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Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source versus a time-dependent, non-equilibrium hadronization off a quark gluon plasma droplet. Due to the time-dependent particle evaporation off the hadronic surface in the latter approach the hadron ratios change (by factors of / 5) in time. The overall particle yields then reflect time averages over the actual thermodynamic properties of the system at a certain stage of evolution.
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.
After a brief introduction on QCD and effective models in the first chapter, I analyze the dependence of the QCD transition temperature on the quark (or pion) mass in the second chapter. I found that a linear sigma model, which links the transition to chiral symmetry restoration, predicts a much stronger dependence of T_c on m_pi than seen in present lattice data for m_pi >~ 0.4 GeV. On the other hand, an effective Lagrangian for the Polyakov loop requires only small explicit symmetry breaking to describe T_c(m_pi) in the above mass range. In the third and fourth chapter, I study the linear sigma model with O(N) symmetry at nonzero temperature in the framework of the Cornwall-Jackiw-Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual Hartree-Fock (or Hartree) contributions, I derive a new approximation scheme which extends the standard Hartree-Fock (or Hartree) approximation by the inclusion of nonzero decay widths.
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.
Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung des ALTRO Chips (ALICE TPC Readout), der ein integraler und wichtiger Bestandteil der Auslesekette des TPC (Time Projection Chamber) Detektors von ALICE (A Large Ion Collider Experiment) ist. ALICE ist ein Experiment am noch im Bau befindlichen LHC (Large Hadron Collider) am CERN mit der zentralen Ausrichtung, Schwerionenkollisionen zu untersuchen. Diese sind von besonderem Interesse, da durch sie ein experimenteller Zugriff zu dem QGP (Quark Gluon Plasma) existiert, dem einzigen vom Standardmodell vorhergesagten Phasenübergang, der unter Laborbedingungen erreichbar ist. Im Jahr 2004 wurden Messungen an einem Teststrahl am CERN PS (Proton Synchrotron) durchgeführt. Der Prototyp wurde voll mit FECs bestückt, was 5400 Kanälen entspricht und einer anderen Gasmixtur (Ne/N2/CO2 90%/5%/5%) befüllt. Für das optimale Leistungsverhalten der ALICE TPC muß der Digitalprozessor im ALTRO, bestehend aus vier Berechnungseinheiten, mit den passenden Werten konfiguriert werden. Der Datenfluss beginnt mit dem BCS1 (Baseline Correction and Subtraction 1) Modul, das systematische Störungen und die Grundlinie entfernt. Da der ALTRO kontinuierlich das anliegende Signal abtastet, entfernt es automatisch langsame Grundlinienveränderungen, die Beispielsweise durch Temperaturänderungen auftreten können. Gefolgt von dem TCF (Tail Cancellation Filter), der den Schweif des langsam fallenden, vom PASA generierten Signals entfernt. Um die nichtsystematischen Störungen der Grundlinie zu entfernen, folgt die BCS2 (Baseline Correction and Subtraction 2), die auf einer gleitenden Mittelwertsberechnung mit Ausschluß von Detektorsignalen über einen doppelten Schwellenwert basiert. Die finale Einheit für die Signalverarbeitung ist die ZSU (Zero Suppression Unit), die Meßpunkte unterhalb eines definierten Schwellwertes entfernt. Hier wird der weg beschrieben die TCF und BCS1 Parameter aus vorhandenen Detektordaten zu extrahieren. Während der Analyse der Daten von kosmischen Teilchen fiel bei Signalen mit hoher Amplitude (>700 ADC) eine zusätzliche Struktur in dem Schweif auf. Der Monitor wurde deswegen mit einem gleitenden Mittelwertfilter erweitert, worauf sich diese Struktur auch in kleineren Signalen (> 200 ADC) zeigte. Dieses Signal wird von Ionen erzeugt, die zur Kathode oder zu den Pads driften, bisher ist jedoch weder die Streuung der Elektronenlawine an der Anode, noch die Variationsbreite in den erzeugten Elektronlawinen verstanden oder gemessen worden. Eine erfolgreiche Messung, sowie Charakterisierung wird in dieser Arbeit beschrieben. Im Jahr 2005 im Sommer beginnt der Einbau der Gaskammern der TPC in ALICE, die Elektronik folgt am Ende dieses Jahres. Parallel hierzu wurde der Prototyp der TPC wieder in Betrieb genommen und im Frühling wird ein kompletter Sektor mit der Detektorelektronik ausgestattet. An diesen zwei Aufbauten wird die ALTRO Charakterisierung fortgeführt, verfeinert und komplettiert.
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.
Abstract: Local thermal and chemical equilibration is studied for central AqA collisions at 10.7 160 AGeV in the Ultrarelativis- . tic Quantum Molecular Dynamics model UrQMD . The UrQMD model exhibits strong deviations from local equilibrium at the high density hadron string phase formed during the early stage of the collision. Equilibration of the hadron resonance matter is established in the central cell of volume Vs125 fm3 at later stages, tG10 fmrc, of the resulting quasi-isentropic expansion. The thermodynamical functions in the cell and their time evolution are presented. Deviations of the UrQMD quasi-equilibrium state from the statistical mechanics equilibrium are found. They increase with energy per baryon and lead to a strong enhancement of the pion number density as compared to statistical mechanics estimates at SPS energies. PACS: 25.75.-q; 24.10.Lx; 24.10.Pa; 64.30.qt
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.
Noneequilibrium models (three-fluid hydrodynamics and UrQMD) use to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that these two models - although they do treat the most interesting early phase of the collisions quite differently(thermalizing QGP vs. coherent color fields with virtual particles) - both yields a reasonable agreement with a large variety of the available heavy ion data.
In dieser Arbeit wurde die Produktion negativ geladener Pionen in zentralen Blei+Blei Kollisionen bei 40 A·GeV am CERN SPS mit dem Experiment NA49 untersucht. Die Analyse der Pionen basiert auf der Tatsache, das sie ungefähr 90% des hadronischen Endzustands aller negativ geladenen Hadronen darstellen, wobei der Rest hauptsächlich aus Kaonen besteht. Diese Analyse deckt die komplette vordere Hemisphäre ab, somit wurden keinerlei Extrapolationen benötigt. Für diese Analyse wurde ein komplett neuer Satz von Schnitten in diversen Variablen der Daten von NA49 gesucht und optimiert. Um einen möglichst gut bestimmten Satz von Spuren zu verwenden, wurde nur ein kleiner Teil aller Spuren verwendet, der aber exakt und einfach zur vollen Akzeptanz zurückkorrigiert werden kann. Um die Spuren aus Zerfällen nahe am Hauptinteraktionspunkt und um Dreckeffekte wie γ-Konversion oder Vielfachstreuung zu entfernen, wurde ein komplett neuer Korrekturalgorithmus entwickelt und getestet. Da bei dieser Energie die Spurmultiplizitäten ungefähr um einen Faktor zwei kleiner sind, wurde beobachtet, daß Ineffizienzen in der Rekonstruktion eine untergeordnete Rolle spielen. Hier wurde im Mittel eine Korrektur von 8% verwendet. Um Spektren negativer Pionen zu erhalten, müssen die negativ geladenen Kaonen aus dem Spursatz entfernt werden, hierfür wurde eine Simulation aufgebaut und eingesetzt. Ein großes Problem stellt die Abschätzung des Systematischen Fehlers dar, da es eine Mannigfaltigkeit von Fehlerquellen gibt. In dieser Arbeit wurden zwei Methoden angewandt, um den Systematischen Fehler abzuschätzen. Das Ergebnis der hier vorgestellten Analyse ergibt eine mittlere Multiplizität für die negativen Pionen von 320±14. Die Präsentation eines vorläufigen Zustands dieser Analyse in Kombination mit den neu gewonnen Kaonwerten [1] vor dem SPSC [2] veränderten den vorhandenen Strahlzeitplan nachhaltig, so daß in extrem kurzer Zeit nach ieser Präsentation eine Energieabtastung gestartet wurde. Schon ein paar Monate später bekam NA49 hierfür einen Bleistrahl bei der Energie von 80 A·GeV und wird im Jahr 2002 auch Energien von 20 und 30 A·GeV geliefert bekommen. Auch wurden diese Daten auf der QM2001 als vorläufige Ergebnisse präsentiert. Desweiteren bilden die Ergebnisse, sowie die aus der 80 A·GeV Analyse und denen bei Top-SPS Energie gewonnenen kombiniert mit den Kaonergebnissen bei den gleichen Energien die Grundlage für ein Physical Review Letter der NA49-Kollaboration zum Thema der Energieabhängigkeit des K+/π + Verhältnis. Die Motivation für diese Arbeit war die Suche nach einer Evidenz des Quark-Gluon-Plasma und bei der analysierten Energie wurde der Übergang in diese Phase vorhergesagt [3]. Man sollte einen Wechsel von der Pionunterdrückung zur Pionvermehrung im Vergleich mit den Daten aus Nukleus+Nukleus Experimenten in dem Verhältnis der mittleren Pionmultiplizität zu der Anzahl der Teilnehmenden Nukleonen beobachten. Diese Vermutung stellte sich als richtig heraus. Diesen Wechsel kann man erklären, wenn man einen Phasenübergang zu einer Phase quasifreier Quarks und Gluonen in diesem Bereich annimmt. Die Pionen stellen, aufgrund ihrer geringen Masse, die häufigsten Teilchen dar und sind somit auch eine gute Meßprobe für die gesamte Entropie des Feuerballs. Da die Anzahl der Freiheitsgrade in einem QGP massiv ansteigen muß, sollte man eine erhöhte Produktion von Pionen beobachten. Der Meßpunkt bei 40 A·GeV liegt genau in dem Bereich des Wechsels. Ein Vergleich mit den Modellen zeigt, das kein Modell, wenn es überhaupt Pionen beschreiben kann, die Produktion von Pionen korrekt wiedergibt, außer das „Statistical Modell of the early Stage“, das die Pionproduktion beschreibt und auch den Wechsel von Pionunterdrückung zu Pionvermehrung im Bereich um 40 A·GeV wiedergibt. Dieses Modell besitzt eine Phasenübergang von gebundener Materie zum QGP. Das Hadrongas-Modell kann die Pionen bei jeder Energie beschreiben, aber eine Vorhersage ist nicht möglich, da die Pionen als Eingabe in dieses Modell benötigt werden. Die Ergebnisse von NA49 haben neuen Schwung in die Erklärung von Schwerionenkollisionen und die Suche nach dem QGP gebracht. Die ersten „Resultate“ sind eine Energieabtastung am CERN-SPS und diverse Änderungen an vorhandenen Modellen, um vor allem das nichtmonotonische Verhalten des K+/Pi + Verhältnisses zu beschreiben. Bis jetzt existiert kein Modell und keine Erklärung, die die Daten beschreibt und auf anderen Hadronischen Erklärungen basiert. Somit kann man feststellen, daß eine sich erhärtende Evidenz für die Produktion des QGP am CERN-SPS vorhanden ist.
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 using 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 energy in Pb+Pb collisions at 160 GeV and found to be in reasonable agreement with existing data.
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 and the semiclassical, quasiparticle, and Born approximations 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 Delta's 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 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 nonrelativistic 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 piN->Delta cross section is in agreement with the experimental data. Medium effects on the piN->Delta cross section and momentum-dependent Delta-decay width are shown to be substantial. PACS-numbers: 24.10.Jv, 13.75.Cs, 21.65.1f, 25.75.2q
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.