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

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.