A new long distance contribution to $B^\pm\to K^\pm/\pi^\pm\ell^+\ell-$ decays

Abstract

We have identified a missing long-distance (one-photon exchange) contribution to the $B^\pm\to K^\pm/\pi^\pm\ell^+\ell^-$ decays. Although it does not help to explain the anomaly measured by the LHCb Coll. in the ratio $R_K = \mathcal{B}(B^\pm\to K^\pm\mu^+\mu^-)/\mathcal{B}(B^\pm\to K^\pm e^+e^-)\sim0.75$ (2.6 $\sigma$ deviation with respect to $R_K=1+\mathcal{O}(10^{-4})$ in the Standard Model), it provides a sizable contribution to the branching ratio of the $B^\pm\to \pi^\pm\ell^+\ell^-$ decays. The new decay mechanism gives rise to a measurable CP asymmetry, which is of order 1\% in both channels. These predictions can be tested in forthcoming LHCb measurements.