Study the isoscalar mesons $\eta_2(1870)$ and X(1870)

An isoscalar resonance, X(1870), with a mass $M=1877.3\pm6.3(stat)^{+3.4}_{-7.4}(syst)$MeV and width $\Gamma=57\pm12(stat)^{+19}_{-4}(syst)$MeV was observed by the BesIII Collaboration recently. The mass of X(1870) is compatible with $\eta_2(1870)$ but the decay width is much smaller. In this paper, we analyzed the mass and the two-body strong decay of $\eta_2(1870)$ and X(1870). According to the mass spectra predicted by the Godfrey-Isgur potential model, X(1870) can be candidates of the states $f'_1(2^3P_1)$, $\eta'_2(1^1D_2)$ or $\eta_2(2^1D_2)$. In the Regge trajectories (RTs) framework, X(1870) favors the $\eta'(3^1S_0)$ and $f'_1(2^3P_1)$ assignments. However, the decay properties of $\eta'(3^1S_0)$, $f'_1(2^3P_1)$, $\eta'_2(1^1D_2)$ disagree with the experiments. The two-body strong decay widths indicate that $\eta_2(1870)$ and X(1870) maybe the two different resonant structures. $\eta_2(1870)$ could be assigned to the $\eta_2(2^1D_2)$ quarkonium as the first radical excited state of $\eta_2(1645)$. X(1870) favors a $\eta_H(0^+2^{-+})$ hybrid assignment. Some significant decay modes are suggested to test in future.