Current progress on the semileptonic form factors for \(\bar{B} \to D^{\ast} \ell \bar{\nu}\) decay using the Oktay-Kronfeld action

Abstract

We present recent progress in calculating the semileptonic form factors \(h_{A_1}(w)\) for the \(\bar{B} \to D^{\ast} \ell \bar{\nu}\) decays. We use the Oktay-Kronfeld (OK) action for the charm and bottom valence quarks and the HISQ action for light quarks. We adopt the Newton method combined with the scanning method to find a good initial guess for the \(\chi^2\) minimizer in the fitting of the 2pt correlation functions. The main advantage is that the Newton method lets us to consume all the time slices allowed by the physical positivity. We report the first, reliable, but preliminary results for \(h_{A_1}(w)/\rho_{A_1}\) at zero recoil (\(w=1\)). Here we use a MILC HISQ ensemble (\(a = 0.12\) fm, \(M_{\pi}\) = 220 MeV, and \(N_f = 2 + 1 + 1\) flavors).