We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay B → D ν at nonzero recoil. We carry out numerical simulations on fourteen 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 parameterize the form factors and extend them to the full kinematic range using modelindependent 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 ± 1.7 QCD+exp ± 0.2 QED ) × 10 −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).
We present a lattice-QCD calculation of the B → π ν semileptonic form factors and a new determination of the CKM matrix element |V ub |. We use the MILC asqtad 2+1-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent z parameterization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolation to the z expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain |V ub |, we simultaneously fit the experimental data for the B → π ν differential decay rate obtained by the BaBar and Belle collaborations together with our lattice form-factor results. We find |V ub | = (3.72 ± 0.16) × 10 −3 where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on |V ub | to the same level as the experimental error. We also provide results for the B → π ν vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely-determined than from our lattice-QCD calculation alone. These results can be used in other phenomenological applications and to test other approaches to QCD.
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