The correlations of the velocities and of the vorticities for pions and nucleons are investigated in frames of the PHSD model for Au+Au collisions at √(s_NN)=7.8 GeV and fixed impact parameter b=7.5 fm. The different behavior of correlations for these kinematic quantities is observed. It is shown that after the time of the separation of the nuclei this difference is due to the ‘microscopic’ Hubble flow. However, for earlier times the reasons are more complicated.

We study self-consistent approximations such as the $\Phi$-derivable and virial approaches to dilute strongly interacting systems in equilibrium. We consider a system of non-relativistic fermions of one kind interacting via a pair potential Thermodynamical quantities are expressed in terms of various spectral functions. We review the $\Phi$ derivable approximation scheme demonstrating the exact conservation of the Noether and the Botermans-Malfliet fermion number densities, and then for $\Phi$ described by the tadpole and sandwich diagrams we show the coincidence of these two number densities. As examples of test pair potentials, we consider the Yukawa central nucleon-nucleon potentials within Walecka, CD Bonn, and Reid parameterizations, and the corresponding classical Lennard-Jones potentials. Expressions for the second and third virial coefficients are derived and analyzed for $\Phi$ described by the tadpole and sandwich diagrams. Next, we focus on the virial approach to the equation of state. Classical, semiclassical, and purely quantum approaches are studied in detail. Then, different extrapolations of the virial equation of state are considered including the van~der~Waals form and excluded-volume models. We derive the expression for the second virial coefficient using the effective range approximation for the scattering amplitude and compare the result with the purely quantum result using the experimental phase shifts. Attention is focused on the problem of anomalously large value of the nucleon-nucleon scattering length appearing due to the presence of the quasi-bound state in nucleon-nucleon scattering, which can be destroyed in the matter because of the action of the Pauli blocking. We present results for the second virial coefficient subtracting this term. We discuss the validity of such a procedure to describe the equation of state of the nuclear matter in the virial limit.

The strange baryon production in Bi+Bi collisions at √(s_NN)=9.0 GeV is studied using the PHSD transport model. Hyperon and anti-hyperon yields, transverse momentum spectra, and rapidity spectra are calculated, their centrality dependence and the effect of rapidity and transverse momentum cuts are studied. The rapidity distributions for Lambda, Ξ, Xi baryons are found to be systematically narrower than for Λs. The p_T slope parameters for anti-hyperons vary more with centrality than those for hyperons. Restricting the accepted rapidity range to |y|<1 increases the slope parameters by 13–30 MeV depending on the centrality class and the hyperon mass. Hydrodynamic velocity and vorticity fields are calculated and the formation of two oppositely rotating vortex rings moving in opposite directions along the collision axis is found. The hyperon spin polarization induced by the medium vorticity within the thermodynamic approach is calculated and the dependence of the polarization on the transverse momentum and rapidity cuts and on the centrality selection is analyzed. The cuts have stronger effect on the polarization of Λ and Ξ hyperons than on the corresponding anti-hyperons. The polarization signal is maximal for the centrality class 60-70%. We show that for the considered hyperon polarization mechanism the structure of the vorticity field makes an imprint on the polarization signal as a function of the azimuthal angle in the transverse momentum plane, ϕ_H, cosϕ_H=p_x/p_T. For particles with positive longitudinal momentum, p_z>0, the polarization increases with cosϕ_H, while for particles with p_z<0 it decreases.

Preliminary results on determination of the microscopic Hubble constant for pions and nucleons in Au + Au collisions at √(s_NN) = 7.8 GeV for a range of times and b = 7.5 fm are presented and discussed. The data are simulated within PHSD model. A typically used method based on the fit of the velocity profile is considered in detail. Also a new method for determination of the Hubble parameter is proposed. It consists in the analysis of the statistical distribution of the divergence of the velocity field and getting the Hubble parameter as a position of a particular peak of the distribution. A comparison of the methods is done.

Analyses for the NICER data indicate that there is no significant variation of the compact star radii within the mass range of 1.4 to 2.0 solar masses. Yamamoto et al. [Phys. Rev. C 108, 035811 (2023)] concluded recently that ``this feature cannot be reproduced by the hadronic matter due to the softening of the equation of state (EoS) by hyperon mixing, suggesting the possible existence of quark phases in neutron-star interiors.'' Using a collection of 162 purely nucleonic, hyperonic, and quarkish EoSs from CompOSE database and some other works, we verify that hyperons indeed lead to a significant difference in radii of stars of 1.4 and 2.0 solar masses, which diminishes in the presence of quarks. We compare the shapes of the mass-radius curves and show that hyperons and quarks in the neutron star cores prefer a particular curve shape with backbending. It is argued that the shape {is controlled by the density dependence} of the nuclear symmetry energy. We draw attention to the existence of a class of purely hadronic relativistic mean-field EoSs with scalar-field dependent hadron masses and coupling constants that satisfy the known constraints on the EoSs including the analyses of the new NICER data and the above requirement of no significant variation of the neutron star radii.

The strange baryon production in Bi + Bi collisions at sNN=9.0 GeV is studied using the PHSD transport model. Hyperon and anti-hyperon yields, transverse momentum spectra, and rapidity spectra are calculated, and their centrality dependence and the effect of rapidity and transverse momentum cuts are studied. The rapidity distributions for Λ¯, Ξ, Ξ¯ baryons are found to be systematically narrower than for Λs. The pT slope parameters for anti-hyperons vary more with centrality than those for hyperons. Restricting the accepted rapidity range to |y|<1 increases the slope parameters by 13–30 MeV, depending on the centrality class and the hyperon mass. Hydrodynamic velocity and vorticity fields are calculated, and the formation of two oppositely rotating vortex rings moving in opposite directions along the collision axis is found. The hyperon spin polarization induced by the medium vorticity within the thermodynamic approach is calculated, and the dependence of the polarization on the transverse momentum and rapidity cuts and on the centrality selection is analyzed. The cuts have stronger effect on the polarization of Λ and Ξ hyperons than on the corresponding anti-hyperons. The polarization signal is maximal for the centrality class, 60–70%. We show that, for the considered hyperon polarization mechanism, the structure of the vorticity field makes an imprint on the polarization signal as a function of the azimuthal angle in the transverse momentum plane, ϕH, cosϕH=px/pT. For particles with positive longitudinal momentum, pz>0, the polarization increases with cosϕH, while for particles with pz<0 it decreases.

The gold-gold collisions at root s(NN) = 7.7 and 11.5GeV are simulated within the PHSD transport model. In each collision event, the spectator nucleons are separated and the fluidization procedure for the participants is performed. The local velocities are determined in the Landau frame and the kinematic and thermal vorticity fields are evaluated. We analyze the thermodynamic properties of the cells where Lambda s and (Lambda) over bars were born or had their last interaction. Such cells contribute to the formation of the observed global polarization of hyperons induced by the thermal vorticity of the medium. The L polarization signal is found to be mainly determined by hot, dense, and highly vortical cells at the earlier stage of the collision, whereas the L polarization signal is accumulated over the longer time and includes cells with lower vorticity. The calculated global polarizations for both Ls and Ls agree well with the experimental finding by the STAR collaboration at energy root s(NN) = 11.5GeV. For collisions at root s(NN) = 7.7GeV, we can reproduce the STAR data for L hyperons, but significantly underpredict the observed global polarization of (Lambda) over bar. Furthermore, we consider the centrality dependence of the hyperon polarization in collisions at 7.7 GeV. It increases with an increase of centrality, reaches a maximum at 65-75% and then starts decreasing rapidly for peripheral collisions.

The gold–gold collisions at sNN=7.7 and 11.5 GeV are simulated within the PHSD transport model. In each collision event, the spectator nucleons are separated and the fluidization procedure for the participants is performed. The local velocities are determined in the Landau frame and the kinematic and thermal vorticity fields are evaluated. We analyze the thermodynamic properties of the cells where Λs and Λ¯s were born or had their last interaction. Such cells contribute to the formation of the observed global polarization of hyperons induced by the thermal vorticity of the medium. The Λ¯ polarization signal is found to be mainly determined by hot, dense, and highly vortical cells at the earlier stage of the collision, whereas the Λ polarization signal is accumulated over the longer time and includes cells with lower vorticity. The calculated global polarizations for both Λs and Λ¯s agree well with the experimental finding by the STAR collaboration at energy sNN=11.5 GeV. For collisions at sNN=7.7 GeV, we can reproduce the STAR data for Λ hyperons, but significantly underpredict the observed global polarization of Λ¯. Furthermore, we consider the centrality dependence of the hyperon polarization in collisions at 7.7 GeV. It increases with an increase of centrality, reaches a maximum at 65–75% and then starts decreasing rapidly for peripheral collisions.

Global polarization of hyperons induced by the local vorticity of the medium created in heavy-ion collisions at energies 2.3\,GeV$\le\sqrt{s_{NN}}\le$11.5 GeV is calculated in the parton-hadron-string dynamic (PHSD) model. The separation of spectator nucleons and the fluidization of the generated particle distributions are performed. The polarization of all anti-hyperon species is found significantly larger than that of hyperons. The $\overline{\Xi}$ hyperons are found to be polarized as strong as $\overline{\Lambda}$s but $\Xi$ hyperons have weaker polarization compared to $\Lambda$s. The $\Omega$ and $\overline{\Omega}$ polarizations show the strongest dependence on the collision energy. Despite the strong polarization of the produced $\Lambda$s and $\overline{\Lambda}$s induced by the vortical flows in the medium, the observed polarization signal is significantly depleted because of the feed down from weak and electromagnetic decays of heavier hyperons. Particularly strong suppression is found to be due to electromagnetic decays of $\Sigma^0$ hyperons, which multiplicities obtained in the transport are poorly constrained both from the microscopic input of the $\Sigma^0$ production reactions and from the experimental data. The final $\Lambda(\overline{\Lambda})$ polarization signal strongly depends on the $\Sigma^0$ multiplicity generated in the model. With all these effects we can reproduce the measured global $\Lambda$ polarization in collisions at $\sqrt{s_{NN}}=7.7$ and $11.5$ GeV and the global $\overline{\Lambda}$ polarization at 11.5 GeV. For energies $< 3$ GeV, the calculated $\Lambda$ polarization is smaller than the observed one. The polarization of $\Xi(\overline{\Xi})$ hyperons is calculated. The signal of $\Xi(\overline{\Xi})$ polarization is argued to be insensitive to feed-down effects and be a more direct probe of the degree of the vorticity in the system.

Heavy-ion collisions at center-of-mass nucleon collision energies 4.5-11.5 GeV are analyzed within the parton-hadron-string dynamics (PHSD) transport model. Spectator nucleons are separated, and the transfer of the initial angular momentum of colliding nuclei to the fireball formed by participants is studied. The maximal angular momentum is carried by the fireball in gold-gold collisions with the impact parameter about 5 fm corresponding to centrality class 10-20%. The obtained participant distributions were fluidized and the energy and baryon number densities, temperature, and velocity fields are obtained in the Landau frame. It is shown that the velocity field has dominantly Hubble-like transversal and longitudinal expansion with the vortical motion being only a small correction on top of it. The vorticity field is calculated and illustrated in detail. The formation of two oppositely rotating vortex rings moving in opposite directions along the z axis is demonstrated. Other characteristics of the vortical motion such as the Lamb vector field and the kinematic vorticity number are considered. The magnitude of the latter one is found to be smaller than that for the Poiseuille flow and close to the pure shear deformation corresponding to just a flattening of fluid cells. The field of hydrodynamic helicity, which is responsible for the axial vortex effect, is calculated. The separation of positive and negative helicities localized in upper and lower semiplanes with respect to the reaction plane is shown. It is proved that the areas with various helicity signs can be probed by the selection of A hyperons with positive and negative projections of their momenta orthogonal to the reaction plane.

Heavy-ion collisions at center-of-mass nucleon collision energies 4.5–11.5 GeV are analyzed within the PHSD transport model. Spectator nucleons are separated, and the transfer of the initial angular momentum of colliding nuclei to the fireball formed by participants is studied. The maximal angular momentum is carried by the fireball in gold-gold collisions with the impact parameter about 5 fm corresponding to centrality class 10–20%. The obtained participant distributions were fluidized and the energy and baryon number densities, temperature, and velocity fields are obtained in the Landau frame. It is shown that the velocity field has dominantly Hubble-like transversal and longitudinal expansion with the vortical motion being only a small correction on top of it. The vorticity field is calculated and illustrated in detail. The formation of two oppositely-rotating vortex rings moving in opposite directions along the z axis is demonstrated. Other characteristics of the vortical motion such as the Lamb vector field and the kinematic vorticity number are considered. The magnitude of the latter one is found to be smaller than that for the Poiseuille flow and close to the pure shear deformation corresponding to just a flattening of fluid cells. The field of hydrodynamic helicity, which is responsible for the axial vortex effect, is calculated. The separation of positive and negative helicities localized upper and lower semi-planes with respect to the reaction plane is shown. It is proved that the areas with various helicity signs can be probed by the selection of Λ hyperons with positive and negative projections of their momenta orthogonal to the reaction plane.

Knowledge of the equation of state (EoS) of cold and dense baryonic matter is essential for the description of properties of neutron stars (NSs). With an increase of the density, new baryon species can appear in NS matter, as well as various meson condensates. In previous works, we developed relativistic mean-field (RMF) models with hyperons and Δ -isobars, which passed the majority of known experimental constraints, including the existence of a 2 M ⊙ neutron star. In this contribution, we present results of the inclusion of ρ − -meson condensation into these models. We have shown that, in one class of the models (so-called KVOR-based models, in which the additional stiffening procedure is introduced in the isoscalar sector), the condensation gives only a small contribution to the EoS. In another class of the models (MKVOR-based models with additional stiffening in isovector sector), the condensation can lead to a first-order phase transition and a substantial decrease of the NS mass. Nevertheless, in all resulting models, the condensation does not spoil the description of the experimental constraints.

We extend our hybrid model HydHSD by taking into account shear viscosity within the Israel-Stewart hydrodynamics. The influence of different forms of π^μν constraints on observables is analyzed. We show that the form of the corresponding condition plays an important role for the sensitivity of viscous hydrodynamics to the ratio of shear viscosity to the entropy density, η/s. It is shown that the constraint used in the vHLLE model, results in most sensitivity of rapidity distributions and transverse momentum spectra to a change of the η/s ratio; however, their applicability for large values of η/s is doubtful. On the contrary, the strict constraints from are very strong but most established. We also found that η/s as a function of the collision energy probably has an extremum at E_ lab=10.7 AGeV. However, we obtain that any considered condition does not allow to reproduce simultaneously pion and proton experimental data within our model.

We consider a non-ideal hot pion gas with the dynamically fixed number of particles in the model with the λφ4 interaction. The effective Lagrangian for the description of such a system is obtained by dropping the terms responsible for the change of the total particle number. Within the self-consistent Hartree approximation, we compute the effective pion mass, thermodynamic characteristics of the system and identify a critical point of the induced Bose-Einstein condensation when the pion chemical potential reaches the value of the effective pion mass. The normalized variance, skewness, and kurtosis of the particle number distributions are calculated. We demonstrate that all these characteristics remain finite at the critical point of the Bose-Einstein condensation. This is due to the non-perturbative account of the interaction and is in contrast to the ideal-gas case.

We study the equation of state of cold and dense baryon matter within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field. We include Δ(1232) isobars into previously developed models with hyperons and consider the possibility of charged ρ-meson condensation. The Δ-isobars, being included with realistic values of the attractive in-medium potential, do not lead to a strong decrease of the maximum predicted neutron star (NS) mass, and our models thus resolve the "Δ-resonance puzzle". The charged ρ−-meson condensation leads to a substantial maximum NS mass decrease. However, the observational constraint on the minimal value of the maximum NS mass remains fulfilled in all our models under consideration. The decrease of NS mass can be lowered, if one assumes a limited decrease of the ρ-meson effective mass at high densities.

We study the formation of fluid vorticity and the hyperon polarization in heavy-ion collisions at energies available at the JINR Nuclotron-based Ion Collider fAcility in the framework of the parton-hadron-string dynamic model, taking into account both hadronic and quark-gluonic (partonic) degrees of freedom. The vorticity properties in peripheral Au+ Au collisions at root s(NN) = 7.7 GeV are demonstrated and confronted with other models. The obtained result for the Lambda polarization is in agreement with the experimental data by the STAR Collaboration, whereas the model is not able to explain the observed high values of the antihyperon (Lambda) over bar polarization.

Exploiting a stiff equation of state of the relativistic mean-field model MKVORH ϕ with σ -scaled hadron effective masses and couplings, including hyperons, we demonstrate that the existing neutron-star cooling data can be appropriately described within “the nuclear medium cooling scenario” under the assumption that different sources have different masses.

We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar sigma field, studied previously to incorporate Delta(1232) baryons. Available empirical information is analyzed to put constraints on the couplings of Delta s with meson fields. Conditions for the appearance of Delta s are studied. We demonstrate that with inclusion of the Delta s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urea and the gravitational baryon mass ratio constraints. (C) 2017 Elsevier B.V. All rights reserved.