Vub|fromB→πℓνdecays and (2+1)-flavor lattice QCD

We present a lattice-QCD calculation of the $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ 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 $z$ parametrization 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 $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find $|{V}_{ub}|=(3.72\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, 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 $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ 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.