Supersymmetric Model-Building in the Era of LHC Data: From Struggles with Naturalness to the Simple Delights of Fine-Tuning by Thomas Zorawski A dissertation submitted to The Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. Baltimore, Maryland May, 2014 c Thomas Zorawski 2014 All rights reserved Abstract The Standard Model (SM) of particle physics has withstood decades of experi- mental tests, making it the crowning achievement of 20th century physics. However, it is not a complete description of nature. Observations have revealed that most of the matter in the universe is not of the baryonic form described in the SM but rather something else known as dark matter. The SM also has theoretical shortcomings: 1) No explanation for the widely-varying masses of different particles (flavor puzzle); 2) Failure of the couplings that characterize the strength of the three SM forces to unify at a high energy scale; 3) Instability of the Higgs mass (hierarchy problem). The simplest version of supersymmetry (SUSY) introduces a partner for each SM particle, resulting in the Minimal Supersymmetric Standard Model (MSSM). The lightest of these is stable and an appealing dark matter candidate, and the extra par- ticle content yields good gauge coupling unification. Most model-building, however, has been inspired by the natural solution that the MSSM provides to the hierarchy problem when the superpartner masses are close to the weak scale, leading to the paradigm of the Natural (weak-scale) MSSM. Although the first run of the Large ii ABSTRACT Hadron Collider (LHC) did not operate at the design energy, the data is already in tension with the idea of naturalness, as the bounds on some superpartner masses in vanilla models are significantly above the weak scale. We address this by con- structing a hybrid of the two most appealing SUSY breaking mechanisms (gauge and anomaly mediation) that compresses part of the superpartner spectrum and reduces experimental sensitivity, thereby loosening the constraints. Nonetheless, the recent discovery of a Higgs-like particle at the LHC with a mass 125 GeV that can only be obtained in the weak-scale MSSM with fairly heavy ≈ superpartners casts serious doubt on naturalness. It does, however, point in the di- rection of a different paradigm in the MSSM known as Split SUSY, where only the superpartners that are potential dark matter candidates are light. We present a sim- ple realization of a modification of Split SUSY, called Mini-Split SUSY, where all of the superpartner masses are determined by just one parameter. We show that it easily accommodates the Higgs mass, preserves gauge coupling unification, and has a good dark matter candidate. We then exploit the defining features of the Mini-Split framework to obtain a radiative solution to the flavor puzzle, where the hierarchy of SM particle masses is explained by successive orders of quantum corrections. Advisor: David E. Kaplan iii Acknowledgments I am very grateful to my advisor David E. Kaplan for his guidance, encouragement, and patience with me. Special thanks also go to Matthew Baumgart and Daniel Stolarski, with whom it was a pleasure to work on the last project that brought all of my research together. I also feel fortunate to have had such a great friend and collaborator in Arpit Gupta, who taught me the invaluable lesson of the importance of wasting time. I also thank Jingsheng Li and Liang Dai for enjoyable chats about physics and other things not as lofty. Although I enjoyed all of my TA assignments, working with Prof. Zsuzsa Kovesi-Domokos for many semesters in undergraduate quantum mechanics was an especially fun and rewarding experience. I would like to thank all the people in the particle theory group with whom I have had helpful discussions, especially the other graduate students and postdocs. Finally, I extend my heartfelt gratitude to my family, knowing that without their love, unwavering support, and belief in me, this work would never have been com- pleted. iv Dedication This thesis is dedicated to my parents, Andrzej and El_zbieta,who from a young age instilled in me a deep respect for education and made many sacrifices to ensure that I always had a nurturing environment in which to learn and grow. v Contents Abstract ii Acknowledgments iv List of Tables xi List of Figures xii 1 Introduction 1 1.1 The Standard Model . .1 1.2 Beyond the Standard Model: Supersymmetry . 14 1.2.1 Introduction . 14 1.2.2 The Minimal Supersymmetric Standard Model (MSSM) . 18 1.3 Supersymmetry Breaking . 24 1.3.1 Gravity Mediation . 25 vi CONTENTS 1.3.2 Anomaly Mediation (AMSB) . 27 1.3.3 Gauge Mediation (GMSB) . 31 1.4 Tension between Experiment and Naturalness . 33 1.4.1 Gaugomaly Mediation . 34 1.4.2 Split SUSY . 35 1.4.3 Mini-Split SUSY . 37 1.4.4 Radiative Models of Flavor and Mini-Split SUSY . 39 2 Gaugomaly Mediation Revisited 44 2.1 Introduction . 44 2.2 Gaugino Pole Masses . 46 2.2.1 Gauge Loops . 46 2.2.2 Matter Loops . 47 2.2.3 NLO Formulae . 50 2.3 Messengers and Sleptons . 52 2.4 Gaugino Spectrum . 55 2.4.1 Soft Masses . 56 2.4.2 No Soft Masses . 58 2.5 Complete Example Spectra . 63 2.6 Addressing the µ Problem . 66 vii CONTENTS 2.7 Conclusions . 69 3 Simply Unnatural (Mini-Split) Supersymmetry 72 3.1 Introduction . 72 3.2 Simplest Tuned Picture of the World . 74 3.2.1 Model and Spectrum . 74 3.2.2 New Vector-Like States . 86 3.2.3 Dark Matter . 89 3.3 New Flavor Physics and Radiative Fermion Masses . 91 3.4 Tests of Un-naturalness . 96 3.4.1 Gaugino Decays and the Next Scale . 99 3.4.2 Gluino Decays and Stop Naturalness . 105 3.5 Conclusions . 107 4 Split SUSY Radiates Flavor 110 4.1 Introduction . 110 4.2 A Model of Flavor . 113 4.2.1 Up Sector . 114 4.2.1.1 Top Yukawa . 116 4.2.1.2 Charm Yukawa . 119 4.2.1.3 Up Yukawa . 121 viii CONTENTS 4.2.2 Down and Lepton Sectors . 123 4.2.3 CKM Matrix . 129 4.3 Computing the Spectrum . 131 4.3.1 Gaugino Spectrum, Unification, and Dark Matter . 131 4.3.2 Higgs Mass and Quartic . 137 4.3.3 Mass Eigenstates and Wavefunction Renormalization . 141 4.3.3.1 Diagonalization . 141 4.3.3.2 Wavefunction renormalization . 146 4.3.4 Standard Model Flavor Parameters . 148 4.4 Experimental Constraints and Signatures . 154 4.4.1 Meson Mixing . 155 4.4.2 (Chromo)Electric Dipole Moments . 157 4.4.3 Lepton Flavor Violation . 160 4.4.4 Proton Decay . 161 4.5 Conclusions . 162 A Field Content and U(1)F Gauge Symmetry 167 B Flavon Sector Details 171 C Constructing the Yukawa Matrices 176 ix CONTENTS C.1 Radiative Yukawa Generation . 176 C.2 Wavefunction Renormalization . 182 D Messenger Threshold Corrections to Gaugino Masses 186 E Formulae for Select Flavor Observables 189 Bibliography 193 Vita 216 x List of Tables 1.1 The SM matter field content and respective charge assignments. .4 1.2 The SM Higgs and gauge field content and respective charge assignments.5 1.3 SM fermion masses, taken from [1]. 11 1.4 The matter and Higgs sectors in the MSSM, represented by chiral supermultiplets (adapted from [2]). 19 1.5 Gauge supermultiplets in the MSSM (adapted from [2]). 19 2.1 Gaugino spectra . 60 2.2 Example spectra for N = 2; 3; 4. All masses are in GeV. 64 4.1 Charge assignments of the Higgs and up-sector messenger fields. 114 4.2 The set of flavon fields needed to break U(1)F , along with their charge assignments. 115 4.3 Fields needed to generate the down and lepton Yukawa couplings in addition to those in Tables 4.1 and 4.2, as well as their charges. 124 4.4 Benchmark parameters for the messenger and Higgs sectors. 135 4.5 Classes of contributions we include for up and down-type Yukawa ma- trix entries. 149 A.1 The full particle content of our model in addition to that of the MSSM. 168 xi List of Figures 1.1 The hierarchy of SM Yukawa couplings on a logarithmic scale. 40 2 2.1 Effect of c for positive msoft ....................... 57 2 2.2 Effect of c for negative msoft ....................... 58 2.3 Squark contribution to gluino mass . 62 2.4 Gluino-LSP Splitting for N =2..................... 62 3.1 A \simply unnatural" spectrum. 80 3.2 The Higgs mass predicted as a function of the scalar masses and tan β. 81 3.3 The allowed parameter space in the tan β Msc plane for a Higgs mass − of 125:7 0:8 GeV, for µ = msc...................... 82 3.4 The running± of the gauge couplings with scalar masses and Higgsinos fixed at 103 TeV. ............................. 84 3.5 The Yukawa coupling ratio (yb=yτ ) evaluated at the GUT scale as a function of the scalar mass. 85 3.6 The gaugino spectrum as a function of Neff (defined in Sec. 2.4) at two-loop order plus threshold corrections. 87 3.7 The running gauge couplings in the case of N = 1 vector-like state (dashed), and N = 4 (solid). 88 3.8 Diagram that generates up-type quark Yukawa couplings from the top Yukawa in the case of large mass mixing between flavors, indicated by the crosses on the scalar lines. 93 3.9 Radiatively generated down-type quark Yukawa couplings seeded by heavy messenger-Higgs Yukawa couplings.