Can contribution from magnetic-penguin operator with real photon to $B_s\to \ell^+\ell^-\gamma$ in the standard model be neglected?

Abstract

Using the $B_s$ meson wave function extracted from non-leptonic $B_s$ decays, we reevaluate the rare decays $B_s\to \ell^+\ell^- \gamma, (\ell=e,\mu)$ in the standard model, including two kinds of contributions from magnetic-penguin operator with virtual and real photon. We find that the contributions from magnetic-penguin operator $b\to s\gamma$ with real photon to the exclusive decays, which is regarded as to be negligible in previous literatures, are large, and the branchings of $B_s\to \ell^+\ell^-\gamma$ are nearly enhanced by a factor 2. With the predicted branching ratios at order of $10^{-8}$, it is expected that the radiative dileptonic decays will be detected in the LHC-b and B factories in near future.