Pion transition form factor and distribution amplitudes in large-NcRegge models

Abstract

We analyze the $\ensuremath{\pi}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}$ amplitude in the framework of radial Regge models in the large-${N}_{c}$ limit. With the assumption of similarity of the asymptotic Regge $\ensuremath{\rho}$ and $\ensuremath{\omega}$ meson spectra we find that the pion distribution amplitude is constant in the large-${N}_{c}$ limit at the scale ${Q}_{0}$ where the QCD radiative corrections are absent---a result found earlier in a class of chiral quark models. We discuss the constraints on the couplings from the anomaly and from the limit of large photon virtualities, and find that the coupling of the pion to excited $\ensuremath{\rho}$ and $\ensuremath{\omega}$ mesons must be asymptotically constant. We also discuss the effects of the QCD evolution on the pion electromagnetic transition form factor. Finally, we use the Regge model to evaluate the slope of the form factor at zero momentum and compare the value to the experiment, finding very reasonable agreement.