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The branching ratio of the electromagnetic rare decays$\eta\to\pi^0\gamma\gamma$ and $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ areanalysed in terms of scalar and vector meson exchange contributions using theframeworks of the Linear Sigma Model and Vector Meson Dominance, respectively.The measured $\eta\to\pi^0\gamma\gamma$ process serves as a test of ourapproach 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 reportedvalues, thus supporting the validity of our framework. Therefore, ourpredictions for the $\eta^\prime\to\pi^0\gamma\gamma$ and$\eta^\prime\to\eta\gamma\gamma$ decays should be taken as a first indicationof the possible values of the associated branching ratios. We hope thesepredictions to be interesting and useful for experiments such as KLOE-2,Crystal Ball, WASA, and BES-III where these processes are expected to bemeasured in the next future.

A first prediction of the electromagnetic rare decays $\eta^\prime\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$