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Nonleptonic decays of $B \to ( f_1(1285),f_1(1420) ) V$ in the perturbative QCD approach

We investigate the branching ratios, the polarization fractions, the direct CP-violating asymmetries, and the relative phases in 20 nonleptonic decay modes of $B \to f_1 V$ within the framework of perturbative QCD approach at leading order with $f_1$ including two $^3\!P_1$-axial-vector states $f_1(1285)$ and $f_1(1420)$. Here, $B$ denotes $B^+$, $B^0$, and $B_s^0$ mesons and $V$ stands for the lightest vector mesons $ρ$, $K^*$, $ω$, and $ϕ$ , respectively. The $B_s^0 \to f_1 V$ decays are studied theoretically for the first time in the literature. Together with the angle $ϕ_{f_1} \approx (24^{+3.2}_{-2.7})^\circ$ extracted from the measurement through $B_{d/s} \to J/ψf_1(1285)$ modes for the $f_1(1285)-f_1(1420)$ mixing system, it is of great interest to find phenomenologically some modes such as the tree-dominated $B^+ \to f_1 ρ^+$ and the penguin-dominated $B^{+,0} \to f_1 K^{*+,0}, B_s^0 \to f_1 ϕ$ with large branching ratios around ${\cal O}(10^{-6})$ or even ${\cal O}(10^{-5})$, which are expected measurable at the LHCb and/or the Belle-II experiments in the near future. The good agreement [sharp contrast] of branching ratios and decay pattern for $B^+ \to f_1 ρ^+, B^{+,0} \to f_1(1285) K^{*+,0} [B^{+,0} \to f_1(1420) K^{*+,0}]$ decays between QCD factorization and perturbative QCD factorization predictions can help us to distinguish these two rather different factorization approaches via precision measurements, which would also be helpful for us to explore the annihilation decay mechanism through its important roles for the considered $B \to f_1 V$ decays.