QCD inequalities for hadron interactions

TL;DR

This paper generalizes QCD mass inequalities to multi-hadron systems, showing that certain meson interactions are inherently repulsive and establishing bounds on nucleon mass, aligning with experimental and lattice QCD results.

Contribution

It introduces new generalized inequalities for multi-hadron systems in QCD, providing constraints on interactions and mass bounds not previously established.

Findings

Interactions between identical pseudo-scalar mesons of maximal isospin are repulsive.

No bound states can form in these meson channels.

A new lower bound on the nucleon mass, m_N ≥ 3/2 m_π, is derived.

Abstract

We derive generalisations of the Weingarten--Witten QCD mass inequalities for particular multi-hadron systems. For systems of any number of identical pseudo-scalar mesons of maximal isospin, these inequalities prove that interactions between the constituent mesons must be repulsive and that no bound states can form in these channels. Similar constraints in less symmetric systems are also extracted. These results are compatible with experimental results (where known) and recent lattice QCD calculations, and also lead to a more stringent bound on the nucleon mass than previously derived, $m_N \ge 3/2 m_\pi$.