A search for the rare decay $\eta \rightarrow e^+e^-$ is performed using the inverse process $e^+e^- \rightarrow \eta$ 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 $ { \cal B} (\eta \rightarrow e^+ e^-) < 7 \times 10^{ -7} $ at the 90\% confidence level.
Categories: hep-ex