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Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130 +/- 10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned.
A brief review of a history of data collection and interpretation of the results on high energy A+A collisions is presented. Basic assumptions and main results of a statistical model of the early stage of the A+A collisions are discussed. It is concluded that a broad set of experimental data is in agreement with the hypothesis that QGP is created in central A+A (S+S and Pb+Pb) collisions at the SPS. Carefull experimental investigation of the A+A collisions in the energy region between top AGS and SPS energies is needed.
In this paper, the concepts of microscopic transport theory are introduced and the features and shortcomings of the most commonly used ansatzes are discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model is described in great detail. Based on the same principles as QMD and RQMD, it incorporates a vastly extended collision term with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin is explicitly treated for all hadrons. The range of applicability stretches from E lab < 100$ MeV/nucleon up to E lab> 200$ GeV/nucleon, allowing for a consistent calculation of excitation functions from the intermediate energy domain up to ultrarelativistic energies. The main physics topics under discussion are stopping, particle production and collective flow.
Dielectron mass spectra are examined for various nuclear reactions recently measured by the DLS collaboration. A detailed description is given of all dilepton channels included in the transport model UrQMD 1.0, i.e. Dalitz decays of π, η, ω, ή mesons and of the (1232) resonance, direct decays of vector mesons and pn bremsstrahlung. The microscopic calculations reproduce data for light systems fairly well, but tend to underestimate the data in pp at high energies and in pd at low energies. These conventional sources, however, cannot explain the recently reported enhancement for nucleus-nucleus collisions in the mass region 0.15GeV ≤ Me+e- ≤ 0.6GeV. Chiral scaling and ω meson broadening in the medium are investigated as a source of this mass excess. They also cannot explain the recent DLS data.
A self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the N (1440) resonance is developed based on an effective Lagrangian of baryons interacting through mesons. The equation is consistent with that of nucleon s and delta s which we derived before. Thus, we obtain a set of coupled equations for the N, Delta and N (1440) distribution functions. All the N (1440)-relevant in-medium two-body scattering cross sections within the N, Delta and N (1440) system are derived from the same effective Lagrangian in addition to the mean field and presented analytically. Medium effects on the cross sections are discussed.
We derive the self-consistent relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed time-path Green's function technique, the semi-classical, quasi-particle and Born approximation are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and deltas which we developed before. Thus, we obtain a self-consistent relativistic transport model which describes the hadronic matter with N, Delta and pi degrees of freedom simultaneously. Within this approach, we investigate the medium effects on the pion dispersion relation as well as the pion absorption and pion production channels in cold nuclear matter. In contrast to the results of the non-relativistic model, the pion dispersion relation becomes harder at low momenta and softer at high momenta as compared to the free one. The theoretically predicted free pi N to Delta cross section is in agreement with the experimental data. Medium effects on the pi N to Delta cross section and momentum-dependent Delta-decay width are shown to be substantial.
Relativistic quantum transport theory of hadronic matter: the coupled nucleon, delta and pion system
(1998)
We derive the relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed time-path Green s function technique, the semi-classical, quasiparticle and Born approximation are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and deltas which we developed before. Thus, we obtain a relativistic transport model which describes the hadronic matter with N,Delta and pi degrees of freedom simultaneously. Within this approach, we investigate the medium e ects on the pion dispersion relation as well as the pion absorption and pion production channels in cold nuclear matter. In contrast to the results of the non-relativistic model, the pion dispersion relation becomes harder at low momenta and softer at high momenta as compared to the free one, which is mainly caused by the relativistic kinetics. The theoretically predicted free pi*N -> Delta cross section is in agreement with the experimental data. Medium e ects on the pi*N -> Delta cross section and momentum-dependent Delta-decay width are shown to be substantial. PACS number(s): 24.10.Cn; 13.75.Cs; 21.65.+f; 25.70.-z
We perform an event-by-event analysis of the transverse momentum distribution of final state particles in central Pb(160AGeV)+Pb collisions within a microscopic non-equilibrium transport model (UrQMD). Strong influence of rescattering is found. The extracted momentum distributions show less fluctuations in A+A collisions than in p+p reactions. This is in contrast to simplified p+p extrapolations and random walk models.
A new chiral SU(3) Lagrangian is proposed to describe the properties of kaons and anti-kaons in the nuclear medium. The saturation properties of nuclear matter are reproduced as well as the results of the Dirac-Brückner theory. After introducing the coupling between the omega meson and the kaon, our results for e ective kaon and anti-kaon energy are quite similar as calculated in the one-boson-exchange model.
We calculate the shadowing of sea quarks and gluons and show that the shadowing of gluons is not simply given by the sea quark shadowing, especially at small x. The calculations are done in the lab frame approach by using the generalized vector meson dominance model. Here the virtual photon turns into a hadronic fluctuation long before the nucleus. The subsequent coherent interaction with more than one nucleon in the nucleus leads to the depletion sigma(gamma* A) < A sigma( gamma*N) known as shadowing. A comparison of the shadowing of quarks to E665 data for 40Ca and 207Pb shows good agreement.
We estimate the energy density epsilon pile-up at mid-rapidity in central Pb+Pb collisions from 2 200 GeV/nucleon. epsilon is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for Elab 30 GeV/nucleon. In Pb+Pb collisions at 160 GeV/nucleon the energy density reaches up to 4 GeV/fm3, 95% of which are contained in partonic degrees of freedom.
In fluid dynamical models the freeze out of particles across a three dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze out surfaces, with both space-like and time-like normals, taking into account conservation laws across the freeze out discontinuity.
The extend to which geometrical effects contribute to the production and suppression of the J/psi and qq minijet pairs in general is investigated for high energy heavy ion collisions at SPS, RHIC and LHC energies. For the energy range under investigation, the geometrical e ects referred to are shadowing and anti-shadowing, respectively. Due to those effects, the parton distributions in nuclei deviate from the naive extrapolation from the free nucleon result; fA 6= AfN. The strength of the shadowing/anti-shadowing e ect increases with the mass number. Therefore it is interesting to see the di erence between cross sections for e.g. S+U vs. Pb+Pb at SPS. The recent NA50 results for the survival probability of produced J/psi s has attracted great attention and are often interpreted as a signature of a quark gluon plasma. This publication will present a fresh look on hard QCD e ects for the charmonium production level. It is shown that the apparent suppression of J/psi s must also be linked to the production process. Due to the uncertainty in the shadowing of gluons the suppression of charmonium states might not give reli- able information on a created plasma phase at the collider energies soon available. The consequences of shadowing e ects for the xF distribution of J/psi s at s = 20 GeV, s = 200 GeV and s = 6 TeV are calculated for some relevant combinations of nuclei, as well as the pT distribution of minijets at midrapidity for Nf = 4 in the final state.
Nuclei can be described satisfactorily in a nonlinear chiral SU(3)-framework, even with standard potentials of the linearmodel. The condensate value of the strange scalar meson is found to be important for the properties of nuclei even without adding hyperons. By neglecting terms which couple the strange to the nonstrange condensate one can reduce the model to a Walecka model structure embedded in SU(3). We discuss inherent problems with chiral SU(3) models regarding hyperon optical potentials.
Signatures of quark gluon plasma formation in high-energy heavy ion collisions : a critical review
(1998)
Ultra-relativistic heavy ion collisions offer the unique opportunity to probe highly excited dense nuclear matter under controlled laboratory conditions. The compelling driving force for such studies is the expectation that an entirely new form of matter may be created from such reactions. That form of matter, called the Quark Gluon Plasma (QGP), is the QCD analogue of the plasma phase of ordinary atomic matter. However, unlike such ordinary plasmas, the deconfined quanta of a QGP are not directly observable because of the fundamental confining property of the physical QCD vacuum. What is observable are hadronic and leptonic residues of the transient QGP state. There is a large variety of such individual probes.
Two-particle correlation functions of negative hadrons over wide phase space, and transverse mass spectra of negative hadrons and deuterons near mid-rapidity have been measured in central Pb+Pb collisions at 158 GeV per nucleon by the NA49 experiment at the CERN SPS. A novel Coulomb correction procedure for the negative two-particle correlations is employed making use of the measured oppositely charged particle correlation. Within an expanding source scenario these results are used to extract the dynamic characteristics of the hadronic source, resolving the ambiguities between the temperature and transverse expansion velocity of the source, that are unavoidable when single and two particle spectra are analysed separately. The source shape, the total duration of the source expansion, the duration of particle emission, the freeze-out temperature and the longitudinal and transverse expansion velocities are deduced.
We report measurements of Xi and Xi-bar hyperon absolute yields as a function of rapidity in 158 GeV/c Pb+Pb collisions. At midrapidity, dN/dy = 2.29 +/- 0.12 for Xi, and 0.52 +/- 0.05 for Xi-bar, leading to the ratio of Xi-bar/Xi = 0.23 +/- 0.03. Inverse slope parameters fitted to the measured transverse mass spectra are of the order of 300 MeV near mid-rapidity. The estimated total yield of Xi particles in Pb+Pb central interactions amounts to 7.4 +/- 1.0 per collision. Comparison to Xi production in properly scaled p+p reactions at the same energy reveals a dramatic enhancement (about one order of magnitude) of Xi production in Pb+Pb central collisions over elementary hadron interactions.
The large acceptance TPCs of the NA49 spectrometer allow for a systematic multidimensional study of two-particle correlations in different part of phase space. Results from Bertsch-Pratt and Yano-Koonin-Podgoretskii parametrizations are presented differentially in transverse pair momentum and pair rapidity. These studies give an insight into the dynamical space-time evolution of relativistic Pb+Pb collisions, which is dominated by longitudinal expansion.
We study J/psi suppression in AB collisions assuming that the charmonium states evolve from small, color transparent configurations. Their interaction with nucleons and nonequilibrated, secondary hadrons is simulated us- ing the microscopic model UrQMD. The Drell-Yan lepton pair yield and the J/psi /Drell-Yan ratio are calculated as a function of the neutral transverse en- ergy in Pb+Pb collisions at 160 GeV and found to be in reasonable agreement with existing data.
The hard contributions to the heavy quarkonium-nucleon cross sections are calculated based on the QCD factorization theorem and the nonrelativistic quarkonium model. We evaluate the nonperturbative part of these cross sections which dominates at psNN 20 GeV at the Cern Super Proton Synchrotron (SPS) and becomes a correction at psNN 6 TeV at the CERN Large Hadron Collider (LHC). J/psi production at the CERN SPS is well described by hard QCD, when the larger absorption cross sections of the states predicted by QCD are taken into account. We predict an A-dependent polarization of the states. The expansion of small wave packets is discussed.