Renormalization group improved pressure for cold and dense QCD

Jean-Loïc Kneur,Tulio Eduardo Restrepo,Marcus Benghi Pinto

doi:10.1103/physrevd.100.114006

Abstract

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. These results indicate that the RGOPT provides an efficient resummation scheme which may be considered as an alternative to lattice simulations at high baryonic densities.

Highlights

First principles evaluations aiming to describe the properties of strongly interacting matter at finite temperatures and/ or baryonic densities are highly complicated by the inherent nonlinear and nonperturbative characteristics displayed by quantum chromodynamics (QCD)
The famous sign problem [2] for nonzero chemical potential is still preventing the method to be reliably applied to regimes of intermediate temperatures and baryonic densities which are relevant to experiments such as the beam energy scan (BES) at the Relativistic Heavy Ion Collider (RHIC) as well as CBM at FAIR and NICA at JINR which aim to locate the eventual QCD critical endpoint
The results show that the pressure has a rather large renormalization scale dependence, especially below the quark chemical potential μ ∼ 1 GeV, which corresponds to a baryon density ∼102ρ0 where ρ0 ∼ 0.16 fm−3 represents the nuclear mass density

Summary

Introduction

First principles evaluations aiming to describe the properties of strongly interacting matter at finite temperatures and/ or baryonic densities are highly complicated by the inherent nonlinear and nonperturbative characteristics displayed by quantum chromodynamics (QCD). At least in regimes of vanishing baryonic densities which concerns high energy heavy ion collisions, this fundamental theory can nowadays be successfully described by numerical lattice simulations (LQCD) [1]. The famous sign problem [2] for nonzero chemical potential is still preventing the method to be reliably applied to regimes of intermediate temperatures and baryonic densities which are relevant to experiments such as the beam energy scan (BES) at the Relativistic Heavy Ion Collider (RHIC) as well as CBM at FAIR and NICA at JINR which aim to locate the eventual QCD critical endpoint.

Objectives

Methods

Findings

Conclusion