Study of $e^{\mathbf{+}}{e}^{\mathbf{-}}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ in the energy range 1.05–2.00 GeV with the SND detector

The cross section for the process $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ has been measured in the center-of-mass energy range 1.05–2.00 GeV. The experiment has been performed at the $e^{+}{e}^{-}$ collider VEPP-2000 with the SND detector. The measured $e^{+}{e}^{-}\to \omega {\pi }^0$ cross section above 1.4 GeV is the most accurate to date. Below 1.4 GeV our data are in good agreement with the previous SND and CMD-2 measurements. Data on the $e^{+}{e}^{-}\to \omega {\pi }^0$ cross section are well described by the vector meson dominance model with two excited $\rho$-like states. From the measured cross section we have extracted the ${\gamma }^{*}\to \omega {\pi }^0$ transition form factor. It has been found that the vector meson dominance model cannot describe simultaneously our data and data obtained from the $\omega \to {\pi }^0{\mu }^{+}{\mu }^{-}$ decay. We have also tested the conserved vector current hypothesis comparing our results on the $e^{+}{e}^{-}\to \omega {\pi }^0$ cross section with data on the ${\tau }^{-}\to \omega {\pi }^{-}{\nu }_{\tau }$ decay and have found that the conserved vector current hypothesis works well within the reached experimental accuracy of about 5%.

Figure 1

The distribution of the ${\pi }^0\gamma$ invariant mass for selected data events (points with error bars) with $E<1.7\mathrm{GeV}$ (left) and $E\ge 1.7\mathrm{GeV}$ (right). The curves are the result of the fit described in the text. The dashed line represents the linear-background contribution.

Figure 2

The $E_r$ dependence of the detection efficiency for the process $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ for $E=1.05\mathrm{GeV}$ (left) and $E=2.00\mathrm{GeV}$ (right).

Figure 3

The ${\chi }_{5\gamma }^2$ (left) and (${\chi }_{{\pi }^0{\pi }^0\gamma }^2-{\chi }_{5\gamma }^2$) (right) distributions for data events with $E<1.7\mathrm{GeV}$ (points with error bars). The open histogram is a sum of the simulated signal distribution and background distribution. The latter is shown by the shaded histogram. The data and the $\mathrm{\text{signal}}+\mathrm{\text{background}}$ distributions are normalized to the same number of events. The arrows indicate the selection criteria used.

Figure 4

The cross section for $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ measured in this work (circles), and in SND [5] (triangles), CMD-2 [6] (stars), and DM2 [10] (squares) experiments. Only statistical errors are shown. The curve is the result of the fit to SND 2000 and SND 2013 data described in the text.

Figure 5

The ${\gamma }^{*}\to \omega {\pi }^0$ transition form factor. The points with error bars represent data from this work (circles), Ref. 5 (triangles), and Ref. 26 (squares). Only statistical errors are shown. The curve represent the result of model prediction with the parameters listed in Table  for model 1. The dashed curve shows the $\rho (770)$ contribution.

Figure 6

The cross section for $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ measured in this work (circles) and in Ref. 5 (triangles). Only statistical errors are shown. The cross-section data shown by squares was calculated under the CVC hypothesis from the spectral function of the $\tau \to \omega \pi {\nu }_{\tau }$ decay measured in the CLEO experiment [27]. The curve is the result of the fit to SND 2013 and SND 2000 data.