The anomalous dimension of the gluon-ghost mass operator in Yang–Mills theory

Abstract

The local composite gluon-ghost operator (12AaμAμa+αc̄aca) is analysed in the framework of the algebraic renormalization in SU(N) Yang–Mills theories in the Landau, Curci–Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MS scheme for the Curci–Ferrari gauge.