Photon--meson transition form factors $\gamma {\pi }^0$, $\gamma \eta$ and $\gamma {\eta }^{\prime }$ at low and moderately high $Q^2$

Abstract

We study photon--meson transition form factors ${\gamma }^{\ast }(Q^2)\gamma \to {\pi }^0,\eta ,{\eta }^{\prime }$ at low and moderately high virtualities $Q^2$ of one of the photons, the second photon being real. For the description of the form factor at low $Q^2$, a nontrivial quark--antiquark $(q\bar{q})$ structure of the photon in the soft region is assumed, i.e. the photon is treated much like an ordinary vector meson. At large $Q^2$, along with a perturbative tail of the soft wave function, as it is for a hadron, the photon wave function contains also a standard QED point-like $q\bar{q}$ component. The latter provides the $1/Q^2$ behavior of the transition form factor at large $Q^2$ in accordance with perturbative QCD. Using the experimental results on $\gamma {\pi }^0$ form factor, we reconstruct the soft photon wave function which is found to have the structure similar to pion's, which has been formerly determined from a study of the elastic pion form factor. Assuming the universality of the ground--state pseudoscalar meson wave functions we calculate the transition form factors $\gamma \eta$, $\gamma {\eta }^{\prime }$ and partial widths $\eta \to \gamma \gamma$, ${\eta }^{\prime }\to \gamma \gamma$, in a perfect agreement with data.

Comments: 13 pages in twocoloumn RevTex, 7 .eps figures automatically inserted by epsfig.sty