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

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