Ω 3⁢𝑐 ⁢𝑁⁢𝑁 and Ω 3⁢𝑐 ⁢Ω 3⁢𝑐 ⁢𝑁 systems with HAL QCD potentials

Abstract

Here, this study employs the Faddeev formalism in configuration space to investigate the Ω 3⁢𝑐 ⁢𝑁⁢𝑁 cluster containing a triply charmed Omega baryon (Ω 3⁢𝑐 ). Using the recently reported HAL QCD 𝑆-wave Ω 3⁢𝑐 ⁢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 Ω 3⁢𝑐 ⁢𝑛⁢𝑝 system. We predict near-threshold resonances in the 𝐽 𝜋 =5/2 + (maximal total spin) and 𝐽 𝜋 =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 Ω 3⁢𝑐⁢ Ω 3⁢𝑐⁢ 𝑁 system likewise reveals no bound states, though a possible resonance is indicated.