The equivalence theorem

The equivalence theorem states that, at an energy {ital E} much larger than the vector-boson mass {ital M}, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghos...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1990-04, Vol.41 (7), p.2294-2311
Main Author: VELTMAN, H
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
ELEMENTARY PARTICLES
EQUIVALENCE PRINCIPLE
Exact sciences and technology
FERMIONS
FUNCTIONS
GREEN FUNCTION
HIGGS BOSONS
LIE GROUPS
MASS FORMULAE
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
PERTURBATION THEORY
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POSTULATED PARTICLES
RENORMALIZATION
S MATRIX
STANDARD MODEL
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TOP PARTICLES
UNIFIED GAUGE MODELS 645400 > High Energy Physics-- Field Theory
WARD IDENTITY
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Summary:The equivalence theorem states that, at an energy {ital E} much larger than the vector-boson mass {ital M}, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region {ital m}{sub {ital f}}{approx}{ital M}{much lt}{ital E}{much lt}{ital m}{sub Higgs}.
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.41.2294