Singly heavy Omega Baryon ($Ω_c^0$ \& $Ω_b^-$) Spectroscopy in the Relativistic Framework of Independent Quark Model

The Independent Quark Model, formulated for a three-body system within a relativistic framework, is applied to singly heavy baryons \( Ω_c^0 \) and \( Ω_b^- \) to investigate their spectroscopic properties. A Martin-like potential with an equal mixture of scalar and vector components is employed, with potential parameters fitted using ground-state experimental data. The resulting mass spectra include both radial and orbital excitations. The spin-parity for the recently observed states \( Ω_c^0(3000) \), \( Ω_c^0(3050) \), \( Ω_c^0(3067) \), \( Ω_c^0(3120) \), and \( Ω_c^0(3185) \) as well as possible spin assignments for the four newly observed excited states of \( Ω_b^- \) (\(Ω_b^-(6316)\), \(Ω_b^-(6330)\), \(Ω_b^-(6340)\), and \(Ω_b^-(6350)\)) are proposed. The magnetic moments of the ground and first excited states are also calculated, along with radiative decay widths and transition magnetic moments. The non-leptonic weak decays of \( Ω_c^0 \) are analyzed, with decay widths and branching ratios computed and compared with experimental data to validate the predictive power of the model. The branching ratios for the non-leptonic decays of $Ω_b^-$ are also predicted for future observations.