Gauge Invariance and the Electromagnetic Current of Composite Pions

Abstract

The Global Color-symmetry Model of QCD is extended to deal with a background electromagnetic field and the associated conserved current is identified for composite $\bar{q}q$ pion modes of the model. Although the analysis is limited to tree level in the bilocal fields that bosonize the model, the identified photon-pion vertex produces the charge form factor associated with ladder Bethe-Salpeter pion amplitudes. A Ward-Takahashi identity for this vertex is derived in terms of the effective inverse propagator for the equivalent local pion field and the intrinsic ladder Bethe-Salpeter amplitudes. This identity is then used to illustrate gauge invariance by showing that identical vertex information is produced from the gauge change of the free action once proper account is taken of the gauge transformation properties of the bilocal pion fields. Comments are made on the location of the vector dominance mechanism in this treatment.