A Dispersive Treatment of $K_{\ell4}$ Decays

Abstract

$K_{\ell4}$ are for several reasons an especially interesting decay channel of $K$ mesons: $K_{\ell4}$ decays allow an accurate measurement of a combination of $S$-wave $\pi\pi$ 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 $K_{\ell4}$ 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.