Tribaryons with lattice QCD and one-boson exchange potentials

Abstract

Motivated by the existence of two-body hadronic molecules composed of $\Omega \Omega$, ${\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}$ predicted by lattice QCD simulations, we use the Gaussian expansion method to investigate whether three-body systems composed of $\Omega \Omega \Omega$, ${\Omega }_{ccc}{\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}{\Omega }_{bbb}$ can bind with the two-body ${}^1{S}_0$ interactions provided by lattice QCD. Our results show that none of the three-body systems bind. On the other hand, we find that with the one-boson exchange potentials the $\Omega \Omega \Omega$ system develops a bound state, for which the ${}^5{S}_2$ interaction plays an important role. Our studies support the existence of the ${\frac{3}{2}}^{+}$ $\Omega \Omega \Omega$ bound state and the nonexistence of the ${\frac{3}{2}}^{+}$ ${\Omega }_{ccc}{\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}{\Omega }_{bbb}$ bound states, due to the suppressed ${}^5{S}_2$ interactions in heavier systems.

Comments: 6 pages, 2 figures, 4 tables, to appear in PRD as a letter