Nonfactorizable charming-loop contribution to FCNC B_s→γ l^+l^- decay

We present the first theoretical calculation of nonfactorizable charm-quark loop contributions to the B_s→γ l^+l^- amplitude. We calculate the relevant form factors, H_A,V^ NF(k'^2,k^2), and provide convenient parametrizations of our results in the form of fit functions of two variables, k'^2 and k^2, applicable in the region below hadron resonances, k'^2 < M_J/ψ^2 and k^2 < M_ϕ^2. We report that factorizable and nonfactorizable charm contributions to the B_s→γ l^+l^- amplitude have opposite signs. To compare the charm and the top contributions, it is convenient to express the NF charming loop contribution as a non-universal (i.e., dependent on the reaction) q^2-dependent correction Δ^ NFC_7(q^2) to the Wilson coefficient C_7. For the B_s→γ l^+l^- amplitude, the correction is found to be positive, Δ^ NF C_7(q^2)/C_7 > 0.