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

TL;DR

This paper revisits the triangle loop effects related to chiral anomaly to explain the BaBar measurements of the $ o o ext{form factor}$, proposing a logarithm squared behavior that aligns with experimental data, contrasting with perturbative QCD predictions.

Contribution

The paper introduces a novel logarithm squared dependence for the $ o o ext{form factor}$ based on triangle loop effects, providing a better fit to experimental data than traditional perturbative QCD models.

Findings

Form factor $F(Q^{2})$ behaves like $(m^{2}/Q^{2}) imes ( ext{ln}(Q^{2}/m^{2}))^{2}$.

The model with $m oughly 132$ MeV matches BaBar data.

Contrasts with flat form factors predicted by perturbative QCD.

Abstract

The recent BaBar measurements of the $\gamma\gamma^{*}\to \pi^{0}$ 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 $\gamma + \gamma^* \to \pi^0$ 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 $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ - 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.