Bound States of $\Omega$ Baryons in Light Nuclei

Abstract

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.

Comments: 13 pages, 3 figures