Precision Higgs Physics, Effective Field Theory, and Dark Matter by Brian Quinn Henning A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Hitoshi Murayama, Chair Professor Wick C. Haxton Professor Phillip L. Geissler Summer 2015 Precision Higgs Physics, Effective Field Theory, and Dark Matter Copyright 2015 by Brian Quinn Henning 1 Abstract Precision Higgs Physics, Effective Field Theory, and Dark Matter by Brian Quinn Henning Doctor of Philosophy in Physics University of California, Berkeley Professor Hitoshi Murayama, Chair The recent discovery of the Higgs boson calls for detailed studies of its properties. As precision measurements are indirect probes of new physics, the appropriate theoretical framework is effective field theory. In the first part of this thesis, we present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on the UV model concerned. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. The covariant derivative expansion dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of renormalization group running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. With a detailed understanding of how to use the SM EFT, we then turn to applications and study in detail two well-motivated test cases. The first is singlet scalar field that enables the first- order electroweak phase transition for baryogenesis; the second example is due to scalar tops in the MSSM. We find both Higgs and electroweak measurements are sensitive probes of these cases. The second part of this thesis centers around dark matter, and consists of two studies. In the first, we examine the effects of relic dark matter annihilations on big bang nucleosynthesis (BBN). The magnitude of these effects scale simply with the dark matter mass and annihilation cross- section, which we derive. Estimates based on these scaling behaviors indicate that BBN severely constrains hadronic and radiative dark matter annihilation channels in the previously unconsidered dark matter mass region MeV . mχ . 10 GeV. Interestingly, we find that BBN constraints on hadronic annihilation channels are competitive with similar bounds derived from the cosmic microwave background. Our second study of dark matter concerns a possible connection with supersymmetry and the keV scale. Various theoretical and experimental considerations motivate models with high scale supersymmetry breaking. While such models may be difficult to test in colliders, we propose 2 looking for signatures at much lower energies. We show that a keV line in the X-ray spectrum of galaxy clusters (such as the recently disputed 3.5 keV observation) can have its origin in a universal string axion coupled to a hidden supersymmetry breaking sector. A linear combination of the string axion and an additional axion in the hidden sector remains light, obtaining a mass of order 10 keV through supersymmetry breaking dynamics. In order to explain the X-ray line, the scale of supersymmetry breaking must be about 1011-12 GeV. This motivates high scale supersymmetry as in pure gravity mediation or minimal split supersymmetry and is consistent with all current limits. Since the axion mass is controlled by a dynamical mass scale, this mass can be much higher during inflation, avoiding isocurvature (and domain wall) problems associated with high scale inflation. In appendix E we present a mechanism for dilaton stabilization that additionally leads to (1) modifications of the gaugino mass from anomaly mediation. O i For my parents, Mark and Mary ii Contents Contents ii 1 Introduction 1 1.1 Precision Higgs physics and effective field theory . ............. 1 1.1.1 The Higgs, dimensional analysis, and the hierarchy problem ........ 2 1.1.2 Naturalsolutions .............................. 5 1.1.3 PrecisionHiggsphysics. 7 1.1.4 TheSMeffectivefieldtheory. 8 1.2 Darkmatter ...................................... 10 1.2.1 Cosmological evidence of dark matter . ..... 10 1.2.1.1 A diversion on the lower bound of allowed DM mass . 12 1.2.2 SearchingforDM............................... 13 1.2.3 Dark matter and Big Bang nucleosynthesis . ..... 14 1.2.4 AkeVstringaxion .............................. 16 2 How to Use the Standard Model Effective Field Theory 18 2.1 Covariant derivative expansion . ....... 23 2.1.1 Covariant evaluation of the tree-level and one-loop effective action . 25 2.1.1.1 Covariant evaluation of the tree-level effective action . 26 2.1.1.2 CDE of the one-loop effective action . 28 2.1.2 CDE for fermions, gauge bosons, and summary formulas . ........ 31 2.1.3 Evaluating the CDE and universal results . ...... 35 2.1.3.1 Evaluating terms in CDE . 35 2.1.3.2 Universalresults . 38 2.1.4 Examplecalculations . 42 2.1.4.1 Electroweak triplet scalar . 44 2.1.4.2 ExtraEWscalardoublet . 49 2.1.4.3 A SU(2)L quartetscalar ...................... 54 2.1.4.4 Kinetic mixing of gauge bosons . 55 2.1.4.5 Heavy vector bosons in the triplet representation of SU(2)L . 56 2.2 Running of Wilson coefficients and choosing an operator set ............ 58 2.2.1 When is RG running important? . 59 iii 2.2.2 Choosing an operator set in light of RG running analysis . ......... 60 2.2.3 Popular operator bases in the literature . ......... 61 2.3 Mapping Wilson coefficients onto observables . ........... 63 2.3.1 Electroweak precision observables . ....... 64 2.3.2 Triple gauge couplings . 67 2.3.3 Deviations in Higgs decay widths . .... 67 2.3.3.1 Brief description of the results . 68 2.3.3.2 Detailed derivation . 71 2.3.4 Deviations in Higgs production cross sections . .......... 73 2.4 Applications.................................... 74 2.4.1 Electroweak baryogenesis from a real singlet scalar . ............ 76 2.4.1.1 Effects on precision observables . 78 2.4.2 Supersymmetry and light scalar tops . ...... 81 2.5 Summaryofresults ................................ 83 3 Constraints on Light Dark Matter from Big Bang Nucleosynthesis 87 3.1 EnergyinjectionintoBBN . 88 3.1.1 Injection of hadronic energy . .... 89 3.1.2 Injection of electromagnetic energy . ....... 90 3.2 ConstraintsfromBBN ................................ 91 3.2.1 Hadronic constraints . 93 3.2.2 Electromagnetic constraints . ...... 93 3.2.3 Other annihilation channels . ..... 94 3.3 Discussion...................................... 96 4 A keV String Axion from High Scale Supersymmetry 97 4.1 Anexplicitmodel ................................. 99 4.2 Cosmology ...................................... 102 4.3 Discussion...................................... 103 A Supplemental details for the CDE 106 A.1 CDE for fermions and gauge bosons . .... 106 A.2 Usefulidentities................................ .... 111 A.3 Evaluating terms in the CDE: results for the ................... 114 In B Universality of Magnetic Dipole Term 116 B.1 AlgebraicProof ................................... 117 B.2 PhysicalProof.................................... 120 C Supplemental Details for Mapping Wilson Coefficients on to Physical Observables 122 C.1 Additional Feynman rules from dim-6 effective operators .............. 122 C.1.1 Feynman rules for vacuum polarization functions . ......... 122 iv C.1.2 Feynman rules for three-point vertices . ....... 125 C.2 Details on interference corrections to the Higgs decay widths ............ 127 C.3 Details on interference corrections to Higgs production crosssection . 131 C.4 Calculation of residue modifications . ....... 134 C.5 Calculation of Lagrangian parameter modifications . ........... 134 D Observational Abundances of Light Elements 137 E Axion Potential and Dilaton Stabilization 138 E.1 Axionpotential .................................. 138 E.1.1 Wtree =0 ................................... 138 E.1.2 Wtree =0 ................................... 141 E.2 DilatonStabilization6 . ..... 142 Bibliography 145 v Acknowledgments This thesis, and my education in general, is the product of numerous educators, collaborators, friends, and family who shaped the path I wandered and supported me as I traveled it. In no reasonable manner can this acknowledgments page do justice to all these wonderful people, but I hope it can at least manage to capture my gratitude. I thank Dr. T.J. Donahue for igniting my interest in scientific research. He opened the door to research and went above and beyond to create opportunities; moreover, he made science cool. The world benefits greatly from high school teachers like Dr. D. I was incredibly fortunate to have the opportunity of working in research labs at the University of Colorado Health Sciences Center while still in high school. For encouraging curiosity and taking the time to share a passion—all the while treating me like a colleague—I am so incredibly grateful to Doug, Holly, Jamie, Jim, Julie, Natalie, Petra, Tammy, and, especially, Adrie van Bokhoven. I may not have ended up studying