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A Pittetd-Thesis Sample 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 ful¯llment 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 °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 ¯rst 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 e®ect modi¯es 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 kfs, function of mass and distribution of WDM particles. We discover WDM acoustic oscillations at small scales about k ¸ 2kfs and an Integrated Sachs-Wolfe (ISW) e®ect in the Radiation Dominant (RD) era which enhances the matter power spectrum for k · kfs. A quasi-degeneracy between the mass and distribution function of WDM on the matter power spectrum is identi¯ed, suggesting an inherent ambiguity of Lyman-® 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 ¤CDM COSMOLOGICAL MODEL ........... 14 2.2 SMALL SCALE PROBLEMS OF ¤CDM 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-® 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 PART I: STERILE NEUTRINOS PRODUCED AT THE ELECTROWEAK 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 Helicity dependence: right-handed sterile neutrinos and standard model 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 IMAGINARY PARTS: WIDTHS FROM VECTOR AND SCALAR BOSON 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 Homogeneous Equation: 2nd-order Associated Legendre Equa- 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 Di®erent 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-® 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
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