Decadimenti semileptonici inclusivi dei mesoni pesanti

The study of inclusive semileptonic decays of heavy mesons is an active research field as they provide direct information on V_ub and V_cb, two important elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix which parameterizes the quark mixing. It is well-known how inclusive and exclusive determinations of these elements have shown tensions. Historically, non-perturbative studies in the lattice regularization of Quantum Chromodynamics (QCD) have mainly focused on exclusive decays, but recent innovative approaches using smearing of spectral densities extracted from 4-point correlators computed on the lattice have enabled inclusive studies. This work focuses on the inclusive semileptonic decays of B and D mesons, whose analytic treatment is based on Heavy Quark Effective Theories (HQETs) and the Operator Product Expansion (OPE). By employing these techniques, we compute the non-perturbative corrections to the differential distribution, rate, and first leptonic moments. We show how to constrain the so-called Weak Annihilation (WA) coefficients by comparing OPE predictions with observables computed from experimental data sets for decays of D mesons, particularly those from CLEO-c and BESIII collaborations. This study also introduces the formalism of lattice QCD and treats the fundamental Euclidean correlators used in hadronic spectroscopy. The main focus, however, is on the spectral densities derived from these correlation functions, which are crucial for computing the matrix elements required for inclusive decays. By considering synthetic data for reconstructed spectral densities, the limits of infinite volume and zero smearing parameter are performed, enabling the reconstruction of the inclusive differential rate for decays of the B meson. In conclusion, this work is part of a wider research area which aims to directly compare experimental data with lattice predictions for inclusive decays, when the results of new lattice QCD simulations will become available in the next few years.