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

Abstract

We revisit $F_{\pi }(Q^2)$ and $F_{P\gamma }(Q^2)$, $P=\pi ,\eta ,{\eta }^{\prime }$, 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 ($\eta ,{\eta }^{\prime })\to \gamma {\gamma }^{\ast }$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the ${\pi }^0\to \gamma {\gamma }^{\ast }$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV${}^2$, at odds with the $\eta ,{\eta }^{\prime }$ case and with the general properties expected for the LD sum rule.

Comments: 17 pages. arXiv admin note: substantial text overlap with arXiv:1103.3781 and arXiv:1110.6904