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

Abstract

We carry out an analysis of the full set of ten $\bar{B}\to D^{(\ast )}$ 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 $\bar{B}\to D^{(\ast )}\{e^{-},{\mu }^{-}\}\bar{\nu }$ 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 $R_{D^{(\ast )}}$, the $\tau$ polarization observables $P_{\tau }^{D^{(\ast )}}$, 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.

Comments: 14 pages, 2 figures, 3 tables, link to ancillary files on Zenodo.org