Three-body decays B -> phi(rho)K gamma in perturbative QCD approach

We study the three-body radiative decays B -> phi(rho)K gamma induced by a flavor-changing neutral current in the perturbative QCD approach. Pseudoscalar-vector (PV) distribution amplitudes (DAs) are introduced for the final-state phi K (rho K) pair to capture important infrared dynamics in the region with a small PV-pair invariant mass. The dependence of these PV DAs on the parton momentum fraction is parametrized in terms of the Gegenbauer polynomials, and the dependence on the meson momentum fraction is derived through their normalizations to timelike PV form factors. In addition to the dominant electromagnetic penguin, the subleading chromomagnetic penguin, quark-loop and annihilation diagrams are also calculated. After determining the PV DAs from relevant branching-ratio data, the direct CP asymmetries and decay spectra in the PV-pair invariant mass are predicted for each B -> phi(rho)K gamma mode.