### Speaker

### Description

The semileptonic form factors, at zero and non-zero recoil, of $B\to D^{(\ast)}\ell\nu$ decays are needed to determine the $V_{cb}$, a Cabibbo-Kobayashi-Maskawa (CKM) matrix element. Typically in the Unitarity Triangle (UT) analysis for the quark flavor mixing angles and the CP violating phase, $V_{cb}$ enters as a normalization of $\vert V_{ub}\vert/\vert V_{cb}\vert$ or with $\varepsilon_K \propto \vert V_{cb} \vert^4$. More precise determination of $V_{cb}$ will make the UT constraints tighter and possibly can reveal a new physics. Other interesting quantity is the ratios of $R(D^{(\ast)}) = \Gamma(B \to D^{(\ast)}\tau\nu)/\Gamma(B \to D^{(\ast)}\ell\nu)$ which can provide a precision test of lepton-flavor universality. A lattice calculation with a non-zero recoils can be used to diagnose the current HQET parameterization of the form factors, which are argued by many of recent articles.

We will present a recent progress in a lattice calculation of these $B \to D^{(\ast)}\ell\nu$ decays form factors. The calculation has been carried out with the MILC HISQ ensemble which simulates 2+1+1-flavor of dynamical quarks. A preliminary results from two different lattice spacings $a=0.12, 0.09$ fm with heavy pion mass 310 MeV will be presented. The valence charm and bottom quarks are simulated with the Oktay-Kronfeld (OK) action [1] by which a highly improved lattice heavy quark action reducing discretization errors with $\mathcal{O}(\lambda_{QCD}^3/m_{b,c}^3)$ matching to continuum QCD at tree-level. Capturing the loop corrections with a tadpole prescription in a numerical simulation, we reported that this tree-level matched OK action, in practice, shows a significant improvement in the heavy quark discretization errors. [2] Anticipating improved measurements of the decay rates from Belle II experiment, our projected error on the $V_{cb}$ is below 1%. Such an improvement will tighten the constraints on the UT analysis, and help resolve the approximate $3\sigma$ discrepancy between estimates using exclusive and inclusive B decays.