Measurement of ππ Scattering Lengths from Ke4 and K3π Decays

In the last few years it has become possible to study low energy pi pi scattering with high precision in kaon decays, thanks to the high statistics measurements of K-+/- -> pi(+/-)pi(0)pi(0) (K-3 pi) and K-+/- -> pi(+)pi(-)e(+/-)nu (K-e4) decays performed by the NA48/2 experiment at the CERN SPS. In K-+/- -> pi(+/-)pi(0)pi(0), at the pi(+)pi(-) threshold, the pi(0)pi(0) mass spectrum exhibits a Wigner-cusp, from which the scattering lengths a(0) and a(2) are extracted. From the study of K-e4 decays a similar precision, but quite independent measurement of a(0) and a(2) can be obtained. The combination of both measurements provides one of the most stringent tests of Chiral Perturbation Theory.