Search for the decay $\eta'\to\gamma\gamma\eta$

Using a data sample of $1.31\times10^{9} ~J/\psi$ events collected with the BESIII detector, a search for $\eta'\to\gamma\gamma\eta$ via $J/\psi\to\gamma\eta'$ is performed for the first time. No significant $\eta'$ signal is observed in the $\gamma\gamma\eta$ invariant mass spectrum, and the %upper limit of the branching fraction of $\eta'\to\gamma\gamma\eta$ is determined to be less than $1.33 \times 10^{-4}$ at the 90$\%$ confidence level.