Dispersion relations for $\eta'\to\eta\pi\pi$

TL;DR

This paper develops a dispersive analysis of the $ ext{η'} o ext{η} ext{π} ext{π}$ decay, incorporating final-state interactions and using scattering phase shifts, to fit experimental Dalitz-plot data and compare with chiral perturbation theory.

Contribution

It introduces a dispersive framework for analyzing $ ext{η'}$ decay that fully accounts for final-state interactions and fits experimental data to determine unknown parameters.

Findings

Dispersive analysis accurately describes decay amplitude.

Fits experimental Dalitz-plot data from VES and BES-III.

Comparison with chiral perturbation theory highlights low-energy behavior.

Abstract

We present a dispersive analysis of the decay amplitude for $\eta'\to\eta\pi\pi$ that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the $\pi\pi$ and $\pi\eta$ scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.