Measurements of $K_{e4}$ and $K^{\pm} \to \pi^{0} \pi^{0} \pi^{\pm}$ decays

The NA48/2 experiment at the CERN SPS collected in 2003 and 2004 large samples of the decays $K^{\pm} \to \pi^{+} \pi^{-} e^{\pm} \nu_{e} (K_{e4}^{+-})$, $K^{\pm} \to \pi^{0} \pi^{0} e^{\pm} \nu_{e}(K^{00}_{e4})$ and $K^{\pm} \to \pi^{0}\pi^{0} \pi^{\pm}$. From the $K_{e4}^{+-}$ form factors and from the cusp in the $M_{00}^{2}$ distribution of the $K^{\pm} \to \pi^{0} \pi^{0} \pi^{\pm}$ events, the $\pi\pi$ scattering lengths $a_{0}^{0}$ and $a^{2}_{0}$ could be extracted. This measurement is a fundamental test of Chiral Perturbation Theory ($\chi PT$). The branching fraction and form factors of the $K_{e4}^{00}$ decay were precisely measured, using a much larger data sample than in previous experiments.