Confined gluon from Minkowski space continuation of the PT-BFM SDE solution

Abstract

Recent lattice studies exhibit infrared finite effective QCD charges. The corresponding gluon propagator in the Landau gauge is finite and nonzero, suggesting that the mechanism of dynamical gluon mass generation is in the operation. In this paper, the analytical continuation of the Euclidean (spacelike) pinch technique–background field method solution of the Schwinger–Dyson equation for the gluon propagator to the timelike region of q2 is found. We found the continuation numerically showing good agreement with a generalized Lehman representation for small Schwinger coupling. The associated non-positive spectral function has an unexpected behavior. Albeit the infrared Euclidean space solution naively suggests a like single-scale ‘massive’ propagator, the obtained spectrum of the gluon propagator does not correspond to the delta function at single scale q = m; instead more possible singularities are generated. The pattern depends on the details of the assumed Schwinger mechanism: for stronger coupling there are a few maxima and minima which appear at the scale Λ, while for perturbatively small Schwinger coupling, the spectral function shows two narrow peaks: particle and ghost excitation, which have mutually opposite signs.