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Register a new userAn effective model for the QCD phase transitions at finite baryon density
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We introduce an effective quark-meson-nucleon model for the QCD phase transitions at finite baryon density. The nucleon and the quark degrees of freedom are described within a unified framework of a chiral linear sigma model. The deconfinement transition is modeled through a simple modification of the distribution functions of nucleons and quarks, where an additional auxiliary field, the bag field, is introduced. The bag field plays a key role in converting between the nucleon and the quark degrees of freedom. The model predicts that the chiral and the deconfinement phase transitions are always separated. Depending on the model parameters, the chiral transition occurs in the baryon density range of $(1.5-15.5)n_0$, while the deconfinement transition occurs above $5 n_0$, where $n_0$ is the saturation density.
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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 $mu_B/T lesssim 6$. We find a critical endpoint at $(T_text{CEP},{mu_B}_{text{CEP}})=(107, 635),text{MeV}$. The curvature of the phase boundary at small chemical potential is $kappa=0.0142(2)$, computed from the renormalised light chiral condensate $Delta_{l,R}$. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for $mu_Bgtrsim 417$ 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.
The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, mu_B and mu_{iso}, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type eight-quark interaction can reproduce lattice QCD data at not only mu_{iso}=mu_B=0 but also mu_{iso}>0 and mu_B=0. In the mu_{iso}-mu_{B}-T space, where T is temperature, the critical endpoint of the chiral phase transition in the mu_B-T plane at mu_{iso}=0 moves to the tricritical point of the pion-superfluidity phase transition in the mu_{iso}-T plane at mu_B=0 as mu_{iso} increases. The thermodynamics at small T is controlled by sqrt{sigma^2+pi^2} defined by the chiral and pion condensates, sigma and pi.
In this work, we revisit the thermodynamical self-consistency of the quasiparticle model with the finite baryon chemical potential adjusted to lattice QCD calculations. Here, we investigate the possibility that the effective quasiparticle mass is also a function of its momentum, $k$, in addition to temperature $T$ and chemical potential $mu$. It is found that the thermodynamic consistency can be expressed in terms of an integro-differential equation concerning $k$, $T$, and $mu$. We further discuss two special solutions, both can be viewed as sufficient condition for the thermodynamical consistency, while expressed in terms of a particle differential equation. The first case is shown to be equivalent to those previously discussed by Peshier et al. The second one, obtained through an ad hoc assumption, is an intrinsically different solution where the particle mass is momentum dependent. These equations can be solved by using boundary condition determined by the lattice QCD data at vanishing baryon chemical potential. By numerical calculations, we show that both solutions can reasonably reproduce the recent lattice QCD results of the Wuppertal-Budapest and HotQCD Collaborations, and in particular, those concerning finite baryon density. Possible implications are discussed.
The QCD equation of state at finite baryon density is studied in the framework of a Cluster Expansion Model (CEM), which is based on the fugacity expansion of the net baryon density. The CEM uses the two leading Fourier coefficients, obtained from lattice simulations at imaginary $mu_B$, as the only model input and permits a closed analytic form. Excellent description of the available lattice data at both $mu_B = 0$ and at imaginary $mu_B$ is obtained. We also demonstrate how the Fourier coefficients can be reconstructed from baryon number susceptibilities.
Fluctuations of conserved charges are sensitive to the QCD phase transition and a possible critical endpoint in the phase diagram at finite density. In this work, we compute the baryon number fluctuations up to tenth order at finite temperature and density. This is done in a QCD-assisted effective theory that accurately captures the quantum- and in-medium effects of QCD at low energies. A direct computation at finite density allows us to assess the applicability of expansions around vanishing density. By using different freeze-out scenarios in heavy-ion collisions, we translate these results into baryon number fluctuations as a function of collision energy. We show that a non-monotonic energy dependence of baryon number fluctuations can arise in the non-critical crossover region of the phase diagram. Our results compare well with recent experimental measurements of the kurtosis and the sixth-order cumulant of the net-proton distribution from the STAR collaboration. They indicate that the experimentally observed non-monotonic energy dependence of fourth-order net-proton fluctuations is highly non-trivial. It could be an experimental signature of an increasingly sharp chiral crossover and may indicate a QCD critical point. The physics implications and necessary upgrades of our analysis are discussed in detail.
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