Search for the double Dalitz decays $ \eta /{\eta }^{\prime }\to {e}^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ and $ {\eta }^{\prime }\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$

Using a data sample of $ (10087\pm 44)\times {10}^{6}$ $ J/\psi $ events collected with the BESIII detector, we search for the decays $ \eta /{\eta }^{\prime }\to {e}^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ and $ {\eta }^{\prime }\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ via the radiative decays $ J/\psi \to \gamma \eta /\gamma {\eta }^{\prime }$. No excess of events over expected background is observed for any of the decays of interest. At 90% confidence level, we report the first upper limits on the branching fractions of $ {\eta }^{\prime }\to {e}^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ and $ {\eta }^{\prime }\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ to be $ 1.75\times {10}^{-6}$ and $ 5.28\times {10}^{-7}$, respectively. In addition, we set an upper limit on the branching fraction of $ \eta \to {e}^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ to be $ 6.88\times {10}^{-6}$, which improves the previous result by about two orders of magnitude.