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

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.