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

Abstract

We study the hadronic $\eta ^{\prime }\rightarrow \eta \pi \pi$ 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 𝜋𝜋 and the subleading S-wave 𝜋𝜂 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 $a=-\,0.072(7)_{\mathrm{stat}}(8)_{\mathrm{syst}},\,b=-\,0.052(1)_{\mathrm{stat}}(2)_{\mathrm{syst}}, d=-\,0.051(8)_{\mathrm{stat}}(6)_{\mathrm{syst}}$ , which lie in the ballpark of the current experimental and theoretical determinations.