$V_{cb}$ puzzle in semi-leptonic $B\to D^{\ast }$ decays revisited

Abstract

Inspired by the newly reported $B\to D^{\ast }(\to D\ddot{I}€)\ell \bar{\hat{I}}{½}_{\ell }$ differential decay rates by the Belle and Belle II Collaborations, we revisit the $V_{cb}$ puzzle in semi-leptonic $B\to D^{\ast }$ 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., $R_{D^{\ast }}$, $F_L^{D^{\ast }}$, and $P_{\ddot{I}}{„}^{D^{\ast }}$, sensitive to new physics in the $B\to D^{\ast }\ell \bar{\hat{I}}{½}_{\ell }$ decays. We conclude that lepton-flavour universality violations still exist in the $b\to c\ddot{I}„\hat{I}½$.

29 pages, 1 figures, 19 tables. Matches published version