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.

China

Zhen-Yu Li

Guo-Liang Yu

Zhi-Gang Wang

Jian-Zhong Gu

Hong-Tao Shen

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

The rigorous calculation of the spin-orbit terms in a three-quark system is realized based on the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions in the framework of the relativized quark model, by ignoring the mixing between different excited states. Then, the complete mass spectra of the singly heavy baryons are obtained rigorously, under the heavy-quark dominance mechanism. Accordingly, systematical analyses are performed for the reliability and predictive power of the model, the fine structure of the singly heavy baryon spectra, the assignments of the excited baryons, and some important topics about heavy baryon spectroscopy, such as the missing states, 'spin-orbit puzzle,' and clustering effect. The results confirm that, under the heavy-quark dominance mechanism, the relativized quark model can describe the excitation spectra and the fine structures of the singly heavy baryons correctly and precisely.

Mass spectra of singly heavy baryons in the relativized quark model with heavy-quark dominance * Supported by the Open Project of Guangxi Key Lab of Nuclear Physics and Technology (NLK2023-04), the Central Government Guidance Funds for Local Scientific and Technological Development in China (Guike ZY22096024), the Natural Science Foundation of Guizhou Province-ZK[2024](General Project)650, the National Natural Science Foundation of China (11675265, 12175068), the Continuous Basic Scientific Research Project (WDJC-2019-13) and the Leading Innovation Project (LC 192209000701)

In the framework of the relativized quark model, the calculation of spin-orbit interactions is improved by considering the contribution from the light-quark cluster in a singly heavy baryon. It modifies the energy level splitting of the orbital excitation significantly and causes the emergence of fine structures for $$\Sigma _{Q}$$ , $$\Xi '_{Q}$$ and $$\Omega _{Q}$$ baryons. Based on this improvement, we systematically analyze the fine structures and retest the heavy quark dominance mechanism. This mechanism is found to be violated in the 1 -wave states of the $$\Sigma _{c}$$ , $$\Xi '_{c}$$ and $$\Omega _{c}$$ baryons although it remains effective overall, which may help to understand the nature of the heavy quarks and strong interactions. With the predicted fine structures, we make the precise assignments of those observed heavy baryons which once could not be accurately explained due to their close mass values. The method used in this work is instructive and applicable for the study of more complex exotic hadrons, such as the heavy tetraquarks and pentaquarks.

Heavy-quark dominance and fine structure of excited heavy baryons $$\Sigma _{Q}$$ , $$\Xi '_{Q}$$ and $$\Omega _{Q}$$

A mechanism of the heavy quark dominance in the orbital excitation is proposed in this paper which is testified to be reasonable for singly and doubly heavy baryons. In the relativistic quark model, an analysis of the Hamiltonian figures out the mechanism that the excitation mode with lower energy levels is always associated with the heavy quark(s), and the splitting of the energy levels is suppressed by the heavy quark(s). So, the heavy quarks dominate the orbital excitation of singly and doubly heavy baryons. Furthermore, a physical understanding of this mechanism is given in a semi-classical way. Accordingly, the predicted mass spectra of singly and doubly heavy baryons confirm the rationality of this mechanism. In addition, an interesting consequence of this mechanism is that a heavy-light meson is more likely to be produced in the strong decay of the high-orbital excited states, which is supported by experiments. This mechanism is rooted in the breakdown of the mass symmetry. Therefore, it may be also valid for other multi-quark systems, such as the tetraquarks Qqqq and QQqq, or the pentaquarks Qqqqq and QQqqq.

Heavy quark dominance in orbital excitation of singly and doubly heavy baryons

Motivated by the experimental progress in the study of heavy baryons, we investigate the mass spectra of strange single heavy baryons in the λ-mode, using the relativistic quark model and the infinitesimally shifted Gaussian basis function method. We show that experimental results are well captured using the predicted masses. The root mean square radii and radial probability density distributions of the wave functions are analyzed in detail. Meanwhile, the mass spectra allow us to successfully construct the Regge trajectories in the   $ (J,M^{2}) $   plane. We also preliminarily assign quantum numbers to the recently observed baryons, including   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  ,   $ (J,M^{2}) $  , and   $ (J,M^{2}) $  . Finally, the spectral structure of strange single heavy baryons is discussed. Accordingly, we predict several new baryons that may be observed in forthcoming experiments.