Uranium on uranium collisions at relativistic energies

Deformation and orientation effects on compression, elliptic flow and particle production in uranium on uranium collisions (UU) at relativistic energies are studied within the transport model ART. The density compression in tip-tip UU collisions is found to be about 30% higher and lasts approximately 50% longer than in body-body or spherical UU reactions. The body-body UU collisions have the unique feature that the nucleon elliptic flow is the highest in the most central collisions and remain a constant throughout the reaction. We point out that the tip-tip UU collisions are more probable to create the QGP at AGS and SPS energies while the body-body UU collisions are more useful for studying properties of the QGP at higher energies.Comment: 8 pages + 4 figure

Pion dispersion relation at finite density and temperature

We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature. We introduce a pion chemical potential to describe the finite pion number density and argue that such description is valid during the hadronic phase of a relativistic heavy-ion collision between chemical and thermal freeze-out. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is computed through the computation of the pion self-energy in a non-perturbative fashion by giving an approximate solution to the Schwinger-Dyson equation for this self-energy. The dispersion relation is described in terms of a density and temperature dependent mass and an index of refraction which is also temperature, density as well as momentum dependent. The index of refraction is larger than unity for all values of the momentum for finite $\mu$ and $T$. We conclude by exploring some of the possible consequences for the propagation of pions through the boundary between the medium and vacuum.Comment: 7 pages, 5 figures, 3 new references, published versio

Thermal and Chemical Equilibration in Relativistic Heavy Ion Collisions

We investigate the thermalization and the chemical equilibration of a parton plasma created from Au+Au collision at LHC and RHIC energies starting from the early moment when the particle momentum distributions in the central region become for the first time isotropic due to longitudinal cooling. Using the relaxation time approximation for the collision terms in the Boltzmann equations for gluons and for quarks and the real collision terms constructed from the simplest QCD interactions, we show that the collision times have the right behaviour for equilibration. The magnitude of the quark (antiquark) collision time remains bigger than the gluon collision time throughout the lifetime of the plasma so that gluons are equilibrating faster than quarks both chemically and kinetically. That is we have a two-stage equilibration scenario as has been pointed out already by Shuryak sometimes ago. Full kinetic equilibration is however slow and chemical equilibration cannot be completed before the onset of the deconfinement phase transition assumed to be at $T_c=200$ MeV. By comparing the collision entropy density rates of the different processes, we show explicitly that inelastic processes, and \emph{not} elastic processes as is commonly assumed, are dominant in the equilibration of the plasma and that gluon branching leads the other processes in entropy generation. We also show that, within perturbative QCD, processes with higher power in \alpha_s need not be less important for the purpose of equilibration than those with lower power. The state of equilibration of the system has also a role to play. We compare our results with those of the parton cascade model.Comment: 17 pages, revtex+psfig style with 14 embedded postscript figures, to appear in Phys. Rev.

Comparison of space-time evolutions of hot/dense matter in sNN\sqrt{s_{NN}}=17 and 130 GeV relativistic heavy ion collisions based on a hydrodynamical model

Based on a hydrodynamical model, we compare 130 GeV/$A$ Au+Au collisions at RHIC and 17 GeV/$A$ Pb+Pb collisions at SPS. The model well reproduces the single-particle distributions of both RHIC and SPS. The numerical solution indicates that huge amount of collision energy in RHIC is mainly used to produce a large extent of hot fluid rather than to make a high temperature matter; longitudinal extent of the hot fluid in RHIC is much larger than that of SPS and initial energy density of the fluid is only 5% higher than the one in SPS. The solution well describes the HBT radii at SPS energy but shows some deviations from the ones at RHIC.Comment: 28 pages, 21 figures, REVTeX4, one figure is added and some figures are replace

Phases of QCD, Thermal Quasiparticles and Dilepton Radiation from a Fireball

We calculate dilepton production rates from a fireball adapted to the kinematical conditions realized in ultrarelativistic heavy ion collisions over a broad range of beam energies. The freeze-out state of the fireball is fixed by hadronic observables. We use this information combined with the initial geometry of the collision region to follow the space-time evolution of the fireball. Assuming entropy conservation, its bulk thermodynamic properties can then be uniquely obtained once the equation of state (EoS) is specified. The high-temperature (QGP) phase is modelled by a non-perturbative quasiparticle model that incorporates a phenomenological confinement description, adapted to lattice QCD results. For the hadronic phase, we interpolate the EoS into the region where a resonance gas approach seems applicable, keeping track of a possible overpopulation of the pion phase space. In this way, the fireball evolution is specified without reference to dilepton data, thus eliminating it as an adjustable parameter in the rate calculations. Dilepton emission in the QGP phase is then calculated within the quasiparticle model. In the hadronic phase, both temperature and finite baryon density effects on the photon spectral function are incorporated. Existing dilepton data from CERES at 158 and 40 AGeV Pb-Au collisions are well described, and a prediction for the PHENIX setup at RHIC for sqrt(s) = 200 AGeV is given.Comment: 31 pages, 15 figures, final versio

Transverse flow and hadro-chemistry in Au+Au collisions at \sqrt{s_{NN}}=200 GeV

We present a hydrodynamic assessment of preliminary particle spectra observed in Au+Au collisions at \sqrt{s_{NN}}=200 GeV. The hadronic part of the underlying equation of state is based on explicit conservation of (measured) particle ratios throughout the resonance gas stage after chemical freezeout by employing chemical potentials for stable mesons, nucleons and anti-nucleons. We find that under these conditions the data (in particular the proton spectra) favor a low freeze-out temperature of around 100 MeV. Furthermore we show that through inclusion of a moderate pre-hydrodynamic transverse flow field the shape of the spectra improves with respect to the data. The effect of the initial transverse boost on elliptic flow and the freeze-out geometry of the system is also elucidated.Comment: as published: more data included in Fig. 1, discussions throughout the text improved, 6 pages, 4 figure

The directed flow maximum near c_s=0

We investigate the excitation function of quark-gluon plasma formation and of directed in-plane flow of nucleons in the energy range of the BNL-AGS and for the E(Lab)=40AGeV Pb+Pb collisions performed recently at the CERN-SPS. We employ the three-fluid model with dynamical unification of kinetically equilibrated fluid elements. Within our model with first-order phase transition at high density, droplets of QGP coexisting with hadronic matter are produced already at BNL-AGS energies, E(Lab)=10AGeV. A substantial decrease of the isentropic velocity of sound, however, requires higher energies, E(Lab)=40AGeV. We show the effect on the flow of nucleons in the reaction plane. According to our model calculations, kinematic requirements and EoS effects work hand-in-hand at E(Lab)=40AGeV to allow the observation of the dropping velocity of sound via an increase of the directed flow around midrapidity as compared to top BNL-AGS energy.Comment: 10 pages, 4 figures; plot of p(e) at various specific entropies shows why mixed phase is not soft at AGS energ

Homogeneous nucleation of quark-gluon plasma, finite size effects and long-lived metastable objects

The general formalism of homogeneous nucleation theory is applied to study the hadronization pattern of the ultra-relativistic quark-gluon plasma (QGP) undergoing a first order phase transition. A coalescence model is proposed to describe the evolution dynamics of hadronic clusters produced in the nucleation process. The size distribution of the nucleated clusters is important for the description of the plasma conversion. The model is most sensitive to the initial conditions of the QGP thermalization, time evolution of the energy density, and the interfacial energy of the plasma-hadronic matter interface. The rapidly expanding QGP is first supercooled by about $\Delta T = T - T_c = 4-6$. Then it reheats again up to the critical temperature T_c. Finally it breaks up into hadronic clusters and small droplets of plasma. This fast dynamics occurs within the first $5-10 fm/c$. The finite size effects and fluctuations near the critical temperature are studied. It is shown that a drop of longitudinally expanding QGP of the transverse radius below 4.5 fm can display a long-lived metastability. However, both in the rapid and in the delayed hadronization scenario, the bulk pion yield is emitted by sources as large as 3-4.5 fm. This may be detected experimentally both by a HBT interferometry signal and by the analysis of the rapidity distributions of particles in narrow p_T-intervals at small p_T on an event-by-event basis.Comment: 29 pages, incl. 12 figures and 1 table; to be published in Phys. Rev.

Hadronic freeze-out following a first order hadronization phase transition in ultrarelativistic heavy-ion collisions

We analyze the hadronic freeze-out in ultra-relativistic heavy ion collisions at RHIC in a transport approach which combines hydrodynamics for the early, dense, deconfined stage of the reaction with a microscopic non-equilibrium model for the later hadronic stage at which the hydrodynamic equilibrium assumptions are not valid. With this ansatz we are able to self-consistently calculate the freeze-out of the system and determine space-time hypersurfaces for individual hadron species. The space-time domains of the freeze-out for several hadron species are found to be actually four-dimensional, and differ drastically for the individual hadrons species. Freeze-out radii distributions are similar in width for most hadron species, even though the Omega-baryon is found to be emitted rather close to the phase boundary and shows the smallest freeze-out radii and times among all baryon species. The total lifetime of the system does not change by more than 10% when going from SPS to RHIC energies.Comment: 11 pages, 4 eps-figures included, revised versio

Antiflow of Nucleons at the Softest Point of the EoS

We investigate flow in semi-peripheral nuclear collisions at AGS and SPS energies within macroscopic as well as microscopic transport models. The hot and dense zone assumes the shape of an ellipsoid which is tilted by an angle Theta with respect to the beam axis. If matter is close to the softest point of the equation of state, this ellipsoid expands predominantly orthogonal to the direction given by Theta. This antiflow component is responsible for the previously predicted reduction of the directed transverse momentum around the softest point of the equation of state.Comment: 13 pages LaTeX, 8 PS figures. Higher-quality PS versions of figures 3 and 4 available at http://www.th.physik.uni-frankfurt.de/~brachman/afl3f/afl3f.htm