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

Abstract: The Independent Quark Model, formulated for a three-body system within a relativistic framework, is applied to singly heavy baryons ( \Omega_c^0 ) and ( \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 ( \Omega_c^0(3000) ), ( \Omega_c^0(3050) ), ( \Omega_c^0(3067) ), ( \Omega_c^0(3120) ), and ( \Omega_c^0(3185) ) as well as possible spin assignments for the four newly observed excited states of ( \Omega_b^- ) ((\Omega_b^-(6316)), (\Omega_b^-(6330)), (\Omega_b^-(6340)), and (\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 ( \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 $\Omega_b^-$ are also predicted for future observations.