Excited $\Omega$ hyperon in charmful $\Omega_b$ weak decays

We investigate the sextet $b$-baryon decay processes $\Omega_b\to J/\psi\Omega^{(*)}$,where $\Omega^*$ represents the $1P$-, $1D$- and $2S$-wave excited $\Omega$ hyperons in the spectroscopy. Using the constituent quark model, we obtain ${\cal B}(\Omega_b \to J/\psi\Omega)=8.8\times 10^{-4}$, which agrees with the previous studies to the order of magnitude. By identifying $\Omega(2012)$ as $\Omega(1^2P_{3/2^-})$, ${\cal B}(\Omega_b \to J/\psi\Omega(2012))=1.1\times 10^{-3}$ can be similarly significant. Additionally, $\Omega(1^2D_{5/2^+})$ and $\Omega(1^4D_{3/2^+},1^4D_{5/2^+})$ states exhibit production rates of 0.5, and (0.6, 0.8), respectively, relative to their ground-state counterpart. Notably, our findings suggest that ${\cal B}(\Omega_b\to J/\psi\Omega(2^2S_{1/2^+},2^4S_{3/2^+}))$ are as large as $(4.5,20)\times 10^{-4}$, making them accessible to experiments at LHCb.