Study of the mass spectra of doubly heavy $Ξ_{QQ^{\prime}}$ and $Ω_{QQ^{\prime}}$ baryons
Ji-Hai Pan, Ji-Si Pan
TL;DR
This work develops a Regge-trajectory framework with relativistic effective quark masses to predict the mass spectra of doubly heavy baryons, treating each baryon as a heavy diquark bound to a light quark. It introduces an all-$JLS$ coupling scheme to compute spin-dependent mass shifts $\Delta M(J,j)$ and derives mass formulas $M(J,j)=\bar{M}+\Delta M(J,j)$ for S-, P-, and D-wave excitations, with scaling relations to propagate parameters from known singly heavy baryons. The authors produce concrete 1S-ground-state predictions for $Ξ^{++}_{cc}$, $Ξ_{bc}$, $Ξ_{bb}$, and $Ω_{cc}$, $Ω_{bc}$, $Ω_{bb}$ (e.g., $Ξ^{++}_{cc}$ 1S: $M=3621.57\pm8.65$ MeV, $J^{P}=1/2^{+}$; $Ξ_{cc}$ 3/2$^{+}$ around $3699.69\pm4.52$ MeV), and provide extensive higher-state predictions to guide experimental exploration. The approach leverages Regge slopes, effective masses, and scaling relations to produce a cohesive set of mass targets and relationships among heavy-baryon spectra. Overall, the results offer a practical theoretical scaffold for future measurements at high-energy experiments.
Abstract
LHCb Collaboration first observed a doubly charmed baryon $Ξ^{++}_{cc}$ in the $Λ^{+}_{c}K^{-}π^{+}π^{+}$ decay with a mass of $3621.40\pm0.72\pm0.27$ MeV. In this paper, we enumerated the mass spectra of the radial and orbital excited states for the doubly heavy $Ξ_{QQ^{\prime}}$ and $Ω_{QQ^{\prime}}$ baryons using the Regge trajectory model and the scaling rules. Our studies suggest that $Ξ^{++}_{cc}$ can be grouped into the $1S$-wave state with the spin-parity quantum number $J^{P} = 1/2^{+}$. On the other hand, the mass of $Ξ_{cc}$ state with $J^{P} = 3/2^{+}$ is predicted to be $3699.69 \pm 4.59$ MeV. We also predict the mass spectra of the unknown ground and excited states for the doubly heavy $Ξ_{QQ^{\prime}}$ and $Ω_{QQ^{\prime}}$ baryons, which provide useful references for the experimental test in the future.