Low-lying doubly heavy baryons: Regge relation and mass scaling

In framework of heavy-diquark$-$light-quark endowed with heavy-pair binding, we explore excited baryons $QQ^{\prime}q$ containing two heavy quarks ($QQ^{\prime}=cc,bb,bc$) by combining the method of Regge trajectory with the perturbative correction due to the heavy-pair interaction in baryons. Two Regge relations, one linear and the other nonlinear, are constructed semi-classically in the QCD string picture, and a mass scaling relation based on the heavy diquark-heavy antiquark symmetry are employed between the doubly heavy baryons and heavy mesons. We employ the ground-state mass estimates compatible with the observed doubly charmed baryon $\Xi_{cc}$ and spectra of the heavy quarkonia to determine the trajectory parameters and the binding energies of the heavy pair, and thereby compute the low-lying masses of the excited baryons $\Xi_{QQ^{\prime}}$ and $\Omega_{QQ^{\prime}}$ up to 2S and 1P excitations of the light quark and heavy diquark. The level spacings of heavy diquark excitations are found to be smaller generally than that of the light-quark excitations, in according with the nature of adiabatic expansion between the heavy and light-quark dynamics.