Eur. Phys. J. A (2023) 59: 126
https://doi.org/10.1140/epja/s10050-023-01044-1

Regular Article –Theoretical Physics

Systematic analysis of doubly charmed baryons ${\mathrm{\Xi }}_{\mathit{cc}}$ and ${\mathrm{\Omega }}_{\mathit{cc}}$

¹ Department of Mathematics and Physics, North China Electric Power University, 071003, Baoding, People’s Republic of China
² School of Physics and Electronic Science, Guizhou Education University, 550018, Guiyang, People’s Republic of China

^a yuguoliang2011@163.com

Received: 19 March 2023
Accepted: 29 May 2023
Published online: 10 June 2023

Abstract

In this work, we perform a systematic study of the mass spectra, the root mean square (r.m.s.) radii and the radial density distributions of the doubly charmed baryons ${\mathrm{\Xi }}_{\mathit{cc}}$ and ${\mathrm{\Omega }}_{\mathit{cc}}$. The calculations are carried out in the frame work of relativized quark model, where the baryon is regarded as a three-body system of quarks. Our results show that the excited energy of doubly charmed baryon with $\rho$-mode is lower than those of the $\lambda$-mode and $\lambda$-$\rho$ mixing mode, which indicates that the lowest state is dominated by the $\rho$-mode. According to this conclusion, we systematically investigate the mass spectra, the r.m.s. radii of the ground and excited states ($1S\sim 4S$, $1P\sim 4P$, $1D\sim 4D$, $1F\sim 4F$ and $1G\sim 4G$) with $\rho$-mode. Using the wave functions obtained from quark model, we also study the radial density distributions. Finally, with the predicated mass spectra, the Regge trajectories of ${\mathrm{\Xi }}_{\mathit{cc}}$ and ${\mathrm{\Omega }}_{\mathit{cc}}$ in the (J,$M^2$) plane are constructed, and the slopes, intercepts are determined by linear fitting. It is found that model predicted masses fit nicely to the constructed Regge trajectories.