Universal behaviour of the $\gamma^*\gamma\to (\pi^0,\eta,\eta')$ transition form factors

Abstract

The photon transition form factors of $\pi$, $\eta$ and $\eta'$ are discussed in view of recent measurements. It is shown that the exact axial anomaly sum rule allows a precise comparison of all three form factors at high-$Q^2$ independent of the different structures and distribution amplitudes of the participating pseudoscalar mesons. We conclude: (i) The $\pi\gamma$ form factor reported by Belle is in excellent agreement with the non-strange I=0 component of the $\eta$ and $\eta'$ form factors obtained from the BaBar measurements. (ii) Within errors, the $\pi \gamma$ form factor from Belle is compatible with the asymptotic pQCD behavior, similar to the $\eta$ and $\eta'$ form factors from BaBar. Still, the best fits to the data sets of $\pi\gamma$, $\eta\gamma$, and $\eta'\gamma$ form factors favor a universal small logarithmic rise $Q^2 F_{P\gamma}(Q^2)\sim \log(Q^2)$.