Eur. Phys. J. C (2020) 80: 74
https://doi.org/10.1140/epjc/s10052-020-7616-4

Regular Article - Theoretical Physics

Theory determination of $\overline{\mathit{B}}\mathbf{\to }{\mathit{D}}^{\mathbf{(}\mathbf{\ast }\mathbf{)}}{\mathit{\ell }}^{\mathbf{-}}\overline{\mathit{\nu }}$ form factors at $\mathcal{O}\mathbf{(}\mathbf{1}\mathbf{/}{\mathit{m}}_{\mathit{c}}^{\mathbf{2}}\mathbf{)}$

¹ Universität Siegen, Walter-Flex Straße 3, 57072, Siegen, Germany
² Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748, Garching, Germany
³ Dipartimento di Fisica, Università di Torino & INFN, Sezione di Torino, 10125, Turin, Italy
⁴ Technische Universität München, James-Franck-Straße 1, 85748, Garching, Germany

^a marzia.bordone@uni-siegen.de

Received: 10 September 2019
Accepted: 6 January 2020
Published online: 31 January 2020

Abstract

We carry out an analysis of the full set of ten $\overline{B}\to D^{(\ast )}$ 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 $\overline{B}\to D^{(\ast )}\{e^{-},{\mu }^{-}\}\overline{\nu }$ 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 $|V_{\mathit{cb}}|$ 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.