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

Abstract

We apply the method of QCD sum rules to study the $ss\bar{s}\bar{s}$ tetraquark states of $J^{PC}=0^{-+}$. We construct all the relevant $ss\bar{s}\bar{s}$ 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 $2.51_{-0.12}^{+0.15}$ 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 $\pi \pi /K\bar{K}$ invariant mass spectra of the $J/\psi \to \gamma \pi \pi {\eta }^{\prime }/\gamma K\bar{K}{\eta }^{\prime }$ decays in BESIII to examine whether there exists the $f_0(980)$ resonance.

Comments: 8 pages, 6 figures, suggestions and comments are welcome