QCD at finite temperature and density within the fRG approach: An overview

TL;DR

This paper reviews recent advances in studying QCD at finite temperature and density using the nonperturbative functional renormalization group approach, highlighting results on phase structure, critical points, and experimental comparisons.

Contribution

It provides a comprehensive overview of fRG applications to QCD, including phase diagram predictions and critical phenomena, with comparisons to other first-principles methods.

Findings

Estimated location of the critical end point around 600 MeV baryon chemical potential.

Identified inhomogeneous instability region at μ_B ≥ 420 MeV.

Explained non-monotonic kurtosis behavior in net-proton fluctuations.

Abstract

In this paper we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated in successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc., are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson-Schwinger Equations, which passes through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with $\mu_B\gtrsim 420$ MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments, could arise from the increasingly sharp crossover in the regime of low collision energy.