B→Dℓνform factors at nonzero recoil and|Vcb|from2+1-flavor lattice QCD

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay $\overline{B}\ensuremath{\rightarrow}D\ensuremath{\ell}\overline{\ensuremath{\nu}}$ at nonzero recoil. We carry out numerical simulations on 14 ensembles of gauge-field configurations generated with $2+1$ flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the $b$ and $c$ valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parametrize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for ${f}_{+}({q}^{2})$ and ${f}_{0}({q}^{2})$, including statistical and systematic errors, as coefficients of a series in the variable $z$ and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, $|{V}_{cb}|=(39.6\ifmmode\pm\else\textpm\fi{}1.{7}_{\mathrm{QCD}+\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}0.{2}_{\mathrm{QED}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio $R(D)$ in the Standard Model, which yields $R(D)=0.299(11)$.