Fermions in Instanton Anti-Instanton Background

Details Fermions in Instanton Anti-Instanton Background Fermions in Instanton Anti-Instanton Background

1993-03-09

arxiv.org/abs/hep-ph/9303232v1

Int.J.Mod.Phys.A9:2613-2644,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

36 PAGES, GEF-Th-8/1993

Scientific paper

10.1142/S0217751X94001059

We consider the behaviour of fermions in the background of instanton-anti\-instanton type configurations. 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 ($\rho $). The situation when the instanton-anti\-instanton overlap and melt, is studied through the behaviour of the Chern Simons number as a function of $ R/\rho$ and $x_4$. Applying our results to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical basis for expecting anomalous cross sections to become observable at energies in $10$ TeV region.

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