The D(M)M perspective on Flavour Physics

Flavour Physics is a a sector of physics able to test the Standard Model of elementary particles with extreme precision. In fact, in the past fty years lots of theoretical predictions of SM parameters and Flavour observables have been found to perfectly agree with the experiments. At present, however, this does not seem to be true in two fundamental cases, both related to semileptonic avour transitions. On the one hand, the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa parameter jVcbj are in tension with each other. This fact is often referred to as the jVcbj puzzle. On the other hand, a non-negligible discrepancy holds beteween the expectations and the measurements of the so-called Flavour Anomalies R(D( )) and R(K( )), which are the = and the =` ratios of the branching fractions of the semileptonic B ! D( )` and B ! K( )`+`􀀀 decays, respectively. In this Thesis we will rstly describe a novel, non-perturbative and model-independent approach, i:e: the Dispersive Matrix method, to describe the hadronic Form Factors entering in the semileptonic charged-current B decays. Our most important ndings are that both the jVcbj puzzle and the R(D ) anomalies are strongly lightened by applying the Dispersive Matrix method to the B ! D ` decays, as will be described in Part I. In particular, for what concerns the CKM matrix element, this is in complete agreement with the indirect UT t prediction for jVcbj. Then, we will extend the discussion to the analysis of Beyond the Standard Model e ects in Flavour Physics, mainly motivated by the strong and still remaining R(K( )) anomalies. In particular, in Part II we will show the impact of several avour observables on two explicit models, the Composite Higgs scenarios and the LeptoQuarks ones. A fundamental link exists between this Part and the previous one since, as we will explicitly appreciate, in the Beyond the Standard Model studies the Standard Model parameters are directly involved, thus the most precise are the theoretical estimates of these parameters, the strongest will be the bounds on the New Physics e ects eventually a ecting the avour sector. In the last Part, we will move to the study of the phenomenology of Dark Matter. Without any doubt, explaining the origin of the Dark Matter abundance is, at present, one of the most important and intriguing challenges of theoretical physics. In Part III we will rstly analyze the proofs of the existence of Dark Matter and then we will describe in detail the Weakly Interacting Massive Particle scenario. We will then show how Dark Matter and the Flavour problem can be related. To this end, we will study another model involving the thermal decays of Dark Matter. It assumes the existence of a precise avour structure and the introduction of the LeptoQuarks, previously described in the context of Flavour Physics, in order to generate interactions between the Dark Matter and the Standard Model particles. As we will see in detail, both these scenarios will allow us to explain the observed value of the Dark Matter abundance. This thesis is based on the work contained in the papers [1{12].