QCD sum rule studies on the $s s \bar s \bar s$ tetraquark states with $J^{PC} = 1^{+-}$

Abstract

We apply the method of QCD sum rules to study the structure $X$ newly observed by the BESIII Collaboration in the $ϕη^\prime$ mass spectrum in 2.0-2.1 GeV region in the $J/ψ\rightarrow ϕηη^\prime$ decay. We construct all the $s s \bar s \bar s$ tetraquark currents with $J^{PC} = 1^{+-}$, and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be $2.00^{+0.10}_{-0.09}$ GeV, suggesting that the structure $X$ can be interpreted as an $s s \bar s \bar s$ tetraquark state with $J^{PC} = 1^{+-}$. The $Y(2175)$ can be interpreted as its $s s \bar s \bar s$ partner having $J^{PC} = 1^{--}$, and we propose to search for the other two partners, the $s s \bar s \bar s$ tetraquark states with $J^{PC} = 1^{++}$ and $1^{-+}$, in the $η^\prime f_0(980)$, $η^\prime K \bar K$, and $η^\prime K \bar K^*$ mass spectra.