Neutrinos and Their Flavor Mixing in Stellar Astrophysics [thesis]

179 Pages·2001·2.564 MB·English

by  S. Choubey

NEUTRINOS AND THEIR FLAVOR
MIXING IN NUCLEAR ASTROPHYSICS
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THESIS SUBMITTED TO

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THE UNIVERSITY OF CALCUTTA
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1 FOR THE DEGREE OF
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DOCTOR OF PHILOSOPHY (SCIENCE)
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By
SANDHYA CHOUBEY
SAHA INSTITUTE OF NUCLEAR PHYSICS
KOLKATA
OCTOBER 2001
ACKNOWLEDGMENTS
I am grateful to my thesis supervisor Prof. Kamales Kar for all his help and guidance
that he has extended to me during my research. He motivated me to take up neutrino
physics and has incessantly encouraged me to pursue my own line of thinking. I thank
him for his incentive, patience and unremitting encouragement which has instilled in me
a world of self confidence.
I am indebted to Dr. Srubabati Goswami with whom I have done most of my research
work. We share a perfect understanding which has helped us work together through thick
and thin, particularly during the development of the solar and the atmospheric neutrino
codes used extensively in this thesis. She has been a friend, teacher and guide and I thank
her for all that she has done for me.
I would like to thank all my collaborators with whom I have worked at various stages
of my research period. In particular, I would like to express my deep gratitude towards
Prof. D.P. Roy with whom I had very stimulating discussions at numerous occasions
which helped me understand the intricate details of neutrino physics. I also thank him for
his constant encouragement which has been of immense help. I thank Prof. S.M. Chitre
and Dr. H.M. Antia who introduced me to the subject of helioseismology and extended
their help whenever needed. It was a pleasure working with them. I wish to thank Dr.
Debasish Majumdar who I worked with during the initial stages of my work. Last but not
the least, I thank Abhijit Bandyopadhyay for all his endurance and perseverance which
helped us work together under the most difficult circumstances.
Thanks are due to Prof. Amitava Raychaudhuri and Prof. Palash Baran Pal for many
useful discussions and their unfailing encouragement.
I wishto thank SergueyPetcov, OsamuYasuda, Eligio Lisiand CarlosPenya Garayfor
their comments and suggestions at various stages which has been of immense importance.
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I thank all members of the Theory Group, SINP for creating a healthy and friendly
atmosphere which made working here most enjoyable. Special thanks are due to Surasri,
Ananda, Amit, Krishnendu, Subhasish, Rajen, Debrupa, Indrajit, Asmita, Sankha, Kaushik,
Somdatta, Dipankar, Rajdeep, Sarmistha, Purnendu, Abhijit, Indranil, Tilak and Tanaya.
Finally, I thank my family, my brother, my sister and particularly my parents. Without
their support and encouragement this thesis would not have been possible. It is impossible
to express my gratitude for them in words.
Kolkata, Sandhya Choubey
October, 2001 Theory Group, SINP
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TABLE OF CONTENTS
Page
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Chapters:
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Plan of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2. Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Neutrino Oscillations in Vacuum . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Neutrino Oscillations in Matter . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Neutrino Survival Probability in Medium with Varying Density . 14
2.2.2 Matter Effects with Sterile Neutrinos . . . . . . . . . . . . . . . . 17
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3. Bounds on Two Flavor Neutrino Mixing Parameters . . . . . . . . . . . . . . . 19
3.1 The Solar Neutrino Problem . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.1 Neutrinos in Standard Solar Models . . . . . . . . . . . . . . . . 23
3.1.2 The Solar Neutrino Experiments . . . . . . . . . . . . . . . . . . 27
3.1.3 The Solar Neutrino Code . . . . . . . . . . . . . . . . . . . . . . 33
3.1.4 Unified Formalism for Analysis of Solar Data . . . . . . . . . . . 36
3.1.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 The Atmospheric Neutrino Anomaly . . . . . . . . . . . . . . . . . . . . 46
iv
3.2.1 Atmospheric Neutrino Flux Predictions . . . . . . . . . . . . . . 49
3.2.2 Results from the Super-Kamiokande . . . . . . . . . . . . . . . . 53
3.2.3 The Atmospheric Neutrino Code . . . . . . . . . . . . . . . . . . 57
3.2.4 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Bounds from Accelerator and Reactor Experiments . . . . . . . . . . . . 61
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4. The Energy Independent Solution to the Solar Neutrino Problem . . . . . . . 71
4.1 Energy Independent Solution . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Regions of Energy Independent Solution in the ∆m2 tan2θ Plane . . . 74
−
4.3 The SMA, LMA, LOW and VO Solutions . . . . . . . . . . . . . . . . . 79
4.4 Comparisons and Discussions . . . . . . . . . . . . . . . . . . . . . . . . 83
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5. A Three Generation Oscillation Analysis of the Super-Kamiokande Atmo-
spheric Neutrino Data Beyond One Mass Scale Dominance Approximation . . 87
5.1 Three-Flavor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.1 The Vacuum Oscillation Probabilities . . . . . . . . . . . . . . . 89
5.1.2 Earth Matter Effects . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 χ2-analysis of the SK Data . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2.1 Zenith-Angle Distribution . . . . . . . . . . . . . . . . . . . . . . 96
5.2.2 Allowed Parameter Region . . . . . . . . . . . . . . . . . . . . . . 100
5.3 χ2 analysis of the SK + CHOOZ Data . . . . . . . . . . . . . . . . . . . 105
5.4 Combined Allowed Area from Short Baseline Accelerator and Reactor
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.6 Discussions and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 115
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6. Decay of Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.1 Neutrino Survival Probabilities . . . . . . . . . . . . . . . . . . . . . . . 122
6.2 Results of the χ2 analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.1 Two-Generation ν ν Oscillations . . . . . . . . . . . . . . . . 124
µ τ
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6.2.2 Neutrino Decay with ∆m2 > 0.1 eV2 . . . . . . . . . . . . . . . . 124
6.2.3 Neutrino Decay with ∆m2 unconstrained . . . . . . . . . . . . . 126
6.3 Comparisons and Discussions . . . . . . . . . . . . . . . . . . . . . . . . 132
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
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7. Massive Neutrinos in Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.1 Effect of Neutrino Oscillations in Vacuum . . . . . . . . . . . . . . . . . 141
7.2 The Effect of Delay in the Time of Flight . . . . . . . . . . . . . . . . . 148
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
8.2 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
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LIST OF FIGURES
Figure Page
3.1 The pp chain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The solar neutrino spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Super-K spectra at day and night. . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Earth regeneration as a function of E . . . . . . . . . . . . . . . . . . 41
∆m2
3.5 The regeneration factor f as a function of neutrino energy . . . . . . . . 42
reg
3.6 The neutrino survival probability vs. energy . . . . . . . . . . . . . . . . . 44
3.7 The allowed areas from global analysis of solar data . . . . . . . . . . . . . 46
3.8 The atmospheric fluxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.9 The zenith angle distribution of the Super-K atmospheric neutrino events. 55
3.10 The C.L. contours for ν ν oscillations of the atmospheric neutrinos . . 61
µ τ
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4.1 The effective energy independent regions . . . . . . . . . . . . . . . . . . . 76
4.2 The solar neutrino rates at maximal mixing . . . . . . . . . . . . . . . . . 78
4.3 Allowed contours for renormalized Cl and X . . . . . . . . . . . . . . . . 81
B
5.1 The variation of ∆χ2 with mixing parameters . . . . . . . . . . . . . . . . 95
5.2 Zenith angle distribution of the lepton events . . . . . . . . . . . . . . . . . 97
5.3 Zenith angle distribution of the lepton events . . . . . . . . . . . . . . . . . 98
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5.4 Allowed regions in ∆ sin2θ plane . . . . . . . . . . . . . . . . . . . . 101
23 23
−
5.5 Allowed regions in tan2θ tan2θ plane . . . . . . . . . . . . . . . . . . 102
12 13
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5.6 Allowed regions in s2 s2 plane . . . . . . . . . . . . . . . . . . . . . . . 103
12 − 23
5.7 Allowed regions in s2 s2 plane . . . . . . . . . . . . . . . . . . . . . . . 105
13 − 23
5.8 Allowed regions in ∆ s2 plane for ∆ 10−5 eV2 . . . . . . . . . . . 106
23 − 23 23 ∼
5.9 Allowed regions in ∆ s2 plane for s2 and s2 small . . . . . . . . . . . 107
23 − 23 12 13
5.10 Combined allowed regions in tan2θ tan2θ plane . . . . . . . . . . . . 110
12 13
−
5.11 Sensitivity of K2K in ∆ s2 plane . . . . . . . . . . . . . . . . . . . . . 112
23 − 23
5.12 Sensitivity of K2K in tan2θ tan2θ plane . . . . . . . . . . . . . . . . 114
12 13
−
6.1 R and Y vs. α for ∆m2 > 0.1 eV2 . . . . . . . . . . . . . . . . . . . . . 125
sg sg
6.2 R and Y vs. α for ∆m2 > 0.1 eV2 . . . . . . . . . . . . . . . . . . . . 126
mg mg
6.3 R and Y vs. ∆m2 for fixed α . . . . . . . . . . . . . . . . . . . . . . . . 127
sg sg
6.4 R and Y vs. ∆m2 at fixed α . . . . . . . . . . . . . . . . . . . . . . . 128
mg mg
6.5 ∆χ2 vs. α for osc+decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.6 Contour in ∆m2 sin22θ plane . . . . . . . . . . . . . . . . . . . . . . . 131
−
6.7 Contour in α sin22θ plane . . . . . . . . . . . . . . . . . . . . . . . . . 132
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6.8 Zenith angle distribution of the atmospheric events . . . . . . . . . . . . . 134
7.1 The supernova (ν d) signal at SNO vs neutrino energy . . . . . . . . . . 146
e
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7.2 The supernova neutrino fluence with and without oscillation . . . . . . . . 147
7.3 Time response of the neutral current events . . . . . . . . . . . . . . . . . 153
7.4 Ratio of CC to NC events as a function of time . . . . . . . . . . . . . . . 154
7.5 Moments of the neutral current events vs. time . . . . . . . . . . . . . . . 156
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7.6 Ratio of CC to NC moments vs. time . . . . . . . . . . . . . . . . . . . . . 158
7.7 Effect of supernova uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 159
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LIST OF TABLES
Table Page
3.1 The BPB00 predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 The observed solar neutrino rates . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 χ2 fits to the solar data for ν ν . . . . . . . . . . . . . . . . . . . . . 45
e active
−
3.4 χ2 fits to the solar data for ν ν . . . . . . . . . . . . . . . . . . . . 47
e sterile
−
3.5 The R and Y from the SK atmospheric data . . . . . . . . . . . . . . . . . 56
l
3.6 The reactor and accelerator experiments . . . . . . . . . . . . . . . . . . . 64
4.1 The energy independent fit . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 Results of MSW fits with X = 1.0 . . . . . . . . . . . . . . . . . . . . . . 79
B
4.3 Results of MSW fits with X = 0.75 . . . . . . . . . . . . . . . . . . . . . 80
B
4.4 Results of MSW fits with X free . . . . . . . . . . . . . . . . . . . . . . . 82
B
4.5 RCC /RNC at the best-fit values . . . . . . . . . . . . . . . . . . . . . . . 84
SNO SNO
5.1 Allowed range of parameters of the 3-gen analysis . . . . . . . . . . . . . . 96
6.1 Individual contributions to χ2 . . . . . . . . . . . . . . . . . . . . . . . . 129
min
7.1 Signal from a galactic supernova with vacuum oscillations . . . . . . . . . . 144
7.2 Signal from a galactic supernova for complete conversion . . . . . . . . . . 151
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