Off-Shell Axial Anomaly via the \gamma^* \pi^0 -> \gamma Transition

Abstract

The $\gamma^* \pi^0 \rightarrow \gamma$ form factor, including the extension off the pion mass-shell, is obtained from a generalized impulse approximation within a QCD-based model field theory known to provide an excellent description of the pion charge form factor. This approach implements dressing of the vertex functions and propagators consistent with dynamical chiral symmetry breaking, gauge invariance, quark confinement and perturbative QCD. Soft nonperturbative behavior, dictated by the axial anomaly, is found to evolve to the perturbative QCD limit only for \mbox{$Q^2 \geq 20~{\rm GeV}^2$}.