[Paper Review] $B o D^\ast\ellν$ at non-zero recoil

Alejandro Vaquero, DeTar, C.+4 more|arXiv (Cornell University)|Jun 3, 2019

Particle physics theoretical and experimental studies9 references4 citations

TL;DR

This paper presents preliminary lattice-QCD calculations of the $B\to D^*\ell\nu$ form factors at non-zero recoil, using the BGL parametrization to compare with experimental data. The results show a large slope at small recoil, conflicting with Belle's untagged data, and highlight discrepancies in $\mathcal{F}_1$ coefficients that affect $R(D^*)$ predictions, underscoring the need for improved lattice precision to resolve the $V_{cb}$ tension.

ABSTRACT

The current status of the lattice-QCD calculations of the form factors of the $B o D^\ast\ellν$ semileptonic decay is reviewed. Particular emphasis is given to the most mature calculation at non-zero recoil coming from the Fermilab Lattice and MILC collaborations. Blinded, preliminary results for the form factors are shown, including a preliminary, but detailed error budget. The lattice results seem to favor a large slope at small recoil, in contrast to the latest untagged results coming from the Belle collaboration. A comprehensive comparison between the latest BGL $z$ expansions of Belle, Babar, the lattice and a joint BGL fit including lattice and Belle data is presented, and a roadmap to improve the current calculation is discussed. The current implications for $V_{cb}$ and $R(D^\ast)$ are discussed.

Motivation & Objective

• To provide first-principles lattice-QCD calculations of $B\to D^*\ell\nu$ form factors at non-zero recoil, addressing the $V_{cb}$ discrepancy.
• To compare lattice results with experimental BGL fits from Belle, Babar, and combined datasets to assess consistency.
• To evaluate the impact of form factor parametrization (BGL vs CLN) on $V_{cb}$ and $R(D^*)$ determinations.
• To identify systematic uncertainties and guide future improvements in lattice calculations.
• To assess the role of lattice QCD in resolving the inclusive-exclusive $V_{cb}$ tension and $R(D^*)$ anomalies.

Proposed method

• Using the Fermilab Lattice and MILC collaborations' gauge configurations, the study computes $B\to D^*\ell\nu$ form factors at non-zero recoil via lattice QCD.
• Employing the BGL parametrization with $z$-expansion to model form factors without relying on HQET assumptions.
• Applying a blinded analysis to ensure objectivity in form factor coefficient extraction and error budgeting.
• Comparing lattice results with experimental BGL fits from Belle (tagged and untagged), Babar, and a joint lattice+Belle fit.
• Using helicity amplitudes $H_{\pm,0}$ and the matrix element decomposition of the $V-A$ current to derive form factors.
• Integrating form factor predictions to compute $R(D^*)$ and comparing with experimental measurements.

Experimental results

Research questions

• RQ1 How do lattice-QCD calculations of $B\to D^*\ell\nu$ form factors at non-zero recoil compare with experimental BGL fits?
• RQ2 What is the impact of the BGL parametrization on resolving the $V_{cb}$ discrepancy compared to CLN?
• RQ3 Why do lattice results show a larger slope at small recoil than Belle's untagged data?
• RQ4 How do the $z$-expansion coefficients of the form factors differ between lattice and experimental fits?
• RQ5 To what extent do discrepancies in $\mathcal{F}_1$ coefficients affect predictions of $R(D^*)$?

Key findings

• The lattice-QCD calculation shows a large slope at small recoil, in tension with Belle's untagged experimental results.
• The $z$-expansion coefficients for $\mathcal{F}_1$ differ significantly between lattice and experimental fits, explaining divergent $R(D^*)$ predictions at large recoil.
• Ratios of BGL coefficients for $f$ and $g$ form factors agree within $2\sigma$ between lattice and combined fits, indicating consistency in low-recoil region.
• The form factor $\mathcal{F}_1$ dominates at large recoil, and its coefficient discrepancies drive the observed differences in $R(D^*)$ predictions.
• The current lattice results suggest that the CLN parametrization may be too restrictive, supporting the need for model-independent BGL fits.
• A roadmap for improving lattice precision is outlined, including three-step enhancements to reduce systematic errors.