Charmless hadronic $B \to (f_1(1285),f_1(1420)) P$ decays in the   perturbative QCD approach
  We study 20 charmless hadronic $B \to f_1 P$ decays in the perturbative QCD(pQCD) formalism with $f_1$ representing axial-vector mesons $f_1(1285)$ and $f_1(1420)$ that result from a mixing of quark-flavor $f_{1q}$ and $f_{1s}$ states with the angle $\phi_{f_1}$. The estimations of branching ratios and CP asymmetries of the considered $B \to f_1 P$ decays are presented in the pQCD approach with $\phi_{f_1} \sim 24^\circ$ from recently measured $B_{d/s} \to J/\psi f_1(1285)$ decays. It is found that (a) the tree(penguin) dominant $B^+ \to f_1 \pi^+(K^+)$ decays with large branching ratios[${\cal O}(10^{-6})$] and large direct CP violations(around 14% $\sim$ 28% in magnitude) simultaneously are believed to be clearly measurable at the LHCb and Belle II experiments; (b) the $B_d \to f_1 K_S^0$ and $B_s \to f_1 (\eta, \eta^{\prime})$ decays with nearly pure penguin contributions and safely negligible tree pollution also have large decay rates in the order of $10^{-6} \sim 10^{-5}$, which can be confronted with the experimental measurements in the near future; (c) as the alternative channels, the $B^+ \to f_1 (\pi^+, K^+)$ and $B_d \to f_1 K_S^0$ decays have the supplementary power in providing more effective constraints on the Cabibbo-Kobayashi-Maskawa weak phases $\alpha$, $\gamma$, and $\beta$ correspondingly, which are explicitly analyzed through the large decay rates and the direct and mixing-induced CP asymmetries in the pQCD approach and are expected to be stringently examined by the measurements with high precision. The complete abstraction can be found in the paper. 
Xin Liu, Zhen-Jun Xiao, Jing-Wu Li, and Zhi-Tian Zou
hep-ph hep-ex