Quasi-two-body decays $$B_{(s)}\rightarrow K^*(892)h\rightarrow K\pi h$$ B(s)→K∗(892)h→Kπh in perturbative QCD approach

Abstract

Abstract 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 $$\Phi _{K \pi }^\mathrm{P}$$ ΦKπP , 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 $$K^*(892)$$ K∗(892) is adopted to parameterize the time-like form factor $$F_{K\pi }$$ FKπ . We calculate the CP-averaged branching ratios and direct CP-violating asymmetries of the quasi-two-body decays $$B_{(s)}\rightarrow K^*(892) h\rightarrow K\pi h$$ B(s)→K∗(892)h→Kπh , with $$h=(\pi , K)$$ h=(π,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.