Large- Q sup 2 behavior of the Higgs mechanism as derived from one-loop diagrams and the renormalization-group equation

Journal Article · Sun Dec 01 00:00:00 EST 1991 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.44.3666· OSTI ID:6091845

Huang, C; Hwang, W P ^[1]

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1. Department of Physics, National Taiwan University, Taipei, Taiwan 10764 (Republic of China)

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-{ital Q}{sup 2} 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 ({proportional to}1/{epsilon}) of the various diagrams regulated in the dimensional-regularization scheme. Using the explicit results on the renormalization constants, we extract the {beta} and {gamma} functions which govern the behavior of the theory through the RG equation as {ital Q}{sup 2}{r arrow}{infinity}. We then solve explicitly the coupled RG equations, obtaining the result that the vacuum expectation value {ital v}{sup 2}({ital Q}{sup 2}) vanishes as {ital Q}{sup 2}{r arrow}{infinity} (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.

• OSTI ID: 6091845
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 44:11; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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