Quasi-two-body decays $B_{(s)}\to K^*\gamma\to K\pi\gamma$ in perturbative QCD approach

TL;DR

This paper analyzes the quasi-two-body decays of B mesons to K* gamma using perturbative QCD, introducing two-meson distribution amplitudes to account for final state interactions, and predicts CP asymmetries consistent with recent experimental data.

Contribution

The study applies the PQCD approach with two-meson DAs to analyze B decays, providing new predictions for CP asymmetries and branching ratios in a three-body framework.

Findings

Results agree with Belle II data.

CP asymmetry for B_{u,d} decays is less than 1%.

CP asymmetry for B_{s} decays can reach a few percent.

Abstract

In this work we study the quasi-two-body decays $B\to K^*\gamma\to K\pi\gamma$ in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $K\pi$ pair, which involve the time-like form factors and the Gegenbauer polynomials. We calculate the CP averaged branching ratios for the decays $B_{(s)}\to K^*\gamma\to K\pi\gamma$. Our results are in agreement with the new update data measured by Belle II, which suggests these quasi-two-body decays are more appropriate to be analyzed in three-body framework than in the two-body one. We also predict the direct CP-violation asymmetries for the considered decay modes and find that $A_{CP}(B_{u,d}\to K^*\gamma\to K\pi\gamma)$ is small and less than $1\%$ in magnitude, while $A_{CP}(B_{s}\to K^*\gamma\to K\pi\gamma)$ is larger and can arrive at a few percent. Our predictions can be tested by the future B meson experiments.