The lattice ghost propagator in Landau gauge up to three loops using Numerical Stochastic Perturbation Theory

TL;DR

This paper advances the calculation of the lattice ghost propagator in Landau gauge up to three loops using Numerical Stochastic Perturbation Theory, providing precise results that align with known one-loop results and improve two-loop estimates.

Contribution

It introduces a systematic method to extract non-logarithmic parts of divergent quantities in lattice ghost propagator calculations up to three loops.

Findings

Excellent agreement with one-loop lattice perturbation theory.

Improved estimate for the two-loop constant contribution.

Comparison with Monte Carlo data shows consistency.

Abstract

We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarithmic parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and $a\to 0$ limits. We find accurate coincidence with the one-loop result for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the ghost self-energy in Landau gauge. Our results for the perturbative ghost propagator are compared with Monte Carlo measurements of the ghost propagator performed by the Berlin Humboldt university group which has used the exponential relation between potentials and gauge links.