High-energy multileg electroweak processes and unitarity

Because of the failure of the dilute-instanton-gas approximation (DIGA) at high energies, recent calculations of ({ital B}+{ital L})-violating processes in the standard model show blatant violations of unitarity, and suggest that these processes may be relatively unsuppressed at multiplicities {ital N}{similar to}{alpha}{sub {ital W}}{sup {minus}1}. We show how to cure the DIGA failure and restore the high-energy behavior necessary for consistency with unitarity in two ways: one in Minkowski space and the other in Euclidean space. In Euclidean space this is done by solving the classical field equations in the presence of space-time-dependent sources; we work out an explicit example. The same techniques allow us to investigate a similar failure of high-energy behavior in perturbation theory (({ital B}+{ital L})-conserving processes) as studied with the DIGA in the manner of Lipatov. An independent Minkowski-space analysis, also dealing with classical solutions in the presence of sources, confirms these results and shows that even with the right high-energy behavior, factors growing rapidly with {ital N} when {ital N}{ge}{alpha}{sub {ital W}}{sup {minus}1} still violate unitarity in the ({ital B}+{ital L})-conserving sector. Within the framework of a simple model which automatically restores unitarity, we investigate whether dispersion integrals relating high- and low-energy ({ital B}+{ital L})-violating processes can restrict the size of the high-energy {ital B}+{ital L} violation, and find that they cannot.