Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

TL;DR

This paper uses Numerical Stochastic Perturbation Theory to estimate a key gluon condensate in a three-dimensional SU(3) + adjoint Higgs theory at four-loop order, revealing significant discretization effects.

Contribution

It provides the first four-loop lattice perturbation theory estimate of the gluon condensate relevant for high-temperature QCD pressure calculations.

Findings

Large discretization effects observed, scaling as a ln(1/a).

Results highlight challenges in continuum extrapolation of lattice measurements.

Suggests need for cross-verification with standard perturbation techniques.

Abstract

The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as non-perturbative contributions from "soft" thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of "large" discretization effects, going like $a\ln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.