Shedding New Light on ${\cal R} (D_{(s)}^{(\ast)} )$ and $|V_{cb}|$ from Semileptonic $\bar B_{(s)} \to D_{(s)}^{(\ast)} \ell \bar {\nu}_{\ell}$ Decays

We compute for the first time the next-to-leading-order QCD corrections to the $\bar B_{(s)} \to D_{(s)}^{(\ast)}$ form factors at large recoil with the power-counting scheme $m_c \sim {\cal O} \left (\sqrt{\Lambda_{\rm QCD} \, m_b }\right)$. Both the charm-quark-mass and the strange-quark-mass dependent pieces in the soft-collinear effective theory Lagrangian can generate the unsuppressed 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-flavour-universality ratios ${\cal R} (D^{(\ast)} )$ significantly.