Neutrinos in Cosmology and Particle Physics

244 Pages·2011·2.46 MB·English

by  Jun Wu

NEUTRINOS IN COSMOLOGY AND PARTICLE
PHYSICS
by
Jun Wu
Bachelor of Science, Beijing Normal University, 2003
Master of Philosophy, The Chinese University of Hong Kong, 2005,
Master of Science, University of Pittsburgh, 2007
Submitted to the Graduate Faculty of
the Department of Physics and Astronomy in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Pittsburgh
2011
UNIVERSITY OF PITTSBURGH
KENNETH P. DIETRICH SCHOOL OF ARTS AND SCIENCES
This dissertation was presented
by
Jun Wu
It was defended on
November 19, 2011
and approved by
Daniel Boyanovsky, Professor, Department Of Physics & Astronomy
Richard Holman, Professor, Department of Physics
Arthur Kosowsky, Associate Professor, Department of Physics & Astronomy
Adam Leibovich, Associate Professor, Department of Physics
Donna Naples, Associate Professor, Department of Physics
Andrew Zentner, Associate Professor, Department of Physics
Dissertation Director: Daniel Boyanovsky, Professor, Department Of Physics & Astronomy
ii
Copyright (cid:176)c by Jun Wu
2011
iii
NEUTRINOS IN COSMOLOGY AND PARTICLE PHYSICS
Jun Wu, PhD
University of Pittsburgh, 2011
This thesis discusses two independent research topics. We first study keV sterile neutrinos
as a Warm Dark Matter (WDM) candidate, focusing on their production at temperatures
of the electroweak scale and the linear structure growth of WDM particles with arbitrary
distribution functions and masses of keV scale. At temperatures of the electroweak scale, the
medium effect modifies the mixing angle between sterile and active neutrinos, introducing
two narrow Mikheev-Smirnov-Wolfenstein (MSW) resonances that break adiabaticity and
enhance the non-thermal production of sterile neutrinos at small momenta. One of the two
MSW resonances is in the absence of a lepton asymmetry and occurs only at temperatures
around the electroweak scale. By solving the linearized collision-less Boltzmann equation,
we obtain a semi-analytical expression of the matter power spectrum for WDM particles
with arbitrary distributions agreeing within a few percent error with results from Boltzmann
codes. This matter power spectrum depends on the horizon size at matter-radiation equality
and the free streaming wave vector k , function of mass and distribution of WDM particles.
fs
We discover WDM acoustic oscillations at small scales about k ≥ 2k and an Integrated
fs
Sachs-Wolfe (ISW) effect in the Radiation Dominant (RD) era which enhances the matter
power spectrum for k ≤ k . A quasi-degeneracy between the mass and distribution function
fs
of WDM on the matter power spectrum is identified, suggesting an inherent ambiguity of
Lyman-α analysis to constrain WDM parameters. Secondly, based on the observation that
neutrinos produced from decay via the charge current interaction are entangled with the
corresponding charged leptons, we re-investigate the theory of neutrino oscillations with
the focus of the dynamics of the entangled state. We study the dynamics of entanglement
iv
and dis-entanglement explicitly in time, which leads to non-conventional expressions for
neutrino oscillation amplitudes and probabilities suggesting possible corrections for short
baseline neutrino oscillation experiments. By applying this method to the GSI anomaly, we
unambiguously show that the GSI anomaly is not a consequence of neutrino oscillations.
v
TABLE OF CONTENTS
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
1.0 OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 INSTRUCTION FOR READERS . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 NEUTRINOS: A WINDOW TO PHYSICS BEYOND THE STANDARD
MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 SUMMARY OF MAIN RESULTS . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Part I (Chapters 2 to 4): keV Sterile Neutrinos as a WDM Candidate 6
1.3.2 Part II (Chapters 5 to 7): Theory on Neutrino Oscillations . . . . . . 9
1.3.3 Chapter 8: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 PUBLICATION LIST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.0 PART I: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 CONCORDANCE ΛCDM COSMOLOGICAL MODEL . . . . . . . . . . . 14
2.2 SMALL SCALE PROBLEMS OF ΛCDM MODEL . . . . . . . . . . . . . 17
2.2.1 Missing Satellite Problem . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Cusp Problems in Galaxy Centers . . . . . . . . . . . . . . . . . . . 20
2.3 STERILE NEUTRINOS AND OBSERVATIONAL CONSTRAINTS . . . 21
2.3.1 Upper Bound from X-ray Constraints . . . . . . . . . . . . . . . . . 22
2.3.2 Lower Bond from Phase Space Density of Dwarf Galaxies . . . . . . 22
2.3.3 Constraints From Lyman-α Forest . . . . . . . . . . . . . . . . . . . 23
2.4 SUMMARY OF OUR WORK . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Sterile Neutrinos Produced at the Electroweak Scale . . . . . . . . . 26
2.4.2 Small Scale Aspects of WDM: Power Spectra and Acoustic Oscillations 29
vi
3.0 PARTI:STERILENEUTRINOSPRODUCEDATTHEELECTROWEAK
SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 THE MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 EQUATION OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 One-Loop Self-Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 Propagator: complex poles and propagating modes in the medium . 48
3.2.3 Helicitydependence: right-handedsterileneutrinosandstandardmodel
interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 REAL PARTS: MIXING ANGLES AND MSW RESONANCES . . . . . . 53
3.3.1 Mixing angles and MSW resonances: . . . . . . . . . . . . . . . . . . 59
3.3.1.1 Case with vanishing lepton asymmetry . . . . . . . . . . . . 59
3.3.1.2 Case With non-vanishing lepton asymmetry . . . . . . . . . 62
3.4 IMAGINARYPARTS:WIDTHSFROMVECTORANDSCALARBOSON
DECAY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Widths from scalar and vector boson decay: . . . . . . . . . . . . . . 67
3.4.2 Imaginary parts: from the width to the production rates. . . . . . . 70
3.4.3 Weak or strong damping? . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.4 Regime of validity of perturbation theory. . . . . . . . . . . . . . . . 73
3.5 NEUTRINO PRODUCTION IN AN EXPANDING UNIVERSE . . . . . . 74
3.6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.0 PART I: LINEAR STRUCTURE GROWTH IN THE WDM SCENARIO 80
4.1 COSMOLOGY PRELIMINARIES: FRIEDMAN EQUATION . . . . . . . 81
4.2 DENSITY PERTURBATION OF DMS: GENERAL ASPECTS . . . . . . 82
4.2.1 Collision-less Boltzmann Equation . . . . . . . . . . . . . . . . . . . 83
4.2.1.1 Unperturbed Collision-less Boltzmann Equation . . . . . . . 84
4.2.1.2 Linearly Perturbed Collision-less Boltzmann Equation . . . . 86
4.2.2 Formal Solution Of The Linearly Perturbed Collision-less Boltzmann
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.3 Initial Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.4 Transfer Function and Super-horizon Mode . . . . . . . . . . . . . . 92
vii
4.3 CDM AND WDM: DIFFERENT EVOLUTION HISTORIES . . . . . . . 93
4.3.1 Our Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.3.2 Free Streaming Distance of CDMs and WDMs . . . . . . . . . . . . 97
4.4 CDM CASE: TIME EVOLUTION AND THE TRANSFER FUNCTION . 101
4.4.1 Density Perturbations of WIMPs in the RD Era . . . . . . . . . . . 102
4.4.1.1 Density Perturbations of Photons in The RD Era . . . . . . 103
4.4.1.2 Radiation Cross-over . . . . . . . . . . . . . . . . . . . . . . 104
4.4.2 Density Perturbations of WIMPs in the MD Era . . . . . . . . . . . 105
4.4.2.1 2nd-order Legendre Equation . . . . . . . . . . . . . . . . . . 106
4.4.2.2 Transfer Function of WIMPs . . . . . . . . . . . . . . . . . . 108
4.4.2.3 An Alternative Method: To Compare with the WDM Case . 109
4.5 WDM CASE: TIME EVOLUTION OF STERILE NEUTRINO DENSITY
PERTURBATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5.1 Stage I: Relativistic Sterile Neutrinos in the RD Era . . . . . . . . . 112
4.5.2 Stage II and III: Non-relativistic Sterile Neutrinos . . . . . . . . . . 115
4.5.2.1 Inhomogeneous Equation for Sterile Neutrino Density Pertur-
bations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.5.2.2 Asymptotic Behavior . . . . . . . . . . . . . . . . . . . . . . 118
4.5.2.3 HomogeneousEquation: 2nd-orderAssociatedLegendreEqua-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.5.2.4 Green’s Function And the Full Solution . . . . . . . . . . . . 121
4.5.2.5 The Born Approximation Of Density Perturbations . . . . . 123
4.6 WDM CASE: TRANSFER FUNCTION AND POWER SPECTRUM . . . 124
4.6.1 Transfer Function of Sterile Neutrinos . . . . . . . . . . . . . . . . . 125
4.6.1.1 Numerical Evaluation . . . . . . . . . . . . . . . . . . . . . . 127
4.6.1.2 Transfer Function of Sterile Neutrinos With Different Masses
And Distributions . . . . . . . . . . . . . . . . . . . . . . . . 129
4.6.1.3 ISW Enhancement . . . . . . . . . . . . . . . . . . . . . . . 129
4.6.1.4 “Acoustic Oscillations” of WDM . . . . . . . . . . . . . . . . 131
4.6.2 Power Spectrum Of Sterile Neutrinos . . . . . . . . . . . . . . . . . . 134
viii
4.6.3 Comparison to Numerical Results From Boltzmann Codes . . . . . . 135
4.6.4 Impact On N-body Simulation And Lyman-α Constraints . . . . . . 137
4.7 SUMMARY AND CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . 139
5.0 PART II: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.1 THEORY OF NEUTRINO OSCILLATION IN PLANE WAVE LIMIT . . 148
5.2 NEUTRINO OSCILLATION UNDER WAVE PACKET TREATMENT . . 151
5.3 SUBTLE ISSUES OF THE THEORY OF NEUTRINO OSCILLATIONS . 156
5.4 SUMMARY OF OUR WORK . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.4.1 Dynamics of Disentanglement And Coherence In Neutrino Oscillations 159
5.4.2 Application of the Plane Wave Result to the GSI Anomaly . . . . . . 159
6.0 PART II: DYNAMICS OF DISENTANGLEMENT AND COHER-
ENCE IN NEUTRINO OSCILLATIONS . . . . . . . . . . . . . . . . . . . 161
6.1 A MODEL OF “NEUTRINO” OSCILLATIONS . . . . . . . . . . . . . . . 161
6.2 INTERACTION NEAR THE SOURCE . . . . . . . . . . . . . . . . . . . 164
6.2.1 Unobserved daughter particles: time evolution of the density matrix 165
6.2.2 Disentangling the neutrino: a two-time measurement . . . . . . . . . 170
6.2.3 Transition amplitudes and event rates . . . . . . . . . . . . . . . . . 173
6.3 INTERACTION AT THE FAR DETECTOR . . . . . . . . . . . . . . . . 173
6.3.1 Transition amplitude and probabilities . . . . . . . . . . . . . . . . . 174
6.3.2 Factorization of the event rates . . . . . . . . . . . . . . . . . . . . . 176
6.4 DISCUSSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.4.1 Possible corrections for short baseline experiments . . . . . . . . . . 178
6.4.2 Wave packet description . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.0 PART II: IS THE GSI ANOMALY DUE TO NEUTRINO OSCILLA-
TIONS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.1 INTRODUCTION TO THE GSI ANOMALY . . . . . . . . . . . . . . . . 183
7.2 A MODEL FOR THE GSI ANOMALY . . . . . . . . . . . . . . . . . . . 186
7.3 NUMBER DENSITIES OF THE PARENT AND THE DAUGHTER PAR-
TICLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
ix
7.3.1 Number Density of Daughter Particles . . . . . . . . . . . . . . . . . 190
7.3.2 Number Density of Parent Particles . . . . . . . . . . . . . . . . . . 194
7.4 CONCLUSION AND DISCUSSIONS . . . . . . . . . . . . . . . . . . . . . 196
8.0 CONCLUSION OF THE THESIS . . . . . . . . . . . . . . . . . . . . . . . 198
8.1 STERILE NEUTRINO PRODUCED AT THE ELECTROWEAK SCALE 198
8.2 LINEAR STRUCTURE GROWTH IN THE WDM SCENARIO . . . . . . 199
8.3 DYNAMICS OF DISENTANGLEMENT AND COHERENCE IN NEU-
TRINO OSCILLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.4 IS THE GSI ANOMALY DUE TO NEUTRINO OSCILLATIONS? . . . . 201
APPENDIX A. APPENDIX FOR STERILE NEUTRINO PRODUCTION 202
A.1 STANDARD MODEL (SM) VECTOR BOSON EXCHANGE . . . . . . . 202
A.2 BEYOND STANDARD MODEL (BSM) SCALAR EXCHANGE . . . . . . 203
APPENDIX B. NUMERICAL MANIPULATION OF I (K,U) . . . . . . . . 204
1
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
x