Inelastice+e−Annihilation in Perturbation Theory

The structure functions for the annihilation process $e^{+}+e^{-}\to \overline{p}+X$ are calculated in the neutral-vector-gluon model in the Bjorken limit. Bjorken scaling is broken by the presence of $\ln q^2$ factors in a way which is closely related to the situation in inelastic scattering. All calculations are carried out in a leading-logarithm approximation. In particular there is a multiplicity $n\sim {\ln }^2{q}^2$ and a close interplay between the damping of the elastic form factor and the excitation of inelastic channels. The annihilation structure functions are shown to be related to their inelastic scattering counterparts by analytic continuation and by a physical-region reciprocal relation. The reciprocal relation is observed to have a number of interesting consequences if it applies, in some approximate sense, to pions, protons, etc. In addition to the leading-logarithm calculations contained in this paper the discussions given here of discontinuities of the virtual Compton amplitude and the longitudinal-impact-parameter representation are of general interest and applicability.