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

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