Strange quark mass effect in $B_s \to \gamma\gamma,\gamma\ell\bar{\ell}$ decays

Abstract

In this paper we investigate the next-to-leading power contribution to the $B_s \to \gamma\gamma$ and $B_s \to \gamma\ell\bar{\ell}$ decays from the strange quark mass effect with the dispersion approach which is QCD inspired and more predictive. We have presented the analytic expression of the quark mass contribution in the $B_s \to \gamma\gamma$ and $B_s \to \gamma\ell\bar{\ell}$ decays, together with a new term that is missed in the previous study. The numerical results of the strange quark mass contribution to the $B_s \to \gamma\gamma$ decay is about 6% relative to the total branching ratio, while it is relatively small in the $B_s \to \gamma\ell\bar{\ell}$ decay due to the large resonance contribuiton