Heavy-heavy current improvement for calculation of $\bar{B}\rightarrow D^{(*)}\ell \bar{\nu}$ semi-leptonic form factors using the Oktay-Kronfeld action

TL;DR

This paper discusses improving the calculation of semi-leptonic form factors for B to D(*) decays using the Oktay-Kronfeld action, which reduces heavy quark discretization errors in lattice QCD.

Contribution

It reports progress in calculating the improvement coefficients for heavy quark currents with bottom and charm quarks using the Oktay-Kronfeld action.

Findings

Preliminary results for current improvement coefficients.

Enhanced accuracy in heavy-light meson form factor calculations.

Reduction of discretization effects in lattice QCD simulations.

Abstract

Lattice calculations of the form factors for $\bar{B}\to D^{(*)}\ell\bar{\nu}$ decays can be used to extract the CKM matrix element $|V_{cb}|$. The Oktay-Kronfeld action is a highly improved version of the Fermilab action, which systematically reduces heavy quark discretization effects through $\mathcal{O}(\lambda^3)$ in HQET power counting, for heavy-light meson quantities. To calculate $\bar{B}\rightarrow D^{(*)}\ell \bar{\nu}$ semi-leptonic form factors using Oktay-Kronfeld heavy quarks, we need to improve the heavy quark currents to the same level. We report our progress in calculating the improvement coefficients for currents composed of bottom and charm quarks. Our results presented in this paper are preliminary.