Two measurements of ππ scattering lengths a0 and a2 from studies of K± decays with the CERN-NA48/2 experiment

The NA48 experiment at the CERN SPS has used and kaons for the precise measurement of the direct CP violation parameter Re(ɛ′/ɛ). In 2002 it was re-designed as NA48/2 to search for CP violation in K±→3π decays. This configuration has also allowed studying several rare decay processes of charged kaons to test chiral perturbation theory. With data samples of ∼106K±→π±π−e±ν decays, precise values of a0 and a2, the isospin I=0 and I=2 s-wave ππ scattering lengths, are extracted with an unprecedented experimental precision. The same scattering lengths are also measured using ∼60×106K±→π±π0π0 decays where a cusp structure in the Dalitz plot has been observed for the first time.