Study of Solar Neutrinos at Super Kamiokande
Yusuke Koshio
University of Tokyo
April 1998

Abstract
Super-Kamiokande started taking data on the 1st of April in 1996. The data used
for the analysis of solar neutrinos in this paper was obtained from the 31st of May, 1996
to the 23rd of June, 1997 and the total live time is 297.4 days. The energy threshold is
6.5MeV and the fiducial volume is 22.5 ktons.
The observed 8 B solar neutrino flux in Super-Kamiokande is
2.42

+0.06
−0.06 (stat.)+0.13−0.09 (sys.)[×106 /cm2 /sec].

The observed flux is smaller than the predicted by Bahcall and Pinsonneault (BP95).
The ratio isData= 0.365
SSM (BP 95)+0.010−0.010 (stat.)+0.019−0.013 (sys.).

Comparing this deficit with the result of the Homestake experiment, the solar neutrino
problem is difficult to explain by changing solar models but is more naturally explainedby neutrino oscillations.
The solar neutrino flux of daytime and night-time agrees within the experimental
errors and the result restricts the allowed neutrino oscillation parameters of the MSW
effect. If we assume the large angle solutions to the solar neutrino problem, according
to the MSW effect, neutrinos would regenerate through the earth. This analysis, whichis independent of the solar models, excludes half of the large angle region which was
obtained from the model-dependent analysis of the combined results from the past experiments. Within five years, the data sample from Super-Kamiokande should be large
enough to study the whole large angle region.
Seasonal flux differences were not seen but currently, the statistical relevance of thedata sample is insufficient. No energy distortion was found within the errors. For the
analysis of the energy spectrum, more statistics and smaller systematic errors are needed.

Acknowledgments
First of all, I would like to express my sincere appreciation to my advisor, Prof.
Yoichiro Suzuki. He gave me the chance to participate in this great experiment fromthe first stage of the construction and also supported me on many occasions during mygraduate studies. His excellent guidance and suggestions helped me to understand what
is important in experimental physics.
I would like to show my appreciation to the leader of the experiment, Prof. Y.Totsuka.
His useful advice and continuous encouragement were helpful for this analysis.
This dissertation and the solar neutrino analysis were highly dependent on cooperation with the subgroup members (the low energy group). I am deeply indebted toProf.M.Nakahata, Dr.K.Inoue, Dr.Y.Fukuda, Dr.Y.Takeuchi and Dr.K.Martens for giving me useful suggestions and for insightful discussions on various occasions. I also wish
to thank the graduate students: Dr.T.Yamaguchi, Dr.H.Okazawa, H.Ishino, E.Ichihara,
N.Sakurai and M.Nemoto, and the members in USA: Prof.B.Svoboda, Dr.J.Hill, Dr.
M.Vagins, Dr.Z.Conner, Dr.M.Smy, Dr.B.K.Kim, R.Sanford and E.Blaufuss, for working together. Without their support and discussions with them, this dissertation would
never have been completed.
I am thankful to all the collaborators of Super-Kamiokande for very useful suggestions. Especially, Prof.T.Kajita, Dr.Y.Itow, Dr.M.Miura, M.Shiozawa, T.Hayakawa,S.Kasuga, K.Ishihara, K.Okumura and J.Kameda who are all members of ICRR at
Kamioka and with whom I often had useful discussions about the experiment, physics andso on. I must thank to Dr.J.Hill and C.Mauger for reading and checking this manuscript
and for some useful comments.
Finally, I gratefully acknowledge the cooperation of Kamioka Mining and Smelting
Company and financial support of the Japan Society for the Promotion of Science.

Contents
1 Introduction

1

2 The solar neutrino problem

5

2.1

The standard solar model . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.2

Solar neutrino experiments . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.2.1

Homestake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.2.2

Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.3

GALLEX and SAGE . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.2.4

Summary of the results in solar neutrino experiments . . . . . . .

17

2.3

The solar neutrino problem . . . . . . . . . . . . . . . . . . . . . . . . .

18

2.4

Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

2.4.1

General description . . . . . . . . . . . . . . . . . . . . . . . . . .

19

2.4.2

MSW effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

2.4.3

Regeneration in the earth . . . . . . . . . . . . . . . . . . . . . .

25

2.4.4

The allowed parameter regions of the MSW effects

27. . . . . . . .

3 The Super-Kamiokande Detector
3.1

3.2

29

Detection method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.1.1

Imaging water Cherenkov detector . . . . . . . . . . . . . . . . .

29

3.1.2

Solar neutrino interactions in the detector . . . . . . . . . . . . .

31

Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.2.1

Detector outline . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.2.2

Water and air purification . . . . . . . . . . . . . . . . . . . . . .

37

3.2.3

Photomultiplier tubes. . . . . . . . . . . . . . . . . . . . . . . .

42

3.2.4

Electronics and Data acquisition . . . . . . . . . . . . . . . . . . .

45

i

CONTENTS

4 Calibration

47

4.1

Relative gain of the PMTs . . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.2

Single photo-electron distribution . . . . . . . . . . . . . . . . . . . . . .

49

4.3

Timing of PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.4

Water transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4.4.1

Direct measurement . . . . . . . . . . . . . . . . . . . . . . . . .

53

4.4.2

Measurement using real data in Super-Kamiokande . . . . . . . .

55

Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.5.1

LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.5.2

Nickel calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

4.5.3

µ-e decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

4.5

4.6

5 Event reconstruction method

69

5.1

Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

5.2

Directional reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.3

Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

5.4

Muon track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

6 Monte Carlo simulation

89

6.1

Solar neutrino event generation . . . . . . . . . . . . . . . . . . . . . . .

89

6.2

Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

6.2.1

Framework of the simulation program . . . . . . . . . . . . . . . .

90

6.2.2

Monte Carlo tuning . . . . . . . . . . . . . . . . . . . . . . . . . .

96

7 Data Analysis and Results

99

7.1

Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

7.2

Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.2.1

First reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.2.2

Bad run selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2.3

Selection of muon events to identify spallation events . . . . . . . 106

7.2.4

Spallation cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.2.5

Fiducial volume cut and gamma ray cut . . . . . . . . . . . . . . 112

7.2.6

Summary of the data reduction . . . . . . . . . . . . . . . . . . . 114
ii

CONTENTS

7.2.7
7.3

Remaining background . . . . . . . . . . . . . . . . . . . . . . . . 115

Results of solar neutrino analysis . . . . . . . . . . . . . . . . . . . . . . 117
7.3.1

Solar neutrino flux and energy spectrum . . . . . . . . . . . . . . 117

7.3.2

Summary of the systematic errors . . . . . . . . . . . . . . . . . . 124

8 Conclusions and Discussions

127

8.1

Implication of the absolute flux measurement . . . . . . . . . . . . . . . . 127

8.2

Neutrino oscillation study using day-night flux difference . . . . . . . . . 131

8.3

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A Electronics

139

B The detail explanation of event reconstruction

145

B.1 Hit-PMT selection for vertex reconstruction . . . . . . . . . . . . . . . . 145
B.2 The definition of effective Nhit . . . . . . . . . . . . . . . . . . . . . . . . 146
B.3 Recent results of LINAC calibration . . . . . . . . . . . . . . . . . . . . . 148
B.4 Another algorithm of vertex reconstruction . . . . . . . . . . . . . . . . . 149
B.5 The method of event clean up using vertex and direction . . . . . . . . . 151
C Spallation events155

C.1 Likelihood function of spallation event . . . . . . . . . . . . . . . . . . . 155
C.2 Spallation events as detector calibration . . . . . . . . . . . . . . . . . . 158

iii

List of Figures
1.1

Proton-proton chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2

CNO cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

2.1

Temperature and Density profile in the sun . . . . . . . . . . . . . . . . .

7

2.2

Radial profiles of solar neutrino flux . . . . . . . . . . . . . . . . . . . . .

8

2.3

Energy spectrum of solar neutrinos . . . . . . . . . . . . . . . . . . . . .

9

2.4

Argon production rate in the Homestake experiment . . . . . . . . . . . .

11

2.5

Solar neutrino flux in Kamiokande as a function of time . . . . . . . . . .

13

2.6

Energy spectrum in Kamiokande . . . . . . . . . . . . . . . . . . . . . .

13

2.7

Day/night difference of solar neutrino flux in Kamiokande . . . . . . . .

14

2.8

Ge production rate in the GALLEX experiment . . . . . . . . . . . . . .

16

2.9

Ge production rate in the SAGE experiment . . . . . . . . . . . . . . . .

17

2.10 Constraint of 8 B/7 Be ratio from solar neutrino experiments . . . . . . . .

18

2.11 Illustration of the MSW effect in the sun . . . . . . . . . . . . . . . . . .

22

2.12 Survival probability of νe through the sun on the adiabatic condition . .

23

2.13 Survival probability of νe through the sun on the non-adiabatic condition24

2.14 Energy distribution of νe by MSW effect . . . . . . . . . . . . . . . . . .

24

2.15 Density profile of the earth . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.16 Survival probability of νe state in the earth . . . . . . . . . . . . . . . . .

26

2.17 Survival probability of νe state as a function of E/∆m2 . . . . . . . . . .

26

2.18 95% C.L. contour of the MSW analysis . . . . . . . . . . . . . . . . . . .

27

3.1

Typical expected event to be observed in Super-Kamiokande . . . . . . .

30

3.2

Differential cross section for neutrino with electron . . . . . . . . . . . .

32

3.3

Spectrum of recoil electrons . . . . . . . . . . . . . . . . . . . . . . . . .

33v

LIST OF FIGURES

3.4

Angular distribution of recoil electrons from incident solar neutrinos . . .

34

3.5

Detector appearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.6

Schematic view of the frame . . . . . . . . . . . . . . . . . . . . . . . . .

37

3.7

Water purification system . . . . . . . . . . . . . . . . . . . . . . . . . .

38

3.8

Resistance of the water . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.9

Number of particles in the water . . . . . . . . . . . . . . . . . . . . . . .

40

3.10 Radon concentration in the air as a function of time . . . . . . . . . . . .

41

3.11 Radon free air system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

3.12 Schematic view of the PMT . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.13 Quantum efficiency of the PMT . . . . . . . . . . . . . . . . . . . . . . .

44

3.14 One photo electron peak of the PMT . . . . . . . . . . . . . . . . . . . .

44

3.15 Dark noise rate of the PMT . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.16 Trigger rate in Super-Kamiokande as a function of time . . . . . . . . . .

46

4.1

Relative gain measurement system. . . . . . . . . . . . . . . . . . . . .

48

4.2

Corrected Q distribution in the relative gain calibration . . . . . . . . . .

48

4.3

Charge distribution of one photon level . . . . . . . . . . . . . . . . . . .

49

4.4

Average occupancy distribution of PMTs in the barrel part . . . . . . . .

50

4.5

Relative timing measurement system . . . . . . . . . . . . . . . . . . . .

51

4.6

TQ-map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4.7

Water transparency measurement system . . . . . . . . . . . . . . . . . .

53

4.8

Picture taken by CCD camera . . . . . . . . . . . . . . . . . . . . . . . .

54

4.9

Water transparency obtained by the direct measurement . . . . . . . . .

54

4.10 Typical event pattern of a muon and a decay electron event. . . . . . .

56

4.11 The relation between the corrected Q and the distance . . . . . . . . . .

57

4.12 Water transparency as a function of time obtained by decay electron events 57
4.13 Relation between Qi × Li /a(θi ) and Li . . . . . . . . . . . . . . . . . . .

58

4.14 Water transparency as a function of time obtained by through going muon
events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.15 Schematic view of LINAC calibration system . . . . . . . . . . . . . . . .

60

4.16 Relation of observed momentum to the magnetic field . . . . . . . . . . .

61

4.17 Transition diagram in the Nickel calibration . . . . . . . . . . . . . . . .

63

4.18 Schematic view of Nickel calibration system . . . . . . . . . . . . . . . .

64vi

LIST OF FIGURES

4.19 Time intervals from the fission trigger in Nickel calibration . . . . . . . .

65

4.20 N50 distribution of Nickel calibration . . . . . . . . . . . . . . . . . . . .

65

4.21 Nef f distribution of decay electron event . . . . . . . . . . . . . . . . . .

66

4.22 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

5.1

Timing distribution of hit-PMTs in one event . . . . . . . . . . . . . . .

70

5.2

Coordinate of the Super-Kamiokande detector . . . . . . . . . . . . . . .

71

5.3

Reconstructed vertex distribution of Nickel calibration . . . . . . . . . .

72

5.4

Definition of the vertex shift and resolution . . . . . . . . . . . . . . . . .

73

5.5

Reconstructed vertex distribution of Linac calibration . . . . . . . . . . .

74

5.6

Likelihood function for the direction and acceptance . . . . . . . . . . . .

76

5.7

Directional cosine distribution . . . . . . . . . . . . . . . . . . . . . . . .

77

5.8

Reconstructed direction distribution of Linac calibration . . . . . . . . .

78

5.9

Directional resolution as a function of position . . . . . . . . . . . . . . .

79

5.10 Reconstructed energy distribution of Linac calibration . . . . . . . . . . .

81

5.11 Nef f distribution of 10MeV electron Monte Carlo events . . . . . . . . .

82

5.12 Mean value of Nef f and energy resolution as a function of energy . . . .

83

5.13 Typical event pattern of an energetic muon . . . . . . . . . . . . . . . . .

85

5.14 Representative event patterns for various muon types . . . . . . . . . . .

86

5.15 Definition of parameters for the muon track reconstruction . . . . . . . .

87

5.16 Difference of entrance and exit positions between auto fit and manual fit

88

6.1

Number of generated Cherenkov photons comparing between GEANT and
EGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

6.2

Tracks of 20 electron events with momentum 10MeV/c . . . . . . . . . .

92

6.3

Refractive index as a function of wavelength . . . . . . . . . . . . . . . .

92

6.4

Number of generated Cherenkov photons as a function of generated electron energy in Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . .

92

6.5

Attenuation coefficiency which put in Monte Carlo. . . . . . . . . . . .

94

6.6

Reflection probability on the surface of a PMT and a black sheet . . . . .

94

6.7

Cherenkov light spectrum . . . . . . . . . . . . . . . . . . . . . . . . . .

95

6.8

Number of hit-PMT belonging to the layer from 21st to 31st in the barrel
as a function of phi angle of the PMT position . . . . . . . . . . . . . . .
vii

97

LIST OF FIGURES

6.9

Direction of recoil electrons distribution in Monte Carlo . . . . . . . . . .

98

7.1

Efficiency of the experimental operation . . . . . . . . . . . . . . . . . . 100

7.2

Total charge of inner hit-PMT distribution . . . . . . . . . . . . . . . . . 101

7.3

Distribution of the time difference from the previous event . . . . . . . . 101

7.4

Typical electronics noise event and the Rnoise distribution . . . . . . . . . 102

7.5

Number of disconnected PMTs as a function of time . . . . . . . . . . . . 103

7.6

Typical flash PMT event and the relation between max charge and thenumber of hit around the cable with max charge . . . . . . . . . . . . . . 103

7.7

Typical event with small goodness and large Nhit . . . . . . . . . . . . . 105

7.8

Typical event including the PMT adjoin noise . . . . . . . . . . . . . . . 105

7.9

Ratio of noise events or flasher events to all events . . . . . . . . . . . . . 107

7.10 Max charge distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.11 Distribution of the distance between the muon and low energy event . . . 109
7.12 Typical spallation likelihood distribution . . . . . . . . . . . . . . . . . . 110
7.13 Vertex distribution of low energy events . . . . . . . . . . . . . . . . . . . 112
7.14 Vertex and directional cosine distribution before and after gamma ray cut 113
7.15 Energy distribution after each reduction step . . . . . . . . . . . . . . . . 114
7.16 Radon concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.17 Distribution of the reconstructed direction of recoil electrons . . . . . . . 117
7.18 Probability function for solar neutrino signal . . . . . . . . . . . . . . . . 118
7.19 Likelihood distribution for extraction of solar neutrino signal . . . . . . . 120
7.20 Solar neutrino flux ratio at the various intermediate analysis steps . . . . 121
7.21 Solar neutrino flux as a function of time . . . . . . . . . . . . . . . . . . 122
7.22 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.1

Individual solar neutrino contributions in various experiments . . . . . . 129

8.2

Deficit energy distribution of νe by MSW effect . . . . . . . . . . . . . . 130

8.3

Solar neutrino flux in each day-night bin . . . . . . . . . . . . . . . . . . 132

8.4

95% C.L. contour of the MSW analysis (exclude region) . . . . . . . . . . 134

8.5

Solar neutrino flux in day, night, mantle and core time regions observedin Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A.1 Logic diagram of the electronics system . . . . . . . . . . . . . . . . . . . 142
viii

LIST OF FIGURES

A.2 ATM Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A.3 Timing chart for signal and trigger . . . . . . . . . . . . . . . . . . . . . 143
B.1 Timing distribution of hit-PMTs in one event . . . . . . . . . . . . . . . 146
B.2 Occupancy value using the definition of Nef f . . . . . . . . . . . . . . . . 147
B.3 The difference of energy scale between data and Monte Carlo . . . . . . . 148
B.4 The distribution of the distance between the original vertex and the vertex
from the new method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
B.5 Typical event pattern of the normal event and the noise event . . . . . . 152
B.6 Relation of the uniformity of the azimuth angle distribution and the difference between the fitted and generated vertex . . . . . . . . . . . . . . 153
B.7 The distribution of the azimuthal angle non-uniformity . . . . . . . . . . 153
B.8 The efficiency of the noise reduction . . . . . . . . . . . . . . . . . . . . . 154
C.1 Residual Q distribution of muons . . . . . . . . . . . . . . . . . . . . . . 156
C.2 Time difference between muon and low energy event . . . . . . . . . . . . 157
C.3 Stability of relative energy scale in time . . . . . . . . . . . . . . . . . . . 158
C.4 Uniformity of relative energy scale in direction . . . . . . . . . . . . . . . 158

ix

List of Tables
2.1

Some measured solar parameters. . . . . . . . . . . . . . . . . . . . . .

6

2.2

Solar neutrino flux predicted by BP95 . . . . . . . . . . . . . . . . . . . .

8

2.3

Predicted solar neutrino rate in some SSMs . . . . . . . . . . . . . . . . .

9

2.4

Solar neutrino flux expected in the Homestake experiment . . . . . . . .

10

2.5

Solar neutrino flux expected in any gallium experiment . . . . . . . . . .

15

2.6

Summary of several solar neutrino experiments and the result . . . . . .

17

3.1

Cherenkov threshold energy . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.2

Several parameters of Super-Kamiokande detector . . . . . . . . . . . . .

36

4.1

Water transparency obtained by the direct measurement . . . . . . . . .

55

4.2

LINAC specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

4.3

Nuclear parameter concerned with the Nickel calibration . . . . . . . . .

62

5.1

Vertex shift and resolution for Nickel calibration . . . . . . . . . . . . . .

73

5.2

Vertex shift and resolution for Linac calibration . . . . . . . . . . . . . .

75

5.3

Vertex resolution in Monte Carlo . . . . . . . . . . . . . . . . . . . . . .

75

5.4

Directional resolution of LINAC data . . . . . . . . . . . . . . . . . . . .

78

5.5

Reconstructed energy and energy resolution of LINAC data . . . . . . . .

82

5.6

Event rate of each muon types . . . . . . . . . . . . . . . . . . . . . . . .

87

7.1

Summary of spallation products . . . . . . . . . . . . . . . . . . . . . . . 111

7.2

Reduction step and the results . . . . . . . . . . . . . . . . . . . . . . . . 115

7.3

Summary of the number of events in each energy bin . . . . . . . . . . . 119

7.4

Summary of systematic errors (%) . . . . . . . . . . . . . . . . . . . . . . 125

8.1

Solar neutrino flux in the daytime and the five night-time bins . . . . . . 132
xi

LIST OF TABLES

8.2

Predicted asymmetry between mantle and core in MSW effect . . . . . . 135

B.1 Differences between data and Monte Carlo in LINAC . . . . . . . . . . . 149
B.2 Number of remained hit-PMTs in several conditions to be neighboring
PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

xiiChapter 1
Introduction
The origin of the energy in main sequence stars like the sun is the following nuclear
fusion reaction,
4p → α + 2e+ + 2νe + 26.73MeV.

(1.1)

In the center of the sun, reaction(1.1) is realized through the reaction chains : pp-chains
and CNO cycle shown in Fig 1.1 and Fig 1.2. This process makes four protons form an
α particle, two positrons, and two neutrinos and generates 27MeV of energy. The CNO
cycle was first studied by H.A.Bethe in the 1930s[1]. The neutrino fluxes and spectra inthese reactions are predicted by so called Standard Solar Models (SSMs)[2]. The SSMs
have been improved over the past decades stimulated by neutrino measurements.
The neutrinos, generated in the center of the sun, go through the sun and appear at
the surface of the sun immediately (∼2sec) unlike the other particles like γ-rays. If theneutrinos from the sun are detected, it would be direct evidence that the nuclear fusion
reaction is the origin of the sun’s energy.
In the late 1960s, the first solar neutrino measurement was started by R.Davis andothers in the Homestake Gold Mine at Lead, South Dakota, USA[3]. This experimentdetected neutrinos by their interaction with 37 Cl, (νe +37 Cl →37 Ar + e). The number of37

Ar atoms generated by this reaction was counted. This kind of experiment is called a“radiochemical experiment”. The flux of neutrinos at the earth can be predicted using
SSM, however, the observed flux by the above measurement was significantly less thanthe expected flux[4].
The second solar neutrino experiment, Kamiokande-II, was operated more than twenty
years later in the Kamioka mine in Gifu, Japan. Kamiokande was a water Cherenkov
1

CHAPTER 1. INTRODUCTION

experiment started in 1983 to search for nucleon decay. The detector was upgraded sothat lower energy events could be detected. The solar neutrino measurement started in
1987. Solar neutrinos were detected by observing the Cherenkov light emitted by relativistic electrons produced by neutrino-electron scattering in the detector volume. The
first result was reported in 1989, and the flux of measured neutrinos was significantly
less than the expected value[5].
After that, two radiochemical experiments were operated in 1990s; those are GALLEX
in the Gran Sasso Laboratory in Italy[6] and SAGE in the Baksan Neutrino observatory in Russia[7]. Those experiments detected neutrinos by their interaction with 71 Ga,(νe +71 Ga →71 Ge +e). The number of 71 Ge atoms generated by this reaction was counted.
An advantage of these experiments was the low energy threshold, so they could detect
neutrinos from the basic pp reaction shown in Fig 1.1 (1). The ambiguity in the predicted solar neutrino flux is smaller than for other reactions. In these experiments a solar
neutrino deficit was also observed.
The solar neutrino experiments up to now will be explained in Section 2.2 in detail.
The newest results from them are summarized in Table 2.6. Compared to the predictionof SSMs, all of the independent solar neutrino measurements observed a solar neutrino
deficit. This is called “the solar neutrino problem”.
Various explanations of the solar neutrino problem have been proposed. Those approaches are mainly classified (1) the modification of the SSM, and (2) the not-yet
resolved properties of neutrinos, especially the MSW effect in neutrino oscillations which
will be explained in Section 2.4 in detail. The most effective method to solve the problem is an independent measurement on solar models, because SSMs have been improved
but the flux calculation from SSMs has remained ambiguous. Super-Kamiokande, whichstarted in 1996, can measure the energy spectrum and the time dependence of the solar
neutrino flux, (day/night or seasonal differences). These are model independent measurements of solar neutrinos. These analyses were studied by Kamiokande[8], but thestatistics were not sufficient to completely solve the problem. In Super-Kamiokande,
the detector volume is more than ten times larger than that of Kamiokande - the fiducial volume is thirty times larger - so we can get extremely high statistics. Therefore,
Super-Kamiokande is expected to provide definitive evidence of any possible new neutrino
physics independent of the uncertainties in the solar models.
2

In this thesis, the first results of solar neutrino observation in Super-Kamiokande from
300days of data are reported in detail. The solar neutrino flux deficit and the daytime
and night-time flux difference are discussed. Special emphasis is placed on the analysisof day/night flux difference which is independent of the solar models, sensitive to the
MSW effect and has small systematic uncertainties.
In Chapter 2, the current status of the solar neutrino problem is explained. In
Chapters 3 and 4, the experimental setup and the calibration are described. After the
event reconstruction method and the Monte Carlo simulation are described in Chapter 5
and in Chapter 6, respectively, the method of data analysis and the results are describedin Chapter 7. Finally, I discuss the results and make conclusions in Chapter 8.

3

CHAPTER 1. INTRODUCTION(1) p + p → D + e+ + νe(2) p + e− + p → D + νe

(99.75%)(0.25%)?

D + p → 3 He + γ?
3?

He + 3 He → α + 2p
(p-p I : 86%)3?

(5) 3 He + p → 4 He + e+ + νe

He + 4 He → 7 Be + γ(0.00002%)

?
7

?
7

7

Li + p → 2α(p-p II : 14%)8−(3) Be + e → Li + νe

Be + p → 8 B + γ

?

?

7

8

(4) B → Be∗ + e+ + νe?
8∗

Be → 2α(p-p III : 0.015%)
Figure 1.1: Proton-proton chain.
e+<E >=0.707MeV
N13
C12
He

C13
p

p

p

p

4

N

15

N14
He4
O15

e+
O
p

16

O17

<E >=0.997MeVp

F17<E >=0.999MeVe+

Figure 1.2: CNO cycle.

4Chapter 2
The solar neutrino problem
2.1

The standard solar model

In the core of the sun, two reaction chains are occurring to realize the net reaction of
Eq(1.1): the pp chain that starts with the direct fusion reaction of two protons; and the
CNO cycle that is a circular chain with carbon, nitrogen, and oxygen as catalysts. These
reactions are shown in Fig 1.1 and Fig 1.2, respectively. With the current knowledge ofthe temperature of the sun, the pp chain is believed to be dominant. The neutrinos fromeach reaction in the pp chain in Fig 1.1 are called: (1) pp neutrinos, (2) pep neutrinos, (3)7Be neutrinos, (4) 8 B neutrinos, and (5) hep neutrinos. As will be explained later, only

8

B neutrinos and hep neutrinos can be detected in Super-Kamiokande, but the expected

rate from hep neutrinos is very small.
In constructing a solar model, some assumptions are used: the sun is in hydrostatic
equilibrium, the transport of energy is caused by radiation or convection, the energy is
generated by nuclear reactions. The basic equations representing the above conditions are
solved numerically, and as the result of that calculation, we can determine the evolution
and inner structure of the sun. The solar models calculated this way are called “Standard
Solar Models” ([9][10][11]). In this section, I will mainly describe “BP95”, which was
published by Bahcall and Pinsonneault in 1995[10] among the several SSMs, and makea comparison with other SSMs will be also made.
The parameters listed in Table 2.1 were used for the input for the SSM calculation.
In addition to that, knowledge of the solar radiative opacity is needed. The energy
generated in the core is transported to the solar surface by photon radiation. The
5

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

photons are absorbed by the following physical processes: photon scattering on freeelectrons and inverse bremsstrahlung. The photon absorption coefficient, the radiative
opacity, appears in the equation of energy transport. It affects the temperature gradientof the solar interior and therefore the neutrino production. The surface abundances of theelements of the sun are measured by an absorption spectrum. The recent measurementsof them are consistent with the chemical composition in the meteorites. The effect of
the back diffusion of heavy elements is included in BP95.
Parameter

Value

Photon luminosity

3.844(1 ± 0.004) × 1033 erg/sec

Mass
RadiusAge

1.99 × 1033 g

6.96 × 1010 cm(4.57 ± 0.02) × 109 year

Table 2.1: Some measured solar parameters[10].
Using the above input data, the basic equations are solved numerically. We candetermine the solar interior as a function of time and space. Fig 2.1 shows the current
temperature and density as a function of the distance from the center. The initial ratioof heavy elements relative to hydrogen is calculated to be 0.0245, and the depth of theconvective zone, where the energy transport is caused by convection, is R = 0.712R⊙ .
(R⊙ is the solar radius.) The results from the standard solar model can be checked byhelioseismological measurements which provide the sound velocity profile in the solar
interior and the depth of the convective zone[12]. Both of these from the SSM agree very
well with the recent helioseismological measurements[13].
The solar neutrino flux depends on the solar core temperature as the following powerlaws[2],φ(pp) ∼ TC−1.2 ,φ(7 Be) ∼ TC8 ,φ(8 B) ∼ TC18 .

(2.1)

The temperature is determined mainly by radiative opacity. If it changes, the flux alsochanges. Particularly, the 8 B neutrino flux is very sensitive to the temperature as shownin Eq(2.1). However, the calculated temperature constrained by the helioseismologicalmeasurements was in excellent agreement with SSMs[54]. This topic will be discussed in
Chapter 8 in detail.
62.1. THE STANDARD SOLAR MODEL

Figure 2.1: Temperature and Density profile in the sun as a function of the
distance from the center of the sun.

For calculating the flux and the energy spectrum of solar neutrinos, the nuclear crosssections of the reactions shown in Fig 1.1 are needed. The cross section is conventionally
written as follows:
σ(E) ≡S(E)
exp(−2πη),Eη = Z1 Z2 (e2 /h̄v),

(2.2)
(2.3)

where v is the relative velocity between two particles with charges Z1 and Z2 . Here,the term exp(−2πη) is called the Gamow penetration factor, which shows the effect of
the Coulomb potential. S(E), “the astrophysical S-factor”, shows only the effect of thenuclear interaction. We need the value of S(E) at zero energy for the calculation ofsolar neutrino flux and the spectrum. The S-factor of each of the reactions in Fig 1.1 isdetermined by experiment or calculation in the case of reactions via the weak interaction.
The most important S-factor for solar neutrinos detected in Super-Kamiokande is forthe 7 Be(p,γ)8 B reaction, which is called S17 . It is directly proportional to the 8 B solar
neutrino flux. The value used in BP95 is S17 (0) = 0.0224(1±0.093) (keV·barn). The error
comes from the uncertainty in the extrapolation of the cross section in the 7 Be(p,γ)8 B
reaction to zero energy, which is caused by the existence of a resonance at 770keV[14].
Recently, the measurement using another method, which is the indirect measurement
using the Coulomb dissociation reaction 208 Pb(8 B,7 Be+p)208 Pb, gives a lower value[15].
7CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

This lower value of S17 (0.017 (keV·barn)) is used in another solar model, DS94 (DarShaviv)[16]. In this model, the 8 B solar neutrinos are reduced and 2.77 ×106 (cm−2

sec−1 ). However there are several disputed issues regarding this model and they are notsettled yet[17].
The predicted solar neutrino flux from BP95 is summarized in Table 2.2. The production point and the energy spectrum of several types of solar neutrinos are shown in Fig 2.2
and Fig 2.3, respectively. Besides BP95, several solar models have been investigated bychanging input parameters and are summarized in Table 2.3.
Source Flux (cm−2 s−1 )
pp
pep
7

Be

8

B

13

N

15

O

17

F

5.91 × 1010

(1.00+0.01−0.01 )

1.40 × 108(1.00+0.01−0.02 )

6.62 × 106(1.00+0.14−0.17 )

5.45 × 108(1.00+0.19−0.22 )

5.15 × 109(1.00+0.06−0.07 )

6.18 × 108(1.00+0.17−0.20 )

6.48 × 106(1.00+0.15−0.19 )

Table 2.2: Total flux of solar neutrinos predicted by BP95.

Figure 2.2: The production fraction ofsolar neutrinos as a function of solar
radius. The fraction of solar luminosity
is also shown by the dashed line.

82.1. THE STANDARD SOLAR MODEL

Figure 2.3: Energy spectrum of solar neutrinos.

SSM

S17 (keV·barn) Predicted rate in Homestake8

BP92[9]0.0224

TL93[11]0.02255.69(1±0.43) × 106

BP95[10]0.02248.0 ± 3.0 (SNU)
6.4 ± 1.4

9.3 +1.2−1.4

B neutrino flux (/cm2 /s)(4.44±1.1) × 106

66.62 +0.93−1.13 × 10

Table 2.3: Predicted solar neutrino rate in some SSMs.

9

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

2.2

Solar neutrino experiments

2.2.1

Homestake

The Homestake experiment operated by R.Davis and others began in 1968. It is
located 1500m underground (4100m of water equivalent) in the Homestake Gold Mineat Lead, South Dakota, USA. This experiment uses the inverse β-decay reaction
νe +37 Cl → e− +37 Ar,

Eth = 0.814MeV,(2.4)

for detecting solar neutrinos. The detector, a 615 ton tank, is filled with pure C2 Cl4liquid, and the isotopic abundance of 37 Cl is 24.23%. Argon atoms generated by theneutrino capture reaction are purged by helium gas and sent to a proportional counter
after each exposure which lasts about one to three months. The 2.82 keV Auger electrons
from electron capture are used to identify 37 Ar (35.0 day half-life).
The expected rate from the standard solar model of BP95 is [10]Rpred = 9.30

+1.2
−1.4

SNU.

(2.5)

“SNU”, the Solar Neutrino Unit is defined as 10−36 captures per target atom per second.
The contribution from each solar neutrino source predicted by BP95 is summarized inTable 2.4. The solar neutrinos detected by Homestake experiment are mainly 7 Be and8

B neutrinos.
solar neutrino expected rate
source

(SNU)

pp

0.00

pep

0.22

7

Be

1.24

8

7.36

B

13

N

0.11

15

O

0.37

Table 2.4: The expected flux of each solar neutrino source in the Homestake
experiment.
10

2.2. SOLAR NEUTRINO EXPERIMENTS

Figure 2.4: Argon production rate (solid line) and sunspot number (dottedline) as a function of time. The sunspot number is plotted inversely. (Higher numbers are lower in the graph.)

The counting rate from 1970 to 1995 is [18]Robs = 2.54 ± 0.14 ± 0.14 SNU(2.6)

on average. Compared to the predicted value, the observed value is significantly smaller,
and the ratio of data to SSM prediction is 0.273 ± 0.015 ± 0.015.

An anti-correlation between solar activity and the solar neutrino flux is reported by

the Homestake experiment. If the 11 year time variation is true, some new property of
the neutrino must be considered, for example, finite neutrino mass or magnetic moment,
since the neutrino production is expected to be stable on the scale of millions of years.
Fig 2.4 shows the Argon production rate and sunspot numbers as a function of time[19].
From this figure, one may note that the anti-correlation is not seen after 1989. This time
variation is not seen in Kamiokande as described in the next section.

2.2.2

Kamiokande

The solar neutrino measurement in Kamiokande started in January 1987 and ended in
February 1995. Kamiokande is located 1000m underground (2700m of water equivalent)
11

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

in the Kamioka mine in Gifu Prefecture, Japan. The detector consists of a cylindricaltank filled with 3000 tons of water and 948 20-inch photomultiplier tubes which arearranged over the surface of the tank providing 20% photo-cathode coverage. The fiducial
volume for the solar neutrino measurement is 680 tons of water.
For detection of solar neutrinos, neutrino-electron elastic scatteringνe + e− → νe + e−

(2.7)

is used. The Cherenkov light generated from the recoil electrons is detected by the PMTs.
The lowest energy threshold achieved in Kamiokande was 7MeV. One of the advantagesof this experiment is that the direction of the incident neutrinos can be determined. The
signal from the sun can be identified clearly.
The total effective live time of Kamiokande was 2079 days[20]. The 8 B solar neutrino
flux observed isφ(8 B)obs = 2.80 ± 0.19(stat.) ± 0.33(syst.) [×106 /cm2 /sec].

(2.8)

The predicted total flux of 8 B solar neutrinos from BP95 isφ(8 B)pred = 6.62

+0.93
−1.13

[×106 /cm2 /sec],(2.9)

which is also shown in Table 2.2. The observed value is less than that predicted, and theratio of data to SSM prediction is 0.423 ± 0.029 ± 0.050.

The period of the solar neutrino measurement in Kamiokande covered the entire pe-

riod of solar cycle 22. Fig 2.5 shows (a) the solar neutrino flux and (b) sunspot numbers.
From this figure, we cannot see any significant correlation within the experimental errors.
The advantage of the Kamiokande experiment is that the energy and the arrival timeof the neutrino events are measured. Fig 2.6 shows the energy distribution of the recoil
electrons (shown in the ratio of data to SSM prediction). No deviation is observed beyond
the errors. Fig 2.7 shows the daytime and night-time solar neutrino flux. No difference
between daytime and night-time is observed within the errors.
The shape of solar neutrino spectrum and the short time variation of the flux likedaytime and night-time difference does not depend on the solar model. These measurements make it possible to do a solar model independent analysis. If a deviation fromprediction is seen in one or both of these measurements, it reflects some new propertyof neutrinos. In Kamiokande, the statistics were insufficient for this analysis. However,122.2. SOLAR NEUTRINO EXPERIMENTS

Super-Kamiokande, which is a larger detector with the same advantages, is expected toobserve enough events for this analysis.

1(a)
D a t a / S S MB P 9 2

0.8

0.6

0.4

0.2

0

8 6

Figure 2.5: (a) The flux ratio of ob8 8

9 0

9 2

9 4

9 6

flux for each 200 day period in

Year
250

Kamiokande; the dashed line is the(b)
Number of sunspots

served solar neutrinos to predicted

average ratio for the entire period.

200(b) The sunspot numbers.

150

100

5 0

0

8 6

8 8

9 0

9 2

9 4

9 6

Year

Figure 2.6: The recoil electron energy spectrum in Kamiokande. The
flux ratio to SSM is shown.

Thehatched area shows the systematic
uncertainty.

13

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

1

D a t a / S S MB P 9 2

0.8

0.6

0.4

0.2

0
-0.8 -0.6 -0.4 -0.2
All
Day Night0

0.2 0.4 0.6 0.8

1

c o sδ s u n

Figure 2.7: The solar neutrino flux measured at Kamiokande during the daytime and night-time. The night-time is divided into 5 regions.
δsun shows the angle between the direction from the sun and thedetector axis.

2.2.3

GALLEX and SAGEThe following reaction is used in two gallium experiments,
νe +71 Ga → e− +71 Ge,

Eth = 0.233MeV.

(2.10)The GALLEX experiment started in 1991 and ended in 1997. It was located in the Gran
Sasso Underground Laboratory in Italy, and the depth is 3300m of water equivalent.
The 71 Ga target is used in the form of a 100-ton gallium chloride solution which contains
30.3 tons of natural gallium, thus 12 tons of 71 Ga. After about 3 weeks of exposure,the generated 71 Ge by the neutrino capture reaction, which is in the form of GeCl4 , istaken out by bubbling nitrogen gas. The final chemical product germane is sent to a
proportional counter where the electron capture decay of 71 Ge occurs, and the Auger
electrons are detected. The half life of the decay is 11.43 days, and the energy of theelectron is 10.37keV (K-peak) or 1.17keV (L-peak).
The SAGE experiment started in 1990, and is located at the Baksan Neutrino observatory in Russia, and the depth is 4715m of water equivalent. As the 71 Ga target, 55
tons of gallium metal is used, and the temperature is raised to extract 71 Ge. (Its melting
14

2.2. SOLAR NEUTRINO EXPERIMENTS

temperature is 29.8◦ C.) The procedure after that is similar to GALLEX. After exposure,the extracted 71 Ge atoms are counted by proportional counters.
Both experiments performed “source experiments” in order to check the absolutedetector efficiency. They used a man-made 51 Cr neutrino source. The source, which is
produced by neutron irradiation of 50 Cr, decays via electron capture to 51 V, and primarily
emits 746 keV neutrinos with 27.7 days of half life. The 71 Ge generated by 51 Cr neutrino
source is counted by the same procedure. The ratio of produced 71 Ge to the known
source activity, R, was measured. The GALLEX result is : R = 0.93 ± 0.08[6], while the

SAGE result is : R = 0.95 ± 0.12[7], This kind of measurement is important because it
demonstrates the validity of the radiochemical methods for solar neutrino detection.

The energy threshold in the reaction Eq(2.10) is low enough to observe the pp neutrinos. It is important to measure pp neutrinos because it is the most fundamental solar
neutrino production reaction and the flux practically depends only on the solar luminosity, so the ambiguity of calculated flux is much smaller than for any of the others. The
predicted counting rate in gallium experiments from BP95 is [10]Rpred = 137

+8
−7

SNU.

(2.11)

The contribution from each solar neutrino source predicted by BP95 is summarized inTable 2.5. It shows that 50.9% of the all solar neutrinos are from pp neutrinos in a
gallium experiment.
solar neutrino expected rate
source

(SNU)

pp

69.7

pep

3.0

7

Be

37.7

8

16.1

B

13

N

3.8

15

O

6.3

Table 2.5: The expected rate of each solar neutrino source in any gallium
experiment.
15

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

The observed counting rate for each experiments is [21][7]GALLEX
Robs= 76.2 ± 6.5(stat.) ± 5(syst.) SNU(2.12)= 69 ± 10(stat.)+5−7 (syst.) SNU(2.13)SAGE
Robs

The observed value is less than that predicted, and the ratio of data to SSM prediction
is 0.556 ± 0.047 ± 0.036 for GALLEX; 0.504 ± 0.073+0.036−0.051 for SAGE.
The time variation of the solar neutrino flux observed by the gallium experiments ischecked. Fig 2.8 and Fig 2.9 shows the Ge production rate as a function of time. It
has very large statistical errors in both experiments, however, from the analysis for time
variation in GALLEX, they find no evidence for any time dependence[6].

Figure 2.8: Ge production rate in each solar neutrino runs of GALLEX.

16

2.2. SOLAR NEUTRINO EXPERIMENTS

Figure 2.9: Ge production rate in SAGE as a function of time. The last pointis the combined 1990-1992 data.

2.2.4

Summary of the results in solar neutrino experiments

In all the solar neutrino experiments up to now, the observed flux is significantly
smaller than expected flux. Here, the deficit in the observed flux of solar neutrinos has
been summarized.

Experiment

Detection method

Energy threshold DATA/SSM (BP95)

Homestake37

0.814MeV

0.273 ± 0.015 ± 0.015

7.0MeV

0.423 ± 0.029 ± 0.050

Cl(νe ,e− )37 Ar

Kamiokande νe + e− → νe + e−
GALLEX
SAGE

71

Ga(νe ,e− )71 Ge

0.233MeV

0.556 ± 0.047 ± 0.036
0.504 ± 0.073+0.036−0.051

Table 2.6: The summary of several solar neutrino experiments and the result.
The deficit from prediction value is also shown.

17

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

2.3

The solar neutrino problem

As described in the previous section, the measured solar neutrino flux is significantly
smaller than the predicted value in all the solar neutrino detectors. This is called thesolar neutrino problem.
The first point of the solar neutrino problem is the 8 B neutrino deficit from theresult of Kamiokande, because Kamiokande is only sensitive 8 B neutrinos. Beyond the
deficit of 8 B solar neutrinos, 7 Be solar neutrinos are “missing” according to results of theradiochemical solar neutrino experiments. Fig 2.10 [22] clearly shows the 7 Be neutrino
deficit.
Explanation of this problem is the major physical issue and this is the subject of thisthesis. I will discuss the solar neutrino problem in detail in Chapter 8 with new resultsfrom Super-Kamiokande. One possibility is to change the model of the solar interior to
explain the problem; that is called an astrophysical solution. The other is to introduce
massive neutrinos which can cause neutrino oscillations. The basic concepts and formula
are described in the next section in detail.
Monte Carlo SSMs
TL SSM
Low Z
Low opacity
WIMP
Large S11
Small S34
Large S33
Mixing models
Dar−Shaviv modelCumming−Haxton model

0.5

BP SSM88

φ( B) / φ( B)SSM

1.0

Smaller S17

Combined fit
90, 95, 99% C.L.

T C power law

0.0

−0.5

0.0
7
7
φ( Be) / φ( Be)SSM

0.5

1.0

Figure 2.10: The constraint of 8 B/7 Be ratio from solar neutrino experiments
at 90, 95, and 99% C.L. Also shown are the predicted fromvarious SSMs.

18

2.4. NEUTRINO OSCILLATIONS

2.4

Neutrino oscillations

2.4.1

General description

One of the possible solutions of the solar neutrino problem is neutrino oscillations. If
neutrinos oscillate among different neutrino flavors, νe , νµ , and ντ , in flight from the sun
to the earth, νe ’s generated in the sun become “missing” when they arrive at the earth.
Neutrino oscillations occur when neutrinos have nonzero mass and a nonzero mixing
angle[23]. Here, for the two neutrino case, the flavor eigenstates of νe and νµ are themixing of the mass eigenstate of ν1 and ν2 as follows,














sin θ   ν1  ν1 
 cos θ
,
≡U

=

ν2
ν2
− sin θ cos θνµ νe 

(2.14)

where θ is the mixing angle. We solve the following equation to obtain the time evolutionof each neutrino flavor;








d  νe  νe 
,
=H

dt νµ
νµ

i

(2.15)

where H is Hamiltonian, diagonal for the mass eigenstate. In vacuum, the eigenvalue isas follows;
Ei =

q

2

m
p2 + m2i ∼
=E+ i
2E

(i = 1, 2),(2.16)

where m1,2 is the mass of the each mass eigenstate, p is the momentum, it is assumed thatthe two mass eigenstates have the same momentum and m1,2 ≪ E. The time evolutionof the mass eigenstates is represented as follows;

−iE1 t00e−iE2 t e ν1 (t) 
=ν2 (t)  ν1 (0) .


ν2 (0)(2.17)

From Eq(2.14) and (2.17), the time evolution of the flavor eigenstate becomes

−iE1 t00e−iE2 t e νe (t) 
=Uνµ (t) −1  νe (0) .
U νµ (0)(2.18)The probability that the state which was generated as νe at t = 0 is νe or νµ at the time
t is calculated from Eq(2.18) and (2.16) as follows;
P (νe → νe ; L) = 1 − sin2 2θ sin2
19

∆m2 L
4E

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM∆m2 (eV2 )L(m)= 1 − sin 2θ sin 1.27,
E(MeV)∆m2 L
P (νe → νµ ; L) = sin2 2θ sin2
4E!
∆m2 (eV2 )L(m)22,= sin 2θ sin 1.27
E(MeV)
22!

(2.19)(2.20)

where L is the distance traveled at the time t, and ∆m2 = m22 − m21 is the difference

between the squared masses.

Neutrino oscillations in vacuum can be applied to the solar neutrino problem. In
the case of ∆m2 /E ≪ L, the probability is averaged over time so that P (νe → νe ) =1 − 12 sin2 2θ[24]. Even in case of the full mixing (sin2 2θ = 1), the probability becomes
0.5 and should be uniform in all the experiments. However, the results in Homestake andKamiokande are much less than 0.5, and the probability obtained by all the experiments
is not constant as shown in Table 2.6. It is difficult to solve the solar neutrino problem
by the above explanation.
The vacuum oscillation parameters can be fine tuned by the results of solar neutrino
deficit. The parameter ranges are calculated to be sin2 2θ > 0.7 and ∆m2 ∼ 10−10 (eV2 ),which implies that the oscillation length is order of the distance from the sun to theearth. This fine-tuned solution is called “just-so” oscillations[25]. The effect could beseen by flux variation with the seasonal difference of the distance between the sun and theearth. Kamiokande and Super-Kamiokande are real time measurement of solar neutrinos.
Therefore, the possible parameter region of just-so oscillation can be checked by theseasonal difference of the observed solar neutrino flux[26].

2.4.2

MSW effects

When neutrinos propagate in matter, they acquire additional potential energy fromtheir forward scattering amplitude. The effect was first pointed out by Wolfenstein[27].
Mikheyev and Smirnov applied the effect to the solar neutrino problem and found thepossibility of resonant enhancement of oscillations in the matter of the sun[28]. Therefore,
it is called the MSW effect.
The potential of νe is different from the other types of neutrinos because of its charged
current interaction of νe -e. This additional potential energy is calculated to beVe =√2GF Ne ,20(2.21)

2.4. NEUTRINO OSCILLATIONS

where GF is the Fermi coupling constant and Ne is the electron number density. In thecase of neutrino propagation in matter, Eq(2.15) can be written








 







νe    E1 0  −1  Ve 0   νe 
d
+
i 
.
 
U
 = U 

dt νµ
νµ
0 0
0 E2

(2.22)Taking out a common diagonal phase factor, the above equation can be rewritten






2
+ Ve
d  νe   − cos 2θ · ∆m
2E
i 
=
2
1
dt νµ
sin 2θ · ∆m
2
2E

2
1
sin 2θ · ∆m
2
2E

0





  νe .
νµ(2.23)

Here, the eigenvector of the above matrix, which is analogous to vacuum oscillations, isdefined as follows,m ν1 



ν2m







− sin θm   νe  cos θm=sin θmcos θm,νµ(2.24)

where ν1m and ν2m are considered as mass eigenstates of neutrinos in matter, and θm is
the neutrino mixing angle in matter which is2

sin 2θ · ∆m2Etan 2θm =.
2
cos 2θ · ∆m
− Ve
2E

(2.25)

The above two equations mean that if the following condition;π∆m2− Ve = 0 (θm = ),cos 2θ ·2E
4(2.26)

is satisfied, oscillation can be amplified greatly even with a small vacuum mixing angle.
This is the resonance condition. From Eq(2.24) and (2.25), we can qualitatively trace
the state of |ν1m i and |ν2m i as follows;m |ν2 i ∼ |νe i



√
m
2
|ν
i
∼
(|ν
i
+
|ν
i)/
e
µ
2


at the very high density region,at the resonance region, |ν m i ∼ cos θ|ν i + sin θ|ν i2eµat the surface of the sun.

If the resonance condition is met and the electron density varies slowly enough (adiabatic condition), the mass eigenstate |ν2m i, which is generated at the core of the sun,changes from |νe i to |νµ i adiabatically, as is illustrated in Fig 2.11. The adiabatic con-dition is as follows;

sin2 2θ ∆m2|dNe /dr|·≥ 2π
cos 2θ
E
Ne
21

!

res

.

(2.27)

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

The survival probability of νe in the adiabatic condition is shown in Fig 2.12. The
explanation of the solar neutrino problem using it is called “the adiabatic solution”.
From Eq(2.26), the critical energy to have an MSW resonance for given parametersiscos 2θ · ∆m2
Ecrit = √2 2GF Nemax(2.28)

where Nemax is the maximum electron density in the sun. Therefore, the neutrino spectrum is suppressed in the region of energies higher than Ecrit .

Figure 2.11: The MSW effect in the sun. The flavor eigenstate νe at the highdensity is approximately the same as the higher mass eigenstateν2 . As the electron density decreases slowly, the flavor eigenstate remains close to ν2 . Therefore, the flavor eigenstate at thesurface of the sun is close to νµ .

If the electron density varies rapidly, “level jumping” from |ν2m i to |ν1m i occurs. The

jumping probability is[29]−π∆m2 sin2 2θ
Pjump = exp
4E cos 2θ
"22

Ne|dNe /dr|

!

res

#

(2.29)

2.4. NEUTRINO OSCILLATIONS

Figure 2.12: The survival probability of νe generated in the core of the sun
at R=0, when E/∆m2 = 105 and sin2 2θ = 0.01.

As a result of level jumping, the conversion from |νe i to |νµ i is suppressed. The explana-tion of the solar neutrino problem using this is called the “non-adiabatic solution”. The
behavior in this parameter region is shown in Fig 2.13.
From Eq(2.29), when the energy is higher, Pjump becomes higher and the probabilityof the conversion becomes smaller. Hence, the neutrino spectrum is suppressed in thelower energy region for the non-adiabatic condition.
The survival probability of νe as a function of energy in several MSW parameters,
which include both the adiabatic region and the non-adiabatic region, are shown in
Fig 2.14.

23

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

Figure 2.13: The survival probability of νe generated in the core of the sun,when E/∆m2 = 6 × 106 and sin2 2θ = 0.01.

Figure 2.14: The survival probability of νe state by MSW effect as a functionof Energy, when sin2 2θ = 0.01 and for several values of ∆m2 .

24

2.4. NEUTRINO OSCILLATIONS

2.4.3

Regeneration in the earth

As in the above discussion, the MSW effect would also occur when neutrinos propagate through the earth[30].

The electron density profile of the earth is shown in

Fig 2.15[31]. Because the density in the earth is different from the one of the sun,the survival probability of νe state in the earth is also different with the case in the sun.
For typical parameters for which the MSW effect would cause a measurable day/nightflux difference, the probability of νe state is shown in Fig 2.16. The example shows thatthe probability of detecting νe increases because of the regeneration through the earth
from νµ generated by the oscillation in the sun. Fig 2.17 shows the MSW effect withand without going through the earth when the equation is solved numerically. We canalso see the enhancement of the MSW effect by the earth. Therefore, the possible parameter region of MSW might be checked by the difference between the observed solar
neutrino rate in the daytime and night-time. The flux at night would be larger than in
the day. This kind of the observation can be performed only by real time measurements
like Kamiokande or Super-Kamiokande. The analysis of the MSW effect in the earth isone of the main topics of this thesis.

Figure 2.15: Density profile of the earth.

25

CHAPTER 2. THE SOLAR NEUTRINO PROBLEM

Figure 2.16: The probability of νe state regenerated in the earth, whenE/∆m2 = 2 × 106 , sin2 2θ = 0.1, and neutrinos go throughthe core of the earth. The horizontal axis is the ratio of thepath length to the diameter of the earth.

Figure 2.17: The expected probability of νe state by MSW effect as afunction of E/∆m2 , when sin2 2θ =0.1. The solid line shows the case ofno earth effect, and the dashed line
shows the earth effect, where neutrinos go through the core of the earth.

26

2.4. NEUTRINO OSCILLATIONS

2.4.4

The allowed parameter regions of the MSW effects

From the results of the past four solar neutrino experiments, the allowed region of the
MSW effect has been studied and estimated. The combined result of all the experiments
gives an allowed region is shown in Fig 2.18. As shown in the figure, two parameterregions are allowed: “the small angle solution” and “the large angle solution”.
In the small angle solution, the deficit of neutrinos depends on its energy as shownin Fig 2.14. Around this parameter region, almost all 7 Be neutrinos and about 40% of
7

B neutrinos have converted such that the results of all the experiments are matched.
The large angle region is sensitive to the solar neutrino flux difference between daytime

and night-time because the electron-neutrino regeneration through the earth occurs inthis parameter region. From the result of the daytime and night-time flux difference in
Kamiokande, the region shown in Fig 2.18 was excluded.
Figure 2.18: The contour of 95%
C.L. allowed region of current
four experiments.

(filled area)

The thin line shows the allowed
region which is calculated by the
deficit of the absolute solar neutrino flux in Kamiokande fromBP95.

The dotted line shows

the result of Homestake and thedashed line shows the result of
Gallium experiments. The insideregion of a thick line is excluded
from the result of day/night flux
variation in Kamiokande.

27

Chapter 3
The Super-Kamiokande Detector
3.1

Detection method

3.1.1

Imaging water Cherenkov detector

Super-Kamiokande is an imaging water Cherenkov detector. It detects Cherenkov
light generated by charged particles scattered by neutrinos in water. In a medium withan index of refraction of n the light velocity is c/n. When a charged particle traverses
the medium with velocity larger than the light velocity, so called Cherenkov light isemitted[32]. The minimum energy of the particles with this velocity (called “Cherenkov
threshold energy”) is,
Particle

Cherenkov threshold in total Energye±0.768(MeV)

µ±

158.7

π±

209.7

Table 3.1: Cherenkov threshold energy of various particle.
Cherenkov light is emitted in a cone of half angle θ from the direction of the particle
track:cos θ =

1
,
nβ

(3.1)

where β = v/c, and θ is 42◦ for β = 1.0 in water. For example, the typical 20MeV
electron simulation event is shown in an exploded view of the cylindrical water tank in
29

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Fig 3.1.
The spectrum of the Cherenkov light as a function of the wavelength λ is
dN
1
2παx
1− 2 2
=
dλ
c
nβ

!

1
,
λ2

(3.2)

where α ≃ 1/137 (fine structure constant) and x is the length of the electron trajectory.

A charged particle emits about 390 photons per 1cm of path length in the water in the
wavelength region, 300nm ∼ 700nm, where the photo multiplier tubes are sensitive.

NUM
7
RUN
0
EVENT
7
DATE 97-Dec- 1
TIME
23:19:35
TOT PE:
102.9
MAX PE:
6.4
NMHIT :
94
ANT-PE:
0.0
ANT-MX:
0.0
NMHITA:
0

RunMODE:MonteCarloTRG ID :00000000
T diff.:
0.
us
:
0.
ms
FSCC:
0
TDC0: 14910.0
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 0

DIR:-0.95, 0.21, 0.25
X: -771.9cm
Y:
0.0cm
Z:
-1.0cmR:
771.9cm
NHIT:
76
good:
0.78

Figure 3.1: Typical expected event to be observed in Super-Kamiokande.
This is a 20MeV electron simulation. The generated vertex anddirection are (-800,0,0)cm and (-1,0,0), respectively.

30

3.1. DETECTION METHOD

3.1.2

Solar neutrino interactions in the detector

Solar neutrinos in Super-Kamiokande are measured through the following reaction;
ν + e− → ν + e− .

(3.3)

The advantage of an experiment using this interaction is that we are able to obtain
information on(1) the direction of the incident neutrinos because the recoil electrons in Eq(3.3) arescattered to almost same direction as the neutrinos,(2) the exact arrival time of the incident neutrinos and(3) the energy distribution of the recoil electrons which reflects the energy spectrumof the incident neutrinos.
The cross section for this scattering can be calculated using standard electroweak theory,and the differential cross section is[33]dσTe 2G2 m eme Te
A0 + B0 (1 −,= F
) + C0
dTe
2π
Eν
Eν Eν




(3.4)

where GF ,me ,Eν ,Te are the Fermi coupling constant, the electron mass ,the incoming
neutrino energy and the kinetic energy of the recoil electron, respectively. The parameters
A0 , B0 and C0 are defined by
A0 = (gV + gA )2 , B0 = (gV − gA )2 , C0 = (gA2 − gV2 ),1
1
gV = 2 sin2 θW + , gA = +for (νe , e),2211gV = 2 sin2 θW − , gA = −for (νµ , e)(ντ , e),22where θW is the Weinberg angle. From Eq(3.4), the overall factor in the differential crosssection isG2F me= 4.31 × 10−452π(cm2 /MeV).

(3.5)

We also consider radiative corrections for the one-loop electroweak and QCD in theinteraction Eq(3.3). A QED radiative correction is also considered. These corrections
reduce the relative probability of observing recoil electrons by about 4% in our energy
region for sin2 θW = 0.2317 [34].
31CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

The cross section as a function of neutrino energy including radiative corrections isshown in Fig 3.2. This cross section can be calculated by integrating Eq(3.4) between
0 and the maximum value, Tmax , of the electron kinetic energy. Here Te for given Eν islimited by kinematics as follows,
Tmax =

Eν
.
1 + me /2Eν

(3.6)

As shown in the figure, when Eν is 10MeV, which is a typical energy of 8 B solar neutrinos,
the cross section of ν-e scattering is:
σtotal = 8.96 × 10−44(cm2 )for (νe , e),(3.7)

1.57 × 10−44(cm2 )for (νµ , e)(ντ , e).

(3.8)

The differences of the cross section between νe and νµ,τ is because the scattering of νµ,τon an electron can take place only through the neutral current interaction, while in caseof νe , both neutral and charged current interactions take place. The (νµ,τ , e) cross section
is approximately six times less than (νe , e) cross section.

Figure 3.2: The cross section of the interaction for νe , νµ , ντ with electron as
a function of neutrino energy.

323.1. DETECTION METHOD

The energy distribution of recoil electrons scattered by solar neutrinos is given by"Z

F (Te )dTe =Eν,max0#dσdEν dTe ,φ(Eν )
dTe(3.9)

where φ(Eν ) is the solar neutrino spectrum at earth (described in Section 2.1 in detail), and Eν,max is the maximum energy of solar neutrinos. Fig 3.3 shows the energy
distribution of recoil electrons with only 8 B and hep solar neutrinos considered.

Figure 3.3: The spectrum of recoil electrons scattered off by 8 B and hep solar
neutrinos.

The angle, θ, between the direction of a recoil electron and an incoming neutrino isgiven by1 + me /Eν
cos θ = q.
1 + 2me /Te(3.10)

The angular distribution of recoil electrons is given by
F (θ)dθ ="Z

0Eν,max#dσ dTedEν dθ.
φ(Eν )dTe dθ

(3.11)

Fig 3.4 shows the angular distribution of recoil electrons with total energy greater than0, 5, 7 and 10MeV. From this figure, the scattering angle is less than 20◦ if the thresholdenergy is greater than 5MeV. For a larger threshold energy, the angular distribution
33

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

becomes much more strongly forward peaked. The angular dispersion defined by thevalue which includes 68% of the distribution, is 12.3◦ , 9.1◦ and 5.7◦ for the electrons
with total energy greater than 5, 7 and 10MeV, respectively

Figure 3.4: The angular distribution of recoil electrons from incident solar
neutrinos. Here, “ALL” means integrated over the 8 B and hep
SSM spectra.

3.2

Detector

3.2.1

Detector outline

The Super-Kamiokande detector consists of about 50000 tons of pure water filled ina cylindrical water tank (diameter 39.3m and height 41.4m), a water and air purification
system, photomultiplier tubes (PMT), electronics and online data acquisition system,and offline computer facilities. Fig 3.5 shows a schematic view of the detector. It is
located 1000m underground (2700m of water equivalent) in the Kamioka mine in Gifu
Prefecture, Japan. Its latitude and longitude are 36◦ 25’ N and 137◦ 18’ E, respectively.
The reason that the detector is underground is to shield against cosmic ray muons.
34

3.2. DETECTOR

Compared to ground level, the intensity of muons is reduced by about 10−5 at the depthof the Super-Kamiokande detector. The muon rate in Super-Kamiokande is 1.88Hz. (See
Section 7.2.3)

Figure 3.5: The detector appearance. Inset at bottom right shows the location within the mountain. (cutaway view)

The wall of the cave is covered by “Mineguard”, a polyurethane material made by
the Canadian company Urylon, which prohibits the radon emanating from the rock.
The water tank is made of stainless steel, and it is divided into an inner part and anouter part. These are summarized in Table 3.2. The reason for the division is mainly
to identify remaining muon events from outside the tank and to reject gamma rays andneutrons from the rock.
The tank is sealed tightly to keep the mine’s radon rich air from entering. Radon gas is
the most serious background for the solar neutrino analysis as described in Section 7.2.7.
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 is caused by the flow of air in the mine.
35

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Tank

Dimensions
VolumeOuter partThickness

39.3m in diameter × 41.4m in height
50 kton

2.6m (7.2 R.L. and 4.3 N.L.) on top and bottom
2.75m (7.6 R.L. and 4.6 N.L.) on barrel

Inner part

Volume32 ktonNum. of PMT

302 (top), 308 (bottom) and 1275 (barrel)

Dimensions

33.8m in diameter × 36.2m in height

VolumeNum. of PMT
Fiducial area Thickness
Volume18 kton1748 (top and bottom) and 7650 (barrel)
2m (5.5 R.L. and 3.3 N.L.) from the inner wall
22ktonTable 3.2: Several parameters of Super-Kamiokande detector. R.L and N.Lmean radiation length and nuclear interaction length, respectively.

Air blows into the mine in the winter and out of the mine in the summer.
We use 11146 20-inch PMTs in the inner detector and 1885 8-inch PMTs in the outerdetector. This is summarized in Table 3.2. The characteristics of the PMTs are describedin Section 3.2.3.
In the inner detector, 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.
In the outer detector, there are 2 outer PMTs in the region behind each 12 inner
PMTs, and they face outward from the support structure. Around each outer PMT,
there is wave length shifter to increase photo coverage. In order to increase the lightdetection efficiency, all surfaces of the outer detector are covered with white tyvek sheetswith a reflectivity of above 80%.
The inner part and outer part are optically isolated using black sheets and tyvek
sheets. There are complicated stainless steel frames for supporting the PMTs and so onin this optically insensitive region. The schematic view of these structures is shown in
Fig 3.6.

36

3.2. DETECTOR

Tyvek

Top

8" PMT

Black seat

Barrel20" PMT

BottomFigure 3.6: The schematic view of the frame which supports PMTs.

Construction started in 1991. First, the cavity was excavated until the middle of1994. After that, water tank construction started, and it finished in the middle of 1995.
From June of 1995, we installed PMTs and set the electronics system simultaneously.
This continued until the end of 1995. Water filling was from January to March in 1996.
After a 1 month test run, we started normal data taking from April 1st in 1996.

3.2.2

Water and air purification

Water purification system
In the Kamioka mine, there is clean water flowing near the detector and it can beused freely in large quantities. This water is circulated through the water purification
37

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

system. The purpose of this water purification system is:
1. To keep the water transparency as high as possible.
Small dust, metal ions like Fe2+ , Ni2+ , Co2+ , and bacteria in the water are removed.
2. To remove the radioactive material, mainly Rn, Ra, and Th. Especially, radon isa serious background for the solar neutrino analysis.

mFigure 3.7: The water purification system.

Fig 3.7 shows the water purification system. The water purification system consistsof the following components,• 1 µm Filter• Heat exchanger:

The water temperature rises due to the heat generated by pumps and PMTs. The

temperature is kept at around 14◦ C to suppress bacteria growth.
38

3.2. DETECTOR• Ion exchanger:

To remove metal ions in the water.

• Ultra-Violet sterilizer:

To kill bacteria. The documentation states the number of bacteria can be reduced

to less than 103 ∼ 104 /100ml.
• Vacuum degasifier:To remove gas resolved in the water. It is able to remove about 99% of the oxygengas and 96% of the radon gas• Cartridge polisher:This is a high performance ion exchanger.

• Ultra filter (UF)To remove small dust even of the order of nanometers. Fig 3.8 shows the resistanceof the water sampled at the inlet and the outlet of the Ultra filter. This can becompared the chemical limit of 18.24 M Ωcm.

Figure 3.8: The resistance of the water sampled at inlet and outlet of the
Ultra filter as a function of time.

39

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Fig 3.9 shows the number of particles after the UF. After the Ultra filter, the water isreturned 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 shown by the dashed line in Fig 3.7.
• Buffer tank
• Reverse osmosis

Figure 3.9: The number of various sizes of particles as a function of time.

The water is taken from the top of the tank using a pump and returned to thebottom of the tank. Its flow rate is about 50 tons/hour. This system keeps the watertransparency above 70m as described in Section 4.4.
Radon free air system
There is ∼60cm space between the surface of the water and the top of the water tank.

Radon gas contaminated in the air in the gap could dissolve in the water. Radon free40

3.2. DETECTOR

air is sent to this region. The concentration of radon in the air is shown in Fig 3.10. It
is of the order of 10 ∼ 103 Bq/m3 . It changes seasonally because the flow of air in themine changes.

Figure 3.10: The radon concentration in the air of various position as a function of time.

Fig 3.11 shows the radon free air system. This system consists of the following
components.
• Compressor:

Air is compressed to 7.0 ∼ 8.5 atm.

• 0.3 µm air filter• Buffer tank
• Air drier:

To remove moisture in the gas to improve the efficiency of removing radon. Thissystem can remove CO2 in the gas as well.
41

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR• Carbon column:

To remove radon gas.

• 0.1 µm and 0.01 µm air filter
As shown in Fig 3.10, the concentration of radon in the air through this system is reduced
to the order of 10−2 Bq/m3 in all seasons.

m

m

m

Figure 3.11: The radon free air system.

3.2.3

Photomultiplier tubes

The photomultiplier tubes (PMTs) used in the inner part of Super-Kamiokande are
20-inch diameter PMTs developed by Hamamatsu Photonics K.K. in cooperation withmembers of Kamiokande[35]. The PMTs used in Super-Kamiokande have some improvement over those used in Kamiokande. The size and shape of this PMT is shown in
Fig 3.12. The photo-cathode is made of bialkali (Sb-K-Cs) that matches the wave lengthof Cherenkov light. The quantum efficiency (Q.E.) is shown in Fig 3.13. As can beseen from this figure, the value of Q.E. at the typical wave length of Cherenkov light(λ = 390nm) is 22%. A Venecian-blind type dynode is used for this PMT because of42

3.2. DETECTOR

its large photosensitive area. However, this large photosensitive area makes the transit
time longer (about 100nsec at 1 photo electron (p.e.) light level) and transit time spread
becomes worse. This type also has a smaller collection efficiency for secondary electrons
compared to other types. The bleeder-chain was optimized in order to achieve goodtiming response and collection efficiency. As the result of this optimization, an 11-stage
voltage divider (the ratio of voltage division is 8 : 3 : 1 : · · · : 1) was used, and three

types of focusing mesh-plates between the cathode and the first dynode were adopted.
The average value of the collection efficiency is more than 70%. The one photo electron
peak can be seen clearly as shown in Fig 3.14. The transit time spread is about 2.2nsec.

These measurements were reported in detail in[36]. It is important for the analysis ofsolar neutrino data to have the ability to see 1 p.e. and good timing resolution, because
the number of photons arriving at the PMT is generally one and the timing resolution
affects the vertex reconstruction.
If the geo-magnetic field is reduced to be less than 100 mG, the PMTs have a uniform
response[36]. The residual geo-magnetic field is kept less than 100 mG in every positionof the tank by using compensation coils.

~ 70000

cable length
φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure( 610 20 )

~ 720

(mm)

Figure 3.12: The schematic view of the PMT used in Super-Kamiokande.

43CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.13: The quantum efficiency of
the PMTs used in Super-Kamiokande
as a function of the wave length of incident light.

Figure 3.14:

One photo electron

peak of the PMTs used in SuperKamiokande.

Fig 3.15 shows the average dark noise rate above the threshold of electronics for the
first one year of operation. It is stable and about 3.1 kHz after May of 1996. The numberof accidental hits caused by the dark noise is estimated about 2 hits in any 50nsec time
window. The dark noise rate is considered in our Monte Carlo simulation program.
The high voltage system for the PMTs consists of a distributor(A933K), a controller(SY527), and an interface module(V288) by CAEN Co. The value of the highvoltage is set for each PMT to have the same gain as described in Section 4.1. The HVvalues of all channels are monitored every 10 minutes.
The PMTs used in the outer part are 8-inch Hamamatsu R1408 PMTs, each witha wave length shifter plate which is 60cm square. Photons in the wave length range
between 300 nm and 400nm are absorbed by the wave length shifter and about 55% of
the photons isotropically re-emitted with a longer wave length.
44

3.2. DETECTOR

Figure 3.15: The dark noise rate of the PMT used in Super-Kamiokande asa function of time.

3.2.4

Electronics and Data acquisition

In this section, the essence of the data acquisition system is described. A detailed
explanation can be seen in Appendix A.
The signal from a PMT is sent to a front end module called an “ATM” (Analog
Timing Module)[37]. We use 934 ATM modules. The signals from 12 PMTs are handledin each ATM module. If the signal exceeds the threshold value, equivalent to about 0.32
p.e., a rectangular pulse (200nsec in width and 11mV in height) is generated. This iscalled the “HITSUM signal”. In the ATM module, both timing and charge of the signal
are also digitized. HITSUM signals are summed and used for the trigger. The summing
signal goes through a discriminator which determines the trigger threshold. The valueof the trigger threshold is now set to 320 mV which is equivalent to about 29 hits, orapproximately 5∼6 MeV. This means that a global trigger is generated when 29 PMTs
are hit in any 200nsec time window. The trigger rate is about 11Hz and has been stable
during the course of the experiment as shown in Fig 3.16. The trigger efficiency will be
described in Section 4.6.
45

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

The digital data from ATM modules are sent to 8 online computers for data acquisition. These data are transferred to an online host computer via FDDI. They are then sent
to the offline computer located outside of the mine via an optical fiber cable. The datais transferred every ten minutes, and the size of the file corresponding to ten minutes isabout 70MByte. The offline host computer saves all the data in a tape library, converts
the data of ADC and TDC counts to the units of photo electrons and nano-seconds,
respectively, and distributes the data to analysis computers for preliminary reduction.

Figure 3.16: The trigger rate in Super-Kamiokande as a function of time.

46

Chapter 4
Calibration
4.1

Relative gain of the PMTs

The high voltage of each PMT is set in order to make the gain of each PMT the same.
Each PMT has a standard high voltage value supplied from Hamamatsu Co. which wasmeasured just after its production by using three methods: DC light source; Xe lightsource; single photo-electron distribution, However, we have re-calibrated the gain of
all PMTs by ourselves in Super-Kamiokande, because a possible long term drift of thecalibration system at Hamamatsu may have caused a systematic gain difference.
The relative gain was measured by the system shown in Fig 4.1. The light generated
by a Xe-lamp is passed through an ultraviolet (U.V.) filter and injected into a scintillator ball via an optical fiber. The scintillator is an acrylic ball with BBOT scintillator(wavelength shifter) and MgO powder. This BBOT scintillator absorbs U.V. light andemits light the wavelength of which is near that of Cherenkov light. MgO powder is used
for diffusing light in the ball. The intensity of the primary U.V. light is monitored by amonitoring system, and one of the outputs is used for a trigger, as shown in Fig 4.1.
In this system, the high voltage value of each PMT is set so that the corrected Q ofeach PMT is same as for all others. Here the “corrected Q” is pulse height corrected
for light attenuation, acceptance, and uniformity of the scintillator ball. It is further
normalized by Xe monitor pulse height. This measurement is done at various positionsof the scintillator ball, and settings of the high voltage value. Fig 4.2 shows the corrected
Q distribution of all PMTs after the adjustment. The relative gain spread is 7%. Thisremaining difference is later corrected in software.
47

CHAPTER 4. CALIBRATIONUV filter ND filter
Xe Flash Lamp

Photo
Diode

SK TANK

Photo
Diode

Optical fiber

ADC

Scintilator Ball
PMT
Scintilator

Monitor20inchPMT

Trigger

Figure 4.1: The relative gain measurement system.

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 4.2: The corrected Q distribution of all PMTs in the relative gain
calibration.

48

4.2. SINGLE PHOTO-ELECTRON DISTRIBUTION

4.2

Single photo-electron distribution

In the previous section, only the relative gain of PMTs is discussed. In this section,
we describe how to measure the absolute gain, particularly at single photo-electron level.
We get only the charge information from the electronics output, in units of pico coulombs.
We have to know how to get the number of photo-electron from this charge value. The
single photo-electron distribution is used for this purpose.
The method is the same as the Nickel calibration, because the number of photonelectrons observed in each PMT is almost one in Nickel calibration. Fig 4.3 shows the
charge distribution of each hit-PMT in units of pico coulombs. The mean value in this
distribution is 2.055 pico coulomb, which is equivalent to single photo-electron.

Figure 4.3: The charge distribution of each hit-PMT in Nickel calibration.
The large spike near 0 is caused that the photoelectron go
through the first dynode.

The “occupancy”, which is hit rate of getting a single photo-electron signal as definedby Eq(B.2), is used in order to check the up-down symmetry of the detector. Fig 4.4 shows
the distribution of average occupancy over PMTs belonging to each layer of the barrel
part. From this figure, occupancy appears higher in the top and bottom layers than the49CHAPTER 4. CALIBRATION

middle layers because of reflections from the surface of PMTs, however, the distribution
is symmetric. Further, we checked that real data and Monte Carlo data were consistent.
This result is crucial for analysis of the day-night effect of solar neutrinos.
Note that there are the layers with high occupancy in Fig 4.4. This occurs because
PMTs belonging to these layers are made older than others and the quality is different.
These PMTs have different single photo-electron detection efficiency even if the relative
gain is adjusted to be same. The difference is 20% on average, and this is corrected forin energy determination as described in Section 5.3.

Figure 4.4: The distribution of average occupancy over PMTs belonging toeach layer of the barrel part. The white squares show the older
PMTs. Their quality is different with others.

4.3

Timing of PMTs

The relative timing of each hit-PMT is important for determination of the vertex. (ref.
Section 5.1) This relative timing depends on observed charge because of the discriminatorslewing effect. The timing difference caused by pulse height has to be measured precisely
50

4.3. TIMING OF PMTS

in each PMT. The timing resolution also depends on pulse height and can be measured
at the same time.
Fig 4.5 shows the system for measuring the relative timing of hit-PMTs. The N2 laser
light source can emit intense light of wavelength 337nm within a very short time (less than
3 nano seconds). The wavelength is converted to 384 nm which is near the Cherenkov
light wavelength by a dye laser module. The light intensity is changed using an opticalfilter, and the measurement of PMT timing at various pulse heights is made. After going
through the optical filter, the light is split into two, one goes to the diffuser ball in thewater tank through an optical fiber, and the other signal is used for monitoring andmaking trigger signals. The schematic view of the diffuser ball is also shown in Fig 4.5.
The diffuser tip which is located at the center of the ball is made from TiO2 suspended
in optical cement. Light emitted from the tip is further diffused by LUDOX, which issilica gel made with 20nm glass fragments. The combination of diffuser tip and LUDOX
can make modestly diffused light without introducing timing spread.

variable
attenuation
filteroptical fiber
N 2 laser
generator
optical fiber

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 4.5: The system of the measurement of the relative timing of hit-PMT.

51

CHAPTER 4. CALIBRATION

A typical 2-dimensional plot of timing and pulse height is shown in Fig 4.6, which wecall a “TQ-map”. Each PMT has its own TQ-map, because the character each PMT is
unique. The vertical axis of this figure shows the hit timing; larger values indicate earlier
hit timing. As shown in the figure, higher charge hits have earlier timing and better
resolution. The typical timing resolution at the single p.e. level, which is important forthe solar neutrino analysis, is 3nsec.

T (nsec)

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

Q (p.e.)Figure 4.6: A typical 2-dimensional plot of timing and pulse height distribution. (TQ-map)

4.4

Water transparency

In Super-Kamiokande, the maximum distance of Cherenkov light traversal reaches
60m. The attenuation of Cherenkov light in water must be measured precisely, because
the energy determination is affected by the water transparency.
52

4.4. WATER TRANSPARENCY

The water transparency is measured two ways: direct measurement using laser and
CCD camera, used for finding the absolute value of the water transparency; and using
the decay electron events from stopping muons, or using penetrating muons observed inSuper-Kamiokande to check the time variation of water transparency on an O(1week)time scale.

4.4.1

Direct measurement

Fig 4.7 shows the system for the direct water transparency measurement, which
consists of laser, diffuser ball, and CCD camera. For the light source, a N2 laser anda dye module are used[38]. This dye module is able to produce mono chromatic laser
output ranging from 337 nm to 600 nm. The light is split, one goes to a 2-inch PMT
for monitoring the light intensity and another goes to an acrylic diffuser ball via an
optical fiber. MgO is used for diffusing light in the ball. The light from the diffuser ballis received by a CCD camera, Fig 4.8 shows the picture of the light from the diffuserball taken by CCD camera. The advantage of using CCD camera is that the effect of
the scattering light is removed if only the region of the ball on a CCD view is used formeasuring pulse height of the ball.

Beam Splitter (50:50)
CCD camera
DYE / N2 laser
Lens

Integrating Sphere<< laser box >>Diffuser Ball
2inch PMT
Optical Fiber (70m)<< SK Tank >>Figure 4.7: The system of the direct water transparency measurement.

53

CHAPTER 4. CALIBRATION

Figure 4.8: The picture of the light from the source taken by CCD camera.

The total number of received photos by CCD camera is measured in various positions,and it is normalized by the monitoring PMT data. For example, Fig 4.9 shows theresult for 400nm wavelength light. The derived water transparency is 72.09m. Thismeasurement is applied to various wavelength light, and the result is summarized inTable 4.1.

Figure 4.9: The result of the direct
water transparency measurement. The
horizontal axis is the distance between
the diffuser ball and CCD camera,
and the vertical axis is the normalized
charge detected by CCD. The wavelength is 400nm.

54

4.4. WATER TRANSPARENCY

Wavelength (nm) Water transparency (m)
337

67.1

400

103.1

500

34.25

580

10.32

Table 4.1: The water transparency obtained by the direct measurement invarious wavelength light.

4.4.2

Measurement using real data in Super-Kamiokande

There are two methods to measure the water transparency using real data in SuperKamiokande; decay electron events from stopping muon and penetrating muon events.
Unlike the direct measurement described above, we can not measure the water transparency dependent on light wave length in these methods. It can not directly be compared with the direct measurement, but these measurements can be done in real time andcontinuously. The value obtained by these methods is defined as the parameter whichindicates the water condition. From these methods, the stability of water quality canbe checked, and the time variation of water transparency measured by decay electron isused for determination of energy.
Measurement by decay electron
Decay electron events from stopping muons are used for the measurement of theaverage water transparency. The selection criteria of decay electron events is that it
follow a stopping muon by 1.5∼8µsec and its Nef f > 70. Fig 4.10 shows the typicalevent pattern of a decay electron event, and we can clearly see the Cherenkov ring. Only
the hit-PMTs with hit timing in a 50nsec window and with opening angle from thereconstructed direction of the decay electron between 32◦ and 52◦ are used for getting
the water transparency in order to neglect the reflected or scattered light. We canget the water transparency from the relation between the corrected Q of the each hitPMT and the distance from the vertex to each hit-PMT. Here, corrected Q is a pulse
height corrected for acceptance. (ref. Section 5.2) Fig 4.11 shows the relation, and thewater transparency is calculated to 8518cm. Fig 4.12 shows the water transparency as
55

CHAPTER 4. CALIBRATION

a function of time. After October in 1996, it is higher and higher, because we clean up
the filter. This value is used for the correction of the energy reconstruction as describedin Section 5.3.
NUM
1
RUN
3999
EVENT
553
DATE 97-May- 6
TIME
19:46:10
TOT PE: 20396.1
MAX PE:
70.6
NMHIT : 4283
ANT-PE:
121.5
ANT-MX:
22.6
NMHITA:
81

RunMODE:NORMALTRG ID :00001011
T diff.:0.727E+04us: 7.27
ms
FSCC:
20F10
TDC0: 8899.8
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 1
NUM
1
RUN
3999
EVENT
554
DATE 97-May- 6
TIME
19:46:10
TOT PE:
576.5
MAX PE:
12.4
NMHIT :
305
ANT-PE:
118.1
ANT-MX:
22.6
NMHITA:
83

RunMODE:NORMALTRG ID :00000011
T diff.: 2.54
us
:0.254E-02ms
FSCC:
60F10
TDC0: 11428.0
Q thr. :0.0
BAD ch.: no mask
SUB EV : 1/ 1

DIR: 0.12,-0.75, 0.65
X: -1290.4cm
Y: -331.7cm
Z:
891.6cm
R: 1332.4cm
NHIT: 237
good:
0.72

Figure 4.10: The typical event pattern of a parent muon event (upper), anddecay electron event (lower). The time difference between these
two events is 2.54µsec.

56

4.4. WATER TRANSPARENCY

Figure 4.11: The relation between the corrected Q of the each hit-PMT and
the distance from the vertex to each hit-PMT. The calculated
water transparency is 8518cm. (χ2 /ν = 108.584/49)

Figure 4.12: The water transparency as a function of time. The decay electron events from stopping muon are used for this calculation.

57

CHAPTER 4. CALIBRATION

Measurement by penetrating muon
Cosmic ray muons which penetrate through the detector are also used to check thewater transparency. When a penetrating muon as shown in Fig 5.13 traverses the detector, the charge observed in each PMT has approximately the following relation;Lia(θi ),exp −Qi = A
Li
λ




(4.1)

where, Li is the distance from muon track to i-th PMT along a ray at 42◦ from the muontrack, θi is the opening angle between the direction of the photon on the surface of i-th
PMT and the relative direction that this PMT is facing, a(θi ) is the PMT acceptancefunction, A is a constant parameter, and λ indicates the water transparency. Fig 4.13
shows the relation between Qi × Li /a(θi ) and Li . This slope in the figure indicates
1/λ, and the water transparency is calculated to 5615cm. Fig 4.14 shows the watertransparency as a function of time calculated by this method, and the time variation isq x travel-length / acceptance(p.e. x m)

consistent with the method using stopping muon event.

403.5

450

/ 20
5.866
-0.1781E-03

P1
P2

0.8726E-03
0.4873E-06

400

350

Super-Kamiokande Preliminary
300

250

200

150

100

50

0

0

500

1000

1500

2000

2500

3000

3500

4000

travel len. v.s. eff. charge, run002120

4500

5000

travel length(cm)Figure 4.13: The relation between Qi ×Li /a(θi ) and Li . The calculated watertransparency is 5615cm.

58

4.5. ENERGY CALIBRATION

Figure 4.14: The water transparency as a function of time. The throughgoing muon events are used for this calculation.

4.5

Energy calibration

Precise energy calibration is an important characteristic of Super-Kamiokande andis essential for solar neutrino measurement. In this section, three methods of energy
calibration are described: using monoenergetic electrons from the LINAC; using a radioactive source for what we call “Nickel calibration”; and using decay electron eventsfrom stopping muons.

4.5.1

LINAC

For MSW analysis using the solar neutrino energy spectrum, the systematic error of
absolute energy scale must be less than 1%.[39] In Super-Kamiokande, “LINAC calibration” is used for precise absolute energy calibration. The advantage of the LINAC is thatthe electron energy is monochromatic and can cover the full energy range relevant forsolar neutrinos, 5∼15MeV. Another advantage compared to the Nickel calibration, which
is described in the next section, is that a direct calibration is available using electrons.
Note that solar neutrinos are observed using electron signals from νe→ νe scattering. In
addition, more precise position calibration and direction calibration is available using a59

CHAPTER 4. CALIBRATION

collimated beam from the LINAC.
The schematic view of LINAC calibration system is shown in Fig 4.15. The LINAC,
which was originally for medical purposes, is a model ML-15MIII from Mitsubishi. The
beam pipe is evacuated to less than 10−4 torr, and the desired beam size and momentum
are obtained by collimators and magnets. On the top of the Super-Kamiokande tankholes are welded every 2.1m along the -x-axis. We insert vertical beam pipe into thedetector through these, and the length of the vertical beam pipe is variable, so we cando LINAC calibration at various positions in the inner detector. The beam intensity is
adjusted to 0.1 electron per bunch so that almost all events are single electron events.
The bunch width is 2µsec, and the maximum rate of bunches is 60Hz. Plastic scintillators
acting as a trigger counter and veto counters are placed at the end of the beam pipe asshown in Fig 4.15.
beam pipe support structure
magnet 2
magnet 1

LINAC

magnet 3
RockTunnelbeam pipe
76mm

Veto
counter
PMTSuper-Kamiokande tank
Trigger counter(1mm)
Ti window(0.1mm)Figure 4.15: The schematic view of LINAC calibration system.

60

4.5. ENERGY CALIBRATIONThe energy of electrons which travel through the beam pipe is measured by a Ge
detector[40]. For estimating the systematic error of the beam energy determination in
the LINAC, the relation of observed momentum by Ge detector to the magnet field ofmagnet 1 is used, as shown in Fig 4.16. The observed momentum can be fitted by a line,
and the deviation from that line is less than ±0.3%.

The specifications of the LINAC are summarized in Table 4.2. The results of LINAC

calibration, the position, angular, and energy calibrations, are described in Chapter 5.

Figure 4.16: The relation of observed momentum by the Ge detector to themagnetic field of magnet 1. The observed momentum can be
fitted by a line.

energy range

5∼16MeVintensity∼ 0.1 electrons / bunch(adjusted by the intensity of electron gun)number of bunches

up to 60 bunches/sec, typical 10∼30 bunches/sec

beam energy spread ≤ ±0.3%

beam size

1∼2cm at end cap

vacuum∼10−7 torr in accelerator tube

≤10−4 torr in beam pipe

Table 4.2: LINAC specification.

61

CHAPTER 4. CALIBRATION

4.5.2

Nickel calibration

The very precise energy calibration is available in LINAC calibration, however, thesetting of LINAC is a hard task and the beam direction is only downward. In addition
to LINAC, we use Nickel calibration. It is so portable that we can do it easily. The
direction of Nickel calibration is uniform. It is possible to reduce the several systematics
using Nickel calibration in addition to LINAC.
The gamma rays emitted from the thermal neutron capture reaction on Nickel areused as a radioactive source for energy calibration of low energy event. Table 4.3 summarizes nuclear parameters of neutron reactions on Nickel, the natural abundances of
Nickel isotopes, the capture cross sections for thermal neutrons, and the total released
energy through gamma emissions[41].
Reaction

natural abundance capture cross section γ energyof Nickel (%)(barns)(MeV)

58

Ni(n,γ)59 Ni∗

67.88

4.4

9.000

60

Ni(n,γ)61 Ni∗

26.23

2.6

7.820

62

Ni(n,γ)63 Ni∗

3.66

15

6.838

64

Ni(n,γ)65 Ni∗

1.08

1.52

6.098

Table 4.3: The nuclear parameter concerned with the Nickel calibration.
Each isotope of the Ni(n,γ)Ni∗ reaction has many branches of transition. Fig 4.17
shows the transition diagram of the 58 Ni(n,γ)59 Ni∗ reaction[41][43]. As shown in the
figure, 52.7% of the decays give an energy release via a single gamma ray of 9 MeV. The
intensity of this gamma ray is the maximum of all branches of any isotope.
For the neutron source, 252 Cf fission is used. Its half life is 2.65 years, and it decays
through α-decay (96.9%) and spontaneous fission (3.1%). When the fission occurs, anaverage of 3.76 neutrons with an average energy of about 2 MeV each and 10.8 γ rays
with energy of about 8 MeV in total are emitted per one fission. The intensity of the252

Cf source used is 1.7 µCi.
The reaction Ni(n,γ)Ni∗ occurs essentially only for thermal neutrons. The moderator

for thermalizing a neutron with 2MeV energy is water. Neutrons are thermalized byprotons in water through about 18 elastic scatterings on average. It takes a few micro
62

4.5. ENERGY CALIBRATION

sec to thermalize. If the thermal neutron is captured by Nickel, a gamma ray with theenergy as shown in Fig 4.17 is emitted. If the thermal neutron is not captured by Nickel,
it is captured by a proton or oxygen in water. The cross section for these is 0.332barn
and 0.178mbarn, respectively. The calculated mean capture time in water is 205µsec.
The energy of emitted gamma rays via H(n,γ)D is 2.2 MeV, this gamma ray is the main
background in this energy calibration.
Ni(n,γ )59 Ni

589.000 9.000 8.534 8.122 7.698 7.265 6.585 6.106

52.7% 25.6 4.65 1.28 0.31 2.74 2.39

5.974

0.87

5.818

3.70

5.621 5.437

0.16

0.72

5.313

1.74

5.270

0.29

4.977

0.26

4.859

1.53

4.284 4.031 3.930

0.39

0.46 0.40

5.069
4.969
4.716
4.141
4.022
3.731
3.687
3.563
3.379
3.182
3.026
2.894
2.415

1.734
1.302
0.36 1.62 0.44 0.321 0.42 1.58

0.23 0.32 0.24 0.47 0.17

0.29

0.96

0.08 0.13

0.87810.46570.33970.00

Figure 4.17: The transition diagram of the 58 Ni(n,γ)59 Ni∗ reaction.

63

CHAPTER 4. CALIBRATION

Fig 4.18 shows the schematic view of the Nickel calibration system. As shown in the
figure, the cylindrical polyethylene container, the diameter and height of which are each
20cm, is filled with 2.84kg Nickel wire of 0.1 mmφ and pure water. At the center of thecontainer, a proportional counter, in which the 252 Cf source is painted on an electrode, islocated. The proportional counter is used for tagging fission and gives a precise trigger
signal of the occurrence of a fission (“fission trigger”). The data is taken only for 500µsec after each fission trigger. Fig 4.19 shows the distribution of the time intervals, andthe mean capture time of the emitted neutron in this setup is 85µsec. For this analysis,
subtraction of the late region from the early region is done in order to suppress thecontinuous backgrounds.
Fig 4.20 shows N50 distribution of the measured and the Monte Carlo data with
the Ni source placed at the center position (x, y, z) = (35.3, −70.7, 0)cm and at the top
position (35.3, −70.7, 1200)cm. From these data, the peak value and resolution of N50

are reproduced for the measurement by the Monte Carlo data. Note that there is a bumpin the low hit region in the measured data. This is caused by the 2.2MeV gamma ray

200mm

130mm

125mm

10mm

30mm

from the H(n,γ)D reaction.

50mm

20mm

Nickel wire + Water

Figure 4.18: The schematic view of Nickel calibration system.

64

4.5. ENERGY CALIBRATION

Figure 4.19: The distribution of the time intervals from the fission trigger.

Figure 4.20: The N50 distribution of the measured and the Monte Carlo dataof Nickel calibration placed at (a) center position (x, y, z) =(35.3, −70.7, 0)cm, and (b) top position (35.3, −70.7, 1200)cm.

65

CHAPTER 4. CALIBRATION4.5.3µ-e decay

Decay electron events can also be used for the energy calibration. The selection
criteria for the decay electron events is as described in Section 4.4.2. The energy spectrumof decay electron is[44]dN
4Ee
G2 2 2mµ Ee 3 −
=
,
3
dEe
12π
mµ
!

(4.2)

where Ee is decay electron energy, G is Fermi coupling constant, and mµ is muon mass.
The maximum energy of a decay electron is 53MeV, and the mean energy is 37MeV.
Fig 4.21 shows Nef f distribution of observed decay electron events both in measurement and in Monte Carlo simulation. The measured and Monte Carlo data are consistentexcept for very low energy region. The difference of low energy region is caused by agamma ray emission from radioactive nuclei such as 16 N generated by capture of a stopping µ− to an oxygen nucleus in water. The ratio of the peak positions of the Nef f
distributions between the measured and the Monte Carlo data is as follows,
 0.982 ± 0.002

22.5kton fiducial

Monte Carlo= 0.984 ± 0.002
measured data  0.986 ± 0.003

11.7kton fiducial
distance from the wall is 2 ∼ 5m.

This confirms that energy scale measured by decay electron event is reproduced by Monte
Carlo to within 1.2%, with no observed position dependence.

Figure 4.21: Nef f distribution of observed decay electron event both inmeasured and Monte Carlo simulation.

66

4.6. TRIGGER EFFICIENCY

4.6

Trigger efficiency

The trigger efficiency of the Super-Kamiokande detector is also important for getting aprecise solar neutrino flux. Note that “trigger efficiency” means the detection efficiency ineach energy region. Of course, because of the energy resolution, the analysis efficiency is
50% at the threshold energy, however, “trigger efficiency” means the detection efficiency
hereafter.
For the measurement of the trigger efficiency, Nickel calibration is used. In addition
to the normal trigger mentioned as Section 3.2.4, the special trigger whose threshold isvery low (150 mV) is applied at the same time. This is called the “super low trigger”.
The trigger efficiency is defined by the ratio at the each energy point of events passing
the normal trigger threshold to those triggering the super low trigger. Fig 4.22 shows thetrigger efficiency at the center and top position. The Nef f at which the trigger efficiency
is 50 % at the center position is 38 hits, which corresponds to 5.8MeV.
As mentioned later (Chapter 7), the energy threshold for solar neutrino analysis is
6.5MeV. The trigger efficiency above 7MeV is almost 100% at all positions in the fiducial
volume both Monte Carlo and Nickel data. However, in the energy region between
6.5MeV and 7MeV, the difference between Monte Carlo and Nickel data is calculated to
1.2%. This difference is corrected for in flux measurements.

Figure 4.22: The trigger efficiency at
the center (solid line) and top position (dashed line).

67Chapter 5
Event reconstruction method
5.1

Vertex reconstruction

The vertex is determined by using timing information of the Cherenkov photons
detected by PMTs. The energy of events important to analysis is around 10MeV. We
call this class of event “low energy events”. Fig 3.1 shows the event pattern of a typical
low energy event. The track length of these events is 10cm at most. Compared to thevertex resolution of 90cm at 10MeV, the track length is negligible and the vertex can beassumed to be a point.
Vertex reconstruction of the event has 2 steps: (1) select hit channels to be used forthe reconstruction and (2) use a grid search method to find the vertex.
(1) Selection of hit channels used for the vertex reconstruction
The timing distribution of hit-PMTs of a typical low energy event is shown in Fig 5.1.
The noise hits shown in the figure are caused by PMT dark current. These noise hits
can be removed effectively by selecting only hit-PMTs in a narrow timing window to use
in reconstruction. The details of this selection are described in Appendix B.1.
(2) Determination of the vertex using grid search method
The vertex is reconstructed by minimizing
T2 =

N
hit
X
i=1

69

t2res,i(5.1)

CHAPTER 5. EVENT RECONSTRUCTION METHOD

Figure 5.1: The timing distribution of hit-PMTs in one event. The time,
which is horizontal axis, is the relative timing of the each hitPMT obtained from ATM data.

In this equation, Nhit is number of hit-PMTs, and tres,i is the residual time of i-th hitPMT after subtracting the time of flight from the arrival time of the photon:
tres,i = t0i − (n/c) ×q(x − xi )2 + (y − yi )2 + (z − zi )2 − tc ,

(5.2)

where
t0i : arrival time of the photon in the i-th PMT,n : index of water,c : light speed in vacuum,(x, y, z) : vertex position,(xi , yi , zi ) : position of the i-th PMT,
tc : the central value of ti ,and the detector coordinate used in Super-Kamiokande is defined shown in Fig 5.2. We
define the following value, “goodness” for vertex reconstruction,
1

goodness = P 1 ×
σi2

t2res,iexp − 2 ,
σi2
2σi

X 1
i

"

#

(5.3)

where σi is timing resolution of the PMT (here 5nsec). The range of this goodness isfrom 0 to 1. A grid search method is used in order to find the vertex where the goodness705.1. VERTEX RECONSTRUCTION

becomes maximum. The search starts on a coarse grid covering the whole inner detector(but 1m away from the surface of the PMTs):
8 divisions in X,Y axis (the step size is 397.5 cm),
9 divisions in Z

axis (the step size is 380.0 cm).

The resultant position at each iteration is used as the initial value for the next, more

Y-axisprecise step. The step size is 150cm at first and goes down to 5cm finally.

X-axis
23

.5
42
55
’
6

ce

ran

Ent

North
Magnetic northFigure 5.2: Coordinate of the Super-Kamiokande detector.

The quality of this vertex reconstruction method was estimated by the Nickel and
LINAC data. Fig 5.3 shows the reconstructed vertex distribution for the Nickel source
placed close to the middle of the detector. Table 5.1 shows the vertex shift and resolution
at various positions. The vertex shift is defined the distance between the Nickel position
and the mean value of the distribution shown in Fig 5.4 (a). The vertex resolution isdefined as the sigma of the distribution. A systematic vertex shift may be present, but
is 16cm at most.
For these figure, the vertex position and resolution are well reproduced by the Monte
Carlo calculation.
71

CHAPTER 5. EVENT RECONSTRUCTION METHOD

Figure 5.3: The reconstructed vertex distribution for the Nickel source placedat (x, y, z) = (35.3, −70.7, 0.0)cm. The left 3 figures show the real

data and the right three are Monte Carlo.

72

5.1. VERTEX RECONSTRUCTION

Position (x,y,z)

△x

△y

△z

σx

σy

σz

σr

(35.3,-70.7,-1200)

-0.3

-2.7

-3.0

47.98 49.28 47.66 115.8(35.3,-70.7,0)

0.7

-0.5

-1.9

47.11 49.23 52.80 114.2(35.3,-70.7,1200)

-1.0

-0.7

-1.0

46.87 48.17 47.88 113.6(35.3,-70.7,1600)-0.6-2.8 -10.0

46.98 46.40 44.67 111.6(35.3,-1201,-1200)

-3.4

7.0

-7.0

46.91 47.65 47.40 110.7(35.3,-1201,0)-1.1 16.0-1.1

42.70 43.16 50.08 113.0(35.3,-1201,1200)

0.6 10.0

2.0

43.74 44.92 48.74 109.4

Table 5.1: The vertex shift and resolution at the various positions of Nickel
source. The unit is (cm).

Figure 5.4: (a) The reconstructed X distribution of Nickel data placed at
x=35.3cm. (b) The distribution of the distance between the
Nickel position and the reconstructed position. The vertex resolution is defined by the value which includes 68%.

73

CHAPTER 5. EVENT RECONSTRUCTION METHOD

LINAC calibration was performed at 2 pipe positions and 7 beam energy points.
Fig 5.5 shows the distance between the pipe position and the reconstructed vertex. This
figure shows that the distribution of the data is reproduced well by the Monte Carlocalculation. Table 5.2 shows the vertex shift and resolution.
distance distribution for each linac energy x = -1237 y=-70.7 z=1228
1000
750
500
250
0

preliminary
0

50

100

150

200

250

300

350

400

450

500

400

450

500

400

450

500

400

450

500

400

450

500

400

450

500

400

450

500

beam energy = 16.301 MeV
1500

preliminary

1000
500
0

0

50

100

150

200

250

300

350

beam energy = 13.6666 MeV

preliminary

1000
500
0

0

50

100

150

200

250

300

350

beam energy = 10.9609 MeV
1000
750
500
250
0

preliminary
0

50

100

150

200

250

300

350

beam energy = 8.826 MeV
800
600
400
200
0

preliminary
0

50

100

150

200

250

300

350

beam energy = 6.983 MeV
1000
750
500
250
0

preliminary
0

50

100

150

200

250

300

350

beam energy = 6.076 MeV

preliminary

400
200
0

0

50

100

150

200

250

300

350

beam energy = 5.145 MeV
distance from end point of beam pipe to vertex position (cm)Figure 5.5: The distribution of the distance between the pipe position andthe reconstructed vertex at 7 energy points in LINAC data andMonte Carlo. The position of the end point of the beam pipe is(-1237,-70.7,1228)cm.

74

5.1. VERTEX RECONSTRUCTION

Position:(-1237,-70.7,1228)cm
Energy(MeV)

△x

△y

△z

σx

σy

σz

σr

16.3

14

2.1

-6

22.38 20.18 42.56 59.89

13.7

14

1.6

-4

23.55 21.91 43.83 63.24

11.0

12

1.8

-3

27.73 25.86 49.14 70.49

8.83

12

2.7

-1

33.16 31.07 56.39 83.02

6.98

9

1.5

-1

41.73 37.96 69.01 104.6

6.08

8

3.3

0

47.12 43.87 80.76 124.7

5.15

5

2.1

2

56.66 51.19 102.2 161.5

Position:(-1237,-70.7,27)cm
Energy(MeV)

△x

△y

△z

σx

σy

σz

σr

16.3

16

1.7

-8.1

21.31 20.88 43.96 62.22

13.7

15

0.4

-6.7

23.18 22.95 46.84 66.28

11.0

15

1.0

-5.5

27.12 26.30 52.46 75.81

8.83

14

0.7

-5.8

32.27 31.75 59.89 90.46

6.98

12

1.1

-5.2

39.42 39.03 72.62 116.8

6.08

10

2.4

-5.3

45.34 44.24 85.71 144.8

5.15

8

1.9

-5.5

55.33 51.60 105.3 207.6

Table 5.2: The vertex shift and resolution of LINAC data. The unit is (cm).

Finally, the vertex resolution for 10MeV and 7MeV Monte Carlo electrons in the
22.5kton fiducial volume, (the distance from the wall is grater than 2m), is calculated.

Energy(MeV)

σx

σy

σz

σr

10.0

43.12 42.31 43.71 88.22

7.0

54.63 53.52 53.93 117.6

Table 5.3: The vertex resolution in Monte Carlo. The unit is (cm).

75

CHAPTER 5. EVENT RECONSTRUCTION METHOD

5.2

Directional reconstruction

Directional reconstruction is very important for solar neutrino analysis because therecoil electron keeps the direction of the solar neutrino. This characteristic is used to
extract the solar neutrino signal in Super-Kamiokande. A maximum likelihood method
using the Cherenkov ring pattern is adopted to determine the direction. The likelihood
function is
~ ≡
L(d)

X
i

log(f (cos θdir ))i ×cos θi.
a(θi )(5.4)

Here, f (cos θdir ) is the function that represents the distribution of the opening angle
between the direction of the generated particle and the vector from reconstructed vertex
to the hit-PMT position. A plot of f (cos θdir ) for 10MeV electrons is shown in Fig 5.6(a).
The distribution is broad with the peak at 42◦ because of the effects of electron multiple
scattering and Cherenkov light scattering in water. θi is the opening angle between the
direction of the vector from reconstructed vertex to the position of i-th hit-PMT and the
direction that hit-PMT is facing, and a(θi ) is acceptance of the photo-cathode of PMTs
as a function of θi , as shown in Fig 5.6(b).

Figure 5.6: (a) The distribution of the opening angle between the direction of
the generated particle and the vector from reconstructed vertex
to the hit-PMT position. This plot is made for 10MeV electronMonte Carlo. (b) The acceptance of hit-PMTs as a function ofangle of incidence. This is made by Monte Carlo simulation.
The direction is d~ determined by maximizing Eq(5.4) using grid search method which76

5.2. DIRECTIONAL RECONSTRUCTION

step sizes are 20◦ , 9◦ , 4◦ , 1.6◦ .
The quality of the directional reconstruction is estimated by Nickel and LINAC data.
The uniformity of the directional reconstruction is checked by Nickel data. The direction
cosine distribution is shown in Fig 5.7. This figure shows Nickel data for a center position.
This is checked at various position and is almost flat in every position.

Figure 5.7: The directional cosine distribution. This is Nickel data at the center position.

Fig 5.8 shows the distribution of the angle between the known direction of the electronfrom LINAC and the reconstructed direction. Fig 5.8 also shows Monte Carlo distributions for the same circumstances. In this figure, the directional reconstruction of Monte
Carlo is reproduced by the measured data. The directional resolution is defined by thevalue which includes 68% in these figures. The directional resolution for each energy of
LINAC data is shown in Table 5.4.
The directional resolution was also calculated by Monte Carlo at various positions77

CHAPTER 5. EVENT RECONSTRUCTION METHOD

angular distribution for each linac energy x = -1237 y=-70.7 z=1228
1000
750
500
250
0

0

20

40

60

80

100

120

140

160

180

500
0

20

40

60

80

100

120

140

160

180

1000
750
500
250
0

preliminary
0

20

40

60

80

100

120

140

60

160

80

100

120

140

180

600
400
200
0

160

0

20

40

60

80

100

120

140

160

20

40

60

80

100

120

beam energy = 8.826 MeV

140

160

preliminary
0

20

40

60

80

100

120

140

beam energy = 5.145 MeV

160

180

Figure 5.8: The distribution of the angle between the direction of the electronfrom LINAC and the reconstructed direction at 7 energy points
in LINAC data and Monte Carlo. The position of the end pointof the beam pipe is (-1237,-70.7,1228)cm.

Position(-1237,-70.7,1228)cm(-1237,-70.7,27)cm

Energy(MeV)

LINAC data Monte Carlo

LINAC data Monte Carlo

16.3

21.37

21.03

21.07

21.78

13.7

22.50

23.69

22.79

24.39

11.0

24.90

26.66

25.72

27.08

8.83

28.48

29.71

28.76

31.43

6.98

31.69

33.35

32.24

35.75

6.08

33.87

35.48

34.60

38.43

5.15

35.62

38.18

36.89

41.94

Table 5.4: The directional resolution of LINAC data. The beam direction is

78

180

theta (degree)

theta (degree)(0,0,-1). The unit is degree.

180

theta (degree)

preliminary
0180

theta (degree)

preliminary

theta (degree)

beam energy = 10.9609 MeV
1000
750
500
250
0

40

beam energy = 6.076 MeV

500
0

20

theta (degree)

beam energy = 13.6666 MeV
1000

0beam energy = 6.983 MeV

preliminary

1000

preliminary

theta (degree)

beam energy = 16.301 MeV

0

800
600
400
200
0

preliminary5.3. ENERGY RECONSTRUCTION

and energies. Fig 5.9 shows that when the distance from the wall is less than 2m, theresolution is dramatically worse. The fiducial volume for solar neutrino analysis is usedwithin 2m from the wall, which is 22.5kton, as described in Section 7.2.
The directional resolution was calculated to 26.7◦ at 10MeV electron Monte Carlowhen the generated vertex is random in 22.5kton fiducial volume.

Figure 5.9: The directional resolution as a function of position for 10MeV
and 7MeV electron Monte Carlo. The parameter distinguishing
the curves is the distance from the tank axis. In each case theright most curve is outside the fiducial volume, as is the top pointof each curve.

5.3

Energy reconstruction

The energy of a charged particle is approximately proportional to the number of
Cherenkov photons, and thus also proportional to the total number of photo-electrons
in hit-PMTs. For analysis of the solar neutrino events in Super-Kamiokande, however,the number of hit-PMTs (Nhit ) with some corrections is used for energy determination
instead of the total photo-electrons. The reason is79

CHAPTER 5. EVENT RECONSTRUCTION METHOD(1) for low energy events, the mean number of Cherenkov photons in each hit-PMT isalmost one, so the total number of photo-electrons and the number of hit-PMTs
are almost the same,(2) the charge resolution at the one photon level is not good enough,(3) PMT or electronics noise can give high p.e. per tube, so the total number of photoelectrons will be strongly affected since the number of hit-PMTs is small for solar
neutrino events.
Only the hit-PMTs whose residual time (ref. Section 5.1) is within a 50nsec window
is used for calculating Nhit , in order to reject accidental hits due to dark noise in the
PMTs. Moreover, we applied several corrections to Nhit . The effective Nhit , Nef f , has
the same value at every position of the detector for a given particle energy. Corrections
are for the variation of the water transparency, the acceptance of the each hit-PMT, thenumber of bad PMTs, the PMT dark noise rate, and so on. A detailed explanation of
Nef f is given in Appendix B.2.
Next, we have to determine the conversion function from Nef f to Energy. For thispurpose, a Monte Carlo simulation, in which several parameters are tuned with the 10
points of LINAC data with the energy grater than 6.5MeV, is used. The energy distributions using this tuned Monte Carlo are well reproduced by the LINAC data at eachenergy. These are shown in Fig 5.10. The greatest difference of the peak value between
Monte Carlo and LINAC data at 7 energy points is ±1.3%. The greatest difference inresolution is ±4.7%. These are summarized in Table 5.5.

One of the most significant uncertainties of Monte Carlo is water transparency. Therefore, we check the position dependence of the energy scale using Nickel data in addition
to LINAC data. Nickel calibration was done at more positions than LINAC. 1 (Thedistance of the Nickel source position from the wall is 2.1m, 4.9m, 6.1m and 16.2m. The
height of the source is ±16m, ±12m and 0m.) The difference of the energy scale at eachposition between Nickel data and Monte Carlo is at most 1.4%.

Fig 5.11 shows the Nef f distribution of 10MeV Monte Carlo electron events. The
mean value is 69.72 in this figure, so events with Nef f = 69.72 are taken to be 10MeV
1

The position measured by LINAC is recently increased[40]. The position dependence calculated byrecent LINAC measurement is described in Appendix B.3.

80

5.3. ENERGY RECONSTRUCTION

electrons. Fig 5.12(a) shows the relation of mean Nef f to generated energy. The energy
resolution as a function of the energy is shown in Fig 5.12(b). This was calculated using
Monte Carlo events. The energy resolution for 10MeV electrons is 14.8%.

energy distribution for each linac energy x = -1237 y=-70.7 z=1228
600
400
200
0

0

2.5

5

7.5

10

12.5

15

17.5

20

beam energy = 16.301 MeV
1000
750
500
250
0

0

2.5

5

7.5

10

12.5

15

17.5

22.5

25

energy (MeV)

20

22.5

25

energy (MeV)beam energy = 13.6666 MeV
1000
500
0

0

2.5

5

7.5

10

12.5

15

17.5

20

22.5

25

energy (MeV)beam energy = 10.9609 MeV
1000
500
0

0

2.5

5

7.5

10

12.5

15

17.5

20

beam energy = 8.826 MeV

800
600
400
200
0

0

2

4

6

8

10

22.5

25

energy (MeV)

1214energy (MeV)beam energy = 6.983 MeV
1000
500
0

0

2

4

6

8

10

12

1000
750
500
250
0

0

2

4

6

8

10

beam energy = 5.145 MeV

14energy (MeV)beam energy = 6.076 MeV

12

14energy (MeV)

Figure 5.10: The reconstructed energy distribution at 7 energy points in LINAC data andMonte Carlo. The position of the end point of the beam pipe is (-1237,-70.7,1228)cm.

81

CHAPTER 5. EVENT RECONSTRUCTION METHOD

Position:(-1237,-70.7,1228)cm(-1237,-70.7,27)cm

reconstructed

resolution

reconstructed

resolutionenergy (MeV)(%)

energy (MeV)

(%)

data

M.C.

data

M.C.

data

M.C.

data

M.C.

16.35

16.57

13.26

12.26

16.51

16.45

13.04 12.26

13.73

13.78

13.32

13.27

13.78

13.72

13.32 12.72

10.93

11.00

14.38

14.12

11.04

10.92

14.54 14.18

8.66

8.71

16.17

16.25

8.74

8.72

16.34 15.58

6.73

6.75

18.15

18.13

6.73

6.74

18.15 17.21

5.72

5.75

19.00

18.96

5.76

5.75

19.06 19.01

4.75

4.79

21.70

20.13

4.77

4.77

20.97 20.19

Table 5.5: The reconstructed energy and the energy resolution of LINAC
data and Monte Carlo.

Figure 5.11: The Nef f distribution of 10MeV electron Monte Carlo events.
The fiducial volume is 22.5kton. The generated vertices are
uniformly distributed in this volume. The fit parameters are fora Gaussian.

82

5.4. MUON TRACK

Figure 5.12: (a) The relation of the mean of Nef f to the generated energy.
Each point is calculated by Monte Carlo as in Fig 5.11, where
the mean from the fit is used here. The fit is to a 4-th orderpolynomial. (b) The energy resolution ( σEE ×100%) as a functionof the energy. This uses the same Monte Carlo samples and thesame Gaussian fits as Fig 5.11.

5.4

Muon track

In Super-Kamiokande, cosmic ray muon events which show up as through going
muons, stopping muons, or edge clipping muons happen at 1.88Hz. This is described in
Section 7.2.3 in detail. The typical energetic muon event pattern is shown in Fig 5.13.
Most are through going muons. Fig 5.14 shows the event pattern of other types of muon
events. The rates for each muon type are summarized in Table 5.6.
Spallation events, which are a background for the solar neutrino analysis, are causedby energetic muons. In order to eliminate spallation events from this analysis, the tracks
of energetic muons must be reconstructed well.
The entrance and the exit positions for the penetrating muon track must be found
for the reconstruction. Two reconstruction methods are applied in sequence. The logicalflow of muon track reconstruction is described below.
(1) Fast reconstruction
The entering position is defined by the position of the earliest hit-PMT with morethan two neighboring hit-PMTs. The exit position is defined by the center position83

CHAPTER 5. EVENT RECONSTRUCTION METHOD~c of hit-PMTs whose charge is saturated (greater than 231p.e.),
~c =

N
hit
X

Qi p~ii=1where Qi and p~i are the charge and the position vector of the i-th hit-PMT, respectively. The charge of hit-PMTs around the exit position is generally saturated
as in Fig 5.13.
(2) A test of the fast reconstruction
The following two distances, (Lent ) and (Lexit ), are calculated in order to test theresult of the fast reconstruction. For each saturated PMT Lent (Lexit ) is its distancefrom the putative entrance (exit) point. It is required that at least one saturated
PMT which satisfies 1) Lent > 300cm and 2) Lexit < 300cm exists. Criteria 1) isfor identification of stopping muons, and 2) is for multi bundle muons.
(3) Precise reconstruction
If an event does not satisfy the criteria described in (2), a precise re-determinationof the exit position is done. A grid search method is applied in order to find the
maximum goodness. The goodness for the search is:1

goodness = P 1 ×
σi2

X 1
i

ti = Ti −1 ti − Texp −2
σi2 1.5σi






lµ n
− lph
c
c

where T is the entering time of muon, σi is the PMT timing resolution, which is
uniformly 3nsec, Ti is time of i-th hit-PMT, c is light velocity, n is the index ofrefraction of water, and lµ and lph are the distances shown in Fig 5.15.
(4) A test of the precise reconstruction
The same criteria as described in (2) is applied first. In addition, we also require
goodness > 0.88. If an event does not satisfy these conditions, it is regarded as anunfitted event. The track reconstruction parameters are not used.
The quality of muon track reconstruction is estimated by comparison of the above
method and manual reconstruction. The manual reconstruction is the method which
determines the entering and exit position using event pattern by eye. Fig 5.16 shows the84

5.4. MUON TRACK

difference between two methods, and the difference is defined by (△Lent + △Lexit )/2,

where △Lent is the distance between the entrance position by the above method andmanual reconstruction, △Lexit is the same for the exit point. 68% in this distribution iswithin 67cm, which we take as the reconstruction resolution.

The failure rates for the reconstruction methods in each type of muon are summarizedin Table 5.6. For the events which are impossible to fit, only the time and total charge
information are used in the spallation cut as described in Section 7.2.4.
NUM
32
RUN
2242
EVENT
30
DATE 96-Jul-19
TIME
3: 9:20
TOT PE: 85126.7
MAX PE:
252.0
NMHIT : 9099
ANT-PE:
374.6
ANT-MX:
53.6
NMHITA:
170

RunMODE:NORMALTRG ID :00001011
T diff.:0.176E+06us: 176.
ms
FSCC:
0
TDC0: -1124.0
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 5.13: The typical event pattern of an energetic muon.

85

CHAPTER 5. EVENT RECONSTRUCTION METHOD

NUM
4
RUN
2242
EVENT
1414
DATE 96-Jul-19
TIME
3:11:59
TOT PE: 32876.6
MAX PE:
238.1
NMHIT : 6876
ANT-PE:
126.1
ANT-MX:
27.6
NMHITA:
75

NUM
343
RUN
2242
EVENT
341
DATE 96-Jul-19
TIME
3: 9:55
TOT PE:277747.8
MAX PE:
265.2
NMHIT : 10884
ANT-PE:
278.0
ANT-MX:
23.5
NMHITA:
154

RunMODE:NORMALTRG ID :00001011
T diff.:0.681E+05us: 68.1
ms
FSCC:
0
TDC0: -1129.5
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 1

RunMODE:NORMALTRG ID :00001011
T diff.:0.949E+05us: 94.9ms
FSCC:
0
TDC0: -1115.5
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

NUM
390
RUN
2242
EVENT
388
DATE 96-Jul-19
TIME
3:10: 3
TOT PE: 13286.5
MAX PE:
248.5
NMHIT : 3931
ANT-PE:
976.1
ANT-MX:
70.0
NMHITA:
262

NUM
26
RUN
2242
EVENT
24
DATE 96-Jul-19
TIME
3: 9:20
TOT PE: 72850.9
MAX PE:
261.6
NMHIT : 7674
ANT-PE:
719.8
ANT-MX:
60.2
NMHITA:
291

RunMODE:NORMALTRG ID :00001011
T diff.:0.201E+06us: 201.
ms
FSCC:
0
TDC0: -1124.5
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

RunMODE:NORMALTRG ID :00001011
T diff.:0.184E+05us: 18.4ms
FSCC:
0
TDC0: -1127.2
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 5.14: Representative event patterns for various muon types. (a) stopping µ, (b) hard interaction µ, (c) edge clipping µ, (d) bundleof multiple µ86

5.4. MUON TRACK

muon type

number of events impossible to fit

normal835

5stopping

10

8

hard

41

2

edge clipper

58

19

multi bundle

56

28

1000

62

Total

Table 5.6: The event rate of each muon types and the failure rate of thereconstruction are summarized. This represents approximately
15minutes of data. Human scanning was done on each event todetermine the event type.

T

Super-Kamiokande
inner tankentrance
positionlµThrough going

µ

42

l ph

CerenkovphotonPMT

exit
position

Ti

Figure 5.15: The definition of lµ and lph for the muon track reconstruction.
For a given photon, lµ is the distance the muon travels from thedetector entrance to the emission point, and lph is the distancetraveled by the photon from there to the detection point.

87

CHAPTER 5. EVENT RECONSTRUCTION METHOD

Figure 5.16: The difference of entrance and exit position between auto fit andmanual fit. The hatched part of the histogram contains 68% of
the events, defining the distance resolution of the automatic fit.

88

Chapter 6
Monte Carlo simulation
6.1

Solar neutrino event generation

The expected total number of recoil electrons from solar neutrinos in the inner detector of Super-Kamiokande is calculated byZ ∞0φ(Eν )σtotal Ne T dEν ,(6.1)

where φ(Eν ) is the solar neutrino flux at earth (here, only 8 B and hep), σtotal is total
scattering cross section, Ne is total number of target electrons in the detector (1.086×1034
electrons/34481tons), and T is live time. The calculated event rate from Eq(6.1) is
55.8events/day for a total flux of 1×106 (cm−2 s−1 ), so if BP95 is taken as the standard
solar model, the rate is 369.7events/day.
However, many more events for Monte Carlo simulation are needed to reduce thestatistical error of the calculation. The generated event rate is 20 per minute for thefull operation time. For this analysis, the total number of generated events is 4428360
events.
The generated position is uniform in the whole volume, and the energy and the
direction of recoil electrons are determined according to the distribution in Eq(3.9) andEq(3.11), respectively.
89

CHAPTER 6. MONTE CARLO SIMULATION

6.2

Detector simulation

6.2.1

Framework of the simulation program

The detector simulation program consists of the following three steps:(1) particle tracking and Cherenkov photon emission in the water,(2) propagation of Cherenkov photons,(3) response of the PMT and electronics.

Particle Tracking
GEANT 3.21[45] was used for detector simulation in Super-Kamiokande. It wasdeveloped at CERN, used generally in high energy physicists, and checked by many
physicists. GEANT is able to simulate the electromagnetic processes which occur in theenergy range from 10keV up to 10TeV.
The electromagnetic interaction in GEANT was also tested against EGS. For example,
Fig 6.1 shows the number of generated Cherenkov photons, in electron and gamma eventswith 9MeV in GEANT and EGS. These are quite consistent. With several comparisons,it was checked that GEANT was accurate enough to use in Super-Kamiokande[46].
Fig 6.2 shows tracks of twenty 10MeV electrons in water using GEANT. The dominant
processes for this energy region are multiple scattering, ionization loss, δ-ray production,bremsstrahlung and annihilation of positrons for electrons, and pair creation, Compton
scattering and photoelectric effect for gammas.
The number of generated Cherenkov photons, the direction of the each photon and its
wavelength are calculated using Eq(3.1) and Eq(3.2). The dependence of the refractive
index on wavelength was used as shown in Fig 6.3[47]. The Cherenkov photons are only
generated between 300nm and 700nm because PMTs are only sensitive to this region
as shown in Fig 3.13. Fig 6.4 shows the total number of emitted Cherenkov photons
from electrons in water as a function of electron kinetic energy. It is approximately
proportional to the electron energy, and this proportionality constant is a good scale forenergy as described in Section 5.3.
90

6.2. DETECTOR SIMULATION

EGS

EGS

(a) electron(b) gamma

GEANT

GEANT
(d) gamma(c) electron

Figure 6.1: The distribution of the number of generated Cherenkov photons.
(a) 9MeV electron events in EGS, (b) 9MeV gamma events in
EGS, (c) 9MeV electron events in GEANT, (b) 9MeV gamma
events in GEANT.

91

CHAPTER 6. MONTE CARLO SIMULATION

Figure 6.2: The tracks of 20 electron
events with momentum 10MeV/c. The
generated starting point is (0,0,0), andthe direction is (1,0,0).

Figure 6.3: The solid line is refractive
index as a function of wavelength. The
dashed line is the “effective index”, asdefined in the text.

Figure 6.4: The number of generated
Cherenkov photons as a function ofgenerated electron energy in Monte
Carlo simulation. The curve is a linear fit to the points.

926.2. DETECTOR SIMULATION

Tracing Cherenkov light in water
We have taken into account the dispersion of the refractive index. The group velocity
vg =

c
∂n(λ)
n(λ) − λ
∂λ

,

(6.2)

where c is light velocity in vacuum, λ is light wavelength, was used for the light velocity
in the water. The so-called “effective index”, which is the denominator of this equation,is shown for water in Fig 6.3.
The generated Cherenkov light can be scattered and absorbed in water. The watertransparency as a function of wave length was determined as follows.
• Short wavelength
We usedC ∝ λ−4
where C is the scattering coefficient and λ is wavelength. If the size of particles
with which a Cherenkov photon interacts is small compared to the wavelength, thescattering length is proportional to the fourth power of light wavelength. This isRayleigh scattering.
• Long wavelength

We used the data given in reference[48].

The absolute water transparency was determined to be consistent with the direct measurement of pure water described in Section 4.4. Fig 6.5 shows the water transparency
as a function of the wave length. This ratio of scattering and absorption is a tunable parameter in the Monte Carlo. This has not been measured directly yet, so the parameteris tuned using LINAC and other calibration data.
When the Cherenkov light arrives at the surface of a PMT or black sheet, reflection
on the surface is possible. The reflection of the PMT glass as a function of the incoming
angle is calculated as shown in Fig 6.6(a)[49]. We also measured it. The calculated value(including the polarization) is used for the simulation.
The reflection by black sheet is calculated and measured in water, and the result isshown in Fig 6.6(b). The measured value is consistent with the calculated one. We haveused the calculated value. The polarization is also considered.
93CHAPTER 6. MONTE CARLO SIMULATION

Figure 6.5: The attenuation coefficiency which put in Monte Carlo. The
circle is the direct measurement data.

Figure 6.6: The reflection probability on the surface of a PMT (a) and a
black sheet (b) as a function of incoming angle. The lines arecalculations: the dashed line is S-wave, the dotted line is P-wave,
the solid line is averaged value. Points show the measured values.

946.2. DETECTOR SIMULATION

response of the PMT and electronics
The quantum efficiency of the PMTs (see Section 3.2.3) is shown in Fig 3.13. Fig 6.7
shows (1) the Cherenkov light spectrum generated, (2) upon arrival on the surface of
PMT, and (3) after convolution of Q.E. for 10MeV electrons generated through entire
volume.
The average value of the collection efficiency of PMT, which is more than 70%, isalso treated as a tunable parameter. This is used for the final adjustment of the energy
scale.
Charge and timing resolution of PMT are considered. (see also Chapter 4) Fig 4.3
shows charge distribution for one photon. The charge value of each hit-PMT in Monte
Carlo is determined by random number distributed as shown in that figure. The timing
distribution dependent on charge is measured using a laser as described in Section 4.3.
Fig 4.6 shows the timing resolution at various charge. In the Monte Carlo, the timing ofeach PMT is a Gaussian random variable with the sigma shown in Fig 4.6.
Finally, trigger simulation is applied. The details of the trigger were described in
Section 3.2.4. A comparison of trigger efficiency in Monte Carlo and the real data wasdescribed in Section 4.6.

Figure 6.7: The Cherenkov light spectrum at various steps: (1) generated,(2) arrival on the surface of PMT,
(3) included Q.E. This is output fromSuper-Kamiokande Monte Carlo simulation.

95

CHAPTER 6. MONTE CARLO SIMULATION

6.2.2

Monte Carlo tuning

The previous section introduced some parameters of the Monte Carlo program. Mostof these parameters are determined independently by direct measurements. Two parameters have to be tuned. They are not completely free, but have standard values andtunable ranges which are based on some measurements. They are:1. the ratio of scattering and absorption.
For long wavelength, infrared absorption is dominant. For short wavelength,
scattering is dominant.
2. the collection efficiency of the PMTs.
This parameter is constrained to be more than 70% which is the result of thedirect measurement in Hamamatsu Co[36].
The ratio of scattering and absorption is determined using the event pattern of Nickel
and LINAC calibration data. For example, Fig 6.8 shows the hit pattern of Nickel
calibration around the center of the barrel PMT. Data and Monte Carlo agree very well.
The collection efficiency for PMTs was used to tune Monte Carlo in the last step. It
is determined by adjusting the energy scale to measured data of LINAC calibration at
various positions. The value used is 78%.
The tuned Monte Carlo as described in this section is consistent with the measured
calibration data. It can be used to predict details of the characteristics of solar neutrino
distributions with great confidence. Fig 7.15 shows the calculated energy distribution ofMonte Carlo events. Fig 6.9 shows the distribution of the reconstructed direction of recoil
electrons relative to the direction from the sun to the earth, for Monte Carlo events withreconstructed energy between 6.5MeV and 20MeV. We can see the clear peak towards
the sun.

966.2. DETECTOR SIMULATION

Figure 6.8: The number of hit-PMT belonging to the layer from 21st to 31st
in the barrel as a function of phi angle of the PMT position. The
source position is (30.3,-1555,0)cm. Phi is the location angle of
the PMT in the X-Y plane. The Monte Carlo (top plot) is after
the final tuning.

97

CHAPTER 6. MONTE CARLO SIMULATION

Figure 6.9: The distribution of the reconstructed direction of recoil electrons
relative to the direction from the sun to the earth for the Monte
Carlo sample.

98Chapter 7
Data Analysis and Results

7.1

Data set

Super-Kamiokande started taking data on the 1st of April in 1996, but the watertransparency in the first two months of the experiment as shown in Fig 4.14 was changing
rapidly and did not have sufficient quality to allow an efficient solar neutrino search. The
data used for the present analysis covers from the 31st of May, 1996 to the 23rd of June,
1997.
Data are taken in runs of at most approximately 24 hours. Each run further consistsof 10 minutes subruns. We removed some runs or subruns as a bad “run” from theanalysis if they did not satisfy the selection criteria. We will describe this in detail later.
“Flash PMTs” described in the next section were the main reason for the rejection. The
live time fraction is shown in Fig 7.1. It became more than 90% after October, 1996.
The total analysis live time between the 31st of May, 1996, the first day of the present
data, and the 23rd of June, 1997 was 297.4 days.
The “raw data” were ∼ 9.5 × 105 events/day which is equivalent to 10.9Hz. Since

the expected observable solar neutrino event rate (assuming the BP95 SSM) is 46.4
events/day above 6.5MeV threshold, the signal to noise ratio (S/N) is O(10−5 ).
99CHAPTER 7. DATA ANALYSIS AND RESULTS

Figure 7.1: The efficiency of the experimental operation. The solid line shows
the data acquisition live time, and the dashed line shows the solar
neutrino analysis live time.

7.2

Data reduction

7.2.1

First reduction

Selection of low energy events
The first step of the reduction is to select the low energy events. Fig 7.2 shows thetotal charge of inner hit-PMT distribution for all events in one run. There are two peaks
which are caused by muon events and low energy events. The following cut to select low
energy events is applied,(1) total charge of inner hit-PMT ≤ 1000 p.e.;Here, 1000 p.e. is equivalent to about 100MeV. The inefficiency of this cut for solar
neutrino events is negligible.

The decay electron events from stopping muons are a background to solar neutrino
analysis because the energy range is close to solar neutrino event. To reject them, the timedifference from the previous event is used. Fig 7.3 shows the time difference distribution.
(2) the time difference from the previous event > 20µsec.;
The dead time caused by this cut is calculated to be 1.8 × 10−4 . It is ignorable.
1007.2. DATA REDUCTION

Figure 7.2: The total charge of inner hit-PMT distribution in one typicalrun. All events acquired by the online
software are represented here. (No cuts
are applied.)

Figure 7.3: The distribution of the timedifference from the previous event in
one typical run. These are the samedata as in the previous figure.

101

CHAPTER 7. DATA ANALYSIS AND RESULTS

Reduction of noise events
Electronics sometimes pick up noise, for example, from turning on a fluorescent light.
Fig 7.4 shows the typical electronics noise event. Most of the charge of each hit-PMT in
this noise event is at the level of less than 0.5 p.e, and sometimes picked up by only one
ATM board. Note that, this kind of noise event occurred especially in the early time ofthe experiment. In order to reject noise events, the following value is defined,
Rnoise =Nnoise,Nhit

where Nnoise is the number of hits with the charge -0.5∼0.5 p.e., and Nhit is the total
number of hits. Fig 7.4 shows the Rnoise distribution. We have applied following two
cuts,(3) Rnoise < 0.4.
(4) if all channels in one ATM board are hit, the event is rejected.
NUM
409
RUN
2926
EVENT
1179
DATE 96-Oct- 7
TIME
10:51:57
TOT PE:
97.1
MAX PE:
19.9
NMHIT :
94
ANT-PE:
101.0
ANT-MX:
70.0
NMHITA:
34

RunMODE:NORMALTRG ID :00000011
T diff.:0.946E+05us: 94.6
ms
FSCC:
20000
TDC0: 8905.2
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 7.4: The typical electronics noise event and the Rnoise distribution in
one typical run.

In Super-Kamiokande, the phenomenon called “flash PMT” is serious problem. Thatis generally caused by electrical discharge due to a leak of water into the PMT. Whena PMT is determined as a flash PMT it is disconnected. The rate of disconnection is0.25 PMTs per day on average and is shown in Fig 7.5. The typical flash PMT event is102

7.2. DATA REDUCTION

shown in Fig 7.6. There is a hit-PMT with high charge and many hit-PMTs around the
flashing PMT. The flash PMT events occur continuously with high rate or sometimes
intermittently, and some of them are hard to identify. In order to reject the flash PMT
event, the relation between max charge of hit-PMT and the number of hit around thecable with max charge is used. Fig 7.6(a) shows the typical run including a lot of flash
PMT events, and (b) shows a normal run, therefore,(5) the region indicated in Fig 7.6(a) is rejected.

Figure 7.5: The number of disconnected PMTs as a function of time.
At some times (for example, early
March, 1997) some previously disconnected PMTs were reconnected
after reanalysis.

NUM
26
RUN
2641
EVENT
1906
DATE 96-Aug-31
TIME
11:54:19
TOT PE:
181.4
MAX PE:
18.1
NMHIT :
104
ANT-PE:
39.4
ANT-MX:
2.5
NMHITA:
46

Here

RunMODE:NORMALTRG ID :00000011
T diff.:0.349E+05us: 34.9
ms
FSCC:
20000
TDC0: -1103.0
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

Figure 7.6: The typical flash PMT event and the relation between max charge of hitPMT and the number of hit around the cable with max charge. (a) The typical run
including a lot of flash PMT events. (b) The normal run. Events above and to the rightof the cut shown in (a) are rejected.

103

CHAPTER 7. DATA ANALYSIS AND RESULTS

Reduction related to reconstruction
After reconstruction (see Chapter 5), the following reductions are applied:(6) Events with less than 10 hit-PMT are rejected.
(7) goodness ≥ 0.4 is required.
The events which have too few hit-PMT are not guaranteed to be reconstructed well,so they are not reconstructed. Fig 7.7 shows scatter plots of goodness and Nhit . Eventswith small goodness but large Nhit are flash PMT events which cannot be rejected by(5). (The typical event is shown in Fig 7.7) Cut (7) is applied to reject these.
Most of the remaining events after the above reduction are caused by gamma raysfrom radioactive elements in the surrounding rock and PMT glass, or very low energy
background events. The following pre fiducial volume cut and energy cut are applied:(8) the distance from the wall >1.5m and the energy >5.5MeV for events to be accepted.
Fig 7.8 shows a remaining noise event and it is a PMT adjoin noise. We suspect it iscaused by the gamma ray from the glass of PMT. This kind of event is usually rejectedby the fiducial volume cut, but occasionally remained after the cut. In order to rejectsuch events, we applied two kinds of cut.
First, we fit the event with different algorithm to select PMTs using the correlationin space and time. The distance between the results of these two kinds of fitting wasused for the reduction. The details of the fit and the selection criteria are described inAppendix B.4. Second, we checked the uniformity of the azimuthal angle distribution of
hit-PMTs. The detailed explanation is in Appendix B.5.
Other criteria
Before the reductions explained above, we rejected the following events: the outertriggered events; events during ATM pedestal data taking; and any events that were notfully acquired by the online software.
The event rate of outer detector triggers is 2.1Hz, which is mostly caused by cosmic
ray muons from outside of the detector.
1047.2. DATA REDUCTION

Pedestals of the ATM modules are measured every 30 minutes taking approximately
about 1 minute. During pedestal data taking, 1/8 of all the ATMs are not active, so we
do not use events in this time for solar neutrino analysis. The dead time caused by thepedestal and incomplete data is calculated to be 2.66% totally.

NUM
48
RUN
2641
EVENT
744
DATE 96-Aug-31
TIME
11:52:49
TOT PE:
164.5
MAX PE:
10.6
NMHIT :
101
ANT-PE:
26.6
ANT-MX:
2.8
NMHITA:41

Max charge

RunMODE:NORMALTRG ID :00000011
T diff.:0.545E+05us: 54.5
ms
FSCC:
20000
TDC0: -1101.2
Q thr. :0.0
BAD ch.: no mask
SUB EV : 0/ 0

flasher

Figure 7.7: The typical event with small goodness and large Nhit . and scatterplots of goodness and Nhit for two runs. The data in (a) have
many remaining flash PMT events. (b) is a normal run.

NUM
1
RUN
1742
EVENT
202650DATE 96-May-31
TIME
9:50:56
TOT PE:
130.0
MAX PE:
16.1
NMHIT :
97
ANT-PE:
193.4
ANT-MX:
10.2
NMHITA:
41

Figure 7.8: The typical event including the
PMT adjoin noise.
DIR: 0.93,-0.37, 0.03
X: -701.6cm
Y:
694.8cmZ:
684.3cmR:
987.4cm
NHIT:
40
good:
0.84

RunMODE:NORMALTRG ID :00000011
T diff.:0.115E+06us: 115.
ms
FSCC:
0
TDC0: -1126.5
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 0105

CHAPTER 7. DATA ANALYSIS AND RESULTS

Summary
Table 7.2 (page 115) summarizes the first reduction and the number of events remaining at each step. After first reduction, the number of remaining events is 1.298×106 ,which is equivalent to 0.0505Hz. Fig 7.15 shows energy distribution of those events.

7.2.2

Bad run selection

The events considered noise are removed event by event as described in the previous
section. As the result of that, if a run or subrun includes a lot of noise events, it should
be designated a bad run or subrun. The selection criteria for bad runs is described inthis section.
Very short runs were first killed by the following criteria,• Run time in one subrun ≤ 30 seconds.
• Live time in one subrun ≤ 0 seconds. The live time is defined by subtract deadtime from run time.

• Total live time in one run ≤ 5 minutes.
Subruns including many electronics noise events or flash tube events are killed. For
this purpose, we check the ratio of number of noise events to all events. Fig 7.9 shows
the ratio distribution and the selection criteria. The number of subruns selected as
bad subruns is 1550 out of a total or 30503 subruns. Note that the bad subruns are
preferentially shorter than good ones.

7.2.3

Selection of muon events to identify spallation events

We have to select muon events to remove spallation events effectively. As shown in
Fig 7.2, there are two peaks in total charge distribution which can be attributed to low
energy events and muon events. The total charge of inner hit-PMT is thus used to selectmuon events.
Also since muon events enter from outside of the detector, there are hit-PMTs withvery high pulse height around the entrance or exit position of the detector. (See Fig 5.13)
Fig 7.10 shows the distribution of max charge of inner hit-PMT. There are two peaks.
106

7.2. DATA REDUCTION

Figure 7.9: The ratio of number of noise events or flasher events to all events.
The selection criteria for bad runs is also shown.

Figure 7.10: The distribution of max charge of inner hit-PMT.

The peak at higher charge represents through going muons. The cuts to select muonsare:• total charge of inner hit-PMT ≥ 10000 p.e.,• max charge of inner hit-PMT ≥ 200 p.e..
The event rate after this selection is 1.88Hz. 96.4% of those events are reconstructedwith sufficiently high quality.
107CHAPTER 7. DATA ANALYSIS AND RESULTS

7.2.4

Spallation cut

Energetic muons produce radioactive elements through the spallation reaction[50]. In
Super-Kamiokande the following reaction occurs,µ +16 O → µ + X,

(7.1)

where X is some radioactive element. Important ones are listed in Table 7.1. We referto these as “spallation products”. There are some calculations[51] to explain muon
spallation processes, however, these results are not very consistent with experimental
results. Therefore, the total rate or branching ratios can not be predicted precisely.
As shown in Table 7.1, the spallation products give β and/or gammas in the energy
range between a few MeV and 20MeV, and the lifetime ranges from 0.01 to 10 seconds
or more. This energy region is near the energy of solar neutrino events, so spallation
events are one of the major backgrounds for solar neutrino analysis.
These events are correlated with muon track and total charge of muon event. The
following correlation is checked in order to eliminate spallation events (“spallation cut”):• distance from muon track to the vertex of the low energy event (△L),• residual pulse height of muon (Qres ),• time difference between muon and low energy event (△t).
Qres is defined as follows,
Qres (p.e.) = Qtot (p.e.) − 24.1(p.e./cm) × Lµ (cm),(7.2)

where Qtot is total pulse height of muon and Lµ is muon track length. In Qres , thephotons generated by muon itself are removed. The total charge per 1cm for a muontrack was calculated to 24.1(p.e./cm) on average.
We used a likelihood method to remove spallation events. For the spallation events,△L and △t are shorter, and Qres is larger. Fig 7.11 shows △L distribution in various Qresregion. The peak caused by spallation events is clearly seen in the region of small △L,compared to the accidental distribution. The spallation likelihood function is expressed
numerically using △L, Qres and △t. The detailed definition of the spallation likelihood
is described in Appendix C.1.

108

7.2. DATA REDUCTION

Figure 7.11: The distribution of the distance between the muon and low energy event in various residual charge regions. This low energy
events are defined by Nef f ≤ 50. The time difference between

the muon and low energy event is less than 0.1sec. The dashedline is the expected accidental distribution.

109

CHAPTER 7. DATA ANALYSIS AND RESULTS

All the muon events before 100sec from the each low energy event are considered tobe candidates for the origin of the spallation events. Since the muon rate is 1.88Hz andthe low energy event rate after the first reduction is 0.0505Hz, there are very many pairsof muon event and low energy event. The spallation likelihood function is calculated foreach pair and we select the pair which gives maximum likelihood value.
Fig 7.12 shows the typical likelihood distribution of spallation events and a random
sample. This random sample was made by taking low energy events (N50 ≤ 25 and
Nef f ≤ 30) and changing the vertex randomly in the fiducial volume. In order todetermine the cut point, the following the “significance” is defined,
Signif icance =1 − deadtime
q

Rspa

(7.3)

where Rspa is the ratio of the remaining events to all the events in real events in Fig 7.12.
Here, it is easy to calculate “dead time” of spallation cut, that is the ratio of rejecting
events in random sample. The cut point is defined such as Signif icance is maximum,
and the dead time is 19.96%.
The number of events after spallation cut is given in Table 7.2, and Fig 7.15 showsenergy distribution before and after spallation cut. As shown in the figure, this cut
affects the high energy region.

Figure 7.12: The typical likelihood distribution in case of including spallation
events (solid line) and only random sample (dashed line).

1107.2. DATA REDUCTION

Isotope τ 1 (sec) Decay mode
2

8
2 He

0.122

Kinetic Energy(MeV)

β−10.66 + 0.99 ( γ )β− n( 11 % )12.5 ∼ 13

8
3 Li

0.84

β−

8
5B

0.77

β+

9
3 Li

0.178

β−

13.73
13.5 ( 75 % )11.0 + 2.5 ( γ )β− n∼ 10 ( 35 % )

9
6C

0.127

β+ p

11
3 Li

0.0085

β−20.77 ( 31 % )β− n∼ 16 ( 61 % )

11
4 Be

13.8

3 ∼ 13β−11.48 ( 61 % )9.32 + 2.1 ( γ ) ( 29 % )

12
4 Be

0.0114

β−

11.66

12
5 B

0.0204

β−

13.37

12
7 N

0.0110

β−

16.38

13
5 B

0.0173

β−

13.42

13
8 O

0.0090β−14
5 B

0.0161β−8 ∼ 1414.07 + 6.09 ( γ )

15
6 C

2.449

β−

9.82 ( 32 % )4.51 + 5.30 ( γ )16
6 C

0.7478

β−

16
7 N

7.134

β−

∼4
10.44 ( 26 % )4.27 + 6.13 ( γ ) ( 68 % )Table 7.1: Summary of spallation products.

111

CHAPTER 7. DATA ANALYSIS AND RESULTS

7.2.5

Fiducial volume cut and gamma ray cut

Fiducial volume cut
The gamma rays from the surrounding rocks became serious backgrounds for solar
neutrino analysis. Fig 7.13 shows the vertex distribution. We applied the cut,
Rwall ≥ 2m,(7.4)

where Rwall is the distance from the wall, in order to remove these backgrounds. The
fiducial volume is 22.5 kton.

Figure 7.13: The vertex distribution of low energy events. The volume withthe distance from the wall greater than 2m is 22.5kton. That isdefined as the fiducial volume. The volume defined by making
the cut 5m is 11.7kton.

Gamma ray cut
In Fig 7.14 where the vertex and directional cosine distribution of the events after
fiducial volume cut are shown, one sees many of the events close to the wall are comingfrom the wall. To further reduce this background, the following cut is applied;Ref f ≥ 450cm,(7.5)

where Ref f is the distance to the wall backward along the event direction. Fig 7.14 also
shows the vertex and direction distribution after gamma ray cut.
112

7.2. DATA REDUCTION

Figure 7.14:

The vertex and direc-

tional cosine distribution before and after gamma ray cut. The hatched one
shows after gamma ray cut.

113

CHAPTER 7. DATA ANALYSIS AND RESULTS

Table 7.2 shows the number of events passing fiducial volume cut and gamma ray
cut in various energy ranges, and Fig 7.15 shows the energy distribution before and after
these cuts.

7.2.6

Summary of the data reduction

We call the data sample through all the reduction step “final sample”. Table 7.2
summarizes the data reduction steps and the number of events. Fig 7.15 shows energy
distribution at each reduction step.

Figure 7.15: The energy distribution after each reduction step. The curveat the bottom is a direct calculation of expectation shown forcomparison.

114

7.2. DATA REDUCTION

reduction step

number of events
Data

Monte Carlo

2.131×108

651310First reduction(1) Total charge ≤ 1000 p.e.

(2) Time to previous event > 20µsec.

1.861×108(3)(4) Noise event cut 1

1.655×108

651271(5) Flash tube cut

1.648×108645770(6) Very low energy event cut

1.036×108645770(7) Goodness cut

1.025×108645769(8) Pre fiducial and energy cut

2.383×106

645769(9) Noise event cut 2

1.298×106

617487

Spallation cut

74351720% dead time

Fiducial volume cut (22.5kton)

426658Gamma ray cut

198111

7.8% dead time

Final sample (6.5 ≤ E ≤ 20MeV)

52368

443282

Table 7.2: The reduction step and the results. Note that the numbers forMonte Carlo are after applying the 22.5kton fiducial cut and6.5MeV energy cut. The numbers for the “First reduction” steps
same as those in the text.

7.2.7

Remaining backgroundAs shown in Table 7.2, the number of remaining events after the reduction steps is52368. (176.1events/day) The signal to noise ratio is O(1/4) assuming the SSM(BP95)

prediction. Many background events are still remaining. The most probable backgroundsource is electrons from β decay of 214 Bi originating from 222 Rn decay in the water tank.
Though the end point energy of this decay is 3.26MeV, those events include in the sample
above 6.5MeV threshold because of the energy resolution. The radon concentration in thewater tank was actually measured[52] and shown in Fig 7.16. It is recently stable at thelevel of 5∼10mBq/m3 as shown in the figure. The estimation of the radon concentrationfrom the event rate of very low energy events is 6.3±2.5mBq/m3 . These are consistent,
however, we do not know whether all of the remaining backgrounds are explained only115

CHAPTER 7. DATA ANALYSIS AND RESULTS

by the radon or not. We are still studying the origin of the background.

Radon Concentration [mBq/m3]

1 04

high
low

1 03

1 02

B.G. 1.9mBq/m3

101
5/1/1996

9/6/1996

1/12/1997

5/20/1997

9/25/1997

1/31/1998

Date

Figure 7.16: The radon concentratin as a function of time.

116

7.3. RESULTS OF SOLAR NEUTRINO ANALYSIS

7.3

Results of solar neutrino analysis

7.3.1

Solar neutrino flux and energy spectrum

Solar neutrino signal extraction
In order to extract solar neutrino signal from the final sample, we make use of thedirectional correlation of electrons to the incident neutrinos in ν-e scattering. We define
an angle θsun , the angle between the direction of low energy event and the directional
vector from the sun. If the signal is coming from the sun, cos θsun distributes around 1
with some angular resolution. Fig 7.17 shows θsun distribution of the final sample withthe energy range from 6.5MeV to 20MeV. As shown in the figure, we can see a clear peaktowards the sun above background.

Figure 7.17: The distribution of the reconstructed direction of recoil electrons
relative to the direction from the sun tothe earth for the final sample.

In order to extract the solar neutrino flux, a maximum likelihood method was used.
The probability function is defined as a function of recoil electron energy (Ee ) andcos θsun ;P (Ee , cos θsun , x) = x × Psignal (Ee , cos θsun ) + (1 − x) × Pbg (Ee , cos θsun ),(7.6)

where x is the ratio of number of solar neutrino events to all the events in the final
sample. It consists of two parts: signal and background. The probability function for
signal, Psignal (Ee , cos θsun ) shown in Fig 7.18, was obtained by Monte Carlo simulation.
117

CHAPTER 7. DATA ANALYSIS AND RESULTS

The probability function for background, Pbg (Ee , cos θsun ), was obtained by the shapeof cos θsun distribution in the final sample in each energy regions. The gamma ray
background has directionality because it goes from the wall. This directionality and thecylindrical shape of the detector geometry causes cosine Z distribution to be non-flat
before gamma ray cut. (See Fig 7.14) The reason to use the shape of the final sample
as background is that the systematic effects caused by this non-flat background can be
reduced even after application of the gamma ray cut.

Figure 7.18: The probability function
for solar neutrino signal obtained byMonte Carlo simulation. The solid line
shows the energy of recoil electron is
10MeV, the dashed line shows 7MeV,
and the dotted line shows 5MeV.

The signal to noise ratio differs in various Ee , namely x varies for different energy
regions. If the energy is larger, it becomes better. Therefore, the probability function
expressed as Eq(7.6) can be applied into various region separately with the energy shape
constraint, in order to make use of smaller background in the larger energy region. The
probability function is represented as follows,
P (Ee , cos θsun , xi ) = xi (x) × Psignal (Ee , cos θsun ) + (1 − xi (x)) × Pbg (Ee , cos θsun ), (7.7)
xi (x) =N
N MC× iM C × x,
Ni N

(7.8)

where N and Ni is total number of events and number of events in each energy regionin final sample, respectively. NiM C and N M C is in expected signal using Monte Carlo
N MC

simulation, so NiM C shows the expected energy shape, which is assumed to be the sameas in the solar model of BP95. Results for this analysis are summarized in Table 7.3.
118

7.3. RESULTS OF SOLAR NEUTRINO ANALYSIS

Ni (final sample)

NiM C

6.5∼ 7.0

12536

75927

2

7.0∼ 7.5

9617

67694

3

7.5∼ 8.0

7867

59306

4

8.0∼ 8.5

6259

51070

5

8.5∼ 9.0

4818

43196

6

9.0∼ 9.5

3580

35428

7

9.5∼10.0

2597

28522

8

10.0∼10.5

1699

22194

9

10.5∼11.0

1132

17410

10

11.0∼11.5

751

13176

11

11.5∼12.0

509

9492

12

12.0∼12.5

326

6819

13

12.5∼13.0

206

4721

14

13.0∼13.5

166

3188

15

13.5∼14.0

107

1994

16

14.0∼20.0

198

3145

N = 52368

N M C = 443282

i

Energy(MeV)

1

Total

Table 7.3: The summary of the number of events in each energy bin for the
final sample and the Monte Carlo sample.
The likelihood function is written as below,
L(x) =Ni
16 Y
Y

Pj (Ee , cos θsun , xi ),

(7.9)

Ni
16 X
X

log Pj (Ee , cos θsun , xi ).

(7.10)

i=1 j=1

orlog L(x) =i=1 j=1

We calculate x with the maximum likelihood value (xmax ) and the number of solar
neutrino events is simplyNν = xmax × N.

(7.11)L(xerror ) = exp(−0.5) × L(xmax )(7.12)The statistical error is derived by

119CHAPTER 7. DATA ANALYSIS AND RESULTS

Fig 7.19 shows the likelihood distribution as a function of x. The results are
xmax= 0.0767,(7.13)

xerror = ±0.002.
The number of recoil electron signals from 8 B solar neutrino was calculated to be
Signal = 4016.6+104.7−104.7 (stat.)+208.9−144.6 (sys.)

events(7.14)

in 297.4 days. For this analysis, the fiducial volume is 22.5 kton and the energy thresholdis 6.5MeV. The systematic errors are described in the next section.

Figure 7.19: The distribution of thelikelihood for extraction of solar neutrino signal. The horizontal axis shows
the signal to noise ratio, which is afree parameter. The exact definitionsof xmax and xerror are given in the text.

8

B solar neutrino flux
Compared to the expected number of signals obtained by Monte Carlo, we can obtain

the observed 8 B solar neutrino flux. As described in Section 6.1, the predicted 8 B solar
neutrino event rate arriving at Super-Kamiokande is 55.8events/day when the total flux
is assumed 1×106 (cm−2 s−1 ) as the unit flux. The number of total generated events
is 4428360 and the number of events after several reduction is 443282. Therefore, theevent rate which is expected to detect in Super-Kamiokande is calculated to be 55.8 ×443282/4428360 = 5.59 events/day. The total live time is 297.4days, so the expected
number of event is 5.59 × 297.4 = 1662.5 events per unit flux 1×106 (cm−2 s−1 ). The

number of observed signal is 4016.6 events, so the observed 8 B solar neutrino flux is
2.42

+0.06
−0.06 (stat.)+0.13−0.09 (sys.)

120[×106 /cm2 /sec].

(7.15)

7.3. RESULTS OF SOLAR NEUTRINO ANALYSIS

Comparing the result to standard solar models, the ratio of data to SSMs prediction is
Data
SSM
Data
SSM
Data
SSM

= 0.365+0.010−0.010 (stat.)+0.019−0.013 (sys.)(BP 95)(7.16)= 0.425+0.011−0.011 (stat.)+0.022−0.015 (sys.)(BP 92)(7.17)= 0.545+0.014−0.014 (stat.)+0.028−0.020 (sys.)(T L93)(7.18)

Fig 7.20 shows the solar neutrino flux obtained at the various intermediate analysis
steps. This is for the systematic check of the solar neutrino flux calculation. From thefigure, we find that the solar neutrino flux is consistent at each analysis step.

Figure 7.20: The calculated solar neutrino flux at the various intermediate
analysis steps. The vertical axis shows the ratio of the flux ateach step to the original one.

Stability of the solar neutrino flux
The present solar neutrino results cover over one year. Fig 7.21 shows the solar
neutrino flux as a function of time. The orbital eccentricity of the earth causes about 7%
flux variation. The measurement is consistent with the expected within the error. The
same data can be used to study seasonal variation of the solar neutrino flux in which
as shown in Fig 7.21 the just-so oscillation[25] can be studied. The current statistics is
unfortunately not very sensitive to check the just-so oscillation, yet.
121CHAPTER 7. DATA ANALYSIS AND RESULTS

Figure 7.21: The solar neutrino flux as a function of time.

Day/Night variation of the solar neutrino flux
We have measured the daytime and the night-time flux separately. The live time is145.1 days 152.3 days for daytime and night-time, respectively. The flux obtained is
Day : 2.39

+0.09
−0.09 (stat.)+0.10−0.07 (sys.)[×106 /cm2 /sec].

(7.19)

Night : 2.44

+0.09
−0.08 (stat.)+0.10−0.07 (sys.)[×106 /cm2 /sec].

(7.20)The relative difference between the daytime and night-time flux isDay − N ight
= −0.0104 ± 0.0258(stat.) ± 0.0135(sys.).
Day + N ight

(7.21)In the ratio Day/Night, many of the systematic errors are cancelled, (See Table 7.4).
Moreover, the advantage of this analysis is independent from the absolute flux calculations. There is no evidence for the difference between daytime and night-time fluxes
within the experimental errors. The implications of these flux measurements are described in the next chapter.
Energy spectrum
The measurement of the solar neutrino energy spectrum is important, because theshape is solar model independent and sensitive to neutrino oscillations, especially the122

7.3. RESULTS OF SOLAR NEUTRINO ANALYSIS

small angle solution of the MSW effect as described in Chapter 2. Fig 7.22 shows theratio of data to SSM prediction in each energy bin. The statistics becomes large inSuper-Kamiokande and the systematic errors have been reduced by LINAC calibration.
Fig 7.22 also shows the expected energy shape if the typical small angle solution of MSW
effect is assumed. (sin2 2θ = 9.12 × 10−3 and ∆m2 = 6.31 × 10−6 ) It is hard to say thatthe spectrum distortion exists, but the small angle solution is more consistent with themeasurement than a flat spectrum. (χ2noosc /ν = 19.7/14, χ2M SW /ν = 18.7/14) However it
is not significant yet and more statistics is needed. Now, we also need further study thesystematic error. The analysis will be very important in the future and we will discuss
it in another paper.

Figure 7.22: Energy spectrum observed in Super-Kamiokande. Inner andouter error bars shows the statistical and systematic errors,
respectively. The dashed line shows the expected spectrum
assuming the typical small angle solution of the MSW effect.
(sin2 2θ = 9.12 × 10−3 and ∆m2 = 6.31 × 10−6 )123CHAPTER 7. DATA ANALYSIS AND RESULTS

7.3.2

Summary of the systematic errors

The systematic errors for the solar neutrino analysis are summarized in Table 7.4.
• Energy scale and resolution.

The systematic error of the absolute energy scale is ±1.5%. This is mainly causedby the variation in each LINAC energy point. (1.3% See Section 5.3) The energy
resolution error, calculated by LINAC, is 4.7%. (See Section 5.3) The systematic
error of solar neutrino flux caused by these errors is calculated to be +4.7% and−3.1%
The uniformity of relative energy scale in direction is calculated using spallation
events as described in Appendix C.2 and to be less than ±0.5%. The systematic

error of day/night flux difference is calculated to be +1.2% and −1.1%• Trigger efficiency.

The trigger efficiency is almost 100% above 7MeV, so the systematic error of thetrigger efficiency is negligible in this energy region. In the energy region between
6.5MeV and 7MeV, it is 1.2% as described in Section 4.6.
• Noise reduction.

Each reduction step of low energy event is summarized in Table 7.2 The main
systematic effects are from noise reduction, items (5) and (9) in the table. The
differences of each cut efficiency between Monte Carlo and the data are 0.2% and0.7%, respectively. All the other reduction steps are negligible.

• Direction.

The difference of the angular resolution between Monte Carlo and the data is

calculated by LINAC in Table 5.4. This difference is considered in the signal
extraction.
• Vertex shift.

As mentioned in Section 5.1, the systematic reconstructed vertex shift from the realpoint is 16cm at most. We estimated the systematic shift of the fiducial volume
from the vertex shift. It is −1.3%.
124

7.3. RESULTS OF SOLAR NEUTRINO ANALYSIS• Calculation of ν-e cross section.

The systematic error in the theoretical calculation of ν-e cross section to the solar

neutrino flux is estimated to be 0.5% [34].
• Livetime calculation.

Livetime is calculated by a few different methods, which use raw data, muon dataor low energy data. The difference between these methods is 0.1% at most.
Flux

Day/Night

Energy scale and

+4.7

+1.2

resolution

−3.1

−1.1

8

+1.2

B spectrum error−1.1

Trigger efficiency
Reduction (5)

+0.2

–

±0.2

±0.1

+1.7

–

±0.7

Reduction (9)Direction

Non-flat background ±0.1

Spallation deadtime<0.1

Vertex shift−1.3

ν-e cross section

–

±0.5

–

±0.4

±0.6
–
–

Live time

±0.1

±0.1

TOTAL

+5.2

+1.4

−3.6

−1.3

Table 7.4: Summary of systematic errors (%). The total is the quadraturesum of the separate items. Currently, energy measurement anddirectional fitting errors dominate.

125Chapter 8
Conclusions and Discussions
We have studied 297.4 days of the solar neutrino data measured in Super-Kamiokande.
The observed 8 B solar neutrino flux,
2.42

+0.06
−0.06 (stat.)+0.13−0.09 (sys.)[×106 /cm2 /sec],(8.1)

has small statistical (±2.5%) and systematic errors (+5.2%−3.6% ) which can be compared tothose of Kamiokande results with error of ±6.8% (stat.) and ±11.8% (sys.)[20].
In this chapter, we discuss the implication of the results of the measurements of theabsolute flux and of the separately measured daytime and night-time fluxes.

8.1

Implication of the absolute flux measurement

The comparison of the results in Super-Kamiokande to SSM
There are several different predicted values of solar neutrino flux as shown in Table 2.3.
It was already shown that the fluxes of BP92 and TL93 were basically same when the
input parameters were taken to be same[11]. The difference of BP95 with BP92 or TL93
is the inclusion of the effect of heavy element diffusion or not. It was shown that the soundspeeds of the solar model which include the diffusion effect agree with helioseismologicalmeasurement with less than 0.2% discrepancy. It is better than the models not including
diffusion effect (the discrepancy is less than 1%)[13].
The flux ratios of Super-Kamiokande to these models are summarized in Eq(7.16) ∼(7.18). The ratio to BP95 which includes the diffusion of the heavy element and now127CHAPTER 8. CONCLUSIONS AND DISCUSSIONS

believed to be the best is,Data= 0.365
SSM (BP 95)+0.010−0.010 (stat.)+0.019−0.013 (sys.).

(8.2)

This shows that the deficit is very significant (30σ) if only the experimental errors aretaking into account. Careful examination on uncertainties of the solar neutrino flux
calculations is indeed needed.
The standard solar models are constrained by the recent precise helioseismologicalmeasurement. Then we are able to build a solar model which is constrained by themeasurement. For example, B.Ricci et al[54] calculated the solar core temperature (T )and its uncertainty in the helioseismologically-constrained solar model. This model used
the same equations as SSM, and they calculated the range of allowed value of T bytuning input parameters (e.g. the radiative opacity, the ratio of heavy elements) to
become consistent with helioseismological data. The central value of T calculated bythem is 1.58×107 K, which is consistent with BP95 (T = 1.57×107 K). Its uncertainty is∆T /T = ±1.4% and becomes smaller than that quoted error in BP95 (∆T /T = ±2.7%).

As a result, the uncertainty of the neutrino flux from the uncertainty of the solar coretemperature becomes also smaller.
However, there are other sources of flux uncertainty, for example, the astrophysicalS-factor, especially S17 for 8 B solar neutrinos. Recently, the new experiment of the crosssection has been done[15] and it is discussed in Section 2.1. B.Ricci et al considered S17
has larger errors (30%) than that in SSM (9.3%). This large error corresponds to a 3σ
uncertainty in S17 , which is 0.0224(1 ± 0.093) (keV·barn)[14].
After all, the total uncertainties in solar neutrino flux calculation by them becomeslarger than that in BP95. The lowest 8 B neutrino flux within their errors is φ(8 B) = 2.97
×106 (cm−2 sec−1 ), (the central value is 5.96 × 106 (cm−2 sec−1 )) which can be compared

to 6.62 × 106 (cm−2 sec−1 ) in BP95. The ratio of the data in Super-Kamiokande to theflux predicted by the lowest 8 B neutrino model isData= 0.815
P rediction+0.020−0.020 (stat.)+0.042−0.029 (sys.).

(8.3)

As described above, the standard solar model is recently supported by helioseismology. However, since there are several parameters which are not entirely constrained by
the helioseismology like the nuclear cross section, the neutrino production rate is still128

8.1. IMPLICATION OF THE ABSOLUTE FLUX MEASUREMENTon the debate. In order to avoid those argument we need the solar model independent
analysis to solve the solar neutrino problem.
The comparison of the results in Super-Kamiokande to Homestake
We compared the results of Super-Kamiokande and Homestake. The sensitivity ofsolar neutrinos in each detectors is shown in Fig 8.1. From the calculation of the BP95,
1.94 SNU of 7 Be, pep and CNO solar neutrinos should be observed in Homestake in
8
addition to the contribution of 2.69 ± 0.07 +0.14−0.10 SNU of B solar neutrinos, corresponding

value to the result of the measurement of Super-Kamiokande. (ref. Eq(8.1) and (8.2))
However, the observed value in Homestake was 2.54 ± 0.14 ± 0.14 SNU, so there is astrong indication that other neutrinos especially 7 Be solar neutrinos are missing.

(φothers < 0.23 SNU (90% C.L.))

Figure 8.1: Individual solar neutrino contributions in various experiments,
which is calculated by BP95.

If we assume the neutrino oscillation, the missing of 7 Be solar neutrinos can benaturally explained because of neutral current contribution to Super-Kamiokande data
and/or non monotonic suppression of neutrinos. (See Fig 2.14)
Homestake experiment can detect only νe , while Super-Kamiokande can detect νµ andντ through the neutral current interaction although the cross section is approximately
129

CHAPTER 8. CONCLUSIONS AND DISCUSSIONS

1/6 of νe . (See Fig 3.2) Therefore, if νe , generated in solar core, changes other typeof neutrino by neutrino oscillation, it can be observed in Super-Kamiokande but not inHomestake. It makes as if the solar neutrino flux observed in Super-Kamiokande is larger
than in Homestake.
When the typical value of oscillation parameters, for example, sin2 2θ = 1.1 × 10−2and ∆m2 = 5 × 10−6 , are assumed, the expected flux observed in each detectors are nonmonotonic as shown in Fig 8.2 and calculated to be φCC = 1.81 × 106

φSK= 2.56 × 106 (cm−2 sec−1 ) = osc φN C = 0.75 × 106

φCl
osc = 2.34 SNU,

where φCC and φN C are expected flux from the charged current and the neutral current
interaction, respectively. These are consistent with both two experimental results within
the errors.

Figure 8.2: The survival probability of νe state by MSW effect as a functionof Energy, when sin2 2θ = 1.1 × 10−2 and ∆m2 = 5 × 10−6 . The

threshold energy of Super-Kamiokande and Homestake are also
shown.

130

8.2. NEUTRINO OSCILLATION STUDY USING DAY-NIGHT FLUXDIFFERENCE
Summary
The absolute solar neutrino flux observed in Super-Kamiokande is significantly smaller
than the expected flux from SSMs, and the experimental errors become particularly
small. Even though the theoretical uncertainty is considered to be still large, this results suggests the neutrino oscillation. The comparison with the result in Homestake areconsistent with a hypothesis of neutrino oscillation.

8.2

Neutrino oscillation study using day-night flux
difference

Introduction
In this section, we will study the flux measured separately for daytime and nighttime in detail. The MSW effect through the earth − the νe regeneration described in

Section 2.4.3 create flux difference between day and night. If we take the ratio of nighttime flux to daytime flux, the analysis for neutrino oscillations becomes independent onsolar model calculations.
With the current statistics the total flux of daytime and night-time agree within theexperimental errors as described in Section 7.3.1. We are able to evaluate the excluded
regions of the neutrino oscillation parameters.
We have divided the night-time into five bins in terms of the angle (δsun ) between thesun and the Z-axis of the detector as shown in the next page. We call each bin as N1,
N2, N3, N4, and N5 (∆ cos δsun = 0.2). By using this division, we are able to make asensitive check on the MSW effect which depend on the distance through the earth andthe different electron density. Table 8.1 and Fig 8.3 shows the solar neutrino flux in thedaytime and the five night-time bins. Fig 8.3 also shows the expected solar neutrino fluxin each bin for the two typical MSW parameters, corresponding to large and small angle
regions. In the large angle region, the flux difference of daytime and average night-timeis larger than in small angle region.
131

CHAPTER 8. CONCLUSIONS AND DISCUSSIONS

Z

all

2.42+0.06
−0.06

day

2.39+0.09
−0.09

night

2.44+0.09
−0.08

N1

2.52+0.22
−0.22

N2

2.17+0.20−0.19

Combined

N3

2.53+0.18−0.17

2.42+0.10
−0.09

N4

2.51+0.20
−0.20

N5

2.61+0.21
−0.21

Day
SK
Horizon
N1
N2
N3
N4
N5

Table 8.1: The solar neutrino flux in the daytime, the five night-time bins
and the combined value between N1 and N4. The definition ofthem are also shown.

Figure 8.3: The solar neutrino flux in the daytime and the five night-timebins observed in Super-Kamiokande. The expected solar neutrino
flux in each day-night bin for the two typical MSW parameters
are also shown. The solid line shows sin2 2θ = 0.631 and ∆m2 =3.16 × 10−5 . The dashed line shows sin2 2θ = 6.31 × 10−3 and∆m2 = 6.92 × 10−6 .

132

8.2. NEUTRINO OSCILLATION STUDY USING DAY-NIGHT FLUXDIFFERENCE
The calculation method
For the analysis of MSW effect, the expected number of solar neutrinos for the various
neutrino oscillation parameters, (sin2 2θ, ∆m2 ) were calculated, and compared with thosefor no MSW effect. The parameter regions considered were 10−4 ≤ sin2 2θ ≤ 1, 10−7.5 ≤∆m2 ≤ 10−3.5 , and the 201×81 points uniformly distributed are picked up from theregion for the calculation.

The generated position of neutrinos is shown in Fig 2.2 [10], and the propagation ofneutrinos through the sun was calculated by the numerical integration of Eq(2.23) fromthe center to the surface of the sun. The electron density used in this calculation isshown in Fig 2.1[10]. From the surface of the sun to the earth, the neutrinos follow theequation of the vacuum oscillation in Eq(2.18). The neutrino propagation in the earth
was calculated by the similar way in the case of the sun. The electron density used wasshown in Fig 2.15[31].
In order to obtain the confidence level contours for the day-night effect, the following
χ2 is defined:
χ2 =

6
X
(Ri − RiM SW × α)2

σi2

i=1

,

(8.4)

where i runs each bin of daytime and five night-time divisions. Ri is the ratio of thedata to SSM in i-th day-night bin and RiM SW is the expected ratio between those withand without MSW effect. σi is the quadratic sum of the statistical error of Ri and thesystematic error of day/night flux shown in Table 7.4. α is the normalization factor
which is free and determined so as to give a minimum χ2 .

The calculation results and discussion
Fig 8.4 shows the contour of the 95% C.L.. The inside region is excluded from theresult for Super-Kamiokande. This figure also shows the result for Kamiokande. As can
be clearly seen, Super-Kamiokande extended the excluded region of the Kamiokande.
As described in Section 2.4.4, if we assume a absolute flux predicted from a solarmodel, we can obtain the allowed parameter region of the MSW effect. In Fig 8.4 wealso show the allowed region from this kind of analysis for all the past four solar neutrino
experiment results assuming BP95. We can exclude about half of the large angle solution
from the result of only 297 days of the day-night flux in Super-Kamiokande.
133

CHAPTER 8. CONCLUSIONS AND DISCUSSIONS

Fig 8.4 also shows the exclude region if the flux difference in daytime and night-time
does not exist in 2 years and 5 years statistics. We can sense all the parameter region inlarge angle solutions in 5 years.

Figure 8.4: The 95% C.L. contour of the MSW analysis. The inside regionof a thick line is excluded from the result of day/night flux variation in Super-Kamiokande. This figure also shows the excluded
region from the day/night flux variation in Kamiokande (a thinline) and the allowed region from the current solar neutrino experiments. (See Section 2.4) The dashed lines show the exclude
region expected from 2 years (inside) and 5 years (outside) statistics.

1348.2. NEUTRINO OSCILLATION STUDY USING DAY-NIGHT FLUXDIFFERENCE
The study of earth core effect in MSW analysis
As shown in Fig 8.3, the study on the day-night effect is not sensitive to the small
angle solution except the N5 bin, because this bin is corresponding to the high density ofcore in the earth. The boundary between core and mantle is 3480km deep in the earth,and cos δsun = 0.8376. Therefore, neutrinos in N1 to N4 go through only mantle, while
neutrinos in N5 go through both core and mantle. It is pointed out by Petkov et al[55]that the small angle region can be precisely studied by the analysis of this core effect.
We separately consider the solar neutrino flux combined from N1 to N4 term (Mantleterm) and N5 term (Core term) in order to see clearly the core effect. We define thefollowing parameters;
Day − N ight,
Day + N ight
Day − M antle,
AM =Day + M antle
Day − CoreAC =.
Day + Core
Table 8.2 shows the expected value for typical two couple of MSW parameters. In small
AN =angle region, the difference between AM and AC becomes large as shown in the table.
sin2 2θ

∆m2

AN

AM

AC

AC
AM

0.631

3.16 × 10−5-0.0307-0.0294-0.0370

1.26-0.00725-0.00108-0.0356 32.96

1

2 6.31 × 10−3

6.92 × 10−6

Table 8.2: The asymmetry defined in the text.

Fig 8.5 and Table 8.1 shows the experimental results in Super-Kamiokande. The
asymmetries are
AN = −0.0104 ± 0.0258(stat.) ± 0.0135(sys.),
AM = −0.0069 ± 0.0273(stat.) ± 0.0135(sys.),
AC = −0.0432 ± 0.0443(stat.) ± 0.0135(sys.).
Fig 8.5 also shows calculate value for the typical MSW parameters in large angle andsmall angle region. From the figure, small angle solution seems good, (χ2large /ν =1.32/4, χ2small /ν = 0.076/4) but it is not conclusive yet, and need more statistics.
135

CHAPTER 8. CONCLUSIONS AND DISCUSSIONS

Figure 8.5: The observed flux in each time region in Super-Kamiokande. The
expected flux assuming the typical MSW parameters as describedin Table 8.2. The solid line shows the large angle and the dashedline shows the small angle region.

8.3

Summary

We summarize the results and the implication of solar neutrino flux observation inSuper-Kamiokande.
1. We have measured solar neutrinos in Super-Kamiokande. The deficit of the observed flux from the predicted by SSMs was seen, and the ratio isData+0.019= 0.365+0.010−0.010 (stat.)−0.013 (sys.).
SSM (BP 95)
The significance of 8 B neutrino flux deficit in Super-Kamiokande is stronger than
the result in Kamiokande because the statistics and the quality of the data were
improved.
2. The results of Super-Kamiokande and Homestake are difficult to be explained bychanging solar models but are natural by neutrino oscillation.
3. The flux of daytime and night-time agree within the experimental errors. From
the result of day-night flux measurement, we calculated the excluded regions of
the neutrino oscillation parameters of MSW effect. It also restricts the large angle
1368.3. SUMMARY

solutions obtained from the combined results of solar neutrino flux in the pastexperiments assuming the absolute flux.
4. By considering future increases of statistics, we can extend on sensitivity in theentire large angle solution.
5. The analysis of the core effect in the earth is sensitive to the small angle solutions.
The result of core effect in Super-Kamiokande suggests that the small angle solution
is better than the large angle solution, but it is not conclusive yet.
In the MSW analysis, the analysis of day-night flux difference is sensitive to the large
angle solutions, and the small angle solutions if the core effect in the earth is considered.
The energy shape is sensitive to the small angle solutions. These analyses are complementary. Further, the analysis of the seasonal flux variation is sensitive to the vacuum
oscillation. Therefore, when the statistics become larger and the analysis is more precise
in future, we can conclude the neutrino oscillation definitely.

137

Appendix A
Electronics
In this chapter the electronics in Super-Kamiokande is described in detail. The electronics for the inner detector consists of TKO(TRISTAN/KEK Online) modules[56] andVME modules. The logic diagram of the electronics system is shown in Fig A.1. These
are arranged in 4 separate electronics huts, each with 12 TKO system crates and 2 VME
crates, for a total of 48 and 8 crates, respectively.
The front-end electronics uses 934 modules called “ATM” (Analog Timing Module)
which process the signals from the PMTs. In general 20 ATM modules are arranged inan each TKO crate. Each crate also contains one interface module called “SCH” (Super
Control Header), one trigger signal distribution module called “GONG” (GO/NoGo),
and one summing circuit. In the VME crates, there are 6 data buffer modules called“SMP” (Super Memory Partner) and one SBus-VME Interface.
Fig A.2 shows the block diagram of the circuit in the ATM. First, each ATM handles
12 PMT channels, and a signal from each PMT is divided into four. One of these four,
after amplification by a factor of 100, goes through a discriminator the threshold of
which is set to 100mV, equivalent to about 0.32 p.e.. When the pulse height of a PMT
signal exceeds this threshold,a rectangular pulse (200nsec in width and 11 mV in height)
is generated. The pulses from each 12 PMT channels are summed and output as the“HITSUM” signal. A rectangular pulse with 900nsec duration is generated as a HIT
signal simultaneously. For this 900nsec, any subsequent PMT signal is rejected. This
discriminator pulse starts the charging of “TAC” (time-to-analog converter), and it willend when the global trigger signal arrives. Another signal from the PMT is sent to the“QAC” (charge-to-analog converter) which accumulates charge for 400nsec after each
139

APPENDIX A. ELECTRONICS

discriminator hit. If the global trigger does not arrive within 1.3µsec after the PMT hit,
the TAC/QAC are flushed. While the global trigger arrives, an ADC begins digitizing
the voltages stored in the TAC/QAC capacitors. The ADC outputs are stored in the1024 word “FIFO”(first-in first-out) memory with event number. It spends 5.5µsec to do
Analog-Digital conversion and store into memory, and the signal is not processed in thisperiod. Therefore, the TAC/QAC has 2 channels, so that if the one is not available, theother channel can be used instead. This reduces the dead time, which is especially usefulfor observation of the decay electron signal from stopping muons. The timing chart ofsignals in the ATM is shown in Fig A.3.
Pedestals for ATMs are measured every 30 minutes. This takes about 1 minute. In
order to reduce dead time for our super nova search, pedestal data taking is done for 1/8
of all the ATM, and normal data taking is operated to the remaining ATM. For solar
neutrino analysis, data taking is dead during all pedestal measurements.
The trigger condition was already described in Section 3.2.4. The trigger signal is
fed to the “TRG” module. This module has a 16 bit event counter, and an internal
clock which runs at 50 MHz, so the relative time of the event is determined with 20nsec
resolution. This event information is stored in the FIFO memory of the TRG module.
The global trigger signal and event counter is distributed to 48 GONG modules in eachTKO crate. GONG modules distribute the trigger signal and event counter to the ATM
modules. The timing chart of the trigger is also shown in Fig A.3.

Data acquisition system and Offline computer facilities
The 20 ATM data are read out via SCH to the SMP (VME module), and stored init. The data stored in SMP are sent via SBus-VME Interface to the online computer. In
each electronics hut, there are two Sun SPARClassic (S4/CL) for inner data acquisition(total 8), and each S4/CL reads out and collects the data of 6 SMP modules. This isshown in Fig A.1. These data are transferred to a Sun SPARCstation 10 (S4/10) as aonline host computer via FDDI which is a network for transferring data at very highspeed. After the data format is changed in the reformat machine (S4/CL, described
below), they are sent to the offline computer which is outside of the mine via an opticalfiber cable.
In the online host computer (S4/10), all the information of hit PMTs including inner140

and outer detector belonging to one global trigger is concatenated and recorded. Thisis regarded as one event. Next, the format of this data is changed to “ZEBRA” format,
by what we call the “reformat” process. ZEBRA is a tool for data management which
is developed in CERN which we use because it is convenient for storage and handlingof large quantities of data, and it is also standard in high-energy physics experiment.
After reformat, the ZEBRA format data is sent to offline host computer (VPX210/10S)
every ten minutes. The size of this file corresponding to ten minutes is about 70MByte.
This host computer saves all the data in a tape library and converts the data of ADC
and TDC counts to units of photo electron and nano second, respectively. These data
are stored in buffers on 1GByte memory temporarily, and distribute to SPARCstation
20 (S4/20), with a total of 20 CPUs connected by the network called “UltraNet1000”.
In these machines, all events are reconstructed by various algorithms for different energy
ranges. There are also 10 work stations for analysis (S4/10) with 2 CPU in each machine,
connected via FDDI to VPX210/10S and S4/20.

141

APPENDIX A. ELECTRONICS

Electronics system
PMT

TKO module

VME module

SCH
ATM..........

× 20
SMP

............

×6............

...................

GONG

Online DAQ

×6

SMP
Sbus-VME
interface..........

................................

SCH
ATM
× 20

GONG

×8

...........

×8

TRG

Work Station

Trigger

Figure A.1: The logic diagram of the electronics system used in SuperKamiokande.

142

PMTSUMstart/stop

Current Splitter

Signalgate

TAC-AchQAC-AchTAC-BchQAC-Bch
ADC

Self Gate

amplifierx100
Threshold (100mV)

w900nsec

DISC.

Trigger signal

w200nsec

HITSUM

Figure A.2: The ATM block diagram.

ATM
PMT signal

A-chThreshold

HIT signal
Gate(charge)

900nsec
400n

B-ch

Start/Stop

200nsec

HITSUM

Trigger proc.

GONG

Summed HITSUM
Trigger threshold

Global Trigger

Figure A.3: The timing chart for signal and trigger.

143

Appendix B
The detail explanation of event
reconstruction
B.1

Hit-PMT selection for vertex reconstruction(1) The hit channels in 200nsec timing window containing the maximum number ofhits are selected. The reason we use 200nsec at first is that the maximum time offlight for a direct photon is approximately that.
(2) The number of background hits in 200nsec window is estimated as follow;
Nbg = (t3 − t2 ) ×

Nhit (t1 : t2 ) + Nhit (t3 : t4 ),(t2 − t1 ) + (t4 − t3 )where Nhit (ti : tj ) is number of hit-PMT in the timing between ti and tj , and t is
as shown in Fig B.1, t1 and t4 are the beginning and end of the event, and t2 andt3 are the limits of the time window under consideration.
(3) The maximum number of hits for each of 11 timing windows of width (200 ×

n/11, n = 11, 10, . . . , 1) inside the 200nsec window determined above is calculated.
For each window, the signif icance defined below is also calculated:(signif icance) =Nhit − Nbg
qNbg(4) The window with maximum significance is selected.
145.

APPENDIX B. THE DETAIL EXPLANATION OF EVENT RECONSTRUCTION(5) It is checked whether any wider timing window than (4) with(signif icance) > (signif icance)max × 0.8
exist or not. If one does exist, all hit channels in this wider window are used forvertex reconstruction are used. If not the timing window which has maximum
significance is taken. This is so that we can use as many signal hits as possible.

t2

t1

t4

t3

Figure B.1: The timing distribution of hit-PMTs in one event. The time,
which is horizontal axis, is the relative timing of each hit-PMT
obtained from ATM data.

B.2

The definition of effective Nhit

. The definition of effective Nhit (Nef f ) is as the following equation,
Nef f =

N
hit
X
i=1

"

!

#

Nall
Rcoverri(Xi + ǫtail − ǫdark ) ×× Gtime (i)× exp×Nnormal S(θi , φi )λ(run)(B.1)

The first factor is the correction to the each hit, where Xi is “occupancy” in order toestimate the effect of multi photo-electrons, ǫtail is for the correction for late hits outside146B.2. THE DEFINITION OF EFFECTIVE NHIT
the 50ns window, and ǫdark is for dark noise correction. The definition of Xi is as follows:1
log 1−x λi =i

Xi =  xi

xi




 3

xi < 1(B.2)
xi = 1

where xi is the ratio of number of hit-PMTs to the number of PMTs around the i-th
hit-PMT (normally nine (3×3)) and λi is the estimated number of photons per one PMT
in this 3×3 PMTs region. This correction is to estimate the number of photons arrived at
the i-th hit-PMT using the number of PMTs which does not hit in the 3×3 PMTs region
around the i-th hit-PMT. Here, the ratio of the PMTs which does not hit is measured tobe 1 − xi . As while, when λi is the average number of photons per one PMT in the 3×3

PMTs region, the probability not to hit is calculated by Poisson distribution as shownin the following equation,
P0 =(λi )0 × e−λi
= 1 − xi .
0!

(B.3)

Fig B.2 shows the occupancy as a function of the number of hit-PMTs around one hitPMT. When xi = 1, the occupancy diverge, therefore, we determined that Xi = 3 at
xi = 1 by extrapolation as is seen in Fig B.2. It also minimizes the position dependenceof Nef f

Figure B.2: The occupancy as a function of the number of hit-PMTs aroundone hit-PMT.

The second factor is the bad PMT correction, where Nall is the total number of PMTs,
11146, and Nnormal is the number of properly operating PMTs for the relevant subrun.
The third factor is the effective photo coverage. The average of the photo coverage,
which is the ratio of the area covered by PMT to all area, is 0.4041, (Rcover ). However,
the effective photo coverage changes as the input angle of the photon to the PMT.
147

APPENDIX B. THE DETAIL EXPLANATION OF EVENT RECONSTRUCTION

Therefore, we applied the coverage correction, where S(θi , φi ) is the photo coverage froma view of θi , φi direction.
The fourth factor is the water transparency correction, where ri is the distance fromthe reconstructed vertex to the i-th hit-PMT position, λ is water transparency as shownin Fig 4.12.
The fifth factor, Gtime (i), is the gain correction at single photo-electron level which
depends on the time of the production of each PMT.

B.3

Recent results of LINAC calibration

We recently took calibration data using an electron LINAC. This data taking was
performed at 6 pipe positions and 7 beam energy points. The positions are (x, z) =(−4, 0), (−4, 12), (−8, 0), (−8, 12), (−12, 0) and (−12, 12) (m), all at y = −0.7m andthe beam energies are shown in Table 5.2. Fig B.3 shows the difference of energy scale

between data and Monte Carlo. The position dependence of the difference is less than
1% and the energy dependence is less than 0.3%. The differences of the energy, positionand directional resolution between data and Monte Carlo are summarized in Table B.1.
0.05

(MC-data)/data(MC-Data)/Data

0.05

Position Dependence

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

0

(-8,0)(-8,12)(-4,0)(-4,12)-0.03(-12,0)(-12,12)
combined

-0.01

-0.01
-0.02

Energy Dependence

0.04

-0.02

combined

-0.03
-0.04

-0.04

-0.05

-0.05

4

6

8

10

12

14

16
18
Ee(MeV)

Figure B.3: The difference of energy scale between data and Monte Carlo.
The left figure shows the position dependence and the right one
shows the energy dependence148B.4. ANOTHER ALGORITHM OF VERTEX RECONSTRUCTION

Energy resolution< 2%

Position resolution< ±5cmDirectional resolution

1.8 degree at 6.5MeV

0.3 degree at 16MeV
Table B.1: The differences of the energy resolution ((data-MC)/data), theposition resolution (data-MC) and the directional resolution(data-MC) between data and Monte Carlo in new LINAC calibration data.

B.4

Another algorithm of vertex reconstruction

As described in Section 7.2, we use a different algorithm of vertex reconstruction inorder to reject the type of noise event shown in Fig 7.8. The essence of this reconstruction
is selecting PMT hits which are considered to be caused by Cherenkov photons. For thispurpose, we use the space-time correlation of hit-PMTs. The following criteria is appliedin selecting PMTs: if a hit-PMT doesn’t have neighboring hit-PMTs which satisfy thefollowing condition,△r ≤ rlimitand△t ≤ tlimit ,we reject this hit-PMT for vertex reconstruction, where △r is the spatial distance be-

tween PMTs and △t is time difference between these PMTs. rlimit and tlimit are limits of

distance and timing difference of given PMTs. These limits are chosen so that they reduce the dark noise as much as possible without reducing good PMT significantly. Theselimits are determined using LINAC data. Table B.2 shows the number of remained hitPMTs in several conditions of rlimit and tlimit . For this analysis we take rlimit = 700cm
and tlimit = 35nsec.

Fig B.4 shows the distribution of the distance (△l) between the original vertex and thevertex from the new method. Some typical events with large △l are shown in Fig 7.8. The

vertex reconstruction of events with large △l is generally clearly mistaken. Therefore,

we use △l for the event reduction as follows; events with △l > 5m are rejected. The

rejected events are classified by the number of small clusters as follows: ∼24% have two
149

APPENDIX B. THE DETAIL EXPLANATION OF EVENT RECONSTRUCTION

rlimit (cm) tlimit (nsec)

Number of hit-PMTs Ratio (%)

400

20

40406

50

500

25

47907

60

600

30

53756

67

700

35

59054

74

800

40

63781

79

Table B.2: The number of remained hit-PMTs in several conditions to beneighboring PMTs, and rlimit and tlimit are given in the text. The
number of all hit-PMTs is 80236. This is 5MeV LINAC data.

clusters;∼57% have one cluster; and ∼19% have none.

∆ l(cm)Figure B.4: The distribution of the distance between the original vertex andthe vertex from the new method. These are the 8 B Monte Carloand the data after spallation cut (hatched region).

150B.5. THE METHOD OF EVENT CLEAN UP USING VERTEX AND DIRECTION

B.5

The method of event clean up using vertex anddirection

In addition to the criteria described above, we use the uniformity of the azimuthal
angle distribution of hit-PMTs for identification of the event as shown in Fig 7.8.
The frame of reference has its center of the reconstructed vertex and the pole isthe event direction. From this, the azimuth angle is calculated. Fig B.5 shows typicalnormal and noise events, and the azimuth angle distributions of each. The expecteddistribution is the dashed line, and we use the length of the arrow shown in the figure
for the identification. If the event is normal, the hit-PMT distribution is uniform andthe value is small, but if there is a cluster, the value is large.
Fig B.6 shows the scatter plot of this value and the difference between fitted andgenerated vertex in solar neutrino Monte Carlo events. This shows only mis-reconstructed
events have large values.
Fig B.7 shows the distribution of the azimuthal angle non-uniformity in the final
sample and in the solar neutrino Monte Carlo in two energy regions. The cut criteria is0.4, and the efficiency is shown in the figure.
Fig B.8 shows the efficiency of the complete reduction combined with both methods
described in Section B.4 and B.5 in real data and Monte Carlo. From the figure, we
can see the real data and Monte Carlo are very consistent above our analysis thresholdenergy; the maximum of difference is 0.7%. This is taken as a systematic error in thesolar neutrino analysis.

151

APPENDIX B. THE DETAIL EXPLANATION OF EVENT RECONSTRUCTION

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
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

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:NORMAL DIR:-0.92, 0.40,-0.07
TRG ID :00000011 X: 1205.2cm
T diff.:0.251E+06us
Y: -688.2cm: 251.
ms -289.4cm
Z:
FSCC:
0
R: 1387.8cm
TDC0: -1117.8
NHIT:
32
Q thr. :0.0 good:
0.63
BAD ch.: no mask
SUB EV : 0/ 0

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 B.5: The left figure is shown as normal event and the right one isthe event with small cluster. Lower distribution fill the azimuth
angle of each hit-PMT from the start of one point.

152

B.5. THE METHOD OF EVENT CLEAN UP USING VERTEX AND DIRECTION

Figure B.6: The relation of the uniformity of the azimuth angle distribution
and the difference between fitted andgenerated vertex in Monte Carlo. The
horizontal axis is normalized to 1.

Figure B.7: The distribution of the azimuthal angle non-uniformity in the
final sample and in the solar neutrino Monte Carlo in two energy
regions. The numbers in the figure show the number of cut event
and all event.

153

APPENDIX B. THE DETAIL EXPLANATION OF EVENT RECONSTRUCTION

Figure B.8: The efficiency of the noise reduction as a function of energy. The
solid line is real data of tightly chosen spallation events, and thedashed line is solar neutrino Monte Carlo.

154

Appendix C
Spallation events
C.1

Likelihood function of spallation event

As described in Section 7.2.4, three values (△L, Qres and △t) are used for the spalla-tion likelihood function. We calculate the probability density functions of △L, Qres and△t by spallation as Fspa (△L), Fspa (Qres ), Fspa (△t), and by events not caused by spalla-tion as Fnon (△L), Fnon (Qres ), Fnon (△t), respectively. Assuming that above three factors
are independent, the spallation likelihood function (Lspallation ) is defined as follows,
Lspallation ≡Fspa (△L) Fspa (Qres ) Fspa (△t)··
Fnon (△L) Fnon (Qres ) Fnon (△t)

(C.1)

For muons with tracks that cannot be well reconstructed, Lspallation is defined using only
two parameters:
Lspallation ≡Fspa (Qres ) Fspa (△t)·
Fnon (Qres ) Fnon (△t)(C.2)

Spallation events have larger values of Lspallation than solar neutrino events.
Here, we describe how to find the probability density function. We gather samples ofpredominantly spallation events using the following selections,• △t ≤ 0.1sec. and Nef f ≥ 50

for △L• △t ≤ 0.1sec. and Nef f ≥ 50

for Qres• Qres ≤ 5.0 × 105 p.e. and △L ≤ 3m

for △twhere we cut on Nef f because very low energy events are often caused by other background sources.
155

APPENDIX C. SPALLATION EVENTS

The distribution of △L is made in six Qres ranges as shown in Fig 7.11. In eachhistogram, the spallation component and phase space shown by dashed line (Fnon (△L))
are included. Subtracting this phase space from the distribution, we get Fspa (△L).
The likelihood function for Qres is defined the same way as for △L. Fig C.1 shows

the Qres distribution of muons accompanied with a spallation event (a), and of muons
without an associate spallation candidates (b). Subtracting (b) from (a), we can get the
Qres distribution from only the spallation component (c) (Fspa (Qres )).

Figure C.1: The Qres distribution of muons accompanied with a spallation
event (a), of muons without any associated spallation candidates(b), and from only the spallation component (c), which is thedifferences (b) and (a).

156

C.1. LIKELIHOOD FUNCTION OF SPALLATION EVENTFig C.2 shows (△t) distribution. One can see a decay curve in correlation with thepenetrating muons. This decay curve is the combination of many isotopes with different
half-lifes as shown in Table 7.1. For making the likelihood function for △t, the decay
curve as shown in Fig C.2 is fitted with the combination of isotopes with known half-life.
The result is:
△t
△t
△t
△t
Fspa (△t)= 33900 × 2− 0.011 + 120100 × 2− 0.0204 + 338.6 × 2− 0.178 + 1254 × 2− 0.84
Fnon (△t)
△t

△t

△t

+ 134.7 × 2− 2.449 + 676.1 × 2− 7.134 + 7.791 × 2− 13.8

Figure C.2: The △t distribution in several time range. The solid lines show
fitting results.

157

(C.3)

APPENDIX C. SPALLATION EVENTS

C.2

Spallation events as detector calibration

Spallation events are generated uniformly in volume, in direction and in time. Therefore, we can use these events as a good relative calibration source. Fig C.3 and Fig C.4
show the stability of relative energy scale in time and as a function of nadir, respectively.

(%)

The uniformity of energy scale both in time and in direction are stable less than ±0.5%.
5
4
3

Figure C.3: The stability of relative

2

energy scale in time using spallation

1

events. The solid, dashed and dotted0line show 0%, ±0.5% and ±1%, respec--1

tively. The y-axis is the (percent) devi--2

ation from the average over the entire-3

sample.

-4

(%)

-5

200

300

400

500
600
700
date since 1996/1/1

5
4
3
2

Figure C.4: The uniformity of relative

1

energy scale in direction using spalla-

0tion events. The solid, dashed and dot--1

ted line show 0%, ±0.5% and ±1%, re-spectively.

-2
-3
-4
-5

-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8 1
cosθz

158

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