Predictions for the rare kaon decays KS,L → π⁰ ⁺ ⁻ from QCD in the limit of a large number of colours

The long-distance and non-local parts of the form factors describing the single-photon mediated KS,L→π⁰γ^*→π⁰⁺⁻ (= e, μ) transitions in the standard model are addressed in QCD in the limit where the number Nc of colours becomes infinite. It is shown that this provides a suitable theoretical framework to study these decay modes and that it allows to predict the decay rates for KS→π⁰⁺⁻. It also unambiguously predicts that the interference between the direct and indirect CP-violating contributions to the decay rate for KL→π⁰ ⁺ ⁻ is constructive.