We introduce a theoretical framework to analyze the thermal properties of a recently proposed "excluded volume" model of quarkyonic matter. This entails proposing finite temperature distribution functions and entropy functionals constrained by internal theoretical consistency. We use the formalism developed here to analyze the effect of temperature on the quark onset as a function of baryon density. We find that the baryon density at which the quarkyonic phase emerges decreases only slightly with temperature, an effect produced by large $N_c$. We furthermore find that a finite temperature increases the density of quarks produced. The framework presented here can be used to compute the equation of state of hot and dense quarkyonic matter which is of relevance to neutron star mergers.
Inspired by the excluded volume model for isospin symmetric quarkyonic matter, we construct an `excluded volume' model for a charge neutral quarkyonic phase whose hadronic sector contains only neutrons. We refer to this model as quarkyonic neutron matter. We compute the equation of state for this model and solve the Tolman-Oppenhermer-Volkoff equations to obtain mass and radius relations relevant for neutron stars. The most straightforward extension of the model for symmetric quarkyonic matter to quarkyonic neutron matter does not satisfy the mass radius constraints from neutron star measureme…
The single-flavor excluded-volume model based on the effective size of baryons reproduces the hard-soft density evolution of the equation of state (EoS) required by the recent studies of GW170817. This phenomenological model basically realizes the concept of quarkyonic matter which is introduced from large-$N_{c}$ gauge theory for dense matter. Enhanced nucleon interactions and dynamically generated quark degrees of freedom can reproduce the hard-soft evolution of the EoS. In this paper, we extend the excluded-volume model to a three-flavor system by considering electromagnetic charge and poss…
We extend the excluded-volume model of isospin symmetric two-flavor dense quarkyonic matter [Phys. Rev. C 101, 035201 (2020)] including strange particles and address its implications for neutron stars. The effective sizes of baryons are defined from the diverging hard-core potentials in the short interdistance regime. Around the hard-core density, the repulsive core between baryons at short distances leads to a saturation in the number density of baryons and generates perturbative quarks from the lower phase space, which leads to the shell-like distribution of baryons by the Pauli exclusion pr…
The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + Δ. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core n…
In this contribution, we outline a new 2-phase description of the quark-nuclear matter hybrid equation of state that takes into account effects of phase space occupation (excluded volume) in both, the hadronic and the quark matter phases. For the nuclear matter phase, the reduction of the available volume at increasing density leads to a stiffening, while for the quark matter phase a reduction of the effective string tension in the confining density functional is obtained. The deconfinement phase transition in the resulting hybrid equation of state is sensitive to both excluded volume effects.…
Both the symmetry energy part and excluded volume corrections to the equation of state play an important role for the neutron star interior structure and composition, namely for the profile of the baryon density and the proton fraction. While the symmetry energy uniquely determines the proton fraction, excluded volume effects control the maximum density values inside neutron stars. Observations of cooling neutron stars indicate that the fast direct Urca cooling is not operative for the typical, low mass stars, pointing at proton fractions that lie below the threshold for the onset of direct Ur…
In this work we discuss a modified version of Excluded Volume Hadron Resonance Gas model and also study the effect of Lorentz contraction of the excluded volume on scaled pressure and susceptibilities of conserved charges. We find that the Lorentz contraction, coupled with the variety of excluded volume parameters reproduce the lattice QCD data quite satisfactorily.
A two-phase description of the quark-nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark matter phases is introduced. The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density functional model DD2 with excluded volume. The quark matter is…
We present a systematic study of production of strange and non-strange hadron yields and their ratios obtained in various experiments using our thermodynamically consistent excluded-volume model. We also analyze the production of light nuclei, hypernuclei and their antinuclei in terms of our excluded-volume model over a broad energy range starting from Alternating Gradient Synchrotron (AGS) to Large Hadron Collider (LHC) energies. Further, we extend our model for studying rapidity spectra of hadrons produced in heavy-ion collisions.
The Monte Carlo (MC) procedure for sampling the hadron yields within hadron resonance gas (HRG) model is presented. The effects of excluded-volume due to the finite hadron eigenvolumes and of exact charge conservation within the canonical ensemble (CE) formulation are simultaneously taken into account with the help of the importance sampling technique combined with the rejection sampling. The MC procedure allows one to calculate arbitrary moments of the event-by-event hadron yields. Note that the CE formulation for the excluded-volume HRG has not been considered before. The MC simulations coin…
We formulate a thermodynamically consistent equation of state (EOS), based on excluded-volume approach, for a hot, dense hadron gas (HG). We calculate various thermodynamical quantities of HG and various hadron ratios and compare our model results with the results of other excluded-volume models and experimental data. We also calculate various transport coefficients such as $η/s$ etc. and compare them with other HG model results. Furthermore, we test the validity of our model in getting the rapidity spectra of various hadrons and the effect of flow on them is investigated by matching our predi…
An analytical formula that accurately accounts for the Lorentz contraction of the excluded volume of two relativistic hadrons with hard-core repulsion is worked out. Using the obtained expression we heuristically derive the equation of state of Boltzmann particles with relativistic excluded volumes in terms of system pressure and its surface and curvature tension coefficients. The behavior of effective excluded volumes of lightest baryons and mesons is studied at very high temperatures (particle number densities) and for very large values of degeneracy factors. Several parameterizations of the…
In this article the role of the supersaturation density equation of state (EOS) is explored in simulations of failed core-collapse supernova explosions. Therefore the nuclear EOS is extended via a one-parameter excluded volume description for baryons, taking into account their finite and increasing volume with increasing density in excess of saturation density. Parameters are selected such that the resulting supernova EOS represent extreme cases, with high pressure variations at supersaturation density which feature extreme stiff and soft EOS variants of the reference case, i.e. without exclud…
The formation of clusters in nuclear matter is investigated, which occurs e.g. in low energy heavy ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean field model. All three models contain bound states of nuclei with mass number A <= 4. It is explored to which extent the complex medium effects can be mimicked by the simpler exclud…
We present temperature ($T$) and baryonic chemical potential ($μ_B$) dependence of higher order fluctuations and correlation between conserved charges in Excluded Volume Hadron Resonance Gas (EVHRG) model. Products of moments, such as ratio of variance to mean ($σ^2/M)$, product of skewness and standard deviation ($Sσ$), product of kurtosis and variance ($κσ^2$), for net-proton, net-kaon and net-charge have been evaluated on the phenomenologically determined freeze-out curve. Further, products of moments for net-proton and net-charge have been compared with the experimental data measured by ST…
The new excluded volume hadron gas model by Singh et al. [1-7] is critically discussed. We demonstrate that in this model the results obtained from relations between thermodynamical quantities disagree with the corresponding results obtained by statistical ensemble averaging. Thus, the model does not satisfy the requirements of thermodynamical consistency.
The shear viscosity $η$ in the van der Waals excluded volume hadron-resonance gas model is considered. For the shear viscosity the result of the non-relativistic gas of hard-core particles is extended to the mixture of particles with different masses, but equal values of hard-core radius r. The relativistic corrections to hadron average momenta in thermal equilibrium are also taken into account. The ratio of the viscosity $η$ to the entropy density s is studied. It monotonously decreases along the chemical freeze-out line in nucleus-nucleus collisions with increasing collision energy. As a fun…
Conventional cluster and virial expansions are generalized to momentum dependent inter-particle potentials. The model with Lorentz contracted hard core potentials is considered, e.g. as hadron gas model. A Van der Waals-type model with a temperature dependent excluded volume is derived. Lorentz contraction effects at given temperature are stronger for light particles and make their effective excluded volume smaller than that of heavy ones.
The relation among the volume coefficient $K$(=incompressibility of the nuclear matter), the Coulomb coefficient $K_c$, and the volume-symmetry coefficient $K_{vs}$ of the nucleus incompressibility are studied in the framework of the relativistic mean field theory with the excluded volume effects of the nucleons, under the assumption of the scaling model. It is found that $K= 300\pm 50$MeV is necessary to account for the empirical values of $K$, $K_c$, and $K_{vs}$, simultaneously, as is in the case of the point-like nucleons. The result is independent on the detail descriptions of the potenti…
Compressional properties of nuclear matter are studied by using the mean field theory with the excluded volume effects of the nucleons. It is found that the excluded volume effects make it possible to fit the empirical data of the Coulomb coefficient $K_{c}$ of nucleus incompressibility, even if the volume coefficient $K$ is small($\sim 150$MeV). However, the symmetry properties favor $K=300\pm 50$MeV as in the cases of the mean field theory of point-like nucleons.
Excluded volume effects are incorporated in the quark meson coupling model to take into account in a phenomenological way the hard core repulsion of the nuclear force. The formalism employed is thermodynamically consistent and does not violate causality. The effects of the excluded volume on in-medium nucleon properties and the nuclear matter equation of state are investigated as a function of the size of the hard core. It is found that in-medium nucleon properties are not altered significantly by the excluded volume, even for large hard core radii, and the equation of state becomes stiffer as…
A canonical partition function for the two-component excluded volume model is derived, leading to two different van der Waals approximations. The one is known as the Lorentz-Berthelot mixture and the other has been proposed recently. Both models are analysed in the canonical and grand canonical ensemble. In comparison with the one-component van der Waals excluded volume model the suppression of particle densities is reduced in these two-component formulations, but in two essentially different ways. Presently used multi-component models have no such reduction. They are shown to be not correct w…
We estimate dissipative properties viz: shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within ambit of excluded volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($η/s$) decreases with temperature while at finite baryon chemical potential this ratio shows same behavior as a function of temperature but reaches close to Kovtun-Son-Starinets (KSS) bound. Further along chemical freezout curve, ratio $η/s$ is almost constant apart from small initial monot…
The multiplicity fluctuations are studied in the van der Waals excluded volume hadron-resonance gas model. The calculations are done in the grand canonical ensemble within the Boltzmann statistics approximation. The scaled variances for positive, negative and all charged hadrons are calculated along the chemical freeze-out line of nucleus-nucleus collisions at different collision energies. The multiplicity fluctuations are found to be suppressed in the van der Waals gas. The numerical calculations are presented for two values of hard-core hadron radius, $r=0.3$ fm and 0.5 fm, as well as for th…
Considering the finite volume of nucleons, a Lagrangian density is given. The first order self-energy of the nucleon and the equation of state of nuclear matter are calculated in the framework of relativistic mean-field approximation. Our results indicate the effects of the volume of nucleons are not negligible.
When the multiplicities of particles produced in heavy-ion collisions are fitted to the hadron-resonance-gas model, excluded-volume effects play a significant role. In this work, we study the impact of such effects on the equation of state of pure Yang-Mills theory at low temperatures, comparing the predictions of the statistical model with lattice results. In particular, we present a detailed analysis of the SU(2) and SU(3) Yang-Mills theories: we find that, for both of them, the best fits to the equilibrium thermodynamic quantities are obtained when one assumes that the volume of different g…
A generalization of the Van der Waals excluded volume procedure for the multicomponent hadron gas is proposed. The derivation is based on the grand canonical partition function for the system of particles of several species interacting by hard core potentials. The obtained formulae for thermodynamical quantities are consistent with underlying principles of statistical mechanics as well as with thermodynamical identities. The model can be applied to the analysis of experimental data for particle number ratios in relativistic nucleus-nucleus collisions.
We recapitulate a thermodynamically consistent excluded volume hadron gas model and examine its differences with other ``thermal models'' used in the literature. Preliminary experimental data for particle number ratios in the collisions of Au+Au at the BNL AGS (11$A$ GeV/$c$) and Pb+Pb at the CERN SPS (160$A$ GeV/$c$) are analyzed. For equal values of the hadron hard-core parameters the excluded volume model gives essentially the ideal gas predictions for the particle number ratios, which is similar to other thermal models. We observe, however, the systematic excess of experimental pion abunda…
Strongly interacting matter with criticality induced by modified excluded volume in core-collapse supernova simulations
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；University of Wroclaw（弗罗茨瓦夫大学）；Silesian University in Opava（奥帕瓦西里西亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung（德国重离子研究中心）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）；Universitat de Valéncia（瓦伦西亚大学）；Observatori Astronòmic, Universitat de València（瓦伦西亚大学天文台）
Repulsive hadronic interactions play a relevant role in the QCD dynamics, attractive ones being represented by resonance formation. In this study we propose different schemes in order to parameterise repulsive interactions, then being able to extract effective sizes of hadrons from fits to lattice QCD simulations. We find that allowing a difference between the strange and light sectors, strange particles are systematically smaller than light ones with equal mass. The very simple implementation of repulsive interactions would in principle allow to extract precise information about all hadronic …
Properties of the 1S0 superfluid phase are studied for symmetric nuclear matter at finite temperature. It is described within a covariant hadronic field model, of the sigma-omega type, with addition of density dependent correlations simulating effects due to finite extension of nucleons. The model is solved in a selfconsistent Hartree-Bogoliubov approach, assuming instantaneous interactions in the superfluid phase. A comparison with the results obtained from several hadronic field models is done. Main characteristics of our description of the superfluid gap are in qualitative agreement with so…
Phase-space excluded-volume approach for light clusters in nuclear medium
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University（中山大学中法核工程与技术学院）；INFN, Laboratori Nazionali del Sud（意大利国家核物理研究所南方实验室）
We study the effects of the finite size of the baryons on the equation of state of homogeneous hadronic matter with hyperons. The finite extension of hadrons is introduced in order to improve the perfomance of field theoretical models at very high densities, simulating the short-range hard-core repulsive part of the baryon-baryon potential. We choose the Quark Meson Coupling model to describe the baryon dynamics because this model provides a density dependent radius of the bag. In addition we calculate finite size corrections for the Zimanyi-Moszkowski model in order to make a definite compari…
From the analysis of light (anti)nuclei multiplicities that were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy $\sqrt{s_{NN}} =2.76$ TeV there arose a highly non-trivial question about the excluded volume of composite particles. Surprisingly, the hadron resonance gas model (HRGM) is able to perfectly describe the light (anti)nuclei multiplicities under various assumptions. Thus, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is…
We match three hadronic equations of state at low energy densities to a perturbatively computed equation of state of quarks and gluons at high energy densities. One of them includes all known hadrons treated as point particles, which approximates attractive interactions among hadrons. The other two include, in addition, repulsive interactions in the form of excluded volumes occupied by the hadrons. A switching function is employed to make the crossover transition from one phase to another without introducing a thermodynamic phase transition. A chi-square fit to accurate lattice calculations wi…
Generalized mean-field approach for thermodynamic description of relativistic single- and multi-component gas in the grand canonical ensemble is formulated. In the framework of the proposed approach different phenomenological excluded-volume procedures are presented and compared to the existing ones. The mean-field approach is then used to effectively include hard-core repulsion in hadron-resonance gas model for description of chemical freeze-out in heavy-ion collisions. We calculate the collision energy dependence of several quantities for different values of hard-core hadron radius and for d…
We study the effects of the finite size of baryons on the equation of state of homogeneous hadronic matter. The finite extension of hadrons is introduced in order to improve the performance of field theoretical models at very high densities. We simulate the in-medium averaged baryon-baryon strong repulsion at very short distances by introducing a Van der Waals like normalization of the fields. This is done in the framework of the Quark Meson Coupling model, that allows to take care of the quark structure of baryons. Since within this model the confinement volume evolves with the fields configu…
The Monte Carlo results in lattice QCD for the pressure and energy density at small temperature $T < 155$ MeV and zero baryonic chemical potential are analyzed within the hadron resonance gas model. Two extensions of the ideal hadron resonance gas are considered: the excluded volume model which describes a repulsion of hadrons at short distances and Hagedorn model with the exponential mass spectrum. Considering both of these models one by one we do not find the conclusive evidences in favor of any of them. The controversial results appear because of rather different sensitivities of the pressu…
The quantum mechanical Beth-Uhlenbeck (BU) approach for repulsive hard-core interactions between baryons is applied to the thermodynamics of a hadron gas. The second virial coefficient $a_2$ -- the "excluded volume" parameter -- calculated within the BU approach is found to be temperature dependent, and it differs dramatically from the classical excluded volume (EV) model result. At temperatures $T =100-200$ MeV, the widely used classical EV model underestimates the EV parameter for nucleons at a given value of the nucleon hard-core radius by large factors of 3-4. Previous studies, which emplo…
We compare two approaches in modeling repulsive interactions among hadrons: the excluded volume approximation and the S-matrix formalism. These are applied to study the thermodynamics of the $πN Δ$ system. It is shown that the introduction of an extraneous repulsion between pions and nucleons via the excluded volume approach, in addition to the interaction that generates the $Δ$-resonance, is incompatible with the analysis based on the physical phase shift of pion-nucleon scattering in the $P_{33}$ channel. This finding suggests that the repulsive force between hadrons is interaction-channel d…
We study the properties of cold asymmetric nuclear matter at high density, applying the quark meson coupling model with excluded volume corrections in the framework of the Landau theory of relativistic Fermi liquids. We discuss the role of the finite spatial extension of composite baryons on dynamical and statistical properties such as the Landau parameters, the compressibility, and the symmetry energy. We have also calculated the low lying collective eigenfrequencies arising from the collisionless quasiparticle transport equation, considering both unstable and stable modes. An overall analysi…
The formalism to augment the classical models of equation of state for real gases with the quantum statistical effects is presented. It allows an arbitrary excluded volume procedure to model repulsive interactions, and an arbitrary density-dependent mean field to model attractive interactions. Variations on the excluded volume mechanism include van der Waals (VDW) and Carnahan-Starling models, while the mean fields are based on VDW, Redlich-Kwong-Soave, Peng-Robinson, and Clausius equations of state. The VDW parameters of the nucleon-nucleon interaction are fitted in each model to the properti…
Thermodynamic properties of hot and dense hadronic systems with a hard-sphere interaction are calculated in the Boltzmann approximation. Two parametrizations of pressure as a function of density are considered: the first one, used in the excluded volume model and the second one, suggested earlier by Carnahan and Starling. The results are given for one-component systems containing only nucleons or pions, as well as for chemically equilibrated mixtures of pions, nucleons and delta resonances. It is shown that the Carnahan-Starling approach can be used in a much broader range of hadronic densitie…
