Semileptonic $B \to D^{**}$ decays in Lattice QCD : a feasibility study and first results
Abstract
We compute the decays $B \to D^*_0$ and $B \to D^*_2$ 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 of the $D^*_0$ and $D^*_2$ 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 $B \to D^*_0$ which turn out not to be vanishing contrary to what happens in the heavy quark limit. This opens a possibility to get a better agreement with experiment, although our extrapolation to the continuum and the physical $B$ mass has more than 100% uncertainty. The $B \to D^*_2$ vanishes at zero recoil and we show a statistically significant signal which is in a range between 1 to 10 times the heavy quark limit prediction. The improvement of these preliminary results will come mainly from adding a smaller lattice spacing to our sample.