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# A study of the gauge invariant, nonlocal mass operator $Tr \int d^4x F_{\mu\nu}(D^2)^{-1} F_{\mu\nu}$ in Yang-Mills theories

Capri, M.A.L.; Dudal, D.; Gracey, J.A.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P. and Verschelde, H. (2005) A study of the gauge invariant, nonlocal mass operator $Tr \int d^4x F_{\mu\nu}(D^2)^{-1} F_{\mu\nu}$ in Yang-Mills theories. Physical Review D, 72 . Article Number: 105016. ISSN 1550-2368 (online);1550-7998 (print)

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## Abstract

The nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is considered in Yang-Mills theories in Euclidean space-time. It is shown that the operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be cast in local form through the introduction of a set of additional fields. A local and polynomial action is thus identified. Its multiplicative renormalizability is proven by means of the algebraic renormalization in the class of linear covariant gauges. The anomalous dimensions of the fields and of the mass operator are computed at one loop order. A few remarks on the possible role of this operator for the issue of the gauge invariance of the dimension two condensates are outlined.

Item Type: Article LTH 659; arXiv Number: arXiv:hep-th/0510240v2. Additional citation information: PHYSICAL REVIEW D 72, 105016 (2005); 1550-7998/2005/72(10)/105016(21). Published 30 November 2005. 21 pages. Issue: November 2005. GLUON POLE MASS; LANDAU GAUGE; COMPOSITE OPERATOR; GRIBOV HORIZON; COVARIANT GAUGES; ANOMALOUS DIMENSION; INFRARED BEHAVIOR; RESONANCE PHYSICS; ABELIAN GAUGE; QCD Q Science > QC Physics Academic Faculties, Institutes and Research Centres > Faculty of Science > Department of Mathematical Sciences 10.1103/PhysRevD.72.105016 ©2005 The American Physical Society http://arxiv.org/abs/hep-th/0510240 Yes Published 412 27 Oct 2008 11:15 20 May 2011 14:57

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