The distribution of the K± → π± π+ π- decays in the Dalitz plot has been measured by the NA48/2 experiment at the CERN SPS with a sample of 4.71 × 108 fully reconstructed events. With the standard Particle Data Group parameterization the following values of the slope parameters were obtained: g = (- 21.134 ± 0.017) %, h = (1.848 ± 0.040) %, k = (- 0.463 ± 0.014) %. The quality and statistical accuracy of the data have allowed an improvement in precision by more than an order of magnitude, and are such as to warrant a more elaborate theoretical treatment, including pion-pion rescattering, which is in preparation.
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