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

Abstract

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 ${}^3{S}_1$ 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 ${\Omega }_{3c}np$ 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.

Comments: 7 pages, 3 figures