Four-loop plaquette in 3d with a mass regulator

TL;DR

This paper introduces a mass regulator for 4-loop perturbative calculations of the 3d plaquette in QCD, enabling lattice and continuum scheme conversion at high loop order.

Contribution

It presents a novel mass regulator implementation for 4-loop lattice perturbation theory, facilitating accurate scheme matching in QCD studies.

Findings

Successfully implemented a mass regulator in 4-loop calculations

Enabled conversion between lattice and continuum regularizations

Provided a method to handle IR singularities at high loop order

Abstract

The QCD free energy can be studied by dimensional reduction to a three-dimensional (3d) effective theory, whereby non-perturbative lattice simulations become less demanding. To connect to the original QCD a perturbative matching computation is required, which is conventionally carried out in dimensional regularization. Therefore the 3d lattice results need to be converted to this regularization scheme as well. The conversion must be carried up to 4-loop order, where the free energy displays an infrared (IR) singularity. We therefore need a regulator which can be implemented both on the lattice and in the continuum computation. We introduce a mass regulator to perform Numerical Stochastic Perturbation Theory computations. Covariant gauge is fixed in the Faddeev-Popov scheme without introducing any ghost fields.