Branching fraction measurement of J /ψ →kSKL and search for J /ψ →kSKS

Using a sample of 1.31×109 J/ψ events collected with the BESIII detector at the BEPCII collider, we study the decays of J/ψ→KSKL and KSKS. The branching fraction of J/ψ→KSKL is determined to be B(J/ψ→KSKL)=(1.93±0.01(stat)±0.05(syst))×10-4, which significantly improves on previous measurements. No clear signal is observed for the J/ψ→KSKS process, and the upper limit at the 95% confidence level for its branching fraction is determined to be B(J/ψ→KSKS)<1.4×10-8, which improves on the previous searches by 2 orders in magnitude and reaches the order of the Einstein-Podolsky-Rosen expectation.