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Sequestered String Models: Supersymmetry Breaking and Cosmological Applications ALMA MATER STUDIORUM - UNIVERSITA’ DI BOLOGNA Dottorato di Ricerca in Fisica Ciclo XXVIII Settore concorsuale di afferenza: 02/A2 Settore scientifico disciplinare: FIS/02 Sequestered String Models: Supersymmetry Breaking and Cosmological Applications Presentata da: Francesco Muia Coordinatore Dottorato: Relatore: arXiv:1603.05845v1 [hep-th] 18 Mar 2016 Prof. Gastone Castellani Dr. Michele Cicoli Esame finale anno 2016 ii “...non per un dio, ma nemmeno per gioco...” F. de André Dedicata alle cinque persone importanti: mamma, papá, Fabrizia, Roxana, Miscell. iii iv Acknowledgements I would like to thank all the collaborators who made the realization of this the- sis possible: Rouzbeh Allahverdi, Luis Aparicio, Michele Cicoli, Bhaskar Dutta, Sven Krippendorf, Anshuman Maharana, Francisco Pedro, Fernando Quevedo. I’m particularly grateful to my supervisor, Michele Cicoli, who taught me how to do re- search, and to Fernando Quevedo, who represents a rare combination of competence and kindness. This thesis has been partially developed during my stays at the DESY Institute in Hamburg, at the ICTP Institute in Trieste and at the IFT Institute in Madrid, where I spent a few months as a visitor. v Declaration This thesis is based on the results presented in the following papers: [1] 2014, November. L. Aparicio, M. Cicoli, S. Krippendorf, A. Maharana, F. Muia, F. Quevedo, “Sequestered de Sitter String Scenarios: Soft-terms”, JHEP 1411 (2014) 071, arXiv:1409.1931 [hep-th]. [2] 2015, May. L. Aparicio, B. Dutta, M. Cicoli, S. Krippendorf, A. Maharana, F. Muia, F. Quevedo, “Non-thermal CMSSM with a 125 GeV Higgs”, JHEP 1505 (2015) 098, arXiv:1502.05672 [hep-ph]. [3] 2015, September. M. Cicoli, F. Muia, F. G. Pedro, “Microscopic Origin of Volume Inflation”, JCAP 1512 (2015) 040, arXiv:1509.07748 [hep-th]. [4] 2015, November. M. Cicoli, F. Muia, “General Analysis of Dark Radiation in Sequestered String Models”, JHEP 1512 (2015) 152, arXiv:1511.05447 [hep-th]. vi Abstract In the present thesis I studied the particle phenomenology and cosmology arising from a class of string models called sequestered compactifications, which were born with the aim of getting low-energy SUSY from strings. This is not an easy task if combined with cosmological constraints, since the mechanism of moduli stabilization fixes both the scale of supersymmetric particles and the scale of moduli, which tend to be of the same order. However, if on the one hand supersymmetric particles with TeV mass are desired in order to address the electroweak hierarchy problem, on the other hand the cosmological moduli problem requires the moduli to be heavier than 100 TeV. The specific setup of sequestered compactifications makes this hierarchy achievable, at least in principle: as in these models the visible sector is located on a stack of D3-branes at singularities, a physical separation between the visible degrees of freedom and the SUSY-breaking sources takes place. Such decoupling translates into a hierarchy between the scale of SUSY-breaking and the spectrum of supersymmetric particles. Moreover, it is interesting to notice that moduli are the four-dimensional manifestation of the existence of extra-dimensions, and then their presence is a common feature of all string compactifications. Since they are only gravitationally coupled, they could decay late in the history of the universe, affecting in a significant way its cosmological evolution. Possible deviations of the cosmological observables from the values predicted by the standard Hot Big Bang Theory constitute an interesting alternative for the discovery of new physics beyond the Standard Model, which is complementary to the particle physics search. For this reason in addition to SUSY-breaking in sequestered models, I also studied several cosmological scenarios arising from them, such as production of non-thermal dark matter and dark radiation, reheating from moduli decay and inflation. vii viii Contents I Introduction 1 1 State of the Art 3 1.1 Current Understanding . .8 1.1.1 Standard Model of Particle Physics . .8 1.1.2 Standard Model of Cosmology . 11 1.2 Beyond the Standard Paradigm . 18 1.2.1 Beyond the Standard Model of Particle Physics . 18 1.2.2 Beyond the Standard Model of Cosmology . 27 1.3 String Theory . 32 1.3.1 Basic Facts About Strings . 33 1.3.2 String Phenomenology . 36 2 Flux Compactifications and Model Building 41 2.1 Flux Compactifications . 42 2.1.1 Calabi-Yau Compactifications . 43 2.1.2 Basic Definitions About Fluxes . 47 2.1.3 Supersymmetry Conditions . 49 2.1.4 Equations of Motion . 57 2.1.5 Moduli Space and Kaluza-Klein Reduction . 60 2.1.6 N = 1 EFT from Type IIB Orientifolds . 63 2.2 Model Building . 71 2.2.1 Moduli Stabilization . 72 2.2.2 Visible Sector . 84 2.2.3 An Explicit Global Model . 93 II Supersymmetry Breaking in Sequestered Models 97 3 Sequestered de Sitter String Models: Soft-Terms 99 3.1 Sequestered LVS Scenarios . 102 ix 3.1.1 Moduli Stabilization . 105 3.1.2 Scenarios for de Sitter Vacua . 107 3.2 F-terms and Soft-terms . 112 3.2.1 Summary of F-terms . 112 3.2.2 Local and Ultra-local Scenarios . 115 3.2.3 Soft-terms . 116 3.2.4 Summary of Soft-terms . 127 3.3 Possible Sources of Desequestering . 129 3.3.1 Loop Corrections . 130 3.3.2 Anomaly Mediated Contributions . 131 3.3.3 Moduli Redefinitions . 132 3.3.4 Superpotential Desequestering . 133 3.4 Conclusions . 133 III Non-Standard Cosmology 137 4 Non-Thermal Dark Matter 139 4.1 Motivation for Non-thermal Dark Matter . 139 4.2 CMSSM Soft-Terms . 142 4.3 Non-thermal CMSSM . 143 4.3.1 Non-thermal Dark Matter Relic Density . 143 4.3.2 Collider and CMB Constraints . 145 4.3.3 Direct and Indirect Detection Constraints . 148 4.4 Discussion of Results . 154 4.4.1 Analysis of the Allowed Parameter Space . 154 4.4.2 Astrophysical Uncertainties . 159 4.5 Conclusions . 162 5 Dark Radiation in Sequestered Models 165 5.1 Introduction . 165 5.2 Dark Radiation in Sequestered Models . 170 5.2.1 Dark Radiation from Moduli Decays . 171 5.2.2 Light Relativistic Axions in LVS Models . 172 5.2.3 Volume Modulus Decay Channels . 173 5.2.4 Dark Radiation Predictions . 177 5.3 Conclusions . 191 x 6 Volume Inflation 193 6.1 Introduction . 193 6.2 Inflection Point Inflation . 197 6.3 Microscopic Origin of the Inflationary Potential . 199 6.4 Single Field Dynamics . 206 6.4.1 Analytical Discussion . 206 6.4.2 Numerical Results . 211 6.5 Two Fields Dynamics . 214 6.6 Conclusions . 217 IV Conclusions 219 7 Summary and final remarks 221 Bibliography 225 xi xii Part I Introduction 1 Chapter 1 State of the Art The higgs boson has been for a long time the last missing block of the Standard Model of particle physics (in the following Standard Model or SM) [5]. With the an- nouncement of the discovery of a new particle in 2012 [6, 7], whose mass is around 125 GeV and whose quantum numbers are compatible with those of the theorized higgs boson [8], the scientific community finally celebrated the complete affirmation of this theory. The Standard Model describes all known particles1 and their inter- actions through three out of the four known forces in nature: the electromagnetic force, the weak force and the strong force. Fermionic particles compose the so-called matter of the universe, and are called leptons and quarks. They are organized in three different families, of which the first one contains the lightest and stable par- ticles, such as the electron. Forces are mediated by bosonic particles called gauge bosons: photon, gluons and the bosons W ± and Z. The Standard Model is an extraordinarily successful scientific theory: to the extent that we can compute physical quantities to make predictions which can be experimentally verified, it has passed every single test. To give an idea of the amazing agreement between Standard Model predictions and experimental data, in Tab. 1.1 we report measured and predicted values for the masses of the W ± and Z bosons, which highlight an impressive accord [5]. In order to locate the Standard Model within a wider scientific context, it is worth recalling that it represents a specific example of a general tool, called quan- tum field theory, which allows to describe the physics of relativistic particles at the quantum level. Quantum field theory represents one of the two main pillars on which the whole understanding of the universe is currently based, and it is useful to de- 1Except massive neutrinos. 3 Measured values (GeV) SM predictions (GeV) Mass of W ± boson 80:376 ± 0:033 80:363 ± 0:006 Mass of Z boson 91:1876 ± 0:0021 91:1880 ± 0:0020 Table 1.1: Predicted and measured values for the masses of W ± and Z [5]. The measured value of W ± is taken from LEP2 results [9]. scribe the physics taking place at small distances: in particular the Standard Model describes the physics up to 10−17 cm. On the other hand, the second main pillar is General Relativity [10], which describes at the classical level the fourth force of nature: gravity. Given the weakness of the force of gravity, which becomes relevant only when extremely large amounts of mass are taken into account, General Rela- tivity is useful to describe the physics involving the largest scales of the universe. The agreement between predictions of General Relativity and experiments has been tested to a high degree of accuracy [11]. The Standard Model supplemented by General Relativity is commonly inter- preted as an Effective Field Theory (EFT) which is valid up to the energies explored at the Large Hadron Collider (LHC) outside Geneve (MEW ∼ 100 GeV).
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