Regge trajectories for the triply heavy bottom-charm baryons in the diquark picture

We present the explicit form of the Regge trajectory relations for the triply heavy bottom-charm baryons, which can be applied to investigate both the \(\lambda \)-mode excited states and the \(\rho \)-mode excited states. We estimate the masses of the \(\lambda \)-excited states and the \(\rho \)-excited states. The results are in agreement with other theoretical predictions. Both the \(\lambda \)-trajectories and the \(\rho \)-trajectories are discussed. Moreover, the behaviors of the \(\lambda \)- and \(\rho \)-trajectories for various baryons are discussed. It is shown that both the \(\lambda \)-trajectories and the \(\rho \)-trajectories for baryons are concave downwards in the \((M^2,\,x)\) plane. The Regge trajectories for the light baryons are approximately linear and become concave as the masses of the light constituents are considered.