Spectroscopy of $ncnc\bar{c}$, $nnnn\bar{c}$, and $nnnc\bar{c}$ pentaquarks within the framework of Regge phenomenology

We investigate the mass spectra of the $ncnc\bar{c}$, $nnnn\bar{c}$, and $nnnc\bar{c}$ pentaquark systems, where $n$ denotes a light $u$ or $d$ quark, within a leading-order linear Regge approximation. The extension of the baryon intercept and inverse-slope additivity relations to these systems is implemented as a minimal cluster-additive ansatz for compact color-antitriplet diquarks, rather than assumed to be an exact QCD relation. By analyzing the corresponding trajectories in the $(J,M^2)$ plane, we first determine the allowed mass range of the ground-state $ncnc\bar{c}$ pentaquark and extract the associated Regge parameters. Using these inputs, we estimate the mass intervals of the excited states of the $ncnc\bar{c}$, $nnnn\bar{c}$, and $nnnc\bar{c}$ systems. We also obtain analytical mass-inequality relations. The resulting spectra exhibit a systematic ordering with increasing total spin and orbital excitation along the Regge trajectories. We further compare the predicted states with selected kinematically compatible meson–baryon thresholds as a qualitative guide to possible nearby channels. Our results provide a useful reference for future theoretical studies and may serve as a guide for experimental searches and spin-parity assignments of pentaquark candidates in the open- and hidden-charm sectors.