Quasi-two-body decays B(s)K(892)hKh in perturbative QCD approach

We extend our recent works on the P-wave two-pion resonant contributions to the kaon-pion cases in the hadronic charmless B meson decays by employing the perturbative QCD approach. The concerned decay modes are analysed in the quasi-two-body framework by parameterizing the kaon-pion distribution amplitude phi KP, which contains the final state interactions between the kaon and pion in the resonant region. The relativistic Breit-Wigner formula for the P-wave resonant state K(892) is adopted to parameterize the time-like form factor FK. We calculate the CP-averaged branching ratios and direct CP-violating asymmetries of the quasi-two-body decays B(s)K(892)hKh, with h=(,K), in this work. It is shown that the agreement of theoretical results with the experimental data can be achieved, through which Gegenbauer moments of the P-wave kaon-pion distribution amplitudes are determined. The predictions in this work will be tested by the precise data from the LHCb and the future Belle II experiments.