Singly heavy Omega Baryon (${\mathrm{\Omega }}_c^0$ \& ${\mathrm{\Omega }}_b^{-}$) 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 ${\mathrm{\Omega }}_c^0$ and ${\mathrm{\Omega }}_b^{-}$ 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 ${\mathrm{\Omega }}_c^0(3000)$, ${\mathrm{\Omega }}_c^0(3050)$, ${\mathrm{\Omega }}_c^0(3067)$, ${\mathrm{\Omega }}_c^0(3120)$, and ${\mathrm{\Omega }}_c^0(3185)$ as well as possible spin assignments for the four newly observed excited states of ${\mathrm{\Omega }}_b^{-}$ (${\mathrm{\Omega }}_b^{-}(6316)$, ${\mathrm{\Omega }}_b^{-}(6330)$, ${\mathrm{\Omega }}_b^{-}(6340)$, and ${\mathrm{\Omega }}_b^{-}(6350)$) 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 ${\mathrm{\Omega }}_c^0$ 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 ${\mathrm{\Omega }}_b^{-}$ are also predicted for future observations.