$B\to D^{\ast }\ell {\nu }_{\ell }$ 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.

45 pages, 19 figures; v2: version published in PRD

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Cited by in corpus (6)

• FLAG Review 2024
• Global fit to $b\to c\tau \nu$ anomalies as of Spring 2024
• Disentangling left and right-handed neutrino effects in $B\to K^{(\ast )}\nu \nu$
• Measurement of the branching fraction ratios $R(D^{+})$ and $R(D^{\ast +})$ using muonic $\tau$ decays
• Right-handed interactions in puzzling $B$-decays
• The QED nonfactorizable correction to the semileptonic charmed three-body $B$ decays