$B \to \pi\ell\nu$ form factors and $|V_{ub}|$ with M\"obius domain wall fermions

TL;DR

This study calculates $B o  ext{pi} u$ form factors using Mb6bius domain wall fermions on fine lattices, enabling a precise determination of the CKM element $|V_{ub}|$ with controlled systematic uncertainties.

Contribution

It presents a novel lattice QCD calculation of $B o  ext{pi} u$ form factors with multiple lattice spacings and pion masses, and performs a physical extrapolation to determine $|V_{ub}|$.

Findings

Form factors depend on pion mass, heavy quark mass, lattice spacing, and momentum transfer.

Extrapolation yields a precise value of $|V_{ub}|$ consistent with experimental data.

Demonstrates the effectiveness of Mb6bius domain wall fermions for heavy-light decay calculations.

Abstract

We report on a calculation of form factors for the semileptonic decay of $B$ meson to pion on $2+1$-flavour lattices with lattice spacings from 0.080 fm down to 0.044 fm. Using the M\"obius domain wall fermion action for both sea and valence quarks, we simulate pions with masses down to 225 MeV. By utilizing a range of heavy quark masses up to 2.44 times the mass of the charm quark we extrapolate to the physical $b$ quark mass. We discuss the dependence of the form factors on the pion mass, heavy quark mass, lattice spacing and the momentum-transfer. We extract the CKM matrix element $|V_{ub}|$ through a simultaneous fit with the $B \to \pi\ell\nu$ differential branching fractions provided by the Belle and BaBar collaborations after a chiral-continuum and physical $b$ quark extrapolations of our lattice data.