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

By analyzing the meson spectra obtained in the constituent quark model, we find that the pseudoscalar mesons ${\eta }^{\mathrm{\prime }}(2^1{S}_0)$, $\eta (4^1{S}_0)$, ${\eta }^{\mathrm{\prime }}(3^1{S}_0)$ and ${\eta }^{\mathrm{\prime }}(4^1{S}_0)$ 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 ${}^3{P}_0$ model. Although the total width of ${\eta }^{\mathrm{\prime }}(2^1{S}_0)$ 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 $\eta (4^1{S}_0)$, 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 ${\eta }^{\mathrm{\prime }}(3^1{S}_0)$ and ${\eta }^{\mathrm{\prime }}(4^1{S}_0)$ is also disfavored in the present calculation because of the incompatibility of the decay widths.