Search for $eta$ and $eta$ Invisible Decays in $J/psitophieta$ and $phieta$

Using a sample of $(225.3pm 2.8)times 10^{6}$ $J/psi$ decays collected with the BESIII detector at BEPCII, searches for invisible decays of $eta$ and $eta^prime$ in $J/psitophieta$ and $phieta^prime$ are performed. Decays of $phi to K^{+}K^{-}$ are used to tag the $eta$ and $eta^prime$ decays. No signals above background are found for the invisible decays, and upper limits at the 90% confidence level are determined to be $2.58times10^{-4}$ for the ratio $frac{mathcal{B}(etatorm{invisible})}{mathcal{B}(etatogammagamma)}$ and $2.39times10^{-2}$ for $frac{mathcal{B}(eta^primetorm{invisible})}{mathcal{B}(eta^prime togammagamma)}$.