$X(1835)$ and the New Resonances $X(2120)$ and $X(2370)$ Observed by the BES Collaboration

TL;DR

This paper investigates the decay properties of excited eta and eta' mesons, comparing theoretical predictions with experimental data to clarify the nature of several observed resonances, and suggests possible mixing with other states like glueballs.

Contribution

It provides a detailed analysis of the decay widths of radial excitations of eta and eta' mesons using the $^3P_0$ model, offering insights into the nature of observed resonances.

Findings

$ ext{X}(1835)$ may contain significant } par{p} ext{ content.

$ ext{X}(2120)$ and $ ext{X}(2370)$ are unlikely to be second radial excitations.

$ ext{X}(2370)$ may be a mixture of } ext{eta'}(4^1S_0) ext{ and a glueball.

Abstract

We calculate the decay widths of both the second and the third radial excitations of $\eta$ and $\eta'$ within the framework of $^3P_0$ model. After comparing the theoretical decay widths and decay patterns with the available experimental data of $\eta(1760)$, $X(1835)$, $X(2120)$ and $X(2370)$, we find that the interpretation of $\eta(1760)$ and $X(1835)$ as the second radial excitation of $\eta$ and $\eta'$ crucially depends on the measured mass and width of $\eta(1760)$, which is still controversial experimentally. We suggest that there may be sizable $p\bar{p}$ content in $X(1835)$. $X(2120)$ and $X(2370)$ can not be understood as the third radial excitations of $\eta$ and $\eta'$, $X(2370)$ probably is a mixture of $\eta'(4{^1}{S}{_0})$ and glueball.