Renormalization group improved pressure for hot and dense quark matter

We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.