QCD sum rule studies on the ssss tetraquark states of JPC=0-+

We apply the method of QCD sum rules to study the ssss tetraquark states of JPC=0-+. We construct all the relevant ssss 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 2.51-0.12+0.15 GeV, suggesting that the X(2370) or the X(2500) can be explained as the ssss tetraquark state of JPC=0-+. To verify this interpretation, we propose to further study the pi pi /KK invariant mass spectra of the J/psi -> gamma pi pi eta ' /gamma KKeta ' decays in BESIII to examine whether there exists the f0(980) resonance.