The Complete High-Energy Behavior of Ladder Diagrams in Perturbation Theory

Abstract

The Mellin‐transform method for obtaining the high‐energy behavior of Feynman integrals is modified and applied to the set of ladder diagrams. The complete set of terms of the form s⁻¹(ln s)ⁿ is summed, and gives an equation for the trajectory function which is analogous to that obtained by Fredholm methods for a Yukawa potential. A perturbation expansion for α(t) valid for t large is given, and the threshold behavior investigated. The results confirm the reliability of the perturbation‐theory method of investigation. They also exhibit directly the connection between high‐energy behavior and the poles of the scattering amplitude.