Motivated by the rapid development of heavy-flavor experiments, phenomenological studies of nonleptonic and () decays are performed within the framework of QCD factorization. Relative to the previous work, 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 decays, the tensions between theoretical results and experimental measurements, i.e. the " puzzle" and " (or ) puzzle", are presented after detailed analyses. For the decays, they have relatively large branching fractions of the order and are in the scope of Belle-II and LHCb experiments. Moreover, they also provide a way to crosscheck the possible puzzles mentioned above through the similar ratios and . More refined experimental measurements and theoretical efforts are required to confirm or refute such two anomalies.
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