Equation of State of QCD with $N_f=3$ flavours up to the electroweak scale

The Equation of State of Quantum Chromodynamics with $N_f=3$ flavours is determined non-perturbatively with a precision of about $0.5\%-1.0\%$ in the range of temperatures between 3 GeV and 165 GeV. The computation is carried out by numerical simulations of the gauge theory discretized on the lattice. At each given temperature the entropy density is computed at several lattice spacings in order to extrapolate the results to the continuum limit. The pressure and energy density are then determined by integrating the entropy density with respect to the temperature. The numerical data show a linear behaviour in the strong coupling constant squared, which points to the Stefan-Boltzmann limit at infinite temperature. They are also compatible with the known perturbative formula supplemented by higher order terms in the coupling constant, containing non-perturbative contributions. This parametrization describes well our data together with those present in the literature down to 500 MeV.