Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (I) The ghost propagator in Landau gauge

TL;DR

This paper uses Numerical Stochastic Perturbation Theory to compute the ghost propagator in Landau gauge for SU(3) lattice gauge theory up to three loops, aiming to compare with non-perturbative lattice results.

Contribution

It introduces a method to calculate ghost propagators perturbatively up to three loops in lattice QCD using NSPT, with detailed analysis of infinite volume and continuum limits.

Findings

Computed ghost propagator up to three loops in Landau gauge

Analyzed infinite volume and continuum limits of results

Provides a foundation for comparing perturbative and non-perturbative lattice data

Abstract

This is the first of a series of two papers on the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to eventually compare with results from lattice simulations in order to enlight the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost propagator in Landau gauge up to three loops. We present results in the infinite volume and $a \to 0$ limits, based on a general strategy that we discuss in detail.