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 lu
minosity 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 $etatopi^0pi^0pi^0$. 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.
The cross section of the process $e^+e^- to K^+K^-$ was measured in the energy range $sqrt{s}$ = 1.04--1.38 GeV in the SND experiment at the VEPP-2M $e^+e^-$ collider. The measured cross section is described by the model of vector meson dominance wit
h contributions from the light vector mesons $rho$, $omega$, $phi$ and their lowest excitations. The mean statistical accuracy of the measurement is 4.4 %, and the systematic uncertainty is 5.2 %.
In the experiment with the SND detector at the VEPP-2M $e^+e^-$ collider measuring the $e^+e^-to etagamma$ cross section in the energy range $0.6<sqrt{s}<1.38 mathrm{GeV}$ the reanalysis of data is performed. The goal is to improve the accuracy of th
e previous results by analysing ambiguities in the approximation of energy dependence of the $e^+e^-to etagamma$ cross section, which were not taken into account in our previous study. We report new results on the approximation of the $e^+e^-to etagamma$ cross section based on Vector Dominance Model under new model parameter assumptions.
