  The QCD evolution of the pion distribution amplitude (DA) $\phi_\pi(x,Q^2)$
is computed for several commonly used models. Our analysis includes the
nonperturbative form predicted by light-front holographic QCD, thus combining
the nonperturbative bound state dynamics of the pion with the perturbative ERBL
evolution of the pion distribution amplitude. We calculate the meson-photon
transition form factors for the $\pi^0$, $\eta$ and $\eta^\prime$ using the
hard-scattering formalism. We point out that a widely-used approximation of
replacing $\phi(x, (1-x) Q)$ with $\phi(x,Q)$ in the calculations will
unjustifiably reduce the predictions for the meson-photon transition form
factors. It is found that the four models of the pion DA discussed give very
different predictions for the $Q^2$ dependence of the meson-photon transition
form factors in the region of $Q^2>30$ GeV$^2$. More accurate measurements of
these transition form factors at the large $Q^2$ region will be able to
distinguish the four models of the pion DA. The rapid growth of the large $Q^2$
data for the pion-photon transition form factor reported by the BaBar
Collaboration is difficult to explain within the current framework of QCD. If
the BaBar data for the meson-photon transition form factor for the $\pi^0$ is
confirmed, it could indicate physics beyond-the-standard model, such as a
weakly-coupled elementary $C=+$ axial vector or pseudoscalar $z^0$ in the few
GeV domain, an elementary field which would provide the coupling $\gamma^*$
$\gamma$ to $z^0$ to $\pi^0$ at leading twist. Our analysis thus indicates the
importance of additional measurements of the pion-photon transition form factor
at large $Q^2$.
