# Ke4 decays and Wigner cusp

## TL;DR

This paper reports precise measurements of Ke4 and Ke400 decays, extracting pi-pi scattering lengths and form factors, providing a fundamental test of Chiral Perturbation Theory and improving understanding of meson interactions.

## Contribution

It presents new, precise measurements of decay form factors, scattering lengths, and decay parameters, with larger data samples than previous studies, advancing the experimental validation of ChPT.

## Key findings

- Measured pi-pi scattering lengths a00 and a20.
- Determined decay form factors and branching fractions with high precision.
- Provided evidence for a non-zero slope parameter k in K+- -> pi0 pi0 pi+- decay.

## Abstract

The NA48/2 experiment at the CERN SPS collected in 2003 and 2004 large samples of the decays K+- -> pi+ pi- e+- nu (Ke4+-), K+- -> pi0 pi0 e+- nu (Ke400) and K+- -> pi0 pi0 pi+-. From the Ke4+- form factors and from the cusp in the M00^2 distribution of the K+- -> pi0 pi0 pi+- events, the pi-pi scattering lengths a00 and a20 could be extracted. This measurement is a fundamental test of Chiral Perturbation Theory (ChPT). The branching fraction and form factors of the Ke400 decay were precisely measured, using a much larger data sample than in previous experiments. An improved measurement of the slope parameters for the decay K+- -> pi0 pi0 pi+- showed evidence for a non-zero value of k.