Lattice QCD calculation of B̄ ̃Dln̄ decay form factors at zero recoil

A lattice QCD calculation of the B̄→Dl n̄ decay form factors is presented. We obtain the value of the form factor h1(w) at the zero-recoil limit w51 with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor h2(w) is calculated, for small recoil momenta, from a similar ratio. In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses. Our results are h1(1) 51.007(6)(2)(3) and h2(1)520.107(28)(04)(30 ). For both the first error is statistical; the second stems from the uncertainty in adjusting the heavy quark masses and the last from omitted radiative corrections. Combining these results, we obtain a precise determination of the physical combination FB→D(1) 51.058(17 ), where the mentioned systematic errors are added in quadrature. The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of FB→D21.