Quark Mean Field Model Research Articles

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU (3) quark mean field model

In the present study, we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3) quark mean field model. Within this model, the properties of the quark matter were modified through the scalar fields , vector fields , ϕ, and Polyakov fields Φ and at finite temperature and chemical potential. Non-extensive effects were introduced through a dimensionless parameter q, and the results were compared to those of the extensive case ( ). In the non-extensive case, the exponential in the Fermi-Dirac (FD) function was modified to a q-exponential form. The influence of the q parameter on the thermodynamic properties, pressure, energy, and entropy density, as well as trace anomaly, was investigated. The speed of sound and specific heat with non-extensive effects were also studied. Furthermore, the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of and s quarks was explored. We found that the critical end point (CEP), which defines the point in the phase diagram where the order of the phase transition changes, shifts to a lower value of temperature, , and a higher value of chemical potential, , as the non-extensivity is increased, that is, 1.

Equation of state of nuclear matter and neutron stars: Quark mean-field model versus relativistic mean-field model

Equation of state of nuclear matter and neutron stars: Quark mean-field model versus relativistic mean-field model

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.

Testing the phase transition parameters inside neutron stars with the production of protons and lambdas in relativistic heavy-ion collisions

We demonstrate the consistency of the quark deconfinement phase transition parameters in the beta-stable neutron star matter and in the nearly symmetric nuclear matter formed in heavy-ion collisions (HICs). We investigate the proton and $\mathrm{\ensuremath{\Lambda}}$ flow in $\mathrm{Au}+\mathrm{Au}$ collisions at 3 and $4.5\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ incident beam energies with the pure hadron cascade version of a multiphase transport model. The phase transition in HICs and neutron stars is described based on a class of hybrid equations of state from the quark mean-field model for the hadronic phase and a constant-speed-of-sound parametrization for the high-density quark phase. The measurements of the anisotropic proton flow at $3\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ by the STAR Collaboration favor a relatively low phase transition density lower than $\ensuremath{\sim}2.5$ times saturation density indicated by the gravitational wave and electromagnetic observations of neutron stars. And the proton flow data at the higher energy of $4.5\text{ }\text{ }\mathrm{GeV}/\mathrm{nucleon}$ can be used to effectively constrain the softness of high-density quark matter equations of state. Finally, compared to the proton flow, the $\mathrm{\ensuremath{\Lambda}}$ flow is found to be less sensitive and not constraining to the equations of state.

Quark matter properties and fluctuations of conserved charges in (2+1)-flavored quark model * *Supported by the DST-SERB, Government of India for funding of research project (CRG/2019/000096)

In this study, the susceptibilities of conserved charges, baryon number, charge number, and strangeness number at zero and low values of chemical potential are presented. Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson (PQM) model and the Polyakov loop extended chiral quark mean-field (PCQMF) model. Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential, as well as the vector interactions. The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed. A comparative analysis of the two models was completed. Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point (CEP). Susceptibilities of conserved quantities were calculated by using the Taylor series method. Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics (QCD) critical-point.

Effect of vector interaction on magnetized strange quark matter and strange quark star

This study investigates the thermodynamical properties of magnetized strange quark matter (MSQM) and magnetized strange quark stars (MSQSs), the longitudinal and transverse equation of state (EoS), the maximum mass, the love number, tidal deformability, and gravitational redshift for MSQSs in chiral SU(3) quark mean-field (CQMF) model. The effects of vector interactions and density-dependent magnetic field are considered in the calculations. The EoS having longitudinal pressure gets soften with an increase in magnetic field and becomes stiffer for transverse pressure. The derived results show that the maximum mass of SQSs depends not only on the strength of the magnetic field but also on the orientation of the magnetic field inside the stars. The maximum mass and tidal deformability of MSQSs show good agreement with both the constraints of PSR J0030+0451 measured by NICER and the tidal deformability of gravitational wave event (GW170817) observed by LIGO and Virgo collaboration. In addition, the structure of MSQS is investigated using an axially symmetric metric with spherical coordinates in which γ- parameter observes the deformation of the star due to magnetic field.

The Ξ-nuclear potential constrained by recent Ξ− hypernuclei experiments

The Ξ-nuclear potential is investigated in the quark mean-field (QMF) model based on recent results on the Ξ− + 14N () system. The experimental data on the binding energy of 1p-state Ξ− hyperon in hypernuclei in KISO, IBUKI, E07-T011, E176-14-03-35 events are merged as MeV. With this constraint, the coupling strengths between the ω vector meson and Ξ hyperon are fixed in three QMF parameter sets. At the same time, the Ξ− binding energy of 1s state in is predicted as MeV with the same interactions, completely consistent with the data from the KINKA and IRRAWADDY events. Finally, the Ξ-nuclear potential is calculated in the symmetric nuclear matter in the same framework. It is found to be U Ξ = −11.96 ± 0.85 MeV at nuclear saturation density, which is important for the discussions of the role of strangeness in a neutron star.

Properties of strange quark matter and strange quark stars

A Polyakov chiral text {SU(3)} quark mean-field (PCQMF) model is applied to study the properties of strange quark matter (SQM) and strange quark star (SQS) in beta -equilibrium. The effect of increasing the strength of vector interactions on the effective constituent quark mass, particle fractions, and the thermodynamical properties such as pressure, energy density, and the speed of sound is investigated. We investigate the above properties for the SQM relevant for various stages of star evolution, i.e., considering with/without trapped neutrinos and zero/finite entropy. The finite lepton fraction and the entropy of the medium is observed to cause the stiffness in the equation of state (EoS). Finally, we calculate the mass-radius relation and the dimensionless tidal deformability within the present model calculations and compare the results to the recent studies.

Quark matter within Polyakov chiral SU(3) quark mean field model at finite temperature

Thermodynamical properties and phase diagram of asymmetric strange quark matter using the Polyakov chiral $$\text {SU(3)}$$ quark mean field (PCQMF) model at finite temperature and chemical potential have been investigated. Within the PCQMF model, the properties of quark matter are calculated through the scalar fields $$\sigma $$ , $$\zeta $$ , $$\delta $$ and $$\chi $$ , the vector fields $$\omega $$ , $$\rho $$ and $$\phi $$ and the Polyakov loop fields $$\Phi $$ and $$\bar{\Phi }$$ . The isospin splitting of constituent quark masses is observed at large isospin asymmetry. The effect of temperature and strangeness fraction on energy per baryon and equation of state is found to be appreciable in quark matter. The effect of the Polyakov loop dynamics on several thermodynamical bulk quantities such as energy density, entropy density and trace anomaly is presented. Furthermore, within the model under mean field approximation, we explore the phase structure in $$T-\mu $$ plane and analyzed the impact of varying the strength of vector coupling and isospin chemical potential on nature of phase transition.

Strange Quark Matter with β-equilibrium condition

Present study explores the properties of strange quark matter (SQM) or strange quark star (SQS) within the Polyakov extended chiral SU(3) quark mean-field (PCQMF) model. Using β-equilibrium condition in the PCQMF model, the analysis of pressure density, and equation of state (EoS) of SQM for different values of vector coupling constant is carried out. Three different conditions of Proto-Quark Star (PQS) along the star evolution (S/nB = 1, Yl = 0.4; S/nB = 2, Yvl = 0; S/nB = 0, Yvl = 0) are considered to perform the theoretical simulation. Providing a significant vector coupling constant, the change in pressure with baryon density is found to be more as compared to zero vector interaction. Further, pressure density shows monotonically and smoothly increasing behavior with an increase in the energy density. The study thus carried out, anticipated to give a better insight in understanding the properties of matter inside the core of supermassive stars in the universe.

Constraining Hadron-quark Phase Transition Parameters within the Quark-mean-field Model Using Multimessenger Observations of Neutron Stars

Abstract We extend the quark mean-field (QMF) model for nuclear matter and study the possible presence of quark matter inside the cores of neutron stars. A sharp first-order hadron-quark phase transition is implemented combining the QMF for the hadronic phase with “constant-speed-of-sound” parameterization for the high-density quark phase. The interplay of the nuclear symmetry energy slope parameter, L, and the dimensionless phase transition parameters (the transition density n trans/n 0, the transition strength Δε/ε trans, and the sound speed squared in quark matter ) are then systematically explored for the hybrid star properties, especially the maximum mass M max and the radius and the tidal deformability of a typical 1.4 M ⊙ star. We show the strong correlation between the symmetry energy slope L and the typical stellar radius R 1.4, similar to that previously found for neutron stars without a phase transition. With the inclusion of phase transition, we obtain robust limits on the maximum mass (M max < 3.6 M ⊙) and the radius of 1.4 M ⊙ stars (R 1.4 ≳ 9.6 km), and we find that a phase transition that is too weak (Δε/ε trans ≲ 0.2) taking place at low densities ≲1.3–1.5 n 0 is strongly disfavored. We also demonstrate that future measurements of the radius and tidal deformability of ∼1.4 M ⊙ stars, as well as the mass measurement of very massive pulsars, can help reveal the presence and amount of quark matter in compact objects.

Decuplet baryons in nuclear and hyperonic medium

Masses and the magnetic moments of baryon decuplet are evaluated in the symmetric nuclear and hyperonic matter at finite temperature using a chiral SU(3) quark mean field model approach. The decuplet baryon masses considerably decrease with the rise in the baryonic density of the medium. With the increase in strangeness (more number of hyperons as compared to nucleons) fraction, the non-strange baryons show an increase in their masses, whereas the strange baryons show a decrease. The contributions coming from the valence quarks, quark sea and the orbital angular momentum of the quark sea have been considered to calculate net magnetic moment. The magnetic moments of decuplet baryons are found to show a considerable increase with the baryonic density of the medium since constituent quark magnetic moment and the quark spin polarizations show significant variation in the nuclear medium especially in the low temperature and baryonic density regime. The increase is however quantitatively less as compared to the case of octet baryon members. With the inclusion of hyperons along with nucleons, the non-strange baryons show a decrease in the magnitude of their effective magnetic moments, whereas the strange baryons show an increase. The strangeness fraction of the medium is found to largely affect the valence quark magnetic moment and quark sea magnetic moment of the baryons.

Single- Λc+ hypernuclei within a quark mean-field model

The quark mean-field (QMF) model is applied to study the single $\Lambda^+_c$ hypernuclei. The charm baryon, $\Lambda^+_c$, is constructed by three constituent quarks, $u, ~d$, and $c$, confined by central harmonic oscillator potentials. The confinement potential strength of charm quark is determined by fitting the experimental masses of charm baryons, $\Lambda^+_c,~\Sigma^+_c$, and $\Xi^{++}_{cc}$. The effects of pions and gluons are also considered to describe the baryons at the quark level. The baryons in $\Lambda^+_c$ hypernuclei interact with each other through exchanging the $\sigma,~\omega$, and $\rho$ mesons between the quarks confined in different baryons. The $\Lambda^+_c N$ potential in the QMF model is strongly dependent on the coupling constant between $\omega$ meson and $\Lambda^+_c$, $g_{\omega\Lambda^+_c}$. When the conventional quark counting rule is used, i. e., $g_{\omega\Lambda^+_c}=2/3g_{\omega N}$, the massive $\Lambda^+_c$ hypernucleus can exist, whose single $\Lambda^+_c$ binding energy is smaller with the mass number increasing due to the strong Coulomb repulsion between $\Lambda^+_c$ and protons. When $g_{\omega\Lambda^+_c}$ is fixed by the latest lattice $\Lambda^+_c N$ potential, the $\Lambda^+_c$ hypernuclei only can exist up to $A\sim 50$.

Octet baryon masses and magnetic moments in hot and dense isospin asymmetric nuclear matter

Medium modification of the magnetic moments of octet baryons in the isospin asymmetric nuclear medium at finite temperature has been calculated using medium modified quark and baryon masses derived in chiral SU(3) quark mean field model. The magnetic moments of baryons are found to vary significantly as a function of density of nuclear medium as well as with the increase in isospin asymmetry of the medium. The rise of temperature is found to decrease the effect of isospin asymmetry on masses and magnetic moments of baryons. The results of present investigation may be helpful to understand the experimentally observed values of octet baryon magnetic moments at different experimental facilities.

Quark mean-field model for nuclear matter with or without bag

We propose the new quark mean-field bag (QMFB) model by incorporating the bag confinement mechanism in the original quark mean-field model. Nuclear matter and neutron star properties are studied with the QMFB model. For the study of the bag effect, we newly fit 12 parameter sets by reproducing the empirical saturation properties of nuclear matter. Quark confinement is found to be mainly demonstrated by the bag after it is included in the model, instead of the confining potential. For nuclear matter, the bag decreases the binding energy and increases the symmetry energy. For neutron star, the bag affects significantly the radius $R$ of a $1.4M_\odot$ star, with the maximum mass only slightly modified. The bag also has a large suppression effect on the well-accepted $R$ vs $L$ dependence, with $L$ the symmetry energy slope at the saturation density.

Neutron Star Equation of State from the Quark Level in Light of GW170817

Abstract The matter state inside neutron stars (NSs) is an exciting problem in astrophysics, nuclear physics, and particle physics. The equation of state (EOS) of NSs plays a crucial role in the present multimessenger astronomy, especially after the event of GW170817. We propose a new NS EOS, “QMF18,” from the quark level, which describes robust observational constraints from a free-space nucleon, nuclear matter saturation, heavy pulsar measurements, and the tidal deformability of the very recent GW170817 observation. For this purpose, we employ the quark mean-field model, which allows us to tune the density dependence of the symmetry energy and effectively study its correlations with the Love number and the tidal deformability. We provide tabulated data for the new EOS and compare it with other recent EOSs from various many-body frameworks.

Magnetic moments of octet baryons in strange matter

The modification of masses as well as magnetic moments of octet baryons in the presence of hot and dense isospin symmetric strange baryonic matter has been studied using the chiral SU(3) quark mean field model. Effective masses of octet baryons are found to decrease considerably as a function of baryonic density of the nuclear medium. The strange baryons show a significant decrease in their masses in the higher baryonic density regime as compared to nucleons. Baryonic magnetic moments comprise the explicit contributions from the valence quarks, sea quarks as well as orbital angular momentum of sea quarks. The magnitudes of magnetic moments of octet baryons are found to increase as a function of the density of the nuclear medium, since the quark spin polarizations corresponding to valence quarks, sea quarks and orbital angular momentum of sea quarks vary significantly in the baryonic medium particularly in the low density and temperature region. The magnetic moments of strange baryons show a consistent behavior as a function of the strangeness fraction with the increase of the temperature of the medium, whereas in the case of nucleons the magnetic moments show an opposite behavior at T = 0 and T = 100 MeV.

Effects of the nucleon radius on neutron stars in a quark mean field model

We study the effects of free space nucleon radius on nuclear matter and neutron stars within the framework of quark mean field model. The nucleon radius is treated self-consistently with this model, where quark confinement is adjusted to fit different values of nucleon radius. Corrections due to center-of-mass motion, quark-pion coupling, and one gluon exchange are included to obtain the nucleon mass in vacuum. The meson coupling constants that describe the behavior of many-body nucleonic system are newly-constructed by reproducing the empirical saturation properties of nuclear matter, including the recent determinations of symmetry energy parameters. Our results show that the nucleon radius in free space have negligible effects on nuclear matter equation of state and neutron star mass-radius relations, which is different from the conclusion drawn in previous studies. We further explore that the sensitivity of star radius on the nucleon radius found in earlier publications is actually from the symmetry energy and its slope.

Massive neutron star with strangeness in a relativistic mean-field model with a high-density cutoff

The properties of strangeness neutron star are studied within relativistic mean-field (RMF) model via including a logarithmic interaction as a function of scalar meson field. This logarithmic interaction, named as the $\sigma$-cut potential, can largely reduce the attractive contributions of scalar meson field at high density without any influence on nuclear structure around normal saturation density. In this work, the TM1 parameter set is chosen as the RMF interaction, while the strengths of logarithmic interaction are constrained by the properties of finite nuclei so that we can obtain a reasonable effective nucleon-nucleon interaction. The hyperons, $\Lambda,~\Sigma$, and $\Xi$ are also considered in neutron stars within this framework, whose coupling constants with mesons are determined by the latest hyperon-nucleon and $\Lambda$-$\Lambda$ potentials extracted from the experimental data of hypernuclei. The maximum mass of neutron star can be larger than two solar mass with these hyperons. Furthermore, the nucleon mass at high density will be saturated due to this additional $\sigma$-cut potential, which is consistent with the conclusions from the microscopic calculations such as, Brueckner-Hartree-Fock theory and quark mean-field model.

Single- Ξ− hypernuclei within a quark mean-field model

The single-${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hypernuclei are studied using a quark mean-field model. At the quark level, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hyperon is composed of one $d$ quark and two $s$ quarks, which are confined by the harmonic oscillator potentials. In the case of hadrons, the baryons interact with each other by exchanging $\ensuremath{\sigma},\ensuremath{\omega}$, and $\ensuremath{\rho}$ mesons between quarks in different baryons. The single-${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ binding energies of $\mathrm{\ensuremath{\Xi}}$ hypernuclei are investigated from $\mathrm{Be}$ to $\mathrm{Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$\mathrm{\ensuremath{\Lambda}}$ and single-$\mathrm{\ensuremath{\Xi}}$ potentials at the nuclear saturation density. For the bound states of ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{14}\mathrm{N}$ (i.e., $\mathrm{C}$) system named as KISO event in the KEK-E373 experiment, it is found that the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ binding energies are around $5.61--5.89$ MeV for $1s$ state and $0.94--1.21$ MeV for $1p$ state with QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets, whose single-$\mathrm{\ensuremath{\Xi}}$ potentials are $\ensuremath{-}12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{12}\mathrm{Be}$ show that in the KISO event, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hyperon may occupy the $1p$ state. Furthermore, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ binding energies are achieved around $27\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{207}\mathrm{Pb}$ (i.e., $\mathrm{Tl}$) system. The energies were nearly comparable to the single-$\mathrm{\ensuremath{\Lambda}}$ binding energy of $\mathrm{Pb}$ observed by experiments. It demonstrates that the $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hyperons seem to appear simultaneously in a neutron star.