Evolved QCD predictions for the meson-photon transition form factors

The QCD evolution of the pion distribution amplitude (DA) φ_π(x,Q²) is computed for several commonly used models. Our analysis includes the nonperturbative form predicted by light-front holographic QCD, thus combining the nonperturbative bound state dynamics of the pion with the perturbative ERBL evolution of the pion DA. We calculate the meson-photon transition form factors for the π⁰, η and η^' using the hard-scattering formalism. We point out that a widely-used approximation of replacing φ(x,(1-x)Q) with φ(x,Q) in the calculations will unjustifiably reduce the predictions for the meson-photon transition form factors. It is found that the four models of the pion DA discussed give very different predictions for the Q² dependence of the meson-photon transition form factors in the region of Q²>30 GeV². More accurate measurements of these transition form factors at the large Q² region will be able to distinguish different models of the pion DA. The rapid growth of the large Q² data for the pion-photon transition form factor reported by the BABAR Collaboration is difficult to explain within the current framework of QCD. If the BABAR data for the pion-photon transition form factor is confirmed, it could indicate physics beyond-the-standard model, such as a weakly coupled elementary $C=+$ axial vector or pseudoscalar z⁰ in the few GeV domain, an elementary field which would provide the coupling γ*γ→z⁰→π⁰ at leading twist. Our analysis thus indicates the importance of additional measurements of the pion-photon transition form factor at large Q².