  We explore the BaBar puzzle within the Regge approach. After reviewing the
chiral quark models in applications to PDF and PDA of the pion, we argue that
variants of these models, fulfilling the chiral anomaly, may in fact violate
the second Terazawa-West unitarity bound, which is based on unverified
assumptions for the real part of the amplitude. Consequently, the transition
form factor need not vanish at large values of the photon virtuality. Then we
show that the experimental data may be properly explained with incomplete
vector-meson dominance in a simple model with one state, as well as in more
sophisticated radial Regge models including infinitely many states. We also
consider the experimental constraint from the rare Z -> pi0 gamma decay, which
is comfortably satisfied in our approach. Finally, we point out that the photon
momentum asymmetry parameter may noticeably influence the precision fits to the
data.
