$B\to \ddot{I}€\ell \hat{I}½$ at zero recoil from lattice QCD with physical $u/d$ quarks

Abstract

The exclusive semileptonic decay $B\to \ddot{I}€\ell \hat{I}½$ 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 $f_0(q_{max}^2)=f_B/f_{\ddot{I}}€$ does hold as $m_{\ddot{I}}€\to 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\ddot{I}}€$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\ddot{I}}€$. We also give results for other processes such as $B_s\to K\ell \hat{I}½$.

16 pages, 6 figures