$\Omega NN$ and $\Omega \Omega N$ states

Abstract

The lattice QCD analysis of the HAL QCD Collaboration has recently derived $\Omega N$ and $\Omega \Omega$ interacting potentials with nearly physical quark masses ($m_{\pi }\simeq$ 146 MeV and $m_K\simeq$ 525 MeV). They found an attractive interaction in the $\Omega N$ ${}^5{S}_2$ channel which supports a bound state with a central binding energy of 1.54 MeV. The $\Omega \Omega$ ${}^1{S}_0$ 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 $\Omega NN$ and $\Omega \Omega N$ three-body systems making use of the latest HAL QCD Collaboration $\Omega N$ and $\Omega \Omega$ interactions. Our results show that the $\Omega d$ system in the state with maximal spin $(I)J^P=(0)5/2^{+}$ is bound with a binding energy of about 20 MeV. The $(I)J^P=(1)3/2^{+}$ $\Omega nn$ state presents a resonance decaying to $\Lambda \Xi n$ and $\Sigma \Xi n$, with a separation energy of $\sim$ 1 MeV. The $(I)J^P=(1/2)1/2^{+}$ $\Omega \Omega N$ state also exhibits a resonance decaying to $\Lambda \Xi \Omega$ and $\Sigma \Xi \Omega$, 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.

Comments: 14 pages. Accepted for publication in Phys. Rev. C