Aspects of Scalar Field Theory and the Dark Matter Problem A Thesis Submitted to the College of Graduate and Postdoctoral Studies in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in the Department of Physics and Engineering Physics University of Saskatchewan Saskatoon By Frederick S. Sage c Frederick S. Sage, January 2019. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Physics and Engineering Physics 162 Physics Building 116 Science Place University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5E2 Dean College of Graduate and Postdoctoral Studies 116 Thorvaldson Building 110 Science Place University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5C9 i Abstract This thesis is comprised of research on the topic of particle dark matter phenomenology, with an emphasis on models in which a scalar field plays an important role. The dark matter problem is reviewed in Chapter 1, including the evidence that it is comprised of. Also included in Chapter 1 is an overview of the standard particle physics and quantum field theory that is used in the thesis. Chapter 2 is a discussion of the con- straints on models of particle dark matter from observations of the abundance, assuming thermal production mechanisms in the early universe. The thermal constraints on scalar Higgs-portal dark matter are discussed as an example. The direct detection of dark matter through nuclear recoils is covered in Chapter 3, which provides an overview of the basic theory and a discussion of the various experiments and their reported and predicted results. Some discussion of the future of direct detection is included, as is the application of the techniques to the example case of scalar Higgs-portal dark matter. Chapter 4 contains some details about the indirect detection of dark matter through observation of the products of its annihilation in the galactic halo, primarily through the gamma ray channel. Several possible gamma ray targets are considered, including the galactic core, dwarf spheroidal galaxies, and searches for signals in the isotropic background. The Chapter closes with the usual example of scalar Higgs-portal dark matter. In Chapter 5 collider signatures of dark matter are discussed. After a lengthy review of collider physics, the basic techniques for placing bounds on dark matter models using collider data are discussed, and finally the scalar Higgs-portal model is discussed in the context of collider signals. Chapter 6 explores a theoretically motivated model of vector-portal fermionic dark matter, including collider bound on the vector mediator, thermal constraints on the dark matter particle based on abundance observations, and bound from direct and indirect detection. The theoretical background renders the phenomenology of the model exceptionally predictive, and the viability of the model given current observations is discussed. Chapter 7 contains some concluding remarks. ii Acknowledgements This thesis, and the research that has gone into it, have taken some time. There are many people who have helped me along the way, without whom I would no doubt never have gotten so far. A great deal of thanks is owed to my doctoral supervisor, Prof. Rainer Dick. Without his patient guidance and firm support over these last several years, I would never have been able to get to this point. I would also like to thank my Advisory Committee, Prof. Masoud Ghezelbash, Prof. Rob Pywell, Prof. Jacek Szmigielski, and Prof. Adam Bourassa, for their helpful advice and support throughout my degree. I must also thank my collaborators, Zhi-Wei Wang, Jason Ho, Tom Steele, and Rob Mann, for putting up with me during our work together. Finally, I must thank the late Prof. Jim Brooke, my undergraduate advisor and the instructor of several of my classes. Without his enthusiastic support, I would have stumbled many years ago. I would like to thank Ben Zitzer and David Hanna for their assistance in sharing the data for the portion of Chapter 4 that deals with VERITAS observations of Segue I, as well as the MAGIC collaboration and Javier Rico in particular for providing the bounds on the annihilation cross sections that were used in Chapter 4. I have been supported during these studies by a William J Rowles Fellowship, a Gerhard Herzberg Fellowship, a Teacher-Scholar Doctoral Fellowship, and several Graduate Research Fellowships. Travel during this time has been supported by several University Travel Awards and Herzberg Travel Awards. And of course there is the inevitable list of graduate students (most of whom are no longer graduate students) who impacted (mostly positively) my academic life here. I would like to thank Tony Bathgate, Ryan Berg, Dena Burnett, Stephanie Goertzen, Adrian Hunt, Darren Hunter, Daryl Janzen, Robin Kleiv, John McLeod, Sarah Purdy, Grant Scouler, Haryanto Siahaan, Paul Smith, Greg Tomney, Niloofar Zarifi, and Dan Zawada. And I guess I should thank my parents, for having me. iii Contents Permission to Use i Abstract ii Acknowledgements iii Contents iv List of Tables vii List of Figures viii List of Abbreviations xiii 1 Background and Motivation1 1.1 The dark matter problem ...................................... 1 1.1.1 Basic statement........................................ 1 1.1.2 Theme of thesis........................................ 2 1.1.3 Outline of thesis ....................................... 3 1.2 Basic particle physics......................................... 4 1.2.1 Conventions and notation.................................. 5 1.2.2 Quantum field theory .................................... 7 1.2.3 Symmetries in quantum field theory ............................ 9 1.2.4 Relativistic quantum field theory.............................. 10 1.2.5 Representations of the Lorentz group............................ 15 1.2.6 Renormalization and the renormalization group equations................ 18 1.2.7 The gauge principle and quantum electrodynamics.................... 23 1.2.8 Nonabelian gauge theory and quantum chromodynamics................. 24 1.2.9 The GSW theory of electroweak interactions ....................... 27 1.2.10 Symmetry breaking in classical field theory ........................ 30 1.2.11 The Higgs mechanism .................................... 34 1.3 Evidence for dark matter ...................................... 37 1.3.1 Galactic scale evidence.................................... 37 1.3.2 Cluster scale evidence .................................... 39 1.3.3 Cosmological scale evidence................................. 43 1.4 Solutions to the dark matter problem ............................... 47 1.4.1 Weakly interacting massive particles............................ 47 1.4.2 Axion-like particles...................................... 48 1.4.3 Right handed neutrinos ................................... 50 1.4.4 Modified theories of gravity................................. 52 2 Thermal Relic Dark Matter 54 2.1 Thermal history of the universe................................... 54 2.2 Particle statistical mechanics in the early universe ........................ 57 2.3 Freeze-out of cold dark matter ................................... 60 2.4 Example - Higgs-portal scalars ................................... 65 3 Direct Detection of Dark Matter 69 3.1 Event Rates.............................................. 69 3.1.1 Basic recoil physics...................................... 70 iv 3.1.2 Recoil cross sections..................................... 71 3.1.3 Nuclear physics effects.................................... 72 3.1.4 Astrophysical parameters .................................. 73 3.1.5 Directional searches ..................................... 74 3.2 Direct detection experiments .................................... 74 3.2.1 Detection channels...................................... 74 3.2.2 Detector materials...................................... 75 3.2.3 Backgrounds ......................................... 78 3.2.4 Experimental collaborations................................. 80 3.3 Current exclusion limits....................................... 81 3.3.1 Spin dependent limits .................................... 81 3.3.2 Spin independent limits ................................... 83 3.3.3 Annual modulation signals ................................. 85 3.3.4 The neutrino floor ...................................... 86 3.4 Example: Scalar Higgs-portal dark matter............................. 89 4 Indirect Detection of Dark Matter 94 4.1 Gamma ray signals.......................................... 95 4.1.1 Prompt photon spectra ..................................