Search for collective transverse flow using particle transverse momentum spectra in relativistic heavy-ion collisions

The particle transverse momentum spectra recently measured in relativistic heavy-ion collisions at CERN and BNL are analysed within an expanding fireball model. All the particle spectra at a given beam energy can be reproduced simultaneously with a single set of intensive parameters for the initial state of the fireball. As typical freeze-out parameters in this beam energy region we find a freeze-out temperatureT _f?110 MeV for most hadrons, and an average transverse expansion velocity at freeze-out of 〈v/c〉?0.4–0.45. The striking enhancement at transverse momentap _T<200 MeV/c in the CERN pion data cannot be fully explained by the existence of transverse flow.     

Hadron spectra from nuclear collisions

We describe high energy nuclear collisions by a superposition of isotropically decaying thermal sources (“fireballs”) of freeze-out temperature T = 0.15 GeV. The longitudinal fireball superposition is taken as boost-invariant, in a rapidity range determined by the average energy loss of nucleons in p?p collisions. The transverse fireball motion is assumed to be due to random walk initial state collisions; it is determined by p?A data and then extrapolated to central A?B interactions. We thus obtain parameter-free predictions for the rapidity and transverse momentum spectra of hadrons produced in high energy nucleus-nucleus collisions. The results account fully for the observed broadening of transverse momentum distributions, so that single-particle spectra require neither collective flow nor temperature increase.     

Initial temperature and EoS of quark matter via direct photons

The time evolution of the quark gluon plasma created in gold-gold collisions of the Relativistic Heavy Ion Collider (RHIC) can be described by hydro-dynamical models. Distribution of hadrons reflects the freeze-out state of the matter. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon spectra. Distributions of low energy photons was published in 2010 by PHENIX. In this paper we analyze a 3 + 1 dimensional solution of relativistic hydrodynamics and calculate momentum distribution of direct photons. Using earlier fits of this model to hadronic spectra, we compare photon calculations to measurements and find that the initial temperature of the center of the fireball is at least 519 ± 12 MeV, while for the equation of state we get c _s = 0.36 ± 0.02.     

Reconstructing the freeze-out state in Pb+Pb collisions at 158 <Emphasis Type="Italic">A</Emphasis>GeV/<Emphasis Type="Italic">c</Emphasis><Superscript>a</Superscript>

For a class of analytical parametrizations of the freeze-out state of relativistic heavy ion collisions, we perform a simultaneous analysis of the single-particle m _⊥-spectra and two-particle Bose-Einstein correlations measured in central Pb+Pb collisions at the CERN SPS. The analysis includes a full model parameter scan with χ² confidence levels. A comparison of different transverse density profiles for the particle emission region allows for a quantitative discussion of possible model dependencies of the results. Our fit results suggest a low thermal freeze-out temperature T≈95±15 MeV and a large average transverse flow velocity \(\bar v_ \bot \approx 0.55 \pm 0.07\). Moreover, the fit favours a box-shaped transverse density profile over a Gaussian one. We discuss the origins and the consequences of these results in detail. In order to reproduce the measured pion multiplicity our model requires a positive pion chemical potential. A study of the pion phase-space density indicates μ_π≈60 MeV for T=100 MeV.     

(1 + 1) dimensional hydrodynamics for high-energy heavy-ion collisions

A (1 + 1)-dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid-dynamical evolution to the equation of state and the parameters of initial state are investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated under the assumption that the transition from the hydrodynamical stage to the collisionless expansion of matter occurs at a certain freeze-out temperature. An important role of resonances in the formation of observed hadronic spectra is demonstrated. The calculated rapidity distributions of pions, kaons, and antiprotons in central Au + Au collisions at √^s NN = 200 GeV are compared with experimental data of the BRAHMS Collaboration. Parameters of the initial state are reconstructed for different choices of the equation of state. The best fit of these data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density, intermediate between the Landau and Bjorken limits. The text was submitted by the authors in English.     

Thermal dileptons from quark and hadron phases of an expanding fireball

A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. A transition from hadronic matter to a quark-gluon plasma at a critical temperature T _C between 130-170 MeV is assumed. We also consider a possible mixed phase scenario. We include thermal corrections to the hadronic spectra below T _C and use perturbation theory above T _C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated. Received: 4 August 2000 / Accepted: 14 November 2000     

Sensitivity of electromagnetic spectra to equation of state and initial energy density in the Pb + Pb collisions at SPS

We study Pb + Pb collisions at 158 A GeV/c using hydrodynamical approach. We test different equations of state (EoSs) and different initial conditions and show that there are more than one initial state for each EoS which reproduce the observed hadronic spectra. We also find that different equations of state favor different freeze-out temperature. Simultaneously we calculate the thermal dilepton and photon spectra for each EoS and initial state. We compare the dilepton mass spectrum to data measured by the CERES collaboration and find that the differences in spectra obtained using different EoSs and initial states are not resolvable within the current experimental resolution. However, at invariant masses over 2 GeV the difference in the yield due to various initial states is close to an order of magnitude. We also study the rapidity distribution of lepton pairs and find that for masses around 800 MeV the shape of the distribution depends strongly on the EoS.     

Equation of state and initial temperature of quark gluon plasma at RHIC

In gold-gold collisions of the Relativistic Heavy Ion Collider a perfect fluid of strongly interacting quark gluon plasma (sQGP) is created. The time evolution of this fluid can be described by hydrodynamical models. After an expansion, hadrons are created during the freeze-out period. Their distribution reveals information about the final state. To investigate the time evolution one needs to analyze penetrating probes: e.g. direct photon observations. In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equations of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507±12 MeV, while for the sound speed we get c _s =0.36±0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also compatible with this model. We also predict a photon source that is significantly larger in the out direction than in the side direction.     

Is there a low-p T “anomaly” in the pion momentum spectra from relativistic nuclear collisions?

The influence of resonance production in relativistic hadron-hadron and nucleus-nucleus collisions, and their role in explaining the so-called “anomalous” behaviour of the hadronic transverse momentum spectra at lowp _T is studied qualitatively and quantitatively in the framework of a simple thermodynamical model. In the discussion effects from the different kinematics in 2- and 3-body decays and from the finite width of the resonances are included. We compare our results with data from the NA35 collaboration for pion, kaon, proton and Λp _T -spectra from 200 A GeV S+S collisions and withpp data at similar energies. The model can successfully describe both S+S andpp data withT=200 MeV, μ _b =250 MeV andT=180 MeV, μ _b =250 MeV, respectively. We discuss the consistency of these parameters by comparing with measured particle ratios and checking the freeze-out conditions. We conclude that the low-p _T part of the pion spectra is dominated by resonance decays, and that there is no low-p _T “anomaly”. We also find, that the flattening of the high-p _T tail in central nuclear collisions compared topp data is probably not of thermal origin but caused by other effects, e.g. collective transverse flow.     

Inflation of fireballs, the gluon wind and the homogeneity of the HBT radii at RHIC

We solve analytically the ellipsoidally expanding fireball hydrodynamics with source terms in the momentum and energy equations, using the non-relativistic approximation. We find that energy transport for high-p _tjets of gluons to the medium leads to a transient, exponential inflation of the fireballs created in high energy heavy ion collisions. In this transient, inflatory period, the slopes of the single particle spectra are exponentially increasing, while the HBT radius parameters are exponentially decreasing with time. This effect is shown to be similar to the development of the homogeneity of our Universe due to an inflatory period. Independently of the initial conditions, and the exact value of freeze-out time and temperature, the measurables (single particle spectra, the correlation functions, slope parameters, elliptic flow, HBT radii and cross terms) become time-independent during the late, non-inflatory stages of the expansion, and they satisfy a new kind of scaling laws. If the expansion starts with a transient inflation caused by the gluon wind, it leads naturally to large transverse flows as well as to the simultaneous equality, and scaling behaviour of the HBT radius parameters, R _side≈R _out≈R _long≈t _f √T _f /m. With certain relativistic corrections, the scaling limit is 281-2, where m _tis the mean transverse mass of the pair.     

The reconstructed final state of Au+AU collisions from PHENIX and STAR data at √s=130 AgeV— Indication for quark deconfinement at RHIC

The final state of Au+Au collisions at √s=130 AGeV at RHIC has been reconstructed within the framework of the Buda-Lund hydrodynamical model, by performing a simultaneous fit to final data on twoparticle Bose-Einstein correlations of the STAR and PHENIX Collaboration, and final identified single-particle spectra as measured by the PHENIX Collaboration. The results indicate a strongly three dimensional expansion, with a four-velocity field that is almost a spherically symmetric Hubble flow. We find large transverse geometrical source sizes, R _G=9.8±1.2 fm, relatively short mean freeze-out time, τ₀=6.1±0.3 fm/c and a short duration of particle emission, Δτ=0.02±1.5 fm/c. Most strikingsly, we find an indication for a hot central part of the hydrodynamically evolving core, characterized by a central temperature T ₀=202±13 MeV that is close to (or even above) the deconfinement temperature of the quark-hadron phase transition. The best fit indicates a cold surface temperature T _s=110±16 MeV. When the possibility of the hot center is excluded, the confidence level of the fit decreases from 28.9% to 1.0%. Predictions are made for the rapidity dependence of the slope parameters and for the transverse mass depedence of the rapidity width of the single-particle spectra, and the transverse mass dependence of the non-identical particle correlations.     

Multiplicity dependence of the pion source in S+A collisions at the CERN SPS

The emission of pions from relativistic heavy-ion collisions of S+S, S+Ag and S+Pb at 200 GeV/nucleon is characterized using two-particle interferometry. The multiplicity dependence of the pion source parameters near midrapidity is studied. The transversal (R _t) and longitudinal (R _l) pion source parameters are independent of the initial nuclei in the interaction and increase with increasing multiplicity. This suggests that the freeze-out process is governed mainly by the particle multiplicity. The multiplicity dependence is weaker than that expected from a simple model of a freeze-out at a constant density.     

Entropy production at RHIC

For central heavy ion collisions at the RHIC energy, the entropy per unit rapidity dS/dy at freeze-out is extracted with minimal model dependence from available experimental measurements of particle yields, spectra, and source sizes estimated from two-particle interferometry. The extracted entropy rapidity density is consistent with lattice gauge theory results for a thermalized quark–gluon plasma with an energy density estimated from transverse energy production at RHIC.     

Identified particle distributions in pp and Au+Au collisions at square root of (sNN)=200 GeV

Transverse mass and rapidity distributions for charged pions, charged kaons, protons, and antiprotons are reported for square root of [sNN]=200 GeV pp and Au+Au collisions at Relativistic Heary Ion Collider (RHIC). Chemical and kinetic equilibrium model fits to our data reveal strong radial flow and long duration from chemical to kinetic freeze-out in central Au+Au collisions. The chemical freeze-out temperature appears to be independent of initial conditions at RHIC energies.     

Backward yields of pions,protons, and deuterons in relativistic 28Si+Pb collisions at 14.6 A GeVc

The production of pions, protons and deuterons is studied at a laboratory angle of 144° in ²⁸Si+Pb collisions at 14.6 GeV/c per nucleon. The centrality dependence of the pion yields is studied over the full impact parameter range using a zero degree calorimeter. The results are compared with the hadronic cascade model RQMD. These calculations are generally in agreement with the experimental results. According to these calculations, the pion yield in our acceptance is completely dominated by Δ-decay at freeze-out. Our measurements thus support the importance of baryon resonance production as one of the central features of relativistic heavy ion collisions at AGS energies. Although the strength of the pion spectrum is adequately described for kinetic energies above 50 MeV, an additional very soft component is observed in the pion spectra which is not predicted by RQMD. This very soft component accounts for a significant fraction of the total pion yield in this rapidity range but remains unexplained.     

Thermal hadron production in Si-Au collisions

The most abundantly produced hadron species in Si - Au collisions at the BNL-AGS (nucleons, pions, kaons, antikaons and hyperons) are shown to be in accord with emission from a thermal resonance gas source. Within the uncertainties of the present data, two freeze-out points are possible. The best agreement is obtained for a temperature T ? 110 MeV and a baryochemical potential μ_B ? 540 MeV, corresponding to about 1/3 standard nuclear density. Another possible point lies at about twice nuclear density, with T ? 160 MeV and μ_B ? 620 MeV. Our analysis takes the isopin asymmetry of the initial state fully into account.     

Transverse momentum spectra of the produced hadrons at SPS energy and a random walk model

The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in thessss nuclear reactions leads to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.     

Initial and Final State Temperatures of Antiproton Emission Sources in High Energy Collisions

The momentum or transverse momentum spectra of antiprotons produced at mid-rapidity in proton-helium (p+He), gold-gold (Au+Au), deuton-gold (d+Au), and lead-lead (Pb+Pb) collisions over an energy range from a few GeV to a few TeV are analyzed by the Erlang distribution, the inverse power-law (the Hagedorn function), and the blast-wave fit, or the superposition of two-component step function. The excitation functions of parameters such as the mean transverse momentum, initial state temperature, kinetic freeze-out temperature, and transverse flow velocity increase (slightly) from a few GeV to a few TeV and from peripheral to central collisions. At high energy and in central collisions, large collision energy is deposited in the system, which results in high degrees of excitation and expansion.

     

200 A GeV Au + Au collisions serve a nearly perfect quark-gluon liquid

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ? 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A GeV Au + Au collisions that v2/ε is a universal function of multiplicity density (1/S)(dN(ch)/dy) that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity ε. Comparing with measurements we find 1<4π(η/s)(QGP) < 2.5 where the uncertainty range is dominated by model uncertainties for the values of ε used to normalize the measured v2.