Probing $NN\Omega_{ccc}$ three-body systems with the modern QCD $N\Omega_{ccc}$ interaction

TL;DR

This study explores the three-body $NN\Omega_{ccc}$ system using lattice QCD-derived potentials, finding a bound state in a specific configuration and analyzing its nature as a virtual state rather than a resonance.

Contribution

It provides the first investigation of the $NN\Omega_{ccc}$ three-body system with modern QCD interactions, identifying a bound state in a particular spin configuration.

Findings

A three-body bound state with $B_3 = -2.255$ MeV was found in the d-$\Omega_{ccc}$ configuration.

Other parameter sets did not produce bound states, indicating sensitivity to interaction details.

Complex scaling suggests the bound state is a virtual state, not a resonance.

Abstract

Newly, first-principles lattice QCD results at the physical pion mass, $ m_\pi \backsimeq 137.1 $ MeV, have been reported by the HAL QCD Collaboration for the S-wave interaction between the nucleon ($N$) and the triply charmed Omega baryon ($\Omega_{ccc}$). The $N\Omega_{ccc}$ potentials in the spin-1 $ \left(^{3}S_{1}\right) $ and spin-2 $ \left(^{5}S_{2}\right) $ channels were derived and found to be attractive, though no two-body bound state was supported in these channels. The present work investigates the $NN\Omega_{ccc}$ three-body system using the Malfliet-Tjon $NN$ potential. Analyses of spin-1, spin-averaged, and spin-2 $N\Omega_{ccc}$ channels (at Euclidean times 16, 17, 18) reveal a three-body bound state only for the d-$\Omega_{ccc}$ configuration with spin $(0)1/2^{+}$ and $t/a=16$. Its binding energy ($B_3 = -2.255$ MeV) lies slightly below the deuteron's ($B_d = -2.23$ MeV). Other parameter sets do not yield a bound state, and complex scaling analysis indicates these configurations correspond to virtual states rather than resonances. The Coulomb potential's role was also examined to differentiate charged states.