Improved currents for $\bar{B}\to D^{(*)}\ell\bar{\nu}$ form factors from Oktay-Kronfeld heavy quarks

The CKM matrix element $|V_{cb}|$ can be extracted by combining experimentally determined branching fractions for $\bar{B}\to D^{(*)}\ell\bar{\nu}$ decays with form factors from the lattice. While successful, the precision of this approach has been limited by heavy-quark discretization effects. An improved version of the Fermilab action, the Oktay-Kronfeld action, can be used to reduce heavy-quark discretization effects in calculations performed at the physical bottom and charm quark masses. Treating charm and bottom quarks as massive, we are carrying out improvement of the flavor-changing currents through third order in the momentum (HQET) expansion.