Universal behaviour of the ${\gamma }^{\ast }\gamma \to ({\pi }^0,\eta ,{\eta }^{\prime })$ transition form factors

Abstract

The photon transition form factors of $\pi$, $\eta$ and ${\eta }^{\prime }$ 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 ${\eta }^{\prime }$ 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 ${\eta }^{\prime }$ form factors from BaBar. Still, the best fits to the data sets of $\pi \gamma$, $\eta \gamma$, and ${\eta }^{\prime }\gamma$ form factors favor a universal small logarithmic rise $Q^2{F}_{P\gamma }(Q^2)\sim \log (Q^2)$.

arXiv comment5 pages

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