Modeling the Landau-Gauge Ghost Propagator in 2, 3 and 4 Space-Time Dimensions

TL;DR

This paper provides an analytic model for the ghost propagator in Landau gauge across 2, 3, and 4 dimensions, based on lattice data and one-loop relations, offering a good fit and a simple parametrization of deviations.

Contribution

It introduces a one-parameter fit for the ghost propagator derived from one-loop relations, and offers a simple parametrization of the discrepancies with lattice data.

Findings

One-loop derived model fits lattice data well.

Good chi-squared values indicate effective modeling.

Provides a simple parametrization of deviations.

Abstract

We present an analytic description of numerical results for the ghost propagator G(p^2) in minimal Landau gauge on the lattice. The data were produced in the SU(2) case using the largest lattice volumes to date, for d = 2, 3 and 4 space-time dimensions. Our proposed form for G(p^2) is derived from the one-loop relation between ghost and gluon propagators, considering a tree-level ghost-gluon vertex and our previously obtained gluon-propagator results \cite{Cucchieri:2011ig}. Although this one-loop expression is not a good description of the data, it leads to a one-parameter fit of our ghost-propagator data with a generally good value of \chi^2/dof, comparable to other fitting forms used in the literature. At the same time, we present a simple parametrization of the difference between the lattice data and the one-loop predictions.