Enhanced Electromagnetic Corrections to the Rare Decay B_{s,d}→μ^{+}μ^{-}

We investigate electromagnetic corrections to the rare B-meson leptonic decay B_{s,d}→μ^{+}μ^{-} from scales below the bottom-quark mass m_{b}. Contrary to QCD effects, which are entirely contained in the B-meson decay constant, we find that virtual photon exchange can probe the B-meson structure, resulting in a "nonlocal annihilation" effect. We find that this effect gives rise to a dynamical enhancement by a power of m_{b}/Λ_{QCD} and by large logarithms. The impact of this novel effect on the branching ratio of B_{s,d}→μ^{+}μ^{-} is about 1%, of the order of the previously estimated nonparametric theoretical uncertainty, and four times the size of previous estimates of next-to-leading order QED effects due to residual scale dependence. We update the standard model (SM) prediction to B[over ¯](B_{s}→μ^{+}μ^{-})_{SM}=(3.57±0.17)×10^{-9}.