Vector-Dominance Model and the Reactionγp→π−Δ++

The vector-dominance-model (VDM) relation between the reactions (a) $\pi p\to \rho \Delta$ and (b) $\pi p\to \omega \Delta$ and the reaction (c) $\gamma p\to \pi \Delta$ is investigated within the context of the Regge-pole model. Parameters for the strong-interaction processes are determined by making a least-squares fit to the differential cross section and spin-density-matrix data. We find that good agreement with the experimental measurements can be obtained by including the $\pi$, $A_1$, and $A_2$ trajectories for reaction (a), while for reaction (b) we need the exchange of the $\rho$ and $B$ trajectories. Using values of the photon-vector-meson coupling constants, as determined from the leptonic decays of these mesons, and the VDM relations between the amplitudes for processes (a)-(c), we calculate the differential cross section for reaction (c). This is found to be in good agreement with the experimental data and yields a ${\chi }^2=3\mathrm{}$ for nine data.