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

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

1994-07-04

arxiv.org/abs/hep-ph/9407220v2

Nucl.Phys. B440 (1995) 521-542

Physics

High Energy Physics

High Energy Physics - Phenomenology

21 pages, 6 figures; McGill/94-24, SHEP 93/94-26 We generalise our results by showing that they are not sensitive to the speci

Scientific paper

10.1016/0550-3213(95)00045-T

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.

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