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We suggest a framework based on the rainbow approximation with effectiveparameters adjusted to lattice data. The analytic structure of the gluon andghost propagators of QCD in Landau gauge is analyzed by means of numericalsolutions of the coupled system of truncated Dyson-Schwinger equations. We findthat the gluon and ghost dressing functions are singular in complex Euclideanspace with singularities as isolated pairwise conjugated poles. These poleshamper solving numerically the Bethe-Salpeter equation for glueballs as boundstates of two interacting dressed gluons. Nevertheless, we argue that, byknowing the position of the poles and their residues, a reliable algorithm fornumerical solving the Bethe-Salpeter equation can be established.

Analytical properties of the gluon propagator from truncated Dyson-Schwinger equation in complex Euclidean space