Semileptonic $B \to D^{(\ast)} \ell\nu$ Decay Form Factors using the Oktay-Kronfeld Action

We report recent progress in calculating semileptonic form factors for the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to D \ell \bar{\nu}$ decays using the Oktay-Kronfeld (OK) action for bottom and charm quarks. We use the second order in heavy quark effective power counting $\mathcal{O}(\lambda^2)$ improved currents in this work. The HISQ action is used for the light spectator quarks. We analyzed four $2+1+1$-flavor MILC HISQ ensembles with $a\approx 0.09\,\mathrm{fm}$, $0.12\,\mathrm{fm}$ and $M_\pi \approx 220\,\mathrm{MeV}$, $310\,\mathrm{MeV}$: $a09m220$, $a09m310$, $a12m220$, $a12m310$. Preliminary results for $B\to D^\ast\ell\nu$ decays form factor $h_{A_1}(w)$ at zero recoil ($w=1$) are reported. Preliminary results for $B \to D\,\ell\nu$ decays form factors $h_\pm(w)$ over a kinematic range $1<w<1.3$ are reported as well.