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We apply the method of QCD sum rules to study the $s s \bar s \bar s$tetraquark states of $J^{PC} = 0^{-+}$. We construct all the relevant $s s \bars \bar s$ tetraquark currents, and find that there are only two independentones. We use them to further construct two weakly-correlated mixed currents.One of them leads to reliable QCD sum rule results and the mass is extracted tobe $2.51^{+0.15}_{-0.12}$ GeV, suggesting that the $X(2370)$ or the $X(2500)$can be explained as the $ss\bar s\bar s$ tetraquark state of $J^{PC} = 0^{-+}$.To verify this interpretation, we propose to further study the $\pi\pi/K \barK$ invariant mass spectra of the $J/\psi \to \gamma \pi \pi \eta^\prime/\gammaK \bar K \eta^\prime$ decays in BESIII to examine whether there exists the$f_0(980)$ resonance.

QCD sum rule studies on the $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$