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

## TL;DR

This paper investigates three-body systems involving $\\Omega$ baryons using lattice QCD potentials, predicting bound and resonant states relevant for understanding hyperon interactions.

## Contribution

It provides the first detailed analysis of $\\Omega NN$ and $\\Omega\\Omega N$ states using recent lattice QCD potentials, identifying bound and resonant states with specific quantum numbers.

## Key findings

- The $\\Omega d$ system with $(I)J^P=0 5/2^+$ is bound with about 20 MeV energy.
- The $(I)J^P=1 3/2^+$ $\\Omega nn$ state is a resonance decaying to $\\Lambda \\Xi n$ and $\\Sigma \\Xi n$.
- The $(I)J^P=1/2 1/2^+$ $\\Omega\\Omega N$ state is a resonance decaying to $\\Lambda \\Xi \\Omega$ and $\\Sigma \\Xi \\Omega$.

## 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 $\Omega N$ $^5S_2$ channel which supports a bound state with a central binding energy of 1.54 MeV. The $\Omega \Omega$ $^1S_0$ 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 $\Omega NN$ 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.