Study of the process $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ in the energy range $\sqrt{s}<2\mathrm{GeV}$ with the SND detector

The process $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ is studied in the energy range 1.45–2.00 GeV using data with an integrated luminosity of $33{\mathrm{pb}}^{-1}$ accumulated by the SND detector at the $e^{+}{e}^{-}$ collider VEPP-2000. The $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ cross section is measured for the first time. The cross section has a threshold near 1.75 GeV. Its value is about 2 nb in the energy range 1.8–2.0 GeV. The dominant intermediate state for the process $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ is found to be $\omega a_0(980)$.

Figure 1

The ${\chi }_{\eta 2{\pi }^0\gamma }^2$ distributions for selected data events (points with error bars) and for simulated $e^{+}{e}^{-}\to \eta 2{\pi }^0\gamma$ events (histogram).

Figure 2

The distributions of the two-photon invariant mass of ${\pi }^0$-meson candidates (left, two entries per events) and of $\eta$-meson candidates (right) for selected data events (points with error bars) and for simulated $e^{+}{e}^{-}\to \eta 2{\pi }^0\gamma$ events (histogram).

Figure 3

The $M_{{\pi }^0\gamma }$ spectrum for selected $e^{+}{e}^{-}\to \eta 2{\pi }^0\gamma$ candidate events (points with error bars, two entries per event). The histogram is the sum of the distributions for simulated $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ and background events. The simulated distribution is normalized to the number of data events. The shaded histogram shows the background distribution.

Figure 4

The $M_{\eta {\pi }^0}$ spectrum for selected $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ candidate events (points with error bars). The solid histogram represents $e^{+}{e}^{-}\to \omega a_0(980)$ simulation, while the dashed histogram represents simulation of the process $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ with uniform phase-space distribution of the final particles.

Figure 5

The dependence of the detection efficiency for $e^{+}{e}^{-}\to \omega a_0(980)\to \omega \eta {\pi }^0\to \eta {\pi }^0{\pi }^0\gamma \to 7\gamma$ events on the energy of the additional photon emitted from the initial state for $\sqrt{s}=2.0\mathrm{GeV}$ (a), 1.76 GeV (b) and 1.6 GeV (c). The points with error bars are obtained from simulation. The curve shows the result of approximation of the ${\epsilon }_r(\sqrt{s},E_r)$ dependence by a smooth function.

Figure 6

The cross section for the process $e^{+}{e}^{-}\to \omega \eta {\pi }^0$ measured in this work. The solid (dashed) curve shows the result of the fit with (without) a resonance contribution.