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We calculate the form factors for the $B \to D^*\ell\nu_\ell$ decay in 2+1flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wallaction, which preserves chiral symmetry to a good precision. Our gaugeensembles are generated at three lattice cutoffs $a^{-1} \sim 2.5$, 3.6 and 4.5GeV 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 directlyexamine FVEs. The bottom quark masses are chosen in a range from the physicalcharm quark mass to $0.7 a^{-1}$ to control discretization effects. Weextrapolate the form factors to the continuum limit and physical quark massesbased on heavy meson chiral perturbation theory at next-to-leading order. Thenthe recoil parameter dependence is parametrized using a model independent formleading 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 StandardModel. A simultaneous fit with recent data from the Belle experiment yields$|V_{cb}| = 39.19(90)\times 10^{-3}$, which is consistent with previousexclusive determinations, and shows good consistency in the kinematicaldistribution of the differential decay rate between the lattice andexperimental data.

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