Chiral symmetry breaking and the pion wave function

We consider here chiral symmetry breaking through a nontrivial vacuum structure with quark-antiquark condensates. We then relate the condensate function to the wave function of the pion as a Goldstone mode. This simultaneously yields the pion also as a quark-antiquark bound state as a localized zero mode in vacuum. We illustrate the above through the Nambu—Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $\sigma$ mesons.