Convergence properties of $\eta$$\,\to$$3\pi$ in low energy QCD

TL;DR

This paper examines the convergence issues of the $ o 3 ext{pi}$ decay widths and Dalitz plot parameters in low energy QCD, analyzing experimental data and theoretical models to assess their compatibility.

Contribution

It provides a comprehensive overview and recent analysis of the convergence properties of chiral series in $ o 3 ext{pi}$ decays within resummed chiral perturbation theory.

Findings

Identifies convergence problems in decay widths and Dalitz parameters.

Assesses compatibility of experimental data with theoretical predictions.

Suggests conditions for improved convergence in chiral expansions.

Abstract

Even today, the convergence of the decay widths and some of the Dalitz plot parameters of the $\eta $$\,\rightarrow $$3\pi$ decays seems problematic in low energy QCD. We provide an overview of the current experimental and theoretical situation with historical background and summarize our recent results, which explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series in the framework of resummed chiral perturbation theory.