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

The exclusive semileptonic decay $B \rightarrow π\ell ν$ 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 $f_0(q^2_{max}) = f_B/f_π$ does hold as $m_π \rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_π$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_π$. We also give results for other processes such as $B_s \rightarrow K \ell ν$.

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