Resonance contribution to electromagnetic structure functions

The part of the pion and proton electromagnetic structure functions due to direct channel resonances in the virtual Compton amplitude is discussed. After a phenomenological discussion, based on the work of Bloom and Gilman, of resonance production in inelastic electroproduction, the single resonance contribution to the pion and proton structure functions is expressed in terms of transition form factors. Froissart-Gribov representations of the Compton amplitude partial waves are presented and are used to specify the spin dependence of the transition form factors. The dependence of the form factors on momentum transfer and resonance mass is assumed on the basis of the behavior of exclusive resonance electroproduction. The single resonance contributions are summed in the Bjorken limit, and the result exhibits Bjorken scaling. Transverse photons are found to dominate in the Bjorken limit, and the threshold behavior of the resonant part of the structure functions is related to the asymptotic behavior of exclusive form factors at large momentum transfer. The resonant parts of the annihilation structure functions are not in general given by simple analytic continuation in the scaling variable ω' of the electroproduction structure functions. (author)