Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ using initial state radiation

We study the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta \gamma$, where the photon is radiated from the initial state. About 8000 fully reconstructed events of this process are selected from the BaBar data sample with an integrated luminosity of 469~fb${}^{-1}$. Using the ${\pi }^{+}{\pi }^{-}\eta$ invariant mass spectrum we measure the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ cross section in the $e^{+}{e}^{-}$ center-of-mass energy range from 1.15 to 3.5 GeV. The cross section is well described by the Vector-Meson Dominance model with four $\rho$-like states. We observe $49\pm 9$ events of the $J\mathrm{/}\psi$ decay to ${\pi }^{+}{\pi }^{-}\eta$, and measure the product $\Gamma_{J/\Psi \to e^+e^-} $\text{B}${J/\Psi \to \pi^+\pi^-\eta} = 2.34 \pm 0.43{$\text{stat}$} \pm 0.16_{$\text{syst}$}$~eV.