Lattice QCD calculation of B̄→Dlv̄ decay form factors at zero recoil

A lattice QCD calculation of the B̄→Dlv̄ decay form factors is presented. We obtain the value of the form factor h₊(w) at the zero-recoil limit w=1 with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor h_(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 h₊(1) = 1.007(6)(2)(3) and h_(1)=-0.107(28)(04)(₃₀¹⁰). 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 ℱ_B→D(1) = 1.058(₁₇²⁰), 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 ℱ_B→D-1.