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We investigate the CP-averaged branching ratios, the polarization fractions,the relative phases, and the CP-violating asymmetries of the penguin-dominated$B \to \phi K_1(1270) $ and $ \phi K_1(1400)$ decays in the perturbativeQCD(pQCD) approach, where $K_1(1270)$ and $K_1(1400)$ are believed to be themixtures of two distinct types of axial-vector $K_{1A}(^3P_1)$ and$K_{1B}(^1P_1)$ states with different behavior, however, their mixing angle$\theta_{K_1}$ is still a hot and controversial topic presently. By numericalevaluations with two different mixing angles $\theta_{K_1} \sim 33^\circ$ and$58^\circ$ and phenomenological analysis, we find that: (a) the pQCDpredictions for the branching ratio, the longitudinal polarization fraction andthe direct CP violation of $B^\pm \to \phi K_1(1270)^\pm$ decay with thesmaller angle $33^\circ$ are in good agreement with the currently availabledata; (b) though the central values significantly exceed the available upperlimit, both pQCD predictions of $Br(B^\pm \to \phi K_1(1400)^\pm)$ with twodifferent mixing angles are consistent with that obtained in QCD factorizationand with the preliminary data in 2$\sigma$ errors. These results and otherrelevant predictions for the considered decays will be further tested by theLHCb and the forthcoming Super-B experiments; (c) the weak annihilationcontributions can play an important role in $B \to \phi K_1(1270)$ and $\phiK_1(1400)$ decays; (d) these pQCD predictions combined with the futureprecision measurements can examine the reliability of the factorizationapproach employed here, but also explore the complicated QCD dynamics andmixing angle $\theta_{K_1}$ of the axial-vector $K_1(1270)$ and $K_1(1400)$system.

Penguin-dominated $B \to \phi K_1(1270)$ and $\phi K_1(1400)$ decays in the perturbative QCD approach