Relations Between Large-Angle Scattering, From Factors, and Structure Functions

Abstract

We study the large-momentum-transfer limit of electromagnetic form factors and the high-energy, large-momentum-transfer limit of exclusive and inclusive scattering under the physical approximation that hadronic states are composite systems which can be decomposed in this kinematic regime into two finite mass and spin constituents. One of these constituents (the parton) is pointlike in accordance with the results of deep-inelastic scattering, while the other (the core) is not. We study in this work only the constituent interchange contribution to scattering, as in a previous work by Gunion, Blankenbecler, and Brodsky. Our approach is to use a general, covariant decomposition of the composite-particle vertex, and then to study relations between the form factors and scattering amplitudes. Rather than taking a phenomenological approach, our aim is to make a careful study of the theoretical underpinnings of such relations. We find that the Drell-Yan-West relation between elastic form factors and deep-inelastic structure functions holds in general, and that the inclusive cross section is proportional to a deep-inelastic structure function. The power dependence of the exclusive and inclusive cross section on elastic form factors is not uniquely determined and we classify various theories according to this dependence. Basically the reason for this is that the elastic and inelastic form factor sample the off-shell behavior of the composite system only in the parton momentum, whereas scattering amplitudes depend intimately on the off-shell behavior of the hadronic vertex in both the core and parton. We also examine a noncovariant integral equation first given by Weinberg to study these problems.