A Dispersive Treatment of Kl4 Decays

K`4 decays are interesting for several reasons: They allow an accurate measurement of a combination of S-wave pp scattering lengths, one form factor of the decay is connected to the chiral anomaly and the decay is the best source for the determination of some low energy constants of ChPT. We present a dispersive approach to K`4 decays, which takes rescattering effects fully into account. Some fits to NA48/2 and E865 measurements and results of the matching to ChPT are shown.

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.