https://doi.org/10.1140/epjc/s10052-019-6554-5
Regular Article - Theoretical Physics
Three-body radiative decay 
in the PQCD approach
1
Department of Physics, Henan University of Technology, Zhengzhou, 450052, Henan, People’s Republic of China
2
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China
* e-mail: guohongxia@zzu.edu.cn
Received:
28
August
2018
Accepted:
27
December
2018
Published online:
28
January
2019
We study the three-body radiative decay by introducing the 
pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative input, the two-meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator 
, the subleading contributions from the chromomagnetic penguin operator 
, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay is about 
, which is much smaller than that for the decay 
. It is mainly because the former decay induced by 
with small CKM matrix element is proportional to 
. The prediction for the direct CP asymmetry is 
, which is well consistent with the result from the U-spin symmetry approach. We also predict the 
decay spectrum, which exhibits a maximum at the invariant masss around 1.95 GeV.
© The Author(s), 2019
