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

Using a data sample of $(1310.6pm7.0)times10^{6}$ $J/psi$ 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 $mathcal{B}(J/psi to eta e^+e^-) = (6.59pm0.07pm0.17) times 10^{-5}$, which improves in precision by a factor of 2 over the previous BESIII measurement. A search for the dark photon ($gamma $) is performed via $J/psi toeta gamma , gamma to e^{+}e^{-}$. 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 $mathcal{B}(J/psi to eta gamma )timesmathcal{B}(gamma to e^+e^-)$, $mathcal{B}(J/psi toeta gamma$) and the mixing strength as a function of dark photon mass. This is among the first searches for dark photons in charmonium decays.