Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

TL;DR

This paper uses local-duality QCD sum rules to analyze the form factors of light pseudoscalar mesons, finding reliable predictions at high momentum transfer and highlighting discrepancies in experimental data for the neutral pion form factor.

Contribution

It demonstrates that the local-duality sum rule provides accurate predictions for meson form factors at high Q^2 and discusses potential violations observed in BaBar data.

Findings

LD sum rule predictions align with data for eta and eta' form factors.

Pion elastic form factor suggests LD limit is reached at Q^2≈4-8 GeV^2.

BaBar results for π^0 form factor show unexpected growth at high Q^2.

Abstract

We revisit $F_\pi(Q^2)$ and $F_{P\gamma}(Q^2)$, $P=\pi,\eta,\eta'$, making use of the local-duality (LD) version of QCD sum rules. We give arguments, that the LD sum rule provides reliable predictions for these form factors at $Q^2 \ge 5-6$ GeV$^2$, the accuracy of the method increasing with $Q^2$ in this region. For the pion elastic form factor, the well-measured data at small $Q^2$ give a hint that the LD limit may be reached already at relatively low values of momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude that large deviations from LD in the region $Q^2=20-50$ GeV$^2$ seem very unlikely. The data on the ($\eta,\eta')\to\gamma\gamma^*$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the $\pi^0\to\gamma\gamma^*$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV$^2$, at odds with the $\eta,\eta'$ case and with the general properties expected for the LD sum rule.