Three-body Final State Interaction in $\eta \to 3 \pi$

TL;DR

This paper develops a dispersive model for the eta to three pions decay, using Khuri-Treiman equations and fits to experimental data to better understand hadronic interactions and quark mass ratios.

Contribution

It introduces a unitary dispersive approach solving Khuri-Treiman equations with Pasquier inversion, fitting recent data to improve decay parameter predictions and quark mass estimates.

Findings

Predicted slope parameter for neutral channel: α = -0.022 ± 0.004

Estimated quark mass double ratio Q = 21.4 ± 0.4

Achieved better agreement with experimental Dalitz plot data

Abstract

We present an unitary dispersive model for the $\eta \to 3 \pi$ decay process based upon the Khuri-Treiman equations which are solved by means of the Pasquier inversion method. The description of the hadronic final-state interactions for the $\eta \to 3\pi$ decay is essential to reproduce the available data and to understand the existing discrepancies between Dalitz plot parameters from experiment and chiral perturbation theory. Our approach incorporates substraction constants that are fixed by fitting the recent high-statistics WASA-at-COSY data for $\eta \to \pi^+ \pi^- \pi^0$. Based on the parameters obtained we predict the slope parameter for the neutral channel to be $\alpha=-0.022\pm 0.004$. Through matching to next-to-leading order chiral perturbation theory we estimate the quark mass double ratio to be $Q=21.4 \pm 0.4$.