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We apply the method of QCD sum rules to study the structure $X$ newlyobserved by the BESIII Collaboration in the $\phi \eta^\prime$ mass spectrum in2.0-2.1 GeV region in the $J/\psi \rightarrow \phi \eta \eta^\prime$ decay. Weconstruct 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 toreliable QCD sum rule results and the mass is extracted to be$2.00^{+0.10}_{-0.09}$ GeV, suggesting that the structure $X$ can beinterpreted 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 $ss \bar s \bar s$ tetraquark states with $J^{PC} = 1^{++}$ and $1^{-+}$, in the$\eta^\prime f_0(980)$, $\eta^\prime K \bar K$, and $\eta^\prime K \bar K^*$mass spectra.

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