Mass spectra of doubly heavy baryons in the relativized quark model with heavy-quark dominance

TL;DR

This paper addresses the mass spectra of doubly heavy baryons within a genuine three-quark framework by employing a relativized quark model with heavy-quark dominance (HQD), solved using the Gaussian expansion method (GEM) and infinitesimally-shifted Gaussian (ISG) basis in JC-3 coordinates. The approach yields 1S–1D states and radii across the $\Xi_{cc}$, $\Xi_{bc}$, and $\Omega_{cc}$ families, with detailed analysis of how each Hamiltonian term shapes the spectrum. A key finding is that orbital excitations are dominated by the $\rho$-mode, while spin splittings are mainly driven by light-quark spin-dependent interactions, leading to a systematic evolution with heavy-quark mass; the ground state is predicted to be $\Xi_{cc}^{++}$ with $J^{P}=\frac{1}{2}^{+}$, and the $\Xi_{cc}^{+}(3520)$ signal is not supported. The results align with lattice QCD for related states and provide precise predictions (uncertainties $<10$ MeV$) and concrete experimental targets, such as searching for $\Xi_{cc}^{*}$ in the 3694–3714 MeV region, informing future HL-LHC investigations.

Abstract

In the framework of the relativized quark model, the mass spectra of the doubly heavy baryons are rigorously calculated in the three-quark system under the heavy-quark dominance mechanism, by using the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions. With the obtained mass spectra of all doubly heavy baryon families, the contribution of each Hamiltonian term to the energy levels is analyzed. It is found that the spin splitting is mainly determined by the spin-dependent interactions associated with the light quark. Moreover, it is shown that the spin splitting evolves regularly with the mass of heavy quarks by the evolution of the spectral structure, which is consistent with the heavy quark symmetry. Meanwhile, the orbital excitation is dominated by the $ρ$-mode, which is different from that of the singly heavy baryons. At last, our analysis indicates that the $Ξ_{cc}^{+}(3520)$ state should not exist truly and the $Ξ_{cc}^{++}(3621)$ should be the true ground state with $J^{P}$ = $\frac{1}{2}^{+}$. It is recommended to design the corresponding experiments to search for the $Ξ_{cc}^{*}$ in the energy range from 3694 to 3714 MeV.

Figures (2)

• Figure 1: There are 3 channels of the Jacobi coordinates for a three-quark system. The channel 3 (JC-3) is selected for defining the spatial wave function of a doubly heavy baryon state. All the quarks are numbered for ease of use in calculations, and the 3rd quark refers specifically to the light quark.
• Figure 2: Calculated spectra of the doubly heavy baryons and the relevant experimental data 04. '++','+', '0' and '-' indicate the charged states of baryons. The open circle denotes the $\Xi_{cc}^{++}$ baryon.