We study the possible existence of bound states of three $\Omega_{bbb}$ baryons. We consider only $S$ wave interactions and we start from recent lattice QCD results which give a strongly attractive potential between two $\Omega_{bbb}$ baryons in the $^1S_0$ channel. We analyze different scenarios. At baryonic level, the $\Omega_{bbb}\Omega_{bbb}$ interaction could be understood to be basically spin-independent, so that the two contributing channels, $^1S_0$ and $^5S_2$, would have a very similar interaction. This baryonic analysis leads to the existence of bound states in the three-body system. At the quark level, repulsive effects would appear in the $^5S_2$ channel, making it more repulsive than the $^1S_0$ channel. We study the effect of such repulsion in terms of its range.

Comment: 9 pages, 2 figures