Recent results from NA48/2 on $K_{e4}$ decays and interpretation in terms of $\pi\pi$ scattering lengths

Preliminary results from a new measurement of the $K_{e4}$ decay $K^{\pm} \rightarrow \pi^{+}\pi^{−}e^{\pm}\nu$ by the Na48/2 collaboration at the CERN SPS are reported. An unprecedented sample of more than 670000 $K_{e4}$ decays in both charged modes have been collected in 2003. The form factors of the hadronic current (F, G, H) and phase shift ($\delta^{0}_{0}−\delta^{1}_{1}$) of the $\pi\pi$ scattering have been measured using a model independent method and their variation with the ππ mass has been investigated. First evidence for a non zero $f_{p}$ term is reported. Thanks to a sizeable acceptance at large $\pi\pi$ mass, a low background and a very good resolution, an improved accuracy $(\pm0.006stat \pm0.005_{syst})$ can be reached when extracting the $\pi\pi$ scattering length $a^{0}_{0}$ . Using more elaborated theory inputs and another NA48/2 result from $K^{\pm} \rightarrow \pi^{0}\pi^{0}\pi^{\pm}$ decays, a consistent picture can be drawn for the scattering lengths $a^{0}_{0}$ and $a^{2}_{0}$ , in good agreement with Chiral Perturbation Theory predictions.