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Title: Renormalization-scheme-invariant QCD and QED: The method of effective charges

Abstract

We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter ..lambda.., even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QEDmore » is discussed as an example of an extension of the method to problems involving several momentum scales.« less

Authors:
Publication Date:
Research Org.:
Centre de Physique Theorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France
OSTI Identifier:
6760328
Resource Type:
Journal Article
Journal Name:
Phys. Rev. D; (United States)
Additional Journal Information:
Journal Volume: 29:10
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; RENORMALIZATION; QUANTUM ELECTRODYNAMICS; COUPLING CONSTANTS; FERMIONS; GREEN FUNCTION; MASS; PERTURBATION THEORY; ELECTRODYNAMICS; FIELD THEORIES; FUNCTIONS; QUANTUM FIELD THEORY; 645400* - High Energy Physics- Field Theory

Citation Formats

Grunberg, G. Renormalization-scheme-invariant QCD and QED: The method of effective charges. United States: N. p., 1984. Web. doi:10.1103/PhysRevD.29.2315.
Grunberg, G. Renormalization-scheme-invariant QCD and QED: The method of effective charges. United States. https://doi.org/10.1103/PhysRevD.29.2315
Grunberg, G. 1984. "Renormalization-scheme-invariant QCD and QED: The method of effective charges". United States. https://doi.org/10.1103/PhysRevD.29.2315.
@article{osti_6760328,
title = {Renormalization-scheme-invariant QCD and QED: The method of effective charges},
author = {Grunberg, G},
abstractNote = {We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter ..lambda.., even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales.},
doi = {10.1103/PhysRevD.29.2315},
url = {https://www.osti.gov/biblio/6760328}, journal = {Phys. Rev. D; (United States)},
number = ,
volume = 29:10,
place = {United States},
year = {Tue May 15 00:00:00 EDT 1984},
month = {Tue May 15 00:00:00 EDT 1984}
}