Search for the process ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{\eta }$

A search for the rare decay $\eta \to e^{+}{e}^{-}$ is performed using the inverse process $e^{+}{e}^{-}\to \eta$ in the decay mode $\eta \to {\pi }^0{\pi }^0{\pi }^0$. We analyze data with an integrated luminosity of 654 nb${}^{-1}$ accumulated at the VEPP-2000 $e^{+}{e}^{-}$ collider with the SND detector at the center-of-mass energy $E=m_{\eta }{c}^2\approx 548$ MeV, and set the upper limit $\mathcal{B}(\eta \to e^{+}{e}^{-})<7\times {10}^{-7}$ at the 90% confidence level.