A Pedagogical Introduction to the Lifshitz Regime

We discuss the phase structure of QCD for N f = 2 and N f = 2 + 1 dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for µB/T 6. We find a critical endpoint at (TCEP, µB CEP ) = (107, 635) MeV. The curvature of the phase boundary at small chemical potential is κ = 0.0142(2), computed from the renormalised light chiral condensate ∆ l,R . Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for µB 417 MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.

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“…For reviews see e.g. [184][185][186][187][188], for applications with the functional RG see e.g. [111,[189][190][191].…”

Section: B Inhomogeneous Regime At Large Chemical Potentialmentioning

confidence: 99%

QCD phase structure at finite temperature and density

2020

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“…A different important issue is the role of fluctuations. One should include them to detect possible instabilities of the space modulation of the condensate [17][18][19], which seem to be particularly important for 1D modulations [8,20,21]. The inclusion of fluctuations in the IGL framework could be implemented following the procedure of [22][23][24].…”

Section: Discussionmentioning

confidence: 99%

The improved Ginzburg-Landau technique

Mannarelli

2018

EPJ Web Conf.

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We discuss an innovative method for the description of inhomogeneous phases designed to improve the standard Ginzburg-Landau expansion. The method is characterized by two key ingredients. The first one is a moving average of the order parameter designed to account for the long-wavelength modulations of the condensate. The second one is a sum of the high frequency modes, to improve the description of the phase transition to the restored phase. The method is applied to compare the free energies of 1D and 2D inhomogeneous structures arising in the chirally symmetric broken phase. *

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“…However, it should be reminded that a negative Z φ,k=0 (0) is not bound to the formation of an inhomogeneous phase, it can also serve as an precursor for the inhomogeneous phase. See, e.g., [135,137,[236][237][238][239][240][241][242][243][244][245] for more related discussions. Most notably, very recently consequence of the inhomogeneous instability indicated by the negative wave function renormalization on the phenomenology of heavy-ion collisions has been studied.…”

Section: Region Of Inhomogeneous Instability At Large Baryon Chemical...mentioning

confidence: 99%

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

2022

Preprint

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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 µB 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.

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A Pedagogical Introduction to the Lifshitz Regime

Cited by 18 publications

References 16 publications

QCD phase structure at finite temperature and density

QCD phase structure at finite temperature and density

The improved Ginzburg-Landau technique

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

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