Shedding new light on $\mathcal{R}(D_{(s)}^{(*)})$ and $|V_{cb}|$ from semileptonic ${\overline{B}}_{(s)}\to D_{(s)}^{(*)}\ell {\overline{\nu }}_{\ell }$ decays

We compute for the first time the next-to-leading-order QCD corrections to the ${\overline{B}}_{(s)}\to D_{(s)}^{(*)}$ form factors at large hadronic recoil. Both the charm-quark-mass- and the strange-quark-mass- dependent pieces can generate the leading-power contributions to these form factors. Including further various power-suppressed contributions, we perform the combined fits of the considered form factors to both our large-recoil theory predictions and the lattice QCD results, thus improving upon the previous determinations of the lepton-flavor-universality ratios $\mathcal{R}(D^{(*)})$ significantly.

Figure 1

Breakdown of the distinct dynamical mechanisms contributing to the form factor ${\mathcal{A}}_0$ for $\overline{B}\to D^{*}\ell {\overline{\nu }}_{\ell }$ in the kinematic range $q^2\in [-3.0,2.0]{\mathrm{GeV}}^2$ with the uncertainties from varying the hard and hard-collinear matching scales.

Figure 2

The determined momentum-transfer dependence of the $\overline{B}\to D^{(*)}$ form factors in the entire kinematic region from (i) the BGL fit against the “only lattice QCD” data points [35, 36, 37, 39, 40], (ii) the simultaneous fit to both the lattice QCD results [35, 36, 37, 39, 40] and our LCSR predictions, and (iii) the combined fit including further the experimental data points [1, 3, 4, 5].

Figure 3

The correlated predictions for $\mathcal{R}(D)$ and $\mathcal{R}(D^{*})$ from the combined BGL fits against the lattice data points [35, 36, 37] and the $\mathrm{NLL}\oplus \mathrm{NLP}$ LCSR predictions. The available measurements from the BABAR [103, 104], Belle [105, 106, 107], LHCb [108, 109], and Belle II Collaborations [110] are also displayed.