Observation of the Dalitz Decay $eta to gamma e^+e^-$

We report the first observation of the Dalitz decay $eta to gamma e^+e^-$, based on a data sample of 1.31 billion $J/psi$ events collected with the BESIII detector. The $eta$ mesons are produced via the $J/psi to gamma eta$ decay process. The ratio $Gamma(eta to gamma e^+ e^-)/Gamma(etatogammagamma)$ is measured to be $(2.13pm0.09(text{stat.})pm0.07(text{sys.}))times10^{-2}$. This corresponds to a branching fraction ${cal B}(eta to gamma e^+e^-)= (4.69 pm0.20(text{stat.})pm0.23(text{sys.}))times10^{-4}$. The transition form factor is extracted and different expressions are compared to the measured dependence on the $e^+e^-$ invariant mass. The results are consistent with the prediction of the Vector Meson Dominance model.