Mass spectra of bottom-charm baryons

In this paper, we investigate the mass spectra of bottom-charm baryons systematically, where the relativistic quark model and the infinitesimally shifted Gaussian basis function method are employed. Our calculation shows that the $\rho$-mode appears lower in energy than the other excited modes. According to this feature, the allowed quantum states are selected and a systematic study of the mass spectra for $\Xi_{bc}^{'}$ ($\Xi_{bc}$) and $\Omega_{bc}^{'}$ ($\Omega_{bc}$) families is performed. The root mean square radii and quark radial probability density distributions of these baryons are analyzed as well. Next, the Regge trajectories in the $(J,M^{2})$ plane are successfully constructed based on the mass spectra. At last, we present the structures of the mass spectra, and analyze the difficulty and opportunity in searching for the ground states of bottom-charm baryons in experiment.