UNIVERSITY OF CALIFORNIA, IRVINE Search for Non-zero … · 2012-09-25 · UNIVERSITY OF...

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UNIVERSITY OF CALIFORNIA, IRVINE Search for Non-zero Neutrino Magnetic Moments Using Super-Kamiokande-I Solar Neutrino Data DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Physics by Dawei Liu Dissertation Committee: Professor Henry W. Sobel, Chair Professor Riley Newman Professor Jonas Schultz Professor Gaurang B. Yodh 2005

Transcript of UNIVERSITY OF CALIFORNIA, IRVINE Search for Non-zero … · 2012-09-25 · UNIVERSITY OF...

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UNIVERSITY OF CALIFORNIA,IRVINE

Search for Non-zero Neutrino Magnetic Moments Using Super-Kamiokande-I SolarNeutrino Data

DISSERTATION

submitted in partial satisfaction of the requirements for the degree of

DOCTOR OF PHILOSOPHY

in Physics

by

Dawei Liu

Dissertation Committee:Professor Henry W. Sobel, Chair

Professor Riley NewmanProfessor Jonas Schultz

Professor Gaurang B. Yodh

2005

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c© 2005 Dawei Liu

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The dissertation of Dawei Liuis approved and is acceptable in qualityand form for publication on microfilm:

Committee Chair

University of California, Irvine2005

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Dedication

To

my parentsMengluan Liu, Feng-e Peng

and my sisterZhaowei Liu

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Contents

List of Figures vii

List of Tables xii

Acknowledgements xiii

Curriculum Vitæ xiv

Abstract of the Dissertation xvi

Chapter 1 Neutrinos 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Vacuum Oscillation . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Neutrino Oscillation In Matter (MSW Effect) . . . . . . . . . 6

1.3 Neutrino Magnetic Moment . . . . . . . . . . . . . . . . . . . . . . . 111.4 Solar Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4.1 Standard Solar Model . . . . . . . . . . . . . . . . . . . . . . 151.4.2 Solar Neutrino Experiments . . . . . . . . . . . . . . . . . . . 22

Radiochemical Experiments . . . . . . . . . . . . . . . . . . . 23Water Cherenkov Experiments . . . . . . . . . . . . . . . . . . 24

1.4.3 Solar Neutrino Problem And Neutrino Oscillation . . . . . . . 281.4.4 Solution Using Neutrino Magnetic Moment . . . . . . . . . . . 291.4.5 KamLAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Chapter 2 Super-Kamiokande Detector 322.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.1.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Detection of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.1 Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.2 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.3 Data Acquisition Systems . . . . . . . . . . . . . . . . . . . . 412.3.4 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.5 Water and Air System . . . . . . . . . . . . . . . . . . . . . . 45

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Water System . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Air Purification System . . . . . . . . . . . . . . . . . . . . . 47

2.3.6 Monitoring System . . . . . . . . . . . . . . . . . . . . . . . . 47Online Monitor System . . . . . . . . . . . . . . . . . . . . . . 47Realtime Supernova Monitor . . . . . . . . . . . . . . . . . . . 48

Chapter 3 Event Reconstruction 493.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 543.3 Energy Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Muon Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 63

Chapter 4 Detector Calibration 684.1 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1.1 PMT Gain Calibration . . . . . . . . . . . . . . . . . . . . . . 69Xe Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 70Ni-Cf Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.2 PMT Timing Calibration . . . . . . . . . . . . . . . . . . . . . 744.2 Water Transparency Measurement . . . . . . . . . . . . . . . . . . . . 76

4.2.1 Measurement of Water Transparency by Laser . . . . . . . . . 764.2.2 Water Transparency Measurement and Monitoring by Decay

Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.3 LINAC Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3.1 LINAC Calibration System . . . . . . . . . . . . . . . . . . . 844.3.2 Energy Calibration By LINAC . . . . . . . . . . . . . . . . . . 87

Beam Energy Measurement . . . . . . . . . . . . . . . . . . . 87SK Energy Calibration . . . . . . . . . . . . . . . . . . . . . . 91Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 96Time And Directional Variations of Energy Scale . . . . . . . 102

4.3.3 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . 1044.3.4 Vertex Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 1044.3.5 Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . 106

4.4 Calibration Using Deuterium-Tritium (DT) Generator . . . . . . . . . 1084.5 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Chapter 5 Data Reduction 1205.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.1.1 Real Time Bad Run Selection . . . . . . . . . . . . . . . . . . 1215.1.2 Manual Bad Run Selection . . . . . . . . . . . . . . . . . . . . 122

5.2 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.2.1 Total Charge Cut . . . . . . . . . . . . . . . . . . . . . . . . . 1245.2.2 Fiducial Volume Cut . . . . . . . . . . . . . . . . . . . . . . . 1255.2.3 Time Difference Cut . . . . . . . . . . . . . . . . . . . . . . . 1255.2.4 Veto Flagged Event Cut . . . . . . . . . . . . . . . . . . . . . 1275.2.5 Pedestal Event Cut . . . . . . . . . . . . . . . . . . . . . . . . 127

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5.2.6 Incomplete Event Cut . . . . . . . . . . . . . . . . . . . . . . 1275.2.7 OD Triggered Cut . . . . . . . . . . . . . . . . . . . . . . . . 1275.2.8 Noise Event Cut and Clustered ATM Hit Event Cut . . . . . . 1275.2.9 Flasher Event Cut . . . . . . . . . . . . . . . . . . . . . . . . 1295.2.10 Goodness Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.2.11 Second Flasher Event Cut . . . . . . . . . . . . . . . . . . . . 131

5.3 Spallation Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.4 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.4.1 Vertex Test - Gringo Cut . . . . . . . . . . . . . . . . . . . . . 1375.4.2 Cherenkov Ring Image Test - Pattern Likelihood Cut . . . . . 140

5.5 Gamma Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Chapter 6 SK Solar Neutrino Results 1466.1 Solar Neutrino Signal Extraction . . . . . . . . . . . . . . . . . . . . 148

6.1.1 Likelihood Method . . . . . . . . . . . . . . . . . . . . . . . . 148Solar Neutrino Signal . . . . . . . . . . . . . . . . . . . . . . . 149Background Estimation . . . . . . . . . . . . . . . . . . . . . . 150

6.1.2 Solfit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1556.2 Solar Neutrino Flux Results . . . . . . . . . . . . . . . . . . . . . . . 155

6.2.1 8B Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . 1556.2.2 Time Variation of the Flux Results . . . . . . . . . . . . . . . 157

6.3 Recoil Electron Energy Spectrum . . . . . . . . . . . . . . . . . . . . 1596.4 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Energy Correlated Systematic Errors . . . . . . . . . . . . . . 169Energy Non-Correlated Systematic Errors . . . . . . . . . . . 172

Chapter 7 Searching For Neutrino Magnetic Moments 1787.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1797.2 Super-K Energy Spectrum And Limit On the Neutrino Magnetic Moment1827.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Bibliography 196

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List of Figures

1.1 Illustration of the MSW Level Crossing . . . . . . . . . . . . . . . . . 10

1.2 Nuclear reaction in the Sun: Proton-proton chain (PP Chain) . . . . 17

1.3 Nuclear reaction in the Sun: Carbon-Nitrogen-Oxygen cycle (CNO

Cycle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.4 Solar neutrino spectrum predicted by the standard solar model (SSM) 19

1.5 Solar neutrino production point as a function of the solar radius . . . 20

1.6 Energy levels of the 8B decay chain . . . . . . . . . . . . . . . . . . . 21

1.7 8B solar neutrino spectrum predicted by the SSM . . . . . . . . . . . 22

1.8 Solar neutrino oscillation solution . . . . . . . . . . . . . . . . . . . . 29

2.1 Location of Super-Kamiokande in Japan. . . . . . . . . . . . . . . . . 33

2.2 A sketch of the Super-Kamiokande detector site, under Mt.Ikenoyama. 35

2.3 Schematic view of support structures for the detector. . . . . . . . . 37

2.4 Schematic view of a 50cm PMT. . . . . . . . . . . . . . . . . . . . . . 38

2.5 Quantum efficiency of the photo-cathode as a function of the wavelength. 38

2.6 Single photo-electron pulse height distribution for a typical PMT . . 39

2.7 Relative transit time distribution of a typical PMT . . . . . . . . . . 39

2.8 Schematic view of the ID data acquisition system . . . . . . . . . . . 44

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2.9 Schematic view of trigger generation. . . . . . . . . . . . . . . . . . . 44

2.10 A schematic view of the water purification system. . . . . . . . . . . . 46

3.1 A typical time distribution of PMT hits . . . . . . . . . . . . . . . . 50

3.2 The grid used in the initial stage of vertex reconstruction. . . . . . . 52

3.3 Projection of the vertex distribution for LINAC calibration events. . . 53

3.4 The goodness distribution for LINAC calibration events. . . . . . . . 54

3.5 The probability density function for the angle of Cherenkov photons . 55

3.6 Definition of the PMT angle . . . . . . . . . . . . . . . . . . . . . . . 55

3.7 The PMT angular acceptance function as a function of the incident angle 56

3.8 The direction cosine distribution of LINAC calibration data . . . . . 57

3.9 Average number of photoelectrons per hit PMT . . . . . . . . . . . . 59

3.10 PMT cathode coverage as a function of the incident photon direction 59

3.11 Reconstructed energy as a function of the effective hit (Neff) . . . . . 63

3.12 Illustration of variables used in the muon track reconstruction . . . . 64

3.13 The track resolution of the muon fitter . . . . . . . . . . . . . . . . . 67

4.1 Illustration of the Xe calibration system . . . . . . . . . . . . . . . . 69

4.2 Spread of the relative PMT gain . . . . . . . . . . . . . . . . . . . . . 70

4.3 Illustration of the Ni-Cf calibration system . . . . . . . . . . . . . . . 72

4.4 The charge distribution for a single p.e. hit . . . . . . . . . . . . . . . 72

4.5 The averaged occupancy for barrel part of the detector . . . . . . . . 73

4.6 Schematic view of the PMT timing calibration system . . . . . . . . . 74

4.7 The time response of a PMT as a function of charge (“TQ-map”) . . 75

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4.8 Illustration of the direct water transparency measurement system . . 77

4.9 Results of the direct measurement of water transparency. . . . . . . . 78

4.10 Wavelength dependence of water transparency. . . . . . . . . . . . . . 78

4.11 Illustration of water transparency calculation using muon decay events 80

4.12 The log(q(r)) distribution for a typical µ-e data sample in water trans-

parency calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.13 Time variation of the water transparency . . . . . . . . . . . . . . . . 82

4.14 Schematic view of LINAC system . . . . . . . . . . . . . . . . . . . . 84

4.15 Schematic view of the first bending magnet of LINAC system . . . . 85

4.16 Schematic view of the second bending magnet of LINAC system . . . 85

4.17 Schematic view of the third bending magnet of LINAC system . . . . 86

4.18 Side view of the end of the beam pipe of LINAC system . . . . . . . 88

4.19 Top view of the end of the beam pipe of LINAC system . . . . . . . . 89

4.20 The observed LINAC beam energy spectrum using the Ge detector. . 90

4.21 Illustration of the trigger logic used in LINAC calibration. . . . . . . 92

4.22 Vertex position distribution from LINAC calibration. . . . . . . . . . 93

4.23 The TOF subtracted timing distribution of the hit PMTs from LINAC

calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.24 Neff distribution from LINAC calibration . . . . . . . . . . . . . . . 95

4.25 Observed energy distribution from LINAC calibration. . . . . . . . . 97

4.26 Deviation of the absolute energy scale between data and MC for all

positions and energies . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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4.27 Position-averaged deviation of the absolute energy scale between data

and MC as a function of energy . . . . . . . . . . . . . . . . . . . . . 99

4.28 The position-dependence of the absolute energy scale deviation be-

tween data and MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.29 Time variation of the energy scale obtained from spallation events . . 104

4.30 Time variation of the energy scale obtained from decay electron events. 105

4.31 Zenith angle dependence of the energy scale obtained from spallation

events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.32 Azimuthal angle dependence of the energy scale obtained from spalla-

tion events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.33 [Deviation of the energy resolution between data and MC for all posi-

tions and energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.34 Position-averaged deviation of the energy resolution between data and

MC as a function of energy . . . . . . . . . . . . . . . . . . . . . . . . 108

4.35 Distribution of the reconstructed vertex from LINAC calibration . . . 109

4.36 Position averaged vertex resolution deviation between LINAC data and

MC data as a function of total energy . . . . . . . . . . . . . . . . . . 110

4.37 Reconstructed angular distribution from LINAC calibration . . . . . 111

4.38 Position-averaged angular resolution deviation between LINAC data

and MC data as a function of total energy . . . . . . . . . . . . . . . 112

4.39 Schematic view of the DT generator. . . . . . . . . . . . . . . . . . . 113

4.40 Energy distribution from DT calibration. . . . . . . . . . . . . . . . . 114

4.41 Position dependence of the energy scale measured by DT calibration . 116

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4.42 The azimuthal angle and zenith angle dependence of the energy scale

measured by DT calibration . . . . . . . . . . . . . . . . . . . . . . . 116

4.43 The LE trigger efficiency as a function of energy . . . . . . . . . . . . 117

4.44 The SLE trigger efficiency as a function of energy . . . . . . . . . . . 119

5.1 Total charge distribution for a typical event sample . . . . . . . . . . 125

5.2 Vertex distribution before and after fiducial volume cut . . . . . . . . 126

5.3 Time from the previous event distribution and time difference cut . . 126

5.4 Noise ratio and ATM ratio distributions . . . . . . . . . . . . . . . . 128

5.5 Event display of a typical flasher event . . . . . . . . . . . . . . . . . 129

5.6 Illustration of the flash event cut . . . . . . . . . . . . . . . . . . . . 130

5.7 Vertex goodness distribution for a typical data sample . . . . . . . . 130

5.8 Illustration of the second flasher cut . . . . . . . . . . . . . . . . . . . 131

5.9 DirKS distribution of a typical data sample . . . . . . . . . . . . . . 132

5.10 Event distribution before and after the second flasher cut . . . . . . . 133

5.11 Spallation likelihood distribution . . . . . . . . . . . . . . . . . . . . 136

5.12 Position dependence of the dead time caused by the spallation cut . . 136

5.13 Rbad distribution for a typical data sample and the Gringo cut . . . 139

5.14 Pattern likelihood distributions from the Cherenkov ring image test . 139

5.15 Likelihood distribution of the Cherenkov ring image test for a typical

data sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.16 Definition of the effective distance from the wall dwall used in the

Gamma-ray cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

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5.17 Event distribution before and after the Gamma-ray cut for a typical

data sample, E = 6.5 ∼ 20.0 MeV . . . . . . . . . . . . . . . . . . . . 142

5.18 Event distribution before and after the Gamma-ray cut for a typical

data sample, E = 5.0 ∼ 5.5 MeV . . . . . . . . . . . . . . . . . . . . 143

5.19 The energy spectrum after each reduction step . . . . . . . . . . . . . 144

5.20 Flow chart illustrating reduction step for the 1496 days data sample . 145

6.1 Illustration of the definition of θSun . . . . . . . . . . . . . . . . . . . 147

6.2 The cos θSun distribution of the final data sample (E=5.0-20.0 MeV) . 147

6.3 The solar neutrino signal probability density functions Psig for various

energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.4 The zenith angle distribution of the Sun position for a typical data

sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.5 The zenith angle distribution of the final data sample for various energies152

6.6 Estimated backgrounds using MC simulation for various energies . . . 153

6.7 Estimated day and night backgrounds for various energies . . . . . . 154

6.8 Ratio of the measured flux to the standard solar model prediction for

all, day, night and different zenith angle data samples . . . . . . . . . 157

6.9 Time variation of the measured solar neutrino flux results . . . . . . . 158

6.10 Number of sunspots as a function of time . . . . . . . . . . . . . . . . 158

6.11 Seasonal variation of the measured solar neutrino flux results . . . . . 159

6.12 cos θSun distributions for various energy bins . . . . . . . . . . . . . . 160

6.13 Measured recoil electron energy spectrum in log scale . . . . . . . . . 161

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6.14 Ratio of the measured recoil electron energy spectrum to the SSM

predicted energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . 162

6.15 Energy spectrum for day time . . . . . . . . . . . . . . . . . . . . . . 165

6.16 Energy spectrum for night time . . . . . . . . . . . . . . . . . . . . . 165

6.17 Summary of systematic errors for flux measurement from various sources167

6.18 Summary of systematic errors for energy spectrum from various sources 168

6.19 Correlated systematic error due to energy scale uncertainty . . . . . . 170

6.20 Correlated systematic error due to energy resolution uncertainty . . . 171

6.21 Correlated systematic error due to 8B neutrino spectrum uncertainty 171

6.22 Azimuth angle φ distribution for events in the energy range from 5.0

to 5.5 MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.23 Azimuth angle φ distribution for events in the energy range from 7 to

10 MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.24 Azimuth angle φ distribution for events in the energy range from 5.0

to 5.5 MeV when the SLE threshold is 250 mV or 260 mV . . . . . . 175

6.25 Azimuth angle φ distribution for events in the energy range from 5.0

to 5.5 MeV when the SLE threshold is 186 mV . . . . . . . . . . . . . 176

6.26 Background estimation considering φ-asymmetry or without consider-

ing φ-asymmetry for 5.0 to 5.5 MeV . . . . . . . . . . . . . . . . . . . 177

7.1 Loop diagram which leads to the neutrino magnetic moment . . . . . 179

7.2 Ratio of the recoil electron magnetic scattering spectrum and weak

scattering spectrum in Super-K for µν = 10−10 µB . . . . . . . . . . . 181

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7.3 Ratio of SK-I observed recoil electron energy spectrum and the ex-

pected non-oscillated weak scattering spectrum . . . . . . . . . . . . 182

7.4 Distortions to the expected weak scattering spectra as results of the

neutrino oscillation for various oscillation parameters . . . . . . . . . 183

7.5 95% C.L. exclusion regions using the SK day/night spectra shape con-

sidering and without considering neutrino magnetic moments . . . . . 187

7.6 Probability distribution of ∆χ2 as function of µ2ν . . . . . . . . . . . . 188

7.7 95% C.L. exclusion regions using the SK day/night spectra shape con-

sidering non-zero neutrino magnetic moment and the allowed regions

using solar neutrino flux measurements . . . . . . . . . . . . . . . . . 190

7.8 The 90% C.L. µν limit contours (in units of 10−10 µB) and solar neu-

trino oscillation allowed regions . . . . . . . . . . . . . . . . . . . . . 191

7.9 95% C.L. solar neutrino data allowed regions taking into account the

effects of neutrino magnetic moments and the KamLAND allowed regions193

7.10 The 90% C.L. µν limit contours (in units of 10−10 µB) and solar plus

KamLAND neutrino oscillation allowed regions. . . . . . . . . . . . . 194

xiv

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List of Tables

1.1 Solar neutrino fluxes predicted by the SSM . . . . . . . . . . . . . . . 20

3.1 Summary of muon fitter efficiency for various types of muons . . . . . 66

4.1 Summary of the beam energy measurement of LINAC system . . . . 91

4.2 List of the injection positions of the LINAC beam . . . . . . . . . . . 92

4.3 Summary of systematic errors obtained from LINAC calibration . . . 102

4.4 Summary of the beta decay modes for 16N . . . . . . . . . . . . . . . 112

4.5 Summary of systematic errors for DT calibration . . . . . . . . . . . 115

4.6 History of the Intelligent Trigger System. . . . . . . . . . . . . . . . . 118

5.1 Summary of spallation products . . . . . . . . . . . . . . . . . . . . . 134

6.1 Summary of the measured recoil electron energy spectrum . . . . . . 163

6.2 Summary of the systematic errors for the energy spectrum . . . . . . 164

6.3 Summary of the measured day and night energy spectra . . . . . . . 166

xv

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Acknowledgements

I would like to express my appreciation and gratitude to many people who have helpedme throughout my graduate study. First and most, I would like to thank my advisor,Hank Sobel, for his guidance, encouragement and support. It is Hank’s trust andbelief helped me to get over many obstacles to obtain this Ph.D.

Next I would like to thank Michael Smy for his advice and help. It was Michaelwho went all the way to the Narita Airport to pick me up and helped me to settledown in my early days in Japan. Michael also helped me get started in the analysiswork. I benefited greatly from the numerous discussion with him. Michael is alwaysvery patient and gives very detailed advice.

I also like to thank Masayuki Nakahata, the leader of Super-K low energy group.It is under Prof. Nakahata’s guidence that this analysis became available. His insightin physics greatly improved the analysis. I also benefited greatly from Mark Vagins’critical comments and suggestions. Special thanks goes to Y. Suzuki, R. Svoboda,Y. Fukuda, Y. Takeuchi, Y. Koshio, K. Martens, K. B. Lee, G. Guillian and othermembers of the low energy group. This work can not be done without their help andhard work.

I also like to thank other UCI members, Bill Kropp is the US leader of the Super-Krebuild and I enjoy talking with him. It is really fun to work with Jeff Griskevich,he makes the work in the tank enjoyable. Danuta Kielczewska and Dave Casper allgave me good advice. I also want to thank Julie Aired and Sylvia Hansen who helpedsending my mails to me while I was in Japan.

I also like to thank my committee, Riely Newman, Jonas Schultz and GaurangYodh, they make the otherwise tedious defense much enjoyable and a good experience.

Hank, Mark, Michael and Jonas read the thesis very carefully and provided manyuseful comments.

I have spent nearly 3 years living in Japan. I really enjoy the good time I had withmy fellow students over there: Nobuyuki Sakurai, Tomasz Barszczak, ChristopherMauger, Dean Takemori, Astuko Kibayashi, Matthew Malek, Shantanu Desai, DusanTurcan, Yoshihito Gando, Chikaori Mitsuda, Jonghee Yoo, Chris Sterner, Wei Wang,Andrew Clough, Joanna Zalipska and John Parker Cravens.

Finally I would like to thank my friends Chunli Zhang and Lina Wong for theirfriendship.

xvi

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Curriculum Vitæ

Dawei Liu

Education

• B.S. : Physics, Peking University, July 1990.

• M.S. : Physics, Peking University, July 1993.

• M.S. : Physics, Florida State University, August 1996.

• Ph.D.: Physics, University of California, Irvine., June 2005.

Publications

• B. L. Brandt, D. W. Liu, L. G. Rubin, LOW TEMPERATURE THERMOM-ETRY IN HIGH MAGNETIC FIELDS VII. CERNOXTM SENSORS TO 32 T,Review of Scientific Instruments 70, 104 (1999).

• S. Fukuda et al., SOLAR 8B AND HEP NEUTRINO MEASUREMENTS FROM1258 DAYS OF SUPER-KAMIOKANDE DATA, Phys. Rev. Lett. 86, 5651(2001).

• S. Fukuda et al., CONSTRAINTS ON NEUTRINO OSCILLATIONS USING1258 DAYS OF SUPER-KAMIOKANDE SOLAR NEUTRINO DATA, Phys.Rev. Lett. 86, 5656 (2001).

• Y. Fukuda et al., THE SUPER-KAMIOKANDE DETECTOR, Nucl. Instrum.Methods. Res. Sect. A 501, 418 (2003).

• S. Fukuda et al., DETERMINATION OF SOLAR NEUTRINO OSCILLATIONPARAMETERS USING 1496 DAYS OF SUPER-KAMIOKANDE I DATA,Phys. Lett. B 539, 179 (2002).

• S. Fukuda et al., SEARCH FOR NEUTRINOS FROM GAMMA-RAY BURSTSUSING SUPER-KAMIOKANDE, Astrophys. J. 578, 317 (2002).

• M. Malek et al., SEARCH FOR SUPERNOVA RELIC NEUTRINOS AT SUPER-KAMIOKANDE, Phys. Rev. Lett. 90, 061101 (2003).

xvii

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• Y. Gando et al., SEARCH FOR νe FROM THE SUN AT SUPER-KAMIOKANDEI, Phys. Rev. Lett. 90, 171302 (2003).

• J. Yoo et al., A SEARCH FOR PERIODIC MODULATIONS OF THE SOLARNEUTRINO FLUX IN SUPER-KAMIOKANDE I, Phys. Rev. D 68, 092002(2003).

• M. B. Smy et al., PRECISE MEASUREMENT OF THE SOLAR NEUTRINODAY / NIGHT AND SEASONAL VARIATION IN SUPER-KAMIOKANDE-1,Phys. Rev. D 69, 011104 (2004).

• D. W. Liu et al., LIMITS ON THE NEUTRINO MAGNETIC MOMENT US-ING 1496 DAYS OF SUPER-KAMIOKANDE-I SOLAR NEUTRINO DATA,Phys. Rev. Lett. 93, 021802 (2004).

• Y. Ashie et al., EVIDENCE FOR AN OSCILLATORY SIGNATURE IN AT-MOSPHERIC NEUTRINO OSCILLATION, Phys. Rev. Lett. 93, 101801(2004).

• S. Desai et al., SEARCH FOR DARK MATTER WIMPS USING UPWARDTHROUGH-GOING MUONS IN SUPER-KAMIOKANDE, Phys. Rev. D 70,083523 (2004), Erratum-ibid. D 70, 109901 (2004).

• Y. Ashie et al., A MEASUREMENT OF ATMOSPHERIC NEUTRINO OS-CILLATION PARAMETERS BY SUPER-KAMIOKANDE I, hep-ex/0501064,Submitted to Phys. Rev. D.

• K. Kobayashi et al., SEARCH FOR NUCLEON DECAY VIA MODES FA-VORED BY SUPERSYMMETRIC GRAND UNIFICATION MODELS IN SUPER-KAMIOKANDE-I, hep-ex/0502026.

Conference Abstracts and posters

• Talk on Limit on the Neutrino Magnetic Moments Using Super-KaimokandeSolar Neutrino Data, THE LAUNCHING OF LA BELLE EPOQUE OF HIGHENERGY PHYSICS AND COSMOLOGY, Proceedings of the 32nd Coral GablesConference, Fort Lauderdale, Florida, USA 17 - 21 December 2003, World Sci-entific.

• Talk given at American Physical Society DPF Meeting 2004 on Neutrino Mag-netic Moments, Riverside, California, to be published by Int. J. Phys.

• Talk given at American Physical Society 2005 April Meeting on Neutrino Mag-netic Moments and Super-K Solar Neutrinos, Tampa, Florida.

xviii

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Abstract of the Dissertation

Search for Non-zero Neutrino Magnetic Moments Using Super-Kamiokande-I Solar

Neutrino Data

by

Dawei Liu

Doctor of Philosophy in Physics

University of California, Irvine, 2005

Professor Henry W. Sobel, Chair

Non-zero neutrino magnetic moments would mean new physics beyond the stan-

dard model. Therefore a search for a nonzero neutrino magnetic moment has been

conducted using the high statistic 1496 live day solar neutrino data from Super-

Kamiokande-I. The search looked for distortions to the energy spectrum of recoil

electrons from ν-e elastic scattering. A nonzero neutrino magnetic moment would

cause an increase of event rates at lower energies. In the absence of clear signal, we

found µν ≤ 3.6 × 10−10 µB at 90% C.L. by fitting to the Super-Kamiokande (Super-

K) day/night energy spectra. The fitting took into account the effect of neutrino

oscillations on the shape of energy spectra. With the results from other neutrino

experiments constraining the oscillation parameter region, a limit of µν ≤ 1.1× 10−10

µB at 90% C.L. was obtained.

xix

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Chapter 1

Neutrinos

The neutrino is one of the most fundamental elementary particles which make up our

universe. They exist copiously in nature. As they interact very weakly with other

particles, and are therefore very difficult to detect, they have remained one of the most

mysterious particles. The challenges in understanding the properties of neutrinos have

often produced new physics. The existence of neutrinos led us to the understanding

of one of the basic interactions - the weak interaction, and later the standard model

of the fundamental particles and interactions. The recent discovery that neutrinos

oscillate from one flavor to another means that neutrinos must have mass. This gives

the first sign of new physics beyond the standard model. Fully understanding the

properties of the neutrinos, such as the neutrino magnetic moment could shed light

onto the ultimate fundamental theory of the world around us.

1

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1.1 Introduction

The Neutrino was proposed by Pauli in 1929 to solve the problem of why the

beta decay spectrum is continuous [1]. He suggested the existence and emission of a

neutral particle with spin half in addition to the observed charged particle in order

to save the principle of conservation of energy. In 1932, Chadwick discovered that

the neutron decays into a proton, electron and neutrino in the process of beta decay

[2]. Fermi then proposed the four-Fermi interaction involving a neutron, proton,

electron and neutrino, which led to a new kind of interaction - the weak interaction

[3]. Neutrinos (or more precisely electron-type anti-neutrinos) were first detected by

Reines and Cowan in 1956 [4]. We now know there are three types of neutrinos, as

there are quarks and charged leptons:

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

(1.1)

In the standard model, neutrinos do not have mass. As only one helicity state of

neutrinos has been observed (left-handed), it follows that the neutrino can not have

a Dirac mass which requires the existence of both helicity states. The neutrino could

possess a Majorana mass which takes the anti-neutrino as the other helicity state,

but this would violate lepton number by 2 units. In the standard model, the lepton

number is conserved for each generation of leptons. Recent results from atmospheric,

2

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solar and reactor neutrino experiments showed strong evidence that neutrinos undergo

flavor oscillation and hence must have finite mass [5, 6, 7, 8, 9]. This leads to new

physics beyond the standard model.

1.2 Neutrino Oscillation

The flavor eigenstates νe, νµ, ντ could be the superposition of the mass eigenstates.

If neutrinos have mass, a neutrino created as one flavor eigenstate could change into

another flavor eigenstate at a later time – neutrino oscillation.

1.2.1 Vacuum Oscillation

Consider a neutrino produced from the lepton charged interaction. By definition,

this neutrino state is flavor eigenstate να. In general, this is not a physical state but

a superposition of mass eigenstates νi:

|να〉 =∑

i

Uαi|νi〉 (1.2)

where U is the unitary mixing matrix. For the simple case of two neutrino oscil-

lation, U is defined as follows:

U =

cos θ sin θ

− sin θ cos θ

(1.3)

where θ is the mixing angle in vacuum.

The neutrino state which is produced propagates according to the following for-

mula after time t:

3

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|να(t)〉 =∑

i

exp (−iEit)Uαi|νi〉 (1.4)

where Ei =√

p2 + m2i is the neutrino energy.

If the neutrino masses are not equal, Equation 1.4 represents a different superpo-

sition of neutrino mass eigenstates from that of Equation 1.2. Therefore, να(t) can

be a superposition of other neutrino flavors. The probability amplitude of finding it

to be the flavor να′ is as follows:

〈να′ |να(t)〉 =∑

i

i′

U †i′α′Uαi exp (−iEit)〈νı′|νı〉

=∑

i

i′

U †i′α′Uαi exp (−iEit)δii′

=∑

i

UαiU∗α′i exp (−iEit) (1.5)

If the neutrino does not interact with other particles, and if we consider the

relativistic case, i.e., the neutrino momentum p is much larger than the neutrino

mass, then Ei can be approximated as follows :

Ei =√

p2 + m2i

' p +m2

i

2p

' E +m2

i

2E(1.6)

4

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At any time t, the probability of finding a να′ from a neutrino να created at t=0

can be calculated from Equation 1.5 as follows:

P (να → να′) = |〈να′ |να(t)〉|2

=∑

i

i′

UαiU∗α′iUαi′U

∗α′i′ exp−i(Ei − Ei′)t

=∑

i

i′

UαiU∗α′iUαi′U

∗α′i′(2 − 2 cos(Ei − Ei′)t) (1.7)

For our simple two neutrino oscillation case, the probability of νe → νx with x 6= e

is:

P (νe → νx) = cos2 θ sin2 θ cos(E1 − E2)t

=1

2sin2 2θ

(

1 − cosm2

1 − m22

2Et

)

=1

2sin2 2θ

(

1 − cosm2

1 − m22

2Et

)

= sin2 2θ sin2

(

∆m2

4EL

)

, (1.8)

where ∆m2 = m21 − m2

2, m21, m

22 E and we choose to use natural units in the

calculation so L = t (as c=1).

From Equation 1.8, the probability of νe → νe is calculated as :

5

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P (νe → νe) = 1 − sin2 2θ sin2

(

∆m2

4EL

)

= 1 − sin2 2θ sin2

(

πL

LV

)

, (1.9)

where LV is called the oscillation length in vacuum and is defined as:

LV =4πE

∆m2(1.10)

The oscillation length gives a measure of the distance scale over which the oscilla-

tion effects is appreciable. Experimentally, we look for Pνeνe< 1 for the disappearance

effects and Pνeνx6=efor the appearance effects of oscillation.

1.2.2 Neutrino Oscillation In Matter (MSW Effect)

Neutrino oscillation in matter is quite different from the oscillation in vacuum as

the different neutrino flavors interact with matter differently. As normal matter only

has electrons but no muons and taus, an electron-type neutrino νe will interact with

the matter through both charged- and neutral-current interactions. On the other

hand, muon type neutrinos νµ and tau type neutrinos ντ will interact with the matter

only through neutral-current interactions. Interactions modify the effective masses

of neutrinos traveling through the matter. If the neutrino mixes in vacuum, when it

travels through matter, its νe component will be modified differently as compared to

other components thus leading to different oscillation probabilities from the oscillation

in vacuum. This effect was first pointed out by Wolfenstein [10] and later it was shown

6

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by Mikheyev and Smirnov that this effect could be used in understanding the neutrino

flux from the Sun [11]. Thus it is called MSW effect.

Consider the simple case of two-flavor oscillation. The equation of motion for the

mass eigenstates is:

id

dt

ν1(t)

ν2(t)

= H

ν1(t)

ν2(t)

(1.11)

where H is the Hamiltonian which is diagonal in the mass eigenstate basis in the

case of no interaction with matter:

H =

E1 0

0 E2

' E +

m21/2E 0

0 m22/2E

(1.12)

The interaction of neutrinos with matter can be written as follows in the flavor

state basis:

V =

VNC + VCC 0

0 VNC

(1.13)

where Vcc and Vnc are the effective potentials for the charged current and neutral

current interactions. Vcc is calculated to be√

2GF Ne, where GF is the Fermi cou-

pling constant and Ne is the electron density. For normal neutral matter, Ne = Np

for charge neutrality, the contributions from the electron and the proton to neutral

current interactions cancel each other and only the contribution from neutrons is left,

which gives Vnc = −√

2GF Nn/2, where Nn is the density of neutrons in the matter.

7

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So, in the flavor state basis the equation of motion is as follows:

id

dt

νe(t)

νµ(t)

= H ′

νe(t)

νµ(t)

(1.14)

where the Hamiltonian can be obtained by the following formula:

H ′ = UHU †

= U

E1 0

0 E2

U−1 +

VNC + VCC 0

0 VNC

= E +m2

1 + m22

4E− 1√

2GFNn

+

−∆m2

4Ecos 2θ +

√2GF Ne

∆m2

4Esin 2θ

∆m2

4Esin 2θ ∆m2

4Ecos 2θ

(1.15)

where ∆m2 = m21 − m2

2.

The eigenstate in matter is defined as follows:

ν1m

ν2m

=

cos θm − sin θm

sin θm cos θm

νe(t)

νµ(t)

(1.16)

where the effective mixing angle in matter θm would be given by:

8

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tan 2θm =2H ′

12

H ′22 − H ′

11

=∆m2 sin 2θ

∆m2 cos 2θ − A(1.17)

where A = 2√

2GFNeE. As seen from Equation 1.17, the effective angle changes

inside matter when the electron density changes. When A = ∆m2 cos 2θ, the mixing

angle in matter becomes maximal, i.e., θm = π/4. So, even if the vacuum mixing is

small, at the resonant point νe and νµ mix maximally. The resonance happens at the

point where the electron density is:

Ne,crit =∆m2 cos 2θ

2√

2GFE(1.18)

The electron density in the Sun decreases as the radius increases. Neutrinos are

produced near the center of the Sun, so when we have neutrinos with energy greater

than the critical energy Ecrit:

Ecrit =∆m2 cos 2θ

2√

2GF Ne,center

= 6.6 × cos 2θ

(

∆m2

10−4eV2

)

MeV (1.19)

Neutrinos will always pass through a point where a resonant condition is satisfied

and the mixing becomes maximal. Ne,center in Equation 1.19 is the electron density

9

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Figure 1.1. MSW effect. The effective masses of neutrinos in matter. The solidlines are the mass squared values of the physical eigenstates, the dashed lines are theexpectation values of squared mass for flavor states νe and νµ. The vertical dashedlines show where the maximal mixing is.

at the center of the Sun.

The eigenvalues of H ′ are the effective masses of the mass eigenstates in the matter:

m2i,m =

m21 + m2

2 + A

2± 1

2

(∆m2 cos 2θ − A)2 + ∆m4 sin2 2θ (i = 1, 2) (1.20)

Figure 1.1 shows effective masses m21,m and m2

2,m as functions of the electron

density. For Ne = 0 which is vacuum, the small effective mass eigenstate ν1 is almost

νe while the large one ν2 is almost νµ. For Ne Ne,crit, the small effective mass

eigenstate is almost νµ while the large one is almost νe. Following the dotted lines of

the effective mass squared of νe and νµ from higher electron density to lower electron

density, the effective mass squared of νe starts from higher than that of νµ to lower

than that of νµ. This is called level crossing. This phenomenon is very important in

10

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understanding oscillation in the Sun. The electron type neutrino νe produced at the

center of the Sun is the main component of the ν2, if it passes through the resonance

region without jumping from ν2 to ν1, i.e., adiabatically, then νe will change to νµ at

the surface of the Sun where the electron density is almost zero. For the case when

the resonance is non-adiabatic, the probability of hopping from ν2 to ν1 is given by:

Phop = exp

−π

4

sin 2θ2

E cos 2θ

∆m2

1Ne

dNe

dr

(1.21)

The adiabatic condition is that Phop 1, i.e.,

sin 2θ2∆m2 ≥ E cos 2θ

1

Ne

dNe

dr

(1.22)

The interaction of neutrinos with matter, matter effect, can also happen when the

neutrinos pass through the Earth. In this case, some of the νµs are converted back

to νes. This could lead to a difference of day and night neutrino fluxes for certain

oscillation parameters. Super-K, as a real time detector, can divide the data sample

into a day sample and a night sample to explore the possible day-night asymmetry.

1.3 Neutrino Magnetic Moment

In field theory, the neutrino magnetic moment is defined as the coefficient of the

following coupling:

νLσαβqβνRAα + νRσβαqβνLAα (1.23)

11

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In the minimal Standard Model, neutrinos are massless and there is no term to

convert the left-handed neutrino to the right-handed neutrino and thus neutrinos do

not have magnetic moments. Introducing neutrino masses to the Standard Model

allows Dirac neutrinos to acquire a magnetic moment by the coupling of the left-

handed neutrino and right-handed neutrino through the mass term [12, 13]:

µν =3GF emν

8√

2π2≈ 3.2 × 10−19(

1eV)µB (1.24)

where µB = e/2me is the Bohr magneton. Considering the small size of the

neutrino mass [14] , the neutrino magnetic moment is too small to have any detectable

astrophysical or physical effects. In some grand unification (GUT) models, the value

of µν has been enhanced to some extent. There are also models in which µν is

decoupled from the mass term, resulting in a large µν without requiring large neutrino

mass. Other models have been constructed to give large µν using different schemes

(See discussions in [15] and references therein). Experimental observation of neutrino

magnetic moment larger than the value given in Equation 1.24 will certainly imply

new physics beyond the Standard Model.

In general, the interaction of neutrino mass eigenstates j and k with a magnetic

field can be characterized by the magnetic moments µjk. Dirac neutrinos can have

both diagonal (j=k) and off-diagonal (j6=k) magnetic moments. Majorana neutri-

nos can only have off-diagonal moments [16, 17]. As Majorana neutrino is its own

antiparticle, we have ν = νC , ν = νL + νCL :

12

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νσµνν = νLσµννCL + νC

L σµννL (1.25)

νLσµννCL = (νC

L )TCσµνCνT

= νL(σµν)T νC

L

= −νLσµννCL (1.26)

where νCL = CνT , ν = (νC)T C and CσµνC = σµν have been used. Similarly, we

can get

νCL σµννL = −νC

L σµννL (1.27)

By combining Equations 1.26 and 1.27, we have νσµνν = 0. Therefore, if the initial

and final neutrino states are the same, the magnetic moment is zero for Majorana

neutrinos, so Majorana neutrinos can only have off-diagonal (transition) moments.

As the fundamental constants µjk are associated with the mass eigenstates, when

neutrinos oscillate, the changing composition of the neutrinos can affect the mea-

sured effective magnetic moments [18]. Consider a beam of electron neutrinos which

propagates in vacuum, Equation 1.2 (where α = e). In principle, different mass eigen-

states are distinguishable in the magnetic scattering and hence combine incoherently.

Therefore the effective magnetic moment is given as follows:

13

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µ2e =

j

|∑

k

Ueke−iEkLµjk|2 (1.28)

=∑

j

kk′

UekU∗

ek′µjkµ

jk′e−2πiL/L

kk′ (1.29)

where j, k, k′

denote mass eigenstates. L is the distance from the source. Lkk′ =

4πEν/∆m2kk′ for k 6= k

is the oscillation length.

Consider Dirac neutrinos with only diagonal magnetic moments µjk = µjδjk, then

Equation 1.29 becomes:

µ2e =

j

|Uej|2|µj|2 (1.30)

there is no dependence on Eν and L.

For Majorana neutrinos with only 2 mass eigenstates, only one magnetic moment

is present:

µ2e = |µ12|2(|Ue1|2 + |Ue2|2) = |µ12|2 (1.31)

which is not only independent of L and Eν but also independent of the mixing

angle.

Similar results for MSW mixing can be obtained. For example, for two flavor

Dirac neutrinos with only diagonal moments, in the adiabatic case, µe = µ2, there is

no energy and distance dependence. For the non-adiabatic case,

14

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µ2e = Phop|µ1|2 + (1 − Phop)|µ2|2 (1.32)

where Phop is the probability of hopping from one mass eigenstate to the other

(Equation 1.21). As Phop depends on the neutrino energy, µe will depend on the

neutrino energy but not on the distance L. For a Majorana particle, the result is the

same as Eq. 1.31.

Considering the complications of oscillations on the neutrino magnetic moment,

the meaning of a measured µν from reactor anti-neutrinos and solar neutrinos could

be different.

1.4 Solar Neutrinos

1.4.1 Standard Solar Model

The Sun is the source of energy for life on the Earth. The Sun is a main sequence

star with an age of about 4.6 billion years. Basic characteristics of the Sun have been

measured as follows [19]:

Solar Mass M = 1.99 × 1033 g,

Solar Radius R = 6.96 × 108 m,

Luminosity L = 3.86 × 1033 erg/sec,

Surface Temperature T = 5.78 × 103 K. (1.33)

15

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Using the above parameters as input and assuming that the Sun is in a hydrostatic

and thermal equilibrium state, a standard solar model (SSM) is constructed based

on the stellar evolution [20, 21, 22]. According to the SSM, the Sun generates power

through the following nuclear fusion reaction in the core of the Sun:

4p → 4He + 2e+ + 2νe (1.34)

Positrons then annihilate with electrons and release energy in the form of photons:

4p + 2e− → 4He + 2νe + 26.73 MeV + Eν (1.35)

where Eν is the energy carried away by the neutrinos.

〈E(2νe)〉 = 0.59MeV (1.36)

The nuclear reaction proceeds through the pp chain (Figure 1.2) and the CNO

cycle Figure (1.3) in the core of the Sun. About 98.5 % of the Sun’s energy is produced

through the pp chain and only 1.5 % of the energy is from CNO cycle. Neutrinos are

the byproducts of the nuclear fusion reactions. For the Sun, the density is the most

in the core which is about 160 g/cm3, with νe-e cross section of 10−43 cm2, the mean

free path for the neutrino is about 1017 cm which is much larger than the radius of the

Sun. So unlike photons, the neutrinos can pass through the Sun carrying the internal

information about the core of the Sun. Therefore, observation of the solar neutrinos

can provide detailed information of energy generation in the Sun and can be used

16

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p+p→D+e++νe

99.75 %

p+e-+p→D+νe

0.25 %

D+p→3He+γ

3He+3He→α+2p86 %p-p I

3He+4He→7Be+γ

7Be+e-→7Li+νe

7Li+p→2α14 %p-p II

7Be+p→8B+γ

8B→8Be*+e++νe

8Be*→2α0.02 %p-p III

Figure 1.2. Nuclear reaction in the Sun: Proton-proton chain (PP Chain).

Figure 1.3. Nuclear reaction in the Sun: Carbon-Nitrogen-Oxygen cycle (CNO Cycle).

17

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to test the validity of the SSM. The neutrinos from in the Sun are listed below and

named according to the nuclear reactions in which they are produced:

From pp chains:

p + p → D + e+ + νe (≤ 0.420 MeV) pp neutrino (1.37)

Eν ≤ 0.420MeV

p + e− + p → D + νe (1.442 MeV) pep neutrino (1.38)

7B + e− → 7Li + νe

0.861 MeV, 90%

0.383 MeV, 10%

7Be neutrino (1.39)

8B → 8Be∗ + e+ + νe (< 15 MeV) 8B neutrino (1.40)

3He + p → 4He∗ + e+ + νe (< 18.77 MeV) Hep neutrino (1.41)

From the CNO cycle:

18

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±1.5%±10%

13N15O

17F

Flu

x at

1 A

U (c

m−2

s−1

MeV

−1) [

for

lines

, cm

−2 s

−1]

7Be

pp

Chlorine SuperKGallium

Neutrino energy (MeV)0.1 0.50.2 1 52 10 20

pep

hep

8B

1012

1010

108

106

104

102

+20% –16%

±?

±1%

Figure 1.4. The solar neutrino spectrum from the standard solar model (SSM). Theunit for the continuous neutrino fluxes is cm−2s−1MeV−1 and for line flux the unit iscm−2s−1. Spectra for neutrinos from pp-chain are shown in solid curves, Spectra forthe CNO neutrinos are shown by the dotted curves [20, 22].

13N → 13C∗ + e+ + νe (< 1.20 MeV) 13N neutrino (1.42)

15O → 15N∗ + e+ + νe (< 1.73 MeV) 15O neutrino (1.43)

17F → 117F∗ + e+ + νe (< 1.74 MeV) 17F neutrino (1.44)

Neutrino fluxes can be calculated in the SSM based on the values of the corre-

sponding nuclear reaction rates and the knowledge of the solar temperature distri-

bution. Table 1.1 gives the various neutrino fluxes predicted by the SSM (BP2000)

19

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source flux(cm−2s−1)

pp chainpp 5.95(1.00 ± 0.01) × 1010

pep 1.40(1.00 ± 0.015) × 108

hep 9.3 × 103

7Be 4.77(1.00 ± 0.10) × 109

8B 5.05(1.00+0.20−0.16) × 106

CNO cycle13N 5.48(1.00+0.21

−0.17) × 108

15O 4.80(1.00+0.25−0.19) × 108

17F 5.63(1.00 ± 0.25) × 106

Table 1.1. Solar neutrino fluxes predicted by the SSM [22].

0

2.5

5

7.5

10

12.5

15

17.5

20

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

pp

8B

7Be

R/RSUN

d(f

ract

ion

of

neu

trin

o p

rod

uct

ion

)/d

(R/R

SU

N)(

%)

Figure 1.5. Production point distribution of solar neutrinos as a function of the solarradius [21].

20

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Figure 1.6. Energy levels of the 8B (β+)8Be(2α) decay chain [23].

[22]. Figure 1.4 gives the expected solar neutrino spectrum at the Earth without

the effects of neutrino oscillation and also the capacities of the various solar neutrino

experiments (SNO observes the same neutrinos as Super-K). Figure 1.5 gives the pro-

duction points of various neutrinos as a function of the distance from the center of

the Sun.

As seen from Figure 1.4, Super-K can only detect 8B neutrinos and Hep neutrinos.

The Hep neutrino flux is about 10−3 of the 8B neutrino flux and becomes relevant

only above 14 MeV, so for this analysis only the 8B neutrino flux is important. 8B

neutrinos are produced from the decay of 8B as shown in Figure 1.6. The spectral

shape of the solar neutrino spectrum can be calculated using results from the ter-

restrial experiments and are not solar model dependent. The 8B neutrino spectrum

is obtained by measuring the β spectrum from 8B decay and the α spectrum of the

21

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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12 14 16

best estimate

-3 σ

+3 σ

neutrino energy (MeV)

ener

gy

spec

tru

m (

1/M

eV)

Figure 1.7. The 8B neutrino energy spectrum with ±σ errors from the SSM [24].

subsequent decay of 8Be. The 8B neutrino flux is proportional to the low-energy cross

section factor S17(0) for the 7Be(p, γ)8B reaction [24]. For this analysis, we use only

the shape of the energy spectrum, the total neutrino flux value is less important. For

the neutrino oscillation analysis, a measured value of the total flux is used to make

the analysis independent of the solar model. Figure 1.7 shows the 8B neutrino energy

spectrum with the uncertainties. This spectrum will be used to calculate the expected

recoil electron spectrum in Super-K.

1.4.2 Solar Neutrino Experiments

There are seven experiments made important contributions in measuring solar

neutrinos. These experiments can be categorized according the methods they em-

ployed to detect the neutrinos: radiochemical experiments and water Cherenkov ex-

periments.

22

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Radiochemical Experiments

In radiochemical experiments, neutrinos interact with nuclei through inverse β

interaction and produce radioactive nuclei with half-life in the range of a few days to a

few weeks. Then the number of these radioactive nuclei is counted using radiochemical

methods.

The first experiment whcih detected solar neutrinos by R. Davis and his col-

laborators used the following interaction in the Homestake mine in South Dakata

[25]:

37Cl + νe → 37Ar + e− (Eth = 814 KeV) (1.45)

As this experiment uses Chlorine (C2Cl4) as the detection material, its result

is usually referred to as the Chlorine rate. The expected rate Chlorine experiment

should see from the SSM model is 7.7+1.3−1.1 SNU, whereas the measured rate is [26]:

Φcl = 2.56 ± 0.16 ± 0.16 SNU (1.46)

where SNU is the solar neutrino unit, 1 SNU = 10−36 captures per atom per second.

The ratio of the measured rate to that from the SSM prediction is 0.34±0.06. Clearly

there is a deficiency in the number of observed neutrinos.

Three solar neutrino experiments (GALLEX and GNO in Gran Sasso in Italy

and SAGE in Baksan in Russia) used gallium as the detection material and used the

following inverse β reaction to detect neutrinos:

23

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71Ga + νe → 71Ge + e− (Eth = 233 KeV) (1.47)

These experiments’ results are usually referred as Gallium rates. They have the

lowest energy threshold and could detect all the solar neutrinos as indicated in Figure

1.4. The expected rate predicted by the SSM is 128+9−7 SNU. The measured results

are [27, 28]:

GALLEX/GNO 69.3 ± 4.1 ± 3.6 SNU

SAGE 69.1+4.3−4.2

+3.8−3.4 SNU (1.48)

These rates are usually combined into a single Gallium rate. The combined Gal-

lium rate is 69.2+3.95−3.84 SNU. So the ratio of the measured rate to the SSM expectation

is 0.54+0.05−0.04. Again the number of observed neutrinos is less than what the SSM has

predicted.

Water Cherenkov Experiments

A Water Cherenkov detector uses water as both the interaction and detection

medium. It is based on the fact that when charged particles travel faster than the

speed of light in water they generate Cherenkov light in a cone about the direction of

the moving particles. Then, the photons are detected by the photomultipliers (PMT)

and the particles’ position and direction can be deduced from the PMT hit patterns.

The energy of the particle can also be determined by the amount of charge deposited

24

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in the PMTs.

Kamiokande and its successor Super-Kamiokande use the ν-e elastic scattering to

detect solar neutrinos:

νx + e− → νx + e− (1.49)

The scattered electrons move in the forward direction of the incoming neutrinos

thus keeping the directional information of the neutrinos. One notable characteristic

of this type of detector is that it detects neutrinos in real time as compared to the

radiochemical detectors. Therefore, it can use the directional correlation with the

Sun’s direction to clearly separate the signal from the background and give explicit

evidence showing that the neutrinos are really coming from the Sun. The energy

thresholds of the water Cherenkov detectors are higher than that of the radiochemical

detectors (7 MeV for Kamiokande and 5 MeV for Super-Kamiokande), so they only

can detect 8B neutrinos and Hep neutrinos. Of these two, the Hep neutrino flux is

about 10−3 of the flux of the 8B neutrinos. In the reaction 1.49, as νµ and ντ interact

with e only through neutral current interaction, their interaction rate with electrons

is less than that of νe, σ(νµ,τ , e)0.16 ≈ σ(νe, e). The measured solar neutrino fluxes

are [6] (in units of 106 cm−2s−1):

ΦKam = 2.80 ± 0.19 ± 0.33 ×

ΦSK = 2.35 ± 0.03+0.07−0.06 (1.50)

25

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When compared to the predicted value 5.05±1.00+0.20−0.16×106 cm−2s−1 from the SSM,

the observed neutrino rate is less than the expectation from the SSM. The ratios of the

observed to the expected are RKam = 0.554+0.135−0.134 and RSK = 0.465+0.095

−0.094. By using

the number of hit PMTs, Kamiokande and Super-Kamiokande can measure the energy

of the recoil electrons with high precision (details can be found in later chapters). The

measured spectral shape shows no obvious distortion from expectation. The measured

energy spectrum is not only very useful in the study of neutrino oscillations but this

is also where we look for the effect of a neutrino magnetic moment.

SNO is also a water Cherenkov detector. It uses 1,000 tons of ultra-pure heavy

water (D2O) to detect 8B neutrinos via the following interactions:

Charge Current (CC) Interaction : νe + d → e− + p + p (1.51)

Neutral Current (NC) Interaction : νx + d → νx + p + n (1.52)

The CC interaction can only detect νe neutrinos while NC interaction can detect

all active neutrinos with equal sensitivity. SNO can also detect neutrinos by the ν-e

elastic scattering Equation 1.49. The contributions from the CC interaction and the

ν-e elastic scattering can be distinguished by their distinct angular distributions as a

function of cos θSun, where θSun is the angle between the directions of the electron and

the Sun. The ν-e elastic scattering event distribution has a strong peak around the

Sun direction while the CC events distribute approximately as 1−1/3 cos θSun. In the

CC interaction, the neutrino energy and the electron energy are strongly correlated

26

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so it can be used to measure the shape of the 8B neutrino energy spectrum more

directly. The NC interaction is detected by the 6.25 MeV γ ray from the neutron

capture by the deuterium. NaCl has been added to the heavy water in a later phase

of the experiment to enhance the detection efficiency of the NC interaction.

SNO’s results are in two phases, with NaCl and without NaCl [7, 8] (in units of

106 cm−2s−1):

Pure D2O:

Pure D2O : 1.76+0.06−0.05 ± 0.09 (CC)

2.39+0.24−0.23 ± 0.12 (νe)

5.09+0.44−0.43

+0.46−0.43 (NC) (1.53)

NaCl in D2O1 :

1.59+0.08−0.07

+0.06−0.08 (CC)

2.21+0.31−0.26 ± 0.10 (νe)

5.21 ± 0.27 ± 0.38 (NC) (1.55)

SNO’s expected flux from the SSM is the same as that of Super-K. The CC and

1Newest SNO salt phase results [29]:

1.68+0.06

−0.06

+0.08

−0.09 (CC)

2.35±−0.22± 0.15 (νe)

4.94± 0.21+0.38

−0.34 (NC) (1.54)

27

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ν-e results show a deficit of neutrinos observed. Although with poorer statistics,

SNO’s ν-e elastic result is in agreement with the high statistics Super-K results. By

comparing the SNO’s CC result with Super-K’s ν-e elastic result, it clearly shows an

active neutrino component besides the νe. The NC result shows that the total solar

neutrino flux is consistent with the prediction of the SSM. Furthermore, the electron

spectral shape is consistent with the expectation.

1.4.3 Solar Neutrino Problem And Neutrino Oscillation

The puzzle that all the measured fluxes except SNO’s NC result are significantly

less than what the SSM predicted is called the solar neutrino problem. The discrep-

ancy between Super-K’s ν-e results (sensitive to all active neutrino flavors) and SNO’s

CC results (sensitive only to electron type neutrino) shows that there exists non-νe

type neutrinos in the solar neutrino flux. And the rather good agreement between

SNO’s NC result and the SSM prediction gives direct evidence of the correctness

of the SSM. The presence of non-νe components implies the change of flavor of the

initially produced νe neutrinos into other flavors. There are several scenarios which

can change the neutrino flavors during their flight from the Sun to the Earth. The

most natural and probable solution to the flavor changing is through neutrino oscil-

lation assuming that neutrinos have non-zero masses. Comparison of the measured

neutrino flux of each experiment with the corresponding prediction from the SSM can

put constraints on the possible values of the oscillation parameters (for solar neutrino

oscillation, it can be approximated by a two-neutrino description) ∆m2 (difference in

mass squared) and θ (mixing angle).

28

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θ2tan

)2 (

eV2

m∆10

-5

10-4

10-1

1

(a)

θ2tan10

-11

90% CL95% CL99% CL99.73% CL

(b)

Figure 1.8. Solar Neutrino Oscillation Solution. (a) Solar Neutrino Global Solution.(b) Solar + KamLAND Neutrino Oscillation Solution [8].

Figure 1.8(a) shows the global solar neutrino oscillation analysis results. It shows

the allowed oscillation parameter region contours of different confidence levels. The

allowed area is in the large mixing angle (LMA) region with the best value at [8]:

∆m2 = 5.5 × 10−5eV2, tan2 θ = 0.42 (1.56)

1.4.4 Solution Using Neutrino Magnetic Moment

If neutrinos have non-zero magnetic moments, the interaction of the neutrinos

with the magnetic field in the Sun can either deplete the number of active neutrinos

or change the flavor of the neutrinos and thus provide an alternative solution to the

solar neutrino problem.

There are two solution to the solar neutrino problem using the non-zero neutrino

magnetic moments. The first method is based on the fact that if neutrinos are Dirac

neutrinos, the flip of the spin of the neutrino by the Sun’s magnet field, νL → νR,

changes the active neutrinos into sterile neutrinos, thus causing fewer neutrinos de-

29

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tected [30, 31]. The reduction due to this approach is neutrino energy independent,

so it can not explain the fact that the depletions are energy dependent from various

solar experiments.

The second approach is called resonant spin flip. This method assumes that

neutrinos are Majorana neutrinos. For Majorana neutrinos, it can not have diagonal

magnetic moments and can only have transition magnetic moments. The magnetic

field in the Sun can change νe,L → νµ,R ≡ νµ. The flavor change means either that

they escape detection or they are detected with less efficiency [32, 33]. This is in

some way similar to the oscillation approach, only different in how the flavor is being

changed. The equation of motion is the same as that in the description of the MSW

effect, but with the Hamiltonian changed as follows:

H =

m2

1

2E+ VCC + VNC µB

µBm2

2

2E− VNC

(1.57)

The effective mixing angle in the medium is:

tan 2θM =2µB

∆ cos 2θ − 2VNC − VCC(1.58)

The profile and the maximum value of the Sun’s magnetic field determine the

eventual probability of flavor changing. It can be seen clearly that the probability is

energy dependent. The lack of knowledge about the exact magnetic field in the Sun

makes this approach more complex and uncertain with many unknown parameters.

30

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1.4.5 KamLAND

KamLAND is a 1,000 ton liquid scintillator detector. It detects anti-neutrinos from

power generating reactors using the inverse β decay interaction νe + p → e+ +n. The

scintillation and annihilation of the positron followed by the neutron capture provides

a coincidence signal to reduce backgrounds. The flux-weighted average distance of

≈ 180 KM and the low energy spectrum of the νe’s makes KamLAND suitable to

probe the oscillations in the region around ∆m2 ≈ 10−5 eV2. So, if the LMA region is

the solution of the solar neutrino problem, under the assumption of CPT invariance,

KamLAND should observe fewer νe’s than that without neutrino oscillations. The

results from KamLAND shows the disappearance of νe’s and the distorted energy

spectrum [9].

NObs − NBG

NExpt= 0.611 ± 0.085 ± 0.041 (1.59)

Figure 1.8(b) shows the combined global analysis of the solar and KamLAND

neutrino data. It clearly identifies the LMA region as the solution to the solar neutrino

problem. It also rules out resonant spin flavor transition as the solution to the solar

neutrino problem since the geomagnetic field is known to be very small [34].

31

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Chapter 2

Super-Kamiokande Detector

Super-Kamiokande (Super Kamioka Neutrino Detection Experiment, SK) is the largest

underground water Cherenkov detector in the world [35]. Its main objective is to

detect neutrinos from various sources, eg., solar neutrinos, atmospheric neutrinos,

supernovae neutrinos etc. It also can be utilized to search for nucleon decays. Re-

sults from SK showed first clear evidence that neutrinos undergo flavor oscillation

and hence neutrinos must have mass. SK’s measurements of solar neutrino flux and

spectrum help to solve the solar neutrino problem [6].

2.1 Introduction

2.1.1 Overview

Super-Kamiokande is located in the Kamioka mine of the Kamioka Mining and

Smelting Company, in the Gifu prefecture of Japan with geographic coordinates

3625′32.6′′N, 13718′37.1′′E. The detector lies about 1000 m under the peak of Mt.

Ikenoyama. The location of Super-Kamiokande is indicated by a black dot in Fig-

32

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Figure 2.1. Location of Super-Kamiokande in Japan.

ure 2.1. The 1,000 m of overburdden reduces the cosmic ray muon flux by a order of

magnitude 5. The muons with an energy less than 1.3 TeV cannot reach the detector.

2.1.2 History

Super-Kamiokande started data taking in April, 1996 and was shut down for

upgrade in July, 2001. This period is referred as Super-Kamiokande I. A cascade of

PMT implosions on Nov.12, 2002 which occurred during the process of refilling the

water tank destroyed more than half of the PMT’s in the detector. Reconstruction

of the detector with reduced inner detector PMT coverage was finished in October

2002. Super-Kamiokande started a second run of data taking thereafter. The data

33

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used for this thesis were taken in Super-Kamiokande -I.

2.2 Detection of Neutrinos

When a charged particle moves faster than the speed of light in a transparent

medium, it will generate Cherenkov light. The Cherenkov light is radiated at angle θ

with respect to the track of the charged particle.

cos θch =1

n(λ)β, (2.1)

where n(λ) is the refractive index of the medium that depends on the wavelength

λ and β is equal to v/c. In water, the refractive index is about 1.334, so the maximum

opening angle is about 42.

The minimum total energy required for a particle to produce Cherenkov photons

is obtained from Eq.(2.1) :

Ethr =n × m√n2 − 1

, (2.2)

where m is mass of the particle. For an electron in water, Ethr is 0.767 MeV.

The number of Cherenkov photons, dNphoton, generated per unit length dL in a

wavelength interval dλ is:

d2Nphoton

dLdλ=

2πα

λ2

(

1 − 1

n2β2

)

, (2.3)

where α is the fine structure constant. For λ = 300 ∼ 660 nm and β ≈ 1, the

number of Cherenkov photons is about 370 per centimeter.

34

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Figure 2.2. A sketch of the Super-Kamiokande detector site, under Mt.Ikenoyama.

Super-Kamiokande can determine the energy of a particle by the number of

Cherenkov photons detected. The position can be tracked by the timing informa-

tion of when the PMT’s detect the Cherenkov photons. The direction of the moving

particle can be deduced from the Cherenkov ring.

2.3 Detector

Figure 2.2 gives a general view of the detector and its associated facilities. The

heart of the Super-Kamiokande detector consists of a cylindrical tank which measures

42 m in height and 39 m in diameter with a volume of 50 kton. On top of the tank, in

the dome area, there are 5 electronic huts and various calibration equipment. There is

an additional hall beyond the dome which houses the electron LINAC that is used to

provide high precision energy calibration. This is very important for the low energy

solar neutrino analysis and also for this thesis.

35

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2.3.1 Tank

The cylindrical tank is made of stainless steel. Reinforced concrete is used be-

tween the tank walls and the surrounding excavation. A cylindrical PMT supporting

structure inside the tank divides the tank into two optically separate regions. The

inner detector (ID) is 36.2 m in height and 33.8 in diameter. It has a volume of

32,000 tons and is viewed by 11146 50 cm Hamamatsu R3600 PMTs. The PMTs

are evenly distributed on a 70 cm grid and cover 40% of the surface area of the ID.

The remaining area is covered by black polyethylene sheets which provide the optical

separation between ID and outer detector (OD) and reduce the reflection of photons.

It also provides a shield against the low energy events from residual radioactivity

entering into the ID. Figure 2.3 gives a schematic view of the support structure of

the ID. The outside of the 55 cm thick structure has 1885 20 cm Hamamatsu R1408

PMTs mounted facing outward. To enhance light collection in the OD, OD PMTs

have wavelength shifting (WS) plates (60 cm by 60 cm ) attached to the PMTs [36].

The OD surface is covered with white Tyvek sheets to increase the reflection of light.

The OD is used to tag incoming charged particles and also provides a passive shield

against neutrons and γ rays from the surrounding rock.

2.3.2 PMT

The 50 cm PMT (Figure 2.4) used in the ID was designed specifically by Hama-

matsu for Super-Kamiokande [37]. The bulb of the PMT is made of 5 mm thick

36

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Figure 2.3. Schematic view of support structures for the detector.

37

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phot

osen

sitiv

e ar

ea >

460

φ

520

7000

0~

720~

)20610(

φ 82

2

φ 25

410

φ 11

6ca

ble

leng

th

water proof structure

glass multi-seal

cable

(mm)

Figure 2.4. Schematic view of a 50cm PMT.

0

0.1

0.2

300 400 500 600 700Wave length (nm)

Qua

ntum

effi

cien

cy

Figure 2.5. Quantum efficiency of the photo-cathode as a function of the wavelength.

38

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Figure 2.6. Single photo-electron pulse height distribution. The peak close to zeroADC count is due to PMT dark current.

Figure 2.7. Relative transit time distribution for a typical PMT tested with 410 nmwavelength light at the single photo-electron intensity level.

39

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Pyrex glass which is transparent to light down to 300 nm in wavelength. The bialkali

(Sb-K-Cs) photo-cathode is sensitive to light in a range from 280 nm to 660 nm. The

quantum efficiency peaks at about 22% around 390 mm (Figure 2.5). The photo-

electron (p.e.) collection efficiency at the first dynode is over 70%. A clear 1 p.e.

peak can be seen in the pulse height spectra (Figure 2.6). The time resolution (tran-

sit time spread) for 1 p.e. is 2.2 ns (Figure 2.7). The high efficiency of photo-electron

detection is important for energy determination. Better time resolution means bet-

ter vertex reconstruction. This is important for observing low energy solar neutrino

events. The dark noise caused by thermal electrons from the photo-cathode is about

3 kHz at the 0.25 p.e. threshold. The gain for the ID PMT depends on the high

voltage applied to the PMT which is in the range of 1700 to 2000 V. This gives a

gain about 107. The gain of each PMT is measured and checked by a Xe calibration

system. Light from a Xe lamp passes through an ultraviolet filter and is injected into

a scintillator ball. The scintillator ball emits light around 440 nm. The intensity of

the primary light and the photons collected by each PMT are compared taking into

account the light attenuation in the water. The high voltage value for each PMT is

adjusted so that the light collection for the all the PMTs are approximately same.

The OD PMTs are equipped with wavelength shifting plates. The WS plates

can absorb UV light and re-emit light in blue-green where the PMTs have better

detection efficiency [36]. The decay time of the fluoride is about 1/3 that of the time

resolution of OD PMTs. Thus is does not seriously effect the time resolution of the

system. In any case, the major use of the OD is to tag the incoming particles and

not to accurately determine their positions.

40

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The presence of geomagnetic fields with a strength of about 450 mG poses a

big problem to the sensitive PMTs. Therefore, 26 sets of horizontal and vertical

Helmholtz coils are utilized on the inner surface of the tank to neutralize the geomag-

netic fields. The resulting field is reduced to about 50 mG inside the tank.

2.3.3 Data Acquisition Systems

Figure 2.8 gives a schematic view of the ID data acquisition system (DAQ). Signals

from PMTs are fed into custom built Analog Timing Modules (ATMs) in Tristan-

KEK-Online (TKO) systems [38]. The ATM records the integrated charge and arrival

time of each PMT signal with an Analog-to-Digital Converter (ADC) and a Time-to-

Digital Converter (TDC). Each ATM can handle up to 12 PMTs. There are a total

of 946 ATM modules. ATMs record ADC/TDC data when a global trigger signal is

set by the VME TRG (Trigger) module. A TKO crate contains a GONG (Go/NoGo)

module which servers as a master module by sending control signals to slave modules

like ATMs. There are 20 ATM modules in one crate. There is also a Super Controller

Header (SCH) module in each TKO which serves as a bus-interface between TKO

and VME. There are a total of 12 TKO crates in 4 electronic huts located on top of

the Super-Kamiokande water tank. Each electronic hut controls 1/4 of the ID PMTs.

A central hut houses the trigger electronics and OD DAQ system.

In the event of a signal, the analog information from a PMT is split into 4 parts in

an ATM module. One part is sent to the TAC (Time to Analog Converter) and one

part is sent to the QAC (Charge to Analog Converter). One copy is amplified 100

times and sent to a discriminator. The last one is used for the purpose of monitoring

41

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analog signals. If the amplified signal at the discriminator exceeds a preset threshold,

a rectangular signal of -15 mV height and 200 nsec width is generated and fed to

the HITSUM output of the ATM module. The threshold at the discriminator is set

to be of 0.2 pe. The addition of the HITSUM of all ATM modules forms the ID

trigger. There are two independent TAC/QAC circuits for each channel in an ATM

which means the ATM has no dead time. This is very useful in handling µ− e decay

events which occur within about 2.2 µsec or any high rate events such as supernovae

bursts. The TAC records the time information by way of an integrated charge which

is proportional to the time delay between the PMT signal and that of the global

trigger. The QAC records the charge information within a 400 nsec window. If a

global trigger is issued within 1.3 µsec after the PMT hit, the charge information

from the QAC is digitized by an ADC (Analog to Digital Converter). The digitized

information is stored in memory. An event number is assigned to this data by a TRG

module in the central hut. High accuracy conversion tables are used to convert ADC

and TDC counts to pico-coulombs (pC) and nano-seconds (nsec) respectively. The

inaccuracies in the conversion using the tables are negligible for the solar neutrino

analysis. The room temperature dependence of the ADC and the TDC is less than

3 counts/C (0.6 pC/C) and 2 counts/C (0.8 nsec/C). Temperature dependence

of the ADC and TDC circuits are checked by sending reference signals with constant

timing and charge every 30 minutes. The measured values are use to convert the ADC

and TDC counts in each of these periods. The temperature is kept within ±0.5C in

the electronics huts. Possible variations coming from the temperature dependence is

less than 0.3 pC and 0.4 nsec for the charge and timing information.

42

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2.3.4 Trigger System

Figure 2.9 gives a schematic view of how the triggers are generated.

In the event of PMT hits, ATM module generates a HITSUM signal with the

height proportional to the number of active channels. The ID HITSUM signal is the

sum of all the HITSUMs from the ATMs. If the HITSUM is more than −320 mV a

low energy (LE) trigger is generated. And the high energy (HE) trigger is generated

with a threshold of −340 mV. The LE trigger corresponds to 29 PMT hits within a

200 ns time window, after subtracting the average dark noise.

Super low energy (SLE) trigger was developed to lower the threshold of the low

energy events down to 5 MeV. The event rate rises dramatically as the threshold is

lowered due to the background events of γ-rays from the surrounding rock, radioactive

decay in the PMT glass, and radon contamination in the water. The hardware trigger

rate of Super-Kamiokande increases by a factor of ten for each MeV the threshold is

lowered. The Intelligent Trigger (IT) system uses two vertex fitting systems to check

the vertex of the SLE triggered events. Only those SLE events which fall within the

22.5 kton fiducial volume according to both fitting routines are kept. Then IT uses a

reformatter machine (which converts the raw data provided by the event builder to

ZEBRA format before sending them to the offline system) to match the fit information

to the raw events and discard those SLE triggers with fits outside the fiducial volume

(except for a small prescaled sample for monitoring).

For the outer detector, the QTC generates a 20 mV by 200 ns square pulse when

an OD PMT got hit with the threshold set at −25 mV, corresponding to 0.25 p.e..

43

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48 SMPs

interface

interupt reg.

TRG

11146 PMTs 9 slave CPUs

VME

TKO

50 cm PMT

x 240

SCH

ATM

x 20

ATM

ATM

TKO

50 cm PMT

x 240

SCH

ATM

x 20

ATM

ATM

CPUslave

SMP

SMP

interface

CPUslave

SMP

SMP

interface

HOST

CPU

CPUslave

FDDI

FDDI

VME

Trigger signal

To ATM

HITSUM from ATM

Triggerlogic

NIM

Sun

Sun

Classic

Sparc10

934 ATMs

Figure 2.8. Schematic view of the earlier ID data acquisition system. Subsequentimprovements have been made to the hardware of the data acquisition system.

900nsec

400nsec

start stop

200 nsec

TDC start and stop

ADC gate

Hit signal

PMT signal

HITSUM

Global trigger

ATM threshold

in ATM

in trigger electronics

Global trigger

Sum of HITSUM

Trigger threshold

Figure 2.9. Schematic view of trigger generation.

44

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The OD trigger is issued when there are 19 OD PMT hits in a 200 ns coincidence

window. When an OD trigger is issued, it will be held for 100 ns to see if a coincident

ID trigger occurs. If there is no ID trigger within this period, the OD trigger will

request the readout of the full detector.

The normal trigger signals (SLE, LE, HE, and OD) are sent to the hardware

trigger module (TRG). There are other type of triggers, such as calibration (CAL),

Veto Start, Stop, etc. If any one of the trigger signals is asserted, the TRG module

generates a global trigger signal and a 16-bit event number, which are distributed to

all quadrant huts to initiate data acquisition for the current event. The TRG module

also records the all trigger types being asserted, trigger time and event number. The

trigger data stored in the TRG module are merged with the PMT data by the online

process.

2.3.5 Water and Air System

Water System

Clean water is very important for a water Cherenkov detector. Impurities in the

water could reduce the water transparency for Cherenkov photons and can be a source

of radioactivity. Figure 2.10 gives a schematic view of the water purification system

in Super-Kamiokande . The water is recycled through this purification system at a

rate of about 30 tons/hour. The water first goes through a series of mesh filters of

size 1 µm to remove small particles in the water. The UV sterilizer is used to kill the

bacteria in the water. A deionizer is used to remove heavy ions in the water. The

resistance of the water is increased from 11 M Ω·cm to 18.24 MΩ·cm.

45

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Figure 2.10. A schematic view of the water purification system.

Radon causes most of the low energy events similar to that from solar neutrinos.

Reducing the Rn in the water is crucial for the solar neutrino experiment. A Reverse

Osmosis (RO) system and a tank to dissolve Rn-free air were installed to achieve

that purpose. A membrane degasifier (MD) consists of 30 hollow fiber membrane

modules and a vacuum pump pumping radon-free air. It can remove radon with an

efficiency of about 83 %. A vacuum degasifier (VD) removes radon gas dissolved in

the water at an efficiency of about 96 %. Radon level in the water is monitored by

several radon detectors at various locations in the water system. The radon level has

been reduced from <2 mBq/m3 to about 0.4± 0.2 mBq/m3 by the water purification

system [39, 40].

The ultra filter (UF) uses fiber membrane filters to eliminate particles as small as

46

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about 10 nm in diameter. The number of particles with size greater than 0.2 µm is

reduced by about a factor of 3.

Air Purification System

The air in the mine is contaminated by radon from the surrounding rock which

causes a problem for low energy neutrino detection. The typical radon level is about

2,000-3,000 Bq/m3 during the warm season and 100-300 Bq/m3 at other times. To

keep radon levels in the dome area and water purification system below 100 Bq/m3,

fresh air is pumped from outside of the mine at a rate of 50 m3/min. The flow rate is

chosen so that it can maintain a slight over-pressure at Super-Kamiokande to keep the

ambient air out. A “Radon Hut” was installed at the entrance of mine to house the

air intake system. The intake air is measured to have a level of about 10-30 Bq/m3.

2.3.6 Monitoring System

Online Monitor System

An online monitor system is installed in the control room which reads data from

the DAQ host computers at real time. It displays the hit PMTs map and shows some

of the events being recorded by the online DAQ system. It also provides current and

recent event histograms to monitor status of the detector. It also can be used by the

shift people to check the performance of the detector and trouble-shooting problems

of the detector and the DAQ system.

A process called the “slow control” is used to monitor the status of the high voltage

supply to the PMTs, the temperatures of each electronics crate and the working of

compensating coils used to cancel the geomagnetic field.

47

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Realtime Supernova Monitor

Large water Cherenkov detector can detect supernova bursts efficiently and promptly

[41, 42]. About 10,000 events are expected in Super-Kamiokande for a supernova ex-

plosion at the center of the Galaxy. Super-Kamiokande can detect up to 30,000 events

within the first second of a burst.

As the supernova bursts occur in few seconds, a candidate cluster within a few

seconds is searched for constantly by the online process. If a candidate cluster is

found, since the supernova events will distribute uniformly in the detector, the average

spatial distance between events is calculated. If this distance is greater than a critical

distance, it will send an “alarm” to the shift people. The shift people will run special

checks on these burst using the vertex reconstruction as well as the PMTs’ hit pattern.

If the burst candidate passes these checks, the data will be re-analyzed using an offline

processes.

Super-Kamiokande with its realtime supernova search system is part of an inter-

national supernova-watch network using neutrinos to detect supernova.

48

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Chapter 3

Event Reconstruction

The raw information of each event includes the PMT hits and the timing of the hits.

For solar neutrino analysis, events can be categorized as neutrino data sample with the

total charge of hit PMTs less than 1000 p.e., and muon data sample for events with the

total charge more than 1000 p.e.. Event reconstruction for the neutrino data sample

includes vertex reconstruction, direction reconstruction and energy reconstruction.

The reconstructed events’ tracks from the muon data sample are used later in the

background reduction. The data sample with reconstructed event information forms

the basis for the solar neutrino analysis.

3.1 Vertex Reconstruction

Vertex reconstruction is the first step in the event reconstruction. It also serves as

the basis for the event direction reconstruction. For solar neutrino events, the energy

is less than 20 MeV. This means the travel length of the recoil electron from neutrino-

electron interaction is less than 10 cm, corresponding to a timing spread of 0.5 nsec,

49

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05

101520253035

600 800 1000 1200 1400 1600 1800

t1 t2 t3 t4

time (nsec)

Figure 3.1. A typical event time distribution of PMT hits [43].

which is far less than the PMT time resolution 2.2 nsec. Therefore the source of the

Cherenkov photons can be treated as a point. The vertex reconstruction algorithm

uses the relative PMT hit timing information to backtrack to the point from which

the Cherenkov photons are generated. In the ideal case, backtracking from each hit

PMT should reach the vertex at the same time, but random noise hits, light scattering

and reflection make this impossible. So instead, the vertex is obtained by minimizing

the residual time of PMT hits. The residual time is calculated as the hit time minus

the photon travel time from the vertex to the hit PMT.

Figure 3.1 gives a typical event PMT hit timing distribution. Selection of the

PMT hits for event vertex reconstruction is based on the following method.

1. Selecting the 200 nsec time window which contains the maximum number of

PMT hits (Nsignal). 200 nsec is chosen because the maximum time for a photon

to traverse the detector is about 200 nsec. t1, t4 are the start and end times of

the event, t2, t3 represents the 200 nsec time window. t2, t3 is also called

’on-time’ and the range outside this time window is called ’off-time’

50

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2. The off-time hits are used to estimate the contribution from dark noise hits,

Nnoise, by the following formula:

Nnoise = (t3 − t2)

[

Nhit(t1 ∼ t2) + Nhit(t3 ∼ t4)

(t2 − t1) + (t4 − t3)

]

(3.1)

3. A series of time windows with smaller size within the on-time time window are

tested to maximize the significance of the signal. The significance, S, is defined

as follows :

S =Nhit(t2 ∼ t3) − Nnoise√

Nnoise

(3.2)

Only those PMT hits within the time window with maximum S are selected for

vertex reconstruction.

The vertex is found by searching a grid of fixed points as shown in Figure 3.2.

The initial grid is spaced at 397.5 cm. A vertex reconstruction goodness is calculated

for each point in the grid using the following formula:

goodness(x, y, z) =

Nhit∑

i=1

exp

(

−(tresidual,i(x, y, z) − tcenter(x, y, z))2

2σ2

)

(3.3)

where (x, y, z) is the position of the grid point. Nhit is the number of PMT hits

in the selected time window. σ is the PMT time resolution, which is 10 nsec for all

51

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-2000

-1500

-1000

-500

0

500

1000

1500

2000

-2000-1500-1000 -500 0 500 1000 1500 2000

x (cm)

y (c

m)

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-2000-1500-1000 -500 0 500 1000 1500 2000

x (cm)

z (c

m)

Figure 3.2. The grid used in the initial stage of the vertex reconstruction. The leftfigure shows a projection on the XY plane and the right figure shows a projectionon the XZ plane. Solid lines and broken lines represent the ID tank and the fiducialvolume, respectively.

PMTs initially and 5 nsec for subsequent grid search. tresidual,i is the residual time of

i-th hit PMT which is calculated with the following formula:

tresidual,i = ti −n

c

(x − xi)2 + (y − yi)2 + (z − zi)2, (3.4)

where ti is the time of the i-th PMT hit; tcenter is the mean time of the distribution of

tresidual,i; n is the refractive index of water and c is the speed of light in vacuum and

(xi, yi, zi) is the position of the i-th hit PMT. The goodness value falls between 0 and

1, where 1 represents the ideal case. After the initial vertex is found, this process is

repeated with reduced grid size until the grid size is reduced to about 5 cm.

Figure 3.3 shows the reconstructed vertexes from a LINAC calibration. Figure

3.4 shows the goodness distribution for the reconstruction. The vertex resolution is

about 75 cm for 10 MeV electrons measured by the LINAC calibration system.

52

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0

2000

4000

6000

-1500 -1000 -500 0 500 1000 1500x(cm)

0

2000

4000

6000

-1500 -1000 -500 0 500 1000 1500y(cm)

0100020003000

-1500 -1000 -500 0 500 1000 1500z(cm)

Figure 3.3. Projection of the reconstructed vertex distribution for LINAC calibrationevents at the position (x=−388.9cm, y=−70.7cm, z=+27cm) with the electron beamenergy set to 8.35 MeV. The broken lines show the electron beam injection position.

53

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0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

goodness

Figure 3.4. The goodness distribution for LINAC calibration events at the position(x=−388.9 cm, y=−70.7cm, z=+27cm) with the electron beam energy set to 8.35MeV.

3.2 Direction Reconstruction

Direction reconstruction is of great importance for solar neutrino analysis as the

directional correlation with the Sun’s direction is used to select solar neutrino events.

After the determination of the vertex position, the direction of the event can be

reconstructed based on the PMT hit pattern. In the ideal case, the hit PMTs should

be on a ring with opening angle about 42 from the vertex position with respect to

the event direction. Since the scatterings of recoil electrons and photons in the water

plus PMT reflection smear the ring pattern, a maximum likelihood method is utilized

to determine the direction of the event, using the PMT hits with residual time within

the 30 nsec time window.

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0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140 160 180

θ

pro

bab

ility

Figure 3.5. The probability density function for the angle of Cherenkov photonsrelative to the recoil electron momentum.

Figure 3.6. Definition of the PMT angles.

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0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80 90

incidence angle (degree)

acce

pta

nce

Figure 3.7. The PMT angular acceptance as a function of the incident angle.

L(~d) =

Nhit∑

i=1

log(Pi(θdir)) ×cos θi

a(θi), (3.5)

where θdir is the angle between the emitted Cherenkov photon and the trial event

direction, and P (θdir) gives the probability density function of the emitted photons

along the direction θdir (Figure 3.5). P (θdir) is obtained from MC simulation of

10 MeV electrons with known direction. The distribution peaks around 42 but is

broadened and extended to 180 due to the smearing effects mentioned earlier. θi is

the incident angle of the Cherenkov photon on the i-th PMT as defined in Figure 3.6.

a(θi) gives the efficiency of acceptance of the PMT as a function of incident angle

(Figure 3.7).

A grid search method is utilized again to find the most likely direction. The grid

56

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0

500

1000

1500

2000

2500

3000

3500

4000

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

direction cosine of z

Figure 3.8. The direction cosine distribution from LINAC calibration data at theposition (x=−388.9cm, y=−70.7cm, z=+27cm) with the electron beam energy of8.35 MeV going downward.

size starts from 20, and goes through 9, 4, 1.6 step sizes until the direction with

the maximum likelihood is found. Figure 3.8 shows the reconstructed direction of the

downward going events from LINAC calibration. The angular resolution for 10 MeV

electrons is about 27.

3.3 Energy Estimation

A non-zero neutrino magnetic moment will manifest itself through the distortion

of the measured recoil electron energy spectrum. So it is of great importance to

determine the event energy as accurately as possible. The energy of the charged

particle can be determined by the number of Cherenkov photons it emits, and the total

number of emitted Cherenkov photons should be proportional to the total number

of photo-electrons detected by all the PMTs in the SK detector. However, for solar

57

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neutrino events, the number of generated Cherenkov photons is relatively small, so

the probability of having 2 or more photons hit one PMT is very small. As the charge

resolution is poor at single p.e. level, it can not give a good estimate of the number of

Cherenkov photons based on the charged deposited in the PMT’s. Also, the charge

measurement depends on the gain of each PMT, which is hard to calibrate and floats

with time and temperature. So, instead, the number of PMT hits (Nhit) within the

50 nsec time window is used as the basis for the estimation of the event energy. The

50 nsec window is chosen to reduce possible noise hits in the PMT’s. The time is the

residual time of PMT hits calculated using the reconstructed vertex mentioned in the

earlier section of this chapter.

The Nhit depends on several factors. The geometry of the detector causes position

dependence of Nhit. For example, the measured Nhit from a Nickel calibration using

Ni(n, γ)Ni interactions shows about 10% variation from center position to a point

close to the edge of the detector. Water transparency and PMT acceptance contribute

to the variation of Nhit. In order to give a uniformed energy calculation through the

whole fiducial volume, various corrections have to be applied to the calculation of the

effective number of hits from Nhit.

Neff =

Nhit∑

i=1

[

(Xi + εtail − εdark) ×Nall

Nalive× S(θi, φi) × exp(

ri

λ) × Gkek(i)

]

(3.6)

where

Xi : Multiple photo-electron hit correction

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0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1

εi

exp

ecte

d n

um

ber

of

ph

oto

n

Figure 3.9. The average number of photo-electrons in a hit PMT as a function of thenumber of hits in the surrounding PMTs (3x3 patch including the hit PMT).

010

2030

4050

6070

8090

010

2030

4050

6070

8090

0.5

0.6

0.7

0.8

0.9

1

θ

φ

cove

rag

e

Figure 3.10. The effective PMT photo-cathode coverage area as a function of theincident photon direction. for PMTs (a 3x3 patch including the hit PMT).

59

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When an event occurs very close to the edge of the fiducial volume and moves

toward the wall next to it, the hit PMTs could have multiple hits. So the

assumption that each PMT has only one hit is not valid. To correct this, the hits

of the surrounding PMTs of the hit PMT are checked. The number of expected

photo-electrons for each hit PMT, Xi, is estimated based on the occupancy of

the 8 surrounding PMTs. Assuming the average number of photon-electrons

is ηi per PMT area in the region surrounding i-th PMT, then the probability

that the surrounding PMTs do not get hit by the photon-electrons is a Possion

distribution, Pi = η0i e

−ηi/0! = e−ηi . If the number of hit PMTs and the number

of live PMTs surrounding the i-th PMT are ni and Ni respectively, then Pi =

(Ni − ni)/Ni = 1 − ni/Ni. So the average number of photon-electrons is

ηi = log1

1 − αi

(3.7)

where αi = ni/Ni. Since the total number of photon-electrons in the region is

Niηi, the expected number of photon-electrons hit the i-th PMT, Xi, is given

as follows:

Xi =

Niηi

ni= 1

αiln [(1 − αi)

−1] for αi < 1

3 by extrapolation for αi = 1

(3.8)

Figure 3.9 shows the corrected number photo-electrons per hit PMT as a func-

tion of αi.

60

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εtail : Reflected light correction

This correction is to take into account of reflected photons. Reflection causes

the photons to arrive at the PMT at a later time which means that the delayed

hits usually will fall outside the 50 nsec time window. The correction is done

by using a larger time window to “recollect” the delayed hits.

εtail =N100 − N50

N50. (3.9)

where N50 and N100 are the number of PMT hits in the 50 nsec time window

and in the 100 nsec time window respectively.

εdark : Dark noise correction

The dark noise rate is about 3.3 KHz which could contribute up to 2 hits in

counting Nhit. The number of dark noise hits in the 50 nsec time window is

calculated as follows and will be subtracted from the calculation of Neff :

εdark =Nalive × Rdark

N50, (3.10)

where Nalive is the number of all live PMTs in the ID and Rdark is the measured

average dark noise rate for the current run.

Nall

Nalive: Dead PMT correction

The number of active PMTs changes with time. This factor accounts for the

time variation of the dead PMTs. Nall is total number of ID PMTs (11,146).

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S(θi, φi) : Effective photo cathode coverage correction

S(θi, φi) gives the effective photo-cathode coverage area of the i-th hit PMT as

a function of incident angle (θi, φi) of the incoming photon. Fig.3.10 shows the

distribution of S(θi, φi). The non-uniformity is caused by the geometry of the

detector and the shadowing effects from surrounding PMTs.

exp( ri

λ(run)) : Water transparency correction

Light attenuation directly affects the number of PMT hits. To compensate for

the time changes of the water transparency, a factor exp( ri

λ(run)) is applied to

the calculation of the Neff , where ri is the distance from the i-th hit PMT to

the reconstructed vertex. λ is the water transparency measured using the decay

electrons events from stopping muons. The water transparency is measured

continuously.

Gkek(i) : Quantum efficiency correction

375 PMTs used in the ID were produced before the main set of PMTs. These

PMTs have larger quantum efficiency than the other PMTs. The correction

factor for PMTs is given as follows :

Gkek(i) =

0.833, for 375 PMTs

1.000, for other PMTs

(3.11)

SK uses an electron linear accelerator (LINAC) to relate Neff to the total electron

energy [44]. The conversion formula is obtained through MC simulation of the known

mono-energy electrons from the LINAC. Figure 3.11 shows the reconstructed energy

62

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Figure 3.11. Reconstructed energy as a function of the effective hit (Neff).

as a function of Neff, the uniformity has been checked to be within 1% over the fidu-

cial volume by the energy calibration procedures described in the Chapter Detector

Calibration.

3.4 Muon Event Reconstruction

Energetic cosmic ray muons from the atmosphere can penetrate 1000 m of rock and

reach the SK detector at a rate of about 2 Hz. These muons interact with the nuclei of

16O in the water and produce radioactive elements. When these elements decay, they

produce electrons, positrons, or γ-rays with energy less than 20 MeV. These events

are called spallation events. These events have similar signatures to those of solar

neutrino events. It is the major source of background for the solar neutrino analysis

above 6 MeV and accounts for about 21% dead time of the detector. Spallation

events have strong temporal and spatial correlations to the parent muon events. A

maximum likelihood method has thus been designed to remove these spallation events

63

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xexitl µ( )

xexitl ( )photon

xexit

entx

i-th PMT

cosmic ray muon

42

Figure 3.12. Variables used in the reconstruction of the muon track

by finding the correlation of these events to the muon events. In order to do this, the

muon events’ track must be reconstructed to extract the spatial correlation between

low energy events to the muon events.

A muon event is defined as those events whose total number of photo-electron

charge is more than 6000 p.e. and one PMT has more than 200 p.e. deposited on it.

To reconstruct the muon track, first the entrance point of the muon is identified by

finding the earliest hit PMT in the ID which has at least 2 hits in neighbor PMTs

within a 5 nsec window. The exit position is identified by finding the central point of

all the charge saturated PMTs (a PMT becomes saturated when it receives more than

231 p.e. at once). The muon track is the line connecting the entrance and exit points.

The quality of this reconstruction is checked by the minimum distance from entrance

point to the saturated PMTs (Lent) and the maximum distance from the exit point to

the saturated PMTs Lext. If Lent > 300 cm and Lext < 300 cm, the reconstruction

is considered good. This criteria can reject stopping muon events and multiple muon

64

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events (2 or more muons enter the detector at the same time). Events that can cause

lots of saturated PMTs can not be reconstructed well by this method. These are the

events with residual charge Qres > 25, 000 p.e.. Qres = Qtotal − p × L, Qtotal is

the total charge for this event and L is the length of the track, p = 23 p.e./cm is

the average number observed photo-electrons per centimeter for the muons. All the

events whose tracks could not be reconstructed are reconstructed using the method

described below with their TDC information. The entrance point is the same. The

exit point is searched for in a method similar to the vertex reconstruction using the

following goodness:

goodness =1

1σ2

i

×∑

i

1

σ2i

exp

−1

2(ti − T

1.5σi

)2

, (3.12)

where

ti = Ti(xi) −lµ(xext)

c− lphoton(xext)

c/n(3.13)

σi = Time resolution of the i-th hit PMT

T = Time when the muon enters the detector

Ti = Time of hit of photon on the i-th PMT

lµ(xext) = Travel distance of the muon as a function xext

lphoton(xext) = Travel distance of the photon as a function of xext

c = Light velocity in vacuum

n = Refractive index of water.

65

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type number of events number of unfittedevents

Single muons 835 5Stopping muons 10 8

Hard muons 41 2Corner clippers 58 19Multiple muons 56 28

total 1000 62

Table 3.1. Summary of muon fitter efficiency for various types of muons.

Figure 3.12 shows the definition of variables used in the search of the muon exit

point.

If goodness > 0.8, the reconstruction is considered good. Events that could not be

reconstructed by the aforementioned methods are considered unfitted muon events.

The efficiency of the muon event reconstruction is estimated with 1000 identified

muon events from data. The muon events can be categorized as follows:

Single muons = Muon events transverse the ID

Stopping muons = Muon events stopped in the ID

Hard muons = Muon events with ResQ > 2.5 × 103 p.e.

Corner clippers = Muon events whose track length is less than 5 m

Multiple muons = Multiple muons in an event.

The reconstruction efficiency for each type of muon events is summarized in Table

3.1. Overall the fitter efficiency is about 94%.

The resolution of the entrance and exit points reconstruction is estimated by using

Monte Carlo generated muon events. The reconstructed entrance and exit points are

66

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Figure 3.13. The track resolution of the muon fitter. The resolution is estimated tobe 67 cm.

compared with generated positions, as shown in Figure 3.13. The 1σ resolution is

found to be 67 cm for a single muon event.

67

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Chapter 4

Detector Calibration

In order to detect solar neutrinos, we first need to understand our detector as much as

possible. We need to know how the PMTs in the water Cherenkov detector respond

to hits by photons, and we need to understand the photon attenuation length in the

water, i.e., the water transparency. The searching for a neutrino magnetic moment

relies on the analysis of the measured energy spectrum, so knowing the energy of

the recoiled electrons from neutrino-electron elastic scattering is of great importance

to this analysis. A proper way of converting the number of PMT hits to energy is

needed, and should be periodically checked and monitored. For a detector of such

a huge size, the aforementioned requirements pose a great challenge and require a

tremendous amount of work. This has been achieved by two means. First, a series

of calibrations are conducted periodically. The PMTs’ charge and timing response

are calibrated by Xe and laser systems respectively. Water transparency is measured

by a laser system and by measurements of muon decay. LINAC ( an electron linear

accelerator) and DTG (Deuterium-Tritium Generator) systems have been used for

68

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Xe Flash LampUV filter ND filter

Optical fiber

Pho

toD

iode

Pho

toD

iode

ADC

Monitor

PMT

Scintilator

Trigger20inchPMT

SK TANK

Scintilator Ball

Figure 4.1. The Xe calibration system.

the energy calibration. A detailed MC simulation of the detector is performed and

is compared to the calibration results to insure an accurate representation of the

detector.

4.1 PMT Calibration

The PMT calibration includes PMT gain and PMT timing calibration, which

checks the PMTs’ charge and timing response to hits by photons.

4.1.1 PMT Gain Calibration

The stability and uniformity of the PMTs’ gain is checked and monitored by two

systems: a Xe calibration system and a Ni-Cf calibration system.

69

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0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

665.1 / 50Constant 1154. 14.51Mean 1.010 0.5944E-03Sigma 0.7246E-01 0.5612E-03

σ=7%

Corrected Q (pC)

Nu

mb

er o

f en

try

Figure 4.2. Typical result from Xe calibration. The spread of the relative gain isestimated to be 7%.

Xe Calibration

The goal of the Xe calibration is to make all of the PMTs’ gain the same, in this

way insuring a uniform detector response. The relative gain of a PMT is controlled

by the high voltage applied to the PMT. The gain G of a PMT is determined by

G = aV b, where a and b (b ' 8.5) are constants, V is the voltage. A typical gain of a

PMT is about 107. A schematic view of the Xe calibration system is shown in Figure

4.1. The Xe lamp can produce a flash of light with a pulse intensity variation less

than 5%. The light then passes through two filters: a ultraviolet (UV) filter which

lets only ultraviolet light pass through and a neutral density (ND) filter which makes

the light intensity independent of the wavelength. After these filters the light is split

into two parts. One is fed into the monitor-trigger subsystem which consists of two

photo-diodes and a 5 cm PMT. The other part is sent to a scintillator ball in the SK

70

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tank via optical fiber. The scintillator ball is a spherical acrylic ball mixed with 50

ppm C26H26N2O2S (BBOT) and 500 ppm MgO. BBOT absorbs UV light and emits

light with wavelength close the Cherenkov light in the water. MgO is used to diffuse

the light uniformly.

As the PMT acceptance, light attenuation in the water and the non-uniformity of

the scintillator ball could affect the charge observed at each PMT, a corrected charge

is defined as follows to take these factors into account:

Qcor =Q × r × exp( r

λ)

faccept(θPMT )fball(θ, φ)(4.1)

where Q is the charge observed at the PMT, r is the distance from the scintillator

ball to the PMT, faccept is the PMT acceptance function and fball is the correction of

the non-uniformity of the scintillator ball.

The corrected charge is then normalized to the light intensity recorded by the

monitor-trigger subsystem. This gives the relative gain of the PMT. The Xe calibra-

tion was first used to determine the high voltage supplied to the PMT. Figure 4.2

shows the relative gain of all the PMTs. The spread of the relative gain is about 7%.

Subsequent periodic Xe calibrations showed that the time variation of the relative

gains is less than 2%.

Ni-Cf Calibration

The light density from the Xe calibration system is about 100-200 photo-electrons

(p.e.). For solar neutrino events, a PMT is usually hit by only one p.e.. Therefore,

the charge response of the PMT at the single p.e. level, absolute gain, should also

71

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20m

m

200m

m

130m

m

125m

m

50mm

10m

m 30m

m

Nickel wire + Water

Figure 4.3. The Ni-Cf calibration system.

10-2

10-1

1

-2 0 2 4 6 8 10

1 p.e. distribution (pC)

Figure 4.4. The charge distribution for a single p.e. hit.

72

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Figure 4.5. The averaged occupancy for each layer of barrel part of the detector.

be checked. This is achieved through the Ni-Cf calibration system. Figure 4.3 shows

the setup of the Ni-Cf source used in the calibration. At the center lies the 252Cf

radioactive source which emits fast neutrons as fission products. The surrounding

Ni wires capture the neutrons and emit γ rays from the Ni(n,γ)Ni reactions with a

maximum energy of 9 MeV. The γ rays interact with electrons in the water through

Compton scattering. The scattered electrons will generate Cherenkov light similar to

that from solar neutrino events with a PMT signal at the 1 p.e. level. Figure 4.4

shows the charge distribution of a typical PMT for a single p.e. hit. The peak value

for each PMT is chosen as the factor for converting the charge into p.e. level for that

tube. The mean value for the converting factor is 2.055 pC/p.e..

The uniformity of the absolute gain of a PMT is checked by occupancy, which

is defined as (number of hits)/(number of events) for each PMT. Distribution of

the averaged occupancy for each layer of the barrel part of the detector is shown in

Figure 4.5. The layers are numbered from bottom (1) to the top (51). It shows an

73

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Super Kamiokande inner tank

diffuser ball

20’PMT

variableattenuation filter

optical fiberN lasergenerator

monitor PMT

trigger elec.

DAQelec.

sig.

optical fiber

sig.

sig.

sig.20’PMT

2

=384nmλ

diffuser tip(TiO )LUDOX 2

Figure 4.6. Schematic view of the PMT timing calibration system.

increase of the occupancy at the bottom and the top parts. This comes from reflection

from the PMTs and from the cylindrical shape of the detector. This phenomena is

reproduced by the detector MC simulation. The open marks at the top parts with

high absolute gains are the so called “KEK” tubes mentioned in Chapter 3 on Event

Reconstruction. These tubes have higher quantum efficiency. This difference has

been taken into account in the calculation of the recoil electron energy.

4.1.2 PMT Timing Calibration

As described in the Chapter on Event Reconstruction, PMT timing is essential in

the event vertex and direction reconstruction. Timing recorded by each PMT relative

to the global trigger could vary due to the intrinsic properties of each PMT and the

different cable length from each PMT to the electronic huts. Also the amount of

charge deposited in the PMT could affect the PMT timing. A laser system with

74

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Typical TQ map

880

890

900

910

920

930

940

950

960

970

980

0 20 40 60 80 100 120 140

Q (p.e.)

T (

nsec

)

Figure 4.7. The PMT time response as function of charge (“TQ-map”).

very short pulse length is used to check the PMT timing (Figure 4.6). The light is

generated by a N2 laser with a wavelength of 337 nm and pulse width of ∼ 3 nsec.

The light then is passed to a dye laser which shifts the light to the wavelength of 384

nm, similar to that of the Cherenkov light. The light is split into two parts with one

going to a trigger subsystem and the other going to a diffuser ball in the SK tank

via optical fiber. To diffuse the light evenly, the diffuser ball contains two diffuser

elements, 3 mm TiO2 at the end of the optical fiber and LUDOX (dioxo-silicon) which

a silica gel with 20 nm glass fragments surrounding the TiO2 tip. This combination

could diffuse the light uniformly without introducing additional time spread of the

light pulse.

By changing the intensity of the light output, the charge dependence of the PMT

timing and timing resolution can be measured. Figure 4.7 shows the PMT timing

75

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response as a function of charge. The small points are the measured values and

the open circles show the mean values with 1 σ error bar. The PMT timing charge

dependence is mainly due to the slewing effect of the ATM discriminator. From this,

a lookup table of timing vs charge for each PMT is made, a “TQ map”, which is used

in the event reconstruction. The PMT timing resolution also depends on the charge.

For 1 p.e. the typical timing resolution is ∼ 2.2 nsec.

4.2 Water Transparency Measurement

Cherenkov photons travel in the water before they are detected by PMTs. The

absorption and scattering of photons in the water directly affects the number of

photons being detected. As the energy of the recoil electrons from neutrino-electron

elastic scattering is closely related to the number of PMT hits, corrections from water

transparency must be done for the accurate determination of the event energy. There

are two aspects of the water transparency measurement, one is the determination

of the wavelength dependence of the water transparency, which is important in the

MC simulation of the Cherenkov photon propagation in the water, the other is time

variation of the water transparency parameter which is important in determination

of event energy.

4.2.1 Measurement of Water Transparency by Laser

The wavelength dependence of the water transparency has been measured by a

wavelength tunable laser system shown in Figure 4.8. The N2 dye laser system can

produce monochromatic light with a tunable wavelength from 337 nm to 600 nm.

76

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Optical Fiber (70m)

CCD cmera

<< SK Tank >>

Beam Splitter (50:50)

Lens

Integrating Sphere

<< laser box >>

Diffuser Ball

2inch PMT

DYE / N2 laser

Figure 4.8. The laser system for direct water transparency measurement

Light from the laser is split into two parts by a beam splitter, one part is sent to a 2

inch PMT for measuring the light intensity, the other part is sent to a MgO diffuser

ball in the tank via optical fiber. The light from the diffuser ball is measured by a

CCD camera at the top the detector. The measured signal is normalized by the light

intensity measured by the reference PMT. By changing the distance of the diffuser

ball to the CCD camera, a series of signals as a function of distance can be obtained.

And the water transparency can be extracted by the following formula:

I(d) = I0exp(−d

λ) (4.2)

where λ is the water transparency, d is the distance from the diffuser ball to the

CCD camera, I(d), I0 are the light intensity measured by the CCD camera and the

reference PMT respectively.

Figure 4.9 shows the measured results for the wavelength of 420 nm. From the fit

to the data, the water transparency can be determined as 97.9 ± 3.5 m. Figure 4.10

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Distance from CCD (m)

I CC

D/I P

MT

λtra = 97.9±3.5m(420nm)

10 4

5 10 15 20 25 30

Figure 4.9. The direct measurement of water transparency using the laser system.Water transparency is obtained from the inverse of the slope of the line fit. In thisfigure, water transparency is obtained at 97.7 m for wavelength of 420 nm.

10-3

10-2

10-1

200 300 400 500 600 700

1996/12/3,4 1996/12/141996/12/17 1997/12/271997/1/18 1997/3/51998/4/18 1998/4/28

Wavelength (nm)

Att

enu

atio

n C

oef

fici

ent

(1/m

)

Figure 4.10. Wavelength dependence of water transparency. Line shows the watertransparency as a function of the wavelength used in the MC simulation.

78

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shows the measured water transparency as a function of the wavelength. The line

represents the value used in the MC simulation of photon propagation.

4.2.2 Water Transparency Measurement and Monitoring by

Decay Muons

The filter performance in the water purification system could cause a change in the

water transparency. Therefore, continuous monitoring of the water transparency is

necessary. The abundant cosmic ray muon events provide a convenient way to measure

and monitor the water transparency. Cosmic ray muons reach the SK detector at a

rate of ∼ 3 Hz. This produces about 6000 stopping muons in the detector per day

which produce decay electrons.

µ− → e− + νe+ νµ,

or

µ+ → e+ + νe + νµ.

The following criteria have been used to select a pure sample of µ-e decay electron

events:

• The µ-e decay electron events must occur within a time window of 2.0 ∼ 8µ sec

after a stopping µ event.

• The reconstructed vertex of the µ-e decay electron events must be within the

SK fiducial volume.

79

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10deg

52deg

32deg

vertex position

direction of decay electron

q j

Delta Q

R

di

i

N hiti

Figure 4.11. Illustration of water transparency calculation using µ-e decay electronevents. Only those hits within the ring of opening angle of 32 to 52 are selected.

• The number of effective PMT hits must be greater than 50. The effective hits

are those PMT hits which are within the 50 nsec timing window after the time-

of-flight (TOF) subtraction.

The averaged number of µ-e decay electron events thus selected is about 1500 per

day. After their vertex and direction have been reconstructed, the PMT hits used

for calculating water transparency are selected according to the following criteria in

order to get rid of the effects of light scattering and reflection (see Figure 4.11 for an

illustration of the selection criteria):

• The PMT hits must be within the 50 nsec timing window after TOF subtraction.

• The PMTs are within a ring of opening angle 32 to 52 with respect to the

decay electron’s direction.

80

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The selected PMT hits on this ring are then divided into 36 equal bins, with the

charge in each bin added together,

∆Qi =

Ni∑

j=1

qjexp(dj

λ) (4.3)

where qj is the charge recorded at the jth hit PMT, Ni is the number of selected

PMTs within the bin, dj is the distance from the reconstructed vertex to the jth hit

PMT, λ is the water transparency. As the bin is rather small, the charge in each bin

can be written as:

∆Qi = exp(r

λ) × q(r) (4.4)

where r =∑Ni

j=1dj

Niis the mean distance from the vertex to the hit PMTs in each

bin, q(r) =∑Ni

j=1 qj is the total charge in this bin. Corrected for attenuation due to

the water transparency, ∆Qi should be equal for all bins. The energy distribution of

the µ-e decay events should follow that of Michel spectrum, so for different event, ∆Qi

could be different. By averaging over the entire Michel spectrum gives the following

relations:

Q(r) = exp(

− r

λ

)

∆Q (4.5)

log(Q(r)) = − r

λ+ log(∆Q) (4.6)

81

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0.9037E-02/ 49P1 -0.1187E-03

r (cm)

log

(q(r

))λe=8425cm

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

10001250150017502000225025002750300032503500

Figure 4.12. The log(q(r)) distribution for a typical µ-e data sample.

Elapsed Days from Jan 1, 1996

Wat

er T

ran

spar

ancy

(cm

)

7000

7500

8000

8500

9000

9500

10000

200 400 600 800 100012001400160018002000

Figure 4.13. Time variation of the measured water transparency as function of elapseddays dating from the starting of Super-Kamiokande -I. Vertical lines shows the sepa-ration of calender years.

82

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By plotting q(r) vs r for the 36 bins of each event for all µ-e events, water trans-

parency can be calculated. Figure 4.12 shows the distribution of log(Q(r)) as a

function of r for a typical µ-e data sample. The inverse of the slope gives the water

transparency. Data from a single week are combined to give a weekly water trans-

parency value. Figure 4.13 shows the weekly transparency as a function of the elapsed

time since the start of Super-Kamiokande -I. Each point in the figure represents a

running average of five weeks of data that are centered on the named week. This

water transparency value is an average for all wavelengths and is used in the calcula-

tion of the event energy to account for the attenuation from water transparency. The

fluctuation of the water transparency is mainly due to the change of the filters in the

water system.

4.3 LINAC Calibration

The determination of the absolute energy scale of the SK detector is of great

importance in the measurement of the energy spectrum of the recoil electrons from

neutrino-electron elastic scattering. And the energy spectrum is in the center of

our quest to search for non-zero neutrino magnetic moment. A non-zero neutrino

magnetic moment will manifest itself in the distortion of the recoil electron energy

spectrum. For neutrino magnetic moment µν = 10−10µB, the maximum distortion

to the weak scattering only spectrum is about 2.4% in the 5-5.5 MeV energy bin.

Therefore the energy scale must be calibrated as accurate as possible in order to be

able to see such small effect in the energy spectrum. At the beginning of the SK

operation, a Ni-Cf source was used for energy calibration, but it has intrinsic system

83

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4000 cm

4200

cm

D1 MAGNET

D2 MAGNET D3 MAGNET

BEAM PIPE

LINAC

TOWER FOR INSERTING BEAM PIPE

1300 cm

A

B

C

D

E

F

H G

X

Z

Y

I

Figure 4.14. LINAC system. The lettered black dots indicate the positions where theend of the beam pipe is positioned in the SK tank during the LINAC data taking.

uncertainties which makes it impossible to obtain the accuracy needed. The LINAC

system has the advantage that it injects electrons which are what being observed by

the SK detector, the energy of the injected electrons can be determined precisely, and

the number of electrons can be controlled. The LINAC system can also be used to

check the vertex and angular resolution.

4.3.1 LINAC Calibration System

Figure 4.14 gives a schematic view of the electron linear accelerator (LINAC)

system [44]. The LINAC system was adapted from a medical grade accelerator (Mit-

subishi ML-15III). It is a traveling-wave type in which electrons are accelerated by

microwaves in the acceleration tube. The electron gun was specially modified to a low

current so that the number of electrons injected into the SK tank could be reduced

84

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KLYSTRON

ELECTRON GUN

ACCELERATING TUBE

VACUUM PUMP

C1 COLLIMATORD1 MAGNET

S1 STEERING

C2 COLLIMATOR

BEAM PIPEIN ROCK

1000 mm

Figure 4.15. Schematic view of the first bending magnet of LINAC system (D1): Thisis where the beam momentum is defined.

RO

CK

C3 COLLIMATOR

M1 BEAM MONITOR

D2 MAGNET

S2 STEERING

HORIZONTAL BEAM PIPE

SUPER-KAMIOKANDE TANK

1350

mm

LEAD SHIELD

LEAD SHIELD

Figure 4.16. Schematic view of the second bending magnet of LINAC system (D2):The beam is directed to move in the horizontal direction on the top of SK tank.

to one at a time. The pulse width of the microwave is 2 µsec and the pulse rate can

be tuned between 10 and 66 Hz. The average momentum of the electrons depends

on the input power to the acceleration tube and the microwave frequency. It is in

the range from 5 to 16 MeV/c which is about the same as that of the recoil electrons

observed from solar neutrino-electron elastic scattering.

The generated electron beam is sent into the SK tank via a magnetically shielded

beam pipe which would be evacuated to 10−4 ∼ 10−5 torr. The beam pipe passes

85

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SUPER-KAMIOKANDE TANK

C4 COLLIMATORQ1 QUADRUPOLE

M2 BEAM MONITOR

D3 BENDING MAGNET

Q2 QUADRU-POLE

TURBO-MOLECULARPUMP

ROTARY PUMP

XY STEERING

HORIZONTAL BEAM PIPE

WATER LEVEL

1350

mm

Figure 4.17. Beam is bent 90 by D3, focused by Q1,Q2 and then injected into SKtank. XY is used to steer the beam to move to the center of the endcap.

through 9 m of rock and goes across the top of the SK tank. It is then bent 90 and

vertically inserted into the SK tank by using a crane. For the electron beam to follow

this path, 3 bending magnets have been installed. The D1 magnet (Figure 4.15)

bends the electron beams by 15 downward to pass through the rock. By setting the

current of the D1 magnet, it also serves as a momentum selector with two collimators

just before it. The rock blocks γ-rays generated by the collisions of the electrons with

the collimators and beam pipe. The electron beam is then bent by 15 at the D2

magnet (Figure 4.16) to go back to the horizontal direction. The electrons are further

selected by the collimators in front of the D2 magnet. The momentum spread after

D2 is about 0.5% FWHM. Lead blocks are placed around the D2 magnet to block

the γ-rays generated by the collisions of electrons with the collimators. Finally, the

electron beam is bent 90 downward by the D3 magnet (Figure 4.17) and vertically

injected into the tank. Electric currents to D2 and D3 are set to minimize the loss of

electrons in the beam. There are two quadrupole magnets (Q1, Q2) installed before

and after D3 magnet for the purpose of focusing the beam to the end of the beam

86

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pipe. A steering magnet is used to fine tune the focusing position in the end cap.

The end part of the LINAC beam line is shown in Figures 4.18 and 4.19. There are

two counters in the end cap. One is a scintillation trigger counter to trigger SK when

an electron leaves the beam pipe. The end cap’s exit window is made of a 50 µm-thick

sheet of titanium. It allows electrons to pass through without significant momentum

loss and also maintains the beam pipe vacuum. In addition to the primary scintillation

counter, four secondary counters are positioned 80 cm from the exit window. These

are used to guide calibration crews to align the beam pipe in the vertical direction

and also used to veto events containing misaligned electrons.

4.3.2 Energy Calibration By LINAC

Beam Energy Measurement

The precise electron beam energy is measured by a germanium (Ge) detector. The

Ge detector uses pure germanium crystal 57.5 mm in diameter and 66.4 mm in length

as the detection medium. This Ge detector has been calibrated by various methods.

Its energy resolution is 1.92 kev measured using 1.33 MeV γ-rays from 60Co. To

measure the beam energy, the current to D3 magnet is turned off and then reversed

to compensate for the remanent field. The beam will go horizontally on the top of

the SK tank in the beam pipe similar to the one used in the tank. The Ge detector

is placed at the end of the beam pipe. The output of the Ge detector is recorded and

digitized by a Multi-Channel-Analyzer. As there is a 500µm beryllium window in

front of the germanium crystal, electrons will lose some energy before being detected

by the germanium crystal. The energy loss has been measured by an air-core beta

87

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Titanium window

Trigger counter

HV, signal cables

Scintillationcounters

PMT

PMT

HV, signal cables

818

mm

102 mm

Figure 4.18. Side view of the of the end of the beam pipe. A scintillation counterlocated directly above the titanium window is used to trigger LINAC events.

88

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SCINTILLATOR FORVETO COUNTER

WAVE-LENGTH- SHIFTER

PMT

SCINTILLATOR FORTRIGGER COUNTER

80 mm

PMT FOR TRIGGERCOUNTER

TITANIUM WINDOW

Figure 4.19. Top view of the end of the beam pipe. The 4 PMTs on the side of thewall are used for the alignment of the beam pipe.

spectrometer using the mono-energetic β-rays from 207Bi. To establish the relation

between the current of the D1 magnet and the energy measured by the Ge detector

with the beam energy in the pipe and the total energy of electrons in the SK tank, MC

simulation has been used to model the beam energy losses in the titanium window,

the beryllium window, and also the inactive region of the germanium detector.

Figure 4.20 shows the energy spectrum measured by the Ge detector for various

beam momenta compared with MC simulation results. The γ-rays which escape from

the Ge detector and the electrons which bounce back from the surface of the crystal

cause the spread of the spectrum. The systematic uncertainties of the beam energy

is evaluated to be 20 keV by comparing different measurements. Table 4.1 gives

the summary of the beam energy measurements by the Ge detector. The difference

between the “Ge energy” and “energy in SK tank” is due to various the energy

losses. For a 8 MeV electron, MC simulation shows that it loses 185 keV in the

trigger counter, 11 keV in the titanium window, 126 keV in the beryllium window

89

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0

100

200

15.2 15.4 15.6

(MeV)

0100200300400

6 6.2

(MeV)

0

100

200

300

12.6 12.8

(MeV)

0

200

400

5 5.2

(MeV)

0

200

400

600

9.8 10 10.2

(MeV)

0200400600800

4 4.1 4.2 4.3 4.4

(MeV)

0

100

200

300

400

7.8 8 8.2

(MeV)

Figure 4.20. The observed LINAC beam energy spectrum from the Ge detector. Solidcircles show data, with statistical error bars. Histograms show the MC simulationresults. The number in the upper left corner is the beam energy.

90

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D1 current Ge energy Beam momentum Energy in SK tank(A) (MeV) (MeV/c) (MeV)

1.8 5.08 4.25 4.892.15 6.03 5.21 5.842.5 7.00 6.17 6.793.2 8.86 8.03 8.674.0 10.99 10.14 10.785.0 13.65 12.80 13.446.0 16.32 15.44 16.09

Table 4.1. Summary of the beam energy measurement. First column gives the currentfor the D1 magnet. 2nd column shows the energy measured by the Ge detector. Thethird and fourth columns give the MC calculated electron energy in the beam pipeand in the SK tank respectively.

and 27 keV in the inactive region of the germanium crystal.

SK Energy Calibration

As mentioned in the Chapter 3 on Event Reconstruction, the energy estimation

is done by relating the number of hit PMTs to the total recoil electron energy. The

relationship is built through the LINAC calibration.

LINAC data have been taken at 8 positions (A-H) as labeled in Figure 4.14. The

coordinates of these positions are listed in Table 4.2. For each position, electrons

are injected with 7 different momenta 4.1 which is defined by the current of the D1

magnet. The absolute energy of the injected electrons is measured by the germanium

detector described earlier. Figure 4.21 shows the trigger logic for the LINAC system.

The LINAC trigger can eliminate most of γ-ray events generated by the LINAC

system. The electron beam spill rate is about 60 Hz. The average number of electrons

which reach the end-cap of the beam pipe is about 0.1/bunch. The choice of this low

occupancy is to minimize triggered events with multiple electrons. LINAC data are

91

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No. x (cm) y (cm) z (cm)

A -388.9 -70.7 1228.B -388.9 -70.7 27.C -813.1 -70.7 1228.D -813.1 -70.7 27.E -1237. -70.7 1228.F -1237. -70.7 27.G -388.9 -70.7 -1173.H -1237. -70.7 -1173.I -813.1 -70.7 -1173.

Table 4.2. The injection position of the LINAC beam. The coordinates are definedin Fig.4.14.

AMP

x25

Triggercounter

Discri.-200mV

LINAC

µ-wave Attn.G.G.3µs

Coin.

LINAC Trigger

µ-wave Trigger

G.G.3µs

Figure 4.21. The trigger logic used in LINAC calibration. The LINAC trigger is usedto select LINAC events in the data. The microwave trigger is used for the purpose ofestimating the background from the LINAC system.

92

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-1500

-1000

-500

0

500

1000

1500

-1500 -1000 -500 0 500 1000 1500

x(cm)

Z (

cm)

0200040006000

-1500 -1000 -500 0 500 1000 1500

010

0020

0030

00

-150

0-1

000

-500

050

010

0015

00

X (cm)

Figure 4.22. Vertex position distribution from LINAC data taken at (x, y, z) =(−388.9cm,−70.7cm, +27cm). The beam momentum is 16.31 MeV/c. Projectionsof the scatter plot are shown on the right and underneath. The scatter plot limitscorrespond to the limits of the ID.

reconstructed with the same event reconstruction algorithms described in the Chapter

on Event Reconstruction. Figure 4.22 shows a typical two-dimensional (x-z plane)

projection of the vertex distribution for one data set taken at one position with a

specific momentum. Also shown are the one-dimensional projections on the x- and

z-axis.

Time information corrected by the time of flight (TOF) from the end of the beam-

pipe is used to reject events with multiple electrons. As shown in Figure 4.23, electrons

that left the end of the beam pipe within a few tens of nanoseconds can be clearly

identified using the timing distribution. Events are rejected as multiple electron events

if multiple peaks with more than 30% of expected signal are found to be more than

93

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1 electron

05

101520

700 800 900 1000 1100 1200 1300 1400 1500nsec

2 electron

05

101520

700 800 900 1000 1100 1200 1300 1400 1500nsec

3 electron

05

101520

700 800 900 1000 1100 1200 1300 1400 1500nsec

Figure 4.23. Examples of TOF subtracted distributions of the hit PMTs for LINACtriggered events containing one, two and three electrons.

30 ns apart in a single event. About 5% of the LINAC triggered events are multiple

electron events.

A simple interpolation between the beam energy and Neff (as described in the

Chapter 3on Event Reconstruction) of the LINAC data events is not used to deter-

mine the SK energy scale since, a) there is about a 1% non-uniformity of Neff in

the fiducial volume, b) the number of the injection positions is limited and c), the

injection direction is only downward for the LINAC calibration data set. The energy

scale should be direction- and position-independent in the fiducial volume of the SK

detector. In order to obtain the absolute energy scale (the relation between effective

number of PMT hits Neff to the total recoil electron energy), the resulting LINAC

calibration data set for the 8 positions and 7 energies is used to tune parameters used

in the detector MC simulation. The absolute energy scale can then be derived from

94

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0

250

500

750

1000

1250

1500

1750

2000

2250

20 40 60 80 100 120

effective hit

nu

mb

er o

f h

its

Figure 4.24. Neff distribution for the MC simulated electron events of total energy10 MeV. A Gaussian fit is applied to the distribution to the get the peak value of thedistribution.

MC simulation whose parameters are tuned to reproduce the obtained LINAC data.

The MC simulation of the detector including the LINAC system (beam pipe in

the tank, LINAC trigger, the end cap etc.) is done for all the positions and beam

energies. The parameters in the MC that could affect energy scale are:

• Light attenuation length

• PMT collection efficiency and reflectiveness of various detector materials

• Coefficients of light scattering and absorption in the water

Various sets of these parameters are used by many MC simulations with the

simulation data analyzed the same way as the LINAC data, and the parameter set

that best reflects the observed distribution of data (not only the energy scale, but also

95

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the angular resolution) is selected. This tuning is done for electrons with total energy

of 4, 5, 6, 7, 10, 15, 30 and 50 MeV. Figure 4.24 shows the Neff distribution for the

MC simulated electron events of total energy 10 MeV. A Gaussian fit is applied to the

distribution to get the peak value of the distribution. The value of Neff and energy

values obtained are then fitted by a 4th order polynomial function to establish the

relationship between Neff and the total electron energy (energy scale) (Figure 4.24).

Figure 4.25 shows the energy distributions for 7 beam energies of LINAC calibra-

tion data and MC simulated data at the position (x = −1237.cm, y = −70.7cm, z =

+1228.cm). The data and MC agree very well with each other spanning the entire

width of the energy distribution.

The LINAC calibration is also used to evaluate the systematic errors from the re-

maining discrepancies between data and MC. Figure 4.26 shows the absolute energy

scale differences (MC−DATADATA

) between data and MC at various positions and energies.

All the error bars around the data points are statistical errors. The position-averaged

deviation in energy scale is done by assigning a weight based on the volume surround-

ing a given point (Figure 4.27). The inner dotted lines are the combined statistical

errors. The right-most mark is the combined deviation for all the positions and beam

energies. The outer lines give the systematic error. The position dependence of the

energy scale is shown in Fig.4.28. All points are within ±0.5%. These values will be

used to estimate energy correlated systematic errors.

Systematic Uncertainties

The systematic errors for the absolute energy come from the following sources:

96

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0200400600800

0 5 10 15 20 25

energy (MeV)

16.09 MeV

0200400600800

0 5 10 15

energy (MeV)

6.79 MeV

0250500750

1000

0 5 10 15 20 25

energy (MeV)

13.44 MeV

0250500750

1000

0 5 10 15

energy (MeV)

5.84 MeV

0250500750

1000

0 5 10 15 20 25

energy (MeV)

10.78 MeV

0250500750

1000

0 5 10 15

energy (MeV)

4.89 MeV

0250500750

1000

0 5 10 15 20 25

energy (MeV)

8.67 MeV

Figure 4.25. Energy distributions for 7 beam energies of LINAC calibration dataand MC simulated data. The beam injection position is at (x = −1237.cm, y =−70.7cm, z = +1228.cm). The cross marks show data with statistical error bars.The histogram shows MC.

97

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-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

4 6 8 10 12 14 16 18

total energy (MeV)

(MC

-LIN

AC

)/L

INA

C

ABCDEFGH

Figure 4.26. The deviation of the absolute energy scale between data and MC for allpositions and energies.

98

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-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

4 6 8 10 12 14 16 18

total energy (MeV)

(MC

-LIN

AC

)/L

INA

C (Energy dependence)(a)

combined

Figure 4.27. The position-averaged deviation of the absolute energy scale betweendata and MC as a function of energy.

99

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-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 2 4 6 8 10

H F E D C G B A

(b)

position tag

((M

C-L

INA

C)/

LIN

AC

)

(position dependence)

Figure 4.28. The position-dependence of the absolute energy scale deviation betweendata and MC.

100

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(A) Uncertainty in the beam energy measurement. This is estimated to be 20 keV

by measuring the beam energy 5 times and taking the full width of the D1

magnet current distribution.

(B) Backgrounds introduced by LINAC calibration system. The sources of these

backgrounds are the γ-rays produced by the run off electrons hitting the col-

limators and the end of the beam pipe. This has been estimated by taking

data with an “empty” (microwave) trigger and with a “random” (clock) trig-

ger. When the former data is taken, a trigger is issued only by the microwave

pulse from the LINAC, as injection is about 0.1 per microwave, 90% of events

thus obtained with this trigger are empty of real electrons but containing pos-

sible background. The random triggered data only contains dark noise from

SK electronics and ID PMTs. A MC simulation of LINAC events without dark

noise is added to both of these data sets event-by-event. By comparing the

peak energy of the energy distribution of “microwave triggered data + MC”

with “random triggered data + MC”, the systematic error in the absolute en-

ergy scale is conservatively estimated to be 0.16%.

(C) Uncertainty in the reflection from the endcap. This poses the most serious

uncertainty to the absolute energy scale. Through MC simulation, it is found

that at 5 MeV/c, 4.7% of Cherenkov photons hit the endcap. Although the

reflectivity of stainless steel and the titanium window can be measured precisely,

the possibility of a small air bubble of unknown size trapped around the titanium

window changes the reflectivity of the endcap. Two sets of MC simulations are

101

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beam momentum fraction hitting error due to total systematic(MeV/c) endcap(%) reflectivity(%) error(%)

5.08 4.7 ±0.68 ±0.716.03 3.3 ±0.40 ±0.557.00 2.8 ±0.22 ±0.448.86 1.3 ±0.18 ±0.3310.99 0.88 ±0.11 ±0.2713.65 0.67 ±0.08 ±0.2416.31 0.51 ±0.06 ±0.21

Table 4.3. Summary of systematic errors obtained from LINAC calibration for variousbeam momenta. The second column shows the percentage of Cherenkov photonshitting the endcap, the third column shows the systematic error due to the uncertaintyin the reflectivity of the endcap, and the fourth shows the total systematic error forthe absolute energy scale calibration.

done with cases of no air bubble and maximum size bubble. And the uncertainty

is conservatively estimated from these two simulations. The results are given in

Table 4.3.

Time And Directional Variations of Energy Scale

Since the LINAC calibration can only be done very few times due to it’s time

consuming nature, other means are required to check the stability of the energy scale.

Spallation events are electrons, positrons, γ-rays and invisible neutrons from the

decay of radioactive nuclei produced by cosmic ray muons passing through the SK de-

tector. They are produced uniformly in the detector and the β decays occur isotrop-

ically which make them ideal to check the time and directional uniformity of the

energy scale.

Spallation events are selected by the following criteria:

1. The time difference between a spallation candidate event and a muon event is

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less than 0.1 sec.

2. The distance from the reconstructed vertex of a spallation candidate event to

the reconstructed muon track is less than 3 m.

3. The spallation likelihood is larger than a threshold value.

The time variation is checked by dividing the spallation data sample into small

samples according to the time. The energy spectrum of that period multiplied by

a scale factor is compared with the whole data sample using a χ2 test. Figure 4.29

shows the time variation of the energy scale factor which is less than 0.5% over the

entire run time.

The time variation of the energy scale can also be studied by examining the energy

spectrum of electrons from the decay of cosmic ray muons in the fiducial volume. The

data sample used to obtain the spectrum is the same as that used to measure the water

transparency. The data sample obtained from decay electrons has high statistics and

low background. Figure 4.30 shows the time variation of the energy scale factor of the

decay electron energy spectrum. The error bars include only statistical error. From

this figure, the time variation of the energy scale is less then ±0.5% which is also

consistent with the result from spallation events.

As the spallation events have uniform directional distribution, they can be used

to check the energy scale directional dependence by dividing the data sample into

sub-samples according to their directional properties and then compare them with

the whole data sample. Figures 4.31 and 4.32 show the energy scale as a function of

The azimuthal angle and zenith angle. The error bars show only the statistical error.

103

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-2-1.5

-1-0.5

00.5

11.5

2

200 400 600 800 1000 1200 1400 1600 1800 2000

Time

days since 1996/1/1

ener

gy

scal

e d

iffe

ren

ce (

%)

(a)

Figure 4.29. The time variation of the energy scale obtained from spallation events.

The directional dependences are within ±0.5%.

4.3.3 Energy Resolution

The energy resolution defined as follows is also studied using the LINAC calibra-

tion data.

Resolution =σenergy

Eobserved(4.7)

Here, σenergy is the width of the Gaussian function which is obtained by fitting to the

energy distribution and Eobserved is the peak energy. Figure 4.33 shows the energy res-

olution deviation between data and MC, MC−DATADATA

, at various positions and energies.

Figure 4.34 shows the position-averaged energy resolution deviation as a function of

energy. All position-averaged deviations between data and MC are consistent with

each other within 2.0%.

4.3.4 Vertex Resolution

The LINAC calibration can also be used to check the vertex reconstruction. Figure

4.35 shows the distribution of the reconstructed vertex to the end point of the beam

pipe which is real event vertex. for injecting position (-1237 cm, -70.7 cm, +1228

104

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Year

Mea

n P

MT

Hit

s (f

or

Mic

hel

Ele

ctro

ns)

256

258

260

262

264

266

268

270

272

274

1996 1997 1998 1999 2000 2001 2002

Figure 4.30. The time variation of the energy scale obtained from decay electronevents.

-5

-4

-3

-2

-1

0

1

2

3

4

5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1cos θz

(%)

Figure 4.31. The zenith angle dependence of the energy scale obtained from spallationevents.

105

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-5

-4

-3

-2

-1

0

1

2

3

4

5

0 50 100 150 200 250 300 350

φ (degree)

(%)

Figure 4.32. The azimuthal angle dependence of the energy scale obtained fromspallation events.

cm). Cross marks show LINAC data. Histograms show MC data. Vertex resolution

is defined as the radius of the sphere centered at the end point of the beam pipe

which includes 68% of the total number of reconstructed vertex. Figure 4.36 shows

the position averaged vertex resolution deviation between LINAC data and MC data

as a function of energy.

4.3.5 Angular Resolution

The angular reconstruction can be checked by the LINAC system as the beam

direction is known precisely downward. Figure 4.37 shows the distribution of the

reconstructed direction with respect to the beam pipe for injecting position (-1237

cm, -70.7 cm, +1228 cm). Cross marks show LINAC data. Histograms show MC

data. The angular resolution is defined as the angle which includes 68% of all the

106

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Figure 4.33. The deviation of the energy resolution between data and MC for allpositions and energies.

107

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-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

4 6 8 10 12 14 16 18

combined

(c)

total energy (MeV)

(MC

-LIN

AC

)/L

INA

C

Figure 4.34. The position-averaged deviation of the energy resolution between dataand MC as a function of energy.

reconstructed directions around the beam direction. Figure 4.38 shows the position

averaged angular resolution deviation between LINAC data and MC data as a function

of total energy. LINAC data and MC data agree well with all the deviations are within

5%.

4.4 Calibration Using Deuterium-Tritium (DT) Gen-

erator

Though the LINAC system can calibrate the detector with high precision, yet it

can only be done with downward direction and requires lots preparation and man-

power in doing the calibration. The DT generator system is developed to check the

directional dependence of the energy scale and cross check and monitor the LINAC

calibration results. DT generator uses the decay of 16N as the source of energy cali-

108

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0

500

1000

0 100 200 300 400 500

distance (cm)

16.09 MeV

0

200

400

600

800

0 100 200 300 400 500

distance (cm)

6.79 MeV

0

500

1000

1500

0 100 200 300 400 500

distance (cm)

13.44 MeV

0200

400600800

0 100 200 300 400 500

distance (cm)

5.84 MeV

0250500750

1000

0 100 200 300 400 500

distance (cm)

10.78 MeV

0

200

400

0 100 200 300 400 500

distance (cm)

4.89 MeV

0

250

500

750

1000

0 100 200 300 400 500

distance (cm)

8.67 MeV

Figure 4.35. The distribution of the reconstructed vertex to the end point of thebeam pipe for injecting position (-1237 cm, -70.7 cm, +1228 cm). Cross marks showLINAC data. Histograms show MC data.

109

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-0.3

-0.2

-0.1

0

0.1

0.2

0.3

4 6 8 10 12 14 16 18

total energy (MeV)

(MC

-LIN

AC

)/L

INA

C

(d)

Figure 4.36. The position averaged vertex resolution deviation between LINAC dataand MC data as a function of total energy.

bration.

In order to check for the directional dependence of the energy scale and to cross-

check the LINAC calibration results, the decay of 16N is used. 16N is produced by an

(n,p) reaction on 16O in the SK water.

The fusion reactions which produce 16N are as follows:

3H + 2H → 4He + n.

The energy of the generated neutron is 14.2 MeV. It interacts with 16O in the

water and produce 16N. The neutron source in the DT generator, the deuterium-

tritium neutron generator (DT generator,MF Physics Model A-211), can produce

about 106 neutrons in each pulse with a rate up to 100 Hz.

n + 16O → 16N + p

110

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0

500

1000

0 50 100 150

theta (degree)

16.09 MeV

0200

400600

800

0 50 100 150

theta (degree)

6.79 MeV

0

500

1000

0 50 100 150

theta (degree)

13.44 MeV

0200400600800

0 50 100 150

theta (degree)

5.84 MeV

0250500750

1000

0 50 100 150

theta (degree)

10.78 MeV

0

200

400

600

0 50 100 150

theta (degree)

4.89 MeV

0200400600800

0 50 100 150

theta (degree)

8.67 MeV

Figure 4.37. Reconstructed angular distribution for injecting position (-1237 cm, -70.7cm, +1228 cm). Cross marks show LINAC data. Histograms show MC data.

111

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-0.15

-0.1

-0.05

0

0.05

0.1

0.15

4 6 8 10 12 14 16 18

total energy (MeV)

(MC

-LIN

AC

)/L

INA

C

(d)

Figure 4.38. The position-averaged angular resolution deviation between LINAC dataand MC data as a function of total energy.

16N most probably decays into 16O, an electron with maximum energy 4.3 MeV

and a γ-ray of energy 6.1 MeV.

16N → 16O + e− + γ + νe

16N’s decay modes are summarized in Table 4.4.

Figure 4.39 shows a schematic view of the DT generator. The DT generator is

Fraction (%) Jpi →Jp

f ∆I Eγ Type

66.2 2− → 3− +1 6.129 GT allowed28.0 2− → 0+ -2 none GT 1st forbidden4.8 2− → 1− +1 7.116 GT allowed1.06 2− → 2− +0 8.872 F+GT allowed0.012 2− → 0+ -2 6.049 GT 1st forbidden0.0012 2− → 1− +1 9.585 GT allowed

Table 4.4. 16N β decay modes. GT means Gamow-Teller transition and F meansFermi transition.

112

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150

cm

Ion Source

Accelerator

Vsource

Vtarget

ElementGas Reservoir

Anode

Anode

Target

Vaccel

AcceleratorHead

PulseForming

Electronics EnvelopeVacuum

AlEndcone

HousingStainless

O-Ring

O-Ring

Spacer

DT Neutron Accelerator

TransformerOil Fill

PVCEndcap

FeedthruEpoxy

SensorLeak

StainlessEndcap

16.5 cm

Figure 4.39. Schematic view the DT generator.

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Energy(MeV)

Num

ber

of e

vent

s

0

1000

2000

3000

4000

5000

6000

7000

8000

2 4 6 8 10 12 14

Figure 4.40. Energy distribution from DT calibration. The DT generator is fired atthe position (x = −388.9cm, y = −70.7cm, z = 0cm). The DT generator was firstput in use when the solar analysis energy threshold was 5.5 MeV.

raised and lowered by a crane. During calibration, the DT generator is raised after

firing 2 m away from the neutron production point to minimize reflection from the

DT generator. Data is taken withing a time window 10 ∼ 40 sec after the firing.

Figure 4.40 shows the observed energy spectrum for a position (x = −388.9cm, y =

−70.7cm, z = 0cm). MC simulation takes into account the reflection of Cherenkov

photons by the DT generator housing. The energy distributions of data and MC are

fit with a Gaussian function between 5.5 MeV and 9.0 MeV. The peak value of each

energy distribution is taken for the evaluation of the energy scale.

Figure 4.41 shows position dependence of the absolute energy scale deviation.

The radial position dependence of the energy scale from DT generator agree with

MC within ±0.5%. The variation of the absolute energy scale as a function of z is

within ±1.0%. They are consistent with the systematic errors for the energy scale

114

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Contamination from natural < 0.01%background16N decay model in MC ±0.1%Decay lines without model < 0.01%Shadowing of Cherenkov photons ±0.1%Data selection ±0.1%Radioactive background from the ±0.05%DT generator

Table 4.5. Summary of systematic errors for DT calibration

obtained by the LINAC system. Fig.4.42 shows the azimuthal angle and zenith angle

dependence of the absolute energy scale deviation. The variation of the energy scale

in the fiducial volume is within ±0.5%.

Tab.4.5 summarizes the systematic errors of the absolute energy scale obtained

by the DT calibration system.

4.5 Trigger Efficiency

There are two types of trigger for the solar neutrino data: Low Energy Trigger

(LE trigger) and Super Low Energy Trigger (SLE trigger). The trigger efficiency has

been measured using the Ni-Cf system and the DT calibration system.

The trigger efficiency is defined as follows:

eLE, SLE =NLE, SLE

Nspecial trigger(4.8)

where e is the trigger efficiency. NLE, SLE is the number of events triggered by

both LE(SLE) trigger and a special low energy trigger with a threshold of -150 mV.

Nspecial trigger is the number of events triggered by the special low energy trigger.

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R-position (cm)

MC

-DA

TA

/DA

TA

(%)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-200 0 200 400 600 800 1000 1200 1400 1600Z-position (cm)

MC

-DA

TA

/DA

TA

(%)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-1500 -1000 -500 0 500 1000 1500

Figure 4.41. The position dependence of the absolute energy scale deviation measuredby the DT calibration.

Azimuthal Angle

MC

-DA

TA

/DA

TA

(%)

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 50 100 150 200 250 300 350Zenith Angle

MC

-DA

TA

/DA

TA

(%)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-80 -60 -40 -20 0 20 40 60 80

Figure 4.42. The angular dependence of the absolute energy scale deviation measuredby the DT calibration.

116

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0

0.2

0.4

0.6

0.8

1

4 5 6 7 8 9 10

DATAMC

Energy (MeV)

LE

tri

gg

er e

ffic

ien

cy

Figure 4.43. The LE trigger efficiency as a function of energy measured by the DTgenerator for position (35.3,−70.7, 41.0).

Figure 4.43 shows the LE trigger efficiency as a function of energy for a typical

data run. The efficiency is 99.8% for energy of 6.5 ∼ 7.0 MeV. The LE trigger

efficiency is 100% above 7 MeV.

A trigger simulator is used to reproduce the energy and position dependence of the

trigger efficiency seen in the data. The open circles in Figure 4.43 show the simulated

trigger efficiency. The deviation between the data and MC is +0.4−1.7% in the energy

region from 6.5 MeV to 7.0 MeV.

The SLE trigger was installed in May 1997 and the threshold has been changed

several times. Table 4.6 summarizes the history of the intelligent trigger (IT) which

is a filtering procedure used to discard SLE triggered events fitted outside the fiducial

volume. Figure 4.44 shows the energy dependence of the SLE trigger efficiency for

different trigger threshold. Filled circles show the data and open circles are for the

117

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MC results. The deviation between the data and MC is +3.2−1.6% in the energy range

from 5.0 MeV to 5.5 MeV, and +0.9−0.5% from 5.5 MeV to 6.0 MeV. The SLE trigger

efficiency is 100% above 6 MeV.

Start Number Online Filtered Hardware Analysis SLEDate of IT Trigger Trigger Threshold Threshold Livetime

Machines Rate (Hz) Rate (Hz) (MeV) (MeV) (%)4/96 0 10 10 5.7 6.5 05/97 1 120 15 4.6 5.5 96.52/99 2 120 15 4.6 5.5 99.39/99 6 580 43 4.0 5.0 99.959/00 12 1700 140 3.5 4.5 99.99

Table 4.6. History of the Intelligent Trigger system [35].

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0

0.2

0.4

0.6

0.8

1

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

DATAMC

threshold:-260mV

Energy (MeV)

SL

E t

rig

ger

eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

DATAMC

threshold:-250mV

Energy (MeV)

SL

E t

rig

ger

eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

3 4 5 6 7 8

DATAMC

threshold:-222mV

Energy (MeV)

SL

E t

rig

ger

eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

3 4 5 6 7 8

DATAMC

threshold:-212mV

Energy (MeV)

SL

E t

rig

ger

eff

icie

ncy

Figure 4.44. The SLE trigger efficiency as a function of energy.

119

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Chapter 5

Data Reduction

The data from the on-line system are sent out of the mine to the off-line system via

optical fiber. The off-line system first converts the ADC and TDC counts of the ATM

data into the charge (pC) and time (nsec) using TQ tables obtained by various detec-

tor calibrations [35]. Afterwards, these data are sent for event reconstruction using

the algorithms described in the Chapter 3 on Event Reconstruction. The resulting

data set is then ready for use by the solar neutrino group. The data set used for this

analysis represents the entire Super-Kamiokande -I period ranging from May 31, 1996

to July 15, 2001 with a live time of 1496 days.

The data set for solar neutrino analysis includes all the low energy events triggered

by the detector system. Therefore, it includes background events from various sources.

Major sources of backgrounds for the solar neutrino events are the following:

• Noise generated by various electronics and by PMT flashing.

• Cosmic ray muons that reached the detector.

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• By-products from these cosmic muons, eg., decay electrons from the stopping

muons.

• Muon-induced spallation products.

• Radioactivity from the detector materials and surrounding rocks.

5.1 Data Set

The data set is organized as series of runs with each run at most 24 hours long.

Each run is subdivided into subruns, which consist of 1 to 10 minute online data.

The size of the subrun is predetermined for easy file management and its run-time

length depends on the trigger rate.

The first reduction applied to the data set is a data quality check called the bad

run selection. There are two ways of implementing this quality check, one is done

by the online process called ”real-time bad run selection” (BADSEL), the other is

manual bad run selection.

5.1.1 Real Time Bad Run Selection

The criteria used for the real-time bad run selection are as follows:

1. Subrun run-time is less than 30 seconds (short subrun)

2. Live-time is 0 seconds (abnormal dead-time)

3. Total run-time is less than 300 seconds (short run)

4. Abnormal flasher event rates (flasher event rates > 0.15 Hz)

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5. Abnormal NSratio (The meaning will be explained later in the Chapter) events

rates

6. Abnormal uncompleted event rates

7. Abnormal anti mis-match event rates

8. Abnormal low-goodness event rates

9. Abnormal number of bad channel

10. Time difference between TQreal and muon vector file is more than 20%

11. Muon rate is less than 1 Hz

12. No muon information

These criteria are applied to all the normal runs (excluding calibration runs and

test runs) by the online processes. The total run time lost due to this bad run selection

is 27.3 days.

5.1.2 Manual Bad Run Selection

For data up to run 3608 (March 1997) the manual bad run selection was done

by several persons with independent criteria. After that, a collective criteria were

established for the bad run selection. Manual bad run selection is done by visually

check the various rates and look for obvious abnormal rates change. More stringent

checks are done in the first reduction 5.2. It consists of the following checks by the

low energy shift personnel.:

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• Log book check

Runs are normally ended with comment “normal end” or “bad/abnormal end”

by the SK shift person. This information is referred to by the low energy

shift person to determine the run quality of the data. For the runs with

“bad/abnormal end” the last 2 subruns are chosen as bad subruns.

• Dark noise rate check

The dark rates are calculated by the BADSEL process for each run using the

hits just before muon events. The normal dark rate is in the range of 3.2∼3.7

kHz.

• Number of ID/OD bad channels

Runs with abnormal number of bad channels are removed as this is usually

caused by malfunction of the electronics system. The criteria for this cut

changes to reflect the number of dead ID and OD PMTs.

• Muon event rate check

Abnormal muon rates are usually the results of incorrect muon analysis. The

runs are chosen as bad runs because the spallation cut could not be properly

applied.

• Delta-T cut event rate check (also see 5.2.3 for details)

If a run consists of a lot of noisy events, a lot of events will be cut by delta-T

cut. So any subrun with an abnormal delta-T cut event rate will be removed.

• Incomplete event rate check

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Incomplete events are usually signs of DAQ system malfunction. Subruns with

abnormal number of incomplete events are removed.

• Strong flasher event check

Strong flashers are identified by those PMTs have abnormal number of hits in

one subrun. If the flasher is extremely intense, it could not be totally removed

by the flasher cuts. Since flasher events have strong directionality, if the event

direction overlaps with the direction of the Sun, it could be mistaken as solar

neutrino events.

• TQreal summary file list and data file list comparison

The live time is calculated using tqreal summary files. They are generated

independently from the data files. The list check could reveal errors in the data

reprocessing.

The last step is to check if the SLE trigger working properly within each subrun.

The total lost time due to manual bad run selection is about 112 days.

5.2 First Reduction

5.2.1 Total Charge Cut

The events for low energy analysis are those with total charge less than 1000 p.e.

This criteria is used to eliminate cosmic muon events and atmospheric neutrino events

from the data sample. 1000 p.e. roughly corresponds to a 130 MeV electron event

which is much higher than the energy of the typical events due to solar neutrinos. So

the cut efficiency for solar neutrino events is 100 %.

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1

10

10 2

10 3

10 4

0 1 2 3 4 5 6

log Q

CUT

Figure 5.1. Total charge distribution of a typical event sample with the hatchedregion shows the events for solar analysis

5.2.2 Fiducial Volume Cut

The fiducial volume is defined as the volume 2 m inward from the ID walls, which

is 28.9 m in diameter and 32.2 m in height with a volume of 22.5 kton. Events

with reconstructed vertex outside the fiducial volume are discarded. Those events

are usually γ-rays from the surrounding rock and PMTs. Figure 5.2 shows the ver-

tex distribution before and after applying the fiducial volume cut for a typical data

sample.

5.2.3 Time Difference Cut

The time difference cut eliminates those events occur within 50 µsec of previous

low energy events. It removes the decay electron events from the the muons and

ringing events from electronic noise after high energy muon events. Figure 5.3 shows

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1

10

10 2

10 3

10 4

-2000 -1500 -1000 -500 0 500 1000 1500 2000

z(cm)

CUT CUT

10 2

10 3

10 4

10 5

0 200 400 600 800 100012001400160018002000

r(cm)

CUT

Figure 5.2. Vertex distributions as function of z and r for a typical data sample. Thehatched regions show the distributions after the fiducial volume cut

10-1

1

10

10 2

10 3

10 4

10 5

10 6

10 7

10 8

2 3 4 5 6 7 8 9 10

log(time difference (nsec))

nu

mb

er o

f ev

ents

50µsec

Figure 5.3. Time from the previous event (∆T ) distribution. If ∆T < 50µsec, theevent will be cut.

126

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the time from the previous event distribution for a typical data sample. The dead

time due to this cut is about 0.7 % of the total livetime.

5.2.4 Veto Flagged Event Cut

Events with the veto trigger set are cut from the data sample. These are normally

events from calibration and test runs.

5.2.5 Pedestal Event Cut

Pedestal events are automatically taken every half hour to adjust for the tem-

perature fluctuation in the electronic huts, therefore events with pedestal flag are

removed.

5.2.6 Incomplete Event Cut

These events are usually due to either the inner detector or the outer detector

being turned off or have incomplete event information from ATM.

5.2.7 OD Triggered Cut

Events with the OD trigger set, which means it has more than 19 OD-PMT-hits

in a 200 nsec window, are rejected in order to remove those cosmic muons with less

than 1000 p.e..

5.2.8 Noise Event Cut and Clustered ATM Hit Event Cut

These cuts are developed to cut those events due to electronic noise such as PMT

flashing, turning on and off the fluorescent lights in the electronic huts, etc. One

characteristic of these events is that a number of PMT hits have smaller charge

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1

10

10 2

10 3

10 4

10 5

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

CUT

10

10 2

10 3

10 4

10 5

10 6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ATM ratio

CUT

Figure 5.4. (a) N/S Noise Ratio Distribution (b) ATM Ratio Distribution. Thearrows point to the events being kept for solar neutrino analysis.

deposited in the PMTs, so a variable is defined as follows to check the noise level:

N/S =Number of Hit Channels With |QPMT| < 0.5 p.e.

Total Number of Hit Channels(5.1)

Figure 5.4(a) shows N/S ratio distribution. If N/S is greater than 0.4, then the

event is removed.

Usually noise events are due to the malfunction of one ATM board, so a lot of

hits will come from one ATM. The following criteria is used to remove those events:

ATMratio = Max(Number of Hit in One ATM Board

Number of Channels in That ATM Board) > 0.95 (5.2)

Figure 5.4(b) shows the ATM ratio distribution and the cut criteria.

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NUM 18RUN 2109SUBRUN 2EVENT 7835DATE 96-Jul- 5TIME 15:49:26TOT PE: 136.8MAX PE: 21.7NMHIT : 88ANT-PE: 176.1ANT-MX: 11.8NMHITA: 35

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

Figure 5.5. Event Display of a Typical Flasher Event.

5.2.9 Flasher Event Cut

The flasher events originate from PMTs’ flashing, which emit light due to electrical

discharge of the dynodes. Figure 5.5 shows the event display of a typical flasher event.

The characteristics of flasher events is that one hit PMT has a high value of charge,

with a cluster of surrounding PMTs being hit. Figure 5.6 shows the scatter plot of

the maximum charge vs the number of hit PMTs around the maximum charged PMT

for a data sample with flasher (a) and a normal data sample (b). Also shown in the

(a) is the criteria used to select the flasher events.

5.2.10 Goodness Cut

The goodness (see Eq. 3.3 for definition) value of the reconstructed vertex shows

how well the event’s vertex has been reconstructed. Low goodness value means the

event could not be reliably reconstructed, so the event is not a good event. Figure 5.7

129

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Figure 5.6. Scatter plot of maximum charge vs the number of PMTs around themaximum charge PMT. (a) Distribution from a sample containing flasher events. (b)Distribution from a normal data sample. The line in (a) shows the cut criteria.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

goodness

CUT

Figure 5.7. Vertex goodness distribution from a typical data sample.

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NUM 1RUN 1742EVENT 604DATE 96-May-31TIME 4:32:18

TOT PE: 155.9MAX PE: 6.8NMHIT : 116ANT-PE: 74.8ANT-MX: 8.5NMHITA: 22

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

DIR:-0.86,-0.14, 0.50X: 963.1cmY: -895.2cmZ: -375.7cmR: 1314.9cmNHIT: 48good: 0.69

NUM 309RUN 1743EVENT 124510DATE 96-Jun- 1TIME 0:59:57

TOT PE: 124.2MAX PE: 12.6NMHIT : 94ANT-PE: 184.0ANT-MX: 10.9NMHITA: 37

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

DIR:-0.92, 0.40,-0.07X: 1205.2cmY: -688.2cmZ: -289.4cmR: 1387.8cmNHIT: 32good: 0.63

Figure 5.8. An example of the directional test to eliminate flasher events. Left figureshows a well constructed event. Right figure shows a badly constructed event, aflasher event.

shows the goodness distribution from a typical data sample and events with goodness

< 0.4 are cut from data set.

5.2.11 Second Flasher Event Cut

For a normal event, the hit PMTs should be uniformly distributed along the

reconstructed direction. A flasher event would cause an uneven distribution of hit

PMTs. The uniformity is checked by the Kolmogorov-Smirnov (KS) test. An example

of the KS test is shown in Figure 5.8. The left figures show a well-constructed good

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0

5000

10000

15000

20000

25000

30000

35000

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

Figure 5.9. DIRKS distribution for a typical data sample. The histogram shows thedistribution from MC data sample.

event. On the bottom, the figure shows the cumulative distribution of the number

of hit PMTs as a function of the azimuthal angle about the reconstruct direction.

Ideally, for the uniform distribution, the hit PMTs will be on the broken lines. The

right figures show a typical flasher event. A variable DIRKS is introduced to represent

the azimuthal deviation of hit PMTs from the ideal case. The cut criteria is chosen

as follows:

DIRKS ≥ 0.25 and goodness < 0.6

Figure 5.9 shows the DIRKS distribution for a data sample and MC data sample.

Figure 5.10 shows the event distribution of the cosine of z (dirz) before and after

applying the second flasher cut. The small peak around dirz = 0.7 disappears after

the cut.

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0

100

200

300

400

500

-1 -0.5 0 0.5 10

100

200

300

400

500

600

700

-1 -0.5 0 0.5 1

d

A B

Ent

ries

Ent

ries

direction cosine of z direction cosine of z

Figure 5.10. The cosine of z distributions before (A) and after (B) applying the secondflasher cut.

5.3 Spallation Cut

When energetic cosmic muons pass through the detector, they could interact with

the 16O in the water as follows:

µ + 16O → µ + X + ......, (5.3)

where X represents radioactive nuclei. A summary of the possible nuclei is listed

in Table 5.1 [45]. The unstable nuclei decay by emitting electrons with half lives in

the range of 0.001 to 14 sec and energies in the order of MeV. As they are produced

along the track of the muons, they are called “spallation events”. As the β decay

events from these spallation events are very similar to the recoil electron events from

the solar neutrino-electron elastic scattering, they are one of the major source of

background to the solar neutrino data sample.

The characteristics of these spallation events are their temporal and spatial corre-

lation with the parent cosmic muon events, so a likelihood method is used to identify

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Isotope Half Life(sec) Decay Mode Kinetic Energy(MeV)82He 0.122 β− 10.66 + 0.99 (γ)

β− n (11%)83Li 0.84 β− 12.5 ∼ 1385B 0.77 β+ 13.7393Li 0.178 β− 13.5 (75%)

11.0 + 2.5 (γ)β− n ∼ 10 (35%)

96C 0.127 β+ p 3 ∼ 13

113 Li 0.0085 β− 20.77 (31%)

β− n ∼ 16 (61%)114 Be 13.8 β− 11.48 (61%)

9.32 + 2.1 (γ) (29%)124 Be 0.0114 β− 11.66125 Be 0.0204 β− 13.37127 N 0.0110 β− 16.38135 B 0.0173 β− 13.42138 O 0.0090 β− 8 ∼ 14145 B 0.0161 β− 14.07 + 6.09 (γ)156 C 2.449 β− 9.82 (32%)

4.51 + 5.31 (γ)166 C 0.7478 β− ∼ 4167 N 7.134 β− 10.44 (26%)

4.27 + 6.13 (γ) (68%)

Table 5.1. Summary of spallation products [45].

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them. There are three parameters used in this likelihood function:

• ∆L : The closest distance from the low energy spallation candidate event to

the reconstructed track of the preceding muon event. Spallation products are

produced along the path of the muon events, so they have strong spatial corre-

lation.

• ∆T : Time difference between the low energy spallation candidate event and

the preceding muon event. Most spallation products have rather short half lives

and therefore are strongly correlated with parent muon events in time.

• Qres: Residual charge of the preceding muon event.

Qres = Qtotal − Qunit × Lµ, (5.4)

where Qtotal is the total charge deposited by the muon in the SK detector, Qunit

is the expected amount of charge deposited in the SK detector by the muon

per unit length, typically 24.1 p.e./cm, and Lµ is the reconstructed path length

of the muon. A positive value of Qres indicates that the muon probably inter-

acts with 16O along its path losing some of its energy and therefore spallation

products are produced.

For muon events without a reconstructed track, only ∆L and ∆T are used for the

evaluation of the likelihood function. Compared with the solar neutrino events, the

spallation events are expected to have shorter ∆L, ∆T and larger Qres. So, for each

event in the data sample, the preceding 200 muon events are used to calculate the

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0

1000

2000

3000

4000

5000

-4 -2 0 2 4 6

CUT

Spallation likelihood1

10

10 2

10 3

10 4

-4 -2 0 2 4 6

CUT

Spallation likelihood

Figure 5.11. The spallation likelihood distributions. The left figure shows the likeli-hood distribution for muon events with reconstructed tracks. The right figure is forthe case where muon track reconstruction failed. The open histogram shows a typicaldata sample and the hatched histogram shows the randomly generated data sample.

0.1

0.125

0.15

0.175

0.2

0.225

0.25

0.275

0.3

0 5 10 15 20 25 30 35

Z(cm)

Dea

d t

ime

(%)

0.1

0.125

0.15

0.175

0.2

0.225

0.25

0.275

0.3

0 2 4 6 8 10 12 14 16

Distance from the ID wall

Dea

d t

ime(

%)

Figure 5.12. Position dependence of the dead time caused by the spallation cut. Leftfigure shows the z-dependence and right figure shows the r-dependence of the deadtime.

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likelihood value with the largest chosen as the likelihood value for the event. Figure

5.11 shows the likelihood distribution for a typical data sample calculated from muon

events with and without reconstructed tracks. Also shown in the figures are the

likelihood distributions for the data sample with their vertex generated randomly

in the detector. These random events are used to estimate the dead time due to

the spallation cut on the solar neutrino data sample. The criteria for identifying

the spallation events are L > 0.98 for muon events with reconstructed tracks and

Lmax > 0.92 for muon events in which track reconstruction failed. These criteria are

chosen by maximizing the significance of the solar neutrino signal.

The dead time due to the spallation cut is estimated by applying the spallation

cut to the randomly generated data sample. The dead time is 21.2%. The dead time

is position dependent. Figure 5.12 shows the position dependence of the spallation

cut as a functions of radial distance and z-position. These position dependencies are

taken into account in the solar neutrino MC simulation.

5.4 Second Reduction

The second reduction cuts are more geared toward data quality checks. They

include a vertex test, a Cherenkov ring image test and a vertex position check (gamma

cut).

5.4.1 Vertex Test - Gringo Cut

All events contain noise hits. Noise hits could degrade the validity of the recon-

structed vertex. As the noise hits are more evenly distributed in time, they would

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broaden the time distribution of in-time hits for a event. So if the vertex position

is artificially shifted around the reconstructed vertex, the goodness value of vertex

reconstruction will undergo small changes as compared to the case which has few

noise hits. So goodness stability check could be used to check the data quality of a

event.

Details of the vertex goodness stability check are done as follows:

1. Make a two dimensional grid with equal spacing on the plane which contains

the reconstructed vertex point and normal to the reconstructed direction.

2. New goodness value is calculated using Eq. 3.3 assuming the vertex is at each

grid point.

3. Calculate the difference between the goodness at the original vertex and at each

grid point.

4. Count the number of grid points at which the deviation exceeds the threshold

(Nbad). The threshold for the selection is a function of the distance of the trial

grid point to the true vertex. The further away the grid point from the true

vertex, the lower the threshold value.

5. Calculate the ratio of Nbad to the total number of grid points (Rbad). If Rbad

is larger then 0.08, then the event is cut.

Figure 5.13 shows a typical Rbad distributions and the Gringo cut. Gringo cut

removes about 50% of the data sample while keeping > 90% of the MC data sample.

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10 3

10 4

10 5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

CUTDataMC

Rbad

Figure 5.13. Rbad distributions for a typical data sample, MC data sample and theGringo cut.

10-3

10-2

10-1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

5 - 5.5MeV 8 - 8.5MeV14 - 20MeV

cosθPMT

Ch

eren

kov

imag

e lik

elih

oo

d

Figure 5.14. Pattern likelihood distributions from the Cherenkov ring image test.The spikes in the figure are due to the binning effect of the PMT spacing.

139

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0

50

100

150

200

250

300

350

-2.3 -2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4

CUT

Cherenkov ring likelihood

cosθsun ≥ 0.8

cosθsun < 0.8 (× 1/9)

Figure 5.15. The likelihood distribution of the Cherenkov ring image test for a typicaldata sample and Patlik cut.

5.4.2 Cherenkov Ring Image Test - Pattern Likelihood Cut

The additional γ-rays from noise in a event could smear the Cherenkov ring image

resulting in erroneous reconstruction of the event direction. To check the validity of

the reconstructed Cherenkov ring, a likelihood function is constructed from the MC

distribution of the angle between the reconstructed direction and the angle from

the reconstructed vertex to each hit PMT. Figure 5.14 shows the Cherenkov ring

likelihood functions for several energy ranges.

The likelihood values are calculated for every hit PMT which is used for the

direction reconstruction. The product is the Cherenkov ring likelihood value for

the event. Figure 5.15 shows the likelihood distributions for a typical data sample.

The points with error bars are for those events whose reconstructed directions are

correlated with the solar direction (the inner products of those directions (cos θsun) is

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wall

reconstructedvertex

directionreconstructed

deff

Figure 5.16. The definition of the effective distance from the wall dwall.

larger then 0.8, means those events are strong solar neutrino candidate events). The

histogram shows the likelihood distribution for events whose cos θsun is smaller than

0.8 (more likely background events). The cut criteria is set at -1.85.

5.5 Gamma Cut

One of the major sources of the background in the solar neutrino analysis is γ-

rays from the PMT glass and the surrounding rock. To remove this background, the

reconstructed direction of each event is projected backward, and the distance from

the reconstructed vertex to the detector wall along this direction (dwall see Figure

5.16 is used to select the γ-ray events. The criteria for the cut is chosen as:

1. dwall ≤ 450cm ( for E ≥ 6.5MeV)

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0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500x 10

3

E = 6.5 - 20MeV

R2 (cm2)

0

500

1000

1500

2000

2500

3000

3500

-2000 -1000 0 1000 2000

E = 6.5 - 20MeV

Z (cm)

0

250

500

750

1000

1250

1500

1750

2000

-1 -0.5 0 0.5 1

E = 6.5 - 20MeV

Dirx

0

250

500

750

1000

1250

1500

1750

2000

-1 -0.5 0 0.5 1

E = 6.5 - 20MeV

Dirz

Figure 5.17. The γ-ray cut for a typical data sample with E = 6.5 ∼ 20.0 MeV. Theupper figures are the vertex distributions and the lower ones are the direction cosinesdistributions along the x and z directions. The hatched regions show the distributionsafter the γ-ray cut.

2. dwall ≤ 800cm ( for 5.0MeV ≤ E < 6.5MeV)

The criteria of the gamma cut is selected by finding the point where the significance

(number of remaining events of M.C.) /√

(number of remaining events of real data)

becomes maximal.

Figure 5.17 shows the vertex distributions for a typical data sample with energy

between 6.5 to 20 MeV. The large peak near the ID wall disappears after this cut.

The inefficiency introduced by this cut in the energy range from 6.5 to 20 MeV is

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10 2

10 3

10 4

10 5

0 500 1000 1500 2000 2500x 10

3

E = 5.0 - 6.5 MeV

R2 (cm2)

10 2

10 3

10 4

10 5

-2000 -1000 0 1000 2000

E = 5.0 - 6.5MeV

Z (cm)

10 2

10 3

-1 -0.5 0 0.5 1

E = 5.0 - 6.5MeV

Dirx

10 2

10 3

-1 -0.5 0 0.5 1

E = 5.0 - 6.5MeV

Dirz

Figure 5.18. The γ-ray cut for a typical data sample with E = 5.0 ∼ 6.5 MeV. Theupper figures are the vertex distributions and the lower ones are the direction cosinesdistributions along the x and z directions. The hatched regions show the distributionsafter the γ-ray cut.

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10-1

1

10

10 2

10 3

10 4

6 8 10 12 14

After 1st reduction

After spallation cut

After 2nd reduction

After gamma cut

SSM(BP2000) * 0.4(efficiencies are considered)

Energy (MeV)

Num

ber

of e

vent

s/da

y/22

.5kt

/0.5

MeV

SK-I 1496day 22.5kt ALL (Preliminary)

Figure 5.19. The energy spectrum after each reduction step.

estimated to be 6.8%.

Figure 5.18 shows the vertex distributions for a typical data sample with energy

between 5.0 to 6.5 MeV. The large peak near the ID wall also disappears after the

gamma cut. The inefficiency introduced by this cut in the energy range from 5.0 to

6.5 MeV is about 20.9%.

5.6 Summary

Figure 5.19 show the energy spectra after each reduction step. Figure 5.20 shows

the flow of the reduction step and number of remaining events after each reduction

cut.

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Figure 5.20. Flow chart illustrating reduction step for the 1496 days data sample.

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Chapter 6

SK Solar Neutrino Results

Super-Kamiokande detects solar neutrinos via the elastic scattering of neutrinos off

electrons in the water. The scattered recoil electrons are detected via Cherenkov

light, allowing their position, direction, timing and total energy to be measured. As

the recoil electrons move in the forward direction of the incoming neutrinos, the

directional correlation with the Sun is utilized to extract solar neutrino signals from

the final data sample by an extended maximum likelihood method.

Super-Kamiokande measures the spectrum of the recoil electrons with high statis-

tical accuracy. The energy-related systematic effects have been minimized by using

the high precision LINAC energy calibration system (Chapter 4 on Detector Cal-

ibration). Details of the systematic errors will be discussed in this chapter. The

precise measurement of the recoil electron energy spectrum is crucial for searching

for a non-zero neutrino magnetic moment.

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Super-Kamiokande

θsun

Figure 6.1. Definition of θSun

0

0.1

0.2

-1 -0.5 0 0.5 1cosθsun

Eve

nt/d

ay/k

ton/

bin

SK-I 1496day 5.0-20MeV 22.5kt

Figure 6.2. The cos θSun distribution of the final data sample (E=5.0-20.0 MeV). Thehistogram is the best fit from the extended maximum likelihood method, the dottedline shows the estimated background.

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6.1 Solar Neutrino Signal Extraction

The basic principle behind the extraction of the solar neutrino signal is that of

the strong directional correlation between the direction of the recoil electrons and the

direction of the Sun. As a realtime detector, the position of the Sun is known, thus an

angle θSun between the reconstructed direction of the event and the direction of the

Sun is defined as shown in Figure 6.1. Figure 6.2 shows the cos θSun distribution of

the final data sample. A peak in the vicinity of the Sun direction (cos θSun = 1) is the

clear evidence that the neutrinos are coming from the Sun. The near-flat component

in the cos θSun distribution (indicated by the dotted line in Figure 6.2) is the remaining

backgrounds due to radioactivity in the detector, γ-rays from surrounding rock, etc.

The excess above the background is due to the solar neutrino events. SK can not

identify individual solar neutrino event. It can only detect solar neutrinos statistically.

Thus an extended maximum likelihood method is used to extract the solar neutrino

signals from the data sample.

6.1.1 Likelihood Method

The program to implement the maximum likelihood method is called solfit. The

likelihood assumes a Possion distribution of the total number of events [46, 6]:

L(x) =

n∏

j=1

e−(Yj ·S+Bj)

Nj!

Nj∏

i=1

[Bj · Pbg(Ei, cos θi) + Yj · S · Psig(Ei, cos θi)] (6.1)

where Ee is the recoil electron energy, Pbg and Psig are the probability density

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0

2.5

5

7.5

10

12.5

15

17.5

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

15MeV

10MeV

7MeV

5MeV

cosθsun

pro

bab

ility

den

sity

Figure 6.3. The solar neutrino signal probability density functions Psig for variousenergies.

functions for background and solar neutrino signal. n is the number of energy bins.

There are 18 bins of size 0.5 MeV between 5 and 14 MeV and 1 bin combines events

from 14 to 20 MeV. S is the total number of signal events, Nj, Bj and Yj are the

number of observed events, the number of background events and the expected frac-

tion of signal events in the jth bin, respectively. The likelihood function is maximized

with respect to S and Bj. For the measurement of energy spectrum, each term in the

product over energy bins is maximized separately.

Solar Neutrino Signal

Psig obtained through MC simulation shows the expected signal shape (Figure

6.3). The energy-dependent smearing around cos θSun ∼ 1 is due to the finite angular

resolution of the SK detector.

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Background Estimation

Backgrounds in SK come mainly from muon-induced spallation events, radioactiv-

ity from the PMT glass and surrounding rock, flashing PMTs and electronic noises.

Most background events enter the detector from outside and thus can be eliminated

by the fiducial volume cut. Some background events remain even after applying

various cuts which are based on the vertex fit quality checks in the data reduction

process. This is due in part to the finite resolution of the vertex reconstruction which

enable some background events escaping the cuts. The basic information we know

about these remaining background events is that they should not correlate with the

direction of the Sun. So, ideally the cos θSun distribution for the background events

should be flat. However, the cylindrical shape of the SK detector causes the number

of PMTs per solid angle to depend on the zenith angle, so the zenith angle distri-

bution of the background events are not flat (Figure 6.5). Adding the fact that the

Sun’s position is not uniformly distributed with respect to the detector (as see from

Figure 6.4), the cos θSun distribution of the background events could be distorted. To

account for this bias, a MC simulation is used to estimate the background shapes.

First we subtract solar neutrino events by assigning a reduced weight for the events

close to the solar direction (cos θSun ≥ 0.7). The weight is based on the ratio of the

number of events less and greater than 0.7. Then, a zenith angle distribution of all

the background events is obtained from a weighted data sample. Then for each real

SK live time Sun direction obtained from the final data sample, the MC generates

many events with their zenith angles according to the aforementioned zenith angle

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Figure 6.4. The zenith angle distribution of the Sun position in the SK detector fora typical data sample.

distribution and their azimuthal angles according to a flat azimuthal angle distribu-

tion. These generated artificial directions are projected on to the Sun direction to get

the background cos θSun distribution. This process can be repeated several times with

each step using the background obtained in the previous step to subtract solar neu-

trino events. The resulting background shapes for various energy regions are shown

in Figure 6.6. Also, Figure 6.7 shows the estimated day and night backgrounds.

The variation of hut gains and azimuthal angle asymmetry in the energy scale

and background sources also leads to a non-flat azimuthal angle distribution of events.

This effect is accounted for in the estimation of systematic error of backgrounds which

will be discussed later in this chapter.

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Figure 6.5. The zenith angle cos θ distribution of the final data sample for variousenergy ranges. Plots are ordered the same as those in the Figure 6.6.

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Figure 6.6. The MC simulated backgrounds for various energy ranges.

153

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Figure 6.7. The MC simulated day and night background for various energy ranges.

154

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6.1.2 Solfit

6.2 Solar Neutrino Flux Results

6.2.1 8B Neutrino Flux

The total live time for Super-Kamiokande -I is 1496 days, consisting of 733 days

in the day and 763 days in the night.

The total number of events with reconstructed recoil electron energy between 5

and 20 MeV is 286,557.

The expected number of events at SK based on BP2000 [22] is 48,173.

Results from solfit gives solar signal as 22385+226−226(stat.)+783

−716(sys.) events.

Thus the ratio of DATA/SSM is

DATA

SSMBP2000= 0.465 ± 0.005(stat.)+0.016

−0.015(sys.) (6.2)

The solar neutrino flux is obtained by multiplying the above ratio with the SSMBP2000

flux prediction (5.05+1.01−0.81 × 106 cm−2s−1).

Φν = 2.35 ± 0.02(stat.) ± 0.08(sys.) × 106 cm−2s−1 (6.3)

Based on the Sun direction with respect to the SK coordinates, the measured 8B

flux can be divided into daytime (cos θz < 0) and nighttime (cos θz > 0) fluxes. θz

is the angle between the z-axis of the detector and the vetor from the Sun to the

detector. These are important to search for matter effects in the analysis of neutrino

oscillations.

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The daytime flux is:

Φν = 2.32 ± 0.03(stat.)+0.08−0.07(sys.) × 106 cm−2sec−1 (6.4)

The ratio of daytime flux to the standard solar model prediction is:

DATAday

SSMBP2000= 0.460 ± 0.007(stat.)+0.016

−0.015(sys.) (6.5)

The nighttime flux is:

Φν = 2.37 ± 0.03(stat.) ± 0.08(sys.) × 106 cm−2sec−1 (6.6)

So the ratio of the nighttime flux to the standard solar model prediction is:

DATAnight

SSMBP2000= 0.470 ± 0.007(stat.)+0.016

−0.015(sys.) (6.7)

Daytime flux and nighttime flux asymmetry is calculated as follows:

Asymdn =Rday − Rnight

(Rday + Rnight)/2= −0.021 ± 0.020(stat.)+0.013

−0.012(sys.) (6.8)

where R is DATA/SSM. The asymmetry is consistent with zero within 0.9 standard

deviation.

Figure 6.8 shows DATA/SSM for all data, daytime, nighttime and as a function

of the zenith angle.

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0.35

0.4

0.45

0.5

0.55

-1 0 1cosθz

Dat

a/S

SM

All

Day

Nig

ht

Day Night

SK-I 1496day 5.0-20MeV 22.5kt

Figure 6.8. Ratio of the measured flux to the standard solar model prediction for all,day, night and different zenith angle data samples.

6.2.2 Time Variation of the Flux Results

Figure 6.9 shows the flux variation as a function time. Each horizontal bin covers

1.5 months. It shows no obvious time-dependent variation other than the orbital

eccentricity effect. It has no correlation with the sunspots Figure 6.10. Figure 6.11

shows the seasonal variation of the measured solar neutrino flux. It has the same

binning as the Figure 6.9. Each bin combines all the data taken at similar time

during the year for the whole Super-Kamiokande -I data. The solid line shows the

predicted value based on the eccentricity of the Earth’s orbit around the Sun. The

1.7% orbital eccentricity causes about 7the inverse square law in the calculation of

the flux. A χ2 fit taking into account of this eccentricity effect gives a χ2 value of 4.7

for 7 degrees of freedom, a C.L. of 69%, showing that the observed flux is consistent

with the predicted modulation.

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0

0.2

0.4

0.6

0.8

1

1998 2000 2002YEAR

Dat

a/S

SM

SK-I 1496day 5.0-20MeV 22.5kt

without eccentricity correction, stat. err. only

Figure 6.9. Time variation of the measured solar neutrino flux results as a functionof time. The binning of the horizontal axis is 1.5 months.

0

50

100

150

200

1998 2000 2002YEAR

Num

ber

of s

unsp

ot

Figure 6.10. Number of sunspots as a function of time.

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0.4

0.5

0.6

JAN

FE

B

MA

R

AP

R

MA

Y

JUN

JUL

AU

G

SE

P

OC

T

NO

V

DE

C

Dat

a/S

SM

SK-I 1496day 5.0-20MeV 22.5kt(Preliminary)

χ2 for eccentricity = 4.7 C.L. = 69%χ2 for flat = 10.3 C.L. = 17%(8-1 d.o.f.) (with sys. err.)

Figure 6.11. Seasonal variation of the measured solar neutrino flux results. The solidline shows the predicted value based on the eccentricity of the Earth’s orbit aroundthe Sun.

6.3 Recoil Electron Energy Spectrum

The energy spectra of 8B neutrinos have been precisely measured by terrestrial

experiments. We make use of the LINAC system to control and minimize the energy

related systematic errors in order to make a high precision measurement of the recoil

electron spectrum. This is crucial for the neutrino oscillation analysis and for the

search for non-zero neutrino magnetic moments as well. The total electron energy is

binned in 0.5 Mev bins from 5 to 14 MeV with one additional bin combining events

from 14 to 20 MeV. Figure 6.12 shows the cos θSun distribution for various energy

bins. The black circles show the data, the histograms show the solfit results and the

dashed lines show the background shape used by solfit to extract the solar signal.

Figure 6.13 shows the measured recoil electron spectrum. Also shown in the figure

is the expected spectrum from the standard solar model. Figure 6.14 shows the ratio

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5.0- 5.5MeV 5.5- 6.0MeV 6.0- 6.5MeV 6.5- 7.0MeV 7.0- 7.5MeV

7.5- 8.0MeV 8.0- 8.5MeV 8.5- 9.0MeV 9.0- 9.5MeV 9.5-10.0MeV

10.0-10.5MeV 10.5-11.0MeV 11.0-11.5MeV 11.5-12.0MeV 12.0-12.5MeV

12.5-13.0MeV 13.0-13.5MeV 13.5-14.0MeV 14.0-20.0MeV

Figure 6.12. cos θSun distributions for various energy bins.

of the measured spectrum to the predicted spectrum. The numerical results are

summarized in Table 6.1 for data and in Table 6.2 for the energy related systematic

errors (detail see section on systematic errors). Figure 6.15 and 6.16 show the day

and night spectra respectively. And Table 6.3 gives the numerical values for the day

and night spectra.

6.4 Systematic Errors

Figure 6.17 and 6.18 show the summaries of the systematic errors for flux measure-

ments and energy spectrum from various sources. Also Table 6.2 gives the summary

of the correlated and uncorrelated systematic errors for the energy spectrum.

The systematic errors generally can be evaluated using the following formula:

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10-1

1

10

5 7.5 10 12.5Energy (MeV)

Num

ber

of e

vent

s / d

ay /

22.5

kt /

0.5M

eV Solar neutrino MC (1496day)

Observed solar neutrino events

(efficiency corrected)SK 1496day 22.5kt (Preliminary)

stat. error

stat.2+sys.2

Figure 6.13. The measured recoil electron energy spectrum. Also shown is the ex-pected spectrum from SSM. The thick error bar shows the statistical error. The thinerror bar shows the total systematic error.

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Figure 6.14. The ratio of the measured recoil electron energy spectrum to the SSMpredicted energy spectrum. The error bars are the results of the statistical errors andenergy non-correlated systematic errors being added in quadrature.

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Energy Data/SSM Number of signal(MeV) (events)

5.0 ∼ 5.5 0.4671 ± 0.0404 1932.8 ± 167.35.5 ∼ 6.0 0.4430 ± 0.0220 1891.1 ± 94.16.0 ∼ 6.5 0.4628 ± 0.0175 1901.9 ± 72.06.5 ∼ 7.0 0.4567 ± 0.0141 2590.6 ± 80.07.0 ∼ 7.5 0.4737 ± 0.0145 2458.5 ± 75.27.5 ∼ 8.0 0.4889 ± 0.0150 2264.2 ± 69.78.0 ∼ 8.5 0.4690 ± 0.0155 1897.4 ± 62.78.5 ∼ 9.0 0.4418 ± 0.0158 1529.0 ± 54.69.0 ∼ 9.5 0.4650 ± 0.0170 1352.9 ± 49.39.5 ∼ 10.0 0.4747 ± 0.0183 1135.9 ± 43.710.0 ∼ 10.5 0.4661 ± 0.0197 896.3 ± 37.910.5 ∼ 11.0 0.4172 ± 0.0206 627.1 ± 31.011.0 ∼ 11.5 0.4813 ± 0.0245 552.8 ± 28.111.5 ∼ 12.0 0.4464 ± 0.0270 384.9 ± 23.312.0 ∼ 12.5 0.4677 ± 0.0316 290.7 ± 19.712.5 ∼ 13.0 0.4715 ± 0.0376 208.7 ± 16.613.0 ∼ 13.5 0.4656 ± 0.0454 139.7 ± 13.613.5 ∼ 14.0 0.5859 ± 0.0604 115.5 ± 11.914.0 ∼ 20.0 0.5415 ± 0.0474 171.1 ± 15.0

Table 6.1. Summary of the measured recoil electron energy spectrum

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Energy Uncorrelated Correlated(MeV) error (%) error (%)

5.0 ∼ 5.5 +3.5 − 2.9 +0.2 − 0.25.5 ∼ 6.0 +1.6 − 1.6 +0.2 − 0.26.0 ∼ 6.5 +1.4 − 1.4 +0.3 − 0.36.5 ∼ 7.0 +1.4 − 1.4 +0.5 − 0.67.0 ∼ 7.5 +1.4 − 1.4 +0.8 − 0.87.5 ∼ 8.0 +1.4 − 1.4 +1.0 − 1.18.0 ∼ 8.5 +1.4 − 1.4 +1.4 − 1.38.5 ∼ 9.0 +1.4 − 1.4 +1.7 − 1.79.0 ∼ 9.5 +1.4 − 1.4 +2.1 − 2.09.5 ∼ 10.0 +1.4 − 1.4 +2.5 − 2.310.0 ∼ 10.5 +1.4 − 1.4 +3.0 − 2.710.5 ∼ 11.0 +1.4 − 1.4 +3.4 − 3.211.0 ∼ 11.5 +1.4 − 1.4 +3.9 − 3.611.5 ∼ 12.0 +1.4 − 1.4 +4.5 − 4.212.0 ∼ 12.5 +1.4 − 1.4 +5.1 − 4.812.5 ∼ 13.0 +1.4 − 1.4 +5.7 − 5.413.0 ∼ 13.5 +1.4 − 1.4 +6.5 − 6.213.5 ∼ 14.0 +1.4 − 1.4 +7.4 − 7.014.0 ∼ 20.0 +1.4 − 1.4 +11.1 − 9.5

Table 6.2. Summary of the systematic errors for the energy spectrum.

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Figure 6.15. The ratio of the measured recoil electron energy spectrum to the SSMpredicted spectrum for daytime.

Figure 6.16. The ratio of the measured recoil electron energy spectrum to the pre-dicted spectrum for nighttime.

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Energy (MeV) Day Night

5.0 ∼ 5.5 0.4514 ± 0.0581 0.4816 ± 0.05625.5 ∼ 6.0 0.4420 ± 0.0315 0.4439 ± 0.03086.0 ∼ 6.5 0.4531 ± 0.0250 0.4715 ± 0.02456.5 ∼ 7.0 0.4576 ± 0.0202 0.4551 ± 0.01977.0 ∼ 7.5 0.4713 ± 0.0208 0.4752 ± 0.02027.5 ∼ 8.0 0.4946 ± 0.0217 0.4833 ± 0.02098.0 ∼ 8.5 0.4614 ± 0.0220 0.4760 ± 0.02188.5 ∼ 9.0 0.4094 ± 0.0222 0.4715 ± 0.02239.0 ∼ 9.5 0.4727 ± 0.0246 0.4578 ± 0.02349.5 ∼ 10.0 0.4731 ± 0.0261 0.4759 ± 0.025610.0 ∼ 10.5 0.4502 ± 0.0280 0.4806 ± 0.027710.5 ∼ 11.0 0.4045 ± 0.0286 0.4286 ± 0.029611.0 ∼ 11.5 0.4716 ± 0.0346 0.4901 ± 0.034611.5 ∼ 12.0 0.4693 ± 0.0397 0.4255 ± 0.036712.0 ∼ 12.5 0.4604 ± 0.0453 0.4748 ± 0.044312.5 ∼ 13.0 0.5105 ± 0.0565 0.4360 ± 0.050013.0 ∼ 13.5 0.4853 ± 0.0677 0.4493 ± 0.061113.5 ∼ 14.0 0.5652 ± 0.0861 0.6064 ± 0.084914.0 ∼ 20.0 0.4664 ± 0.0646 0.6167 ± 0.0690

Table 6.3. Summary of the measured day and night recoil electron energy spectra.

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Figure 6.17. Summary of systematic errors for flux measurement from various sources.

167

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Figure 6.18. Summary of systematic errors for energy spectrum from various sources.

168

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F (Eobs) =

∫ Emax

0

F (Ee)R(Eobs, Ee)ε(Eobs)dEe, (6.9)

where Eobs is the total energy reconstructed in the SK detector, F (Eobs) is mea-

sured energy spectrum given the original energy spectrum F (Ee), Ee is the real recoil

electron energy, R(Eobs, Ee) is the detector response function which gives the proba-

bility that a recoil electron with energy Ee is observed with total energy Eobs by the

SK detector, ε(Eobs) is the detection efficiency function. By varying R(Eobs, Ee) and

ε(Eobs), one can simulate the expected results that include the uncertainties. The sys-

tematics due to the uncertainties can then be estimated by comparing the simulated

results with the observed results.

Energy Correlated Systematic Errors

Energy Scale and Resolution Uncertainties in energy scale and resolution are

the source of energy correlated systematic errors which could affect the shape of the

measured recoil electron spectrum. Since we look for the effect of a neutrino magnetic

moment in the distortion of the energy spectrum, it is very important to correctly

estimate these effects.

The uncertainties of the energy scale and energy resolution come from the following

sources:

• Due to position dependence: 0.21 % measured by LINAC.

• Due to time variation: 0.11 % measured by LINAC.

• Due to accuracy of MC simulation: 0.1 %.

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0

0.2

0.4

0.6

0.8

1

6 8 10 12 14Energy(MeV)

Dat

a/S

SM

20

Figure 6.19. Energy correlated systematic errors due to energy scale uncertainty.

• Due to direction dependence: ±0.5% using spallation events.

• Due to the electron beam uncertainty in LINAC calibration: 0.21%.

• Due to the water transparency measurement: ±0.22%.

Varying the response function in Equation 6.9 with the above uncertainties, the

systematic errors for flux and energy spectrum can be obtained. The systematic error

on flux is estimated to be ±1.6%. The total uncertainty of Super-K’s absolute energy

scale is estimated to be 0.64 %. The systematic errors for the energy spectrum due

to the uncertainties of energy scale and resolution are shown in Figure 6.19 and 6.20.

8B Neutrino Spectrum The uncertainty in the 8B neutrino energy spectrum can

also lead to energy correlated systematic errors. Varying F (Ee) in Equation 6.9 the

systematic error on flux is estimated to be +1.1%−1.0%. The correlated systematic error due

to uncertainty in 8B neutrino energy spectrum is shown in Figure 6.21.

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0

0.2

0.4

0.6

0.8

1

6 8 10 12 14Energy(MeV)

Dat

a/S

SM

20

Figure 6.20. Energy correlated systematic errors due to energy resolution uncertainty.

0

0.2

0.4

0.6

0.8

1

6 8 10 12 14Energy(MeV)

Dat

a/S

SM

20

Figure 6.21. Energy correlated systematic errors due to 8B neutrino spectrum uncer-tainty.

171

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Energy Non-Correlated Systematic Errors

Trigger Efficiency The vertex position and water transparency can affect trigger

efficiency. These effects are taken into account in the MC simulation. The systematic

error is estimated by comparing the measured trigger efficiency with the MC trigger

simulation.

For the LE trigger, the efficiency is 100% above 7.0 MeV. For the energy region

from the 6.5 MeV to 7.0 MeV, the deviation is between +0.4−1.7%.

For the SLE trigger, the trigger efficiency changes with the hardware thresholds.

The difference between the data and MC is obtained by taking the livetime-weighted

average of the difference of each threshold period. The differences for each energy bin

are as follows : 5.0 ∼ 5.5MeV, +3.2−1.6%, 5.5 ∼ 6.0MeV, +0.9

−0.5%. The trigger efficiency is

100% above 6.0 MeV for both data and MC, thus the systematic error is zero above

6.0 MeV.

The uncertainty due to the IT is studied by using Ni-Cf calibration data. The

volume averaged differences of IT reduction efficiency between data and MC for each

energy bin are as follows: 5.0 ∼ 5.5 MeV, ±2.8%, 5.5 ∼ 6.0 MeV, ±0.7%, and

6.0 ∼ 6.5 MeV, ±0.3%. The systematic error due to IT is zero above 6.5 MeV.

Reduction The uncertainty in reduction comes from the difference in reduction

efficiency between real data and MC data.

Systematic errors due to first reduction on flux measurement is ±1.0% and ±0.3%

on the energy spectrum. For the second reduction, systematic errors are +1.9−1.3% for

flux and ±0.8% for the energy spectrum.

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Spallation Dead Time Uncertainty of the spallation dead time comes from the

position and time dependence of the spallation deadtime. The systematic errors due

to the uncertainty in spallation time are estimated to be ±0.2% for flux measurement

and to be negligible for the energy spectrum.

γ-Ray Cut As the γ-ray cut uses the reconstructed vertex and direction, the

vertex and angular resolution differences between real data and MC data can lead to

systematic effects.

To estimate the influence of these differences, the following method is adopted.

1. Shift the reconstructed vertex and direction of events within the differences in

the vertex and angular resolution between data and MC.

2. Apply the γ-ray cut to the modified data and compare the reduction efficiency

with the result of original data.

These effects are estimated by artificially shift the event’s vertex and direction within

the resolution difference between data and MC. Then after applying the γ-ray cut to

the modified data, compare the reduction efficiency with the original one.

The systematic error due to γ-ray cut for the flux measurement is ±0.05% and

that for the energy spectrum measurement is ±0.1%.

Vertex Shift The difference between the reconstructed vertex position and real

vertex position is studied using Ni-Cf calibration at various positions in the SK de-

tector. The systematic errors are estimated to be 1.3% for the flux measurement and

±0.2% for the energy spectrum measurement.

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Figure 6.22. Azimuth angle φ distribution for events in the energy range from 5.0 to5.5 MeV (Zero has been suppressed).

Non-flat Background As mentioned in the section on background estimation, the

variation of hut gains and φ asymmetry in the energy scale and background sources

can also lead to a non-flat azimuthal angle distribution of events . Figure 6.22 shows

the φ distribution for events in the energy range from 5 to 5.5 MeV. There is a 16 %

asymmetry in the event distribution. The reasons for this asymmetry are as follows:

• Gains at the 4 electronic huts, which are each responsible for one quarter of the

total PMTs, are not the same.

• Trigger efficiencies at very low energies might not be 100 %. The φ asymmetry

is less evident in the high energy regions (Figure 6.23).

If this is the case, by lowering the trigger threshold and increasing the trigger effi-

ciencies, the φ asymmetry should be much less. Figure 6.24 shows the φ distribution

when the SLE threshold is 250 mV or 260 mV. Figure 6.25 shows the φ distribution

with much less asymmetry when SLE threshold is 186 mV.

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Figure 6.23. Azimuth angle φ distribution for events in the energy range from 7 to10 MeV (Zero has been suppressed).

Figure 6.24. Azimuth angle φ distribution for events in the energy range from 5.0 to5.5 MeV when the SLE threshold is 250 mV or 260 mV using 1200 day data set (Zerohas been suppressed).

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Figure 6.25. Azimuth angle φ distribution for events in the energy range from 5.0 to5.5 MeV when the SLE threshold is 186 mV using 1200 day data set (Zero has beensuppressed).

The uncertainty in φ asymmetry is treated as a systematic effect. To estimate the

systematic error due to this asymmetry, background with both non-flat zenith angle

and azimuthal angle distributions are generated (Figure 6.26). Solfit is run with this

generated background. The systematic errors are obtained by comparing the results

using the non-φ background and flat-φ background. The systematic error on the flux

measurement is ±0.1% and ±0.4% on the day-night flux asymmetry. The systematic

errors for the energy spectrum are ±0.6% for 5.0-5.5 MeV, ±0.5% for 5.5-6.0 MeV

and ±0.1% for the energies above 6.0 MeV.

Angular Resolution Uncertainty in the angular resolution is estimated by com-

paring real LINAC data and MC simulation. The difference depends on the energy

and has been corrected in flux and spectrum measurements. The estimated difference

of 1.2% for the flux measurement is assigned as a systematic error.

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Figure 6.26. Background estimation considering φ-asymmetry or without consideringφ-asymmetry for 5.0 to 5.5 MeV (Zero has been suppressed).

Cross Section The uncertainty of the cross section of the neutrino-electron elastic

scattering comes from the uncertainty of the Weinberg angle θW . The estimated

systematic error is ±0.5% for flux and ±0.2% for energy spectrum [20].

Livetime The uncertainty in the livetime comes from the difference in the calcula-

tion using different data samples (raw data, muon data or low energy triggered data).

The systematic error due to livetime on the flux measurement is estimated as ±0.1%.

177

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Chapter 7

Searching For Neutrino Magnetic

Moments

The interest in the neutrino magnetic moment started with the original idea of a

neutrino. In Pauli’s famous letter in which he proposed the existence of the neutrino,

he suggested that neutrinos interact with other particles by electromagnetic force

through neutrino magnetic moments [1]. We know this is not true. In the standard

model, neutrinos are massless and have no magnetic moments. Recent experiments

show that neutrinos have tiny masses, consequently neutrinos can acquire magnetic

moments from the coupling of the left-hand and the right-hand currents through the

mass term [12, 13], Figure 7.1, µν ≈ 3.2 × 10−19( mν

1eV) µB, which is several orders of

magnitude smaller than the current limits on the neutrino magnetic moment. There-

fore an observation of a neutrino magnetic moment larger than this could imply new

physics beyond the standard model.

The general interaction of neutrino mass eigenstates j and k with a magnetic field

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Figure 7.1. Loop diagram which leads to the neutrino magnetic moment. The blackdots reprent the mass term. The loop induced neutrino magnetic moment is propor-tional to the mass of the neutrinos.

can be characterized by constants µjk, the magnetic moments. Both diagonal (j = k)

and off-diagonal (j 6= k) moments are possible.

While there have been attempts to use the neutrino magnetic moments to ex-

plain the solar neutrino problem [30, 31], e.g. spin flavor precession (SFP) [32, 33],

SFP cannot explain the suppressed reactor anti-neutrino flux detected at KamLAND

[9]. Under the assumption of CPT invariance, KamLAND’s results give independent

support to neutrino oscillations [6, 7], not SFP [34], being the solution to the solar

neutrino problem.

A search for neutrino magnetic moments has been conducted using the high statis-

tics 1496 live-days solar neutrino data from Super-Kamiokande-I [47].

7.1 Introduction

The neutrino magnetic moments have been searched for in the neutrino-electron

scattering experiments using reactor νe’s with the first of such experiments being

done by the UCI group [48]. These experiments give limits on the neutrino magnetic

moments in the range of (1 − 4) × 10−10 µB, where µB is Bohr magneton. Various

astrophysical observations also yield limits on the neutrino magnetic moment in the

range from 10−12 µB to 4 × 10−10 µB [14].

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Super-K is the first experiment to use solar neutrinos to search for the neutrino

magnetic moment. The idea behind this search is that if neutrinos have non-zero

magnetic moments, in addition to the usual weak contribution to the neutrino-electron

elastic scattering, Equation 7.1, there is an additional incoherent contribution from

the magnetic scattering, Equation 7.2 [18]:

(

dT

)

WK

= C

[

g2L + g2

R ( 1 − T

)2 − gLgRmeT

E2ν

]

(7.1)

where C = 2G2F me/π, gL = sin2 θW +1/2 for νe, gL = sin2 θW − 1/2 for νµ and ντ ,

and gR = sin2 θW .

(

dT

)

EM

= µ2ν

πα2em

m2e

(

1

T− 1

)

(7.2)

where µν is in units of µB, Eν is the neutrino energy, T = Ee − me, and T (Ee)

is the kinetic (total) energy of the recoil electrons. While the weak contribution is

relatively flat with respect to energy, the magnetic contribution increases at lower

energies, Figure 7.2. So the signature of a non-zero neutrino magnetic moment would

be an excess of events at lower energies.

As mentioned in earlier chapters, to control energy-related systematic effects, the

number of hit photomultiplier tubes (PMT) is related to the total electron energy

using electrons injected by an electron linear accelerator (LINAC). The number of

hit PMTs in the Monte Carlo simulation of those LINAC electrons is tuned to agree

with LINAC data. As a result of this tuning, the systematic uncertainty of the

reconstructed energy of electrons between 5 and 20 MeV is less than 0.64%. The

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Figure 7.2. Ratio of the recoil electron magnetic scattering spectrum and weak scat-tering spectrum in Super-K for µν = 10−10 µB. It clearly shows that the magneticscattering increases at lower energies.

uncertainty of the energy resolution is less than 2%. This absolute energy scale is

monitored and cross checked by (1) muon decay electrons, (2) spallation products

induced by cosmic ray muons, and (3) decay of artificially produced 16N. The data

used for this analysis were collected from May 31, 1996 to July 15, 2001 with a

livetime of 1496 days. The results are binned in 0.5 MeV bins of the total electron

energy from 5 to 14 MeV and one bin combining events from 14 to 20 MeV. As a real

time detector, SK can divide the data sample into day and night data samples which

give the day/night spectra. The number of events in each energy bin is extracted

individually by utilizing the directional correlation between the recoil electrons and

the Sun. The angular distribution in the region far from the solar direction is used to

estimate the background. The estimation of the backgrounds, along with the expected

angular distributions of the solar neutrino signals, are incorporated into an extended

maximum likelihood method to extract the number of solar neutrino events.

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SK-I 1496day 5.0-20MeV

Figure 7.3. Ratio of SK-I observed recoil electron energy spectrum and the expectednon-oscillated weak scattering spectrum. The error bars are the results of the sta-tistical and energy non-correlated systematic errors being added in quadrature. Thedotted lines are the correlated systematic errors. The dash-dotted line is the expectedoscillated weak scattering spectrum for ∆m2 = 6.6 × 10−5 eV2, tan2 θ = 0.48. Thedashed line shows the addition of magnetic scattering with µν = 1.1 × 10−10 µB ontop of the oscillated weak spectrum. (The zero has been suppressed).

7.2 Super-K Energy Spectrum And Limit On the

Neutrino Magnetic Moment

In a method first pioneered by Beacom and Vogel to extract the neutrino magnetic

moment from Super-Kamiokande’s early solar data [18], we search for the effects of

the neutrino magnetic moments by looking for distortions in the shape of the recoil

electron spectrum relative to the expected weak scattering spectrum. Figure 7.3 shows

the ratio of SK measured recoil electron energy spectrum and the expected weak

scattering spectrum assuming no oscillation. It is flat, with no obvious increase of

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Figure 7.4. Distortions to the expected weak scattering spectra as results of theneutrino oscillation for various oscillation parameters (Zeros have been suppressed).

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event rates in the lower energy bins. As neutrino oscillation could change the expected

weak scattering spectrum, Figure 7.4, the flatness could be due to a combination of

a decrease of the weak scattering rate by oscillation and an increase of the magnetic

scattering rate at lower energies. To investigate this, the observed SK day/night

energy spectra are examined using the following χ2, similar to the one used in SK’s

standard solar spectrum analysis [49] with the addition of the oscillation effects and

the contribution of magnetic scattering:

χ2 =∑

a=d,n

18∑

i=1

[

α1+β δi

(W ai + µ2

10Mi) − Dai

σai

]2

+ β2 (7.3)

where W d,ni is the ratio of the oscillated day/night weak scattering spectra to

the non-oscillated weak scattering spectrum. We approximate the solar neutrino os-

cillations by a two-neutrino description with parameters θ (mixing angle) and ∆m2

(difference in mass squared between mass eigenstates) [5]. Mi is the ratio of the mag-

netic scattering spectrum to the non-oscillated weak scattering spectrum assuming

µν = 10−10 µB. Dd,ni is the ratio of the measured day/night spectra to the non-

oscillated weak scattering spectrum. δi is the energy bin correlated systematic error,

σd,ni is the day/night statistical and uncorrelated systematic errors added quadrat-

ically. α is the normalization factor of the measured 8B flux to the expected flux;

the 8B flux is not constrained in this analysis. µ210 is magnetic moment squared in

units of (10−10 µB)2. β is a parameter used to constrain the variation of correlated

systematic errors which come from the uncertainties in the energy scale, resolution

and 8B neutrino energy spectrum.

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Considering neutrinos with only diagonal magnetic moments [18]. As shown be-

low,the survival probability of neutrinos passing through the magnetic field in the Sun

is independent of neutrino energy [15]. The neutrinos can flip their spins when they

travel through the magnetic field in the Sun. The evolution equation is as follows

assuming the neutrinos are relativistic:

id

dt

νL

νR

=

m2L/2E µνB

µνB m2R/2E

νL

νR

(7.4)

where mL and mR are the masses of the left-handed and the right-handed neutri-

nos, µν is the neutrino magnetic moment and B is the magnetic field in the Sun.

The survival probabilities of the left-handed neutrinos after traveling a distance x

is obtained as follows:

PνLνL(x) = | 〈νL(x) | νL(0)〉 |2

= 1 − sin2 β sin2 Ωx (7.5)

where

∆LR ≡ m2L − m2

R = 4EΩ cos β

µνB = Ω sin β (7.6)

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The effective mass of left-handed neutrino is m2L = m2 + 2E(Vcc + Vnc) due to the

interaction of neutrinos with matter, Vcc and Vnc are the same as those in Equation

1.13. For right-handed neutrinos, m2R = m2, so ∆LR = 2E(Vcc + Vnc). Thus we get

the following relations from Equation 7.6:

2Ω cos β = Vcc + Vnc

µνB = Ω sin β (7.7)

There is no energy dependence in Equation 7.7, so the solutions for Ω and β are

energy independent. Therefore, the survival probability in Equation 7.5 is energy

independent. Thus the shape of the 8B neutrino spectrum will not be changed by

the magnetic field in the Sun. In this paper we use the SK day/night spectra from

5 to 14 MeV and consider only the 8B solar neutrino flux. Furthermore, we assume

µν1 = µν2, so the magnetic scattering spectrum would not be affected by neutrino

oscillations.

The χ2 is minimized with respect to the parameters α, β and µ2ν in the whole

oscillation parameter space. We impose the physical condition µ2ν ≥ 0 in the process

of minimization. As there is no strong distortion of the observed energy spectra, this

χ2 can be used to exclude certain regions in the oscillation parameter space.

In Figure 7.5, the shaded regions are excluded by SK day/night spectra at 95%

C.L. considering only weak scattering, while the hatched regions are excluded at the

same confidence level but including the contribution from the magnetic scattering.

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SK 1496 Days

Day/Night Spectrum νe→νµ/τ (95%C.L.)

∆m2 in

eV

2

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

tan2(Θ)10-4 10-3 10-2 10-1 1 10 102

Figure 7.5. 95% C.L. exclusion regions using the SK day/night spectra shape. Theshaded area assumes only weak scattering. The hatched region takes into account thecontribution from magnetic scattering.

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µν2 (1x10-20 µB

2)

Pro

bab

ility

Dis

trib

uti

on

Fu

nct

ion

Figure 7.6. The probability distribution of ∆χ2 as function of µ2ν. The solid line

is for the case of no oscillation. The dashed line is for ∆m2 = 2.8 × 10−5 eV2 andtan2 θ = 0.42 (LMA). The dash-dotted line is for ∆m2 = 3.13 × 10−11 eV2 andtan2 θ = 0.91 (VAC). The arrows point to the place where the 90% C.L. limits are.The hatched areas to the right of the arrows are 10% of the total areas under thecurves.

188

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The exclusion regions shrink with the addition of the magnetic scattering because

there is one more parameter with which to minimize the χ2. As there is no obvious

increase of event rates at lower energies, we instead derive a limit on the neutrino

magnetic moment. For each point in the oscillation parameter space, the probability

distribution of ∆χ2 = χ2 − χ2min as a function of the square of the magnetic moment

is used. Figure 7.6 shows the probability distributions of ∆χ2 as function of µ2ν for

some oscillation parameters.

A 90% C.L. upper limit µ0 on the neutrino magnetic moment is obtained by

Equation 7.8 for each point in the oscillation parameter space.

Prob(∆χ2(µ2 ≥ µ20)) = 0.1 × Prob(∆χ2(µ2 ≥ 0)) (7.8)

The overall limit on the neutrino magnetic moment is obtained by finding the

maximum of the aforementioned limits in the oscillation parameter space. Discarding

the regions excluded by SK day/night spectra, we found at 90% C.L. µν ≤ 3.6 ×

10−10 µB with the limit at ∆m2 = 3.13× 10−11 eV2 and tan2 θ = 0.91 which is in the

VAC region.

Results from other solar neutrino experiments can further constrain the allowed

regions in the oscillation parameter space. Radiochemical experiments Homestake

[26], SAGE [28] and Gallex/GNO [27] (combined into a single “Gallium” rate) detect

solar neutrinos via charged current interactions with nucleons. The presence of a

non-zero neutrino magnetic moment would not affect their measurements of solar

neutrino flux rates. SNO [7] extracts the charged current, neutral current and elastic

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Spectrum Excluded, Flux Allowed Regions

∆m2 in

eV

2

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

tan2(Θ)10-4 10-3 10-2 10-1 1 10 102

Figure 7.7. 95% C.L. exclusion regions using the SK day/night spectra shape consid-ering non-zero neutrino magnetic moment and the allowed regions using solar neutrinoflux measurements. The regions within the broken lines are the SK spectra excludedregions. The regions within the solid lines are the solar neutrino rates allowed regions.

190

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0.6

0.70.8

0.9 1.0 1.11.2

1.3

1.4

1.5

1.6

1.71.8

∆m2 in

eV

2

10-5

10-4

tan2(Θ)10-1 1

Figure 7.8. The 90% C.L. µν limit contours (in units of 10−10 µB) and soalr neutrinooscillation allowed regions. The shaded area is the solar neutrino experiments’ allowedregion considering both weak and magnetic scattering.

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scattering rates by utilizing their distinctive angular distributions. Inclusion of the

neutrino magnetic moment will not affect the charged current interaction. The effects

of non-zero neutrino magnetic moment on the SNO neutral current interaction are

estimated to be very small [50, 51]. Such a magnetic moment could change the

elastic scattering rates but would not change the angular distribution of the elastic

scattering events. Therefore, SNO’s charged current and neutral current rates will

be essentially unaffected by a non-zero neutrino magnetic moment. The combination

of these charged current rates with SNO’s neutral current rate and SK’s day/night

spectra constrains the neutrino oscillation to an area in the large mixing angle (LMA)

region as shown in Figure 7.8.

Limiting the search for the neutrino magnetic moment within the region allowed by

solar neutrino experiments, we get an upper limit on the neutrino magnetic moment of

µν ≤ 1.3×10−10 µB at 90% C.L. with the limit at ∆m2 = 2.8×10−5 eV2, tan2 θ = 0.42.

KamLAND uses inverse β-decay interactions to detect reactor νe’s [9]. The signa-

ture of magnetic scattering with non-zero neutrino magnetic moment bears no similar-

ity to that used to detect the inverse β-decay interactions. Therefore, KamLAND’s

detection of anti-neutrinos would not be affected by a non-zero neutrino magnetic

moment. Assuming CPT invariance, the inclusion of the KamLAND results further

constrains the neutrino oscillation solutions in the LMA region (the shaded area in

Figure 7.10). This results in a limit on the neutrino magnetic moment at 90% C.L.

of µν ≤ 1.1 × 10−10 µB with the limit at ∆m2 = 6.6 × 10−5 eV2 and tan2 θ = 0.48.

This result is comparable to the most recent magnetic moment limits from reactor

neutrino experiments of 1.3 × 10−10 µB (TEXONO) [52] and 1.0 × 10−10 µB (MUNU)

192

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Solar And KamLAND Allowed Regions

∆m2 in

eV

2

10-6

10-5

10-4

10-3

tan2(Θ)10-2 10-1 1 10

Figure 7.9. 95% C.L. solar neutrino data allowed regions taking into account theeffects of neutrino magnetic moments and the KamLAND allowed regions. The regionwithin the broken lines shows the solar neutrino data allowed region. The regionswithin the solid lines are the KamLAND data allowed regions.

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0.6

0.70.8

0.9 1.0 1.11.2

1.3

1.4

1.5

1.6

1.71.8

∆m2 in

eV

2

10-5

10-4

tan2(Θ)10-1 1

Figure 7.10. The 90% C.L. µν limit contours (in units of 10−10 µB) and neutrinooscillation allowed regions. The shaded area shows the allowed region for solar ex-periments plus KamLAND results.

194

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[53], albeit for neutrinos and not anti-neutrinos.

If neutrinos have off-diagonal moments, the magnetic field in the Sun can affect the

8B neutrino flux spectrum, so the results on the limits of neutrino magnetic moment

could in principle be changed. But for the LMA region, the effect of the solar magnetic

field is negligible [34, 54, 55], so the same limits on the neutrino magnetic moment in

the LMA region would be obtained.

7.3 Conclusion

Limits on the neutrino magnetic moment have been obtained by analyzing the SK

day/night energy spectra. The oscillation effects on the shape of the weak scattering

spectrum have been taken into account when analyzing energy spectra. A limit of

3.6×10−10 µB using Super-Kamiokande ’s 1496 days of solar neutrino data is obtained.

By constraining the search to only the regions allowed by all neutrino experiments, a

limit of 1.1 × 10−10 µB is obtained.

195

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[3] E. Fermi, Z. Phys 88, 161 (1934).

[4] C. L. Cowan et al., Science 124, 103 (1956).

[5] Y. Fukuda et al., Phys. Rev. Lett, 81, 1562 (1998);

[6] S. Fukuda et al., Phys. Rev. Lett, 86, 5656, (2001); S. Fukuda et al., Phys. Lett.

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