One loop renormalization of the non-local gauge invariant operator min_U (A^U_mu)^2 in QCD

Abstract

We compute the one loop anomalous dimension of the gauge invariant dimension two operator min_U (A^U_mu)^2, where U is an element of the gauge group, by exploiting Zwanziger's expansion of the operator in terms of gauge invariant non-local n leg operators. The computation is performed in an arbitrary linear covariant gauge and the cancellation of the gauge parameter in the final anomalous dimension is demonstrated explicitly. The result is equivalent to the one loop anomalous dimension of the local dimension two operator (A^a_mu)^2 in the Landau gauge.

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Cited by in corpus (10)

• An exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge
• QCD effective charges from lattice data
• Nontrivial ghost-gluon vertex and the match of RGZ, DSE and lattice Yang-Mills propagators
• Six dimensional QCD at two loops
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• The factorisation of glue and mass terms in SU(N) gauge theories
• Physical charges in QED and QCD
• Three loop MSbar anomalous dimension for renormalizable gauge invariant non-local gluon mass operator in QCD
• A gauge invariant infrared stabilization of 3D Yang-Mills gauge theories
• Study of the nonlocal gauge invariant mass operator $\mathrm{Tr}\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the maximal Abelian gauge