On ${\mathrm{\Omega }}_{3c}NN$ and ${\mathrm{\Omega }}_{3c}{\mathrm{\Omega }}_{3c}N$ systems with HAL QCD potentials

This study employs the Faddeev formalism in configuration space to investigate the ${\mathrm{\Omega }}_{3c}NN$ cluster containing a triply charmed Omega baryon (${\mathrm{\Omega }}_{3c}$). Using the recently reported HAL QCD $S$-wave ${\mathrm{\Omega }}_{3c}N$ potentials in the ${}^3{S}_1$ and ${}^5{S}_2$ channels, together with the MT-I–III nucleon–nucleon potential and neglecting the Coulomb force, we find no bound state for the ${\mathrm{\Omega }}_{3c}np$ system. We predict near-threshold resonances in the $J^{\pi }=5\mathrm{/}{2}^{+}$ (maximal total spin) and $J^{\pi }=1\mathrm{/}{2}^{+}$ (minimal total spin) states, with resonance energies of $1.1\mathrm{M}\mathrm{e}\mathrm{V}$ below and $0.0\mathrm{M}\mathrm{e}\mathrm{V}$ at the three-body breakup threshold, respectively, at Euclidean time $t\mathrm{/}a=16$. A similar analysis of the ${\mathrm{\Omega }}_{3c}{\mathrm{\Omega }}_{3c}N$ system likewise reveals no bound states, though a possible resonance is indicated. The short-distance behavior of the HAL QCD ${\mathrm{\Omega }}_{3c}N$ potential is also discussed.