Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates

TL;DR

This paper analyzes lattice simulation data for the Landau-gauge SU(2) gluon propagator across multiple dimensions, confirming a massive infrared behavior and estimating associated mass scales and condensates, with implications for the Gribov-Zwanziger framework.

Contribution

It provides an analytic fit to lattice data in 2, 3, and 4 dimensions, supporting the refined Gribov-Zwanziger model and estimating dynamical mass scales from the propagator's pole structure.

Findings

Good agreement with RGZ predictions in 3d and 4d

D(0) approaches zero in 2d, indicating a different infrared behavior

Estimates of dimension-two condensate mass scales

Abstract

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p^2), 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(p^2) 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 non-integer power of the momentum p in the numerator of the expression for D(p^2). 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.