Branching fraction measurement of $J/psi rightarrow K_S K_L$ and search for $J/psi rightarrow K_S K_S$

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