$B\to D^{\ast }\ell {\nu }_{\ell }$ semileptonic form factors from lattice QCD with Möbius domain-wall quarks

Abstract

We calculate the form factors for the $B\to D^{\ast }\ell {\nu }_{\ell }$ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the Möbius 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 $M_{\pi }L\ge 4$ 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 $0.7a^{-1}$ 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 $R(D^{\ast })=0.252(22)$ 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.

arXiv comment45 pages, 19 figures; v2: version published in PRD

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