Isospin symmetry violating effects and scattering length extraction from kaon decays

The isospin symmetry breaking effects in the charged kaons decays to two or three pions are considered. In semileptonic decay K ± → π + π −e± ν (called K e4) these effects turn out to be crucial for correct extraction of ππ scattering lengths. Taking in account electromagnetic interaction between the pions in the final state and isospin symmetry breaking due to different masses of charged and neutral pions allows to adjust the values of scattering lengths obtained from experimental data on K e4 decay and predictions of Chiral Perturbation Theory (ChPT). Final state interactions of pions in the decay K ± → π ± π 0 π 0 leading to the anomaly (cusp) in the π 0 π 0 invariant mass distribution in the vicinity of charged pions’ threshold are discussed and recent results of accounting of the electromagnetic interaction among charged pions leading to π + π − bound states (pioniumatom) just under the charged pions’ threshold are presented.