On the gluon content of the eta and eta' mesons

A phenomenological analysis of radiative $V\to P\gamma$ and $P\to V\gamma$ decays is performed with the purpose of determining the gluonic content of the $\eta$ and $\eta^\prime$ wave functions. Our results show that within our model there is no evidence for a gluonium contribution in the $\eta$, $Z_\eta^2=0.00\pm 0.12$, or the $\eta^\prime$, $Z_{\eta^\prime}^2=0.04\pm 0.09$. In terms of a mixing angle description this corresponds to $\phi_P=(41.4\pm 1.3)^\circ$ and $|\phi_{\eta^\prime G}|=(12\pm 13)^\circ$. In addition, the $\eta$-$\eta^\prime$ mixing angle is found to be $\phi_P=(41.5\pm 1.2)^\circ$ if we don't allow for a gluonium component.