Effective potential for spontaneously broken gauge theories and gauge hierarchies

Journal Article · Mon Oct 15 04:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.1988· OSTI ID:6001111

Hagiwara, T; Ovrut, B

The Appelquist-Carazzone effective-field-theory method, where one uses effective light-field coupling constants dependent on the heavy-field sector, is explicitly shown to be valid for the discussion of the gauge-hierarchy problem in grand unified gauge models. Using the method of functionals we derive an expression for the one-loop approximation to the scalar-field effective potential for spontaneously broken theories in an arbitrary R/sub xi/ gauge. We argue that this potential generates, through its derivatives, valid zero-momentum, one-particle-irreducible vertices for any value of xi (not just the xi..-->..infinity Landau gauge). The equation that the one-loop vacuum correction must satisfy is presented, and we solve this equation for a number of spontaneously broken theories including gauge theories with gauge groups U(1) and SO(3). We find that a one-loop vacuum shift in a massless, non-Goldstone direction occurs via the Coleman-Weinberg mechanism with an effective coupling constant dependent on the heavy-field sector.

• Research Organization: Department of Physics, Brandeis University, Waltham, Massachusetts 02154
• OSTI ID: 6001111
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 20:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645301 -- High Energy Physics-- Particle Invariance Principles & Symmetries-- General-- (-1987)
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
FUNCTIONS
GREEN FUNCTION
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
RENORMALIZATION
SCALAR FIELDS
SO GROUPS
SO-3 GROUPS
SYMMETRY BREAKING
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS
UNIFIED GAUGE MODELS
VACUUM STATES