Pauli principle forbids $\Omega_{QQQ}\Omega_{QQQ}\Omega_{QQQ}$ bound states

TL;DR

This paper argues that the Pauli principle prevents the existence of bound states of three $ ext{Omega}_{QQQ}$ baryons, despite attractive interactions observed in lattice QCD studies for two-baryon systems.

Contribution

It provides a theoretical analysis showing that quantum mechanical constraints inhibit the formation of three-baryon bound states of $ ext{Omega}_{QQQ}$ baryons due to the Pauli principle.

Findings

Pauli principle forbids $ ext{Omega}_{QQQ} ext{Omega}_{QQQ} ext{Omega}_{QQQ}$ bound states

Two effects of Pauli principle at baryon and quark levels prevent binding

Bound states are unlikely in any flavor sector

Abstract

Lattice QCD studies have shown the attractive character of the $^1S_0$ $\Omega_{QQQ}\Omega_{QQQ}$, $Q=s,c,b$, interaction, predicting deeply bound states as the mass of the heavy quark increases. This has led to the question of the possible existence of bound states of more than two $\Omega_{QQQ}$ baryons, in particular $\Omega_{QQQ}\Omega_{QQQ}\Omega_{QQQ}$ bound states. We discuss how these states might not exist in nature in any flavor sector. The reason would be due to the simultaneous action of two consequences of the Pauli principle in the different partial waves: one at the baryon level, affecting the $^1S_0$ partial wave, and the other due to the quark substructure, affecting the $^5S_2$ partial wave.