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

Abstract In framework of heavy-diquark–light-quark endowed with heavy-pair binding, we explore excited baryons $$QQ^{\prime }q$$ Q Q ′ q containing two heavy quarks ( $$QQ^{\prime }=cc,bb,bc$$ Q Q ′ = c c , b b , b c ) 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 $$\Xi _{cc}$$ Ξ 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 $$\Xi _{QQ^{\prime }}$$ Ξ Q Q ′ and $$\Omega _{QQ^{\prime }}$$ Ω Q Q ′ 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