Prediction of the  Ω_3cNN and  Ω_3cΩ_3cN  resonances with HAL QCD potentials.

In this study, we investigate the baryon clusters Ω_3cNN and  Ω_3cΩ_3cN, which contain a triply charmed Omega baryon (Ω_3c, C=3). The HAL QCD Collaboration has recently reported S-wave Ω_3c-nucleon potentials for the spin channels ³S₁ and ⁵S₂ and Ω_3cΩ_3c attractive interaction in the ¹S₀ spin channel. Our calculations confirm the result of HAL QCD Collaboration that the Ω_3cN two-body system in the ³S₁ and ⁵S₂ channels is not bound. We employ the Faddeev formalism in configuration space to investigate the Ω_3cNN  cluster using the same Ω_3cN  potential together with the MT-I-III nucleon-nucleon potential, neglecting the Coulomb force. No bound state is found for the Ω_3cnp system. However, we predict near-threshold resonances for the J^π=5/2⁺ (maximal total spin) and J^π=1/2⁺ (minimal total spin) states. The corresponding resonance energies are 1.1 MeV below and 0.0 MeV at the three-body breakup threshold, respectively. A similar analysis of the  Ω_3cΩ_3cN system likewise reveals no bound states, though a possible resonance is indicated. The short-range attractive behavior of the HAL QCD Ω_3cN potential is also discussed.