Four loop stochastic perturbation theory in 3d SU(3)

TL;DR

This paper performs four-loop stochastic perturbation theory calculations in 3d SU(3) gauge theory to understand ultrasoft degrees of freedom in finite temperature QCD, providing detailed perturbative matching results.

Contribution

It introduces a four-loop numerical stochastic perturbation theory approach for 3d SU(3) gauge theory, advancing the precision of perturbative calculations in finite temperature field theory.

Findings

Computed the pure gauge plaquette at four loops in 3d SU(3)

Extracted the logarithmic divergence at order g^8

Provided data for perturbative matching in dimensional reduction

Abstract

Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g^8, which had already been computed in the continuum.