Large Q**2 behavior of the Higgs mechanism as derived from one loop diagrams and the renormalization group equation
Journal
Phys. Rev.
Journal Volume
D44
Pages
3666-3679
Date Issued
1991
Author(s)
Abstract
The renormalization-group (RG) approach generalized by Lee and Weisberger to the case of gauge theories with spontaneous symmetry breaking is adopted in order to study the large-Q2 behavior of the Higgs mechanism. The approach amounts to a generalization of the well-known concept of "running coupling constants" to all the couplings involved in the theory. To simplify our consideration, we have considered scalar electrodynamics (QED) in which a U(1) gauge field interacts with both fermions and scalar fields (the latter responsible for spontaneous symmetry breaking). We first carry out a perturbative calculation including all one-loop diagrams with the explicit results on the various renormalization constants obtained by separating out pole parts (1) of the various diagrams regulated in the dimensional-regularization scheme. Using the explicit results on the renormalization constants, we extract the and functions which govern the behavior of the theory through the RG equation as Q2. We then solve explicitly the coupled RG equations, obtaining the result that the vacuum expectation value v2(Q2) vanishes as Q2 (i.e., the broken symmetry is restored) but the gauge sector (consisting of the gauge field and fermions) does not decouple from the strongly self-interacting Higgs sector. In the case of non-Abelian gauge theories, we suggest looking for theories which allow for an eventual decoupling between the strongly interacting Higgs sector and the asymptotically free gauge sector. © 1991 The American Physical Society.
Type
journal article