Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order

We extend previous next-to-next-to leading order (NNLO) calculations of the QCD pressure at zero temperature and non-zero baryonic densities using the renormalization group optimized perturbation theory (RGOPT), which entails an all-order RG-invariant resummation. First, we consider the approximation of three massless quark flavors, and then adding the running strange quark mass dependence. The resulting pressure displays a sizeably reduced sensitivity to variations of the arbitrary renormalization scale as compared to the state-of-the-art NNLO results. This confirms previous NLO investigations that the RGOPT resummation scheme provides improved convergence properties and reduced renormalization scale uncertainties, thus being a promising prescription to improve perturbative QCD at high and mid range baryonic densities.