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 $J^{\pi }=5/2^{+}$ (maximal total spin) and $J^{\pi }=1/2^{+}$ (minimal total spin) states, with resonance energies of 1.1 MeV below and 0.0 MeV at the three-body breakup threshold, respectively, at Euclidean time $t/a=16$. A similar analysis of the ${\mathrm{\Omega }}_{3c}{\mathrm{\Omega }}_{3c}N$ system likewise reveals no bound states, though a possible resonance is indicated.

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• Hypernuclei & mesic nuclei
• Few-body systems