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Results from various theoretical approaches and ideas presented at this exciting meeting (summary talk at the 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP - 2005)) are reviewed. I also point towards future directions, in particular hydrodynamic behaviour induced by jets traveling through the quark-gluon plasma, which might be worth looking at in more detail.
We calculate thermal photon and neutral pion spectra in ultrarelativistic heavy-ion collisions in the framework of three-fluid hydrodynamics. Both spectra are quite sensitive to the equation of state used. In particular, within our model, recent data for S + Au at 200 AGeV can only be understood if a scenario with a phase transition (possibly to a quark-gluon plasma) is assumed. Results for Au+Au at 11 AGeV and Pb + Pb at 160 AGeV are also presented.
We predict the formation of highly dense baryon-rich resonance matter in Au+Au collisions at AGS energies. The final pion yields show observable signs for resonance matter. The Delta1232 resonance is predicted to be the dominant source for pions of small transverse momenta. Rescattering e ects consecutive excitation and deexcitation of Delta's lead to a long apparent life- time (> 10 fm/c) and rather large volumina (several 100 fm3) of the Delta-matter state. Heavier baryon resonances prove to be crucial for reaction dynamics and particle production at AGS.
Triple differential cross sections of pions in heavy ion collisions at 1 GeV/nucl. are studied with the IQMD model. After discussing general properties of resonance and pion production we focus on azimuthal correlations: At projectile- and target-rapidities we observe an anticorrelation in the in-plane transverse momentum between pions and protons. At c.m.-rapidity, however, we find that high pt pions are being preferentially emitted perpendicular to the event-plane. We investigate the causes of those correlations and their sensitivity on the density and momentum dependence of the real and imaginary part of the nucleon and pion optical potential.
The rapidity distribution of thermal photons produced in Pb+Pb collisions at CERN-SPS energies is calculated within scaling and three- fluid hydrodynamics. It is shown that these scenarios lead to very different rapidity spectra. A measurement of the rapidity dependence of photon radiation can give cleaner insight into the reaction dynamics than pion spectra, especially into the rapidity dependence of the temperature.
Spectra of various particle species have been calculated with the Quantum Molecular Dynamics (QMD) model for very central collisions of Au+Au. They are compatible with the idea of a fully stopped thermal source which exhibits a transversal expansion besides the thermal distribution of an ideal gas. How- ever, the microscopic analyses of the local flow velocities and temperatures indicate much lower temperatures at densities associated with the freeze-out. The results express the overall impossibility of a model-independent determi- nation of nuclear temperatures from heavy ion spectral data, also at other energies (e.g. CERN) or for other species (i.e. pions, kaons, hyperons)
In the framework of RQMD we investigate antiproton observables in massive heavy ion collisions at AGS energies and compare to preliminary results of the E878 collaboration. We focus here on the considerable influence of the real part of an antinucleon nucleus optical potential on the ¯p momentum spectra. Pacs-numbers: 14.20 Dh, 25.70.-z
In the framework of the relativistic quantum molecular dynamics approach (RQMD) we investigate antideuteron (d) observables in Au+Au collisions at 10.7 AGeV. The impact parameter dependence of the formation ratios d/p2 and d/p2 is calculated. In central collisions, the antideuteron formation ratio is predicted to be two orders of magnitude lower than the deuteron formation ratio. The d yield in central Au+Au collisions is one order of magnitude lower than in Si+Al collisions. In semicentral collisions di erent configuration space distributions of p s and d s lead to a large squeeze out e ect for antideuterons, which is not predicted for the p s.
We calculate the evolution of quark-gluon-plasma droplets during the hadronization in a thermodynamical model. It is speculated that cooling as well as strangeness enrichment allow for the formation of strangelets even at very high initial entropy per baryon S/Ainit H 500 and low initial baryon numbers of Ainit B H 30. It is shown that the droplet with vanishing initial chemical potential of strange quarks and a very moderate chemical potential of up/down quarks immediately charges up with strangeness. Baryon densi- ties of H 2 0 and strange chemical potentials of µs > 350 MeV are reached if strangelets are stable. The importance of net baryon and net strangeness fluctuations for the possible strangelet formation at RHIC and LHC is em- phasized. Pacs-Classif.: 25.15.tr, 12.38.Mh, 24.85.tp
The extension of the Periodic System into hitherto unexplored domains - anti- matter and hypermatter - is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is stud- ied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that abso- lutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters ( / 10 10s) and on intensity interferometry of multi-strange-baryon correlations.
Abstract: An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is proposed, namely the transverse and longitudinal momentum distribution of all outgoing (or actually detectable) particles. The neural network approach yields an improvement in performance of a factor of two as compared to classical techniques. To achieve this improvement simple network architectures and a 5 × 5 input grid in (pt, pz) space are suffcient.
We want to draw the attention to the dynamics of a (finite) hadronizing quark matter drop. Strange and antistrange quarks do not hadronize at the same time for a baryon-rich system1. Both the hadronic and the quark matter phases enter the strange sector fs 6= 0 of the phase diagram almost immediately, which has up to now been neglected in almost all calculations of the time evolution of the system. Therefore it seems questionable, whether final particle yields reflect the actual thermodynamic properties of the system at a certain stage of the evolution. We put special interest on the possible formation of exotic states, namely strangelets (multistrange quark clusters). They may exist as (meta-)stable exotic isomers of nuclear matter 2. It was speculated that strange matter might exist also as metastable exotic multi-strange (baryonic) objects (MEMO s 3). The possible creation in heavy ion collisions of long-lived remnants of the quark-gluon-plasma, cooled and charged up with strangeness by the emission of pions and kaons, was proposed in 1,4,5. Strangelets can serve as signatures for the creation of a quark gluon plasma. Currently, both at the BNL-AGS and at the CERN-SPS experiments are carried out to search for MEMO s and strangelets, e. g. by the E864, E878 and the NA52 collaborations9,
The microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. We find no gap in the baryon rapidity distribution even at RHIC. For CERN energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters at midrapidity.
The stopping behaviour of baryons in massive heavy ion collisions ( s k 10AGeV) is investigated within di erent microscopic models. At SPS-energies the predictions range from full stopping to virtually total transparency. Experimental data are indicating strong stopping. The initial baryo-chemical potentials and temperatures at collider energies and their impact on the formation probability of strange baryon clusters and strangelets are discussed.
Nuclear clusters as a probe for expansion flow in heavy ion reactions at 10-A/GeV - 15-A/GeV.
(1996)
A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters d,t and He are predicted for central Au(11.6AGeV)Au and Si(14.6AGeV)Si reactions in the framework of the RQMD transport approach. Transverse expansion leads to a strong shoulderarm shape and di erent inverse slope parameters in the transverse spectra of nuclear clusters deviating markedly from thermal distributions. A clear bounce-o event shape is seen: the averaged transverse flow velocities in the reaction plane are for clusters larger than for protons. The cluster yields particularly at low pt at midrapidities and the in-plane (anti)flow of clusters and pions change if suitably strong baryon potential interactions are included. This allows to study the transient pressure at high density via the event shape analysis of nucleons, nucleon clusters and other hadrons.
We investigate the properties of di erent modifications to the linear -model (including a dilaton field associated with broken scale invariance) at finite baryon density and nonzero temperature T. The explicit breaking of chiral symmetry and the way the vector meson mass is generated are significant for the appearance of a phase of nearly vanishing nucleon mass besides the solution describing normal nuclear matter. The elimination of the abnormal solution prohibits the onset of a chiral phase transition but allows to lower the compressibility to a reasonable range. The repulsive contributions from the vector mesons are responsible for the wide range of stability of the normal phase in the (µ, T)-plane. The abnormal solution becomes not only energet- ically preferable to the normal state at high temperature or density, but also mechanically stable due to the inclusion of dilatons. PACS number:12.39.F
We discuss the properties of two distinct forms of hypothetical strange matter, small lumps of strange quark matter (strangelets) and of hyperon matter (metastable exotic multihypernuclear objects: MEMOs), with special empha- sis on their relevance for present and future heavy ion experiments. The masses of small strangelets up to AB = 40 are calculated using the MIT bag model with shell mode filling for various bag parameters. The strangelets are checked for possible strong and weak hadronic decays, also taking into account multiple hadron decays. It is found that strangelets which are stable against strong decay are most likely highly negative charged, contrary to previous findings. Strangelets can be stable against weak hadronic decay but their masses and charges are still rather high. This has serious impact on the present high sensitivity searches in heavy ion experiments at the AGS and CERN facilities. On the other hand, highly charged MEMOs are predicted on the basis of an extended relativistic mean field model. Those objects could be detected in future experiments searching for short lived, rare composites. It is demonstrated that future experiments can be sensitive to a much wider variety of strangelets.
According to the Walecka mean field theory of nuclear interaction the collective mutual deceleration of the colliding nuclei gives rise to the bremsstrahlung of real and virtual ! mesons. It is shown that decays of these mesons may give a noticeable contribution to the observed yields of the baryon antibaryon pairs, dileptons and pions. Excitation functions and rapidity distributions of particles produced by this mechanism are calculated under some simplifying assumptions about the space time variation of meson fields in nuclear collisions. The calculated multiplicities of coherently produced particles grow fast with the bombarding energy, reaching a saturation above the RHIC bombarding energy. In the case of central Au+Au collisions the bremsstrahlung mechanism becomes comparable with particle production in incoherent hadron hadron collisions above the AGS energies. The rapidity spectra of antibaryons and pions exhibit a characteristic two hump structure which is a consequence of incomplete projectile target stopping at the initial stage of the reaction. The predicted distribution of e+e pairs has a strong peak at invariant masses Me+e < 0.5 GeV.
We study the time scale for pressure equilibration in heavy ion collisions at AGS energies within the three-fluid hydrodynamical model and a microscopic cascade model (UrQMD). We find that kinetic equilibrium is reached in both models after a time of 5 fm/c (center-of-mass time). Thus, observables which are sensitive to the early stage of the reaction differ considerably from the expectations within the instant thermalization scenario (one-fluid hydrodynamical model).
Basic problems of the semiclassical microscopic modelling of strongly interacting systems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic interactions on a large variety of observables and phenomena occur- ring in heavy ion collisions at relativistic energies. It is shown that the same predictions can be obtained with several numerically completely di erent and independently written programs as far as the same model parameters are employed and the same basic approximations are made. Many observ- ables are robust against variations of the details of the model assumptions used. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei, which di ers among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given.
Abstract: We study transverse expansion and directed flow in Au(11AGeV)Au reactions within a multi-fluid dynamical model. Although we do not employ an equation of state (EoS) with a first order phase transition, we find a slow increase of the transverse velocities of the nucleons with time. A similar behaviour can be observed for the directed nucleon flow. This is due to non-equilibrium e ects which also lead to less and slower conversion of longitudinal into transverse momentum. We also show that the proton rapidity distribution at CERN energies, as calculated within this model, agrees well with the preliminary NA44-data.
To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium e ects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time teq CM H 5 fm/c C 2RAu/³CM. Observables which are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore di er considerably from those calculated in the one-fluid model.
We examine the properties of both forms of strange matter, small lumps of strange quark matter (strangelets) and of strange hadronic matter (Metastable Exotic Multihypernuclear Objects: MEMOs) and their relevance for present and future heavy ion searches. The strong and weak decays are discussed separately to distinguish between long-lived and short-lived candidates where the former ones are detectable in present heavy ion experiments while the latter ones in future heavy ion experiments, respectively. We find some long-lived strangelet candidates which are highly negatively charged with a mass to charge ratio like a anti deuteron (M/Z 2) but masses of A=10 to 16. We predict also many short-lived candidates, both in quark and in hadronic form, which can be highly charged. Purely hyperonic nuclei like the (2 02 ) are bound and have a negative charge while carrying a positive baryon number. We demonstrate also that multiply charmed exotics (charmlets) might be bound and can be produced at future heavy ion colliders.
Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source vs. a time-dependent, nonequilibrium hadronization o a quark-gluon plasma droplet. Due to the time-dependent particle evapora- tion o the hadronic surface in the latter approach the hadron ratios change (by factors of <H 5) in time. Final particle yields reflect time averages over the actual thermodynamic properties of the system at a certain stage of the evolution. Calculated hadron, strangelet and (anti-)cluster yields as well as freeze-out times are presented for di erent systems. Due to strangeness distillation the system moves rapidly out of the T, µq plane into the µs-sector. Classif.: 25.75.Dw, 12.38.Mh, 24.85.+p
We discuss the early evolution of ultrarelativistic heavy-ion collisions within a multi- fluid dynamical model. In particular, we show that due to the finite mean-free path of the particles compression shock waves are smeared out considerably as compared to the one-fluid limit. Also, the maximal energy density of the baryons is much lower. We discuss the time scale of kinetic equilibration of the baryons in the central region and its relevance for directed flow. Finally, thermal emission of direct photons from the fluid of produced particles is calculated within the three-fluid model and two other simple expansion models. It is shown that the transverse momentum and rapidity spectra of photons give clue to the cooling law and the early rapidity distribution of the photon source.
Hadron and hadron cluster production in a hydrodynamical model including particle evaporation
(1997)
We discuss the evolution of the mixed phase at RHIC and SPS within boostinvariant hydrodynamics. In addition to the hydrodynamical expansion, we also consider evaporation of particles o the surface of the fluid. The back-reaction of this evaporation process on the dynamics of the fluid shortens the lifetime of the mixed phase. In our model this lifetime of the mixed phase is d 12 fm/c in Au + Au at RHIC and d 6.5 fm/c in Pb + Pb at SPS, even in the limit of vanishing transverse expansion velocity. Strong separation of strangeness occurs, especially in events (or at rapidities) with relatively high initial net baryon and strangeness number, enhancing the multiplicity of MEMOs (multiply strange nuclear clusters). If antiquarks and antibaryons reach saturation in the course of the pure QGP or mixed phase, we find that at RHIC the ratio of antideuterons to deuterons may exceed 0.3 and even 4He/4He > 0.1. In S + Au at SPS we find only N/N H 0.1. Due to fluctuations, at RHIC even negative baryon number at midrapidity is possible in individual events, so that the antibaryon and antibaryon-cluster yields exceed those of the corresponding baryons and clusters.
A study of secondary Drell-Yan production in nuclear collisions is presented for SPS energies. In addition to the lepton pairs produced in the initial collisions of the projectile and target nucleons, we consider the potentially high dilepton yield from hard valence antiquarks in produced mesons and antibaryons. We calculate the secondary Drell-Yan contributions taking the collision spectrum of hadrons from the microscopic model URQMD. The con- tributions from meson-baryon interactions, small in hadron-nucleus interac- tions, are found to be substantial in nucleus-nucleus collisions at low dilepton masses. Preresonance collisions of partons may further increase the yields.
A generalized Lagrangian for the description of hadronic matter based on the linear SU(3)L × SU(3)R -model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale invariance is incorporated. The observed values for the vacuum masses of the baryons and mesons are reproduced. In mean-field approximation, vector and scalar interactions yield a saturating nuclear equation of state. We discuss the di culties and possibilities to construct a chiral invariant baryon-meson interaction that leads to a realistic equation of state. It is found that a coupling of the strange condensate to nucleons is needed to describe the hyperon potentials correctly. The effective baryon masses and the appearance of an abnormal phase of nearly massless nucleons at high densities are examined. A nonlinear realization of chiral symmetry is considered, to retain a Yukawa-type baryon-meson interaction and to establish a connection to the Walecka-model.
Abstract. A generalized Lagrangian for the description of hadronic matter based on the linear SU(3)L × SU(3)R -model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale invariance is incorporated. The observed values for the vacuum masses of the baryons and mesons are reproduced. In mean-field approximation, vector and scalar interactions yield a saturating nuclear equation of state. Finite nuclei can be reasonably described, too. The condensates and the e ective baryon masses at finite baryon density and temperature are discussed.
The deconfinement transition region between hadronic matter and quark-gluon plasma is studied for finite volumes. Assuming simple model equations of state and a first order phase transition, we find that fluctuations in finite volumes hinder a sharp separation between the two phases around the critical temperature, leading to a rounding of the phase transition. For reaction volumes expected in heavy ion experiments, the softening of the equation of state is reduced considerably. This is especially true when the requirement of exact color-singletness is included in the QGP equation of state.
A self-consistent relativistic integral-di erential equation of the Boltzmann- Uehling-Uhlenbeck-type for the N*(1440) resonance is developed based on an effective Lagrangian of baryons interacting through mesons. The closed time-path Green s function technique and semi-classical, quasi-particle and Born approxima- tions are employed in the derivation. The non-equilibrium RBUU-type equation for the N*(1440) 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, which can be directly used in the study of relativistic heavy-ion collisions. The theoreticalprediction of the free pp - pp* (1440) cross section is in good agreement with the experimental data. We calculate the in-medium N+N - N+N* , N* +N - N+N and N*+N - N* +N cross sections in cold nuclear matter up to twice the nuclear matter density. The influence of different choices of the N* N* coupling strengths, which can not be obtained through fitting certain experimental data, are discussed. The results show that the density dependence of predicted in-medium cross sections are sensitive to the N* N* coupling strengths used. An evident density dependence will appear when a large scalar coupling strength of g^(sigma) N*N* is assumed. PACS number(s): 24.10.Cn; 25.70.-z; 21.65.+f
Preliminary experimental data for particle number ratios in the collisions of Au+Au at the BNL AGS (11A GeV/c) and Pb+Pb at the CERN SPS (160A GeV/c) are analyzed in a thermodynamically consistent hadron gas model with excluded volume. Large values of temperature, T = 140 185 MeV, and baryonic chemical potential, µb = 590 270 MeV, close to the boundary of the quark-gluon plasma phase are found from fitting the data. This seems to indicate that the energy density at the chemical freezeout is tremendous which would be indeed the case for the point-like hadrons. However, a self-consistent treatment of the van der Waals excluded volume reveals much smaller energy densities which are very far below a lowest limit estimate of the quark-gluon plasma energy density. PACS number(s): 25.75.-q, 24.10.Pa
We study the bremsstrahlung of virtual omega mesons due to the collective deceleration of nuclei at the initial stage of an ultrarelativistic heavy ion collision. It is shown that electromagnetic decays of these mesons may give an important contribution to the observed yields of dileptons. Mass spectra of e+e and µ+µ pairs produced in central Au+Au collisions are calculated under some simplifying assumptions on the space time variation of the baryonic current in a nuclear collision process. Comparison with the CERES data for 160 AGev Pb+Au collisions shows that the proposed mechanism gives a noticeable fraction of the observed e+e pairs in the intermediate region of invariant masses. Sensi tivity of the dilepton yield to the in medium modification of masses and widths of vector mesons is demonstrated.
Collective bremsstrahlung of vector meson fields in relativistic nuclear collisions is studied within the time dependent Walecka model. Mutual deceleration of the colliding nuclei is described by introducing the e ective stopping time and average rapidity loss of baryons. It is shown that electromagnetic decays of virtual ω mesons produced by bremsstrahlung mechanism can provide a substantial contribution to the soft dilepton yield at the SPS bombarding energies. In particular, it may be responsible for the dilepton enhancement observed in 160 AGev central Pb+Au collisions. Suggestions for future experiments to estimate the relative contribution of the collective mechanism are given.
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.
The transverse momentum distribution of prompt photons coming from the very early phase of ultrarelativistic heavy ion collisions for the RHIC and LHC energies is calculated by means of perturbative QCD. We calculate the single photon cross section (A + B -> gamma + X) by taking into account the partonic sub processes q + q -> gamma + g and q + g -> gamma + q as well as the Bremsstrahlung corrections to those processes. We choose a lower momentum cut-off k0 = 2 GeV separating the soft physics from perturbative QCD. We compare the results for those primary collisions with the photons produced in reactions of the thermalized secondary particles, which are calculated within scaling hydrodynamics. The QCD processes are taken in leading order. Nuclear shadowing corrections, which alter the involved nuclear structure functions are explicitly taken into account and compared to unshadowed results. Employing the GRV parton distribution parametrizations we find that at RHIC prompt QCD-photons dominate over the thermal radiation down to transverse momenta kT ≈ 2 GeV. At LHC, however, thermal radiation from the QGP dominates for photon transverse momenta kT ≤ 5 GeV, if nuclear shadowing effects on prompt photon production are taken into account.
Direct photon production in central Pb+Pb collisions at CERN-SPS energy is calculated within the relativistic microscopic transport model UrQMD, and within distinctly di erent versions of relativistic hydrodynamics. We find that in UrQMD the local momentum distributions of the secondaries are strongly elongated along the beam axis initially. Therefore, the preequilibrium contribution dominates the photon spectrum at transverse momenta above H 1.5 GeV. The hydrodynamics prediction of a strong correlation between the temperature and radial expansion velocities on the one hand and the slope of the transverse momentum distribution of direct photons on the other hand thus is not recovered in UrQMD. The rapidity distribution of direct photons in UrQMD reveals that the initial conditions for the longitudinal expansion of the photon source (the meson fluid ) resemble rather boostinvariance than Landau-like flow.
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
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.
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.
We reexamine the scenario of homogeneous nucleation of the quark-gluon plasma produced in ultra-relativistic heavy ion collisions. A generalization of the standard nucleation theory to rapidly expanding system is proposed. The nucleation rate is derived via the new scaling parameter Z. It is shown that the size distribution of hadronic clusters plays an important role in the dynamics of the phase transition. The longitudinally expanding system is supercooled to about 3 6%, then it is reheated, and the hadronization is completed within 6 10 fm/c, i.e. 5 10 times faster than it was estimated earlier, in a strongly nonequilibrium way. PACS: 12.38.Mh; 12.39.Ba; 25.75.-q; 64.60.Qb
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.
A new chiral SU(3) Lagrangian is proposed to describe the properties of kaons and antikaons in the nuclear medium, the ground state of dense matter and the kaon-nuclear interactions consistently. The saturation properties of nuclear matter are reproduced as well as the results of the Dirac-Brückner theory. After taking into account the coupling between the omega meson and the kaon, we obtain similar results for the e ective kaon and antikaon energies as calculated in the one-boson-exchange model while in our model the parameters of the kaon-nuclear interactions are constrained by the SU(3) chiral symmetry. PACS number(s): 14.40.Aq, 12.39.Fe, 21.30.Fe
We study the effects of strict conservation laws and the problem of negative contributions to final momentum distribution during the freeze out through 3-dimensional hypersurfaces with space-like normal. We study some suggested solutions for this problem, and demonstrate it on one example. PACS: 24.10.Nz, 25.75.-q
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.
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.
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.
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.
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
Dissociation rates of J / psi's with comoving mesons : thermal versus nonequilibrium scenario.
(1998)
We study J/psi dissociation processes in hadronic environments. The validity of a thermal meson gas ansatz is tested by confronting it with an alternative, nonequilibrium scenario. Heavy ion collisions are simulated in the frame- work of the microscopic transport model UrQMD, taking into account the production of charmonium states through hard parton-parton interactions and subsequent rescattering with hadrons. The thermal gas and microscopic transport scenarios are shown to be very dissimilar. Estimates of J/psi survival probabilities based on thermal models of comover interactions in heavy ion collisions are therefore not reliable.
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.
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.
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.
Homogeneous nucleation of quark gluon plasma, finite size effects and longlived metastable objects
(1998)
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 nucle- ation 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 den- sity, and the interfacial energy of the plasma hadronic matter interface. The rapidly expanding QGP is first supercooled by about T = T Tc = 4 6%. Then it reheats again up to the critical temperature Tc. 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 e ects 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 pT -intervals at small |pT | on an event-by-event basis. PACS numbers: 12.38.Mh, 24.10.Pa, 25.75.-q, 64.60.Qb
Chemically non equilibrated quark antiquark matter is studied within the Nambu Jona-Lasinio model. The equations of state of non strange (q = u, d) and strange (q = s) qq systems are calculated in the mean field approximation. The existence of metastable bound states with zero pressure is predicted at finite densities and temperatures T 50 MeV. It is shown that the minimum energy per particle occurs for symmetric systems, with equal densities of quarks and antiquarks. At T = 0 these metastable states have quark number densities of about 0.5 fm 3 for q = u, d and of 1 fm 3 for q = s. A first order chiral phase transition is found at finite densities and temperatures. The critical temperature for this phase transition is approximately 75 MeV (90 MeV) for the non strange (strange) baryon free quark antiquark matter. For realistic choices of parameters, the model does not predict a phase transition in chemically equilibrated systems. Possible decay channels of the metastable qq droplets and their signatures in relativistic heavy ion collisions are discussed.
Irreversibility, steady state, and nonequilibrium physics in relativistic heavy ion collisions
(1999)
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve according to Prigogine s steady states rather than towards statistical equilibrium. These results are general and can be easily checked by any microscopic string-, transport-, or cascade model for heavy ion collisions. The absence of pure equilibrium states sheds light on the di culties of thermal models in describing the yields and spectra of hadrons, especially mesons, in heavy ion collisions at bombarding energies above 10 GeV/nucleon. PACS numbers: 25.75.-q, 05.70.Ln, 24.10.Lx
We discuss a model for the space-time evolution of ultrarelativistic heavy-ion collisions which employs relativistic hydrodynamics within one region of the forward light-cone, and microscopic transport theory (i.e. UrQMD) in the complement. Our initial condition consists of a quark-gluon plasma which expands hydrodynamically and hadronizes. After hadronization the solution eventually changes from expansion in local equilibrium to free streaming, as determined selfconsistently by the interaction rates between the hadrons and the local expansion rate. We show that in such a scenario the inverse slopes of the mT -spectra of multiple strange baryons ( Xi,Omega) are practically una ected by the purely hadronic stage of the reaction, while the flow of p's and Lambda's increases. Moreover, we find that the rather soft transverse expansion at RHIC energies (due to a first-order phase transition) is not washed out by strong rescattering in the hadronic stage. The earlier kinetic freeze-out as compared to SPS-energies results in similar inverse slopes (of the mT -spectra of the hadrons in the final state) at RHIC and SPS energies.
Hot hypernuclear matter is investigated in an explicit SU(3) quark model based on a mean field description of nonoverlapping baryon bags bound by the self-consistent exchange of scalar sigma, zeta and vector omega,phi mesons. The sigma, omega mean fields are assumed to couple to the u, d-quarks while the zeta ,phi mean fields are coupled to the s-quark. The coupling constants of the mean fields with the quarks are assumed to satisfy SU(6) symmetry. The calculations take into account the medium dependence of the bag parameter on the scalar fields sigma, zeta. We consider only the octet baryons N,Lambda,Sigma, Xi in hypernuclear matter. An ideal gas of the strange mesons K and K is introduced to keep zero net strangeness density. Our results for symmetric hypernuclear matter show that a phase transition takes place at a critical temperature around 180 MeV in which the scalar mean fields sigma, zeta take nonzero values at zero baryon density. Furthermore, the bag contants of the baryons decrease significantly at and above this critical temperature indicating the onset of quark deconfinement. The present results imply that the onset of quark deconfinement in SU(3) hypernuclear matter is much stronger than in SU(2) nuclear matter. PACS:21.65.+f, 24.85.+p, 12.39Ba
We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. Freeze-out times and transverse radii increase by factors of 2 3 depending on the hadron species.
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 di er drastically for the individual hadrons species. Freeze-out radii distributions are similar in width for most hadron species, even though the 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.
Charmonium production and absorption in heavy ion collisions is studied with the Ultrarelativisitic Quantum Molecular Dynamics model. We compare the scenario of universal and time independent color-octet dissociation cross sections with one of distinct color-singlet J/psi, psi 2 and CHIc states, evolving from small, color transparent configurations to their asymptotic sizes. The measured J/psi production cross sections in pA and AB collisions at SPS energies are consistent with both purely hadronic scenarios. The predicted rapidity dependence of J/psi suppression can be used to discriminate between the two experimentally. The importance of interactions with secondary hadrons and the applicability of thermal reaction kinetics to J/psi absorption are in- vestigated. We discuss the e ect of nuclear stopping and the role of leading hadrons. The dependence of the 2/J/psi ratio on the model assumptions and the possible influence of refeeding processes is also studied.
Event-by-event multiplicity fluctuations in nucleus-nucleus collisions are studied within the HSD and UrQMD transport models. The scaled variances of negative, positive, and all charged hadrons in Pb+Pb at 158 AGeV are analyzed in comparison to the data from the NA49 Collaboration. We find a dominant role of the fluctuations in the nucleon participant number for the final hadron multiplicity fluctuations. This fact can be used to check di erent scenarios of nucleus-nucleus collisions by measuring the final multiplicity fluctuations as a function of collision centrality. The analysis reveals surprising e ects in the recent NA49 data which indicate a rather strong mixing of the projectile and target hadron production sources even in peripheral collisions. PACS numbers: 25.75.-q,25.75.Gz,24.60.-k
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.
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.
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.
Kinetic freeze out models
(1999)
Freeze out of particles across a space-time hypersurface is discussed in kinetic models. The calculation of final momentum distribution of emitted particles is described for freeze out surfaces, with spacelike normals. The resulting non-equilibrium distribution does not resemble, the previously proposed, cut Jüttner distribution, and shows non-exponential pt-spectra similar to the ones observed in experiments. PACS: 24.10.Nz, 25.75.-q
We investigate event-by-event fluctuations for ensembles with non-fixed multiplicity. Moments of event observable distributions, like total energy distribution, total transverse momentum distribution, etc, are shown to be related to the multi-body correlations present in the system. For classical systems, these moments reduce in the absence of any correlations to the mo- ments of particle inclusive momentum distribution. As a consequence, a zero value for the recently introduced Phi-variable is shown to indicate the van- ishing of two-body correlations from one part, and of correlations between multiplicity and momentum distributions from the other part. It is often misunderstood as a measure of the degree of equilibration in the system.
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.
Using a microscopic transport model together with a coalescence after-burner, we study the formation of deuterons in Au + Au central collisions at s = 200 AGeV . It is found that the deuteron transverse momentum distributions are strongly a ected by the nucleon space-momentum correlations, at the moment of freeze-out, which are mostly determined by the number of rescatterings. This feature is useful for studying collision dynamics at ultrarelativistic energies.
In continuum and fluid dynamical models, particles, which leave the system and reach the detectors, can be taken into account via freeze-out (FO) or final break-up schemes, where the frozen out particles are formed on a 3-dimensional hypersurface in space-time. Such FO descriptions are important ingredients of evaluations of two-particle correlation data, transverse-, longitudinal-, radial- and cylindrical- flow analyses, transverse momentum and transverse mass spectra and many other observables. The FO on a hypersurface is a discontinuity, where the pre FO equilibrated and interacting matter abruptly changes to non-interacting particles, showing an ideal gas type of behavior.
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.
Freeze out of particles across three dimensional space-time hypersurface is discussed in a simple kinetic model. The final momentum distribution of emitted particles, for freeze out surfaces with space-like normal, shows a non-exponential transverse momentum spectrum. The slope parameter of the pt distribution increases with increasing pt, in agreement with recently measured SPS pion and h spectra.
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
Introduction: Until now it is not possible to determine the equation of state (EOS) of hadronic matter from QCD. One succesfully applied alternative way to describe the hadronic world at high densities and temperatures are effective models like the RMF-models [1], where the relevant degrees of freedom are baryons and mesons instead of quarks and gluons. Since approximate chiral symmetry is an essential feature of QCD, it should be a useful concept for building and restricting e ective models. It has been shown [2,3] that effective sigma-omega models including SU(2) chiral symmetry are able to obtain a reasonable description of nuclear matter and finite nuclei. Recently [4] we have shown that an extended SU(3) × SU(3) chiral sigma-omega model is able to describe nuclear matter ground state properties, vacuum properties and finite nuclei satisfactorily. This model includes the lowest SU(3) multiplets of the baryons (octet and decuplet[5]), the spin-0 and the spin-1 mesons as the relevant degrees of freedom. Here we will discuss the predictions of this model for dense, hot, and strange hadronic matter.
Last year the E866-group of the Fermilab measured the xF dependence of J/Psi and 2 suppression in pA collisions. We discuss two of the effects found in that experiment with regard to color coherence effects: the di erent suppression of the J/Psi and the 2 at xF < 0 and the significant suppression of both at large xF . The small xF regions is dominated by fully formed charmonium states and thus enables us to discuss the formation time and the cross section of the different charmonium states. In the large xF region the interaction of the charmonium states with nuclear matter has to be described by partonic degrees of freedom, because in that kinematic domain the formation time is much larger than the nuclear radii. The understanding of this region will be crucial for the interpretation of the data of the future heavy ion colliders RHIC and LHC.
We calculate the yields of pions, kaons, and Æ-mesons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities differing strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
UrQMD at RHIC energies
(1999)
We calculate the yields of a variety of hadrons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities di ering strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
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.
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.
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
Job creation schemes (JCS) have been one important programme of active labour market policy in Germany aiming at the re-integration of hard-to-place unemployed individuals into regular employment. In ontrast to earlier evaluation studies of these programmes based on survey data, we use administrative data containing more than 11,000 participants for our analysis and hence, can take effect heterogeneity explicitly into account. We focus on effect heterogeneity caused by differences in the implementation of programmes (economic sector, types of support and implementing institutions). The results are rather discouraging and show that in general, JCS are unable to improve the re-integration chances of participants into regular employment.
We investigate in stable strange hadronic matter (SHM) the modifica- tion of the masses of the scalar (sigma,sigma') and the vector (omega,phi) mesons. The baryon ground state is treated in the relativistic Hartree approximation in the nonlinear sigma-omega and linear sigma'- phi model. In stable SHM, the masses of all the mesons reveal considerable reduction due to large vacuum polarization contribution from the hyperons and small density dependent effects caused by larger binding. PACS: 21.65+f, 24.10Jv
We investigate the excitation function of quark-gluon plasma formation and of directed in-plane flow of nucleons in the energy range of the BNLAGS and for the Ekin Lab = 40A GeV 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, Ekin Lab C 10A GeV. A substantial decrease of the isentropic velocity of sound, however, requires higher energies, Ekin Lab C 40A GeV. We show the e ect on the flow of nucleons in the reaction plane. According to our model calculations, kinematic requirements and EoS effects work hand-in-hand at Ekin Lab = 40A GeV 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.
A nonlinear chiral SU(3) approach including the spin 3 2 decuplet is developed to describe dense matter. The coupling constants of the baryon resonances to the scalar mesons are determined from the decuplet vacuum masses and SU(3) symmetry relations. Di erent methods of mass generation show significant differences in the properties of the spin- 3 2 particles and in the nuclear equation of state
Properties of dense quark matter in and out of chemical equilibrium are studied within the SU(3) Nambu Jona-Lasinio model. In addition to the 4 fermion scalar and vector terms the model includes also the 6 fermion flavour mixing interaction. First we study a novel form of deconfined matter, meso-matter, which is composed of equal number of quarks and antiquarks. It can be thought of as a strongly compressed meson gas where mesons are melted into their elementary constituents, quarks and antiquarks. Strongly bound states in this quark antiquark matter are predicted for all flavour combinations of qq pairs. The maximum binding energy reaches up to 180 MeV per qq pair for mixtures with about 70% of strange (s¯s) pairs. Equilibrated baryon rich quark matter with various flavour compositions is also studied. In this case only shallow bound states appear in systems with a significant admixture(about 40%) of strange quarks (strangelets). Their binding energies are quite sensitive to the relative strengths of scalar and vector interactions. The common property of all these bound states is that they appear at high particle densities when the chiral symmetry is nearly restored. Thermal properties of meso-matter as well as chemically equilibrated strange quark matter are also investigated. Possible decay modes of these bound states are discussed.
Conventional cluster and virial expansions are generalized to momentum dependent interparticle potentials. The model with Lorentz contracted hard core potentials is considered, e.g. as hadron gas model. A Van der Waals-type model with a temperature dependent excluded volume is derived. Lorentz contraction effects at given temperature are stronger for light particles and make their effective excluded volume smaller than that of heavy ones.
The quantum mechanical formula for Mayer s second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The proper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second cluster integral for the pion gas is calculated in quantum mechanical approach with account for both attractive and hard-core repulsive interactions. It is shown that, in the second cluster approximation, the repulsive -interactions as well as the finite width of resonances give important but almost canceling contributions. In contrast, an appreciable deviation from the ideal gas of pions and pion resonances is observed beyond the second clus- ter approximation in the framework of the Van der Waals excluded-volume model.
We investigate the excitation function of directed flow, which can provide a clear signature of the creation of the QGP and demonstrate that the minimum of the directed flow does not correspond to the softest point of the EoS for isentropic expansion. A novel technique measuring the compactness is introduced to determine the QGP transition in relativistic-heavy ion collisions: The QGP transition will lead to higher compression and therefore to higher compactness of the source in coordinate space. This e ect can be observed by pion interferometry. We propose to measure the compactness of the source in the appropriate principal axis frame of the compactness tensor in coordinate space.
Compelling evidence for a new form of matter has been claimed to be formed in Pb+Pb collisions at SPS. We critically review two suggested signatures for this new state of matter: First the suppression of the J/psi , which should be strongly suppressed in the QGP by two different mechanisms, the color-screening [1] and the QCD-photoe ect [2]. Secondly the measured particle, in particular strange hadronic, ratios might signal the freeze-out from a quark-gluon phase.
Recent progress in the understanding of the high density phase of neutron stars advances the view that a substantial fraction of the matter consists of hyperons. The possible impacts of a highly attractive interaction between hyperons on the properties of compact stars is investigated. We find that the equation of state exhibits a second stable minimum at large hyperon contents which is in accord with existing hypernuclear data. This second solution gives rise to new effects for neutron star properties which are similar to the ones proposed for the deconfinement transition to strange quark matter and absolutely stable strange stars. We find that the corresponding hyperstars can have rather small radii of R=6-8 km independent of the mass. PACS: 26.60+c, 21.65+f, 97.60.Gb, 97.60.Jd
Recent progress in the understanding of the high density phase of neutron stars advances the view that a substantial fraction of the matter consists of hyperons. The possible impacts of a highly attractive interaction between hyperons on the properties of compact stars are investigated. We find that a hadronic equation of state with hyperons allows for a first order phase transition to hyperonic matter. The corresponding hyperon stars can have rather small radii of R ~ 8 km. PACS: 26.60+c, 21.65+f, 97.60.Gb, 97.60.Jd
A sign reversal of the directed flow parameter v1 in the central rapidity region in Au+Au collisions at s = 200 AGeV is predicted. This anti-flow is shown to be linked to the expansion of the hot matter created. In line with this observation the predicted elliptic flow parameter v2 of various particle species is linked to the mean free path of these particles.
A model for the production of quarkonium states in the midrapidity region at RHIC and LHC energy range is presented which explores well understood properties of QCD only. An increase of the quarkonium hadronisation time with the initial energy leads to a gradual change of the most important phenomena from fixed target- to collider-energies. We evaluate nuclear e ects in the quarkonium production due to medium modification of the momentum distribution of the heavy quarks produced in the hard interactions, i.e. due to the broadening of the transverse momentum distribution. Other nuclear effects, i.e. nuclear shadowing and parton energy loss, are also evaluated.
In ultra-relativistic heavy ion collisions, early stage multiple scatterings may lead to an increase of the color electric field strength. Consequently, particle production - especially heavy quark (and di-quark) production - is greatly enhanced according to the Schwinger mechanism. We test this idea via the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) for Au+Au collisions at the full RHIC energy (ps = 200 AGeV). Relative to p+p collisions, a factor of 60, 20 and 7 enhancement respectively, for (sss), (ss), and , (s) is predicted for a model with increased color electric field strength.
We study b¯b and c¯c production and the influence of nuclear shadowing at LHC and RHIC energies. We find a significant reduction in the production cross section of both charm and bottom at RHIC and LHC. Bound states such as and J/psi are suppressed by this reduction in the charm production cross sections. Therefore, J/psi suppression may not be useful as a signature for the quark gluon plasma. PACS: 12.38.Mh, 25.75.-q, 24.85.+p, 14.65.Dw