Chiral anomaly, triangle loop and the the $γγ^{*}\to π^{0}$ form factor

The recent BaBar measurements of the $γγ^{*}\to π^{0}$ form factor show spectacular deviation from perturbative QCD computations for large space-like $Q^{2}$. At $34\,\rm GeV^{2}$ 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 $γ+ γ^* \to π^0$ form factor measured in the single tag mode $e^{+} + e^{-}\to e^{+} + e^{-} + π^{0}$ 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 $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ - shows a striking agreement with BaBar data for $m \approx 132\,\rm MeV$. 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.

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