Discretization Errors for the Gluon and Ghost Propagators in Landau Gauge using NSPT

TL;DR

This paper explores using numerical stochastic perturbation theory to compute higher-order lattice corrections for gluon and ghost propagators in Landau gauge, aiming to improve the removal of lattice artifacts beyond 1-loop order.

Contribution

It demonstrates the feasibility of NSPT for calculating 3-loop lattice corrections for SU(3) gluon and ghost propagators in Landau gauge, surpassing traditional 1-loop methods.

Findings

NSPT successfully computes 3-loop corrections.

Higher-order corrections improve artifact removal.

Comparison with H(4) method provides validation.

Abstract

The subtraction of hypercubic lattice corrections, calculated at 1-loop order in lattice perturbation theory (LPT), is common practice, e.g., for determinations of renormalization constants in lattice hadron physics. Providing such corrections beyond 1-loop order is however very demanding in LPT, and numerical stochastic perturbation theory (NSPT) might be the better candidate for this. Here we report on a first feasibility check of this method and provide (in a parametrization valid for arbitrary lattice couplings) the lattice corrections up to 3-loop order for the SU(3) gluon and ghost propagators in Landau gauge. These propagators are ideal candidates for such a check, as they are available from lattice simulations to high precision and can be combined to a renormalization group invariant product (Minimal MOM coupling) for which a 1-loop LPT correction was found to be insufficient to remove the bulk of the hypercubic lattice artifacts from the data. As a bonus, we also compare our results with the ever popular H(4) method.