One-photon exchange contribution to $B^{\pm}\to (\pi^{\pm},K^{\pm}) \ell^+\ell^-$ decays

A so far neglected long-distance (also called one-photon exchange) contribution to the rare semileptonic $B^{\pm}\to (\pi^{\pm},K^{\pm})\ell^+\ell^-$ ($\ell=e,\,\mu$) transitions is evaluated. Although it does not contribute to solve the possible breaking of lepton-universality observed by LHCb in the $B^{\pm}\to K^{\pm}(\mu^+\mu^-/e^+e^-)$ ratio, nor provides an important hadronic contamination to their decay rates, its contribution to the branching ratios of the $B^{\pm}\to \pi^{\pm}\ell^+\ell^-$ transitions turns out to be significant. This hadronic pollution should be taken into account when looking for new physics effects in decays into pions, which suggests to restrict these searches to squared lepton-pair invariant mass in the $(1,8)$ GeV$^2$ range. The interference of the one-photon exchange contribution with the dominant short-distance one-loop amplitude induces a sizable CP asymmetry in these rare decays, which calls for dedicated measurements.