Three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ in the PQCD approach

Abstract

We study the three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ by introducing the $\varphi K$ pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative inputs, the two meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator $O_{7\gamma }$, the subleading contributions from chromomagnetic penguin operator $O_{8g}$, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay $B_s\to \varphi {\bar{K}}^0\gamma$ is about $(9.26_{-1.61-3.86-0.49}^{+1.79+3.12+0.64})\times 10^{-8}$, which is much smaller compared with that for the decay $B^0\to \varphi K^0\gamma$. It is mainly because that the former decay induces by $b\to d\gamma$ with small CKM matrix element being proportional to ${\lambda }^3$. The prediction for the direct CP asymmetry is $A_{CP}^{dir}(B_s\to \varphi {\bar{K}}^0\gamma )=(-4.1_{-0.6-1.2-0.1}^{+0.4+1.7+0.2})\%$, which is well consistent with the result from the U-spin symmetry approach. we also predict the $B_s\to \varphi {\bar{K}}^0\gamma$ decay spectrum, which exhibits a maximu at the $\varphi K$ invariant masss around 1.95 GeV.

arXiv comment17 pages,6 figures, Accepted for publication in EPJC

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