Analytic structure of the quark propagator in a model with an infrared vanishing gluon propagator

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Abstract
The Dyson-Schwinger equation for the quark self-energy is solved in the rainbow approximation using an infrared (IR) vanishing gluon propagator that introduces an IR mass scale b. There exists a b-dependent critical coupling indicating the spontaneous breakdown of chiral symmetry. If one chooses realistic QCD coupling constants the strength and the scale of spontaneous chiral symmetry breaking decouple from the IR scale for small b while for large b no dynamical chiral symmetry breaking occurs. At timelike momenta the quark propagator possesses a pole, at least for a large range of the parameter b. Therefore, it is suggestive that quarks are not confined in this model for all values of b. Furthermore, we argue that the quark propagator is analytic within the whole complex momentum plane except on the timelike axis. Hence the naive Wick rotation is allowed. © 1995 The American Physical Society.