Mass spectrum of the $\Omega\bar{\Omega}$ states

In this study, we investigate the mass spectrum of the $\Omega\bar{\Omega}$ states with quantum numbers $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, and $1^{++}$ within the framework of QCD sum rules. Employing suitably constructed interpolating currents, the analyses are carried out with the operator product expansion (OPE) including condensate contributions up to dimension $12$. Our results indicate the existence of four possible baryonium states with masses $m_{0^{-+}}=(3.22\pm0.07)$ GeV, $m_{1^{--}}=(3.28\pm0.08)$ GeV, $m_{0^{++}}=(3.46\pm0.09)$ GeV, and $m_{1^{++}}=(3.54\pm0.11)$ GeV. For the $0^{-+}$ and $1^{--}$ states, the predicted masses lie below the corresponding dibaryon thresholds, suggesting possible bound-state configurations. In contrast, the $0^{++}$ and $1^{++}$ states are found above the respective thresholds, implying resonance-like behavior. Potential decay channels for these baryonium candidates are discussed, with emphasis on those accessible to current experimental facilities such as BESIII, Belle II, and LHCb.