Search for the double Dalitz decays $η/η' \to e^+e^-μ^+μ^-$ and $η' \to μ^+μ^-μ^+μ^-$
Using a data sample of $(10087 \pm 44) \times {10^{6}}$ $J/ψ$ events collected with the BESIII detector, we search for the decays $η/η'\to e^+e^-μ^+μ^-$ and $η' \to μ^+μ^-μ^+μ^-$ via the radiative decays $J/ψ\toγη$/$γη'$. No excess of events over expected background is observed for any of the decays of interest. At 90% confidence level, we report the first upper limits on the branching fractions of $η' \to e^{+}e^{-}μ^{+}μ^{-}$ and $η' \to μ^{+}μ^{-}μ^{+}μ^{-}$ to be $ 1.75 \times {10^{-6}}$ and $5.28 \times {10^{-7}}$, respectively. In addition, we set an upper limit on the branching fraction of $η\to e^{+}e^{-}μ^{+}μ^{-}$ to be $6.88 \times {10^{-6}}$, which improves the previous result by about two orders of magnitude.