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The Interplay Between Natural and Accidental Supersymmetry

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The Interplay Between Natural and Accidental Supersymmetry THE INTERPLAY BETWEEN NATURAL AND ACCIDENTAL SUPERSYMMETRY by Christopher P. Brust A dissertation submitted to The Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. Baltimore, Maryland February, 2014 c Christopher P. Brust 2014 ⃝ All rights reserved Abstract In this thesis, we will explore the subject of the little hierarchy problem which plagues solutions to the big hierarchy problem of the Standard Model of particle physics. In the first half of this thesis, we study the theoretical framework for a supersym- metric resolution of the little hierarchy problem, known as natural supersymmetry, and argue that regions of the parameter space of this model have been missed by search strategies employed at the large hadron collider, but could be searched for with new search strategies. In the second half of this thesis, we explore the possibility of embedding natural supersymmetry in models of warped extra dimensions in order to UV-complete them by utilizing a mechanism known as accidental supersymmetry. We study the mech- anism of accidental supersymmetry in the Randall-Sundrum framework by focusing on a toy model, and argue that accidental supersymmetry is capable solving the little hierarchy problem in that toy model. Finally, as models in the Randall-Sundrum framework themselves require UV completions, we demonstrate that it is possible to ii ABSTRACT realize the mechanism of accidental supersymmetry within the UV-complete frame- work of type IIB superstring theory. iii Acknowledgments I would first like to thank my advisor, Raman Sundrum, for his continual support, useful advice, collaboration and friendship over the duration of my time at Johns Hopkins. He has truly been the best kind of advisor a graduate student could hope to have. I would also like to thank David E. Kaplan, who has served as a co-advisor and collaborator to me over the years. His support and insight have been invaluable to me. I am very grateful for the support from all of my friends, both within and outside of the PHA community, without whose friendship I surely would be lost. I am wonderfully grateful for the continual love and support of my family over the years, and for all of the sacrifices they have made on my behalf. Finally, I am extremely grateful to my finace´e,April, who has loved me, encour- aged me to pursue my dreams and supported me in every way possible. iv Dedication This thesis is dedicated to April, for everything she has done for me. v Contents Abstract ii Acknowledgments iv List of Tables xi List of Figures xiii 1 Introduction and Background 1 1.1 The Standard Model and Motivations for its Extension . 4 1.1.1 The Standard Model . 4 1.1.2 The Hierarchy Problem . 8 1.1.3 Other Concerns with the SM . 11 1.2 Extensions of the SM . 14 1.2.1 The Minimal Supersymmetric Standard Model . 14 1.2.2 Warped Extra Dimensions . 20 1.2.3 The Little Hierarchy Problem . 23 vi CONTENTS 2 Natural SUSY: The Story Below 10 TeV 26 2.1 Introduction and General Concerns . 28 2.2 Natural SUSY . 10 TeV with Light Higgsinos . 31 2.2.1 Effective Lagrangian, Neglecting Third-Generation Mixing .33 2.2.2 Higgs Mass . 36 2.2.3 Naturalness in Natural SUSY . 37 2.3 Natural SUSY . 1 TeV with Light Higgsinos . 43 2.3.1 Effective Lagrangian, Neglecting Third-Generation Mixing .46 2.3.2 Dark Matter Considerations . 47 2.4 Natural SUSY . 10 TeV with Heavy Higgsinos . 48 2.4.1 Effective Lagrangian, Neglecting Third-Generation Mixing .49 2.4.2 Higgsino Mass . 50 2.5 Natural SUSY . 1 TeV with Heavy Higgsinos . 50 2.5.1 Effective Lagrangian, Neglecting Third-Generation Mixing .51 2.5.2 Effective Lagrangian with Neutralino LSP . 51 2.6 Flavor-Changing Neutral Currents and CP Violation . 52 2.7 R-Parity versus R-Parity Violation . 57 2.7.1 Proton Decay . 58 2.7.2 Unification . 59 2.7.3 Dark Matter . 60 2.7.4 RPV and FCNCs . 61 vii CONTENTS 2.7.5 RPV with Lepton Number Conservation . 62 2.7.6 R-Parity Violation with Baryon Number Conservation . 63 2.8 Dirac Gauginos . 64 2.8.1 Naturalness . 66 2.8.2 R-Parity Violation . 67 2.8.3 Electric Dipole Moments . 69 3 Natural SUSY at the LHC 71 3.1 Collider Phenomenology of R-Parity Conserving Natural SUSY . 72 3.1.1 Neutralino and Squarks . 74 3.1.2 Overview of Some Other Possibilities . 79 3.1.2.1 Gluinos . 79 3.1.2.2 Collider-Stable Squarks . 81 3.1.2.3 Neutralino and Chargino LSPs . 82 3.2 R-Parity Violating Phenomenology . 83 3.3 Reduction to the RPV Simplified Model . 88 3.3.1 Spectrum . 88 3.3.2 Couplings . 90 3.3.3 Higgsinos . 92 3.4 Signals and Strategy of Search . 93 3.5 Details of Event Simulations, Backgrounds and Reach . 100 3.6 Brief Comments on Neutral Current Decays . 107 viii CONTENTS 3.7 Outlook . 114 4 Accidental SUSY and RS: The Story Above 10 TeV 118 4.1 Intro to Accidental SUSY . 120 4.2 A Toy Model of Accidental SUSY . 122 4.3 Further Considerations . 132 5 Accidental SUSY and String Theory: The Story Above The Story Above 10 TeV 134 5.1 Accidental SUSY Ingredients . 135 5.2 The Conifold and its Deformation . 138 5.3 The Complex Cone Over F0 . 142 5.3.1 The Supergravity Side . 143 5.3.2 The Gauge Side . 151 5.3.3 The AdS/CFT Matching . 160 5.4 Conclusions . 161 6 Looking Forward 165 A Notations and Conventions 168 B Relevant Mathematical Results 170 B.1 Groups, Algebras and Representations . 170 B.2 Differential Geometry . 171 ix CONTENTS B.3 Grassmann Variables . 175 C Relevant Physics Results 176 C.1 Introduction to SUSY . 176 C.2 Anti-de Sitter Space . 182 C.3 Conformal Field Theory . 189 C.4 The AdS/CFT correspondence . 190 C.5 IIB Supergravity . 192 C.6 The Conifold . 197 Bibliography 205 Vita 226 x List of Tables 1.1 The fields in the Standard Model. .5 2.1 R-charges of particles in theory with eqn. (2.33) and Dirac gaugino masses. 68 3.1 Pair production cross sections for stop at NLO for center of mass en- ergy ps = 8 TeV. Sbottom production cross-sections are very similar, slightly bigger though due to electro-weak effects. 95 3.2 Benchmark points for the charged-current decay search. The produc- tion cross sections are given only for sbottoms . 100 3.3 Expected yields of events in the \golden" channel in the multilepton ∗ search of [1], ps = 7 TeV with assumption BR(t~2 Z t~1) = 100%. ! Channels with high HT , low MET are the most informative. All pos- sible leptonic decays of Z∗ have been simulated including leptonic τs. We define the Z window such that the invariant mass of the OSSF pair is 76 GeV < mll < 106 GeV. We do not simulate channels with hadronic τs due to difficulties to mimic one-prong τh detection with our theoretical tools. Three right columns cite the results of [1] where Exp. stands for the expected yield of the SM, Err. is the systematic error as it was estimated by the experimentalists, and Obs. stands for the observed number of events at = 4:98 fb−1. 112 L 5.1 The scaling dimensions and quantum numbers of the first few scalar harmonics on T 1;1. ............................ 146 5.2 The scaling dimensions and quantum numbers of scalar harmonics of τ with ∆ 4. 146 5.3 The scaling≤ dimensions and quantum numbers of scalar harmonics of A2 with ∆ 4. 149 ≤ 5.4 The scaling dimensions and quantum numbers of harmonics of Φ− with ∆ 4. 150 ≤ xi LIST OF TABLES 5.5 The representations of the fields in the orbifold of KS. G1 and G3 are SU(n + m), G2 and G4 are SU(n), and B, BA, BB, A and R are all U(1)s. 153 5.6 The representations of the fields in the orbifold of KS after a Seiberg 0 0 dual. G and G are SU(n m), G2 and G4 are SU(n), and B, BA, 1 3 − BB, A and R are all U(1)s. 157 5.7 A matching of SUGRA and SCFT scalar modes with ∆ 4. The columns include: scalars in their respective superoperators,≤ why their dimensions might be protected, whether they are even under the outer Z2-automorphism of KW, their symmetry structure under our orbifold, their scaling dimension, what mode they are dual to in SUGRA, and their quantum numbers under SU(2) SU(2) U(1)R. 164 × × xii List of Figures 1.1 The SM top-loop contribution to the Higgs mass. 9 1.2 The stop-loop contribution to the Higgs mass. 17 2.1 Higgs mass corrections . 38 2.2 Higgs mass correction . 40 2.3 Higgs mass correction . 41 2.4 Stop mass correction . 42 2.5 Contributions to K K¯ mixing . 55 − 3.1 Exclusion curves for our minimal model, eqn. (2.29), from three rele- vant searches as a function of masses for squarks and neutralino. We assume roughly equal masses for all three squark species, two stops and a sbottom. The green line represents exclusion by αT search, the blue line is an exclusion by H= T search and the red one is exclusion by tt¯+ E= T search. 77 3.2 Exclusion of a single sbottom due to jets + H= T search as a function of a sbottom and neutralino masses.
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