When skyrmions representing nucleons are put on crystal lattice and compressed to simulate high density, there is a transition above the normal nuclear matter density $n_0$ from a matter consisting of skyrmions with integer baryon charge to a state of half-skyrmions with half-integer baryon charge. We exploit this observation in an effective field theory formalism to access dense baryonic system. We find that the topology change involved implies a changeover from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate in the nucleon "melted off." The $\sim 80%$ of the nucleon mass that remains, invariant under chiral transformation, points to the origin of the (bulk of) proton mass that is not encoded in the standard mechanism of spontaneously broken chiral symmetry. The topology change engenders a drastic modification of the nuclear tensor forces, thereby nontrivially affecting the EoS, in particular, the symmetry energy, for compact star matter. It brings in stiffening of the EoS needed to accommodate a neutron star of $\sim 2$ solar mass. The strong effect on the EoS in general and in the tensor force structure in particular will also have impact on processes that could be measured at RIB-type accelerators.
An EOS-Driven Extension of NSCool for Compact Star Cooling with Hadronic and Quark Degrees of Freedom
Università degli Studi della Campania “Luigi Vanvitelli”（坎帕尼亚路易吉范维特利大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati（意大利国家核物理研究所弗拉斯卡蒂国家实验室）；Universidad Rey Juan Carlos（胡安卡洛斯国王大学）
A mean field calculation is carried out to obtain the equation of state (EoS) of nuclear matter from a density dependent M3Y interaction (DDM3Y). The energy per nucleon is minimized to obtain ground state of the symmetric nuclear matter (SNM). The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of SNM. The energy variation of the exchange potential is treated properly in the negative energy domain of nuclear matter. The EoS of SNM, thus obtained, is not only free from the superluminosity probl…
I discuss how to access dense baryonic matter of compact stars by combining hidden local symmetry (HLS) of light-quark vector mesons with spontaneously broken scale invariance of a (pseudo) Nambu-Goldstone boson, dilaton, in a description that parallels the approach to dilatonic Higgs. Some of the surprising observations are that the bulk of proton mass is not Nambu-Goldstonian, parity doubling emerges at high density and the EoS of baryonic matter can be soft enough for heavy-ion processes at low density and stiff enough at high density for $\sim 2$ solar mass neutron stars.
We describe the on-going effort to formulate the baryon-quark continuity in terms of a topology change in the equation of state (EoS) of dense baryonic matter in analogy to -- and inspired by -- the mapping of the characteristics of Chern-Simon topological field theory to Kohn-Sham density functional theory in the fractional quantized Hall effect (FQHE). This is done by translating the density-dependent characteristics of the skyrmion-half-skyrmion transition formulated in the presence of hidden local symmetry and (hidden) scale symmetry to the density-dependent parameters of a renormalization…
Using the Callan-Klebanov bound state model for hyperons simulated on crystal lattice to describe strange baryonic matter, we argue that to ${\cal O} (1)$ in the large $N_c$ counting to which the theory is robust, hyperons can figure only when -- or after -- kaons condense in compact-star matter. We also discuss how the skyrmion-half-skyrmion topological transition affects the equation of state (EoS) of dense baryonic matter. The observations made in this note open wide the issue of how to theoretically access the EoS of compact stars.
We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with the thermodynamic quantities. The formulation is the NSE description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with the atomic number up to ~ 1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our EOS occurs i…
We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a stiff quark matter EoS with color superconductivity at high densities within a finite region of baryonic chemical potentials $μ_B^h < μ_B < μ_B^q$. We consider two scenarios corresponding to a cross-over and a strong first-order transition between quark and hadron phases considered at finite and zero temperatures. This allows us to analyze the effects of finite entropy on the EoS and mass-radius relation …
When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar $f_0(500)$ may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudo-scalar pNG bosons $π$ and the matter fields $V=(ρ,ω)$ as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large $N_c$ in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter,…
We clarify and extend further the idea developed in \cite{PKLMR,MLPR} that baryonic matter at high density has an emergent "pseudo-conformal symmetry." It is argued that as baryonic density exceeds $n \simeq n_{1/2} \gtrsim 2n_0$, a topology change mimicking the baryon-quark continuity takes place at $n_{1/2}$. In terms of skyrmions, this corresponds to the transition from skyrmions to half-skyrmions and impacts on the equation of state of dense baryonic matter. The emergence in medium at $n_{1/2}$ of parity-doublet symmetry -- which is invisible in QCD in matter-free vacuum -- plays the cruci…
We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory so constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are "local flavor symmetry" of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden "quantum scale symmetry" with an IR fixed point with a "genuine dilaton (GD)" characterized …
Exploiting certain robust topological inputs from the skyrmion description of compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict the equation of state that is consistent with the properties of nuclear matter at the equilibrium density, supports the maximum mass of massive compact star $\sim 2 M_\odot$ and surprisingly gives the sound velocity close to the "conformal velocity" $1/\sqrt{3}$ at densities $\gtrsim 3 n_0$. At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above $\sim 2n_0$ with a chiral-si…
This is a summary of the talks I gave at Korean Physical Society meeting (April 26, 2012, Daejeon, Korea) and the 4th Asian Triangle Heavy Ion Conference (ATHIC) (November 14, 2012, Pusan, Korea). They are based on the series of work done at Hanyang University in the World Class University III Program under the theme of "From Dense Matter to Compact Stars." The program was conceived and executed to understand highly compressed baryonic matter in anticipation of the forthcoming RIB machine "RAON" which is in construction in the Institute for Basic Science (IBS) in Korea. The problems treated ra…
We analyze the recent astrophysical constraints in the context of a hadronic equation of state (EoS), in which the baryonic matter is subject to chiral symmetry restoration. We show that with such EoS it is possible to reconcile the modern constraints on the neutron star (NS) mass, radius, and tidal deformability (TD). We find that the softening of the EoS, required by the TD constraint of a canonical $1.4~M_\odot$ NS, followed by a subsequent stiffening, required by the $2~M_\odot$ constraint, is driven by the appearance of $Δ$ matter due to partial restoration of chiral symmetry. Consequentl…
In this paper we present a simple discussion on the properties of compact stars using an EoS obtained in effective field theory anchored on scale and hidden-local symmetric Lagrangian endowed with topology change and a unequivocal prediction on the deformation of the compact star, that could be measured in gravitational waves. The objective is not to offer a superior or improved EoS for compact stars but to confront with a forthcoming astrophysical observable the given model formulated in what is considered to be consistent with the premise of QCD. The model so obtained is found to satisfactor…
Compact stars with significant high densities in their interiors can give rise to quark deconfined phases that can open a window for the study of strongly interacting dense nuclear matter. Recent observations on the mass of two pulsars, PSR J1614-2230 and PSR J0348+0432, have posed a great restriction on their composition, since their equations of state must be hard enough to support masses of about at least two solar masses. The onset of quarks tends to soften the equation of state, but due to their strong interactions, different phases can be realized with new parameters that affect the corr…
The chiral soliton lattice (CSL) has been studied in condensed-matter system such as chiral magnets, which arises as a parity-violating topological soliton. In hadron physics, various attempts have also been made to apply the idea of CSL to baryonic matter. In this work, we explore the CSL effects on the baryonic matter based on the skrymion crystal approach. It is found that the CSL causes an inverse catalysis for the topology change in the dense baryonic matter. Furthermore, we observe that the CSL makes the single-baryon shape deformed to be highly oscillating as the frequency of the CSL ge…
Bayesian Constraints on Bosonic Dark Matter in Neutron Stars within a Covariant Density-Functional Equation-of-State Ensemble
University of Wrocław（弗罗茨瓦夫大学）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Alikhanyan National Science Laboratory (Yerevan Institute of Physics)（阿利哈尼扬国家科学实验室（埃里温物理研究所））；Frankfurt Institute for Advanced Studies（法兰克福高级研究所）
After the first predictions in seventies that in dense nuclear matter, for example, in neutron stars there could be pion condensation phenomenon, it was shown that at least s-wave pion condensation is unlikely to occur in such a medium in different approaches including NJL model consideration with neutrality and $β$-equilibrium condition. Then it has been found a condition that can promote this phenomenon in dense baryonic matter, it is chiral imbalance, so now it is interesting if this generation can survive rather strict requirement of electric neutrality and $β$-equilibrium. Here in this pa…
We consider the parity doublet model for nucleonic and delta matter to investigate the structure of neutron stars. We show that it is possible to reconcile the multi-messenger astronomy constraints within a purely hadronic equation of state (EOS), which accounts for the self-consistent treatment of the chiral symmetry restoration in the baryonic sector. We demonstrate that the characteristics of the EOS required by the astrophysical constraints do not necessarily imply the existence of a hadron-quark phase transition in the stellar core.
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the $ρ$ pole. Except for S+Au collisions our calculations reproduce the CERES data.
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Effects of a density dependent pole of the $ρ$-meson propagator on dilepton spectra are studied for different systems and centralities at CERN energies.
Understanding the equation of state (EOS) of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of energetic heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova all depend critically on the nuclear-matter EOS. In this contribution I focus on the EOS of cold baryonic matter with special emphasis on its impact on the structure, dynamics, and composition of neutron stars. In particular, I discuss how laboratory experiments on neutron skins as well as on Pygmy…
We construct a new effective field theory approach to the equation of state (EoS), dubbed pseudo-confomal model "PCM," for nuclear and compact star matter entirely in terms of effective hadron degrees of freedom. The possible transition at $n\sim (2-4) n_0$ (where $n_0$ is the normal nuclear matter density) from hadron degrees of freedom to strongly-coupled quark degrees of freedom, giving rise to a soft-to-hard changeover in the EoS that can accommodate the massive stars observed, is effectuated by the topology change at $n_{1/2}\gsim 2n_0$ from skyrmions to half-skyrmions without involving l…
We derive the equation of state (EOS) for electrically charge neutral dense matter using Quantum Hadrodynamics (QHD) model. This is carried out in a nonperturbative manner including quantum corrections for baryons through a realignment of vacuum with baryon-antibaryon condensates. This yields the results of relativistic Hartree approximation of summing over baryonic tadpole diagrams. The quantum corrections from the scalar meson is also taken into account in a similar way. This leads to a softening of the equation of state for the hyperonic matter. The formalism also allows us to do a self con…
The nuclear symmetry energy figures crucially in the structure of asymmetric nuclei and, more importantly, in the equation of state (EoS) of compact stars. At present it is almost totally unknown, both experimentally and theoretically, in the density regime appropriate for the interior of neutron stars. Basing on a strong-coupled structure of dense baryonic matter encoded in the skyrmion crystal approach with a topology change and resorting to the notion of generalized HLS (hidden local symmetry) in hadronic interactions, we address a variety of hitherto unexplored issues of nuclear interactio…
The equation of state (EoS) of hot and dense matter is a fundamental input to describe static and dynamical properties of neutron stars, core-collapse supernovae and binary compact-star mergers. We review the current status of the EoS for compact objects, that have been studied with both ab-initio many-body approaches and phenomenological models. We limit ourselves to the description of EoSs with purely nucleonic degrees of freedom, disregarding the appearance of strange baryonic matter and/or quark matter. We compare the theoretical predictions with different data coming from both nuclear phy…
Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first…
We present an updated general purpose nuclear equation of state (EoS) for use in simulations of core-collapse supernovae, neutron star mergers and black hole collapse. This EoS is formulated in the context of Density Functional Theory (DFT) and is generalized to include all DFT EoSs consistent with known nuclear and astrophysical constraints. This EoS also allows for the possibility of the formation of material with a net proton excess ($Y_p > 0.5$) and has an improved treatment of the nuclear statistical equilibrium and the transition to heavy nuclei as the density approaches nuclear matter d…
Understanding the equation of state (EOS) of cold nuclear matter, namely, the relation between the pressure and energy density, is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova, all depend critically on the equation of state of hadronic matter. In this contribution I will concentrate on the special role that nuclear physics plays in constraining the EOS of cold baryonic matter and its impact on the properties of neutron…
A general formula of the symmetry energy for many-body interaction is proposed and the commonly used two-body interaction symmetry energy is recovered. Within Landau's theory (Lt), we generalize two equations of state (EoS) CCS$δ$3 and CCS$δ$5 to asymmetric nuclear matter. We assume that the density and density difference between protons and neutrons divided by their sum are order parameters. We use different EoS to study neutron stars by solving the TOV equations. We demonstrate that different EoS give different mass and radius relation for neutron stars even when they have exactly the same g…
We present an updated and improved equation of state (which we call the NDL EoS) for use in neutron-star structure and supernova simulations. This EoS is based upon a framework originally developed by Bowers & Wilson, but there are numerous changes. Among them are: (1) a reformulation in the context of density functional theory; (2) the possibility of the formation of material with a net proton excess (Ye > 0.5); (3) an improved treatment of the nuclear statistical equilibrium and the transition to heavy nuclei as the density approaches nuclear matter density; (4) an improved treatment of the …
Neutron stars with large masses $\sim 2M_{\odot}$ require the hard stiffness of equation of state (EoS) of neutron-star matter. On the other hand, hyperon mixing brings about remarkable softening of EoS. In order to solve this problem, a multi-pomeron exchange potential (MPP) is introduced as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) baryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The interactions in $Λ\!N$, $Σ\!N$ and $Ξ\!N$ channels ar…
Hyperonic compact stars with vector portal dark matter
Utkal University（乌塔卡尔大学）；University of Coimbra（科英布拉大学）；Indian Institute of Science Education and Research Berhampur（印度科学教育研究学院贝尔汉普尔分校）；National Institute of Science Education and Research（国家科学教育研究中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Institute of Physics Bhubaneswar（布巴内斯瓦尔物理研究所）；Indian Institute of Technology Bhilai（印度理工学院比莱分校）
The equation of state of symmetric nuclear matter has been investigated within Brueckner approach adopting the charge-dependent Argonne $V_{18}$ two-body force plus a microscopic three-body force based on a meson-exchange model. The effects on the equation of state of the individual processes giving rise to the three-body force are explored up to high baryonic density. It is found that the major role is played by the competition between the strongly repulsive $(σ, ω)$ exchange term with virtual nucleon-antinucleon excitation and the large attractive contribution due to $(σ, ω)$ exchange with $…
The half-skyrmions that appear in dense baryonic matter when skyrmions are put on crystals modify drastically hadron properties in dense medium and affect strongly the nuclear tensor forces, thereby influencing the equation of state (EoS) of dense nuclear and asymmetric nuclear matter. The matter comprised of half skyrmions has vanishing quark condensate but non-vanishing pion decay constant and could be interpreted as a hadronic dual of strong-coupled quark matter. We infer from this observation combined with certain predictions of hidden local symmetry in low-energy hadronic interactionsa a …
The possible $^{1}S_{0}$ protonic superfluidity is investigated in neutron star matter, and the corresponding energy gap as a function of baryonic density is calculated on the basis of BCS gap equation. We have discussed particularly the influence of hyperon degrees of freedom on $^{1}S_{0}$ protonic superfluidity. It is found that the appearance of hyperons leads to a slight decrease of $^{1}S_{0}$ protonic pairing energy gap in most density range of existing $^{1}S_{0}$ protonic superfluidity. However, when the baryonic density $ρ_{B}>$0.377 (or 0.409) fm${^{-3}}$ for TM1 (or TMA) parameter …
Phases of nuclear matter are crucial in the determination of physical properties of neutron stars~(NS). In the core of NS, the density and pressure become so large that the nuclear matter possibly undergoes phase transition into a deconfined phase, consisting of quarks and gluons and their colour bound states. Even though the quark-gluon plasma has been observed in ultra-relativistic heavy-ion collisions\cite{Gyulassy, Andronic}, it is still unclear whether exotic quark matter exists inside neutron stars. Recent results from the combination of various perturbative theoretical calculations with…
We analyze the effects of chiral symmetry restoration in hadronic matter, including the lowest-lying baryonic resonance $Δ$ based on the parity doublet model. We study the role of $Δ$ and its chiral partner on the equation of state (EoS) of dense matter under neutron star (NS) conditions of $β$-equilibrium and charge neutrality. We find that the softening of the EoS driven by the early onset of $Δ$ matter due to partial restoration of chiral symmetry allows accommodating the modern multi-messenger astrophysical constraints on the mass, radius, and tidal deformability. The softening above the s…
The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely …
The uncertainties in neutron star (NS) radii and crust properties due to our limited knowledge of the equation of state (EOS) are quantitatively analysed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core EOS based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\sim 30\%$ for the crust thickness and $4\%$ for the radius. Necessary conditions for causal and thermodynamically consistent matchings betwe…
The properties of hybrid stars formed by hadronic and quark matter in beta-equilibrium at fixed entropies are described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. In this work we include the possibility of neutrino trapped EOS and compare the star properties with the ones obtained after deleptonization, when neutrinos have already diffused out. We use the nonlinear Walecka model for the hadron matter with two different sets for the hyperon couplings and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a…
The Compressed Baryonic Matter (CBM) experiment planned at Facility for Antiproton and Ion Research (FAIR) will provide a major scientific effort for exploring the properties of strongly interacting matter in the high baryon density regime. One of the important goal behind such experiment is to precisely determine the equation of state (EOS) for the strongly interacting matter at extreme baryon density. In this paper, we have used a thermal model EOS incorporating excluded volume description for the hot and dense hadron gas (HG). We then predict different particle ratios and the total multipli…
Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the rho and omega vector mesons are introduced as hidden gauge bosons, valid up to O(p^4) terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants - apart from f_pi and m_rho - are fixed by the master formula derived from the relation between 5-D hQCD and 4-D HLS. This allows one to pin down the density n_1/2 at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the EoS of den…
The role of anti-kaons in the symmetry energy to be determined in heavy-ion collisions as for instance in such observables as the $π^-/π^+$ ratio is discussed using a simple chiral Lagrangian. It is shown, with some mild assumptions, that kaons, when present in the system, can affect the EoS appreciably for both symmetric and asymmetric nuclear matter. For nuclear matter with small asymmetry with which heavy-ion collisions are studied, it may be difficult to distinguish a stiff symmetry energy and the supersoft symmetry energy, even with kaons present. However the effect of kaon is found to be…
The fundamental properties of dense nuclear matter, as it exists in the core of massive stellar objects, are still largely unknown. The investigation of the high-density equation of state (EOS), which determines mass and radii of neutron stars and the dynamics of neutron star mergers, is in the focus of astronomical observations and of laboratory experiments with heavy-ion collisions. Moreover, the microscopic degrees-of-freedom of strongly interacting matter at high baryon densities are also unknown. While Quantum-Chromo-Dynamics (QCD) calculations on the lattice find a smooth chiral crossove…
Indian Institute of Science Education and Research Berhampur（印度科学教育研究所布兰普尔分校）；Rajdhani College, Bhubaneswar（布巴内斯瓦尔拉吉达尼学院）；Institute of Physics Bhubaneswar（布巴内斯瓦尔物理研究所）；National Institute of Science Education and Research（国家科学教育研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Indian Institute of Technology Bhilai（比莱印度理工学院）
The hadron-quark/gluon duality formulated in terms of a topology change at a density $n\gsim 2n_0$ $n_0\simeq 0.16$fm$^{-3}$ is found to describe the core of massive compact stars in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. This can be considered as the Cheshire-Cat mechanism~\cite{CC} for the hadron-quark continuity arrived at bottom-up from skyrmions that is equivalent to the "MIT-bag"-to-skyrmion continuity arrived at top-down from quarks/gluons. Hidden symmetries, both local gauge and pseudo-conformal (or broken sc…
