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The branching ratio of the electromagnetic rare decays $\eta\to\pi^0\gamma\gamma$ and $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ are analysed in terms of scalar and vector meson exchange contributions using the frameworks of the Linear Sigma Model and Vector Meson Dominance, respectively. The measured $\eta\to\pi^0\gamma\gamma$ process serves as a test of our approach while the non yet measured $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ reactions are predicted for the first time. Our prediction for the $\eta\to\pi^0\gamma\gamma$ decay agrees with recent experimental reported values, thus supporting the validity of our framework. Therefore, our predictions for the $\eta^\prime\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$ decays should be taken as a first indication of the possible values of the associated branching ratios. We hope these predictions to be interesting and useful for experiments such as KLOE-2, Crystal Ball, WASA, and BES-III where these processes are expected to be measured in the next future.

A first prediction of the electromagnetic rare decays \eta ^{\prime} \rightarrow \pi °\gamma \gamma and \eta ^{\prime} \rightarrow \eta \gamma \gamma