Mass spectra of $0^{--}$ and $0^{+-}$ hidden-heavy baryoniums

In this work, the spectra of the prospective exotic hidden-charm and hidden-bottom baryonium, viz. the baryon-antibaryon states, with $J^{PC}=0^{--}$ and $0^{+-}$ are investigated in the framework of QCD sum rules. The non-perturbative contributions up to dimension 12 are taken into account. Numerical results indicate that there might exist 3 possible $0^{--}$ hidden-charm baryonium states with masses $(5.22\pm 0.26)$, $(5.52\pm 0.25)$, and $(5.46\pm 0.24)$ GeV, and 5 possible $0^{+-}$ hidden-charm baryonium states with masses $(4.76\pm 0.28)$, $(5.24\pm 0.28)$, $(5.16\pm 0.27)$, $(5.52\pm 0.27)$, and $(5.69\pm 0.27)$ GeV, respectively. The corresponding hidden-bottom partners are found lying in the range of $11.68-12.28$ GeV and $11.38-12.33$ GeV, respectively. The possible baryonium decay modes are analyzed, which are hopefully measurable in LHC experiments.