QCD Equation of State with $N_f=3$ Flavors up to the Electroweak Scale

TL;DR

This paper non-perturbatively determines the QCD equation of state for three flavors across a wide temperature range up to the electroweak scale, achieving high precision through lattice simulations.

Contribution

It provides the first high-precision lattice calculation of the QCD equation of state from 3 to 165 GeV, bridging non-perturbative and perturbative regimes.

Findings

Results approach the Stefan-Boltzmann limit at high temperatures.

Data are compatible with perturbative formulas including higher-order terms.

Continuum extrapolation confirms the reliability of lattice results.

Abstract

The equation of state of Quantum Chromodynamics with $N_f=3$ flavors is determined non-perturbatively in the range of temperatures between $3$ and $165$~GeV with a precision of about $0.5$-$1.0$\%. The calculation is carried out by numerical simulations of lattice gauge theory discretized \`a la Wilson with shifted boundary conditions in the compact direction. At each given temperature the entropy density is computed at several lattice spacings in order to extrapolate the results to the continuum limit. Taken at face value, data point straight to the Stefan-Boltzmann value by following a linear behavior in the strong coupling constant squared. They are also compatible with the known perturbative formula supplemented by higher order terms in the coupling constant, a parametrization which describes well our data together with those present in the literature down to $500$ MeV.