FERMIONS IN THE INSTANTON-ANTI-INSTANTON VALLEY AND HIGH-ENERGY ELECTROWEAK INTERACTIONS

Abstract

We consider the behavior of fermions in the background of instanton-anti-instanton valley fields. Several different physics problems, from the high-energy electroweak interactions to the study of vacuum structure of QCD and of large orders of perturbation theory, are related to this problem. The spectrum of the Dirac operator in such a background is studied in detail. We present an approximation for the fermion correlation function when the instanton-anti-instanton separation (R) is large compared to their sizes (ρ). The situation where the instanton-anti-instanton overlap and melt is studied through the behavior of the Chern-Simons number as a function of R/ρ and x4. Applying our results to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there is no theoretical basis for expecting anomalous cross-sections to become observable at energies in the 10 TeV region.