Stability of the pion and the pattern of chiral symmetry breaking

TL;DR

This paper explores the stability of the pion within the chiral quark model, revealing that its zero pressure, linked to chiral symmetry breaking, is consistent beyond the chiral limit, highlighting fundamental symmetry principles.

Contribution

It demonstrates that pion stability and zero pressure naturally emerge from the Gell-Mann-Oakes-Renner relation in the chiral quark model beyond the chiral limit.

Findings

Pion pressure vanishes nontrivially via the Gell-Mann-Oakes-Renner relation.

Pion stability is deeply connected to spontaneous chiral symmetry breaking.

Physical quantities related to the energy-momentum tensor are discussed.

Abstract

We investigate the pressure of the pion, which should be equal to zero to ensure the stability of the pion, within the framework of the chiral quark model beyond the chiral limit. The pressure of the pion turns out to vanish nontrivially by the Gell-Mann-Oakes-Renner relation within the present framework. It implies that the stability of the pion might be deeply rooted in spontaneous chiral symmetry breaking. We also discuss physical quantities relevant to the energy-momentum tensor operator.