Theory determination of $$\varvec{\bar{B}\rightarrow D^{(
Marzia Bordone (Universität Siegen, Walter-Flex Straße 3, Siegen, 57072, Germany); Martin Jung (Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, Garching, 85748, Germany, Dipartimento di Fisica, Università di Torino & INFN, Sezione di Torino, Turin, 10125, Italy); Danny Dyk (Technische Universität München, James-Franck-Straße 1, Garching, 85748, Germany)
We carry out an analysis of the full set of ten $$\bar{B}\rightarrow D^{(*)}$$ form factors within the framework of the Heavy-Quark Expansion (HQE) to order $$\mathcal {O}\left( \alpha _s,\,1/m_b,\,1/m_c^2\right) $$ , both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in $$\bar{B}\rightarrow 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.