Pion-pion scattering lengths from Ke4 and Cusp at NA48/2 experiment

Abstract

In kaon decays the measurement of ππ scattering lengths ( a 0 and a 2 ) are accessible mainly through the study of kinematical properties in two decay modes. The classic way is based on the form factors analysis in K ± → π + π − e ± ν ( K e 4 ) decay. Thanks to the absence of other hadrons in the final state the ππ interaction can be analyzed in terms of phase shift variation with the ππ invariant mass. The preliminary results on a set of ∼ 1150000 K ± events collected in two years of data taking, will be discussed. The second way to evaluate the ππ scattering lengths is based on the accurate study of K ± → π ± π 0 π 0 Dalitz plot, in which the strong rescattering process π + π − → π 0 π 0 introduces a singularity in the shape of the distribution. The preliminary result based on more than ∼ 60 ⋅ 10 6 K ± → π ± π 0 π 0 decays is in good agreement with the measurement in K e 4 .