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

By analyzing the meson spectra obtained in the constituent quark model, we find that the pseudoscalar mesons $η'(2^1S_0)$, $η(4^1S_0)$, $η'(3^1S_0)$ and $η'(4^1S_0)$ are the possible candidates of $η(1760)$, 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 $η'(2^1S_0)$ is compatible with the experimental value of BES for $η(1760)$, the partial decay width to $ωω$ is too small, which is not consistent with the result of BES. If the state X(1835) is interpreted as $η(4^1S_0)$, the total decay width is compatible with the experimental data, and the main decay modes will be $πa_0(980)$ and $πa_0(1450)$, which needs to be checked. The assignment of X(2120) and X(2370) to $η'(3^1S_0)$ and $η'(4^1S_0)$ is also disfavored in the present calculation because of the incompatibility of the decay widths.