Mass Spectra of $Λ_Q\barΣ_Q$ Bound States
Xuan-Heng Zhang, Cong-Feng Qiao
TL;DR
This work uses QCD sum rules to predict the masses and decay constants of ground-state hidden-charm and hidden-bottom baryon–antibaryon bound states $Λ_Q\bar{Σ}_Q$ with $J^P = 0^-,0^+,1^-,1^+$. Two independent interpolating currents are employed (Type-I and Type-II), and the operator product expansion is carried out up to dimension-12 to form the spectral densities, with a Borel transform enforcing quark-hadron duality. The analysis finds central masses near $5.8$ GeV for $Λ_c\bar{Σ}_c$ and near $12$ GeV for $Λ_b\bar{Σ}_b$, with Type-II currents providing robust windows across all four $J^P$ assignments, and the bottom-sector couplings significantly larger than the charm-sector ones. The results offer mass-region guidance for experimental searches and highlight how quark-level condensates, rather than hadron-level potentials, can underpin binding in these molecular-like baryonium states, consistent with BESIII exclusions near threshold and distinct from Bethe-Salpeter-based predictions.
Abstract
Recently, the BESIII Collaboration indicate that no $Λ_c\barΣ_c$ bound-state with a mass near threshold in the range $4715$--$4735~\mathrm{MeV}$ was observed. In order to determine the plausible mass region of the bound states in this structure, we calculate the mass spectrum of the $Λ_c\barΣ_c$ molecular configuration with the method of QCD sum rules. Two linearly independent interpolating currents are constructed, and contributions from nonperturbative condensates up to dimension 12 are included in the numerical results. Consequently, we obtain the masses of the candidate bound states with quantum numbers $J^P = 0^-,\,0^+,\,1^-,\,1^+$. Our results show that the central values of the $Λ_c\barΣ_c$ bound-state masses lie around the $5.8~\mathrm{GeV}$ region, consistent with the findings reported by the BESIII Collaboration. Furthermore, we compute the mass spectrum of the $Λ_b\barΣ_b$ bound states with quantum numbers $J^P = 0^-,\,0^+,\,1^-,\,1^+$, which could be served as hidden-bottom candidates in the experimental detecting.