Three-body final state interaction in $\eta \to 3 \pi$ updated

TL;DR

This paper uses a dispersive model to analyze three-pion final state interactions in eta decay, fitting recent high-statistics data to determine quark mass ratios and decay parameters.

Contribution

It introduces a dispersive approach that incorporates rescattering effects to accurately describe eta decay Dalitz plots and extract fundamental quark mass ratios.

Findings

Determined quark mass double ratio Q=21.6 ± 1.1

Predicted slope parameter α=-0.025 ± 0.004

Achieved consistent fit with KLOE and WASA-at-COSY data

Abstract

In view of the recent high-statistic KLOE data for the $\eta \to \pi^+ \pi^- \pi^0$ decay, a new determination of the quark mass double ratio has been done. Our approach relies on a dispersive model that takes into account rescattering effects between three pions via subenergy unitarity. The latter is essential to reproduce the Dalitz plot distribution. A simultaneous description of the KLOE and WASA-at-COSY data is achieved in terms of just two real parameters. From a global fit, we determine $Q=21.6 \pm 1.1$. The predicted slope parameter for the neutral channel $\alpha=-0.025\pm 0.004$ is in reasonable agreement with the PDG average value.