Using NSPT for the Removal of Hypercubic Lattice Artifacts

TL;DR

This paper investigates the use of Numerical Stochastic Perturbation Theory (NSPT) to calculate and subtract hypercubic lattice artifacts in non-perturbative renormalization, extending beyond 1-loop order for Wilson fermion operators.

Contribution

It demonstrates the feasibility of using NSPT to compute hypercubic corrections at higher loops, surpassing traditional 1-loop LPT limitations for non-perturbative renormalization.

Findings

NSPT can compute hypercubic corrections up to 3-loop order.

Comparison of boosted and unboosted perturbative corrections shows significant differences.

Results improve the accuracy of non-perturbative renormalization constants.

Abstract

The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI'-MOM scheme a large part of these artifacts can be calculated and subtracted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.