Analytic properties of the Landau gauge gluon and quark propagators

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Abstract
We explore the analytic structure of the gluon and quark propagators of Landau gauge QCD from numerical solutions of the coupled system of renormalized Dyson-Schwinger equations and from fits to lattice data. We find sizable negative norm contributions in the transverse gluon propagator indicating the absence of the transverse gluon from the physical spectrum. A simple analytic structure for the gluon propagator is proposed. For the quark propagator we find evidence for a masslike singularity on the real timelike momentum axis, with a mass of 350 to 500 MeV. Within the Green’s function approach that is employed, we identify a crucial term in the quark-gluon vertex that leads to a positive definite Schwinger function for the quark propagator.