Leading logarithmic QCD corrections to the B_s --> \gamma \gamma decay rate including long-distance effects through B_s --> \phi \gamma --> \gamma \gamma

Abstract

We present leading logarithmic QCD corrections to the decay B_s --> \gamma\gamma in the Standard Model. Further, the form factor F_{1}(0) of B_s --> \phi\gamma is calculated in the framework of QCD sum rules and found to be in agreement with the result existing in the literature. Using Vector Meson Dominance model, the amplitude for B_s --> \phi \gamma -->\gamma\gamma is calculated as an estimate of the O_7-type contributions to the long-distance effects in the B_s --> \gamma\gamma decay. The resulting branching ratio B(B_s --> \gamma \gamma)_{SD+LD_{O_7}} is analysed in view of its strong dependence on the non-perturbative parameter $\bar{\Lambda}_s$, describing bound state effects, and the renormalization scale $\mu$. .