Resolving the Puzzle of the Pion-Photon Transition Form Factor

Abstract

We investigate the form factors for pseudoscalar-meson-photon transitions by means of dispersive QCD sum rules and demonstrate that most of the measurements done so far (in particular, those by BaBar for $\eta ,$ ${\eta }^{\prime },$ and ${\eta }_c$ and those by Belle for ${\pi }^0$) are, on the one hand, compatible with each other and with the saturation required by factorization theorems obtained from perturbative QCD and, on the other hand, give a hint that saturation is effective already at relatively low momentum transfers $Q^2;$ this hypothesis is supported by experimental data for the charged-pion elastic form factor available in the range Q^2\approx2-4\;\{GeV}^2. The only exception are the BaBar results for the ${\pi }^0\gamma$ transition form factor, which do not fit into such picture. We point out that results expected from SHMS at JLab on the pion elastic form factor in the region Q^2\approx5-8\;\{GeV}^2 will provide the ultimate test of saturation and factorization and strongly impact our general view of the form factors up to infinitely large $Q^2.$

Comments: 7 pages, 4 figures, talk presented at the European Physical Society Conference on High Energy Physics - EPS-HEP2013, 18-24 July 2013, Stockholm, Sweden