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

Abstract

We revisit $F_π(Q^2)$ and $F_{Pγ}(Q^2)$, $P=π,η,η'$, 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 ($η,η')\toγγ^*$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the $π^0\toγγ^*$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV$^2$, at odds with the $η,η'$ case and with the general properties expected for the LD sum rule.