Dispersive representation of K -> 3 pi amplitudes and cusps

The NA48/2 collaboration has shown clear experimental evidence for a cusp in the data for K → π π 0 π 0 . This effect can be used to extract information on the ππ scattering lengths. We address this issue using a two-loop dispersive construction of π π → π π and K → π π π amplitudes in the presence of isospin breaking.