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

Abstract

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 $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$ 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.

Comments: 8 pages, 2 figures, Lattice 2017 proceeding, references updated, typos fixed