Light baryonium states with exotic quantum numbers

The existence of baryonium-bound or resonant states composed of a baryon and an antibaryon has long been postulated as a natural extension of conventional hadron spectroscopy. In the present work, we conduct a systematic investigation of the mass spectrum and internal configurations of light baryonium candidates exhibiting exotic quantum numbers that are inaccessible within the framework of the traditional quark model. Employing the method of QCD sum rules, we analyze nucleon-antinucleon and light hyperon-anti-hyperon systems with quantum numbers $J^{PC}=0^{--}$ and $0^{+-}$, which are quantum number combinations prohibited for conventional mesonic states. Our analysis reveals the potential existence of two $0^{--}$ $\Lambda$-$\bar{\Lambda}$ baryonium states with masses $(2.90\pm0.09)$ GeV and $(3.36\pm0.09)$ GeV, respectively, as well as two $0^{+-}$ $\Lambda$-$\bar{\Lambda}$ states with masses $(2.91\pm0.07)$ GeV and $(3.29\pm0.07)$ GeV, respectively. In addition, corresponding nucleon-antinucleon partner states are identified at $(2.69\pm0.07)$ GeV, $(3.07\pm0.08)$ GeV, $(2.86\pm0.07)$ GeV, and $(3.22\pm0.07)$ GeV, respectively. Furthermore, analogous $\Xi$-$\bar{\Xi}$ configurations are predicted with masses of $(3.10\pm0.09)$ GeV, $(3.54\pm0.07)$ GeV, $(3.08\pm0.08)$ GeV, and $(3.45\pm0.08)$ GeV, respectively. The possible decay modes of the light exotic baryonium states are analyzed, which are hopefully measurable in BESIII, BELLEII, and LHCb experiments.