Wigner-cusp in kaon decays and determination of $\pi\pi$ scattering lengths

In the last few years it has become possible to study low energy pi pi scattering in kaon decays to three pions, thanks to the high statistics measurement of $K^{\pm} \rightarrow \pi^{\pm}\pi^{0}\pi^{0}$ decays performed by the NA48/2 experiment at the CERN SPS. At the $\pi^{+}\pi^{-}$ threshold, the $\pi^{0}\pi^{0}$ mass spectrum exhibits a Wigner-cusp, from which the S-wave $\pi\pi$ scattering lengths are extracted with high precision. This measurement is complementary to the extraction of the scattering lengths from $K_{e4}$ decays, which is also performed by the NA48/2 experiment.