Theory determination of $\bar{B}\to D^{(*)}\ell^-\bar\nu$ form factors at $\mathcal{O}(1/m_c^2)$

TL;DR

This paper performs a comprehensive theoretical analysis of $ar{B} o D^{(*)}$ form factors at order $rac{1}{m_c^2}$ using HQE, QCD sum rules, and lattice data, improving the understanding of semileptonic B decays.

Contribution

It provides the first full-order HQE calculation of all ten form factors with combined theoretical and experimental constraints, confirming convergence and refining $|V_{cb}|$ and $R_{D^{(*)}}$ predictions.

Findings

Good agreement among theoretical methods.

Form factors show convergence at $rac{1}{m_c^2}$ order.

Updated $|V_{cb}|$ and $R_{D^{(*)}}$ predictions.

Abstract

We carry out an analysis of the full set of ten $\bar{B}\to D^{(*)}$ form factors within the framework of the Heavy-Quark Expansion (HQE) to order $\mathcal{O}(\alpha_s,\,1/m_b,\,1/m_c^2)$, both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in $\bar{B}\to D^{(*)}\lbrace e^-,\mu^-\rbrace\bar\nu$ measurements. The coefficients entering at the $1/m_c^2$ level are found to be of $\mathcal{O}(1)$, indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of $|V_{cb}|$ in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios $R_{D^{(*)}}$, the $\tau$ polarization observables $P_\tau^{D^{(*)}}$, and the longitudinal polarization fraction $F_L$. Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.