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

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.