Abstract

The CKM matrix is a key ingredient in the study of CP violation and in New Physics searches within the flavour sector. Therefore, precise determinations of its matrix elements are of utmost importance. |Vub| and |Vcb| can be extracted from both exclusive semileptonic b —> u and b —> c decays and the inclusive channels B —> Xu l nu and B —> Xc l nu. Exclusive and inclusive determinations of these matrix elements have been in tension for a long time, with even different theoretical frameworks not agreeing well with one another. In this seminar, I am going to review some of the techniques employed in the study of inclusive semileptonic B-meson decays and present the results of our latest inclusive determination of |Vcb|. Then, I will discuss the challenges one needs to face in order to obtain a solid description for B —> Xu l nu and some of the solutions proposed. Finally, I will present the first calculation of power-suppressed perturbative corrections in B —> Xu l nu and show the first preliminary results of our determination of the necessary non-perturbative functions within a neural network approach.