We present an updated discussion of K → πll decays in a combined framework of chiral perturbation theory and Large-Nc QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of thell pair. The proposed picture reproduces very well, both the experimental K + → π + e + e − decay rate and the invariant e + e − mass spectrum. The predicted Br(KS → π 0 e + e − ) is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the K → π µ + µ − modes are also obtained. We find that the resulting interference between the direct and indirect CP-violation amplitudes in KL → π 0 e + e − is constructive.

It is shown that the integral representation of Feynman diagrams in terms of the traditional Feynman parameters, when combined with properties of the Mellin-Barnes representation and the so called converse mapping theorem, provide a very simple and efficient way to obtain the analytic asymptotic behaviours in both the large and small ratios of mass scales.

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The Froissart-Martin bound for total ππ scattering cross sections is reconsidered in the light of QCD properties such as spontaneous chiral symmetry breaking and the counting rules for a large number of colours N c .