One loop renormalization of the non-local gauge invariant operator min{U}∫d4x(AμaU)2 in QCD

We compute the one loop anomalous dimension of the gauge invariant dimension two operator min{U}∫d4x(AμaU)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 (Aμa)2 in the Landau gauge.