A lattice QCD calculation of the $\overline{B}\to \mathrm{Dl}\overline{\nu }$ decay form factors is presented. We obtain the value of the form factor $h_{+}\mathrm{}\left(w\right)\mathrm{}$ at the zero-recoil limit $w=1\mathrm{}$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor $h_{-}\mathrm{}\left(w\right)\mathrm{}$ 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 $h_{+}\mathrm{}\left(1\right)=1.007\mathrm{}\left(6\right)\mathrm{}\left(2\right)\mathrm{}\left(3\right)\mathrm{}$ and $h_{-}\mathrm{}\left(1\right)=-{0.107\left(28\right)\mathrm{}\left(04\right)(}_{30}^{10}).\mathrm{}$ 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 ${\mathcal{F}}_{\overrightarrow{B}D}{\mathrm{}\left(1\right)=1.058(}_{17}^{20}),$ 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 ${\mathcal{F}}_{\overrightarrow{B}D}-1.$

• Received 16 June 1999

DOI:https://doi.org/10.1103/PhysRevD.61.014502