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Singly heavy Cascade Baryon $Ξ^0_{c}$ \& $Ξ^-_{b}$ Spectroscopy in the Relativistic Framework of Independent Quark Model

In this work, the potential parameters of the independent quark model are systematically reduced using previously determined inputs from a broad range of baryons. The reduced-parameter formulation, developed within the relativistic Dirac formalism and employing a Martin-like potential, is then applied to the spectroscopy of the singly heavy baryons $Ξ_c^0$ and $Ξ_b^-$. This enables an explicit verification of the linear relation obtained between the potential parameters. Radially and orbitally excited state masses are calculated, and the resulting Regge trajectories are used to assign spin-parity to experimentally observed states. The states $Ξ_c^0(2923)$, $Ξ_c^0(3080)$, $Ξ_c^0(2882)$, and $Ξ_c^0(2970)$ are identified as having $J^P = \tfrac{1}{2}^-$, $\tfrac{3}{2}^+$, $\tfrac{3}{2}^-$, and $\tfrac{1}{2}^+$, respectively, while the observed $Ξ_b^-(6227)$ state is assigned $J^P = \tfrac{5}{2}^+$. To investigate the electromagnetic structure of these baryons, their magnetic moments and radiative decay widths are computed. Additionally, the two-body weak decay branching ratios of $Ξ_c^0$ are evaluated and contrasted with experimental data to assess the robustness of the approach. The two-body nonleptonic decays of $Ξ_b^-$ are also analyzed, providing predictions for branching ratios that may be tested in future experiments. Overall, the results demonstrate the effectiveness of the parameter-reduction procedure and support its applicability in the spectroscopy of baryons.