$B \rightarrow \pi \ell \nu$ at zero recoil from lattice QCD with physical $u/d$ quarks

TL;DR

This paper presents the first lattice QCD calculations of the $B ightarrow \pi \ell u$ decay form factors at physical u/d quark masses, resolving previous uncertainties and confirming theoretical predictions at zero recoil.

Contribution

It provides the first lattice QCD results for $B ightarrow \pi \ell u$ form factors at physical quark masses, including a precise test of the soft-pion theorem at zero recoil.

Findings

Form factor $f_0$ at zero recoil determined to 3% accuracy.

Confirmed the soft-pion theorem $f_0(q^2_{max}) = f_B/f_{\pi}$ as $m_\pi ightarrow 0$.

Demonstrated the effectiveness of staggered chiral perturbation theory for light quark mass dependence.

Abstract

The exclusive semileptonic decay $B \rightarrow \pi \ell \nu$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3\%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q^2_{max}) = f_B/f_{\pi}$ does hold as $m_{\pi} \rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\pi}$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\pi}$. We also give results for other processes such as $B_s \rightarrow K \ell \nu$.