K_{l4} decays have several features of interest: they allow an accurate measurement of ππ-scattering lengths; the decay is the best source for the determination of some low-energy constants of chiral perturbation theory (χPT); one form factor of the decay is connected to the chiral anomaly. We present the final results of our dispersive analysis of K_{l4} decays, which provides a resummation of ππ- and Kπ-rescattering effects [1,2]. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 [3,4] and NA48/2 [5,6]. The data input is corrected for additional isospin-breaking effects, which were not taken into account in the experimental analyses [7]. By matching to χPT at NLO and NNLO, we determine the low-energy constants L1r, L2r, and L3r. Recently published data [6] from NA48/2 allow even a determination of L9r. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the K_{l4} form factors, which we understand as an effect of rescattering beyond NNLO.
References
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