Abelian anomaly and neutral pion production

TL;DR

This paper demonstrates that fully self-consistent treatments of the pion's properties do not exceed the asymptotic limit of the transition form factor, and shows that contact interactions produce unrealistic flat pion distribution amplitudes incompatible with experimental data.

Contribution

It provides a detailed analysis contrasting contact interactions with QCD-like interactions, clarifying their impact on pion form factors and distribution amplitudes, and challenges interpretations of BaBar data.

Findings

Contact interactions yield flat, endpoint nonvanishing pion distribution amplitudes.

QCD-like interactions produce soft pions with form factors consistent with experiments.

The asymptotic limit of the transition form factor is not exceeded at finite spacelike momenta.

Abstract

We show that in fully-self-consistent treatments of the pion; namely, its static properties and elastic and transition form factors, the asymptotic limit of the product Q^2 G_{\gamma * \gamma \pi ^0}(Q^2), determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer. Furthermore, in such a treatment of a vector-vector contact-interaction one obtains a \gamma * \gamma -> \pi ^0 transition form factor that disagrees markedly with all available data. We explain that the contact interaction produces a pion distribution amplitude which is flat and nonvanishing at the endpoints. This amplitude characterises a pointlike pion bound-state. Such a state has the hardest possible form factors; i.e., form factors which become constant at large momentum transfers and hence are in striking disagreement with completed experiments. On the other hand, interactions with QCD-like behaviour produce soft pions, a valence-quark distribution amplitude that vanishes as ~(1-x)^2 for x~1, and results that agree with the bulk of existing data. Our analysis supports a view that the large-Q^2 data obtained by the BaBar Collaboration is not an accurate measure of the \gamma * \gamma -> \pi ^0 form factor.