The gluon content of the $\eta$ and ${\eta }^{\prime }$ mesons and the $\eta \gamma$, ${\eta }^{\prime }\gamma$ electromagnetic transition form factors

Abstract

We compute power-suppressed corrections to the \eta\gamma and \eta^{\prime}\gamma transition form factors Q^2F_{\eta(\eta^{\prime})\gamma}(Q^2) arising from the end point regions x \to 0,1 by employing the infrared-renormalon approach. The contribution to the form factors from the quark and gluon content of the \eta,\eta^{\prime} mesons is taken into account using for the \eta-\eta^{\prime} mixing the SU_f(3) singlet \eta_1 and octet \eta_8 basis. The theoretical predictions obtained this way are compared with the corresponding CLEO data and restrictions on the input parameters (Gegenbauer coefficients) B_2^q(\eta_1), B_2^g(\eta_1), and B_2^q(\eta_8) in the distribution amplitudes for the \eta_1,\eta_8 states with one nonasymptotic term are deduced. Comparison is made with the results from QCD perturbation theory.

Comments: 25 pages, RevTeX4 used. 9 figures as EPS files. Text significantly changed to include variation of theoretical parameters. Figures modified. Corrected typo in equation (34) and trivial mistake in ${\beta }_1$-coefficient. References added. Conclusions unchanged