QCD effective action with dressing functions: Consistency checks in the perturbative regime

Abstract

In a previous paper, we presented solution to the Slavnov--Taylor identity for the QCD effective action, and argued that the action terms containing (anti)ghost fields are unique. These terms have the same form as those in the classical action, but the gluon and (anti)ghost effective fields are convoluted with gluon and ghost dressing functions G_A and G_c, the latter containing perturbative and nonperturbative effects (but not including the soliton-like vacuum effects). In the present work we show how the perturbative QCD (pQCD) can be incorporated into the framework of this action, and we present explicit one-loop pQCD expressions for G_A and G_c. We then go on to check the consistency of the obtained results by considering an antighost Dyson--Schwinger equation (DSE). By solving the relations that result from the Legendre transformation leading to the effective action, we obtain the effective fields as power expansions of sources. We check explicitly that the aforementioned one-loop functions G_A and G_c fulfil the antighost DSE at the linear source level. We further explicitly check that these one-loop G_A and G_c have the regularization-scale and momentum dependence consistent with the antighost DSE at the quadratic source level. These checks suggest that the the effective action with dressing functions represents a consistent framework for treating QCD, at least at the one-loop level.