<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> </mml:math> a

This study employs the Faddeev formalism in configuration space to investigate the ${\mathrm{\ensuremath{\Omega}}}_{3c}NN$ cluster containing a triply charmed Omega baryon (${\mathrm{\ensuremath{\Omega}}}_{3c}$). Using the recently reported HAL QCD $S$-wave ${\mathrm{\ensuremath{\Omega}}}_{3c}N$ 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 ${\mathrm{\ensuremath{\Omega}}}_{3c}np$ system. We predict near-threshold resonances in the ${J}^{\ensuremath{\pi}}=5/{2}^{+}$ (maximal total spin) and ${J}^{\ensuremath{\pi}}=1/{2}^{+}$ (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 ${\mathrm{\ensuremath{\Omega}}}_{3c}{\mathrm{\ensuremath{\Omega}}}_{3c}N$ system likewise reveals no bound states, though a possible resonance is indicated.