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The analytic structure of the lattice Landau gauge gluon and ghost propagators
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abstract
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pad\'e approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pad\'e analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Pad\'e analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise estimates for the gluon complex poles, that agree well with other estimates found in the literature. For the branch cut the Pad\'e analysis gives, at least, a rough estimate of the corresponding branch point.
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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.
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