Exclusive Determination of $|V_{cb}|$ from Semileptonic Decays $B\to D^{(*)}\ell \nu_{\ell}$
We present an updated exclusive determination of the CKM matrix element \(|V_{cb}|\) from the semileptonic decays \(B\to D^{(*)}\ell\bar{\nu}_{\ell}\). Our analysis combines the latest Belle II measurements, updated lattice-QCD calculations of the \(B\to D^{(*)}\) form factors at small hadronic recoil, and correlated large-recoil SCET sum-rule predictions incorporating next-to-leading-order QCD corrections and several power-suppressed contributions. We consider three fit scenarios with progressively enlarged input sets and find that the inclusion of the large-recoil sum-rule constraints substantially reduces the form-factor uncertainties. From the full global fit, we obtain\(|V_{cb}|=(39.18 \pm0.47)\times10^{-3}\). Using the combined lattice-QCD and LCSR fit, we predict \(R(D)=0.3069\pm0.0080,\qquad R(D^*)=0.2548\pm0.0043\), and provide differential decay distributions in the momentum transfer and angular variables for both the muon and tau channels. Comparisons of the individual and correlated predictions for \(R(D)\) and \(R(D^*)\) with the experimental averages reveal a persistent tension. In particular, our theoretical 68\% confidence region shows little overlap with the experimental average. All correlations among the fitted parameters are retained in the uncertainty propagation. Our results therefore provide updated Standard Model benchmarks for tests of lepton-flavor universality. Improved lattice-QCD calculations, sum-rule predictions, and Belle II measurements will be essential for determining whether the remaining discrepancies originate from theoretical systematic uncertainties or from physics beyond the Standard Model.