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 fifty 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 flavour 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 τ/μ and the μ/l ratios of the branching fractions of the semileptonic B→D( *)lν and B→K(*)l+l- decays, respectively. In this Thesis we will firstly 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 findings are that both the jVcbj puzzle and the R(D*) anomalies are strongly lightened by applying the Dispersive Matrix method to the B→D* lν 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 UTfit prediction for |Vcb|. Then, we will extend the discussion to the analysis of Beyond the Standard Model effects 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 effects eventually affecting the avour sector.