$ΩNN$ and $ΩΩN$ states

Abstract

The lattice QCD analysis of the HAL QCD Collaboration has recently derived $ΩN$ and $ΩΩ$ interacting potentials with nearly physical quark masses ($m_π\simeq $ 146 MeV and $m_K \simeq $ 525 MeV). They found an attractive interaction in the $ΩN$ $^5S_2$ channel which supports a bound state with a central binding energy of 1.54 MeV. The $ΩΩ$ $^1S_0$ channel shows an overall attraction with a bound state with a central binding energy of 1.6 MeV. In this paper we looked closely at the $ΩNN$ and $ΩΩN$ three-body systems making use of the latest HAL QCD Collaboration $ΩN$ and $ΩΩ$ interactions. Our results show that the $Ωd$ system in the state with maximal spin $(I)J^P=(0)5/2^+$ is bound with a binding energy of about 20 MeV. The $(I)J^P=(1)3/2^+$ $Ωnn$ state presents a resonance decaying to $ΛΞn$ and $ΣΞn$, with a separation energy of $\sim$ 1 MeV. The $(I)J^P=(1/2)1/2^+$ $ΩΩN$ state also exhibits a resonance decaying to $ΛΞΩ$ and $ΣΞΩ$, with a separation energy of $\sim$ 4.6 MeV. We have calculated the contribution of the Coulomb potential to differentiate among the different charged states.