Fixed Poles in High-Energy Compton Scattering, Electroproduction, and the Vector-Dominance Models

It is shown that the vector dominance of $s$-channel helicity amplitudes requires the existence of a nonsense wrong-signature fixed pole at $J=1\mathrm{}$ in virtual photon-hadron scattering. Furthermore, in the amplitudes for electroproduction, where the virtual photon masses are spacelike, it is argued that such fixed poles must exist simply from such general requirements as analyticity, gauge invariance, and positivity of cross sections. This fixed pole occurs multiplicatively with the Pomeranchuk pole if the photon-hadron cross sections ${\sigma }_L$ or ${\sigma }_S$ are constant asymptotically with energy. A minimal amount of analyticity then allows one to extend this result to general values of the virtual photon masses. If the asymptotic cross section for photoproduction of $\rho$ mesons is dominated by Pomeranchuk exchange and if it conserves helicity, then the multiplicative fixed pole is present there, too. Further, the presence of this fixed pole tests for the compositeness of the $\rho$ meson or third-double-spectral-function effects.