Estimate of the long-distance contribution through b --> s \psi to the B_{s} --> \gamma\gamma decay rate

Abstract

The B_{s} --> \phi\psi decay is modeled through the inclusive b --> s\psi decay. Using the Vector Meson Dominance model, the amplitude for the chain process B_{s} --> \phi\psi --> \phi\gamma --> \gamma\gamma is estimated and it is found to be at most 4 % of the corresponding amplitude from the O_7 type LD contribution. The intermediate amplitude for the process B_{s} --> \phi\gamma is compared with the corresponding one obtained by a different approach based on the interaction of the virtual charm quark loop with soft gluons \cite{Ruckl}. Both amplitudes are found to agree within 10 %. Further the influence on the branching ratio B(B_{s} --> \gamma\gamma)_{SD+LD_{O7}} from inclusive b --> s \psi is estimated as less than 1 %.