Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p²), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in $d=2$, 3 and 4 space-time dimensions. Fits to the gluon data in $3d$ and in $4d$ show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p²) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the $2d$ case, fitting the data requires a noninteger power of the momentum p in the numerator of the expression for D(p²). In this case, an infinite-volume-limit extrapolation gives $D(0)=0$. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.