Precision study of K^\pm\toπ^\pmπ^0π^0 and K^\pm\toπ^\pmπ^+π^- Dalitz plot distributions by NA48/2

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The NA48/2 experiment at the CERN SPS has collected an unprecedented sample of $K^\pm\to3π$ 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 $K^\pm\toπ^\pmπ^0π^0$ decays turned out to be a powerful tool for extraction of the S-wave $ππ$ scattering lengths. The large statistics also allowed a precise measurement of the Dalitz plot slope parameters for the $K^\pm\to3π^\pm$ decays.
Talk given at Kaon'07 Conference, LNF, Frascati, Italy, 21--25 May, 2007. A version revised by PoS referee

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