Resolving the Puzzle of the Pion-Photon Transition Form Factor

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 $\eta,$ $\eta',$ 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 $Q^2.$