Photon--meson transition form factors $γπ^0$, $γη$ and $γη'$ at low and moderately high $Q^2$

Abstract

We study photon--meson transition form factors $γ^*(Q^2)γ\to π^0,η,η'$ 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 $γπ^0$ 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 $γη$, $γη'$ and partial widths $η\toγγ$, $η'\toγγ$, in a perfect agreement with data.