Chiral Anomaly Effects and the BaBar Measurements of the $\gamma {\gamma }^{\ast }\to {\pi }^0$ Transition Form Factor

Abstract

The recent BaBar measurements of the $\gamma {\gamma }^{\ast }\to {\pi }^0$ transition form factor show spectacular deviation from perturbative QCD prediction for large space-like $Q^2$ up to $34\mathrm{Ge}{\mathrm{V}}^2$. When plotted against $Q^2$, $Q^{2}F(Q^2)$ shows steady increase with $Q^2$ in contrast with the flat $Q^2$ behavior predicted by perturbative QCD, and at $34\mathrm{Ge}{\mathrm{V}}^2$ is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes $Z^0\to {\pi }^0\gamma$, $e^{+}{e}^{-}\to {\pi }^0\gamma$ and apply our results to the ${\gamma }^{\ast }\gamma \to {\pi }^0$ transition form factor measured in the $e^{+}{e}^{-}\to e^{+}{e}^{-}{\pi }^0$ process with one highly virtual photon. We find that, the transition form factor $F(Q^2)$ behaves as $(\frac{m^2}{Q^2})\times (\ln (Q^2/m^2){)}^2$ and produces a striking agreement with the BaBar data for $Q^{2}F(Q^2)$ with $m=132\mathrm{MeV}$ which also reproduces very well the CLEO data at lower $Q^2$.

Comments: v4, LaTeX, 8 pages, one figure, minor changes(references), to appear in Int. J. Mod. Phys. A