Three-body decays $B \to \phi(\rho) K \gamma$ in perturbative QCD approach

TL;DR

This paper investigates three-body radiative B meson decays into a vector meson, a kaon, and a photon using perturbative QCD, introducing new distribution amplitudes to account for infrared dynamics and predicting CP asymmetries and spectra.

Contribution

It develops a novel approach with pseudoscalar-vector distribution amplitudes for the final state to better understand infrared effects in B decays and predicts observables based on data-driven parameters.

Findings

Predicted direct CP asymmetries for B decays.

Calculated decay spectra in the PV-invariant mass.

Provided a framework for incorporating infrared dynamics in decay calculations.

Abstract

We study the three-body radiative decays $B\to \phi(\rho) K\gamma$ 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 time-like $PV$ 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 $B\to \phi(\rho) K\gamma$ mode.