Study of $\eta^\prime \to \eta \pi\pi $ Decays in Large-$N_C$ Chiral Perturbation Theory

TL;DR

This paper models the $ ext{eta'} o ext{eta} ext{pi} ext{pi}$ decay using large-$N_C$ chiral perturbation theory, incorporating final-state interactions to match experimental data and extract Dalitz-plot parameters.

Contribution

It advances the theoretical understanding of $ ext{eta'}$ decay by including $ ext{pi} ext{pi}$ final-state interactions and fitting to precise experimental data.

Findings

Including $ ext{pi} ext{pi}$ final-state interactions improves agreement with data.

Dalitz-plot parameters are extracted with quantified uncertainties.

Theoretical decay descriptions are refined with unitarization and higher-order calculations.

Abstract

We investigate the $\eta^\prime \to \eta \pi\pi$ decays within the framework of large-$N_{C}$ chiral perturbation theory, by calculating the decay amplitudes up to next-to-next-to-leading order in a simultaneous expansion in powers of external momenta, quark masses, and $1/N_C$. Projecting the amplitudes onto partial waves allows us to implement a unitarization procedure to account for the $S$- and $D$-wave $\pi\pi$ final-state interactions. The relevant low-energy constants are determined by fitting our theoretical results to the precise experimental data from the A2 collaboration. A comparison of fits with and without $\pi\pi$ final-state interactions demonstrates that including these effects significantly improves the agreement of our theoretical predictions with the experimental measurements. Consequently, the Dalitz-plot parameters are extracted as $a=-0.085(18)_{\mathrm{stat}}(4)_{\mathrm{syst}}$, $b=-0.081(10)_{\mathrm{stat}}(6)_{\mathrm{syst}}$, and $d=-0.045(6)_{\mathrm{stat}}(8)_{\mathrm{syst}}$. Our results provide therefore a refined theoretical description of the $\eta^\prime \to \eta \pi\pi$ decay dynamics.