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UrQMD at RHIC energies
(1999)
The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.
Dilepton spectra are calculated within the microscopic transport model UrQMD and compared to data from the CERES experiment. The invariant mass spectra in the region between 300 MeV and 600 MeV depend strongly on the mass dependence of the rho meson decay width which is not sufficiently determined by the Vector Meson Dominance model. A consistent explanation of both the recent Pb+Au data and the proton induced data can be given without additional medium effects.
A selection of recent data referring to Pb+Pb collisions at the SPS CERN energy of 158 GeV per nucleon is presented which might describe the state of highly excited strongly interacting matter both above and below the deconfinement to hadronization (phase) transition predicted by lattice QCD. A tentative picture emerges in which a partonic state is indeed formed in central Pb+Pb collisions which hadronizes at about T = 185 MeV, and expands its volume more than tenfold, cooling to about 120 MeV before hadronic collisions cease. We suggest further that all SPS collisions, from central S+S onward, reach that partonic phase, the maximum energy density increasing with more massive collision systems.
Hadronic yields and yield ratios observed in Pb+Pb collisions at the SPS energy of 158 GeV per nucleon are known to resemble a thermal equilibrium population at T=180 +/- 10 MeV, also observed in elementary e+ + e- to hadron data at LEP. We argue that this is the universal consequence of the QCD parton to hadron phase transition populating the maximum entropy state. This state is shown to survive the hadronic rescattering and expansion phase, freezing in right after hadronization due to the very rapid longitudinal and transverse expansion that is inferred from Bose-Einstein pion correlation analysis of central Pb+Pb collisions.
The centrality dependence of (multi-)strange hadron abundances is studied for Pb(158 AGeV)Pb reactions and compared to p(158 GeV)Pb collisions. The microscopic transport model UrQMD is used for this analysis. The predicted Lambda/pi-, Xi-/pi- and Omega-/pi- ratios are enhanced due to rescattering in central Pb-Pb collisions as compared to peripheral Pb-Pb or p-Pb collisions. A reduction of the constituent quark masses to the current quark masses m_s \sim 230 MeV, m_q \sim 10 MeV, as motivated by chiral symmetry restoration, enhances the hyperon yields to the experimentally observed high values. Similar results are obtained by an ad hoc overall increase of the color electric field strength (effective string tension of kappa=3 GeV/fm). The enhancement depends strongly on the kinematical cuts. The maximum enhancement is predicted around midrapidity. For Lambda's, strangeness suppression is predicted at projectile/target rapidity. For Omega's, the predicted enhancement can be as large as one order of magnitude. Comparisons of Pb-Pb data to proton induced asymmetric (p-A) collisions are hampered due to the predicted strong asymmetry in the various rapidity distributions of the different (strange) particle species. In p-Pb collisions, strangeness is locally (in rapidity) not conserved. The present comparison to the data of the WA97 and NA49 collaborations clearly supports the suggestion that conventional (free) hadronic scenarios are unable to describe the observed high (anti-)hyperon yields in central collisions. The doubling of the strangeness to nonstrange suppression factor, gamma_s \approx 0.65, might be interpreted as a signal of a phase of nearly massless particles.
A microscopic model of deconfined matter based on color interactions between semi-classical quarks is studied. A hadronization mechanism is imposed to examine the properties and the disassembly of a thermalized quark plasma and to investigate the possible existence of a phase transition from quark matter to hadron matter.
The modification of the width of rho mesons due to in-medium decays and collisions is evaluated. The decay width is calculated from the imaginary part of the one-loop selfenergy at finite temperature. The collision width is related to the cross sections of the rho + pion and the rho + nucleon reactions. A calculation based on an e ective Lagrangian shows the importance of including the direct pho pi - > pho pi scattering which is dominated by the a1 exchange. A large broadening of the spectral function is found, accompanied by a strength suppression at the pole. http://www.arxiv.org/abs/nucl-th/9812059
The modification of the width of the rho meson due to in-medium decays and collisions is evaluated. In high temperature and/or high density hadronic matter, the collision width is much larger than the one-loop decay width. The large width of the meson in matter seems to be consistent with some current interpretations of the e+e mass spectra measured at the CERN/SPS.
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon s Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the e ective interactions in addition to the positive-energy spectra.
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the effective interactions in addition to the positive-energy spectra.
Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model
(1999)
Hadron-hadron collisions at high energies are investigated in the Ultra- relativistic-Quantum-Molecular-Dynamics approach. This microscopic trans- port model describes the phenomenology of hadronic interactions at low and intermediate energies ( s < 5 GeV) in terms of interactions between known hadrons and their resonances. At higher energies, s > 5 GeV, the excitation of color strings and their subsequent fragmentation into hadrons dominates the multiple production of particles in the UrQMD model. The model shows a fair overall agreement with a large body of experimental h-h data over a wide range of h-h center-of-mass energies. Hadronic reaction data with higher precision would be useful to support the use of the UrQMD model for relativistic heavy ion collisions.
Pseudorandom function tribe ensembles based on one-way permutations: improvements and applications
(1999)
Pseudorandom function tribe ensembles are pseudorandom function ensembles that have an additional collision resistance property: almost all functions have disjoint ranges. We present an alternative to the construction of pseudorandom function tribe ensembles based on oneway permutations given by Canetti, Micciancio and Reingold [CMR98]. Our approach yields two different but related solutions: One construction is somewhat theoretic, but conceptually simple and therefore gives an easier proof that one-way permutations suffice to construct pseudorandom function tribe ensembles. The other, slightly more complicated solution provides a practical construction; it starts with an arbitrary pseudorandom function ensemble and assimilates the one-way permutation to this ensemble. Therefore, the second solution inherits important characteristics of the underlying pseudorandom function ensemble: it is almost as effcient and if the starting pseudorandom function ensemble is efficiently invertible (given the secret key) then so is the derived tribe ensemble. We also show that the latter solution yields so-called committing private-key encryption schemes. i.e., where each ciphertext corresponds to exactly one plaintext independently of the choice of the secret key or the random bits used in the encryption process.
Nonequilibrium models (three-fluid hydrodynamics, UrQMD, and quark molecular dynamics) are used to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions from the SPS via RHIC to LHC. It is demonstrated that these models - although they do treat the most interesting early phase of the collisions quite differently (thermalizing QGP vs. coherent color fields with virtual particles) -- all yield a reasonable agreement with a large variety of the available heavy ion data. Hadron/hyperon yields, including J/Psi meson production/suppression, strange matter formation, dileptons, and directed flow (bounce-off and squeeze-out) are investigated. Observations of interesting phenomena in dense matter are reported. However, we emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data. The role of future experiments with the STAR and ALICE detectors is pointed out.
We investigate the hadronic cooling of a quark droplet within a microscopic model. The color flux tube approach is used to describe the hadronization of the quark phase. The model reproduces experimental particle ratios equally well compared to a static thermal hadronic source. Furthermore, the dynamics of the decomposition of a quark-gluon plasma is investigated and time dependent particle ratios are found.
We calculate the initial non-equilibrium conditions from perturbative QCD (pQCD) within Glauber multiple scattering theory for s = 200 AGeV and s = 5.5 ATeV. At the soon available collider energies one will particularly test the small x region of the parton distributions entering the cross sections. Therefore shadowing effects, previously more or less unimportant, will lead to new e ects on variables such as particle multiplicities dN/dy, transverse energy production d T /dy, and the initial temperature Ti. In this paper we will have a closer look on the effects of shadowing by employing di erent parametrizations for the shadowing effect for valence quarks, sea quarks and gluons. Since the cross sections at midrapidity are dominated by processes involving gluons the amount of their depletion is particularly important. We will therefore have a closer look on the results for dN/dy, d ¯E T /dy, and Ti by using two different gluon shadowing ratios, di ering strongly in size. As a matter of fact, the calculated quantities di er significantly.
The effects of internal quark structure of baryons on the composition and structure of neutron star matter with hyperons are investigated in the quark- meson coupling (QMC) model. The QMC model is based on mean-field description of nonoverlapping spherical bags bound by self-consistent exchange of scalar and vector mesons. The predictions of this model are compared with quantum hadrodynamic (QHD) model calibrated to reproduce identical nuclear matter saturation properties. By employing a density dependent bag constant through direct coupling to the scalar field, the QMC model is found to exhibit identical properties as QHD near saturation density. Furthermore, this modified QMC model provides well-behaved and continuous solutions at high densities relevant to the core of neutron stars. Two additional strange mesons are introduced which couple only to the strange quark in the QMC model and to the hyperons in the QHD model. The constitution and structure of stars with hyperons in the QMC and QHD models reveal interesting di erences. This suggests the importance of quark structure e ects in the baryons at high densities. PACS number(s): 26.60.+c, 21.65.+f, 12.39.Ba, 24.85.+p
We investigate various properties of neutron star matter within an e ective chiral SU(3)L × SU(3)R model. The predictions of this model are compared with a Walecka-type model. It is demonstrated that the importance of hy- peron degrees are strongly depending on the interaction used, even if the equation of state near saturation density is nearly the same in both models. While the Walecka-type model predicts a strange star core with strangeness fraction fS 4/3, the chiral model allows only for fS 1/3 and predicts that 0, + and 0 will not exist in star, in contrast to the Walecka-type model. PACS: 26.60+c, 21.65+f, 24.10Jv