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

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 $a=-0.072(7{)}_{\mathrm{stat}}(8{)}_{\mathrm{syst}},b=-0.052(1{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}},d=-0.051(8{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$, which lie in the ballpark of the current experimental and theoretical determinations.

45 pages, 12 figures