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

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.Comment: 20 pages, 6 figure