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Supersymmetry Phenomenology in IIB String Theory

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Supersymmetry Phenomenology in IIB String Theory Supersymmetry Phenomenology in IIB String Theory by Kevin Mitchell Givens B.S., Vanderbilt University, 2006 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2012 This thesis entitled: Supersymmetry Phenomenology in IIB String Theory written by Kevin Mitchell Givens has been approved for the Department of Physics Senarath P. de Alwis Prof. William T. Ford Prof. Oliver DeWolfe Prof. K. T. Manhanthappa Prof. J. Michael Shull Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Givens, Kevin Mitchell (Ph.D., Physics) Supersymmetry Phenomenology in IIB String Theory Thesis directed by Prof. Senarath P. de Alwis IIB string theory represents one of the most promising realizations of string theory studied to date because it successfully handles a variety of phenomenological issues. These issues include mechanisms for stabilizing all relevant moduli fields, generating a small cosmological constant and breaking supersymmetry on a low scale. In this dissertation we examine these issues and describe the phenomenological consequences of a class of realistic IIB models that have the potential to effect both LHC physics and cosmology. In addition, we explore ways to embed interesting physical models, such as the QCD axion, within this class of IIB models. Dedication First, I would like to express my sincerest appreciation to my advisor, Shanta de Alwis, for his steadfast support and encouragement throughout the entire course of my dissertation. His wisdom, compassion and genial nature are truly outstanding human traits, traits I can only hope to emulate in my own life. Second, I would like to thank my parents, Stan and Joyce Givens, for their love and en- couragement throughout my entire education. They have gone to great lengths to ensure that all of their children receive excellent educations. These educations rightly deserve to be my parents’ greatest legacy. Finally, I would like to thank my girlfriend Rocio Vargas for her love and support during my years as a graduate student. She has stood by me and helped me to overcome many challenges along the way. Without her love and humor I’m not sure I would have succeeded as a graduate student. Any success I achieve in life belongs to her. v Acknowledgements This work was supported in part by the United States Department of Energy under grant • DE-FG02-91-ER-40672. Most of the papers that constitute this dissertation were directly of indirectly affected by • the research of Prof. Howie Baer at the University of Oklahoma. Prof. Baer coauthored papers (chapters) 1 and 2 as well as provided invaluable assistance in papers 3 and 5. For paper 2 we thank Yuri Gershtein of Rutgers University for discussions. • For paper 4 we thank James Gray of the Arnold Sommerfield Center for Theoretical Physics • for correspondence concerning the STRINGVACUA program. vi Contents Chapter 1 Introduction 1 1.1 StringTheoryGeneralities. ......... 1 1.2 IIBStringTheory ................................. .... 6 1.3 SummaryofWork ................................... 9 2 Gaugino Anomaly Mediated SUSY Breaking: phenomenology and prospects for the LHC 11 2.1 Introduction.................................... ..... 12 2.2 Effective supergravity from IIB strings: Overview of Models.............. 15 2.2.1 EffectiveSupergravityTheory. ....... 15 2.2.2 SingleK¨ahlermodulusscenario . ........ 17 2.2.3 LargeVolumeScenario(LVS) . ..... 17 2.2.4 GauginoMasses-WeylAnomalyEffects. ...... 18 2.2.5 Scalar Masses, Trilinear Couplings, µ and Bµ terms .............. 20 2.3 Mass spectra, parameter space and constraints for the inoAMSBmodel . 22 2.3.1 Sparticle mass spectra and parameter space . .......... 22 2.3.2 BF (b sγ) and (g 2) ininoAMSB...................... 31 → − µ 2.4 TheinoAMSBmodelandtheLHC . 35 2.4.1 SparticleproductionatLHC . ..... 35 2.4.2 SparticledecaysininoAMSBmodels . ....... 36 vii 2.4.3 LHC collider events for the inoAMSB models . ........ 38 2.4.4 ThereachofLHCintheinoAMSBmodelline . ..... 42 2.5 Discussionandconclusions. ......... 47 3 Testing the gaugino AMSB model at the Tevatron via slepton pair production 49 3.1 Introduction.................................... ..... 49 3.2 ThegauginoAMSBmodel............................. 51 3.3 Production and decay of inoAMSB sleptons at the Tevatron .............. 53 3.4 Signalandbackgroundaftercuts . ......... 56 3.4.1 SleptonpairproductioninmAMSB . ..... 59 3.5 Conclusions ..................................... 59 4 Dark Matter density and the Higgs mass in LVS String Phenomenology 67 4.1 Introduction.................................... ..... 67 4.2 CosmologicalIssues.............................. ....... 72 4.2.1 CosmologicalModulusProblem. ...... 72 4.2.2 DarkMatterRelicAbundance . 73 4.3 PhenomenologicalIssues . ........ 73 4.3.1 FCNC and Anomalous Magnetic Moment of the Muon . ...... 73 4.4 ProspectsfortheLHC .............................. ..... 75 4.5 Conclusion ...................................... 75 5 Physical Vacua in IIB Compactifications with a Single K¨ahlerModulus 77 5.1 Introduction.................................... ..... 77 5.2 Single K¨ahler Modulus + α′ +Non-PerturbativeTerm. 80 5.2.1 AnalyticResults ............................... 81 5.3 Single K¨ahler Modulus with S and T SUSYbreaking. 86 viii 5.3.1 SeriesExpansionAnalysis . ...... 86 5.3.2 NumericalExample .............................. 88 5.4 Conclusion ...................................... 91 5.5 Appendix: Single K¨ahler Modulus + α′ +RaceTrack.................. 92 5.5.1 AnalyticResults ............................... 92 6 A QCD Axion from a IIB Local Model in the Large Volume Scenario 96 6.1 Introduction.................................... ..... 96 6.2 TheSUSYLagrangian ............................... 98 6.2.1 TheFieldContent ............................... 100 6.2.2 ScalarPotentialConsiderations . .........101 6.3 SparticleMasses ................................. 102 6.3.1 ScalarMasses.................................. 104 6.3.2 FermionMasses................................. 106 6.3.3 PhysicalCouplings . 107 6.4 CosmologicalConsiderations. ..........107 6.4.1 SaxionDominatedEpoch . 108 6.4.2 BBNConstraints................................ 108 6.4.3 DarkMatterOverabundance . 109 6.5 Conclusion ...................................... 109 6.6 Appendix ........................................ 110 6.6.1 SuperfieldExpansions . 110 6.6.2 ThePhysicalCouplings . 112 7 Conclusion 116 Bibliography 117 ix Tables Table 1.1 Basic information about various 10D superstring constructions. ............ 3 2.1 Masses and parameters in GeV units for four case study points mAMSB1, HCAMSB1, inoAMSB1 and inoAMSB2 using Isajet 7.80 with mt = 172.6 GeV and µ > 0. We also list the total tree level sparticle production cross sectioninfbattheLHC. 26 2.2 Estimated SM background cross sections (plus the inoAMSB1 benchmark point) in miss c fb for various multi-lepton plus jets +ET topologies after cuts C2 with ET = 100 GeV. ............................................ 43 1 2.3 Estimated reach of 100 fb− LHC for m3/2 (TeV) in the inoAMSB model line in varioussignalchannels. ..... 44 4.1 Masses and parameters in GeV units for four case study points inoAMSB1,2,3,4 using ISAJET 7.79 with mt = 172.6 GeV and µ> 0. We also list the total tree level sparticle production cross section in fb at the LHC with 14 TeV center of mass energy. 71 4.2 Phenomenological constraints for inoAMSB with m3/2 = 500 TeV, m0 = 407 GeV, A0 = 50 GeV, tan β = 40 using ISAJET 7.79 with mt = 172.6 GeV and µ> 0. 74 5.1 Moduli field vev’s, F-terms, Gravitino mass and the Cosmological Constant for SKM + 4 Non-Pert Terms at a non-SUSY minimum of the scalar potential (in MP = 1 units)............................................. 90 x Figures Figure 1.1 Stringtheorywebofduality. ........ 2 1.2 Swiss Cheese Manifold with = V V ....................... 9 V L − i Si P 2.1 Running of soft SUSY breaking parameters as a function of energy scale Q for m3/2 = 50 TeV, tan β = 10 and µ> 0 in the inoAMSB model, with Mstring = MGUT . 24 2.2 Plot of sparticle masses for the inoAMSB1 case study with m3/2 = 50 TeV, tan β = 10 and µ> 0. ....................................... 25 2.3 Sparticle mass spectrum versus m3/2 in the inoAMSB with Mstring = MGUT , tan β = 10, with µ> 0 and mt = 172.6GeV. ........................... 27 2.4 Sparticle mass spectrum versus tan β for m3/2 = 50 TeV in the inoAMSB with Mstring = MGUT and with µ> 0. ............................ 28 2.5 Allowed parameter space of the inoAMSB models in the m3/2 vs. tan β plane with µ> 0. We plot also contours of mg˜. ........................... 29 2.6 Plot of sparticle masses for the inoAMSB1 case study with m3/2 = 50 TeV, tan β = 10 and µ> 0, but with variable value of Mstring. .................... 30 2.7 Plot of sparticle masses for the inoAMSB with m3/2 = 50 TeV, tan β = 10 and µ> 0, but with an additional universal contribution m0 added to all scalar masses. 31 2.8 Branching fraction for b sγ versus m and tan β variation in the inoAMSB → 3/2 model with Mstring = MGUT . ............................... 33 xi 2.9 SUSY contribution to ∆aµ versus m3/2 and tan β variation in the inoAMSB model with Mstring = MGUT . We also take µ> 0 and mt = 172.6GeV. ........... 34 2.10 Sparticle pair production cross sections at LHC with √s = 14 TeV for
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