Photon-meson transition form factorsγπ0,γη, andγη′at low and moderately highQ2

Abstract

We study photon-meson transition form factors ${\ensuremath{\gamma}}^{*}{(Q}^{2})\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$ at low and moderately high ${Q}^{2}$ assuming a nontrivial hadronlike $q\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}$ structure of the photon in the soft region. In the hard region, the $q\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}$ photon wave function contains both a perturbative tail of the soft wave function such as the wave function of an ordinary hadron and a standard QED pointlike $q\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}$ component. The latter provides the ${1/Q}^{2}$ asymptotical behavior of the transition form factor in accordance with QCD. The data on the $\ensuremath{\gamma}{\ensuremath{\pi}}^{0}$ form factor are used for fixing the soft photon wave function which is found to have the same structure as the soft wave function of the pion reconstructed from the elastic pion form factor. Assuming universality of the ground-state pseudoscalar meson wave functions we calculate the $\ensuremath{\gamma}\ensuremath{\eta}$, $\ensuremath{\gamma}{\ensuremath{\eta}}^{\ensuremath{'}}$ transition form factors and $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ partial widths and found them to be in perfect agreement with the data.