Bound States of $\Omega$ Baryons in Light Nuclei

We investigate bound states of light $\Omega_{3x}$-clusters ($x = s, c$), motivated by the $\Omega_{3s}N$ potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at $r < 0.4~\mathrm{fm}$ and parametrize the long-range component ($r > 0.4~\mathrm{fm}$) using a two-range Gaussian form. This procedure preserves the relevant two-body bound state energy while having a negligible effect on the $\Omega_{3s}NN$ and $\Omega_{3s}\Omega_{3s}N$ systems. An effective $\Omega_{3s}\alpha$ potential is then constructed by fitting a two-range Gaussian function to the long-range component of the folding potential, enabling calculations of the bound state energies of the $\Omega_{3s}\alpha$, $\Omega_{3s}\alpha\alpha$, and $\Omega_{3s}\Omega_{3s}\alpha$ systems. The regularization procedure leads to a substantial reduction in bound state energies compared to those obtained with the original potential. We further extend the analysis to $\Omega_{3c}$-cluster systems by introducing an $\Omega_{3c}N$ interaction, derived by comparing the existing $\Omega_{3s}\Omega_{3s}$ and $\Omega_{3c}\Omega_{3c}$ potentials. Our results suggest that several parametrizations predict bound states in $\Omega_{3c}$-containing clusters. Finally, the $\Omega_{3s}\Omega_{3s}$ interaction is described using a contact-like potential approach, motivated by the effective field theory.