Rare Kaon Decays Revisited

Abstract

We present an updated discussion of $K\text{ra}\pi \bar{l}l$ 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 $K^{+}\text{ra}{\pi }^{+}{e}^{+}{e}^{-}$ decay rate and the invariant $e^{+}{e}^{-}$ mass spectrum. The predicted Br$(K_S\text{ra}{\pi }^0{e}^{+}{e}^{-})$ is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the $K\text{ra}\pi {\mu }^{+}{\mu }^{-}$ modes are also obtained. We find that the resulting interference between the {\it direct} and {\it indirect} CP--violation amplitudes in $K_L\text{ra}{\pi }^0{e}^{+}{e}^{-}$ is constructive.