$B$ meson semileptonic decays from lattice QCD

Abstract

$B$ processes are a rich source of potential anomalies that could lead to the discovery of BSM physics. The long-standing tension between the inclusive and the exclusive determinations of the CKM matrix elements $|V_{xb}|$, or the current tensions in the $R(D)$-$R(D^\ast)$ plane are some examples of active areas of research where we might find signals of new physics. Heavy-to-heavy $B$ semileptonic decays, $B_{(s)}\to D^{(\ast)}_{(s)}\ell\nu$, and in particular, decays with a vector product ($D^\ast_{(s)}$) are especially interesting from an experimental point of view, but experiment and theory must walk together in order to reach conclusions in the intensity frontier. In this review I talk about the current status of the lattice-QCD calculations of the $B\to D^{\ast}\ell\nu$ form factors at non-zero recoil, I discuss the implications they have for the determination of $B$ anomalies, and finally I give some hints of what we can expect from future calculations.