High-Energy Behavior near Threshold: Massive Quantum Electrodynamics

Abstract

In this paper we study all scattering amplitudes in quantum electrodynamics in the limit $s\to \infty$, with $t$ near or at the two-photon threshold. In this limit, the power of $s$ for a diffractive amplitude with a two-photon cut is found to be promoted from 1 to $\frac{3}{2}$. The fourth-order electron-electron scattering amplitude is first studied by the method of Feynman parameters. The method of impact diagrams is next generalized to handle the more complicated cases. We then apply the new method explicitly to the lowest-order diffractive amplitude for electron-electron scattering, Compton scattering, and photon-photon scattering. A general case $a+b\to a^{\prime }+b^{\prime }$ is also discussed. We find that the scattering amplitude is now factorized and the existence of a Regge pole is suggested. This is then verified by a study of the tower diagrams. Thus the leading singularity in the $J$ plane, while being a pair of branch points for $t\le 0$, is a moving Regge pole located to the right of $J=\frac{3}{2}$ as $t$ is near $4{\lambda }^2$. The Gribov paradox is thereby automatically resolved.