Branching fraction measurement of $J\mathrm{/}\psi \to K_S{K}_L$ and search for $J\mathrm{/}\psi \to K_S{K}_S$

Using a sample of $1.31\times {10}^9$ $J\mathrm{/}\psi$ events collected with the BESIII detector at the BEPCII collider, we study the decays of $J/\psi \rightarrow K_S K_L$and$K_S K_S$\mathrm{.}Thebranchingfractionof$J/\psi\rightarrow K_S K_L$isdeterminedtobe${\cal B}(J/\psi \rightarrow K_S K_L)=(1.93\pm0.01~(\rm{stat.})\pm0.05~(\rm{syst.}))\times10^{-4}$, which significantly improves on previous measurements. No clear signal is observed for the $J\mathrm{/}\psi \to K_S{K}_S$ process, and the upper limit at the 95% confidence level for its branching fraction is determined to be ${\cal B}(J/\psi \rightarrow K_S K_S)<1.4\times10^{-8}$, which improves on the previous searches by two orders in magnitude and reaches the order of the Einstein-Podolsky-Rosen expectation.