%0 Journal Article %T On a search for the $¦Ç\rightarrow e^+ e^-$ decay at the VEPP-2000 $e^+e^-$ collider %A M. N. Achasov %A A. Yu. Barnyakov %A K. I. Beloborodov A. V. Berdyugin %A A. G. Bogdanchikov %A A. A. Botov %A T. V. Dimova %A V. P. Druzhinin %A V. B. Golubev %A L. V. Kardapoltsev %A A. G. Kharlamov %A I. A. Koop %A L. A. Korneev %A A. A. Korol %A D. P. Kovrizhin %A A. S. Kupich %A A. P. Lysenko %A K. A. Martin %A N. Yu. Muchnoi %A A. E. Obrazovsky %A E. V. Pakhtusova %A E. A. Perevedentsev %A Yu. A. Rogovsky %A A. I. Senchenko %A S. I. Serednyakov %A Z. K. Silagadze %A Yu. M. Shatunov %A D. A. Shtol %A D. B. Shwartz %A A. N. Skrinsky %A I. K. Surin %A Yu. A. Tikhonov %A Yu. V. Usov %A A. V. Vasiljev %A I. M. Zemlyansky %J Physics %D 2015 %I arXiv %X A sensitivity of the VEPP-2000 $e^+e^-$ collider in a search for the rare decay $\eta \rightarrow e^+ e^-$ has been studied. The inverse reaction $e^+ e^- \rightarrow \eta$ is proposed for this search. We have analyzed a data sample with an integrated luminosity of 108 nb$^{-1}$ collected with the SND detector in the center-of-mass energy range 520-580 MeV and found no background events for the reaction $e^+ e^- \rightarrow \eta$ in the decay mode $\eta\to\pi^0\pi^0\pi^0$. In the absence of background, a sensitivity to ${\cal B}(\eta \rightarrow e^+ e^-)$ of $10^{-6}$ can be reached during two weeks of VEPP-2000 operation. Such a sensitivity is better than the current upper limit on ${\cal B}(\eta \rightarrow e^+ e^-)$ by a factor of 2.3. %U http://arxiv.org/abs/1507.02073v2