Cusps in K→3π decays: A theoretical framework

Based on the analysis of 6.031×107K±→π0π0π± decays, the NA48/2 Collaboration has recently determined the S-wave ππ scattering lengths a0−a2 with high precision. In addition, the scattering length a2 has been independently measured, although less precisely so. The present article discusses in detail one of the theoretical frameworks used in the data analysis.