A dispersive treatment of K ℓ 4 decays

Kℓ4 decays have several features of interest: they allow an accurate measurement of ππ-scattering lengths; they provide the best source for the determination of some low-energy constants of χPT; one form factor is directly related to the chiral anomaly, which can be measured here. We present a dispersive treatment of Kℓ4 decays that provides a resummation of ππ- and Kπ-rescattering effects. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. The matching to χPT at NLO and NNLO enables us to determine the LECs Lr1, Lr2 and Lr3. With recently published data from NA48/2, the LEC Lr9 can be determined as well. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the form factors, which we understand as a rescattering effect beyond NNLO.