Updated measurement of the $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ cross section with the SND detector

We analyze a $37{\mathrm{pb}}^{-1}$ data sample collected with the SND detector at the VEPP-2000 $e^{+}{e}^{-}$ collider in the center-of-mass energy range 1.05–2.00 GeV and present an updated measurement of the $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ cross section. In particular, we correct the mistake in radiative correction calculation made in our previous measurement based on a part of the data. The measured cross section is fitted with the vector meson dominance model with three $\rho$-like states and used to test the conserved vector current hypothesis in the ${\tau }^{-}\to \omega {\pi }^{-}{\nu }_{\tau }$ decay.

Figure 1

The distribution of the ${\pi }^0\gamma$-invariant mass for selected data events (points with error bars) with $E=1494\mathrm{MeV}$. The curve is the result of the fit by the sum of the signal and background distribution. The dashed curve represents the background contribution.

Figure 2

The cross section for $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ measured in this work (circles), and in the SND@VEPP-2M [3, 4] (triangles), CMD-2 [7] (stars), and DM2 [9] (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 (Model 1).

Figure 3

The ${\gamma }^{*}\to \omega {\pi }^0$ transition form factor. The points with error bars represent data from this work (circles), Ref. [3] (triangles), and Ref. [20] (squares). Only statistical errors are shown. The curve is the result of of the fit to the $e^{+}{e}^{-}\to \omega {\pi }^0$ cross-section data. The dashed curve shows the $\rho (770)$ contribution.