Semileptonic decays of B mesons provide a rich source of knowledge for determining fundamental parameters of the Standard Model. This work reports mainly on the study of two semileptonic decay channels: the Bs → D_{s}ℓν¯_{ℓ} and B → D**ℓν¯_{ℓ} (where the D** are the first orbitally excited states of the D mesons having a positive parity). The theoretical framework is Lattice QCD which is considered as the only satisfying approach which calculates in a non perturbative way the transition amplitudes from first principles. By using the twisted mass QCD on the lattice with Nf=2 dynamical flavors we studied, first, the spectroscopy of the scalar D₀* and the tensor D₂* states. Then, we determined the normalization G_s(1) of the form factor dominating Bs → D_{s}ℓν¯_{ℓ} in the Standard Model which provides a means of extracting the CKM matrix element V_{cb}. Next, we make the first lattice determination of F₀(q²)/F₊(q²) and F_T(q²)/F₊(q²) near the zero recoil. The obtained results are important for the discussion of this decay in various scenarios of physics beyond the Standard Model. Finally, we did a preliminary study of B → D₀* where we have obtained a non vanishing matrix element corresponding to the decay of B into the D₀* at zero recoil contrary to what was known in the heavy quark limit. Moreover, the computations corresponding to B → D₂* show a signal indicating a difference with respect to the infinite mass limit prediction. These results are important to draw a firm conclusion on the "1/2 vs 3/2 puzzle".
Semileptonic B decays into charmed D** mesons from lattice QCD