Electromagnetic transition form factors of light mesons

Abstract

We study selected meson transition processes and associated form factors within a model of QCD based on the Dyson-Schwinger equations truncated to the ladder-rainbow level. The infrared structure of the ladder-rainbow kernel is described by two parameters, the ultraviolet behavior is fixed by the one-loop renormalization group behavior of QCD. The work is restricted to the u and d quark sector and allows a Poincar\'e-covariant study of the radiative decays $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}\ensuremath{\pi}\ensuremath{\gamma},$ $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\pi}\ensuremath{\gamma},$ and ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}.$ Particular attention is paid to the form factors for the associated transitions ${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma},$ ${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{*},$ ${\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}}\ensuremath{\rho},$ and ${\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}\ensuremath{\pi}.$ The latter two processes are of interest as contributors to meson electroproduction from hadronic targets away from the s-channel resonance region. We use the present QCD model to explore limitations to the assumption that coupling to a t-channel virtual $\overline{q}q$ correlation can be modeled as meson exchange.