Chiral anomaly, triangle loop and the the $\gamma {\gamma }^{\ast }\to {\pi }^0$ form factor

The recent BaBar measurements of the $\gamma {\gamma }^{\ast }\to {\pi }^0$ form factor show spectacular deviation from perturbative QCD computations for large space-like $Q^2$. At $34\mathrm{G}\mathrm{e}{\mathrm{V}}^2$ the data are more than 50% larger than theoretical predictions. Stimulated by these new experimental results, we revisit our previous paper on triangle loop effects related to chiral anomaly, and apply our method to the $\gamma +{\gamma }^{\ast }\to {\pi }^0$ form factor measured in the single tag mode $e^{+}+e^{-}\to e^{+}+e^{-}+{\pi }^0$ with one highly virtual photon. The resultant form factor $F(Q^2)$ - which depends on only one parameter (the mass $m$ of up, down quark circulating in the triangle loop) behaves like $(\frac{m^2}{Q^2})\times (\ln (Q^2\mathrm{/}{m}^2){)}^2$ - shows a striking agreement with BaBar data for $m\approx 132\mathrm{M}\mathrm{e}\mathrm{V}$. The rising logarithm squared form factor, surprisingly unnoticed in the literature, is in sharp contrast with the rather flat ones derived from perturbative QCD approaches.