Abstract
The weak-coupling expansion of the QCD pressure is known up to the order g 6 log g . However, at experimentally relevant temperatures, the corresponding series is poorly convergent. In this proceedings, we discuss at which extent the gauge-invariant resummation scheme, Hard-Thermal-Loop perturbation theory (HTLpt), improves the apparent convergence. We first present HTLpt results for QCD thermodynamic functions up to three-loop order at vanishing chemical potential. Then, we report a preliminary HTLpt result of one-loop quark number susceptibility, probing the finite density equation of state. Our results are consistent with lattice data down to 2 − 3 T c , reinforcing the weakly-coupled quasiparticle picture in the intermediate coupling regime.
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