Precision study of $K^\pm\to\pi^\pm\pi^0\pi^0$ and $K^\pm\to\pi^\pm\pi^+\pi^-$ Dalitz plot distributions by NA48/2

The NA48/2 experiment at the CERN SPS has collected an unprecedented sample of $K^\pm\to3\pi$ decays. The high statistics and the good resolution of the detectors allow a unique investigation of the detailed phase space distributions of these decays. The effects of final state pion rescattering observed in the Dalitz plot distribution of the $K^\pm\to\pi^\pm\pi^0\pi^0$ decays turned out to be a powerful tool for extraction of the S-wave $\pi\pi$ scattering lengths. The large statistics also allowed a precise measurement of the Dalitz plot slope parameters for the $K^\pm\to3\pi^\pm$ decays.