[Paper Review] $B o D^*\ellν_\ell$ semileptonic form factors from lattice QCD with Möbius domain-wall quarks

Yasumichi Aoki, Brian Colquhoun+6 more|arXiv (Cornell University)|Jun 9, 2023

Particle physics theoretical and experimental studies16 references4 citations

TL;DR

This lattice QCD study computes $B\to D^*\ell\nu_\ell$ semileptonic form factors using Möbius domain-wall fermions across three lattice spacings and light pion masses down to 230 MeV, achieving high chiral symmetry preservation. The analysis yields $R(D^*) = 0.252(22)$ in the Standard Model and $|V_{cb}| = 39.19(90)\times10^{-3}$ when combined with Belle data, showing improved consistency with experimental differential decay rates compared to prior lattice results.

ABSTRACT

We calculate the form factors for the $B o D^*\ellν_\ell$ 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 $M_π\sim 230$ MeV. The physical lattice size $L$ satisfies the condition $M_πL \geq 4$ to control finite volume effects (FVEs), while we simulate a smaller size at the smallest $M_π$ 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 ($\ell = τ$) and light lepton ($\ell = e,μ$) channels $R(D^*) = 0.252(22)$ in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields $|V_{cb}| = 39.19(91) imes 10^{-3}$, 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.

Motivation & Objective

• To compute $B\to D^*\ell\nu_\ell$ semileptonic form factors with controlled systematic uncertainties using unquenched 2+1-flavor lattice QCD.
• To reduce discretization and finite-volume effects by employing Möbius domain-wall fermions and multiple lattice spacings down to $a^{-1} \sim 4.5$ GeV with $M_\pi L \geq 4$.
• To enable a precise determination of $|V_{cb}|$ and $R(D^*)$ by extrapolating form factors to the continuum and physical quark masses using heavy meson chiral perturbation theory at next-to-leading order.
• To improve consistency with experimental differential decay rate distributions by employing a model-independent BGL parametrization and high-statistics lattice data.
• To resolve the long-standing $|V_{cb}|$ tension between exclusive and inclusive determinations by providing a first-principles lattice calculation with controlled systematics.

Proposed method

• The study uses Möbius domain-wall fermions for all valence and sea quarks to preserve chiral symmetry and eliminate $O(a)$ discretization errors.
• Lattice gauge ensembles are generated at three inverse lattice spacings ($a^{-1} \sim$ 2.5, 3.6, 4.5 GeV) with pion masses as low as 230 MeV and physical volumes satisfying $M_\pi L \geq 4$.
• Bottom quark masses are tuned from the physical charm mass up to $0.7a^{-1}$ to suppress $O(a^2)$ and higher discretization effects.
• Correlator ratios are computed at four source-sink separations to ensure ground state saturation and reduce excited-state contamination.
• Form factors are extrapolated to the continuum and physical quark masses using heavy meson chiral perturbation theory at next-to-leading order.
• The BGL parametrization is applied to model the recoil parameter dependence, enabling a model-independent fit to experimental data and extraction of $R(D^*)$ and $|V_{cb}|$.

Experimental results

Research questions

• RQ1 What is the value of $R(D^*)$ in the Standard Model, computed from first-principles lattice QCD with controlled systematics?
• RQ2 How well do the lattice form factors reproduce the differential decay rate distribution measured by the Belle experiment?
• RQ3 To what extent do the lattice form factors reduce the tension in $|V_{cb}|$ determinations between exclusive and inclusive decays?
• RQ4 How do the form factor expansion coefficients from this study compare with those from other lattice calculations and phenomenological fits to Belle data?
• RQ5 What is the impact of finite-volume effects and discretization errors on the form factor extrapolation, and how are they controlled?

Key findings

• The study computes synthetic form factor data for $g$, $f$, $\mathcal{F}_1$, and $\mathcal{F}_2$ at three reference recoil parameters ($w = 1.025$, 1.060, 1.100), providing a high-precision input for future $|V_{cb}|$ determinations.
• The lattice result for $R(D^*)$ in the Standard Model is $0.252(22)$, consistent with the world average and indicating no significant lepton flavor universality violation in the SM.
• A simultaneous fit with Belle experimental data yields $|V_{cb}| = 39.19(90)\times10^{-3}$, which is consistent with previous exclusive lattice determinations and shows good agreement with the measured differential decay rate distribution.
• The expansion coefficient for $\mathcal{F}_1$ is slightly larger than in earlier lattice studies and shows better consistency with a phenomenological fit to Belle data, improving agreement with experiment.
• Finite-size effects are found to be small, confirmed by direct simulations at two volumes with the lightest pion mass, supporting the validity of the $M_\pi L \geq 4$ condition.
• The use of Möbius domain-wall fermions ensures high chiral symmetry preservation, suppressing $O(a)$ errors and enabling direct calculation of form factors without explicit renormalization.