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

## TL;DR

This study uses QCD sum rules to analyze the $s s ar s ar s$ tetraquark states with $J^{PC} = 1^{+-}$, identifying a candidate for the structure $X$ observed by BESIII and proposing searches for related states.

## Contribution

The paper constructs specific tetraquark currents and applies QCD sum rules to interpret the structure $X$ as an $s s ar s ar s$ tetraquark with $J^{PC} = 1^{+-}$, and predicts related partner states.

## Key findings

- Mass of $X$ estimated at $2.00^{+0.10}_{-0.09}$ GeV.
- Interpretation of $Y(2175)$ as an $s s ar s ar s$ partner with $J^{PC} = 1^{--}$.
- Proposal to search for other tetraquark partners in specific mass spectra.

## Abstract

We apply the method of QCD sum rules to study the structure $X$ newly observed by the BESIII Collaboration in the $\phi \eta^\prime$ mass spectrum in 2.0-2.1 GeV region in the $J/\psi \rightarrow \phi \eta \eta^\prime$ 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 $\eta^\prime f_0(980)$, $\eta^\prime K \bar K$, and $\eta^\prime K \bar K^*$ mass spectra.