Constraints on the light pseudoscalar meson distribution amplitudes from their meson-photon transition form factors

The meson-photon transition form factors γγ*→P (P stands for π, η and η^') 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 nonvalence quarks' contributions have been taken into consideration. To be consistent, a unified wave function model is adopted to analyze these form factors. It is shown that with the proper charm component f_η^'ᶜ~-30 MeV and a moderate DA with B~0.30, the experimental data on Q²F_ηγ(Q²) and Q²F_η^'γ(Q²) in the whole Q² region can be explained simultaneously. Furthermore, a detailed discussion on the form factors' uncertainties caused by the constituent quark masses mq and mₛ, the parameter B, the mixing angle φ, and f_η^'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 cannot solve the puzzle for Q²F_πγ(Q²), especially to explain the behavior of the π-γ form factor within the whole Q² region consistently. We hope further experimental data on these form factors in the large Q² region can clarify the present situation.