Complete Analyses on the Short-Distance Contribution of B_s→?⁺?^?γ in the Standard Model

Using the B_s meson wave function extracted from non-leptonic B_s decays, we evaluate the rare decays B_s→?⁺?^? γ(?=e,μ) in the standard model, including contributions from all four kinds of diagrams. We focus on the contribution from the four-quark operators, which were not taken into account properly in previous studies. We find that the contribution is large, leading to the branching of B_s→?⁺?^?γ being nearly enhanced by a factor 3 and up to 1.6×10^?8. The predictions for such processes can be tested in the LHC-b and B factories in the near future.