No Massless Pions in Nambu-Jona-Lasinio Model due to Chiral Fluctuations

TL;DR

This paper demonstrates that in the Nambu-Jona-Lasinio model, strong chiral fluctuations prevent the existence of massless pions, resulting in pions having a nonzero mass comparable to sigma mesons, contrary to common belief.

Contribution

It shows that chiral fluctuations eliminate massless pions in the NJL model, challenging the traditional view of spontaneous chiral symmetry breaking.

Findings

Pions have nonzero mass equal to sigma mesons.

Chiral fluctuations are strong enough to prevent massless pions.

Results are consistent across various cutoff schemes.

Abstract

In contrast to common belief, the chirally symmetric Nambu--Jona-Lasinio model does not contain massless pions, due to strong chiral fluctuations. Although quarks acquire spontaneously a nonzero constituent mass $M$, pions have a nonzero mass equal to the mass of $ \s $-mesons, both being of the order of $M$. This result is found in several cutoff schemes. Our derivation is nonperturbative, but involves a simple approximation (London limit) which should, however, receive only quantitative, no qualitative corrections.