Search for $K_S^0$ invisible decays

Based on $(1.0087\pm 0.0044)\times {10}^{10}$ $J\mathrm{/}\psi$ events collected with the BESIII detector at the BEPCII $e^{+}{e}^{-}$ storage ring, we search for $K_S^0$ invisible decays via the $J\mathrm{/}\psi \to \phi K_S^0{K}_S^0$ process. No significant signal is observed, and the upper limit of the branching fraction of these invisible decays is set at 8.4 $\times$ ${10}^{-4}$ at the 90% confidence level. This is the first experimental search for $K_S^0$ invisible decays.