Higher-Order Radiative Corrections to Eikonal Functions in Massive Electrodynamics at Very High Energy

Abstract

We show that the assumptions of an impact-parameter representation and energy-independent $\frac{d\sigma }{\mathrm{dt}}$ for fermion-fermion scattering at high energy imply that the amplitude is proportional to square of the vector form factors, multiplied by the bare eikonal functions, to all orders in radiative corrections without vacuum polarization. This is done in the framework of massive electrodynamics. We explicitly demonstrate that these two assumptions are satisfied for some sets of graphs in the two-photon exchanged amplitude with fourth-order radiative correction, where the radiative particle is taken to be a pseudoscalar in order to simplify the algebra.