Study of the mass spectra of doubly heavy ${\mathrm{\Xi }}_{Q{Q}^{\mathrm{\prime }}}$ and ${\mathrm{\Omega }}_{Q{Q}^{\mathrm{\prime }}}$ baryons

LHCb Collaboration first observed a doubly charmed baryon ${\mathrm{\Xi }}_{cc}^{++}$ in the ${\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+}{\pi }^{+}$ decay with a mass of $3621.40\pm 0.72\pm 0.27$ MeV. In this paper, we enumerated the mass spectra of the radial and orbital excited states for the doubly heavy ${\mathrm{\Xi }}_{Q{Q}^{\mathrm{\prime }}}$ and ${\mathrm{\Omega }}_{Q{Q}^{\mathrm{\prime }}}$ baryons using the Regge trajectory model and the scaling rules. Our studies suggest that ${\mathrm{\Xi }}_{cc}^{++}$ can be grouped into the $1S$-wave state with the spin-parity quantum number $J^P=1\mathrm{/}{2}^{+}$. On the other hand, the mass of ${\mathrm{\Xi }}_{cc}$ state with $J^P=3\mathrm{/}{2}^{+}$ 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 ${\mathrm{\Xi }}_{Q{Q}^{\mathrm{\prime }}}$ and ${\mathrm{\Omega }}_{Q{Q}^{\mathrm{\prime }}}$ baryons, which provide useful references for the experimental test in the future.