The puzzle of the \pi -> \gamma \gamma* transition form factor

TL;DR

This paper investigates the transition form factors of pseudoscalar mesons using QCD sum rules, finding good agreement for eta and eta' but a puzzling discrepancy with BaBar data for the pion at high momentum transfer.

Contribution

It applies the local-duality QCD sum rule approach to meson transition form factors and highlights a surprising disagreement with experimental data for the pion form factor at high Q^2.

Findings

LD model describes eta and eta' form factors well

Discrepancy observed between LD predictions and BaBar data for pion form factor at high Q^2

Quantum mechanical analogy shows LD sum rule accuracy for bound states at Q^2 ≥ a few GeV^2

Abstract

We study the $P\to\gamma\,\gamma^*$ ($P=\pi^0,\eta,\eta'$) transition form factors by means of the local-duality (LD) version of QCD sum rules. For the case of $\eta$ and $\eta'$, the conventional LD model provides a good description of the existing data. However, for the $\pi$ form factor we find disagreement with recent BaBar results for high $Q^2$ even though the accuracy of the LD approximation is expected to increase with $Q^2$. It remains mysterious why the $\eta$ and $\eta'$ form factors to virtual photons, on the one hand, and the $\pi$ form factor, on the other hand, show a qualitatively different behaviour corresponding to a rising with $Q^2$ violation of local duality in the pion case. In a quantum mechanical example we show that, for a bound-state size of about 1 fm, the LD sum rule provides an accurate prediction for the form factor for $Q^2\ge$ a few GeV$^2$.