Isospin Asymmetric Matter Research Articles

Isospin asymmetric matter in uniform and nonuniform strong magnetic fields

Isospin asymmetric matter in uniform and nonuniform strong magnetic fields

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

We use the two-flavor Linear Sigma Model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral and isospin condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counterterms that are added respecting the original structure of the theory. These counterterms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the noncondensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges

In the current work, we present the influence of finite volume and magnetic field on the thermodynamic properties of isospin asymmetric quark matter using the Polyakov loop extended chiral SU(3) quark mean field (PCQMF) model at finite chemical potential and temperature. Within the PCQMF model, we use the scalar and vector field values in mean-field approximation to obtain the thermodynamic properties: pressure density, entropy density and energy density. The susceptibilities of conserved charges for strongly interacting matter for different system sizes as well as for different values of the magnetic field have been studied. A sizable shift in phase boundary towards the higher values of quark chemical potential ($\mu_q$) and temperature (T) has been observed for decreasing values of system volume as well as an opposite shift towards lower temperature and quark chemical potential for increasing magnetic field. We observe an enhancement in fluctuations of conserved charges in the regime of the transition temperature. These studies may have a significant role in understanding the thermodynamic observables extracted from heavy-ion collisions data.

The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

Elliptic flow splitting of charged pions in relativistic heavy-ion collisions

Relativistic heavy-ion collisions are an important experimental way of studying the new state of matter as well as the phase diagram of the quantum chromodynamics (QCD) under extremely high temperatures and high densities. In recent years, the beam-energy scan program has been carried out on the relativistic heavy-ion collider at Brookhaven National Laboratory in USA, and the STAR collaboration at relativistic heavy ion collision (RHIC) has measured the difference in the elliptic flow <inline-formula><tex-math id="M5">\begin{document}$v_2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M5.png"/></alternatives></inline-formula> between <inline-formula><tex-math id="M6">\begin{document}$\pi^-$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M6.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$\pi^+$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M7.png"/></alternatives></inline-formula> on an event-by-event basis, and found a linear dependence on the charge asymmetry <i>A</i><sub>ch</sub> of the collision system, which is considered as a possible signal of the chiral magnetic wave. Based on the extended multi-phase transport model (AMPT), this paper uses a 3 flavor Nambu-Jona-Lasinio (NJL) model to study the quark isospin Mean-field potential, which provides a new idea for explaining the experimental phenomenon of the linear relationship between the pion elliptic flow splitting <inline-formula><tex-math id="M8">\begin{document}$\Delta v_2=v_2(\pi^-)- $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M8.png"/></alternatives></inline-formula><inline-formula><tex-math id="M8-1">\begin{document}$ v_2(\pi^+)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M8-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M8-1.png"/></alternatives></inline-formula> and charge asymmetry <i>A</i><sub>ch</sub>. Our results show that isovector interaction can cause a splitting of the isospin asymmetric quark matter mean-field potential, manifesting as <inline-formula><tex-math id="M9">\begin{document}$d(\bar{u})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M9.png"/></alternatives></inline-formula> quarks experiencing a mean-field potential greater than <inline-formula><tex-math id="M10">\begin{document}$u(\bar{d})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M10.png"/></alternatives></inline-formula> quarks. Therefore, <inline-formula><tex-math id="M11">\begin{document}$d(\bar{u})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M11.png"/></alternatives></inline-formula> quarks experience more repulsion than <inline-formula><tex-math id="M12">\begin{document}$u(\bar{d})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M12.png"/></alternatives></inline-formula> quarks in collision processes, resulting in a small increase in the elliptic flow of the partial subflow <inline-formula><tex-math id="M13">\begin{document}$v_2(d)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M13.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$v_2(\bar{u})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M14.png"/></alternatives></inline-formula>, while <inline-formula><tex-math id="M15">\begin{document}$v_2(u)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M15.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M16">\begin{document}$v_2(\bar{d})$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M16.png"/></alternatives></inline-formula> decrease slightly. In the hadronization process, the <inline-formula><tex-math id="M17">\begin{document}$\pi$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M17.png"/></alternatives></inline-formula> elliptic flow splitting occurs due to the split of <inline-formula><tex-math id="M18">\begin{document}$d$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M18.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M19">\begin{document}$u$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M19.png"/></alternatives></inline-formula> elliptic flows combined with the split of <inline-formula><tex-math id="M20">\begin{document}$\bar{u}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M20.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M21">\begin{document}$\bar{d}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M21.png"/></alternatives></inline-formula> elliptic flows. We also found a linear correlation between charge asymmetry and isospin asymmetry at mid-rapidity region from our transport model, and thus explained the experimental phenomenon of the linear relationship between the pion elliptic flow splitting <inline-formula><tex-math id="M22">\begin{document}$\Delta v_2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230454_M22.png"/></alternatives></inline-formula> and charge asymmetry <i>A</i><sub>ch</sub> by using the isospin mean-field potential of quark matter. Further, isospin properties of quark matter also provide a theoretical basis for isobar collisions and the equation of state of compact star matter.

Zero-temperature thermodynamics of dense asymmetric strong-interaction matter

Employing constraints derived from the microscopic theory of the strong interaction, we estimate the zero-temperature phase structure of dense isospin-asymmetric matter with two quark flavors. We find indications that strong-interaction matter along trajectories relevant for astrophysical applications undergoes a first-order phase transition from a color-superconducting phase to an ungapped quark-matter phase when the density is increased. Such a phase transition is found to be absent in isospin-symmetric matter. Moreover, by taking into account constraints from $\ensuremath{\beta}$ equilibrium, charge neutrality, and color neutrality, we provide an estimate for the speed of sound in neutron-star matter. Notably, we observe that the speed of sound in neutron-star matter exceeds the asymptotic value associated with the noninteracting quark gas and even increases toward lower densities across a wide range, in agreement with recent results for isospin-symmetric matter. Considering results from studies based on chiral effective field theory at low densities, our findings suggest the existence of a maximum in the speed of sound for $n/{n}_{0}\ensuremath{\lesssim}10$, where ${n}_{0}$ is the nuclear saturation density.

Low Density Neutron Star Matter with Quantum Molecular Dynamics: The Role of Isovector Interactions

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.

Slope parameter of the symmetry energy and the structure of three-particle interactions in nuclear matter

In the first part of this paper, we present a study of the symmetry energy ${a}_{s}$ and its slope parameter $L$ for nuclear matter in the framework of the Fermi-liquid theory of Landau and Migdal. We derive an exact relation between ${a}_{s}$ and $L$, which involves the nucleon effective masses and three-particle Landau-Migdal parameters. We present simple estimates which suggest that there are two main mechanisms to explain the empirical values of $L$: The proton-neutron effective-mass difference in isospin asymmetric matter and the $\ensuremath{\ell}=0$ moment of the isovector in-medium three-particle scattering amplitude. In the second part of this paper, we discuss the general structure of three-particle interactions in nuclear matter in the framework of the Fermi-liquid theory. The connections to the Bethe-Brueckner-Goldstone theory and other approaches are also discussed. We show explicitly how the first few terms in the Faddeev series, together with medium-induced three-particle interactions, emerge naturally in the Fermi-liquid theory.

Quarkyonic stars with isospin-flavor asymmetry

We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $\beta$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps differentiating the nucleon and the quark sectors. In addition, we impose the conservation of the isospin-flavor asymmetry in the nucleon and the quark phases. Within this model, several quarkyonic stars are constructed on top of the SLy4 model for the nucleon sector, producing a bump in the sound speed, which implies that quarkyonic stars are systematically bigger and have a larger maximum mass than the associated neutron stars. They also predict lower proton fraction at $\beta$-equilibrium, which potentially quenches fast cooling in massive compact stars.

Isospin asymmetric matter in a nonlocal chiral quark model

We analyze the features of strongly interacting matter in the presence of nonzero isospin chemical potential $\mu_I$, within a nonlocal two-flavor Polyakov-Nambu-Jona-Lasinio (PNJL) model. For a system at finite temperature $T$, we describe the behavior of various thermodynamic quantities and study the phase diagram in the $\mu_I - T$ plane. In particular, it is found that for values of $\mu_I$ larger than the pion mass and temperatures lower than a critical value of about 170 MeV the system lies in an isospin symmetry broken phase signaled by the presence of a nonzero pion condensate. Our results for the phase diagram are found to be in better agreement with those arising from lattice QCD calculations, as compared to the predictions from other theoretical approaches like the local PNJL model.

Isospin effect on quark matter instabilities

We have studied the mechanical and chemical instabilities as well as the liquid-gas-like phase transition in isospin asymmetric quark matter based on the NJL and the pNJL model. Areas of the mechanical instability region and the liquid-gas coexistence region are seen to be enlarged with a larger quark matter symmetry energy or in the presence of strange quarks. Our study shows that the light cluster yield ratio observed in relativistic heavy-ion collisions may not be affected much by the uncertainties of the isospin effect, and favors a smooth hadron-quark phase transition in compact stars as well as their mergers.

Isospin Effect on Baryon and Charge Fluctuations from the pNJL Model

We have studied the possible isospin corrections on the skewness and kurtosis of net-baryon and net-charge fluctuations in the isospin asymmetric matter formed in relativistic heavy-ion collisions at RHIC-BES energies, based on a 3-flavor Polyakov-looped Nambu–Jona–Lasinio model. With typical scalar–isovector and vector–isovector couplings leading to the splitting of u and d quark chiral phase transition boundaries and critical points, we have observed considerable isospin effects on the susceptibilities, especially those of net-charge fluctuations. Reliable experimental measurements at even lower collision energies are encouraged to confirm the observed isospin effects.

Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

The three-body cluster energy for the [formula omitted] asymmetric [formula omitted] matter in the [formula omitted] formalism

The equation of state (EOS) of the isospin asymmetric nucleonic matter (IASM) is studied in the Lowest Order Constrained Variational (LOCV) formalism, using the AV18 two-body potential with a density-dependent three-body interaction (TBI), which was proposed by Lagaris and Pandharipande (LP) in 1981. In the LOCV framework, an adjustment mechanism is introduced for finding the appropriate parameters of the TBI. It is shown that, assuming the TBI, the corresponding LOCV symmetric nuclear (pure neutron) matter results fairly agree with those of Fermi Hypernetted Chain (FHNC). Also, the contribution of the averaged three-body cluster (TBC) energy is evaluated, at different proton to neutron ratios R. Employing the TBI, up to ρ=0.5 fm−3, the TBC energy ranges from −6 to 6 MeV per particle which considerably changes the IASMEOS, especially at low densities. Moreover, employing the TBI, the LOCVIASM state-averaged correlation functions (effective potentials) and the nucleon–nucleon distribution functions (NNDF) are reported. It is illustrated that, by increasing the density (ratio R), the impact of the TBI becomes much more evident. Finally, it should be noted that, the IASMFHNC and Monte Carlo (MC) data are not available for comparison.

Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in the framework of effective model

It has been shown in [15, 70] in the framework of Nambu-Jona-Lasinio model with the assumption of spatially homogeneous condensates that in the large-Nc limit (Nc is the number of quark colours) there exist three dual symmetries of the thermodynamic potential, which describes dense quark matter with chiral and isospin imbalances. The main duality is between the chiral symmetry breaking and the charged pion condensation phenomena. There have been a lot of studies and hints that the ground state could be characterized by spatially inhomogeneous condensates, so the question arises if duality is a rather deep property of the phase structure or just accidental property in the homogeneous case. In this paper we have shown that even if the phase diagram contains phases with spatially inhomogeneous condensates, it still possesses the property of this main duality. Two other dual symmetries are not realized in the theory if it is investigated within an inhomogeneous approach to a ground state. Based on various previously studied aspects of the QCD phase diagram of dense isospin asymmetric matter with possible inhomogeneous condensates, in the present paper a unified picture and full phase diagram of dense quark matter with isospin imbalance have been assembled. Acting on this diagram by a dual transformation, we obtained, in the framework of an approach with spatially inhomogeneous condensates and without any calculations, a full phase diagram of chirally asymmetric dense medium. This example shows that the duality is not just entertaining mathematical property but an instrument with very high predictivity power. The obtained phase diagram is quite rich and contains various spatially inhomogeneous phases.

The density- and isospin-dependent Δ-formation cross section and its decay width

The energy-, density-, and isospin-dependent Δ-formation cross section σ*Nπ→Δ and Δ-decay width are calculated based on the relativistic BUU approach in which the effective mass splitting of nucleon and Δ baryons in isospin-asymmetric matter is considered by the inclusion of the δ meson exchange in the effective Lagrangian density and the density-dependent coupling constants of Hofmann et al. The results show that the σ*Nπ→Δ is decreased (increased) moderately with increasing density with (without) the consideration of medium modifications on pion mass. Meanwhile, if the invariant mass of the system is not far from the Δ pole mass, the Δ-decay width is also weakly dependent on density. The mass splitting effect of differently charged nucleon and Δ baryons on σ*Nπ→Δ is found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard Δ production channel NN → NΔ. Further, the largest mass-splitting influence is seen in the π−p → Δ0 and π+n → Δ+ channels but not in the production of Δ − and Δ++ isobars.

Dense quark matter with chiral and isospin imbalance: NJL-model consideration

Isospin asymmetry is the well-known property of dense quark matter, which exists in the compact stars and is produced in heavy ion collisions. On the other hand, the chiral imbalance between left- and right- handed quarks is another highly anticipated phenomenon that could occur in the dense quark matter. To investigate quark matter under these conditions, we take into account baryon –μB, isospin –μIand chiral isospin –μI5chemical potentials and study QCD phase portrait using NJL4model generalized to two massive quarks that could condense into the pion condensation. We have shown that the chiral isospin chemical potentialμI5generates pion condensation in isospin asymmetric quark matter. Also, we have investigated discrete symmetry (duality) between chiral and pion condensates in the case of massless quarks, which stay relatively instructive even if the quarks have bare mass. To describe hot dense quark matter, in addition to the above-mentioned chemical potentials, we introduce non-zero temperatures into consideration.

Isospin properties of quark matter from a 3-flavor NJL model

We have studied the properties of hot and dense quark matter based on the 3-flavor Nambu-Jona-Lasinio (NJL) model as well as its Polyakov-loop extension (pNJL) with scalar-isovector and vector-isovector couplings. Provided a considerable large isospin asymmetry or isospin chemical potential, isospin splittings of constituent mass, chiral phase transition boundary, and critical point for $u$ and $d$ quarks can be observed for positive isovector coupling constants but are suppressed for negative ones. The quark matter symmetry energy decreases with the increasing isovector coupling constant, and is mostly enhanced in the pNJL model than in the NJL model. A positive scalar-isovector coupling constant is more likely to lead to an unstable isospin asymmetric quark matter. The isovector coupling has been further found to affect particle fractions as well as the equation of state in hybrid stars. Possible effects on the isospin properties of quark matter have also been discussed if the strangeness sector is further broken among the flavor symmetry.

Probing the hadron-quark mixed phase at high isospin and baryon density

We discuss the isospin effect on the possible phase transition from hadronic to quark matter at high baryon density and finite temperatures. The two-Equation of State (Two-EoS) model is adopted to describe the hadron-quark phase transition in dense matter formed in heavy-ion collisions. For the hadron sector we use Relativistic Mean Field (RMF) effective models, already tested on heavy ion collision (HIC). For the quark phase we consider various effective models, the MIT-Bag static picture, the Nambu--Jona-Lasinio (NJL) approach with chiral dynamics and finally the NJL coupled to the Polyakov-loop field (PNJL), which includes both chiral and (de)confinement dynamics. The idea is to extract mixed phase properties which appear robust with respect to the model differences. In particular we focus on the phase transitions of isospin asymmetric matter, with two main results: i) an earlier transition to a mixed hadron-quark phase, at lower baryon density/chemical potential with respect to symmetric matter; ii) an "Isospin Distillation" to the quark component of the mixed phase, with predicted effects on the final hadron production. Possible observation signals are suggested to probe in heavy-ion collision experiments at intermediate energies, in the range of the NICA program.

Relativistic mean-field models with scaled hadron masses and couplings: Hyperons and maximum neutron star mass

An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson–nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector–meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector–meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint for the pulsar J0737-3039B, and the constraint on the maximum mass of the neutron stars.