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

TL;DR

This paper calculates the mass spectra of doubly heavy baryons using a relativized quark model, revealing how spin and orbital excitations depend on heavy quark mass and suggesting experimental searches for specific states.

Contribution

It applies the relativized quark model with Gaussian basis functions to systematically analyze doubly heavy baryons, including spin splitting and orbital modes, under heavy-quark dominance.

Findings

Spin splitting mainly due to light quark spin-dependent interactions.

Spin splitting evolves with heavy quark mass consistent with heavy quark symmetry.

The $ ho$-mode dominates orbital excitation in doubly heavy baryons.

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 $\rho$-mode, which is different from that of the singly heavy baryons. At last, our analysis indicates that the $\Xi_{cc}^{+}(3520)$ state should not exist truly and the $\Xi_{cc}^{++}(3621)$ should be the true ground state with $J^{P}$ = $\frac{1}{2}^{+}$. It is recommended to design the corresponding experiments to search for the $\Xi_{cc}^{*}$ in the energy range from 3694 to 3714 MeV.