Vector-Meson Dominance and High-Energy Electroproduction of theρMeson

The vector-meson dominance (VMD) model is applied to the high-energy electroproduction of $\rho$ mesons off unpolarized protons. It is shown that an experimental study of the angular distribution of the two pions produced from the decay of the final $\rho$ can be used to measure directly the total $\rho p$ cross sections for transversely and longitudinally polarized $\rho$ mesons. The ratio of these cross sections is important in the VMD theory of $\mathrm{ep}$ inelastic scattering. An expression for the differential cross section of the electroproduction of $\rho$ mesons in the forward direction of the $\rho p$ scattering is also given in terms of these two cross sections. The $q^2$ dependence of the $\rho$-electroproduction amplitude is predicted, and certain checks of the model are also given.