$B \to D^*\ell\nu_\ell$ semileptonic form factors from lattice QCD with M\"obius domain-wall quarks

Abstract

We calculate the form factors for the $B \to D^*\ell\nu_\ell$ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with pion masses as low as $M_\pi \sim 230$ MeV. The physical lattice size $L$ satisfies the condition $M_\pi L \geq 4$ to control finite volume effects (FVEs), while we simulate a smaller size at the smallest $M_\pi$ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to $0.7 a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau ($\ell = \tau$) and light lepton ($\ell = e,\mu$) channels $R(D^*) = 0.252(22)$ in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields $|V_{cb}| = 39.19(91)\times 10^{-3}$, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data.