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

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.

Comments: 15 pages, 6 figures, 3 tables