Some Properties of the Five-Point Function in Perturbation Theory

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.