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

In a previous paper, we presented a 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 GA and Gc, the latter containing perturbative and nonperturbative effects (but not including the solitonlike vacuum effects). In the present work we show how perturbative QCD (PQCD) can be incorporated into the framework of this action, and we present explicit one-loop PQCD expressions for GA and Gc. We then go on to check the consistency of the results obtained 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 GA and Gc satisfy the antighost DSE at the linear source level. We further explicitly check that these one-loop GA and Gc have a regularization scale and momentum dependence consistent with the antighost DSE at the quadratic source level. These checks suggest that the effective action with dressing functions represents a consistent framework for treating QCD, at least at the one-loop level