Hadronic decays of the (pseudo-)scalar charmonium states $\eta_c$ and $\chi_{c0}$ in the extended Linear Sigma Model

TL;DR

This paper models the decay behaviors of scalar and pseudoscalar charmonium states using an extended linear sigma model, exploring glueball mixing effects and providing predictions relevant for current and future experiments.

Contribution

It extends the linear sigma model to include OZI-suppressed decays of charmonia, analyzing glueball-quark mixing and predicting decay widths for unmeasured channels.

Findings

Decay widths align with experimental data where available.

Predictions for unmeasured states can guide future experiments.

Analysis of glueball and quark-antiquark mixing impacts decay patterns.

Abstract

We study the phenomenology of the ground-state (pseudo-)scalar charmonia $\eta_c$ and $\chi_{c0}$ in the framework of a $U(4)_r \times U(4)_l$ symmetric linear sigma model with (pseudo-)scalar and (axial-) vector mesons. Based on previous results for the spectrum of charmonia and the spectrum and (OZI-dominant) strong decays of open charmed mesons, we extend the study of this model to OZI-suppressed charmonia decays. This includes decays into 'ordinary' mesons but also particularly interesting channels with scalar-isoscalar resonances $f_0(1370),\, f_0(1500),\, f_0(1710)$ that may include sizeable contributions from a scalar glueball. We study the variation of the corresponding decay widths assuming different mixings between glueball and quark-antiquark states. We also compute the decay width of the pseudoscalar $\eta_c$ into a pseudoscalar glueball. In general, our results for decay widths are in reasonable agreement with experimental data where available. Order of magnitude predictions for as yet unmeasured states and channels are potentially interesting for BESIII, Belle II, LHCb as well as the future PANDA experiment at the FAIR facility.