Search for a proper and realistic equation of state (EOS) for strongly interacting matter used in the study of the QCD phase diagram still appears as a challenging problem. Recently, we constructed a hybrid model description for the quark gluon plasma (QGP) as well as hadron gas (HG) phases where we used an excluded volume model for HG and a thermodynamically consistent quasiparticle model for the QGP phase. The hybrid model suitably describes the recent lattice results of various thermodynamical as well as transport properties of the QCD matter at zero baryon chemical potential ($μ_{B}$). In this paper, we extend our investigations further in obtaining the properties of QCD matter at finite value of $μ_{B}$ and compare our results with the most recent results of lattice QCD calculation.
Thermodynamics properties of an interacting system of bosons are considered at finite temperatures and zero chemical potential within the Skyrme-like mean-field model. An interplay between attractive and repulsive interactions is investigated. As a particular example an equilibrium system of pions is discussed. Several modifications of thermodynamic properties in the considered system are found with increasing a strength of attractive forces. Different types of the first order phase transition are classified. Some of these transitions exist also in the Boltzmann approximation. However, effects…
We investigate the phase structure of strongly interacting matter at non-vanishing isospin before the onset of pion condensation in the framework of the unquenched Polyakov-Quark-Meson model with 2+1 quark flavors. We show results for the order parameters and all relevant thermodynamic quantities. In particular, we obtain a moderate change of the pressure with isospin at vanishing baryon chemical potential, whereas the chiral condensate decreases more appreciably. We compare the effective model to recent lattice data for the decrease of the pseudo-critical temperature with the isospin chemical…
We explore the highly non-perturbative hot region of the QCD phase diagram close to Tc by use of an imaginary chemical potential mu which avoids the sign problem. The number density and the quark number susceptibility are consistent with a critical behaviour associated with the transition line in the negative mu^2 half-plane. We compare the analytic continuation of these results with various phenomenological models, none of which provides a satisfactory description of data, a failure on which we make some comments. These results complement and extend the information obtained via the analysis o…
The energy dependence of various particle ratios is calculated within the Ultra-Relativistic Quantum Molecular Dynamics approach and compared with the hadron resonance gas (HRG) model and measurements from various experiments, including RHIC-BES, SPS and AGS. It is found that the UrQMD particle ratios agree well with the experimental results at the RHIC-BES energies. Thus, we have utilized UrQMD in simulating particle ratios at other beam energies down to 3 GeV, which will be accessed at NICA and FAIR future facilities. We observe that the particle ratios for crossover and first-order phase tr…
We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $μ_π$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $μ_π\ne…
We use a "hybrid" method, mixing variationally-determined triaxial nuclear Slater determinants, to calculate the response of Ge73 to hypothetical dark-matter particles such as neutralinos. The method is a hybrid in that rotational invariance is approximately restored prior to variation and then fully restored before the mixing of intrinsic states. We discuss such features of Ge73 as shape coexistence and triaxiality, and their effects on spin-dependent neutralino cross sections. Our calculations yield a satisfactory quadrupole moment and an accurate magnetic moment in this very complicated nuc…
We review the transport properties of the strongly interacting quark-gluon plasma (QGP) created in heavy-ion collisions at ultrarelativistic energies, i.e. out-of equilibrium, and compare them to the equilibrium properties. The description of the strongly interacting (non-perturbative) QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. We study the transport coefficients such as the ratio of shear…
We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation Theory at low and moderate temperatures, below any phase transition to a quark-gluon plasma phase. We argue that inelastic processes are irrelevant and exponentially suppressed at low temperatures. Since the system falls out of chemical equilibrium upon expansion,a pion chemical potential must be introduced, so we extend the existing theory to include it. We control the zero modes of the collision operator and Landau's conditions of fit when solving the Boltzmann equation with the elastic collision kernel. The dependen…
We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems of quasi-particles whose masses depend on both the temperature and the chemical potential. We work out several solutions for an interacting system of quarks and gluons and show that there is only one type of solution that reproduce both perturbative and lattice QCD.
The meson exchange interaction based on relativistic mean-field (RMF) theory has been introduced in the hadron resonance gas (HRG) model, called interacting HRG (iHRG) model. This model can be used to explain the experimental data both at finite temperature ($T$) with finite chemical potential ($μ_B$) and finite temperature at vanishing chemical potential. The nuclear matter equation of state also can be explained at zero temperature with finite baryon density (finite chemical potential) due to the presence of attractive and repulsive interactions between the hadrons in the iHRG model. Similar…
The equation of state and fluctuations of conserved charges in a strongly interacting medium under equilibrium conditions form the baseline upon which various possible scenarios in relativistic heavy-ion collision experiments are built. Many of these quantities have been obtained in the lattice QCD framework with reliable continuum extrapolations. Recently the Polyakov$-$Nambu$-$Jona-Lasinio model has been reparametrized to some extent to reproduce quantitatively the lattice QCD equation of state at vanishing chemical potentials. The agreement was precise except at low temperatures, possibly d…
We study finite volume effects within the Polyakov loop Nambu-Jona-Lasinio model for two light and one heavy quarks at vanishing baryon chemical potential and finite temperatures. We include three different Polyakov loop potentials and ensure that the predictions of our effective model in bulk are compatible with lattice QCD results. Finite size effects are taken into account by means of the Multiple Reflection Expansion formalism. We analyze several thermodynamic quantities including the interaction measure, the speed of sound, the surface tension, and the curvature energy and find that they …
Search of a proper and realistic equations of state (EOS) for strongly interacting matter used in the study of QCD phase diagram still appears as a challenging task. Recently, we have constructed a hybrid model description for the quark gluon plasma (QGP) as well as hadron gas (HG) phases where we use a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase. We attempt to use them to get a QCD phase boundary and a critical point. We test our hybrid model by reproducing the entire lattice QCD data for strongly interacting matter at zero baryon …
QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential $μ_{\text B}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu-Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu-Jona-Lasinio model describes the weakly …
There are two possible methods for the inclusion of the chemical potential in a relativistic bosonic field theory. The most popular method has recently been criticised by some authors, so much so as to require a re-analysis of the entire problem. I here present a new approach to the inclusion of the chemical potential that uses the second method and zeta-function regularisation techniques. I first apply it to the non-interacting field, obtaining an expression for the effective potential which is formally coincident with the well-known one from the first method. My approach, however, seems here…
We extend the hadronic SU(3) non-linear sigma model to include quark degrees of freedom. The choice of potential for the Polyakov loop as a function of temperature and chemical potential allows us to construct a realistic phase diagram from the analysis of the order parameters of the system. These parameters are the chiral condensate, for the chiral symmetry restoration and the Polyakov loop, for the deconfinement to quark matter. Besides reproducing lattice QCD results, for zero and low chemical potential, we are in agreement with neutron star observations for zero temperature.
Intensive search for a proper and realistic equations of state (EOS) is still continued for studying the phase diagram existing between quark gluon plasma (QGP) and hadron gas (HG) phases. Lattice calculations provide such EOS for the strongly interacting matter at finite temperature ($T$) and vanishing baryon chemical potential ($μ_{B}$). These calculations are of limited use at finite $μ_{B}$ due to the appearance of notorious sign problem. In the recent past, we had constructed a hybrid model description for the QGP as well as HG phases where we make use of a new excluded-volume model for H…
Instanton liquid in heated and strongly interacting matter is studied using the variational principle. The dependence of the instanton liquid density (gluon condensate) on the temperature and the quark chemical potential is determined under the assumption that, at finite temperatures, the dominant contribution is given by an ensemble of calorons. The respective one-loop effective quark Lagrangian is used.
A quasiparticle model of the quark-gluon plasma is compared with lattice QCD data for purely imaginary chemical potential. Net quark number density, susceptibility as well as the deconfinement border line in the phase diagram of strongly interacting matter are investigated. In addition, the impact of baryo-chemical potential dependent quasiparticle masses is discussed. This accomplishes a direct test of the model for non-zero baryon density. The found results are compared with lattice QCD data for real chemical potential by means of analytic continuation and with a different (independent) set …
The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the standard ground state energy and pressureas function of the particle density. At finite temperatures it is found necessary to include ring corrections to the one-loop result in order to satisfy the Goldstone theorem. It is natural to introduce an effective chemical potential directly related to the order parameter and which uniformly decreases with increasing …
Analytical solutions are obtained to the nonlinear equations describing neutrino oscillations when explicit neutrino-antineutrino asymmetries are present. Such a system occurs in the early Universe if neutrinos have a non-zero chemical potential. Solutions to the equations lead to a new type of coherent behavior governed by two modes. These bimodal solutions provide new insights into dense neutrino gases and into neutrino oscillations in the early Universe, thereby allowing one to surmise the flavor behavior of neutrinos with a non-zero chemical potential.
We employ a conformal mapping to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $μ$. This method allows us to identify the singularity corresponding to the critical point of a second-order phase transition at finite $μ$, given information only at $μ=0$. The scheme is potentially useful for computing thermodynamic properties of strongly interacting hot and dense matter in lattice gauge theory. The technique is illustrated by an application to a chiral effective model.
