QCD sum rule studies on the $ss\overline{s}\overline{s}$ tetraquark states of J${}^{PC}$=0${}^{\text{â}\text{ˆ}\text{’}+}$

We apply the method of QCD sum rules to study the $ss\overline{s}\overline{s}$ tetraquark states of J${}^{PC}$=0${}^{\text{â}\text{ˆ}\text{’}+}$. We construct all the relevant $ss\overline{s}\overline{s}$ tetraquark currents, and find that there are only two independent ones. 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 to be 2.51+0.15−0.12 GeV, suggesting that the X(2370) or the X(2500) can be explained as the $ss\overline{s}\overline{s}$ tetraquark state of J${}^{PC}$=0${}^{\text{â}\text{ˆ}\text{’}+}$. To verify this interpretation, we propose to further study the ππ/$K\overline{K}$ invariant mass spectra of the J/ψ→γππη′/γ$K\overline{K}$η′ decays in BESIII to examine whether there exists the f${}_0$(980) resonance.