A lattice QCD calculation of the B̅ →Dlν̅ 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 FB→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 FB→D-1.
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