon is able to move by about 10 cm [105].
The schematic view of estimated background contamination is like figure 7.13.

44% External Gamma Ray or
Rn from U/Th
44% Rn from Top or Bottom PMT
12% Rn from Wall PMT by Convection
56% Rn for total B.G

Bottom
1.6 mBq/m^3

Center
<0.6mBq/m^3

Top

Figure 7.13: The schematic view the ratio of background contamination in SK detector.

131

7.9

Future prospects

Since the radon in the supplied water was reduced to a level acceptable for the solar neutrino
analysis, we need to reduce the radon emanating from detector materials and to suppress theconvection in the SK tank. We plan to do the following things for this purpose.
1. We changed the shape of the water outlet pipes in order to reduce the height of theconvective zone as far as possible. We asked Mitsui-zosen Co. (SK tank company) tomake a simulation program for the SK water flow. We found the optimized shape andlength of the outlet pipes using the simulation. The improved pipes were replaced during
the PMT replacement between July. 2001 and October. 2001 after SK-I. Figure 7.14
shows the improvement of the shape of the water outlet pipe. A new outlet pipe, which
is made by transparent acrylic resin, was attached to the top of the old PVC outlet pipe.
The new outlet pipe has many holes on the side of the pipe in order to let the water out
in the horizontal direction.
2. We will measure radium concentration in SK tank water. As seen in the data of January. 2001 in figure 7.7, we still have background in the non-convective zone in the tank(continuum background from top to center). Is it due to radon produced from radiumin water? We have installed RO system in March 2000 in order to increase the efficiencyof removing radium. But, apparently the continuum background did not disappear. We
need to measure radium in the SK water and understand the source of the continuum
background.
         ! " ;=<?>;=<?>9>' $& 

#%$ & ' $( 

35  6"7  98/7:)+*,- '. ! / 0)2143

]^

_Y^

T M9UVIJHJIJM9WXM9O
LYFZHJDC[P\9IJ\9D
T IJ\9IJW9`@ACB9DCEGFCHJIJAK9IJDCLNM9OP@QSR9M9HJHJM9E

Figure 7.14: The improvement of SK water supply pipe to control water convection in SK tank.

132

Chapter 8

Tight data reduction for 4.5 MeV
In chapter 7, the Rn reduction approach to observe low energy solar neutrino was presented from
hardware aspect In this chapter, the probability to lower energy threshold by the improvementsof analysis tools is described from soft-ware aspect.
To lower energy threshold from 5.0 to 4.5 MeV, we need to install new reduction tools adding
to general reductions, and need to improve Signal-Noise ratio. So, we applied the “Tight data
reduction” to the data sample after “General data reduction which has already been describedin chapter 6. First, the applied tight data reduction is explained. Then, the quality of the madedata sample after tight data reduction is described in this chapter.

8.1

Tight Data Reduction

The tight data reduction is applied to the data sample after general data reduction in two stages.
The data reduction in the first stage is named “Tight cut” from now on in this thesis. Thiscut is based on the “General data reduction” which is mentioned in the chapter 6. The data
reduction in the second stage is called “New fitting cut” which is a developed new fitter in order
to increase the efficiency of the vertex re-construction performance. Because the number of hit
PMTs becomes small in low energy region, current fitting tool has no enough performance inthe energy region of 4.5∼5.0 MeV. All reduction methods are optimized in order to analyze 4.5
MeV energy bin. Then, the remaining backgrounds are reduced as much as possible keeping the
maximum signal significance for the background.
A special mentioned thing is that the new reduction for 4.5 MeV energy bin analysis has beendeveloped by blind analysis in this time in order to remove the bias for the solar neutrino signal
extraction. In the optimization of new reduction tool, we did not confirm the cos θsun distribution.
After the all tight data reduction, we opened the data and saw the cos θsun distribution for the
first time.

8.1.1

Tight cutFirst, tight cut is applied the data sample after general data reduction. The remaining background events are removed in this stage basically. The applied reduction is based on the generaldata reduction optimized to 4.5 MeV analysis. First of this stage, the basic data set is madein order to collect useful 4.5∼5.0 MeV data, then applied the various reductions for remaining
background.
Trigger efficiency cut
A trigger efficiency cut makes the basic data set for 4.5∼5.0 MeV energy region. The SLE
analysis was started from May 5th in 1997. The analysis threshold is set 5.0 MeV for all SLE
analysis. The trigger efficiency for 5.0 MeV data in the SLE analysis is more than 95%. However,133the trigger efficiency for the 4.5 MeV data has no enough efficiency in the beginning of the SLE
analysis. The trigger thresholds of SLE analysis were changed seven times during SK-I datataking. The changing periods and the thresholds are already explained in chapter 3. Therefore,
the trigger threshold of 260 mV and 250 mV has no enough efficiency for 4.5 MeV data becauseof the high threshold. Table 8.1 explains the summary of the trigger efficiency from 4.5 to 5.0
MeV and the energy of the trigger efficiency 50% and 100% for each trigger threshold. The
trigger thresholds are calculated using solar neutrino MC. Figure 8.1 shows the run progress ofthe trigger threshold for 50% and 95% of trigger efficiency estimated by the solar neutrino MC.
The empty circle and filled circle shows the progress of the trigger threshold for SLE trigger
efficiency 50% and LE trigger efficiency 50% respectively in the right figure. Otherwise, the left
figure shows the run progress of the trigger efficiency 95%.
222 mV 186 mV

186 mV
250 mV
222 mV
MeV

MeV

250 mV
8

8

7.5

7.5

212 mV

260 mV

6.5

6.5

6

6

5.5

5.5

5

5

4.5

4.5

4

4

3.5

3.5

3

212 mV

260 mV

7

7

2000

3000

4000

5000

6000

7000

8000

9000

3

10000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Run number

Run number

Figure 8.1: The run progress of the trigger threshold for 50% and 95% of trigger efficiency.

SLE
trigger threshold
260 mV
250 mV
222 mV
212 mV
186 mV

Average of trigger efficiency
from 4.5 to 5.0 MeV
60%
70%
95%
97%
100%

Energy of trigger efficiency( 50%/100%)
4.7 MeV/5.5 MeV
4.5 MeV/5.3 MeV
4.2 MeV/4.8 MeV
3.9 MeV/4.6 MeV
3.5 MeV/4.3 MeV

Table 8.1: The summary of the trigger efficiency from 4.5 to 5.0 MeV and the energy at thetrigger efficiency of 50% and 100% for each trigger threshold.
Figure 8.2 shows the run progress of the trigger efficiency estimated by the solar neutrino
MC. The empty circle and filled circle shows the progress of the SLE trigger efficiency and LE
trigger efficiency from 4.5 to 5.0 MeV respectively. The progress sometimes fluctuates becauseof the fluctuation of the water transparency.
From above results, the useful 4.5 MeV data which has enough trigger efficiency more than
95% started from the SLE trigger threshold of 222 mV. The remaining live-time after this trigger
efficiency cut is 566 days. This data set is the most basic data set including useful data from
4.5 to 5.0 MeV.

134

222 mV
186 mV
Efficiency(%)

250 mV100

260 mV80

212 mV
60

40

20

0

2000

3000

4000

5000

6000

7000

8000

9000

10000

Run number

Figure 8.2: The run progress of the trigger efficiency estimated by the solar neutrino MC.

Radon high rate run cut
After the trigger efficiency cut, the radon high rate run cut is applied to 566 days data set
by a run unit. In chapter 7, the high event rate in low energy region was occurred by thelarge convection in the SK tank when the circulating water was supplied from the top of thetank. The data in the period is bad quality because there are many radon events in the fiducial
volume coming from the wall PMT. Figure 8.3 shows the progress of the background event rate(event/day) from 4.5 to 6.5 MeV in fiducial volume of 22.5 ktons after trigger efficiency cut.
The background event rate means events per day in less than 0.8 of cos θ sun distribution. The
switching points of the trigger thresholds are also drawn by the solid lines. There are somejumpings of the event rate. The jumpings of the event rate from 4.5 to 6.0 MeV are due toradon background transferring from the wall PMTs by the large convection in the SK tank.
Figure 8.4 shows the event rates for each energy region, which are from 4.5 to 5.0, from 5.0 to
5.5, from 5.5 to 6.5 and from 6.5 to 20.0 MeV from top figure. From this figure, the fluctuationof the event rate in low energy region from 4.5 to 5.0 MeV is mainly caused by the fluctuationin the energy region from 4.5 to 5.0 MeV which includes the dominant background source ofradon.
Because the most of the events in the fluctuating periods were the radon events and it isdifficult to extract the solar neutrino events in the data, the radon high rate data is removed by
run unit. The rejected runs are selected by judging whether the event rate is over a event rate
threshold. The event rate threshold is defined by searching the maximum significance which is
Signif icance =Total solar neutrino events w/o high event rate run.
Total background events w/o high event rate run(8.1)

The background events are the events which are distributed in less than 0.8 of cos θ sun
distribution. Assuming the solar neutrino event rate is constant in the all period of the dataset, solar neutrino events are in proportion to the live time of a run.
Solar neutrino events run ∝ Live timerun
135

(8.2)

event/day

1800

1600

222mV

1400

186mV186mV
212mV

1200

212mV

1000

800

600

400

200

0

8000

8500

9000

9500

10000

4.5-6.5MeV’ Run’

event/dayevent/dayevent/dayevent/dayevent/dayFigure 8.3: The progress of the background event rate (events/day) from 4.5 to 6.5 MeV.

10

3

10

2

8000

8500

9000

9500

10000

4.5-5MeV’ Run’

10

2

8000

8500

9000

9500

10000

5-5.5MeV’ Run’
10

2

8000

8500

9000

9500

10000

5.5-6MeV’ Run’
10

2

8000

8500

9000

9500

10000

6-6.5MeV’ Run’
10

2

8000

8500

9000

9500

10000

6.5-20MeV’ Run’

Figure 8.4: The event rates for each energy region.

136

Signif icance =Total Live time w/o high event rate run.
Background events w/o high event rate run(8.3)

The event rate threshold is searched by maximizing the calculated significance without thehigh event rate run which is over the event rate threshold.
Pnrun
Ti
Signif icance = Pni=1
run
N
i
i=1

(8.4)

events/day

where n is the number of runs whose event rate are less than the event rate threshold, i is therun number, T is the live time of a run, N i is the number of background events of the run whose
event rate is less than a event rate threshold. The maximum significance search was applied forthe energy region from 4.5 to 5.0 MeV. Figure 8.5 shows the progress of the background event
rate (events/day) from 4.5 to 5.0 MeV. The decided event rate threshold of 597.0 events per day
was shown by a solid line. After this radon high rate run cut, the remaining live-time is 511.5
days. In this calculation, for the all events including solar neutrino events without the bias ofcos θsun distribution, the event rate threshold is searched by the same method. The result of
the event rate threshold for all events is 795.2 events per day. The remaining live-time is 511.7
days. The both results are consistent. So, in this reduction, there is no systematic bias. Thisdata set after radon high rate run cut is the final data set for 4.5 MeV data analysis.

1800

1600

1400

1200

1000

800

600

400

200

0

8000

8500

9000

9500

10000

4.5−5MeV ’elapsed Run from Run#7859’

Figure 8.5: The progress of the background event rate (events/day) from 4.5 to 5.0 MeV andthe decided event rate threshold of 597.0 events/day.

Strong gamma cut
After the radon high rate run cut, the strong gamma cut is applied to the final data set. From
this reduction step, the various cuts are applied by the event by event. The definition of the
gamma cut is explained in chapter 6. In this section, the optimization of the strong gamma
cut to the 4.5 MeV data analysis is explained. The default gamma cut is optimized to the SLE
region from 5.0 to 6.5 MeV and to the LE region from 6.5 to 20.0 MeV. The distance of the
gamma cut from the wall for the LE and the SLE region are 4.5 m and 8.0 m respectively.
137

However, the external γ rays from the wall materials are remaining in the energy region from
4.5 to 5.0 MeV. So, the distance of the gamma cut is optimized to the energy region from 4.5
to 5.0 MeV by the maximum significance search. The significance is defined by the following
formulation.
Remaining solar neutrino events after gamma cut
Signif icance = √Remaining background events after gamma cut(8.5)

eventsSolar MC is used as the solar neutrino events. The events distributed in less than 0.8 ofcos θsun distribution is used as the background events. The distance which make the significancemaximal is the best cut point. The distance optimized to 4.5 MeV data is 9.7 m.
Figure 8.6 shows the significance result for the distance of the gamma cut. The significancefor the distance from 0.0 to 8.0 m is 0 because the gamma cut is already applied by the default
value. At the distance of 9.7 m, the significance becomes maximum remarkably. Figure 8.7
shows the vertex R2 distribution in the energy region from 4.5 to 5.0 MeV at each distance ofthe gamma cut. The distances are 8.0 m, 9.0 m and 10.0 m from the top figure respectively.
There is abnormal peak at the R2 from 500×103 to 1000×103 for the distance of 8.0 m. However,after 10 m gamma cut, the abnormal peak is removed completely by the strong gamma cut. The
strong gamma cut is applied for all energy region by this gamma cut distance.
4000
2000
0

0

2000 
x 10

4.5−5MeV,800m

2.32

2.3

eventsSignificance2.34

 

2.28

2.26

4000
3000
2000
1000
0

2.24

0


2000
x 10

4.5−5MeV,900m

2.2

4000
3000

events

2.22

2.18

2.16
0

200

400

600

800

1000

1200

1400

4.5−5MeV’ Radius(cm) ’

2000
1000
0

Figure 8.6: The significance results for the
gamma cut distance.

0

2000
x 10



4.5−5MeV,1000m

Figure 8.7: The vertex R2 distribution in the energy region from 4.5
to 5.0 MeV for each gamma cut distance.

Strong goodness stability cut
The definition of the goodness stability cut (GRINGO cut) is also already explained in chapter 6.
So, in this section, the optimization to the energy region from 4.5 to 5.0 MeV data is explained.
The criterion of the GRINGO cut is optimized to the energy above 5.0 MeV. The default value138

of the criterion is 0.08 for ratio of number of failed point over number of grid point. In the lower
energy region from 4.5 to 5.0 MeV, because the number of hit PMTs is smaller than it in theenergy region above 5.0 MeV, the number of mis-fit event becomes large. So, the cut criterion
need to be re-optimized to the energy region from 4.5 to 5.0 MeV.
The optimization was done by searching the maximum significance after the GRINGO cut.
The significance is defined by the following formulation which is same as the strong gamma cut.
Remaining solar neutrino events after GRINGO cut
Signif icance = √Remaining background events after GRINGO cut(8.6)

Solar neutrino events are the events of the solar neutrino MC after the GRINGO cut. The
background events are the events distributed in less than 0.8 of cos θ sun distribution after the
GRINGO cut. Figure 8.8 shows the significance plots with the GRINGO cut value which isratio of number of failed point over number of grid point. The horizontal axis is the GRINGO
cut value. The significance becomes maximum at the GRINGO cut value of 0.031.
Significance

2.5

2.45

2.4

2.35

2.3

 

2.25

2.2

2.15

2.1

2.05

2

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

4.5−5MeV’ GRINGO Ratio’Figure 8.8: The significance plots for the GRINGO cut value.
Figure 8.9 shows the vertex distribution before and after the strong GRINGO cut of 0.031.
The left figure is the R2 vertex distribution and the right figure is the Z vertex distribution. The
histogram is the vertex distribution before the strong GRINGO cut and the hatched region isthe vertex distribution after the strong GRINGO cut. From the figures, the mis-fit events are
removed for all vertex area uniformly.
Tight Fiducial Volume cut
The fiducial volume is determined 22.5 ktons at 2 m from the wall in the general data reduction.
However, the background events from the wall, for example, a external γ ray from detectormaterials and radon , are remaining near the edge of the fiducial volume and the bottom regionof the tank which is caused by the small convection by the water supply from the bottom. It
is difficult to remove remaining events by the event by event. So, the best fiducial volume isre-estimated for the energy region from 4.5 to 5.0 MeV. The best fiducial volume is determinedby the best radius and best height of the tank. The best parameter of the fiducial volume
is searched by using the significance maximum after the fiducial volume cut. The best cut
139event

event

6000

7000

6000

5000

5000

4000
4000

3000
3000

2000

2000

1000

0

1000

0

250

500

750

1000

1250

1500

1750

2000
3
x 10

0

−1500

−1000

−500

0

500

1000

1500

Figure 8.9: The vertex distribution before and after the strong GRINGO cut of 0.031.

parameter for the height and the radius of the tank is searched independently. Specially, forthe height parameter, the height is separated with the bottom region and the top region of thetank. The significance is ratio between the solar neutrino events and the sqrt of the background
events which is same definition as the gamma cut and the GRINGO cut.
The summary of the best parameters of the fiducial volume are shown in table 8.2. The values
are optimized to the energy region from 4.5 to 5.0 MeV. The default value is also explained in
the parenthesis of the table.
Parameter
RadiusHeight from center to bottom

Height from center to top

Region-1610<Z<1610-1619<Z<-1000-1000<Z<-500-500<Z<0
0<Z<500
500<Z<1000
1000<Z<1610
4.5<E<5.0
5.0<E<5.5
5.5<E<6.0
6.0<E<6.5
4.5<E<5.0
5.0<E<5.5
5.5<E<6.0
6.0<E<6.5

Values(cm)1430 (1490)
1490 (1490)
1410 (1490)
1380 (1490)
1360 (1490)
1430 (1490)
1480 (1490)
1100 (1610)
1160 (1610)
1590 (1610)
1590 (1610)
1580 (1610)
1590 (1610)
1590 (1610)
1590 (1610)

Table 8.2: The summary of the best parameters of the fiducial volume cut.
From the summary, the estimated best radius is the 1430 cm for all volume in the energy
from 4.5 to 5.0 MeV. As a reference, the best radiuses for each height of the SK tank are also
shown in the table. Except for the center, the radius cut is not required the tight value. The
center region is required the tight value because of the remaining external γ rays from the wall,
top and bottom materials. The left side of figure 8.10 shows the vertex distribution of R 2 andthe best radius is also drawn by a solid line. The events outer of the best radius are removed.
The best heights for the energy region from 4.5 to 5.0 MeV are -1100 cm from the centerin the bottom region and +1590 cm from the center in the top region. The right side of the140Events

Eventsfigure 8.10 shows the vertex distribution for the tank height and the best height is also drawn
by a solid line. In above 5.5 MeV, the best height is no asymmetry for the top and bottom
region. However, in lower energy region, the best height produces the asymmetry because of theaccumulation of the radon in bottom region. So, if the best height is optimized to the energy
region from 4.5 to 5.0 MeV, the asymmetry cut is needed. In this thesis, we want to analysis day
and night spectrum as possible. Therefore, the fiducial volume is not optimized to the height of
the tank.
18000

12000



16000

   

10000
14000

12000

8000

10000
6000
8000

6000

4000

4000
2000
2000

0
−500

0

500

1000

1500

2000

2

2500

R (cm)
x 10

0
−2000

3

−1500

−1000

−500

0

500

1000

1500

2000

Z(cm)

Figure 8.10: The vertex distribution of R 2 with the best radius cut is shown in left plot. The
vertex distribution of the tank height with the best height cut is shown in right plot.

The noise cut from the water pipe
In the background study, the abnormal event accumulation was found in the center of top of the
SK tank. The energy distribution of the events are from 4.5 to 5.5 MeV. These events have astrong correlation with the position of the water pipe which was used for supplying of the waterfrom the center of the top of the tank. So, it is supposed that the events are like γ rays from thepipe. Figure 8.11 shows the vertex distributions in 2 dimensions (x versus y cm) from 4.5 to 5.0
MeV. The right plot is the distribution of the bottom, and the left plot is the top. The upper
figures are the 3 dimensional plots, and the lower figures are plane plots. In the bottom andtop distributions, the abnormal peak exists in the really center position of the tank. The mis-fit
events are accumulated in the center position. But, in the top figure, in the slightly shifted
position from the center around x = 100 and y = -400, there are some accumulated events. The
position is almost consistent with the water pipe position (x = 50 and y = -400 cm).
Therefore, the events around the water pipe were removed. The criterion is that the events
inner of the square of 3 m around the water pipe were rejected. After this cut and the best
fiducial volume cut, the fiducial volume changed from 22.5 ktons to 20.5 ktons.

8.1.2

New fitting cut

In chapter 4, the event reconstruction methods were explained. Now, the basic principle is shown
again. The vertex point is searched by the chi square testing assuming a Gaussian distribution
for the true vertex point. The definition of the goodness function for the testing is as follows.
NhitX∆ti (x, y, z)2
)
2σi2

(8.7)

∆ti (x, y, z) = ti − tofi (x, y, z) − t0

(8.8)

goodness =

exp(−

i=1

141

events

events

225
200
175
150
125
100
75
50
25
0

300
250
200
150
100
50
0

1000

1000
0

-1000

y( 0
cm
-1000
)

1000

x(cm)

y(cm)

y( 0
cm
-1000
)

y(cm)

350

1000

500

0

0

-500

-500

-1000

-1000

0

1000

-1000

x(cm)

1000

x(cm)

1000

500

-1000

0

-1000

0

1000

x(cm)

Figure 8.11: The vertex distribution in 2 dimensions (x versus y cm) from 4.5 to 5.0 MeV.

where (x,y,z) is the positions of grid points, ∆t i is the residual time of i-th hit PMT, t i is
the time of the i-th hit PMT, tofi is the time of flight of i-th hit PMT, t 0 is the mean time ofthe distribution of ∆ti .
In this vertex reconstruction, the important assumption is that the distribution of the hit
PMT is the Gaussian distribution. However, in the low energy region, 5.0 MeV, the expected
number of hit PMTs is about 30. So, the small number of hit PMTs in the lower energy region
gives the wrong vertex point sometimes. The current vertex reconstruction does not work wellin the energy region from 4.5 to 5.0 MeV (below about 25 signal hits). In SK-I data set, there
are some mis-fit events in the lower energy region from 4.5 to 5.0 MeV. The most of these events
are the γ rays. So, if the corrected vertex point is given, the gamma like events can be removed
combining with the general data reduction tools. In this thesis, the new vertex reconstruction
method was tried for the SK-I 4.5 MeV data set in order to improve the above problems.
The new developed vertex reconstruction tool is named BONSAI (Branch Optimization
Navigating Successive Annealing Iterations) fitter from now on. The hit selection of the BONSAI
fitter is same as the before vertex reconstruction of the cluster fitting in chapter 6. The definitionof goodness is different from the current vertex reconstruction in order to treat small numberof hit PMTs. The goodness is defined by the following formulation.
NhitY

pdf (∆ti (x, y, z))(8.9)∆ti (x, y, z) = ti − tofi (x, y, z) − t0(8.10)

goodness = log(

i=1

where ∆ti is same definition as the before vertex reconstruction, pdf is the probability density
function. The goodness is the log timing likelihood function for the Poisson distribution. At
the maximum goodness, the vertex point gives the correct information.
However, sometimes, the reconstructed vertex point agrees with the local maximum point.
So, the BONSAI fitter searches a tree tracing all branches for a range of the likelihood. This
principle is the origin of the name. The technical order to search the starting point to search
the true vertex point are as follows.
1. Hit selection using cluster fitting method.
142

2. Time ordering of the hit.
3. Use the four suitable combination in order to search the start position of searching true
vertex position. The results of each combination gives the two or three candidates.
4. Use the best vertex point which has the maximum likelihood.
After above preparing, the search of the true vertex point starts from the starting point. In
the current vertex reconstruction, the grid point is used and the fitting is applied to all ∆t i,jfor the pairs of the hits when the fitter searches the true vertex point. However, BONSAI fitter
does not do that.
Figure 8.12 shows the performance of the BONSAI vertex reconstruction in the energy region
from 4.5 to 5.0 MeV. The right side plot of the upper figures is the x vertex distribution, and left
side is the y vertex distribution. In the lower figures, the right side is the z vertex distribution,and the left side is the R2 vertex distribution. The histograms are the results by the current
vertex reconstruction. The hatched areas are the results by the BONSAI vertex reconstruction.
The some events exist outer of the fiducial volume as a result of the correction of the vertex
point. Especially, in the R 2 distribution, the mis-fit events accumulated in the center of thetank are reduced and the remaining external γ ray at R 2 ∼ 500 is also reduced.






 3000

3000
2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

−1000

0

0

1000

−1000

0

x


 

1000

y


3000


 

2500

4500
4000
3500

2000

3000
2500

1500

2000
1000

1500
1000

500
0
−2000

500
−1000

0

1000

2000

0

0

1000
R

z

2000
3
x 10

Figure 8.12: The performance of the BONSAI vertex reconstruction in the energy region from
4.5 to 5.0 MeV.
Figure 8.13 shows the difference of the vertex position between current fitter and BONSAI
fitter. The number of events which has the difference less than 2.0 m are 85% for the total
events.
We applied the some reduction which has an effect on the γ ray using the new reconstructedvertex information by BONSAI fitter. The used reductions are PATLIK cut, strong gamma cut
and fiducial volume cut. First of all, we searched the best combination of the cuts. Figure 8.14
shows the reduction efficiency for each reductions. The empty circles are the reduction efficienciesof the data and the filed circles are the reduction efficiencies of the solar neutrino MC. The data
is extracted from less than 0.8 of the cos θ sun distribution as background events. The large
difference between data and MC means that the reduction is optimized to the background
reduction well. The left plot shows the reduction efficiency for the single reduction of fiducial
cut (F), Gamma cut (G) and PATLIK cut (P). The right plot shows the reduction efficiency for
143




10

5

10

4

10

3

10

2



10

1
−500

0

500

1000

1500

2000

2500

3000

 3500  4000 4500
Figure 8.13: The difference of the vertex position between current fitter and BONSAI fitter.

Efficiency

Efficiency

the combination cut. The largest reduction efficiency appears when using the three combination
cuts. Table 8.3 shows the summary of the reduction efficiency for the MC. Therefore, the three
reductions were applied to the data set with new vertex information by BONSAI fitter.
0.14

0.25

0.225

0.2

0.12

0.175
0.1
0.15
0.08
0.125

0.1

0.06

0.075
0.04
0.05
0.02

F+G+P

G+P

F+P

0

Cut

F+G

PatlikGamma

0

Fiducial

0.025

Cut

Figure 8.14: The reduction efficiencies for each reduction using BONSAI vertex.
Figure 8.15 shows the R2 and Z vertex distribution before and after the three reductions
using the BONSAI vertex information in energy region from 4.5 to 5.0 MeV. The hatchedarea shows after reductions and the histogram is before reductions. Basically, the events are
uniformly reduced for all vertex area. The remarkable reduction is seen in the left figure of theR2 vertex distribution. The mis-fit events accumulated in the center of the tank by current
vertex reconstruction tool are reduced remarkably. Figure 8.16 shows the direction distribution
before and after the three reductions using BONSAI vertex information in energy region from
144

Cut
Fiducial volume cut (F)Gamma cut (G)PATLIK cut (P)
F+G
F+P
G+P
F+G+P

reduction efficiency for MC
6%
9.2 %
3.6 %
9.9 %
9.6 %
12.9 %
13.4 %

Table 8.3: The summary of the reduction efficiencies for the solar neutrino events using BONSAI
vertex.
4.5 to 5.0 MeV.
3000

4500

4000
2500
3500

2000

3000

2500
1500
2000

1000

1500

1000
500
500

0
−500

0

500

1000
r2

1500

2000

0
−2000

2500
3
x 10

−1500

−1000

−500

0

500

1000

1500

2000

z

Figure 8.15: The R2 and Z vertex distribution before and after the three reductions using
BONSAI vertex information in energy region from 4.5 to 5.0 MeV.

8.2

Monte Carlo simulation of the solar neutrino events

In order to estimate the reduction efficiency of the solar neutrino signal, the whole analysis chain
was applied to the solar neutrino MC events. The solar neutrino MC events are generated 10
events per minute along the solar neutrino analysis live-time for 8 B neutrinos and hep neutrinos,
which corresponds to 51 times of the event rate predicted by BP2000 (284.4 events/day), in the
inner volume (32 ktons).

8.3

Summary and Data quality

Table 8.4 shows the summary of the reduction steps. The number is the number of the remaining
events after each reduction. The reduced rate means the reduction efficiency simply calculated
from the ratio between before and after each reduction. After all reductions, the remaining
events are 141539 events (20% remaining for first entries).
Figure 8.17 shows the energy distribution for each reduction step, which are first entries,
after the tight cut and after the new fitting cut.
Figure 8.18 shows the energy distribution of the S/N ratio for each reduction step. The S/Nratio is calculated from the ratio between the data and MC results after each reduction step for
145

1400

1200

1200

1000

1000
800
800
600
600
400

400

200

200
0

−1

−0.5

0

0.5

0

1

−1

dirx

−0.5

0

0.5

1

diry

1200
1000
800
600
400
200
0

−1

−0.5

0

0.5

1

dirz

Figure 8.16: The direction distribution before and after the three reductions using BONSAI
vertex information in energy region from 4.5 to 5.0 MeV.

first
Tight cut

New fitting cut

Reduction step
all events
Trigger efficiency cut
Radon high rate run cut
Strong GAMMA cut
Strong GRINGO cut
Best F.V R cut
Water Pipe cut
final number of events
F.V cut
PATLIK cut
Strong GAMMA cut
final number of events

Real Data
692556385640313406298099226988175758173012173012
163953151432141539141539MC data
3544686
141314412774291235504
995836917912908809908809895709854918819050819050

Reduced rate of Data
44%
19%
5%
24%
23%
1.5%
75%
12%
8%
7%
80%

Table 8.4: The table of the reduction steps. ’MC data’ is the solar neutrino MC simulation in
the energy range of 4.5∼20.0 MeV in the 20.5kt fiducial volume.

146

Event

10

6

10

5

Final sample
After tight cut
After new fitting cut

10

4

10

3

10

2

10

1

6

8

10

12

14

16

18

20

Energy(MeV)

Figure 8.17: The energy distribution for summarized reduction steps of first entries, after thetight cut and after the new fitting cut.

the second entries which is after the trigger efficiency cut. The S/N ratio from 4.5 to 5.0 MeV
increased by a factor of about 1.9 for the second entries. Since the S/N ratio was improved
remarkably in the low energy region, the optimization to reduce the background events in the
low energy region is done well. The improvement of the data quality for the second entries is+53% (the background events are reduced by 53%).
We estimated the improvement of the data quality for the first entries from the following
calculation of the S/N ratio and the Significance values.

S/N ratio =Signal(Solar MC after all reductions) × Oscillation factor
Data(Data cos θsun < −0.8 after all reductions)

Significance =Signal(Solar MC after all reductions) × Oscillation factorp
Data(Data cos θsun < 0.8 after all reductions)(8.11)(8.12)

where the oscillation factor is the following equation.
Oscillation factor =284.4[events/day]
× 0.465
24. × 60. × 10.

(8.13)The value of 0.465 is the official number of the data over SSM in SK-I. Table 8.5 shows thesummary of the calculation results in the energy region from 4.5 to 5.0 MeV. If it is assumed theonly background events are reduced after all reductions, the improvement of the data quality
for the first entries is +25% (the background events are reduced by 25%).
Figure 8.19 shows the vertex distribution in the energy region from 4.5 to 5.0 MeV after
all reductions. Figure 8.20 shows the direction distribution in same energy region as vertex
distribution. The histogram means before the tight data reduction, and the hatched area means
the after all reductions. The tight data reduction reduced the events uniformly. Especially,in the R2 distribution, the reductions have an effect on the mis-fit events in the center of the147

S/N=MC(after/before)/DATA(after/before)

3

2.5

2

1.5

1

0.5

’After strong GAMMA cut ’’After strong GRINGO ’’After F.V R cut ’’After Center pipe cut ’’After BONSAI tight cut ’

0

−0.5

−1

4.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2

6.4

Energy(MeV)

Figure 8.18: The energy distribution of the S/N ratio for each reduction step.

Cut
S/N
Significance

SK-I 1496 days data
0.06
2.70

511 days data
0.08
2.74

Table 8.5: The summary of the calculation results for the S/N ratio and the significance in theenergy region from 4.5 to 5.0 MeV.

148

tank and the remaining γ ray around the R 2 = 500 ∼ 1000. This reduction performance forγ ray is appeared in the direction distributions. The events from wall materials were reduced
remarkably.




12000

7000


















10000



6000











5000

8000

4000

6000
3000

4000
2000

2000
1000

0
−500

0

500

1000

1500

2000

r2

0
−2000

2500
3
x 10

−1500

−1000

−500

0

500

1000

1500

2000

z

Figure 8.19: The vertex distribution in the energy region 4.5 to 5.0 MeV after all reductions.

"

#

3000
!

"

#

3000
!







2500





2500










2000




2000













1500

1500

1000

1000

500

500

0

−1

−0.5

0

0.5

1

dirx
"

0

−1

−0.5

0

0.5

1

diry

#

!

3000






2500






2000






1500
1000
500
0

−1

−0.5

0

0.5

1

dirz

Figure 8.20: The direction distribution in the energy region 4.5 to 5.0 MeV after all reductions.

8.4

Remaining background

In Z distribution, there are remaining radon events transported from bottom PMTs by theconvection of water supply. This is exactly the pure radon background after all reductions.
However, if it is assumed that the distribution of the top region is applicable to the bottom
region, the ratio for background contamination looks like small. In the future, one can hopethese events will be reduced by the controller system of the water convection.
The final estimation of the radon concentration in bottom region is shown in table 8.6 basedon above assumption. The calculation is done as follows.

149

Radon concentration =Nbottom [events] − Ntop [events](8.14)
mBq/m2
F.V./2[ton] × Live Time[day] × Rn detection efficiency[ events/day/ton]

where Nbottom is the remaining events in the bottom region under the center of the tank.
Ntop is the remaining events in the top region above the center of the tank. F.V. means thefiducial volume which is 20.5 ktons in this analysis. Rn detection efficiency which is the radonobserved rate in the SK tank is estimated as follows.
1.0[mBq/m3 ] = 0.0074[events/day/ton](8.15)The radon detection efficiency depends on the trigger threshold. The estimated value is theaveraged number by weighting the live time of each trigger threshold for each radon detection
efficiency in each trigger threshold. The radon detection efficiencies for another hardware trigger
thresholds without the tight data reduction in all volume of the SK tank are shown in table 8.7.
Data set
SK-I 566 days data
(only trigger efficiency cut)
SK-I 511 days data
(after all reduction)

F.V.
22.5 ktons

Live-time
566 days

Efficiency
0.0074

Radon conc.
-

20.5 ktons

511 days0.0027(0.0074×0.37)

1.52±0.03 mBq/m 3

Table 8.6: The summary of the expected radon concentration in the bottom region of the SK
tank in the energy region from 4.5 to 5.0 MeV. The value of 0.37 is the reduction efficiency of
the tight data reduction.
RunperiodMay. 1997∼
Sep. 1999∼
Dec. 1999∼
Sep. 2000∼

Hardwaretrigger threshold-260mV,-250mV-222mV-212mV-186mV

Radon detection
efficiency for 1.0mBq/m 3
0.0050[events/day/ton]
0.0057[events/day/ton]
0.0065[events/day/ton]
0.0086[events/day/ton]Table 8.7: The radon detection efficiency after the general data reduction for each hardware
trigger threshold.
The final expected radon concentration of 1.52±0.03 mBq/m 3 is consistent with the absolutemeasurements of the radon concentration in the SK tank (1.6±0.5 mBq/m 3 ).

150

Chapter 9

Results

Event/day/kton/bin

Solar neutrino events are detected by recoil electrons via ν − e scattering. The strong angularcorrelation between the incident neutrino direction and the scattered electron direction is used
to extract the solar neutrino flux.
Figure 9.2 shows the distribution of cos θ sun for all events passing the reduction cuts describedin chapter 6, 8. θsun is defined as the angle reconstructed momentum and the radius vector fromthe Sun. It is shown in figure 9.1. The energy range of the event is 4.5 ∼ 20.0 MeV in the figure.
The filled circles show data, and the histogram shows MC normalized to data. The dotted line
shows the background shape which is used in extracting the neutrino signal.
A clear peak due to solar neutrinos is seen, as described above. The flat component in thecos θsun distribution is due to radon background in the water, radioactive spallation productsand γ rays from the surrounding rock and materials comprising the ID wall.
In this chapter, the method used to extract the solar neutrino signal is explained. The flux
measurement and the observed recoil electron energy spectrum of new data above 4.5 MeV is
described. The day and night time energy spectrum is presented in appendix G.

   0.3

SK−I 511days 4.5−20MeV 20.5kt

0.25

0.2

0.15

0.1

θ             

0.05

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

cosθsunFigure 9.1: The definition ofcos θsun .

Figure 9.2: The cosθsun distribution of all events(E =4.5 ∼ 20.0MeV)

151

9.1

Solar neutrino signal extraction

In order to obtain the measured flux relative to the SSM, a extended maximum likelihood method(EMLM) is used. In old solar neutrino extraction, the simple maximum likelihood method had
been used. But, in the most recent analysis, the EMLM has been used. The details of thereasons is explained later.
The probability function for the likelihood consists of signal and background components in
old method:
P (Ee , cos θsun , x) = Pbg × (1 − x) + Psig × x(9.1)

Probability density

where Ee is the recoil electron energy and x is the fraction of the solar neutrino signals
relative to the observed total number of events.
The probability function for the signal (P sig ) is obtained by the solar neutrino MC simulation
at various energy regions. Figure 9.3 shows the distributions of P sig at 4.5, 8, 10, 14 MeV. The
distribution is named XANG. The XANG is made by the smoothed probability function for thesignal distribution of MC by the smoothing functions. The details is described in appendix F. In
this thesis, the smoothing function is different from current analysis. The smoothing functions
are changed from the sorting method to the function fitting method. It was problem that theold smoothing function created a artificial shape for original MC cos θ sun distribution. So, the
new smoothing method was developed. It has a small artificial effect.
20

18

4.5 MeV

16

8.0 MeV

1410.0 MeV

12

14.0 MeV

10

8

6

4

2

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CosθsunFigure 9.3: The probability density function for signal, P sig at various energy.
The background shape is almost flat. But, asymmetries in the γ ray background fromthe surrounding rocks and PMT gain variations may slightly distort the background shape.
Especially, the effect is most important factor for extracting solar signals in low energy region,
for example, 4.5 ∼ 5.0 MeV. Small deviations from a flat background shape are taken into accountby simulating the background distribution. In order to obtain the background shape, the zenith
angle (cos θz ) distribution of the events is fit with 8-th degree polynomial. The backgroundprobability function (Pbg ) is obtained by transforming this fit function into a function cos θ sun .
The fitting function was weighted by the cos θ sun distribution of the real data. Then, it was
distributed cos θsun with cos θx,y of the random number. By this method, the background which
has enough statistics is simulated. Here, it is assumed that the background shape does not152Probability density

dependent on the azimuth angle. Possible azimuth dependence (φ asymmetry of the background)is discussed in the systematic errors. Figure 9.4 shows the distributions of P bg at 4.5,8.0,10.0,
and 14.0 MeV.
0.52

0.515

0.51

0.505

0.5

0.495

0.49

4.5 MeV
0.485

8.0 MeV
0.48

10.0 MeV
0.475

14.0 MeV
0.47

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CosθsunFigure 9.4: The probability density function for background, P bg at various energy.

The fraction of signal x differs between energy regions. In order to get this fraction at various
energy regions separately, the probability function is defined as follows:
P (Ee , cos θsun , xi (x)) = Pbg (Ee , cosθsun ) × (1 − xi (x)) + Psig (Ee , cos θsun ) × xi (x)(9.2)

where xi (x) of a scale factor is defined by following steps.
1. Assuming 8 B spectrum and no spectrum distortion, the following equation is defined.
data
Sall
Sidata
=
SSM
Nall
NiSSM

(9.3)

2. From probability function fitting, one can obtainx=

Sidata.
Nidata(9.4)

3. Therefore, one can obtain xi (x) by following equation.
xi (x) =data
NiSSM Nall
× x.
SSM N data
Nall
i

(9.5)

where i is the index of the energy region. N all and Ni are the total number of events andthe number of events in each energy region respectively. S all and Si are the extracted total
solar neutrino signals and the number of solar neutrino signals in each energy region.
From the probability function, the traditional likelihood function is defined as follows.

153

L(x) =

Ni
N
ene Y
Y

Pij (Ee , cos θsun , xi (x))(9.6)

i=1 j=1

where Nene is the number of the energy regions and N i is the number of events in i-th energy
region. In this function, there was a problem. The problems was the total number of events isfixed. The problems produced the harmful effect as following lists.
• Fitted results using the likelihood function is just a number of signal events in our particular
data sample. (and it does not correspond to the absolute value of the true number of signal
rate)• For small Ni bin, the scale factor xi tend to fluctuate largely and make many negative
likelihood values.
To avoid these harmful effect, we improved the smoothing technique for scale factor (x i ) andused the extended maximum likelihood function [90] [5]. The extended maximum likelihood
function is as follows:e−T · T N
· LT (x)(9.7)
N!
where LE and LT are the extended maximum likelihood function and the traditional maximum likelihood function respectively. T is the extracted true all number of events which is total
number of true extracted signals adding to total number of true fitted background events. N is
the total observed number of events. Therefore, the extended likelihood function is transfered
as follows.
LE (x) =L(x) =

N
ene
Y
i=1

N

Bi + xi · S Yi
Pij (Ee , cos θsun , xi )
N!

(9.8)

j=1

xi is the new scale factor for the signal. B i is the number of true fitted background events ini-the energy bin. S is the total number of the true extracted signals. The probability function
with new scale factor is as follows.
P (Ee , cos θsun , xi ) = Pbg,i (Ee , cosθsun ) × Bi + Psig,i (Ee , cos θsun ) × S · xi

(9.9)

SM C,i = xi × SM C .

(9.10)

where

SM C,i is the number of the expected signal events in i-th bin for total expected signal eventsof SM C . In this analysis, the data are divided into 20 energy regions. From 4.5 to 14.0 MeV,
data are divided into regions 0.5 MeV width. The last region is from 14.0 to 20.0 MeV.

9.2

Results of the flux measurement

In this section, the flux measurement is summarized. For the flux measurement, the events withreconstructed recoil electron from 4.5 to 20.0 MeV is used. In this thesis, the flux measurement
is done for three data sets. The data set I (dsI) is the full 1496 days data set of SK-I. The data
set II (dsII) is the periodical 566 days data set of SK-I, which is same period as the data set ofthe 4.5∼5.0 MeV analysis but without tight data reduction. The data set III (dsIII) is the final
511 days data set of SK-I with 4.5∼5.0 MeV data.
1549.2.1

The results of total 8 B neutrino flux

First of all, the total number of recoil electron events by the solar neutrino is shown for each data
set. The total systematic error is given +3.5% and -3.2% for data set I,II. The total systematic
error is given +5.8% and -5.3% for data set III.
+780
Nsignal,dsI = 222967+226−225 (stat.)−713 (syst.)+312
Nsignal,dsII = 8920+146−145 (stat.)−285 (syst.)+338
Nsignal,dsIII = 5823+120−119 (stat.)−309 (syst.)(9.11)(9.12)(9.13)The expected number of solar neutrino events in total, N expect is obtained as follows.

Nexpect =

N
thr
X
i=1

Nred,i× Tlivetime,i × Nssm
NM C,i(9.14)The expected number of solar neutrino events in j-th energy bin, N expect,j is obtained asfollows.

Nexpect,j =

N
thr
X
i=1

Nred,i,j
× Tlivetime,i,j × Nssm
NM C,i,j(9.15)

where Nthr is the number of trigger thresholds. As described in chapter 3, there are 7
different trigger thresholds. NM C is the number of the solar neutrino MC events in i-th run
period of each trigger threshold. N red,i is the number of solar neutrino MC events after the
reduction steps in i-th run period. T livetime,i is the live-time of i-th run period. N SSM is the
SSM prediction of the number of solar neutrino recoil electrons in SK, which is 284.4 events/day.
The live-time is summarized in table 9.1 for the data set I,II and in table 9.2 for the data set
III.
triggerLE
LE+SLE
LE+SLE
LE+SLE
LE+SLE
LE+SLE
LE+SLE
LE+SLE
total(dsII)
total(dsI)

LE/SLE-320mV-320mV -260mV-320mV -250mV-320mV -222mV-302mV -212mV-302mV -186mV-302mV -212mV-302mV -186mV

run number
R1742-4141
R4142-7333
R7334-7858
R7859-8233
R8234-8995
R8996-9093
R9094-9267
R9268-10417
R7859-10417
R1742-10417

live time(day/night time)
280.026(135.29/144.73) day
548.375(270.77/277.61) day
101.701(56.96/44.74) day
78.072(33.84/44.23) day
173.492(84.41/89.08) day
17.147(10.02/7.13) day
50.610(26.4/24.25) day
246.693(115.49/131.20) day
566.01(270.13/295.88) day
1496.12(733.15/762.97) day

Table 9.1: The live-time summary for each trigger threshold in the data set I,II.
Figure 9.5 shows the SSM prediction of the number of solar neutrino recoil electrons in SK.
The expected numbers of events for the flux analysis are:Nexpect,SSMBP2000 ,dsI = 48173 events(9.16)

Nexpect,SSMBP2000 ,dsII = 19316 events(9.17)

Nexpect,SSMBP2000 ,dsIII = 12209 events(9.18)

155

trigger
LE+SLE
LE+SLE
LE+SLE
LE+SLE
LE+SLE
total(dsIII)

LE/SLE-320mV -222mV-302mV -212mV-302mV -186mV-302mV -212mV-302mV -186mV

run number
R7859-8233
R8234-8995
R8996-9093
R9094-9267
R9268-10417
R7859-10417

live time(day/night time)
72.95(31.78/41.16) day
173.408(84.33/89.08) day
7.72(4.49/3.23) day
31.83(15.90/15.93) day
225.58(107.36/118.22) day
511.48(243.86/267.62) day

Table 9.2: The live-time summary for each trigger threshold in the data set III.

0.5

event/day/kev

event/day/kev

x 10

0.45

0.4

0.1

0.09

0.08

0.35

0.07

0.3

0.06

B8

0.25

0.04

0.15

0.03

0.1

0.02

0.05

0.01

0

5

10

15

HEP

0.05

0.2

0

-2

20

energy

0

0

5

10

15

20

energyFigure 9.5: The SSM prediction of the number of solar neutrino recoil electrons in SK detector.

156

Therefore, the ratios Data/SSMBP2000 are obtained as:+0.016
Data/SSM(SSMBP2000 , dsI) = 0.462+0.005−0.005 (stat.)−0.015 (syst.)+0.016
Data/SSM(SSMBP2000 , dsII) = 0.463+0.008−0.007 (stat.)−0.015 (syst.)+0.028
Data/SSM(SSMBP2000 , dsIII) = 0.478+0.01−0.01 (stat.)−0.025 (syst.)(9.19)(9.20)(9.21)The solar neutrino flux Φν is obtained for each data set by multiplying this ratio by the
SSMBP200,v2 flux prediction.
+0.08
6
2
Φν (SSMBP2000 , dsI) = 2.34+0.02−0.02 (stat.)−0.08 (syst.)(×10 /cm /sec)(9.22)+0.14
62
Φν (SSMBP2000 , dsIII) = 2.41+0.05−0.05 (stat.)−0.13 (syst.)(×10 /cm /sec)(9.24)+0.08
62Φν (SSMBP2000 , dsII) = 2.33+0.04−0.04 (stat.)−0.08 (syst.)(×10 /cm /sec)(9.23)The result of the data set III is used in this thesis for energy spectrum analysis. The
Data/SSM result is consistent with the another results within 1.3 sigma. Therefore, the result
from new analysis including 4.5∼5.0 MeV data has no systematic bias.

9.2.2

The results of 8 B neutrino flux from 4.5 to 5.0 MeV

The details of the 4.5∼5.0 MeV data is described in this section. The event rates as shown intable 9.3 can be observed for each energy region in the SK detector by SSM prediction.
Energy8B
4.5-5.0
5.0-5.5
5.5-6.0
6.0-6.5
6.5-7.0
7.0-7.5
4.5-6.5
6.5-20.0
hep
4.5-5.0
5.0-5.5
5.5-6.0
6.0-6.5
6.5-7.0
7.0-7.5
4.5-6.5
6.5-20.0

Event rate (events/day)
11.18
13.29
15.27
17.02
18.45
19.50
56.75
199.560.00960.01220.01500.01790.02100.02400.05480.6767

Table 9.3: The expected event rates in the SK detector by prediction.
Figure 9.6 shows the cos θsun distribution of the data set III with 4.5∼5.0 MeV data. In the
figure, the cos θsun distributions for 5.5∼6.0 and 5.0∼5.5 MeV energy regions are also drawn.
Figure 9.7 shows the expanded plot of the cos θ sun distribution for 4.5∼5.0 MeV energy region.
We can see the clear solar neutrino peak to the solar direction in this energy region. The
histogram shows the result of the likelihood fits. The dashed line shows the background shape.
The black circles show the data with statistical error.
157

Event/day/kton

4.5−5.0MeV

0.2

0.175

SK−I 511days
20.5kton

0.15

0.125

0.1

5.0−5.5MeV

0.075

0.05

5.5−6.0MeV

0.025

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

cosθsunEvent/day/kton

Figure 9.6: The cos θsun distribution for 5.5∼6.0, 5.0∼5.5 and 4.5∼5.0 MeV energy regions of
the data set III.

0.22

0.21

4.5−5.0MeV

0.2

0.19

0.18

0.17

0.16

0.15

SK−I 511days
20.5kton

0.14

0.13

0.12

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

cosθsunFigure 9.7: The expanded plot of the cos θ sun distribution for 4.5∼5.0 MeV energy region.

158

The number of the extracted solar neutrino signals in this energy region with a systematic
error of ±5.9% is as follows:+43
Nsignal,4.5−5.0 = 722+139−137 (stat.)−43 (syst.)(9.25)The expected solar neutrino events in this energy region is as follows:
Nexpect,SSMBP2000 ,4.5−5.0 = 1109 events(9.26)

We obtained the solar neutrino flux in this energy region for the first time in the world as
follows:+0.19
62
Φν (SSMBP2000 , 4.5 − 5.0) = 3.28+0.63−0.62 (stat.)−0.19 (syst.)(×10 /cm /sec)(9.27)The Data/SSM in this energy region is as follows:+0.038
Data/SSM(SSMBP2000 , 4.5 − 5.0) = 0.651+0.13−0.12 (stat.)−0.038 (syst.)(9.28)In this energy region, the observed solar neutrino events are also deficits by the solar neutrino
oscillation comparing with the SSM prediction.

9.3

Results of the energy spectrum measurement

Figure 9.8, figure 9.9, figure 9.10 present the cos θ sun distribution in various energy bins. The
filled circles show the data with statistical error, the histograms show the result of the likelihood
fit, and the dashed lines show the background shape used to extract the solar neutrino signals.
The width of each energy bin is divided as follows:• 4.5∼14.0 : 0.5 MeV for each bin• 14.0∼20.0 : combined into one bin
As described in figure 9.5, 8 B neutrino energy spectrum endpoint is about 15 MeV. The hep
flux is predicted to be 0.04% of the expected 8 B neutrino flux, although the end point energy is
18.77 MeV. Therefore, the number of solar neutrino events with recoil electron energy above 14
MeV is expected to be much smaller than that below 14 MeV. This is the reason for the large
width of the last bin.
Figure 9.11 shows the measured solar neutrino recoil electron energy spectrum and the
expected spectrum from the SSM prediction. This figure is result of the data set III which
includes the 4.5 MeV data. We can see the deficit of the observed solar neutrino flux in all overthe energy region.
Figure 9.12 shows the ratio of the measured recoil electron energy spectrum to the predicted
spectrum. This figure is the result of the data set III which includes the 4.5 MeV data. Figure 9.13 also shows the ratio of the measured recoil electron energy spectrum to the predicted
spectrum for the results of data set I and II. In the right side plot, the result of the data set III isoverlaid with the result of the data set II. The data set I is the SK-I full data. The data set II is
the periodical data which has same time period as data set III but no any tight data reduction.
Comparing these three figures, although the fluctuation of the data by the poor statistics, thetendency is consistent in all energy region. It is concluded that the new made data set III with
4.5∼5.0 MeV data has no systematic bias. In table 9.4, the numerical summary of the recoil
electron energy spectrum is represents. The error is statistical only.
159

0.04

0.08

0.2

0.03

0.06

0.15
0.1

0.04

0.02

0.05

0.02

0.01

0

0

−1

0

1

−1

4.5− 5.0MeV

0

1

0

0.03

0.03

0.02

0.02

0.02

0.01

0.01

0.01

−1

0

1

0

−1

6.0− 6.5MeV

0

1

1

0.01

0.01

0.005

0.005

0

0

1

0.015

0.01

0

−1

0.02

0.015

−1

1

7.0− 7.5MeV

0.02

0

0

6.5− 7.0MeV

0.02

05.5− 6.0MeV

0.03

0

−1

5.0− 5.5MeV

−1

0

1

0

−1

8.0− 8.5MeV

7.5− 8.0MeV01

8.5− 9.0MeV

Figure 9.8: The cos θsun distribution in each energy bin from 4.5 to 9.0 MeV. The unit of thevertical axis is events/day/kton/bin.

0.015
0.015

0.015

0.005

0.005

0.005
0

0.01

0.01

0.01

−1

0

1

0

−1

9.0− 9.5MeV
0.008

0.008

0.006

0.006

0.004

0.004

0.002

0.002

0

−1

0

0

1

−1

1

0

−1

0

1

0
x 10

0.003

0.003

1

0.002

11.0−11.5MeV

0.004

0
10.0−10.5MeV

0.004

10.5−11.0MeV

−1

−2

0

1

11.5−12.0MeV

0.2
0.15

0.002

0.1

0.002
0.001

0.001
0

0

9.5−10.0MeV−10
12.0−12.5MeV

1

0

0.05
−1

0
12.5−13.0MeV

1

0

−1

0

1

13.0−13.5MeV

Figure 9.9: The cos θsun distribution in each energy bin from 9.0 to 13.5 MeV. The unit of thevertical axis is events/day/kton/bin.

160

x 10

−2

0.15
0.002
0.1
0.001

0.05
0

−1

0

1

0

13.5−14.0MeV

−1

0

1

14.0−20.0MeV

Number of events / day / 20.5kt / 0.5MeV

Figure 9.10: The cos θsun distribution in each energy bin from 13.5 to 20.0 MeV. The unit of
the vertical axis is events/day/kton/bin.

Solar neutrino MC
Observed solar neutrino

10

stat. error
2stat. +sys.

2

1

-1

10

(efficiency corrected)
SK 511day 20.5kt
6

8

10

12

14

Energy (MeV)

Figure 9.11: The measured solar neutrino recoil electron energy spectrum. The expected spectrum from SSM is also shown. The thick error bar shows the statistical error only. The thinerror bar shows the total error including systematic error.

161

Data/SSM

1

0.9

0.8

SK-I 511 days 4.5-20MeV 20.5kt
Data/SSM : 0.477+-0.01

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

6

8

10

12

14

Energy(MeV)

Figure 9.12: The ratio of the measured recoil electron energy spectrum to the predicted spectrum. The error bars shows total errors including systematic error and statistical errors. The
center value of the best fit for the total recoil electron is shown by the solid center line. The
dashed line shows the systematic errors for the predicted 8 B spectrum including energy resolution, energy scale resolution and uncertainty for the 8 B spectrum.

Energy4.5- 5.0
5.0- 5.5
5.5- 6.0
6.0- 6.5
6.5- 7.0
7.0- 7.5
7.5- 8.0
8.0- 8.5
8.5- 9.0
9.0- 9.5
9.5-10.0
10.0-10.5
10.5-11.0
11.0-11.5
11.5-12.0
12.0-12.5
12.5-13.0
13.0-13.5
13.5-14.0
14.0-20.0

Data/SSM
0.649
0.444
0.438
0.501
0.445
0.492
0.484
0.422
0.470
0.479
0.534
0.583
0.405
0.480
0.414
0.490
0.528
0.410
0.411
0.627

Statistical error+0.125-0.123+0.061-0.060+0.037-0.036+0.032-0.031+0.031-0.029+0.033-0.031+0.033-0.031+0.034-0.032+0.035-0.033+0.038-0.036+0.042-0.039+0.048-0.044+0.046-0.041+0.054-0.048+0.059-0.051+0.074-0.063+0.093-0.078+0.106-0.083+0.130-0.096+0.120-0.099

Flux(×10 6 /cm/s)
3.27
2.24
2.21
2.53
2.25
2.48
2.44
2.13
2.37
2.42
2.69
2.94
2.04
2.42
2.09
2.47
2.66
2.07
2.08
3.16

Statistical error+0.63-0.62+0.31-0.30+0.19-0.18+0.16-0.15+0.15-0.15+0.16-0.15+0.16-0.16+0.17-0.16+0.18-0.17+0.19-0.18+0.21-0.19+0.24-0.22+0.23-0.21+0.27-0.24+0.30-0.26+0.37-0.32+0.47-0.39+0.53-0.42+0.65-0.48+0.60-0.50

Table 9.4: The numerical summary of the recoil electron energy spectrum.

162

0.9

0.8

Data/SSM

Data/SSM

1

SK-I 1496 days 5.0-20MeV 22.5kt
Data/SSM : 0.463+-0.005

1

0.9

SK-I 566 days 5.0-20MeV 22.5kt

0.8

SK-I 511 days 4.5-20MeV 20.5kt

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

6

8

10

12

0

14

6

8

10

Energy(MeV)1214Energy(MeV)

Figure 9.13: The definition in the figure is same as Figure 9.12. The left figure is the result of
the data set I (1496 days). The right figure shows the result of the data set II (566 days, notight data reduction) with empty circles and data set III (511 days) with filled circles.

9.4

systematic uncertainties

Systematic uncertainties in the energy spectrum measurement are classified into two categories.
The one are errors that are correlated with energy. And they are called correlated errors. The
other are errors that are not correlated error basically, and they are called uncorrelated errors.
In the uncorrelated errors, some error has the correlation with energy, In this case, the error iscalled uncorrelated-correlated error. In this section, the correlated errors and the uncorrelated
errors are explained separately. The all uncertainties is updated in order to analyze the newdata set III which includes 4.5∼5.0 MeV data in this thesis. Especially, the main factor for theuncertainties of 4.5∼5.0 MeV data is described in detail.

9.4.1

Correlated errors

Uncertainties in the absolute energy scale and the energy resolution directly affect the shape ofthe observed energy spectrum. Moreover, the effect in each energy bin is the independent. So
the correlation between each energy bin should be considered in evaluating the systematic errorof each bin.
The uncertainty in the energy scale and the energy resolution are summarized here.
• Position dependence of the energy scale deviation, (Data-MC)/MC, is measured to bewithin ±0.5 % by LINAC calibration. For the energy resolution, it is within ±2.0 %.
• Energy dependence of the energy scale deviation is also studied using LINAC calibration
data and it is obtained to be within ± 2.0 %• The systematic uncertainty due to the LINAC system itself is 0.33 % for electron energyof 8.9 MeV.
• Directional dependence of the energy scale deviation measured using spallation data isfound to be within ± 0.5 %.
• The uncertainty due to the water transparency measurement is ± 0.22 %.

163

The effect of above uncertainties are obtained are evaluated as follows. In order to simulate
the observed energy spectrum f (Eobs ) given the original spectrum fo (Ee ) which uses SSM BP2000
and 8 B spectrum by Ortiz, the following function is defined:f (Eobs ) =Z ∞f0 (E0 )R(Eobs , Ee )P (Ee )dEe ,(9.29)

0where R(Eobs , Ee ) is a function to simulate the energy resolution, and P (E e ) is a function
for the detection efficiency.
By varying R(Eobs , Ee ) and P (Ee ), one can simulate the expected results that include theuncertainties. Then the effects of the uncertainties can be estimated by comparing the simulated
results with the observed results. The effect of the theoretical uncertainty in the 8 B neutrinoenergy spectrum is estimated in the same way. The estimated systematic errors are given intable 9.5. Figure 9.14 shows the total correlated errors for each energy bin.
Energy4.5-5.0
5.0-5.5
5.5-6.0
6.0-6.5
6.5-7.0
7.0-7.5
7.5-8.0
8.0-8.5
8.5-9.0
9.0-9.5
9.5-10.0
10.0-10.5
10.5-11.0
11.0-11.5
11.5-12.0
12.0-12.5
12.5-13.0
13.0-13.5
13.5-14.0
14.0-20.0

Total error(%)+0.39 -0.20+0.25 -0.16+0.21 -0.16+0.32 -0.33+0.51 -0.56+0.75 -0.81+1.03 -1.07+1.35 -1.35+1.70 -1.65+2.09 -1.97+2.51 -2.32+2.97 -2.71+3.46 -3.15+3.98 -3.64+4.54 -4.20+5.13 -4.81+5.75 -5.47+6.39 -6.18+7.04 -6.90+10.85 -9.45

Error with Res. + Scal.(%)+0.35 -0.19+0.24 -0.16+0.20 -0.16+0.29 -0.30+0.45 -0.50+0.66 -0.71+0.89 -0.93+1.16 -1.16+1.44 -1.40+1.75 -1.65+2.09 -1.93+2.45 -2.24+2.84 -2.60+3.26 -3.00+3.71 -3.45+4.19 -3.96+4.70 -4.52+5.24 -5.12+5.81 -5.75+9.05 -8.32

Error with 8 B(%)
+0.17 -0.08+0.08 -0.01+0.05 -0.01+0.14 -0.13+0.24 -0.25+0.37 -0.39+0.52 -0.54+0.70 -0.69+0.90 -0.87+1.14 -1.06+1.39 -1.27+1.68 -1.51+1.98 -1.78+2.29 -2.07+2.62 -2.39+2.96 -2.73+3.30 -3.09+3.64 -3.45+3.98 -3.81+5.99 -4.49

Table 9.5: The numerical results for the correlated error.

9.4.2

Uncorrelated error

Trigger efficiency
The trigger efficiency dependents on the vertex position and water transparency. These dependences are considered in the solar neutrino MC simulation. The systematic error with the trigger
efficiency is estimated by comparing the measured trigger efficiency with the trigger simulationof the solar neutrino MC. The estimation of systematic uncertainty with it is a important factor
of all uncertainties in low energy region, specially 4.5∼5.0 MeV, because the trigger efficiency isexactly relative to the number of hit PMTs. By comparing the measured trigger efficiency withthe trigger efficiency of the solar neutrino MC, the precision of the solar neutrino MC simulation
is evaluated.
164

× 100(%)

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

4

6

8

10

12

14

16

18

20

Ee (MeV)Figure 9.14: The total correlated errors for each energy bin.

For the LE trigger, the efficiency is almost 100% above 6.5 MeV. The summary of LE trigger
efficiency is presented in table 9.6. In the energy region from 6.5 to 7.0 MeV and from 7.0
to 7.5 MeV, the uncertainties with the trigger efficiencies are ±0.3% and ±0.1% respectively.
The result is obtained by the maximum deviation between the DT calibration data and solar
neutrino MC considering the live time in the period of each trigger threshold.
LE threshold
Data set I-320 mV(R1742-R8239)-302 mV(R8239-R10417)
Data set II-320 mV(R7859-R8239)-302 mV(R8239-R10417)
Data set III-320 mV(R7859-R8239)-302 mV(R8239-R10417)

Energy (50%/95% trigger efficiency)

Live time

5.5 MeV/6.3 MeV
5.4 MeV/6.1 MeV

1013.8 days (for 1496 days)
483.3 days (for 1496 days)

5.5 MeV/6.3 MeV
5.4 MeV/6.1 MeV

83.7 days (for 566 days)
483.3 days (for 566 days)

5.5 MeV/6.3 MeV
5.4 MeV/6.1 MeV

78.6 days (for 511 days)
433.9 days (for 511 days)

Table 9.6: The summary of the LE trigger efficiency.
The details of the SLE trigger efficiency is already described in chapter 8. For the SLE
trigger, the trigger efficiency varies with the hardware threshold change. The trigger efficiency
is measured for every SLE trigger threshold by DT calibration described in chapter 5. The result
is obtained by the maximum deviation between the DT calibration data and solar neutrino MC
considering the live time in the period of each trigger threshold. Table 9.7 shows the summaryof the live time average of SLE trigger efficiency by DT calibration in 4.5∼5.0 MeV.
Figure 9.15 shows the progress of the simulated trigger efficiency by solar neutrino MC andthe live time average of the trigger efficiency by the DT calibration. The solid lines in the figure
present the DT calibration in each trigger threshold. The dot points present the simulated
trigger efficiency by the solar neutrino MC.
Figure 9.16 shows the summary of the live time average of the trigger efficiency for the solar
neutrino MC and DT calibration in each trigger threshold. The MC is almost consistent with165

SLE threshold-260 mV-250 mV-222 mV-212 mV-186 mV

Trigger efficiency
70.8 %
82.1 %
97.7 %
87.2 %
99.9 %

Efficiency(DT,B8MC)(%)

Table 9.7: The summary of the live time average of the SLE trigger efficiency by the DT
calibration in 4.5∼5.0 MeV.

102

101

   

10099

  

98

97

96

95

94

8000

8500

9000

9500

10000

Run number

Figure 9.15: The progress of the simulated trigger efficiency by solar neutrino MC and the live
time average of the trigger efficiency by the DT calibration.

166

Trigger Efficiency(%)

DT data.
105

102.5

   

100

97.5

95

92.5

B8MC

90

87.5

DT

85

82.5

80
−230

−225

−220

−215

−210

−205

−200

−195

−190

−185

−180

SLE threshold

Figure 9.16: The summary of the trigger efficiency for the solar neutrino MC and the DT
calibration in each trigger threshold.
Table 9.8 shows the numerical results of uncertainties with the trigger efficiency for eachenergy region.
Energy region
4.5 - 5.0
5.0 - 5.5
5.5 - 6.0
6.0 - 6.5
6.5 - 7.0
7.0 - 7.5
7.5 - 20.0

Uncertainty (Data set III)
±1.1%
±0.4%
±0.7%
±0.4%
±0.3%
±0.1%
±0.0%

Uncertainty (Data set I,II)+2.2 -1.0 %+0.6 -0.3 %+0.0 -0.0 %+0.2 -0.2 %+0.0 -0.0 %+0.0 -0.0 %Table 9.8: The numerical results of uncertainties with the trigger efficiency for each energy
region.

IT trigger efficiency
The systematic error due to the IT is studied using the Ni-Cf source. The deviation between
the reduction efficiency of the IT data and that for Ni-Cf MC simulation is calculated at various
positions in the ID. The volume average of those deviations in each energy bin is obtained intable 9.9.
1st reduction
The systematic error due to reduction comes from the reduction efficiency between data andMC simulation. In 1st reduction, the relatively largest systematic errors come from flasher cuts.
The reduction efficiency of the flasher cut is obtained by comparing the reduction efficiency
is spallation event data with that in 8 B The deviation (Data-MC)/MC is less than ± 0.3%.
Table 9.10 shows the summary.
167

Energy region
4.5 - 5.0
5.0 - 5.5
5.5 - 6.0
6.0 - 6.5
6.5 - 7.0
7.0 - 20.0

Uncertainty (Data set III)
±1.1%
±1.1%
±0.5%
±0.1%
±0.0%
±0.0%

Uncertainty (Data set I,II)
±1.1%
±0.5%
±0.1%
±0.0%
±0.0%

Table 9.9: The uncertainty with the IT trigger efficiency.
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.3%
±0.3%

Uncertainty (Data set I,II)±0.3%

Table 9.10: The uncertainty with the 1st reduction.
Spallation cut
The uncertainty with the spallation cut is due to spallation dead time. The position dependentsof the spallation dead time is presented in the figure of chapter 6, and it is used to simulate thespallation cut in MC simulation. The systematic error due to this position dependence of thedead time is estimated to be 0.05% by comparing the dead time calculated in MC with the deadtime calculated from data. This uncertainty is considered only for flux measurement.
Flux
Total flux

Uncertainty (Data set III)
±0.3%

Uncertainty (Data set I,II)±0.2%

Table 9.11: The uncertainty with the spallation cut.

2nd reduction
The systematic uncertainty with the GRINGO cut is obtained using the LINAC (or Ni-Cf)
calibration data at various positions and the LINAC (or Ni-Cf) MC at each corresponding
position. In order to obtain the energy dependence of the uncertainty, a volume average iscalculated. In 4.5∼5.0 energy region, the deviation (Data-MC)/MC is calculated using the
LINAC calibration. Above 5.0 MeV data, the deviation (Data-MC)/MC is calculated using the
Ni-Cf calibration.
The systematic uncertainty with the Cluster fit cut is estimated using Ni-Cf calibration data
at various positions.
The systematic uncertainty caused by PATLIK cut is estimated using LINAC data and
LINAC MC in 4.5∼5.0 energy region. The deviation (Data-MC)/MC is calculated using the
LINAC calibration. In SK-I full data set, the systematic error is estimated using spallation
products with short time (∼30 msec). The reduction efficiency for the spallation events iscompared with that in solar neutrino MC simulation.
Gamma cut
The gamma cut uses the reconstructed vertex and direction in events. So the differences of vertex
and angular resolution between data and MC simulation introduce systematic uncertainties. To
estimate the influence of these differences, the following method is adopted.
168

Cut
GRINGO cut
Cluster cut
PATLIK cut
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±1.2% (<5.0 MeV)
±0.3% (<5.0 MeV)
±1.9% (<5.0 MeV)
Total error (Data set III)
±2.3%
±0.8%

Uncertainty (Data set I,II)±0.2% (>5.0 MeV)
±0.3% (>5.0 MeV)
±0.7% (>5.0 MeV)
Total error (Data set I,II)±0.8%

Table 9.12: The uncertainty with the 2nd reduction.
1. Shift the reconstructed vertices and direction of events within the differences in the vertex
and angular resolution between data and MC.
2. Apply the gamma cut to the modified data and compare the reduction efficiency with theresult of original data.
The used differences in the vertex and angular resolution are measured with LINAC as
described in chapter 5.
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.1%
±0.1%

Uncertainty (Data set I,II)±0.1%

Table 9.13: The uncertainty with the gamma cut.

Tight data reduction for 4.5sim5.0 MeV data
The systematic uncertainties for new installed tight data reduction is also estimated in thistime. The systematic errors for strong GRINGO cut, fiducial volume cut, and PATLIK cut
with BONSAI reconstructed vertex information is calculated using the LINAC calibration data.
The errors are estimated the deviation (Data-MC)/MC of the LINAC calibration for each reduction. The systematic errors for the strong gamma cut and strong gamma cut with BONSAI
reconstructed vertex information is estimated by above described method.
Cut
Strong GAMMA cut
Strong GRINGO cut
F.V cut with BONSAI vertex
GAMMA cut with BONSAI vertex
PATLIK cut with BONSAI vertex
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.2% (4.5 - 20.0 MeV)
±1.3%
±0.2% (4.5 - 20.0 MeV)
±0.4% (4.5 - 20.0 MeV)
±2.0% (4.5 - 20.0 MeV)
Uncertainty (Data set III)
±2.4%
±2.4%

Uncertainty (Data set I,II)
Uncertainty (Data set I,II)-

Table 9.14: The uncertainty with the tight data reduction for the 4.5∼5.0 MeV data analysis.

Vertex shift
Systematic shifts in the reconstructed vertex relative to the original vertex is studied with Ni-Cf
calibration at various positions.
169

Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.2%
±0.2%

Uncertainty (Data set I,II)±0.2%

Table 9.15: The uncertainty with the vertex-shift.
Non-flat Background

Probability density

Non-flat background shape is the largest systematic uncertainty in all systematic uncertainties
for the energy spectrum analysis above 4.5 MeV, because the fluctuation of background becomeslarge in lower energy region by the remaining radon and gamma rays background.
In order to obtain the background shape used in the solar neutrino signal extraction, it
is assumed that the background is independent of azimuth angle φ. So, the asymmetry is
considered about θ. But, the φ asymmetry in the energy scale and background sources withpossible asymmetric φ distribution may introduce deviations from flatness in the backgroundcos θsun distribution.
So the difference between the originally measured signal events and the obtained using thebackground shape considering energy scale φ asymmetry and flatness background is treated as
the systematic error.
Figure 9.17 shows the background shapes for each asymmetries and flatness in energy region
from 4.5 to 5.0 MeV. The solid flat line indicates the flatness background. The solid wavingline indicates the θ asymmetry background. The dashed line indicates the background shapeconsidering about φ asymmetry.
2.7

2.65

2.6

2.55

2.5

2.45

2.4

2.35

2.3

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

ALL

Figure 9.17: The fluctuation of probability function of P bg as cos θsun function.

Angular resolution
The measured angular resolution in MC simulation is slightly worse than in data as describedin chapter 5. In solar neutrino signal extraction, the MC angular resolution is corrected sothat it agrees with data. The systematic uncertainty due to angular resolution is the difference
between the number of the obtained signal events using the MC angular resolution and using
the corrected angular resolution.
170

Energy region
4.5 - 5.0
5.0 - 5.5
5.5 - 6.0
6.0 - 6.5
6.5 - 7.0
7.0 - 20.0

Uncertainty (Data set III)
±4.5%
±0.5%
±0.5%
±0.3%
±0.3%
±0.1%

Uncertainty (Data set I,II)
±0.6%
±0.5%
±0.1%
±0.1%
±0.1%

Table 9.16: The uncertainty with the non-flat background.
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±1.0%
±1.0%

Uncertainty (Data set I,II)±1.0%

Table 9.17: The uncertainty with the angular resolution.
Likelihood fit resolution
The solar signal extraction is done by the likelihood function fit. Therefore, the signal extraction
is dependent on the numerical method exactly. The systematic uncertainty with likelihood
function fit is estimated as following steps.
1. The background events and the background shape is extracted from the final data sample(cos θsun < 0).
2. Using the energy distribution and cos θ sun distribution of the solar neutrino MC, the signal
is generated by random number basing on Poisson function. This number of signals is true
number.
3. Simulated data is made by combining the extracted background events and the generated
signals. Then, the likelihood fit is applied to this simulated data.
4. The true number of signals is compared with the results from the likelihood fit. The
difference of them is the uncertainty by the numerical method of the solar signal extraction.
Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.5%
±0.5%

Uncertainty (Data set I,II)±1.0%

Table 9.18: The uncertainty with the likelihood fit.

Cross section
The uncertainty with the cross section between neutrino-electron elastic scattering is 0.2% allover energy region.
Live time
The systematic uncertainty due to live-time calculation is evaluated from the difference between
calculations using several different data samples (raw data, muon data or low energy triggered
171

Energy region
4.5 - 5.0
5.0 - 20.0

Uncertainty (Data set III)
±0.2%
±0.2%

Uncertainty (Data set I,II)±0.2%

Table 9.19: The uncertainty with the cross section.
Flux
Total flux

Uncertainty (Data set III)
±0.1%

Uncertainty (Data set I,II)±0.1%

Table 9.20: The uncertainty with the live time calculation.

Error(%)data). The systematic error has an effect on the flux measurement and Day/Night flux measurement.
Figure 9.18 shows the summary of the error for each energy bin. The empty circle means
the error with data set I,II. The filled circle means the error with data set III which include 4.5
MeV data. Table 9.21 is a numerical summary of the figure.
15Black Correlated error
Red UnCorrelated error
Blue Total error

10

5

0

-5

-10

-15

4

6

8

10

12

14

16

18

20

Energy(MeV)

Figure 9.18: The total uncertainty with the energy spectrum.

172

Energy
4.5 5.0
5.0 5.5
5.5 6.0
6.0 6.5
6.5 7.0
7.0 7.5
7.5 8.0
8.0 8.5
8.5 9.0
9.0 9.5
9.5 10.0
10.0 10.5
10.5 11.0
11.0 11.5
11.5 12.0
12.0 12.5
12.5 13.0
13.0 13.5
13.5 14.0
14.0 20.0

Total error(%) for dsIII+5.94 -5.93+3.07 -3.06+2.97 -2.97+2.86 -2.86+2.87 -2.88+2.90 -2.91+2.98 -3.00+3.11 -3.11+3.28 -3.25+3.49 -3.42+3.76 -3.66+4.08 -3.89+4.45 -4.21+4.87 -4.59+5.34 -5.05+5.84 -5.57+6.39 -6.15+6.97 -6.78+7.58 -7.45+11.21 -9.86

Total error(%) for dsI,II+3.54 -2.95+1.65 -1.56+1.39 -1.39+1.46 -1.47+1.55 -1.57+1.70 -1.73+1.91 -1.91+2.17 -2.13+2.49 -2.39+2.85 -2.68+3.26 -3.03+3.71 -3.43+4.21 -3.89+4.74 -4.41+5.31 -5.00+5.90 -5.64+6.53 -6.33+7.17 -7.04
10.94 -9.55

p
Table 9.21: The numerical results for the total error ( Corr2err + Uncorr2err ).

173

Chapter 10

Discussions
In this chapter, the distortion of the solar neutrino energy spectrum and the effect of 4.5∼5.0
MeV bin for the constraints on the solar neutrino oscillation is discussed basing on the resultsof chapter 9. First, the distortion of the solar neutrino energy spectrum is inspected. After
that, the effect of 4.5∼5.0 MeV bin for the constraints on the oscillation parameter decision is
discussed.

10.1

The distortion of solar neutrino energy spectrum

In order to compare the shape of the observed energy spectrum with the expectation of SSM,
the ratio of observed and expected numbers of events for each energy bin is taken; These ratios
are plotted in chapter 9 as Data/SSM.
In order to inspect the distortion caused by solar neutrino oscillation, the observed energy
spectrum is examined using the following χ 2 definition [7]:

2

χ =

1
n
ene n ( Data ) − α ·
o
X
SSM i
ficorr (scl ,res ,b8 ) 2i=1σi+ 2scl + 2res + 2b8

(10.1)

where σi is a 1σ error for each i-th energy bin defined as a sum of statistical error anduncorrelated errors added quadratically, and α is a free parameter which normalizes the measured
8 B solar neutrino flux relative to the expected flux, and f corr is the response function and definedi
as follow:
ficorr = (1 + σi,res × res )(1 + σi,scl × scl )(1 + σi,b8 × b8 )(10.2)

where σi,res , σi,scl , σi,b8 are 1σ errors of the absolute energy scale, the energy resolution,and the expected solar neutrino spectrum shape.  res , scl , b8 are also free parameters used forconstraining the variation of correlated systematic errors.
The minimum value of this χ2 is obtained by numerically varying the free parameters. Table 10.1 shows the summary of the numerical results for the examination.
The resulting minimum χ2 corresponds to an agreement of the measured energy shape withthe expected energy shape at the 51.0 % confidence level, for example, data set I. The rather
poor fit of χ2 for the data set II is due mainly to fluctuation in the observed energy spectrum
at lower energy region unless the statistics is almost enough. This fluctuation comes from thewrongness of S/N ratio without any tight data reduction unless the statistics is smaller than full
data set I. Comparing the χ2 result of data set III with data set I, the result is almost consistent.
This means the data quality of the data set III is good unless the statistics is poorer than thedata set I.
174

Data set
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)

Energy region (d.o.f)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

χ2
17.19
27.23
18.29
20.11

α
0.457
0.453
0.471
0.472

C.L.
51.0%
7.5%
43.7%
38.8%

Table 10.1: The minimum value of this χ 2 is obtained by numerically varying the free parameters
for energy spectrum distortion.
The data set IV indicates the distortion of the solar neutrino energy spectrum. This poorer
fit of χ2 than the χ2 of data set I comes from the rise of the first 4.5∼5.0 energy bin in theobserved spectrum. So, a comparison of the observed recoil electron energy spectrum from solar
neutrino with the expectation exhibits a poorer agreement at the 38.8 % confidence level thanthe energy spectrum of 19 bins. By including the 4.5∼5.0 energy bin, the distortion of theenergy spectrum becomes more certain.

10.2

Constraints on neutrino oscillation from energy spectrum

10.2.1

The allowed solutions from flux measurements

The observed flux in SK is 46.2% for the SSM prediction in full data set I, as described inchapter 9. The Chlorine experiments and Gallium experiments, which sensitive to lower energy
neutrino, also show flux deficits in chapter 2. SNO experiment confirmed flux deficits as well.
From these flux measurement results, 5 solutions resulted from local minimum χ 2 is indicatedby the parameter of two-flavor neutrino oscillation. In order to fit the observed flux from four
experiments, a standard χ2 method is adopted. The definition on χ 2 is as follows:
Nexp

χ2 =

X

−1
(Ridata − Riosc )Vi,j(Rjdata − Rjosc )(10.3)

i,j=1

Nexp is the number of the flux measurements, which is 4 in this analysis. R idata is the ratio of
the measured solar neutrino flux to the SSM predicted flux for each experiment. R iosc is the ratioof the solar neutrino flux calculated assuming neutrino oscillations to the SSM prediction. V i,jis the error matrix which includes errors from the theoretical uncertainty in the solar neutrino
flux. The definition in Vi,j is as follows :
exp 2
cs 2
ssm 2
Vi,j = (σi,j) + (σi,j) + (σi,j)(10.4)

cs is an error matrix which includes the uncertainty in the neutrino cross sections.
where σi,jexp
ssm is an error matrix for the uncertainty in theσi,j is an error matrix for each experiment. σ i,jSSM. The uncertainties in the SSM are as follows :• Uncertainty in the interaction cross section for reactions in the PP-chain and the CNOcycle.
• Uncertainty in the solar luminosity.
• Uncertainty in the abundances of heavy elements.
• Uncertainty in the radiative opacity of the Sun.
175

Mechanism
Vacuum Oscillation
MSW effectGlobal minimum

Solution
Vacuum solution
Quasi vacuum solution
SMA
LMA
LOW
LMA

∆m2
7.9×10 −11
6.7×10−10
4.6×10−6
6.6×10−5
7.2×10−8
6.0×10−5tan2 θ
0.26/3.81.50
0.0016
0.42
0.63
0.42

Table 10.2: The local minimum of χ2 for global analysis of all solar neutrino experiments. (Ga,Cl, SK, and SNO(CC))• Uncertainty in the element diffusion in the Sun.
The local minimum of χ2 is shown in table 10.2. Figure 2.17 shows the iso-χ 2 contours ofχ2 − χ2globalmin corresponding to an allowed region at 95% C.L.. As shown in figure 2.17, there
are several allowed regions.

10.2.2

Constraints from energy spectrum measurements

In this section, the distortion of the energy spectrum is inspected which solution is most flavoredby comparing the observed energy spectrum with the expected energy spectrum by each solution.
The solutions by each allowed regions are described above section.
When the distortion is examined for the expected energy spectrum, in the analysis, χ 2 isdefined as follows.

χ2 =Data exp)i( SSMn
ene n ( Data )data −
o
X
corr
i
SSM
fi
(scl ,res ,b8 ) 2

i=1

σi

+ 2scl + 2res + 2b8

(10.5)

Data exp
The definitions of the parameters in above equation is same as previous section. ( SSM)i isthe ratio of the flux calculated assuming neutrino oscillations to the SSM prediction and defined
as follows.

(

Data exp α × Pi,osc (8 B)φi (8 B) + β × Pi,osc (hep)φi (hep)
)
=
SSM i
φi (8 B) + φi (hep)(10.6)

where Pi,osc (8 B, hep) is the oscillation probability function in i-th energy bin for 8 B and hep
flux, φi (8 B, hep) is the each flux predicted by SSM. α and β are free parameters so that one
can perform a solar model independent analysis of neutrino oscillation parameters. Since theSSM prediction of the hep neutrino flux has large uncertainty, the hep contribution to the recoil
electron spectrum can be treated as an additional free parameter.
Figure 10.1, figure 10.2, and figure 10.3 show the results of comparison between the observed
energy spectrum and expected energy spectrum for each solution. The right plot in the figures is
the results of data set III including 4.5∼5.0 MeV data. The left plot in the figures is the resultsof full data set I without 4.5∼5.0 MeV data. Figure 10.1, figure 10.2, and figure 10.3 are thecomparisons for the vacuum oscillation solutions, the MSW solutions, and the global minimum
χ2 of all solar neutrino experiments respectively. In table 10.3, the summary of the numericalresults for the χ2 examination is presented.
The energy spectrum with 4.5∼5.0 MeV data does not favor the VO and the SMA solutions.
It favors the LMA, the LOW, the Quasi VO solutions at almost same C.L.. However, the full
data set favor LMA and Quasi VO solutions. The dominant factor of this difference is due to176

Data/SSM

Data/SSM

0.8

0.7

0.8

0.7

0.6

0.6

0.5

0.5

0.4

0.4

−10

0.2

−10

Quasi Yellow (1.5,6.7*10 )−11Vacuum Cian (0.26,7.85*10 )

0.3

4

6

8

10

Quasi Yellow (1.5,6.7*10 )−11Vacuum Cian (0.26,7.85*10 )

0.3

12

0.2

14

4

6

8

10

12

Energy14

Energy0.8

Data/SSM

Data/SSM

Figure 10.1: The comparison between the energy spectrum and the expected energy spectrum
for the vacuum oscillation solutions.

0.7

0.8

0.7

0.6

0.6

0.5

0.5

0.4

0.4

−6

0.2

−6

SMA Red (0.0016,4.6*10 )−5
LMA Green (0.42,6.6*10 )−8
LOW Blue (0.63,7.2*10 )

0.3

4

6

8

10

SMA Red (0.0016,4.6*10 )−5
LMA Green (0.42,6.6*10 )−8
LOW Blue (0.63,7.2*10 )

0.3

12

0.2

14

Energy

4

6

8

10

12

14

EnergyFigure 10.2: The comparison between the energy spectrum and the expected energy spectrum
for the MSW solutions.

177

Data set
VO
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)
Quasi VO
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)
SMA
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)
LMA
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)
LOW
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)
Solar best
Data set I(1496d)
Data set II(566d)
Data set III(511d)
Data set IV(511d)

Energy region (d.o.f)

χ2

α

β

C.L.

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

36.86
37.53
27.34
28.15

0.91
0.88
0.91
0.91

1.04
5.36
4.30
4.31

0.5%
0.4%
7.3%
8.1%

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

13.24
24.5
17.51
19.37

0.77
0.75
0.79
0.79

2.50
6.27
2.30
2.49

77.7%
13.9%
48.8%
43.3%

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

28.84
29.79
21.27
24.4

0.98
0.96
0.99
1.01

3.88
3.62
1.01
1.01

5.0%
4.0%
26.6%
18.1%

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

14.82
25.04
18.14
19.78

1.03
1.01
1.05
1.05

6.42
9.00
6.75
6.88

67.4%
12.4%
44.6%
40.8%

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

14.92
24.33
17.63
19.62

0.90
0.87
0.91
0.92

4.91
7.56
4.59
3.90

66.7%
14.4%
48.0%
41.8%

5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
5.0 - 20.0 (19-1=18)
4.5 - 20.0 (20-1=19)

14.69
24.84
18.05
19.72

1.04
1.01
1.06
1.06

6.29
10.45
6.72
6.85

68.3%
12.9%
45.2%
41.1%

Table 10.3: The summary of the numerical results for χ 2 examination for each oscillation solution.

178

Data/SSM

Data/SSM

0.8

0.7

0.8

0.7

0.6

0.6

0.5

0.5

0.4

0.4

−5

−5

Solar Best Red (0.42,6.0*10 )

0.3

0.2

4

6

8

10

Solar Best Red (0.42,6.0*10 )

0.3

12

0.2

14

4

6

8

10

12

Energy14

EnergyFigure 10.3: The comparison between the energy spectrum and the expected energy spectrum
for the global minimum χ2 of all solar neutrino experiments.

the statistical uncertainty with the data set III. The comparison between data set III without
4.5∼5.0 data and data set IV with 4.5∼5.0 data means the 4.5∼5.0 data has no strong effect tothe decision of oscillation solution, because the 4.5∼5.0 has large uncertainty in this analysis.
Although the results of χ2 for 4.5∼5.0 data can not give a impact, one can understand in visualthat the bin of 4.5∼5.0 MeV is key to decide the oscillation parameter.

10.3

Combined constraints on neutrino oscillation

Using the measured flux from the Chlorine and Gallium experiments, SK, SNO, and SK recoil
electron energy spectrum, the allowed regions obtained.
The combinations of the analysis are as follows:• Energy spectrum analysis– Constraints from the flux measurements of all solar neutrino experiments (Chlorine,
Gallium, SK, and SNO). : make allowed region (Green area in the contour plot).
– Constraints from the energy spectrum measurements by SSM independent analysis(flux(rate) not constrained). : make excluded region (Orange area in the contourplot).
Nexp

χ

2

=

X

−1
(Ridata − Riosc )Vi,j(Rjdata − Rjosc )

i,j=1

+

Data exp( SSM)in
ene n ( Data )data −
o
X
SSM i
ficorr (scl ,res ,b8 ) 2

i=1

σi

+ 2scl + 2res + 2b8

(10.7)

where α and β are free parameters.
• Energy spectrum and global analysis– Constraints from the flux measurements of all solar neutrino experiments (Chlorine,
Gallium, SK, and SNO). : make allowed region (Green area in the contour plot).
179

– Constraints from the energy spectrum measurements by SSM independent analysis(flux(rate) not constrained). : make excluded region (Orange area in the contourplot).
– Constraints from the energy spectrum measurements by SSM dependent analysis(flux(rate) constrained). : make allowed region. (Sky blue area in the contour plot).
Nexp

χ2 =

X

−1
(Ridata − Riosc )Vi,j(Rjdata − Rjosc )

i,j=1

+

Data exp( SSM)in
ene n ( Data )data −
o
X
corr
i
SSM
fi
(scl ,res ,b8 ) 2

σi

i=1

+

+ 2scl + 2res + 2b8

Data exp)i( SSMn
ene n ( Data )data − γ ·
o
X
SSM i
ficorr (scl ,res ,b8 ) 2

σi

i=1

+ 2scl + 2res + 2b8 + 2γ(10.8)

where γ is a free parameter which is constrained by the SSM flux. The uncertainty in γ
comes from the uncertainty in the 8 B neutrino flux. The γ is the error factor due to theuncertainty in the 8 B neutrino flux.
• Energy spectrum and global analysis with SNO(CC) flux constraints– Constraints from the flux measurements of all solar neutrino experiments (Chlorine,
Gallium, SK, and SNO). : make allowed region (Green area in the contour plot).
– Constraints from the energy spectrum measurements by SSM independent analysis(flux(rate) not constrained). : make excluded region (Orange area in the contourplot).
– Constraints from the energy spectrum measurements by SSM dependent analysis(flux(rate) constrained by SNO(CC) result). : make allowed region (Sky blue area inthe contour plot).
Nexp

χ

2

=

X

−1
(Ridata − Riosc )Vi,j(Rjdata − Rjosc )

i,j=1

+

Data exp)i( SSMn
ene n ( Data )data −
o
X
SSM i
ficorr (scl ,res ,b8 ) 2

i=1

+

σi

+ 2scl + 2res + 2b8

Data exp( SSM)in
ene n ( Data )data − γ ·
o
X
corr
SSM i
fi
(scl ,res ,b8 ) 2

i=1

σi

+ 2scl + 2res + 2b8 + 2γ(10.9)

where γ is a free parameter which is constrained by the SNO(CC) flux measurement. The
uncertainty in γ comes from the uncertainty in the result of 8 B neutrino flux measurementby SNO(CC) flux measurement. The γ is the error factor due to the uncertainty of the
8 B neutrino flux by SNO(CC) flux measurement.
Figure 10.4, figure 10.5 and figure 10.6 shows the allowed and excluded regions in “ Energy
spectrum analysis”, “Energy spectrum and global analysis” and “Energy spectrum and global
analysis with SNO(CC) flux constraints” respectively. In the figure 10.4, the distortion of recoil
electron energy spectrum excluded the solutions of the Vacuum, the Quasi Vacuum oscillation
and almost all of the SMA just by itself. In the global analysis with the SNO(CC) flux constraint,
the LOW and a part of the LMA solution is favored by the distortion of the energy spectrum.
180

2
2

∆m in eV

10
10
10
10
10
10
10
10
10
10

−3

SK 511 Days,20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7
excluded(rate not−8 constrained)−9
allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

2∆m in eV2

Figure 10.4: The allowed and excluded region in “ Energy spectrum analysis”.

10
10
10
10
10

−3

SK 511 Days, 20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7

excluded(rate not−8 constrained) allowed
10(rate con−strained tosolar model)

10
10
10
10

−9

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

Figure 10.5: The allowed and excluded region in “ Energy spectrum and global analysis”

181

2
2

∆m in eV

10
10
10
10
10

−3

SK 511 Days, 20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7

excluded(rate not−8 constrained) allowed
10(rate con−strained by
SNO CC)

10
10
10
10

−9

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

Figure 10.6: The allowed and excluded region in “Energy spectrum and global analysis with
SNO(CC) constrain”.

Figure 10.7 shows the comparison of the global analysis with the SNO(CC) flux constraint
between the data set II without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV data.
The excluded region becomes large in the SMA allowed region and the allowed region becomes
small in the LMA region. The dominant factor for the changes are the new added bin (4.5∼5.0
MeV) in spite of the low statistics of the data set IV.
Figure 10.8 shows the comparison of the global analysis with SNO(CC) flux constraints
between the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV
data. The difference is just number of bins. The excluded region in the SMA solution becomesslightly large. But, the energy bin from 4.5 to 5.0 MeV has no effect on the LMA allowed region
in this analysis. This is why the statistical uncertainty is still large for the decision for the LMA
solution.

182

2
2

∆m in eV

10
10
10
10
10

−3

SK 566 Days, 22.5 kton w/o 4.5 − 5.0 MeV
−4

−5

−6

−7

excluded(rate not−8 constrained) allowed
10(rate con−strained by
SNO CC)

10
10
10
10

−9

−10

−11

−12

2

∆m in eV

2

10
10
10
10
10
10
10
10
10
10
10

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

−3

10
10
2
tan (Θ)2

SK 511 Days, 20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7
excluded(rate not−8 constrained) allowed(rate con−strained by
SNO CC)−9

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

Figure 10.7: The comparison of the global analysis with the SNO(CC) flux constraint between
the data set II without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV data.

183

2
2

∆m in eV

10
10
10
10
10

−3

SK 511 Days, 20.5 kton w/o 4.5 − 5.0 MeV
−4

−5

−6

−7

excluded(rate not−8 constrained) allowed
10(rate con−strained by
SNO CC)

10
10
10
10

−9

−10

−11

−12

2

∆m in eV

2

10
10
10
10
10
10
10
10
10
10
10

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

−3

10
10
2
tan (Θ)2

SK 511 Days, 20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7
excluded(rate not−8 constrained) allowed(rate con−strained by
SNO CC)−9

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

Figure 10.8: The comparison of the global analysis with the SNO(CC) flux constraint between
the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV data.

184

Chapter 11

Conclusions and future prospect
11.1

Conclusions

SK-I observed the flux of the energy region from 4.5 to 5.0 MeV for the first time basing on 511
days new data set from the collection from May 31, 1996 to July 15, 2001. SK-I get a clear solar
neutrino peak in the cos θsun distribution of this energy region. The number of signals in thisenergy region is :+43
Nsignal,4.5−5.0 = 722+139−137 (stat.)−43 (syst.).

(11.1)The 8 B solar neutrino flux in the energy region from 4.5 to 5.0 MeV is obtained to be :
+0.19
6
2
Φν (SSMBP2000 , 4.5 − 5.0) = 3.28+0.63−0.62 (stat.)−0.19 (syst.)(×10 /cm /sec)(11.2)The ratio to the SSM prediction is :+0.038
Data/SSM(SSMBP2000 , 4.5 − 5.0) = 0.651+0.13−0.12 (stat.)−0.038 (syst.)(11.3)In this energy region, the deficit of the solar neutrino to the SSM prediction is confirmed byabout 3 sigma.
For the total flux, the ratio to the SSM prediction is obtained to be :+0.028
Data/SSM(SSMBP2000 ) = 0.479+0.014−0.013 (stat.)−0.025 (syst.)(11.4)

This ratio is consistent with the ratio for the 1496 days full data set within 1.3 sigma. It
is concluded that the new data set to analyze 4.5∼5.0 MeV data has no systematic bias. The
new results give the strong credit to the various SK-I results gathered up to now from different
aspect.
The measured recoil electron energy spectrum from 4.5 to 5.0 MeV is presented. The energy
spectrum is examined the distortion to the predicted SSM energy spectrum without the neutrino
oscillation. The probability of the distortion is higher than full data analysis by including 4.5∼5.0
energy bin.
The energy spectrum is inspected which neutrino oscillation solution is most flavored bycomparing with the expected energy spectrum of each solution in the SSM independent analysis.
It is confirmed the 4.5∼5.0 MeV bin indicates the tendency of the LMA solution energy spectrum.
In combined constraints on neutrino oscillation, the excluded and allowed regions were obtained by the energy spectrum with 4.5∼5.0 MeV data. Almost of the SMA, all of vacuum

185solution and quasi vacuum solution is excluded at 95% C.L. only by SK energy spectrum measurements. By combined global analysis, a part of the LMA solution were also excluded at 95%
C.L.. From the various comparisons between with 4.5∼5.0 MeV data and without 4.5∼5.0 MeV
data, it is found that the allowed region around the LMA solution becomes slightly small andexcluded regions around the SMA solution becomes slightly large. The 4.5∼5.0 MeV data has
an effect on the decision of the oscillation parameter.
However, the statistical uncertainty of the 4.5∼5.0 MeV data is too large to discuss thedecision of the oscillation parameter. In order to make this energy bin effective, we need morestatistics of this energy bin with the smaller background.

11.2

Future prospect

Figure 11.1 shows the result of KamLAND (Kamioka Liquid scintillator Anti Neutrino Detector)
experiment which has observe the disappearance of the anti-electron neutrino coming from thereactor [20]. The allowed region for neutrino two flavor oscillation by KamLAND is shown withthe result of the global analysis for solar neutrino experiments (Chlorine, Gallium, SK, SNO).
KamLAND also confirmed LMA solution as a most favored neutrino oscillation mechanism froma different point of view. The following equations are the oscillation probability and the best fit
values for oscillation parameters in KamLAND Nails Neutrino Oscillations.
Pνe →νe = 0.611 ± 0.085 ± 0.041∆m2 = 6.9 × 10−5 eV2 , tan2 θ = 0.0(11.5)

Figure 11.2 shows the result of this thesis including 4.5∼5.0 MeV data overlaid with the
expected spectrum of KamLAND result.
So, now, solar neutrino observation is shifting new phase. So far, it is searched whether thesolar neutrino oscillation is correct or not and which oscillation solution is true. Now, we cansearch what parameter number of LMA solution is. In the figure 11.1, the green line shows the
expected constraints by the asymmetry between day and night time flux.
To determine the oscillation parameter,• We need more statistics, (the statistical uncertainty with asymmetry between day andnight time flux is 2 times larger than the systematic uncertainty.)• We need to observe the lower energy spectrum with high statistics.
It is important to improve the S/N ratio in the low energy region as much as possible inorder to satisfy above requirements in the future. All solar neutrino experiments locate inunderground. Radon is the most dominant source of the background for the solar neutrino observation. So, primary subjects is to reduce radon background in all solar neutrino experiments.
Our development of the technique to lower energy threshold will be useful in the future.
In SK detector, the dominant background source is the radon transported by the water
convection from PMTs. In SK-II, PMTs are covered with acrylic case. And, the controller
system of the water convection is installed in the tank of the SK-II detector. We confirmed
the zone of the water convection becomes smaller than SK-I by measuring the temperature in
the SK-II tank. Figure 11.3 shows the water temperature with height of the SK-I tank and the
SK-II tank.
The zone of the water convection in the SK-II becomes smaller than the SK-I by the effectof controller system. In the future, we can hope to lower the energy threshold and improve theS/N ratio in the solar neutrino observation.

186

2

-3

Data/SSM

2∆m in eV

10

0.1%

0.8

0.7

0.32%
0.6

10

-4

1%
0.5

3.2%
0.4

10%
-5

10

νe→νµ/τ (95%C.L.)
-1

1

0.2

2

tan (Θ)Temperature (degree)

6

8

10

12

14

EnergyFigure 11.1: The KamLAND result isoverlaid with the results of global analysis
for solar neutrino experiments (Chlorine,
Gallium, SK, SNO). [2]

4

Figure 11.2: The expected spectrum from
KamLAND result and the energy spectrum of this thesis with 4.5∼5.0 MeV
data.

12.9
13.74

Effect of water convection in SKII
12.85

13.72

Effect of water convection in SKI
13.7



13.68

12.8



13.66

12.75

13.64

Temperature (degree)

10−5

KAM Best Red (1.0,6.9*10 )

0.3



12.7

13.62
12.65
13.6

13.58

12.6

13.56
−15

−10

−5

0

5

10

15

12.55

Z (m)

Figure 11.3: The water temperature with the height of the tank in SK-I and SK-II. The box
with solid line and dashed line shows the SK-I and SK-II convection zone in the bottom region
respectively.

187

Appendix A

The 7Be and hep neutrino flux
The most important nuclear physics experiment for solar neutrino research is an accurate measurement of the low energy proton capture rate on 7 Be. The largest astrophysical uncertainties
in the calculation of the 8 B neutrino flux are about 5% [60]. Therefore, the low energy crosssection for the production of 8 B by proton capture on 7 Be must be measured to an accuracy of
5 % in order to prevent this nuclear physics measurement from dominating the error budget in
inferring astrophysical and neutrino properties from solar neutrino experiments.
The flux of the higher energy neutrinos (from 8 B beta-decay) that is measured in the
Kamiokande, Super-Kamiokande, and SNO solar neutrino experiments is proportional to thelow energy value for the proton capture cross section. According to the combined standard
model (standard solar model and standard electroweak theory), the rate measured in the chlorine solar neutrino experiment is also proportional to this cross section. The rate at which 8 B
is produced in the Sun is so slow that the value of the proton capture cross section on 7 Be thatis assumed in the solar model calculations has no perceptible effect on the solar models. This is
the reason for the linear dependence of the 8 B neutrino flux on the 8 B production cross section.
7

Be(beam) + H(target) → 8 B + γ(A.1)

The 3 He +4 He fusion cross section must also be measured more precisely. The uncertainties
in this cross section dominate the uncertainties in the prediction of the 7 Be neutrino flux andare also an important source of uncertainty in the prediction of the 8 B neutrino flux.

A.1

The 7 Be neutrino flux

T he flux of 7 Be solar neutrinos is relatively accurately determined by standard solar models,
but-if one assumes nothing happens to solar neutrinos after they are created-the 7 Be neutrinos
appear to be almost entirely absent in the gallium and chlorine solar neutrino experiments. Thisis one of the most severe aspects of the “solar neutrino problem.” This viewgraph shows thatthe flux of 7 Be solar neutrinos is independent of the rate at which 8 B neutrinos are producedby the relatively less certain cross section for proton capture on 7 Be. The reason is that the
proton capture, which gives rise to 8 B neutrinos, is very much slower than the electron capturethat gives rise to 7 Be neutrinos.
R(e)R(e) + R(p)R(p) ≈ 0.001R(e)φ(7 Be) ∝

(A.2)
(A.3)

The figure A.1 shows the fractional differences between the calculated sound speeds forthe standard model and what may e the most accurate available sound speeds measured by188

helioseismology, the LOWL1 + BiSON measurements presented in Basu et al. (1997) [62].
These sound speeds are derived from a combination of the data obtained by the Birmigham Solar
Oscillation Network(BiSON) and the Low-` instrument (LOWL). The rms fractional difference
between the calculated and the measured sound speeds is 10.4 × 10 −4 over the entire region inwhich the sound speeds are well measured, 0.05 ≤ r ≤ 0.95R . In the solar core, 0.05 ≤ r ≤0.25R (in which about 95%of the solar energy and neutrino flux are produced in a standard
solar model), the rms fractional difference 6.3 × 10 −4 . The standard model sound speeds agreewith the measured sound speeds to 0.1% whether or not one limits the comparison to the solar
interior or averages over the entire Sun. Systematic uncertainties ∼ 3 × 10 −4 are contributes
to the sound speed profile by each of three sources: the assumed reference model, the width of
the inversion kernel, and the measurement errors(BPB00 [62]). The vertical scale of the figure
was chosen so as to include the arrow marked “ 7 Be lowered (σ off Ga)”. This arrow indicates
the typical difference between solar model speeds and helioseismological measurements thatwould be expected if the discrepancy between the gallium solar neutrino measurements and thepredictions were due to errors in the solar physic of the standard solar model (BBP98 [63]).
The figure shows the excellent agreement between the calculated sound speeds for the Standard solar model (BP2000) and the helioseismologically measured (Sun) sound speeds. The
horizontal line at 0.0 represents the hypothetical case in which the calculated sound speeds andthe measured sound speeds agree exactly everywhere in the Sun. The rms fractional difference between the calculated and the measured sound speeds is 0.10% for all solar radii between
between 0.05 R and 0.95 R and is 0.08% for the deep interior region, r 0.25 R , in which
neutrinos are produced. Taken from figure A.2 of “Solar Models: current epoch and time dependences of normalized luminosity”.

Figure A.1: Predicted versus measured sound speeds. (http://www.sns.ias.edu/ j̃nb/)

A.2

The hep neutrino flux

In the hep neutrino flux calculation of the BP2000, the most recent and detailed calculation(Marcucci et al. 2000a [64]) is used for the S 0 -factor for the 3 He(p, e+ +νe )4 He reaction:S0 (hep) =10.1 × 10−20 keVb, which is a factor of 4.4 times larger than the previous best estimate. For
values of S0 (hep) in the range of current estimates, the assumed rate of the hep-reaction only
affects in a noticeable way the calculation flux of hep neutrinos and does not affect the calculated

189

Figure A.2: Normalized solar luminosity vs. solar age for the standard solar model (solid curve)
and for three ”deficient” solar models: the No Diffusion model (dotted curve), the S 34 = 0 model(short-dashed curve), and the Mixed model (long-dashed curve). (http://www.sns.ias.edu/ j̃nb/)
flux fluxes of other neutrinos, helioseismological characteristics, or other physical properties of
the Sun.
An estimated uncertainty for the hep flux is not quoted. The difficulty of calculating fromfirst principles the nuclear cross section factor S 0 (hep) is an uncertainty in the hep flux. The
hep-reaction is uniquely difficult to calculate among the light-element fusion reactions since theone-body and two-body contributions to the reaction rate are comparable in magnitude but
opposite in sign, so that the net results is sensitive to a delicate cancellation. Also two-body
axial currents from excitations of δ isobars are model dependent. In addition, the calculated
rate is sensitive to a small components in the wave function, particularly D − state admixture
generated by tensor interactions. These complications have been discussed most recently andmost throughly by Marcucci et al. (2000b).
From the analysis using the recoil electron energy spectrum from 18 MeV to 25 MeV in 1496
days of data, the preliminary upper limit of the hep neutrino is obtained to be 7.9 times the hep
flux predicted by the SSM (BP2000).

190

Appendix B

Detector simulation
In order to investigate solar neutrino physics, the detector response for solar neutrino events has
to be known. In order to understand the detector response, a Monte Carol (MC) simulation of
the detector is carried out. The simulation program is based on GEANT [91] which is developedat CERN (European laboratory for particle physics). The program reproduces the behavior ofelectrons and photons in materials faithfully with the consideration of physical processes such as
Coulomb multiple scattering, ionization loss, bremsstrahlung, etc. for electrons, and Compton
scattering, pair creation, etc. for photons in energy range of a few keV to a few TeV.
In the SK detector simulation, the production and propagation of Čerenkov photons generated by recoil electrons have to be considered also [99]. The production of these is based onequation (3.2). The propagation of these is slightly complicated. When the Čerenkov photons
travel in water, they suffer Rayleigh scattering and absorption. Rayleigh scattering is dominatedfor short wavelength (λ ≤400nm) due to wavelength dependence of ∝ 1/λ 4 , and the absorption
effect is dominant for long wavelength (λ ≥ 400nm). These effects are related to the water
attenuation length. The theoretical wavelength dependence of Rayleigh scattering and absorption are calculated [80] separately, however, the magnitude of these effects is not known sincethese factors depend on the purity of water. Therefore, these parameters are tuned in the MC.
These parameters with a collection factor (described later) are turned so that the simulation of
the LINAC calibration (see chapter 5) reproduces the real data. In figure B.1, the wavelength
dependence of attenuation coefficient for light in the water in SK, which is calculated from thetuned parameters, is shown together with the results of a direct measurement (A description ofthis direct measurement is given in chapter 5.).
The speed of Čerenkov light in water depends on the wavelength. The speed is the groupvelocity vg which is given by:
vg =

c
dn(λ)
n(λ) − λdλ(B.1)

where n(λ) is index of refraction as a function of wavelength λ and is parameterized as [81]:ra1+ a 2 + a 3 λ2 + a 4 λ4 + a 5 λ6
(B.2)n(λ) =2λ − λ2a
The unit of λ is µm and the parameters are tabulated in table B.1. These values were obtainedby fitting equation (B.2) to the results of measurements. This index of refraction and groupvelocity is also put into the detector simulation.
The Čerenkov photons are reflected by the surface of PMTs and black sheet. The reflectivities
of PMT and black sheet are calculated under the law of optics (The structure of the surface
of a PMT is composed of 4mm thickness glass (n = 1.47) and 20nm thickness bi-alkali (n =3.50)and the layer of bi-alkali is inside of the glass layer. The index of refraction of black sheet(polyethylene) is 1.6.) and the results are again put into the simulation. The polarization of
191attenuation coefficient(1/m)

10measurement

1

-1

10

-2

10

-3

10

250

300

350

400

450

500

550

600

650

700

750

wave length (nm)Figure B.1: The water attenuation coefficient for the water in SK tank which is calculated fromthe tuned parameter. Open marks are the measured value (see chapter 5).

parameter
λ2a
a1
a2
a3
a4
a5

value
0.018085
5.743534×10−3
1.769238-2.797222×10−2
8.715348×10−3-1.413942×10−3

Table B.1: The values of parameters in equation (B.2).

192

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

averagep-waves-wave

0

20

40

(a)

60

80

reflectivity

reflectivityČerenkov photon is considered at the reflection step. The reflectivities of the PMT and black
sheet are shown in figure B.2 for p-wave and s-wave and the average of both polarization.

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

incident angle

averagep-waves-wave

0

20

40

(b)

60

80

incident angle

Figure B.2: The reflectivity of the PMT and black sheet. Figure(a) is for black sheet and (b)for the PMT. The horizontal axis of each figure is the incident angle (degree) and the verticalaxis is reflectivity.
The PMT response to Čerenkov photons has to be considered. To begin with, the wavelength
dependence of the quantum efficiency (see figure 3.12), which was measured by HAMAMATSU,
is taken into account. For a solar neutrino event, most PMTs are given only 1 photo-electron,
therefore it is important to know the output charge distribution of a PMT which is given bya single photo-electron, in order to choose the threshold on the analog signals at the ATM.
This distribution is measured using the Ni-Cf source. A typical distribution of output charges
in response to single photo-electron hits is shown in figure B.3. The output charge in the MC
simulation is determined by random number distribution of figure B.3. The time resolution ofa PMT is also taken into account. The resolution is calibrated using the vertex resolution of
LINAC data.
Finally, the contribution of the dark noise is taken into account. PMT dark noise is simulatedby distributing random hits according to the observed average dark rate of the ID PMTs. The
charge for these hits is distributed according to the single photo-electron distribution. The
dynode collection efficiency, which is the probability that an electron generated by the photoelectric effect reaches the dynode, is not known. Accordingly, this factor is also tuned in theMC simulation.
The ID-PMTs have two kinds of after-pulses. One after-pulse arrives about 15µsec after thesignal. This kind of after-pulse happens when a large amount of Čerenkov photons (greater than
400p.e.) hit the PMT. The reason is that the many electrons generated by the photons ionize
the remaining gas in the PMT on their way from cathode to dynode. The ions move to thecathode with a smaller velocity due to their large mass, and many electrons are generated again
when the ions hit the cathode. Another after-pulse, which is more serious for solar neutrino
observation, arrives about 100nsec after signal. This after-pulse is caused by an electron whichis scattered by the first dynode elastically and goes back to the dynode with a time lag. As
a result, the timing response of the PMT can be delayed by about 100nsec. In the detector
simulation, this after-pulse is generated with 2% probability, which is measured by LINAC andNi-Cf calibration, and a time delay which is distributed in a Gaussian of 10nsec width and a
193

1

-1

10

-2

10

-2

0

2

4

1 p.e. distribution

6

8

10

(pC)

Figure B.3: The charge distribution of a PMT after a single photo-electron hit.

mean of 100nsec.
The result of the detector simulation is recorded in the same format as real data, and thesame analysis is applied.

194

Appendix C

Reconstruction of cosmic ray muonsCosmic ray muons are generated by the interactions of the primary cosmic ray particles highin the atmosphere. They penetrate 1000m rock and reach the ID at a rate of about 2Hz.
The energetic muons often break 16 O nuclei and produce radioactive elements, which decay byemitting electrons or positrons or γ-rays with energies ranging up to about 20 MeV. Since theenergy of these events is similar to that of the recoil electrons from solar neutrinos, these events(spallation events) become a serious background. In order to reject spallation events, precise
reconstruction of the muon tracks is crucial, because the vertex position of spallation eventsis strongly correlated with the track of the parent muon. In this section, brief explanations ofmuon fitting and quality of the reconstruction are given.
A muon event is defined as an event where the total number of photo-electrons is greaterthan 6000p.e. (For reference, note that if a muon travels 1m in the ID, about 2300p.e. areobserved.) and one PMT exists which recorded a charge greater than 200p.e.. Reconstruction of
the muon event proceeds in two steps. The first step is called ’fast reconstruction’. This methodfinds the entrance point and the exit point of the muon as follows. The entrance position isdefined as the position of the PMT which is hit earliest and has more than 2 neighboring hits
within 5nsec. The exit point is defined as the center of gravity of the PMTs which detect
more than 231p.e. (from now on these PMTs are called ’charge-saturated PMTs’). The trackof the muon is the line connecting the entrance and exit points. The success or failure of thefirst reconstruction method is tested as follows. Two variables are defined: L ent , which is theminimum distance between each charge-saturated PMT position and the entrance point, andLexit , which is the maximum distance between each charge-saturated PMT position and theexit point. If Lent > 300cm and Lexit < 300cm, the reconstruction is regarded as success. Thisrequired condition rejects stopping muons (the muons which stop in the ID) and multiple muon
events (more than 2 muons enter the ID at the same time). The events whose reconstruction
fails go to the second reconstruction step.
When the number of the charge-saturated PMTs is large, the first reconstruction may havefailed. Therefore, events with a residual charge Q res greater than 25,000p.e. are always sent tothe second reconstruction step even though the requirements on L ent and Lexit in the first step
are met. Qres is defined by:
Qres = Qtotal − pL

(C.1)

and Qtotal is the total photo-electrons observed in the event, L(cm) is the track length, andp = 23p.e./cm is the average number of observed photo-electrons per unit track length formuons.
The second step reconstruction is based on the vertex reconstruction method of solar neutrino
events. The difference is that the track of a muon is not point-like. In this reconstruction method,the entrance point is same as that used by the fast reconstruction method and the exit point is

195searched for so as to maximize the goodness g µ defined by:
(
 )

X 1
1 ti − T 2
2 exp − 2
1.5σi
σ
i
i
gµ =
X 1
i

ti = Ti (xi ) −

(C.2)

σi2

lµ (xexit ) lphoton (xexit )
−
c
c0

(C.3)

where xexit is the exit point and T is the arrival time of the muon. l µ (xexit ) and lphoton (xexit ) aredefined in figure C.1. If Lent > 300cm, Lexit < 300cm and gµ > 0.88, this muon fit is regarded

xent

lphoton ( xexit )l µ ( xexit )i-th PMT
42xexit

cosmic ray
muon

Figure C.1: The definition of the variables used by the second muon reconstruction.
as successful. Events which do not satisfy this condition are regarded as unfitted.
The efficiency of the muon event reconstruction is checked by visual inspection for 1000 muon
events. For this purpose, muon events are classified as follows• single muon events : events which contain only a single muon track• stopping muon events : muon events stopping in the ID• hard interaction events : events with Q res ≥25000p.e.
• edge clipping events : muons with track length less than 5m• multiple muon events : events which contain more than or equal to 2 muon tracks
Table C.1 summarizes the fitting efficiency. About 6% of the muon events are not fit.
The precision of the muon track reconstruction is evaluated by comparing the results of above
fitting and manual fitting, which is carried out by visual scan. This comparison is performedin the following way: (1) calculate the distance between the entrance points obtained by bothprogram and manual fits (dent ), (2) calculate the distance between exit points obtained by bothfits (dexit ), (3) define the average distance between them ((d ent + dexit )/2 ≡ d). The distributionof d is shown in figure C.2. The track resolution is defined as shown in figure C.2; i.e. it is the
distance which 68% of all entries fill below. It is evaluated to be 67cm.
196

muon typesingle muon
stopping muon
hard interactionedge clipping
multiple muon
total

number of events
835
10
41
58
56
1000

number of unfitted events
5
8
2
19
28
62

number of events

Table C.1: The fitting efficiency for the classified muon events.

70

67cm (68% included)

60

50

40

30

20

10

0

0

50

100

150

200

250

300

350

400

track resolution of muon (cm)Figure C.2: The track resolution. The resolution is evaluated to be 67cm.

197Appendix D

Systematic uncertainties with
LINAC calibration
D.1

LINAC beam energy calibration

In order to calibrate the SK detector within 1% accuracy, the precise beam energy has to be
known. The beam energy is measured by a Ge detector. The Ge detector has a germanium
crystal of 57.5mm diameter and 66.4mm length. Energy resolution of the detector is 1.92 keV forthe 1.33 MeV γ-rays of 60 Co. Reading out the output charge of the Ge detector and digitizationof it is done by a Multi-Channel-Analyzer. After pulling up the vertical pipe in figure 5.13 anddisconnecting the D3 magnet, the end-cap with the trigger counter is connected horizontally
just before the D3 magnet. The Ge detector is located just after the end-cap. Relation between
deposit energy in the crystal and digital counts is calibrated using γ-rays in energy range from
0.662 MeV of 137 Cs to 9.000 MeV of Ni(n,γ)Ni reaction. Linearity is kept within 0.03% error in
the energy range.
The primary purpose of using a Ge detector is to measure energy of not electrons but γ-rays.
In a case of electrons, they go through a thin beryllium window, which is the entrance windowof it, and inactive region surrounding the Ge crystal before they reach the active region. As aresult, the electrons lose some of their energy before being detected. In order to measure theenergy loss, the Ge detector was calibrated using an air-core beta spectrometer at the Tanashibranch of KEK. A view of the spectrometer is shown in figure D.1. A radioactive elementof β-rays used for that purpose is 207 Bi. A 207 Bi emits a monochromatic electron by internalconversion process with a half life of 38 years. Ratio of momentum spread to momentum ∆p/p
at focus place is about 0.01% [72]. The 975.7 and 1682.2 keV electrons are used to calibrate.
Figure D.2 shows comparisons between background subtracted data and MC simulation, where
the depth of the inactive layer and the thickness of the beryllium window are tuned to be 41µm
and 500µm respectively.
With the knowledge of the energy loss at the Ge detector, energies of the electron beam
injected into the water tank are measured for various D1 magnet electric current. Table D.1
lists correlation of the D1 magnet current and the measured energy by the Ge detector. The
beam energies in the beam pipe are evaluated by taking into account energy losses of the trigger
counter, the Ti window, the Be window and the inactive region by MC simulation. The totalenergy in SK tank is calculated from the evaluated beam momentum and the energy loss of thetrigger counter and the Ti window.
Figure D.3 shows the energy spectrum measured by the Ge detector for various beam momentum with MC simulation. The measurements were done five times for three x positions. The
uncertainty of the beam energy is evaluated by comparing different measurements and estimatedto be ±20 keV for full width.

198

To turbo-molecular pump

Baffle No.3
Baffle No.2

Baffle No.4

40
75cm

12

0

Resolution Adj.
Baffle No.1

π <τωο>Gate valve

Gate valve

GERMANIUM DETECTOR

SOURCE BOX
0

LIQUID N2 TANK

100cm

50cm

events/bin

Figure D.1: A view of the air-core beta spectrometer.

300
250
200
150
100
50

events/bin

0
0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87
MeV

200
150
100
50
0
1.48

1.5

1.52

1.54

1.56

1.58

1.6
MeV

Figure D.2: The results of the Ge detector calibration using the air-core beta spectrometer withthe monochromatic internal conversion electron ray from 207 Bi. The upper figure is for 975 keVand lower figure is for 1682.2 keV electrons.

199

D1 magnet current
(A)
6.0
5.0
4.0
3.2
2.5
2.15
1.8

Ge energy
(MeV)
16.31
13.65
10.99
8.86
7.00
6.03
5.08

beam momentum(MeV/c)
15.44
12.80
10.14
8.03
6.17
5.21
4.25

energy in-tank
(MeV)
16.09
13.44
10.78
8.67
6.79
5.84
4.89

Table D.1: The correlation between the D1 magnet current and the measured energy by the Ge
detector, the beam momentum in the beam pipe and the total energy in SK water tank.

200
100
0

15.2

15.4

15.6

400
300
200
100
0

6

6.2

(MeV)
300

(MeV)
400

200
200

100
0

12.6

0

12.8

5

5.2

(MeV)
600
400
200
0

9.8

10

(MeV)
800
600
400
200
0

10.2

(MeV)

4

4.1

4.2

4.3

4.4

(MeV)

400
300
200
100
0

7.8

8

8.2

(MeV)

Figure D.3: The measurement of the beam momentum by the Ge detector. The cross marks aredata and histograms are MC simulation.

200

D.2

Systematic uncertainty with the LINAC system

In order to confirm that the absolute energy is determined within 1%, systematic uncertaintyof the LINAC calibration system have to be considered. The source of the systematic error isclassified as follows.

D.2.1

Uncertainty of the beam energy determination

This value is determined by measuring the beam energy five times and taking full width of the
distribution for each D1 magnet current, and it is estimated to be ±20 keV for all 7 momenta.

D.2.2

Beam correlated background

When the electron beam is injected to the tank, there is a possibility that beam correlated
background exists. The source of the background is thought to be the γ-rays produced by
the run off electrons, which hit the collimator before the D2 magnet or the vertical beam pipe
between the D3 magnet and the end point of the beam pipe. In order to evaluate level of the
background, data taking with ”empty” (microwave) trigger and ”random” (clock) trigger wasdone. The trigger logic of these trigger modes is shown in figure 5.15. As described above,since the injection rate of single electron is 0.1 per microwave, 90% microwave triggered data
are empty with possible background. By comparing the background level of the empty trigger
data and the random trigger data, the background level is estimated. Differences between the
background level fluctuate around zero, and conservative estimation is done, i.e. averaging over
the absolute values of these differences, and the systematic uncertainty of the beam correlated
background is evaluated to be ±0.16%.

D.2.3

Reflectivity of the end point of the beam pipe

The most serious uncertainty of the LINAC system is reflectivity of the end point cap of thebeam pipe. In the MC simulation, it is found that about 5% Čerenkov photons hit the end
point at the electron momentum of 5 MeV/c. Although the reflectivity of the end point wasmeasured, it is found that there is a possibility that an air bubble is trapped in a hollow space
enclosing the Ti window and the unknown size of the bubble changes the reflectivity of the end
point. In order to estimate the effect, two set of MC simulations for the extreme case of no air
and maximum bubble size are carried out. And conservative uncertainty of this is estimated.
The results are given in table D.2.

D.2.4

Summary

Energy dependence of combined systematic uncertainty (the sum of square of all uncertainties)
is also shown in table D.2. The uncertainty is large for small beam momentum due to the larger
fraction of Čerenkov photons that hit the end point. The systematic uncertainty is shown as
outside error bars in figure 5.24(a).

D.3

The time and directional uniformity of the energy scale

There are two other important aspects for the energy calibration, i.e. the time and directional
uniformity of the energy scale. The former is checked by the spallation events, the Ni-Cf γ-ray
source, and the µ decay electron events. The latter is checked by only the spallation events. In
this section, a description of these two aspects of the energy calibration is given.

201

beam momentum(MeV/c)
16.31
13.65
10.99
8.86
7.00
6.03
5.08

fraction hitting
beam pipe
0.51%
0.67%
0.88%
1.3%
2.2%
3.3%
4.7%

error due toreflectivity±0.06%±0.08%±0.11%±0.18%±0.28%±0.40%±0.68%

total systematic
error±0.21%±0.24%±0.27%±0.33%±0.44%±0.55%±0.81%

Table D.2: The list of the LINAC systematic error.

D.3.1

The time uniformity

number of events

As mentioned in section 5.3, the water transparency have been changing since the beginning ofdata taking of SK. The time variation of the water transparency affects the energy scale of thedetector strongly. In order to correct for the variation, the water transparency obtained by theµ decay electron events is substituted for the equation (4.7) event by event. In order to checkthe validity of the method, radioactive sources, such as the spallation events, the Ni-Cf γ-ray
events and the µ decay electron events, are used.
These products emit β-rays whose energy are similar to that of the recoil electrons scatteredby the solar neutrinos. Further, the elements are produced almost uniformly in space and timein the ID and emit β-rays with uniform direction. Hence, the spallation products are goodcalibrator to investigate the directional and time uniformity of the energy scale of ID. However,branching ratio of the spallation products generated by the interaction is not known in detail,therefore it is difficult to use these radioactive elements as a calibrator for the absolute energy
determination. Figure D.4 shows energy spectrum of the spallation events. In order to study

4500

4000

3500

3000

2500

2000

1500

1000

500

0

0

2

4

6

8

10

12

14

16

18

20

energy (MeV)

Figure D.4: Energy spectrum of the spallation events.
the time variation of the energy scale using the spallation events, the following manipulation isdone. At first, the total spallation sample is separated into time periods. For each period, theenergy scale is changed artificially by multiplying a factor and the energy spectrum of the each202

5total energy (MeV)

factor(%)

period is compared with that of the whole sample. Comparison is done by a χ 2 test in a energy
range of 6.5∼15 MeV. The lower bound of 6.5 MeV is determined by taking into account thetrigger efficiency and Rn event contamination. The upper bound is set to 15 MeV, because,above 15 MeV, statistics of the spallation events become poor. Figure D.5(a) shows the time
variation of the factor. The figure shows that the energy scale is consistent within ±0.5%.
Though the Ni-Cf source has large systematic uncertainty by itself, this source is useful forthis purpose, since only the relative energy scale is important. Unfortunately, the data taking
with this source is not carried out frequently, therefore this source is used for an additional
check. Figure D.5(b) shows the time variation of averaged energy of recoil electrons scatteredby the Ni-Cf γ-rays. This figure shows also that the energy scale is consistent within ±0.5%.
Third radioactive source is the µ decay electron events. The µ decay electron events usedhere are the same as those used for the calculation of the water transparency. Advantages tousing the events for this purpose are that statistics of the events are large and backgroundcontamination is almost negligible. Figure D.5(c) shows the time variation of energy of theevents. One point corresponds to two weeks. The figure also shows that the energy scale isstable within ±0.5%.

(a)

4

8

(b)

7.8

3

±0.5 %±1.0 %

7.6

2

7.4

1
0

7.2

-1
7

-2

6.8

-3
-4
-5

6.6
0

100 200 300 400 500 600 700 800 900

0100 200 300 400 500 600 700 800 900

total energy (MeV)

elapse day from 1996/1/1

elapsed day from 1996/1/1

38

37.5

±0.5 %

37±1.0 %

(c)

36.5
36
35.5
35
34.5
34
33.5
33

0

100

200

300

400

500

600

700

800

900

elapse day from 1996/1/1

Figure D.5: The time variation of the energy scale for three calibration sources. (a) the spallation
events, (b) the Ni-Cf source, (c) the µ decay electron events.

In summary, three radioactive sources indicate that the time variation of the energy scale
for long time period (∼2 years) is stable within ±0.5%.

203D.3.2The directional uniformity(%)

To know the directional uniformity of the energy scale and to extrapolate the precise energy calibration achieved by the LINAC calibration to all directions are quit important when studying
the energy spectrum distortion and the day/night effect caused by the MSW effect. Unfortunately, the only reliable source to check the uniformity is the spallation events. The Ni-Cf
calibration source has directional asymmetry caused by asymmetrical configuration of the Ni
wire and material such a pulling stainless steel wire, a signal cable, etc. The µ decay electron
events have direction dependent energy spectrum due to polarization of the parent stopping
muon.
Figure D.6 shows zenith angle dependence of the energy scale for the spallation events. The
way of estimating the factor is the same as that used for the time variation investigation. The
figure indicates that the directional dependence of the energy scale is consistent within ±0.5%.
5
4
3
2
1
0
-1
-2
-3
-4
-5

-1

-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8
1
cosθz

Figure D.6: The directional dependence of the energy scale.

204

Appendix E

Bad run selection to make data set
The basic unit of the data set is a run. Each run is at most 24 hours long. Each run is divided
into sub-runs, which are about 2∼10 minutes long. The length of each sub-run depends on thetrigger rate.
To make the basic data set, real-time bad run (sub-runs) selection and non-real-time badrun (sub-runs) selection are applied to the all runs in order. The bad run selections are appliedby the unit of Run and Sub-run.

E.1

Real-time bad run selection

First of all, the real-time bad run selection is applied to the all normal runs. At the online
real-time reduction process, obvious bad sub-runs are automatically selected as bad sub-runs.
In this real-time bad run selection, there are 12 categories for bad run selection. So, real-time
bad run selection is done by the following criteria.
1. Run-time with less than 30 seconds (short sub-run)
2. Live-time is less than 0 seconds (abnormal dead-time)
3. Total-run time is less than 300 seconds (short run)
4. Abnormal flasher event rates
rate of flasher events > 0.5Hz(E.1)

5. Abnormal NS-ratio (Noise/Signal ratio) events rates
Number of events with NS-ratio<0.4> 0.01
Total number of events(E.2)

6. Abnormal incomplete event rates
Number of events with incomplete flag
> 0.1
Total number of events(E.3)

7. Abnormal anti mis-match event rates
Number of events with the number of antihit>20> 0.01
Total number of events(E.4)

8. Abnormal Low-goodness event rates
Number of events with goodness<0.4> 0.05
Total number of events
205

(E.5)

9. Abnormal number of bad channel
Number of bad PMTs > 500(E.6)

10. Time difference between TQ(Time and Charge)-real information and muon information
file is greater than 20 %11. Muon rate is less than 1 Hz
12. No muon information table file
Criterion
number
1
2
3
4
5
6
7
8
9
10
11
12

Rejected unit
Number of rejected(Run or Sub-run)Sub-runs
Sub-runs
3270
Sub-runs1593
Sub-runs
1566
Sub-runs
2956
Sub-runs
1977
Sub-runs
3795
Sub-runs
3325
Sub-runs
210
Sub-runs274
Sub-runs
2872
Sub-runs
1131
Sub-runs
121
Total Lost time

Lost time(days)
0.1
1.2
1.8
4.6
7.1
6.8
4.1
0.5
0.4
0.7
2.2
0.5
27.3

Table E.1: The summary of number of the rejected sub-runs by the real-time bad run selection.
The summary of number of the rejected sub-runs by real-time bad run selection is presented
in table E.1 The most largest bad run was selected by Abnormal NS-ratio rates or abnormal
incomplete flag rates. They might be related to the hardware trouble.

E.2

Non-real-time bad run selection

The non-real-time bad run selection is applied all normal Runs after the Real-time bad run
selection. People checked the quality of the runs and sub-runs remaining after real-time bad run
selection manually and reject the bad runs.
The manual bad run selection is applied by the following of selection steps.

E.2.1

Bad run selection• Log book check
Looking the log book and run summary, the useless run is rejected by several persons.
Figure E.1 shows the rejected time by the log book check. The left figure shows therejected time versus the categorized reason. The right figure shows the rejected time by
the log book check for each run number from 1742 to 10417.
• Dark rate
The dark rates are calculated for each run by using the hits before muon events. The
current criteria is 3.2∼3.7 kHz.

206

Lost time(min)Lost time(hours)

180
160
140

1750

1500

120

1250
100

1000

80
60

750
40
20

500

Online test
Online trouble
HV maintenance
OD trouble
No OD data
OD testSome hard ware troubles
LE trigger test
SLE trigger test
LINAC calibration
DT calibration
XE calibration
Not useful data
Water system maintenance
Abnormal system trouble
Test run
A lot of noise
Abnormal high rate by flasher
OD trouble by unknown reason
ID trouble by unknown reason
SLE trigger maintenance
LINAC pipe installed in SK tank
LINAC clibration source on SK tank
Scintilation ball in SK tank0

Category Key words

250

0
2000

4000

6000

8000

10000

Run number
LOST%RUNNUM

Figure E.1: The rejected time by the log book check. The left figure shows the rejected time
versus the categorized reason. The right figure shows the rejected time by the log book checkfor each run number from 1742 to 10417.

• Number of ID/OD bad channels
The run with too many bad channels are removed because there may exist some anisotropy.
The run with too small bad channels are also removed because the bad run selection may
fail.
• Muon event rate
Checking muon files for spallation cut, if muon rate is too small (most case, it becomes 0),
there are something wrong in the muon analysis or file. So, spallation cut is wrong for therun. The sub-runs with too large muon event rate is also removed because muon analysis
has something wrong.
• Delta-T cut event rate
If run is very noisy, the number of event cut by delta-T is increase. The sub-run withtoo large event rate cut by delta-T (this cut is called ”delta-T cut event rate”) is removed
because the quality of the data may differ from the run with usual delta-T cut event rate.
• Pedestal event rate
If there are some hardware trouble around trigger flags, dead-time calculation may become
incorrect. Pedestal event rate is used to monitor whether trigger flag system is working
well or not. We can not judge easily if the pedestal event is too small or not. Therefore,
only the sub-run with too many pedestal events is removed.
• Incomplete event rate
To check hardware trouble around trigger flags, this selection is used. If there are something
wrong about hardware, incomplete event rate becomes too large.
• Strong flasher event rate
We have some good flasher cut tools. But if the flasher is extremely strong, some amount offlasher events remain in the final sample.Flasher event has strong directional correlations.
So, if it overlaps with the direction of the sun, it could make some amount of fake solar
neutrino flux.
• External flush event rate
If the following list of event rate are extremely high, there are something wrong. External
flush event happens under the following condition of high event rate.
207

– OD triggered event rate
– OD mismatch event rate
– NS ratio cut event rate
– ATM ratio cut event rate
– Unfitted event rate
• Live run list in tqreal summary files and in data file
The live time is calculated from tqreal summary files. The final data sample is of course
made from data files. They are independently generated. So, the list of sub runs in bothtqreal summary and data files after the 1st reductions are compared to make sure that weare using the same run list. The trouble found here is a bunch of ”no data files”. Thismeans real-time process may have some trouble at some step. So, usually re-process isneeded for these sub runs. There is only a small afraid. If the run time is very short(the current shortest sub run time is 30 sec), all the events are really removed at the 1st
reductions.
• Others– Gamma source on the SK tank for LINAC calibration– High radon rate for Radon calibration– Bad trigger level at hard-ware trigger threshold changing.

E.2.2

Summary

Live time (day)The following table E.2 shows the manual bad run selection summary of the total lost time fromthe rejected run as bad run.
Thus, we see that 112 days of live-time can be accounted for by the LE manual bad run
selection cuts. In figure E.2, the detector live time after bad run selection is plotted as afunction of elapsed run number from May 5, 1996. The highest plot, middle plot and the lowest
plot shows total detector live time, solar neutrino analysis live time after real-time bad run
rejection and solar neutrino analysis live time after non-real-time bad run rejection respectively.
1600

1400

1200

1000

800

600

400

200

0

2000

3000

4000

5000

6000

7000

8000

9000

10000

Elapsed Run number from 1996.5.31

Figure E.2: The detector live time after bad run selection for elapsed run number from May
5, 1996. The highest plot, middle plot and the lowest plot shows total detector live time, after
real-time bad run rejection and after non-real-time bad run rejection respectively.

208

Step
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
20

Cut criteria

Rejected unit
(Run or Sub-run)
Log book checking
Log book check(Bad run)Runs
Log book check(Bad run end)
Sub-runs
Gamma source on the top of the tank
Runs
Radon water injection for radon calibration
Runs
Bad trigger level
Runs
Dark rate
Runs
Number of OD bad channels
Sub-runs
Number of ID bad channels
Sub-runs
Abnormal muon rate
Sub-runs
Muon event rate
Sub-runs
Delta cut event rate
Sub-runs
Pedestal event rate
Sub-runs
Incomplete event rate
Sub-runs
Strong flasher event rate
Sub-runs
OD triggered event rate
Sub-runs
OD mismatch event rate
Sub-runs
NS ratio event rate
Sub-runs
ATM ratio cut event rate
Sub-runs
External flasher event rate
Sub-runs
Live runs list
Sub-runs
Low goodness
Sub-runs
Data problem
Sub-runs
Total Lost time

Rejected Runs
or Sub-runs

Lost time(days)

553
2912
52
31
22
148
1345
276
222
116
453
52
212
4
85
14
33
64
41
223
41
107

49.4
2.2
20.2
13.1
2.0
18.0
2.5
1.2
0.2
0.00
0.9
0.1
0.6
0.0
0.2
0.0
0.1
0.1
0.3
0.8
0.0
0.0
112

Table E.2: The manual bad run selection summary of the total lost time.

209

Appendix F

The probability function of solar
signal for solar signal extraction
The probability function for the signal (P sig ) is obtained by the solar neutrino MC simulation at
various energy regions. The distribution is named XANG. The XANG is made by smoothing theprobability function of the MC by smoothing functions. In this thesis, the smoothing function
is different from current analysis. The smoothing function is changed from sorting method tofunction fitting method. It was problem that the old smoothing function created a artificial
shape for the cos θsun distribution of the original MC. So, the new smoothing method which has
small artificial effect was developed.

F.1

Old way to make the signal probability function

The cos θsun distribution made from the signals of solar neutrino MC is applied following smoothing method in order to smooth because it has some fluctuation due to statistics. If the fluctuation is large, the extraction of the solar neutrino signal from real data is not done correctly.
The cos θsun distribution of the signal before smoothing is called original XANG from now
on. Figure F.2 shows the original XANG in 8.0∼9.0 MeV energy region. After smoothing,
it is called smoothing XANG from now on. Figure F.3 shows the smoothing XANG for eachsmoothing step in 8.0∼9.0 MeV energy region. The original XANG is made for 12 energy regions (4.5∼5.0, 5.0∼5.5, 5.5∼6.0...12.5∼100.0 MeV) and 7 zenith angles (All-time, Day-time,
Night-time:Mantle1... Mantle5, Core) as shown in figure F.1. The region is given in table F.1.
Zenith angle
MANTLE1
MANTLE2
MANTLE3
MANTLE4
MANTLE5
CORE

region0.00< cos θz ≤ 0.16
0.16< cos θz ≤ 0.33
0.33< cos θz ≤ 0.50
0.50< cos θz ≤ 0.67
0.67< cos θz ≤ 0.84
0.84< cos θz ≤ 1.00

Table F.1: The region of the zenith angle division.
1. Tail fitting
In small statistical region of the cos θ sun < 0.0, the distribution is replaced with theexponential function.
2. Sorting
In the cos θsun > 0.0, the fluctuation due to statistics appears. Some bins which is near
210

Z

Day

SK
Mantle1(Night1)
Mantle2(Night2)
Core
Mantle3(Night3)
MantleMantle4(Night4)
Mantle5(Night5)
Core

Figure F.1: The definition of the zenith angle division.

to the solar direction have smaller statistics than some bins farther from solar direction.
This fluctuation is improved by the sorting method. It means a smaller statistical bin is
exchanged a higher statistical bin for each bin.
3. Spline
The numerical method of Spline [92] is applied to smooth.
4. Secondary sorting
Above sorting is applied again.
5. Running average of first differential
The running average of first differential is applied to the cos θ sun < 0.99.
6. Normalization
The distribution is transfered to the probability function.
These smoothing methods have an large effect on small statistical distribution, for example,
in energy region from 12.5 to 100.0 MeV and zenith angle of Mantle 1 from 0.00 to 0.16.
Figure F.4 shows the bad example due to smoothing method.

F.2

The effect of smoothing for spectrum analysis

The original XANG has some fluctuations. It is not smooth because of low statistics of the MC.
So, the high statistics MC which has 10 times larger statistics than usual MC is generated inorder to skip the smoothing. Comparing the observed solar neutrino flux for SK-I full data of
1496 days between the result by using the smoothing XANG and by using the original XANG
which can skip the smoothing by the high statistics MC, the smoothing effect is estimated. The
original XANG which can skip the smoothing is called no smoothing XANG from now on.
Figure F.5 shows the ratio between the energy spectrum result by using smoothing XANG
and by using no smoothing XANG.
The energy spectrum by using no smoothing XANG is slightly down uniformly by 0.5%.
This result is due to the running average effect in the smoothing.

211

Number of Events

10

10

10

10

10

6

   
  !"$#    

5

4

3

2

10

1

−0.4

−0.2

0

0.2

0.4

0.6

%&(' θ' )*
0.8

1

10

10

10

10

TVUNM W$L[5\LNW$],3^3W_RNSS3X O W$Y

5

4

3

Number of Events

Number of Events

Figure F.2: The original XANG of cosθ sun distribution of all events(E = 8.0 ∼ 9.0MeV).

78:9;=<=> ;@?(;=8:9ACBC;=BC> D E@F$G HBC<=> D ACBIEJ9C9F D ;=?

1010TVUNM W$L. ,3LNM O 23PQRNS3S3X O W$Y

5

4K$,3LNM O 23P+-,/.0. 1323465
Z RNO XUNO M

10

2

10

10

3

2

K$,3LNM O 23PQ. M0RNLNMS3,O 23M

10

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

−0.4

8−ene−9

−0.2

0

10

10

10

10

TVUNM W$L. S3X O 23W_RNS3SX O W$Y

54

KK$gS3X RNO S323W_W23. X ,3O P MIg . M ,\X h ]b$1 g b$RNg 23P3W$W$UNUNY W b M O ^3W

10

10

3

10

j3kOl 2\i3i3O X2 13Wb$g b RNO 23L b P3X W$W Y

2

0.2

0.4

0.6

0.8

1

8−ene−9work

Number of Events

Number of Events

work

10

10

TVUNM W$L[LN132323O 2PQRN^3W$L$RNP3W_RNS3S3X O W$Y

5

4

3

` 132323. M0O RN23LNPQMS3RN,3^3O W$23L$M RNP3W
a b ,/.0. 132\4c5/d e3e3f

2

10

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

8−ene−9

work

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

8−ene−9work

Figure F.3: The smoothing XANG of cosθ sun distribution of all events(E = 8.0 ∼ 9.0MeV).

212

3

Number of Events

Number of Events10!"$#%& ')(*#++& +-,./
0  )12 3+& +(+& #546 ,718 #910

3   :;< 2!=118 >
10

10

2

2

10

10

1
1

−0.4

−0.2

0

0.2

0.4

0.6

0.8

  

1

−0.4

−0.2

0

0.2

0.4

0.6

   1

0.8

θ

θ

Figure F.4: The bad example of the smoothing XANG for cosθ sun distribution.

Ratio(No Smoothing/Smoothing(Official plot))

1.025

1.02

Ratio =

1.015

Using no Smoothing XANG
Using Smoothing XANG

1.01

1.005

1.000

1

0.995

0.995
0.99

0.990

0.985

0.98

0.975

5

6

7

8

9

10

11

12

13

14

15

Energy(MeV)

Figure F.5: The ratio between the energy spectrum result by using smoothing XANG and it byusing no smoothing XANG.

213

Figure F.6 shows the ratio between the zenith energy spectrum result by using smoothing
XANG and by using no smoothing XANG. The zenith energy spectrum is obtained by dividing
the energy spectrum into each zenith angles region as shown in figure F.1.

Ratio

Zenith Spectrum Ratio =Using no Smoothing XANG
Using smoothing XANG
1.02
1
0.98

DAY

0.96
5

10

ALL
15

1.02

Ratio

Ratio

Energy(MeV)

1
0.98

MAN1

0.96
5

10

ALL

1.02
1
0.98

MAN2

0.96

15

5

10

1.02

Energy(MeV)

Ratio

Ratio

Energy(MeV)

1
0.98

1.02
1
0.98

MAN3

0.96
5

10

ALL

MAN4

0.96

15

5

10

Energy(MeV)
1.02
1
0.98

MAN5

0.96
5

10

ALL
15

Energy(MeV)

Ratio

Ratio

ALL
15

ALL

1.02
1
0.98

CORE

0.96

15

5

10

Energy(MeV)ALL
15

Energy(MeV)

Figure F.6: The ratio between the zenith energy spectrum result by using smoothing XANG
and it by using no smoothing XANG.
In the high energy region, the spectrum is down largely by 2∼3%. This result is due to thetail fitting effect in the smoothing because the tail fitting changes the normalization factor fororiginal XANG.
In the estimation of the smoothing effect, the largest change is 2∼3 % in zenith energy
spectrum. Figure F.7 shows the results of the oscillation analysis by using the zenith energy
spectrum. The left figure is the result by using smoothing XANG, and the right figure is theresult by using no smoothing XANG. It is concluded that the oscillation analysis results did notchange.

F.3

New way to make the signal probability function

The smoothing method has some wrong effects on the original shape of XANG. So, this method
need to be improved. In this improvement, the following contents is required.
• The shape of original xang is not changed.
• The fluctuation in the low statistical region is improved.
From above requirements, the new smoothing method is developed. The developed smoothing method is a high order exponential function fitting with polynomial function. The originalxang is replaced with the fitting result in the small statistical region.
214

2

−3

SK 1496 Days

10
10
10
10
10
10
10
10

−4

2

10

∆m in eV22

∆m in eV10−5excluded(rate not−8 constrained)10 

10

−9

10

−10

10

−11

10

10

10

−7



Zenith Spectrum νν
−4

10

−3

10

−2

10

10
ννµ,τ (95%
Ψ C.L.)
−1

1

10
10
2
tan (Θ)10

2−3

SK 1496 Days

10

−6

−12

10

−4

−5

−6

−7
excluded(rate not−8 constrained)  

−9

−10

−11

−12

10



Zenith Spectrum νν
−4

10

−3

10

−2

10

ννµ,τ(95%
Ψ C.L.)
−1

1

10
10
2
tan (Θ)2

Figure F.7: The results of oscillation analysis by using zenith energy spectrum. The left figureis the result by using smoothing XANG, and the right figure is the result by using no smoothing
XANG.

Figure F.8 shows the outline of the new method. The way to fit polynomial function is asfollows:
1. The original xang is divided into three regions as figure F.8.
2. In the peak region, the shape of original XANG is used as it is, because the statistics inthis region is enough. The fluctuation does not appear.
3. In the region from middle to tail, the exponential function with polynomial function isapplied. The function is as following equation.

f (x) = exp(Pn (x))
Pn = p1 · x + p2 · x2 · · · +pn · xn

x = cos θsun

(F.1)

where f (x) is the fitting function, n is the order of polynomial function which has 4,6,12
or 16 in this method, pn is fitting free parameter.
The various combined order for n is used in this fitting. For example, in the middle region,n = 12 is used, and in the tail region, n = 8 is used. Or, the single function with n = 16
or n = 12 is used in all over the region from middle to tail. These combinations is selectedfrom a point of view of the best agreement with the original XANG by χ 2 testing.
Figure F.9 shows the agreement between the fitting results and the original XANG in theenergy region from 8.0 to 9.0 MeV and the zenith angle from 0.00 to 0.16. In the top and left
figure, the fitting result (solid line) is overlaid on the original XANG (histogram). The anotherfigures show the ratios between the fitting result and the original XANG for each cos θ sun region
with the statistical uncertainties of 1σ of solid line. The difference is suppressed within statisticaluncertainties in all regions.
215

32

&'"$
1, "!#!%$"



/0 .
+ ,-*
()
89:<;>="?9@;ABA9DC =FEHG
I8I::<; =H?9@;ABA9<C>=FEHG

465

7
    

5  θ  

Ratio(Fit/Xang)

number of event

Figure F.8: The outline of the new method.

1.1

NPOQ K M RZY\[]R R ^]U

1.075

4

10

10

3

10

2

1.05

1.025
1
0.975
0.95

10
0.925

−0.5

0

0.5

cos θJLK M

1.1

NPOQ K>M RTS>UWVBX

1.075

0.9

1

Ratio(Fit/Xang)

Ratio(Fit/Xang)

−1

1.05

1.025

0.5

0.6

0.7

0.8

0.9

1

cos θJLK M

1

cos θJLK M

1.5_P` U OI` [HUBa

1.4
1.3
1.2
1.1

1

1
0.9

0.975

0.8
0.95
0.7
0.925
0.9

0.75

0.6
0.8

0.85

0.9

0.95

cos θJLK M

1

0.5

−0.5

0

0.5

Figure F.9: The agreement between the fitting results and the original XANG in the energy
region from 8.0 to 9.0 MeV and the zenith angle from 0.00 to 0.16.

216

Appendix G

Day and Night flux with 4.5∼5.0
MeV data
SK can measure the 8 B neutrino flux in real time, so one can compare the day time flux withnight time flux. For certain values of ∆m 2 and sin2 2θ, these fluxes are different because of
re-generation in the earth.
The data sample is divided into day time and night time samples defined by the zenith angleof the direction of the sun as shown in figure 2.16 and the region is given in table G.2. The
systematic uncertainties for day and night time flux are same as energy spectrum measurement
except for the live-time uncertainty.

G.1

Flux measurements

The day time flux is obtained as follows.
6
2
+0.08
Φν (day, SSMBP2000 , dsI) = 2.31+0.03−0.03 (stat.)−0.08 (syst.)(×10 /cm /sec)

+0.08
6
2
Φν (day, SSMBP2000 , dsII) = 2.34+0.06−0.05 (stat.)−0.08 (syst.)(×10 /cm /sec)
+0.14
6
2
Φν (day, SSMBP2000 , dsIII) = 2.40+0.07−0.07 (stat.)−0.13 (syst.)(×10 /cm /sec)

(G.1)
(G.2)
(G.3)

The night time flux is obtained as follows.
+0.08
6
2
Φν (night, SSMBP2000 , dsI) = 2.36+0.03−0.03 (stat.)−0.08 (syst.)(×10 /cm /sec)

+0.08
6
2
Φν (night, SSMBP2000 , dsII) = 2.33+0.05−0.05 (stat.)−0.08 (syst.)(×10 /cm /sec)
+0.14
6
2
Φν (night, SSMBP2000 , dsIII) = 2.42+0.07−0.07 (stat.)−0.13 (syst.)(×10 /cm /sec)

(G.4)
(G.5)
(G.6)

The mean distance between the sun and the earth is summarized in table G.1. The measured
flux is correlated for the eccentricity of the earth’s orbit at 1 AU.
Data set
I
II
III

All
1.001
0.998
0.997

Day
1.004
1.001
1.000

Night
0.998
0.995
0.994

Table G.1: The mean distance between the sun and the earth in this analysis.
The ratios of the measured flux to the SSM prediction for day and night time fluxes are as
follows:217

+0.016
Data/SSM(day, SSMBP2000 , dsI) = 0.458+0.007−0.007 (stat.)−0.015 (syst.)(G.7)+0.016
Data/SSM(day, SSMBP2000 , dsII) = 0.463+0.011−0.011 (stat.)−0.015 (syst.)+0.028
Data/SSM(day, SSMBP2000 , dsIII) = 0.475+0.014−0.014 (stat.)−0.025 (syst.)

(G.8)
(G.9)

+0.016
Data/SSM(night, SSMBP2000 , dsI) = 0.468+0.007−0.007 (stat.)−0.015 (syst.)(G.10)+0.016
Data/SSM(night, SSMBP2000 , dsII) = 0.461+0.011−0.010 (stat.)−0.015 (syst.)+0.028
Data/SSM(night, SSMBP2000 , dsIII) = 0.479+0.014−0.013 (stat.)−0.025 (syst.)(G.11)(G.12)The difference (R day ) between the day time flux and night time flux is calculated as follows:night

R day =night

Φday − Φnight(Φday 0 + Φnight )/2(G.13)

Therefore, some neutrino oscillation parameters predict a non-zero difference for R day duenight

to the matter effect in the earth’s mantle and core [86].
+0.013R day ,dsI = −0.021+0.020−0.020 (stat.)−0.012 (syst.)(G.14)+0.013R day ,dsII = 0.004+0.095−0.095 (stat.)−0.012 (syst.)(G.15)+0.022R day ,dsIII = −0.008+0.098−0.098 (stat.)−0.020 (syst.)(G.16)

night

night

night

0.65

Data/SSM

0.6

0.55

SK-I 1496day 5.0-20MeV 22.5kt

0.5

0.5

0.45

0.45

Day

Night
0.35

0.3

0.25

Night

Night

Day

0.4

All

0.4

0.35

SK-I 566day(no cut) 5.0-20MeV 22.5kt
SK-I 511day 4.5-20MeV 20.5kt

0.6

Day

0.55

0.65

All

Data/SSM

Figure G.1 shows the fluxes for day time and night time. The night time period is divided
into 5 bins. Numerical results for each data set are given in table G.2. The error is statisticalerror only. In the figure, the left plot shows the result of the data set I, and the right plot shows
the results of the data set II, III. The black circle indicates the result of the data set III. The
white circle indicates the result of the data set II.

Day

Night

0.3

-1.5

-1

-0.5

0

0.5

0.25

1

cosθz

-1.5

-1

-0.5

0

0.5

1

cosθz

Figure G.1: The time variation of the ratio of the measured flux to the SSM prediction.

The Data/SSM of 4.5∼5.0 MeV data analysis (data set III) is almost consistent with theanother data sets within ∼ 1.0 sigma. It is shows the data set for the energy spectrum with218

Time bin
Data set I
N1
N2
N3
N4
N5
Data set II
N1
N2
N3
N4
N5
Data set III
N1
N2
N3
N4
N5

cos θzData/SSM

Observed flux(×106 cm−2 s−1 )0.0∼-0.2-0.2∼-0.4-0.4∼-0.6-0.6∼-0.8-0.8∼-1.0

0.474+0.016-0.016
0.458+0.015-0.015
0.474+0.013-0.013
0.469+0.015-0.015
0.459+0.016-0.015

2.394+0.083-0.080
2.312+0.076-0.074
2.393+0.066-0.064
2.368+0.075-0.073
2.318+0.078-0.076

0.0∼-0.2-0.2∼-0.4-0.4∼-0.6-0.6∼-0.8-0.8∼-1.0

0.458+0.026-0.025
0.438+0.024-0.023
0.476+0.022-0.021
0.452+0.023-0.022
0.473+0.024-0.023

2.310+0.132-0.126
2.210+0.122-0.117
2.402+0.109-0.105
2.284+0.117-0.113
2.388+0.120-0.115

0.0∼-0.2-0.2∼-0.4-0.4∼-0.6-0.6∼-0.8-0.8∼-1.0

0.525+0.036-0.034-0.494+0.032-0.031
0.474+0.028-0.027
0.466+0.031-0.029
0.442+0.030-0.028

2.650+0.180-0.171
2.496+0.164-0.156
2.393+0.142-0.136
2.354+0.154-0.147
2.231+0.150-0.142

Table G.2: Numerical results of the flux of night time divided into 5 for each data set.
4.5∼5.0 MeV has no systematic bias in the time variation. However, the fluctuation and statistical error is very large in the data set III because of the poor statistics. So, the time variation
analysis is not described in this thesis.
Figure G.2 shows the ratio of the measured recoil electron day time and night time energy
spectrum to the predicted spectrum. The numerical summary of the day time and the nighttime recoil electron energy spectrum is given in table G.3. Figure G.2 is the result of the data
set III, and figure G.3 is the the results of the data set I,II.

G.2

Oscillation analysis

Figure G.4 shows the comparison between day-night energy spectrum and the expected daynight spectrum for each allowed solution. The right figure is night time energy spectrum, andthe left figure is day time energy spectrum.
When the combined constraints on neutrino oscillation is examined by the expected energy
spectrum, χ2 is defined as follows:
Nexp

χ

2

=

X

−1
(Ridata − Riosc )Vi,j(Rjdata − Rjosc )

i,j=1

+

( Data )exp

SSM i
ndn n
ene n ( Data )data −
o
X
X
SSM i
f corr (scl ,res ,b8 ) 2i

σii=1 i=1+

Data exp( SSM)in
ene n ( Data )data − γ ·
o
X
corr
SSM i
fi
(scl ,res ,b8 ) 2

i=1

σi

+ 2scl + 2res + 2b8

+ 2scl + 2res + 2b8 + 2γ(G.17)

where ndn is the number of day and night bins, which is 2 in this analysis. Figure G.5
shows the comparison of the result for global analysis with SNO(CC) flux constraints between
219

EnergyDay
4.5- 5.0
5.0- 5.5
5.5- 6.0
6.0- 6.5
6.5- 7.0
7.0- 7.5
7.5- 8.0
8.0- 8.5
8.5- 9.0
9.0- 9.5
9.5-10.0
10.0-10.5
10.5-11.0
11.0-11.5
11.5-12.0
12.0-12.5
12.5-13.0
13.0-13.5
13.5-14.0
14.0-20.0Night
4.5- 5.0
5.0- 5.5
5.5- 6.0
6.0- 6.5
6.5- 7.0
7.0- 7.5
7.5- 8.0
8.0- 8.5
8.5- 9.0
9.0- 9.5
9.5-10.0
10.0-10.5
10.5-11.0
11.0-11.5
11.5-12.0
12.0-12.5
12.5-13.0
13.0-13.5
13.5-14.0
14.0-20.0

Data/SSM

Statistical error

Flux(×10 6 /cm/s)

Statistical error

0.563
0.448
0.405
0.519
0.438
0.462
0.481
0.424
0.432
0.440
0.531
0.683
0.428
0.576
0.424
0.516
0.567
0.251
0.379
0.531

+0.186-0.182+0.091-0.088+0.054-0.051+0.048-0.045+0.045-0.042+0.048-0.045+0.049-0.045+0.050-0.046+0.051-0.046+0.055-0.050+0.062-0.055+0.075-0.067+0.069-0.059+0.087-0.074+0.091-0.074+0.112-0.090+0.147-0.115+0.144-0.094+0.192-0.122+0.175-0.128

2.84
2.26
2.05
2.62
2.21
2.33
2.42
2.14
2.18
2.22
2.68
3.45
2.16
2.91
2.14
2.60
2.86
1.27
1.91
2.68

+0.94-0.92+0.46-0.44+0.27-0.25+0.24-0.22+0.22-0.21+0.24-0.22+0.24-0.23+0.25-0.23+0.26-0.23+0.28-0.25+0.31-0.28+0.38-0.34+0.34-0.29+0.44-0.37+0.46-0.37+0.56-0.45+0.74-0.58+0.72-0.47+0.97-0.61+0.88-0.65

0.726
0.440
0.468
0.484
0.452
0.517
0.487
0.420
0.504
0.512
0.536
0.494
0.381
0.403
0.406
0.466
0.499
0.552
0.444
0.709

+0.169-0.166+0.084-0.081+0.053-0.050+0.044-0.042+0.044-0.041+0.045-0.042+0.046-0.043+0.047-0.043+0.051-0.047+0.054-0.050+0.059-0.053+0.063-0.056+0.064-0.056+0.072-0.061+0.082-0.067+0.104-0.083+0.127-0.100+0.166-0.124+0.196-0.130+0.176-0.138

3.66
2.22
2.36
2.44
2.28
2.61
2.46
2.12
2.54
2.58
2.70
2.49
1.92
2.03
2.05
2.35
2.51
2.78
2.24
3.58

+0.85-0.84+0.42-0.41+0.26-0.25+0.22-0.21+0.22-0.20+0.23-0.21+0.23-0.21+0.23-0.22+0.25-0.23+0.27-0.25+0.30-0.27+0.32-0.28+0.32-0.28+0.36-0.30+0.41-0.34+0.52-0.42+0.64-0.50+0.84-0.62+0.98-0.65+0.89-0.69

Table G.3: The numerical summary of the day time and the night time recoil electron energy
spectrum.

220

Data/SSM

1

SK-I 511 days 4.5-20MeV 20.5kt
Day
Night

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

6

8

10

12

14

Energy(MeV)

1

0.9

0.8

Data/SSM

Data/SSM

Figure G.2: The ratio of the measured day time and night time energy spectrum to the predicted
spectrum. The error bars shows the total errors including systematic error and statistical errors.
The dashed line shows the systematic errors for the predicted 8 B spectrum including energy
resolution, energy scale resolution and uncertainty for 8 B spectrum.

SK-I 1496 days 5.0-20MeV 22.5kt
Day
Night

1

0.9

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

6

8

10

12

0

14

Energy(MeV)

SK-I 566 days 5.0-20MeV 22.5kt
Day
Night

6

8

10

12

14

Energy(MeV)

Figure G.3: The definition in the figure is same as figure G.2. The left plot is the result of thedata set I (1496 days). The right plot shows the results of the data set II (566 days, no tightdata reduction).

221

Data/SSM

Data/SSM

0.9

0.8

0.9

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

−6

−6

SMA Red (0.0016,4.6*10−5)
LMA Green (0.42,6.6*10)−8
LOW Blue (0.63,7.2*10 )

0.3

0.2

0.1

SMA Red (0.0016,4.6*10−5)
LMA Green (0.42,6.6*10)−8
LOW Blue (0.63,7.2*10 )

0.3

0.2

4

6

8

10

12

0.1

14

Energy

4

6

8

10

12

14

EnergyFigure G.4: The comparison between day-night energy spectrum and the expected day-night
spectrum for each allowed solution.

the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV data using
day-night energy spectrum. The difference is just number of bins Green area in the contour
plot indicates allowed area by constraints from the flux measurements of all solar neutrino
experiments. Orange area in the contour plot indicates allowed area by constraints from theenergy spectrum measurements by SSM independent analysis. Sky blue area in the contour
plot indicates allowed area by constraints from the energy spectrum measurements by SSM
dependent analysis (flux(rate) constrained by SNO(CC) result).
The allowed region in SMA solution becomes small by 4.5∼5.0 MeV data. Then, the allowed
region by day-night energy spectrum with SSM independent analysis disappeared by 4.5∼5.0
MeV data. It also became small in LMA region.

222

10
10
10

2

SK 511 Days, 20.5 kton w/o 4.5 − 5.0 MeV
−4

2

10

−3

∆m in eV22

∆m in eV

10

−5

10
10
10

−6

10

−7

10

10

allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

10

−11

10

10
Day/Night Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−3

SK 511 Days, 20.5 kton w/ 4.5 − 5.0 MeV
−4

−5

−6

−7

allowed(rate not−8 constrained) allowed
10(rate con−strained by
SNO CC)

−9

−12

10
10

allowed(rate not−8 constrained) allowed
10(rate con−strained by
SNO CC)

10

10

−1

1

10
10
2
tan (Θ)10

2−9allowed(Ga, Cl, SK & SNO
rate+SSM pred.)

−10

−11

−12

10

Day/Night Spectrum νe νµ/τ (95%C.L.)
−4

10

−3

10

−2

10

−1

1

10
10
2
tan (Θ)2

Figure G.5: The comparison of result for global analysis with SNO(CC) flux constraints between
the data set III without 4.5∼5.0 MeV data and the data set IV with 4.5∼5.0 MeV data.

223

Bibliography[1] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Nucl. Instr. & Meth. A 501
418-462 (2003)[2] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Lett. B539 (2002) 179-187[3] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 77 (1996) 1683
[4] K. Hirata, et al. (Kamiokande-II Collaboration), Phys. Rev. Lett. 63 (1989) 16[5] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 86 (2001)
5651-5655[6] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 86 5656-5660(2001)[7] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 82 (1999)
2430-2434[8] Davis, R., Phys. Rev. Lett. 12 (1964) 303-305[9] Davis, Raymond, Jr., Harmer, Don S., Hoffman, Kenneth C., Phys. Rev. Lett. 20 (1968)
1205-1209[10] Davis, R., Prog. Part. Nucl. Phys. 32 (1994) 13-32[11] Cleveland, Bruce T., et al., Astrophys. J. 496 (1998) 505-526[12] M. Altmann, et al., (GNO-Collaboration), Physics Letters B 490(1-2) (2000) 16-26[13] E. Bellotti, Nuclear Physics B (Procceedings Supplements) 91(1-3) (2000) 44-49[14] Hampel, W. et al. (GALLEX Collaboration), Phys. Lett. B447 (1999) 127-133.
[15] Hampel, W. et al. (GALLEX Collaboration), Phys. Lett. B388 (1996) 384-396.
[16] Anselmann, P. et al. (GALLEX Collaboration), Phys. Lett. B357 (1995) 237-247.
[17] Anselmann, P. et al. (GALLEX Collaboration), Phys. Lett. B314 (1993) 445-458.
[18] Anselmann, P. et al. (GALLEX Collaboration), Phys. Lett. B285 (1992) 376-389.
[19] W. Hampel et al. Physics Letters B 420(1-2) (1998) 114-126[20] K. Eguchi et al. (KamLAND Collaboration), Phys. Rev. Lett. 90 (2003) 021802[21] Abdurashitov, J. N. et al. (SAGE Collaboration), Phys. Rev. C60 (1999) 055801[22] Abazov, A. I. et al., Phys. Rev. Lett. 67 (1991) 3332-3335.
[23] Abdurashitov, J. N. et al. (SAGE Collaboration), Phys. Rev. C59 (1999) 2246-2263
224

[24] Abdurashitov, Dzh. N. et al., Phys. Rev. Lett. 77 (1996) 4708-4711.
[25] Ahmad, Q. R. et al. (SNO Collaboration), Phys. Rev. Lett. 89 (2002) 011302[26] Ahmad, Q. R. et al. (SNO Collaboration), Phys. Rev. Lett. 89 (2002) 011301[27] Ahmad, Q. R. et al. (SNO Collaboration), Phys. Rev. Lett. 87 (2001) 071301[28] Dick, R.H., J.R. Kuhn, and K.G. Libbrecht Nature, 316, (1985) 687[29] J.N Bahcall, M.H. Pinosonneault, and S. Basu, Astrophys.J. 555, (2001) 990 (BP2000)[30] S. Turck-Chieze et al., Astrophys. J. 555, (2001) L69[31] A.R. Junghans et al., Phys. Rev. Lett. 88, (2002) 041101[32] J.N Bahcall, M.C. Gonzalez-Garcia, and C. Pena-Garay, JHEP 0204, 007 (2002).
[33] C.A Iglesias and F.J. Rogers, Astrophys.J. 371 (1991) 408[34] Frohlich, C., Lean, J., Geophysical Research Letters 25, (1998) 4377
[35] Frohlich, C., Crommelynck et al. Solar Phys., 162 (1995) 101[36] J.N.Bahcall and M.H.Pinsonneault 1992, Rev. Mod. Physics, 64, 885.
[37] Adelberger EG, et al., Rev. Mod. Phys. 70, (1998) 1265
[38] Gruzinov, J.N. Bahcall, Astrophys.J. 504 (1998) 996-1001[39] Salpeter, E.E., Australian Journal of Physics 7, (1954) 373[40] Thoul, A. A., Bahcall, J. N., and Loeb, A.: ApJ 421, (1994) 828[41] Bahcall J.N., Pinsonneault M.H., Rev. Mod. Phys. 67, (1995) 781[42] Turcotte S., Richer J., Michaud G., ApJ 504, (1998) 559 NASA ADS[43] Grevesse, N. & Suaval, A. J., Space Sci Rev, 85, (1998) 161[44] Bahcall J.N., Pinsonneault M.H., Rev. Mod. Phys. 67, (1995) 781[45] J.N. Bahcall Phys. Rev. D, 49, No. 8, (1994) 3923
[46] J.N. Bahcall Phys. Rev. C, 56, No. 6, (1997) 3391
[47] J.N. Bahcall, L. Lisi, D.E. Alburger, et al. Phys. Rev. C, 54, (1996) 411[48] Bahcall, J. N., & Pinsonneault, M. H. Rev. Mod. Phys., 67, (1995) 781[49] Thoul, A. A., Bahcall, J. N., & Loeb, A. ApJ, 421, (1994) 828[50] Bahcall, J. N., & Pinsonneault, M. H. Rev. Mod. Phys., 64, (1992) 885[51] Grevesse, N. Phys. Scripta, T8, (1984) 49[52] Grevesse N., & Noels A. 1993, in Origin and Evolution of the Elements, ed. N. Prantzos,
E. Vangioni-Flam, & M. Cass (Cambridge: Cambridge University Press)[53] Grevesse, N., & Sauval, A. J. Space Sci. Rev., 85, (1998) 161[54] Bahcall, J. N., & Ulrich, R. K. Rev. Mod. Phys., 60, (1988) 297

225

[55] J. Napolitano, S.J. Freedman, and J. Camp, Phys. Rev. C 36 (1987) 298[56] D.H. Wilkinson and D.E. Alburger, Phys. Rev. Lett. 26, (1971) 1127
[57] B.J. Farmer and C.M. Class, Nucl. Phys. 15. (1960) 626[58] L. De Braeckeleer and D. Wright (unpablished data), as quated in L. De Braeckeleer et al.,Phys. Rev. C 51, (1995) 2778
[59] J.N. Bachall and M.H.Pinsonneault, Rev. Mod. Phys. 67, (1995) 781[60] J.N Bahcall, S. Basu, MH Pinsonneaul Phys. Lett. B, 433, (1998) 1-8[61] Basu, S., et al., MNRAS, 292, (1997) 243[62] Basu, S., Pinsonneault, M.H., & Bahcall, J.N. ApJ, 529, (2000) 1084 (BPB00)[63] J. Bahcall, S. Basu and M. Pinsonneault, Phys. Lett. B433, (1998) 1[64] Marcucci, L. E., Schiavilla, R., Viviani, M., Kievsky, A., & Rosati, S. Phys. Rev. Lett., 84,(2000a) 5959
[65] W. Hamptel and L. P. Remsberg, Phys. Rev. C31, (1985) 666[66] W. Hamptel et al., Phys. Lett. B420, (1998) 114[67] J.N. Bachall. and U.K. Urrich, Rev. Mod. Phys. 60, (1988) 297[68] W. Hamptel et al., Phys. Lett. B447, (1999) 127[69] J.N. Bachall, Phys. Rev. C56, (1997) 3391
[70] T.Kajita, talk at ”XVIII International Conference on Neutrino Physics and Astrophysics”(1998)[71] Felix Boehm and Petr Vogel ”Physics of Massive Neutrinos” (Cambridge 1987) p146
[72] M.Fukugita and A.Suzuki, ”Physics and Astrophysics of Neutrinos”, (Springer-Verlag,
1994)[73] D.L.Anderson, ”Theory of the Earth” (Blackwell scientific publication, 1989)[74] J.N Bachall, P.I. Krastev, and Ayu. Smirnov, JHEP05, 015, (2001)[75] “Physicas and Astrophysics of Neutrinos”, edited by M.Fkukugita and A. Suzuki, SpringerVerlag.
[76] Eric G. Adelberger et al., Rev. Mod. Phys., 70, (1998) 1265-1292[77] J.N.Bahcall, M.Kamionkowski, and A.Sirlin, Phys.Rev.D 51 (1995) 6146
[78] H.Ikeda,et.al, Nucl.Instr.and.Meth.,A320 (1992) 310[79] T.Tanimori, et.al, IEEE Tran.on.Nucl.Sci 36 (1989) 497[80] A.Morel, et.al, Limnology and Oceanography 22 (1977) 709[81] I.Thorm äheln, K.Scheffler, and J.Scaub, in Water and Steam, Proceedings of the 9th ICPS
(Pergamon, Oxford, 1980)[82] A.Suzuki et.al Nucl.Instr.and Meth.,A329 (1993) 299

226

[83] W. Y. Chang, M. Goldhaber, R. Sagane, Nature 139 (1937) 962.
[84] V. McLane, C.L. Dunford, P.F. Rose, Neutron Cross Sections, Vol. 2 (Academic Press,
Boston, 1982) 48.
[85] R. B. Firestone, Table Of Isotopes, Vol. 1 (John Wiley and Sons, New York, 1996) 20.
[86] E. D. Carlson, Phys. Rev. D 34, (1986) 1454
J. Bouchez et al., Z. Phys. C32, (1986) 499[87] J.N. Bachall, “Neutrino Astrophysics”, Cambridge University, Cambridge (1998)[88] Klaus. Winter, “Neutrino Physics”, Cambridge University, Cambridge (2000)[89] Thomas. K. Gaisser, “Cosmic Rays and Particle Physics”, Cambridge University, Cambridge (1990)[90] L. LYONS, “Statistics for nuclear and particle physicists” Cambridge university, Cambridge[91] GEANT Detector Description and Simulation Tool, Cern Program Library W5013, (1994)[92] William H. Press, “Numerical Recipes in FORTRAN 77”, Cambridge University, Cambridge(1993)[93] K. Hagiwara et al.l. (particle Data Group), Phys. Rev. D 66, 010001 (2002) (URL:
http://pdg.lbl.gov)[94] M. Nemoto, Master theisis, Tokai University (1998) (unpublished)[95] C. Mitsuda, Master theisis, Niigata University (2000) (unpublished)[96] Yusuke Koshio, PhD Thesis, University of Tokyo, Apr. 1998
[97] Measurement of the solar neutrino energy spectrum at Super-Kamiokande Hirokazu Ishino,
PhD Thesis, University of Tokyo, Jan. 1999
[98] Nobuyuki Sakurai, PhD Thesis, University of Tokyo, Dec 2000
[99] Y.Koshio, master thesis, Tokyo University (1994) (unpublished)[100] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Phys. Lett. 452 (1999) 418-422[101] Y.Takeuchi, et al., Nucl. Instr. & Meth. A421 (1999) 334-341[102] C.Mitsuda, et al., Nucl. Instr. & Meth. A 497 (2003) 414-428[103] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Nucl. Instr. & Meth. A 458(2001) 636-647[104] Y. Fukuda, et al., (The Super-Kamiokande Collaboration), Nucl. Instr. Meth. A421 (1999)
113-129[105] M. Nakahata, private communication

227