In a spectral DSE computation, the quark propagator develops complex-conjugate poles when the classical quark-gluon vertex strength exceeds a critical value, while the full QCD strength is predicted to stay below that value.
On Gribov's supercriticality picture of quark confinement
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abstract
Some years ago Gribov developed the so-called supercritical light quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back-reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back-reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson-Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme.
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The causal structure of the quark propagator
In a spectral DSE computation, the quark propagator develops complex-conjugate poles when the classical quark-gluon vertex strength exceeds a critical value, while the full QCD strength is predicted to stay below that value.