Renormalization group improved pressure for cold and dense QCD

Understand

We apply the renormalization group optimized perturbation theory (RGOPT)to evaluate the QCD (matter) pressure at the two-loop level considering three flavors of massless quarks in a dense and cold medium.

• Already at leading order ($\alpha_s^0$), which builds on the simple one loop (RG resummed) term, our technique provides a non-trivial non-perturbative approximation which is completely renormalization group invariant.
• At the next-to-leading order the comparison between the RGOPT and the pQCD predictions shows that the former method provides results which are in better agreement with the state-of-the-art $higher \, order$ perturbative results, which include a contribution of order $\alpha_s^3 \ln^2 \alpha_s$.
• At the same time one also observes that the RGOPT predictions are less sensitive to variations of the arbitrary $\bar{\rm MS}$ renormalization scale than those obtained with pQCD.