Semileptonic B → D** decays in lattice QCD: a feasability

We compute the decays B → D₀^* and B → D₂^* with finite masses for the b and c quarks. We first discuss the spectral properties of both the B meson as a function of its momentum and the D₀^* and D₂^* at rest. We compute the theoretical formulae leading to the decay amplitudes from the three-point and two-point correlators. We then compute the amplitudes at zero recoil of B → D₀^*, which turns out not to be vanishing contrary to what happens in the heavy quark limit. This opens the possibility to get better agreement with experiment. To improve the continuum limit we have added a set of data with smaller lattice spacing. The B → D₂^* vanishes at zero recoil and we show a convincing signal but only slightly more than 1 sigma from 0. In order to reach quantitatively significant results we plan to exploit fully smaller lattice spacings as well as another lattice regularisation. (orig.)