X(1835), X(2120), X(2370) and $\eta(1760)$ in chiral quark model

TL;DR

This paper investigates the nature of several pseudoscalar mesons, including X(1835), X(2120), X(2370), and η(1760), using the constituent quark model and the $^3P_0$ decay framework to compare theoretical predictions with experimental data.

Contribution

The study assigns possible quark model states to these mesons and evaluates their decay widths, providing insights into their internal structure and challenging some previous interpretations.

Findings

The η'(2^1S_0) state matches the total width of η(1760) but not the partial decay to ωω.

X(1835) fits the η(4^1S_0) assignment with compatible total decay width.

X(2120) and X(2370) are unlikely to be the η'(3^1S_0) and η'(4^1S_0) states due to decay width discrepancies.

Abstract

By analyzing the meson spectra obtained in the constituent quark model, we find that the pseudoscalar mesons $\eta'(2^1S_0)$, $\eta(4^1S_0)$, $\eta'(3^1S_0)$ and $\eta'(4^1S_0)$ are the possible candidates of $\eta(1760)$, X(1835), X(2120) and X(2370). The strong decay widths of these pseudoscalars to all the possible decay modes are calculated within the framework of the $^3P_0$ model. Although the total width of $\eta'(2^1S_0)$ is compatible with the experimental value of BES for $\eta(1760)$, the partial decay width to $\omega\omega$ is too small, which is not consistent with the result of BES. If the state X(1835) is interpreted as $\eta(4^1S_0)$, the total decay width is compatible with the experimental data, and the main decay modes will be $\pi a_0(980)$ and $\pi a_0(1450)$, which needs to be checked. The assignment of X(2120) and X(2370) to $\eta'(3^1S_0)$ and $\eta'(4^1S_0)$ is also disfavored in the present calculation because of the incompatibility of the decay widths.