Quasi-two-body Decays in the Perturbative QCD Approach*

In this study, we investigate quasi-two-body B-(s) (sic) K*gamma (sic) K pi gamma decays in the perturbative QCD approach. Two-meson distribution amplitudes are introduced to describe the final state interactions of the K pi pair, which involve time-like form factors and Gegenbauer polynomials. We calculate the CP averaged branching ratiosof the B-(s) (sic) K*gamma (sic) K pi gamma decays. Our results are in agreement with newly updated data measured by Belle II. This suggests that it is more appropriate to analyze these quasi-two-body B decays in the three-body framework than the two-body framework. We also predict direct CP asymmetries for the considered decay modes and find that A(CP)(B-u,B-d (sic) K*gamma (sic) K pi gamma) is small and less than % in magnitude, whereas A(CP)(B-s (sic) K*gamma (sic) K pi gamma) is larger and can reach a few percent. Our predictions can be tested in future B meson experiments.