On $\Omega_{3c}NN$ and $\Omega_{3c} \Omega_{3c} N$ systems with HAL QCD potentials

This study employs the Faddeev formalism in configuration space to investigate the $\Omega_{3c}NN$ cluster containing a triply charmed Omega baryon ($\Omega_{3c}$). Using the recently reported HAL QCD $S$-wave $\Omega_{3c}N$ potentials in the $^3S_1$ and $^5S_2$ channels, together with the MT-I--III nucleon--nucleon potential and neglecting the Coulomb force, we find no bound state for the $\Omega_{3c}np$ 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 $1.1~\mathrm{MeV}$ below and $0.0~\mathrm{MeV}$ at the three-body breakup threshold, respectively, at Euclidean time $t/a = 16$. A similar analysis of the $\Omega_{3c}\Omega_{3c}N$ system likewise reveals no bound states, though a possible resonance is indicated. The short-distance behavior of the HAL QCD $\Omega_{3c}N$ potential is also discussed.