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
c© 2005 Dawei Liu
The dissertation of Dawei Liuis approved and is acceptable in qualityand form for publication on microfilm:
Committee Chair
University of California, Irvine2005
ii
Dedication
To
my parentsMengluan Liu, Feng-e Peng
and my sisterZhaowei Liu
iii
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
iv
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
v
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
vi
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
vii
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
ix
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
x
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
xi
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
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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
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
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
• 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
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
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
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
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
|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
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
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
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
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
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
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
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
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(
mν
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
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
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
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
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
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
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
±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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Figure 2.3. Schematic view of support structures for the detector.
37
phot
osen
sitiv
e ar
ea >
460
φ
<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
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
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
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
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
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
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
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
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
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
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
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
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
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
-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
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
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.
54
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.
55
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
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
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
58
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
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
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).
61
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
77
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
-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
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
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
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
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
-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
-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
-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
(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
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
102
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
-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
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
-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
Figure 4.33. The deviation of the energy resolution between data and MC for allpositions and energies.
107
-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
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
-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
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
-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
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.
113
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
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.
115
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
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
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].
118
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
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.
120
• 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)
121
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.:
122
• 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
123
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 %.
124
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
125
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
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
127
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.
128
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
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.
130
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
131
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.
132
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
133
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].
134
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
135
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.
136
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
137
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.
138
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
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
140
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)
141
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
142
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.
143
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.
144
Figure 5.20. Flow chart illustrating reduction step for the 1496 days data sample.
145
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.
146
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.
147
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
148
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.
149
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
150
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.
151
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.
152
Figure 6.6. The MC simulated backgrounds for various energy ranges.
153
Figure 6.7. The MC simulated day and night background for various energy ranges.
154
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.
155
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.
156
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.
157
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.
158
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
159
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:
160
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.
161
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.
162
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
163
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.
164
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.
165
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.
166
Figure 6.17. Summary of systematic errors for flux measurement from various sources.
167
Figure 6.18. Summary of systematic errors for energy spectrum from various sources.
168
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 %.
169
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.
170
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
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.
172
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.
173
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.
174
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).
175
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.
176
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
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
178
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].
179
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]:
(
dσ
dT
)
WK
= C
[
g2L + g2
R ( 1 − T
Eν
)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 .
(
dσ
dT
)
EM
= µ2ν
πα2em
m2e
(
1
T− 1
Eν
)
(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
180
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.
181
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
182
Figure 7.4. Distortions to the expected weak scattering spectra as results of theneutrino oscillation for various oscillation parameters (Zeros have been suppressed).
183
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.
184
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)
185
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.
186
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.
187
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
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
189
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
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.
191
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
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.
193
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
[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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