The analytic structure of the non-perturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.

We formulate a framework to determine the mass of glueball states of Landau gauge Yang-Mills theory in the continuum. To this end we derive a Bethe-Salpeter equation for two gluon bound states including the effects of Faddeev-Popov ghosts. We construct a suitable approximation scheme such that the interactions in the bound state equation match a corresponding successful approximation of the Dyson-Schwinger equations for the Landau gauge ghost and gluon propagators. Based upon a recently obtained solution for the propagators in the complex momentum plane we obtain results for the mass of the 0 ++ and 0 −+ glueballs. In the scalar channel we find a mass value in agreement with lattice gauge theory.

We consider the running coupling from the four-gluon vertex in Landau gauge, SU(Nc) Yang-Mills theory as given by a combination of dressing functions of the vertex and the gluon propagator. We determine these functions numerically from a coupled set of Dyson-Schwinger equations. We reproduce asymptotic freedom in the ultraviolet momentum region and find a coupling of order one at mid-momenta. In the infrared we find a nontrivial (i.e. nonzero) fixed point which is three orders of magnitude smaller than the corresponding fixed point in the coupling of the ghost-gluon vertex. This result explains why the Dyson-Schwinger and the functional renormalization group equations for the two point functions can agree in the infrared, although their structure is quite different. Our findings also support Zwanziger's notion of an infrared effective theory driven by the Faddeev-Popov determinant.

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We present results on the scalar glueball with PC = ++ in Landau gauge Yang-Mills theory within the Dyson-Schwinger/ Bethe-Salpeter equation approach. To this end, the gluon and ghost propagators are determined non-perturbatively in the whole complex momentum plane by numerical solutions of the respective Dyson-Schwinger equations. The resulting propagators are analytic apart from a cut structure on the real, timelike momentum axis and violate the OsterwalderSchrader positivity condition. The mass of the scalar glueball is obtained using a generalized ladder truncation to the Poincare-covariant Bethe-Salpeter equation. Xth Quark Confinement and the Hadron Spectrum,