Predictions for $\eta_c \to \eta \pi^+ \pi^-$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$

TL;DR

This paper predicts the production of scalar mesons in the decay of eta_c into eta and pions using SU(3) symmetry and chiral unitary methods, providing results that can be compared with recent experimental data.

Contribution

It introduces a novel theoretical approach combining SU(3) symmetry and chiral unitary methods to predict scalar meson production in eta_c decay.

Findings

Clear signals for $f_0(500)$, $f_0(980)$, and $a_0(980)$ in mass distributions.

Predictions align with recent BESIII measurements of similar reactions.

Provides insights into the nature of low mass scalar mesons.

Abstract

We perform calculations for the $\eta_c \to \eta \pi^+ \pi^-$ decay using elements of SU(3) symmetry to see the weight of different trios of pseudoscalars produced in this decay, prior to the final state interaction of the mesons. After that, the interaction of pairs of mesons, leading finally to $\eta \pi^+ \pi^-$, is done using the chiral unitary approach. We evaluate the $\pi^+ \pi^-$ and $\pi \eta$ mass distributions and find large and clear signals for $f_0(500)$, $f_0(980)$ and $a_0(980)$ excitation. The reaction is similar to the $\chi_{c1} \to \eta \pi^+ \pi^-$, which has been recently measured at BESIII and its implementation and comparison with these predictions will be very valuable to shed light on the nature of the low mass scalar mesons.