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

## TL;DR

This paper measures the cross section of the process $e^{+}e^{-}
ightarrow ext{eta} ext{pi}^+ ext{pi}^-$ using the CMD-3 detector, fitting the energy dependence to extract resonance parameters and testing vector current conservation.

## Contribution

First measurement of the $e^{+}e^{-}
ightarrow ext{eta} ext{pi}^+ ext{pi}^-$ cross section at VEPP-2000, with analysis within vector meson dominance framework and comparison to tau decay spectral functions.

## Key findings

- Measured cross section agrees with previous data.
- Extracted resonance parameters for $
ho(1450)$ and $
ho(1700)$.
- Confirmed the relationship between $e^{+}e^{-}$ and tau decay spectral functions.

## Abstract

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.