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.

8 latex pages

References in corpus (2)

• Quantum properties of a non-Abelian gauge invariant action with a mass parameter
• Renormalization group aspects of the local composite operator method

Cited by in corpus (4)

• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• Three loop MSbar anomalous dimension for renormalizable gauge invariant non-local gluon mass operator in QCD
• 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
• A gauge invariant infrared stabilization of 3D Yang-Mills gauge theories