Rare Kaon Decays Revisited

Abstract

We present an updated discussion of $K\ra\pi \bar{l} l$ decays in a combined framework of chiral perturbation theory and Large--$N_c$ QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of the $ \bar{l} l$ pair. The proposed picture reproduces very well, both the experimental $K^+\ra\pi^+ e^+ e^-$ decay rate and the invariant $e^+ e^-$ mass spectrum. The predicted Br$(K_S\ra\pi^0 e^+ e^-)$ is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the $K\ra\pi \mu^{+}\mu^{-}$ modes are also obtained. We find that the resulting interference between the {\it direct} and {\it indirect} CP--violation amplitudes in $K_L\ra\pi^0 e^+ e^-$ is constructive.