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Title: Renormalization of composite operators in Yang-Mills theories using a general covariant gauge

Abstract

Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear when gluonic matrix elements are taken on shell at zero momentum transfer.

Authors:
;  [1]
  1. The Pennsylvania State University, Department of Physics, 104 Davey Laboratory, University Park, Pennsylvania 16802 (United States)
Publication Date:
OSTI Identifier:
7073177
Resource Type:
Journal Article
Journal Name:
Physical Review, D (Particles Fields); (United States)
Additional Journal Information:
Journal Volume: 50:6; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; YANG-MILLS THEORY; RENORMALIZATION; ENERGY-MOMENTUM TENSOR; FACTORIZATION; GAUGE INVARIANCE; GREEN FUNCTION; MATRIX ELEMENTS; MOMENTUM TRANSFER; OPERATOR PRODUCT EXPANSION; QUANTUM CHROMODYNAMICS; SINGULARITY; FIELD THEORIES; FUNCTIONS; INVARIANCE PRINCIPLES; QUANTUM FIELD THEORY; SERIES EXPANSION; TENSORS; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-); 662230 - Quantum Chromodynamics- (1992-)

Citation Formats

Collins, J C, and Scalise, R J. Renormalization of composite operators in Yang-Mills theories using a general covariant gauge. United States: N. p., 1994. Web. doi:10.1103/PhysRevD.50.4117.
Collins, J C, & Scalise, R J. Renormalization of composite operators in Yang-Mills theories using a general covariant gauge. United States. https://doi.org/10.1103/PhysRevD.50.4117
Collins, J C, and Scalise, R J. 1994. "Renormalization of composite operators in Yang-Mills theories using a general covariant gauge". United States. https://doi.org/10.1103/PhysRevD.50.4117.
@article{osti_7073177,
title = {Renormalization of composite operators in Yang-Mills theories using a general covariant gauge},
author = {Collins, J C and Scalise, R J},
abstractNote = {Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear when gluonic matrix elements are taken on shell at zero momentum transfer.},
doi = {10.1103/PhysRevD.50.4117},
url = {https://www.osti.gov/biblio/7073177}, journal = {Physical Review, D (Particles Fields); (United States)},
issn = {0556-2821},
number = ,
volume = 50:6,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 1994},
month = {Thu Sep 15 00:00:00 EDT 1994}
}