\(V_{cb}\) puzzle in semi-leptonic \(B\rightarrow D^*\) decays revisited

Inspired by the newly reported \(B\rightarrow D^*(\rightarrow D\pi )\ell \bar{\nu }_\ell \) differential decay rates by the Belle and Belle II Collaborations, we revisit the \(V_{cb}\) puzzle in semi-leptonic \(B\rightarrow D^*\) decays, considering the latest lattice QCD (LQCD) simulations and light-cone sum rule (LCSR) results. We examine the commonly used Caprini–Lellouch–Neubert (CLN), Boyd–Grinstein–Lebed (BGL), and heavy quark effective theory (HQET) parameterizations. We demonstrate that these three parameterizations yield consistent results and reconfirm the \(V_{cb}\) puzzle. Then, we use a state-of-the-art Bayesian method to estimate the impact of higher-order terms beyond the present HQET expansion on the uncertainty of \(V_{cb}.\) We show that higher-order effects cannot eliminate the deviation between the exclusive and inclusive determinations of \(V_{cb}.\) Finally, utilizing the best-fit results obtained in the HQET parameterization via fitting LQCD and LCSR data only as inputs, we predict the relevant observables, i.e., \(R_{D^*},\) \(F_L^{D^*},\) and \(P_\tau ^{D^*},\) sensitive to new physics in the \(B\rightarrow D^*\ell \bar{\nu }_\ell \) decays. We conclude that lepton-flavour universality violations still exist in the \(b\rightarrow c\tau \nu \) transitions.