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.
The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
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abstract
The hadronic vacuum polarization function $\Pi_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $\Pi_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.
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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.