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.

• Received 9 September 2003

DOI:https://doi.org/10.1103/PhysRevD.70.014014