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

TL;DR

This paper introduces a dispersive method for analyzing $K_{ ext{l}4}$ decays, accurately accounting for rescattering effects, and compares the approach with experimental data and chiral perturbation theory.

Contribution

It presents a novel dispersive framework for $K_{ ext{l}4}$ decays that fully incorporates rescattering effects and matches experimental data with chiral perturbation theory.

Findings

Fits to NA48/2 and E865 data are successful.

Rescattering effects are fully accounted for in the dispersive approach.

Results align well with chiral perturbation theory predictions.

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.