The elegant instanton calculus of Lipatov and others used to find factorially divergent behavior (${\mathit{g}}^{\mathit{N}}$N!) for ${\mathit{N}}_{\mathit{g}}$≫1 in g${\mathrm{\phi }}^4$ perturbation theory is strictly only applicable when all external momenta vanish; a description of high-energy 2→N scattering with N massive particles is beyond the scope of such techniques. On the other hand, a standard multiperipheral treatment of scattering with its emphasis on leading logarithms gives a reasonable picture of high-energy behavior but does not result in factorial divergences. Using a straightforward graphical analysis we present a unified picture of both these phenomena as they occur in the two-particle total cross section of g${\mathrm{\phi }}^4$ theory. We do not attempt to tame the unitarity violations associated with either multiperipheralism or the Lipatov technique at strong coupling.

• Received 12 August 1994

DOI:https://doi.org/10.1103/PhysRevD.51.4844