Constraints on the Light Pseudoscalar Meson Distribution Amplitudes from Their Meson-Photon Transition Form Factors

TL;DR

This paper calculates meson-photon transition form factors using light-cone perturbative QCD, constraining pseudoscalar meson distribution amplitudes and analyzing their compatibility with experimental data.

Contribution

It provides a unified analysis of meson-photon transition form factors considering both valence and non-valence quark contributions, and discusses parameter effects on the form factors.

Findings

Proper charm component and moderate DA can explain experimental data.

Adjusting parameters improves form factor fits but cannot fully resolve the pion form factor puzzle.

Further experimental data are needed for clarification.

Abstract

The meson-photon transition form factors $\gamma\gamma^*\to P$ ($P$ stands for $\pi$, $\eta$ and $\eta'$) provide strong constraints on the distribution amplitudes of the pseudoscalar mesons. In this paper, these transition form factors are calculated under the light-cone perturbative QCD approach, in which both the valence and non-valence quarks' contributions have been taken into consideration. To be consistent, an unified wavefunction model is adopted to analyze these form factors. It is shown that with proper charm component $f^{c}_{\eta'}\sim -30$ MeV and a moderate DA with $B\sim 0.30$, the experimental data on $Q^{2}F_{\eta\gamma}(Q^2)$ and $Q^{2}F_{\eta'\gamma}(Q^2)$ in whole $Q^2$ region can be explained simultaneously. Further more, a detailed discussion on the form factors' uncertainties caused by the constituent quark masses $m_q$ and $m_s$, the parameter $B$, the mixing angle $\phi$ and $f_{\eta'}^c$ are presented. It is found that by adjusting these parameters within their reasonable regions, one can improve the form factor to a certain degree but can not solve the puzzle for $Q^{2}F_{\pi\gamma}(Q^2)$, especially to explain the behavior of $\pi-\gamma$ form factor within the whole $Q^2$ region consistently. We hope further experimental data on these form factors in the large $Q^2$ region can clarify the present situation.