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

Abstract

We present the explicit form of the Regge trajectory relations for the doubly heavy baryons ${\Xi }_{Q{Q}^{\prime }}$ and ${\Omega }_{Q{Q}^{\prime }}$ $(Q,Q^{\prime }=b,c)$ 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.

Comments: 10 pages, 4 figures, and 12 tables. arXiv admin note: substantial text overlap with arXiv:2407.18280, arXiv:2407.04222