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Lepton Flavour Violation and Dark Matter Phenomenology UNIVERSIDAD AUTONOMA´ DE MADRID FACULTAD DE CIENCIAS DEPARTAMENTO DE F´ISICA TEORICA´ Lepton Flavour Violation and Dark Matter Phenomenology Memoria de Tesis Doctoral realizada por Bryan Zald´ıvar Montero presentada ante el Departamento de F´ısica Teorica´ de la Universidad Autonoma´ de Madrid para la obtencion´ del T´ıtulo de Doctor en Ciencias. Tesis Doctoral dirigida por Alberto Casas Jesus´ Moreno del I.F.T. de la Universidad Autonoma´ de Madrid Madrid, Febrero 2013. AGRADECIMIENTOS CONTENTS 1 General Introduction and Motivations 1 2 Supersymmetry and Lepton Flavour Violation 5 2.1 Elements of SUSY .............................. 5 2.1.1 Neutrino masses and mixings .................... 9 2.1.2 Supersymmetric See-saw ....................... 9 2.1.3 LFV processes in the supersymmetric See-saw ........... 11 2.2 Leptogenesis ................................. 14 3 Dark Matter phenomenology 17 3.1 Experimental evidences of Dark Matter ................... 17 3.2 Dark Matter candidates ............................ 18 3.2.1 Baryonic Dark Matter? ........................ 18 3.2.2 Non-baryonic Dark Matter ...................... 19 3.3 Early universe ................................. 20 3.3.1 The dynamics of the universe’s evolution .............. 20 3.3.2 Thermodynamics ........................... 23 3.4 Dark Matter abundance ............................ 29 3.4.1 Freeze-out of cold Dark Matter .................... 31 3.5 Dark Matter Detection ............................ 33 3.5.1 Indirect detection ........................... 33 3.5.2 Direct Detection ........................... 35 3.5.3 Collider searches ........................... 36 4 Fair Scans of the Seesaw I 39 5 Collider Bounds on Dark Matter 63 6 Complementarity among different strategies of Dark Matter Searches 79 7 Conclusions 121 8 Conclusiones 125 Appendices 129 Appendix A Corrected Boltzmann equation 131 List of Figures 135 CHAPTER 1 GENERAL INTRODUCTION AND MOTIVATIONS One of the open questions in particle physics nowadays is the so-called flavour puzzle: why there is a hierarchical structure of fermion masses and mixings, and why there are two repli- cas of the lightest fermions? The leptonic sector presents even more challenging features than the quark sector, where the mixings between flavour eigenstates show an approximately perturbative texture. Indeed, in the neutrino sector the values of the mixing angles appear ‘randomly’ distributed, and one of the mixing angles is close to maximal. On the other hand, the masses of neutrinos are believed to be below 0.3 eV, i.e. six orders of magnitude ∼ smaller than the lightest charged fermion (the electron). This should be compared with the five orders of magnitude expanded by the masses of the nine charged fermions (from the ∼ electron to the top mass), more or less equally distributed in between. Certainly, the Standard Model (SM) can be trivially extended to accommodate neutrino masses. However, the previous huge gap between the neutrinos and the rest of SM particles has posed a strong motivation to develop theoretical models that could explain it. One of the most popular theoretical frameworks to accommodate such small neutrino masses is the so- called Seesaw mechanism. The idea is that right-handed (RH) neutrinos, which are singlets under the SM gauge group, can have large Majorana masses (as they are not controlled by the electroweak-breaking scale). Then the lightest (approximately pure left-handed) neutrinos get masses suppressed by the ratio of the Higgs VEV and the right-handed Majorana mass, thus becoming extremely light. The Seesaw scenario can be easily formulated within a supersymmetric framework. Indeed, this is highly motivated by the fact that the massive right-handed neutrinos introduce large (logarithmic) corrections to the Higgs mass, which worsens the notorious Hierarchy- Problem of the Standard Model. On the other hand, the neutrino Yukawa couplings must present an off-diagonal structure (to generate the neutrino mixings), which in turn induces off-diagonal entries in the slepton matrices. The latter may potentially trigger processes which violate Lepton flavour, for example µ eγ. → 2 General Introduction and Motivations The results of the first part of this thesis have been worked out in this context. In partic- ular we have derived an algorithm to scan the large parameter space of the (supersymmetric or not) Seesaw in a complete way. We have done this using the so-called R parametrisation − and show that the results are consisted with those obtained using other parametrisations. In particular, we demonstrate that if the scan is complete, the branching ratio BR(µ eγ) is → not sensitive to the angle θ13 of the neutrino (PMNS) mixing matrix. This result rectifies previous claims in the literature stating that there was a strong dependence between these two quantities. We explain that the reason for those previous results was essentially that they were based on an incomplete scan of the Seesaw parameter space. The second part of the thesis is devoted to the study of Dark Matter (DM) issues. The existence of DM is probably the strongest evidence to believe that the Standard Model is an incomplete theory, since in order to account for the assorted observations of DM one has to extend the SM with extra degrees of freedom. There are many candidates to play the role of the DM particles. One of the best-motivated ones are the so called WIMPs (weakly inter- acting massive particles). The reason is the following. If one assumes that the DM-genesis occurs in the early universe, in a similar fashion to the rest of the particles, then the DM- particles lived in thermal equilibrium until the global temperature decreased below a certain threshold. Then the DM particles decoupled from the thermal bath, annihilating massively until -due to the expansion of the universe- no DM particle were able to find a partner to annihilate with. After this moment the DM abundance became “frozen”. The calculation shows that for DM-masses of electroweak size (from GeV to TeV) with weak interactions (similar to neutrinos) the final DM-abundance is in the range consistent with observations. In this context, the DM particles are expected to participate not only in gravitational interac- tions with the rest of SM particles, but also in other kind of processes, e.g. in electroweak interactions, behaving similarly to neutrinos but with a much larger mass. There are three basic experimental strategies to search for DM nowadays. The first one is the so-called “Indirect Detection”, in which one attempts to detect the DM annihilation or decay subproducts generated in the Galactic Centre (or in Galaxy Clusters). For example, the electrons and positrons produced in processes like DM DM e+e taking place in re- → − gions where there are strong magnetic fields, will produce synchrotron radiation which can directly point towards us. Thus by measuring synchrotron fluxes from different directions in the sky, we may detect DM signals. The second experimental approach is “Direct De- tection”. The idea is that the DM particles of the galactic halo can interact, from time to time, with nucleons of a heavy material, e.g. xenon placed in containers deep underground, producing recoil energies which could be measured if the process is energetic enough. The third experimental strategy is the DM production in colliders. E.g. the LHC, the idea is that the DM particles could be directly produced in some proton-proton collisions. Once produced, the DM particles would escape the detector, as neutrinos do, contributing to the missing energy. In this way a DM signal can be identified indirectly by studying the other 3 -visible- products of the scattering. This occurs for instance in processes like qq¯ j DM → DM, in which a quark-antiquark pair annihilate into a pair of DM particles plus a jet (which can be originated by a gluon emitted by the initial states). In our results, we first combine different bounds coming from collider searches of assorted (leptonic or hadronic) nature, as LEP and Tevatron. We show that, considering leptonic and hadronic bounds at the same time constrains much further the parameter space of generic DM models, which we study in a model-independent fashion through different classes of effective theories. We include in the analysis additional bounds coming from Di- rect Detection searches, as well as the requirement of a correct relic abundance. All this results in quite severe exclusion limits, excluding a particular class of effective theories. Finally, we perform a detailed study of possible synchrotron signals coming from DM an- nihilation at the Galactic Centre, comparing the corresponding bounds with those obtained from other searches, e.g. direct production in colliders (LEP, Tevatron and LHC) and other indirect-detection searches. We study the DM induced synchrotron-signal not only in the effective theory, but also in two particular ultraviolet realisations, which represent the most simple extensions of the SM to account for Dark Matter, obtaining important restrictions on their parameter-spaces. The thesis is organised as follows. In chapter 2 I expose some introductory elements and motivations of Supersymmetry, the MSSM and the Seesaw mechanism. I also give the basis of the calculation of Lepton-Flavor violation effects and Leptogenesis in this context. In chapter 3 I introduce the Dark Matter subject, describing the first experimental evidences, the theoretical formalism and the present experimental strategies. Finally, the original works and results are presented in chapters 4, 5 and 6, which are a compendium of the main ac- complishments of my thesis. 4 General Introduction and Motivations CHAPTER 2 SUPERSYMMETRY AND LEPTON FLAVOUR VIOLATION 2.1 Elements of SUSY Nowadays, Supersymmetry (SUSY) is an usual ingredient in theories beyond the Standard Model (SM). There are indeed strong theoretical reasons supporting the idea that SUSY is a good symmetry of nature in some region of scales. Maybe the first motivation about its existence came from the idea of generalising the Poincare symmetry, allowing for transformations that take fermions into bosons and vice- versa.
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