Magnetic-dipole corrections to RK and RK* in the Standard Model and dark photon scenarios

In this work we evaluate the long-distance QED contributions, induced by the magnetic-dipole corrections to the final charged leptons, on the B meson decay widths B → (K, K*)ℓ+ℓ− and ratios RK,K* = Γ(B → (K, K*)μ+μ−)/Γ(B → (K, K*)e+e−), as well as on ,∗RK,K∗τ (with μ replaced by the τ lepton). QED long-distance contributions induced by the Coulomb potential corrections (Fermi-Sommerfeld factors) were also included. Corresponding corrections to the inclusive decay widths of B → Xsℓ+ℓ−, with ℓ = e, μ, τ, are also analyzed for completeness. The magnetic-dipole corrections, which are manifestly Lepton Flavor Universality violating and gauge-invariant, are expected to be particularly enhanced in RK* for the dilepton mass region close to the threshold. However, we find that the largest contribution of all these corrections to the RK,K* observables do not exceed a few per mille effect, thus reinforcing the validity of previous estimates about the leading QED corrections to RK,K*. Finally, viable new physics contributions to RK,K* induced by the exchange of a massless dark-photon via magnetic-dipole interactions, which provide the leading contribution to the corresponding B → (K, K*)ℓ+ℓ− amplitudes in this scenario, are analyzed in light of the present RK,K* anomalies.