Evolved QCD predictions for the meson-photon transition form factors

The QCD evolution of the pion distribution amplitude (DA) $\phi_\pi(x,Q^2)$ 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 distribution amplitude. We calculate the meson-photon transition form factors for the $\pi^0$, $\eta$ and $\eta^\prime$ using the hard-scattering formalism. We point out that a widely-used approximation of replacing $\phi(x, (1-x) Q)$ with $\phi(x,Q)$ 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 $Q^2$ dependence of the meson-photon transition form factors in the region of $Q^2>30$ GeV$^2$. More accurate measurements of these transition form factors at the large $Q^2$ region will be able to distinguish the four models of the pion DA. The rapid growth of the large $Q^2$ 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 meson-photon transition form factor for the $\pi^0$ is confirmed, it could indicate physics beyond-the-standard model, such as a weakly-coupled elementary $C=+$ axial vector or pseudoscalar $z^0$ in the few GeV domain, an elementary field which would provide the coupling $\gamma^*$ $\gamma$ to $z^0$ to $\pi^0$ at leading twist. Our analysis thus indicates the importance of additional measurements of the pion-photon transition form factor at large $Q^2$.