LEADING-ORDER FERMION-NUMBER NON-CONSERVATION IN THE (1+1)-DIMENSIONAL ABELIAN HIGGS MODEL

Abstract

We consider fermion-number violating Green’s functions involving also gauge and Higgs bosons in the axial (1+1)-dimensional Abelian Higgs model. We show that the Fourier transform of the classical vortex solution has (in the unitary gauge) an isolated pole at the position of the Higgs and gauge boson mass. In a certain sense the vortex, an Euclidean pseudoparticle, is capable to describe particles, i.e. physical gauge and Higgs bosons. From that it follows that, in the leading-order semiclassical approximation around the unit winding number vortex solution, the S-matrix elements for the fermion-number violating processes are local and of order [Formula: see text], where ν is the vacuum expectation value and n is the number of external boson legs. This suggests that, at high energy, fermion-number violating processes with associated production of many gauge and Higgs bosons have large probabilities reaching the unitarity limit, and puts the recent observation of a similar phenomenon in the standard electroweak theory on much firmer ground.