Measurement of the $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ cross section in the center-of-mass energy range 1.22–2.00 GeV with the SND detector at the VEPP-2000 collider

In the experiment with the SND detector at the VEPP-2000 $e^{+}{e}^{-}$ collider the cross section for the process $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ has been measured in the center-of-mass energy range from 1.22 to 2.00 GeV. Obtained results are in agreement with previous measurements and have better accuracy. The energy dependence of the $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ cross section has been fitted with the vector-meson dominance model. From this fit the product of the branching fractions $B(\rho (1450)\to \eta {\pi }^{+}{\pi }^{-})B(\rho (1450)\to e^{+}{e}^{-})$ has been extracted and compared with the same products for $\rho (1450)\to \omega {\pi }^0$ and $\rho (1450)\to {\pi }^{+}{\pi }^{-}$ decays. The obtained cross section data have been also used to test the conservation of vector current hypothesis.

Figure 1

The diagram for the process $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ in the VMD model.

Figure 2

The two-photon invariant-mass spectrum for simulated $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ events at $\sqrt{s}=1.5\mathrm{GeV}$ (points with error bars) fitted with the double-Gaussian function.

Figure 3

The two-photon invariant-mass spectrum for data events selected in the energy range $\sqrt{s}=1.45–1.60\mathrm{GeV}$. The curve is the result of the fit described in the text.

Figure 4

The ${\pi }^{+}{\pi }^{-}$ invariant-mass spectrum for data (points with error bars) and simulated (histogram) $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ events from the energy range $\sqrt{s}=1.45–1.60\mathrm{GeV}$. The simulation uses a model of the $\eta \rho (770)$ intermediate state.

Figure 5

The $\cos {\theta }_{\eta }$ distribution for data (points with error bars) and simulated (histogram) $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ events from the energy range $\sqrt{s}=1.45–1.60\mathrm{GeV}$. The simulation uses a model of the $\eta \rho (770)$ intermediate state.

Figure 6

The detection efficiency for simulated $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$, $\eta \to \gamma \gamma$ events.

Figure 7

The Born cross section for $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ measured in this (SND@VEPP2000) and previous experiments (BABAR [4] and SND@VEPP2M [5]). The solid curve is the result of the VMD fit with the $\rho (770)$, $\rho (1450)$ and $\rho (1700)$ resonances. The dashed curve is the same fit without the $\rho (1700)$ contribution.