Updated Σc excitation spectrum including the 2P- and 1F-wave fine structures
Abstract
In order to study the new Σc baryons observed by the LHCb collaboration recently, we update the previously predicted Σc excitation spectrum by extending the excited states up to the highly excited 2P- and 1F-wave states. The calculation is performed in the framework of the relativized quark model and Gaussian expansion method by considering the mixing effect. The radially and orbitally excited states in the calculation are determined by the truncation convention proposed in this work and the mechanism of the heavy-quark dominance. The contribution of each Hamiltonian term to the energy levels is precisely calculated by using the two-step Gaussian expansion method. Then, the concerned Σc states are obtained and the Σc excitation spectrum including the 2P- and 1F-wave fine structures is established. Based on these, several important topics are discussed and analyzed, including the root-mean-square radii, off-diagonal matrix elements, mixing effect, fine structures and assignments of the newly observed Σc(2800)0, Σc(2900)0 and Σc(3200)0 states. Meanwhile, it is found that the approximate decoupling phenomenon emerges in different nL-wave groups. This implies the reasonability of the truncation convention and is of great significance for further improving the calculation scheme for all the baryon spectra. Moreover, it is demonstrated that in the very high-lying nL-wave groups such as the 1F-wave group, the energy level gaps become small even degenerate, and each of the baryon states has a big radius and therefore a loosely bound structure. In addition, by examining the experimental and calculated data, we suggest more precise experiments to search for more Σc baryon states in the predicted 1P- and 2P-wave fine structures whose central energies are around 2822 and 3210 MeV, respectively.
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BibTeX
@misc{li2026updated,
title = {{Updated $Σ_c$ excitation spectrum including the $2P$- and $1F$-wave fine structures}},
author = {Zhen-Yu Li and Guo-Liang Yu and Zhi-Gang Wang and Jian-Zhong Gu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41339},
eprint = {2610.41339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Updated Σ_c excitation spectrum including the 2P- and 1F-wave fine structures
AU - Zhen-Yu Li
AU - Guo-Liang Yu
AU - Zhi-Gang Wang
AU - Jian-Zhong Gu
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41339
UR - https://arxiv.org/abs/2610.41339
AB - In order to study the new Σ_c baryons observed by the LHCb collaboration recently, we update the previously predicted Σ_c excitation spectrum by extending the excited states up to the highly excited 2P- and 1F-wave states. The calculation is performed in the framework of the relativized quark model and Gaussian expansion method by considering the mixing effect. The radially and orbitally excited states in the calculation are determined by the truncation convention proposed in this work and the mechanism of the heavy-quark dominance. The contribution of each Hamiltonian term to the energy levels is precisely calculated by using the two-step Gaussian expansion method. Then, the concerned Σ_c states are obtained and the Σ_c excitation spectrum including the 2P- and 1F-wave fine structures is established. Based on these, several important topics are discussed and analyzed, including the root-mean-square radii, off-diagonal matrix elements, mixing effect, fine structures and assignments of the newly observed Σ_c(2800)^0, Σ_c(2900)^0 and Σ_c(3200)^0 states. Meanwhile, it is found that the approximate decoupling phenomenon emerges in different nL-wave groups. This implies the reasonability of the truncation convention and is of great significance for further improving the calculation scheme for all the baryon spectra. Moreover, it is demonstrated that in the very high-lying nL-wave groups such as the 1F-wave group, the energy level gaps become small even degenerate, and each of the baryon states has a big radius and therefore a loosely bound structure. In addition, by examining the experimental and calculated data, we suggest more precise experiments to search for more Σ_c baryon states in the predicted 1P- and 2P-wave fine structures whose central energies are around 2822 and 3210 MeV, respectively.
ER -