  We point out the problems affecting most quark--antiquark bound state
approaches when they are faced with the electromagnetic processes dominated by
Abelian axial anomaly. However, these problems are resolved in the consistently
coupled Schwinger-Dyson and Bethe-Salpeter approach. Using one of the most
successful variants of this approach, we find the dynamically dressed
propagators of the light u and d quarks, as well as the heavy c and b quarks,
and find the Bethe-Salpeter amplitudes for their bound states pi0, eta_c and
\eta_b. Thanks to incorporating the dynamical chiral symmetry breaking, the
pion simultaneously appears as the (pseudo)Goldstone boson. We give the
theoretical predictions for the gamma-gamma decay widths of pi0, eta_c and
eta_b, and for the pi0 gamma* -> gamma transition form factor, and compare them
with experiment. In the chiral limit, the axial-anomaly result for
pi0->gamma-gamma is reproduced analytically in the consistently coupled
Schwinger-Dyson and Bethe-Salpeter approach, provided that the quark-photon
vertex is dressed consistently with the quark propagator, so that the vector
Ward-Takahashi identity of QED is obeyed. On the other hand, the present
approach is also capable of quantitatively describing systems of heavy quarks,
concretely eta_c and possibly eta_b, and their gamma-gamma decays. We discuss
the reasons for the broad phenomenological success of the bound-state approach
of Jain and Munczek.
