Some models for the decay of timelike, highly virtual particles

Abstract

We calculate some tree-graph models for the decay of a timelike virtual particle. Using bare propagators and vertices we find that there exist strong coupling solutions in which the decay rates grow with increasing energy much faster than would be predicted from the consideration of individual graphs. However, we show that self-energy corrections to the propagators and the condition that no ghost poles should exist lead to much more conventional behavior, whatever assumptions we make about the vertex functions. In particular, within the framework of our approximations we show that the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation cross section must eventually decrease as $\frac{1}{s}$.