Some Properties of the Five-Point Function in Perturbation Theory

Abstract

A preliminary investigation of the five‐point function in its dependence on two complex variables is presented. Only single‐loop diagrams are examined. The approach involves a determination of the singularity curves and of their regular and singular parts. The geometrical properties of singularity curves are described in detail; in particular, a method for determining the tangency of two curves is given. The following general conclusions are drawn: First, real and complex vertex singularities are near the physical regions and, therefore, can produce significant experimental effects. On the other hand, scattering singularities and five‐point poles seem to be further removed from the physical regions. Second, it is not likely that a simple scheme can be found for the description of the analytic properties of the five‐point function. A short discussion of scattering singularities involving unstable masses is also given.