${\bar{B}}_{d,s}\to D_{d,s}^{\ast }V$ and ${\bar{B}}_{d,s}^{\ast }\to D_{d,s}V$ decays within QCD Factorization and Possible Puzzles

Abstract

Motivated by the rapid development of heavy-flavor experiments, phenomenological studies of nonleptonic ${\bar{B}}_{d,s}\to D_{d,s}^{\ast }V$ and ${\bar{B}}_{d,s}^{\ast }\to D_{d,s}V$~($V=\rho ,K^{\ast }$) decays are performed within the framework of QCD Factorization. Relative to previous works, the QCD corrections to the transverse amplitudes are evaluated at next-to-leading order. The theoretical predictions of the observables are updated. For the measured ${\bar{B}}_{d,s}\to D_{d,s}^{\ast }V$ decays, two tensions between theoretical results and experimental measurements, {\it i.e.} "$R_{ds}^V$ puzzle" and "$D^{\ast }V$~(or $R_{V/\ell {\bar{\nu }}_{\ell }}$) puzzle", are presented after detailed analyses. For the ${\bar{B}}_{d,s}^{\ast }\to D_{d,s}V$ decays, they have relatively large branching fractions of the order $\gtrsim \mathcal{O}(10^{-9})$ and are in the scope of Belle-II and LHCb experiments. Moreover, they also provide a way to crosscheck the above-mentioned possible puzzles through the similar ratios $R_{ds}^{\prime V}$ and $R_{V/\ell {\bar{\nu }}_{\ell }}^{\prime }$. More refined experimental measurements and theoretical efforts are required to confirm or refute such two anomalies.

Comments: 20 pages, 1 figure, 3 tables; revised version