$B\to\pi\ell\nu$ semileptonic form factors from unquenched lattice QCD and determination of $|V_{ub}|$

TL;DR

This paper calculates the $B o ext{pi} u ext{l}$ form factors using unquenched lattice QCD and updates the value of $|V_{ub}|$, combining theoretical and experimental data for a precise determination.

Contribution

It provides the first unquenched lattice QCD calculation of $B o ext{pi} u ext{l}$ form factors with multiple lattice spacings and a combined analysis to extract $|V_{ub}|$.

Findings

Preliminary $|V_{ub}|$ value: $(3.72 extpm 0.14) imes 10^{-3}$

Lattice and experimental uncertainties are comparable

Form factors extrapolated to full kinematic range using $z$-parameterization

Abstract

We compute the $B\to\pi\ell\nu$ semileptonic form factors and update the determination of the CKM matrix element $|V_{ub}|$. We use the MILC asqtad ensembles with $N_f=2+1$ sea quarks at four different lattice spacings in the range $a \approx 0.045$~fm to $0.12$~fm. The lattice form factors are extrapolated to the continuum limit using SU(2) staggered chiral perturbation theory in the hard pion limit, followed by an extrapolation in $q^2$ to the full kinematic range using a functional $z$-parameterization. The extrapolation is combined with the experimental measurements of the partial branching fraction to extract $|V_{ub}|$. Our preliminary result is $|V_{ub}|=(3.72\pm 0.14)\times 10^{-3}$, where the error reflects both the lattice and experimental uncertainties, which are now on par with each other.