|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.