Study of the mass spectra of doubly heavy $Ξ_{QQ^{\prime}}$ and $Ω_{QQ^{\prime}}$ baryons

Abstract: LHCb Collaboration first observed a doubly charmed baryon $\Xi^{++}_{cc}$ in the $\Lambda^{+}_{c}K^{-}\pi^{+}\pi^{+}$ decay with a mass of $3621.40\pm0.78$ MeV. In this paper, we enumerated the mass spectra of the radial and orbital excited states for the doubly heavy $\Xi_{QQ^{\prime}}$ and $\Omega_{QQ^{\prime}}$ baryons using the Regge trajectory model and the scaling rules. Our studies suggest that $\Xi^{++}_{cc}$ 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 $\Xi_{cc}$ state with $J^{P} = 3/2^{+}$ is predicted to be $3699.69$ MeV. We also predict the mass spectra of the unknown ground and excited states for the doubly heavy $\Xi_{QQ^{\prime}}$ and $\Omega_{QQ^{\prime}}$ baryons, which provide useful references for the experimental test in the future.