In this paper we study the $t$ dependence of the $\gamma \pi \omega$ vertex functions on the basis of partial-wave dispersion relations and unitarity. The right-hand cut is approximated by the $2\pi$ contribution and the left-hand cut by the nearest $s$- and $u$-channel poles. The electromagnetic $\pi \omega$ transition form factor is calculated as a function of $t$ in the timelike and spacelike region and is compared with predictions of the $\rho$-dominance model and with recent experimental data for $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ near threshold. The influence of the left-hand cut and the finite width of the $\rho$ resonance is explicitly shown.

• Received 8 April 1974

DOI:https://doi.org/10.1103/PhysRevD.10.932