The quark propagator from the Dyson-Schwinger equations: (I). The chiral solution Original Research Article

Within the framework of the Dyson-Schwinger equations in the axial gauge, and using a truncation procedure which respects the Ward-Takahashi identities, we study the effect that nonperturbative glue has on the quark propagator. We show that within this truncation scheme, the requirement of matching perturbative QCD at high momentum transfer leads to a multiplicatively renormalisable equation. Technically, the matching with perturbation theory is accomplished by the introduction of a transverse part to the quark-gluon vertex. In the case of an analytic gluon propagator, this truncation scheme can lead to chiral symmetry breaking only after the introduction of such a transverse vertex: massless solutions do not exist beyond a critical value of as. Using the gluon propagator that we previously obtained, we obtain small corrections to the quark propagator, which keeps a pole at the origin in the chiral phase.