Chiral Anomaly, Triangle Loop and the \(\gamma\gamma^{*}\to \pi^{0}\) Transition Form Factor

Pham Tri Nang, Pham Xuan Yem


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 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 \(\gamma +\gamma ^{ * }  \to  \pi ^{0 }\) transition form factor measured in the single tag mode \(e^{ + }+e^{ - } \to   e^{ + }+ e^{ - }+\pi ^{0 }\) with one highly virtual photon \(\gamma ^{ * }\). 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 \((m^{2}/Q^{2}) \times  [\ln (Q^{2}/m^{2})]^{2}\)- shows a striking agreement with BaBar data for \(m \approx   132\) 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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