Lattice QCD (focus on Charm and Beauty form factors, $R(D^*)$, $b$- & $c$-quark masses)

Abstract

We present an overview of state of the art lattice quantum chromodynamcis calculations for heavy-light quantities. Special focus is given to the calculation of form factors for semi-leptonic decays of $B_{(s)}$ and $D$ mesons, the extraction of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{ub}|$ and $|V_{cb}|$ as well as the determination of $R(D^{(*)})$ testing the universality of lepton flavors in $b\to c$ transitions. In addition we report on the determination of $b$ and $c$ quark masses as well as on neutral $B_{(s)}$ meson mixing. Recent results are summarized and new developments highlighted.