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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.
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.