Measurement of the \(e^{+}e^{-}\rightarrow\eta\pi^{+}\pi^{-}\) cross section with the CMD-3 detector at the VEPP-2000 collider

The cross section of the process \(e^{+}e^{-}\rightarrow\eta\pi^{+}\pi^{-}\) is measured using the data collected with the CMD-\(3\) detector at the VEPP-\(2000\) collider in the center-of-mass energy range from \(1.1\) to \(2.0\) GeV. The decay mode \(\eta\rightarrow\gamma\gamma\) is used for \(\eta\) meson reconstruction in the data sample corresponding to an integrated luminosity of \(78.3\) pb\(^{-1}\). The energy dependence of the \(e^{+}e^{-}\rightarrow\eta\pi^{+}\pi^{-}\) cross section is fitted within the framework of vector meson dominance in order to extract the \(\Gamma(\rho(1450)\rightarrow{^{+}e^{-}})\mathcal{B}(\rho(1450)\rightarrow\eta\pi^{+}\pi^{-})\) and the \(\Gamma(\rho(1700)\rightarrow{e^{+}e^{-}})\mathcal{B}(\rho(1700)\rightarrow\eta\pi^{+}\pi^{-})\) products. Based on conservation of vector current, the analysed data are used to test the relationship between the \(e^{+}e^{-}\rightarrow\eta\pi^{+}\pi^{-}\) cross section and the spectral function in \(\tau^-\rightarrow\eta\pi^-\pi^0\nu_\tau\) decay. The \(e^{+}e^{-}\rightarrow\eta\pi^{+}\pi^{-}\) cross section measured with the CMD-\(3\) detector is in good agreement with the previous measurements.