$\lambda$ and $\rho$ trajectories for the doubly heavy baryons in the diquark picture

We present the explicit form of the Regge trajectory relations for the doubly heavy baryons $\Xi_{QQ'}$ and $\Omega_{QQ'}$ $(Q,Q'=b,c)$ in the diquark picture. Using the derived Regge trajectory relations, we estimate the masses of the $\lambda$-excited states and the $\rho$-excited states, which are consistent with other theoretical predictions. Both the $\lambda$-trajectories and $\rho$-trajectories are discussed. We show that the $\rho$-trajectories behave differently from the $\lambda$-trajectories. Specifically, the $\rho$-trajectories behave as $M{\sim}x_{\rho}^{2/3}$ $(x_{\rho}=n_r,l)$, whereas the $\lambda$-trajectories follow $M{\sim}x_{\lambda}^{1/2}$ $(x_{\lambda}=N_r,L)$. By using the obtained relations, the baryon Regge trajectory provides a straightforward and easy method for estimating the spectra of both the $\lambda$-excited states and $\rho$-excited states.