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

Motivated by the rapid development of heavy-flavor experiments, phenomenological studies of nonleptonic $\bar{B}_{d,s} \to D^{*}_{d,s} V$ and $\bar{B}_{d,s}^* \to D_{d,s} V$~($V=\rho\,,K^*$) 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 $\bar{B}_{d,s} \to D^{*}_{d,s} V$ decays, two tensions between theoretical results and experimental measurements, {\it i.e.} "$R_{ds}^{V}$ puzzle" and "$D^{*} V$~(or $R_{V/\ell\bar{\nu}_\ell}$) puzzle", are presented after detailed analyses. For the $\bar{B}_{d,s}^* \to D_{d,s} V$ decays, they have relatively large branching fractions of the order $\gtrsim{\cal O}(10^{-9})$ 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.