Anomalous Action of QCD from the General Quark Propagator
  The anomalous action of the chiral effective theory to $\mathcal{O}(p^4)$ is investigated by generalizing the consideration in \cite{ma02} with including the wave function part in the general quark propagator. It is found that the QCD dynamics dependence of the Wess-Zumino term is explicit and this dependence means that the QCD chiral symmetry must be broken dynamically in the low energy region for dynamically generating the Wess-Zumino term. In addition, we found that the next to leading order anomalous action in the momentum expansion of the chiral perturbation theory is gauge invariant and QCD dynamics dependent. 
Yong-Liang Ma, Qing Wang and Yue-Liang Wu