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

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 $654{\mathrm{nb}}^{-1}$ accumulated at the VEPP-2000 $e^{+}{e}^{-}$ collider with the SND detector at the center-of-mass energy $E=m_{\eta }{c}^2\approx 548\mathrm{MeV}$, and set the upper limit $\mathcal{B}(\eta \to e^{+}{e}^{-})<7\times {10}^{-7}$ at the 90% confidence level.

Figure 1

The diagram for the $\eta \to e^{+}{e}^{-}$ decay.

Figure 2

The measurements of the c.m. energy during data taking. The errors are statistical. The band indicates the $\pm 1\sigma$ range for $E=m_{\eta }{c}^2$ [14].

Figure 3

The visible $e^{+}{e}^{-}\to \eta$ cross section evaluated for ${\mathcal{B}}^{\mathrm{UL}}(\eta \to e^{+}{e}^{-})=1.78\times {10}^{-9}$ and ${\sigma }_E=226\mathrm{keV}$. The points with error bars represent the cross section values at the energy points where data were recorded. The errors of the cross section are determined by the statistical errors in the measurement of the beam energy.

Figure 4

The ${\chi }^2$ distribution for simulated $e^{+}{e}^{-}\to \eta$ events passed the selection criteria of six-photon events.