Systematic analysis of doubly charmed baryons $\Xi_{cc}$ and $\Omega_{cc}$

TL;DR

This paper systematically analyzes the mass spectra, radii, and density distributions of doubly charmed baryons $\\Xi_{cc}$ and $\Omega_{cc}$ using the Godfrey-Isgur quark model, revealing the dominance of the $\rho$-mode in their lowest states.

Contribution

It provides a comprehensive study of doubly charmed baryons' properties and their Regge trajectories within the relativized quark model, highlighting the $\rho$-mode as dominant in the lowest states.

Findings

The lowest energy state is dominated by the $\rho$-mode.

Predicted masses fit well with Regge trajectories.

Radial density distributions are obtained from wave functions.

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 $\Xi_{cc}$ and $\Omega_{cc}$. The calculations are carried out in the frame work of Godfrey-Isgur (GI) relativized quark model, where the baryon is regarded as a real 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($1S\sim4S$, $1P\sim4P$, $1D\sim4D$, $1F\sim4F$ and $1G\sim4G$) 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 $\Xi_{cc}$ and $\Omega_{cc}$ 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.