Universal behaviour of the $γ^*γ\to (π^0,η,η')$ transition form factors

The photon transition form factors of $π$, $η$ and $η'$ 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 $πγ$ form factor reported by Belle is in excellent agreement with the non-strange I=0 component of the $η$ and $η'$ form factors obtained from the BaBar measurements. (ii) Within errors, the $πγ$ form factor from Belle is compatible with the asymptotic pQCD behavior, similar to the $η$ and $η'$ form factors from BaBar. Still, the best fits to the data sets of $πγ$, $ηγ$, and $η'γ$ form factors favor a universal small logarithmic rise $Q^2 F_{Pγ}(Q^2)\sim \log(Q^2)$.

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