Hot Quark Matter Research Articles

Erratum: Phase diagrams in the three-flavor Nambu–Jona-Lasinio model with the Polyakov loop [Phys. Rev. D77, 114028 (2008)

We present extensive studies on hot and dense quark matter with two light and one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop (so-called PNJL model). First we discuss prescription dependence in choosing the Polyakov loop effective potential and propose a simple and rather sensible ansatz. We look over quantitative comparison to the lattice measurement to confirm that the model captures thermodynamic properties correctly. We then analyze the phase structure with changing the temperature, quark chemical potential, quark masses, and coupling constants. We particularly investigate how the effective U_A(1) restoration and the induced vector-channel interaction at finite density would affect the QCD critical point.

Phase diagrams in the three-flavor Nambu–Jona-Lasinio model with the Polyakov loop

We present extensive studies on hot and dense quark matter with two light and one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop (so-called PNJL model). First we discuss prescription dependence in choosing the Polyakov loop effective potential and propose a simple and rather sensible ansatz. We look over quantitative comparison to the lattice measurement to confirm that the model captures thermodynamic properties correctly. We then analyze the phase structure by changing the temperature, quark chemical potential, quark masses, and coupling constants. We particularly investigate how the effective ${\mathrm{U}}_{\mathrm{A}}(1)$ restoration and the induced vector-channel interaction at finite density would affect the QCD critical point.

WHAT'S THE MATTER AT RHIC?

I present here a concise review of the experimental results obtained at the Relativistic Heavy Ion Collider (RHIC), which shed light on the hot and dense quark gluon matter produced at these high temperature and density conditions.

Relativistic quark matter in light front field theory

We consider correlations in hot and dense quark matter within the framework of light front quantization. We have computed the masses of two-body boundstates M 2 ( T , μ ) in the pionic and scalar diquark channel using a T -matrix approach. The quark interaction is given by a NJL model. The gap equation is generalized to finite temperature T and quark chemical potential μ and we determine the medium dependent quark mass. Further we calculate the critical temperature of two flavor color superconductivity.

Light Front Approach to Correlations in Hot Quark Matter

We investigate two-quark correlations in hot and dense quark matter. To this end we use the light front field theory extended to finite temperature T and chemical potential μ. Therefore it is necessary to develop quantum statistics formulated on the light front plane. As a test case for light front quantization at finite T and μ we consider the NJL model. The solution of the in-medium gap equation leads to a constituent quark mass which depends on T and μ. Two-quark systems are considered in the pionic and diquark channel. We compute the masses of the two-body system using a T-matrix approach.

Restoration of Chiral Symmetry in Light-Front Finite-Temperature Field Theory

We investigate the properties of $qq$ and $q\bar q$ states in hot and dense quark matter in the framework of light-front finite temperature field theory. Presently we use the Nambu Jona-Lasinio model of QCD and derive the gap equation at finite temperature and density. We study pionic and scalar diquark dynamics in quark matter and calculate the masses and the Mott dissociation as a function of the temperature $T$ and the chemical potential $\mu$. For the scalar diquark we determine the critical temperature of color superconductivity.

Erratum: General effective action for high-density quark matter [Phys. Rev. D70, 114029 (2004)

We derive a general effective action for quark matter at nonzero temperature and/or nonzero density. For this purpose, we distinguish irrelevant from relevant quark modes, as well as hard from soft gluon modes by introducing two separate cut-offs in momentum space, one for quarks, $\Lambda_q$, and one for gluons, $\Lambda_g$. We exactly integrate out irrelevant quark modes and hard gluon modes in the functional integral representation of the QCD partition function. Depending on the specific choice for $\Lambda_q$ and $\Lambda_g$, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the ``Hard Thermal Loop'' or the ``Hard Dense Loop'' action, as well as the high-density effective theory proposed by Hong and others. We then apply our effective action to review the calculation of the color-superconducting gap parameter to subleading order in weak coupling, where the strong coupling constant $g \ll 1$. In this situation, relevant quark modes are those within a layer of thickness $2 \Lambda_q$ around the Fermi surface. The non-perturbative nature of the gap equation invalidates naive attempts to estimate the importance of the various contributions via power counting on the level of the effective action. Nevertheless, once the gap equation has been derived within a particular many-body approximation scheme, the cut-offs $\Lambda_q, \Lambda_g$ provide the means to rigorously power count different contributions to the gap equation. We recover the previous result for the QCD gap parameter for the choice $\Lambda_q \alt g \mu \ll \Lambda_g \alt \mu$, where $\mu$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

General effective action for high-density quark matter

We derive a general effective action for quark matter at nonzero temperature and/or nonzero density. For this purpose, we distinguish irrelevant from relevant quark modes, as well as hard from soft gluon modes by introducing two separate cutoffs in momentum space, one for quarks, ${\ensuremath{\Lambda}}_{q}$, and one for gluons, ${\ensuremath{\Lambda}}_{g}$. We exactly integrate out irrelevant quark modes and hard gluon modes in the functional integral representation of the QCD partition function. Depending on the specific choice for ${\ensuremath{\Lambda}}_{q}$ and ${\ensuremath{\Lambda}}_{g}$, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the ``Hard Thermal Loop'' or the ``Hard Dense Loop'' action, as well as the high-density effective theory proposed by Hong and others. We then apply our effective action to review the calculation of the color-superconducting gap parameter to subleading order in weak coupling, where the strong coupling constant $g\ensuremath{\ll}1$. In this situation, relevant quark modes are those within a layer of thickness $2{\ensuremath{\Lambda}}_{q}$ around the Fermi surface. The nonperturbative nature of the gap equation invalidates naive attempts to estimate the importance of the various contributions via power counting on the level of the effective action. Nevertheless, once the gap equation has been derived within a particular many-body approximation scheme, the cutoffs ${\ensuremath{\Lambda}}_{q},{\ensuremath{\Lambda}}_{g}$ provide the means to rigorously power count different contributions to the gap equation. We recover the previous result for the QCD gap parameter for the choice ${\ensuremath{\Lambda}}_{q}\ensuremath{\lesssim}g\ensuremath{\mu}\ensuremath{\ll}{\ensuremath{\Lambda}}_{g}\ensuremath{\lesssim}\ensuremath{\mu}$, where $\ensuremath{\mu}$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

Pseudogap of color superconductivity in heated quark matter

We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the decaying process of quarks near Fermi surface to a hole and the diquark soft mode $(\mathrm{q}\mathrm{q}{)}_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ is responsible for the formation of the pseudogap. Our result suggests that the pseudogap is a universal phenomenon in strong coupling superconductors.

Fluctuations of the color-superconducting gap in hot and dense quark matter

Fluctuations of the color superconducting gap in hot and dense quark matter are investigated in terms of the phenomenological Ginzburg-Landau approach. Our estimates show that fluctuations of the di-quark gap may strongly affect some of thermodynamic quantities even far below and above the critical temperature. If the critical temperature of the di-quark phase transition were rather high one could expect a manifestation of fluctuations of the di-quark gap in the course of heavy ion collisions.

Energy release due to antineutrino untrapping and diquark condensation in hot quark star evolution

We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation. Due to the conditions of charge neutrality and β-equilibrium the flavor asymmetry increases with the number density of trapped antineutrinos. Above a critical value of the antineutrino chemical potential of 30 MeV, diquark condensation is inhibited at low densities and a two-phase structure emerges: a superconducting quark matter core surrounded by a shell of normal quark matter. When the quark star cools below a temperature T ∼ 1 MeV, the mean free path of antineutri nos becomes larger than the thickness of the normal quark matter shell so that they become suddenly untrapped. By comparing the masses of configurations with the same baryon number we estimate that the release of energy due to the antineutrino untrapping transition can be in the range of 10 51 -10 52 erg.

Pseudogap of Color Superconductivity

We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the soft mode of the di-quark pair field gives rise to a peculiar behavior of the quark dispersion relation and a short life-time of the quasiparticles near the Fermi surface, both of which make a depression of the density of states of quarks. Our result suggests that the appearance of the pseudogap is a universal phenomenon of strong coupling superconductors, irrespective of the dimensionality.

Correlations in Hot and Dense Quark Matter

We present a relativistic three-body equation to investigate three-quark clusters in hot and dense quark matter. To derive such an equation we use the Dyson equation approach. The equation systematically includes the Pauli blocking factors as well as the self energy corrections of quarks. Special relativity is realized through the light front form. Presently we use a zero-range force and investigate the Mott transition.

PION AND KAON DISSOCIATION IN HOT QUARK MEDIUM

Pion and kaon dissociation in a medium of hot quark matter is studied in the Nambu–Jona-Lasinio model. The decay widths of pion and kaon are found to be large but finite at temperatures much higher than the so-called critical temperature of chiral or deconfinement transition, kaon decay width being larger. Consequently, pions and even kaons (with a lower density compared to pions) should coexist with quarks and gluons at such high temperatures. The implication of the above result in the study of quark–gluon plasma is discussed.

Coherent amplification of classical pion fields during the cooling of droplets of quark plasma

In the framework of the linear sigma model, we study the time evolution of a system of classical $\sigma$ and pion fields coupled to quarks. For this purpose we solve numerically the classical transport equation for relativistic quarks coupled to the nonlinear Klein-Gordon equations for the meson fields. We examine evolution starting from variety of initial conditions corresponding to spherical droplets of hot quark matter, which might mimic the behaviour of a quark plasma produced in high-energy nucleus-nucleus collisions. For large droplets we find a strong amplification of the pion field that oscillates in time. This leads to a coherent production of pions with a particular isospin and so would have similar observable effects to a disoriented chiral condensate which various authors have suggested might be a signal of the chiral phase transition. The mechanism for amplification of the pion field found here does not rely on this phase transition and is better thought of as a "pion laser" which is driven by large oscillations of the $\sigma$ field.

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.

Instantaneous chiral quark model for relativistic mesons in a hot and dense medium

A chiral quark model with covariant instantaneous interactions is formmulatd using relativistic thermodynamic Green functions. The approach is applied to the description of mesons as relativistic bound states in hot and dense quark matter. The Schwinger-Dyson equation for the quark-mass operator and the Salpeter equations for quark-antiquark bound states are obtained for a nonlocal covariant four-point interaction kernel. Special attention is paid to the medium modification of meson properties as a function of their total momentum. Numerical results for the pion mass and the pion decay constant at finite temperature are presented for the special case of a separable interaction. We obtain a “protection” of the pseudoscalar bound state against medium influence due to the finite (thermal) velocity relative to the surrounding matter.

Strange matter lumps in the early Universe.

We study the stability of hot strange matter lumps formed in the early Universe. As the Universe cools below the hadronization temperature, these lumps normally become unstable against boiling. They can stabilize themselves against this process if their mass is sufficiently large to hold a hadronic crust by gravitational attraction. Our analysis improves on previous studies of the internal structure of such stable hot quark matter lumps with hadronic crust by correctly treating the constraints from chemical equilibrium of baryonic and electric charge between crust and core. Since the expansion rate of the early Universe is much faster than the cooling rate of the strange matter lumps, their internal structure is characterized by constant entropy per baryon. Our improved analysis confirms the earlier finding that such stable quark matter lumps require a mass well above the total mass inside the horizon.

Dilepton spectra from expanding hot quark matter

The previous dilepton spectrum expression and relativistic hydrodynamic equations derived from the energy-momentum conservation, are generalized to include the effect of the space-time distribution of particles. The influences of the particle distribution and the latent heat released by the phase transition on the dilepton spectrum are studied on the basis of the generalized formalism. We find that these two influences significantly change the characteristic dilepton spectrum for the formation of quark matter given by previous authors, they especially cause the non-monotony of the total dilepton yield with respect to the initial temperature. It is shown that these two influences must be included in order to get a more reasonable characteristic dilepton spectrum for the formation of the quark matter.

Damping of vibrations and of the secular instability in quark stars

We calculate the bulk viscosity of hot quark matter, or “strange” matter, which could be present in neutron stars. In the temperature range characteristic of young neutron stars, the bulk viscosity arising from non-leptonic strangeness-changing quark-quark interactions is orders of magnitude larger than that which has been calculated for ordinary nuclear matter. The gravitational wave secular instability should be completely suppressed for quark stars, and the damping times for pulsations will be very short.