Cusps in K_L --> 3 pi decays

TL;DR

This paper uses an effective field theory approach to analyze the cusp effect in K_L --> 3 pi decays caused by pion mass differences, linking it to pi pi scattering lengths.

Contribution

It provides a systematic evaluation of decay amplitudes respecting analyticity and unitarity, extending to eta --> 3 pi decays.

Findings

Quantitative predictions for cusp effects in K_L --> 3 pi decays.

Amplitudes for eta --> 3 pi decays are also calculated.

Framework respects fundamental principles like analyticity and unitarity.

Abstract

The pion mass difference generates a pronounced cusp in K --> 3 pi decays, the strength of which is related to the pi pi S-wave scattering lengths. We apply an effective field theory framework developed earlier to evaluate the amplitudes for K_L --> 3 pi decays in a systematic manner, where the strictures imposed by analyticity and unitarity are respected automatically. The amplitudes for the decay eta --> 3 pi are also given.