Theoretical progress on cusp effect and Kl4 decays

Abstract

The cusp effect in K \to 3\pi and data on K_e4 decays allow one to extract experimental information on the elastic \pi\pi scattering amplitude near threshold, and to confront the outcome of the analyses with predictions made in the framework of QCD. In my talk I pointed out that these predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin breaking effects -- generated by electromagnetic interactions and by the mass difference of the up and down quarks -- are always present. I discussed the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, I pointed out that there is a spectacular isospin breaking effect in K_e4 decays, overlooked so far. Once it is taken into account, the previous discrepancy between NA48/2 data on K_e4 decays and the prediction of \pi\pi scattering lengths disappears.