No Spontaneous Breakdown of Chiral Symmetry in Nambu-Jona-Lasinio Model

TL;DR

This paper argues that in the Nambu-Jona-Lasinio model, spontaneous chiral symmetry breaking does not occur as previously thought, because of strong fluctuations, resulting in equal heavy masses for sigma and pi fields instead of light pions.

Contribution

It challenges the conventional understanding by showing that strong fluctuations prevent spontaneous symmetry breaking in the model.

Findings

Quarks gain a constituent mass.

Sigma and pi fields have equal heavy masses.

No spontaneous chiral symmetry breaking occurs.

Abstract

We argue that the spontaneous breakdown of symmetry in the chirally symmetric Nambu--Jona-Lasinio model which was supposed to illustrate the origin of the low mass of pions in hadron physics does not occur due to strong fluctuations in the sigma - pi field space. Although quarks acquire a constituent mass, sigma and pi turn out to have equal heavy masses of the order of the constituent quark mass.