The Renormalization of Composite Operators in Yang-Mills Theories Using 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 infra-red singularities that appear when gluonic matrix elements are taken on-shell at zero momentum transfer. Keywords: twist-two covariant gluon operator, finite part, mixing, non-abelian, anomalous dimension, Ward identity, BRST, modified LSZ reduction, Dixon, Taylor, Joglekar, Lee.

52 pages, uuencoded compressed PostScript, PSU/TH/141. [Minor typo- graphical errors in the references and in Eqs. (A.5) and (A.7) corrected.]

References in corpus (1)

• Remarks on the renormalization of gauge invariant operators in Yang-Mills theory

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