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

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.

Low energy effective theories on the lattice with coloured noise

“…Potentially, this gives an access to regions of the QCD phase diagram that are inaccessible to full QCD simulations. Moreover, LEFT actions, still coupled to glue dynamics, emerge dynamically in the Wilsonian functional approach at low momentum scales, see the functional renormalisation group (fRG) reviews [1,2]. Hence, lattice results for these LEFTs provide benchmark tests for this part of first principle functional computations in QCD, as well as functional computations directly in LEFTs.…”

Four-quark scatterings in QCD I

“…We use the functional renormalisation group approach to QCD, in which the evolution of the full effective action of QCD is described by its functional flow equation for the effective action Γ k [Φ] where k is an infrared cutoff scale that regularises the infrared propagation of all fields, for recent reviews see [43,44]. Including dynamical hadronisation, the flow equation reads [5,45],…”

“…In (1) we have introduced the effective fields for the scalar-pseudoscalar channel (t-channel), the σ-mode and the pions π. More details can be found in [5], or the reviews [43,44]. This QCD setup will be used in the subsequent works [40] and in particular [41], while in the present work we concentrate on the matter sector in the infrared regime for cutoff scales k ≲ 1 GeV.…”

“…So far, respective fRG computations in QCD have been done within the framework of dynamical hadronisation [5, 17, 18, 20-22, 24, 55], see also the reviews [43,44]. In short, in this framework composite bilinear fields qT q are introduced, that comprises the full dynamics of one momentum channel of a four-quark exchange (qT q) 2 with the given tensor structure T .…”

Numerical RG-time integration of the effective potential: Analysis and Benchmark

“…Dealing with collective phenomena and phase transitions, one may employ a derivative expansion, i.e., a truncation up to some power of momenta in the 1PI effective action Γ k [φ]. In spite of neglecting higher momentum dependencies, derivative expansions are usually a good choice to explore these systems in the fRG, as they allow * nicolas.wink@tu-darmstadt.de to focus on taking into account higher interaction processes, i.e., model the effective action for high orders in the fields, see e.g., [2][3][4][5].…”