Three-body radiative decay BsφK0 in the PQCD approach

We study the three- body radiative decay Bs. f K 0. by introducing the fK 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 O7., the subleading contributions from the chromomagnetic penguin operator O8g, quark- loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay Bs. f K 0. is about ( 9.26 + 1.79+ 3.12+ 0.64 - 1.61- 3.86- 0.49) x10 - 8, which is much smaller than that for the decay B0. fK0.. It is mainly because the former decay induced by b. d. with small CKM matrix element is proportional to.3. The prediction for the direct CP asymmetry is Adir CP( Bs. f K 0.) = (- 4.1 + 0.4+ 1.7+ 0.2 - 0.6- 1.2- 0.1)%, which is well consistent with the result from the U- spin symmetry approach. We also predict the Bs. f K 0. decay spectrum, which exhibits a maximum at the fK invariant masss around 1.95 GeV.