# Towards a precise determination of the equation of state of QCD at high-temperature

## TL;DR

This paper reports preliminary non-perturbative results for the QCD equation of state at high temperatures using lattice QCD in a moving frame, focusing on entropy density calculations with improved Wilson fermions.

## Contribution

It introduces a lattice formulation of QCD in a moving frame to accurately determine the entropy density at high temperatures, advancing non-perturbative methods.

## Key findings

- Preliminary results for QCD at 3-80 GeV temperatures.
- Validation of lattice formulation in a moving reference frame.
- Analysis of O(a)-improvement for expectation values.

## Abstract

We present preliminary results towards a fully non-perturbative determination of the equation of state of QCD at very high-temperatures, $T\approx 3-80\,{\rm GeV}$. The key ingredient is the lattice formulation of QCD in a moving reference frame, which allows us for a neat determination of the entropy density from simple expectation values of the momentum-components of the energy-momentum tensor. For the computation we employ $N_{\rm f}=3$ flavours of non-perturbatively O($a$)-improved Wilson-fermions. We present an analysis of the O($a$)-improvement of the expectation values entering the determination, and show how these can be accurately computed in simulations.