Mass spectrum, magnetic moments and Regge trajectories of $\Omega_{ccb}$ and $\Omega_{cbb}$ baryons in the nonrelativistic quark--diquark model

In this work, we investigate the mass spectra, magnetic moments, and Regge trajectories of the triply heavy baryons $\Omega_{ccb}$ and $\Omega_{cbb}$ within a nonrelativistic constituent quark model based on the quark--diquark approximation, which reduces the three-body problem to an effective two-body system. For each baryon, all three possible diquark clusterings are considered, providing a qualitative indication of the sensitivity of the results to the quark--diquark decomposition. The model parameters are fixed by a fit to the measured $B_c$ meson spectrum, thereby anchoring the baryon predictions to experimentally constrained inputs and establishing a consistent link between the heavy meson and baryon sectors. We obtain ground-state masses of approximately $8.0$~GeV for $\Omega_{ccb}$ and $11.0$~GeV for $\Omega_{cbb}$, with radial and orbital excitation patterns in good agreement with the results reported in the literature. The computed magnetic moments of the spin-$\tfrac{1}{2}$ and spin-$\tfrac{3}{2}$ states are consistent with the results of various approaches. A radial Regge analysis in the $(n_r, M^2)$ plane reveals approximately linear $P$-wave trajectories and mildly curved $S$-wave trajectories, with slope and intercept parameters that scale systematically with the heavy-quark content of the baryon. These results suggest that the nonrelativistic quark--diquark framework provides a reliable description of triply heavy baryons and serves as a useful reference for future experimental searches, particularly at LHCb.