Penguin-dominated B -> phi K-1(1270) and phi K-1(1400) decays in the perturbative QCD approach

We investigate the CP-averaged branching ratios, the polarization fractions, the relative phases, and the CP-violating asymmetries of the penguin-dominated B -> phi K-1(1270) and phi K-1(1400) decays in the perturbative QCD (pQCD) approach, where K-1(1270) and K-1(1400) are believed to be the mixtures of two distinct types of axial-vector K-1A(P-3(1)) and K-1B(P-1(1)) states with different behavior, however, their mixing angle theta(K1) is still a hot and controversial topic presently. By numerical evaluations with two different mixing angles theta(K1) similar to 33 degrees and 58 degrees and phenomenological analysis, we find that: (i) the pQCD predictions for the branching ratio, the longitudinal polarization fraction and the direct CP violation of B-+/- -> phi K-1(1270)(+/-) decay with the smaller angle 33 degrees are in good agreement with the currently available data; (ii) though the central values significantly exceed the available upper limit, both pQCD predictions of Br(B-+/- -> phi K-1(1400)(+/-)) with two different mixing angles are consistent with that obtained in QCD factorization and with the preliminary data in 2 sigma errors. These results and other relevant predictions for the considered decays will be further tested by the LHCb and the forthcoming Super-B experiments; (iii) the weak annihilation contributions can play an important role in B -> phi K-1(1270) and phi K-1(1400) decays; (d) these pQCD predictions combined with the future precision measurements can examine the reliability of the factorization approach employed here, but also explore the complicated QCD dynamics and mixing angle theta K-1 of the axial-vector K-1(1270) and K-1(1400) system.