Perturbation Theory of Scattering Amplitudes at High Energies

The asymptotic behavior of Feynman-Dyson graphs for elastic scattering at high energies is studied by means of the Mellin transform. The leading terms of a set of graphs involving three-particle intermediate states are summed. Under certain conditions the asymptotic behavior of the sum is found to contain a factor ${\left(\ln s\right)}^{-\frac{3}{2}}$. This is incompatible with Regge behavior, but is consistent instead with a cut in the complex angular momentum plane.