TOPICS IN SUPERSYMMETRY AND PHYSICS BEYOND THE STANDARD MODEL BY JEAN-FRANC¸OIS FORTIN A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Professor Thomas Banks and approved by New Brunswick, New Jersey October, 2009 ABSTRACT OF THE DISSERTATION Topics in Supersymmetry and Physics Beyond the Standard Model by Jean-Fran¸cois Fortin Dissertation Director: Professor Thomas Banks In this thesis we explore different aspects related to the central concepts of supersymmetry and physics beyond the Standard Model. We start by investigating fine-tuning in the minimal su- persymmetric extension of the Standard Model, where the regions with the minimal amount of fine-tuning of electroweak symmetry breaking are found. Afterwards, we concentrate on a more formal aspect of supersymmetry, studying spontaneous symmetry breaking in supersymmetry using the superspace formalism. Thereafter we direct our attention to supersymmetry as physics beyond the Standard Model, looking more specifically at supersymmetry breaking in metastable states. First, we discuss possible undetected Higgs decays in the Pentagon model with renor- malizable lepton number violating couplings which also explain neutrino masses. Second, we generalize metastable supersymmetry breaking in supersymmetric quantum chromodynamics to phenomenologically viable models of direct gauge mediation by adding single and multitrace deformations. Third, we introduce a new model of physics beyond the Standard Model, the Pyramid Scheme, and study its implications, focusing on dark matter and its astrophysical signatures in particular. Four, we examine tunneling constraints in models of Cosmological Su- persymmetry Breaking, arguing that these models can have no supersymmetric vacuum states in the infinite Planck mass limit. Finally, we present a general study of the possible gamma ray signatures coming from dark matter annihilation or decay. ii Acknowledgements In the first place, I wish to thank my advisor Professor Tom Banks for his support and guidance, and for sharing his profound knowledge of physics. It has been a great intellectual challenge and privilege to work with him and I have learned a great deal from him. I am also indebted to all professors from Rutgers University, University of California in Santa Cruz and Laval University. In particular, I would like to thank several professors for many enlightening discussions over the years, especially Professors Scott Thomas, Matthew Strassler and Pierre Mathieu. Moreover, I am grateful to Michael Dine, Kenneth Intriligator, Nathan Seiberg, and also to the members of my PhD committee, for their interest and useful discussions. A special thank you also goes to my graduate director, Ronald Ransome. It is my pleasure to thank many friends and colleagues at Rutgers University, SCIPP and other places for interesting discussions from which I learned. A very partial list includes Evgeny Andriyash, Manjul Apratim, Louis-Francois Arsenault, Aatish Bhatia, Dmitriy Belov, Linda Carpenter, Carl-Johan Eklund, Rouven Essig, Adam Falkowski, Guido Festuccia, Al- berto Garc´ıa Raboso, Deepak Iyer, Jos´eJuknevich, Michael Kavic, Semyon Klevtsov, Zohar Komargodski, Sergio Lukic, Dmitry Malyshev, John Mason, Jan Manschot, Dmitry Melnikov, Samuel Monnier, Alexander Morisse, Haile Owusu, Guang Pan, Stefano Profumo, Shidhar Ra- manujam, Robert Schabinger, Jesse Shelton, David Shih, Warren Siegel, Kuver Sinha, Martin Roˇcek, Gonzalo Torroba, Brian Vancil, Dieter van den Bleeken, Korneel van den Broek, Peter van Nieuwenhuizen, Yi Zhang, Yue Zhao and Iskander Ziyatdinov. I gratefully acknowledge the hospitality of the members of SCIPP at University of California in Santa Cruz during the month of May 2008. Also a special word of gratitude to Diane Soyak. Finally, I would like to thank my parents, my siblings and Silvia for their care and patience. iii Dedication Pour mes parents, mon fr`ere, ma soeur & mon amour iv Table of Contents Abstract ............................................ ii Acknowledgements ..................................... iii Dedication ........................................... iv List of Tables .......................................... viii List of Figures ......................................... ix 1. Introduction ........................................ 1 1.1. Supersymmetry and Physics Beyond the Standard Model . ........... 1 1.2. Outline of the Thesis and Summary of the Results . .......... 5 2. Fine-tuning in the MSSM ................................ 8 2.1. Introduction................................... .... 8 2.2. ElectroweakSymmetryBreaking . ....... 10 2.3. TheTuningMeasure ............................... ... 13 2.4. Minimal Model Independent Tuning . ....... 15 2.5. Minimal Fine-Tuning as a Function of the Higgs Mass . ........... 27 2.6. Conclusions .................................... ... 31 2.7. Appendix: Semi-numerical Solutions of the MSSM One-LoopRG-Equations. 32 2.8. Appendix: Fine-tuning Components . ........ 36 3. Spontaneous Symmetry Breaking in Supersymmetry .............. 38 3.1. Introduction................................... .... 38 3.2. SU(Nc)supersymmetricQCDwithmatter . 39 3.3. Non-local terms in the effective action at one-loop . ............. 42 3.4. Conclusion ..................................... .. 46 3.5. Appendix:Notation .............................. .... 46 v 3.6. Appendix:Ghostaction . ..... 48 4. Undetected Higgs Decays in Supersymmetry .................... 50 4.1. The little hierarchy problem and its solutions . ............. 50 4.2. Constraints on h0 χ0χ0 : χ0 (τ, ν )jj ..................... 51 → → τ 4.3. Bounds on jets + E ................................. 58 6 T 4.4. Neutrinomasses ................................. ... 61 4.5. Conclusions .................................... ... 67 5. Metastable Supersymmetry Breaking ........................ 68 5.1. Introduction................................... .... 68 5.2. SQCDwithamultitracesuperpotential . ......... 70 5.3. Metastable DSB in the R-symmetric limit . ......... 73 5.4. Singletracedeformation . ....... 76 5.5. The deformation with γ =0.............................. 82 6 5.6. Commentsonthephenomenology. ...... 85 5.7. Appendix: Oneloopcalculations . ........ 90 6. A Pyramid Scheme for Particle Physics ....................... 96 6.1. Introduction................................... .... 96 6.2. Discrete R-symmetry:themodel . .101 6.3. Breaking R-symmetryandSUSY . .. .. .. .. .. .. .. .. .. .. ..102 6.4. The Higgs sector and SU (2) U (1)breaking. .108 L × Y 6.5. APyramidSchemeforcosmology. ......112 6.6. Conclusions .................................... 118 6.7. Appendix: CosmologicalSUSY breaking . .........120 6.8. Appendix: Non-thermaldarkmatter . ........122 6.9. Appendix: Somecomputations . ......123 7. Tunneling Constraints in Cosmological Supersymmetry Breaking ...... 126 7.1. Introduction................................... .126 7.2. Tunneling for meta-stable field theory states . .............129 7.3. LowenergymodelscompatiblewithCSB . .......131 7.4. Pyramid Schemes with a triplet of singlets . ...........132 vi 7.5. SUP (3) Landau pole and SUP (4)completion . .135 7.6. DiscreteR-symmetry. .136 7.7. Conclusions .................................... 139 8. Gamma Ray Spectra from Dark Matter Annihilation and Decay ....... 141 8.1. Introduction................................... .141 8.2. Direct production of photons through subsequent two-bodydecaychain . 143 8.3. Photons from final states with charged particles . .............146 8.4. Photonsfromtaus ................................ 154 8.5. Photonspectraandflux .. .. .. .. .. .. .. .. .. .. .. .. .158 8.6. Conclusion ..................................... 160 8.7. Appendix: Densityofstates . .......161 8.8. Appendix: FSRcollineardivergence . .........162 8.9. Appendix: Higher-orderoperators . .........164 References ........................................... 173 9. Curriculum Vitae ..................................... 186 vii List of Tables 2.1. Low-scale values for the stop soft trilinear coupling, the average of the left- and right-handed stop soft masses and the two physical stop masses. These low scale values give the minimal fine-tuning for arbitrary messenger scales. .. .. .. 19 4.1. Higgs mass and production cross-section bounds for varioussearches.. 59 4.2. AllowedR-charges. .. .. .. .. .. .. .. .. .. .. .. .. .. ..... 66 5.1. The classical mass spectrum, grouped in sectors with Str M 2 = 0. Since super- symmetry is spontaneously broken only after including one loop effects, there is no Goldstino at tree level. gmag is the magnetic gauge coupling. A subscript “NGB” indicates the particle is massless because it is a Nambu-Goldstone boson. Subscripts in the third column indicate the charge under the U(1) subgroup. Note this table gives the spectrum before the Standard Model gauge group is gauged. 77 5.2. The mass spectrum, including one loop corrections (but without Standard Model gauge interactions), grouped in sectors with Str M 2 = 0. Notice the appearance of the Goldstino in the tr (X) sector. The details of the spectrum are described further in the text. Notation is as in Figure 1. ........ 84 8.1. Relevant electron-positron operators in the effective Lagrangian approach. The empty boxes correspond to operators which are not needed in the analysis. 164 8.2. Relevant photon operators