A. J. Gentles | Searcharxiv

arXiv1996

Chiral Symmetry Breaking in Axial Gauge QCD from the Dyson Schwinger Equations

We investigate the nonperturbative behaviour of the quark propagator in axial gauge using a truncation of the Dyson-Schwinger equations which respects the Ward-Takahashi identity and multiplicative renormalisability. We demonstrate that above a critical coupling $α_c$, which depends on the form of the gluon propagator, one can obtain massive solutions for both explicit and dynamically generated quark masses. The stability of these is discussed in the context of the Cornwall-Jackiw-Tomboulis effective action.

hep-ph↗

arXiv1994

The Quark Propagator from the Dyson-Schwinger Equations: I. the Chiral Solution

Within the framework of the Dyson-Schwinger equations in the axial gauge, we study the effect that non-perturbative glue has on the quark propagator. We show that Ward-Takahashi identities, combined with the requirement of matching perturbative QCD at high momentum transfer, guarantee the multiplicative renormalisability of the answer. Technically, the matching with perturbation theory is accomplished by the introduction of a transverse part to the quark-gluon vertex. We show that this transverse vertex is crucial for chiral symmetry breaking, and that massless solutions exist below a critical value of the strong coupling constant. Using the gluon propagator that we previously calculated, we obtain small corrections to the quark propagator, which keeps a pole at the origin in the chiral phase.

hep-ph↗