Calculation of Semileptonic Form Factor for $\bar B\to D^\ast \ell \bar \nu$ Decay Using the Oktay-Kronfeld Action

Abstract

We study the calculation of $\bar{B}\to D^\ast \ell \bar{\nu}$ semileptonic form factor using the lattice QCD technique. Our first target is the zero recoil process which is gold-plated channel to determine the flavor mixing between bottom and charm: $V_{cb}$ of the Cabbibo-Kobayashi-Maskawa (CKM) matrix.<br/> <br/> The simulation is done on the $N_{f}=2+1+1$ MILC Highly-improved staggered-quark (HISQ) lattices where the lattice spacing $a\approx 0.12~\fm$, and the sea pion mass $M_\pi\approx 300~\MeV$. For valence quarks, we use the HISQ action for the light and strange quarks and the Oktay-Kronfeld (OK) action for the bottom and charm quarks. Here the OK action is improved version of the Fermilab action such that the bilinear operators are tree-level matched to QCD through $\CO(\lambda^3)$ in HQET power counting where $\lambda\sim a\Lambda\sim \Lambda/(2m_Q)$ and $m_Q$ is the heavy quark mass.<br/> <br/> We present preliminary results of the $\BtoDst$ semileptonic form factor at zero recoil. For the OK action inputs, we determine the critical hopping parameter $\kcrit$ nonperturbatively, and tune the hopping parameters $\kappa_b$ and $\kappa_c$ for physical bottom and charm.