The Landau gauge lattice ghost propagator in stochastic perturbation theory

TL;DR

This paper computes the ghost propagator in Landau gauge using Numerical Stochastic Perturbation Theory at one- and two-loop levels, comparing results with standard lattice perturbation theory and estimating unknown constants.

Contribution

It introduces a method to perform limits in NSPT and a recipe for handling logarithmic terms, providing new two-loop results for the ghost propagator.

Findings

Agreement with one-loop standard lattice perturbation theory

Estimated the unknown constant in the ghost self-energy, found to be negligible

Developed a procedure for finite-lattice logs in NSPT

Abstract

We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs''. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI'-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.