  Many meson processes are related to the U_A(1) axial anomaly, present in the
Feynman graphs where fermion loops connect axial vertices with vector vertices.
However, the coupling of pseudoscalar mesons to quarks does not have to be
formulated via axial vertices. The pseudoscalar coupling is also possible, and
this approach is especially natural on the level of the quark substructure of
hadrons. In this paper we point out the advantages of calculating these
processes using (instead of the anomalous graphs) the graphs where axial
vertices are replaced by pseudoscalar vertices. We elaborate especially the
case of the processes related to the Abelian axial anomaly of QED, but we
speculate that it seems possible that effects of the non-Abelian axial anomaly
of QCD can be accounted for in an analogous way.
