Predictions for the Rare Kaon Decays KS,L → π0ℓ+ℓ− 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*→π0ℓ+ℓ− (ℓ=e,μ) transitions in the standard model are addressed in QCD regarding 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 enables predicting the decay rates for KS→π0ℓ+ℓ−. It also unambiguously predicts that the interference between the direct and indirect CP-violating contributions to the decay rate for KL→π0ℓ+ℓ− is constructive.