Quark stars: features and findings

Under extreme conditions of temperature and/or density, quarks and gluons are expected to undergo a deconfinement phase transition. While this is an ephemeral phenomenon at the ultra-relativistic heavy-ion collider (BNL-RHIC), quark matter may exist naturally in the dense interior of neutron stars. Here, we present an appraisal of the possible phase structure of dense quark matter inside neutron stars, and the likelihood of its existence given the current status of neutron star observations. We conclude that quark matter inside neutron stars cannot be dismissed as a possibility, although recent observational evidence rules out most soft equations of state. PACS 97.60.Jd; 26.60.+c     

Hybrid stars and quark hadron phase transition in chiral colour dielectric model

We investigate the properties of hybrid stars consisting of quark matter in the core and hadron matter in outer region. The hadronic equation of state (EOS) is calculated by using nonlinear Walecka model. Strange baryons are included in the hadronic EOS calculation. The chiral colour dielectric (CCD) model, in which quarks are confined dynamically, is used to calculate quark matter EOS. We find that the phase transition from hadron to quark matter is possible in a narrow range of the parameters of nonlinear Walecka and CCD models. The transition is strong or weak first order depending on the parameters used. The EOS thus obtained, is used to study the properties of hybrid stars. We find that the calculated hybrid star properties are similar to those of pure neutron stars.     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

Breached pairing superfluidity: possible realization in QCD

We propose a wide universality class of gapless superfluids, and analyze a limit that might be realized in quark matter at intermediate densities. In the breached pairing color superconducting phase heavy s quarks, with a small Fermi surface, pair with light u or d quarks. The ground state has a superfluid and a normal Fermi component simultaneously. We expect a second-order phase transition, as a function of increasing density, from the breached pairing phase to the conventional color-flavor locked phase.     

Flavor ordering of elliptic flows at high transverse momentum

Based on the quark coalescence model for the parton-to-hadron phase transition in relativistic heavy ion collisions, we relate the elliptic flow (upsilon(2)) of high p(T) hadrons to that of high p(T) quarks. For high p(T) hadrons produced from an isospin-symmetric and quark-antiquark-symmetric partonic matter, magnitudes of their elliptic flows follow a flavor ordering as (upsilon(2,pi)=upsilon(2,N))>(upsilon(2,Lambda)=upsilon(2,Sigma))>upsilon(2,K)>upsilon(2,Xi)>(upsilon(2,phi)=upsilon(2,Omega)) if strange quarks have a smaller elliptic flow than light quarks. The elliptic flows of high p(T) hadrons further follow a simple quark counting rule if strange quarks and light quarks have the same high p(T) spectrum and coalescence probability.     

The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

Energy dependence of transverse quark flow in heavy ion collisions

Energy dependence of quark transverse flow carries information about dynamical properties (equation of state, initial conditions) of deconfined matter produced in heavy ion collisions. We assume quark-antiquark matter formation in Pb+Pb collisions at CERN SPS and Au+Au collisions at RHIC energies and determine quark transverse flow at the critical temperature of the quark-hadron phase transition. Coalescence of massive quarks is calculated in the MICOR hadronization model and hadronic final state effects are considered using the GROMIT cascade program. Comparing theoretical results to data, transverse flow values are determined and energy dependence is discussed.     

Quark matter formation in dense stellar objects

It is expected that at very large densities and/or temperatures a quark-hadron phase transition takes place. Lattice QCD calculations at zero baryon density indicate that the transition occurs at T _c ∼ 150–170 MeV. The transition is likely to be second order or a cross over phenomenon. Although not much is known about the density at which the phase transition takes place at small temperatures, it is expected to occur around the nuclear densities of few times nuclear matter density. Also, there is a strong reason to believe that the quark matter formed after the phase transition is in colour superconducting phase. The matter densities in the interior of neutron stars being larger than the nuclear matter density, the neutron star cores may possibly consist of quark matter which may be formed during the collapse of supernova. Starting with the assumption that the quark matter, when formed consists of predominantly u and d quarks, we consider the evolution of s quarks by weak interactions in the present work. The reaction rates and time required to reach the chemical equilibrium are computed here. Our calculations show that the chemical equilibrium is reached in about 10⁻⁷ seconds. Further more during the equilibration process enormous amont of energy is released and copious numbers of neutrinos are produced. Implications of these on the evolution of supernovae will be discussed.     

Chiral-symmetry restoration in clustered hadronic matter

Chiral-symmetry restoration is usually discussed in the context of quark matter, a system of deconfined quarks. However, many systems like stable nuclei and neutron stars have quarks confined within nucleons. In the present paper we use a Fermi sea of three-quark clusters instead of a Fermi sea of deconfined quarks to investigate the in-medium quark condensate. We find that an enhancement of the chiral breaking in clustered matter as claimed in the literature is not a consequence of the clustering but rather dependent on the microscopic model dynamics.Received: 30 September 2002, Published online: 22 October 2003PACS: 21.65. + f Nuclear matter - 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processes - 12.39.-x Phenomenological quark models     

Possible pseudogap phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally, and quarks acquire constituent masses in the pseudogap phase, despite the fact that chiral symmetry is restored.     

Quark core stars,quark stars and strange stars

A recent one flavor (zero temperature) quark matter equation of state is generalized to several flavors. It is shown that quarks undergo a first order phase transition. In addition, this equation of state depends on few parameters, one in the two flavor case, two in the three flavor case, and these parameters can be constrained by phenomenology. This equation of state is then applied to 1) the hadronquark transition in neutron stars and the determination of quark star stability, 2) the investigation of strange matter stability and possible strange star existence.     

Open quantum system approach for heavy quark thermalization

We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schr?dinger equation (SSE) from the full Schr?dinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.     

Quark matter influence on observational properties of compact stars

Densities in compact stars may be such that quarks are no longer confined in hadrons, but instead behave as weakly interacting particles. In this regime perturbative calculations are possible. Yet, due to high pressures and an attractive channel in the strong force, condensation of quarks in a superfluid state is likely. This can have interesting consequences for magnetic fields, especially in relation to the discovery of slow-period free precession in a compact star. In this proceedings there will be a discussion of the mass-radius relations of compact stars made from quark matter and magnetic field behaviour in compact stars with a quark matter core.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

QCD phase transition with strange quark in wilson formalism for fermions

The nature of QCD phase transition is studied with massless up and down quarks and a light strange quark, using the Wilson formalism for quarks on a lattice with the temporal direction extensionN _t=4. We find that the phase transition is of first order for the physical strange quark mass.