Investigating $\Omega_c$ spectroscopy in two-body $\Omega_b$ decays

We investigate the $1S$-, $1P$-, $2S$-, and $1D$-wave $\Omega_c(css)$ spectroscopy through the non-leptonic decays of $\Omega_b^-$ baryon within the constituent quark model. For the lowest-lying $1S$-wave $\Omega_c$ state, we obtain the branching fractions ${\cal B}(\Omega_b^- \to \Omega_c^0 \pi^-,\Omega_c^0 \rho^-)=(1.2,6.3) \times 10^{-3}$, which are consistent with existing model predictions. For $\Omega_c(3000)$, $\Omega_c(3050)$, $\Omega_c(3065)$, and $\Omega_c(3090)$, observed in the proton-proton and $e^+ e^-$ collisions and interpreted as members of the $1P$-wave multiplet (collectively denoted as $\Omega_c^{**}$), we predict the branching fractions of $\Omega_b^-\to\Omega_c^{**}\pi^-,\Omega_c^{**}\rho^-$ at the level of $10^{-3}$. Assigning the newly observed $\Omega_c(3327)$ baryon to a $1D$-wave excitation with $J^P=5/2^+$ or $7/2^+$, we obtain ${\cal B}[\Omega_b^-\to \Omega_c(3327)^0\pi^-,\Omega_c(3327)^0\rho^-] =(2.0,5.7)\times 10^{-3}$ or $(4.6,0.8)\times 10^{-3}$, respectively. The pronounced differences between these two scenarios provide a clear discriminant that can be tested in future measurements at LHCb.