Mass Spectra of $\Lambda_Q\bar{\Sigma}_Q$ Hexaquark States in QCD Sum Rules

TL;DR

This paper uses QCD sum rules to calculate the mass spectrum of $ ext{Lambda}_Qar{ ext{Sigma}}_Q$ hexaquark states, finding their masses are too high to be bound states near the observed thresholds.

Contribution

It provides the first detailed QCD sum rule analysis of $ ext{Lambda}_Qar{ ext{Sigma}}_Q$ hexaquark states, including nonperturbative effects up to dimension 12.

Findings

Ground-state masses around 5.8 GeV do not support bound states.

Results align with BESIII findings that no near-threshold bound states exist.

Mass spectrum for bottom counterparts suggests potential experimental candidates.

Abstract

Recently, the BESIII Collaboration indicate that no $\Lambda_c\bar{\Sigma}_c$ 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 states in this structure, we calculate the mass spectrum of the $\Lambda_c\bar{\Sigma}_c$ 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 states with quantum numbers $J^P = 0^-,\,0^+,\,1^-,\,1^+$. Our results show that the central values of the $\Lambda_c\bar{\Sigma}_c$ ground-state masses lie around the $5.8~\mathrm{GeV}$ region, which do not support them as bound states and consistent with the findings reported by the BESIII Collaboration. Furthermore, we compute the mass spectrum of the $\Lambda_b\bar{\Sigma}_b$ states with quantum numbers $J^P = 0^-,\,0^+,\,1^-,\,1^+$, which could be served as hidden-bottom candidates in the experimental detecting.