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arXiv · hep-ph/9309263

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

Frederick T. Hawes·Craig D. Roberts·Anthony G. Williams
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Abstract

We study a model Dyson-Schwinger equation for the quark propagator closed using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim q^2/[(q^2)^2 + b^4]$} and two {\it Ansätze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the model {\bf is not} confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behaviour of QCD.

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Frederick T. Hawes, Craig D. Roberts, Anthony G. Williams. 1994-01-18. Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?. https://doi.org/10.1103/physrevd.49.4683

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