Flavor symmetry breaking and mixing effects in the $\eta \gamma$ and $\eta'\gamma$ transition form factors

Abstract

We reanalyze the \(\eta\gamma\) and \(\eta'\gamma\) transition form factors within the modified hard scattering approach on the basis of new experimental data from CLEO [1] and L3 [2]. Our approach perfectly describes the experimental data over a wide range of the virtuality of the probing photon, 1 GeV\(^2\leq Q^2 \leq 15\) GeV\(^2\). The analysis provides hints that the conventional flavor octet-singlet scheme for the \(\eta\)-\(\eta'\) mixing is too simple. A more general mixing scheme on the other hand, involving two mixing angles, leads to a very good description of the transition form factors and also accounts for the two-photon decay widths of the \(\eta\) and \(\eta'\) mesons as well as for the ratio of the widths for the \(J/\psi \to \eta'\gamma\) and \(J/\psi \to \eta\gamma\) decays. We also investigate the questions of possible deviations of the \(\eta\) and \(\eta'\) distribution amplitudes from the asymptotic form and of eventual intrinsic charm in the \(\eta\) and \(\eta'\) mesons. We estimate the charm decay constant of the \(\eta'\) meson to lie within the range \(-65\) MeV \(\leq f_{\eta'}^c\leq 15\) MeV.