On the rare $K\to \pi \bar{l}l$ decays

Abstract

In this talk, we present our recent work on the $K\text{ra}\pi \bar{l}l$ decays in a combined framework of chiral perturbation theory and Large--$N_c$ QCD under the dominance of a minimal narrow resonance structure. The proposed description reproduces very well the experimental Br$(K^{+}\text{ra}{\pi }^{+}{e}^{+}{e}^{-})$ and Br$(K_S\text{ra}{\pi }^0{e}^{+}{e}^{-})$. Predictions for the $K\text{ra}\pi {\mu }^{+}{\mu }^{-}$ modes are also obtained and we can conclude to the constructive type for the interference between the {\it direct} and {\it indirect} CP--violation amplitudes in $K_L\text{ra}{\pi }^0{e}^{+}{e}^{-}$.

Comments: Talk given at the $11^{th}$ High-Energy Physics International Conference on Quantum Chromodynamics, 5-10 July (2004), Montpellier (France)