The Equation of State of QCD up to very high temperatures

TL;DR

This paper non-perturbatively computes the entropy density of QCD at very high temperatures using a novel, efficient lattice approach with shifted boundary conditions, achieving high accuracy and comparing with perturbative predictions.

Contribution

It introduces a new computational strategy for calculating QCD thermodynamics at high temperatures using shifted boundary conditions and continuum extrapolation.

Findings

Entropy density computed with 0.5-1.0% accuracy.

Results agree with high-temperature perturbation theory.

Method applicable to other thermodynamic quantities.

Abstract

We present the non-perturbative computation of the entropy density in QCD for temperatures ranging from 3 GeV up to the electro-weak scale, using $N_f=3$ flavours of massless O$(a)$-improved Wilson fermions. We adopt a new strategy designed to be computationally efficient and based on formulating thermal QCD in a moving reference frame, where the fields satisfy shifted boundary conditions in the temporal direction and periodic boundary conditions along the spatial ones. In this setup the entropy density can be computed as the derivative of the free-energy density with respect to the shift parameter. For each physical temperature, we perform Monte Carlo simulations at four values of the lattice spacing in order to extrapolate the numerical data of the entropy density to the continuum limit. We achieve a final accuracy of approximatively $0.5$-$1.0\%$ and our results are compared with predictions from high-temperature perturbation theory.