Heavy meson decays as precision tools for new physics: A search for beyond Standard Model signals

During the years several tensions were found between experimental results and Standard Model (SM) predictions, in particular in the flavour sector. Individually, these anomalies are not large enough to disproof SM but all together they are telling us that a theory beyond it is required. In particular, measurements of semileptonic $B$ decays are pointing out a violation of the lepton flavour universality (LFU) of the SM, an accidental symmetry broken only by the Yukawa interactions. Furthermore, two different determinations of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements $\lvert V_{ub} \lvert$ and $\lvert V_{cb} \lvert$ from exclusive and inclusive $B$ decays are in tension between them. These issues related to $B$ decays indicate that these processes are an interesting subject to investigate for the presence of new physics (NP) that can explain one or all of the anomalies. The tool for such investigations is the Effective Field Theory, which can avoid the knowledge of the exact extension of the Standard Model. In the thesis we use such an approach to assess the role of general constraints provided by the cancellation of gauge anomalies, in the case the extension is an abelian $U(1)^\prime$. We also investigate the constraints provided on the coefficients of generalized semileptonic Hamiltonian using measured quantities such as a set of angular distribution functions. Efforts are devoted to investigate the role of $B_c$ in the search of new physics effects, and how quantities as the hadronic form factors can be treated using general properties of QCD. The studies are extended to the semileptonic and nonleptonic $B_c$ decays to positive parity hidden charm mesons, showing that predictions can be obtained allowing, among other consequences, to assess the structure of a debated state, as $\chi_{c1}(3872)$. Finally, an excursion on the hadron spectroscopy is represented by the characterization of the Dalitz decays of positive parity mesons with open charm.