Measurement of $\mathcal{B}(J/\psi \to \eta' e^+ e^- $) and search for a dark photon

Using a data sample of $(1310.6\pm7.0)\times10^{6}$ $J/\psi$ decay events collected with the BESIII detector at BEPCII, we study the electromagnetic Dalitz decay $J/\psi \to \eta' e^+e^-$ with two dominant $\eta'$ decay modes, $\eta' \to \gamma \pi^+ \pi^-$ and $\eta' \to \pi^+\pi^-\eta$. The branching fraction is determined to be $\mathcal{B}(J/\psi \to \eta' e^+e^-) = (6.59\pm0.07\pm0.17) \times 10^{-5}$, which improves in precision by a factor of 2 over the previous BESIII measurement. A search for the dark photon ($\gamma '$) is performed via $J/\psi \to\eta' \gamma ', \gamma' \to e^{+}e^{-}$. Excluding the $\omega$ and $\phi$ mass regions, no significant signal is observed in the mass range from 0.1 to 2.1 GeV/$c^{2}$. We set upper limits at the 90\% confidence level on $\mathcal{B}(J/\psi \to \eta' \gamma ')\times\mathcal{B}(\gamma ' \to e^+e^-)$, $\mathcal{B}(J/\psi \to\eta' \gamma'$) and the mixing strength as a function of dark photon mass. This is among the first searches for dark photons in charmonium decays.