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

TL;DR

This paper demonstrates that the photon transition form factors of $$, $ta$, and $ta'$ mesons exhibit a universal behavior at high momentum transfer, consistent with axial anomaly sum rules and recent experimental data.

Contribution

It establishes a universal pattern for the transition form factors of these mesons using axial anomaly sum rules, aligning with recent measurements and pQCD predictions.

Findings

The Belle and BaBar measurements are in good agreement.

Form factors follow a universal logarithmic rise at high Q^2.

Data supports the asymptotic pQCD behavior for all three mesons.

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 $Q^2 F_{P\gamma}(Q^2)\sim \log(Q^2)$.