Chiral Symmetry Breaking and Pion Wave Function

Abstract

We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with 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 $σ$ mesons.