The CKM matrix element $|V_{ cb}|$ can be extracted by combining data from experiments with lattice QCD results for the semileptonic form factors for the $\bar{ B}\to D^{ (*)} \ell \bar{ \nu}$ decays. The Oktay-Kronfeld (OK) action was designed to reduce heavy-quark discretization errors to below $1\%$, or through $\mathcal{ O}(\lambda^3)$ in HQET power counting. Here we describe recent progress on bottom-to-charm currents improved to the same order in HQET as the OK action, and correct formerly reported results of our matching calculations, in which the operator basis was incomplete.
Categories: hep-lat hep-ph