No spontaneous breakdown of chiral symmetry in Nambu–Jona-Lasinio model

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 σ– π field space. Although quarks acquire a constituent mass, σ and π turn out to have equal heavy masses of the order of the constituent quark mass.