Finite Baryon Density Research Articles

A Study of the Thermodynamic Properties of a Hot, Dense Hadron Gas Using an Event Generator: Hadro-Molecular-Dynamical Calculation

We investigate the equilibration and the equation of state of a hot hadron gas at finite baryon density using an event generator which is designed to approximately satisfy detailed balance at finite temperatures and finite baryon densities of the hadronic scale (80 MeV <T <170 MeV and 0.157 fm −3 <n B < 0.315 fm −3 ). Molecular-dynamical simulations were performed for a system of hadrons in a box with periodic boundary conditions. Starting from an initial state composed of only nucleons with a uniform phase-space distribution, the evolution takes place through interactions such as collisions, productions and absorptions. The system approaches a stationary state of baryons, mesons and their resonances, which is characterized by the value of the exponent in the energy distribution common to the different particles, i.e., the temperature. After the equilibration, thermodynamic quantities, such as the energy density, particle density, entropy and pressure are calculated. Above T ∼ mπ, the obtained equation of state exhibits a significant deviation from the naive mixed free gas model. Large values of the entropy per baryon are also notable. In our system, the excitation of heavy baryon resonances and meson production are enhanced simultaneously, and the increase of the temperature becomes moderate, but a Hagedorn-type artificial temperature saturation does not occur. The pressure exhibits a linear dependence on the energy density.

Finite baryon density effects on gauge field dynamics

We discuss the effective action for QCD gauge fields at finite temperatures and densities, obtained after integrating out the hardest momentum scales from the system. We show that a non-vanishing baryon density induces a charge conjugation (C) odd operator to the gauge field action, proportional to the chemical potential. Even though it is parametrically smaller than the leading C even operator, it could have an important effect on C odd observables. The same operator appears to be produced by classical kinetic theory, allowing in principle for a non-perturbative study of such processes.

Intermediate Mass Dilepton Production in a ChemicallyEquilibrating Quark-Gluon Matter

Dilepton production during the chemical equilibration of quark-gluonmatter with a finite baryon density has been studied. We find that dueto the slowing down of the cooling rate and the high initial temperature of thequark-gluon matter produced at RHIC energies, the quark phasecontribution to dileptons with intermediate masses is significantlyheightened and is much larger than that calculated by the evolutionof the thermodynamic equilibrium system. The latter has shown anenhancement of intermediate mass dileptons from the quark phase.Therefore, such an enhancement of dileptons should be asignature for quark-gluon matter formation.

QCD-like theories at finite baryon and isospin density

We use two-color QCD as a model to study the effects of the simultaneous presence of chemical potentials for isospin charge ${\ensuremath{\mu}}_{I}$ and for baryon number ${\ensuremath{\mu}}_{B}.$ We determine the phase diagrams for two and four flavor theories using the method of effective chiral Lagrangians at low densities and weak-coupling perturbation theory at high densities. We determine the values of various condensates and densities as well as the spectrum of excitations as functions of ${\ensuremath{\mu}}_{I}$ and ${\ensuremath{\mu}}_{B}.$ A similar analysis of QCD with quarks in the adjoint representation is also presented. Our results can be of relevance for lattice simulations of these theories. We predict a phase of inhomogeneous condensation (Fulde-Ferrel-Larkin-Ovchinnikov phase) in the two color, two flavor theory, while we do not expect it in the four flavor case or in other realizations of QCD with a positive measure.

Dileptons from a quark-gluon plasma with finite baryon density

We investigate the effects of a baryon-antibaryon asymmetry on the spectrum of dileptons radiating from a quark gluon plasma. We demonstrate the existence of a new set of processes in this regime. The dilepton production rate from the corresponding diagrams is shown to be as important as that obtained from the usual quark-antiquark annihilation.

Quark-gluon plasma fireball

Lattice quantum chromodynamics results provide an opportunity to model, and extrapolate to finite baryon density, the properties of the quark-gluon plasma (QGP). Upon fixing the scale of the thermal coupling constant and vacuum energy to the lattice data, the properties of resulting QGP equations of state (EoS) are developed. We show that the physical properties of the dense matter fireball formed in heavy ion collision experiments at CERN-SPS are well described by the QGP-EoS we presented. We also estimate the properties of the fireball formed in early stages of nuclear collision, and argue that QGP formation must be expected down to $40A$ GeV in central Pb-Pb interactions.

Strange-quark matter within the Nambu-Jona-Lasinio model

Equation of state of baryon rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavour mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of strangeness fraction S/3B. The model predictions are very sensitive to the ratio of vector (Gv) and scalar (Gs) coupling constants. At Gv/Gs=0.5 and zero temperature the maximum binding energy (about 15 MeV per baryon) takes place when strangeness fraction is about 0.4. Such strangelets are negatively charged and have typical life times of the order of 100 ns. Calculations are carried out also at finite temperatures. They show that bound states exist up to temperatures of about 15 MeV. The model predicts a first order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as function of strangeness fraction.

Color dynamics in phase space

We describe the properties of quark matter at zero temperature and finite baryon densities within microscopic Vlasov/molecular dynamics approaches. We use an inter-quark Richardson's potential consistent with the indications of Lattice QCD calculations. The color degrees of freedom are explicitly taken into account. We explicitly demonstrate that the Vlasov approach alone is insufficient in the hadronization region. In order to overcome this problem we prepare the initial condition for many events using molecular dynamics with frictional cooling and a Thomas-Fermi approximation to the Fermi motion. These events are averaged and propagated in time using the Vlasov approach. We find some evidence for a second order phase transition from nuclear to quark matter at high baryon densities. An order parameter suitable to describe the phase transition is discussed. At low densities the quark condensate into approximately color white clusters (nucleon).

Quark hadron continuity in QCD with one flavor

We study QCD with one flavor at finite baryon density. In the limit of very high baryon density the system is expected to be a color superconductor. In the case of one flavor, the order parameter is in a $\bar 3$ of color and has total angular momentum one. We show that in weak coupling perturbation theory, the energetically preferred phase exhibits ``color-spin-locking'', i.e. the color and spin direction of the condensate are aligned. We discuss the properties of this phase and argue that it shares important features of the hadronic phase at low density. In particular, we find an unbroken rotational symmetry, spin 3/2 quasiparticles, and an unusual mechanism for quark-anti-quark condensation. Our results are relevant to three flavor QCD in the regime where the strange quark mass is bigger than the critical value for color-flavor-locking. We find that the gaps in this case are on the order of one MeV.

Emergence of the Skyrme crystal in Gross-Neveu and ’t Hooft models at finite density

We study two-dimensional, large $N$ field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out.

Predictions of multiparticle Bose-Einstein correlations of pions and kaons for hadronization of quark-gluon plasma droplets

We calculate the multiparticle Bose-Einstein correlations of pions and kaons produced by a surface hadronization of quark-gluon plasma droplets with initial baryon densities of 0.5 and $0{\mathrm{fm}}^{\ensuremath{-}3}.$ For a finite initial baryon density, the multiparticle correlations of ${K}^{+}$ are weaker than those of $\ensuremath{\pi},$ and the average multiparticle correlation intensities of ${K}^{\ensuremath{-}}$ decrease greatly with the increase of the number of the droplets, ${N}_{d}.$ For zero initial baryon density the differences between the average multiparticle correlation intensities of ${K}^{+}$ and $\ensuremath{\pi}$ become obvious with increasing ${N}_{d}.$

QCD-like theories at finite baryon density

We study QCD-like theories with pseudoreal fermions at finite baryon density. Such theories include two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint color representation. In all such theories the lightest baryons are diquarks. At zero chemical potential μ they are, together with the pseudoscalar mesons, the Goldstone modes of a spontaneously broken enlarged chiral symmetry group. Using symmetry principles, we derive the low-energy effective Lagrangian for these particles. We find that a second order phase transition occurs at a value of μ equal to half the mass of the Goldstone modes. For values of μ beyond this point the scalar diquarks Bose condense and the diquark condensate is nonzero. We calculate the dependence of the chiral condensate, the diquark condensate, the baryon charge density, and the masses of the diquark and pseudoscalar excitations on μ at finite bare quark mass and scalar diquark source. The relevance of our results to lattice QCD calculations and to real three-color QCD at finite baryon density is discussed.

Modifications of the rho-meson from the virtual pion cloud in hot and dense matter

The modification of the ρ-meson self-energy due to the coupling to in-medium pions is calculated consistently at finite baryon density and temperature, keeping the full 3-momentum dependence in a gauge invariant way. As a function of nucleon density, the ρ-meson spectral function is strongly enhanced in the invariant mass region M≲650 MeV , while the maximum, i.e., the pole mass, is slightly shifted upwards. As a function of temperature, for fixed nucleon density, the imaginary part of the self-energy increases further due to Bose-enhancement. At the same time the mass shift from the real part becomes very large. As a consequence of these medium effects, the dilepton rate in the low-mass region M≲650 MeV increases strongly, while the peak at M≈770 MeV disappears.

Effect of baryon density on parton production, chemical equilibration, and thermal photon emission from the quark gluon plasma

The effect of baryon density on parton production processes of $gg\rightleftharpoons ggg$ and $gg\rightleftharpoons q{\bar q}$ is studied using full phase space distribution function and also with inclusion of quantum statistics i.e. Pauli blocking and Bose enhancement factors, in the case of both saturated and unsaturated quark gluon plasma. The rate for the process $gg \rightleftharpoons q{\bar q}$ is found to be much less as compared to the most commonly used factorized result obtained on the basis of classical approximation. This discrepancy, which is found both at zero as well as at finite baryon densities, however, is not due to the lack of quantum statistics in the classical approximation, rather due to the use of Fermi-Dirac and Bose-Einstein distribution functions for partons instead of Boltzmann distribution which is appropriate under such approximation. Interestingly, the rates of parton production are found to be insensitive to the baryo-chemical potential particularly when the plasma is unsaturated although the process of chemical equilibration strongly depends on it. The thermal photon yields, have been calculated specifically from unsaturated plasma at finite baryon density. The exact results obtained numerically are found to be in close agreement with the analytic expression derived using factorized distribution functions appropriate for unsaturated plasma. Further, it is shown that in the case of unsaturated plasma, the thermal photon production is enhanced with increasing baryon density both at fixed temperature and fixed energy density of the quark gluon plasma.

Finite density fat QCD

Lattice formulation of finite baryon density QCD is problematic from the computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For a large bare quark mass, problems related to the phase of the determinant are still present but restricted to a small region in the chemical potential $\ensuremath{\mu}.$ We present evidence for a transition line that, starting from the temperature critical point at $\ensuremath{\mu}=0,$ moves towards a smaller $\ensuremath{\beta}$ with increasing $\ensuremath{\mu}.$

Strongly coupled QCD at finite baryon density

The analytical results obtained in the infinite mass and strong coupling limits of QCD are difficult to reconcile with the predictions of the Monomer Dimer Polymer algorithm. We have reconsidered in detail the results obtained with this simulation scheme and evidences of severe convergence problems are presented for the SU(3) and SU(2) gauge group cases.

Strongly Coupled QCD at Finite Baryon Density

Strongly Coupled QCD at Finite Baryon Density

Renormalization group flow equation at finite density

For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high density. In the latter solution, the formation of droplets of massless quarks is realized even at low density.

Dissipative phenomena in a chemically nonequilibrated quark gluon plasma

The dissipative corrections to the hydrodynamic equations describing the evolution of energy-momentum tensor and parton densities are derived in a simple way using the scaling approximation for the expanding quark gluon plasma at finite baryon density. This procedure has been extended to study the process of chemical equilibration using a set of rate equations appropriate for a viscous quark gluon plasma. It is found that in the presence of dissipation, the temperature of the plasma evolves slower, whereas the quark and gluon fugacities evolve faster than their counterparts in the ideal case without viscosity.

Pion scalar density and chiral symmetry restoration at finite temperature and density

This paper is devoted to the evaluation of the pionic scalar density at finite temperature and baryonic density. We express the latter effect in terms of the nuclear response evaluated in the random phase approxima- tion. We discuss the density and temperature evolution of the pionic density which governs the quark condensate evolution. Numerical evalua- tions are performed.