Dressed perturbation theory: a perturbative approach to Dyson-Schwinger and Bethe-Salpeter equations in QCD

Abstract

Dressed perturbation theory (DPT) is a perturbative approach based on the idea of using dressed propagators, instead of free propagators like in ordinary perturbation theory. Quark and gluon self-energies are added to the free part of the QCD action and subtracted from the interaction part. The added self-energies are determined self-consistently via a devised symmetry-preserving power counting scheme. Correlation functions are then calculated using the modified QCD interaction according to the devised power counting. At zeroth order, DPT is very similar to the rainbow-ladder truncation scheme for Dyson-Schwinger and Bethe-Salpeter equations; the first nontrivial perturbative contribution introduces vertex corrections. Dynamical chiral symmetry breaking is realized in the light-quark sector; Goldstone’s theorem and the axial-vector WardTakahashi identity are satisfied in the chiral limit. Higher order contributions can be calculated in a systematic, symmetry-preserving and controllable way, like in ordinary perturbation theory.