Unifying logarithmic and factorial behavior in high-energy scattering.

The elegant instanton calculus of Lipatov and others used to find factorially divergent behavior ({ital g}{sup {ital N}}{ital N}!) for {ital N}{sub {ital g}}{much_gt}1 in {ital g}{phi}{sup 4} perturbation theory is strictly only applicable when all external momenta vanish; a description of high-energy 2{r_arrow}{ital N} scattering with {ital 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 {ital g}{phi}{sup 4} theory. We do not attempt to tame the unitarity violations associated with either multiperipheralism or the Lipatov technique at strong coupling.