Improvement of heavy-heavy current for calculation of $\bar{B}\to D^{(\ast )}\mathrm{\ell }\bar{\nu }$ form factors using Oktay-Kronfeld heavy quarks

The CKM matrix element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ can be extracted by combining data from experiments with lattice QCD results for the semileptonic form factors for the $\bar{B}\to D^{(\ast )}\mathrm{\ell }\bar{\nu }$ decays. The Oktay-Kronfeld (OK) action was designed to reduce heavy-quark discretization errors to below $1\mathrm{\%}$, 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.