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

The cross section for the process e(+)e(-) -> omega pi(0) -> 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(-) -> 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(-) -> 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* -> 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 -> pi(0)mu(+)mu(-) decay. We have also tested the conserved vector current hypothesis comparing our results on the e(+)e(-) -> omega pi(0) cross section with data on the tau(-) -> omega pi(-)nu(tau) decay and have found that the conserved vector current hypothesis works well within the reached experimental accuracy of about 5%.