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Grand Unification Phenomenology at the LHC and Beyond

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Grand Unification Phenomenology at the LHC and Beyond UNIVERSITY OF GLASGOW SCHOOL OF PHYSICS AND ASTRONOMY PARTICLE PHYSICS THEORY GROUP Grand Unification Phenomenology at the LHC and Beyond Ant´onioPestana Morais Presented as a thesis for the degree of Doctor of Philosophy December 2013 Abstract We investigate models of supersymmetric grand unification based on the gauge groups SU(5), SO(10) and E6, as well as in a class of orbifolds inspired by four dimensional Strings. We follow a stepwise analysis starting our journey with a revisit to the Standard Model and commenting on major issues that are motivation for new physics. We then introduce supersymmetry and discuss the Minimal Supersymmetric Standard Model (MSSM), with a detailed analysis of its mass spectrum. We study the evolution of the strong and electroweak forces with the energy scale, and interpret the near match of the gauge couplings at the high scale as a clue for the unification of strong and electroweak interactions. The second half of our journey starts with the introduction of the SU(5), SO(10) and E6 symmetries. We provide a review of main aspects such as proton stability, split multiplets and Yukawa unification, and show how the MSSM soft parameters may be constrained by these groups. We demonstrate how the measurement of the first and second generation supersymmetric spectrum may be used to probe the underlying grand unification structure and compare our expressions with numerical calculations. We consider SU(5) and SO(10) models with non-universal gaugino masses and confront them with low energy constraints, including the Higgs boson mass and the Dark Matter relic density. We also discuss fine-tuning and show the effect of not including the µ-parameter into fine tuning determinations. With this relaxation, we find viable scenarios with low fine tuning and study some model choices for gaugino mass ratios. We demonstrate that gaugino masses inspired by some orbifold models may provide low fine-tuning and the preferred relic abundance of Dark Matter while evading all experimental constraints. We also determine high scale Yukawa coupling ratios and confront the results with theoretical predictions. We finally consider orbifold models to constrain the full set of soft parameters, and argue that a String inspired framework presents definite theoretical background to relax fine-tuning constraints. We present benchmarks for all our scenarios that should be explored at the LHC and future colliders. i Acknowledgements I want to thank the University of Glasgow for welcoming me during the last four years and always providing the essential facilities for a healthy student life. I also want to thank to all members of the particle physics theory group for their constant cheer and availability to discuss physics and non-physics related topics, which contributed for a very pleasant working environment. In particular I want to thank Brian, Dan, Gordon, Kate, Liam, Stacey, Bipasha and Ben for the amusing times spent with them, and will never forget the ”points game”, or the ”would you rather game”. I am very grateful to David Miller for his availability in becoming my supervisor, even without knowing me at first. David early understood my working method and gave me all the conditions to consistently grow as a physicist. I will not forget our weekly meetings, as well as the conferences in Bonn, Chicago and Stockholm, which have decisively contributed to my motivation and learning. I would also like to express my sincere and special thanks to David Sutherland, who had an important participation in our weekly meetings, raising crucial questions, providing restless support, criticism and, above all, very fruitful discussions. David Sutherland undoubtedly became a physicist of reference for me that I will not forget. I also want to thank Prof. Christine Davies as head of the PPT group, for welcoming me in the group even before being awarded with my scholarship. I want to thank the members of the Gr@v group at the Physics Department of the University of Aveiro, particularly Marco Sampaio, Carlos Herdeiro and Joao˜ Rosa for fruitful discussions and hospitality during visits to Aveiro. I am also very grateful for their availability in supporting my application for a Post-Doc grant, and I am looking forward to become a member of the group as soon as possible. I acknowledge FCT for the grant SFRH/BD/62203/2009 and partial support by the grants PTDC/FIS/116625/2010 and PTDC/FIS/117951/2010. iii I want to thank my parents for being present in all moments of my life and never denying me any help or support. They also supported part of my academic and scientific life, so this thesis is also for them. Without their care, I am sure that I would not be here writing these words. A very special word for Rita, my girlfriend, who is responsible for one of the best periods of my life and always gave me all the emotional support needed to carry on doing physics and running after my dreams. Thank you Rita for being a special and unique person!! This thesis is also dedicated to you! Finally, I want to remember my grandmother, and thank her for everything she was for me. She may no longer be around, but I am sure she is very happy about this moment of my life... wherever she is. Declaration I declare that the research presented in this thesis is my original work and has not been previously presented for a degree. Furthermore, citations were always included whenever published material was used. Chapters 2 to 5 provide a general overview of my field of research and serve as theoretical introduction for the remaining chapters. The work presented in chapter 6 was accomplish in collaboration with Prof. Pran Nath Pandita and my supervisor Dr. David Miller. Chapters 7, 8 and 9 contain work that was carried out in close collaboration with Dr. David Miller. v Contents 1. Introduction1 2. The Standard Model5 2.1. Symmetries in the Standard Model6 2.2. The Gauge Structure of the Standard Model8 2.2.1. Quantum Electrodynamics8 2.2.2. Yang-Mills Theories 10 2.3. Electroweak Symmetry Breaking in the Standard Model 14 2.3.1. The Higgs Mechanism 15 2.4. Renormalization and Running of the Gauge Couplings 21 2.5. Motivations for Physics Beyond the Standard Model 26 2.5.1. The Hierarchy Problem 27 3. Supersymmetry 31 3.1. Supersymmetric Algebra 31 3.2. Lagrangians for Chiral and Gauge Superfields 34 3.2.1. Chiral Interactions 34 3.2.2. Gauge Interactions 36 3.2.3. Solution to the Hierarchy Problem 38 3.3. Soft Supersymmetry Breaking 40 3.3.1. Soft Scalar Masses and Bilinear Couplings 42 3.3.2. Soft Trilinear Couplings 42 3.3.3. Gaugino Masses 43 4. The Minimal Supersymmetric Standard Model 45 4.1. Superfields in the MSSM 45 4.2. Superpotential and Soft Lagrangian 46 4.3. Physical Masses in the MSSM 48 4.3.1. Electroweak Symmetry Breaking 48 4.3.2. Higgs and Gauge Boson Masses 50 4.3.3. Fermion and Sfermion Masses 55 4.3.4. Gluino, Neutralino and Chargino Masses 58 4.4. Running of the Gauge Couplings in the MSSM 60 vii Contents 5. Grand Unification 63 5.1. SU(5) Grand Unification 63 5.1.1. Proton Decay via Heavy Boson Exchange 66 5.1.2. Doublet-Triplet Splitting Problem 69 5.1.3. Yukawa Coupling Unification 71 5.2. SO(10) Grand Unification 72 5.2.1. Breaking Chains 72 5.2.2. Yukawa Couplings and Higgs Representations 75 5.3. E6 Grand Unification 76 6. Constraining Grand Unification using the First and Second Generation Sfermions 79 6.1. Integration of the Renormalization Group Equations 81 6.2. Boundary Conditions 83 6.2.1. SU(5) 83 6.2.2. SO(10) 86 6.2.3. E6 89 6.3. Including Additional Matter: The E6SSM 91 6.4. A Comparison with SOFTSUSY 95 6.4.1. SU(5) Boundary Conditions 95 6.4.2. SO(10) Boundary Conditions 96 6.5. Extension for Non-Universal Gaugino Masses 98 7. SU(5) Grand Unification Phenomenology 101 7.1. The SU(5) GUT Model 101 7.1.1. Soft Scalar Masses 102 7.1.2. Soft Trilinear Couplings 103 7.1.3. Gaugino Masses 103 7.1.4. Summary of the Parameter Space 103 7.2. Constraints on the Particle Spectrum 103 7.2.1. Experimental Constraints 104 7.2.2. Fine-tuning 106 7.3. Universal Gaugino Masses 108 7.4. Non-Universal Gaugino Masses 112 7.4.1. An Inclusive Scan 114 7.4.2. An Enhanced Scan Over M1=2, ρ1 and ρ2 118 7.5. Scenarios with Fixed Gaugino Mass Ratios 122 7.5.1. SU(5)200 Model 124 7.5.2. BIM Orbifold Models 126 7.5.3. First and Second Generation Squarks and Gluinos 129 viii Contents 7.6. Benchmark Points 132 8. SO(10) Grand Unification Phenomenology 137 8.1. The SO(10) GUT Model 137 8.1.1. Soft Scalar Masses 138 8.1.2. Soft Trilinear Couplings 139 8.1.3. Gaugino Masses 139 8.1.4. Summary of the Parameter Space 139 8.2. Constraints on the Particle Spectrum 140 8.3. Universal Gaugino Masses 140 8.4. Non-Universal Gaugino Masses 146 8.4.1. An Inclusive Scan 146 8.4.2. An Enhanced Scan Over M1=2, ρ1 and ρ2 151 8.5. Scenarios with Fixed Gaugino Mass Ratios 153 8.5.1. GG75 + 200 Model 160 8.5.2. FL75 + 1 Model 162 8.5.3. PS1 Model 167 8.5.4. First and Second Generation Squarks and Gluinos 170 8.6.
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