  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.
