Observation of $\psi(3770)\to\eta J/\psi$

The Born cross section of the process $e^+e^-\to\eta J/\psi$ at a center-of-mass energy $\sqrt{s}=3.773 ~\mathrm{GeV}$ is measured to be ($8.89\pm0.88\pm0.42$)$~\mathrm{pb}$, using a data sample collected with the BESIII detector operating at the BEPCII storage ring. The decay $\psi(3770)\rightarrow\eta J/\psi$ is observed for the first time with a statistical significance of $7.4\sigma$. From a fit to the dressed cross-section line-shape of $e^+e^-\to\eta J/\psi$ from $\sqrt{s}=3.773$ to $4.600~\mathrm{GeV}$ we obtain the branching fraction of the decay $\psi(3770)\to \eta J/\psi$ to be $(11.6\pm6.1\pm1.0)\times 10^{-4}$ when the $\psi(3770)$ decay amplitude is added coherently to the other contributions, and $(7.9\pm1.0\pm0.7)\times 10^{-4}$ when it is added incoherently. Here the first uncertainties are statistical and the second are systematic.