$|V_{ub}|$ from $B\to\pi\ell\nu$ decays and (2+1)-flavor lattice QCD

TL;DR

This paper presents a lattice-QCD calculation of B to pi semileptonic form factors and a new determination of the CKM matrix element |V_{ub}|, combining lattice data with experimental results for improved precision.

Contribution

It introduces a comprehensive lattice-QCD analysis with a novel functional method and combined fit to experimental data to accurately determine |V_{ub}| and form factors.

Findings

|V_{ub}| = (3.72 ± 0.16) × 10^{-3} from combined fit

Form factors are more precise than previous lattice-only results

Systematic error budget and covariance matrix provided

Abstract

We present a lattice-QCD calculation of the $B\to\pi\ell\nu$ 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 $z$ 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 $B\to\pi\ell\nu$ differential decay rate obtained by the BaBar and Belle collaborations together with our lattice form-factor results. We find $|V_{ub}|=(3.72\pm 0.16)\times 10^{-3}$ 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 $B\to\pi\ell\nu$ 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.