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Three decades of work on the quantum field equations of pure Yang-Millstheory have distilled two families of solutions in Landau gauge. Both coincidefor high (Euclidean) momentum with known perturbation theory, and both predictan infrared suppressed transverse gluon propagator, but whereas the solutionknown as "scaling" features an infrared power law for the gluon and ghostpropagators, the "massive" solution rather describes the gluon as a vectorboson that features a finite Debye screening mass.  In this work we examine the gauge dependence of these solutions by adoptingstochastic quantization. What we find, in four dimensions and in a rainbowapproximation, is that stochastic quantization supports both solutions inLandau gauge but the scaling solution abruptly disappears when the parametercontrolling the drift force is separated from zero (soft gauge-fixing),recovering only the perturbative propagators; the massive solution seems tosurvive the extension outside Landau gauge. These results are consistent withthe scaling solution being related to the existence of a Gribov horizon, withthe massive one being more general.  We also examine the effective action in Faddeev-Popov quantization thatgenerates the rainbow and we find, for a bare vertex approximation, that thethe massive-type solutions minimise the quantum effective action.

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism