$\eta^{\prime}\to\eta\pi\pi$ decays in unitarized resonance chiral theory

TL;DR

This paper analyzes the decay process $ta^{} ota\u0012$ using unitarized resonance chiral theory, fitting parameters to recent experimental data and calculating Dalitz-plot parameters.

Contribution

It introduces a unitarized chiral perturbation theory approach including resonance states and one-loop corrections for decay analysis.

Findings

Determined scalar multiplet mass and coupling from Dalitz plot data.

Calculated Dalitz-plot slope parameters consistent with experimental values.

Provided a detailed theoretical framework for $ta^{} ota\u0012$ decay analysis.

Abstract

We study the hadronic $\eta^{\prime}\to\eta\pi\pi$ decays within the framework of $U(3)_{L}\otimes U(3)_{R}$ Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the $N/D$ method resumming both the important $S$-and $D$-wave $\pi\pi$ and the subleading $S$-wave $\pi\eta$ final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associated Dalitz-plot slope parameters are found to be $a=-0.072(7)_{\rm{stat}}(8)_{\rm{syst}}\,, b=-0.052(1)_{\rm{stat}}(2)_{\rm{syst}}\,, d=-0.051(8)_{\rm{stat}}(6)_{\rm{syst}}$, which lie in the ballpark of the current experimental and theoretical determinations.