Exploring Supersymmetry and Naturalness in Light of New Experimental Data

Exploring supersymmetry and naturalness in light of new experimental data by Kevin Earl A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics Carleton University Ottawa-Carleton Institute for Physics Ottawa, Canada August 27, 2019 Copyright ⃝c 2019 Kevin Earl Abstract This thesis investigates extensions of the Standard Model (SM) that are based on either supersymmetry or the Twin Higgs model. New experimental data, primar- ily collected at the Large Hadron Collider (LHC), play an important role in these investigations. Specifically, we examine the following five cases. We first consider Mini-Split models of supersymmetry. These types ofmod- els can be generated by both anomaly and gauge mediation and we examine both cases. LHC searches are used to constrain the relevant parameter spaces, and future prospects at LHC 14 and a 100 TeV proton proton collider are investigated. Next, we study a scenario where Higgsino neutralinos and charginos are pair produced at the LHC and promptly decay due to the baryonic R-parity violating superpotential operator λ00U cDcDc. More precisely, we examine this phenomenology 00 in the case of a single non-zero λ3jk coupling. By recasting an experimental search, we derive novel constraints on this scenario. We then introduce an R-symmetric model of supersymmetry where the R- symmetry can be identified with baryon number. This allows the operator λ00U cDcDc in the superpotential without breaking baryon number. However, the R-symmetry will be broken by at least anomaly mediation and this reintroduces baryon number violation. Under these conditions, we investigate baryon number violating processes and flavour physics, as well as the collider phenomenology of both stops andthe 00 first two generations of squarks assuming they decay due to a single non-zero λ3jk coupling. There have been several experimental anomalies related to the quark level tran- sition b ! s``. We investigate these anomalies with the R-parity violating superpotential operator λ0LQDc. By examining diagrams featuring winos we find new pa- ii rameter space capable of explaining these anomalies while at the same time avoiding other experimental bounds. Finally, a variation of the Twin Higgs model is presented. These models stabilize the electroweak scale with particles uncharged under the SM colour group. This is accomplished by introducing a mirror sector to the SM and requiring an approximate Z2 symmetry between the two sectors. It is shown that it is beneficial to break the Z2 symmetry spontaneously rather than explicitly. iii Acknowledgments This thesis would not be possible without the considerable support I have received from many different people during my graduate studies at Carleton University. As such, I would like to acknowledge those who have helped me during the last six years. I apologize in advance to anyone who I have missed. First and foremost, I would like to express my immense gratitude to my su- pervisor Dr. Thomas Grégoire. I have benefitted greatly from not only his deep understanding of elementary particle physics, but also his unending patience and willingness to assist and guide me in my studies. Next, I would like to personally thank Dr. Hugues Beauchesne. During the first three years of my graduate studies, Hugues and I worked very closely on research projects. Perhaps the most important thing Hugues taught me during this time was the dedication and work ethic required to truly perform innovative research. I would also like to thank the other faculty members of the theory group: Dr. Heather Logan, Dr. Bruce Campbell, Dr. Stephen Godfrey, Dr. Daniel Stolarski, and Dr. Pat Kalyniak. Also deserving of recognition are my fellow graduate stu- dents: Katy Hartling, Terry Pilkington, Paul Smith, Dylan Linthorne, Jerome Claude, Rouzbeh Modarresi Yazdi, and Alex Poulin. I would also like to acknowledge the ad- ministrative staff of the physics department, particularly Joanne Martin and Karina Auclair for helping me print tutorial materials for PHYS 1007 and PHYS 1008. I would also like to acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) and the government of Ontario for providing very gen- erous and much appreciated financial assistance. Finally, I would like to thank my family: my parents Cheryl and David, my older brothers Brian and Steven, and my younger sister Megan. iv Statement of Originality Chapters2 and3 present reviews of the Standard Model and supersymmetry, respec- tively. The information contained in these chapters is well known and can be found in the references provided. Other than reviewing the preexisting literature, chapters4, 5,6,7, and8 present new results derived from original research. Each of these chapters are based on publications except chapter5 which is based on currently ongoing work. We list below which chapters correspond to which publications as well as detail the contributions made by myself and my collaborators to each of these projects. • The results presented in chapter4 are published in [1]. This project was also worked on by Hugues Beauchesne, a more senior graduate student. As such, the results from this chapter are also presented in Hugues Beauchesne's thesis. All results were individually derived (and cross-checked) by both of us except for the following points. { The gaugino pole mass calculations for both anomaly and gauge mediation presented in section 4.2.2 were computed by Hugues Beauchesne. { The writing of codes to recast experimental searches was split between the author and Hugues Beauchesne. { The scripts used to determine the efficiencies for different topologies to pass the cuts of experimental searches were written by the author. • The results presented in chapter5 are based on work that has yet to be published. All results in this chapter were derived by the author. • The results presented in chapter6 are published in [2]. The bounds on the λ00 couplings derived from baryon number violating processes and flavour physics v presented in section 6.2.1 were initially computed by Thomas Grégoire and were independently verified by the author. Except for the bounds coming from displaced vertices which were determined by Hugues Beauchesne, the analysis of the collider phenomenology presented in section 6.3 was performed by the author. • The results presented in chapter7 are published in [3]. All results in this chapter were derived by the author. • The results presented in chapter8 are published in [4]. This project was also worked on by Hugues Beauchesne. As such, the results from this chapter are also presented in Hugues Beauchesne's thesis. The main idea in this chapter, to break the Z2 symmetry spontaneously, was thought of by Hugues Beauch- esne. Many of the details of the model were also initially worked out by Hugues Beauchesne and subsequently confirmed by the author. The radiative correc- tions presented in section 8.2.3 were originally computed by the author and confirmed by Hugues Beauchesne. Except for the reservations described above, the research presented in this thesis is new and original (to my knowledge) and has not been published or submitted as a final project by any other individual. vi Contents 1 Introduction1 2 The Standard Model8 2.1 Introduction . .8 2.2 The symmetries of spacetime . .9 2.3 Quantum fields and their Lagrangians . 12 2.4 Non-abelian gauge theories . 22 2.5 Field content of the Standard Model . 24 2.6 Electroweak symmetry breaking . 27 2.7 The Standard Model as an effective field theory and the hierarchy problem . 33 3 Supersymmetry 35 3.1 Introduction . 35 3.2 The supersymmetry algebra . 37 3.3 Superfields . 40 3.3.1 Chiral superfields . 42 3.3.2 Vector superfields . 44 3.4 Supersymmetrically invariant Lagrangians . 47 vii 3.4.1 Kinetic terms for chiral superfields . 48 3.4.2 Kinetic terms for vector superfields . 50 3.4.3 The superpotential . 52 3.5 Soft supersymmetry breaking terms . 53 3.6 The scalar potential . 54 3.7 The MSSM . 55 3.7.1 Kinetic terms . 55 3.7.2 Superpotential . 58 3.7.3 Soft supersymmetry breaking terms . 59 3.7.4 Electroweak symmetry breaking . 61 3.8 Mediation mechanisms . 64 3.8.1 Gravity mediation . 65 3.8.2 Gauge mediation . 66 3.8.3 Anomaly mediation . 67 3.9 R-symmetries . 69 4 Phenomenology of Mini-Split supersymmetry 72 4.1 Introduction . 72 4.2 Theory . 74 4.2.1 Mini-Split models . 74 4.2.2 Gaugino mass spectrum . 77 4.2.3 Gaugino decays . 80 4.2.4 Higgs mass . 81 4.3 Methodology and results . 83 4.3.1 Parameter space . 83 4.3.2 Current LHC constraints . 86 viii 4.3.3 Prospects at LHC 14 . 91 4.3.4 Prospects at a 100 TeV collider . 97 4.4 Conclusion . 101 5 Phenomenology of Higgsinos with baryonic R-parity violation at the LHC 103 5.1 Introduction . 103 5.2 Majorana versus Dirac Higgsinos . 106 5.3 Higgsino masses . 114 5.4 Constraining Higgsinos at the LHC . 117 5.4.1 Higgsino decays . 118 5.4.2 Constraining points in the parameter space . 120 5.4.3 Parameter scan . 122 5.4.4 Results . 125 5.5 Conclusion . 129 6 Phenomenology of supersymmetric models with a U(1)R baryon number 131 6.1 Introduction . 131 6.2 The model . 133 6.2.1 Bounds on λ00 ........................... 135 6.2.1.1 Bounds from baryon number violating processes . 136 6.2.1.2 Bounds from flavour physics . 139 6.2.2 Spectrum and parameter space . 140 6.3 Collider constraints . 142 6.3.1 Placing limits on stops . 143 ix 6.3.1.1 Stop production . 143 6.3.1.2 Stop LSP .

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