Towards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure

TL;DR

This paper advances the calculation of a key condensate contribution to hot QCD pressure by applying 4-loop Numerical Stochastic Perturbation Theory within an effective 3D model, addressing convergence issues.

Contribution

It demonstrates the use of NSPT to determine the lattice spacing dependence of a condensate up to 4-loop order, improving precision in hot QCD pressure calculations.

Findings

Successfully extended NSPT to 4-loop order for the condensate.

Identified and addressed discretization artifacts in lattice measurements.

Sharpened computational tools with a 2-loop example.

Abstract

Thanks to dimensional reduction, the contributions to the hot QCD pressure coming from so-called soft modes can be studied via an effective three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields plus an adjoint Higgs scalar). The poor convergence of the perturbative series within EQCD suggests to perform lattice measurements of some of the associated gluon condensates. These turn out, however, to be plagued by large discretization artifacts. We discuss how Numerical Stochastic Perturbation Theory can be exploited to determine the full lattice spacing dependence of one of these condensates up to 4-loop order, and sharpen our tools on a concrete 2-loop example.