Infrared and high energy fixed angle domains of scattering and the role of eikonal approximation

Abstract

We examine the infrared structure and fixed angle behaviour of generalised ladder diagrams in spinor electrodynamics. The external line rules for infrared divergence is proved within the framework of parametric representation of the amplitudes. We derive a set of rules for computing the precise form of the leading infrared behaviour of any generalised ladder diagram. The same set of rules is shown to yield the leading term in the high energy fixed angle limit. Our analysis shows that both in the infrared and in the fixed-angle high energy limits the usual propagator eikonal approximation fails even in the leading order. The deficiencies of eikonal approximation can be partially removed if one also makes the small angle approximation. Leading corrections of relative O( |t | 1 2 /s 1 2 ) to the small-angle eikonal amplitude are calculated.