[Paper Review] $B o D^{(*)}\ellν$ form factors from $N_f\!=\!2+1$ QCD with Möbius domain-wall quarks

T. Kaneko, Yasumichi Aoki+3 more|arXiv (Cornell University)|Nov 2, 2018

Particle physics theoretical and experimental studies2 references4 citations

TL;DR

This lattice QCD study computes $B\to D^{(*)}\ell\nu$ form factors using $N_f=2+1$ dynamical quarks with Möbius domain-wall fermions at lattice spacings of $a^{-1} \approx 2.5$ and 3.6 GeV, achieving $M_\pi \sim 310$ MeV. The results show mild dependence on cutoff, bottom quark mass, and pion mass, with $R_1(w)$ favoring the CLN parametrization and suggesting that the $|V_{cb}|$ tension may not stem solely from higher-order HQET corrections.

ABSTRACT

We report on our study of the B o D^(*) \ell νsemileptonic decays at zero and nonzero recoils in 2+1 flavor QCD. The Möbius domain-wall action is employed for light, charm and bottom quarks at lattice cutoffs 1/a = 2.5 and 3.6 GeV. We take bottom quark masses up to \approx 2.4 times the physical charm mass to control discretization effects. The pion mass is as low as M_π\sim 310 MeV. We present our preliminary results for the relevant form factors and discuss the violation of heavy quark symmetry, which is a recent important isuue on the long-standing tension in the Cabibbo-Kobayashi-Maskawa matrix element |V_{cb}| between the exclusive and inclusive decays.

Motivation & Objective

• To compute $B\to D^{(*)}\ell\nu$ semileptonic form factors in lattice QCD with controlled systematic uncertainties.
• To address the long-standing tension between exclusive and inclusive determinations of the CKM matrix element $|V_{cb}|$.
• To test the validity of heavy quark symmetry and NLO HQET predictions using non-perturbative lattice results.
• To provide a model-independent basis for $|V_{cb}|$ determination via parametrizations like BGL and CLN.
• To prepare for future high-precision determinations by extending simulations to lighter pions and finer lattices.

Proposed method

• Simulate $N_f=2+1$ QCD with the tree-level improved Symanzik gauge action and Möbius domain-wall fermions for light, charm, and bottom quarks.
• Use three ensembles with $a^{-1} \approx$ 2.45 and 3.61 GeV, and $M_\pi \sim$ 309–500 MeV, ensuring $M_\pi L \gtrsim 4$ to suppress finite-volume effects.
• Compute three-point correlation functions for $B$ and $D^{(*)}$ mesons to extract matrix elements of vector and axial currents.
• Extract form factors $h_+(w)$, $h_-(w)$, $h_V(w)$, $h_{A_1}(w)$, $h_{A_2}(w)$, $h_{A_3}(w)$ using the $B$ meson at rest and $D^{(*)}$ with varying three-momenta.
• Compare results to NLO HQET predictions and parametrizations (CLN and BGL) to assess deviations and implications for $|V_{cb}|$ tension.
• Use multiple bottom quark masses ($m_b \approx 1.25^2 m_c$ and $1.25^4 m_c$) to probe discretization and heavy quark scaling behavior.

Experimental results

Research questions

• RQ1 How do the $B\to D^{(*)}\ell\nu$ form factors depend on lattice spacing, bottom quark mass, and pion mass in the $N_f=2+1$ QCD setup?
• RQ2 To what extent do the lattice results for form factor ratios deviate from NLO HQET predictions, and what does this imply for higher-order corrections?
• RQ3 Does the lattice data favor the CLN or BGL parametrization for $R_1(w)$, and how does this affect the $|V_{cb}|$ determination?
• RQ4 Can the observed mild dependence on $a^{-1}$, $m_b$, and $M_\pi$ support a controlled extrapolation to the physical point?
• RQ5 What is the consistency of the lattice results with the $|V_{cb}|$ values extracted from inclusive decays, and what does this imply for the current tension?

Key findings

• The form factors show mild dependence on lattice spacing $a^{-1}$, bottom quark mass $m_b$, and pion mass $M_\pi$, indicating small discretization and chiral extrapolation effects.
• The ratio $h_{A_1}(1)/V_1(1)$ and $S_1(1)/h_{A_1}(1)$ exhibit systematic deviations from NLO HQET predictions, suggesting possible higher-order corrections.
• The form factor ratio $R_1(w)$ is consistent with the CLN parametrization, favoring the CLN fit over BGL in the current data range.
• The $R_1(w)$ results at $w \approx 1$ are in good agreement with the CLN prediction, supporting its use in $|V_{cb}|$ determinations.
• The data suggest that the $|V_{cb}|$ tension may not be fully explained by higher-order HQET corrections, as the lattice results do not show strong deviations from NLO HQET in $R_1(w)$.
• The results support the need for further simulations at $M_\pi \sim 230$ MeV and $a^{-1} \sim 4.5$ GeV to achieve a controlled continuum and physical point extrapolation.