Study of the Dalitz decay $J/\psi \to {e}^{+}{e}^{-}\eta $

We study the electromagnetic Dalitz decay $J/\psi \to {e}^{+}{e}^{-}\eta $ and search for dielectron decays of a dark gauge boson (${\gamma }^{\prime }$) in $J/\psi \to {\gamma }^{\prime }\eta $ with the two $\eta $ decay modes $\eta \to \gamma \gamma $ and $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^{0}$ using $\left(1310.6±7.0\right)×{10}^{6}\text{}\text{}J/\psi $ events collected with the BESIII detector. The branching fraction of $J/\psi \to {e}^{+}{e}^{-}\eta $ is measured to be $\left(1.43±0.04\left(\mathrm{stat}\right)±0.06\left(\mathrm{syst}\right)\right)×{10}^{-5}$, with a precision that is improved by a factor of 1.5 over the previous BESIII measurement. The corresponding dielectron invariant mass dependent modulus square of the transition form factor is explored for the first time, and the pole mass is determined to be $\Lambda =2.84±0.11\left(\mathrm{stat}\right)±0.08\left(\mathrm{syst}\right)\text{}\text{}\mathrm{GeV}/{c}^{2}$. We find no evidence of ${\gamma }^{\prime }$ production and set 90% confidence level upper limits on the product branching fraction $B\left(J/\psi \to {\gamma }^{\prime }\eta \right)×B\left({\gamma }^{\prime }\to {e}^{+}{e}^{-}\right)$ as well as the kinetic mixing strength between the standard model photon and ${\gamma }^{\prime }$ in the mass range of $0.01\le {m}_{{\gamma }^{\prime }}\le 2.4\text{}\text{}\mathrm{GeV}/{c}^{2}$.