On the high-energy behavior of weakly-coupled gauge theories

Abstract

Motivated by recent investigations in sphaleron physics, we discuss several ways in which even weakly-coupled gauge theories, like the standard model, show non-perturbative features at energies E > M w/ α w and multiplicity N∼ α w −1. For B + L-violating processes we show how to modify the canonical dilute instanton gas approximation (DIGA) so that it gives sensible answers at high energy in Minkowski space; in the fixed-angle regime, cross sections decrease like E −2 and show a Poisson distribution in N, peaked at N ≌2π/α w ; this is essentially the limiting multiplicity. The total cross section is many orders of magnitude larger than would be expected from the DIGA at small N, but exactly how many orders of magnitude larger is extremely difficult to calculate. We show that perturbation theory breaks down at similar energies and multiplicities for B + L-conserving processes, and give a simple model of a cure through unitarization. Finally, we speculate on such issues as large-multiplicity diffractive events and sphaleron processes.